Preface

The demand for electricity and heat production is still largely covered by conventional ther‐ mal power plants based on fossil fuel combustion. Thermal power stations face a big chal‐ lenge to meet the environmental requirements constantly keeping high process efficiency and avoiding lifetime shortening of critical components. In recent years, many activities have been observed to reduce pollutant emissions and optimize performance in thermal power plants.

Increased share of renewable sources of energy in domestic markets enforces flexible opera‐ tion of plant units and fast adjustment to actual electricity demand. Gas power plants start to play a very important role in this process, allowing for rapid change of load and to reduce emission of gas pollutants. Operation under changing load together with keeping emissions at the accurate level requires constantly introducing new solutions and technologies as well as carrying out many research and development activities for optimization of the electricity and heat production process.

The present edited book intends to cover recent research and development activities dedi‐ cated to thermal power plants, new approaches and future perspectives. This book consists of 8 chapters covering research issues as analysis of coal-fired power unit operation for flexi‐ bility improvement, algorithm dedicated to detect certain abnormal conditions and malfunc‐ tions of coal mills, numerical analysis of creep-fatigue damage in a steam turbine rotor. The book also includes work on new potential solutions to enhance fluid flow and heat ex‐ change, modelling of dilute phase transportation, engineering approach for fast fluidization dynamics and also recent trends and discussions about a concept strategy for concentrating solar power management.

The editor is indebted to all the colleagues who have contributed to this volume and pre‐ sented results of latest research, to InTechOpen for the opportunity to work on this book and to its members for the help and support.

> **Paweł Madejski** PGE Energia Ciepła S.A. Research and Development Kraków, Poland

**Chapter 1**

Provisional chapter

**Introductory Chapter: New Trends and Recent**

DOI: 10.5772/intechopen.74723

The largest share of sources for electricity generation still belongs to fossil fuels such as coal, natural gas, and oil. Conventional thermal power plants based on the fossil fuel combustion are currently facing new challenges. The challenges and recent activities mainly result from the development of technologies that use renewable energy sources and activities aimed at reduc-

The new challenges are a decisive impulse for introducing changes in power plants and combined heat and power plants, as well as for the implementation and continuous development of new technologies allowing for the electricity and heat production in the least harmful way to the environment. In recent years, many activities have been observed to reduce pollutant emissions and optimize the performance of thermal power plants. Ensuring a continuous supply of electricity and heat is necessary and requires a continuous monitoring of all pro-

Based on the data provided by International Energy Agency [1], we can observe how electricity generation during almost last 50 years is changing (Figure 1). Total electricity generation was increased almost 6 times, reaches in 2015 value 24,255 TWh, with the share of fossil fuel on the level around 66% (75% in 1973). The share of renewable energy sources (Figure 1) includes mainly geothermal, solar, wind, ocean, biofuels, and waste was increased from 0.6 to 7.1% of total electricity generation sources. Despite these changes and the intensive development of technologies based on renewable energy sources, fossil fuels still dominate. The values presented in Figure 1 confirm current trends indicating the continuous use of coal (39.3% in

2015) as the main source and a large increase of natural gas utilization (22.9% in 2015).

The use of various sources for the electricity generation is strongly diversified and depends on the geographical location which determines the possibility of using renewable resources, as

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Introductory Chapter: New Trends and Recent

**Developments for Thermal Power Plants**

Developments for Thermal Power Plants

Additional information is available at the end of the chapter

ing the emission of harmful substances into the atmosphere.

cesses and conduct of maintenance and optimization works.

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.74723

1. New trends and challenges

Paweł Madejski

Paweł Madejski

#### **Introductory Chapter: New Trends and Recent Developments for Thermal Power Plants** Introductory Chapter: New Trends and Recent Developments for Thermal Power Plants

DOI: 10.5772/intechopen.74723

Paweł Madejski Paweł Madejski

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.74723

## 1. New trends and challenges

The largest share of sources for electricity generation still belongs to fossil fuels such as coal, natural gas, and oil. Conventional thermal power plants based on the fossil fuel combustion are currently facing new challenges. The challenges and recent activities mainly result from the development of technologies that use renewable energy sources and activities aimed at reducing the emission of harmful substances into the atmosphere.

The new challenges are a decisive impulse for introducing changes in power plants and combined heat and power plants, as well as for the implementation and continuous development of new technologies allowing for the electricity and heat production in the least harmful way to the environment. In recent years, many activities have been observed to reduce pollutant emissions and optimize the performance of thermal power plants. Ensuring a continuous supply of electricity and heat is necessary and requires a continuous monitoring of all processes and conduct of maintenance and optimization works.

Based on the data provided by International Energy Agency [1], we can observe how electricity generation during almost last 50 years is changing (Figure 1). Total electricity generation was increased almost 6 times, reaches in 2015 value 24,255 TWh, with the share of fossil fuel on the level around 66% (75% in 1973). The share of renewable energy sources (Figure 1) includes mainly geothermal, solar, wind, ocean, biofuels, and waste was increased from 0.6 to 7.1% of total electricity generation sources. Despite these changes and the intensive development of technologies based on renewable energy sources, fossil fuels still dominate. The values presented in Figure 1 confirm current trends indicating the continuous use of coal (39.3% in 2015) as the main source and a large increase of natural gas utilization (22.9% in 2015).

The use of various sources for the electricity generation is strongly diversified and depends on the geographical location which determines the possibility of using renewable resources, as

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

well as on the availability of fossil fuels (coal, gas). The next very important factor is the change in the demand for electricity, which is conditioned by the development dynamics of individual regions of the world. Figure 2 presents data illustrating changes in the quantities of electricity produced in particular regions of the world. It is noticeable that in recent years, the increase in electricity generation has changed in many regions of the world with different rates. Organization for Economic Co-operation and Development (OECD) countries have the largest share all the time (44.7% in 2015), but for some time the rate of growth has decreased and this level is

Introductory Chapter: New Trends and Recent Developments for Thermal Power Plants

http://dx.doi.org/10.5772/intechopen.74723

3

Coal-fired power plants currently face a big challenge to reduce the level of gaseous pollutants and to adopt new flue-gases treatment methods and devices. Regulations for reducing NOx, Sox, and dust emissions become more strict [2], and the required limits of gas emission levels are different for old and for new units. In case of old units, with the fuel power above 300 MW, permitted emission levels have been changed during last year's [2]. The upper limits of the average annual values for pulverized coal-fired boilers and for sources above 300 MWt are presented in Figure 3. In addition to these values, the future regulations can also include limits of emission levels for HCl, HF, Hg, and NH3, as well as CO indicator levels. Emission limit values are developed every few years based on the best available techniques (BATs) that exist

Due to mandatory environmental regulations, coal-fired power stations in many countries need to install denitrification plants (DeNOx) for nitrogen oxide (NOx) and desulphurization plants (DeSOx) for sulfur oxide (SOx) removal from the flue gases. The most popular methods for removing sulfur oxides from exhaust gases are calcium methods. There are several types of this calcium method such as dry, semi-dry, but the Wet Flue Gas Desulfurization (WFGD) method is the most common technology for SOx control. The reduction of NOx emission levels is currently possible using primary and secondary measures. Primary measures are used inside the combustion chamber including methods as proper selection of the excess air ratio and temperature, modification of combustion techniques (re-burning, exhaust gas recirculation, air staging, cooling the flame and burners re-design). The use of primary measures allows to reduce NOx emission with an efficiency about 35%, so in many cases is not enough to meet the environmental concerns. The other solution is to use secondary measures of NOx reduction, such as Selective Non-Catalytic Reduction (SNCR) and Selective Catalytic Reduction (SCR). These techniques based on the auxiliary installations are located behind the boiler combustion zone. Secondary measures are more effective than primary methods and NOx reduction efficiency can reach about 50 and 95% for SNCR and SCR techniques, respectively. Many research activities are currently focused on the developed methodology of prediction and assessment [3–6], optimization [7–10], and improving the efficiency of NOx

However, to avoid efficiency reduction of the production process by applying these methods, the thermal efficiency of the boiler needs to be constantly at a high level. It is necessary to perform optimization work of combustion process using dedicated and novel measurement techniques, optimization algorithms, consequently developed by many researchers and boilers

almost constant.

or will be available in the future.

reduction using primary as well as secondary measures.

Figure 1. World electricity generation by fuel between 1971 and 2015 [1].

well as on the availability of fossil fuels (coal, gas). The next very important factor is the change in the demand for electricity, which is conditioned by the development dynamics of individual regions of the world. Figure 2 presents data illustrating changes in the quantities of electricity produced in particular regions of the world. It is noticeable that in recent years, the increase in electricity generation has changed in many regions of the world with different rates. Organization for Economic Co-operation and Development (OECD) countries have the largest share all the time (44.7% in 2015), but for some time the rate of growth has decreased and this level is almost constant.

Coal-fired power plants currently face a big challenge to reduce the level of gaseous pollutants and to adopt new flue-gases treatment methods and devices. Regulations for reducing NOx, Sox, and dust emissions become more strict [2], and the required limits of gas emission levels are different for old and for new units. In case of old units, with the fuel power above 300 MW, permitted emission levels have been changed during last year's [2]. The upper limits of the average annual values for pulverized coal-fired boilers and for sources above 300 MWt are presented in Figure 3. In addition to these values, the future regulations can also include limits of emission levels for HCl, HF, Hg, and NH3, as well as CO indicator levels. Emission limit values are developed every few years based on the best available techniques (BATs) that exist or will be available in the future.

Due to mandatory environmental regulations, coal-fired power stations in many countries need to install denitrification plants (DeNOx) for nitrogen oxide (NOx) and desulphurization plants (DeSOx) for sulfur oxide (SOx) removal from the flue gases. The most popular methods for removing sulfur oxides from exhaust gases are calcium methods. There are several types of this calcium method such as dry, semi-dry, but the Wet Flue Gas Desulfurization (WFGD) method is the most common technology for SOx control. The reduction of NOx emission levels is currently possible using primary and secondary measures. Primary measures are used inside the combustion chamber including methods as proper selection of the excess air ratio and temperature, modification of combustion techniques (re-burning, exhaust gas recirculation, air staging, cooling the flame and burners re-design). The use of primary measures allows to reduce NOx emission with an efficiency about 35%, so in many cases is not enough to meet the environmental concerns. The other solution is to use secondary measures of NOx reduction, such as Selective Non-Catalytic Reduction (SNCR) and Selective Catalytic Reduction (SCR). These techniques based on the auxiliary installations are located behind the boiler combustion zone. Secondary measures are more effective than primary methods and NOx reduction efficiency can reach about 50 and 95% for SNCR and SCR techniques, respectively. Many research activities are currently focused on the developed methodology of prediction and assessment [3–6], optimization [7–10], and improving the efficiency of NOx reduction using primary as well as secondary measures.

However, to avoid efficiency reduction of the production process by applying these methods, the thermal efficiency of the boiler needs to be constantly at a high level. It is necessary to perform optimization work of combustion process using dedicated and novel measurement techniques, optimization algorithms, consequently developed by many researchers and boilers

Figure 1. World electricity generation by fuel between 1971 and 2015 [1].

2 Thermal Power Plants - New Trends and Recent Developments

manufacturers [11–18]. Introduction of primary and secondary measures for NOx reduction can result in a higher level of carbon in fly ash. Many research activities are observed regarding the quality of fly ash [19, 20] and its potential utilization [21, 22] as well as ash monitoring and

fuels with the exception of gas turbines and gas engines, and for the total nominal power delivered in fuel >300 MW.

) for SO2, NO2, and dust for fossil fuel-fired power plants using solid or liquid

Introductory Chapter: New Trends and Recent Developments for Thermal Power Plants

http://dx.doi.org/10.5772/intechopen.74723

5

Currently, one of the big challenges is to assess the possibilities of CO2 capture and to develop a technology that allows limiting the emission of this greenhouse gas. For this reason, many theoretical studies, as well as experimental work, have been carried out, among others in order to evaluate the possibilities of CO2 capture, and the impact of applying technology on produc-

The increased share of electricity produced from renewable energy sources [36] requires from coal-fired power plants more flexible operation to balance power grids and compensate the variable electricity demand [37]. Coal-fired power plants need to adopt these requirements and to operate in the flexible regime. Flexibility in the power plants operation is characterized by the necessity of frequent load changes, the need to work outside the nominal operating conditions, and the need of more frequent power units start-ups as well as shortening the time of start-up, shutdown or changing a partial load. The necessary flexibility can be achieved with acceptable impacts on component life, efficiency, and emissions but it needs continuous monitoring and controlling of basic operating parameters [38–47]. In Figure 4, the forecasted

In recent years, an intense increase in the use of gas-fired systems can be observed. Gas-fired plants are characterized by high efficiency and the ability to provide fast response to variable electricity demand. Production of electricity and heat using gas technology is widely used in the power industry, and from year to year more and more units start the operation [48–50]. The efficiency of the gas turbine is mainly responsible for the high efficiency of the system, as well as the ability to quickly change the load and operate under high flexible regime [51, 52]. Ensuring

electricity generation (2012–2040) based on renewable energy sources is presented.

optimization of cleaning methods of ash deposits formation inside the boilers [23–30].

tion efficiency in both old production units and newly built [31–35].

Figure 3. Emission limit values (mg/Nm<sup>3</sup>

Figure 2. World electricity generation by region between 1971 and 2015 [1].

Introductory Chapter: New Trends and Recent Developments for Thermal Power Plants http://dx.doi.org/10.5772/intechopen.74723 5

Figure 3. Emission limit values (mg/Nm<sup>3</sup> ) for SO2, NO2, and dust for fossil fuel-fired power plants using solid or liquid fuels with the exception of gas turbines and gas engines, and for the total nominal power delivered in fuel >300 MW.

manufacturers [11–18]. Introduction of primary and secondary measures for NOx reduction can result in a higher level of carbon in fly ash. Many research activities are observed regarding the quality of fly ash [19, 20] and its potential utilization [21, 22] as well as ash monitoring and optimization of cleaning methods of ash deposits formation inside the boilers [23–30].

Currently, one of the big challenges is to assess the possibilities of CO2 capture and to develop a technology that allows limiting the emission of this greenhouse gas. For this reason, many theoretical studies, as well as experimental work, have been carried out, among others in order to evaluate the possibilities of CO2 capture, and the impact of applying technology on production efficiency in both old production units and newly built [31–35].

The increased share of electricity produced from renewable energy sources [36] requires from coal-fired power plants more flexible operation to balance power grids and compensate the variable electricity demand [37]. Coal-fired power plants need to adopt these requirements and to operate in the flexible regime. Flexibility in the power plants operation is characterized by the necessity of frequent load changes, the need to work outside the nominal operating conditions, and the need of more frequent power units start-ups as well as shortening the time of start-up, shutdown or changing a partial load. The necessary flexibility can be achieved with acceptable impacts on component life, efficiency, and emissions but it needs continuous monitoring and controlling of basic operating parameters [38–47]. In Figure 4, the forecasted electricity generation (2012–2040) based on renewable energy sources is presented.

In recent years, an intense increase in the use of gas-fired systems can be observed. Gas-fired plants are characterized by high efficiency and the ability to provide fast response to variable electricity demand. Production of electricity and heat using gas technology is widely used in the power industry, and from year to year more and more units start the operation [48–50]. The efficiency of the gas turbine is mainly responsible for the high efficiency of the system, as well as the ability to quickly change the load and operate under high flexible regime [51, 52]. Ensuring

Figure 2. World electricity generation by region between 1971 and 2015 [1].

4 Thermal Power Plants - New Trends and Recent Developments

Shale gas deposits belong to unconventional resources (tight gas, shale gas) and are under detailed consideration as a chance for replacing fuels from conventional resources. Finding of shale formations is easier than conventional, but exploitation of hydrocarbons is more difficult [53–56]. Nevertheless, on the basis of the data presented in Figure 5, it can be observed that the

Introductory Chapter: New Trends and Recent Developments for Thermal Power Plants

http://dx.doi.org/10.5772/intechopen.74723

7

Nowadays, power companies need to modify their management method and models and adapt to strongly changing requirements and regulation on the electricity generation and sale market. Development of more marketable approaches focused on high-quality services needs to be prepared in a careful way. All activities need to be scheduled taking into account upcoming requirements maintaining optimal parameters and efficiency of all processes. The demand for electricity and heat production is still largely covered by conventional Thermal Power Plants which face a big challenge to meet the environmental requirements. Constant keeping high efficiency of processes, avoiding shortening of a critical component lifetime is one of the most important tasks to accomplish. Increased share of renewable energy sources enforces more flexible operation of existing Thermal Power Plants and the necessity to provide fast response to variable electricity demand. Because of these limitations, Gas Power Plants can start to play an important role, allowing for rapid change of load and to reduce the emission of harmful gas pollutants. New environmental restrictions together with the need for operation under changing load, requires constantly introducing new solutions and technologies, as well as carrying out research and development activities to create and

gas resources are located in every region of the world.

2. Conclusions

implement new optimal solutions.

Address all correspondence to: pawel.madejski@gkpge.pl

PGE Energia Ciepła S.A., Research and Development, Kraków, Poland

org/publications/freepublications/publication/KeyWorld2017.pdf

cial Journal of the European Union. 2010;334:17-119

[1] International Energy Agency. Key World Energy Statistics 2017. Paris. https://www.iea.

[2] Directive 2010/75/EU of the European Parliament and of the Council of 24 November 2010 on Industrial Emissions (integrated pollution prevention and control, Recast). Offi-

Author details

Paweł Madejski

References

Figure 4. Electricity generation by sources (2012–2040) [36].

Figure 5. Shale gas resources [36].

the optimal operating conditions together with the changing demand requires the use of proper tools for monitoring and optimizing the production process.

For several years, it has been observed a great interest in the growing possibilities of obtaining gas from the unconventional gas resources. The shale gas supply can play an important role and lead to a substitution of a coal-fired plant by gas-fired plants. In Figure 5, the technically recoverable shale gas resources are presented.

Shale gas deposits belong to unconventional resources (tight gas, shale gas) and are under detailed consideration as a chance for replacing fuels from conventional resources. Finding of shale formations is easier than conventional, but exploitation of hydrocarbons is more difficult [53–56]. Nevertheless, on the basis of the data presented in Figure 5, it can be observed that the gas resources are located in every region of the world.

## 2. Conclusions

Nowadays, power companies need to modify their management method and models and adapt to strongly changing requirements and regulation on the electricity generation and sale market. Development of more marketable approaches focused on high-quality services needs to be prepared in a careful way. All activities need to be scheduled taking into account upcoming requirements maintaining optimal parameters and efficiency of all processes. The demand for electricity and heat production is still largely covered by conventional Thermal Power Plants which face a big challenge to meet the environmental requirements. Constant keeping high efficiency of processes, avoiding shortening of a critical component lifetime is one of the most important tasks to accomplish. Increased share of renewable energy sources enforces more flexible operation of existing Thermal Power Plants and the necessity to provide fast response to variable electricity demand. Because of these limitations, Gas Power Plants can start to play an important role, allowing for rapid change of load and to reduce the emission of harmful gas pollutants. New environmental restrictions together with the need for operation under changing load, requires constantly introducing new solutions and technologies, as well as carrying out research and development activities to create and implement new optimal solutions.

## Author details

Paweł Madejski

Address all correspondence to: pawel.madejski@gkpge.pl

PGE Energia Ciepła S.A., Research and Development, Kraków, Poland

## References

the optimal operating conditions together with the changing demand requires the use of proper

For several years, it has been observed a great interest in the growing possibilities of obtaining gas from the unconventional gas resources. The shale gas supply can play an important role and lead to a substitution of a coal-fired plant by gas-fired plants. In Figure 5, the technically

tools for monitoring and optimizing the production process.

recoverable shale gas resources are presented.

Figure 5. Shale gas resources [36].

Figure 4. Electricity generation by sources (2012–2040) [36].

6 Thermal Power Plants - New Trends and Recent Developments


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**Chapter 2**

Provisional chapter

**Analysis of Coal-Fired Power Unit Operation in**

Analysis of Coal-Fired Power Unit Operation in Reduced

DOI: 10.5772/intechopen.72954

Large coal-fired power plants were typically designed as a base load units. Any changes in load level, as well as start-up time, are noticeably slow on that kind of units. However, in order to adapt to changing market conditions with increasing number of renewable energy sources, coal-fired power plants need to improve their flexibility. In the paper, 200 MWe class unit has been taken into consideration. During the test campaign, a minimum safe load of the unit was decreased from 60 to 40%. Paper presents results of a model that was made using Ebsilon®Professional software. The simulation model is comprised of boiler and turbine part of the power unit. Obtained results were validated using measurements collected from the test campaign. Parameters important from the technical and economical point of view were investigated. Results revealed that simulation model can be utilised successfully to scrutinise coal-fired units under off-design operation conditions. As the outcome of the performed analysis, a number of issues related to low load operation of the coal-fired unit are presented and discussed. Paper indicates sensitive areas that need to be addressed when operation in decreased safe load is considered. Finally, overall potential for flexibility improvement for 200 MWe

Keywords: flexibility, simulation modelling, power plant, power production, coal

Large coal-fired power plants used to be designed as a base load unit for electricity market. Power units in such power plants can only change their load level in limited range. What is more, any load changes as well as start-up periods, are considerably slow. That has not been the case for many years, currently though, power units require much more flexibility in operation. The reason for that is a growing number of intermittent energy sources, like wind or

> © The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

**Reduced Minimum Safe Load Regime**

Piotr Żymełka, Maciej Żyrkowski and Maciej Bujalski

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

class coal-fired units has been evaluated.

Minimum Safe Load Regime

Piotr Żymełka, Maciej Żyrkowski and

http://dx.doi.org/10.5772/intechopen.72954

Maciej Bujalski

Abstract

1. Introduction

#### **Analysis of Coal-Fired Power Unit Operation in Reduced Minimum Safe Load Regime** Analysis of Coal-Fired Power Unit Operation in Reduced Minimum Safe Load Regime

DOI: 10.5772/intechopen.72954

Piotr Żymełka, Maciej Żyrkowski and Maciej Bujalski Piotr Żymełka, Maciej Żyrkowski and

Additional information is available at the end of the chapter Maciej Bujalski

http://dx.doi.org/10.5772/intechopen.72954 Additional information is available at the end of the chapter

#### Abstract

Large coal-fired power plants were typically designed as a base load units. Any changes in load level, as well as start-up time, are noticeably slow on that kind of units. However, in order to adapt to changing market conditions with increasing number of renewable energy sources, coal-fired power plants need to improve their flexibility. In the paper, 200 MWe class unit has been taken into consideration. During the test campaign, a minimum safe load of the unit was decreased from 60 to 40%. Paper presents results of a model that was made using Ebsilon®Professional software. The simulation model is comprised of boiler and turbine part of the power unit. Obtained results were validated using measurements collected from the test campaign. Parameters important from the technical and economical point of view were investigated. Results revealed that simulation model can be utilised successfully to scrutinise coal-fired units under off-design operation conditions. As the outcome of the performed analysis, a number of issues related to low load operation of the coal-fired unit are presented and discussed. Paper indicates sensitive areas that need to be addressed when operation in decreased safe load is considered. Finally, overall potential for flexibility improvement for 200 MWe class coal-fired units has been evaluated.

Keywords: flexibility, simulation modelling, power plant, power production, coal

## 1. Introduction

Large coal-fired power plants used to be designed as a base load unit for electricity market. Power units in such power plants can only change their load level in limited range. What is more, any load changes as well as start-up periods, are considerably slow. That has not been the case for many years, currently though, power units require much more flexibility in operation. The reason for that is a growing number of intermittent energy sources, like wind or

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

PV units. Due to the currents EU's policy, they are privileged on the electricity market, therefore other units role is to balance power level in the system. Power plants with the highest ability to balance renewable energy sources are those equipped with gas turbines, because of a very high speed of load changes as well as short start-up time they are able to provide. However, many energy markets still rely on large coal-fired plants and therefore they need to increase their flexibility. Two aspects of the flexible operation are taken into consideration. The first is the ability to start and change load faster. The second aspect is related to load level of considered units and possibility of its extension [1]. Paper refers to the latter case and tries to evaluate the potential for flexibility improvement of 200 MWe class coal-fired power unit, including both turbine and boiler part.

Flexibility issues with the steam turbine are mostly related to start-up periods. Material limitations impose a maximum temperature gradient that is allowed when the turbine warms up, which for saturated steam is equal to about 1 K/min and for superheated steam about 5 K/min [2]. Minimum power output that steam turbine can produce depends on the pressure in the condenser, which must be kept close to zero. Much more problems however, are associated with the boiler. In case of the reference unit, the most critical element in terms of thermal stress is a drum, for which maximum allowed temperature gradient for is equal to about 4.5 K/min [2]. Next flexibility limitation is related to combustion process itself, which in case of largescale boilers cannot be controlled too fast. In fact, any changes in boiler operation must be done gradually. When it comes to the boiler load range, it mainly depends on its water circulation technology. Natural circulation boilers have limited flexibility, due to the fact that certain level of heat from combustion process must be delivered to the evaporator, to maintain water circulation. Boilers with forced circulation can operate with much lower minimum safe load. In the reference unit, that is natural circulation boiler, the minimum safe load was designed to 60%, which is equal roughly to 390 t/h of steam flow and 135 MWe of power output. As a matter of fact, minimum safe load operation of the boiler is crucial in this investigation as it indicates overall minimum load of the entire unit. That is because steam turbine has typically wider range of operation than the boiler. Decreasing minimum safe load of the boiler would subsequently allow to decrease the electric power output of the unit. This, in turn, can be strongly beneficial during periods with low energy consumption, when coal-fired units are often forced to shut down. Avoiding the latter, by ability to decrease the power production, is highly desirable by power plant operators. The reason for that, is because shutting down and starting-up coal fired power plants is a rather costly and time consuming process. In the chapter, authors present outcomes of in situ tests as well as simulation modelling of reference unit operation at 40% load level that is below its safe design minimum.

outlet temperature is equal to 540C. The boiler is comprised of 5 superheaters and 2 reheaters as well as double water heater and three rotary air preheaters. At the boiler's outlet, there is

Analysis of Coal-Fired Power Unit Operation in Reduced Minimum Safe Load Regime

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15

For coal-fired units, it is important if the start-up is being done from the cold, warm or hot state [2, 3]. Figures 1 and 2 present parameter like electric power output and critical factors (drum wall and turbine casing temperatures) of reference unit during cold and warm start-ups. According to presented data, the warm start-up time of the unit is equal to about 7 h 20 min, while cold start-up is equal to about 10 h 40 min. Typical load variation of the reference unit is presented in Figure 3 and it changes from about 140 to 220 MWe. The minimum safe load for

one electrostatic precipitation unit (ESP).

Figure 1. Reference unit cold start-up.

the reference unit is equal to 60%.

Figure 2. Reference unit warm start-up.

#### 2. Flexibility of reference coal-fired power unit

Reference coal-fired units were produced between 1970 and 1974 in Poland. It is comprised of 225 MWe condensing steam turbine and pulverised coal boiler with a nominal steam output of 650 t/h. Turbine consists of the high, medium and low-pressure part. Inlet steam pressure equals to about 13.5 MPa. The boiler has natural water circulation and is equipped with the drum as well as front wall burners configuration with additional over fire air nozzles. Fuel mixed with primary air is supplied by six coal mills to low-NOx burners and steam nominal Analysis of Coal-Fired Power Unit Operation in Reduced Minimum Safe Load Regime http://dx.doi.org/10.5772/intechopen.72954 15

Figure 1. Reference unit cold start-up.

PV units. Due to the currents EU's policy, they are privileged on the electricity market, therefore other units role is to balance power level in the system. Power plants with the highest ability to balance renewable energy sources are those equipped with gas turbines, because of a very high speed of load changes as well as short start-up time they are able to provide. However, many energy markets still rely on large coal-fired plants and therefore they need to increase their flexibility. Two aspects of the flexible operation are taken into consideration. The first is the ability to start and change load faster. The second aspect is related to load level of considered units and possibility of its extension [1]. Paper refers to the latter case and tries to evaluate the potential for flexibility improvement of 200 MWe class coal-fired power unit,

Flexibility issues with the steam turbine are mostly related to start-up periods. Material limitations impose a maximum temperature gradient that is allowed when the turbine warms up, which for saturated steam is equal to about 1 K/min and for superheated steam about 5 K/min [2]. Minimum power output that steam turbine can produce depends on the pressure in the condenser, which must be kept close to zero. Much more problems however, are associated with the boiler. In case of the reference unit, the most critical element in terms of thermal stress is a drum, for which maximum allowed temperature gradient for is equal to about 4.5 K/min [2]. Next flexibility limitation is related to combustion process itself, which in case of largescale boilers cannot be controlled too fast. In fact, any changes in boiler operation must be done gradually. When it comes to the boiler load range, it mainly depends on its water circulation technology. Natural circulation boilers have limited flexibility, due to the fact that certain level of heat from combustion process must be delivered to the evaporator, to maintain water circulation. Boilers with forced circulation can operate with much lower minimum safe load. In the reference unit, that is natural circulation boiler, the minimum safe load was designed to 60%, which is equal roughly to 390 t/h of steam flow and 135 MWe of power output. As a matter of fact, minimum safe load operation of the boiler is crucial in this investigation as it indicates overall minimum load of the entire unit. That is because steam turbine has typically wider range of operation than the boiler. Decreasing minimum safe load of the boiler would subsequently allow to decrease the electric power output of the unit. This, in turn, can be strongly beneficial during periods with low energy consumption, when coal-fired units are often forced to shut down. Avoiding the latter, by ability to decrease the power production, is highly desirable by power plant operators. The reason for that, is because shutting down and starting-up coal fired power plants is a rather costly and time consuming process. In the chapter, authors present outcomes of in situ tests as well as simulation modelling of reference

unit operation at 40% load level that is below its safe design minimum.

Reference coal-fired units were produced between 1970 and 1974 in Poland. It is comprised of 225 MWe condensing steam turbine and pulverised coal boiler with a nominal steam output of 650 t/h. Turbine consists of the high, medium and low-pressure part. Inlet steam pressure equals to about 13.5 MPa. The boiler has natural water circulation and is equipped with the drum as well as front wall burners configuration with additional over fire air nozzles. Fuel mixed with primary air is supplied by six coal mills to low-NOx burners and steam nominal

2. Flexibility of reference coal-fired power unit

including both turbine and boiler part.

14 Thermal Power Plants - New Trends and Recent Developments

outlet temperature is equal to 540C. The boiler is comprised of 5 superheaters and 2 reheaters as well as double water heater and three rotary air preheaters. At the boiler's outlet, there is one electrostatic precipitation unit (ESP).

For coal-fired units, it is important if the start-up is being done from the cold, warm or hot state [2, 3]. Figures 1 and 2 present parameter like electric power output and critical factors (drum wall and turbine casing temperatures) of reference unit during cold and warm start-ups. According to presented data, the warm start-up time of the unit is equal to about 7 h 20 min, while cold start-up is equal to about 10 h 40 min. Typical load variation of the reference unit is presented in Figure 3 and it changes from about 140 to 220 MWe. The minimum safe load for the reference unit is equal to 60%.

Figure 2. Reference unit warm start-up.

Figure 3. Reference unit critical operation parameters (during September 2017).

The output load of the reference unit has been studied between January and October 2017. Histogram of the electric power is presented in Figure 4. During this period, the unit was under flexible operation with frequent load changes over a single day. Most of the time the unit worked with output power below 180 MW which corresponds to the load level below 80%. The unit worked almost 30 h with maximum capacity—225 MW and was shut down several times a month. Table 1 shows the number of start-ups with the start-up type (from the cold or warm state) during individual months. Aggregated stand-by and average start-up time are also provided. Until the end of October, the unit was launched 28 times. The critical factors (load, drum wall and casing turbine temperatures) of the reference unit during September are presented in Figure 3. Over this month, the unit was launched 7 times in total (including one

Table 1. A number of different start-ups of the reference unit between January and October 2017.

Month Avg. start-up time, h No. of cold start-ups, – No. of warm start-ups, – Stand-by time, h

Analysis of Coal-Fired Power Unit Operation in Reduced Minimum Safe Load Regime

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17

January 7.3 1.0 2.0 227.7 February 9.9 1.0 0 520 March 7.0 1.0 2.0 225.7 April 0 0 0 0 May 10.1 1.0 0 571.5 June 9.6 2.0 0 106.0 July 8.1 1.0 1.0 63.0 August 7.9 1.0 2.0 111.3 September 6.0 1.0 6.0 183.2 October 5.1 0 6.0 230.6

Steam turbine of a 225 MW power unit is considered for the simulation analysis. The mathematical model of the coal-fired power unit was developed using the Ebsilon®Professional computer software [4], including detailed models of turbine and boiler part. Boiler model

The subcritical steam cycle structure of analysed power unit is presented in Figure 5. The hatched areas show the main components of analysed thermal system: steam boiler, three casing turbine (consisting of a high-pressure part HP, an intermediate-pressure part IP and a low-pressure part LP), eight regenerative heat exchangers (consisting of three high-pressure HPH and five low-pressure LPH), two-part condenser (CO-1 and CO-2), an electric generator (G), a feed-water tank with deaerator (FW), condensate pumps (CP-1 and CP-2) and feed water

The superheated steam from the steam boiler at 535C temperature under 12.17 MPa pressure and 180.6 kg/s mass flow feed the high-pressure turbine. The steam after the expansion process in HP part is reduced to the pressure equal to 2.67 MPa. The HP turbine part supplies two regenerative heat exchangers (HPH-3 and HPH-2) and at the outlet of HP section, the mass flow rate is reduced to 158.8 kg/s. After the HP part, the steam is reheated from 324 to 535C. The nominal pressure drop in the reheated system is equal to 0.36 MPa. The reheated steam at

description and simulation results are presented in the next chapter.

cold start-up).

pump (FWP).

3. Turbine modelling

3.1. Description of simulation model

Figure 4. Histogram of the output power (from 1 January to 30 October 2017).

Analysis of Coal-Fired Power Unit Operation in Reduced Minimum Safe Load Regime http://dx.doi.org/10.5772/intechopen.72954 17


Table 1. A number of different start-ups of the reference unit between January and October 2017.

times a month. Table 1 shows the number of start-ups with the start-up type (from the cold or warm state) during individual months. Aggregated stand-by and average start-up time are also provided. Until the end of October, the unit was launched 28 times. The critical factors (load, drum wall and casing turbine temperatures) of the reference unit during September are presented in Figure 3. Over this month, the unit was launched 7 times in total (including one cold start-up).

## 3. Turbine modelling

The output load of the reference unit has been studied between January and October 2017. Histogram of the electric power is presented in Figure 4. During this period, the unit was under flexible operation with frequent load changes over a single day. Most of the time the unit worked with output power below 180 MW which corresponds to the load level below 80%. The unit worked almost 30 h with maximum capacity—225 MW and was shut down several

Figure 3. Reference unit critical operation parameters (during September 2017).

16 Thermal Power Plants - New Trends and Recent Developments

Figure 4. Histogram of the output power (from 1 January to 30 October 2017).

#### 3.1. Description of simulation model

Steam turbine of a 225 MW power unit is considered for the simulation analysis. The mathematical model of the coal-fired power unit was developed using the Ebsilon®Professional computer software [4], including detailed models of turbine and boiler part. Boiler model description and simulation results are presented in the next chapter.

The subcritical steam cycle structure of analysed power unit is presented in Figure 5. The hatched areas show the main components of analysed thermal system: steam boiler, three casing turbine (consisting of a high-pressure part HP, an intermediate-pressure part IP and a low-pressure part LP), eight regenerative heat exchangers (consisting of three high-pressure HPH and five low-pressure LPH), two-part condenser (CO-1 and CO-2), an electric generator (G), a feed-water tank with deaerator (FW), condensate pumps (CP-1 and CP-2) and feed water pump (FWP).

The superheated steam from the steam boiler at 535C temperature under 12.17 MPa pressure and 180.6 kg/s mass flow feed the high-pressure turbine. The steam after the expansion process in HP part is reduced to the pressure equal to 2.67 MPa. The HP turbine part supplies two regenerative heat exchangers (HPH-3 and HPH-2) and at the outlet of HP section, the mass flow rate is reduced to 158.8 kg/s. After the HP part, the steam is reheated from 324 to 535C. The nominal pressure drop in the reheated system is equal to 0.36 MPa. The reheated steam at

Extraction Bleed number Pressure, MPa Temperature, C Mass flow rate, kg/s

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19

I 9 4.03 (3.72) 376.4 (368.0) 8.56 (7.64) II 12 2.70 (2.48) 324.0 (317.0) 13.17 (11.83) III 15 1.23 (1.14) 447.0 (447.0) 7.50 (6.72) IV 19 0.51 (0.47) 334.0 (334.0) 3.72 (3.31) V 21 0.28 (0.26) 268.0 (268.0) 5.28 (4.78) VI 23 0.13 (0.12) 188.0 (188.0) 7.39 (6.75) VII 25 0.026 (0.025) 63.0 (64.6) 5.50 (4.89)

Table 2. Design steam parameters at selected turbine extractions.

Figure 6. Course of steam expansion line for nominal load of power unit.

Figure 5. A simulation model of the power unit.

535C and with 2.31 MPa pressure enters the intermediate-pressure (IP) turbine. In the IP turbine part, the steam is expanded to the of temperature 188.0C and the pressure of 0.13 MPa. The IP section has four extractions to the regeneration system (HPH-1, LPH-5, LPH-4 and LPH-3). The steam mass flow leaving the IP part of the turbine is reduced to 134.9 kg/s. Steam from the IP turbine section feeds the low-pressure LP part. The LP section has one extraction to the low-pressure regeneration heat exchangers (LPH-1/2), so the mass flow rate at the outlet of LP part of the turbine is equal to 129.4 kg/s. The low-pressure steam from the outlet of LP turbine part goes to condensers where is subcooled and then is pumped to the LPH regeneration system. In the LPH section water is reheated to the temperature of 146C and then enters the deaerator and feed water tank. The water pressure after the deaerator is increased to 16.7 MPa and then it flows to the HPH regeneration system. In the HPH section water is reheated to the 250C under 15.5 MPa and then feeds the steam boiler. The design steam parameters (pressure, temperature and mass flow rate) at selected turbine extractions are presented in Table 2.

The steam expansion line for nominal conditions of the analysed power unit is presented in Figure 6. The numerical designation on the expansion curves correspond with the steam parameters in the following locations in turbine system: 1—after shut-off valve, 2—HPregulating stage, 3—exhaust I (to HPH-3), 4—exhaust II (to HPH-2), 5—before IP stage, 6 exhaust III (to HPH-1), 7—exhaust IV (to LPH-5), 8—exhaust V (to LPH-4), 9—exhaust VI (to LPH-3), 10—exhaust VII (to LPH-1/2), 11—turbine outlet.

The structure of simulation model of 225 MW power unit was developed on the basis of information and data included in the turbine operational manual and performance documentation (power unit energy balance). In the design phase, the average numerical values from thermal measurements included in the in the performance measurements report were used for the unit power load equal to 225 MW. Additionally, values of thermal parameters according to operational data from the measuring system were assumed during the simulation model preparation. The efficiencies of main power plant components (turbine, pumps, generator) Analysis of Coal-Fired Power Unit Operation in Reduced Minimum Safe Load Regime http://dx.doi.org/10.5772/intechopen.72954 19


Table 2. Design steam parameters at selected turbine extractions.

535C and with 2.31 MPa pressure enters the intermediate-pressure (IP) turbine. In the IP turbine part, the steam is expanded to the of temperature 188.0C and the pressure of 0.13 MPa. The IP section has four extractions to the regeneration system (HPH-1, LPH-5, LPH-4 and LPH-3). The steam mass flow leaving the IP part of the turbine is reduced to 134.9 kg/s. Steam from the IP turbine section feeds the low-pressure LP part. The LP section has one extraction to the low-pressure regeneration heat exchangers (LPH-1/2), so the mass flow rate at the outlet of LP part of the turbine is equal to 129.4 kg/s. The low-pressure steam from the outlet of LP turbine part goes to condensers where is subcooled and then is pumped to the LPH regeneration system. In the LPH section water is reheated to the temperature of 146C and then enters the deaerator and feed water tank. The water pressure after the deaerator is increased to 16.7 MPa and then it flows to the HPH regeneration system. In the HPH section water is reheated to the 250C under 15.5 MPa and then feeds the steam boiler. The design steam parameters (pressure, temperature and mass flow rate) at selected turbine

The steam expansion line for nominal conditions of the analysed power unit is presented in Figure 6. The numerical designation on the expansion curves correspond with the steam parameters in the following locations in turbine system: 1—after shut-off valve, 2—HPregulating stage, 3—exhaust I (to HPH-3), 4—exhaust II (to HPH-2), 5—before IP stage, 6 exhaust III (to HPH-1), 7—exhaust IV (to LPH-5), 8—exhaust V (to LPH-4), 9—exhaust VI (to

The structure of simulation model of 225 MW power unit was developed on the basis of information and data included in the turbine operational manual and performance documentation (power unit energy balance). In the design phase, the average numerical values from thermal measurements included in the in the performance measurements report were used for the unit power load equal to 225 MW. Additionally, values of thermal parameters according to operational data from the measuring system were assumed during the simulation model preparation. The efficiencies of main power plant components (turbine, pumps, generator)

extractions are presented in Table 2.

Figure 5. A simulation model of the power unit.

18 Thermal Power Plants - New Trends and Recent Developments

LPH-3), 10—exhaust VII (to LPH-1/2), 11—turbine outlet.

Figure 6. Course of steam expansion line for nominal load of power unit.

were assumed to achieve the nominal operating conditions (in the design mode) and are presented in Table 3. The topology constructing process of the analysed power unit thermal cycle was conducted with the following simplifications:

3.2. Verification of steam turbine simulation model

Figure 7. High-pressure regeneration system in the local design mode.

Figure 8. Low-pressure regeneration system in the local design mode.

The simulation model of power unit was verified with available measurements from the DCS system and also with the performance documentation which contains the results of power unit energy balances. Results obtained from simulation calculations in the design mode were compared to results of the guarantee measurements for four different load levels: 100% (225 MW), 80% (180 MW), 60% (135 MW) and 40% (90 MW). In the verification process of simulation model built in the Ebsilon®Professional software, over 50 measurement points (temperature, pressure and mass flow rate) were used at the characteristic points of the thermal structure of analysed power unit. The off-design calculations were performed by entering the required generator active power (power load) and the external (ambient) conditions for the temperature of cooling water inlet to the steam turbine condenser. The characteristic lines were developed for each of steam turbine stages based on the turbine performance data. The real characteristics of a turbine stage group allow to determine the

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The steam turbine simulation model was developed as a number of turbine stages. The number of turbine sections was determined in terms of main inlets and outlets (extractions) in steam turbine cycle. The simulation model of steam turbine was divided into the high-pressure part, intermediate-pressure part and low-pressure part in accordance with its actual construction. The steam turbine model is based on the variable isentropic efficiency, what allows to receive accurate results of simulation calculations for the different load operation. This is very important in part load modelling of steam turbine which is working in sliding pressure mode. The performance operation of steam turbine cycle dependents from many operational parameters, e.g. the temperature, pressure and speed of the working medium. This fact also applies to other elements in the thermal cycle of power systems. The characteristics are used in simulation modelling for an accurate thermodynamic description of components behaviour under part load operation. The characteristic lines describing steam turbine performance were developed for each of turbine stage and then implemented in a simulation model of power unit [4, 5].

The local design mode was assumed for high and low-pressure feed water heaters during the model constructing phase in the design mode. The special off-design mode was used for HPH and LPH regeneration sections in the off-design calculations (at different load levels). The regeneration heat exchangers of HP/LP sections and also the condenser system was developed in separate files for design values and then was subsequently transferred to the simulation model of the power unit. The special off-design mode enables maintenance of constant rated values for given components during the development of the whole power unit designing without the possibility of such values overwriting after operation parameters change of the components directly influencing their functioning [5]. The nominal parameters of HP and LP regeneration system developed in the local design mode are presented in Figures 7 and 8, respectively.


Table 3. Power unit components efficiency.

### 3.2. Verification of steam turbine simulation model

were assumed to achieve the nominal operating conditions (in the design mode) and are presented in Table 3. The topology constructing process of the analysed power unit thermal

• deaerator is supplied from the third turbine extraction (IP turbine section) for power load above 190 MW, whereas for power load below 190 MW—from the second turbine extrac-

• steam distribution in the outer glands of the turbine shaft and the turbine sealing system

The steam turbine simulation model was developed as a number of turbine stages. The number of turbine sections was determined in terms of main inlets and outlets (extractions) in steam turbine cycle. The simulation model of steam turbine was divided into the high-pressure part, intermediate-pressure part and low-pressure part in accordance with its actual construction. The steam turbine model is based on the variable isentropic efficiency, what allows to receive accurate results of simulation calculations for the different load operation. This is very important in part load modelling of steam turbine which is working in sliding pressure mode. The performance operation of steam turbine cycle dependents from many operational parameters, e.g. the temperature, pressure and speed of the working medium. This fact also applies to other elements in the thermal cycle of power systems. The characteristics are used in simulation modelling for an accurate thermodynamic description of components behaviour under part load operation. The characteristic lines describing steam turbine performance were developed for each of turbine stage and then implemented in a simulation model of power unit [4, 5].

The local design mode was assumed for high and low-pressure feed water heaters during the model constructing phase in the design mode. The special off-design mode was used for HPH and LPH regeneration sections in the off-design calculations (at different load levels). The regeneration heat exchangers of HP/LP sections and also the condenser system was developed in separate files for design values and then was subsequently transferred to the simulation model of the power unit. The special off-design mode enables maintenance of constant rated values for given components during the development of the whole power unit designing without the possibility of such values overwriting after operation parameters change of the components directly influencing their functioning [5]. The nominal parameters of HP and LP regeneration system developed in the local design mode are presented in Figures 7 and 8,

Efficiency, % Turbine Pumps Generator

HP IP LP

Isentropic 0.852 0.837 0.823 0.800 – Mechanical 0.996 0.996 0.996 0.985 0.996 Electrical – ––– 0.986

cycle was conducted with the following simplifications:

20 Thermal Power Plants - New Trends and Recent Developments

were not included in the simulation model calculations.

tion (HP turbine section),

respectively.

Table 3. Power unit components efficiency.

The simulation model of power unit was verified with available measurements from the DCS system and also with the performance documentation which contains the results of power unit energy balances. Results obtained from simulation calculations in the design mode were compared to results of the guarantee measurements for four different load levels: 100% (225 MW), 80% (180 MW), 60% (135 MW) and 40% (90 MW). In the verification process of simulation model built in the Ebsilon®Professional software, over 50 measurement points (temperature, pressure and mass flow rate) were used at the characteristic points of the thermal structure of analysed power unit. The off-design calculations were performed by entering the required generator active power (power load) and the external (ambient) conditions for the temperature of cooling water inlet to the steam turbine condenser. The characteristic lines were developed for each of steam turbine stages based on the turbine performance data. The real characteristics of a turbine stage group allow to determine the

Figure 7. High-pressure regeneration system in the local design mode.

Figure 8. Low-pressure regeneration system in the local design mode.

changes of the isentropic efficiencies in part load calculations and to obtain the reliable results of thermodynamic parameters in steam turbine system.

The relative error for different parameters at the characteristic points in the power unit thermal cycle was used to assess the quality of the developed simulation model. The values of relative error δxi of selected parameters were calculated according to the following formula:

$$\delta \mathbf{x}\_i = \frac{|\mathbf{x}\_{i\ REF} - \mathbf{x}\_{i\ EBS}|}{\mathbf{x}\_{i\ REF}} \tag{1}$$

To determine the technical-operational parameters of the power unit in off-design conditions the following indices were determined based on the results of simulation calculations: gross power of steam turbine generator, isentropic efficiency of steam turbine, isentropic efficiency of HP, IP and LP part of steam turbine, gross thermal efficiency of power unit, heat supplied to the steam cycle and specific consumption of heat. The mathematical formulas concerning

Nel,G ¼ ð Þ Ni,HP þ Ni,IP þ Ni,LP ∙ηmS,T∙η<sup>G</sup> (2)

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(3)

23

(4)

quantities and indices specified above are presented below [8].

where:

where:

where:

where:

The gross power of steam turbine generator is defined as follows:

Ni,HP—internal power of the HP section of the steam turbine, MW Ni,IP—internal power of the IP section of the steam turbine, MW Ni,LP—internal power of the LP section of the steam turbine, MW

The isentropic efficiency of the steam turbine is calculated from the following equation:

i2s—enthalpy at the outlet from the turbine after isentropic expansion, kJ/kg

<sup>η</sup><sup>i</sup> <sup>¼</sup> <sup>i</sup><sup>1</sup> � <sup>i</sup><sup>2</sup> i<sup>1</sup> � i2<sup>s</sup>

The values of the gross thermal efficiency of power unit result from the following equation:

<sup>η</sup>el,G <sup>¼</sup> Nel,G Q\_ ch

The values of the flux of chemical energy of fuel were taken from the simulation calculations of boiler performance in off-design conditions. The amount of heat supplied to the steam cycle in

<sup>Q</sup>\_ sc <sup>¼</sup> <sup>m</sup>\_ LS∙ð Þþ iLS � iFW <sup>m</sup>\_ RH∙ð Þ iHRH � iCRH (5)

ηmS,T—mechanical efficiency of the steam turbine,

i1—enthalpy at the inlet to the turbine, kJ/kg

i2—enthalpy at the outlet from the turbine, kJ/kg

Q\_ ch—the flux of chemical energy of the fuel, MW

coal-fired boiler result from the equation:

m\_ LS—live steam mass flow rate, kg/s

ηG—generator efficiency.

where:

xi REF—reference value of the i-th parameter,

xi EBS—simulation model value of the i-th parameter.

The values of relative errors calculated using Eq. (1) for different groups of the parameter at part load conditions are presented in Table 3. The values of relative errors obtained from the verification process of steam turbine cycle confirm the correctness and accuracy of the simulation model. The analysis shows that the difference between simulation model results and measured data varying from 1.94 to 6.17%. Based on the obtained results it can be concluded that the simulation model of steam turbine cycle may be used for off-design investigation of the analysed 225 MWe power unit. Results in Table 4 show that with the decrease of power unit load the average relative error increases. This means that the accuracy of the simulation model is the highest for nominal conditions and in the steam turbine part load operation the precision decreases. The main cause of this is the various simulation model assumptions and the accuracy of the developed characteristics of turbine stages. However, it must be also taken into account the uncertainties of measured data used in the verification process.

#### 3.3. Thermodynamic analysis of power unit in off-design conditions

Through simulation analysis, it is possible to determine the specific parameters of thermal power systems under conditions which are different from the nominal. In this chapter, the thermodynamic analysis was carried out to demonstrate the impact of changes in power unit performance under part load operation. One-dimensional simulation modelling is sufficient to obtain the detailed results of power systems behaviour in steady-state conditions. However, it does not give any information about the effects of dynamic changes in power system operation. This type of thermodynamic modelling is a perfect engineering tool to give a global view of the thermal cycle performance [5–7].


Table 4. Relative errors in the verification process of power unit under different load.

To determine the technical-operational parameters of the power unit in off-design conditions the following indices were determined based on the results of simulation calculations: gross power of steam turbine generator, isentropic efficiency of steam turbine, isentropic efficiency of HP, IP and LP part of steam turbine, gross thermal efficiency of power unit, heat supplied to the steam cycle and specific consumption of heat. The mathematical formulas concerning quantities and indices specified above are presented below [8].

The gross power of steam turbine generator is defined as follows:

$$N\_{el,G} = (N\_{i,HP} + N\_{i,IP} + N\_{i,LP}) \cdot \eta\_{mS,T} \cdot \eta\_G \tag{2}$$

where:

(1)

changes of the isentropic efficiencies in part load calculations and to obtain the reliable

The relative error for different parameters at the characteristic points in the power unit thermal cycle was used to assess the quality of the developed simulation model. The values of relative

> <sup>δ</sup>xi <sup>¼</sup> j j xi REF � xi EBS xi REF

The values of relative errors calculated using Eq. (1) for different groups of the parameter at part load conditions are presented in Table 3. The values of relative errors obtained from the verification process of steam turbine cycle confirm the correctness and accuracy of the simulation model. The analysis shows that the difference between simulation model results and measured data varying from 1.94 to 6.17%. Based on the obtained results it can be concluded that the simulation model of steam turbine cycle may be used for off-design investigation of the analysed 225 MWe power unit. Results in Table 4 show that with the decrease of power unit load the average relative error increases. This means that the accuracy of the simulation model is the highest for nominal conditions and in the steam turbine part load operation the precision decreases. The main cause of this is the various simulation model assumptions and the accuracy of the developed characteristics of turbine stages. However, it must be also taken

Through simulation analysis, it is possible to determine the specific parameters of thermal power systems under conditions which are different from the nominal. In this chapter, the thermodynamic analysis was carried out to demonstrate the impact of changes in power unit performance under part load operation. One-dimensional simulation modelling is sufficient to obtain the detailed results of power systems behaviour in steady-state conditions. However, it does not give any information about the effects of dynamic changes in power system operation. This type of thermodynamic modelling is a perfect engineering tool to give a global view

Pressure 2.40% 3.78% 4.47% 5.08% Temperature 2.89% 4.97% 5.38% 6.17% Mass flow 1.94% 4.32% 5.24% 5.23% Average 2.42% 4.24% 4.72% 5.48%

100% load 80% load 60% load 40% load

into account the uncertainties of measured data used in the verification process.

3.3. Thermodynamic analysis of power unit in off-design conditions

Table 4. Relative errors in the verification process of power unit under different load.

error δxi of selected parameters were calculated according to the following formula:

results of thermodynamic parameters in steam turbine system.

xi REF—reference value of the i-th parameter,

22 Thermal Power Plants - New Trends and Recent Developments

of the thermal cycle performance [5–7].

xi EBS—simulation model value of the i-th parameter.

where:

Ni,HP—internal power of the HP section of the steam turbine, MW

Ni,IP—internal power of the IP section of the steam turbine, MW

Ni,LP—internal power of the LP section of the steam turbine, MW

ηmS,T—mechanical efficiency of the steam turbine,

ηG—generator efficiency.

The isentropic efficiency of the steam turbine is calculated from the following equation:

$$\eta\_i = \frac{i\_1 - i\_2}{i\_1 - i\_{2s}} \tag{3}$$

where:

i1—enthalpy at the inlet to the turbine, kJ/kg

i2—enthalpy at the outlet from the turbine, kJ/kg

i2s—enthalpy at the outlet from the turbine after isentropic expansion, kJ/kg

The values of the gross thermal efficiency of power unit result from the following equation:

$$
\eta\_{el,G} = \frac{N\_{el,G}}{\dot{Q}\_{ch}} \tag{4}
$$

where:

Q\_ ch—the flux of chemical energy of the fuel, MW

The values of the flux of chemical energy of fuel were taken from the simulation calculations of boiler performance in off-design conditions. The amount of heat supplied to the steam cycle in coal-fired boiler result from the equation:

$$
\dot{Q}\_{sc} = \dot{m}\_{LS} \cdot (\dot{\mathbf{i}}\_{LS} - \dot{\mathbf{i}}\_{FW}) + \dot{m}\_{RH} \cdot (\dot{\mathbf{i}}\_{HRH} - \dot{\mathbf{i}}\_{CRH}) \tag{5}
$$

where:

m\_ LS—live steam mass flow rate, kg/s

iLS—live steam enthalpy at the outlet from the boiler, kJ/kg

iFW—feed water enthalpy at the inlet to the boiler, kJ/kg

m\_ RH—reheat steam mass flow rate, kg/s

iHRH—hot reheat steam enthalpy at the outlet from the intermediate superheater, kJ/kg

iCRH—cold reheat steam enthalpy at the inlet to the intermediate superheater, kJ/kg

The specific consumption of heat in a steam turbine is calculated from the following equation:

$$q\_{h,ST} = 3600 \cdot \frac{\dot{Q}\_{sc}}{N\_{el,G}} \tag{6}$$

isentropic efficiency of IP turbine for which this indices at nominal conditions is equal to 86.6% while in 40% load increases to 87.6%. The thermodynamic analysis of selected power unit performance factors shows that the difference between simulation results and reference data varying from 0.11 to 1.21%. Based on the obtained results it can be concluded that the simulation model of steam turbine cycle accurately confirms the results of the reference

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Boiler modelling was performed using Ebsilon®Professional software with EbsBoiler package. The simulation was made for 100%, 80%, 60% and 40% load of the boiler and results were validated using data from in-situ test campaign. Ebsilon®Professional software allows creating a boiler model using graphical interface embedded in the software. Figure 9 presents schematic of the reference boiler, with superheaters (SH), reheaters (RH) and water heater (WH) depicted. A number of particular heat exchanger represents the degree of overheating of the steam—SH 5, for instance, is a final superheater with steam outlet temperature equal to about 535�C. Figure 10 depicts part of the model, that represents combustion chamber and evaporator. Furthermore, simulated processes are controlled in the same way it is done on the reference unit—for instance amount of air supplied to the combustion chamber in the model is controlled by the level of oxygen at the boiler outlet. Values depicted in Figure 10 present different parameters of the combustion process in full load operation. Fuel flow is equal to

flows are modelled as a single stream. However, if more precision in calculations of combustion chamber itself is required, air staging would have to be modelled. Level of oxygen at the outlet of combustion zone is equal to 4.499% while air-fuel ratio is equal to 1.302. The latter value does not represent real stoichiometry of combustion in the reference boiler, due to simplification that was made in case of primary and secondary air streams. Figure 11 depicts

particular heat exchangers—for instance, heat flows from area D<sup>0</sup> to the superheater 4 and 1 subsequently. There is also a water spray injection model, with water flow equal to 3.722 t/h. In steady-state modelling of the boiler, water spray injection is difficult to simulate. In reality, this value varies heavily during operation, therefore it can only be simulated as an average value. In general, this way of modelling requires deep knowledge about the simulated object and its

Results of the simulation indicate boiler behaviour in different load levels, including load 40% which is below minimum safe design load of the reference boiler. Figure 12 presents result of flue gas temperature distribution inside the boiler, for live steam flow equal to 650 t/h (100% load), 520 t/h (80% load), 390 t/h (60% load) and 260 t/h (40% load). Temperature values depicted in Figure 12 should be treated as average from given boiler areas (perpendicular to the flue gas flow direction) and not as exact temperature points. What can be seen, is that the difference in temperatures is more significant between 60 and 40% load than between 80 and

/h. Primary and secondary air

, D00) from where heat is taken to

98.697 t/h while total air to combustion is equal to 618012.633 m<sup>3</sup>

part of the model that represents areas of the boiler (D, D<sup>0</sup>

performance measurements.

4. Boiler modelling

operating conditions.

60% load.

The values of selected characteristic indices obtained from the simulation modelling of steam turbine system are presented in Table 4. The part load calculations were performed for four different loads of power unit: 100%, 80%, 60% and 40%. For each of off-design conditions, the simulation results were compared with the data obtained from the performance documentation of the steam turbine. The EBS and REF abbreviations used in Table 5 mean the calculation results from the Ebsilon®Professional simulation model and the values of selected parameters from the reference documentation, respectively. The obtained results show that with the decrease in power load, the gross thermal efficiency decreases from 40.0% (for 100% load) to 36.8% (40% load). This means that for 40% part load of the power unit, the gross thermal efficiency is 3.2% less than for the nominal conditions. The steam turbine heat rate of 100% load is equal to 8119 kJ/kWh. The steam turbine heat rate increase with power load drop and for 40% load is 9021 kJ/kWh. On this basis, it can be concluded that for 40% load of power unit it is necessary to supply to the steam cycle about 902 kJ of an additional amount of energy for each of kWh produced in the generator. The isentropic efficiency of a steam turbine for nominal conditions is equal to 85.1% and it decreases to 79.1% in 40% load. The isentropic efficiency of HP and LP section of steam turbine also decreases with the power load from the 81.5 to 65.2% and from 87.2 to 84.1%, respectively. The only exception is an


Table 5. Selected technical-operational parameters of power unit under different load.

isentropic efficiency of IP turbine for which this indices at nominal conditions is equal to 86.6% while in 40% load increases to 87.6%. The thermodynamic analysis of selected power unit performance factors shows that the difference between simulation results and reference data varying from 0.11 to 1.21%. Based on the obtained results it can be concluded that the simulation model of steam turbine cycle accurately confirms the results of the reference performance measurements.

## 4. Boiler modelling

iLS—live steam enthalpy at the outlet from the boiler, kJ/kg

iHRH—hot reheat steam enthalpy at the outlet from the intermediate superheater, kJ/kg

The specific consumption of heat in a steam turbine is calculated from the following equation:

qh,ST <sup>¼</sup> <sup>3600</sup><sup>∙</sup> <sup>Q</sup>\_

The values of selected characteristic indices obtained from the simulation modelling of steam turbine system are presented in Table 4. The part load calculations were performed for four different loads of power unit: 100%, 80%, 60% and 40%. For each of off-design conditions, the simulation results were compared with the data obtained from the performance documentation of the steam turbine. The EBS and REF abbreviations used in Table 5 mean the calculation results from the Ebsilon®Professional simulation model and the values of selected parameters from the reference documentation, respectively. The obtained results show that with the decrease in power load, the gross thermal efficiency decreases from 40.0% (for 100% load) to 36.8% (40% load). This means that for 40% part load of the power unit, the gross thermal efficiency is 3.2% less than for the nominal conditions. The steam turbine heat rate of 100% load is equal to 8119 kJ/kWh. The steam turbine heat rate increase with power load drop and for 40% load is 9021 kJ/kWh. On this basis, it can be concluded that for 40% load of power unit it is necessary to supply to the steam cycle about 902 kJ of an additional amount of energy for each of kWh produced in the generator. The isentropic efficiency of a steam turbine for nominal conditions is equal to 85.1% and it decreases to 79.1% in 40% load. The isentropic efficiency of HP and LP section of steam turbine also decreases with the power load from the 81.5 to 65.2% and from 87.2 to 84.1%, respectively. The only exception is an

Indices 100% load 80% load 60% load 40% load

Gross thermal efficiency, % 40.0 39.9 39.6 39.7 38.4 38.6 36.8 36.7 Steam turbine heat rate, kJ/kWh 8119 8100 8164 8175 8358 8380 9021 8999 Isentropic efficiency of turbine, % 85.1 85.2 83.6 83.7 82.1 82.0 79.1 79.0 Isentropic efficiency of HP, % 81.5 81.5 78.1 78.0 74.0 74.3 65.2 65.3 Isentropic efficiency of IP, % 86.6 86.7 86.3 86.5 87.0 87.1 87.6 87.6 Isentropic efficiency of LP, % 87.2 87.0 86.2 86.4 85.2 85.1 84.1 84.0

Gross power, MW 222.8 179.6 134.9 90.7

Table 5. Selected technical-operational parameters of power unit under different load.

EBS REF EBS REF EBS REF EBS REF

sc Nel,G

(6)

iCRH—cold reheat steam enthalpy at the inlet to the intermediate superheater, kJ/kg

iFW—feed water enthalpy at the inlet to the boiler, kJ/kg

m\_ RH—reheat steam mass flow rate, kg/s

24 Thermal Power Plants - New Trends and Recent Developments

Boiler modelling was performed using Ebsilon®Professional software with EbsBoiler package. The simulation was made for 100%, 80%, 60% and 40% load of the boiler and results were validated using data from in-situ test campaign. Ebsilon®Professional software allows creating a boiler model using graphical interface embedded in the software. Figure 9 presents schematic of the reference boiler, with superheaters (SH), reheaters (RH) and water heater (WH) depicted. A number of particular heat exchanger represents the degree of overheating of the steam—SH 5, for instance, is a final superheater with steam outlet temperature equal to about 535�C. Figure 10 depicts part of the model, that represents combustion chamber and evaporator. Furthermore, simulated processes are controlled in the same way it is done on the reference unit—for instance amount of air supplied to the combustion chamber in the model is controlled by the level of oxygen at the boiler outlet. Values depicted in Figure 10 present different parameters of the combustion process in full load operation. Fuel flow is equal to 98.697 t/h while total air to combustion is equal to 618012.633 m<sup>3</sup> /h. Primary and secondary air flows are modelled as a single stream. However, if more precision in calculations of combustion chamber itself is required, air staging would have to be modelled. Level of oxygen at the outlet of combustion zone is equal to 4.499% while air-fuel ratio is equal to 1.302. The latter value does not represent real stoichiometry of combustion in the reference boiler, due to simplification that was made in case of primary and secondary air streams. Figure 11 depicts part of the model that represents areas of the boiler (D, D<sup>0</sup> , D00) from where heat is taken to particular heat exchangers—for instance, heat flows from area D<sup>0</sup> to the superheater 4 and 1 subsequently. There is also a water spray injection model, with water flow equal to 3.722 t/h. In steady-state modelling of the boiler, water spray injection is difficult to simulate. In reality, this value varies heavily during operation, therefore it can only be simulated as an average value. In general, this way of modelling requires deep knowledge about the simulated object and its operating conditions.

Results of the simulation indicate boiler behaviour in different load levels, including load 40% which is below minimum safe design load of the reference boiler. Figure 12 presents result of flue gas temperature distribution inside the boiler, for live steam flow equal to 650 t/h (100% load), 520 t/h (80% load), 390 t/h (60% load) and 260 t/h (40% load). Temperature values depicted in Figure 12 should be treated as average from given boiler areas (perpendicular to the flue gas flow direction) and not as exact temperature points. What can be seen, is that the difference in temperatures is more significant between 60 and 40% load than between 80 and 60% load.

Figure 11. Flue gas path, superheaters and water spray injection depicted in the model.

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Figure 12. Flue gas temperature distribution inside the boiler for different load levels.

Figure 9. Reference boiler description (SH—superheater, RH—reheater, WH—water heater).

Figure 10. Combustion chamber and evaporator depicted in the model.

Figure 13 presents results of live and reheated steam temperature at the boiler outlet for different load levels. What can be observed, is that both temperatures undergo a steep descent between 60 and 40% load. In the latter case, the live steam temperature is below 520C and reheated steam temperature falls down below 490C. Both values are considerably lower than designed Analysis of Coal-Fired Power Unit Operation in Reduced Minimum Safe Load Regime http://dx.doi.org/10.5772/intechopen.72954 27

Figure 11. Flue gas path, superheaters and water spray injection depicted in the model.

Figure 12. Flue gas temperature distribution inside the boiler for different load levels.

Figure 13 presents results of live and reheated steam temperature at the boiler outlet for different load levels. What can be observed, is that both temperatures undergo a steep descent between 60 and 40% load. In the latter case, the live steam temperature is below 520C and reheated steam temperature falls down below 490C. Both values are considerably lower than designed

Figure 9. Reference boiler description (SH—superheater, RH—reheater, WH—water heater).

26 Thermal Power Plants - New Trends and Recent Developments

Figure 10. Combustion chamber and evaporator depicted in the model.

Figure 13. Steam temperatures in different load levels.

5. Discussion

Outcomes from simulation modelling revealed that reference power unit can experience a variety of issues when operating with the decreased minimum safe load. Steam temperatures presented in Figure 8 indicate, that operation in 40% load is much less efficient than in 60% load. However, there is an economic sense of such configuration when shut down and start-up costs are taken into consideration. Flue gas temperatures presented in Figure 12 indicate other potential issues. The vastly important threat is related to sulphuric acid (H2SO4) condensation. Formation of H2SO4 occurs in a temperature range between 200 and 400C while its content depends on the amount of sulphur trioxide SO3 and water vapour in the flue gas. The temperature of condensation decreases proportionally to the content of sulphuric acid or water vapour in flue gas and it is in the range of 95–160C [9–11]. However, roughly 90% of sulphuric acid condenses in a temperature range between 115 and 138C [12]. According to data presented in Figures 12 and 15, in 40% load temperature at the outlet of air preheater is close to 100C. That increases the probability of sulphuric acid condensation inside the air preheater, which can eventually lead to corrosion problems. Corrosion can also be an issue when it comes to electrostatic precipitator (ESP) operation, however low flue gas temperature is in general

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Another concern with low load boiler operation is related to de-NOx installations. Temperature value at the outlet of combustion zone depicted in Figure 12 decreases from about 1190 to 1090C. Considering low load operation on boilers equipped with SNCR technology, it must be confirmed that reagent injection system is able to adjust to the new conditions—optimal injection temperature window for NOx removal is roughly between 950 and 1025C [14]. Regarding

favourable here because it decreases dust resistivity [13].

Figure 15. Flue gas temperature at the outlet of air preheater.

Figure 14. Heating power delivered to each heat exchanger for different load levels (100%, 60%, 40%).

temperature equal to 535C. Figure 14 presents results from heating power Q taken by each heat exchanger in the boiler. What is interesting, is that second superheater (SH 2) has got higher power in 40% than in 60% load. Also, power taken by fourth superheater (SH 4) in 40% load is almost negligible. Figure 15 depicts descend of flue gas temperature at the outlet of air preheater.

Figure 15. Flue gas temperature at the outlet of air preheater.

#### 5. Discussion

temperature equal to 535C. Figure 14 presents results from heating power Q taken by each heat exchanger in the boiler. What is interesting, is that second superheater (SH 2) has got higher power in 40% than in 60% load. Also, power taken by fourth superheater (SH 4) in 40% load is almost negligible. Figure 15 depicts descend of flue gas temperature at the outlet of air preheater.

Figure 14. Heating power delivered to each heat exchanger for different load levels (100%, 60%, 40%).

Figure 13. Steam temperatures in different load levels.

28 Thermal Power Plants - New Trends and Recent Developments

Outcomes from simulation modelling revealed that reference power unit can experience a variety of issues when operating with the decreased minimum safe load. Steam temperatures presented in Figure 8 indicate, that operation in 40% load is much less efficient than in 60% load. However, there is an economic sense of such configuration when shut down and start-up costs are taken into consideration. Flue gas temperatures presented in Figure 12 indicate other potential issues. The vastly important threat is related to sulphuric acid (H2SO4) condensation. Formation of H2SO4 occurs in a temperature range between 200 and 400C while its content depends on the amount of sulphur trioxide SO3 and water vapour in the flue gas. The temperature of condensation decreases proportionally to the content of sulphuric acid or water vapour in flue gas and it is in the range of 95–160C [9–11]. However, roughly 90% of sulphuric acid condenses in a temperature range between 115 and 138C [12]. According to data presented in Figures 12 and 15, in 40% load temperature at the outlet of air preheater is close to 100C. That increases the probability of sulphuric acid condensation inside the air preheater, which can eventually lead to corrosion problems. Corrosion can also be an issue when it comes to electrostatic precipitator (ESP) operation, however low flue gas temperature is in general favourable here because it decreases dust resistivity [13].

Another concern with low load boiler operation is related to de-NOx installations. Temperature value at the outlet of combustion zone depicted in Figure 12 decreases from about 1190 to 1090C. Considering low load operation on boilers equipped with SNCR technology, it must be confirmed that reagent injection system is able to adjust to the new conditions—optimal injection temperature window for NOx removal is roughly between 950 and 1025C [14]. Regarding SCR operation, most of the current commercial installations are based on V2O5/TiO2 catalyst, which has considerably high working temperature, roughly between 300 and 400C. Furthermore, the activity of such catalysts decreases with temperature [15, 16]. SCR installation is normally designed for full load operation temperatures, but it should also work well in minimum load conditions. In case of reference boiler, that would be 60% load. Simulation outcomes reveal, that in 40% load flue gas temperature in SCR relevant region drops below 300C.

conventional coal-fired power plants strongly influences operation of the steam turbine. The turbine ventilation is one of the main limiting factors in the load range of steam turbine. Insufficient steam flow causes temperature increase and thermal stresses in turbine stages. It is important to revise all of the control loops and measuring devices in case the of power unit operation at low loads to avoid exploitation and performance problems [7, 17]. The steadystate simulation analysis of the power unit model shows a good accordance to reference operating data throughout the power unit operating range. Based on the results of verification process it can be stated that simulation model of steam turbine cycle developed in Ebsilon®Professional can be used as an engineering tool for investigation of power unit perfor-

Analysis of Coal-Fired Power Unit Operation in Reduced Minimum Safe Load Regime

http://dx.doi.org/10.5772/intechopen.72954

31

Simulation modelling described in the paper can be recommended as an efficient and accurate method to evaluate power unit operation in different conditions. Authors investigated the operation of '200 MWe' class coal-fired power unit in reduced minimum load regime. Performed tests revealed, that this is a technically feasible way of operation that can improve the flexibility of that sort of units. However, reducing the unit load from designed minimum safe load, can bring about variety of problems. Vastly decreased efficiency, inaccurate measurements and operation problems derived from low flue gas temperature are the most important ones. On the other hand, ability to work in extended load range may decrease number of shut down and start-ups of the unit, which is very desirable from power plant operator point of view. To conclude, it must be said that reference 200 MWe class coal-fired unit, as well as other similar units, have potential of flexibility improvement that is worth

[1] Huber M, Dimkova D, Hamacher T. Integration of wind and solar power in Europe:

[2] Taler J, Węglowski B, Taler D, Sobota T, Dzierwa P, Trojan M, Madejski P, Pilarczyk M. Determination of start-up curves for a boiler with natural circulation based on the analy-

sis of stress distribution in critical pressure components. Energy. 2015;92:153-159

mance in off-design conditions.

6. Conclusions

considering.

Author details

References

Piotr Żymełka, Maciej Żyrkowski\* and Maciej Bujalski

\*Address all correspondence to: maciej.zyrkowski@gkpge.pl R&D Department, PGE Energia Ciepla S.A., Krakow, Poland

Assesment of flexibility requirements. Energy. 2014;69:236-246

Operation of the steam turbine in part load conditions as well as below current technical minimum involves many technical and economic aspects. The simulation results for a selected different load of power unit shows that analysed power unit can operate stably in the range between 90 and 225 MW. The thermodynamic analysis demonstrates, that the gross thermal efficiency varies between 40.0 and 36.8%. The steam turbine heat rate was calculated to determine the quality of steam turbine performance in off-design conditions. The heat rate of steam turbine cycle increases from 8119 kJ/kWh (for 100% load) to 9021 kJ/kWh (40% load). Figure 16 shows the course of gross thermal efficiency and steam turbine heat rate. What can be seen, is that the heat rate and efficiency have non–linear characteristic. Presented indices rapidly change in the range between 90 and 135 MW. The thermal efficiency decrease from 38.6 to 36.8% and the steam turbine heat rate increases from 8358 to 9021 kJ/kWh in load range below the current technical minimum.

The simulation calculations reveal that the 225 MW power unit can operate between 40 and 100% load with reasonable efficiency. Power unit operation with reduced minimum load allows decreasing start-up and shut-down operation costs. Reducing the minimum load of

Figure 16. Power unit heat rate and thermal efficiency for part load conditions.

conventional coal-fired power plants strongly influences operation of the steam turbine. The turbine ventilation is one of the main limiting factors in the load range of steam turbine. Insufficient steam flow causes temperature increase and thermal stresses in turbine stages. It is important to revise all of the control loops and measuring devices in case the of power unit operation at low loads to avoid exploitation and performance problems [7, 17]. The steadystate simulation analysis of the power unit model shows a good accordance to reference operating data throughout the power unit operating range. Based on the results of verification process it can be stated that simulation model of steam turbine cycle developed in Ebsilon®Professional can be used as an engineering tool for investigation of power unit performance in off-design conditions.

## 6. Conclusions

SCR operation, most of the current commercial installations are based on V2O5/TiO2 catalyst, which has considerably high working temperature, roughly between 300 and 400C. Furthermore, the activity of such catalysts decreases with temperature [15, 16]. SCR installation is normally designed for full load operation temperatures, but it should also work well in minimum load conditions. In case of reference boiler, that would be 60% load. Simulation outcomes reveal, that in 40% load flue gas temperature in SCR relevant region drops below 300C.

Operation of the steam turbine in part load conditions as well as below current technical minimum involves many technical and economic aspects. The simulation results for a selected different load of power unit shows that analysed power unit can operate stably in the range between 90 and 225 MW. The thermodynamic analysis demonstrates, that the gross thermal efficiency varies between 40.0 and 36.8%. The steam turbine heat rate was calculated to determine the quality of steam turbine performance in off-design conditions. The heat rate of steam turbine cycle increases from 8119 kJ/kWh (for 100% load) to 9021 kJ/kWh (40% load). Figure 16 shows the course of gross thermal efficiency and steam turbine heat rate. What can be seen, is that the heat rate and efficiency have non–linear characteristic. Presented indices rapidly change in the range between 90 and 135 MW. The thermal efficiency decrease from 38.6 to 36.8% and the steam turbine heat rate increases from 8358 to 9021 kJ/kWh in load range

The simulation calculations reveal that the 225 MW power unit can operate between 40 and 100% load with reasonable efficiency. Power unit operation with reduced minimum load allows decreasing start-up and shut-down operation costs. Reducing the minimum load of

below the current technical minimum.

30 Thermal Power Plants - New Trends and Recent Developments

Figure 16. Power unit heat rate and thermal efficiency for part load conditions.

Simulation modelling described in the paper can be recommended as an efficient and accurate method to evaluate power unit operation in different conditions. Authors investigated the operation of '200 MWe' class coal-fired power unit in reduced minimum load regime. Performed tests revealed, that this is a technically feasible way of operation that can improve the flexibility of that sort of units. However, reducing the unit load from designed minimum safe load, can bring about variety of problems. Vastly decreased efficiency, inaccurate measurements and operation problems derived from low flue gas temperature are the most important ones. On the other hand, ability to work in extended load range may decrease number of shut down and start-ups of the unit, which is very desirable from power plant operator point of view. To conclude, it must be said that reference 200 MWe class coal-fired unit, as well as other similar units, have potential of flexibility improvement that is worth considering.

## Author details

Piotr Żymełka, Maciej Żyrkowski\* and Maciej Bujalski \*Address all correspondence to: maciej.zyrkowski@gkpge.pl R&D Department, PGE Energia Ciepla S.A., Krakow, Poland

## References


[3] Talej J, Dzierwa P, Taler D, Harchut P. Optimization of the boiler start-up taking into account thermal stresses. Energy. 2015;92:160-170

**Chapter 3**

Provisional chapter

**Detection of Malfunctions and Abnormal Working**

DOI: 10.5772/intechopen.72952

Detection of Malfunctions and Abnormal Working

Coal mill malfunctions are some of the most common causes of failing to keep the power plant crucial operating parameters or even unplanned power plant shutdowns. Therefore, an algorithm has been developed that enable online detection of abnormal conditions and malfunctions of an operating mill. Based on calculated diagnostic signals and defined thresholds, this algorithm informs about abnormal operating conditions. Diagnostic signals represent the difference between the measured and the modeled values of two selected mill operating parameters. Models of mill motor current and outlet temperature of pulverized fuel were developed based on the linear regression theory. Various data analysis and feature selection procedures have been performed to obtain the best possible model. The model based on linear regression has been compared with two alternative models. The algorithm validation was carried out based on historical data containing values of operating parameters from 10 months of mill operation. Historical data were downloaded from distributed control system (DCS) of a 200-MW coal-fired power plant. Tests carried out on historical data show that this algorithm can be successfully used to detect certain abnormal conditions and malfunctions of the operating

**Conditions of a Coal Mill**

Conditions of a Coal Mill

Teresa Kurek, Konrad Wojdan,

http://dx.doi.org/10.5772/intechopen.72952

Daniel Nabagło and Konrad Świrski

Konrad Świrski

Abstract

diagnostic

1. Introduction

Teresa Kurek, Konrad Wojdan, Daniel Nabagło and

mill, such as feeder blockage, lack of coal and mill overload.

Keywords: predictive maintenance, coal mill, fault detection, digital twin, online

Safety, reliability and flexibility are some of the most important operation features of any power plant. The abnormal operation conditions and malfunctions of coal mills negatively

> © The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter


## **Detection of Malfunctions and Abnormal Working Conditions of a Coal Mill** Provisional chapter Detection of Malfunctions and Abnormal Working

DOI: 10.5772/intechopen.72952

Teresa Kurek, Konrad Wojdan, Daniel Nabagło and Konrad Świrski Teresa Kurek, Konrad Wojdan,

Additional information is available at the end of the chapter Daniel Nabagło and Konrad Świrski

http://dx.doi.org/10.5772/intechopen.72952 Additional information is available at the end of the chapter

Conditions of a Coal Mill

#### Abstract

[3] Talej J, Dzierwa P, Taler D, Harchut P. Optimization of the boiler start-up taking into

[4] STEAG Energy Services GmbH. Ebsilon Professional software. [Online]. December, 2017.

[5] Szega M, Żymełka P. Thermodynamic and economic analysis of the production of electricity, heat and cold in the combined heat and power unit with the absorption chillers.

[6] Alobaid F, Mertens N, Starkloff R, Lanz T, Heinze C, Epple B. Progress in dynamic simulation of thermal power plants. Progress in Energy and Combustion Science. 2017;59:

[7] Madejski P, Janda T, Modliński N, Nabagło D. A combustion process optimization and numerical analysis for the low emission operation of pulverized coal-fired boiler. In:

[8] Kotowicz J, Łukowicz H, Bartela Ł, Michalski S. Validation of a program for supercritical

[9] Sporl R, Maier J, Scheffknecht G. Sulfur oxide emissions from dust-fired oxy-fuel com-

[10] Chen H, Pan P, Shao H, Wang Y, Zhao Q. Corrosion and viscous ash deposition of a rotary air preheater in a coal-fired power plant. Applied Thermal Engineering. 2017;113:

[11] Wei W, Sun F, Shi Y, Ma L. Theoretical prediction of acid dew point and safe operating temperature of heat exchangers for coal-fired power plants. Applied Thermal Engineering.

[12] Wang Y, Zhao Q, Zhang Z, Zhang Z, Tao W. Mechanism research on coupling effect between dew point corrosion and ash deposition. Applied Thermal Engineering. 2013;54:

[13] Guo B, Yang D, Su Y, Yu AB. Process modelling of low temperature electrostatic precipi-

[14] Daood S, Javed M, Gibbs N, Nimmo W. NOx control in a coal combustion by combining

[15] Hu X, Shi Q, Zhang H, Wang P, Zhan S, Li Y. NH3-SCR performance improvement over Mo modified Mo(x)-MnOx nanorods at low temperatures. Catalysis Today. 2017;297:17-26

[16] Tang X, Li C, Yi H, Wang L, Yu Q, Gao F, Cui X, Chu C, Li J, Zhang R. Facile and fast synthesis of novel Mn2CoO4@rGO catalysts for the NH3-SCR of NOx at low temperature.

[17] Richter M, Möllenbruck F, Obermüller F, Knaut A, Weiser F, Lens H, Lehmann D. Flexibilization of steam power plants as partners for renewable energy systems. In: Power Systems Computation Conference (PSCC); 2016. DOI: 10.1109/PSCC.2016.7540840

biomass co-firing, oxygen enrichment and SNCR. Fuel. 2013;105:283-292

Developments in Combustion Technology. Croatia: InTechOpen; 2016. pp. 33-76

power plant calculations. Archives of Thermodynamics. 2011;32(4):81-89

http://www.steag-systemtechnologies.com/ebsilon\_professional.html

ASME Journal of Energy Resources Technology. 2018;140(5)

bustion of coal. Energy Procedia. 2013;37:1435-1447

tators. Powder Technology. 2017;314:567-576

Chemical Engineering Journal. 2018;333:467-476

account thermal stresses. Energy. 2015;92:160-170

32 Thermal Power Plants - New Trends and Recent Developments

79-162

373-385

102-110

2017;123:782-790

Coal mill malfunctions are some of the most common causes of failing to keep the power plant crucial operating parameters or even unplanned power plant shutdowns. Therefore, an algorithm has been developed that enable online detection of abnormal conditions and malfunctions of an operating mill. Based on calculated diagnostic signals and defined thresholds, this algorithm informs about abnormal operating conditions. Diagnostic signals represent the difference between the measured and the modeled values of two selected mill operating parameters. Models of mill motor current and outlet temperature of pulverized fuel were developed based on the linear regression theory. Various data analysis and feature selection procedures have been performed to obtain the best possible model. The model based on linear regression has been compared with two alternative models. The algorithm validation was carried out based on historical data containing values of operating parameters from 10 months of mill operation. Historical data were downloaded from distributed control system (DCS) of a 200-MW coal-fired power plant. Tests carried out on historical data show that this algorithm can be successfully used to detect certain abnormal conditions and malfunctions of the operating mill, such as feeder blockage, lack of coal and mill overload.

Keywords: predictive maintenance, coal mill, fault detection, digital twin, online diagnostic

#### 1. Introduction

Safety, reliability and flexibility are some of the most important operation features of any power plant. The abnormal operation conditions and malfunctions of coal mills negatively

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

affect the boiler operation and furthermore can be the cause of emergency boiler shutdown. Coal mills produce the air and pulverized fuel mixture, which is burned in the boiler; hence, abnormal operating conditions can decrease boiler efficiency and increase CO2 and NOx emissions. Undetected at the right time, mill faults are the causes of numerous issues like failing to keep steam parameters, reduction of generated power, and the flame instability in the furnace, which enforces fuel oil burner usage to maintain continuity of combustion; the flame instability can lead to flame loss and that is one of the most dangerous situations that may appear in power plant.

models are presented in Section 6, and the comparison between two other models' approaches is derived in Section 7. Section 8 presents the algorithm evaluation, and Section 9 shows

Detection of Malfunctions and Abnormal Working Conditions of a Coal Mill

http://dx.doi.org/10.5772/intechopen.72952

35

The work presented in this chapter is based on a MKM-33 ball mill used at Rybnik Unit 4 (rated capacity 220 MW). The mill is one of six mills supplying the 650-k (steam production of 650 t/h) boiler. However, the proposed method in this chapter is so generic that it can be

The coal is fed to the coal mill through the central inlet pipe, where it is pulverized by a series of large balls separated by two types of rings. The pulverized material is carried out in the mill by the flow of air moving through it. The primary air is a mixture of cold air and air heated by the preheaters. The ratio of the hot and cold air flows is used to control the temperature and the flow of the primary air. The size of the pulverized particles released from the grinding section of the mill is determined by a classifier separator. Too large and heavy particles fall

applied to other types of coal mills. The coal mill is illustrated in Figure 1.

back on the gridding table and will be crushed by bowls again.

algorithm fault detection performance.

2. The coal mill

Figure 1. Coal mill scheme.

As a consequence of these problems, coal mill control and fault detection have been the main focus in many research activities. General overview of control and fault diagnostic methods are the topics in [1, 2]. The authors in [3] investigated models based on the mass and heat balance together with the energy model. This model has been used in [4, 5]. In [4], observer-based models are developed. The fault detection is based on energy balance analysis, producing fault residuals that are used in detection schemes. It has been shown that the fault (blocked coal inlet pipe) is detected as soon as the fault occurs. A dynamic coal mil model using conservation laws and empirical relations has been developed in [6]. Unknown model parameters are estimated using differential evolution algorithm, and data set contains parameters from 7 days of mill operation. From the validation results, it is concluded that the model fits the on-site measured data very well, but model has not been tested in control or diagnostic application. Non-linear coal mill modeling and its application to model predictive control are presented in [7]. Three system output parameters of vertical roller coal mill (the pressure drop over the mill, power consumed by the mill and outlet temperature) models have been developed and used in non-linear model predictive control with results in improving coal load response time and temperature control. The observer-based approach presented in [3, 4] is compared with the regression-based approach in [8, 9]. The methods have been tested on data with one given fault that is dramatic increasing of the moisture content. Results show that both methods detect faults as it emerges, but the observer-based model detects the tested fault earlier than regression-based model.

In this chapter, a novel coal mill fault detection approach is presented. This is done through applying the linear regression theory to model two mill operating parameters: motor current and outlet temperature of pulverized fuel. Even though the regression theory has been tested and compared in [8], this chapter presents complex approach with high volume of data analysis containing around 2 million of measurements, while model in [8] has been trained on 300 samples. Additionally, the parameter's time delay influence has been tested as it was not used before and the input variables have been selected with the usage of advanced techniques of feature selection. The regression-based models are also compared with two alternative models that are artificial neural network-based models and physical equation-based models. Finally, developed algorithm has been implemented in fault detection algorithm implemented in 200 MW power unit.

The outlier of this chapter is as follows. The coal mill is introduced in Section 2. Real data analysis downloaded from Rybnik power plant is presented in Section 3. Section 4 focuses on feature selection process. In Section 5, moisture content estimation is presented. Developed models are presented in Section 6, and the comparison between two other models' approaches is derived in Section 7. Section 8 presents the algorithm evaluation, and Section 9 shows algorithm fault detection performance.

## 2. The coal mill

affect the boiler operation and furthermore can be the cause of emergency boiler shutdown. Coal mills produce the air and pulverized fuel mixture, which is burned in the boiler; hence, abnormal operating conditions can decrease boiler efficiency and increase CO2 and NOx emissions. Undetected at the right time, mill faults are the causes of numerous issues like failing to keep steam parameters, reduction of generated power, and the flame instability in the furnace, which enforces fuel oil burner usage to maintain continuity of combustion; the flame instability can lead to flame loss and that is one of the most dangerous situations that

As a consequence of these problems, coal mill control and fault detection have been the main focus in many research activities. General overview of control and fault diagnostic methods are the topics in [1, 2]. The authors in [3] investigated models based on the mass and heat balance together with the energy model. This model has been used in [4, 5]. In [4], observer-based models are developed. The fault detection is based on energy balance analysis, producing fault residuals that are used in detection schemes. It has been shown that the fault (blocked coal inlet pipe) is detected as soon as the fault occurs. A dynamic coal mil model using conservation laws and empirical relations has been developed in [6]. Unknown model parameters are estimated using differential evolution algorithm, and data set contains parameters from 7 days of mill operation. From the validation results, it is concluded that the model fits the on-site measured data very well, but model has not been tested in control or diagnostic application. Non-linear coal mill modeling and its application to model predictive control are presented in [7]. Three system output parameters of vertical roller coal mill (the pressure drop over the mill, power consumed by the mill and outlet temperature) models have been developed and used in non-linear model predictive control with results in improving coal load response time and temperature control. The observer-based approach presented in [3, 4] is compared with the regression-based approach in [8, 9]. The methods have been tested on data with one given fault that is dramatic increasing of the moisture content. Results show that both methods detect faults as it emerges, but the observer-based model detects the tested fault earlier than regression-based model.

In this chapter, a novel coal mill fault detection approach is presented. This is done through applying the linear regression theory to model two mill operating parameters: motor current and outlet temperature of pulverized fuel. Even though the regression theory has been tested and compared in [8], this chapter presents complex approach with high volume of data analysis containing around 2 million of measurements, while model in [8] has been trained on 300 samples. Additionally, the parameter's time delay influence has been tested as it was not used before and the input variables have been selected with the usage of advanced techniques of feature selection. The regression-based models are also compared with two alternative models that are artificial neural network-based models and physical equation-based models. Finally, developed algorithm has been implemented in fault detection algorithm implemented

The outlier of this chapter is as follows. The coal mill is introduced in Section 2. Real data analysis downloaded from Rybnik power plant is presented in Section 3. Section 4 focuses on feature selection process. In Section 5, moisture content estimation is presented. Developed

may appear in power plant.

34 Thermal Power Plants - New Trends and Recent Developments

in 200 MW power unit.

The work presented in this chapter is based on a MKM-33 ball mill used at Rybnik Unit 4 (rated capacity 220 MW). The mill is one of six mills supplying the 650-k (steam production of 650 t/h) boiler. However, the proposed method in this chapter is so generic that it can be applied to other types of coal mills. The coal mill is illustrated in Figure 1.

The coal is fed to the coal mill through the central inlet pipe, where it is pulverized by a series of large balls separated by two types of rings. The pulverized material is carried out in the mill by the flow of air moving through it. The primary air is a mixture of cold air and air heated by the preheaters. The ratio of the hot and cold air flows is used to control the temperature and the flow of the primary air. The size of the pulverized particles released from the grinding section of the mill is determined by a classifier separator. Too large and heavy particles fall back on the gridding table and will be crushed by bowls again.

Figure 1. Coal mill scheme.

## 3. Real data analysis

#### 3.1. Data set

The research has been performed on data set downloaded from Rybnik power plant DCS system. Data contain measurements values of 22 parameters from 10 months of mill operation (January 2014 to October 2014) with 10-s sampling period, except outside temperature and temperature in coal bunker which have 1-min sampling period. All parameters are presented in Table 1. In this chapter, variable names presented in Table 1 have been used.

#### 3.2. Data filtration and distribution analysis

Models presented in this chapter have been developed to describe mill normal working conditions based on historical data. Therefore, from the data set starts up, shuts down and work with feeder speed less than 10% has been removed. Additionally, seven new columns have been added to improve process description. Newly added columns are presented in Table 2.

> Finally, an additional column has been added for each input variable (all variables except AMPS and MILL\_OUT\_TEMP), and newly added columns contained the rolling mean of each

> where x is measured value at time t. The final data set contained 56 columns: 27 columns each for one depended variable, 27 columns for theirs means and two columns each for one independent

> MW\_DMD, MILL\_OUT\_TEMP\_DMD, MILL\_OUT\_TEMP, PRESS\_CORR, STEAM\_FLOW, FUEL\_DMD\_REG. Bimodal distribution of power is a result of unit working conditions (high power demand during morning hours, and low power demand during evening hours). Bimodal distribution of outlet temperature is caused by milled fuel type. During periods of coal and biomass co-milling, the mill outlet temperature demand has been set at 115�C. If the mill was gridding, only coal mill outlet temperature demand has been set at 105�C. Histograms are

> As presented in Section 2, the process of coal pulverizing in the mill consists of some subprocesses, for example hot and cold air mixtures before entering the mill. Some variable measurements (data set columns) can influence the main process with different time delay. To

variable. Histogram plots show that we can split data parameters into two groups:

x tð Þþ � 20s x tð Þþ � 10s x tð Þ

2

Detection of Malfunctions and Abnormal Working Conditions of a Coal Mill

FUEL\_DMD MW

<sup>r</sup><sup>∗</sup> TPPIN ð Þ <sup>þ</sup><sup>273</sup> <sup>P</sup>\_AIR\_FLOW\_kgs <sup>¼</sup> PAIRFLOW <sup>∗</sup>gair

3600

10∗ð Þ MP\_PP\_IN\_AVGkPa � P\_PP\_IN\_AVG\_kPa

http://dx.doi.org/10.5772/intechopen.72952

37

0:0749435882327∗MW þ 26:9627419581

FUEL\_DMD � FUEL\_DMD\_REG

STEAM\_FLOW∗TEMP\_ON\_LOAD

<sup>3</sup> (1)

column calculated according to the formula 1

1. Variables with normal distribution

presented in Figures 2 and 3.

2. Variables with bimodal distribution: MW,

3.3. Co-correlations between model output and inputs

xmean\_3ðÞ¼ t

New variable Description Formula

DELTA\_PA\_mbar Pressure difference between mill inlet and primary air collector

FUEL\_DMD\_REG Mean value FUEL\_DMD for a given power

FUEL2POWER Proportion FUEL\_DMD/MW, possible estimation of fuel quality

FQUALITY Difference between FUEL\_DMD and

SUPPLIED\_HEAT Product of STEAM\_FLOW and

supplied)

Table 2. Added variable.

estimation quality

data

P\_PP\_IN\_AVG\_kPa Pressure difference in primary air [kPa] P\_PP\_IN\_LþP\_PP\_IN\_P

P\_AIR\_FLOW\_kgs Unit change from Nm^3/h to kg/s gair <sup>¼</sup> MILL\_IN\_PRESS

obtained from linear regression for all historical

FUEL\_DMD\_REG - second, more accurate fuel

TEMP\_ON\_LOAD (proportional to the heat


Table 1. Data set variable description.


Table 2. Added variable.

/h

/h

/h

3. Real data analysis

3.2. Data filtration and distribution analysis

36 Thermal Power Plants - New Trends and Recent Developments

Table 1. Data set variable description.

The research has been performed on data set downloaded from Rybnik power plant DCS system. Data contain measurements values of 22 parameters from 10 months of mill operation (January 2014 to October 2014) with 10-s sampling period, except outside temperature and temperature in coal bunker which have 1-min sampling period. All parameters are presented

Models presented in this chapter have been developed to describe mill normal working conditions based on historical data. Therefore, from the data set starts up, shuts down and work with feeder speed less than 10% has been removed. Additionally, seven new columns have been

No. Variables Description Units MW Unit power MW MW\_DMD Unit power demand MW TURB\_PRESS Steam pressure at turbine inlet MPa PRESS\_CORR Corrected pressure demand for the boiler MPa STEAM\_FLOW Steam flow t/h FUEL\_DMD Fuel demand % FAN\_DMPR The fan blade setting % MILL\_IN\_PRESS Primary air inlet pressure kPa MILL\_OUT\_TEMP Temperature of pulverized fuel C P\_AIR\_FLOW\_DMD Primary air flow demand Nm<sup>3</sup>

11 P\_AIR\_FLOW\_BIAS Primary air flow demand correction (manual) Nm<sup>3</sup>

12 P\_AIR\_FLOW Measured primary air flow Nm<sup>3</sup>

 HOT\_AIR\_DMPR The opening of the hot air dumper % MILL\_OUT\_TEMP\_DMD Mill outlet temperature demand C COLD\_AIR\_DMPR The opening of the cold air dumper % FEEDER\_LOAD Feeder speed % AMPS Mill motor current A TEMP\_MILL\_IN Primary air inlet temperature C PRESS\_FAN\_IN\_L Pressure in primary air collector (left side) Pa PRESS\_FAN\_IN\_R Pressure in primary air collector (right side) Pa TEMP\_ON\_LOAD Temperature in coal bunker C TEMP\_OUTSIDE Ambient temperature C

added to improve process description. Newly added columns are presented in Table 2.

in Table 1. In this chapter, variable names presented in Table 1 have been used.

3.1. Data set

Finally, an additional column has been added for each input variable (all variables except AMPS and MILL\_OUT\_TEMP), and newly added columns contained the rolling mean of each column calculated according to the formula 1

$$\mathbf{x}\_{\text{mean\\_3}}(t) = \frac{\mathbf{x}(t-20\mathbf{s}) + \mathbf{x}(t-10\mathbf{s}) + \mathbf{x}(t)}{3} \tag{1}$$

where x is measured value at time t. The final data set contained 56 columns: 27 columns each for one depended variable, 27 columns for theirs means and two columns each for one independent variable. Histogram plots show that we can split data parameters into two groups:


MW\_DMD, MILL\_OUT\_TEMP\_DMD, MILL\_OUT\_TEMP, PRESS\_CORR, STEAM\_FLOW, FUEL\_DMD\_REG. Bimodal distribution of power is a result of unit working conditions (high power demand during morning hours, and low power demand during evening hours). Bimodal distribution of outlet temperature is caused by milled fuel type. During periods of coal and biomass co-milling, the mill outlet temperature demand has been set at 115�C. If the mill was gridding, only coal mill outlet temperature demand has been set at 105�C. Histograms are presented in Figures 2 and 3.

#### 3.3. Co-correlations between model output and inputs

As presented in Section 2, the process of coal pulverizing in the mill consists of some subprocesses, for example hot and cold air mixtures before entering the mill. Some variable measurements (data set columns) can influence the main process with different time delay. To

FEEDER\_LOAD\_mean3 (correlation value is equal to 0.395). The correlation coefficient higher than 0.3 has also variables: FEEDER\_LOAD, FAN\_DMPR, MILL\_IN\_PRESS, P\_AIR\_FLOW\_kgs, DELTA\_PA\_mbar and theirs means. The best correlated with MILL\_OUT\_TEMP is variable: MILL\_OUT\_TEMP\_DMD\_mean3. With correlation coefficient 0.926 (for the rest of variables,

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Variables Delay [s] Correlation coefficient

Variables Delay [s] Correlation coefficient

MILL\_OUT\_TEMP\_DMD 300 0.926 COLD\_AIR\_DMPR 300 0.497 TEMP\_MILL\_IN 300 0.467 P\_AIR\_FLOW\_kgs 300 0.362 TEMP\_OUTSIDE 300 0.327 DELTA\_PA\_mbar 10 0.269 MILL\_IN\_PRESS 10 0.259 P\_AIR\_FLOW\_DMD 200 0.247 P\_AIR\_FLOW 300 0.240 TEMP\_ON\_LOAD 300 0.202

FEEDER\_LOAD 150 0.393 FAN\_DMPR 80 0.390 MILL\_IN\_PRESS 130 0.369 P\_AIR\_FLOW\_kgs 130 0.347 DELTA\_PA\_mbar 130 0.340 FUEL\_DMD 150 0.289 P\_AIR\_FLOW\_DMD 90 0.287 SUPPLIED\_HEAT 30 0.282 FUEL\_DMD\_REG 20 0.281 MW 20 0.281 MW\_DMD 30 0.281 STEAM\_FLOW 30 0.276 P\_AIR\_FLOW 20 0.239 PRESS\_CORR 300 0.220 HOT\_AIR\_DMPR 20 0.208 TURB\_PRESS 10 0.199 COLD\_AIR\_DMPR 300 0.195

correlation coefficient is not greater than 0.5).

Table 3. Variable delays best correlated with AMPS.

Table 4. Variable delays best correlated with MILL\_OUT\_TEMP.

Figure 2. MILL outlet temperature (MILL\_OUT\_TEMP) histogram.

Figure 3. Unit power (MW) histogram.

explore the delay values, the Pearson correlation analysis has been made. Pearson correlation coefficient is a measure of the linear correlation between two variables.

For each depended variable, new columns have been added containing delayed variable values for 10, 20, 30,…,300 s. Afterwards, for each column presented in Tables 1 and 2 and their mean values, the Pearson correlation coefficient has been calculated and the delay with the highest Pearson coefficient has been chosen. The results are presented in Tables 3 and 4.

For MILL\_OUT\_TEMP, most of the parameters are the best correlated with 6-min delay. This time shows the automatic process control reaction time for mill outlet temperature demand changes. Only the parameters which do not influence directly into demanded outlet temperature are correlated with very slow delay (10, 20 s) For the AMPS variable, the system is reacting for AIR\_FLOW\_DMD changes with around 6-min delay. However, parameters with strong influence into process are correlated with small delay. The best correlated with AMPS is variable FEEDER\_LOAD\_mean3 (correlation value is equal to 0.395). The correlation coefficient higher than 0.3 has also variables: FEEDER\_LOAD, FAN\_DMPR, MILL\_IN\_PRESS, P\_AIR\_FLOW\_kgs, DELTA\_PA\_mbar and theirs means. The best correlated with MILL\_OUT\_TEMP is variable: MILL\_OUT\_TEMP\_DMD\_mean3. With correlation coefficient 0.926 (for the rest of variables, correlation coefficient is not greater than 0.5).


Table 3. Variable delays best correlated with AMPS.

explore the delay values, the Pearson correlation analysis has been made. Pearson correlation

For each depended variable, new columns have been added containing delayed variable values for 10, 20, 30,…,300 s. Afterwards, for each column presented in Tables 1 and 2 and their mean values, the Pearson correlation coefficient has been calculated and the delay with the highest

For MILL\_OUT\_TEMP, most of the parameters are the best correlated with 6-min delay. This time shows the automatic process control reaction time for mill outlet temperature demand changes. Only the parameters which do not influence directly into demanded outlet temperature are correlated with very slow delay (10, 20 s) For the AMPS variable, the system is reacting for AIR\_FLOW\_DMD changes with around 6-min delay. However, parameters with strong influence into process are correlated with small delay. The best correlated with AMPS is variable

coefficient is a measure of the linear correlation between two variables.

Figure 2. MILL outlet temperature (MILL\_OUT\_TEMP) histogram.

38 Thermal Power Plants - New Trends and Recent Developments

Figure 3. Unit power (MW) histogram.

Pearson coefficient has been chosen. The results are presented in Tables 3 and 4.


Table 4. Variable delays best correlated with MILL\_OUT\_TEMP.

## 4. Feature selection

So far, input data set used to evaluate models contains all parameters. Obviously, not all of them have the impact on modeling parameters. The process of feature selection has been made to extract all variables with the influence on modeling output. This process is also developed to:

In Table 6, the best model evaluated for AMPS independent variable after feature selection process is presented; the number of features has been decreased from 55 to 4 with minor model

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The model variables have been chosen from the RFECV feature selection method, with ridge

In Table 7, the best model evaluated for MILL\_OUT\_TEMP independent variable is presented. The feature number has been decreased from 55 to 15, and the model accuracy has been improved. The features have been chosen from the RFECV feature selection method. The

The autoregressive models have not been considered because of future model's use that is fault detection. Autoregressive models in case of fault development will model malfunction, and

Hypothesis 1: Continuous historical data updating can improve model fitting. An assumption has been made that if we will train model progressively based on defined period of historical data, the accuracy of the model will be improved in comparison with model based on all historical data. The hypothesis has been tested by algorithm that idea is presented in Figure 4. First model is trained on data located in history window, then the model output prediction is made for samples located in prediction window. Afterwards, data widow is moved by the length of prediction window; then, process of model training and output prediction is repeated. The windows are

The algorithm has been implemented to forward feature selection but without particular success (the feature selection algorithm has stopped after first iteration). Furthermore, the algorithm has been used to obtain model coefficient for models presented in Tables 6 and 7; for this model, numerous configurations of data history window and data prediction window

The best growth of MAPE coefficient has been observed for short historical data windows (from 14 to 28 days) though training model on such short period of time can be dangerous. If

R2

[�] 0.930 RMS[�C] 1.831 MAPE[%] 1.253

Features Accuracy coefficients

model accuracy has been improved in comparison with the reference model.

Afterwards, few additional hypotheses have been investigated:

have been examined. The summary of results is presented in Table 8.

accuracy diminution.

regression model fitting estimator (∝ =1e 07).

consequently, the fault will be undetected.

moved after each iteration until the end of data set.

MILL\_OUT\_TEMP\_DMD\_mean3–300,FUEL2POWER\_mean3–300, P\_AIR\_FLOW\_DMD\_mean3–190,COLD\_AIR\_DMPR-300, TEMP\_MILL\_IN\_mean3–300,P\_AIR\_FLOW\_BIAS\_mean3–10, FEEDER\_LOAD\_mean3–180,COLD\_AIR\_DMPR\_mean3–300,

HOT\_AIR\_DMPR-300, FQUALITY\_mean3–300,

PRESS\_FAN\_IN\_L-300,FUEL\_DMD\_mean3–300,

MW-300,TURB\_PRESS\_mean3–300, P\_AIR\_FLOW\_DMD-200,PRESS\_CORR-300, P\_AIR\_FLOW\_BIAS-10,MW\_DMD\_mean3–300, STEAM\_FLOW-10,P\_AIR\_FLOW-300,

Table 7. MILL\_OUT\_TEMP model.


The main assumption during feature selection is that the initial data set contains variables which are redundant, strongly correlated with one another or irrelevant and, therefore, can be deleted without information losses [10, 11].

The wage of model improvement is determined by model accuracy coefficient, and in this chapter, the root mean square (RMS) coefficient has been used. Forward feature selection has been made with the usage of author algorithms. The comparison between various developed models has been made by comparing calculated model accuracy coefficients. For each model, the following model fitting parameters have been calculated: coefficient of determination (R2 ), root mean square (RMS) and mean average percentage error (MAPE). Those parameters have been calculated with the usage of threefold cross-validation technics [12]. Comparison between models has been made by comparing RMS coefficient value.

The determination of unknown regression coefficient has been made with linear and ridge regression usage [13].

In Table 5, the reference model is presented. The reference model has been fitted to initial data set containing variables presented in Tables 1 and 2 and their means (no feature selection process).


Table 5. Reference models.


Table 6. AMPS model.

In Table 6, the best model evaluated for AMPS independent variable after feature selection process is presented; the number of features has been decreased from 55 to 4 with minor model accuracy diminution.

The model variables have been chosen from the RFECV feature selection method, with ridge regression model fitting estimator (∝ =1e 07).

In Table 7, the best model evaluated for MILL\_OUT\_TEMP independent variable is presented. The feature number has been decreased from 55 to 15, and the model accuracy has been improved. The features have been chosen from the RFECV feature selection method. The model accuracy has been improved in comparison with the reference model.

The autoregressive models have not been considered because of future model's use that is fault detection. Autoregressive models in case of fault development will model malfunction, and consequently, the fault will be undetected.

Afterwards, few additional hypotheses have been investigated:

4. Feature selection

quality of the modeling;

regression usage [13].

Table 5. Reference models.

MILL\_IN\_PRESS\_mean3–120, P\_PP\_IN\_AVG\_kPa-30, FUEL2POWER-10, FUEL2POWER\_mean3–10

Table 6. AMPS model.

process).

3. decrease the model training time.

deleted without information losses [10, 11].

40 Thermal Power Plants - New Trends and Recent Developments

models has been made by comparing RMS coefficient value.

Features Accuracy coefficients

So far, input data set used to evaluate models contains all parameters. Obviously, not all of them have the impact on modeling parameters. The process of feature selection has been made to extract all variables with the influence on modeling output. This process is also developed to:

2. increase the generalization of the model by limiting overfitting, and by that, increasing the

The main assumption during feature selection is that the initial data set contains variables which are redundant, strongly correlated with one another or irrelevant and, therefore, can be

The wage of model improvement is determined by model accuracy coefficient, and in this chapter, the root mean square (RMS) coefficient has been used. Forward feature selection has been made with the usage of author algorithms. The comparison between various developed models has been made by comparing calculated model accuracy coefficients. For each model, the following model fitting parameters have been calculated: coefficient of determination (R2

root mean square (RMS) and mean average percentage error (MAPE). Those parameters have been calculated with the usage of threefold cross-validation technics [12]. Comparison between

The determination of unknown regression coefficient has been made with linear and ridge

In Table 5, the reference model is presented. The reference model has been fitted to initial data set containing variables presented in Tables 1 and 2 and their means (no feature selection

Depended variables R2 RMS MAPE AMPS 0.256 0.707 1.903 MILL\_OUT\_TEMP 0.85 2.21 1.43

> MAPE [%] 1.965 RMS [A] 0.622 R2 [] 0.179

),

1. simplify the model. Simple models are easier to interpret and maintain;

Hypothesis 1: Continuous historical data updating can improve model fitting. An assumption has been made that if we will train model progressively based on defined period of historical data, the accuracy of the model will be improved in comparison with model based on all historical data. The hypothesis has been tested by algorithm that idea is presented in Figure 4. First model is trained on data located in history window, then the model output prediction is made for samples located in prediction window. Afterwards, data widow is moved by the length of prediction window; then, process of model training and output prediction is repeated. The windows are moved after each iteration until the end of data set.

The algorithm has been implemented to forward feature selection but without particular success (the feature selection algorithm has stopped after first iteration). Furthermore, the algorithm has been used to obtain model coefficient for models presented in Tables 6 and 7; for this model, numerous configurations of data history window and data prediction window have been examined. The summary of results is presented in Table 8.

The best growth of MAPE coefficient has been observed for short historical data windows (from 14 to 28 days) though training model on such short period of time can be dangerous. If


Table 7. MILL\_OUT\_TEMP model.

Figure 4. The idea of progressive prediction.

abnormal condition has occurred during this period, the model will fit coefficients into these data obviously; furthermore, model would not achieve its function. It has been assumed that safe historical data length is greater than 800,000 s (around 3 months). For such cases, model accuracy has not improved significantly, and this is why the algorithm has been rejected. Nevertheless, it has to be kept in mind that after some periods, the model coefficient has to be updated, for example in case of mill or boiler renovation. In such cases, it is recommended to train the model on at least 2-month history data set.

Hypothesis 2: The fuzzy regression will improve model accuracy. As shown in Section 3.3, some parameters have bimodal distribution; in such cases, fuzzy regression can be successfully implemented. An algorithm has been developed which creates two linear models, model for high load and model for low load. The model output is the sum of those sub model outputs, multiplied by wages that are depended on load. The formula for wages is presented in Eqs. (2) and (3):

$$
\mu\_{low\ demand} = \begin{cases} 1 & \text{for } \mathbf{x} < 150 \\\\ \frac{190 - \mathbf{x}}{190 - 150} & \text{for } \mathbf{x} \text{ } \epsilon < 150, 190 > \\\\ 0 & \text{for } \mathbf{x} > 190 \end{cases} \tag{2}
$$

$$
\mu\_{high\ demand} = \begin{cases} 1 & \text{for } \mathbf{x} < 150 \\\\ \frac{\mathbf{x} - 150}{190 - 150} & \text{for } \mathbf{x} \text{ } \epsilon < 150, 190 > \\\\ 0 & \text{for } \mathbf{x} > 190 \end{cases} \tag{3}
$$

Hypothesis 3: Non-linear input variable transformation may increase model accuracy. Since the processes occurring in the mill are non-linear, some input parameters' manipulation has been investigated. To perform, an algorithm has been created which was adding a new parameter that was obtained by changing selected parameters values according to defined manipulation; however, during one iteration, only one parameter with one manipulation has been investigated; after iteration, the algorithm was returning to initial data set. The parameter modifications have been based on functions such as quadratic function, cubic function, square, natural logarithm, decimal logarithm and exponential function. The results show that for none of the parameter's

AMPS 0.719 1.922 MILL\_OUT\_TEMP 9.428 1.224

RMS MAPE

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History window (s) Prediction window (s) R2 [] RMS [A] MAPE [%] 50,000 100 0.495 0.488 1.551 100,000 100 0.375 0.543 1.732 100,000 500 0.317 0.568 1.755 5,000,000 100 0.184 0.590 1.890 5,000,000 500 0.164 0.597 1.890 5,000,000 1000 0.142 0.605 1.891

To improve model accuracy and abnormal working conditions' detection ability, the estimation of the moisture content has been evaluated. Two main processes, coal gridding and moisture evaporation from the coal dust, are taking place in the mill, and the quality and performance of those processes are highly depended on coal milling quality and moisture content. Online measurements of those parameters are not possible; however, the moisture

A simple energy balance model of the coal mill is derived based on [2, 3]. The coal mill is

In Figure 5, T(t) is the temperature in the mill, Q\_air (t) is the energy in the primary air flow, Q\_coal (t) is the energy in the coal flow, Q\_moisture (t) is the energy in moisture, Q\_e (t) is energy losses to environment, Q\_pf (t) is energy in air-fuel mixture, Q\_steam (t) is energy in steam, Q\_evap (t) is energy used to evaporate moisture and Q\_cum (t) is accumulated energy

modification, the model accuracy coefficients have improved significantly.

content can be determined by evaluating the energy balance.

considered as one body with the mass m\_m, as illustrated in Figure 5.

5. Coal moisture content

Table 8. AMPS moved historical window.

Table 9. Fuzzy regression.

where x is the unit power. As presented in Table 9, the model accuracy has not been improved.


Table 8. AMPS moved historical window.


Table 9. Fuzzy regression.

abnormal condition has occurred during this period, the model will fit coefficients into these data obviously; furthermore, model would not achieve its function. It has been assumed that safe historical data length is greater than 800,000 s (around 3 months). For such cases, model accuracy has not improved significantly, and this is why the algorithm has been rejected. Nevertheless, it has to be kept in mind that after some periods, the model coefficient has to be updated, for example in case of mill or boiler renovation. In such cases, it is recommended to

Hypothesis 2: The fuzzy regression will improve model accuracy. As shown in Section 3.3, some parameters have bimodal distribution; in such cases, fuzzy regression can be successfully implemented. An algorithm has been developed which creates two linear models, model for high load and model for low load. The model output is the sum of those sub model outputs, multiplied by wages that are depended on load. The formula for wages is presented in Eqs. (2) and (3):

190 � x

x � 150

where x is the unit power. As presented in Table 9, the model accuracy has not been improved.

8 >>>><

>>>>:

8 >>>><

>>>>:

1 for x < 150

<sup>190</sup> � <sup>150</sup> for x <sup>E</sup> <sup>&</sup>lt; <sup>150</sup>, <sup>190</sup> <sup>&</sup>gt; 0 for x > 190

1 for x < 150

<sup>190</sup> � <sup>150</sup> for x <sup>E</sup> <sup>&</sup>lt; <sup>150</sup>; <sup>190</sup> <sup>&</sup>gt; 0 for x > 190

(2)

(3)

train the model on at least 2-month history data set.

Figure 4. The idea of progressive prediction.

42 Thermal Power Plants - New Trends and Recent Developments

μlow demand ¼

μhigh demand ¼

Hypothesis 3: Non-linear input variable transformation may increase model accuracy. Since the processes occurring in the mill are non-linear, some input parameters' manipulation has been investigated. To perform, an algorithm has been created which was adding a new parameter that was obtained by changing selected parameters values according to defined manipulation; however, during one iteration, only one parameter with one manipulation has been investigated; after iteration, the algorithm was returning to initial data set. The parameter modifications have been based on functions such as quadratic function, cubic function, square, natural logarithm, decimal logarithm and exponential function. The results show that for none of the parameter's modification, the model accuracy coefficients have improved significantly.

## 5. Coal moisture content

To improve model accuracy and abnormal working conditions' detection ability, the estimation of the moisture content has been evaluated. Two main processes, coal gridding and moisture evaporation from the coal dust, are taking place in the mill, and the quality and performance of those processes are highly depended on coal milling quality and moisture content. Online measurements of those parameters are not possible; however, the moisture content can be determined by evaluating the energy balance.

A simple energy balance model of the coal mill is derived based on [2, 3]. The coal mill is considered as one body with the mass m\_m, as illustrated in Figure 5.

In Figure 5, T(t) is the temperature in the mill, Q\_air (t) is the energy in the primary air flow, Q\_coal (t) is the energy in the coal flow, Q\_moisture (t) is the energy in moisture, Q\_e (t) is energy losses to environment, Q\_pf (t) is energy in air-fuel mixture, Q\_steam (t) is energy in steam, Q\_evap (t) is energy used to evaporate moisture and Q\_cum (t) is accumulated energy

Figure 5. Scheme of coal mill heat balance.

in the mill. The specific heat capacity of the mill is C\_m. Even though this assumption is only entirely true for steady state, it is assumed in this chapter for simplifying the model.

The energy balance is given by [2, 3](4):

$$Q\_{\rm air}(t) + Q\_{\rm coal}(t) + Q\_{\rm moisture}(t) = \left[Q\_{\rm pf}(t) + Q\_{\rm cum}(t) + Q\_{\rm e}(t) + Q\_{\rm steam}(t)\right] \tag{4}$$

The Q\_cum (t) + Q\_e (t) + Q\_steam (t) coefficients have been neglected due to relatively small influence into balance or lack of information. The heating and evaporation of the moisture in the coal are modeled by combined heating coefficients. The latent energy of the evaporation dominates the energy required for a few degrees of heating of the moisture. The combined heat coefficient, H\_st, is defined as follows: H\_st = C\_w + L\_steam/100, where C\_w is the specific heat of the water and L\_steam is the latent heat. This combined heat coefficient does not deal with the fact that the specific heats of water and steam are different. However, the model error is due to heat if steam to a couple of degrees above 100�C is negligible in this context. The moisture content has been determined by [4](5):

$$\gamma = \frac{\mathbf{m}\_{\text{air}} \mathbf{C} \mathbf{p}\_{\text{air}} \* (\mathbf{T}\_{\text{air}\_{\text{in}}} - \mathbf{T}\_{\text{out}}) + \mathbf{m}\_{\text{coal}} \mathbf{C} \mathbf{p}\_{\text{coal}} (\mathbf{T}\_{\text{on}\_{\text{lead}}} - \mathbf{T}\_{\text{out}})}{\mathbf{m}\_{\text{coal}} \mathbf{C} \mathbf{p}\_{\text{coal}} (\mathbf{T}\_{\text{on}\_{\text{lead}}} - \mathbf{T}\_{\text{out}}) + \mathbf{m}\_{\text{coal}} (\mathbf{T}\_{\text{out}} - \mathbf{T}\_{\text{on load}}) + \mathbf{m}\_{\text{coal}} \mathbf{h}\_{\text{ev}}} \tag{5}$$

where mair is the primary air flow, mcoal is the coal flow into mill, Cpair, Cpcoal are specific heat of air and coal, Tairin is primary air flow temperature,Tout is outlet temperature of pulverized fuel, and Tonload is temperature in coal bunker. The modeling results are presented in Figure 6.

The moisture content together with the heat accumulation determined by (6) has been added to AMPS model selected features.

$$Q\_{\text{acumulated}} = Q\_{\text{air}} + Q\_{\text{coal}} - Q\_{\text{coal\\_dust}} \tag{6}$$

6. Modeling results

MILL\_IN\_PRESS\_mean3–120, P\_PP\_IN\_AVG\_kPa-30, FUEL2POWER-10, FUEL2POWER\_mean3–10

Table 10. Adding moisture content.

γ ¼ Qacumulated

Figure 6. The plot of moisture content estimation.

a noticeable difference from the measurements.

Features Accuracy coefficients

The best obtained models have been based on variables presented in Tables 7 and 10. The predicted values are compared with the measured values in Figures 7 and 8. From this figure, it can be seen that the models are quite similar to the dynamical changes as the measurements show. However, for periods with co-milling the biomass, model behavior with comparison to measurements is not sufficient. The analyzed power plant does not continue co-firing of biomass with such way; therefore, these periods are not the main focus of this algorithm. It has also been noticed that during fault occurring in data sets, the models have been presenting

> MAPE [%] 1.946 RMS [A] 0.601 <sup>R</sup><sup>2</sup> [�] 0.21

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The model accuracy has been slightly improved, and it has also been noticed that the model presents high differences from measurements during faults.

Figure 6. The plot of moisture content estimation.

### 6. Modeling results

in the mill. The specific heat capacity of the mill is C\_m. Even though this assumption is only

The Q\_cum (t) + Q\_e (t) + Q\_steam (t) coefficients have been neglected due to relatively small influence into balance or lack of information. The heating and evaporation of the moisture in the coal are modeled by combined heating coefficients. The latent energy of the evaporation dominates the energy required for a few degrees of heating of the moisture. The combined heat coefficient, H\_st, is defined as follows: H\_st = C\_w + L\_steam/100, where C\_w is the specific heat of the water and L\_steam is the latent heat. This combined heat coefficient does not deal with the fact that the specific heats of water and steam are different. However, the model error is due to heat if steam to a couple of degrees above 100�C is negligible in this context. The

<sup>γ</sup> <sup>¼</sup> mairCpair∗ð Þþ Tairin � Tout mcoal Cpcoal Tonload � Tout

where mair is the primary air flow, mcoal is the coal flow into mill, Cpair, Cpcoal are specific heat of air and coal, Tairin is primary air flow temperature,Tout is outlet temperature of pulverized fuel, and Tonload is temperature in coal bunker. The modeling results are presented in Figure 6. The moisture content together with the heat accumulation determined by (6) has been added

The model accuracy has been slightly improved, and it has also been noticed that the model

Qairð Þþ t Qcoalð Þþ t QmoistureðÞ¼ t Qpfð Þþ t Qcumð Þþ t Qeð Þþ t Qsteamð Þt (4)

<sup>þ</sup> mcoalðTout � Ton loadÞ þ mcoalhev

Qacumulated ¼ Qair þ Qcoal � Qcoal\_dust (6)

(5)

entirely true for steady state, it is assumed in this chapter for simplifying the model.

The energy balance is given by [2, 3](4):

Figure 5. Scheme of coal mill heat balance.

44 Thermal Power Plants - New Trends and Recent Developments

moisture content has been determined by [4](5):

to AMPS model selected features.

mcoal Cpcoal Tonload � Tout

presents high differences from measurements during faults.

The best obtained models have been based on variables presented in Tables 7 and 10. The predicted values are compared with the measured values in Figures 7 and 8. From this figure, it can be seen that the models are quite similar to the dynamical changes as the measurements show. However, for periods with co-milling the biomass, model behavior with comparison to measurements is not sufficient. The analyzed power plant does not continue co-firing of biomass with such way; therefore, these periods are not the main focus of this algorithm. It has also been noticed that during fault occurring in data sets, the models have been presenting a noticeable difference from the measurements.


Table 10. Adding moisture content.

Figure 7. The plot of measured and modeled values of mill motor current (AMPS) date: 15 Feburary 2015, fuel: Coal.

Figure 8. The plot of measured and modeled values of mill outlet temperature (MILL\_OUT\_TEMP) AMPS 15 Feburary 2015, fuel: Coal.

## 7. Comparison with artificial neural network and physical model

As presented in Section 1, the mill models have been the subject of investigation by many researches; nevertheless, the main scope of models creation is to develop model as simple as possible without significant model accuracy losses. Processes occurring in the coal mill are dynamic and nonlinear; this is why so many methods have been investigated. The model based on linear regression has been compared with the model based on artificial neural network and the model based on physical equations with genetic algorithm usage to determine unknown parameters.

set have been standardized [15, 16]. The MPLPNN hidden and output layers are activated with tangent-sigmoid function. Numerous combinations of architecture have been investigated to develop the best possible model. The architecture combinations are presented in Table 11. During training and testing procedures, the accuracy parameters have been calculated with cross-validation [12] technique usage. The ANN has been trained with usage of backpropagation supervised ANN learning algorithm. The ANN consists also the bias coefficients. The best

First hidden layer Second hidden layer AMPS MILL\_OUT\_TEMP

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 8 1.961 1.12 6 1.959 1.10 2 1.984 1.18 0 1.971 1.15 0 2.21 1.29

7.2. Model based on physical equations with the use of a genetic algorithm to determine

This method has been developed by [16, 17], and the model is derived through the analysis of energy transferring, heat exchange and mass flow balances. A non-linear mathematical model for a normal mill grinding process was developed in the previous work [16], which was based on the following assumptions: (1) the pulverizing mechanism in the mill is simplified, and coal classification is not considered; (2) grinding and pneumatic transport in the milling process are separated into two stages; and (3) coal size is grouped into only two categories, namely pulverized coal and unpulverized coal. The mill model for the steady-state milling process can

obtained structure and results are presented in Table 11.

Figure 9. Example of artificial neural network architecture.

Number of neurons MAPE [%]

the unknown model coefficients

Table 11. ANN modeling results.

#### 7.1. Model based on artificial neural network

Artificial neural network (ANN)-based modeling is non-linear statistical technique [14]. Recently, there has been increasing interest in neural network modeling of industrial processes such as gridding in coal mills [19]. The design of ANN includes the choice of architecture, training function and training algorithm. The architecture of a network is determined by the number of hidden layers in the network, the number of neurons and the transfer function in each layer, and how the layers are connected to one another. The basic neural network is shown in Figure 9.

The multi-layer perception neural network (MLPNN) is one of the most widely applied neural network topologies, and this topology has been applied to develop non-linear models. The input variables are the features selected and presented in Sections 4 and 5. The values of data Detection of Malfunctions and Abnormal Working Conditions of a Coal Mill http://dx.doi.org/10.5772/intechopen.72952 47

Figure 9. Example of artificial neural network architecture.


Table 11. ANN modeling results.

7. Comparison with artificial neural network and physical model

mine unknown parameters.

2015, fuel: Coal.

7.1. Model based on artificial neural network

46 Thermal Power Plants - New Trends and Recent Developments

As presented in Section 1, the mill models have been the subject of investigation by many researches; nevertheless, the main scope of models creation is to develop model as simple as possible without significant model accuracy losses. Processes occurring in the coal mill are dynamic and nonlinear; this is why so many methods have been investigated. The model based on linear regression has been compared with the model based on artificial neural network and the model based on physical equations with genetic algorithm usage to deter-

Figure 8. The plot of measured and modeled values of mill outlet temperature (MILL\_OUT\_TEMP) AMPS 15 Feburary

Figure 7. The plot of measured and modeled values of mill motor current (AMPS) date: 15 Feburary 2015, fuel: Coal.

Artificial neural network (ANN)-based modeling is non-linear statistical technique [14]. Recently, there has been increasing interest in neural network modeling of industrial processes such as gridding in coal mills [19]. The design of ANN includes the choice of architecture, training function and training algorithm. The architecture of a network is determined by the number of hidden layers in the network, the number of neurons and the transfer function in each layer, and how the layers are connected to one another. The basic neural network is shown in Figure 9.

The multi-layer perception neural network (MLPNN) is one of the most widely applied neural network topologies, and this topology has been applied to develop non-linear models. The input variables are the features selected and presented in Sections 4 and 5. The values of data set have been standardized [15, 16]. The MPLPNN hidden and output layers are activated with tangent-sigmoid function. Numerous combinations of architecture have been investigated to develop the best possible model. The architecture combinations are presented in Table 11. During training and testing procedures, the accuracy parameters have been calculated with cross-validation [12] technique usage. The ANN has been trained with usage of backpropagation supervised ANN learning algorithm. The ANN consists also the bias coefficients. The best obtained structure and results are presented in Table 11.

#### 7.2. Model based on physical equations with the use of a genetic algorithm to determine the unknown model coefficients

This method has been developed by [16, 17], and the model is derived through the analysis of energy transferring, heat exchange and mass flow balances. A non-linear mathematical model for a normal mill grinding process was developed in the previous work [16], which was based on the following assumptions: (1) the pulverizing mechanism in the mill is simplified, and coal classification is not considered; (2) grinding and pneumatic transport in the milling process are separated into two stages; and (3) coal size is grouped into only two categories, namely pulverized coal and unpulverized coal. The mill model for the steady-state milling process can be described by numerous equations [16, 17], containing five algebraic equations describing primary air flow based on pressure differences and air density, coal flow based on feeder speed, pulverized coal flow based on pressure differences and actual amount of pulverized fuel in mill and four differential equations describing mass balance in coal mill based on coal flow, actual coal content in mill, pulverized fuel flow and content in coal mill following equation describing mill motor current, mill pressure differences, and outlet temperature variability.

The main focus in developing this model is unknown coefficients K\_i, where i ∈{1,2,3,…,17} definition is such way that the model has the lowest prediction error (the difference between measured and modeled values is minimalized). One approach [16] uses the genetic algorithm to determine unknown coefficients. The same method has been developed and applied to analyzed coal mill [18], and the results are presented in Table 12.

#### 7.3. Comparison

In this chapter, three coal mill models' evaluation approaches are presented, and the methods are linear regression (Sections 4, 5 and 6), artificial neural network (Section 7.1) and physical equations with the use of a genetic algorithm to determine the unknown model coefficients (Section 7.2). All mentioned methods have been applied to data set containing values of operating parameters from 10 months of mill operation presented in Section 3. The results presented in Table 13 show that the AMPS models have similar performance with the MAPE coefficient close to 2%, which is less than 0.5A mean error. The results presented in Table 14 show that the MILL\_OUT\_TEMP models have more varied results.

Although ANN-based model of MILL\_OUT\_TEMP has the best accuracy, and the Ridge regression-based model has lower as it can be seen in Figures 10 and 11; the behavior of models, response to parameter changes and places of higher difference from measures are the same. The ANN better adapts to periods with high temperature increasing mainly in case of mill start-up. However, both models have the same sudden changes of predicted value as presented in Figures 10 and 11; ANN generates the valued bit proximal to measurement than ridge regression but without significant influence into further application to fault detection. It has been also tested that both models detect abnormal working condition present at nearly the same time. It seems reasonable to use Ridge regression-based models in algorithm since they are easier to train, maintain and adapt.


The models' application into industrial process control and fault detection usually depends on the model accuracy and the model complexity. As presented in the chapter, the three different approaches of AMPS model evaluations gave comparable model accuracy; however, their complexity differs. It seems natural that the model with the lowest complexity level is implemented, and still, furthermore, complex comparison tests should be performed. Model

Model based on MAPE Ridge regression 1.26 Artificial neural network 1.10 Physical equations 1.15

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Table 14. MILL\_OUT\_TEMP comparison.

Figure 10. ANN and ridge regression comparison.

Figure 11. ANN and ridge regression comparison.

Table 13. AMPS comparison.


be described by numerous equations [16, 17], containing five algebraic equations describing primary air flow based on pressure differences and air density, coal flow based on feeder speed, pulverized coal flow based on pressure differences and actual amount of pulverized fuel in mill and four differential equations describing mass balance in coal mill based on coal flow, actual coal content in mill, pulverized fuel flow and content in coal mill following equation describing

The main focus in developing this model is unknown coefficients K\_i, where i ∈{1,2,3,…,17} definition is such way that the model has the lowest prediction error (the difference between measured and modeled values is minimalized). One approach [16] uses the genetic algorithm to determine unknown coefficients. The same method has been developed and applied to

In this chapter, three coal mill models' evaluation approaches are presented, and the methods are linear regression (Sections 4, 5 and 6), artificial neural network (Section 7.1) and physical equations with the use of a genetic algorithm to determine the unknown model coefficients (Section 7.2). All mentioned methods have been applied to data set containing values of operating parameters from 10 months of mill operation presented in Section 3. The results presented in Table 13 show that the AMPS models have similar performance with the MAPE coefficient close to 2%, which is less than 0.5A mean error. The results presented in Table 14

Although ANN-based model of MILL\_OUT\_TEMP has the best accuracy, and the Ridge regression-based model has lower as it can be seen in Figures 10 and 11; the behavior of models, response to parameter changes and places of higher difference from measures are the same. The ANN better adapts to periods with high temperature increasing mainly in case of mill start-up. However, both models have the same sudden changes of predicted value as presented in Figures 10 and 11; ANN generates the valued bit proximal to measurement than ridge regression but without significant influence into further application to fault detection. It has been also tested that both models detect abnormal working condition present at nearly the same time. It seems reasonable to use Ridge regression-based models in algorithm since they

MAPE [%] 1.15 2.02

Model based on MAPE Ridge regression 1.946 Artificial neural network 1.981 Physical equations 2.020

MILL\_OUT\_TEMP [C] AMPS [A]

mill motor current, mill pressure differences, and outlet temperature variability.

analyzed coal mill [18], and the results are presented in Table 12.

48 Thermal Power Plants - New Trends and Recent Developments

show that the MILL\_OUT\_TEMP models have more varied results.

are easier to train, maintain and adapt.

Table 12. Genetic algorithm.

Table 13. AMPS comparison.

7.3. Comparison

Figure 10. ANN and ridge regression comparison.

Figure 11. ANN and ridge regression comparison.

The models' application into industrial process control and fault detection usually depends on the model accuracy and the model complexity. As presented in the chapter, the three different approaches of AMPS model evaluations gave comparable model accuracy; however, their complexity differs. It seems natural that the model with the lowest complexity level is implemented, and still, furthermore, complex comparison tests should be performed. Model based on physical equation is the most understandable, but the process of unknown coefficient estimation is time-consuming and non-deterministic; the neural network-based model is the most complex and the least comprehensible; consequently, its implementation does not seem to be needed. The advantage of regression model is its simplicity and comprehension; therefore, it seems appropriate to implement model in algorithm designed to detect mill faults.

## 8. Fault detection algorithm

The models presented in Tables 6 and 7 have been used to develop the algorithm and enabled to detect abnormal operation conditions and malfunction of analyzed mill. The algorithm during mill operation determines diagnostic signals (7) which represents the difference between measured y\_measured and predicted y\_predicted values of mill current and outlet temperature:

$$r = y\_{predicted} - y\_{measured} \tag{7}$$

Figure 13. MILL\_OUT\_TEMP histogram of residuals.

Table 15. Thresholds.

Model Threshold for level 1 Threshold for level 2 Threshold for disabling

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AMPS 1,2 2 0,8 MILL\_OUT\_TEMP 8 15 6

Figure 12. AMPS histogram of residuals.

If the value exceeds defined threshold, the algorithm infers about abnormal working condition presence. The predicted values are calculated based on coefficients determined for model presented in Tables 8 and 10 with consideration of variable delays presented in Tables 3 and 4.

#### 8.1. Threshold definition

The appropriate threshold value definition is crucial; if the threshold is low, the algorithm will often falsely infer the presence of abnormal condition; on the other hand, if threshold will be too high, the algorithm may not infer abnormal conditions while it occurs. The threshold values have been determined based on residual valued r, and the distribution of residuals is presented in Figures 12 and 13.

After analyzing the model behavior, it has been decided that the algorithm will infer with two levels:

LEVEL 1—abnormal operation conditions.

LEVEL 2—fault.

The thresholds for each level are presented in Table 15, and the alarm disabling will occur when the diagnostic signal value is decreased to determine value.

#### 8.2. Fault cause distinction

When algorithm informs about appearance of abnormal working conditions, which mean that at least one diagnostic signal has exceeded the threshold, the most likely cause of these conditions is estimated and provided. There are three main fault causes that algorithm detects: feeder blockage, lack of coal in the mill and mill overload. Inference mechanism combines the algorithm performance and unit operator's experience.

Detection of Malfunctions and Abnormal Working Conditions of a Coal Mill http://dx.doi.org/10.5772/intechopen.72952 51

Figure 12. AMPS histogram of residuals.

based on physical equation is the most understandable, but the process of unknown coefficient estimation is time-consuming and non-deterministic; the neural network-based model is the most complex and the least comprehensible; consequently, its implementation does not seem to be needed. The advantage of regression model is its simplicity and comprehension; therefore, it seems appropriate to implement model in algorithm designed to detect mill faults.

The models presented in Tables 6 and 7 have been used to develop the algorithm and enabled to detect abnormal operation conditions and malfunction of analyzed mill. The algorithm during mill operation determines diagnostic signals (7) which represents the difference between measured y\_measured and predicted y\_predicted values of mill current and outlet

If the value exceeds defined threshold, the algorithm infers about abnormal working condition presence. The predicted values are calculated based on coefficients determined for model presented in Tables 8 and 10 with consideration of variable delays presented in Tables 3 and 4.

The appropriate threshold value definition is crucial; if the threshold is low, the algorithm will often falsely infer the presence of abnormal condition; on the other hand, if threshold will be too high, the algorithm may not infer abnormal conditions while it occurs. The threshold values have been determined based on residual valued r, and the distribution of residuals is

After analyzing the model behavior, it has been decided that the algorithm will infer with two

The thresholds for each level are presented in Table 15, and the alarm disabling will occur

When algorithm informs about appearance of abnormal working conditions, which mean that at least one diagnostic signal has exceeded the threshold, the most likely cause of these conditions is estimated and provided. There are three main fault causes that algorithm detects: feeder blockage, lack of coal in the mill and mill overload. Inference mechanism combines the

r ¼ ypredicted � ymeasured (7)

8. Fault detection algorithm

50 Thermal Power Plants - New Trends and Recent Developments

temperature:

levels:

LEVEL 2—fault.

8.2. Fault cause distinction

8.1. Threshold definition

presented in Figures 12 and 13.

LEVEL 1—abnormal operation conditions.

when the diagnostic signal value is decreased to determine value.

algorithm performance and unit operator's experience.

Figure 13. MILL\_OUT\_TEMP histogram of residuals.


Table 15. Thresholds.

First, algorithm determines whether in the mill there is too much (r > 0) or too little of coal (r < 0). If there is too little of coal, the second step is to compare temperature in coal bunker. If there is no coal in feeder, the temperature instantly is rising and the feeder motor current is lower that usually. In case of r > 0, the algorithm also is checking the mill inlet presser since it is main parameter observed by operators during mill diagnostic; if the pressure is significantly higher than usual, the algorithm also informs about it. Those mechanisms have been implemented in operator graphic which informs about current mill conditions and estimated risks.

#### 8.3. Algorithm

Algorithm presented in Figure 14 is designed to inform online about coal mill working conditions. History window contains the measurements from last 5 min (due to input signal time delay), and diagnostic signal is generated in way presented in Section 8. The operators are informed about actual coal mill conditions and estimated risk by dedicated operator graphic containing information about diagnostic signals and estimated risks presented in Section 8.2.

9. Fault detection performance

Figure 15. AMPS11 September 2014 fault: Screw blockage.

operators enough time to react safely.

Table 16. 11 September 2014 fault: Screw blockage.

Figure 16. MILL\_OUT\_TEMP 2014.09.11 fault: Screw blockage.

The algorithm has been tested to analyze its fault detection performance. In historical data set, the faults occur six times and were caused by lack of coal in coal bunker, feeder blockage and mill overload. For each malfunction type, the algorithm infers abnormal working conditions with some ahead of time. Particularly, the algorithm detects the feeder blockage. For fault in 11 September 2014, the algorithm infers abnormal working conditions around 40 min ahead the mill shutdown and 6 min before mill shutdown algorithm inferring about fault. More detailed times are presented in Table 16. It can be seen that the failure has been developing during period between first alarm occupancy at LEVEL1 and LEVEL 2. This gives the unit

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In Figures 15–16, the comparison of measured and modeled values is presented. The same type of fault appeared in 22 January 2014, and the LEVELS 1 and 2 appeared at similar time around 11 min before emergency mill shutdown. Details are presented in Table 17, and

Model Level 1 Level 2 AMPS 2550 s 390 s MILL\_OUT\_TEMP 240 s 240

Figure 14. The idea of online diagnostic algorithm.

Figure 15. AMPS11 September 2014 fault: Screw blockage.

## 9. Fault detection performance

First, algorithm determines whether in the mill there is too much (r > 0) or too little of coal (r < 0). If there is too little of coal, the second step is to compare temperature in coal bunker. If there is no coal in feeder, the temperature instantly is rising and the feeder motor current is lower that usually. In case of r > 0, the algorithm also is checking the mill inlet presser since it is main parameter observed by operators during mill diagnostic; if the pressure is significantly higher than usual, the algorithm also informs about it. Those mechanisms have been implemented in

Algorithm presented in Figure 14 is designed to inform online about coal mill working conditions. History window contains the measurements from last 5 min (due to input signal time delay), and diagnostic signal is generated in way presented in Section 8. The operators are informed about actual coal mill conditions and estimated risk by dedicated operator graphic containing information about diagnostic signals and estimated risks presented in Section 8.2.

operator graphic which informs about current mill conditions and estimated risks.

8.3. Algorithm

52 Thermal Power Plants - New Trends and Recent Developments

Figure 14. The idea of online diagnostic algorithm.

The algorithm has been tested to analyze its fault detection performance. In historical data set, the faults occur six times and were caused by lack of coal in coal bunker, feeder blockage and mill overload. For each malfunction type, the algorithm infers abnormal working conditions with some ahead of time. Particularly, the algorithm detects the feeder blockage. For fault in 11 September 2014, the algorithm infers abnormal working conditions around 40 min ahead the mill shutdown and 6 min before mill shutdown algorithm inferring about fault. More detailed times are presented in Table 16. It can be seen that the failure has been developing during period between first alarm occupancy at LEVEL1 and LEVEL 2. This gives the unit operators enough time to react safely.

In Figures 15–16, the comparison of measured and modeled values is presented. The same type of fault appeared in 22 January 2014, and the LEVELS 1 and 2 appeared at similar time around 11 min before emergency mill shutdown. Details are presented in Table 17, and


Table 16. 11 September 2014 fault: Screw blockage.

Figure 16. MILL\_OUT\_TEMP 2014.09.11 fault: Screw blockage.

Figure 17. AMPS 12 July 2014 fault: Lack of coal in coal bunker.

comparison of modeled and predicted values is presented in Figures 19 and 20. It can be seen that the failure occurred suddenly unlike the failure on 11.09 where before failure the mill has been working with abnormal conditions for around 30 min; however, the algorithm has been informing at LEVEL 2 10 min before mill shut down. The fault caused by lack of coal in the bunker is presented in Figures 17 and 18, and the times of algorithm abnormal working condition inference are presented in Table 18. The algorithm infer at LEVEL 1 and LEVEL 2 around 2 min before emergency mill shutdown; although this is not a lot this types of faults forms and evolve relatively fast and inexpertly and algorithm allows inform and give for the

MODEL Level 1 Level 2 AMPS 100 100 MILL\_OUT\_TEMP 120 120

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This chapter presents the models of two coal mill operation parameters: motor current and outlet temperature of pulverized fuel, implemented in algorithm designed to detect faults and abnormal operating conditions in coal mills. During extended data analysis, it has been shown that some depended variables influence independent variables with certain delay. The models have been developed with usage of multiple regression theory and compared with model based on an artificial neural network and model based on physical equations. It has been demonstrated that regression-based models have comparable model accuracy and fault detection performance. Based on developed models, an algorithm that detects abnormal working conditions and faults of coal mill has been developed. Tests carried out on historical data show that this algorithm can be successfully used to detect certain abnormal conditions and malfunctions of the operating mill, such as feeder blockage, lack of coal and mill overload.

The algorithm is implemented in the power plant on 200 MW power unit.

operator a time for propel reaction.

Figure 20. MILL\_OUT\_TEMP 22 January 2014. Fault: Screw blockage.

Table 18. 12 July 2014 fault: Lack of coal in coal bunker.

10. Conclusion

Figure 18. MILL\_OUT\_TEMP 12 July 2014 fault: Lack of coal in coal bunker.


Figure 19. AMPS 22 January 2014. Fault: Screw blockage.

Figure 20. MILL\_OUT\_TEMP 22 January 2014. Fault: Screw blockage.


Table 18. 12 July 2014 fault: Lack of coal in coal bunker.

comparison of modeled and predicted values is presented in Figures 19 and 20. It can be seen that the failure occurred suddenly unlike the failure on 11.09 where before failure the mill has been working with abnormal conditions for around 30 min; however, the algorithm has been informing at LEVEL 2 10 min before mill shut down. The fault caused by lack of coal in the bunker is presented in Figures 17 and 18, and the times of algorithm abnormal working condition inference are presented in Table 18. The algorithm infer at LEVEL 1 and LEVEL 2 around 2 min before emergency mill shutdown; although this is not a lot this types of faults forms and evolve relatively fast and inexpertly and algorithm allows inform and give for the operator a time for propel reaction.

## 10. Conclusion

Figure 18. MILL\_OUT\_TEMP 12 July 2014 fault: Lack of coal in coal bunker.

Figure 17. AMPS 12 July 2014 fault: Lack of coal in coal bunker.

54 Thermal Power Plants - New Trends and Recent Developments

Table 17. 22 January 2014 fault: Screw blockage.

Figure 19. AMPS 22 January 2014. Fault: Screw blockage.

MODEL Level 1 Level 2 AMPS 670 600 MILL\_OUT\_TEMP 590 s 590

> This chapter presents the models of two coal mill operation parameters: motor current and outlet temperature of pulverized fuel, implemented in algorithm designed to detect faults and abnormal operating conditions in coal mills. During extended data analysis, it has been shown that some depended variables influence independent variables with certain delay. The models have been developed with usage of multiple regression theory and compared with model based on an artificial neural network and model based on physical equations. It has been demonstrated that regression-based models have comparable model accuracy and fault detection performance. Based on developed models, an algorithm that detects abnormal working conditions and faults of coal mill has been developed. Tests carried out on historical data show that this algorithm can be successfully used to detect certain abnormal conditions and malfunctions of the operating mill, such as feeder blockage, lack of coal and mill overload. The algorithm is implemented in the power plant on 200 MW power unit.

## Author details

Teresa Kurek<sup>1</sup> \*, Konrad Wojdan<sup>1</sup> , Daniel Nabagło<sup>2</sup> and Konrad Świrski<sup>1</sup>

\*Address all correspondence to: teresa.bil@itc.pw.edu.pl

1 Institute of Heat Engineering, Faculty of Power and Aeronautical Engineering, Warsaw University of Technology, Warszawa, Poland

[12] Arlot S, Celisse A. A survey of cross-validation procedures for model selection. Statistics

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[13] Lium X-Q, H-Y J. Optimal generalized ridge estimator under the generalized crossvalidation criterion in linear regression. Linear Algebra and its Applications. 2012;436:1238-

[14] Guoqiang Zhang, Patuwo BE, Hu MY. Forecasting with artificial neural networks: The

[15] Shanker M, Hu MY, Hung MS. Effect of data standardization on neural network training.

[16] Zhang YG, Wu QH, Wang J, Oluwande G, Matts D, Zhou XX. Coal mill modeling by machine learning based on on-site measurement. IEEE Transactions on Energy Conver-

[17] Wei JL, Wang JH, Wu QH. Further study of coal mill modeling by machine learning based on on-site measurement. In: Proc.. 16th Int. Conf. Syst. Eng. Conf. 2003, Conventry, U.K.

[18] Krosnicki M. Current diagnosis of coal mill using evolutionary algorithm. WUT Masther

[19] Guo-you L, Min D. A wavelet and neural networks based on fault diagnosis for HAGC system of strip rolling mill. Journal of Iron and Steel Research, International. 2011;18(1):31-35

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Author details

\*, Konrad Wojdan<sup>1</sup>

56 Thermal Power Plants - New Trends and Recent Developments

University of Technology, Warszawa, Poland

\*Address all correspondence to: teresa.bil@itc.pw.edu.pl

, Daniel Nabagło<sup>2</sup> and Konrad Świrski<sup>1</sup>

1 Institute of Heat Engineering, Faculty of Power and Aeronautical Engineering, Warsaw

[1] Agrawal V, Panigrahi BK, Subbarao PMV. Review of control and fault diagnosis methods

[2] Rees NW, Fan GQ. Modeling and control of pulverized fuel coal mills. Institution of Electrical Engineers, Thermal power plant simulation and control: Chapter3. 2003. 63-99

[3] Rees N, Fan F. Modeling and control of pulverized fuel coal mills in Thermal power plant simulation and control. Flynn D, editor. 1st ed. Institution of Electrical Engineers. 2003 [4] Odgaard PF, Mataji B. Observer-based fault detection and moisture estimating in coal

[5] Guo S, Wang J, Wei J, Zachariades P. A new model-based approach for power plant tubeball mill condition monitoring and fault detection. Energy Convertion and Management.

[6] Agrawal V, Panigrahi BK, Subbarao PMV. A unified thermo-mechanical model for coal

[7] Cortinovi A. Mercangöz M, Mathur T, Poland J, Blaumann M. Nonlinear coal mill modeling and its application to model predictive control. Control Engineering Practice.

[8] Odgaard PF, Lin B, Jorgensen SB. Observer based and regression model-based detection of emerging faults in coal mills. Supervision and Safety of Technical Processes Beijing.

[9] Odgaard PF, Mataji B. Fault Detection in Coal Mills Used in Power Plants. Kananaskis,

[10] D'Ambrosio JPR, Dupont P. Kernel methods for heterogeneous feature selection.

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**Chapter 4**

Provisional chapter

**Numerical Modeling of Cyclic Creep-Fatigue Damage**

DOI: 10.5772/intechopen.73186

The paper presents the results of numerical analysis of creep-fatigue damage development in a steam turbine rotor under cyclic duty. Investigations were performed for a full cycle representing the most accurate description of real operation and three simplified cycles representative of different levels of simplification in inelastic strains modeling. It was shown by numerical simulations that significant inaccuracies in creep-fatigue damage predictions, reaching an order of magnitude in deviation of inelastic strains, cannot be excluded when simplified models are used. It is thus concluded that full consideration of creep-fatigue damage at real operating conditions requires proper modeling of stress/

The increasing demand for higher thermal efficiency and higher operational flexibility of modern power generation plants results in severe mechanical and thermal loading conditions experienced by plant components in service [1]. In order to increase the thermal efficiency, it is often necessary to increase the power plant operating temperature, while the higher operational flexibility requires frequent and faster turbine start-ups and shutdowns. The extremely severe service conditions of the plant components are subjected to produce a progressive material deterioration due to the accumulation of creep and fatigue damage and can lead to

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Numerical Modeling of Cyclic Creep-Fatigue Damage

**Development for Lifetime Assessment of Steam**

Development for Lifetime Assessment of Steam

**Turbine Components**

Turbine Components

Additional information is available at the end of the chapter

strain histories using visco-elastic-plastic material models.

Keywords: creep, low-cycle fatigue, steam turbine, lifetime assessment

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.73186

Mariusz Banaszkiewicz

Mariusz Banaszkiewicz

Abstract

1. Introduction

component failure [2].

#### **Numerical Modeling of Cyclic Creep-Fatigue Damage Development for Lifetime Assessment of Steam Turbine Components** Numerical Modeling of Cyclic Creep-Fatigue Damage Development for Lifetime Assessment of Steam Turbine Components

DOI: 10.5772/intechopen.73186

Mariusz Banaszkiewicz Mariusz Banaszkiewicz

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.73186

#### Abstract

The paper presents the results of numerical analysis of creep-fatigue damage development in a steam turbine rotor under cyclic duty. Investigations were performed for a full cycle representing the most accurate description of real operation and three simplified cycles representative of different levels of simplification in inelastic strains modeling. It was shown by numerical simulations that significant inaccuracies in creep-fatigue damage predictions, reaching an order of magnitude in deviation of inelastic strains, cannot be excluded when simplified models are used. It is thus concluded that full consideration of creep-fatigue damage at real operating conditions requires proper modeling of stress/ strain histories using visco-elastic-plastic material models.

Keywords: creep, low-cycle fatigue, steam turbine, lifetime assessment

## 1. Introduction

The increasing demand for higher thermal efficiency and higher operational flexibility of modern power generation plants results in severe mechanical and thermal loading conditions experienced by plant components in service [1]. In order to increase the thermal efficiency, it is often necessary to increase the power plant operating temperature, while the higher operational flexibility requires frequent and faster turbine start-ups and shutdowns. The extremely severe service conditions of the plant components are subjected to produce a progressive material deterioration due to the accumulation of creep and fatigue damage and can lead to component failure [2].

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Steam turbine components operating at high and highly variable temperatures, e.g., rotors, casings and valve chests, are among the most critical components of power plant units, and their lifetime is already limited at the design stage [3]. Safe and reliable operation of steam turbines can only be ensured with proper monitoring systems, periodic inspections and comprehensive lifetime assessment studies [4–6].

Typical operation cycle of a steam turbine consists of a start-up, steady state, load change, shutdown and natural cooling. During transient phases, the low-cycle fatigue damage is generated, while steady-state operation brings about the creep wear [7]. In order to accurately determine the creep-fatigue life exhaustion, inelastic material models and a proper approach to multiple cycles consideration have to be applied [8].

Traditional methods of lifetime assessment basing on the use of representative operation data and elastic material models can result in significant inaccuracies in damage prediction and lead to non-optimal decisions regarding future operation [9]. That is why the use of inelastic material models and long-term operation data is becoming mandatory for reliable calculation of creep-fatigue damage and residual life prediction.

The paper presents the results of investigations performed for a steam turbine rotor showing possible inaccuracies and, in particular, differences in predicted strain accumulation and damage depending on the material model and cycles analysis method used.

## 2. Cyclic operation of steam turbines

The lifetime of steam turbine components depends on variable loading conditions resulting in fatigue and creep-fatigue damage. Typical service start-stop cycle includes start-up, full load, part load and shutdown phase, generating variable temperature and stress-strain distributions in turbine components. A schematic illustration of different operation phases and the resulting temperature and stress variations on a rotor surface is shown in Figure 1. During turbine runup, rotor rotational speed increases from turning gear to rated speed (0–1) and steam parameters start rising from the initial values. After unit synchronization (1), turbine loading starts (1–2) with continued increase of steam temperature and pressure, and after some time, all the parameters reach their nominal values. The start-up process is finished and steady-state phase (2–3) with constant process parameters is reached. During steady-state operation, load changes (3–4, 5–6) with different rate can take place, which are accompanied by steam temperature and pressure variations. The operating cycle is closed by the shutdown (7–8) and natural cooling phases when all the process parameters go down.

during the shutdown phase. The major stress range Δσ is thus formed by the start-up and

Figure 1. Typical operating cycle of conventional steam turbine unit: (a) process parameters and (b) rotor surface stress.

Numerical Modeling of Cyclic Creep-Fatigue Damage Development for Lifetime Assessment of Steam Turbine…

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61

Full consideration of creep-fatigue damage at real operating conditions requires modeling of long stress/strain histories using visco-elastic-plastic material models. Such a modeling approach is impractical when 2D or 3D models are used to represent the real component geometry and the balance equations solved by means of a finite element method. For the purpose of numerical investigation of creep-fatigue damage development in steam turbine rotors, simplified cycles are defined with different material models prescribed to transient and steady-state phases. It was done in order to investigate the effect of material model applied and number of cycles analyzed on the creep-fatigue damage accumulation. The four

1. Full multiple cycle: fatigue simulated with elastic-plastic model and creep with viscous

2. Simplified multiple viscous cycle 1: fatigue simulated with elastic-plastic model for one

shutdown stresses, while the minor stress range is defined by the load change stresses.

cycle types are schematically shown in Figure 2. They are as follows:

cycle and creep with viscous model for multiple start-stop cycles.

model for multiple start-stop cycles.

The corresponding stress variations at a rotor surface are presented in Figure 1b. During startup, the rotor surface temperature increases with a higher rate than the center temperature, which results in compressive stresses at the surface [10]. The stress attains maximum and then slowly decays to a steady-state stress. The following load changes generate transient thermal stresses of different sign, but usually the highest tensile stress is generated on the rotor surface Numerical Modeling of Cyclic Creep-Fatigue Damage Development for Lifetime Assessment of Steam Turbine… http://dx.doi.org/10.5772/intechopen.73186 61

Steam turbine components operating at high and highly variable temperatures, e.g., rotors, casings and valve chests, are among the most critical components of power plant units, and their lifetime is already limited at the design stage [3]. Safe and reliable operation of steam turbines can only be ensured with proper monitoring systems, periodic inspections and com-

Typical operation cycle of a steam turbine consists of a start-up, steady state, load change, shutdown and natural cooling. During transient phases, the low-cycle fatigue damage is generated, while steady-state operation brings about the creep wear [7]. In order to accurately determine the creep-fatigue life exhaustion, inelastic material models and a proper approach to

Traditional methods of lifetime assessment basing on the use of representative operation data and elastic material models can result in significant inaccuracies in damage prediction and lead to non-optimal decisions regarding future operation [9]. That is why the use of inelastic material models and long-term operation data is becoming mandatory for reliable calculation

The paper presents the results of investigations performed for a steam turbine rotor showing possible inaccuracies and, in particular, differences in predicted strain accumulation and

The lifetime of steam turbine components depends on variable loading conditions resulting in fatigue and creep-fatigue damage. Typical service start-stop cycle includes start-up, full load, part load and shutdown phase, generating variable temperature and stress-strain distributions in turbine components. A schematic illustration of different operation phases and the resulting temperature and stress variations on a rotor surface is shown in Figure 1. During turbine runup, rotor rotational speed increases from turning gear to rated speed (0–1) and steam parameters start rising from the initial values. After unit synchronization (1), turbine loading starts (1–2) with continued increase of steam temperature and pressure, and after some time, all the parameters reach their nominal values. The start-up process is finished and steady-state phase (2–3) with constant process parameters is reached. During steady-state operation, load changes (3–4, 5–6) with different rate can take place, which are accompanied by steam temperature and pressure variations. The operating cycle is closed by the shutdown (7–8) and natural

The corresponding stress variations at a rotor surface are presented in Figure 1b. During startup, the rotor surface temperature increases with a higher rate than the center temperature, which results in compressive stresses at the surface [10]. The stress attains maximum and then slowly decays to a steady-state stress. The following load changes generate transient thermal stresses of different sign, but usually the highest tensile stress is generated on the rotor surface

damage depending on the material model and cycles analysis method used.

prehensive lifetime assessment studies [4–6].

60 Thermal Power Plants - New Trends and Recent Developments

multiple cycles consideration have to be applied [8].

of creep-fatigue damage and residual life prediction.

2. Cyclic operation of steam turbines

cooling phases when all the process parameters go down.

Figure 1. Typical operating cycle of conventional steam turbine unit: (a) process parameters and (b) rotor surface stress.

during the shutdown phase. The major stress range Δσ is thus formed by the start-up and shutdown stresses, while the minor stress range is defined by the load change stresses.

Full consideration of creep-fatigue damage at real operating conditions requires modeling of long stress/strain histories using visco-elastic-plastic material models. Such a modeling approach is impractical when 2D or 3D models are used to represent the real component geometry and the balance equations solved by means of a finite element method. For the purpose of numerical investigation of creep-fatigue damage development in steam turbine rotors, simplified cycles are defined with different material models prescribed to transient and steady-state phases. It was done in order to investigate the effect of material model applied and number of cycles analyzed on the creep-fatigue damage accumulation. The four cycle types are schematically shown in Figure 2. They are as follows:


3. Simplified multiple viscous cycle 2: fatigue simulated with elastic model for one cycle and creep with viscous model for multiple start-stop cycles.

The first cycle describes the most realistic representation of actual operating conditions, while the other three cycles represent simplified approaches in terms of material models and number

Numerical Modeling of Cyclic Creep-Fatigue Damage Development for Lifetime Assessment of Steam Turbine…

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63

The problem under consideration is cyclic heating up and cooling down of a steam turbine rotor taking place during start-up and the subsequent shutdown. Rotor heating and cooling are caused by hot steam flow through the turbine with varying temperature, pressure and velocity. Non-stationary heat transfer takes place via forced convection, and the thermal load is a primary load of the rotor [11]. The rotor rotates with a constant rotational speed ω in steadystate operation. Steam pressure and rotational body forces due to rotation are also considered in the model. Non-uniform temperature distribution in the rotor induces thermal stresses due

• The rotor material is isotropic and its physical and mechanical properties are temperature

• Heating and cooling process is described by the linear theory of heat conduction and non-

• The resulting thermal stresses are determined from the solution of system of equations of

• Due to the geometrical and load symmetry of the rotor about its axis, the computational

Based on the above assumptions, a boundary problem of heat conduction and thermoelasticity

Heat conduction in a homogeneous isotropic solid is described by the Fourier-Kirchhoff

where T is the metal temperature, k is the thermal conductivity, g is the heat source, ρ is the

Neglecting the heat source g and assuming heat conduction in the radial and axial direction

∂T xð Þ ; t

<sup>∂</sup><sup>t</sup> (1)

div½ �þ kgradT xð Þ ; t g xð Þ¼ ; t ρcp

• Mechanical loads are modeled as surface pressure and volumetric body force.

is formulated and solved by means of a finite element method [12].

only, Eq. (1) is rewritten in cylindrical coordinate system as follows:

of cycles, which are used in engineering practice.

The following assumptions are adopted in the model:

linear convective boundary conditions.

uncoupled thermoelasticity and plasticity.

region is assumed axisymmetric.

3.1. Heat conduction problem

density and cp is the specific heat.

differential equation [13]

3. Problem formulation

to thermal expansion.

dependent.

4. Simplified multiple elastic-plastic cycle: fatigue simulated with elastic-plastic model for multiple start-stop cycles and no creep.

Figure 2. Different cycle types adopted for analyses: (a) full multiple cycle, (b) simplified multiple viscous cycle 1, (c) simplified multiple viscous cycle 2 and (d) simplified multiple elastic-plastic cycle.

The first cycle describes the most realistic representation of actual operating conditions, while the other three cycles represent simplified approaches in terms of material models and number of cycles, which are used in engineering practice.

## 3. Problem formulation

3. Simplified multiple viscous cycle 2: fatigue simulated with elastic model for one cycle and

4. Simplified multiple elastic-plastic cycle: fatigue simulated with elastic-plastic model for

Figure 2. Different cycle types adopted for analyses: (a) full multiple cycle, (b) simplified multiple viscous cycle 1, (c)

simplified multiple viscous cycle 2 and (d) simplified multiple elastic-plastic cycle.

creep with viscous model for multiple start-stop cycles.

multiple start-stop cycles and no creep.

62 Thermal Power Plants - New Trends and Recent Developments

The problem under consideration is cyclic heating up and cooling down of a steam turbine rotor taking place during start-up and the subsequent shutdown. Rotor heating and cooling are caused by hot steam flow through the turbine with varying temperature, pressure and velocity. Non-stationary heat transfer takes place via forced convection, and the thermal load is a primary load of the rotor [11]. The rotor rotates with a constant rotational speed ω in steadystate operation. Steam pressure and rotational body forces due to rotation are also considered in the model. Non-uniform temperature distribution in the rotor induces thermal stresses due to thermal expansion.

The following assumptions are adopted in the model:


Based on the above assumptions, a boundary problem of heat conduction and thermoelasticity is formulated and solved by means of a finite element method [12].

## 3.1. Heat conduction problem

Heat conduction in a homogeneous isotropic solid is described by the Fourier-Kirchhoff differential equation [13]

$$\text{div}[\text{kgrad}T(\mathbf{x},t)] + \text{g}(\mathbf{x},t) = \rho \mathbf{c}\_p \frac{\partial T(\mathbf{x},t)}{\partial t} \tag{1}$$

where T is the metal temperature, k is the thermal conductivity, g is the heat source, ρ is the density and cp is the specific heat.

Neglecting the heat source g and assuming heat conduction in the radial and axial direction only, Eq. (1) is rewritten in cylindrical coordinate system as follows:

$$
\rho c\_p \frac{\partial T}{\partial t} = \frac{1}{\mathbf{r}} \frac{\partial}{\partial r} \left( kr \frac{\partial T}{\partial r} \right) + \frac{\partial}{\partial z} \left( k \frac{\partial T}{\partial z} \right) \tag{2}
$$

A non-uniform temperature distribution T rð Þ ; z is assumed as initial condition at t ¼ 0. For rotor free surfaces, the boundary conditions are:

$$\left. \frac{\partial T}{\partial r} \right|\_{r=r\_{\rm in}} = 0 \text{ for } t \ge 0 \tag{3}$$

3.2. Thermoelasticity problem

<sup>∇</sup><sup>2</sup><sup>u</sup> � <sup>u</sup>

where the following definitions were employed:

<sup>∂</sup>r2 <sup>þ</sup> <sup>1</sup> r ∂ <sup>∂</sup><sup>r</sup> <sup>þ</sup> <sup>∂</sup><sup>2</sup> ∂z2

• At the outer cylindrical surfaces of the discs

• At the outer surfaces in contact with steam

coordinate system are expressed as [19]:

r<sup>2</sup> þ

<sup>∇</sup><sup>2</sup><sup>w</sup> <sup>þ</sup>

<sup>∂</sup><sup>r</sup> <sup>þ</sup> <sup>u</sup> <sup>r</sup> <sup>þ</sup> <sup>∂</sup><sup>w</sup> ∂z In Eq. (7), ν is the Poisson's ratio and β is the thermal expansion coefficient.

σ<sup>r</sup> ¼ pbð Þz —pressure due to centrifugal forces of blades

σ<sup>n</sup> ¼ �p zð Þ—steam pressure acting normal to the surface

1 1 � 2ν

> 1 1 � 2ν

∂e ∂r

∂e

<sup>þ</sup> ρω<sup>2</sup><sup>r</sup>

<sup>∂</sup><sup>z</sup> <sup>¼</sup> 2 1ð Þ <sup>þ</sup> <sup>ν</sup> 1 � 2ν

The system of partial differential equations (7) is solved with the following boundary condi-

The relations between strains and displacements for an axisymmetric body in the cylindrical

<sup>ε</sup><sup>r</sup> <sup>¼</sup> <sup>∂</sup><sup>u</sup> ∂r

εφ <sup>¼</sup> <sup>u</sup> r

<sup>ε</sup><sup>z</sup> <sup>¼</sup> <sup>∂</sup><sup>w</sup> ∂z

<sup>γ</sup>rz <sup>¼</sup> <sup>∂</sup><sup>u</sup> ∂z þ ∂w ∂r

<sup>G</sup> <sup>¼</sup> 2 1ð Þ <sup>þ</sup> <sup>ν</sup> 1 � 2ν

∂ βð Þ T � T<sup>0</sup> ∂r

http://dx.doi.org/10.5772/intechopen.73186

(7)

65

(8)

∂ βð Þ T � T<sup>0</sup> ∂z

respectively [19]:

• Laplacian <sup>∇</sup><sup>2</sup> <sup>¼</sup> <sup>∂</sup><sup>2</sup>

• At the left end face

• w ¼ 0 at z ¼ 0

tions:

• Volumetric strain e <sup>¼</sup> <sup>∂</sup><sup>u</sup>

Knowing the axisymmetric temperature field in the rotor, a solution of the problem of stress state induced by it can be obtained. The equilibrium conditions written for stresses are transformed, taking into account the relations between stresses, strains and displacements, to obtain differential equations with unknown displacements u and w in the r and z direction,

Numerical Modeling of Cyclic Creep-Fatigue Damage Development for Lifetime Assessment of Steam Turbine…

$$\left.k(z,t)\frac{\partial T}{\partial r}\right|\_{r=r\_{\text{sur}}(z)} = -\alpha(z,t)\left(T\_s - T\_f(z,t)\right) \text{ for } t \ge 0 \tag{4}$$

where αð Þ z; t is the heat transfer coefficient varying with time and axial co-ordiante, Ts is the metal surface temperature and Tfð Þ z; t is the fluid temperature depending on time and axial coordiante. The outer radius of the rotor r zð Þ varies with the axial coordinate z defining its outer contour.

The material physical properties are temperature dependent and their variation is described by polynomial functions. The variation of heat transfer coefficient in time and space αð Þ z; t is considered by the Nusselt number Nu changing in time as a function of the Reynolds number Re and Prandtl number Pr:

$$\mathbf{Nu} = \mathbf{f}(\mathbf{Re}, \mathbf{Pr}) \tag{5}$$

The Nusselt number is defined as follows:

$$\text{Nu} = \frac{\alpha d}{k} \tag{6}$$

where d denotes a characteristic diameter. A detailed form of Eq. (6) depends on the surface type and flow character [11]. The heat transfer model adopted in this study is based on the well-proven formulae for heat transfer coefficients in steam turbine rotors and can be employed in online calculations of temperatures and thermal stresses [14], which is not possible when more advanced thermal FSI (fluid-structure interaction) modeling is adopted [15–18].

Geometrical model of the rotor is shown in Figure 3.

Figure 3. Rotor geometrical model.

#### 3.2. Thermoelasticity problem

ρcp ∂T <sup>∂</sup><sup>t</sup> <sup>¼</sup> <sup>1</sup> r ∂ ∂r

rotor free surfaces, the boundary conditions are:

64 Thermal Power Plants - New Trends and Recent Developments

k zð Þ ; t ∂T ∂r r¼routð Þz

contour.

Re and Prandtl number Pr:

Figure 3. Rotor geometrical model.

The Nusselt number is defined as follows:

Geometrical model of the rotor is shown in Figure 3.

kr <sup>∂</sup><sup>T</sup> ∂r 

A non-uniform temperature distribution T rð Þ ; z is assumed as initial condition at t ¼ 0. For

where αð Þ z; t is the heat transfer coefficient varying with time and axial co-ordiante, Ts is the metal surface temperature and Tfð Þ z; t is the fluid temperature depending on time and axial coordiante. The outer radius of the rotor r zð Þ varies with the axial coordinate z defining its outer

The material physical properties are temperature dependent and their variation is described by polynomial functions. The variation of heat transfer coefficient in time and space αð Þ z; t is considered by the Nusselt number Nu changing in time as a function of the Reynolds number

Nu <sup>¼</sup> <sup>α</sup><sup>d</sup>

where d denotes a characteristic diameter. A detailed form of Eq. (6) depends on the surface type and flow character [11]. The heat transfer model adopted in this study is based on the well-proven formulae for heat transfer coefficients in steam turbine rotors and can be employed in online calculations of temperatures and thermal stresses [14], which is not possible when more advanced thermal FSI (fluid-structure interaction) modeling is adopted [15–18].

∂T ∂r r¼rin þ ∂ ∂z k ∂T ∂z 

¼ 0 for t ≥ 0 (3)

¼ �αð Þ <sup>z</sup>; <sup>t</sup> Ts � Tfð Þ <sup>z</sup>; <sup>t</sup> for <sup>t</sup> <sup>≥</sup> <sup>0</sup> (4)

Nu ¼ f Re ð Þ ; Pr (5)

<sup>k</sup> (6)

(2)

Knowing the axisymmetric temperature field in the rotor, a solution of the problem of stress state induced by it can be obtained. The equilibrium conditions written for stresses are transformed, taking into account the relations between stresses, strains and displacements, to obtain differential equations with unknown displacements u and w in the r and z direction, respectively [19]:

$$\begin{aligned} \nabla^2 u - \frac{u}{r^2} + \frac{1}{1 - 2\nu} \frac{\partial e}{\partial r} + \frac{\rho a^2 r}{G} &= \frac{2(1 + \nu)}{1 - 2\nu} \frac{\partial \left(\beta(T - T\_0)\right)}{\partial r} \\\\ \nabla^2 w + \frac{1}{1 - 2\nu} \frac{\partial e}{\partial z} &= \frac{2(1 + \nu)}{1 - 2\nu} \frac{\partial \left(\beta(T - T\_0)\right)}{\partial z} \end{aligned} \tag{7}$$

where the following definitions were employed:


In Eq. (7), ν is the Poisson's ratio and β is the thermal expansion coefficient.

The system of partial differential equations (7) is solved with the following boundary conditions:

• At the outer cylindrical surfaces of the discs

σ<sup>r</sup> ¼ pbð Þz —pressure due to centrifugal forces of blades

• At the outer surfaces in contact with steam

σ<sup>n</sup> ¼ �p zð Þ—steam pressure acting normal to the surface


The relations between strains and displacements for an axisymmetric body in the cylindrical coordinate system are expressed as [19]:

$$\begin{aligned} \varepsilon\_r &= \frac{\partial u}{\partial r} \\ \varepsilon\_\phi &= \frac{u}{r} \\ \varepsilon\_z &= \frac{\partial w}{\partial z} \end{aligned} \tag{8}$$
 
$$\gamma\_{rz} = \frac{\partial u}{\partial z} + \frac{\partial w}{\partial r}$$

Stress components are obtained from the solution of the constitutive equation of linear thermoelasticity [13] and for an axisymmetric body in the cylindrical coordinate system they are given as [19]:

$$\begin{aligned} \sigma\_r &= 2G \left\{ \varepsilon\_r + \frac{1}{1 - 2\nu} \left[ \nu e - (1 + \upsilon)\beta (T - T\_0) \right] \right\} \\\\ \sigma\_\psi &= 2G \left\{ \varepsilon\_\psi + \frac{1}{1 - 2\nu} \left[ \nu e - (1 + \upsilon)\beta (T - T\_0) \right] \right\} \\\\ \sigma\_z &= 2G \left\{ \varepsilon\_z + \frac{1}{1 - 2\nu} \left[ \nu e - (1 + \upsilon)\beta (T - T\_0) \right] \right\} \end{aligned} \tag{9}$$
 
$$\sigma\_{rz} = G \gamma\_{rz}$$

where ε\_ p

3.4. Creep model

Eq. (15) can be written as:

relationship is adopted:

where μ is a positive scalar coefficient.

as a fraction of creep rupture strength σ<sup>R</sup> [24]:

ij is a plastic flow rate and <sup>λ</sup>\_ denotes here a plastic work. In the linear kinematic

Numerical Modeling of Cyclic Creep-Fatigue Damage Development for Lifetime Assessment of Steam Turbine…

<sup>α</sup>\_ij <sup>¼</sup> μ σ \_ ij � <sup>α</sup>ij (13)

http://dx.doi.org/10.5772/intechopen.73186

<sup>σ</sup> � <sup>1</sup> (15)

<sup>σ</sup> � <sup>1</sup> (16)

(18)

(14)

67

(17)

hardening model, translation of the yield surface is described by the backstress tensor αij

For creep strain predictions, the characteristic strain model proposed by Bolton was employed [24, 25]. The model is simple and effective in description of creep deformation at long times. Based on the analyses of creep test data, Bolton extended the classical Norton model [26] and proposed the following isochronous relation between the stress exponent and stress expressed

<sup>∂</sup>log<sup>σ</sup> <sup>¼</sup> <sup>n</sup> <sup>¼</sup> <sup>1</sup>

where σ<sup>R</sup> denotes the creep rupture strength for a given time at constant temperature. Integrating the above relationship, he obtained an equation for the creep strain ε<sup>C</sup> in the form:

> <sup>ε</sup><sup>C</sup> <sup>¼</sup> εχ σR

where εχ is a characteristic creep strain, which is a material constant at a given time and temperature. The characteristic creep strain can be evaluated using Eq. (15) and by knowing two stresses, i.e. the creep rupture strength σR<sup>1</sup> at time t<sup>1</sup> and the stress σD<sup>1</sup> to produce datum creep strain ε<sup>D</sup> at time t1. With this assumption, the isochronous stress-strain relation of

> ε<sup>D</sup> <sup>σ</sup>R<sup>1</sup> <sup>σ</sup>D<sup>1</sup> � 1

> > σR

To close the model, a relationship for the rupture strength described by a simple power-law

where m denotes the exponent in the power-law relationship. The exponent m can be evalu-

log <sup>t</sup><sup>2</sup> t1 

log <sup>σ</sup>R<sup>1</sup> σR<sup>2</sup>

t1 t 1=<sup>m</sup>

σ<sup>R</sup> ¼ σR<sup>1</sup>

m ¼

ated from two values of rupture strengths at time t<sup>1</sup> and t2:

<sup>1</sup> � <sup>σ</sup> σR

whose evolution in time is determined by the Prager-Ziegler linear hardening law

∂ log ε<sup>c</sup>

ε<sup>C</sup> ¼

where <sup>G</sup> <sup>¼</sup> <sup>E</sup> 2 1ð Þ <sup>þ</sup><sup>ν</sup> is the shear modulus and <sup>E</sup> is the Young's modulus.

Eq. (9) is known as the Duhamel-Neumann relations and has a fundamental importance in thermal stress analysis within the validity of Hooke's law [20].

#### 3.3. Plasticity model

At stress concentration areas, thermal stresses induced by nonuniform temperature field can exceed the material yield stress and give rise to plastic deformation. Instead of estimating the plastic strains based on thermoelastic stresses and using analytical notch stress-strain correction methods [4, 14], a more accurate approach with direct use of elastic-plastic material was adopted. Numerical calculations were performed using Abaqus [21], employing elastic-plastic material model with the Prager-Ziegler linear kinematic hardening. The plasticity surface is defined by the Huber-Mises-Hencky function [22]:

$$F = f\left(\sigma\_{i\bar{\jmath}} - \alpha\_{i\bar{\jmath}}\right) - \sigma\_y = 0 \tag{10}$$

where <sup>f</sup> <sup>σ</sup>ij � <sup>α</sup>ij � � is the equivalent stress related to the backstress <sup>α</sup>ij defining translation of the yield surface. The yield function is traditionally defined as follows

$$f(\sigma\_{i\dot{\eta}} - \alpha\_{i\dot{\eta}}) = \sqrt{\frac{3}{2} \left( s\_{i\dot{\eta}} - \alpha\_{i\dot{\eta}}^d \right) \left( s\_{i\dot{\eta}} - \alpha\_{i\dot{\eta}}^d \right)} \tag{11}$$

where sij is a deviatoric part of the stress tensor σij, while α<sup>d</sup> ij is a deviatoric part of the backstress tensor αij.

The linear kinematic hardening model assumes the associated plastic flow rule in the form [23]:

$$\dot{\varepsilon}^{p}\_{ij} = \dot{\lambda} \frac{\partial F}{\partial \sigma\_{ij}} = \dot{\lambda} \left( s\_{ij} - \alpha^{d}\_{ij} \right) \tag{12}$$

where ε\_ p ij is a plastic flow rate and <sup>λ</sup>\_ denotes here a plastic work. In the linear kinematic hardening model, translation of the yield surface is described by the backstress tensor αij whose evolution in time is determined by the Prager-Ziegler linear hardening law

$$
\dot{\alpha}\_{\vec{\eta}} = \dot{\mu} \left( \sigma\_{\vec{\eta}} - \alpha\_{\vec{\eta}} \right) \tag{13}
$$

where μ is a positive scalar coefficient.

#### 3.4. Creep model

Stress components are obtained from the solution of the constitutive equation of linear thermoelasticity [13] and for an axisymmetric body in the cylindrical coordinate system they

νe � ð Þ 1 þ v βð Þ T � T<sup>0</sup>

νe � ð Þ 1 þ v βð Þ T � T<sup>0</sup>

(9)

(11)

(12)

ij is a deviatoric part of the

νe � ð Þ 1 þ v βð Þ T � T<sup>0</sup>

� � � <sup>σ</sup><sup>y</sup> <sup>¼</sup> <sup>0</sup> (10)

� � � �

� � � �

� � � �

σrz ¼ Gγrz

Eq. (9) is known as the Duhamel-Neumann relations and has a fundamental importance in

At stress concentration areas, thermal stresses induced by nonuniform temperature field can exceed the material yield stress and give rise to plastic deformation. Instead of estimating the plastic strains based on thermoelastic stresses and using analytical notch stress-strain correction methods [4, 14], a more accurate approach with direct use of elastic-plastic material was adopted. Numerical calculations were performed using Abaqus [21], employing elastic-plastic material model with the Prager-Ziegler linear kinematic hardening. The plasticity surface is

� � is the equivalent stress related to the backstress αij defining translation of

<sup>2</sup> sij � <sup>α</sup><sup>d</sup> ij � �

The linear kinematic hardening model assumes the associated plastic flow rule in the form

<sup>¼</sup> <sup>λ</sup>\_ sij � <sup>α</sup><sup>d</sup>

ij � �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>r</sup> � �

sij � <sup>α</sup><sup>d</sup> ij

F ¼ f σij � αij

3

the yield surface. The yield function is traditionally defined as follows

f σij � αij � � <sup>¼</sup>

where sij is a deviatoric part of the stress tensor σij, while α<sup>d</sup>

ε\_ p ij <sup>¼</sup> <sup>λ</sup>\_ <sup>∂</sup><sup>F</sup> ∂σij

1 1 � 2ν

1 1 � 2ν

1 1 � 2ν

2 1ð Þ <sup>þ</sup><sup>ν</sup> is the shear modulus and <sup>E</sup> is the Young's modulus.

σ<sup>r</sup> ¼ 2G ε<sup>r</sup> þ

66 Thermal Power Plants - New Trends and Recent Developments

σφ ¼ 2G εφ þ

σ<sup>z</sup> ¼ 2G ε<sup>z</sup> þ

thermal stress analysis within the validity of Hooke's law [20].

defined by the Huber-Mises-Hencky function [22]:

are given as [19]:

where <sup>G</sup> <sup>¼</sup> <sup>E</sup>

3.3. Plasticity model

where f σij � αij

backstress tensor αij.

[23]:

For creep strain predictions, the characteristic strain model proposed by Bolton was employed [24, 25]. The model is simple and effective in description of creep deformation at long times. Based on the analyses of creep test data, Bolton extended the classical Norton model [26] and proposed the following isochronous relation between the stress exponent and stress expressed as a fraction of creep rupture strength σ<sup>R</sup> [24]:

$$\frac{\partial \log \varepsilon\_{\varepsilon}}{\partial \log \sigma} = n = \frac{1}{1 - \frac{\sigma}{\sigma\_{\mathbb{R}}}} \tag{14}$$

where σ<sup>R</sup> denotes the creep rupture strength for a given time at constant temperature. Integrating the above relationship, he obtained an equation for the creep strain ε<sup>C</sup> in the form:

$$
\varepsilon\_{\mathbb{C}} = \frac{\varepsilon\_{\chi}}{\frac{\sigma\_{\mathbb{R}}}{\sigma} - 1} \tag{15}
$$

where εχ is a characteristic creep strain, which is a material constant at a given time and temperature. The characteristic creep strain can be evaluated using Eq. (15) and by knowing two stresses, i.e. the creep rupture strength σR<sup>1</sup> at time t<sup>1</sup> and the stress σD<sup>1</sup> to produce datum creep strain ε<sup>D</sup> at time t1. With this assumption, the isochronous stress-strain relation of Eq. (15) can be written as:

$$\varepsilon \varepsilon = \frac{\varepsilon\_D \left(\frac{\sigma\_{\rm R1}}{\sigma\_{\rm D1}} - 1\right)}{\frac{\sigma\_{\rm R}}{\sigma} - 1} \tag{16}$$

To close the model, a relationship for the rupture strength described by a simple power-law relationship is adopted:

$$
\sigma\_R = \sigma\_{R1} \left(\frac{t\_1}{t}\right)^{1/n} \tag{17}
$$

where m denotes the exponent in the power-law relationship. The exponent m can be evaluated from two values of rupture strengths at time t<sup>1</sup> and t2:

$$m = \frac{\log\left(\frac{t\_2}{t\_1}\right)}{\log\left(\frac{\sigma\_{\mathbb{R1}}}{\sigma\_{\mathbb{R2}}}\right)}\tag{18}$$

Finally, combining Eqs. (16) and (17), the model relationship between creep strain and time at a constant stress assumes the form:

$$\varepsilon\_{\mathcal{C}} = \frac{\varepsilon\_D \left(\frac{\sigma\_{\rm R1}}{\sigma\_{\rm D1}} - 1\right)}{\frac{\sigma\_{\rm R1}}{\sigma} \left(\frac{t\_1}{t}\right)^{1/m} - 1} \tag{19}$$

<sup>D</sup> <sup>¼</sup> <sup>D</sup>cr <sup>þ</sup> <sup>D</sup><sup>f</sup> (24)

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The total damage D cannot exceed a critical value Dc above which creep-fatigue crack initiation can be expected. The rules of calculating the critical damage are given in different national

Numerical Modeling of Cyclic Creep-Fatigue Damage Development for Lifetime Assessment of Steam Turbine…

Creep-fatigue damage calculation using the linear damage accumulation rule, creep and plasticity models and the proposed cycle descriptions can be used in lifetime calculations of both new and old turbines that have been in service for a longer period of time. For new machines, the following input data are typically required in order to perform lifetime calculations:

• Variation in time of the basic process parameters like steam temperature and pressure, rotor rotational speed and turbine load for cold, warm and hot starts and shutdown (these

Creep-fatigue damage calculations are performed for the cycles defined using the above data. For old machines, lifetime calculations are carried out in order to determine the current damage and predict the residual life assuming unchanged operating conditions. The accuracy of lifetime calculations strongly depends on the range and quality of operation data provided by the turbine user. In this case, long-term data characterizing turbine operation in the whole operation time or at least representative operation period should be used for computations. The range of data required for such analyses is similar to that required for new machines with the difference that the data were recorded and characterize real operation instead of the ideal operation assumed at the design phase. Creep-fatigue damage calculations are performed for

The difference between design and real conditions can be high and result in a huge deviation

According to the strain-based damage accumulation rules, damage due to a load cycle depends on the inelastic strain accumulated in the cycle and the strain at failure. For a given material and loading conditions, the failure strain can be assumed as constant, thus the accumulated strain can be adopted as a direct measure of creep or fatigue damage. This property was utilized in the present study to examine creep-fatigue damage development in a steam turbine rotor. In particular, the effect of prior creep and plastic deformation on the creep and plastic strain evolution is investigated, and its impact on damage development is

of damage and residual life predictions exceeding an order of magnitude.

5. Damage development in a steam turbine rotor

• Number of cold, warm and hot starts that the turbine has to perform.

• Requested operation time with given steam parameters and loads.

data are provided in the turbine design start-up diagrams).

the cycles defined using the real operation data.

discussed in detail.

standards [32–35].

The creep model is thus described by three constants: σR1—creep rupture strength at time t1; σR2—creep rupture strength at time t<sup>2</sup> and σD1—stress of creep strain ε<sup>D</sup> at time t1, which clearly have physical significance and can be derived from readily available data from standard creep tests.

#### 4. Creep-fatigue damage modeling

Creep damage is assessed on the basis of accumulated creep strain and is calculated using the ductility exhaustion rule [27, 28]. For a given load cycle i of duration th, creep damage dcr <sup>i</sup> is calculated from the formula [29]

$$d\_i^{cr} = \int\_0^{t\_h} \frac{\dot{\varepsilon}^{cr}}{\varepsilon\_R(\dot{\varepsilon}^{cr})} dt \tag{20}$$

where ε<sup>R</sup> is the creep ductility depending on the creep strain rate. The total creep damage Dcr due to n cycles is obtained by summing up the fractional creep damage values:

$$D^{cr} = \sum\_{i=1}^{n} d\_i^{cr} \tag{21}$$

Fatigue damage is assessed on the basis of accumulated plastic strain. For a given load cycle i, fatigue damage d f <sup>i</sup> is calculated from the formula [30]:

$$d\_i^f = \oint \frac{d\varepsilon^{pl}}{\varepsilon\_f} \tag{22}$$

where ε<sup>f</sup> is the plastic strain at failure. The total fatigue damage D<sup>f</sup> due to n cycles is obtained by summing up the fractional fatigue damage values:

$$D^f = \sum\_{i=1}^n d\_i^f \tag{23}$$

According to the linear damage accumulation rule, the total creep-fatigue damage D is a sum of that due to creep and fatigue [31]:

Numerical Modeling of Cyclic Creep-Fatigue Damage Development for Lifetime Assessment of Steam Turbine… http://dx.doi.org/10.5772/intechopen.73186 69

$$D = D^{cr} + D^{\ell} \tag{24}$$

The total damage D cannot exceed a critical value Dc above which creep-fatigue crack initiation can be expected. The rules of calculating the critical damage are given in different national standards [32–35].

Creep-fatigue damage calculation using the linear damage accumulation rule, creep and plasticity models and the proposed cycle descriptions can be used in lifetime calculations of both new and old turbines that have been in service for a longer period of time. For new machines, the following input data are typically required in order to perform lifetime calculations:


Finally, combining Eqs. (16) and (17), the model relationship between creep strain and time at a

ε<sup>D</sup> <sup>σ</sup>R<sup>1</sup> <sup>σ</sup>D<sup>1</sup> � 1 � �

The creep model is thus described by three constants: σR1—creep rupture strength at time t1; σR2—creep rupture strength at time t<sup>2</sup> and σD1—stress of creep strain ε<sup>D</sup> at time t1, which clearly have physical significance and can be derived from readily available data from stan-

Creep damage is assessed on the basis of accumulated creep strain and is calculated using the ductility exhaustion rule [27, 28]. For a given load cycle i of duration th, creep damage dcr

ε\_ cr

<sup>ε</sup><sup>R</sup> <sup>ε</sup>\_ cr ð Þ dt (20)

<sup>i</sup> (21)

<sup>i</sup> (23)

0

where ε<sup>R</sup> is the creep ductility depending on the creep strain rate. The total creep damage Dcr

<sup>D</sup>cr <sup>¼</sup> <sup>X</sup><sup>n</sup>

i¼1 dcr

Fatigue damage is assessed on the basis of accumulated plastic strain. For a given load cycle i,

where ε<sup>f</sup> is the plastic strain at failure. The total fatigue damage D<sup>f</sup> due to n cycles is obtained

<sup>D</sup><sup>f</sup> <sup>¼</sup> <sup>X</sup><sup>n</sup> i¼1 d f

According to the linear damage accumulation rule, the total creep-fatigue damage D is a sum

d f <sup>i</sup> <sup>¼</sup> <sup>∮</sup> <sup>d</sup>εpl εf

dcr <sup>i</sup> ¼ ðth

due to n cycles is obtained by summing up the fractional creep damage values:

<sup>i</sup> is calculated from the formula [30]:

by summing up the fractional fatigue damage values:

(19)

<sup>i</sup> is

(22)

σR<sup>1</sup> σ t1 t � �1=<sup>m</sup> � <sup>1</sup>

ε<sup>C</sup> ¼

constant stress assumes the form:

68 Thermal Power Plants - New Trends and Recent Developments

4. Creep-fatigue damage modeling

calculated from the formula [29]

dard creep tests.

fatigue damage d

f

of that due to creep and fatigue [31]:

• Variation in time of the basic process parameters like steam temperature and pressure, rotor rotational speed and turbine load for cold, warm and hot starts and shutdown (these data are provided in the turbine design start-up diagrams).

Creep-fatigue damage calculations are performed for the cycles defined using the above data.

For old machines, lifetime calculations are carried out in order to determine the current damage and predict the residual life assuming unchanged operating conditions. The accuracy of lifetime calculations strongly depends on the range and quality of operation data provided by the turbine user. In this case, long-term data characterizing turbine operation in the whole operation time or at least representative operation period should be used for computations. The range of data required for such analyses is similar to that required for new machines with the difference that the data were recorded and characterize real operation instead of the ideal operation assumed at the design phase. Creep-fatigue damage calculations are performed for the cycles defined using the real operation data.

The difference between design and real conditions can be high and result in a huge deviation of damage and residual life predictions exceeding an order of magnitude.

## 5. Damage development in a steam turbine rotor

According to the strain-based damage accumulation rules, damage due to a load cycle depends on the inelastic strain accumulated in the cycle and the strain at failure. For a given material and loading conditions, the failure strain can be assumed as constant, thus the accumulated strain can be adopted as a direct measure of creep or fatigue damage. This property was utilized in the present study to examine creep-fatigue damage development in a steam turbine rotor. In particular, the effect of prior creep and plastic deformation on the creep and plastic strain evolution is investigated, and its impact on damage development is discussed in detail.

#### 5.1. Thermal and elastic analysis

Temperature and elastic stress distributions in the examined rotor were obtained by solving the heat conduction and thermoelasticity equations given in Sections 3.1 and 3.2. Numerical solutions were obtained by means of the finite element method [12] using Abaqus code [21]. Transient and steady-state temperature distributions in the rotor are shown in Figure 4. During turbine start-up, highest temperature gradients, predominantly in the radial direction, are present in the rotor hottest region close to the steam inlet (Figure 4a). In steady-state, temperature distribution shown in Figure 4b, mainly axial temperature gradients are present which result from steam expansion in the turbine steam path and gland system. Transient temperature gradients produce high thermal stresses in the rotor leading to thermal fatigue cracking in stress concentration areas. High temperature in the rotor hottest sections in combination with centrifugal stresses lead to the creep damage which can also be localized in the stress concentration zones [36, 37]. In the examined rotor, the area of highest stress and temperature is located in the gland section where several heat relief grooves are present (Figure 5). High elastic stresses are developed at the bottom of the grooves and they frequently exceed the material yield stress. This results in local plastic deformation whose repetitive occurrence leads to thermal fatigue cracking often found in the heat grooves [38]. The heat relief grooves are thus the most critical locations of the rotor and their creep-fatigue damage development is analyzed in detail in the subsequent sections.

Throughout the entire analysis, the elastic-plastic material model was enabled with plasticity model defined in Section 3.3. Two types of cycles were utilized in order to examine the effect of creep deformation on plastic strain accumulation, namely full multiple cycle (Figure 2a) and simplified multiple elastic-plastic cycle (Figure 2d). The former accounts for creep during steady-state operation, whereas the latter cycle neglects the viscous effects and stress relaxation under constant load. The duration of one full cycle was 386 h, which results in the total time to complete three cycles equal 1158 h. The comparison of equivalent plastic strain distribution after each cycle for both types of analysis is shown in Figure 6. The zone of plastic deformation increases in size during cycling and its shape remains almost unchanged being close to semi-elliptical. Both models, i.e. elasto-plastic and visco-elasto-plastic, predict similar development of the plastic zone but with slightly higher equivalent plastic strains at the bottom of the groove observed in the elastic-plastic model predictions (without creep effects). The evolution in time of the maximum equivalent plastic strain at the groove is shown in Figure 7 together with the corresponding temperature cycles. The equivalent plastic strain gradually increases over time and so does the difference between the two models. It is thus found that creep deformation decelerates the plastic strain accumulation, which can be explained by the stress relaxation taking place during steady-state phase. As it is seen from Figure 7b, the first deviation in equivalent strains occurs after c.a. 110 h, which corresponds to

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Figure 6. Equivalent plastic strain distribution in heat grooves for: (a) full multiple cycle and (b) simplified elastic-plastic

cycle.

Figure 5. Elastic stress distribution in the rotor during cold start at 130 min.

#### 5.2. Effect of creep deformation on plastic strain accumulation

Cyclic operation of the turbine and the resulting plastic strain accumulation in the heat grooves were simulated by three start-stop cycles, each consisting of cold start-up, steadystate operation and shutdown followed by natural cooling to the subsequent cold start.

Figure 4. Temperature distribution in the rotor: (a) during cold start at 130 min and (b) at steady-state operation.

Numerical Modeling of Cyclic Creep-Fatigue Damage Development for Lifetime Assessment of Steam Turbine… http://dx.doi.org/10.5772/intechopen.73186 71

Figure 5. Elastic stress distribution in the rotor during cold start at 130 min.

5.1. Thermal and elastic analysis

70 Thermal Power Plants - New Trends and Recent Developments

analyzed in detail in the subsequent sections.

5.2. Effect of creep deformation on plastic strain accumulation

Temperature and elastic stress distributions in the examined rotor were obtained by solving the heat conduction and thermoelasticity equations given in Sections 3.1 and 3.2. Numerical solutions were obtained by means of the finite element method [12] using Abaqus code [21]. Transient and steady-state temperature distributions in the rotor are shown in Figure 4. During turbine start-up, highest temperature gradients, predominantly in the radial direction, are present in the rotor hottest region close to the steam inlet (Figure 4a). In steady-state, temperature distribution shown in Figure 4b, mainly axial temperature gradients are present which result from steam expansion in the turbine steam path and gland system. Transient temperature gradients produce high thermal stresses in the rotor leading to thermal fatigue cracking in stress concentration areas. High temperature in the rotor hottest sections in combination with centrifugal stresses lead to the creep damage which can also be localized in the stress concentration zones [36, 37]. In the examined rotor, the area of highest stress and temperature is located in the gland section where several heat relief grooves are present (Figure 5). High elastic stresses are developed at the bottom of the grooves and they frequently exceed the material yield stress. This results in local plastic deformation whose repetitive occurrence leads to thermal fatigue cracking often found in the heat grooves [38]. The heat relief grooves are thus the most critical locations of the rotor and their creep-fatigue damage development is

Cyclic operation of the turbine and the resulting plastic strain accumulation in the heat grooves were simulated by three start-stop cycles, each consisting of cold start-up, steadystate operation and shutdown followed by natural cooling to the subsequent cold start.

Figure 4. Temperature distribution in the rotor: (a) during cold start at 130 min and (b) at steady-state operation.

Throughout the entire analysis, the elastic-plastic material model was enabled with plasticity model defined in Section 3.3. Two types of cycles were utilized in order to examine the effect of creep deformation on plastic strain accumulation, namely full multiple cycle (Figure 2a) and simplified multiple elastic-plastic cycle (Figure 2d). The former accounts for creep during steady-state operation, whereas the latter cycle neglects the viscous effects and stress relaxation under constant load. The duration of one full cycle was 386 h, which results in the total time to complete three cycles equal 1158 h. The comparison of equivalent plastic strain distribution after each cycle for both types of analysis is shown in Figure 6. The zone of plastic deformation increases in size during cycling and its shape remains almost unchanged being close to semi-elliptical. Both models, i.e. elasto-plastic and visco-elasto-plastic, predict similar development of the plastic zone but with slightly higher equivalent plastic strains at the bottom of the groove observed in the elastic-plastic model predictions (without creep effects). The evolution in time of the maximum equivalent plastic strain at the groove is shown in Figure 7 together with the corresponding temperature cycles. The equivalent plastic strain gradually increases over time and so does the difference between the two models. It is thus found that creep deformation decelerates the plastic strain accumulation, which can be explained by the stress relaxation taking place during steady-state phase. As it is seen from Figure 7b, the first deviation in equivalent strains occurs after c.a. 110 h, which corresponds to

Figure 6. Equivalent plastic strain distribution in heat grooves for: (a) full multiple cycle and (b) simplified elastic-plastic cycle.

5.3. Effect of plastic deformation on creep strain accumulation

the total time of creep strain accumulation in 3 cycles equal 300 h.

plastic effects.

cycle 1, and (c) simplified multiple viscous cycle 2.

Similar to the effect of creep deformation on plastic strain accumulation, the effect of plastic deformation on creep strain accumulation can be expected. In order to investigate this phenomenon, different simplified cycles were adopted for analysis, namely simplified multiple viscous cycle 1 (Figure 2b) and simplified multiple viscous cycle 2 (Figure 2c). The duration of one full cycle was the same as in previous analyses, i.e. 386 h, but creep calculations with viscous model enabled were performed for steady-state phase lasting 100 h. This resulted in

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The comparison of equivalent creep strain distribution after each cycle for all types of analysis is shown in Figure 9. Similar to the behavior of the plastic zone, the zone of creep deformation increases in size during cycling and its shape remains almost unchanged. But this time, the applied models predict visibly different development rate of the creep zone. The largest zone size and equivalent creep strain are obtained for the full multiple cycle (Figure 9a), which takes into account both viscous and plastic effects in each individual start-stop cycle (Figure 2a). A smaller creep zone size and equivalent creep strain are obtained for the simplified multiple viscous cycle 1 (Figure 9b), which includes viscous effects in each individual start-stop cycle but neglects plastic strain development in cycles 2 and 3 (Figure 2b). The creep strain zone is nearly invisible in case of the simplified multiple viscous cycle 2, which completely neglects

The differences in creep strain accumulation are better seen from Figure 10a, which shows development of the maximum equivalent creep strain at the groove bottom. After the first start-stop cycle, a higher difference in the creep strain reaching 150% is found between the

Figure 9. Equivalent creep strain distribution in heat grooves for: (a) full multiple cycle, (b) simplified multiple viscous

Figure 7. Temperature variation and equivalent plastic strain accumulation in heat groove with and without prior creep: (a) in 3 cycles and (b) in 1 cycle.

the beginning of shutdown phase that started with different stress distributions in the groove computed with and without creep. Creep relaxation has thus a positive effect on the fatigue damage measured by the plastic strain accumulation. By neglecting the viscous effects in the steady-state operation, the plastic strains are overpredicted, and consequently the calculated fatigue damage will be too high as compared with the results of the visco-elastic-plastic model.

Figure 8 presents the evolution of plastic strain components in the groove bottom over 3 cycles. The strain state is very close to plane strain, with the radial and axial components having the same value and opposite sign, and the circumferential plastic strain being close to zero. It is interesting to see that initially the radial and axial strain components have different signs during operation and natural cooling but after the second cycle the radial strain becomes positive and the axial component remains negative.

Figure 8. Plastic strain accumulation in heat groove for full multiple cycle.

## 5.3. Effect of plastic deformation on creep strain accumulation

the beginning of shutdown phase that started with different stress distributions in the groove computed with and without creep. Creep relaxation has thus a positive effect on the fatigue damage measured by the plastic strain accumulation. By neglecting the viscous effects in the steady-state operation, the plastic strains are overpredicted, and consequently the calculated fatigue damage will be too high as compared with the results of the visco-elastic-plastic model. Figure 8 presents the evolution of plastic strain components in the groove bottom over 3 cycles. The strain state is very close to plane strain, with the radial and axial components having the same value and opposite sign, and the circumferential plastic strain being close to zero. It is interesting to see that initially the radial and axial strain components have different signs during operation and natural cooling but after the second cycle the radial strain becomes

Figure 7. Temperature variation and equivalent plastic strain accumulation in heat groove with and without prior creep:

positive and the axial component remains negative.

Figure 8. Plastic strain accumulation in heat groove for full multiple cycle.

(a) in 3 cycles and (b) in 1 cycle.

72 Thermal Power Plants - New Trends and Recent Developments

Similar to the effect of creep deformation on plastic strain accumulation, the effect of plastic deformation on creep strain accumulation can be expected. In order to investigate this phenomenon, different simplified cycles were adopted for analysis, namely simplified multiple viscous cycle 1 (Figure 2b) and simplified multiple viscous cycle 2 (Figure 2c). The duration of one full cycle was the same as in previous analyses, i.e. 386 h, but creep calculations with viscous model enabled were performed for steady-state phase lasting 100 h. This resulted in the total time of creep strain accumulation in 3 cycles equal 300 h.

The comparison of equivalent creep strain distribution after each cycle for all types of analysis is shown in Figure 9. Similar to the behavior of the plastic zone, the zone of creep deformation increases in size during cycling and its shape remains almost unchanged. But this time, the applied models predict visibly different development rate of the creep zone. The largest zone size and equivalent creep strain are obtained for the full multiple cycle (Figure 9a), which takes into account both viscous and plastic effects in each individual start-stop cycle (Figure 2a). A smaller creep zone size and equivalent creep strain are obtained for the simplified multiple viscous cycle 1 (Figure 9b), which includes viscous effects in each individual start-stop cycle but neglects plastic strain development in cycles 2 and 3 (Figure 2b). The creep strain zone is nearly invisible in case of the simplified multiple viscous cycle 2, which completely neglects plastic effects.

The differences in creep strain accumulation are better seen from Figure 10a, which shows development of the maximum equivalent creep strain at the groove bottom. After the first start-stop cycle, a higher difference in the creep strain reaching 150% is found between the

Figure 9. Equivalent creep strain distribution in heat grooves for: (a) full multiple cycle, (b) simplified multiple viscous cycle 1, and (c) simplified multiple viscous cycle 2.

Based on the performed investigations, the following observations can be formulated:

strains increases over subsequent cycles.

the cycle and over subsequent cycles.

(creep strain) in stationary conditions.

Author details

References

100 p

Mariusz Banaszkiewicz

dictions and optimal decisions regarding units' future operation.

Address all correspondence to: mbanaszkiewicz@imp.gda.pl

ponents. ASM International: Ohio; 1989. 497 p

Fairmont Press Inc.; 2008. 537 p

tional Journal of Fatigue. 2015;73:39-47

• Prior creep deformation affects the plastic strain accumulation by reducing the plastic strain as compared with no creep conditions. The difference in the accumulated plastic

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75

• Local plastic deformation in heat grooves accelerates the creep strain accumulation during

• Neglecting the creep overestimates the fatigue damage (plastic strain) generated during cycling, and neglecting the plasticity in cyclic duty underestimates the creep damage

It was shown by numerical simulations that significant inaccuracies in creep-fatigue damage predictions, reaching an order of magnitude in deviation of inelastic strains already after first few cycles, cannot be excluded when simplified models are used. It is thus concluded that full consideration of creep-fatigue damage at real operating conditions requires appropriate modeling of stress/strain histories using visco-elastic–plastic material models. Lifetime assessment studies employing such methodologies ensure the highest possible accuracy of life pre-

The Szewalski Institute of Fluid-Flow Machinery Polish Academy of Sciences, Gdańsk, Poland

[1] Colombo F. Service-Like Thermo-Mechanical Fatigue Characteristic of 1CrMoV Rotor Steel Creep-Fatigue [Dissertation]. Swiss Federal Institute of Technology: Zurich; 2007.

[2] Viswanathan R. Damage Mechanisms and Life Assessment of High-Temperature Com-

[3] Leyzerovich AS. Steam Turbines for Modern Fossil-Fuel Power Plants. Lilburn: The

[4] Banaszkiewicz M. Multilevel approach to lifetime assessment of steam turbines. Interna-

[5] Banaszkiewicz M, Bzymek G, Radulski W. Management and optimization of a steam turbine life by using an on-line monitoring system. Power Engineering. 2015;8:519-524

Figure 10. Creep strain accumulation in heat grooves: (a) equivalent creep strain for different cycles and (b) creep strain components for full multiple cycle.

elastic and elastic-plastic models (cycles with and without plasticity). After the second cycle, the deviation increases, but a significant difference in creep strain reaching 100% occurs between the elastic-plastic models, i.e. full multiple cycle and simplified multiple viscous cycle 1. This is due to neglecting the plastic strain development in cycles 2 and 3. It follows from the evolution of the equivalent creep strains that the secondary creep regime is reached already after 100 h (the first cycle) for all simplified modeling approaches, while for the full multiple cycle the heat grooves are still in the primary creep regime after 300 h (third cycle). This qualitative difference is very important from the point of view of creep damage, which on one hand depends on the accumulated creep strain and on the other hand is a function of the failure strain (creep ductility) primarily depending on the creep strain rate, which is very different in the three creep regimes.

The evolution in time of the creep strain components at the groove is shown in Figure 10b. The creep strain state at the bottom of the groove is three dimensional with all three components having comparable values. The radial and circumferential strain components are negative, and the axial component is positive and has the largest absolute value. In contrast to the plastic strain components, all the creep strain components increase continuously with continuous slope within the cycle and discontinuous slope change between two subsequent cycles.

#### 6. Summary

Creep-fatigue damage development in a steam turbine rotor in cyclic operation was numerically investigated using different material models and cycle modeling approaches. Creep strain was adopted as a creep damage parameter, and plastic strain was adopted as a damage parameter for fatigue. Four different operation cycles were defined and used in numerical simulations to examine the effect of various simplifications on the creep fatigue-damage prediction. The analyzed multiple cycles included different combinations of material models and number of individual cycles used in damage calculations during steady-state and transient conditions.

Based on the performed investigations, the following observations can be formulated:


It was shown by numerical simulations that significant inaccuracies in creep-fatigue damage predictions, reaching an order of magnitude in deviation of inelastic strains already after first few cycles, cannot be excluded when simplified models are used. It is thus concluded that full consideration of creep-fatigue damage at real operating conditions requires appropriate modeling of stress/strain histories using visco-elastic–plastic material models. Lifetime assessment studies employing such methodologies ensure the highest possible accuracy of life predictions and optimal decisions regarding units' future operation.

## Author details

elastic and elastic-plastic models (cycles with and without plasticity). After the second cycle, the deviation increases, but a significant difference in creep strain reaching 100% occurs between the elastic-plastic models, i.e. full multiple cycle and simplified multiple viscous cycle 1. This is due to neglecting the plastic strain development in cycles 2 and 3. It follows from the evolution of the equivalent creep strains that the secondary creep regime is reached already after 100 h (the first cycle) for all simplified modeling approaches, while for the full multiple cycle the heat grooves are still in the primary creep regime after 300 h (third cycle). This qualitative difference is very important from the point of view of creep damage, which on one hand depends on the accumulated creep strain and on the other hand is a function of the failure strain (creep ductility) primarily depending on the creep strain rate, which is very

Figure 10. Creep strain accumulation in heat grooves: (a) equivalent creep strain for different cycles and (b) creep strain

The evolution in time of the creep strain components at the groove is shown in Figure 10b. The creep strain state at the bottom of the groove is three dimensional with all three components having comparable values. The radial and circumferential strain components are negative, and the axial component is positive and has the largest absolute value. In contrast to the plastic strain components, all the creep strain components increase continuously with continuous slope within the cycle and discontinuous slope change between two subsequent cycles.

Creep-fatigue damage development in a steam turbine rotor in cyclic operation was numerically investigated using different material models and cycle modeling approaches. Creep strain was adopted as a creep damage parameter, and plastic strain was adopted as a damage parameter for fatigue. Four different operation cycles were defined and used in numerical simulations to examine the effect of various simplifications on the creep fatigue-damage prediction. The analyzed multiple cycles included different combinations of material models and number of individual cycles used in damage calculations during steady-state and tran-

different in the three creep regimes.

components for full multiple cycle.

74 Thermal Power Plants - New Trends and Recent Developments

6. Summary

sient conditions.

Mariusz Banaszkiewicz

Address all correspondence to: mbanaszkiewicz@imp.gda.pl

The Szewalski Institute of Fluid-Flow Machinery Polish Academy of Sciences, Gdańsk, Poland

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[9] Schaaf T, Mohr W, Helbig K. Flexibility improvement of steam turbines for conventional

[10] Dinh C, Marriner B, Tadros R, Kim SY, Farineau T. Design and Operation of Large Fossil-Fueled Steam Turbines in Cyclic Duty. GE Technical Paper GER4933. July 2016 [11] Chmielniak T, Kosman G. Thermal Loads of Steam Turbines. Warsaw: WNT; 1990

[12] Zienkiewicz OC, Taylor RL, Zhu JZ. The Finite Element Method: It's Basis and Funda-

[13] Hetnarski RB, Eslami MR. Thermal Stresses—Advanced Theory and Applications.

[14] Banaszkiewicz M. Online monitoring and control of thermal stresses in steam turbine

[15] Badur J, Ziółkowski P, Sławiński D, Kornet S. An approach for estimation of Water Wall

[16] Banaś K, Badur J. Influence of strength differential effect on material effort of a turbine guide vane based on a thermoelastoplastic analysis. Journal of Thermal Stresses.

[17] Badur J, Ziółkowski P, Kornet S, Stajnke M, Bryk M, Banaś K, Ziółkowski PJ. The effort of the steam turbine caused by a flood wave load. In: AIP Conference Proceedings; 2017 [18] Badur J, Ziółkowski P, Zakrzewski W, Sławiński D, Kornet S, Kowalczyk T, Hernet J, Piotrowski R, Felicjancik J, Ziółkowski PJ. An advanced thermal-FSI approach to flow

[22] Kleiber M, Kowalczyk P. Introduction to Non-linear Mechanics of Deformable Bodies.

steam turbines. In: PowerGen Europe; June 2016; Milan

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[19] Orłoś Z. Thermal Stresses. Warsaw: PWN; 1991

[21] Abaqus User's Manual. Dassault Systems; 2008

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[20] Nowacki W. Thermoelasticity. Warsaw: PWN; 1986

mentals. Elsevier Butterworth-Heinemann: Burlington; 2005. 733 p

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[23] Olszak W, Perzyna P, Sawczuk A. Theory of Plasticity. Warsaw: PWN; 1965

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76 Thermal Power Plants - New Trends and Recent Developments

San Antonio

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2017;40(11):1368-1385


**Chapter 5**

**Provisional chapter**

**Ti Microholes Potential for Thermal Power Plants**

**Ti Microholes Potential for Thermal Power Plants** 

DOI: 10.5772/intechopen.73308

The use of microholes is a potential approach to enhance fluid flow and heat exchange within thermal power plants, especially for the turbines. Ascribed to eco environmental competition, micropunching is extremely suitable for the mass production of micro features with friendly eco effects. Therefore, the morphology variation of micropunch and microhole during the punching with WC/Co micropunches was investigated by scanning electron microscopy (SEM), energy dispersive spectrometer (EDS) and confocal laser. Results reveal that due to the optimal joint contribution of WC and Co, the formed microholes satisfy with the practical requirements in the quasi stable period. Moreover, the serious wear of micropunch occurs with the wear loss both of Co and WC when the punching number exceeds 1525. With the further increment in punching numbers, the dominant factors of the wear loss would mainly rely on the easily peeled off WC due to the serious loss of Co. In addition, the microholes can be adequately processed after about 30 min by natural sand grains. The quality of the hole would decrease with further

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

It is well known that the thermal power plants can be classified by the source of the energy used to generate the steam that it is expanded in the turbine to produce electricity, which are listed as follows classified by heat source: (1) heat sources for fossil fuel power stations: (i) a steam turbine generator and (ii) the natural gas-fired plants. They may use a combustion turbine. To date, a coal-fired power station produces heat by burning coal in a steam boiler. The steam drives a steam turbine coupled to a generator producing electricity. It is well known that the fossil fuel power stations are still currently the dominating plants for generation

**Application Punched by WC/Co Micropunch**

increase in processing time and sand accumulation becomes severe.

**Keywords:** microhole, thermal power plants, WC/Co, micropunch, morphology

**Application Punched by WC/Co Micropunch**

Kelvii Wei Guo and Hon Yuen Tam

Kelvii Wei Guo and Hon Yuen Tam

http://dx.doi.org/10.5772/intechopen.73308

**Abstract**

**1. Introduction**

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

**Provisional chapter**

## **Ti Microholes Potential for Thermal Power Plants Application Punched by WC/Co Micropunch Application Punched by WC/Co Micropunch**

**Ti Microholes Potential for Thermal Power Plants** 

DOI: 10.5772/intechopen.73308

Kelvii Wei Guo and Hon Yuen Tam Kelvii Wei Guo and Hon Yuen Tam Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.73308

#### **Abstract**

The use of microholes is a potential approach to enhance fluid flow and heat exchange within thermal power plants, especially for the turbines. Ascribed to eco environmental competition, micropunching is extremely suitable for the mass production of micro features with friendly eco effects. Therefore, the morphology variation of micropunch and microhole during the punching with WC/Co micropunches was investigated by scanning electron microscopy (SEM), energy dispersive spectrometer (EDS) and confocal laser. Results reveal that due to the optimal joint contribution of WC and Co, the formed microholes satisfy with the practical requirements in the quasi stable period. Moreover, the serious wear of micropunch occurs with the wear loss both of Co and WC when the punching number exceeds 1525. With the further increment in punching numbers, the dominant factors of the wear loss would mainly rely on the easily peeled off WC due to the serious loss of Co. In addition, the microholes can be adequately processed after about 30 min by natural sand grains. The quality of the hole would decrease with further increase in processing time and sand accumulation becomes severe.

**Keywords:** microhole, thermal power plants, WC/Co, micropunch, morphology

## **1. Introduction**

It is well known that the thermal power plants can be classified by the source of the energy used to generate the steam that it is expanded in the turbine to produce electricity, which are listed as follows classified by heat source: (1) heat sources for fossil fuel power stations: (i) a steam turbine generator and (ii) the natural gas-fired plants. They may use a combustion turbine. To date, a coal-fired power station produces heat by burning coal in a steam boiler. The steam drives a steam turbine coupled to a generator producing electricity. It is well known that the fossil fuel power stations are still currently the dominating plants for generation

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

of energy production around the world. (2) A nuclear power plant is a steam turbine plant where the steam is generated by a nuclear reactor. Up to now, about 10% of all electric generation worldwide is produced by nuclear power plants. It should be noted that after the Fukushima disaster, all the plants are scheduled to be shut down in a few years, and the rest of the world is very hesitant with respect to what role nuclear energy should have in future energy planning. (3) Geothermal power plants use steam extracted from hot underground rocks. This kind of energy plant only contributes a minor energy output compared with the global demand. (4) Biomass-fueled power plants are fueled with wood pellets, wood chips, straw and waste from the agricultural industry such as sugar cane and nut scale, municipal solid waste, landfill methane or other forms of bio gas. (5) In integrated steel mills, blast furnace exhaust gas is a low cost, although low energy-density, fuel. This recycled gas is available to produce about 60% of the total electricity consumption. (6) Waste heat from industrial processes is occasionally concentrated enough to use for power generation, usually in a steam boiler and turbine. (7) Solar thermal electric plants use sunlight to boil water and produce steam, which turns the generator. (8) IGCC (integrated gasification combined cycle) with carbon capture and storage (CCS) technology allows coal to be used to generate power as cleanly as natural gas [1, 2].

It is well known that microtechnology describes the technological approach, directed to the miniaturization of components and systems, down to micrometer scale. Microtechnological components, such as distributed holes, bear the potential to provide further functionality, for example, enhancing fluid flow and heat exchange within thermal power plants, especially for

Ti Microholes Potential for Thermal Power Plants Application Punched by WC/Co Micropunch

http://dx.doi.org/10.5772/intechopen.73308

81

Up to now, the ever increasing demand for smaller, higher quality and lower priced products from almost all fields of industry, household equipment and entertainment electronics involves the optimisation of already existing and the development of new manufacturing methods

However, these kinds of micro devices are mainly fabricated by using micromachining technique, and fabrication technology with stable and low cost as one of the important issues [11,

Therefore, the microholes formed by micropunching at low cost and in large quantities, applied for thermal power plants application and micro-parts fabrication have been researched. This research aims at investigating the wear characteristics of micropunch (150 μm in diameter) and the morphology variation of microholes formed by punching pure titanium (Ti) in various processing periods to overcome current problems in the micro-metal-forming technology. In the long run, this research can lead to making microholes distributed in the thermal power materials (both non-metals and metals) at low cost and in large quantities with this eco-friendly

Micropunch with 75% volume fraction WC particle and 25% volume fraction Co particle of 50 μm mean size, 150 μm in diameter, is shown in **Figure 1**. **Figure 2** shows the surface texture of micropunch. Pure titanium sheet with 200 μm in thickness was used as the substrate.

which are tailor-made for the micro systems technique with higher precision [19, 20].

the turbine blades [15–18].

12, 14, 19].

technique.

**2.1. Experimental material**

**Figure 1.** Profile of micropunch.

**2. Experimental materials and procedures**

In most of the countries, thermal power plants are playing an important role in the energy production. Therefore, the research work should be taken enough attention toward the optimization of these power plants. In the developing countries, energy supplies are less secure because of its costlier price. Indeed, there is a need to reconsider lowest cost energy options and the relevant techniques. Since, from an energy performance point of view, first law analysis has been found to be insufficient. So, in thermodynamic analysis of various thermal processes and plant systems, exergy analysis is getting its own importance. It is well known that the total conversion of heat into work is not possible.

Consequently, that part which is available for conversion is termed as exergy. It is a property associated with the state of system and environment, nowadays a useful tool to differentiate between internal irreversibility and energy losses in a process [2]. Thermal power plant performance can be evaluated through energetic performance criteria, which are electrical power and thermal efficiency. In recent decades, exergy analysis of plant has been found as a useful method in the design, evaluation, optimization and improvement of thermal power plants [3–5]. Exergy analysis helps in finding the losses taking place in a system. By this method, energy conversion at different points, various component efficiencies and points of largest losses are easily obtainable and hence it helps in taking necessary action to decrease them [6, 7].

Some researchers have contributed review paper on exergy analysis, which helps the young researchers to get in touch with the previous year's problems [8]. In power plants, insights have been provided into various energy and exergy efficiencies which are helpful for design engineers [9, 10]. As a result, improvement in thermal performance of power generation units and consuming devices can be achieved significantly by combining exergy analyses with the related techniques upgraded.

In recent years, microtechnology has become one of the key disciplines with a significant effect on the development of new products and production technologies [11–14].

It is well known that microtechnology describes the technological approach, directed to the miniaturization of components and systems, down to micrometer scale. Microtechnological components, such as distributed holes, bear the potential to provide further functionality, for example, enhancing fluid flow and heat exchange within thermal power plants, especially for the turbine blades [15–18].

Up to now, the ever increasing demand for smaller, higher quality and lower priced products from almost all fields of industry, household equipment and entertainment electronics involves the optimisation of already existing and the development of new manufacturing methods which are tailor-made for the micro systems technique with higher precision [19, 20].

However, these kinds of micro devices are mainly fabricated by using micromachining technique, and fabrication technology with stable and low cost as one of the important issues [11, 12, 14, 19].

Therefore, the microholes formed by micropunching at low cost and in large quantities, applied for thermal power plants application and micro-parts fabrication have been researched. This research aims at investigating the wear characteristics of micropunch (150 μm in diameter) and the morphology variation of microholes formed by punching pure titanium (Ti) in various processing periods to overcome current problems in the micro-metal-forming technology. In the long run, this research can lead to making microholes distributed in the thermal power materials (both non-metals and metals) at low cost and in large quantities with this eco-friendly technique.

## **2. Experimental materials and procedures**

## **2.1. Experimental material**

of energy production around the world. (2) A nuclear power plant is a steam turbine plant where the steam is generated by a nuclear reactor. Up to now, about 10% of all electric generation worldwide is produced by nuclear power plants. It should be noted that after the Fukushima disaster, all the plants are scheduled to be shut down in a few years, and the rest of the world is very hesitant with respect to what role nuclear energy should have in future energy planning. (3) Geothermal power plants use steam extracted from hot underground rocks. This kind of energy plant only contributes a minor energy output compared with the global demand. (4) Biomass-fueled power plants are fueled with wood pellets, wood chips, straw and waste from the agricultural industry such as sugar cane and nut scale, municipal solid waste, landfill methane or other forms of bio gas. (5) In integrated steel mills, blast furnace exhaust gas is a low cost, although low energy-density, fuel. This recycled gas is available to produce about 60% of the total electricity consumption. (6) Waste heat from industrial processes is occasionally concentrated enough to use for power generation, usually in a steam boiler and turbine. (7) Solar thermal electric plants use sunlight to boil water and produce steam, which turns the generator. (8) IGCC (integrated gasification combined cycle) with carbon capture and storage (CCS) technology allows coal to be used to generate power as cleanly

In most of the countries, thermal power plants are playing an important role in the energy production. Therefore, the research work should be taken enough attention toward the optimization of these power plants. In the developing countries, energy supplies are less secure because of its costlier price. Indeed, there is a need to reconsider lowest cost energy options and the relevant techniques. Since, from an energy performance point of view, first law analysis has been found to be insufficient. So, in thermodynamic analysis of various thermal processes and plant systems, exergy analysis is getting its own importance. It is well known that

Consequently, that part which is available for conversion is termed as exergy. It is a property associated with the state of system and environment, nowadays a useful tool to differentiate between internal irreversibility and energy losses in a process [2]. Thermal power plant performance can be evaluated through energetic performance criteria, which are electrical power and thermal efficiency. In recent decades, exergy analysis of plant has been found as a useful method in the design, evaluation, optimization and improvement of thermal power plants [3–5]. Exergy analysis helps in finding the losses taking place in a system. By this method, energy conversion at different points, various component efficiencies and points of largest losses are easily obtain-

Some researchers have contributed review paper on exergy analysis, which helps the young researchers to get in touch with the previous year's problems [8]. In power plants, insights have been provided into various energy and exergy efficiencies which are helpful for design engineers [9, 10]. As a result, improvement in thermal performance of power generation units and consuming devices can be achieved significantly by combining exergy analyses with the

In recent years, microtechnology has become one of the key disciplines with a significant

effect on the development of new products and production technologies [11–14].

as natural gas [1, 2].

related techniques upgraded.

the total conversion of heat into work is not possible.

80 Thermal Power Plants - New Trends and Recent Developments

able and hence it helps in taking necessary action to decrease them [6, 7].

Micropunch with 75% volume fraction WC particle and 25% volume fraction Co particle of 50 μm mean size, 150 μm in diameter, is shown in **Figure 1**. **Figure 2** shows the surface texture of micropunch. Pure titanium sheet with 200 μm in thickness was used as the substrate.

**Figure 1.** Profile of micropunch.

**Figure 2.** Surface texture of micropunch.

#### **2.2. Experimental procedures**

In order to clean the contaminants in the prepared pure titanium sheet, it was carefully washed by acetone and pure ethyl alcohol before putting into the microdie. After that, the microprocessing machine MP50 (made in Japan) was taken to punch the titanium sheet with 20 pulses per minute, and feedrate of 2 mm.

The wear of the micropunch and the variation of the morphology of microholes in different processing periods were investigated using confocal microscopy, scanning electron microscopy (SEM), energy dispersive spectrometer (EDS) and confocal laser.

## **3. Results and discussion**

#### **3.1. Initial wear characteristic of micropunch**

The relationship between the wear loss of micropunch and punching numbers is shown in **Figure 3**. It illustrates that the weight of micropunch (each for five times) has an obvious decrease with the increment of punching number in the initial. Its corresponding surface texture is expressed in **Figure 4**. It depicts that the particles distributed more uniformly than that of parent material (cf. **Figures 2** and **4**).

as depicted in **Figure 3**, particularly for punching number from 500 to 1200. The surface texture of micropunch is shown in **Figure 7** correspondingly. It expresses small pieces of WC particles on the surface. Meanwhile, WC particles distribute uniformly on the micropunch surface.

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**Figure 4.** Surface texture of micropunch in the initial condition (punching number lower than 500).

The morphologies of the formed microhole are shown in **Figure 8**. It expresses that although some substrate debris still distribute in the backside (**Figure 8b**), the quality of the quasi stable-period-microhole is definitely superior to the initial period (compared **Figure 5** with **Figure 8**). It illustrates that because of the joint contribution of WC and Co, the wear loss of

The surface texture of micropunch with punching number over 1525 is shown in **Figure 9**. It shows that large amounts of WC particles distributes on the micropunch surface because of

micropunch in the quasi stable period is little.

**Figure 3.** Relationship between wear loss of micropunch and punching numbers.

**3.3. Severe wear characteristic of micropunch**

According to **Figures 3** and **4**, it shows that the wear of micropunch in the initial increases significantly, and WC particles cannot be easily observed. Consequently, the dominant factor of the wear loss in the initial period is mainly due to Co. The morphology of the formed microhole is expressed in **Figure 5**. Some substrate debris is distributed sparsely in the backside as shown in **Figure 5b**, and its EDS results are illustrated in **Figure 6**.

#### **3.2. Quasi stable wear characteristic of micropunch**

With the increment of punching numbers, the phenomena of the initial distinct wear of micropunch disappears, the wear loss of the micropunch becomes relatively stable with a little variation Ti Microholes Potential for Thermal Power Plants Application Punched by WC/Co Micropunch http://dx.doi.org/10.5772/intechopen.73308 83

**Figure 3.** Relationship between wear loss of micropunch and punching numbers.

**2.2. Experimental procedures**

**Figure 2.** Surface texture of micropunch.

**3. Results and discussion**

20 pulses per minute, and feedrate of 2 mm.

82 Thermal Power Plants - New Trends and Recent Developments

**3.1. Initial wear characteristic of micropunch**

of parent material (cf. **Figures 2** and **4**).

**3.2. Quasi stable wear characteristic of micropunch**

In order to clean the contaminants in the prepared pure titanium sheet, it was carefully washed by acetone and pure ethyl alcohol before putting into the microdie. After that, the microprocessing machine MP50 (made in Japan) was taken to punch the titanium sheet with

The wear of the micropunch and the variation of the morphology of microholes in different processing periods were investigated using confocal microscopy, scanning electron micros-

The relationship between the wear loss of micropunch and punching numbers is shown in **Figure 3**. It illustrates that the weight of micropunch (each for five times) has an obvious decrease with the increment of punching number in the initial. Its corresponding surface texture is expressed in **Figure 4**. It depicts that the particles distributed more uniformly than that

According to **Figures 3** and **4**, it shows that the wear of micropunch in the initial increases significantly, and WC particles cannot be easily observed. Consequently, the dominant factor of the wear loss in the initial period is mainly due to Co. The morphology of the formed microhole is expressed in **Figure 5**. Some substrate debris is distributed sparsely in the back-

With the increment of punching numbers, the phenomena of the initial distinct wear of micropunch disappears, the wear loss of the micropunch becomes relatively stable with a little variation

side as shown in **Figure 5b**, and its EDS results are illustrated in **Figure 6**.

copy (SEM), energy dispersive spectrometer (EDS) and confocal laser.

**Figure 4.** Surface texture of micropunch in the initial condition (punching number lower than 500).

as depicted in **Figure 3**, particularly for punching number from 500 to 1200. The surface texture of micropunch is shown in **Figure 7** correspondingly. It expresses small pieces of WC particles on the surface. Meanwhile, WC particles distribute uniformly on the micropunch surface.

The morphologies of the formed microhole are shown in **Figure 8**. It expresses that although some substrate debris still distribute in the backside (**Figure 8b**), the quality of the quasi stable-period-microhole is definitely superior to the initial period (compared **Figure 5** with **Figure 8**). It illustrates that because of the joint contribution of WC and Co, the wear loss of micropunch in the quasi stable period is little.

#### **3.3. Severe wear characteristic of micropunch**

The surface texture of micropunch with punching number over 1525 is shown in **Figure 9**. It shows that large amounts of WC particles distributes on the micropunch surface because of

**Figure 7.** Surface texture of micropunch with punching number between 500 and 1200.

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**Figure 8.** Morphology of microhole. (a) Front side, (b) back side.

**Figure 9.** Surface texture of micropunch in the severe wear condition.

**Figure 5.** Morphology of microhole. (a) Front side, (b) back side.

**Figure 6.** EDS results of debris in the backside.

Ti Microholes Potential for Thermal Power Plants Application Punched by WC/Co Micropunch http://dx.doi.org/10.5772/intechopen.73308 85

**Figure 7.** Surface texture of micropunch with punching number between 500 and 1200.

**Figure 8.** Morphology of microhole. (a) Front side, (b) back side.

**Figure 9.** Surface texture of micropunch in the severe wear condition.

**Figure 6.** EDS results of debris in the backside.

**Figure 5.** Morphology of microhole. (a) Front side, (b) back side.

84 Thermal Power Plants - New Trends and Recent Developments

serious wear loss of Co, which matches well with **Figure 3**. As a result, the wear of micropunch increases distinctly (**Figure 3**). Furthermore, with the punching numbers increasing further, the dominant factors of the wear loss would mainly rely on WC (which is easily peeled off during the micropunching) as shown in **Figure 9**. Meanwhile, the quality of the machined microhole decreases distinctly (cf. **Figures 5**, **8**, **10** and **11**). It illustrates that a large amount of micropunch materials are peeled off and adhered to the Ti substrate. At the same time, the substrate material could not be punched successfully and it would stick to the substrate. Also, with the effect of feedrate, the unsuccessfully removed materials would be sheared and form the larger debris as shown in **Figure 11**.

**Figure 13**. Compared with **Figure 3**, it indicates that the diameter of microhole changes in the different micropunching periods. At the beginning of the micropunching, the obvious decrement of the diameter of microhole varies with the punching number increasing, which surely matches well with results expressed in **Figure 3**. The attractive results are addressed with the relatively stable diameter of microhole when the micropunching number varies from 500 to 1200. When the punching number increases further, the obvious decrement of the diameter of microhole becomes more and more clear on account of the serious Co loss, especially for the punching number over 1525 as depicted in **Figure 13**. As a result, in the severe wear period of micropunching, due to the serious loss of bonding material Co, the wear of micropunch mainly relies on the easily peeled off WC particles. Simultaneously, because the temperature of the micropunch increases with the increment of the punching number, WC particles are more easily detached off from the micropunch. Consequently, the wear loss of the micropunch becomes more intensive. Furthermore, if the pulses per minute increases, the wear of micropunch will drastically lose. In order to improve the quality of the micropunch, besides the abovementioned, the microstructure of micropunch should be considered further with the composition of the micropunch, especially for the distribution of WC and Co particles.

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**Figure 12.** Profile of microhole punched by micropunch measured by OLS3000.

**Figure 13.** Relationship between diameter of microhole and punching number.

#### **3.4. Profile of the microhole punched by micropunch**

The diameter of the punched microhole by micropunch was measured by LEXT confocal laser-OLS3000 as shown in **Figure 12**. Its corresponding results (each for five times) are shown in

**Figure 10.** Morphology of microhole in the severe wear condition. (a) Front side, (b) back side.

**Figure 11.** Morphology of microhole in the intensively severe wear condition. (a) Front side, (b) back side.

**Figure 13**. Compared with **Figure 3**, it indicates that the diameter of microhole changes in the different micropunching periods. At the beginning of the micropunching, the obvious decrement of the diameter of microhole varies with the punching number increasing, which surely matches well with results expressed in **Figure 3**. The attractive results are addressed with the relatively stable diameter of microhole when the micropunching number varies from 500 to 1200. When the punching number increases further, the obvious decrement of the diameter of microhole becomes more and more clear on account of the serious Co loss, especially for the punching number over 1525 as depicted in **Figure 13**. As a result, in the severe wear period of micropunching, due to the serious loss of bonding material Co, the wear of micropunch mainly relies on the easily peeled off WC particles. Simultaneously, because the temperature of the micropunch increases with the increment of the punching number, WC particles are more easily detached off from the micropunch. Consequently, the wear loss of the micropunch becomes more intensive. Furthermore, if the pulses per minute increases, the wear of micropunch will drastically lose. In order to improve the quality of the micropunch, besides the abovementioned, the microstructure of micropunch should be considered further with the composition of the micropunch, especially for the distribution of WC and Co particles.

**Figure 12.** Profile of microhole punched by micropunch measured by OLS3000.

serious wear loss of Co, which matches well with **Figure 3**. As a result, the wear of micropunch increases distinctly (**Figure 3**). Furthermore, with the punching numbers increasing further, the dominant factors of the wear loss would mainly rely on WC (which is easily peeled off during the micropunching) as shown in **Figure 9**. Meanwhile, the quality of the machined microhole decreases distinctly (cf. **Figures 5**, **8**, **10** and **11**). It illustrates that a large amount of micropunch materials are peeled off and adhered to the Ti substrate. At the same time, the substrate material could not be punched successfully and it would stick to the substrate. Also, with the effect of feedrate, the unsuccessfully removed materials would be sheared and form

The diameter of the punched microhole by micropunch was measured by LEXT confocal laser-OLS3000 as shown in **Figure 12**. Its corresponding results (each for five times) are shown in

**Figure 11.** Morphology of microhole in the intensively severe wear condition. (a) Front side, (b) back side.

**Figure 10.** Morphology of microhole in the severe wear condition. (a) Front side, (b) back side.

the larger debris as shown in **Figure 11**.

86 Thermal Power Plants - New Trends and Recent Developments

**3.4. Profile of the microhole punched by micropunch**

**Figure 13.** Relationship between diameter of microhole and punching number.

## **4. Post-treatment for microholes by natural sand grains**

Features of microholes (such as **Figures 5** and **8**) in the micropunching include debris (for example, shear marks and burrs). Because of the combination of shear and ductile fracture in the micropunching, the debris produced. Moreover, the property of the processing materials is also one of the crucial effective influence factors on the final features of the microhole. In the meantime, the uniformity of the clearance can affect the microhole features during the micropunching (cf. **Figures 5**, **8**, **10** and **11**). The debris can hinder the normal functionality of micro features and prevent the proper assembly of micro components to form micro systems. Therefore, the microholes shall be post treated to improve its finishing.

friendliness. It expresses the results of a 20 min processing microhole. The hole is basically free from loosely attached debris. Burrs at the back side edge are further lowered. Those flattened fragments are slimmer than before. More aggregation of the microscopic grains is observed, both the fragment regions and the edge regions (**Figure 14a**, insets). Their sizes range from the micron to sub-micron. Continued aggregation might possibly be on account of van der Waals

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With further increment of the processing time, the quality of the hole continues to improve. **Figure 15** reveals that the burrs in the back side edge are no longer existed, except for some small isolated pieces (**Figure 15b**, inset). Burrs are protrusions from the edge. Their bonding with the substrate is much stronger than that of the re-attached debris. Tiny burrs are particularly hard to be removed. It is well known that the impact energy from a grain of sand depends on the grain size besides its velocity. Those burrs could not be effectively cleaned by the impact from smaller grains. Yet, the chance that tiny burrs are impacted by the larger sand grains is relatively low.

The fragment terraces on the front side become very thin. As a result, they are noticeable mainly under higher magnification (**Figure 15a**, right inset). In addition, more grains are gathered around the edge of the hole as well as stuck to the inner wall of the hole through attrac-

The quality of the holes cannot improve with further processing. Spontaneously, more sand aggregates after 40 min (**Figure 16**). The attachment of sand grains to the edge regions and

inner wall could be visible from the back side as well as from the front side.

**Figure 15.** Morphology of a microhole after 30 min processing. (a) Front side, (b) back side.

or inter-molecular forces.

tion forces (**Figure 15a**, left inset).

**Figure 14** shows the post treated microhole realized with the agitation of abrasive grains through planetary stirring, where natural sand was used as the abrasive due to its environmental

**Figure 14.** Morphology of a microhole after 20 min processing. (a) Front side, (b) back side.

friendliness. It expresses the results of a 20 min processing microhole. The hole is basically free from loosely attached debris. Burrs at the back side edge are further lowered. Those flattened fragments are slimmer than before. More aggregation of the microscopic grains is observed, both the fragment regions and the edge regions (**Figure 14a**, insets). Their sizes range from the micron to sub-micron. Continued aggregation might possibly be on account of van der Waals or inter-molecular forces.

**4. Post-treatment for microholes by natural sand grains**

88 Thermal Power Plants - New Trends and Recent Developments

**Figure 14.** Morphology of a microhole after 20 min processing. (a) Front side, (b) back side.

Features of microholes (such as **Figures 5** and **8**) in the micropunching include debris (for example, shear marks and burrs). Because of the combination of shear and ductile fracture in the micropunching, the debris produced. Moreover, the property of the processing materials is also one of the crucial effective influence factors on the final features of the microhole. In the meantime, the uniformity of the clearance can affect the microhole features during the micropunching (cf. **Figures 5**, **8**, **10** and **11**). The debris can hinder the normal functionality of micro features and prevent the proper assembly of micro components to form micro systems. Therefore, the microholes shall be post treated to improve its finishing. **Figure 14** shows the post treated microhole realized with the agitation of abrasive grains through planetary stirring, where natural sand was used as the abrasive due to its environmental

With further increment of the processing time, the quality of the hole continues to improve. **Figure 15** reveals that the burrs in the back side edge are no longer existed, except for some small isolated pieces (**Figure 15b**, inset). Burrs are protrusions from the edge. Their bonding with the substrate is much stronger than that of the re-attached debris. Tiny burrs are particularly hard to be removed. It is well known that the impact energy from a grain of sand depends on the grain size besides its velocity. Those burrs could not be effectively cleaned by the impact from smaller grains. Yet, the chance that tiny burrs are impacted by the larger sand grains is relatively low.

The fragment terraces on the front side become very thin. As a result, they are noticeable mainly under higher magnification (**Figure 15a**, right inset). In addition, more grains are gathered around the edge of the hole as well as stuck to the inner wall of the hole through attraction forces (**Figure 15a**, left inset).

The quality of the holes cannot improve with further processing. Spontaneously, more sand aggregates after 40 min (**Figure 16**). The attachment of sand grains to the edge regions and inner wall could be visible from the back side as well as from the front side.

**Figure 15.** Morphology of a microhole after 30 min processing. (a) Front side, (b) back side.

**Author details**

Hong Kong

**References**

79-162

**378**:11-14

Francis; 2006

Entropy. 2001;**3**(3):116-149

Kelvii Wei Guo\* and Hon Yuen Tam

\*Address all correspondence to: kelviiguo@yahoo.com

Department of Mechanical and Biomedical Engineering, City University of Hong Kong,

Ti Microholes Potential for Thermal Power Plants Application Punched by WC/Co Micropunch

http://dx.doi.org/10.5772/intechopen.73308

91

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**Figure 16.** Morphology of a microhole after 40 min processing. (a) Front side, (b) back side.

A band of jagged foil material is detected around the front surface near the edge of the hole. It is mainly produced as substrate material breaks from the punch when it is pulled back from the hole. It cannot be clearly detected before because (1) the feature size is relatively small compared with those fragments detected at earlier times and (2) parts of the band are rolled back against the surface of the substrate material. Apparently sand abrasion could only reduce the width of the band to a few microns. Occasionally, parts of the band are bent toward the microhole. On account of the support of sand gathered underneath, it is unlikely that their posture could be reversed in subsequent processing.

## **5. Conclusion**

The wear characteristic of the WC/Co micropunch used for micromachining microhole potential for thermal power plants application had been researched. It shows that the wear of micropunch increases significantly in the initial and the dominant factor of the wear loss mainly relies on Co. With the punching number increasing, the quasi stable wear of WC/Co micropunch varies with a little wear loss. However, when the punching number exceeds 1525, the serious wear loss of Co and WC of micropunch takes place. Moreover, with the increment of the punching numbers further, the dominant factor of the wear loss would mainly rely on the easily peeled off WC. Meanwhile, the quality of microhole decreases intensively. In addition, the microholes can be adequately processed after about 30 min by natural sand grains. The quality of the hole would decrease with further increase in processing time and sand accumulation becomes severe and no further improvement is observed.

## **Acknowledgements**

The work is supported by the Strategic Research Grant (SRG) from City University of Hong Kong (Grant No.: 7004860).

## **Author details**

Kelvii Wei Guo\* and Hon Yuen Tam

\*Address all correspondence to: kelviiguo@yahoo.com

Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Hong Kong

## **References**

A band of jagged foil material is detected around the front surface near the edge of the hole. It is mainly produced as substrate material breaks from the punch when it is pulled back from the hole. It cannot be clearly detected before because (1) the feature size is relatively small compared with those fragments detected at earlier times and (2) parts of the band are rolled back against the surface of the substrate material. Apparently sand abrasion could only reduce the width of the band to a few microns. Occasionally, parts of the band are bent toward the microhole. On account of the support of sand gathered underneath, it is unlikely

The wear characteristic of the WC/Co micropunch used for micromachining microhole potential for thermal power plants application had been researched. It shows that the wear of micropunch increases significantly in the initial and the dominant factor of the wear loss mainly relies on Co. With the punching number increasing, the quasi stable wear of WC/Co micropunch varies with a little wear loss. However, when the punching number exceeds 1525, the serious wear loss of Co and WC of micropunch takes place. Moreover, with the increment of the punching numbers further, the dominant factor of the wear loss would mainly rely on the easily peeled off WC. Meanwhile, the quality of microhole decreases intensively. In addition, the microholes can be adequately processed after about 30 min by natural sand grains. The quality of the hole would decrease with further increase in processing time and sand

The work is supported by the Strategic Research Grant (SRG) from City University of Hong

that their posture could be reversed in subsequent processing.

**Figure 16.** Morphology of a microhole after 40 min processing. (a) Front side, (b) back side.

90 Thermal Power Plants - New Trends and Recent Developments

accumulation becomes severe and no further improvement is observed.

**5. Conclusion**

**Acknowledgements**

Kong (Grant No.: 7004860).


[14] Fecht HJ, Werner M. The Nano-micro Interface: Bridging the Micro and Nano Worlds. Weinheim: Wiley-VCH; 2004

**Chapter 6**

Provisional chapter

**A Review on Supercritical Fluidization**

A Review on Supercritical Fluidization

Supercritical water fluidized bed (SCWFB) has been used to gasify biomass, coal and solid waste to produce gas fuel. Supercritical carbon dioxide fluidized bed (SCCO2FB) was applied in the coating industry. Both the two fluidized bed treats the supercritical fluids as fluidization medium. The fluidization behaviours of particles in the supercritical fluids are quite important issues for achieving the basic two phase flow pattern. Few research institutions have conducted experimental and numerical investigations on the fluidization in supercritical conditions. The authors try to establish a comprehensive insight of fluid dynamics of the supercritical fluidized bed. For the SCWFB, the fluidization transitions of fixed bed, homogeneous bed expansion and bubbling were demarcated by discrimination number Dn. A flow pattern map of Reynolds number vs. Archimedes number was available for describing the flow patterns and their boundaries of the SCCO2FB. Ergun equation was acceptable for calculating the fixed bed pressure drop for both SCWFB and SCCO2FB. Wei and Lu correlations of the minimum fluidization velocity, minimum bubbling velocity and homogeneous bed expansion rate are suggested to design the SCWFB. Wen and Yu equation of the minimum fluidization velocity, Vogt et al. correlation of the homogeneous bed expansion rate and their method for determining the minimum bubbling velocity, Nakajima et al. equation of transition velocity, and Bi and Fan correlation of turbulent

DOI: 10.5772/intechopen.68180

Keywords: supercritical fluids, fluidized bed, flow pattern, simulation, experiment

Supercritical fluidized bed fluidizes solids with supercritical fluids. The supercritical fluids is the fluid phase, and the solid particles including silica sand, biomass, coal or some coating particles are used in specific applications. Normally, supercritical fluidized bed can be divided into two types according the different supercritical fluids: supercritical water (SCW) and supercritical

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

distribution, and reproduction in any medium, provided the original work is properly cited.

Youjun Lu, Liping Wei and Jikai Huang

Youjun Lu, Liping Wei and Jikai Huang

http://dx.doi.org/10.5772/intechopen.68180

Abstract

1. Introduction

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

velocity were recommended to calculate SSCO2FB.


Provisional chapter

## **A Review on Supercritical Fluidization**

A Review on Supercritical Fluidization

Youjun Lu, Liping Wei and Jikai Huang

Additional information is available at the end of the chapter Youjun Lu, Liping Wei and Jikai Huang

http://dx.doi.org/10.5772/intechopen.68180 Additional information is available at the end of the chapter

#### Abstract

[14] Fecht HJ, Werner M. The Nano-micro Interface: Bridging the Micro and Nano Worlds.

[15] Horn A, Weichenhain R, Albrecht S, Kreutz EW, Michel J, Niessen M, Kostrykin V, Schulz W, Etzkorn A, Bobzin K, Lugscheider E, Poprawe R. Microholes in zirconia coated Ni-superalloys for transpiration cooling of turbine blades. High-Power Laser

[16] Lugscheider E, Bobzin K, Moes M, Lackner K, Poprawe R, Kreutz EW, Willach J. Laser drilled microholes in zirconia coated surfaces using two variants to implement the effusion cooling of first stage turbine blades. Advanced Engineering Materials. 2005;**7**(3):145-152

[17] Kaur N, Kumar M, Sharma SK, Kim DY, Kumar S, Chavan NM, Joshi SV, Singh N, Singh H. Study of mechanical properties and high temperature oxidation behavior of a novel cold-spray Ni-20Cr coating on boiler steels. Applied Surface Science. 2015;**328**:13-25 [18] Moon HW, Yoon YJ, Park JH, Myung BS, Kim DE. Dynamic wetting and boiling characteristics on micro-structured and micro/nano hierarchically structured surfaces.

[19] Knobloch H, Kaminorz Y. MicroNano Integration. Berlin Heidlberg: Springer-Verlag; 2004

[20] Mohamed GH. The MEMS Handbook. Boca Raton, FL: CRC/Taylor & Francis; 2006

Weinheim: Wiley-VCH; 2004

92 Thermal Power Plants - New Trends and Recent Developments

Ablation III. SPIE. 2000;**4065**:218-226

Experimental Thermal and Fluid Science. 2016;**74**:19-26

Supercritical water fluidized bed (SCWFB) has been used to gasify biomass, coal and solid waste to produce gas fuel. Supercritical carbon dioxide fluidized bed (SCCO2FB) was applied in the coating industry. Both the two fluidized bed treats the supercritical fluids as fluidization medium. The fluidization behaviours of particles in the supercritical fluids are quite important issues for achieving the basic two phase flow pattern. Few research institutions have conducted experimental and numerical investigations on the fluidization in supercritical conditions. The authors try to establish a comprehensive insight of fluid dynamics of the supercritical fluidized bed. For the SCWFB, the fluidization transitions of fixed bed, homogeneous bed expansion and bubbling were demarcated by discrimination number Dn. A flow pattern map of Reynolds number vs. Archimedes number was available for describing the flow patterns and their boundaries of the SCCO2FB. Ergun equation was acceptable for calculating the fixed bed pressure drop for both SCWFB and SCCO2FB. Wei and Lu correlations of the minimum fluidization velocity, minimum bubbling velocity and homogeneous bed expansion rate are suggested to design the SCWFB. Wen and Yu equation of the minimum fluidization velocity, Vogt et al. correlation of the homogeneous bed expansion rate and their method for determining the minimum bubbling velocity, Nakajima et al. equation of transition velocity, and Bi and Fan correlation of turbulent velocity were recommended to calculate SSCO2FB.

DOI: 10.5772/intechopen.68180

Keywords: supercritical fluids, fluidized bed, flow pattern, simulation, experiment

### 1. Introduction

Supercritical fluidized bed fluidizes solids with supercritical fluids. The supercritical fluids is the fluid phase, and the solid particles including silica sand, biomass, coal or some coating particles are used in specific applications. Normally, supercritical fluidized bed can be divided into two types according the different supercritical fluids: supercritical water (SCW) and supercritical

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

carbon dioxide (SCCO2). The critical point of SCW and SCCO2 is Tc = 374C and PC = 22.1 MPa, and Tc = 31.26C, PC = 7.36 MPa, respectively. The properties including density, viscosity, conductivity, and specific heat capacity vary with operating temperature and pressure. The properties of water are calculated by ISAWP-IF97 equations based on the operating temperature and pressure [1]. The drastic and fast variation of property under temperatures near the pseudocritical temperature greatly affects the multiphase flow and heat transfer processes [2, 3].

velocity, minimum bubbling velocity, bed expansion rate, etc.) of the supercritical fluidized bed

Although the experimental investigations of the supercritical fluidized bed are still limited, the flow patterns and their boundaries of the supercritical fluidized bed have been gradually obtained, and the correlations of the minimum fluidization velocity, homogenous bed expansion rate and minimum bubbling velocity, transition velocity and turbulent velocity were also partially proposed based on the experimental data. They can help readers to understand the

Tarmy et al. [8] studied the three-phase flow characteristics of fluidized beds under a pressure of 17 MPa and temperature of 450C. Jiang et al. [9] investigated bed contraction and expansion in a gas–liquid–solid fluidized bed at pressures from 0.1 to 17.4 MPa and temperatures from 20 to 94C. Liu et al. [10] operated a CO2-fluidized bed system from ambient to 9.4 MPa. The fluidized bed is a stainless steel column with 25 mm i.d. and 1.2 m height. They experimentally studied the fluidization of Geldart Group A, B, and D particles in CO2 under ambient to supercritical conditions. They found that fluidization of the supercritical CO2 fluidized bed was intermediate between the classical aggregative (gas-solid system) and particulate (liquidsolid system) fluidizations. Marzocchella and Salatino [11] fluidized Geldart Group A and B particles by CO2 at temperature of 35C with pressure ranging from 1 to 8 MPa. The fluidization column consisted of a lower section made of a polycarbonate pipe with height of 600 mm and inner diameter of 30 mm and a higher stainless steel upper section with height of 700 mm. The temperature of CO2 varies from ambient to 80C. The pressure varies from ambient to 100 bar and regulated by a back pressure regulating valve. The maximum flow rate was up to 100 kg h-1. Pressure drop transducer and a hot wire anemometer were applied to measure the fluctuations signals, pressure drop, and average voidage. The fluidization regimes of fixed bed, homogeneous bed expansion, bubbling zone, and turbulent regime were mapped. Vogt et al. investigated the fluidization behaviors of supercritical CO2-fluidized bed with pressure up to 30 MPa [12]. The experimental system was designed with a maximum operating pres-

volume of 2.5 · 10<sup>3</sup> m<sup>3</sup> with inner diameter of 39 or 21 mm. They provided a comprehensive picture for the supercritical CO2-fluidized bed when the superficial velocity was not very high. Potic et al. [13] visually studied the fluidization process of Geldart Group A particles in high pressure water within a cylindrical quartz reactor with an internal diameter of 1.0 mm in the range of 0.1–24.4 MPa and 20–500. Lu et al. [14] experimentally obtained the minimum fluidization velocity by measuring the pressure drops of a SCWFB with a diameter of 35 mm for temperature ranging from 360 to 420C and pressure ranging from 23 to 27 MPa. Wei and Lu [15] built a SCWFB fluid dynamics teasing systems; the fluidized bed section is made of stainless steel with 1.2 m height and 35 mm inner diameter. It is designed for the temperature up to 550C and the pressure up to 30 MPa. A porous metal foam with bore diameter of 30 μm

. The largest steel autoclave had a

A Review on Supercritical Fluidization http://dx.doi.org/10.5772/intechopen.68180 95

are important issues for perfecting the theory of the supercritical fluidized bed.

basic two-phase flow characteristics and achieve a calculation of design work.

2. Experiment and simulation

sure of 35 MPa and a maximum CO2 flow of 50 kg <sup>h</sup><sup>1</sup>

2.1. Experiment study

#### 1.1. Applications of supercritical fluidized bed

The supercritical water fluidized bed (SCWFB) has been used for gasifying biomass and coal for hydrogen production. The concept of SCWFB reactor was proposed first by Matsumura and Minowa [4]. In 2008, State Key Laboratory of Multiphase Flow in Power Engineering (SKLMF) of Xi'an Jiaotong University developed a SCWFB reactor for hydrogen production by gasifying wet biomass [5]. The reactor could avoid plugging, increase the hydrogen yield and improve gasification efficiency. Then, SKLMF successfully applied the SCW fluidized bed reactor to gasify coal and established pilot plant for gasification of biomass or coal [6]. In addition, the water fluidized bed operating in high pressure and temperature is a promising reactor for other high temperature water reactions to produce gas or liquid fuels.

The SCCO2 is treated as a solvent and fluidization medium in the fluidized bed. Coating some inert substrate or pharmaceutical particle within the supercritical carbon dioxide fluidized bed (SCCO2FB) can help to improve the material performance or control the release processes of the active substance. The SCCO2FB coating processes have many advantages: narrow particle size distribution, simple process step, simple solvents, moderate temperatures, and easily controlling the particle fluidizations. A further advantage is that they offer control over solid state properties, producing either amorphous or crystalline material and sometimes polymorphs [7].

### 1.2. Challenges of supercritical fluidized bed

One of the challenges for industrial applications of chemical technology of the supercritical fluidized bed is the reliability of continuous running of the reactor. Another challenge of the supercritical fluidized bed is enlargement. The inner diameter or size of the fluidized bed are limited to the operating high temperature and high pressure. An increase in the inner diameter leads to larger wall thickness, which may reduce the heat transfer coefficient. The unclear flow pattern and transitions processes may affect the chemical reaction efficiency. The theories of optimal matching of mass, momentum, heat, and chemical reaction are still not perfect.

### 1.3. Important issues within the supercritical fluidization

The design and operation of the fluidized bed reactor are greatly dependent on the understanding of the two-phase flow characteristics in the fluidized bed. An exact determination of flow patterns in fluidized bed reactor will help to keep the chemical reaction under suitable conditions. The evolution of flow patterns, key design parameters (minimum fluidization velocity, minimum bubbling velocity, bed expansion rate, etc.) of the supercritical fluidized bed are important issues for perfecting the theory of the supercritical fluidized bed.

Although the experimental investigations of the supercritical fluidized bed are still limited, the flow patterns and their boundaries of the supercritical fluidized bed have been gradually obtained, and the correlations of the minimum fluidization velocity, homogenous bed expansion rate and minimum bubbling velocity, transition velocity and turbulent velocity were also partially proposed based on the experimental data. They can help readers to understand the basic two-phase flow characteristics and achieve a calculation of design work.

## 2. Experiment and simulation

#### 2.1. Experiment study

carbon dioxide (SCCO2). The critical point of SCW and SCCO2 is Tc = 374C and PC = 22.1 MPa, and Tc = 31.26C, PC = 7.36 MPa, respectively. The properties including density, viscosity, conductivity, and specific heat capacity vary with operating temperature and pressure. The properties of water are calculated by ISAWP-IF97 equations based on the operating temperature and pressure [1]. The drastic and fast variation of property under temperatures near the pseudo-

The supercritical water fluidized bed (SCWFB) has been used for gasifying biomass and coal for hydrogen production. The concept of SCWFB reactor was proposed first by Matsumura and Minowa [4]. In 2008, State Key Laboratory of Multiphase Flow in Power Engineering (SKLMF) of Xi'an Jiaotong University developed a SCWFB reactor for hydrogen production by gasifying wet biomass [5]. The reactor could avoid plugging, increase the hydrogen yield and improve gasification efficiency. Then, SKLMF successfully applied the SCW fluidized bed reactor to gasify coal and established pilot plant for gasification of biomass or coal [6]. In addition, the water fluidized bed operating in high pressure and temperature is a promising

The SCCO2 is treated as a solvent and fluidization medium in the fluidized bed. Coating some inert substrate or pharmaceutical particle within the supercritical carbon dioxide fluidized bed (SCCO2FB) can help to improve the material performance or control the release processes of the active substance. The SCCO2FB coating processes have many advantages: narrow particle size distribution, simple process step, simple solvents, moderate temperatures, and easily controlling the particle fluidizations. A further advantage is that they offer control over solid state properties, producing either amorphous or crystalline material and sometimes poly-

One of the challenges for industrial applications of chemical technology of the supercritical fluidized bed is the reliability of continuous running of the reactor. Another challenge of the supercritical fluidized bed is enlargement. The inner diameter or size of the fluidized bed are limited to the operating high temperature and high pressure. An increase in the inner diameter leads to larger wall thickness, which may reduce the heat transfer coefficient. The unclear flow pattern and transitions processes may affect the chemical reaction efficiency. The theories of optimal matching of mass, momentum, heat, and chemical reaction are still not perfect.

The design and operation of the fluidized bed reactor are greatly dependent on the understanding of the two-phase flow characteristics in the fluidized bed. An exact determination of flow patterns in fluidized bed reactor will help to keep the chemical reaction under suitable conditions. The evolution of flow patterns, key design parameters (minimum fluidization

critical temperature greatly affects the multiphase flow and heat transfer processes [2, 3].

reactor for other high temperature water reactions to produce gas or liquid fuels.

1.1. Applications of supercritical fluidized bed

94 Thermal Power Plants - New Trends and Recent Developments

1.2. Challenges of supercritical fluidized bed

1.3. Important issues within the supercritical fluidization

morphs [7].

Tarmy et al. [8] studied the three-phase flow characteristics of fluidized beds under a pressure of 17 MPa and temperature of 450C. Jiang et al. [9] investigated bed contraction and expansion in a gas–liquid–solid fluidized bed at pressures from 0.1 to 17.4 MPa and temperatures from 20 to 94C. Liu et al. [10] operated a CO2-fluidized bed system from ambient to 9.4 MPa. The fluidized bed is a stainless steel column with 25 mm i.d. and 1.2 m height. They experimentally studied the fluidization of Geldart Group A, B, and D particles in CO2 under ambient to supercritical conditions. They found that fluidization of the supercritical CO2 fluidized bed was intermediate between the classical aggregative (gas-solid system) and particulate (liquidsolid system) fluidizations. Marzocchella and Salatino [11] fluidized Geldart Group A and B particles by CO2 at temperature of 35C with pressure ranging from 1 to 8 MPa. The fluidization column consisted of a lower section made of a polycarbonate pipe with height of 600 mm and inner diameter of 30 mm and a higher stainless steel upper section with height of 700 mm. The temperature of CO2 varies from ambient to 80C. The pressure varies from ambient to 100 bar and regulated by a back pressure regulating valve. The maximum flow rate was up to 100 kg h-1. Pressure drop transducer and a hot wire anemometer were applied to measure the fluctuations signals, pressure drop, and average voidage. The fluidization regimes of fixed bed, homogeneous bed expansion, bubbling zone, and turbulent regime were mapped. Vogt et al. investigated the fluidization behaviors of supercritical CO2-fluidized bed with pressure up to 30 MPa [12]. The experimental system was designed with a maximum operating pressure of 35 MPa and a maximum CO2 flow of 50 kg <sup>h</sup><sup>1</sup> . The largest steel autoclave had a volume of 2.5 · 10<sup>3</sup> m<sup>3</sup> with inner diameter of 39 or 21 mm. They provided a comprehensive picture for the supercritical CO2-fluidized bed when the superficial velocity was not very high. Potic et al. [13] visually studied the fluidization process of Geldart Group A particles in high pressure water within a cylindrical quartz reactor with an internal diameter of 1.0 mm in the range of 0.1–24.4 MPa and 20–500. Lu et al. [14] experimentally obtained the minimum fluidization velocity by measuring the pressure drops of a SCWFB with a diameter of 35 mm for temperature ranging from 360 to 420C and pressure ranging from 23 to 27 MPa. Wei and Lu [15] built a SCWFB fluid dynamics teasing systems; the fluidized bed section is made of stainless steel with 1.2 m height and 35 mm inner diameter. It is designed for the temperature up to 550C and the pressure up to 30 MPa. A porous metal foam with bore diameter of 30 μm is used as the distributor of the fluidized bed test section, and a metal foam filter is installed in the exit of the fluidized bed to avoid the escape of the bed materials. They measured the fixed bed pressure drop, minimum fluidization velocity, and bed expansion, minimum fluidization bubbling velocity of a water-solid fluidized bed from ambient to supercritical conditions, and they proposed a flow pattern map of the SCWFB.

3.1. Fixed bed pressure drop

Table 2. Properties of SCCO2.

ΔP <sup>L</sup> <sup>¼</sup> <sup>a</sup> ð1 � εÞ 2 <sup>ε</sup><sup>3</sup> · <sup>μ</sup><sup>u</sup>

predicating fixed bed pressure drop in the sub-critical and supercritical zones.

fixed bed flow with a supercritical fluid.

3.2. Minimum fluidization velocity

Ergun equation,

μf/10�<sup>5</sup>

Fixed bed pressure drop is greatly affected by properties of fluid (density and viscosity), solid properties (diameter, density, and shape factor), and superficial velocity and operation conditions. The description of the fixed bed pressure drop is a key element in the calculation of the minimum fluidization velocity. The calculation of fixed bed pressure drop can be achieved by

P/MPa 0.1 2 4 6 8 9.1 10.1 14.8 17.9 24.8 T/�C 18 35 35 35 35 54 57 56 57 57 ρf/kg.m�<sup>3</sup> 1.8 36 85 150 480 266.8 316.4 637.2 707.1 799.1

Pa∙s 1.46 1.65 1.73 1.91 4.18 2.25 2.49 4.92 5.77 7.13

ðψdpÞ

where ΔP is the pressure drop, μ is the viscosity of fluid, ρ<sup>f</sup> is the density of fluid, ε is the fixed bed voidage, dp is the equivalent volume diameter of the particle, and ψ is the sphericity. The parameters a and b are 1.50 and 1.75, respectively, which are from the investigations of Ergun [22]. Ergun equation has been accepted to calculate the fixed bed pressure drop widely in literature [23].

Figure 1(a) shows the bed pressure drop vs. superficial velocity at temperature from ambient to supercritical zone. The pressure drop increased with an increase in the superficial velocity. An elevated temperature greatly affects bed pressure drop, and the main reason is the density and viscosity of high pressure water decrease with an increase in temperature. Figure 1(b) shows the simulated instantaneous bed pressure drop under each superficial velocity was time-averaged, and the relationship between bed pressure drop and fluidization number (superficial velocity divided by umf). When the superficial velocity is below the minimum fluidization velocity umf, the bed pressure drop increases with the increasing superficial velocity. When the superficial velocity is above the minimum fluidization velocity, the curve of the bed pressure become flat. Wei and Lu [15] found the deviation of Ergun equation was about �30%, which was suitable for

Figure 2 shows the pressure drop of SCCO2-fluidized bed. The experimental data are provided by Marzocchella and Salatino [11], and Vogt et al. [12]. It was found that Ergun equation was generally giving a good description of the measured relationship between pressure drop and superficial velocity. Considering the different supercritical fluids and operating pressures and temperature from ambient to supercritical zone, Ergun's equation is also well applicable for

The minimum fluidization velocity serves as a critical parameter for the design and operation of fluidized bed. The determination of minimum fluidization velocity is conventionally based on the

<sup>2</sup> þ b

1 � ε <sup>ε</sup><sup>3</sup> · ρ<sup>f</sup> u<sup>2</sup> ψdp

ð1Þ

97

A Review on Supercritical Fluidization http://dx.doi.org/10.5772/intechopen.68180

#### 2.2. Simulation advance

The fluidization of particles in the supercritical fluidized beds has been simulated by few researchers. Potic et al. [13] applied a DPM model to qualitatively simulate a micro-fluidized bed with an inner diameter of 1 mm. The model provided consistent flow structures with the tested results in the sub-critical and supercritical zones. Vogt et al. [16] developed a compromised model to compute the movement of bubbles in a SCCO2FB on the basis of empirical correlations. The model describes local fluid dynamics within the SCCO2FB by treating the surrounding emulsion phase as a continuum and bubble as the other phase. Rodriguez-Rojo and Cocero [17] simulated a SCCO2FB with an Eulerian two-flow model incorporating the classical drag model of Gidaspow. Wei et al. [18] simulated the feeding methods of a SCW fluidized bed reactor based on the Eulerian two-flow model incorporating particle kinetic theory. Bubbling phenomenon of Geldart Group B particles was observed in the simulation results. Lu et al. [19] derived a non-sphere drag equation to determine the momentum transfer between non-sphere particles and fluid in a dilute suspension system. A combination drag of the non-spherical particle drag model and the Ergun equation has been validated by comparing experimental data of the SCWFB. More recently, Lu et al. [20, 21] studied the fluidization process of Geldart Group B particles in SCW by a CFD-DEM model. Fluidization transition of fixed–homogeneous-bubbling zone was observed in the simulation work. The two-fluid model and CFD-DEM model are two effective simulation method to investigate the fluid dynamics of the supercritical fluidized bed.

## 3. Flow dynamic in the supercritical fluidized bed

Fixed bed pressure drop, minimum fluidization velocity, minimum bubbling velocity, homogenous expansion rate, bubble properties and transitions, and turbulence flow regimes of the supercritical fluidized bed are summarized. The flow characteristics of each flow regime are analyzed. The correlations for the key parameters are proposed. In this part, the results of measured method or simulated method for obtaining these parameters are discussed. The properties of SCW and SCCO2 used in the experiments were shown in Tables 1 and 2, respectively.


Table 1. Properties of SCW.


Table 2. Properties of SCCO2.

is used as the distributor of the fluidized bed test section, and a metal foam filter is installed in the exit of the fluidized bed to avoid the escape of the bed materials. They measured the fixed bed pressure drop, minimum fluidization velocity, and bed expansion, minimum fluidization bubbling velocity of a water-solid fluidized bed from ambient to supercritical conditions, and

The fluidization of particles in the supercritical fluidized beds has been simulated by few researchers. Potic et al. [13] applied a DPM model to qualitatively simulate a micro-fluidized bed with an inner diameter of 1 mm. The model provided consistent flow structures with the tested results in the sub-critical and supercritical zones. Vogt et al. [16] developed a compromised model to compute the movement of bubbles in a SCCO2FB on the basis of empirical correlations. The model describes local fluid dynamics within the SCCO2FB by treating the surrounding emulsion phase as a continuum and bubble as the other phase. Rodriguez-Rojo and Cocero [17] simulated a SCCO2FB with an Eulerian two-flow model incorporating the classical drag model of Gidaspow. Wei et al. [18] simulated the feeding methods of a SCW fluidized bed reactor based on the Eulerian two-flow model incorporating particle kinetic theory. Bubbling phenomenon of Geldart Group B particles was observed in the simulation results. Lu et al. [19] derived a non-sphere drag equation to determine the momentum transfer between non-sphere particles and fluid in a dilute suspension system. A combination drag of the non-spherical particle drag model and the Ergun equation has been validated by comparing experimental data of the SCWFB. More recently, Lu et al. [20, 21] studied the fluidization process of Geldart Group B particles in SCW by a CFD-DEM model. Fluidization transition of fixed–homogeneous-bubbling zone was observed in the simulation work. The two-fluid model and CFD-DEM model are two effective simulation method to

Fixed bed pressure drop, minimum fluidization velocity, minimum bubbling velocity, homogenous expansion rate, bubble properties and transitions, and turbulence flow regimes of the supercritical fluidized bed are summarized. The flow characteristics of each flow regime are analyzed. The correlations for the key parameters are proposed. In this part, the results of measured method or simulated method for obtaining these parameters are discussed. The properties of SCW and SCCO2 used in the experiments were shown in Tables 1 and 2, respectively.

P/MPa 27 27 27 27 27 25 23 23 T/�C 201 350 400 430 479 386 421 406 <sup>ρ</sup>f/kg.m�<sup>3</sup> 880.1 616.1 200.0 150.5 108.2 283.8 112.2 136.5 <sup>μ</sup>f/10�<sup>5</sup> Pa∙s 13.5 7.16 3.12 2.96 3.04 3.67 2.71 2.75

they proposed a flow pattern map of the SCWFB.

96 Thermal Power Plants - New Trends and Recent Developments

investigate the fluid dynamics of the supercritical fluidized bed.

3. Flow dynamic in the supercritical fluidized bed

2.2. Simulation advance

Table 1. Properties of SCW.

#### 3.1. Fixed bed pressure drop

Fixed bed pressure drop is greatly affected by properties of fluid (density and viscosity), solid properties (diameter, density, and shape factor), and superficial velocity and operation conditions. The description of the fixed bed pressure drop is a key element in the calculation of the minimum fluidization velocity. The calculation of fixed bed pressure drop can be achieved by Ergun equation,

$$\frac{\Delta P}{L} = a \frac{\left(1 - \varepsilon\right)^2}{\varepsilon^3} \times \frac{\mu u}{\left(\psi d\_p\right)^2} + b \frac{1 - \varepsilon}{\varepsilon^3} \times \frac{\rho\_f u^2}{\psi d\_p} \tag{1}$$

where ΔP is the pressure drop, μ is the viscosity of fluid, ρ<sup>f</sup> is the density of fluid, ε is the fixed bed voidage, dp is the equivalent volume diameter of the particle, and ψ is the sphericity. The parameters a and b are 1.50 and 1.75, respectively, which are from the investigations of Ergun [22]. Ergun equation has been accepted to calculate the fixed bed pressure drop widely in literature [23].

Figure 1(a) shows the bed pressure drop vs. superficial velocity at temperature from ambient to supercritical zone. The pressure drop increased with an increase in the superficial velocity. An elevated temperature greatly affects bed pressure drop, and the main reason is the density and viscosity of high pressure water decrease with an increase in temperature. Figure 1(b) shows the simulated instantaneous bed pressure drop under each superficial velocity was time-averaged, and the relationship between bed pressure drop and fluidization number (superficial velocity divided by umf). When the superficial velocity is below the minimum fluidization velocity umf, the bed pressure drop increases with the increasing superficial velocity. When the superficial velocity is above the minimum fluidization velocity, the curve of the bed pressure become flat. Wei and Lu [15] found the deviation of Ergun equation was about �30%, which was suitable for predicating fixed bed pressure drop in the sub-critical and supercritical zones.

Figure 2 shows the pressure drop of SCCO2-fluidized bed. The experimental data are provided by Marzocchella and Salatino [11], and Vogt et al. [12]. It was found that Ergun equation was generally giving a good description of the measured relationship between pressure drop and superficial velocity. Considering the different supercritical fluids and operating pressures and temperature from ambient to supercritical zone, Ergun's equation is also well applicable for fixed bed flow with a supercritical fluid.

#### 3.2. Minimum fluidization velocity

The minimum fluidization velocity serves as a critical parameter for the design and operation of fluidized bed. The determination of minimum fluidization velocity is conventionally based on the

In literature, Wen and Yu [24] equation has been usually used to calculate the minimum fluidization velocity of fluidized bed, even at high pressure conditions. Vogt et al. [12] found Wen and Yu equation predicated the minimum fluidization velocity with an average error of 14.3% in a SCCO2 fluidized bed. Rodríguez-Rojo and Cocero [17] also used Wen and Yu equation to determine the minimum fluidization velocity in the simulation work. Marzocchella and Salatino [11] used Chitester et al. [25] equation to calculate the minimum fluidization velocity of the supercritical CO2 fluidized bed. Wei and Lu [15] have examined the applicability of those reported correlations in SCW fluidized bed. It was found that Wen and Yu equation predicated acceptable minimum fluidization velocity from ambient to supercritical conditions, and the deviations of most predicated results are within �30%. However, Chitester et al. equation predicated much higher minimum fluidization velocities than the experimental

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

� 28:7 ð3Þ

A Review on Supercritical Fluidization http://dx.doi.org/10.5772/intechopen.68180 99

<sup>0</sup>:<sup>5</sup> � <sup>33</sup>:<sup>7</sup> <sup>ð</sup>4<sup>Þ</sup>

<sup>2</sup> <sup>þ</sup> <sup>0</sup>:0494Ar <sup>q</sup>

Figure 3 shows the curves of bed voidage vs. superficial velocity in typical operating conditions for the SCW fluidized bed. The slopes of the curves after the turning point were obviously lower than that before the turning point. Similar phenomena were also observed in the SCCO2 fluidized bed, as shown in Figure 4. The turning points of the voidage curves indicated bubbling occurrence in the fluidized bed. The homogenous bed expansion existed before the turning point and after which bubbling was formed. The experimental results show that the transitions from homogenous to bubbling occur in several supercritical conditions for both Geldart A and B particles.

Figure 5 shows the relation curve of bed pressure drop and superficial velocity vs. time. It can be observed that the curve of bed pressure drop vs. time can be divided into three stages.

ð28:7Þ

Remf ¼ ð33:72 <sup>þ</sup> <sup>0</sup>:0408Ar<sup>Þ</sup>

data.

Chitester et al. equation

Wen and Yu equation

3.3. Bed expansion

Remf ¼

Figure 3. Typical results of voidage vs. superficial velocity for the SCW fluidized bed [20].

Figure 1. Bed pressure drop vs. superficial velocity for water-solid fluidized bed: (a) experimental data [15] and (b) simulation results by CFD-DEM model [20].

Figure 2. Bed pressure drop vs. superficial velocity for SCCO2 fluidized bed: (a) Marzocchella and Salatino [11], and (b) Vogt et al. [12].

curve of experimentally measured pressure drop vs. superficial velocity. The minimum fluidization velocity was determined by the turning point of the curves, as shown in Figures 1 and 2. The minimum fluidization velocity is a function of temperature and pressure for Geldart-A and Geldart-B particles. The minimum fluidization velocity increased with an increase in temperature. The results are attributed to the decrease in density and viscosity of water induces a larger relative velocity for achieving force balance of particles in fluidization. Wei and Lu [15] proposed that an empirical equation of minimum fluidization velocity was achieved for fluidization of Geldart-B and Geldart-A particles in water from ambient zone to supercritical zone. The correlation combined the experimental data in supercritical zone and the expression is shown as follows

$$Re\_{\rm mf} = 6.17 \times 10^{-4} Ar^{0.9324}, \ 70 < Ar < 52000 \tag{2}$$

where Ar is the Archimedes number Ar <sup>¼</sup> <sup>g</sup>d<sup>3</sup> <sup>p</sup>ρfðρ<sup>s</sup> � <sup>ρ</sup>fÞ=μ<sup>2</sup> f . In literature, Wen and Yu [24] equation has been usually used to calculate the minimum fluidization velocity of fluidized bed, even at high pressure conditions. Vogt et al. [12] found Wen and Yu equation predicated the minimum fluidization velocity with an average error of 14.3% in a SCCO2 fluidized bed. Rodríguez-Rojo and Cocero [17] also used Wen and Yu equation to determine the minimum fluidization velocity in the simulation work. Marzocchella and Salatino [11] used Chitester et al. [25] equation to calculate the minimum fluidization velocity of the supercritical CO2 fluidized bed. Wei and Lu [15] have examined the applicability of those reported correlations in SCW fluidized bed. It was found that Wen and Yu equation predicated acceptable minimum fluidization velocity from ambient to supercritical conditions, and the deviations of most predicated results are within �30%. However, Chitester et al. equation predicated much higher minimum fluidization velocities than the experimental data.

Chitester et al. equation

$$Re\_{\rm mf} = \sqrt{\left(28.7\right)^2 + 0.0494Ar} - 28.7\tag{3}$$

Wen and Yu equation

$$Re\_{\rm mf} = (33.7^2 + 0.0408Ar)^{0.5} - 33.7 \tag{4}$$

#### 3.3. Bed expansion

curve of experimentally measured pressure drop vs. superficial velocity. The minimum fluidization velocity was determined by the turning point of the curves, as shown in Figures 1 and 2. The minimum fluidization velocity is a function of temperature and pressure for Geldart-A and Geldart-B particles. The minimum fluidization velocity increased with an increase in temperature. The results are attributed to the decrease in density and viscosity of water induces a larger relative velocity for achieving force balance of particles in fluidization. Wei and Lu [15] proposed that an empirical equation of minimum fluidization velocity was achieved for fluidization of Geldart-B and Geldart-A particles in water from ambient zone to supercritical zone. The correlation combined the experimental data in supercritical zone and the expression is shown as follows

Figure 2. Bed pressure drop vs. superficial velocity for SCCO2 fluidized bed: (a) Marzocchella and Salatino [11], and (b)

Figure 1. Bed pressure drop vs. superficial velocity for water-solid fluidized bed: (a) experimental data [15] and (b)

<sup>p</sup>ρfðρ<sup>s</sup> � <sup>ρ</sup>fÞ=μ<sup>2</sup>

f .

Ar<sup>0</sup>:<sup>9324</sup>, <sup>70</sup> <sup>&</sup>lt; Ar <sup>&</sup>lt; <sup>52000</sup> <sup>ð</sup>2<sup>Þ</sup>

Remf <sup>¼</sup> <sup>6</sup>:<sup>17</sup> · <sup>10</sup>�<sup>4</sup>

where Ar is the Archimedes number Ar <sup>¼</sup> <sup>g</sup>d<sup>3</sup>

simulation results by CFD-DEM model [20].

98 Thermal Power Plants - New Trends and Recent Developments

Vogt et al. [12].

Figure 3 shows the curves of bed voidage vs. superficial velocity in typical operating conditions for the SCW fluidized bed. The slopes of the curves after the turning point were obviously lower than that before the turning point. Similar phenomena were also observed in the SCCO2 fluidized bed, as shown in Figure 4. The turning points of the voidage curves indicated bubbling occurrence in the fluidized bed. The homogenous bed expansion existed before the turning point and after which bubbling was formed. The experimental results show that the transitions from homogenous to bubbling occur in several supercritical conditions for both Geldart A and B particles.

Figure 5 shows the relation curve of bed pressure drop and superficial velocity vs. time. It can be observed that the curve of bed pressure drop vs. time can be divided into three stages.

Figure 3. Typical results of voidage vs. superficial velocity for the SCW fluidized bed [20].

Figure 4. Typical results of voidage vs. superficial velocity for the SCCO2 fluidized bed Vogt et al. [12], and Marzocchella and Salatino [11].

<sup>u</sup> <sup>¼</sup> utε<sup>n</sup> <sup>ð</sup>5<sup>Þ</sup>

A Review on Supercritical Fluidization http://dx.doi.org/10.5772/intechopen.68180 101

<sup>n</sup> <sup>¼</sup> <sup>11</sup>:8Re�0:<sup>23</sup> <sup>t</sup> <sup>ð</sup>6<sup>Þ</sup>

<sup>ð</sup><sup>1</sup> � <sup>ε</sup>Þε�4:<sup>8</sup> <sup>ð</sup>8<sup>Þ</sup>

<sup>n</sup> <sup>¼</sup> <sup>10</sup>:364Re�0:<sup>09973</sup> <sup>t</sup> , <sup>2</sup> <sup>&</sup>lt; Ret <sup>&</sup>lt; <sup>270</sup> <sup>ð</sup>7<sup>Þ</sup>

where ut is the terminal velocity, which can be calculated by correlation from Haider and

Vogt et al. [12] proposed an empirical correlation for homogeneous bed expansion in the

Wei and Lu [15] provided a modified correlation for homogeneous bed expansion in the SCW

The exponent n obtained from linear fitting of experimental data, thus they diverge each other greatly. The deviation of Eqs. (6) and (7) may indicate that the effects of fluid properties or operating conditions on bed expansion rates are remarkable. Care should be taken to use the bed expansion correlation. The correlation should be carefully used for the design of sub- and

The Gibilaro's equation [28] was used to predicate the bed expansion of SCCO2 fluidized bed

ρ<sup>f</sup> u<sup>2</sup>H dp

Levenspiel [27].

in literature [17].

SCCO2 fluidized bed, which was given:

Figure 6. Snapshots of particles in various fluidization regimes [20].

fluidized bed, which is shown as follows,

supercritical water or SCCO2 fluidized bed.

<sup>Δ</sup><sup>P</sup> <sup>¼</sup> <sup>18</sup> Rep <sup>þ</sup> <sup>0</sup>:<sup>33</sup> �

Figure 5. Bed pressure drop and superficial velocity vs. time for the SCW fluidized bed [21].

Stage I, the bed pressure drop increases step by step with the superficial velocity and without fluctuation when u < umf. Stage II, the pressure drop stops increasing with superficial velocity and fluctuates around a fixed value and decays rapidly when umf < u < umb. Stage III, the pressure fluctuates more violently with the increasing of superficial velocity when u > umb.

Figure 6 shows three snapshots of particles in the three stages. Figure 6(a) shows the fixed bed almost no particle moves. Figure 6(b) shows the homogeneous fluidization regime without bubbling fluidization in SCW fluidized bed. Figure 6(c) shows a bubble fluidization. Bubbles are quite small and scattered in SCW fluidized bed and the bed expansion is more obvious. The distribution characteristics of bubbles benefit the mixing state of fluid phase and solid phase.

For predicating the homogenous bed expansion rate at supercritical pressure, Richardson and Zaki equation [26] was modified based on the experimental data. The basic equation was given:

Figure 6. Snapshots of particles in various fluidization regimes [20].

Stage I, the bed pressure drop increases step by step with the superficial velocity and without fluctuation when u < umf. Stage II, the pressure drop stops increasing with superficial velocity and fluctuates around a fixed value and decays rapidly when umf < u < umb. Stage III, the pressure fluctuates more violently with the increasing of superficial velocity when u > umb. Figure 6 shows three snapshots of particles in the three stages. Figure 6(a) shows the fixed bed almost no particle moves. Figure 6(b) shows the homogeneous fluidization regime without bubbling fluidization in SCW fluidized bed. Figure 6(c) shows a bubble fluidization. Bubbles are quite small and scattered in SCW fluidized bed and the bed expansion is more obvious. The distribution characteristics of bubbles benefit the mixing state of fluid phase and solid phase. For predicating the homogenous bed expansion rate at supercritical pressure, Richardson and Zaki equation [26] was modified based on the experimental data. The basic equation was given:

Figure 5. Bed pressure drop and superficial velocity vs. time for the SCW fluidized bed [21].

Figure 4. Typical results of voidage vs. superficial velocity for the SCCO2 fluidized bed Vogt et al. [12], and Marzocchella

and Salatino [11].

100 Thermal Power Plants - New Trends and Recent Developments

$$
\mu = \mu\_t \varepsilon^n \tag{5}
$$

where ut is the terminal velocity, which can be calculated by correlation from Haider and Levenspiel [27].

Vogt et al. [12] proposed an empirical correlation for homogeneous bed expansion in the SCCO2 fluidized bed, which was given:

$$n = \mathbf{1}1.8 \text{Re}\_t^{-0.23} \tag{6}$$

Wei and Lu [15] provided a modified correlation for homogeneous bed expansion in the SCW fluidized bed, which is shown as follows,

$$m = 10.364 \text{Re}\_t^{-0.09973}, \text{ } 2 < \text{Re}\_t < 270 \tag{7}$$

The exponent n obtained from linear fitting of experimental data, thus they diverge each other greatly. The deviation of Eqs. (6) and (7) may indicate that the effects of fluid properties or operating conditions on bed expansion rates are remarkable. Care should be taken to use the bed expansion correlation. The correlation should be carefully used for the design of sub- and supercritical water or SCCO2 fluidized bed.

The Gibilaro's equation [28] was used to predicate the bed expansion of SCCO2 fluidized bed in literature [17].

$$
\Delta \mathbf{P} = \left(\frac{18}{\mathcal{Re}\_p} + 0.33\right) \cdot \frac{\rho\_f u^2 H}{d\_p} (1 - \varepsilon) \varepsilon^{-4.8} \tag{8}
$$

#### 3.4. Bubbling fluidization

#### 3.4.1. Minimum bubbling velocity

The minimum bubble velocity can be obtained from the figure of the standard deviation σ of pressure drop and heat transfer coefficient vs. superficial velocity in the vicinity of the incipient fluidization and incipient bubbling velocities. Figure 7 shows the simulated and experimentally measured method of the minimum bubbling velocity. As shown in Figure 7, before bubbling, the standard deviations kept nearly invariable with an increase in the superficial velocity. After bubbling, an approximately linear relationship between the standard deviation σ and superficial velocity were observed. The onset increase in σ was related to the bubble occurrence. Based on the two methods, the minimum bubbling velocities were obtained.

fluidization velocity and minimum fluidization voidage. Foscolo and Gibilaro found system is homogeneous when the kinematic wave velocity is higher than the dynamic wave velocity, otherwise bubble occurs. When the two velocities are equal, the limit of stability of the system

> þ : Homogeneous 0 : Stability limit � : Bubbling

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3:2gdpð1 � εÞðρ<sup>s</sup> � ρfÞ=ρ<sup>s</sup>

However, Wen and Lu [15] evaluated the adaptability of Foscolo and Gibilaro criterion for the water-solid fluidized bed from ambient to supercritical conditions. They found that Foscolo and Gibilaro's criterion qualitatively predicated bubbling occurrence, the transformation processes of homogenous to bubbling were not captured. Therefore, it was difficult to use Foscolo and Gibilaro's criterion to predicate the minimum bubbling velocity for the SCW fluidized bed. They provided a polynomial function of Archimedes number for calculating the mini-

Based on the investigations of Vogt et al. [12], the visible bubble flow is multiplying the bubble

The linear relationship between the visible bubble flow and the excess velocity was observed in

where ϕ = 0.6. When the emulsion phase voidage and bed average voidage are known, the bubble voidage can be obtained ε<sup>b</sup> ¼ ðε � εeÞ=ð1 � εeÞ. Then the bubble rising velocity can be calculated by Eq. (13). Eq. 14 reflects a linear relationship between the visible bubble flow and the excess velocity, which is adapted to the ambient conditions. Although the correlation has not been validated for the SCWFB, the equation is suggested to evaluate bubble rising velocity

Uk <sup>¼</sup> nutð<sup>1</sup> � <sup>ε</sup>Þε<sup>n</sup>�<sup>1</sup> <sup>ð</sup>10<sup>Þ</sup>

Ar þ 1:4608, 700 < Ar < 34000 ð12Þ

Vb ¼ εbub ð13Þ

Vb ¼ ϕðu � umbÞ ð14Þ

ð9Þ

103

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ð11Þ

Ud � Uk Uk

Ud ¼

q

Ar<sup>2</sup> � <sup>9</sup> · <sup>10</sup>�<sup>8</sup>

¼

8 ><

>:

is reached. The criterion is expressed as:

The kinematic wave speed is

The dynamic wave velocity is

mum bubbling velocity for the SCWFB.

3.4.2. Visible bubble flow rate

Figure 8.

Remb <sup>¼</sup> <sup>2</sup> · <sup>10</sup>�<sup>8</sup>

gas holdup with the local mean bubble rise velocity,

in the situation of lack of reliable formula for predication.

For the classical gas-solid fluidized bed, Abrahamsen and Geldart correlation is usually used to calculate the minimum bubbling velocity [29]. However, Vogt et al. [12] found Abrahamsen and Geldart correlation predicated a much higher minimum bubbling velocity for the SCCO2 fluidized bed. They suggested to use Foscolo and Gibilaro [30] criterion to predicate the εb, and then use Eqs. (5) and (6) to calculate the minimum bubbling velocity by intruding the minimum

Figure 7. Typical results of variance of variables in the vicinity of incipient fluidization and bubbling: (a) SCW fluidized bed [15], (b) SCCO2 fluidized bed [11], and (c) SCW fluidized bed by CFD-DEM simulation [21].

fluidization velocity and minimum fluidization voidage. Foscolo and Gibilaro found system is homogeneous when the kinematic wave velocity is higher than the dynamic wave velocity, otherwise bubble occurs. When the two velocities are equal, the limit of stability of the system is reached. The criterion is expressed as:

$$\frac{\mathcal{U}\_d - \mathcal{U}\_k}{\mathcal{U}\_k} = \begin{cases} + : \text{Homogeneous} \\ 0 : \text{Stability limit} \\ - : \text{Bubbling} \end{cases} \tag{9}$$

The kinematic wave speed is

3.4. Bubbling fluidization

3.4.1. Minimum bubbling velocity

102 Thermal Power Plants - New Trends and Recent Developments

The minimum bubble velocity can be obtained from the figure of the standard deviation σ of pressure drop and heat transfer coefficient vs. superficial velocity in the vicinity of the incipient fluidization and incipient bubbling velocities. Figure 7 shows the simulated and experimentally measured method of the minimum bubbling velocity. As shown in Figure 7, before bubbling, the standard deviations kept nearly invariable with an increase in the superficial velocity. After bubbling, an approximately linear relationship between the standard deviation σ and superficial velocity were observed. The onset increase in σ was related to the bubble occurrence. Based on the two methods, the minimum bubbling velocities were obtained.

For the classical gas-solid fluidized bed, Abrahamsen and Geldart correlation is usually used to calculate the minimum bubbling velocity [29]. However, Vogt et al. [12] found Abrahamsen and Geldart correlation predicated a much higher minimum bubbling velocity for the SCCO2 fluidized bed. They suggested to use Foscolo and Gibilaro [30] criterion to predicate the εb, and then use Eqs. (5) and (6) to calculate the minimum bubbling velocity by intruding the minimum

Figure 7. Typical results of variance of variables in the vicinity of incipient fluidization and bubbling: (a) SCW fluidized

bed [15], (b) SCCO2 fluidized bed [11], and (c) SCW fluidized bed by CFD-DEM simulation [21].

$$
\mathcal{U}L\_k = m\mu\_t (1 - \varepsilon) \varepsilon^{n-1} \tag{10}
$$

The dynamic wave velocity is

$$\mathcal{U}\_d = \sqrt{3.2gd\_p(1-\varepsilon)(\rho\_s - \rho\_f)/\rho\_s} \tag{11}$$

However, Wen and Lu [15] evaluated the adaptability of Foscolo and Gibilaro criterion for the water-solid fluidized bed from ambient to supercritical conditions. They found that Foscolo and Gibilaro's criterion qualitatively predicated bubbling occurrence, the transformation processes of homogenous to bubbling were not captured. Therefore, it was difficult to use Foscolo and Gibilaro's criterion to predicate the minimum bubbling velocity for the SCW fluidized bed. They provided a polynomial function of Archimedes number for calculating the minimum bubbling velocity for the SCWFB.

$$Re\_{\rm mb} = 2 \times 10^{-8} Ar^2 - 9 \times 10^{-8} Ar + 1.4608, \; 700 < Ar < 34000 \tag{12}$$

#### 3.4.2. Visible bubble flow rate

Based on the investigations of Vogt et al. [12], the visible bubble flow is multiplying the bubble gas holdup with the local mean bubble rise velocity,

$$V\_b = \varepsilon\_b \mu\_b \tag{13}$$

The linear relationship between the visible bubble flow and the excess velocity was observed in Figure 8.

$$V\_b = \phi(\mathfrak{u} - \mathfrak{u}\_{\mathfrak{m}b}) \tag{14}$$

where ϕ = 0.6. When the emulsion phase voidage and bed average voidage are known, the bubble voidage can be obtained ε<sup>b</sup> ¼ ðε � εeÞ=ð1 � εeÞ. Then the bubble rising velocity can be calculated by Eq. (13). Eq. 14 reflects a linear relationship between the visible bubble flow and the excess velocity, which is adapted to the ambient conditions. Although the correlation has not been validated for the SCWFB, the equation is suggested to evaluate bubble rising velocity in the situation of lack of reliable formula for predication.

intermediate fluidization has the characteristics of the two-phase flow in both bubbling and homogeneous fluidization. Obviously, the present simulation results showed an intermediate state of the SCW fluidized bed, which was a pseudo-homogeneous expansion with a large number of small bubbles. With an increase in the discrimination number Dn, the fluidization of

Fluid states Ambient Subcritical SCW Steam

No. (a) (b) (c) (d) (e) (f) (g) (h) P/MPa 0.1 6.3 25.1 25.4 25.2 25.5 6 0.1 T/�C 20 207 224 387 403 428 400 400 ρf/kg.m�<sup>3</sup> 998.2 859.9 854.1 296.7 162.9 128.7 21.1 0.322 μf/10�<sup>5</sup> Pa∙s 100.1 13.06 12.48 3.787 2.913 2.87 2.437 2.446

ΔP1=ΔP<sup>2</sup>

<sup>1</sup> increase first and then decrease. Gas superficial velocities at which σ<sup>2</sup>

is the well-known bell-shaped curve, as shown in Figure 10. With an increase in superficial

is at a maximum and at which it levels off, have been assumed, respectively, as the beginning UC and the end Uk of the transition to the turbulent fluidization regime. Note that no detectable decrease in the pressure drop across the bed was observed over several minutes of operation of the bed even at fluid superficial velocities over Uk. Based on the experimental investigations, Marzocchella and Salatino [11] suggested Nakajima et al. [31] equation to calculate the transi-

Figure 10. Dimensionless variance of the bed pressure drop vs. superficial fluid velocity for the SCCO2 fluidized bed.

<sup>1</sup> vs. u pattern of the SCCO2 fluidized bed

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ΔP1=ΔP<sup>2</sup> 1

water-solid system evolved from particulate to intermediate to aggregative.

tion velocity, and Bi and Fan [32] correlation to determine the turbulent velocity.

3.5. Turbulence fluidization and transition zone

Table 3. Simulation conditions and parameters in Figure 9.

Marzocchella and Salatino [11] observed the σ<sup>2</sup>

velocity, σ<sup>2</sup>

ΔP1=ΔP<sup>2</sup>

Figure 8. Visible bubble flow for glass beads in the SCCO2 fluidized bed [12].

#### 3.4.3. Effects of fluid states on the bubbling fluidization

Based on the Eulrian two fluid models and non-spherical particle drag model, the fluidized processes of the SCWFB were simulated [19]. Figure 9 shows the solid distribution of the fluidized bed using different states of water as the fluidization medium and the properties of the SCW were shown in Table 3. The superficial velocity was set as 3.5 umf. Figure 9(a)–(c) describes the ambient and sub-critical water-solid system, in which particulate fluidization and homogeneous bed expansion are two typical characteristics. Figure 9(g) and (h) represents the flow characteristics of the vapor-solid system. Figure 9(d)–(f) represents the SCW-solid flow system. In the SCW zone, the pseudo-homogeneous expansion of the bed was similar to the liquid-solid system, but the bubbles occurrence was similar to the gas-solid system. Liu et al. [10] stated that the fluidization in the supercritical CO2 fluidized bed was an intermediate state between bubbling and homogeneous fluidization through an experimental analysis. The

Figure 9. Solid distribution of fluidized bed at different states of water with u / umf = 3.5 [19].


Table 3. Simulation conditions and parameters in Figure 9.

intermediate fluidization has the characteristics of the two-phase flow in both bubbling and homogeneous fluidization. Obviously, the present simulation results showed an intermediate state of the SCW fluidized bed, which was a pseudo-homogeneous expansion with a large number of small bubbles. With an increase in the discrimination number Dn, the fluidization of water-solid system evolved from particulate to intermediate to aggregative.

#### 3.5. Turbulence fluidization and transition zone

3.4.3. Effects of fluid states on the bubbling fluidization

104 Thermal Power Plants - New Trends and Recent Developments

Figure 8. Visible bubble flow for glass beads in the SCCO2 fluidized bed [12].

Figure 9. Solid distribution of fluidized bed at different states of water with u / umf = 3.5 [19].

Based on the Eulrian two fluid models and non-spherical particle drag model, the fluidized processes of the SCWFB were simulated [19]. Figure 9 shows the solid distribution of the fluidized bed using different states of water as the fluidization medium and the properties of the SCW were shown in Table 3. The superficial velocity was set as 3.5 umf. Figure 9(a)–(c) describes the ambient and sub-critical water-solid system, in which particulate fluidization and homogeneous bed expansion are two typical characteristics. Figure 9(g) and (h) represents the flow characteristics of the vapor-solid system. Figure 9(d)–(f) represents the SCW-solid flow system. In the SCW zone, the pseudo-homogeneous expansion of the bed was similar to the liquid-solid system, but the bubbles occurrence was similar to the gas-solid system. Liu et al. [10] stated that the fluidization in the supercritical CO2 fluidized bed was an intermediate state between bubbling and homogeneous fluidization through an experimental analysis. The

Marzocchella and Salatino [11] observed the σ<sup>2</sup> ΔP1=ΔP<sup>2</sup> <sup>1</sup> vs. u pattern of the SCCO2 fluidized bed is the well-known bell-shaped curve, as shown in Figure 10. With an increase in superficial velocity, σ<sup>2</sup> ΔP1=ΔP<sup>2</sup> <sup>1</sup> increase first and then decrease. Gas superficial velocities at which σ<sup>2</sup> ΔP1=ΔP<sup>2</sup> 1 is at a maximum and at which it levels off, have been assumed, respectively, as the beginning UC and the end Uk of the transition to the turbulent fluidization regime. Note that no detectable decrease in the pressure drop across the bed was observed over several minutes of operation of the bed even at fluid superficial velocities over Uk. Based on the experimental investigations, Marzocchella and Salatino [11] suggested Nakajima et al. [31] equation to calculate the transition velocity, and Bi and Fan [32] correlation to determine the turbulent velocity.

Figure 10. Dimensionless variance of the bed pressure drop vs. superficial fluid velocity for the SCCO2 fluidized bed.

Nakajima et al. equation is,

$$Re\_t = 0.663Ar^{0.46V} \tag{15}$$

Dn < 1:2 · 104 1:2 · 104 ≤ Dn < 6:4 · 10<sup>4</sup> Dn ≥ 6:4 · 104

The discrimination number Dn of 1.2 · 104 is little higher than the experimental results by Liu et al. [10]. The boundary of F-H fluidization can be determined by the minimum fluidization velocity correlation Eq. (2), and the boundary of F-B and H-B fluidization can be calculated by

Marzocchella and Salatino [11] gave a flow pattern map of Reynolds numbers Re vs. Archimedes number for the SCCO2 fluidized bed. In the original map, they calculated Remf according to Chitester et al. [25] correlation, Rec by Nakajima et al. [31] correlation, and Rek could be calculated by Bi and Fan [32]. Here, the map was redrawn by adding the Wen and Yu equation to evaluate the minimum fluidization velocity as shown in Figure 11. What's more, the minimum bubble velocity is suggested to be determined according to Foscolo and

Supercritical bed is a kind of new and promising reactors. This work tries to conduct a comprehensive study on supercritical fluidized bed to provide information of basic two-phase flow and theories of design and operation. A review of main research progress is illustrated

and important results were summarized. The main conclusions are obtained as follow:

8 >><

Figure 11. Flow pattern for the SCCO2 fluidized bed.

>>:

the minimum bubbling velocity correlation Eq. (12).

4.2. SSCO2FB

Gibilaro's criterion.

5. Conclusion

F � H F � H � B F � B

ð18Þ

A Review on Supercritical Fluidization http://dx.doi.org/10.5772/intechopen.68180 107

Bi and Fan correlation is,

$$Re\_k = \begin{cases} 0.601Ar^{0.695} & Ar \le 125\\ 2.28Ar^{0.419} & Ar > 125 \end{cases} \tag{16}$$

### 4. Flow pattern maps of supercritical fluidized bed

Mapping flow pattern based on experimental data is a useful method to characterize the flow regimes and transitions. For the classical gas-solid or liquid-solid fluidized bed, maps of pressure drop vs. supercritical velocity, slip velocity vs. solid fraction, voidage vs. supercritical velocity, DP standard deviations vs. voidage, non-linear parameters vs. supercritical velocity, dimensionless diameter vs. dimensionless gas velocity, and Reynolds number vs. Archimedes number have been investigated [33, 34, 35]. Those maps can be classified into two groups: dimension and dimensionless. Obviously, the dimensional flow pattern maps are hard to be used in present situation because the fluid state varies greatly from ambient to supercritical conditions. For example, although a plot of velocity vs. fluid density shows a clear physical meaning, it cannot include all the cases for different particles. The dimensionless flow pattern maps are promising to solve the shortcoming. The horizontal ordinates of dimensionless gas velocity or Archimedes number in the traditional flow maps have been proved effective to the classical fluidized bed. However, they are useless for present situations because they cannot discriminate the different transitions of flow regimes. The transitions of flow regimes are mainly depending on the properties of each phases and operating parameters. Obviously, just using Archimedes number cannot reflect effects of both sides. The main obstacle of mapping the flow pattern is describing the horizontal ordinates reasonably.

#### 4.1. SCWFB

Wei and Lu [15] drew the flow pattern maps with abscissa Dn demarcating the three transitions processes and ordinate charactering the operating parameters. The discrimination number Dn was proposed by Liu et al. [10] to demarcate the fluidization quality.

$$D\_n = \left(\frac{Ar}{Re\_{m\sharp}}\right) \left(\frac{\rho\_s - \rho\_f}{\rho\_f}\right) \tag{17}$$

The discrimination umber shows the effect of properties of two phases in Ar � <sup>ρ</sup>s�ρ<sup>f</sup> ρf � �, and the effect of operating parameters in <sup>1</sup> Remf. This paper found the discrimination number Dn can demarcate the flow pattern evolution processes. Based on the experimental analysis, fluidization state of fixed-homogeneous (F-H), fixed-homogeneous-bubbling (F-H-B) and fixedbubbling (F-B) was summarized as follows:

Figure 11. Flow pattern for the SCCO2 fluidized bed.

$$\begin{cases} \begin{aligned} D\_n &< 1.2 \times 10^4 & F - H \\ 1.2 \times 10^4 \le D\_n &< 6.4 \times 10^4 & F - H - B \\ D\_n &\ge 6.4 \times 10^4 & F - B \end{aligned} \end{cases} \tag{18}$$

The discrimination number Dn of 1.2 · 104 is little higher than the experimental results by Liu et al. [10]. The boundary of F-H fluidization can be determined by the minimum fluidization velocity correlation Eq. (2), and the boundary of F-B and H-B fluidization can be calculated by the minimum bubbling velocity correlation Eq. (12).

#### 4.2. SSCO2FB

Nakajima et al. equation is,

106 Thermal Power Plants - New Trends and Recent Developments

Bi and Fan correlation is,

4.1. SCWFB

effect of operating parameters in <sup>1</sup>

bubbling (F-B) was summarized as follows:

Rec <sup>¼</sup> <sup>0</sup>:663Ar<sup>0</sup>:<sup>467</sup> <sup>ð</sup>15<sup>Þ</sup>

ð16Þ

ð17Þ

, and the

ρf � �

Rek <sup>¼</sup> <sup>0</sup>:601Ar<sup>0</sup>:<sup>695</sup> Ar <sup>≤</sup> <sup>125</sup>

Mapping flow pattern based on experimental data is a useful method to characterize the flow regimes and transitions. For the classical gas-solid or liquid-solid fluidized bed, maps of pressure drop vs. supercritical velocity, slip velocity vs. solid fraction, voidage vs. supercritical velocity, DP standard deviations vs. voidage, non-linear parameters vs. supercritical velocity, dimensionless diameter vs. dimensionless gas velocity, and Reynolds number vs. Archimedes number have been investigated [33, 34, 35]. Those maps can be classified into two groups: dimension and dimensionless. Obviously, the dimensional flow pattern maps are hard to be used in present situation because the fluid state varies greatly from ambient to supercritical conditions. For example, although a plot of velocity vs. fluid density shows a clear physical meaning, it cannot include all the cases for different particles. The dimensionless flow pattern maps are promising to solve the shortcoming. The horizontal ordinates of dimensionless gas velocity or Archimedes number in the traditional flow maps have been proved effective to the classical fluidized bed. However, they are useless for present situations because they cannot discriminate the different transitions of flow regimes. The transitions of flow regimes are mainly depending on the properties of each phases and operating parameters. Obviously, just using Archimedes number cannot reflect effects of both sides. The main obstacle of mapping

Wei and Lu [15] drew the flow pattern maps with abscissa Dn demarcating the three transitions processes and ordinate charactering the operating parameters. The discrimination num-

� � ρ<sup>s</sup> � ρ<sup>f</sup>

demarcate the flow pattern evolution processes. Based on the experimental analysis, fluidization state of fixed-homogeneous (F-H), fixed-homogeneous-bubbling (F-H-B) and fixed-

ρf !

Remf. This paper found the discrimination number Dn can

�

4. Flow pattern maps of supercritical fluidized bed

the flow pattern is describing the horizontal ordinates reasonably.

ber Dn was proposed by Liu et al. [10] to demarcate the fluidization quality.

Dn <sup>¼</sup> Ar Remf

The discrimination umber shows the effect of properties of two phases in Ar � <sup>ρ</sup>s�ρ<sup>f</sup>

2:28Ar<sup>0</sup>:<sup>419</sup> Ar > 125

Marzocchella and Salatino [11] gave a flow pattern map of Reynolds numbers Re vs. Archimedes number for the SCCO2 fluidized bed. In the original map, they calculated Remf according to Chitester et al. [25] correlation, Rec by Nakajima et al. [31] correlation, and Rek could be calculated by Bi and Fan [32]. Here, the map was redrawn by adding the Wen and Yu equation to evaluate the minimum fluidization velocity as shown in Figure 11. What's more, the minimum bubble velocity is suggested to be determined according to Foscolo and Gibilaro's criterion.

#### 5. Conclusion

Supercritical bed is a kind of new and promising reactors. This work tries to conduct a comprehensive study on supercritical fluidized bed to provide information of basic two-phase flow and theories of design and operation. A review of main research progress is illustrated and important results were summarized. The main conclusions are obtained as follow:


## Acknowledgements

This work is currently supported by the National Natural Science Foundation of China through contract No. 91634109, 51676158, and 51606153.

Author details

P Pressure (Pa) Re Reynolds number

Re<sup>p</sup> Particle Reynolds number Re<sup>t</sup> Terminal Reynolds number

SCCO2 Supercritical carbon dioxide

u Superficial fluid velocity (m s�<sup>1</sup>

umb Minimum bubbling velocity (m s�<sup>1</sup>

umf Minimum fluidization velocity (m s�<sup>1</sup>

SCW Supercritical water

T Temperature (K or �C)

ut Terminal velocity (m s�<sup>1</sup>

t Time (s)

ε Voidage ρ Density

c Transition f Fluid k Turbulence o Initial state s Particle phase t Terminal state

Greek letters

Subscripts

University, Xi'an, Shaanxi, China

\*, Liping Wei1,2 and Jikai Huang<sup>1</sup>

1 State Key Laboratory of Multiphase Flow in Power Engineering (SKLMF), Xi'an Jiaotong

[1] Wagner W, Kruse A. Properties of water and steam-the industrial standard IAPWS-IF97 for the thermodynamic properties and supplementary equations for other properties:

2 School of Chemical Engineering, Northwest University, Xi'an, Shaanxi, China

)

)

)

)

A Review on Supercritical Fluidization http://dx.doi.org/10.5772/intechopen.68180 109

tables based on these equations. Berlin: Springer Verlag; 1998

\*Address all correspondence to: yjlu@mail.xjtu.edu.cn

Youjun Lu1

References

## Nomenclature



#### Greek letters

1. Fixed bed pressure drop in supercritical conditions can be predicated by Ergun equation. 2. Wei and Lu correlation Eq. (2) was suggested as a new correlation for minimum fluidization velocity of water-solid fluidized bed in high pressure, near-critical and supercritical conditions. Wen and Yu equation Eq. (4) was acceptable for calculating the minimum

3. The homogeneous bed expansion rate of supercritical fluidized bed can be described by modified Richard and Zaki equation. The index function n can be correlated by Wei and Lu equation Eq. (7) and Vogt et al. equation Eq. (6) for the SCWFB and SCCO2FB, respectively.

4. The bubbling fluidization was found for both Geldart A and B particles in the supercritical fluidized bed. An empirical correlation of minimum bubbling velocity in Eq. (12) was achieved by Wei and Lu for the SCWFB. Vogt et al. provided a method to determine the minimum bubbling velocity of the SCCO2FB by using Foscolo and Gibilaro criterion. 5. The fluidization state of the supercritical fluidized bed can be viewed as an intermediate between classical gas-solid and liquid-solid fluidizations. The visible bubble flow rate can

6. For the SCWFB, discrimination number Dn was used to determine the fluidization regimes from ambient to supercritical conditions. Fluidization of F-H was found when

, and fluidization of F-B was found when Dn was above 6 · 104

This work is currently supported by the National Natural Science Foundation of China

<sup>v</sup>ρfðρ<sup>s</sup> � <sup>ρ</sup>fÞ=μ<sup>2</sup>

)

f )

by Marzocchella and Salatino [11], Nakajima et al. [31] equation was used to calculate the transition velocity, and Bi and Fan [32] correlation was applied to determine the turbulent velocity of the SSCO2FB. A flow pattern map of Reynolds numbers Re vs. Archimedes

; fluidization of F-H-B was found when Dn was between 1.2 · 104

. As suggested

fluidization velocity of the SCWFB and SCCO2FB.

108 Thermal Power Plants - New Trends and Recent Developments

be predicated by Vogt et al. equation Eq. (14).

number has been provided for the SSCO2FB.

through contract No. 91634109, 51676158, and 51606153.

Dn was below 1.2 · 10<sup>4</sup>

and 6 · 104

Acknowledgements

Nomenclature

Ar Archimedes number (Ar <sup>¼</sup> <sup>g</sup>d<sup>3</sup>

db Bubble equivalent diameter (m)

g Acceleration due to gravity (m s�<sup>2</sup>

d Particle diameter (m)

Dn Discrimination number

FB Fluidized bed

n Index function


## Author details

Youjun Lu1 \*, Liping Wei1,2 and Jikai Huang<sup>1</sup>

\*Address all correspondence to: yjlu@mail.xjtu.edu.cn

1 State Key Laboratory of Multiphase Flow in Power Engineering (SKLMF), Xi'an Jiaotong University, Xi'an, Shaanxi, China

2 School of Chemical Engineering, Northwest University, Xi'an, Shaanxi, China

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[33] Bi H, Grace J, Zhu J. Regime transitions affecting gas-solids suspensions and fluidized beds. International Journal of Multiphase Flow. 1996;22(97):154-161

**Chapter 7**

Provisional chapter

**Introductory Review on an Engineering Approach for**

**Fast‐Bed Modeling in Mimic to Bubbling Bed Practice**

Fast-Bed Modeling in Mimic to Bubbling Bed Practice

Based on the downward-penetrating particle flow through clusters and the analogy between a falling cluster and a rising bubble identified by the authors, a "type-Achoking-oriented separate-phase-coexistence model" for the upper dilute region of fast beds was established first. Without any model parameter adjustment, the unified model predicted successfully the type C choking, the solids holdup of upper dilute region, and

The model was then integrated with the sub-models of "cluster rebound at the dense bottom," "the momentum flux balances for acceleration and transition zones" in the lower and middle parts of the bed. The integrated model predicted successfully the axial solids holdup distributions of literature data under extremely wide operation conditions covering dilute-phase transportation, the premature fast bed, the classical fast bed, and

Keywords: fast fluidization, separate-phase model, type A choking, cluster rebound,

After several decades of development, fast fluidization or circulating fluidized bed (CFB) has been applied widely, nowadays, in different industries, such as chemical, metallurgy, and energy engineering [1–3]. Thanks to the particle agglomeration in CFB risers, small particles could be fluidized under quite high gas velocity, resulting in very high rates of heat and mass transfers in the bed. A unique feature of a fast fluidized bed is its nonuniform axial distribution of particle concentration. On top of the bed, the solids holdup is small, while it is large at the bottom. To form a fast fluidized bed, both of the two conditions are usually required [4]: (i) the

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

distribution, and reproduction in any medium, provided the original work is properly cited.

transitions to the high-density fast bed and the dense suspension up-flow.

Introductory Review on an Engineering Approach for

Ming‐Chuan Zhang and Chu Zhang

Ming-Chuan Zhang and Chu Zhang

http://dx.doi.org/10.5772/68107

the high-density fast bed.

solids holdup distribution

1. Introduction

Abstract

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter


Provisional chapter

## **Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice** Introductory Review on an Engineering Approach for

Fast-Bed Modeling in Mimic to Bubbling Bed Practice

Ming‐Chuan Zhang and Chu Zhang

Additional information is available at the end of the chapter Ming-Chuan Zhang and Chu Zhang

http://dx.doi.org/10.5772/68107 Additional information is available at the end of the chapter

#### Abstract

[33] Bi H, Grace J, Zhu J. Regime transitions affecting gas-solids suspensions and fluidized

[34] Bai D, Shibuya E, Nakagawa N, et al. Characterization of gas fluidization regimes using

[35] Zhu J, Karamanev D, Bassi A, et al. (Gas-) liquid-solid circulating fluidized beds and their potential applications to bioreactor engineering. Canadian Journal of Chemical Engineer-

beds. International Journal of Multiphase Flow. 1996;22(97):154-161

pressure fluctuations. Powder Technology. 1996;87(2):105-111

ing. 2009;78(1):82-94

112 Thermal Power Plants - New Trends and Recent Developments

Based on the downward-penetrating particle flow through clusters and the analogy between a falling cluster and a rising bubble identified by the authors, a "type-Achoking-oriented separate-phase-coexistence model" for the upper dilute region of fast beds was established first. Without any model parameter adjustment, the unified model predicted successfully the type C choking, the solids holdup of upper dilute region, and transitions to the high-density fast bed and the dense suspension up-flow.

The model was then integrated with the sub-models of "cluster rebound at the dense bottom," "the momentum flux balances for acceleration and transition zones" in the lower and middle parts of the bed. The integrated model predicted successfully the axial solids holdup distributions of literature data under extremely wide operation conditions covering dilute-phase transportation, the premature fast bed, the classical fast bed, and the high-density fast bed.

Keywords: fast fluidization, separate-phase model, type A choking, cluster rebound, solids holdup distribution

## 1. Introduction

After several decades of development, fast fluidization or circulating fluidized bed (CFB) has been applied widely, nowadays, in different industries, such as chemical, metallurgy, and energy engineering [1–3]. Thanks to the particle agglomeration in CFB risers, small particles could be fluidized under quite high gas velocity, resulting in very high rates of heat and mass transfers in the bed. A unique feature of a fast fluidized bed is its nonuniform axial distribution of particle concentration. On top of the bed, the solids holdup is small, while it is large at the bottom. To form a fast fluidized bed, both of the two conditions are usually required [4]: (i) the

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

solid circulating rate G<sup>s</sup> is larger than the minimum value of that Gsm; (ii) and at a given solid circulating rate G<sup>s</sup> > Gsm, the superficial gas velocity u<sup>f</sup> should be higher than the critical velocity for type C choking, but lower than that for type A choking, that is, uch,C < u<sup>f</sup> < uch,A.

To predict the two-phase flow characteristics in this very special flow regime, different kinds of modeling methods have been developed. They are, for examples, two-fluid modeling based on kinetic theory established by Gidaspow [5], two-fluid modeling with energy minimization multiscale (EMMS) approach suggested by Li and Kwauk [6], CFD modeling coupled with discrete element method (DEM) [7], CFD modeling with multiphase particle-in-cell (MP-PIC) approach [8], and so on. Nowadays, these methods have been developed to an extent that three-dimensional (3D) simulation of large-scale reactors including the full-solids loop, heat and mass transfer, and reaction kinetics can be realized [9]. However, all these methods expend great amount of computer efforts, sometimes super computers are even needed [9], which is usually not affordable for engineering application.

To overcome the problems met in practice, an engineering approach for fast fluidization dynamics was proposed by the authors recently [10, 11]. This paper will give an introductory review on this approach as follows.

> into clusters instead of suspending in dilute broth (phase), whereas the gas tends to pass around, instead of penetrating through, the dense cluster phase" [14]. Thus, it might be possible that some results obtained from bubbling beds could be applied also to the fast

> Figure 1. PIV measurement of particle moving in a CFB riser [12] compared with the flow field around a rising bubble [13]: (a) snapshots of instantaneous particle positions when a falling cluster (denoted by the small circle on the right wall)

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice

http://dx.doi.org/10.5772/68107

115

(a) (b) (c)

passing by; (b) corresponding particles' velocity field; and (c) flow pattern around a rising bubble.

In the research progress of traditional fluidization, though people understood the phenomenon of minimum fluidization and its prediction method long time ago [15], the knowledge on fluidization had not been an applied science, to some extent, until Davidson and Harrison's bubble model appeared in 1963 [13]. This excellent model explained successfully many important phenomena of bubbling beds, and based on that, a series of reactor models of this type,

What can we learn from the research success of bubbling beds? First, to grasper the critical boundary of this flow regime, that is, minimum fluidization (or minimum bubbling) in this case, is extremely important, since predicting the flow characteristics of a bubbling bed from its boundary not far away is much easier than extrapolating the flow transformation from the force analysis with a single particle. It can be seen clearly that the corresponding boundary in fast fluidization is the type A choking. And at a given gas velocity uf, the saturation-carrying

velocity for minimum fluidization umf. Thus, the critical boundary condition of fast fluidiza-

\* corresponds to the superficial gas

fluidization, as depicted below.

2.2. Modeling strategies learned from bubbling beds

capacity or the solid flux at type A choking in a riser G<sup>s</sup>

tion, that is, the type A choking, should be studied carefully first.

that is, "bubble models," were developed [9].

## 2. Analogy between fast beds and bubbling beds

### 2.1. Analogy of flows around a cluster and a bubble

To explain how a cluster is formed in a CFB riser, the wake effect was applied quite often in the literature. Recently, He et al. [12] conducted an excellent PIV investigation in a CFB riser, shown in Figure 1(a) and (b), from which some details of this phenomenon can be seen clearly. They declared in their article, "it can be easily seen that a cluster is followed by a wake, in which particles move downward quickly," and "when a cluster is passing by, the particles are dragged down at a higher velocity." It is very clear that those particles move toward the cluster at quite high velocities, which will cause a notable deposition, yet not the one negligible, on the back side of the cluster. Considering the size limitation for a stable cluster, the same quantity of particles must be poured out from its nose. Therefore, the continuous deposition and pour out of those particles together with the downward displacement inside can be viewed as an integrated penetration of particles through the cluster. From this point of view, the phenomenon was thought quite analogous to what happens around a rising bubble in a bubbling bed, shown as in Figure 1(c) [13].

It can be seen that the flow patterns of the two are quite similar, except their directions being opposite-down. Moreover, the following correspondences could be easily recognized if phasereversing is applied: (1) a rising bubble with null or few particles against a falling cluster with concentrated particles; (2) the relatively downward dense particle flow around the bubble against the upward dilute flow around the cluster; and (3) the upward-penetrating gas flow through the bubble against the downward-penetrating particle flow through the cluster. The scenarios in a CFB riser described are very close to the detailed numerical simulation results using two-fluid model combined with EMMS approach [14], that is, "the particles tend to enter

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice http://dx.doi.org/10.5772/68107 115

Figure 1. PIV measurement of particle moving in a CFB riser [12] compared with the flow field around a rising bubble [13]: (a) snapshots of instantaneous particle positions when a falling cluster (denoted by the small circle on the right wall) passing by; (b) corresponding particles' velocity field; and (c) flow pattern around a rising bubble.

into clusters instead of suspending in dilute broth (phase), whereas the gas tends to pass around, instead of penetrating through, the dense cluster phase" [14]. Thus, it might be possible that some results obtained from bubbling beds could be applied also to the fast fluidization, as depicted below.

#### 2.2. Modeling strategies learned from bubbling beds

solid circulating rate G<sup>s</sup> is larger than the minimum value of that Gsm; (ii) and at a given solid circulating rate G<sup>s</sup> > Gsm, the superficial gas velocity u<sup>f</sup> should be higher than the critical velocity for type C choking, but lower than that for type A choking, that is, uch,C < u<sup>f</sup> < uch,A. To predict the two-phase flow characteristics in this very special flow regime, different kinds of modeling methods have been developed. They are, for examples, two-fluid modeling based on kinetic theory established by Gidaspow [5], two-fluid modeling with energy minimization multiscale (EMMS) approach suggested by Li and Kwauk [6], CFD modeling coupled with discrete element method (DEM) [7], CFD modeling with multiphase particle-in-cell (MP-PIC) approach [8], and so on. Nowadays, these methods have been developed to an extent that three-dimensional (3D) simulation of large-scale reactors including the full-solids loop, heat and mass transfer, and reaction kinetics can be realized [9]. However, all these methods expend great amount of computer efforts, sometimes super computers are even needed [9],

To overcome the problems met in practice, an engineering approach for fast fluidization dynamics was proposed by the authors recently [10, 11]. This paper will give an introductory

To explain how a cluster is formed in a CFB riser, the wake effect was applied quite often in the literature. Recently, He et al. [12] conducted an excellent PIV investigation in a CFB riser, shown in Figure 1(a) and (b), from which some details of this phenomenon can be seen clearly. They declared in their article, "it can be easily seen that a cluster is followed by a wake, in which particles move downward quickly," and "when a cluster is passing by, the particles are dragged down at a higher velocity." It is very clear that those particles move toward the cluster at quite high velocities, which will cause a notable deposition, yet not the one negligible, on the back side of the cluster. Considering the size limitation for a stable cluster, the same quantity of particles must be poured out from its nose. Therefore, the continuous deposition and pour out of those particles together with the downward displacement inside can be viewed as an integrated penetration of particles through the cluster. From this point of view, the phenomenon was thought quite analogous to what happens around a rising bubble in a bubbling bed, shown as

It can be seen that the flow patterns of the two are quite similar, except their directions being opposite-down. Moreover, the following correspondences could be easily recognized if phasereversing is applied: (1) a rising bubble with null or few particles against a falling cluster with concentrated particles; (2) the relatively downward dense particle flow around the bubble against the upward dilute flow around the cluster; and (3) the upward-penetrating gas flow through the bubble against the downward-penetrating particle flow through the cluster. The scenarios in a CFB riser described are very close to the detailed numerical simulation results using two-fluid model combined with EMMS approach [14], that is, "the particles tend to enter

which is usually not affordable for engineering application.

2. Analogy between fast beds and bubbling beds

2.1. Analogy of flows around a cluster and a bubble

review on this approach as follows.

114 Thermal Power Plants - New Trends and Recent Developments

in Figure 1(c) [13].

In the research progress of traditional fluidization, though people understood the phenomenon of minimum fluidization and its prediction method long time ago [15], the knowledge on fluidization had not been an applied science, to some extent, until Davidson and Harrison's bubble model appeared in 1963 [13]. This excellent model explained successfully many important phenomena of bubbling beds, and based on that, a series of reactor models of this type, that is, "bubble models," were developed [9].

What can we learn from the research success of bubbling beds? First, to grasper the critical boundary of this flow regime, that is, minimum fluidization (or minimum bubbling) in this case, is extremely important, since predicting the flow characteristics of a bubbling bed from its boundary not far away is much easier than extrapolating the flow transformation from the force analysis with a single particle. It can be seen clearly that the corresponding boundary in fast fluidization is the type A choking. And at a given gas velocity uf, the saturation-carrying capacity or the solid flux at type A choking in a riser G<sup>s</sup> \* corresponds to the superficial gas velocity for minimum fluidization umf. Thus, the critical boundary condition of fast fluidization, that is, the type A choking, should be studied carefully first.

Secondly, the classical two-phase theory of fluidization, that is, "above the minimum fluidization velocity, all the extra gas passes through the bed in the form of bubbles, while the rest part of the bed remains at the minimum fluidization condition" [13], is probably one form of a general law caused by the agglomeration nature of gas-solid systems. The appearing form of the general law in fast beds should be further excavated, too. It will be shown later that the formation of clusters at G<sup>s</sup> > G<sup>s</sup> \* corresponds to the formation of bubbles at u<sup>f</sup> > umf. And also, when clusters are formed, in the case of fast bed, the upward dilute flow will still be at the solid-saturated condition, as if at type A choking. All these ideas will be used for the derivation of our model below.

#### 3. Constitutive equations for solid-saturated up-flow

#### 3.1. Yang's formula for type A choking

To predict the happening of type A choking, much research work was carried out in the past. Among the different types of methods developed, the form of Yang's formula [16, 17] looks the one most reasonable, as the formula was derived from two simple theoretical deductions. The first one is used to calculate the terminal velocity u<sup>0</sup> <sup>t</sup> for uniformly suspended particles with voidage ε in a riser of diameter Dt, in relative with the original value u<sup>t</sup> for a single particle

$$u'\_{\mathbf{t}} = u\_{\mathbf{t}} \sqrt{\left(1 + \frac{f\_p u\_p^2}{2gD\_{\mathbf{t}}}\right)} \times \epsilon^{4.7}.\tag{1}$$

3.2. Physical essence of Yang's formula

increases, the real gas velocity (1/√ε<sup>2</sup>

too [14].

voidage on u<sup>0</sup>

3.3. Reconstruction of Yang's formula

data collected by Xu et al. [20], resulting in

by the first item with square root sign √[1þfpu<sup>p</sup>

From Eq. (1), it can be easily recognized that the influence of wall friction on u<sup>0</sup>

particle F<sup>f</sup> and the surplus F<sup>s</sup> due to the surrounding particles. Then, we have

2

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice

will always be unity. With a decrease of Dt, the wall friction increases, then ut' increases. And the influence of bed voidage, that is, the influence of surrounding particles, is reflected by the second item with square root sign √ε4.7. With an increase of particle concentration (1–ε), ε decreases, and then ut' decreases. This is because when the concentration of particles

considered becomes more flexuous, and then the drag force coefficient will increase (1/√ε2.7),

To quantitatively analyze further the overall force balance for a uniform suspension of particles in a gas flow, we can resolve the increased fluid drag into the basal fluid drag on a single

where G is the gravity of particle suspension, while W stands for the friction of riser wall.

uniformity, since the force balance of any single particle depends more on the others.

Therefore, the criteria of Fs¼ W or F<sup>f</sup> ¼ G can be used to separate the two different situations just mentioned. Clearly, this critical condition is the type A choking, where the influence of bed

<sup>t</sup> is just compensated by the influence of riser wall, leading to u<sup>0</sup>

unique condition, a moving particle looks as if there is neither surrounding particles nor the riser wall. From the authors' opinion, this is the real physical essence of type A choking. Then, the functional dependence of the bed voidage on the superficial gas velocity at type A choking, that is, Eq. (3), could be used as the "constitutive equation" for solid-saturated up-flow.

According to a comprehensive review paper on choking for vertical conveying systems by Xu et al. [20], the prediction accuracy of Yang's formula is not satisfactory for type A choking, though it was suggested to be applied for a pretty long time [21]. In conserving its form, the solid-wall friction factor f<sup>p</sup> in Yang's formula was recorrelated by the authors [10] with the

If we compare the values of F<sup>s</sup> and W, we will have two different situations. When the suspension is quite dilute, the surplus drag force is relatively small. Then, we will have F<sup>s</sup> < W, and F<sup>f</sup> > G. The latter means that subtracting particle gravity the basal fluid drag F<sup>f</sup> still have something rest with its own freedom, resulting in F<sup>f</sup> – G ¼ W – F<sup>s</sup> and a simple dynamic system centered on each single particle. That is the case of normal dilute transportation, because the relatively independent movement of these particles will let themselves disperse uniformly. On the other hand, if we have F<sup>s</sup> > W and F<sup>f</sup> < G, the basal fluid drag F<sup>f</sup> will no longer be able, by itself, to support the particle but requires help from surrounding particles, as F<sup>f</sup> þ (F<sup>s</sup> – W) ¼ G. That makes the dynamic system more complex and easier to lose its

<sup>t</sup> is reflected

117

http://dx.doi.org/10.5772/68107

<sup>t</sup> ¼ ut. At this

/(2gDt)], since for an infinitely wide riser it

) increases, and the flow path of gas around the particle

F<sup>f</sup> þ F<sup>s</sup> ¼ G þ W, ð5Þ

where up¼ Gs/[ρs(1�ε)] stands for the particle velocity, and f<sup>p</sup> is the solid-wall friction factor. The formula is theoretically correct, and the detailed derivations of that can be found in the series work of Yang from 1973 to 1975 [16, 18, 19].

The second deduction is that the terminal velocity of a particle suspension in a finite diameter riser u<sup>0</sup> t , that is, the slip velocity between gas and solid, is just equal to the terminal velocity of a single particle in the infinity ut, when type A choking occurs [16, 17]

$$
\mu'\_t = \mu\_t. \tag{2}
$$

In the derivation of Yang's predictive equation (Eq. (3)), this deduction was actually applied [16, 17], yet not declared clearly

$$\frac{2D\_t g(\varepsilon\_{\rm ch}^{-4.7} - 1)}{\left(\mu\_{\rm ch} - \mu\_t\right)^2} = f\_{\rm p}. \tag{3}$$

The original value of solid-wall friction factor f<sup>p</sup> was taken as 0.01 in 1975 [16], but it was changed in 1983 to the present form as [17]

$$f\_{\rm p} = 6.81 \times 10^5 \left(\frac{\rho\_{\rm g}}{\rho\_s}\right)^{2.2}. \tag{4}$$

#### 3.2. Physical essence of Yang's formula

Secondly, the classical two-phase theory of fluidization, that is, "above the minimum fluidization velocity, all the extra gas passes through the bed in the form of bubbles, while the rest part of the bed remains at the minimum fluidization condition" [13], is probably one form of a general law caused by the agglomeration nature of gas-solid systems. The appearing form of the general law in fast beds should be further excavated, too. It will be shown later that the

when clusters are formed, in the case of fast bed, the upward dilute flow will still be at the solid-saturated condition, as if at type A choking. All these ideas will be used for the derivation

To predict the happening of type A choking, much research work was carried out in the past. Among the different types of methods developed, the form of Yang's formula [16, 17] looks the one most reasonable, as the formula was derived from two simple theoretical deductions. The

voidage ε in a riser of diameter Dt, in relative with the original value u<sup>t</sup> for a single particle

1 þ

where up¼ Gs/[ρs(1�ε)] stands for the particle velocity, and f<sup>p</sup> is the solid-wall friction factor. The formula is theoretically correct, and the detailed derivations of that can be found in the

The second deduction is that the terminal velocity of a particle suspension in a finite diameter

In the derivation of Yang's predictive equation (Eq. (3)), this deduction was actually applied

ch � 1Þ

The original value of solid-wall friction factor f<sup>p</sup> was taken as 0.01 in 1975 [16], but it was

ρs � �<sup>2</sup>:<sup>2</sup>

u0

<sup>2</sup>Dtgðε�4:<sup>7</sup>

ðuch � utÞ

<sup>f</sup> <sup>p</sup> <sup>¼</sup> <sup>6</sup>:<sup>81</sup> · <sup>105</sup> <sup>ρ</sup><sup>g</sup>

, that is, the slip velocity between gas and solid, is just equal to the terminal velocity of a

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

· ε<sup>4</sup>:<sup>7</sup>

f <sup>p</sup>u<sup>2</sup> p 2gD<sup>t</sup> !

3. Constitutive equations for solid-saturated up-flow

u0 <sup>t</sup> ¼ u<sup>t</sup>

single particle in the infinity ut, when type A choking occurs [16, 17]

\* corresponds to the formation of bubbles at u<sup>f</sup> > umf. And also,

<sup>t</sup> for uniformly suspended particles with

vuut : <sup>ð</sup>1<sup>Þ</sup>

<sup>t</sup> ¼ ut: ð2Þ

<sup>2</sup> ¼ f <sup>p</sup>: ð3Þ

: ð4Þ

formation of clusters at G<sup>s</sup> > G<sup>s</sup>

116 Thermal Power Plants - New Trends and Recent Developments

3.1. Yang's formula for type A choking

first one is used to calculate the terminal velocity u<sup>0</sup>

series work of Yang from 1973 to 1975 [16, 18, 19].

[16, 17], yet not declared clearly

changed in 1983 to the present form as [17]

of our model below.

riser u<sup>0</sup> t From Eq. (1), it can be easily recognized that the influence of wall friction on u<sup>0</sup> <sup>t</sup> is reflected by the first item with square root sign √[1þfpu<sup>p</sup> 2 /(2gDt)], since for an infinitely wide riser it will always be unity. With a decrease of Dt, the wall friction increases, then ut' increases. And the influence of bed voidage, that is, the influence of surrounding particles, is reflected by the second item with square root sign √ε4.7. With an increase of particle concentration (1–ε), ε decreases, and then ut' decreases. This is because when the concentration of particles increases, the real gas velocity (1/√ε<sup>2</sup> ) increases, and the flow path of gas around the particle considered becomes more flexuous, and then the drag force coefficient will increase (1/√ε2.7), too [14].

To quantitatively analyze further the overall force balance for a uniform suspension of particles in a gas flow, we can resolve the increased fluid drag into the basal fluid drag on a single particle F<sup>f</sup> and the surplus F<sup>s</sup> due to the surrounding particles. Then, we have

$$F\_{\text{f}} + F\_{\text{s}} = G + W\_{\text{\\_}} \tag{5}$$

where G is the gravity of particle suspension, while W stands for the friction of riser wall.

If we compare the values of F<sup>s</sup> and W, we will have two different situations. When the suspension is quite dilute, the surplus drag force is relatively small. Then, we will have F<sup>s</sup> < W, and F<sup>f</sup> > G. The latter means that subtracting particle gravity the basal fluid drag F<sup>f</sup> still have something rest with its own freedom, resulting in F<sup>f</sup> – G ¼ W – F<sup>s</sup> and a simple dynamic system centered on each single particle. That is the case of normal dilute transportation, because the relatively independent movement of these particles will let themselves disperse uniformly. On the other hand, if we have F<sup>s</sup> > W and F<sup>f</sup> < G, the basal fluid drag F<sup>f</sup> will no longer be able, by itself, to support the particle but requires help from surrounding particles, as F<sup>f</sup> þ (F<sup>s</sup> – W) ¼ G. That makes the dynamic system more complex and easier to lose its uniformity, since the force balance of any single particle depends more on the others.

Therefore, the criteria of Fs¼ W or F<sup>f</sup> ¼ G can be used to separate the two different situations just mentioned. Clearly, this critical condition is the type A choking, where the influence of bed voidage on u<sup>0</sup> <sup>t</sup> is just compensated by the influence of riser wall, leading to u<sup>0</sup> <sup>t</sup> ¼ ut. At this unique condition, a moving particle looks as if there is neither surrounding particles nor the riser wall. From the authors' opinion, this is the real physical essence of type A choking. Then, the functional dependence of the bed voidage on the superficial gas velocity at type A choking, that is, Eq. (3), could be used as the "constitutive equation" for solid-saturated up-flow.

#### 3.3. Reconstruction of Yang's formula

According to a comprehensive review paper on choking for vertical conveying systems by Xu et al. [20], the prediction accuracy of Yang's formula is not satisfactory for type A choking, though it was suggested to be applied for a pretty long time [21]. In conserving its form, the solid-wall friction factor f<sup>p</sup> in Yang's formula was recorrelated by the authors [10] with the data collected by Xu et al. [20], resulting in

$$f\_{\text{p}} = 0.01 \left(\frac{u\_{\text{f}} - u\_{\text{t}}}{u\_{\text{t}}}\right)^{a} \left(\frac{gD\_{\text{t}}}{0.8u\_{\text{t}}^{2}}\right)^{\text{g}} \tag{6}$$

riser diameter on type A choking velocity was not monotonic. Since the new correlation is given in a dimensionless form and the application ranges are quite wide, it is hoped that this correlation could be used, to some extent, in practically large units. For instance, if the particle terminal velocity is around 0.3 m/s (typical in CFB boilers), the riser diameter could be used up

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice

Described above, Eq. (3) gives the functional dependence of bed voidage εch on superficial gas velocity uch under solid-saturated conditions. For a given fluidizing system, with an increase of uch, εch decreases and (1–εch) increases, and then the solid flux at type A choking G<sup>s</sup>

Taking an FCC-air fluidizing system as an example, Figure 4 shows the calculated (1–εch) and

system will not completely collapse when the circulating solid flux is greater than G<sup>s</sup>

corresponded to the superficial gas velocity uf. Some particles will segregate from the gas stream to form a free-sedimentary dense phase, that is, the so-called cluster. The fluidizing system then runs in a more complicated separate-phase-coexistence mode. The cluster occupies a part of the cross-sectional area of the riser, but without any outer gas invading in. Meanwhile in the rest part of the riser, all gas squeezes into the dilute phase and carries much

Let β stand for the fraction of cross-sectional area occupied by the falling clusters, and m<sup>s</sup>

, dp¼ 100 µm, Dt¼ 0.1 m).

1 � εch εch

þ represent the solid flux upward in the dilute phase. Both

\* and its concentration <sup>ð</sup><sup>1</sup> � <sup>ε</sup>ch<sup>Þ</sup> at type A choking on superficial gas velocity <sup>u</sup><sup>f</sup> for

<sup>s</sup> ¼ ρsðuch � utÞ

\* will

119

\*

– for

: ð8Þ

http://dx.doi.org/10.5772/68107

\* on u<sup>f</sup> (uch in the equation), the

4. Separate-phase-coexistence model for fast bed

G�

\* varied with uf. Thanks to this special dependence of G<sup>s</sup>

4.1. Physical description of the model

increase more rapidly

more particles upward.

the solid flux downward, while m<sup>s</sup>

Figure 4. Dependences of solid flux G<sup>s</sup>

an FCC-air system (ρs<sup>¼</sup> 1620 kg/m<sup>3</sup>

to 10 m.

Gs

$$\alpha = -(1.0723 + 0.0017 \text{Ar}).\tag{7}$$

When gDt=u<sup>2</sup> <sup>t</sup> <sup>&</sup>gt; <sup>0</sup>:8, <sup>ϑ</sup> <sup>¼</sup> 0.71; while gDt=u<sup>2</sup> <sup>t</sup> < 0:8, ϑ ¼ �1.27, as shown in Figure 2. This correlation is applied with Ar <sup>¼</sup> <sup>1</sup>–1000, <sup>u</sup>ch,A/ut<sup>¼</sup> <sup>3</sup>–40, and gDt=u<sup>2</sup> <sup>t</sup> ¼ 0:2–1000. And the values of f<sup>p</sup> should range from 0.001 to 0.1. As can be seen in Figure 3, the predicted saturation-carrying capacities G<sup>s</sup> \* are in good consistency with the experimental data, if some observation delays in these experiments are considered.

The dependence of dimensionless solid-wall friction factor <sup>~</sup><sup>f</sup> <sup>p</sup> on dimensionless riser diameter gDt=u<sup>2</sup> <sup>t</sup> changes abruptly at gDt=u<sup>2</sup> <sup>t</sup> ¼ 0:8, which corresponds to the transit of general flow pattern from confined slugging to free bubbling [10]. It further confirms that type A choking is a riser-diameter-dependent phenomenon, as we discussed before. However, most of the previous work ignored this dependence except Xu et al. [20], showing that the influence of

Figure 2. Log-log plot of <sup>~</sup><sup>f</sup> <sup>p</sup> with gDt/u<sup>t</sup> <sup>2</sup> for experimental data collected by Xu et al. [20].

Figure 3. Predictions of G<sup>s</sup> \* for type A choking compared with experimental data of [20].

riser diameter on type A choking velocity was not monotonic. Since the new correlation is given in a dimensionless form and the application ranges are quite wide, it is hoped that this correlation could be used, to some extent, in practically large units. For instance, if the particle terminal velocity is around 0.3 m/s (typical in CFB boilers), the riser diameter could be used up to 10 m.

## 4. Separate-phase-coexistence model for fast bed

#### 4.1. Physical description of the model

<sup>f</sup> <sup>p</sup> <sup>¼</sup> <sup>0</sup>:<sup>01</sup> <sup>u</sup><sup>f</sup> � <sup>u</sup><sup>t</sup>

<sup>t</sup> <sup>&</sup>gt; <sup>0</sup>:8, <sup>ϑ</sup> <sup>¼</sup> 0.71; while gDt=u<sup>2</sup>

vation delays in these experiments are considered.

0.1

10

*G*\*

(kg/m2s,cal)

s

100

*f*

~

Figure 2. Log-log plot of <sup>~</sup><sup>f</sup> <sup>p</sup> with gDt/u<sup>t</sup>

Figure 3. Predictions of G<sup>s</sup>

p


1

10

<sup>t</sup> changes abruptly at gDt=u<sup>2</sup>

118 Thermal Power Plants - New Trends and Recent Developments

correlation is applied with Ar <sup>¼</sup> <sup>1</sup>–1000, <sup>u</sup>ch,A/ut<sup>¼</sup> <sup>3</sup>–40, and gDt=u<sup>2</sup>

When gDt=u<sup>2</sup>

gDt=u<sup>2</sup>

tion-carrying capacities G<sup>s</sup>

ut

values of f<sup>p</sup> should range from 0.001 to 0.1. As can be seen in Figure 3, the predicted satura-

The dependence of dimensionless solid-wall friction factor <sup>~</sup><sup>f</sup> <sup>p</sup> on dimensionless riser diameter

pattern from confined slugging to free bubbling [10]. It further confirms that type A choking is a riser-diameter-dependent phenomenon, as we discussed before. However, most of the previous work ignored this dependence except Xu et al. [20], showing that the influence of

0.1 <sup>1</sup> <sup>10</sup> 100 1000 0.01

*gD*<sup>t</sup> /*u*<sup>2</sup> t

<sup>1</sup> <sup>10</sup> <sup>100</sup> <sup>1</sup>

<sup>s</sup> (kg/m2s,exp)

*G*\*

\* for type A choking compared with experimental data of [20].

<sup>2</sup> for experimental data collected by Xu et al. [20].


+3SD

<sup>α</sup> gD<sup>t</sup>

0:8u<sup>2</sup> t <sup>ϑ</sup>

α ¼ �ð1:0723 þ 0:0017ArÞ: ð7Þ

<sup>t</sup> ¼ 0:8, which corresponds to the transit of general flow

\* are in good consistency with the experimental data, if some obser-

<sup>t</sup> < 0:8, ϑ ¼ �1.27, as shown in Figure 2. This

ð6Þ

<sup>t</sup> ¼ 0:2–1000. And the

Described above, Eq. (3) gives the functional dependence of bed voidage εch on superficial gas velocity uch under solid-saturated conditions. For a given fluidizing system, with an increase of uch, εch decreases and (1–εch) increases, and then the solid flux at type A choking G<sup>s</sup> \* will increase more rapidly

$$\mathcal{G}\_s^\* = \rho\_s (\mu\_{\rm ch} - \mu\_t) \frac{1 - \varepsilon\_{\rm ch}}{\varepsilon\_{\rm ch}}. \tag{8}$$

Taking an FCC-air fluidizing system as an example, Figure 4 shows the calculated (1–εch) and Gs \* varied with uf. Thanks to this special dependence of G<sup>s</sup> \* on u<sup>f</sup> (uch in the equation), the system will not completely collapse when the circulating solid flux is greater than G<sup>s</sup> \* corresponded to the superficial gas velocity uf. Some particles will segregate from the gas stream to form a free-sedimentary dense phase, that is, the so-called cluster. The fluidizing system then runs in a more complicated separate-phase-coexistence mode. The cluster occupies a part of the cross-sectional area of the riser, but without any outer gas invading in. Meanwhile in the rest part of the riser, all gas squeezes into the dilute phase and carries much more particles upward.

Let β stand for the fraction of cross-sectional area occupied by the falling clusters, and m<sup>s</sup> – for the solid flux downward, while m<sup>s</sup> þ represent the solid flux upward in the dilute phase. Both

Figure 4. Dependences of solid flux G<sup>s</sup> \* and its concentration <sup>ð</sup><sup>1</sup> � <sup>ε</sup>ch<sup>Þ</sup> at type A choking on superficial gas velocity <sup>u</sup><sup>f</sup> for an FCC-air system (ρs<sup>¼</sup> 1620 kg/m<sup>3</sup> , dp¼ 100 µm, Dt¼ 0.1 m).

ms <sup>þ</sup> and m<sup>s</sup> – are calculated based on the total cross-sectional area of the riser, but not their own occupied. Then, the circulating solid flux in the riser G<sup>s</sup> should be

$$G\_s = m\_s^+ - m\_s^-.\tag{9}$$

which there is always an upward interstitial gas flow subject to the pressure gradient of the bed. There have not been direct experimental evidences for the sufficient condition, that is, the two opposite flows should be completely compensated with each other. However, it is speculated that this situation could be the one with least flow resistance for a gas-solid two-phase system with agglomerative nature, and then tends to be most possible. In analogy with the bubbling beds, "no outer-gas invading clusters" is surely corresponding to "no solid particles

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice

At the very beginning of cluster formation (β ≈ 0), the terminal velocity of a single particle u<sup>t</sup> can still be used as the gas-solid slip velocity, the same value at type A choking. It is surely expected, when clusters visibly appear, the gas-solid slip velocity will increase due to the impact of falling clusters. To facilitate the calculation, this impact can be realized with decreasing the effective gas velocity of dilute phase by an effective velocity factor of F(β) < 1. Therefore,

> ufFðβÞ <sup>1</sup> � <sup>β</sup> � <sup>u</sup><sup>t</sup> <sup>1</sup> � <sup>ε</sup>ch

Meanwhile, the solid-saturated dilute-phase voidage εch and the nominal gas velocity

ch ¼ uf FðβÞ=ð1–βÞ should still fit the revised Yang's formula. Then, the kernel model for dilute phase, that is, the superficial upward solid flux based on unit cross-sectional area of the riser, is

<sup>s</sup> <sup>¼</sup> <sup>ρ</sup>s½ufFðβÞ � <sup>u</sup>tð<sup>1</sup> � <sup>β</sup>Þ� <sup>1</sup> � <sup>ε</sup>ch

Meanwhile, to keep the outer-gas flow within the cluster being zero, the modified Richardson-Zaki's equation [22] must be satisfied for the cluster voidage εcl and its falling velocity ucl.

> εcl 1 <sup>m</sup>

and the value of voidage at minimum fluidization εmf ¼ 0.45 was taken in later calculations.

<sup>¼</sup> <sup>u</sup>tε<sup>m</sup>

The form of the kernel model for dense phase or falling clusters is quite simple as

m�

ucl ¼ u<sup>t</sup>

<sup>m</sup> <sup>¼</sup> lg <sup>u</sup>mf ut

εch

εch

<sup>s</sup> ¼ ρsβuclð1 � εclÞ: ð15Þ

lgεmf, <sup>ð</sup>17<sup>Þ</sup>

: ð13Þ

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121

: ð14Þ

cl: ð16Þ

the upward solid flux based on unit dilute-phase area should be

m<sup>þ</sup>

G<sup>þ</sup> <sup>s</sup> ¼ ρ<sup>s</sup>

falling into bubbles."

4.2.1. Model kernels

u�

expressed as

Then, we have

Here,

4.2. Mathematical model kernels

Figure 5 shows the schematic diagram of m<sup>s</sup> <sup>þ</sup> and m<sup>s</sup> – calculated for varied β at a given gas velocity.

This figure shows when

$$
\left.\frac{\mathbf{d}m\_s^+}{\mathbf{d}\beta}\right|\_{\beta=0} > \left.\frac{\mathbf{d}m\_s^-}{\mathbf{d}\beta}\right|\_{\beta=0} \,, \tag{10}
$$

more particles, compared with those at type A choking, can be transported upward in the separate-phase-coexistence mode, that is, G<sup>s</sup> ¼ m<sup>s</sup> <sup>þ</sup>– m<sup>s</sup> – > G<sup>s</sup> \* . However, when β increases to a critical value βch

dm<sup>þ</sup> s <sup>d</sup><sup>β</sup> <sup>β</sup>¼βch <sup>¼</sup> <sup>d</sup>m� s <sup>d</sup><sup>β</sup> <sup>β</sup>¼βch , ð11Þ

the net solid flux transported upward reaches its maximum value Gs,max. Beyond that point, the system will be abruptly collapsed, that is, the case of type C choking.

Therefore, the basal requirement for separate-phase-coexistence mode should be

$$
\left. \frac{\mathbf{d}m\_s^+}{\mathbf{d}\beta} \right|\_{\beta=0} > = \left. \frac{\mathbf{d}m\_s^-}{\mathbf{d}\beta} \right|\_{\beta=0}. \tag{12}
$$

This criterion will be applied later to predict Gsm, the minimum solid flux for fast bed.

"Without outer-gas invaded in clusters" is a primary assumption used in our model. Its necessary condition is met by the downward penetration of solid particles into the cluster, in

Figure 5. Schematic diagram of m<sup>s</sup> <sup>þ</sup>and m<sup>s</sup> – changed with β at given gas velocity.

which there is always an upward interstitial gas flow subject to the pressure gradient of the bed. There have not been direct experimental evidences for the sufficient condition, that is, the two opposite flows should be completely compensated with each other. However, it is speculated that this situation could be the one with least flow resistance for a gas-solid two-phase system with agglomerative nature, and then tends to be most possible. In analogy with the bubbling beds, "no outer-gas invading clusters" is surely corresponding to "no solid particles falling into bubbles."

#### 4.2. Mathematical model kernels

#### 4.2.1. Model kernels

ms

<sup>þ</sup> and m<sup>s</sup>

velocity.

This figure shows when

critical value βch

Figure 5. Schematic diagram of m<sup>s</sup>

<sup>þ</sup>and m<sup>s</sup> –

– are calculated based on the total cross-sectional area of the riser, but not their own

<sup>s</sup> : ð9Þ

– calculated for varied β at a given gas

. However, when β increases to a

ð10Þ

ð11Þ

ð12Þ

<sup>s</sup> � m�

<sup>þ</sup> and m<sup>s</sup>

> dm� s <sup>d</sup><sup>β</sup> <sup>β</sup>¼<sup>0</sup> , 

more particles, compared with those at type A choking, can be transported upward in the

<sup>¼</sup> <sup>d</sup>m� s <sup>d</sup><sup>β</sup> <sup>β</sup>¼βch

<sup>&</sup>gt;<sup>¼</sup> <sup>d</sup><sup>m</sup> � s <sup>d</sup><sup>β</sup> <sup>β</sup>¼<sup>0</sup>

the net solid flux transported upward reaches its maximum value Gs,max. Beyond that point,

<sup>þ</sup>– m<sup>s</sup>

  – > G<sup>s</sup> \*

,

: 

G<sup>s</sup> ¼ m<sup>þ</sup>

dm<sup>þ</sup> s <sup>d</sup><sup>β</sup> <sup>β</sup>¼<sup>0</sup>

dm<sup>þ</sup> s <sup>d</sup><sup>β</sup> <sup>β</sup>¼βch

the system will be abruptly collapsed, that is, the case of type C choking.

dm<sup>þ</sup> s <sup>d</sup><sup>β</sup> <sup>β</sup>¼<sup>0</sup>

 

Therefore, the basal requirement for separate-phase-coexistence mode should be

 

This criterion will be applied later to predict Gsm, the minimum solid flux for fast bed.

"Without outer-gas invaded in clusters" is a primary assumption used in our model. Its necessary condition is met by the downward penetration of solid particles into the cluster, in

changed with β at given gas velocity.

 

occupied. Then, the circulating solid flux in the riser G<sup>s</sup> should be

Figure 5 shows the schematic diagram of m<sup>s</sup>

120 Thermal Power Plants - New Trends and Recent Developments

separate-phase-coexistence mode, that is, G<sup>s</sup> ¼ m<sup>s</sup>

At the very beginning of cluster formation (β ≈ 0), the terminal velocity of a single particle u<sup>t</sup> can still be used as the gas-solid slip velocity, the same value at type A choking. It is surely expected, when clusters visibly appear, the gas-solid slip velocity will increase due to the impact of falling clusters. To facilitate the calculation, this impact can be realized with decreasing the effective gas velocity of dilute phase by an effective velocity factor of F(β) < 1. Therefore, the upward solid flux based on unit dilute-phase area should be

$$\mathcal{G}\_s^+ = \rho\_s \left[ \frac{u\_t F(\beta)}{1 - \beta} - u\_t \right] \frac{1 - \varepsilon\_{\rm ch}}{\varepsilon\_{\rm ch}}.\tag{13}$$

Meanwhile, the solid-saturated dilute-phase voidage εch and the nominal gas velocity u� ch ¼ uf FðβÞ=ð1–βÞ should still fit the revised Yang's formula. Then, the kernel model for dilute phase, that is, the superficial upward solid flux based on unit cross-sectional area of the riser, is expressed as

$$
\rho m\_s^+ = \rho\_s[\mu\_\text{f} F(\beta) - \mu\_\text{t} (1 - \beta)] \frac{1 - \varepsilon\_{\text{ch}}}{\varepsilon\_{\text{ch}}}.\tag{14}
$$

The form of the kernel model for dense phase or falling clusters is quite simple as

$$m\_s^- = \rho\_s \beta \mu\_{\rm cl} (1 - \varepsilon\_{\rm cl}).\tag{15}$$

Meanwhile, to keep the outer-gas flow within the cluster being zero, the modified Richardson-Zaki's equation [22] must be satisfied for the cluster voidage εcl and its falling velocity ucl. Then, we have

$$
\mu\_{\rm cl} = \mu\_{\rm t} \left( \frac{\varepsilon\_{\rm cl}}{1} \right)^{m} = \mu\_{\rm t} \varepsilon\_{\rm cl}^{m}. \tag{16}
$$

Here,

$$m = \lg\left(\frac{\mu\_{\rm mf}}{\mu\_{\rm t}}\right) \Big/ \lg \varepsilon\_{\rm mf} \tag{17}$$

and the value of voidage at minimum fluidization εmf ¼ 0.45 was taken in later calculations.

#### 4.2.2. Empirical closures for F(β) and εcl

To make the kernel model for dilute phase closed, an empirical expression for the effective velocity factor F(β) was given as [10]

$$F(\beta) = 1 - [1 - F(1)]\beta^n,\tag{18}$$

where F(1) is the value of F(β) at β=1 and can be calculated as

$$F(1) = \left(1 - \frac{\mu\_{\rm t}}{\mu\_{\rm f}}\right) \frac{1 - \varepsilon\_{\rm ch, A}}{\varepsilon\_{\rm ch, A}} \frac{\varepsilon\_{\rm sl}}{1 - \varepsilon\_{\rm sl}},\tag{19}$$

εsl and εch,A are the bed voidages for slugging (β=1) and type A choking (β=0), respectively. Here,

$$
\varepsilon\_{\rm sl} = 1 - (1 - \varepsilon\_{\rm mf})/2. \tag{20}
$$

From this kind of "calibration," the model parameter n ¼ 4.5 was chosen for a simplified version of the model without iteration. Figure 7 shows comparisons between the model predicted uch,C with n ¼ 4.5 and those given by Eq. (23), for both FCC-air and sand-air systems with different

Figure 6. Variations of dilute-phase voidage εch with gas velocity u<sup>f</sup> calculated from different n for an FCC-air system

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice

s)).

From a meso-scale analysis in mimic to bubbling beds [10], the effective velocity factor in

Figure 7. Comparison of model predictions for type C choking (n ¼ 4.5, Dt¼ 0.1 m) and those from Yousfi and Gau [24].

where upen stands for the superficial percolation velocity in a packed bed of voidage εcl under pressure gradient of the bed, and φ is the influence factor of penetrating particles in clouds

� <sup>ε</sup>ch 1 � εch

� 1 β

1 � β

� β � φ, ð24Þ

: ð25Þ

<sup>F</sup>ðβÞ ¼ <sup>1</sup> � <sup>3</sup>upen

uf � 1 � εcl εcl

<sup>φ</sup> <sup>¼</sup> <sup>u</sup>cl <sup>þ</sup> <sup>2</sup>usd;<sup>∞</sup> ucl � usd;<sup>∞</sup>

s)) in a riser of

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123

particle sizes (50, 100, 150, and 200 μm) and solid fluxes (50, 100 and 200 kg/(m2

0.1 m, typical scale in laboratories. The result looks quite satisfactory.

, <sup>d</sup>p<sup>¼</sup> 100 µm, <sup>G</sup>s<sup>¼</sup> 100 kg/(m<sup>2</sup>

4.2.3. Mechanistic closures for F(β) and εcl

dilute phase F(β) was determined as

(Dt<sup>¼</sup> 0.1 m, <sup>ρ</sup>s<sup>¼</sup> 1620 kg/m<sup>3</sup>

To make the kernel model for dense phase closed, Harris's correlation [23] for solid concentration in clusters εs, cl was suggested be applied [11].

$$1 - \varepsilon\_{\rm cl} = \varepsilon\_{\rm s,d} = \frac{0.58 \left(\varepsilon\_{\rm s}^{\*}\right)^{1.48}}{0.013 + \left(\varepsilon\_{\rm s}^{\*}\right)^{1.48}}\tag{21}$$

where ε� <sup>s</sup> is the solids holdup in upper dilute region, which will be discussed in Section 4.4. Or, an even rough estimation directly from εch could be used as

$$1 - \varepsilon\_{\rm cl} = 2(1 - \varepsilon\_{\rm ch}) + 0.45\beta. \tag{22}$$

With these equations derived, the calculation procedure is quite straightforward. (i) Type A choking velocity uch,A is calculated for a given solid flux G<sup>s</sup> > Gsm. (ii) Decreasing superficial gas velocity to make u<sup>f</sup> < uch,A; then, m<sup>s</sup> <sup>þ</sup> and m<sup>s</sup> – are calculated by using different β until G<sup>s</sup> ¼ m<sup>s</sup> <sup>þ</sup>– m<sup>s</sup> � is satisfied; the voidage of upward dilute phase εch at the operating gas velocity u<sup>f</sup> is then determined. (iii) Repeating the steps above until type C choking occurs, the type C choking velocity uch,C is finally obtained.

Using different model parameter n, the variations of dilute-phase voidage εch with operating gas velocity u<sup>f</sup> for an FCC-air system are shown in Figure 6. It can be seen from the figure that when the operating gas velocity u<sup>f</sup> is close to uch,C, a small reduction of gas velocity will cause a great increase of solid concentration (1�ε) and then pressure drop of the bed. Thus, it can be recognized as the occurrence of type C choking.

The figure also shows that the type C choking velocity calculated decreases with an increase of n used. Since Yousfi and Gau's empirical correlation for type C choking [24] (Eq. (23)) had been considered as the best in the literature [20], it was applied to estimate the proper value of n

$$\frac{\mu\_{\rm ch,C}}{\sqrt{gd\_{\rm p}}} = 32 \text{Re}\_{\rm t}^{-0.06} \left( \frac{G\_{\rm s}}{\rho\_{\rm g} \mu\_{\rm ch,C}} \right)^{0.28} \,. \tag{23}$$

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice http://dx.doi.org/10.5772/68107 123

Figure 6. Variations of dilute-phase voidage εch with gas velocity u<sup>f</sup> calculated from different n for an FCC-air system (Dt<sup>¼</sup> 0.1 m, <sup>ρ</sup>s<sup>¼</sup> 1620 kg/m<sup>3</sup> , <sup>d</sup>p<sup>¼</sup> 100 µm, <sup>G</sup>s<sup>¼</sup> 100 kg/(m<sup>2</sup> s)).

From this kind of "calibration," the model parameter n ¼ 4.5 was chosen for a simplified version of the model without iteration. Figure 7 shows comparisons between the model predicted uch,C with n ¼ 4.5 and those given by Eq. (23), for both FCC-air and sand-air systems with different particle sizes (50, 100, 150, and 200 μm) and solid fluxes (50, 100 and 200 kg/(m2 s)) in a riser of 0.1 m, typical scale in laboratories. The result looks quite satisfactory.

Figure 7. Comparison of model predictions for type C choking (n ¼ 4.5, Dt¼ 0.1 m) and those from Yousfi and Gau [24].

#### 4.2.3. Mechanistic closures for F(β) and εcl

4.2.2. Empirical closures for F(β) and εcl

122 Thermal Power Plants - New Trends and Recent Developments

velocity factor F(β) was given as [10]

Here,

where ε�

G<sup>s</sup> ¼ m<sup>s</sup>

<sup>þ</sup>– m<sup>s</sup>

where F(1) is the value of F(β) at β=1 and can be calculated as

tion in clusters εs, cl was suggested be applied [11].

gas velocity to make u<sup>f</sup> < uch,A; then, m<sup>s</sup>

the type C choking velocity uch,C is finally obtained.

recognized as the occurrence of type C choking.

uch;<sup>C</sup> ffiffiffiffiffiffiffi gd<sup>p</sup>

<sup>p</sup> <sup>¼</sup> 32Re�0:<sup>06</sup> <sup>t</sup>

an even rough estimation directly from εch could be used as

<sup>F</sup>ð1Þ ¼ <sup>1</sup> � <sup>u</sup><sup>t</sup>

uf � � <sup>1</sup> � <sup>ε</sup>ch;<sup>A</sup>

εsl and εch,A are the bed voidages for slugging (β=1) and type A choking (β=0), respectively.

To make the kernel model for dense phase closed, Harris's correlation [23] for solid concentra-

With these equations derived, the calculation procedure is quite straightforward. (i) Type A choking velocity uch,A is calculated for a given solid flux G<sup>s</sup> > Gsm. (ii) Decreasing superficial

<sup>þ</sup> and m<sup>s</sup>

velocity u<sup>f</sup> is then determined. (iii) Repeating the steps above until type C choking occurs,

Using different model parameter n, the variations of dilute-phase voidage εch with operating gas velocity u<sup>f</sup> for an FCC-air system are shown in Figure 6. It can be seen from the figure that when the operating gas velocity u<sup>f</sup> is close to uch,C, a small reduction of gas velocity will cause a great increase of solid concentration (1�ε) and then pressure drop of the bed. Thus, it can be

The figure also shows that the type C choking velocity calculated decreases with an increase of n used. Since Yousfi and Gau's empirical correlation for type C choking [24] (Eq. (23)) had been considered as the best in the literature [20], it was applied to estimate the proper value of n

<sup>1</sup> � <sup>ε</sup>cl <sup>¼</sup> <sup>ε</sup><sup>s</sup>;cl <sup>¼</sup> <sup>0</sup>:58ðε�

εch;<sup>A</sup>

To make the kernel model for dilute phase closed, an empirical expression for the effective

<sup>F</sup>ðβÞ ¼ <sup>1</sup> � ½<sup>1</sup> � <sup>F</sup>ð1Þ�βn, <sup>ð</sup>18<sup>Þ</sup>

εsl ¼ 1 � ð1 � εmfÞ=2: ð20Þ

1 � εcl ¼ 2ð1 � εchÞ þ 0:45β: ð22Þ

, ð19Þ

<sup>1</sup>:<sup>48</sup> , ð21Þ

– are calculated by using different β until

: ð23Þ

εsl 1 � εsl

s Þ 1:48

� is satisfied; the voidage of upward dilute phase εch at the operating gas

Gs ρguch;<sup>C</sup>

!<sup>0</sup>:<sup>28</sup>

s Þ

0:013 þ ðε�

<sup>s</sup> is the solids holdup in upper dilute region, which will be discussed in Section 4.4. Or,

From a meso-scale analysis in mimic to bubbling beds [10], the effective velocity factor in dilute phase F(β) was determined as

$$F(\beta) = 1 - \frac{3u\_{\text{pen}}}{u\_{\text{f}}} \cdot \frac{1 - \varepsilon\_{\text{cl}}}{\varepsilon\_{\text{cl}}} \cdot \frac{\varepsilon\_{\text{ch}}}{1 - \varepsilon\_{\text{ch}}} \cdot \beta \cdot \varphi\_{\text{\prime}} \tag{24}$$

where upen stands for the superficial percolation velocity in a packed bed of voidage εcl under pressure gradient of the bed, and φ is the influence factor of penetrating particles in clouds

$$
\varphi = \left(\frac{\mu\_{\rm cl} + 2\mu\_{\rm sd,\rm co}}{\mu\_{\rm cl} - \mu\_{\rm sd,\rm co}} - 1\right) \frac{\beta}{1 - \beta}.\tag{25}
$$

Detailed definitions and calculation methods of these parameters in Eqs. (24) and (25) can be found in Ref. [10].

It will be discussed later in Section 5.1, the weight of clusters should be balanced by the interphase drag between the dilute and the dense phases. This requirement can be used to determine the cluster voidage εcl independently, rather than using Harris's correlation. Certainly, all these calculations need iterations.

As an example, Figure 8 shows that the meso-scale model determined F (β) compared with those with constant n for an FCC-air system. It can be seen that n ¼ 4.5 is a pretty good approximation for the simplified version without iterations. And Figure 9 shows the solid concentration of clusters predicted by inter-phase balance compared with Harris's correlation. It can be seen that they are also in agreement with each other pretty well.

4.3. Minimum solid flux for fast bed

Figure 10. Predictions of G<sup>s</sup>

have already

And, as we have also [11]

As mentioned before, the critical requirement for separate-phase-coexistence mode is

  <sup>¼</sup> <sup>d</sup>m� s <sup>d</sup><sup>β</sup> <sup>β</sup>¼<sup>0</sup> , 

<sup>C</sup> for type C choking compared with the experimental data collected by Xu et al. [20].

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice

which can be used for the determination of Gsm, the minimum solid flux for fast bed. And we

<sup>s</sup> <sup>¼</sup> <sup>ρ</sup>s½ufFðβÞ � <sup>u</sup>tð<sup>1</sup> � <sup>β</sup>Þ� <sup>1</sup> � <sup>ε</sup>ch

¼ ρsuclj

<sup>β</sup>!<sup>0</sup>Þ

The first statement means that at the very beginning of phase separation, the original formation of cluster is due to a noncollided convergence of two dilute solid pockets. The second statement with equal signs is required for the force balance of gas and particles inside the clusters settled freely, that is, the modified Richardson-Zaki equation should be fitted [11]. Because the solid concentration of the originally formed cluster is very small, the voidage is

εch

<sup>β</sup>!<sup>0</sup>ð<sup>1</sup> � <sup>ε</sup>clÞj<sup>β</sup>!<sup>0</sup>:

<sup>s</sup> ¼ ρsβuclð1 � εclÞ: ð15aÞ

<sup>ð</sup><sup>1</sup> � <sup>ε</sup>clÞj<sup>β</sup>!<sup>0</sup> <sup>¼</sup> <sup>2</sup>ð<sup>1</sup> � <sup>ε</sup>ch;<sup>A</sup>Þ ð27<sup>Þ</sup>

<sup>m</sup> <sup>¼</sup> <sup>u</sup>t½<sup>1</sup> � <sup>2</sup>ð<sup>1</sup> � <sup>ε</sup>ch;<sup>A</sup>Þ�<sup>m</sup> <sup>≈</sup> <sup>u</sup>t: <sup>ð</sup>28<sup>Þ</sup>

ð12aÞ

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125

ð14aÞ

ð26Þ

dm<sup>þ</sup> s <sup>d</sup><sup>β</sup> <sup>β</sup>¼<sup>0</sup>

m�

m<sup>þ</sup>

The derivation of Eq. (15a) is quite straightforward, that is,

uclj

dm� s <sup>d</sup><sup>β</sup> <sup>β</sup>!<sup>0</sup>

<sup>β</sup>!<sup>0</sup> <sup>¼</sup> <sup>u</sup><sup>t</sup> · <sup>ð</sup>εcl<sup>j</sup>

 

Figure 8. F(β) calculated by Eq. (24) compared with constant <sup>n</sup> (FCC-air system, <sup>ρ</sup><sup>s</sup> <sup>¼</sup> 1600 kg/m<sup>3</sup> , d<sup>p</sup> ¼ 70 μm, D<sup>t</sup> ¼ 0.1 m, u<sup>f</sup> ¼ 6 m/s).

Figure 9. Predicted solid concentration of clusters εs,cl compared with Harris's correlation [23].

As a first check, Figure 10 shows the solid flux G<sup>s</sup> <sup>C</sup> at type C choking predicted by the mechanistic model. The model predictions were compared with the experimental data collected by Xu et al. [20]. Noting that some data points of type B choking due to blower and/or standpipe limitation of the system [21] could also be included, the accuracy of model prediction is reasonably accepted.

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice http://dx.doi.org/10.5772/68107 125

Figure 10. Predictions of G<sup>s</sup> <sup>C</sup> for type C choking compared with the experimental data collected by Xu et al. [20].

#### 4.3. Minimum solid flux for fast bed

Detailed definitions and calculation methods of these parameters in Eqs. (24) and (25) can be

It will be discussed later in Section 5.1, the weight of clusters should be balanced by the interphase drag between the dilute and the dense phases. This requirement can be used to determine the cluster voidage εcl independently, rather than using Harris's correlation. Certainly, all

As an example, Figure 8 shows that the meso-scale model determined F (β) compared with those with constant n for an FCC-air system. It can be seen that n ¼ 4.5 is a pretty good approximation for the simplified version without iterations. And Figure 9 shows the solid concentration of clusters predicted by inter-phase balance compared with Harris's correlation.

<sup>C</sup> at type C choking predicted by the

, d<sup>p</sup> ¼ 70 μm, D<sup>t</sup> ¼ 0.1 m,

It can be seen that they are also in agreement with each other pretty well.

Figure 8. F(β) calculated by Eq. (24) compared with constant <sup>n</sup> (FCC-air system, <sup>ρ</sup><sup>s</sup> <sup>¼</sup> 1600 kg/m<sup>3</sup>

Figure 9. Predicted solid concentration of clusters εs,cl compared with Harris's correlation [23].

As a first check, Figure 10 shows the solid flux G<sup>s</sup>

tion is reasonably accepted.

mechanistic model. The model predictions were compared with the experimental data collected by Xu et al. [20]. Noting that some data points of type B choking due to blower and/or standpipe limitation of the system [21] could also be included, the accuracy of model predic-

found in Ref. [10].

u<sup>f</sup> ¼ 6 m/s).

these calculations need iterations.

124 Thermal Power Plants - New Trends and Recent Developments

As mentioned before, the critical requirement for separate-phase-coexistence mode is

$$
\left.\frac{\mathbf{d}m\_s^+}{\mathbf{d}\beta}\right|\_{\beta=0} = \left.\frac{\mathbf{d}m\_s^-}{\mathbf{d}\beta}\right|\_{\beta=0},\tag{12a}
$$

which can be used for the determination of Gsm, the minimum solid flux for fast bed. And we have already

$$m\_s^+ = \rho\_s[\mu\_t F(\beta) - \mu\_t(1-\beta)]\frac{1-\varepsilon\_{\rm ch}}{\varepsilon\_{\rm ch}}\tag{14a}$$

$$
\rho m\_s^- = \rho\_s \beta \mu\_{\rm cl} (1 - \varepsilon\_{\rm cl}).\tag{15a}
$$

The derivation of Eq. (15a) is quite straightforward, that is,

$$\left. \frac{\mathbf{d}m\_s^-}{\mathbf{d}\beta} \right|\_{\beta \to 0} = \rho\_s u\_{\rm cl}|\_{\beta \to 0} (1 - \varepsilon\_{\rm cl})|\_{\beta \to 0}. \tag{26}$$

And, as we have also [11]

$$(1 - \varepsilon\_{\rm cl})|\_{\beta \to 0} = 2(1 - \varepsilon\_{\rm ch,A}) \tag{27}$$

$$\left.u\_{\rm cl}\right|\_{\beta\to 0} = u\_{\rm t} \times \left(\varepsilon\_{\rm cl}|\_{\beta\to 0}\right)^{\rm m} = \mu\_{\rm t}[1 - 2(1 - \varepsilon\_{\rm ch,A})]^{\rm m} \approx u\_{\rm t}.\tag{28}$$

The first statement means that at the very beginning of phase separation, the original formation of cluster is due to a noncollided convergence of two dilute solid pockets. The second statement with equal signs is required for the force balance of gas and particles inside the clusters settled freely, that is, the modified Richardson-Zaki equation should be fitted [11]. Because the solid concentration of the originally formed cluster is very small, the voidage is close to unity, its falling velocity can then be estimated as the particle terminal velocity ut. Putting Eqs. (27) and (28) into Eq. (26), we have approximately

$$\frac{\text{d}m\_{\text{s}}}{\text{d}\beta}|\_{\beta \to 0} \approx 2\rho\_{\text{s}}u\_{\text{t}}(1-\varepsilon\_{\text{ch},\text{A}}).\tag{29}$$

it can be concluded that the coefficient k under the condition of β!0 is approximately one, that

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice

Correspondingly, the minimum solid flux Gsm for fast fluidization can be estimated by the

Figure 12 shows comparison between the values of Gsm determined from 3u<sup>t</sup> and those from uch,C and uch,A becoming equal, for 60-µm FCC particles in a 0.1�m diameter riser. It can be

The minimum solid flux for fast bed is generally more important in theory than in practice, since in most practical circulating fluidized bed systems the solid flux is usually much higher than Gsm. However, there might be a potential practical application for circulating fluidized bed combustion of coal, where particle size distribution is quite wide, but the gas velocity is relatively low. Therefore, it is possible that the gas velocity is higher than the minimum value required for fast fluidization with respect to the average particle size 3ut(dp,ave), but not high enough for some coarse particle fractions. In this case, the value of ut(dp,crit) ¼ uf/3 may be used as a criterion, by which the whole particle size distribution can be divided into two relatively narrow groups, d<sup>p</sup> ≤ dp,crit and d<sup>p</sup> > dp,crit. It is suggested that only the finer particle group with its own average size be calculated with the model, while the coarse particle group be treated as

Figure 12. Gsm determined from 3u<sup>t</sup> compared with uch,C and uch,A becoming equal, for 60-µm FCC particles in a 0.1-m

As we mentioned earlier, Eq. (1) was proposed by Yang to amend the terminal velocity of a

the gas drag at ut' will also conquer the wall friction. Considering the influence of wall friction

<sup>t</sup> [16, 17]. The influence of wall friction on ut'

/(2gDt)]. In a finite diameter riser, besides the particle gravity

ch,<sup>A</sup> ≈ 3ut: ð34Þ

http://dx.doi.org/10.5772/68107

127

u�

≈1. Finally, we have a very simple result, that is,

revised Yang's formula at superficial gas velocity of 3ut.

seen from the figure that the comparison is quite satisfactory.

is, k \*

a stationary fluidized bed.

diameter riser.

appears in the form of √[1þfpu<sup>p</sup>

4.4. Solids holdup in upper dilute region

uniform particle suspension in a CFB riser u<sup>0</sup>

2

as additional particle gravity, the equivalent gravity factor is determined as

To obtain the derivative of m<sup>s</sup> <sup>þ</sup> with respect to β directly is difficult, since both F(β) and εch in Eq. (14a) change with β in very complicated manners. However, the expression for m<sup>s</sup> þ can be linearized, under conditions of very small β (β ≈ 0) as

$$\left.m\_{\rm s}^{+}\right|\_{\beta\simeq0} = (1+k\beta)G\_{\rm s}^{\ast}.\tag{30}$$

Here, k stands for an unknown coefficient to be determined numerically later. Then, the derivative can be written as

$$\left. \frac{\mathrm{d}m\_{\mathrm{s}}^{+}}{\mathrm{d}\beta} \right|\_{\beta=0} = kG\_{\mathrm{s}}^{\*} \quad = k\rho\_{\mathrm{s}}(\mathrm{u\_{\mathrm{ch},\mathrm{A}}} - \mu\_{\mathrm{t}}) \frac{1 - \varepsilon\_{\mathrm{ch},\mathrm{A}}}{\varepsilon\_{\mathrm{ch},\mathrm{A}}} \quad. \tag{31}$$
 
$$\approx k\rho\_{\mathrm{s}}(\mathrm{u\_{\mathrm{ch},\mathrm{A}}} - \mu\_{\mathrm{t}})(1 - \varepsilon\_{\mathrm{ch},\mathrm{A}})$$

Let the terms on the right side of Eqs. (29) and (31) be equal, we have

$$k^\* \rho\_s (\mu\_{\text{ch},\text{A}}^\* - \mu\_\text{t}) \approx 2 \rho\_s \mu\_\text{t}.\tag{32}$$

Here, u� ch;<sup>A</sup> and k \* are uch,A and k evaluated at the minimum solid flux Gsm, respectively. Therefore, we obtain

$$
\mu\_{\rm ch,A}^\* \approx \left(\frac{2}{k^\*} + 1\right) \mu\_{\rm t}.\tag{33}
$$

The values of k can be calculated numerically for different small values of β, according to the definition of k ¼ (m<sup>s</sup> <sup>þ</sup>/G<sup>s</sup> þ�1)/β. Taking 60-µm FCC particles fluidized in a 0.1�m diameter riser as an example, the results obtained are shown in Figure 11. From reasonable extrapolation,

Figure 11. Variation of coefficient k in Eq. (30) with β for 60-µm FCC particles in a 0.1-m diameter riser.

it can be concluded that the coefficient k under the condition of β!0 is approximately one, that is, k \* ≈1. Finally, we have a very simple result, that is,

$$
\mu^\*\_{\text{ch},\text{A}} \approx \mathfrak{Z}u\_{\text{t}}.\tag{34}
$$

Correspondingly, the minimum solid flux Gsm for fast fluidization can be estimated by the revised Yang's formula at superficial gas velocity of 3ut.

Figure 12 shows comparison between the values of Gsm determined from 3u<sup>t</sup> and those from uch,C and uch,A becoming equal, for 60-µm FCC particles in a 0.1�m diameter riser. It can be seen from the figure that the comparison is quite satisfactory.

Figure 12. Gsm determined from 3u<sup>t</sup> compared with uch,C and uch,A becoming equal, for 60-µm FCC particles in a 0.1-m diameter riser.

The minimum solid flux for fast bed is generally more important in theory than in practice, since in most practical circulating fluidized bed systems the solid flux is usually much higher than Gsm. However, there might be a potential practical application for circulating fluidized bed combustion of coal, where particle size distribution is quite wide, but the gas velocity is relatively low. Therefore, it is possible that the gas velocity is higher than the minimum value required for fast fluidization with respect to the average particle size 3ut(dp,ave), but not high enough for some coarse particle fractions. In this case, the value of ut(dp,crit) ¼ uf/3 may be used as a criterion, by which the whole particle size distribution can be divided into two relatively narrow groups, d<sup>p</sup> ≤ dp,crit and d<sup>p</sup> > dp,crit. It is suggested that only the finer particle group with its own average size be calculated with the model, while the coarse particle group be treated as a stationary fluidized bed.

#### 4.4. Solids holdup in upper dilute region

close to unity, its falling velocity can then be estimated as the particle terminal velocity ut.

<sup>β</sup> <sup>≈</sup> <sup>0</sup> ¼ ð1 þ kβÞG�

<sup>s</sup> ¼ kρsðuch;<sup>A</sup> � utÞ

≈ kρsðuch;<sup>A</sup> � utÞð1 � εch;<sup>A</sup>Þ

\* are uch,A and k evaluated at the minimum solid flux Gsm, respectively.

þ�1)/β. Taking 60-µm FCC particles fluidized in a 0.1�m diameter

Here, k stands for an unknown coefficient to be determined numerically later. Then, the

Eq. (14a) change with β in very complicated manners. However, the expression for m<sup>s</sup>

<sup>β</sup>!<sup>0</sup> <sup>≈</sup> <sup>2</sup>ρsutð<sup>1</sup> � <sup>ε</sup>ch;<sup>A</sup>Þ: <sup>ð</sup>29<sup>Þ</sup>

<sup>s</sup> : ð30Þ

: ð31Þ

þ can be

<sup>þ</sup> with respect to β directly is difficult, since both F(β) and εch in

1 � εch;<sup>A</sup> εch;<sup>A</sup>

ch,<sup>A</sup> � utÞ ≈ 2ρsut: ð32Þ

ut: ð33Þ

Putting Eqs. (27) and (28) into Eq. (26), we have approximately

linearized, under conditions of very small β (β ≈ 0) as

126 Thermal Power Plants - New Trends and Recent Developments

dm<sup>þ</sup> s dβ

 β ≈ 0

To obtain the derivative of m<sup>s</sup>

derivative can be written as

ch;<sup>A</sup> and k

Therefore, we obtain

definition of k ¼ (m<sup>s</sup>

<sup>þ</sup>/G<sup>s</sup>

Here, u�

dm � s dβ j

> m<sup>þ</sup> s j

¼ kG�

Let the terms on the right side of Eqs. (29) and (31) be equal, we have

k � ρsðu�

> u� ch,<sup>A</sup> <sup>≈</sup> <sup>2</sup> k � þ1

Figure 11. Variation of coefficient k in Eq. (30) with β for 60-µm FCC particles in a 0.1-m diameter riser.

The values of k can be calculated numerically for different small values of β, according to the

riser as an example, the results obtained are shown in Figure 11. From reasonable extrapolation,

As we mentioned earlier, Eq. (1) was proposed by Yang to amend the terminal velocity of a uniform particle suspension in a CFB riser u<sup>0</sup> <sup>t</sup> [16, 17]. The influence of wall friction on ut' appears in the form of √[1þfpu<sup>p</sup> 2 /(2gDt)]. In a finite diameter riser, besides the particle gravity the gas drag at ut' will also conquer the wall friction. Considering the influence of wall friction as additional particle gravity, the equivalent gravity factor is determined as

$$k\_{\mathbf{w}} = \left(1 + \frac{f\_{\mathbf{p}} u\_{\mathbf{p}}^2}{2gD\_{\mathbf{t}}}\right). \tag{35}$$

The concept of k<sup>w</sup> can also be applied to the case of separate-phase-coexistence if the falling clusters are considered as a moving wall, in which the dilute-phase flows upward. In this case, the slipping velocity of those particles relative to the "cluster wall" will increase from u<sup>p</sup> to

$$
\mu\_{\rm p}^{'} = \mu\_{\rm p} + \beta \mu\_{\rm cl} = \frac{G\_{\rm s}^{+}}{\rho\_{\rm s}(1 - \varepsilon\_{\rm ch})} + \beta \mu\_{\rm cl}.\tag{36}
$$

Meanwhile, the equivalent diameter of the flow path will decrease from D<sup>t</sup> to Dt', which is determined as [10, 11]

$$\frac{1}{D\_{\rm t}^{\prime}} = \frac{1}{D\_{\rm t1}} + \beta \left(\frac{1}{D\_{\rm t2}} - \frac{1}{D\_{\rm t1}}\right) \tag{37}$$

where Dt1 is the equivalent flow-path diameter for very small cluster fraction β, while clusters tend to move close to the wall

$$D\_{\rm t1} = D\_{\rm t} \sqrt{1 - \beta}. \tag{38}$$

� <sup>d</sup><sup>p</sup>

1E-3

0.01

*D*cl(m,cal)

0.1

the particle weight in dilute phase, (1�εch)ρsg · fpup'

ε� <sup>s</sup> ¼ � <sup>d</sup><sup>p</sup> dz

<sup>D</sup>cl (Eqs. (40) or (41)) involves (1�ε-

reason for under-prediction of ε�

) for iteration is suggested as (1�ε-

pressure probe.

predicted as

[23].

(1�ε-

<sup>d</sup><sup>z</sup> ¼ ð<sup>1</sup> � <sup>ε</sup>chÞρs<sup>g</sup> <sup>1</sup> <sup>þ</sup>

Harris This model

> f <sup>p</sup>u<sup>0</sup> p 2

!

where εch is the dilute-phase voidage calculated by this model. In the equation, (1�εch)ρsg is

1E-4 1E-3 0.01 0.1 1E-4

Figure 13. Cluster size predictions from different correlations compared with experimental data collected by Harris et al.

*D*cl(m,exp)

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice

while (1�β) represents the time fraction when the upward dilute phase is sensed by the

From the analysis above, the apparent solids holdup in the upper dilute region can be easily

Here, εs,ch¼ (1�εch) is the solid concentration in upward dilute phase. Since the calculation of

)0 ¼ εs,chþ0.25β. There were quite a lot of theoretical and experimental investigations on the solids holdup of the upper dilute region in the literature. Among them, Ouyang and Potter compiled abundant data available at that time [25], where the solids holdups of the upper dilute regions and the corresponding operating conditions were both reported in detail. Using the operating conditions provided, the solids holdups of the upper dilute regions were calculated with the model and compared with the experimental data in Figure 14. In the figure, symbols of 1–4 indicate the conditions of dilute transportation, traditional fast fluidization, high-density fast fluidization (HDFF) (to be discussed later in Section 5), and pseudo type C choking, respectively. The figure shows that the predictions for traditional fast fluidization, high-density fast fluidization,

tion (denoted as hollow squares in the figure) are all lower than those from experiments. The

=ðρsgÞ ¼ ε<sup>s</sup>;ch 1 þ

) ¼ ε�

and pseudo type C choking are reasonably good. However, predicted ε�

velocity ut. It would often be met for particles with certain size distribution.

2gD<sup>0</sup> t

2

<sup>f</sup> <sup>p</sup>u0<sup>2</sup> p 2gD<sup>0</sup> t

!

ð1 � βÞ, ð42Þ

http://dx.doi.org/10.5772/68107

129

ð1 � βÞ: ð43Þ

<sup>s</sup> for dilute transporta-

<sup>s</sup> , iterations should be applied. The initial value of

<sup>s</sup> in those cases might be under-evaluation of the terminal

/(2gDt') is the equivalent "wall" friction,

And Dt2 is the equivalent flow-path diameter for very big cluster fraction β, while clusters have to distribute uniformly in the riser

$$D\_{t2} = \frac{4F}{U} = D\_t \frac{1-\beta}{1+1.5\beta \frac{D\_t}{D\_{\rm cl}}} \, \tag{39}$$

where F and U are the cross-sectional area and the wetted perimeter of the "tubing" dilute flow, respectively, while Dcl is the diameter of cluster, which can be estimated from the empirical correlation given by Harris and Davidson (Eq. (40)) [23] or the dimensionless form suggested by the authors (Eq. (41)) [10] (see also Figure 13).

$$D\_{\rm cl} = \frac{1 - \overline{\varepsilon}}{40.8 - 94.5(1 - \overline{\varepsilon})} \, [\rm m] \tag{40}$$

$$\frac{D\_{\rm cl}}{D\_{\rm t}} = 27.34(1 - \overline{\varepsilon})^{1.26} \left(\frac{gD\_{\rm t}}{2\mu\_{\rm t}^2} + 1.5\right)^{-1} \tag{41}$$

where ε� is the average voidage of the upper dilute region.

The reason that we could treat the meso-scale drag using the concept of equivalent wall friction with viscous drag only, same as the riser wall, is due to the suppression effect of penetrating particles on the wake separation behind the cluster, which is discussed in detail in Ref. [11].

By using the concept of equivalent gravity, the pressure gradient in the upper dilute region can be expressed as [10]

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice http://dx.doi.org/10.5772/68107 129

k<sup>w</sup> ¼ 1 þ

<sup>p</sup> <sup>¼</sup> <sup>u</sup><sup>p</sup> <sup>þ</sup> <sup>β</sup>ucl <sup>¼</sup> <sup>G</sup><sup>þ</sup>

u 0

128 Thermal Power Plants - New Trends and Recent Developments

1 D0 t ¼ 1 Dt1 þ β

determined as [10, 11]

tend to move close to the wall

to distribute uniformly in the riser

be expressed as [10]

The concept of k<sup>w</sup> can also be applied to the case of separate-phase-coexistence if the falling clusters are considered as a moving wall, in which the dilute-phase flows upward. In this case, the slipping velocity of those particles relative to the "cluster wall" will increase from u<sup>p</sup> to

Meanwhile, the equivalent diameter of the flow path will decrease from D<sup>t</sup> to Dt', which is

where Dt1 is the equivalent flow-path diameter for very small cluster fraction β, while clusters

And Dt2 is the equivalent flow-path diameter for very big cluster fraction β, while clusters have

where F and U are the cross-sectional area and the wetted perimeter of the "tubing" dilute flow, respectively, while Dcl is the diameter of cluster, which can be estimated from the empirical correlation given by Harris and Davidson (Eq. (40)) [23] or the dimensionless form

40:8 � 94:5ð1 � εÞ

The reason that we could treat the meso-scale drag using the concept of equivalent wall friction with viscous drag only, same as the riser wall, is due to the suppression effect of penetrating particles on the wake separation behind the cluster, which is discussed in detail in Ref. [11].

By using the concept of equivalent gravity, the pressure gradient in the upper dilute region can

<sup>1</sup>:<sup>26</sup> gD<sup>t</sup> 2u<sup>2</sup> t þ 1:5 � ��<sup>1</sup>

Dt1 ¼ D<sup>t</sup>

<sup>U</sup> <sup>¼</sup> <sup>D</sup><sup>t</sup>

<sup>D</sup>cl <sup>¼</sup> <sup>1</sup> � <sup>ε</sup>

¼ 27:34ð1 � εÞ

<sup>D</sup>t2 <sup>¼</sup> <sup>4</sup><sup>F</sup>

suggested by the authors (Eq. (41)) [10] (see also Figure 13).

Dcl Dt

where ε� is the average voidage of the upper dilute region.

1 Dt2

� 1 Dt1 � �

ffiffiffiffiffiffiffiffiffiffiffi

1 � β <sup>1</sup> <sup>þ</sup> <sup>1</sup>:5<sup>β</sup> <sup>D</sup><sup>t</sup> Dcl

f <sup>p</sup>u<sup>2</sup> p 2gD<sup>t</sup> !

> s ρsð1 � εchÞ

: ð35Þ

þ βucl: ð36Þ

, ð37Þ

, ð39Þ

½m� ð40Þ

, ð41Þ

<sup>1</sup> � <sup>β</sup> <sup>p</sup> : <sup>ð</sup>38<sup>Þ</sup>

Figure 13. Cluster size predictions from different correlations compared with experimental data collected by Harris et al. [23].

$$-\frac{\mathbf{d}p}{\mathbf{d}z} = (1 - \varepsilon\_{\rm ch})\rho\_{\rm s}\mathbf{g}\left(1 + \frac{f\_{\rm p}u\_{\rm p}'^2}{2gD\_{\rm t}'}\right)(1 - \beta),\tag{42}$$

where εch is the dilute-phase voidage calculated by this model. In the equation, (1�εch)ρsg is the particle weight in dilute phase, (1�εch)ρsg · fpup' 2 /(2gDt') is the equivalent "wall" friction, while (1�β) represents the time fraction when the upward dilute phase is sensed by the pressure probe.

From the analysis above, the apparent solids holdup in the upper dilute region can be easily predicted as

$$\varepsilon\_s^\* = -\frac{\mathrm{d}p}{\mathrm{d}z} / (\rho\_s \mathrm{g}) = \varepsilon\_{s,\mathrm{ch}} \left( 1 + \frac{f\_p u\_p'^2}{2 \mathrm{g} D'\_t} \right) (1 - \beta). \tag{43}$$

Here, εs,ch¼ (1�εch) is the solid concentration in upward dilute phase. Since the calculation of <sup>D</sup>cl (Eqs. (40) or (41)) involves (1�ε- ) ¼ ε� <sup>s</sup> , iterations should be applied. The initial value of (1�ε- ) for iteration is suggested as (1�ε- )0 ¼ εs,chþ0.25β.

There were quite a lot of theoretical and experimental investigations on the solids holdup of the upper dilute region in the literature. Among them, Ouyang and Potter compiled abundant data available at that time [25], where the solids holdups of the upper dilute regions and the corresponding operating conditions were both reported in detail. Using the operating conditions provided, the solids holdups of the upper dilute regions were calculated with the model and compared with the experimental data in Figure 14. In the figure, symbols of 1–4 indicate the conditions of dilute transportation, traditional fast fluidization, high-density fast fluidization (HDFF) (to be discussed later in Section 5), and pseudo type C choking, respectively. The figure shows that the predictions for traditional fast fluidization, high-density fast fluidization, and pseudo type C choking are reasonably good. However, predicted ε� <sup>s</sup> for dilute transportation (denoted as hollow squares in the figure) are all lower than those from experiments. The reason for under-prediction of ε� <sup>s</sup> in those cases might be under-evaluation of the terminal velocity ut. It would often be met for particles with certain size distribution.

Figure 14. Predictions of solids holdup for the upper dilute region ε� <sup>s</sup> compared with experimental data collected by Ouyang and Potter [25].

#### 5. Transition to high-density fast bed

#### 5.1. Force balance of falling clusters

As discussed above, besides its gravity the upward dilute phase should also conquer the equivalent "wall" friction F<sup>w</sup> in a fast-bed riser [10]

$$F\_{\mathbf{w}} = (1 - \varepsilon\_{\rm ch}) \rho\_{\rm s} \mathbf{g} \frac{f\_{\mathbf{p}} \boldsymbol{\mu}\_p^{\prime}}{2 \mathbf{g} \boldsymbol{D}\_{\mathbf{t}}^{\prime}}. \tag{44}$$

its voidage εcl decrease simultaneously, until type C choking happens. This is the case of

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice

On the other hand, if the operating velocity of gas is high enough, the situation could be different.

longer reciprocally supported, since the voidage of clusters is fixed to εcl,min. Therefore, the adjustment for ΔFw¼ Gcl can be performed by reducing the cluster-falling velocity along. Compared with its original value, that is, the one determined by the modified Richardson-Zaki's equation for the voidage εcl ¼ εcl,min, the minus adjustment for falling velocity of clusters can be

cluster gets a tendency of moving upward, but no longer be free settling. This phenomenon might be termed as "secondary fluidization of clusters" (SFC), somewhat similar to the fluidiza-

. To keep the relative velocity of gas and particles inside the cluster unchanged, a

<sup>Þ</sup>GðβÞ � <sup>u</sup>tð<sup>1</sup> � <sup>β</sup>Þ� <sup>1</sup> � <sup>ε</sup>ch

\*\*, the cluster voidage εcl reaches its minimum value εcl,

\*\* can be found in Ref. [10], in which the most

Þð1 � εclÞ: ð49Þ

� β � φ for 0 < u� < upen, ð50Þ

\*\*. And Figure 15(b) shows that the final

εch

<sup>u</sup><sup>f</sup> � <sup>β</sup>u� for <sup>u</sup>� <sup>&</sup>gt; <sup>u</sup>pen: <sup>ð</sup>51<sup>Þ</sup>

<sup>¼</sup> <sup>u</sup>cl-u\* (opposite direction of <sup>u</sup><sup>f</sup> as positive) decreases continuously

\* becomes negative, this means all the clusters will move

\*\*, the adjustments of ucl and εcl are no

http://dx.doi.org/10.5772/68107

131

. As a result, the

\*\*

ð48Þ

traditional fast fluidization, where clusters settle down freely as we discussed above.

small quantity of outer gas has to invade into the cluster at the same velocity u\*

5.2. Secondary fluidization of clusters

When G<sup>s</sup> increases to a certain value of G<sup>s</sup>

Detailed model modifications for G<sup>s</sup> > G<sup>s</sup>

m<sup>þ</sup>

<sup>G</sup>ðβÞ ¼ <sup>1</sup> � <sup>3</sup>ðupen � <sup>u</sup>�Þ

do not change obviously with further increase of G<sup>s</sup> > G<sup>s</sup>

\*

<sup>s</sup> ¼ ρs½ðu<sup>f</sup> � βu�

m �

uf

<sup>s</sup> ¼ ρsβðucl � u�

Here, G(β) stands for the modified effective velocity factor of dilute phase for G<sup>s</sup> > G<sup>s</sup>

� <sup>ε</sup>ch 1 � εch

The model predictions to Issangya's experiment [26] for u<sup>f</sup> ¼ 6 m/s are shown in Figure 15(a). It can be seen from the figure that the model properly predicted the unique feature of high-density fast fluidization, that is, the solids holdups of the upper dilute region and the bottom-dense region

upward. This is the flow regime defined by Grace et al. as "dense suspension up-flow" (DSU) [27]. According to Issangya's experiment [26], the solid-gas mass ratio at the onset of high-density fast fluidization was about 40. And Grace et al. proposed a more general correlation for the

� 1 � εcl εcl

<sup>G</sup>ðβÞ ¼ <sup>u</sup><sup>f</sup> � <sup>β</sup>upen

signed as (-)u\*

tion of packed particles.

important ones are listed below:

5.3. Prediction to transition of HDFF

with an increase of Gs. When u\* >ucl, ucl

onset of dense suspension up-flow as [27]

falling velocity of clusters ucl

min, the minimum voidage of clusters. In the case of G<sup>s</sup> > G<sup>s</sup>

The equivalent friction is caused by both falling clusters and the riser wall. The latter can be estimated from the wall friction at the type A choking Fw0, since falling clusters have not yet formed at that moment

$$F\_{\rm w0} = (1 - \varepsilon\_{\rm ch,A}) \rho\_{\rm s} g \frac{f\_{\rm p} u\_{\rm p}^2}{2gD\_{\rm t}}.\tag{45}$$

Then, the net inter-phase drag between the upward dilute phase and falling clusters can be estimated as

$$
\Delta F\_{\rm w} = F\_{\rm w} - F\_{\rm w0}.\tag{46}
$$

On the other hand, the gravity of falling clusters is easily calculated as

$$\mathbf{G}\_{\rm cl} = \beta (1 - \varepsilon\_{\rm cl}) \rho\_{\rm s} \mathbf{g}. \tag{47}$$

As we mentioned above in Section 4.2.3 (closure to dense phase model), the weight of clusters should always be balanced with the inter-phase drag. By using the initial value of εcl,0 (Eq. (22)), the inter-phase drag ΔF<sup>w</sup> calculated is usually not just equal to the cluster gravity Gcl. Then, sequence adjustments for ucl and/or εcl will be done with iterations until a new balance of ΔFw¼ Gcl is reached. At a relatively low-operating velocity of gas, the adjustment of ucl and εcl is reciprocally supported. With an increase of Gs, the cluster-falling velocity ucl and its voidage εcl decrease simultaneously, until type C choking happens. This is the case of traditional fast fluidization, where clusters settle down freely as we discussed above.

#### 5.2. Secondary fluidization of clusters

5. Transition to high-density fast bed

130 Thermal Power Plants - New Trends and Recent Developments

Figure 14. Predictions of solids holdup for the upper dilute region ε�

equivalent "wall" friction F<sup>w</sup> in a fast-bed riser [10]

As discussed above, besides its gravity the upward dilute phase should also conquer the

The equivalent friction is caused by both falling clusters and the riser wall. The latter can be estimated from the wall friction at the type A choking Fw0, since falling clusters have not yet

Then, the net inter-phase drag between the upward dilute phase and falling clusters can be

As we mentioned above in Section 4.2.3 (closure to dense phase model), the weight of clusters should always be balanced with the inter-phase drag. By using the initial value of εcl,0 (Eq. (22)), the inter-phase drag ΔF<sup>w</sup> calculated is usually not just equal to the cluster gravity Gcl. Then, sequence adjustments for ucl and/or εcl will be done with iterations until a new balance of ΔFw¼ Gcl is reached. At a relatively low-operating velocity of gas, the adjustment of ucl and εcl is reciprocally supported. With an increase of Gs, the cluster-falling velocity ucl and

<sup>f</sup> <sup>p</sup>u0<sup>2</sup> p 2gD<sup>0</sup> t

> f <sup>p</sup>u<sup>2</sup> p 2gD<sup>t</sup>

ΔF<sup>w</sup> ¼ F<sup>w</sup> � Fw0: ð46Þ

Gcl ¼ βð1 � εclÞρsg: ð47Þ

: ð44Þ

<sup>s</sup> compared with experimental data collected by

: ð45Þ

F<sup>w</sup> ¼ ð1 � εchÞρsg

Fw0 ¼ ð1 � εch;<sup>A</sup>Þρsg

On the other hand, the gravity of falling clusters is easily calculated as

5.1. Force balance of falling clusters

formed at that moment

Ouyang and Potter [25].

estimated as

On the other hand, if the operating velocity of gas is high enough, the situation could be different. When G<sup>s</sup> increases to a certain value of G<sup>s</sup> \*\*, the cluster voidage εcl reaches its minimum value εcl, min, the minimum voidage of clusters. In the case of G<sup>s</sup> > G<sup>s</sup> \*\*, the adjustments of ucl and εcl are no longer reciprocally supported, since the voidage of clusters is fixed to εcl,min. Therefore, the adjustment for ΔFw¼ Gcl can be performed by reducing the cluster-falling velocity along. Compared with its original value, that is, the one determined by the modified Richardson-Zaki's equation for the voidage εcl ¼ εcl,min, the minus adjustment for falling velocity of clusters can be signed as (-)u\* . To keep the relative velocity of gas and particles inside the cluster unchanged, a small quantity of outer gas has to invade into the cluster at the same velocity u\* . As a result, the cluster gets a tendency of moving upward, but no longer be free settling. This phenomenon might be termed as "secondary fluidization of clusters" (SFC), somewhat similar to the fluidization of packed particles.

Detailed model modifications for G<sup>s</sup> > G<sup>s</sup> \*\* can be found in Ref. [10], in which the most important ones are listed below:

$$m\_s^+ = \rho\_s[(u\_\text{f} - \beta u^\*)G(\beta) - u\_\text{t}(1-\beta)]\frac{1-\varepsilon\_{\text{ch}}}{\varepsilon\_{\text{ch}}}\tag{48}$$

$$m\_s^{-} = \rho\_s \beta (\mu\_{\rm cl} - \mu^\*) (1 - \varepsilon\_{\rm cl}).\tag{49}$$

Here, G(β) stands for the modified effective velocity factor of dilute phase for G<sup>s</sup> > G<sup>s</sup> \*\*

$$G(\beta) = 1 - \frac{\Im(u\_{\rm pen} - u^\*)}{u\_{\rm f}} \cdot \frac{1 - \varepsilon\_{\rm cl}}{\varepsilon\_{\rm cl}} \cdot \frac{\varepsilon\_{\rm cl}}{1 - \varepsilon\_{\rm cl}} \cdot \beta \cdot \boldsymbol{\wp} \text{ for} \, 0 < u^\* < u\_{\rm pen} \tag{50}$$

$$G(\beta) = \frac{\mu\_{\text{f}} - \beta \mu\_{\text{pen}}}{\mu\_{\text{f}} - \beta \mu^\*} \text{ for } u^\* > u\_{\text{pen}}. \tag{51}$$

#### 5.3. Prediction to transition of HDFF

The model predictions to Issangya's experiment [26] for u<sup>f</sup> ¼ 6 m/s are shown in Figure 15(a). It can be seen from the figure that the model properly predicted the unique feature of high-density fast fluidization, that is, the solids holdups of the upper dilute region and the bottom-dense region do not change obviously with further increase of G<sup>s</sup> > G<sup>s</sup> \*\*. And Figure 15(b) shows that the final falling velocity of clusters ucl \* <sup>¼</sup> <sup>u</sup>cl-u\* (opposite direction of <sup>u</sup><sup>f</sup> as positive) decreases continuously with an increase of Gs. When u\* >ucl, ucl \* becomes negative, this means all the clusters will move upward. This is the flow regime defined by Grace et al. as "dense suspension up-flow" (DSU) [27].

According to Issangya's experiment [26], the solid-gas mass ratio at the onset of high-density fast fluidization was about 40. And Grace et al. proposed a more general correlation for the onset of dense suspension up-flow as [27]

Figure 15. Transition from traditional fast bed to HDFF for an FCC-air system (ρ<sup>s</sup> <sup>¼</sup> 1600 kg/m<sup>3</sup> , dp¼ 70 μm, Dt¼ 0.076 m, uf¼ 6 m/s): (a) solids holdups of upper dilute region and bottom-dense region; (b) falling velocity of clusters.

$$\mathcal{U}\_{\rm DSU} = 0.0113 \mathcal{G}\_{\rm s}^{1.192} \rho\_{\rm g}^{-1.064} [\mu\_{\rm g} \mathbf{g}(\rho\_{\rm s} - \rho\_{\rm g})]^{-0.064} \,. \tag{52}$$

this region. However, it is generally agreed that two different types of axial solids holdup distributions can be found in this region, that is, the S-shaped distribution and the one exponentially decayed with height. According to Bai and Kato's systematical studies, the two different distributions would happen in a riser depending on the circulated solid flux, whether

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice

It is also agreed that fluctuations, with respect to both time and space, in the bottom dense region are very strong. Based on their measurements, Bai et al. [29] described the bottom dense region as "a more radial homogeneous cluster-dominating turbulent pattern," while Brereton and Grace [30] called it as "the cluster-like structure" indicated by its high intermittency index. Very detailed experimental investigations to the bottom region of a CFB riser were also carried out by Zhu and Zhu [31]. From their investigations, the solid concentrations at the intermittent peaks were much higher than those in free-settled clusters. Even more, in the near-wall region,

On the basis of the investigations, the authors of the paper put forward a new hypothetic model called "cluster rebound at the dense bottom" [11]. The model declares that (1) during the time that a cluster falls down and decelerates in the dense bottom, it will still absorb surrounding particles from its wake, but there will be no more particles pouring out from its nose, because of the high-flow resistance there. Thus, the solid concentration inside the cluster

mixing and interaction with the upward-moving gas-solid flow in the bottom, the much denser cluster will then be "bounced back" and leave the bottom at its original falling velocity |ucl| yet in the opposite direction; (3) just because of this unbalanced cluster rebound, the gas flow will gain an additional carrying capacity in this region at the basis of a uniformly

<sup>s</sup> <sup>þ</sup> βρsuclðε<sup>d</sup>

where ρ<sup>s</sup> is the particle density. From this equation, the solid concentration in rebounding

by Leva [15]; the total solid flux reaches a critical value, the saturated solid flux with once-

<sup>s</sup> <sup>þ</sup> βρsuclðεmax

through the bottom directly. Yet, some of the particles will stay longer in this region, causing built-up of a higher dense bottom; (6) therefore, the saturated solid flux with once-through

distributions of axial solids holdup in the bottom region, thus it is comparable to GBai

<sup>s</sup>;cl can be determined; (4) when the solid concentration in the rebounding clusters

<sup>s</sup> , the gas flow will have no more ability to carry over all solid particles passing

<sup>s</sup> (in their paper

133

http://dx.doi.org/10.5772/68107

<sup>s</sup>;cl is reached; (2) thanks to very strong

. Then, we obtain

<sup>s</sup>;cl � ε<sup>s</sup>;clÞ, ð53Þ

<sup>s</sup>;cl � ε<sup>s</sup>;clÞ; ð54Þ

<sup>s</sup> in Ref. [28].

\*

<sup>s</sup>;cl ¼ 0:45, the average value of the loosest parked beds suggested

<sup>s</sup> can be used as a criterion to distinguish the two different

greater or smaller than the so-called "saturated carrying capacity of gas" GBai

noted as G<sup>s</sup>

clusters ε<sup>d</sup>

(5) above Grb

reaches its maximum value εmax

cluster rebound at the bottom Grb

through cluster rebound at the bed bottom

\* ) [28].

the values at some plateaus reached around 0.45.

will increase continuously until a determinate value of ε<sup>d</sup>

saturated suspension, that is, the solid flux at type A choking G<sup>s</sup>

Grb <sup>s</sup> ¼ G�

G<sup>s</sup> ¼ G�

The model predictions to the onsets of high-density fast bed and dense suspension up-flow for FCC and sand particles fluidized by ambient air are compared with those given by Issangya et al. [26] and Grace et al. [27] in Figure 16, respectively. The results are also reasonably good.

Figure 16. Comparisons of onsets of HDFF and DSU predicted from different models or criteria: (a) FCC-air, <sup>ρ</sup>s<sup>¼</sup> 1600 kg/m3 , <sup>d</sup>p<sup>¼</sup> <sup>70</sup> <sup>μ</sup>m, <sup>D</sup>t<sup>¼</sup> 0.076 m; (b) sand-air, <sup>ρ</sup>s<sup>¼</sup> 2500 kg/m3 , dp¼ 100 μm, Dt¼ 0.1 m.

#### 6. Submodels for bottom-dense region

#### 6.1. Cluster rebound at dense bottom

Unlike the upper dilute region, the dense bottom region of a fast bed was less investigated in the past. And significant controversies appeared in the literature on the actual mechanism of this region. However, it is generally agreed that two different types of axial solids holdup distributions can be found in this region, that is, the S-shaped distribution and the one exponentially decayed with height. According to Bai and Kato's systematical studies, the two different distributions would happen in a riser depending on the circulated solid flux, whether greater or smaller than the so-called "saturated carrying capacity of gas" GBai <sup>s</sup> (in their paper noted as G<sup>s</sup> \* ) [28].

It is also agreed that fluctuations, with respect to both time and space, in the bottom dense region are very strong. Based on their measurements, Bai et al. [29] described the bottom dense region as "a more radial homogeneous cluster-dominating turbulent pattern," while Brereton and Grace [30] called it as "the cluster-like structure" indicated by its high intermittency index. Very detailed experimental investigations to the bottom region of a CFB riser were also carried out by Zhu and Zhu [31]. From their investigations, the solid concentrations at the intermittent peaks were much higher than those in free-settled clusters. Even more, in the near-wall region, the values at some plateaus reached around 0.45.

On the basis of the investigations, the authors of the paper put forward a new hypothetic model called "cluster rebound at the dense bottom" [11]. The model declares that (1) during the time that a cluster falls down and decelerates in the dense bottom, it will still absorb surrounding particles from its wake, but there will be no more particles pouring out from its nose, because of the high-flow resistance there. Thus, the solid concentration inside the cluster will increase continuously until a determinate value of ε<sup>d</sup> <sup>s</sup>;cl is reached; (2) thanks to very strong mixing and interaction with the upward-moving gas-solid flow in the bottom, the much denser cluster will then be "bounced back" and leave the bottom at its original falling velocity |ucl| yet in the opposite direction; (3) just because of this unbalanced cluster rebound, the gas flow will gain an additional carrying capacity in this region at the basis of a uniformly saturated suspension, that is, the solid flux at type A choking G<sup>s</sup> \* . Then, we obtain

<sup>U</sup>DSU <sup>¼</sup> <sup>0</sup>:0113G<sup>1</sup>:<sup>192</sup>

132 Thermal Power Plants - New Trends and Recent Developments

Figure 15. Transition from traditional fast bed to HDFF for an FCC-air system (ρ<sup>s</sup> <sup>¼</sup> 1600 kg/m<sup>3</sup>

6. Submodels for bottom-dense region

6.1. Cluster rebound at dense bottom

<sup>d</sup>p<sup>¼</sup> <sup>70</sup> <sup>μ</sup>m, <sup>D</sup>t<sup>¼</sup> 0.076 m; (b) sand-air, <sup>ρ</sup>s<sup>¼</sup> 2500 kg/m3

<sup>s</sup> ρ<sup>g</sup>

uf¼ 6 m/s): (a) solids holdups of upper dilute region and bottom-dense region; (b) falling velocity of clusters.

The model predictions to the onsets of high-density fast bed and dense suspension up-flow for FCC and sand particles fluidized by ambient air are compared with those given by Issangya et al. [26] and Grace et al. [27] in Figure 16, respectively. The results are also reasonably good.

Unlike the upper dilute region, the dense bottom region of a fast bed was less investigated in the past. And significant controversies appeared in the literature on the actual mechanism of

Figure 16. Comparisons of onsets of HDFF and DSU predicted from different models or criteria: (a) FCC-air, <sup>ρ</sup>s<sup>¼</sup> 1600 kg/m3

, dp¼ 100 μm, Dt¼ 0.1 m.

�1:<sup>064</sup>½μggðρ<sup>s</sup> � <sup>ρ</sup>g��<sup>0</sup>:<sup>064</sup>: <sup>ð</sup>52<sup>Þ</sup>

, dp¼ 70 μm, Dt¼ 0.076 m,

,

$$\mathbf{G}\_{\rm s} = \mathbf{G}\_{\rm s}^{\*} + \beta \rho\_{\rm s} \mu\_{\rm cl} (\varepsilon\_{\rm s,cl}^{\rm d} - \varepsilon\_{\rm s,cl}) \,\tag{53}$$

where ρ<sup>s</sup> is the particle density. From this equation, the solid concentration in rebounding clusters ε<sup>d</sup> <sup>s</sup>;cl can be determined; (4) when the solid concentration in the rebounding clusters reaches its maximum value εmax <sup>s</sup>;cl ¼ 0:45, the average value of the loosest parked beds suggested by Leva [15]; the total solid flux reaches a critical value, the saturated solid flux with oncethrough cluster rebound at the bed bottom

$$\mathbf{G}\_{\rm s}^{\rm rb} = \mathbf{G}\_{\rm s}^{\*} + \beta \rho\_{\rm s} \mu\_{\rm cl} (\varepsilon\_{\rm s, cl}^{\rm max} - \varepsilon\_{\rm s, cl});\tag{54}$$

(5) above Grb <sup>s</sup> , the gas flow will have no more ability to carry over all solid particles passing through the bottom directly. Yet, some of the particles will stay longer in this region, causing built-up of a higher dense bottom; (6) therefore, the saturated solid flux with once-through cluster rebound at the bottom Grb <sup>s</sup> can be used as a criterion to distinguish the two different distributions of axial solids holdup in the bottom region, thus it is comparable to GBai <sup>s</sup> in Ref. [28].

#### 6.2. Average solids holdup in dense bottom

According to the hypotheses proposed above, the modeling method for average solids holdup in the dense bottom of the bed was established as follows [11]:

1. Calculate the solid concentration in rebounding clusters ε<sup>d</sup> <sup>s</sup>, cl and the corresponding solids holdup in the dense bottom ε� <sup>s</sup>,d, as

$$
\varepsilon\_{\rm s,cl}^{\rm d} = \varepsilon\_{\rm s,cl} + \frac{G\_{\rm s} - G\_{\rm s}^\*}{\beta \rho\_{\rm s} \mu\_{\rm cl}} \tag{55}
$$

$$
\hbar \overline{\varepsilon}\_{\rm s,d} = \beta \varepsilon\_{\rm s,cl}^{\rm d} + (1 - \beta) \varepsilon\_{\rm s,cb} \tag{56}
$$

2. Calculate the solids holdup in the dense bottom εs,d, corresponding to the maximum solid concentration in rebounding clusters εmax <sup>s</sup>;cl ¼ 0:45:

$$
\varepsilon\_{\rm s,d} = \beta \varepsilon\_{\rm s,cl}^{\rm max} + (1 - \beta) \varepsilon\_{\rm s,ch} \tag{57}
$$

6.3. Height of built-up section in dense bottom

data and correlations [28].

Grb

The mechanism of how a vertical section with nearly constant solids holdup is built-up in the dense bottom has seldom been investigated. Li [33] ever tried to explain and model this process by a dynamic balance of the elutriated solid particles from the bottom region with the particles accumulated in it, which were in turn proportional to the "height of the built-up section," or simply "the dense bottom height". Using this assumption, a semi-empirical corre-

Figure 17. Predicted variation of bottom solids holdup with solid flux, and compared with Bai and Kato's experimental

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice

The above-depicted mechanism is simple enough and looks reasonable. However, from our

<sup>s</sup> , but not the total one Gs. Using the data collected by Ouyang and Potter [25], the rate

ðu<sup>f</sup> � νsÞ 2

" #<sup>0</sup>:<sup>471</sup>

dpg

rb), the extra portion beyond

http://dx.doi.org/10.5772/68107

135

: ð58Þ

lation between the solid flux G<sup>s</sup> and the dense bottom height h was established [33].

ρ<sup>s</sup> � ρ<sup>g</sup>

Figure 18. Multiregression result for dense bottom height h using the data collected by Ouyang and Potter [25].

!<sup>1</sup>:<sup>581</sup>

understanding, the solid flux to be correlated ought to be (Gs-G<sup>s</sup>

constant for elutriation was then reregressed [11], shown as in Figure 18.

<sup>k</sup><sup>0</sup> <sup>¼</sup> <sup>102</sup>:<sup>366</sup> <sup>ρ</sup><sup>g</sup>


The postulated behaviors of particle movement in the bottom region, that is, "once-through" or "stay longer," are also well consistent with the experimental visualizations using PEPT imaging in Ref. [32]. To distinguish the two different cases easily, we will call the case of Sshaped solids holdup distribution as a "classical" fast bed (G<sup>s</sup> > G<sup>s</sup> rb), while call the case of exponentially decayed solids holdup as a "premature" fast bed (G<sup>s</sup> ≤ G<sup>s</sup> rb). Both the classical and premature cases are "traditional" fast beds in comparison with the "high-density" fast bed characterized in Ref. [26].

Based on the above analysis, increasing solid flux G<sup>s</sup> continuously at a constant gas velocity will lead to transitions from dilute transportation, through the premature fast bed, to the classical fast bed. Taking Bai and Kato's experiment [28] as an example, Figure 17 gives the predicted variation of bottom solids holdup with solid flux, showing clearly these kinds of transition. The bottom solids holdup calculated by Bai and Kato's empirical correlations and the so-called "saturated carrying capacity of gas" GBai <sup>s</sup> [28] are also given in the figure. From the figure, it is clear that the εs,d–G<sup>s</sup> curves are deflected indeed near Grb <sup>s</sup> or GBai <sup>s</sup> , but the curves are not flattened for G<sup>s</sup> > G<sup>s</sup> rb or GBai <sup>s</sup> . The curves will be flattened at a much higher solid flux G<sup>s</sup> \*\* with the onset of high-density fast bed, as explained before in Section 5.3. To avoid confusing this deflection with type A choking, it is better to call Grb <sup>s</sup> in its full termination "saturated solid flux with once-through cluster rebound at the bottom" or simply "saturated solid flux with cluster rebound," while calling "saturation carrying capacity" only for type A choking.

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice http://dx.doi.org/10.5772/68107 135

Figure 17. Predicted variation of bottom solids holdup with solid flux, and compared with Bai and Kato's experimental data and correlations [28].

#### 6.3. Height of built-up section in dense bottom

6.2. Average solids holdup in dense bottom

134 Thermal Power Plants - New Trends and Recent Developments

holdup in the dense bottom ε�

concentration in rebounding clusters εmax

average solids holdup for the dense bottom;

once-through cluster rebound at the bottom.

the so-called "saturated carrying capacity of gas" GBai

rb or GBai

this deflection with type A choking, it is better to call Grb

shaped solids holdup distribution as a "classical" fast bed (G<sup>s</sup> > G<sup>s</sup>

figure, it is clear that the εs,d–G<sup>s</sup> curves are deflected indeed near Grb

exponentially decayed solids holdup as a "premature" fast bed (G<sup>s</sup> ≤ G<sup>s</sup>

get the curves of ε�

characterized in Ref. [26].

not flattened for G<sup>s</sup> > G<sup>s</sup>

in the dense bottom of the bed was established as follows [11]: 1. Calculate the solid concentration in rebounding clusters ε<sup>d</sup>

<sup>s</sup>,d, as

εd

<sup>ε</sup><sup>s</sup>;<sup>d</sup> <sup>¼</sup> βε<sup>d</sup>

<sup>ε</sup><sup>s</sup>;<sup>d</sup> <sup>¼</sup> βεmax

<sup>s</sup>;cl ¼ ε<sup>s</sup>;cl þ

2. Calculate the solids holdup in the dense bottom εs,d, corresponding to the maximum solid

3. Compare the values calculated from Eqs. (56) and (57) and take the smaller one as the

4. At a given superficial gas velocity, repeat steps 2 and 3 with an increase of solid flux, and

The postulated behaviors of particle movement in the bottom region, that is, "once-through" or "stay longer," are also well consistent with the experimental visualizations using PEPT imaging in Ref. [32]. To distinguish the two different cases easily, we will call the case of S-

and premature cases are "traditional" fast beds in comparison with the "high-density" fast bed

Based on the above analysis, increasing solid flux G<sup>s</sup> continuously at a constant gas velocity will lead to transitions from dilute transportation, through the premature fast bed, to the classical fast bed. Taking Bai and Kato's experiment [28] as an example, Figure 17 gives the predicted variation of bottom solids holdup with solid flux, showing clearly these kinds of transition. The bottom solids holdup calculated by Bai and Kato's empirical correlations and

with the onset of high-density fast bed, as explained before in Section 5.3. To avoid confusing

flux with once-through cluster rebound at the bottom" or simply "saturated solid flux with

cluster rebound," while calling "saturation carrying capacity" only for type A choking.

<sup>s</sup>,<sup>d</sup> and εs,d crossed, which determines G<sup>s</sup>

<sup>s</sup>;cl ¼ 0:45:

According to the hypotheses proposed above, the modeling method for average solids holdup

G<sup>s</sup> � G� s βρsucl

<sup>s</sup>, cl and the corresponding solids

rb, the saturated solid flux with

rb), while call the case of

<sup>s</sup> [28] are also given in the figure. From the

<sup>s</sup> in its full termination "saturated solid

<sup>s</sup> or GBai

<sup>s</sup> . The curves will be flattened at a much higher solid flux G<sup>s</sup>

rb). Both the classical

<sup>s</sup> , but the curves are

\*\*

<sup>s</sup>;cl þ ð1 � βÞε<sup>s</sup>;ch; ð56Þ

<sup>s</sup>;cl þ ð1 � βÞε<sup>s</sup>;ch; ð57Þ

ð55Þ

The mechanism of how a vertical section with nearly constant solids holdup is built-up in the dense bottom has seldom been investigated. Li [33] ever tried to explain and model this process by a dynamic balance of the elutriated solid particles from the bottom region with the particles accumulated in it, which were in turn proportional to the "height of the built-up section," or simply "the dense bottom height". Using this assumption, a semi-empirical correlation between the solid flux G<sup>s</sup> and the dense bottom height h was established [33].

The above-depicted mechanism is simple enough and looks reasonable. However, from our understanding, the solid flux to be correlated ought to be (Gs-G<sup>s</sup> rb), the extra portion beyond Grb <sup>s</sup> , but not the total one Gs. Using the data collected by Ouyang and Potter [25], the rate constant for elutriation was then reregressed [11], shown as in Figure 18.

$$k'=10^{2.366} \left(\frac{\rho\_{\rm g}}{\rho\_{\rm s}-\rho\_{\rm g}}\right)^{1.581} \left[\frac{\left(\mu\_{\rm f}-\nu\_{\rm s}\right)^{2}}{d\_{\rm pg}}\right]^{0.471}.\tag{58}$$

Figure 18. Multiregression result for dense bottom height h using the data collected by Ouyang and Potter [25].

And finally, the height of the built-up dense bottom can be calculated as

$$h = 10^{-2.366} \left(\frac{\rho\_s - \rho\_g}{\rho\_g}\right)^{1.581} \left[\frac{d\_\text{pg}}{(u\_\text{f} - v\_\text{s})^2}\right]^{0.471} \times \frac{G\_\text{s} - G\_\text{s}^\text{rb}}{\rho\_s \varepsilon\_{\text{s,d}}},\tag{59}$$

<sup>h</sup><sup>t</sup> <sup>¼</sup> <sup>M</sup>out � <sup>M</sup>in ρsgε<sup>s</sup>;<sup>t</sup>ð1 � ηÞ

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice

Putting the expressions of Min and Mout for acceleration/transition zones, respectively, in, we

<sup>s</sup> � GsV<sup>d</sup>

where δ stands for the coefficient of the converse momentum flux caused by the recycled solid

<sup>s</sup> <sup>¼</sup> <sup>m</sup><sup>þ</sup>

V�

Then, the equivalent momentum balance heights based on the average solids holdup of dense

<sup>s</sup> � GsV<sup>d</sup>

Adding the two equivalent momentum balance heights for the acceleration and transition

As depicted in the above section, the axial solids holdup distribution exponentially decayed with height in a premature fast bed can be considered as a special case of a classical fast bed with null built-up section. Therefore, it is possible that the functional description of the acceleration/transition zones for both classical fast bed and premature fast bed can be unified to a single one. Actually, this attempt can be easily realized by the ordinate transfer from z to (z-h) for the transition zone of a classical fast bed, where h stands for the height of built-up section in the bottom. Thus, the commonly accepted exponential decay of solids holdup with bed height for the premature fast bed can be used for the unified functional description of the

s ρsð1 � βÞε<sup>s</sup>;ch

<sup>h</sup>t1 <sup>¼</sup> <sup>m</sup><sup>þ</sup>

<sup>H</sup>t1 <sup>¼</sup> <sup>m</sup><sup>þ</sup>

<sup>s</sup> V<sup>þ</sup> <sup>s</sup> þ m� <sup>s</sup> V�

zones together, we get the total momentum balance height as

7.2. Functional description of acceleration/transition zones

<sup>H</sup>t2 <sup>¼</sup> <sup>G</sup>sVdð<sup>1</sup> <sup>þ</sup> <sup>δ</sup><sup>Þ</sup>

bottom εs,d can be calculated as

acceleration/transition zones as

<sup>s</sup> V<sup>þ</sup> <sup>s</sup> þ m� <sup>s</sup> V�

particles moving downwards. And velocities in the equations are

<sup>h</sup>t2 <sup>¼</sup> <sup>G</sup>sVdð<sup>1</sup> <sup>þ</sup> <sup>δ</sup><sup>Þ</sup>

V<sup>þ</sup>

have

: ð62Þ

http://dx.doi.org/10.5772/68107

ð65Þ

137

<sup>ρ</sup>sgε<sup>s</sup>;t1ð<sup>1</sup> � <sup>η</sup><sup>Þ</sup> for transition zone, <sup>ð</sup>63<sup>Þ</sup>

<sup>ρ</sup>sgε<sup>s</sup>;t2ð<sup>1</sup> � <sup>η</sup><sup>Þ</sup> for acceleration zone, <sup>ð</sup>64<sup>Þ</sup>

<sup>s</sup> ¼ ucl ð66Þ

V<sup>d</sup> ¼ ν<sup>s</sup> ¼ Gs=ðρsε<sup>s</sup>;<sup>d</sup>Þ: ð67Þ

<sup>ρ</sup>sgε<sup>s</sup>;<sup>d</sup>ð<sup>1</sup> � <sup>η</sup><sup>Þ</sup> for transition zone, <sup>ð</sup>68<sup>Þ</sup>

<sup>ρ</sup>sgε<sup>s</sup>;<sup>d</sup>ð<sup>1</sup> � <sup>η</sup><sup>Þ</sup> for acceleration zone: <sup>ð</sup>69<sup>Þ</sup>

H<sup>t</sup> ¼ Ht1 þ Ht2: ð70Þ

where u<sup>f</sup> stands for the superficial gas velocity, ρ<sup>g</sup> for gas density, while vs¼ Gs/(ρsεs,d) is the nominal particle velocity in the dense bottom.

## 7. Axial solids holdup distribution

#### 7.1. Momentum balance for acceleration/transition zones

In addition to the fully developed upper dilute region described in Section 4.4 and the built-up dense bottom region we have just discussed, there are also two less important zones in a classical fast bed. They are a transition zone between the two regions and an acceleration zone prior to the built-up dense section. In the acceleration zone, the particles recycled from the standpipe should be accelerated from their original downward movement to a finite upward velocity. It was assumed that in a premature fast bed, the axial solids holdup distribution decayed exponentially with height was a direct conjunction of the two zones with null builtup section in between [11].

As selecting an adequate drag coefficient is very difficult for those complicated gas-solid flows, the detailed flow mapping from commercial CFD software is usually less reliable. However, the most important principle involved in the software, that is, the momentum conservation, can still be applied when those integrated zones are considered. Compared with the solid phase, the momentum of gas and the wall friction can be neglected; the conservation of momentum between the inlet and the outlet cross sections is then written as

$$M\_{\rm out} - M\_{\rm in} = \Delta P - \mathcal{G}\_{\prime} \tag{60}$$

where Mout and Min are the solid momentum fluxes at the outlet and inlet cross sections, respectively, while ΔP stands for the pressure difference of the two sections, and G for the solid gravity per unit area within the zone.

The apparent solids holdup ε� <sup>s</sup>,<sup>t</sup> averaged in the zone can be used to calculate the pressure difference between the lower and the upper cross sections of the acceleration/transition zones, that is, ΔP ¼ htρsgε� <sup>s</sup>,t, where h<sup>t</sup> is the height of the zone. And the real solid concentration ε's,t averaged can be used to calculate the solid gravity per unit area within the zone, that is, G ¼ htρsgε<sup>0</sup> <sup>s</sup>,t. It is supposed that ε<sup>0</sup> <sup>s</sup>,<sup>t</sup> ¼ ηε� <sup>s</sup>,t, where η can be considered as the contribution factor of gravity for the pressure drop. Then, we obtain

$$M\_{\rm out} - M\_{\rm in} = h\_{\rm t} \rho\_{\rm s} \mathbf{g}(\overline{\varepsilon}\_{\rm s,t} - \varepsilon\_{\rm s,t}') = h\_{\rm t} \rho\_{\rm s} \overline{\mathbf{g}} \overline{\varepsilon}\_{\rm s,t} (1 - \eta). \tag{61}$$

Therefore, the height of acceleration/transition zones can be calculated from the momentum flux deference between the inlet and the outlet, and the average apparent solids holdup ε� <sup>s</sup>,<sup>t</sup> as

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice http://dx.doi.org/10.5772/68107 137

$$h\_{\rm t} = \frac{M\_{\rm out} - M\_{\rm in}}{\rho\_s g \overline{\varepsilon}\_{s,t} (1 - \eta)}.\tag{62}$$

Putting the expressions of Min and Mout for acceleration/transition zones, respectively, in, we have

And finally, the height of the built-up dense bottom can be calculated as

ρg

!<sup>1</sup>:<sup>581</sup>

dpg ðu<sup>f</sup> � vsÞ 2 " #<sup>0</sup>:<sup>471</sup>

where u<sup>f</sup> stands for the superficial gas velocity, ρ<sup>g</sup> for gas density, while vs¼ Gs/(ρsεs,d) is the

In addition to the fully developed upper dilute region described in Section 4.4 and the built-up dense bottom region we have just discussed, there are also two less important zones in a classical fast bed. They are a transition zone between the two regions and an acceleration zone prior to the built-up dense section. In the acceleration zone, the particles recycled from the standpipe should be accelerated from their original downward movement to a finite upward velocity. It was assumed that in a premature fast bed, the axial solids holdup distribution decayed exponentially with height was a direct conjunction of the two zones with null built-

As selecting an adequate drag coefficient is very difficult for those complicated gas-solid flows, the detailed flow mapping from commercial CFD software is usually less reliable. However, the most important principle involved in the software, that is, the momentum conservation, can still be applied when those integrated zones are considered. Compared with the solid phase, the momentum of gas and the wall friction can be neglected; the conservation of

where Mout and Min are the solid momentum fluxes at the outlet and inlet cross sections, respectively, while ΔP stands for the pressure difference of the two sections, and G for the solid

difference between the lower and the upper cross sections of the acceleration/transition zones,

averaged can be used to calculate the solid gravity per unit area within the zone, that is,

Therefore, the height of acceleration/transition zones can be calculated from the momentum flux deference between the inlet and the outlet, and the average apparent solids holdup ε�

<sup>s</sup>,<sup>t</sup> ¼ ηε�

Mout � Min ¼ htρsgðε<sup>s</sup>;<sup>t</sup> � ε<sup>0</sup>

momentum between the inlet and the outlet cross sections is then written as

·

Mout � Min ¼ ΔP � G, ð60Þ

<sup>s</sup>,<sup>t</sup> averaged in the zone can be used to calculate the pressure

<sup>s</sup>,t, where η can be considered as the contribution

<sup>s</sup>;<sup>t</sup>Þ ¼ htρsgε<sup>s</sup>;<sup>t</sup>ð1 � ηÞ: ð61Þ

<sup>s</sup>,<sup>t</sup> as

<sup>s</sup>,t, where h<sup>t</sup> is the height of the zone. And the real solid concentration ε's,t

<sup>G</sup><sup>s</sup> � <sup>G</sup>rb s ρsε<sup>s</sup>;<sup>d</sup>

, ð59Þ

<sup>h</sup> <sup>¼</sup> <sup>10</sup>�2:<sup>366</sup> <sup>ρ</sup><sup>s</sup> � <sup>ρ</sup><sup>g</sup>

7.1. Momentum balance for acceleration/transition zones

nominal particle velocity in the dense bottom.

136 Thermal Power Plants - New Trends and Recent Developments

7. Axial solids holdup distribution

up section in between [11].

gravity per unit area within the zone.

<sup>s</sup>,t. It is supposed that ε<sup>0</sup>

factor of gravity for the pressure drop. Then, we obtain

The apparent solids holdup ε�

that is, ΔP ¼ htρsgε�

G ¼ htρsgε<sup>0</sup>

$$h\_{t1} = \frac{m\_s^+ V\_s^+ + m\_s^- V\_s^- - G\_s V\_d}{\rho\_s g \overline{\varepsilon}\_{s,t1} (1 - \eta)}\text{ for transition zone,}\tag{63}$$

$$h\_{t2} = \frac{G\_s V\_d (1 + \delta)}{\rho\_s g \overline{\varepsilon}\_{s,t2} (1 - \eta)} \text{ for acceleration zone,} \tag{64}$$

where δ stands for the coefficient of the converse momentum flux caused by the recycled solid particles moving downwards. And velocities in the equations are

$$V\_s^+ = \frac{m\_s^+}{\rho\_s(1-\beta)\varepsilon\_{s,\text{ch}}}\tag{65}$$

$$V\_s^- = \mu\_{\rm cl} \tag{66}$$

$$V\_{\mathbf{d}} = \nu\_{\mathbf{s}} = \mathbf{G}\_{\mathbf{s}} / (\rho\_{\mathbf{s}} \varepsilon\_{\mathbf{s}, \mathbf{d}}). \tag{67}$$

Then, the equivalent momentum balance heights based on the average solids holdup of dense bottom εs,d can be calculated as

$$H\_{t1} = \frac{m\_s^+ V\_s^+ + m\_s^- V\_s^- - G\_s V\_d}{\rho\_s g \varepsilon\_{s,d} (1 - \eta)}\text{ for transition zone,}\tag{68}$$

$$H\_{\rm t2} = \frac{G\_{\rm s}V\_{\rm d}(1+\delta)}{\rho\_{\rm s}g\varepsilon\_{\rm s,d}(1-\eta)}\text{ for acceleration zone.}\tag{69}$$

Adding the two equivalent momentum balance heights for the acceleration and transition zones together, we get the total momentum balance height as

$$H\_{\rm t} = H\_{\rm t1} + H\_{\rm t2}.\tag{70}$$

#### 7.2. Functional description of acceleration/transition zones

As depicted in the above section, the axial solids holdup distribution exponentially decayed with height in a premature fast bed can be considered as a special case of a classical fast bed with null built-up section. Therefore, it is possible that the functional description of the acceleration/transition zones for both classical fast bed and premature fast bed can be unified to a single one. Actually, this attempt can be easily realized by the ordinate transfer from z to (z-h) for the transition zone of a classical fast bed, where h stands for the height of built-up section in the bottom. Thus, the commonly accepted exponential decay of solids holdup with bed height for the premature fast bed can be used for the unified functional description of the acceleration/transition zones as

$$
\varepsilon\_s = \varepsilon\_{s0} e^{-\gamma z},
\tag{71}
$$

riser of 0.076-m inner diameter. The operating conditions varied from dilute transportation, through the premature fast bed, the classical fast bed, until the high-density fast bed [26].

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice

The coefficient of converse momentum flux δ ¼ 2, for the recycled particles, was applied in the calculation. As an example, Figure 20 shows the comparisons of model predictions and the experimental data [26] for a constant gas velocity uf¼ 4 m/s yet different solid fluxes of 18, 44,

Based on the downward-penetrating particle flow through clusters and the analogy between a falling cluster and a rising bubble identified by the authors, a "type-A-choking-oriented separate-phase-coexistence model" for the upper dilute region of fast beds was established first. The model was then integrated with the sub-models of "cluster rebound at the dense bottom," "the momentum flux balances for acceleration and transition zones" in the lower and middle parts of the bed. The integrated model predicted successfully the axial solids holdup distributions of literature data under extremely wide operation conditions covering dilute-phase transportation, the premature fast bed, the classical fast bed, and the high-density fast bed.

Figure 20. Axial solids holdup distributions from present model and Issangya's data, uf¼ 4 m/s [26].

To make the model system for fast fluidization have even sounder theoretical basis, more fundamental studies are expected in the future, especially those to explain further the reasons for "the four simplest integer numbers" as: "0"—in the regime of traditional fast fluidization, clusters settle down freely without outer-gas invasion; "1"—at type A choking, the terminal velocity of a particle suspension in a finite diameter riser is just equal to the terminal velocity of a single particle in an infinite fluid; "2"—at the very beginning of particle aggregation, the solid concentration in clusters is twice that in the dilute phase; "3"—the minimum solid circulating flux for fast fluidization corresponds to the type A chocking at the gas velocity of

s), respectively. It can be seen from the figure that the results are

http://dx.doi.org/10.5772/68107

139

68, 138, 200, and 240 kg/(m2

8. Conclusions and outlook

triple particle terminal velocity.

somewhat reasonable.

where εs0 stands for the solids holdup just above the air distributor of the riser, and γ for the decay constant.

Since the equivalent momentum balance heights of acceleration/transition zones have been determined above, we can simply transfer the values to the actual solids holdup distributions, in accordance with their equal impacts on the total bed pressure drop.

By some mathematical deduction, the final expressions for εs0 and γ were obtained as [11]

$$
\varepsilon\_{s0} = \frac{\varepsilon\_{s,d} - m' \varepsilon\_s^\*}{1 - m'} \tag{72}
$$

$$\gamma = \frac{\varepsilon\_{\rm s0} - \varepsilon\_{\rm s,d}}{\varepsilon\_{\rm s,d} H\_{\rm t2}} = \frac{1}{H\_{\rm t2}} \left( \frac{\varepsilon\_{\rm s0}}{\varepsilon\_{\rm s,d}} - 1 \right),\tag{73}$$

where m'¼ Ht2/Ht, and ε� <sup>s</sup> stands for the solids holdup of the upper dilute region.

Under the same conditions of experiments in Ref. [25], the heights of transition zones were calculated with δ ¼ 0 assumed. Then, a proportionality coefficient (1�η) ¼ 0.212 was determined from comparing those results with experimental data [25], shown as in Figure 19. From that, η ¼ 0.788 was obtained, which meant that the particle gravity contributed roughly fourfifths of the total pressure drop for the zone. Now, the method to predict the axial solids holdup distribution of fast beds has been established completely.

Figure 19. Comparison of the predicted heights of transition zones and the experimental data collected by Ouyang and Potter [25].

#### 7.3. Prediction of axial solids holdup distribution

Though there were quite a lot of experimental data available in the literature, Issangya's investigation [26] for axial solids holdup distributions seemed the most systematical. FCC particles of 70 μm in diameter and 1600 kg/m3 in density were fluidized by ambient air in a riser of 0.076-m inner diameter. The operating conditions varied from dilute transportation, through the premature fast bed, the classical fast bed, until the high-density fast bed [26].

The coefficient of converse momentum flux δ ¼ 2, for the recycled particles, was applied in the calculation. As an example, Figure 20 shows the comparisons of model predictions and the experimental data [26] for a constant gas velocity uf¼ 4 m/s yet different solid fluxes of 18, 44, 68, 138, 200, and 240 kg/(m2 s), respectively. It can be seen from the figure that the results are somewhat reasonable.

Figure 20. Axial solids holdup distributions from present model and Issangya's data, uf¼ 4 m/s [26].

## 8. Conclusions and outlook

ε<sup>s</sup> ¼ εs0e

decay constant.

138 Thermal Power Plants - New Trends and Recent Developments

where m'¼ Ht2/Ht, and ε�

Potter [25].

where εs0 stands for the solids holdup just above the air distributor of the riser, and γ for the

Since the equivalent momentum balance heights of acceleration/transition zones have been determined above, we can simply transfer the values to the actual solids holdup distributions,

By some mathematical deduction, the final expressions for εs0 and γ were obtained as [11]

<sup>ε</sup>s0 <sup>¼</sup> <sup>ε</sup><sup>s</sup>;<sup>d</sup> � <sup>m</sup><sup>0</sup>

¼ 1 Ht2

Under the same conditions of experiments in Ref. [25], the heights of transition zones were calculated with δ ¼ 0 assumed. Then, a proportionality coefficient (1�η) ¼ 0.212 was determined from comparing those results with experimental data [25], shown as in Figure 19. From that, η ¼ 0.788 was obtained, which meant that the particle gravity contributed roughly fourfifths of the total pressure drop for the zone. Now, the method to predict the axial solids

Though there were quite a lot of experimental data available in the literature, Issangya's investigation [26] for axial solids holdup distributions seemed the most systematical. FCC particles of 70 μm in diameter and 1600 kg/m3 in density were fluidized by ambient air in a

Figure 19. Comparison of the predicted heights of transition zones and the experimental data collected by Ouyang and

ε� s

εs0 ε<sup>s</sup>;<sup>d</sup> � 1 

<sup>s</sup> stands for the solids holdup of the upper dilute region.

in accordance with their equal impacts on the total bed pressure drop.

<sup>γ</sup> <sup>¼</sup> <sup>ε</sup>s0 � <sup>ε</sup><sup>s</sup>;<sup>d</sup> ε<sup>s</sup>;<sup>d</sup>Ht2

holdup distribution of fast beds has been established completely.

7.3. Prediction of axial solids holdup distribution

�γz

, ð71Þ

<sup>1</sup> � <sup>m</sup><sup>0</sup> <sup>ð</sup>72<sup>Þ</sup>

, ð73Þ

Based on the downward-penetrating particle flow through clusters and the analogy between a falling cluster and a rising bubble identified by the authors, a "type-A-choking-oriented separate-phase-coexistence model" for the upper dilute region of fast beds was established first. The model was then integrated with the sub-models of "cluster rebound at the dense bottom," "the momentum flux balances for acceleration and transition zones" in the lower and middle parts of the bed. The integrated model predicted successfully the axial solids holdup distributions of literature data under extremely wide operation conditions covering dilute-phase transportation, the premature fast bed, the classical fast bed, and the high-density fast bed.

To make the model system for fast fluidization have even sounder theoretical basis, more fundamental studies are expected in the future, especially those to explain further the reasons for "the four simplest integer numbers" as: "0"—in the regime of traditional fast fluidization, clusters settle down freely without outer-gas invasion; "1"—at type A choking, the terminal velocity of a particle suspension in a finite diameter riser is just equal to the terminal velocity of a single particle in an infinite fluid; "2"—at the very beginning of particle aggregation, the solid concentration in clusters is twice that in the dilute phase; "3"—the minimum solid circulating flux for fast fluidization corresponds to the type A chocking at the gas velocity of triple particle terminal velocity.

## Acknowledgements

The authors would like to acknowledge the financial support from the Chinese National Natural Science Fund, Grant No. 50676062.

[10] Zhang M C, Zhang C. A type-A-choking-oriented unified model for fast fluidization

Introductory Review on an Engineering Approach for Fast‐Bed Modeling in Mimic to Bubbling Bed Practice

http://dx.doi.org/10.5772/68107

141

[11] Zhang M C, Zhang C. Further integration of the type-A-choking-oriented unified model

[12] He Y, Deen N G, ven Annaland S, Kuipers J A M. Gas-solid turbulent flow in a circulating fluidized bed riser: Experimental and numerical study of mono-disperse particle system.

[14] Yang N, Wang W, Ge W, Wang L N, Li J H. Simulation of heterogeneous structure in a circulating fluidized bed riser by combining the two-fluid model with the EMMS

[16] Yang W C. A mathematical definition of choking phenomenon and a mathematical model for predicting choking velocity and choking volume fraction. AIChE Journal. 1975;21:1013-

[17] Yang W C. Criteria for choking in vertical pneumatic conveying lines. Powder Technol-

[18] Yang W C. Estimating the solid particle velocity in vertical pneumatic conveying lines.

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[24] Yousfi Y, Gau G. Aerodynamique de l'ecoulement vertical de suspensions concentrees gaz-solides-I: regimes d'ecoulement et stablilite aerodynamique. Chemical Engineering

[25] Ouyang S, Potter O E. Consistency of circulating fluidized bed experimental data. Indus-

[26] Issangya A S, Bai D, Bi H T, Lim K S, Zhu J, Grace J R. Suspension densities in a highdensity circulating fluidized bed riser. Chemical Engineering Science. 1999;54:5451-5460

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near wall region of a vertical riser. Powder Technology, 2002;127:128-143

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[15] Leva M. Fluidization. New York: McGraw-Hill Book Company, 1959

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dynamics. Powder Technology, 2013;241:126-141

## Author details

Ming-Chuan Zhang\* and Chu Zhang

\*Address all correspondence to: mczhang@sjtu.edu.cn

School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China

## References


Acknowledgements

Author details

References

Natural Science Fund, Grant No. 50676062.

140 Thermal Power Plants - New Trends and Recent Developments

Ming-Chuan Zhang\* and Chu Zhang

\*Address all correspondence to: mczhang@sjtu.edu.cn

demic & Professional; 1997, Chapter 12

tions. Boston: Academic Press, 1994

Method. Beijing: Metallurgical Industry Press, 1994

sional; 1997, Chapter 14

3741-3751

2014. p. 1-21

The authors would like to acknowledge the financial support from the Chinese National

School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China

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[2] Avidan A A. Fluid catalytic cracking. In: Grace J R, Avidan A A & Knowlton T M, editors. Circulating Fluidized Beds. London: Black Academic & Professional; 1997, Chapter 13

[3] Masten J M. Design and scale-up of CFB catalytic reactors. In: Grace J R, Avidan A A & Knowlton T M, editors. Circulating Fluidized Beds. London: Black Academic & Profes-

[4] Du B, Warsito W, Fan L S. Behavior of the dense phase transportation regime in a circulating fluidized bed. Industrial and Engineering Chemistry Research. 2006;45:

[5] Gidaspow D. Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descrip-

[6] Li J, Kwauk M. Particle-Fluid Two-Phase Flow—The Energy-Minimization Multi-Scale

[7] Zhu H P, Zhou Z Y, Yang R Y, Yu A B. Discrete particle simulation of particulate systems:

[8] Snider D M. An incompressible three-dimensional multiphase particle-in-cell model for

[9] Werther J, Hartge E. Bridges between industrial practice and fundamental research in fluidization technology. In: Proceedings of CFB-11. Beijing: Chemical Industry Press;

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dense particle flows. Journal of Computational Physics, 2001;170:523-549


[27] Grace J R, Issangya A S, Bai D, Bi H, Zhu J. Situating the high-density circulating fluidized bed. AIChE Journal. 1999;45:2108-2116

**Chapter 8**

Provisional chapter

**Economic Future of Concentrating Solar Power for**

DOI: 10.5772/intechopen.74334

Worldwide, the climate change is a major universal concern. CO2 is the main cause of international warming, and at least 85% emission results of CO2 came from conventional energy depleted sources (oil, natural gas and coal) for energy generation. Hence, renewable energy has been the focal point of most regulations of governments to aim at greenhouse gas reduced. In Egypt, greenhouse gas emissions from rural activities amount to some 25% of national greenhouse gas emissions, amounting to approximately 27 million t CO2 equivalent annually. Moreover, these emissions are supposed to increase rapidly in the coming decades, more than doubling in the next 15 years, as rural populations grow and activities become increasingly energy intensive. The Mediterranean region embraces Europe, North Africa and Middle East and has enormous potential in solar energy. It has abundant solar radiation, cheap land and high electricity demand, which could make this region the universal hub for concentrating solar power (CSP) generation. This chapter discusses the Egypt market potential of CSP. The chapter covers recent CSP trends and discusses in detail the CSP market development. The chapter aims to obtain the data sources to compare the CSP and levelized electricity cost. Enas Shouman presents a strategy for CSP plant market entrance in Egypt and a comparison between the electricity cost for Egypt model case and the cost evolution of CSP plants on the basis of expectations for the expansion as an international level. This chapter proposes a concept strategy for management CSP in Egypt. The chapter included two applied parts. The first part is to calculate the generating electricity cost from conventional power sources and its expansion in the future. Then, the second part will be followed by identifying the CSP cost and

Keywords: solar energy, CSP, renewable energy, economics, levelized cost, electricity

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Economic Future of Concentrating Solar Power for

**Electricity Generation**

Electricity Generation

Enas Raafat Maamoun Shouman

Enas Raafat Maamoun Shouman

http://dx.doi.org/10.5772/intechopen.74334

Abstract

its growth in the future.

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter


#### **Economic Future of Concentrating Solar Power for Electricity Generation** Economic Future of Concentrating Solar Power for Electricity Generation

DOI: 10.5772/intechopen.74334

Enas Raafat Maamoun Shouman Enas Raafat Maamoun Shouman

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.74334

#### Abstract

[27] Grace J R, Issangya A S, Bai D, Bi H, Zhu J. Situating the high-density circulating fluidized

[28] Bai D, Kato K. Quantitative estimation of solids holdups at dense and dilute regions of

[29] Bai D, Shibuya E, Masuda Y, Nakawaga N, Kato K. Flow structure in a fast fluidized bed.

[30] Brereton C M H, Grace J R. Microstructure aspects of the behavior of circulating fluidized

[31] Zhu H, Zhu J. Characterization of fluidization behavior in the bottom region of CFB

[32] Chen C W, Seville J, Yang Z, Baeyens J. Particle motion in the CFB riser with special emphasis on PEPT-imaging of the bottom section. Powder Technology, 2009;196:318-325

[33] Li Y C. Introduction of Fluidization Process Engineering (in Chinese). Beijing: Science

circulating fluidized beds. Powder Technology, 1999;101:183-190

bed. AIChE Journal. 1999;45:2108-2116

142 Thermal Power Plants - New Trends and Recent Developments

Press; 2008

Chemical Engineering Science, 1996;51:957-966

beds. Chemical Engineering Science, 1993;48:3565-2572

risers. Chemical Engineering Journal, 2008;141:169-179

Worldwide, the climate change is a major universal concern. CO2 is the main cause of international warming, and at least 85% emission results of CO2 came from conventional energy depleted sources (oil, natural gas and coal) for energy generation. Hence, renewable energy has been the focal point of most regulations of governments to aim at greenhouse gas reduced. In Egypt, greenhouse gas emissions from rural activities amount to some 25% of national greenhouse gas emissions, amounting to approximately 27 million t CO2 equivalent annually. Moreover, these emissions are supposed to increase rapidly in the coming decades, more than doubling in the next 15 years, as rural populations grow and activities become increasingly energy intensive. The Mediterranean region embraces Europe, North Africa and Middle East and has enormous potential in solar energy. It has abundant solar radiation, cheap land and high electricity demand, which could make this region the universal hub for concentrating solar power (CSP) generation. This chapter discusses the Egypt market potential of CSP. The chapter covers recent CSP trends and discusses in detail the CSP market development. The chapter aims to obtain the data sources to compare the CSP and levelized electricity cost. Enas Shouman presents a strategy for CSP plant market entrance in Egypt and a comparison between the electricity cost for Egypt model case and the cost evolution of CSP plants on the basis of expectations for the expansion as an international level. This chapter proposes a concept strategy for management CSP in Egypt. The chapter included two applied parts. The first part is to calculate the generating electricity cost from conventional power sources and its expansion in the future. Then, the second part will be followed by identifying the CSP cost and its growth in the future.

Keywords: solar energy, CSP, renewable energy, economics, levelized cost, electricity

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## 1. Introduction

## 1.1. Outlook for CSP in Europe and MENA

The solar direct normal irritation (DNI) plays a great role for the of electricity generation amount from CSP plants. Europe has vast variations in solar radiation unlike the Middle East and North Africa. It has enormous potential for generating electricity from solar energy, with great average solar energy irradiance (Figure 1). This allows the Middle East and North Africa to export energy to Europe [1, 2].

This would open up new opportunities for economic and technical cooperation between the two regions and protect environmental considerations by reducing the CO2 emissions in Europe. World energy demand is growing by over 50% up to the year 2030; Figure 2 shows the energy consumption per capita up to the year 2050 [3, 4].

The CSP economic potential is limited to Spain, Portugal, Greece, Turkey and the Mediterranean Islands and amounts to 1570 TWh/y of which 1280 TWh/y are located in Southern Spain. Mediterranean Sea is a more attractive site for CSP, with direct solar irradiance of about 2800 kWh/m<sup>2</sup> /y.

### 1.2. Universal cumulative installed CSP capacity

☁ Spain and the USA have 69 and 29% of installed capacity, respectively, and they have dominated the market; United States used to be a leader actor in solar power generation until 2007 when Spain design its first plant (PS10).

☁ Spain developed 1.9 GW of CSP, and it dominates the market with 69% of the universal installed capacity.

☁ Between 2010 and 2011, Middle Eastern and African countries (Algeria, Morocco and Egypt) have generated 65 MW. The UAE has a 100 MW plant (Shams 1) which is established in 2013. ☁ China and India have started to generate CSP since 2010, and at the end of 2012, their

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☁ Australia, France, Thailand, Germany and Italy have developed CSP plants with nominal

installed capacity was about 1.5 and 2.5 MW, respectively (Figure 3).

Figure 3. Universal cumulative installed CSP capacities, MW, 2007–2012 [5, 6].

capacities of 1–9 MW.

Figure 2. Energy consumption per capita [3, 4].

Figure 1. Sum of universal irradiation annually [1, 2].

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Figure 2. Energy consumption per capita [3, 4].

1. Introduction

kWh/m<sup>2</sup>

/y.

installed capacity.

1.1. Outlook for CSP in Europe and MENA

144 Thermal Power Plants - New Trends and Recent Developments

the energy consumption per capita up to the year 2050 [3, 4].

1.2. Universal cumulative installed CSP capacity

2007 when Spain design its first plant (PS10).

Figure 1. Sum of universal irradiation annually [1, 2].

to export energy to Europe [1, 2].

The solar direct normal irritation (DNI) plays a great role for the of electricity generation amount from CSP plants. Europe has vast variations in solar radiation unlike the Middle East and North Africa. It has enormous potential for generating electricity from solar energy, with great average solar energy irradiance (Figure 1). This allows the Middle East and North Africa

This would open up new opportunities for economic and technical cooperation between the two regions and protect environmental considerations by reducing the CO2 emissions in Europe. World energy demand is growing by over 50% up to the year 2030; Figure 2 shows

The CSP economic potential is limited to Spain, Portugal, Greece, Turkey and the Mediterranean Islands and amounts to 1570 TWh/y of which 1280 TWh/y are located in Southern Spain. Mediterranean Sea is a more attractive site for CSP, with direct solar irradiance of about 2800

☁ Spain and the USA have 69 and 29% of installed capacity, respectively, and they have dominated the market; United States used to be a leader actor in solar power generation until

☁ Spain developed 1.9 GW of CSP, and it dominates the market with 69% of the universal

Figure 3. Universal cumulative installed CSP capacities, MW, 2007–2012 [5, 6].

☁ Between 2010 and 2011, Middle Eastern and African countries (Algeria, Morocco and Egypt) have generated 65 MW. The UAE has a 100 MW plant (Shams 1) which is established in 2013.

☁ China and India have started to generate CSP since 2010, and at the end of 2012, their installed capacity was about 1.5 and 2.5 MW, respectively (Figure 3).

☁ Australia, France, Thailand, Germany and Italy have developed CSP plants with nominal capacities of 1–9 MW.

#### 1.3. CSP deployment beyond 2030

By 2040, the universal installed CSP capacity will be about 715 GW, with an average capacity factor of 45% (3900 h/year), thereby providing 2790 TWh yearly. The solar share of 85%, or 2370 TWh, represents 8.3% of universal electricity generation [7, 8]. By 2050, the universal installed capacity will reach 1089 GW, with an average capacity factor of 50% (4380 h/y). In the year 2010, the total electricity demand for 30 countries in Europe was 3530 TWh/y, which is projected to reach a maximum of 4310 TWh/y in 2040 [9, 10].

Figure 4 represents the future electricity demand expected in Europe in 2050, which would cover the demand with a surplus of 45%. However, it must be considered that about 30% of the countries which have been analyzed show considerable deficits, while on the other side considerable surpluses are concentrated in seven countries as shown in Figure 4.

Figure 5 shows where CSP electricity will be produced and consumed by 2050. North America would be the leader in producing solar energy, followed by Africa, India and the Middle East. Africa would be the largest exporter and Europe the largest importer. Indeed, the Middle East and North Africa are the largest reproducers when all solar products are considered [11].

2. Future energy demand

sources from 2000 to 2050.

Figure 6. MENA region installed capacity by sources.

2.1. World electricity consumption

In North Africa, as a result of increasing population from 150 million in 2005 to a projected 250

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Total electricity consumption is prospective to increase at a compound yearly growth rate of 3.17% with a rise in population. Total installed generating capacity is also expected to rise at a compound annual growth rate of 3.28% to meet the growing demand of electricity and to fill the shortfall of supply and demand. Figure 6 represents electricity production by different

Total electricity generation from CSP has been supposed to increase to contribute by more than 40% of the total electricity produced in North Africa by 2030 through efficiencies

million in 2050, an increasing electricity demand and production is expected.

Figure 5. Production and consumption of CSP electricity by 2050 (in TWh) [12, 13].

Figure 4. Electricity consumption of European countries between 2010 and 2050.

Figure 5. Production and consumption of CSP electricity by 2050 (in TWh) [12, 13].

## 2. Future energy demand

1.3. CSP deployment beyond 2030

146 Thermal Power Plants - New Trends and Recent Developments

considered [11].

projected to reach a maximum of 4310 TWh/y in 2040 [9, 10].

Figure 4. Electricity consumption of European countries between 2010 and 2050.

By 2040, the universal installed CSP capacity will be about 715 GW, with an average capacity factor of 45% (3900 h/year), thereby providing 2790 TWh yearly. The solar share of 85%, or 2370 TWh, represents 8.3% of universal electricity generation [7, 8]. By 2050, the universal installed capacity will reach 1089 GW, with an average capacity factor of 50% (4380 h/y). In the year 2010, the total electricity demand for 30 countries in Europe was 3530 TWh/y, which is

Figure 4 represents the future electricity demand expected in Europe in 2050, which would cover the demand with a surplus of 45%. However, it must be considered that about 30% of the countries which have been analyzed show considerable deficits, while on the other side

Figure 5 shows where CSP electricity will be produced and consumed by 2050. North America would be the leader in producing solar energy, followed by Africa, India and the Middle East. Africa would be the largest exporter and Europe the largest importer. Indeed, the Middle East and North Africa are the largest reproducers when all solar products are

considerable surpluses are concentrated in seven countries as shown in Figure 4.

#### 2.1. World electricity consumption

In North Africa, as a result of increasing population from 150 million in 2005 to a projected 250 million in 2050, an increasing electricity demand and production is expected.

Total electricity consumption is prospective to increase at a compound yearly growth rate of 3.17% with a rise in population. Total installed generating capacity is also expected to rise at a compound annual growth rate of 3.28% to meet the growing demand of electricity and to fill the shortfall of supply and demand. Figure 6 represents electricity production by different sources from 2000 to 2050.

Total electricity generation from CSP has been supposed to increase to contribute by more than 40% of the total electricity produced in North Africa by 2030 through efficiencies

Figure 6. MENA region installed capacity by sources.

achieved on account of advancements in CSP technology [14]. Figure 7 shows MENA region renewable energy resources.

2.2. Egypt electricity consumption

than 30% and will reach 55% in 2050 [16, 17].

The German Aerospace Center has produced statistic studies on forecasted electricity consumption for Egypt up until 2050. Egypt will largely depend on CSP to satisfy the electricity demand due to the unpredictable population increase as well as the prospective economic growth (Figures 9 and 10). In 2020, in Egypt, electricity generated from CSP will likely contribute more

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Figure 9. Electricity scenarios by primary energy sources for power generation in Egypt [16, 17].

Figure 10. Installed capacities required for the electricity supply in Egypt [16, 17].

Figure 8 shows the comparison between El-Kharga in Egypt and different areas in Europe and North Africa. Figure 8 represents the monthly electricity yield of a best-case CSP plant with 24-h storage capacity throughout the year.

Figure 7. Renewable power generation potential by sources in TWh/y [15].

Figure 8. Proportional monthly electricity generation simulation of CSP plant with 24-h storage for equivalent annual full load hours in different sites with different DNI, Freiburg in Germany 2260 h/y, Madrid in Spain 5150 h/y, El Kharga in Egypt 8500 h/y/May 2005/.

#### 2.2. Egypt electricity consumption

achieved on account of advancements in CSP technology [14]. Figure 7 shows MENA region

Figure 8 shows the comparison between El-Kharga in Egypt and different areas in Europe and North Africa. Figure 8 represents the monthly electricity yield of a best-case CSP plant with

Figure 8. Proportional monthly electricity generation simulation of CSP plant with 24-h storage for equivalent annual full load hours in different sites with different DNI, Freiburg in Germany 2260 h/y, Madrid in Spain 5150 h/y, El Kharga in

renewable energy resources.

Egypt 8500 h/y/May 2005/.

24-h storage capacity throughout the year.

148 Thermal Power Plants - New Trends and Recent Developments

Figure 7. Renewable power generation potential by sources in TWh/y [15].

The German Aerospace Center has produced statistic studies on forecasted electricity consumption for Egypt up until 2050. Egypt will largely depend on CSP to satisfy the electricity demand due to the unpredictable population increase as well as the prospective economic growth (Figures 9 and 10). In 2020, in Egypt, electricity generated from CSP will likely contribute more than 30% and will reach 55% in 2050 [16, 17].

Figure 9. Electricity scenarios by primary energy sources for power generation in Egypt [16, 17].

Figure 10. Installed capacities required for the electricity supply in Egypt [16, 17].

## 3. Economic methods for solar energy financial analyses

There are five economic methods of financial analysis for making investment decisions. Enas R. Shouman et al. have mentioned different methods including payback analysis (Annex 1), saving-to-investment ratio (SIR) (Annex 2), life-cycle cost (LCC) (Annex 3) and an adjusted internal rate of return (AIRR) (Annex 4). These studies evaluated the economics of PV applications by using these financial methods [18].

## 3.1. Levelized cost of electricity generation

The most significant parameters that determine at 2011 the levelized cost of electricity (LCOE) of CSP plants are as follows:


The economics of CSP technologies are substantially different from that of fossil fuel power technologies. Solar energy has high investment costs, modest operation and maintenance costs and very low or no fuel costs when compared to conventional fossil fuel power which is only very sensitive to the price volatility of the fossil fuel international markets. On the other hand, solar energy technologies are more sensitive to change in the capital and financing condition costs. The levelized cost of electricity of CSP plants is strongly correlated with DNI. Supposing a base of 2100 kWh/m<sup>2</sup> /year (a typical value for Spain), the estimated LCOE of a CSP plant is declined by 4.5% for every 100 kWh/m<sup>2</sup> /year that the DNI exceeds 2100 (Figure 11). In Egypt, the estimated average value of the DNI is around 2500.

Egypt is in an advantageous position for generating solar energy. It enjoys 2900–3200 h of sunshine annually with annual direct normal energy density 1980–3200 kWh/m<sup>2</sup> and technical solar-thermal electricity generating potential of 73.6 PWh, so the CSP is a promising technology in Egypt.

CSP capacity growth and cost learning curves from different project locations were taken as a basis for the modeling of the levelized CSP for generating the cost of electricity plants. The chapter uses Spain as a reference value for the successful market in 2010–2011 which its electricity tariff is around 27 €ct/kWh and define an equivalent value for MENA region in US(\$) currency. Supposing an exchange rate of 1.19 \$/€ and Egypt DNI reference of about 2500 kWh/m<sup>2</sup> /a compared to Southern Spain DNI of about 2900 kWh/m<sup>2</sup> /a, our equivalent demand tariff for CSP in the model case reached to 28 UScent/kWh in 2010 [19, 20] (Figure 12).

CSP capacity is expected to increase from 20,000 MW to 150,000 MW by 2020 and about 230,000–340,000 MW by 2030. In 2050, expectation range for installed CSP capacity will be from 850,000 MW to 1,500,000 MW worldwide. In order to calculate the cost of decreased effects for the model reference case, we have selected a moderate universal expansion scenario, reaching about 39,000–240,000 MW in 2020–2030. This assumption will be the basis for the cost model scenario. In 2050, about 950,000 MW is supposed to be installed. The

Figure 12. Expansion of universally installed CSP capacity and resulting reduction of demand tariff for the model

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Figure 11. LCOE of CSP plants as a function of DNI [19].

parameters shown in Table 1.

Figure 11. LCOE of CSP plants as a function of DNI [19].

3. Economic methods for solar energy financial analyses

tions by using these financial methods [18].

150 Thermal Power Plants - New Trends and Recent Developments

3.1. Levelized cost of electricity generation

structure, grid connection and capitalized costs;

• CSP power plant capacity and efficiency factor.

• Level of DNI at the project location;

• The capital cost, economic lifecycle, etc.

declined by 4.5% for every 100 kWh/m<sup>2</sup>

the estimated average value of the DNI is around 2500.

of CSP plants are as follows:

a base of 2100 kWh/m<sup>2</sup>

ogy in Egypt.

about 2500 kWh/m<sup>2</sup>

20] (Figure 12).

There are five economic methods of financial analysis for making investment decisions. Enas R. Shouman et al. have mentioned different methods including payback analysis (Annex 1), saving-to-investment ratio (SIR) (Annex 2), life-cycle cost (LCC) (Annex 3) and an adjusted internal rate of return (AIRR) (Annex 4). These studies evaluated the economics of PV applica-

The most significant parameters that determine at 2011 the levelized cost of electricity (LCOE)

• Cost of initial investment, including location design for plants, with component costs,

The economics of CSP technologies are substantially different from that of fossil fuel power technologies. Solar energy has high investment costs, modest operation and maintenance costs and very low or no fuel costs when compared to conventional fossil fuel power which is only very sensitive to the price volatility of the fossil fuel international markets. On the other hand, solar energy technologies are more sensitive to change in the capital and financing condition costs. The levelized cost of electricity of CSP plants is strongly correlated with DNI. Supposing

Egypt is in an advantageous position for generating solar energy. It enjoys 2900–3200 h of sunshine annually with annual direct normal energy density 1980–3200 kWh/m<sup>2</sup> and technical solar-thermal electricity generating potential of 73.6 PWh, so the CSP is a promising technol-

CSP capacity growth and cost learning curves from different project locations were taken as a basis for the modeling of the levelized CSP for generating the cost of electricity plants. The chapter uses Spain as a reference value for the successful market in 2010–2011 which its electricity tariff is around 27 €ct/kWh and define an equivalent value for MENA region in US(\$) currency. Supposing an exchange rate of 1.19 \$/€ and Egypt DNI reference of

equivalent demand tariff for CSP in the model case reached to 28 UScent/kWh in 2010 [19,

/a compared to Southern Spain DNI of about 2900 kWh/m<sup>2</sup>

/year (a typical value for Spain), the estimated LCOE of a CSP plant is

/year that the DNI exceeds 2100 (Figure 11). In Egypt,

/a, our

• Operation and maintenance (O&M) (\$/y) costs (including insurance) costs; and.

Figure 12. Expansion of universally installed CSP capacity and resulting reduction of demand tariff for the model parameters shown in Table 1.

CSP capacity is expected to increase from 20,000 MW to 150,000 MW by 2020 and about 230,000–340,000 MW by 2030. In 2050, expectation range for installed CSP capacity will be from 850,000 MW to 1,500,000 MW worldwide. In order to calculate the cost of decreased effects for the model reference case, we have selected a moderate universal expansion scenario, reaching about 39,000–240,000 MW in 2020–2030. This assumption will be the basis for the cost model scenario. In 2050, about 950,000 MW is supposed to be installed. The


electricity generation of about 22,179 ktoe and total electricity generation of about 101,898

Eq. (3) will be followed to measure efficiency which plays a significant role in consumption and fuel cost. The equation would calculate the fuel cost estimated for the medium load and

toe ½ �<sup>∗</sup>USD EGP

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153

Electricityoutput MWh ½ � (2)

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<sup>η</sup>medium=peak (3)

Specific fuel cost USD <sup>½</sup> <sup>=</sup>MWh� ¼ fuelconsumption toe ½ �∗fuelcost EGP

COFmedium=peak <sup>¼</sup> COFbase<sup>∗</sup> <sup>η</sup>base

where η is the efficiency (%). This will result in a cost of fuel (CoF) medium load of 8.2 USD/MWh

The investment cost of the conventional energy plants has three main types of energy generation: combined cycle plants, gas turbine plants and steam turbine energy plants. By multiplying the installed capacity and the share of the production of each type and then these costs with the share of the installed capacity as shown in Table 3, we calculate the weighted average for the CSP plant investment cost of 1114.77 USD/kW [23] which is very significant to deter-

The fixed O&M costs vary between the different types of generation, as Combined Cycle Charge around 2 US/kW, Gas about 13 USD/kW while the most expensive ones are the Steam energy plants with 28 USD/kW. Using the weighted average according to the, respectively, installed capacity about 7178, 1641 and 11,458 MW, the average fixed operation and maintenance cost

Figure 13 shows the levelized cost of electricity (LCOE) calculated as in Annex 5 for the peak load, medium load and base load segments as well as for the resulting weighted average cost

Type of energy generation Combine cycle Gas turbines Steam turbine energy plants

Investment cost (USD/kW) 800 500 1400 Share of the installed capacity 35% 8% 57%

peak load with the fuel efficiency of 35 and 30%, respectively.

and cost of fuel peak load of 9.6 USD/MWh.

3.2.4. Cost of operation and maintenance

could be calculated as 17.58 USD/kW/year [23].

3.3. LCOE for conventional power in Egypt

Table 3. Weighted average for the CSP plant investment cost.

3.2.3. Investment cost of the conventional power plants

GWh/a [22].

mine the LCOE.

of electricity.

Table 1. Installing CSP model parameters for capacity.

demand tariff for CSP is decreased according to the universal installed capacity, with a progress ratio of about 0.88 according to a model by Neij, that the cost is cut the price by 12% every time worldwide installed capacity doubles [21]. In 2020, with these conditions the required CSP tariff will cut the price to 14 and 10 cent/kWh by 2030. In the long term, a cost below 8 cent/kWh is achieved.

### 3.2. A strategy for CSP finance in Egypt

### 3.2.1. Calculating levelized cost parameter of electricity (LCOE)

#### 3.2.1.1. Assuming the electricity output per capita

For this model, the electricity output per capita is needed, while only the total electricity output value is known, which is 101,898 GWh/a [1, 2]. From the reference model for MENA region, the share of each capita could be calculated and supposed to be the same distribution in Egypt. Multiplying this share by the total annual electricity output will give us the electricity output per capita as shown in Table 2 [22].

#### 3.2.2. Cost of fuel (CoF)

The objective of the coming calculations is to determine the Cost of fuel for the different segments (peak-, medium, and base load). In the annual report of the EEHC a case was given that showed savings of 581 million EGP, when 3195 k toe were saved in the year 2008–2009, fuel cost [EGP/toe] was 181.84 according to the following equation [22].

$$\text{Specific fuel cost} \left[ \text{EGP/Toe} \right] = (\text{fuelcost} [\text{EGP}]) / \text{fuel} [\text{ktoe}] \tag{1}$$

The fuel cost could be about 7.19 \$/MWh according to the following equation, taking into consideration the value proposition in Eq. (1), as well as knowing the total fuel consumed in


Table 2. Electricity output/capita in Egypt.

electricity generation of about 22,179 ktoe and total electricity generation of about 101,898 GWh/a [22].

$$\text{Specific fuel cost} \left[ \text{USD/MWh} \right] = \frac{\text{fuel consumption} \left[ \text{to} \right] \* \text{fuel cost} \left[ \frac{\left[ \frac{\text{LGP}}{\text{W}} \right] \* \text{LSD}}{\text{EGP}} \right]}{\text{Electricityout} \left[ \text{MWh} \right]} \tag{2}$$

Eq. (3) will be followed to measure efficiency which plays a significant role in consumption and fuel cost. The equation would calculate the fuel cost estimated for the medium load and peak load with the fuel efficiency of 35 and 30%, respectively.

$$\mathbf{COF\_{medium/peak}} = \mathbf{COF\_{base}}^{\*} \underset{\eta \text{ } phase\text{ }}{}{\text{ }}}{\text{ }} \underset{\eta \text{ } medium/peak}{} \tag{3}$$

where η is the efficiency (%). This will result in a cost of fuel (CoF) medium load of 8.2 USD/MWh and cost of fuel peak load of 9.6 USD/MWh.

#### 3.2.3. Investment cost of the conventional power plants

The investment cost of the conventional energy plants has three main types of energy generation: combined cycle plants, gas turbine plants and steam turbine energy plants. By multiplying the installed capacity and the share of the production of each type and then these costs with the share of the installed capacity as shown in Table 3, we calculate the weighted average for the CSP plant investment cost of 1114.77 USD/kW [23] which is very significant to determine the LCOE.

### 3.2.4. Cost of operation and maintenance

demand tariff for CSP is decreased according to the universal installed capacity, with a progress ratio of about 0.88 according to a model by Neij, that the cost is cut the price by 12% every time worldwide installed capacity doubles [21]. In 2020, with these conditions the required CSP tariff will cut the price to 14 and 10 cent/kWh by 2030. In the long term, a cost

Preference LCOE of CSP in 2010 \$/kWh 0.280 Preference DNI kWh/M2/a 2400 CSP progress ratio % 88.0%

For this model, the electricity output per capita is needed, while only the total electricity output value is known, which is 101,898 GWh/a [1, 2]. From the reference model for MENA region, the share of each capita could be calculated and supposed to be the same distribution in Egypt. Multiplying this share by the total annual electricity output will give us the electricity output

The objective of the coming calculations is to determine the Cost of fuel for the different segments (peak-, medium, and base load). In the annual report of the EEHC a case was given that showed savings of 581 million EGP, when 3195 k toe were saved in the year 2008–2009,

The fuel cost could be about 7.19 \$/MWh according to the following equation, taking into consideration the value proposition in Eq. (1), as well as knowing the total fuel consumed in

Peak load 1000 2000 5 4852 Medium load 2500 10,000 24 24,261 Base load 4000 30,000 71 72,784 Total 7500 42,000 100 101898

Specific fuel cost EGP ½ �¼ =Toe ð Þ fuelcost EGP ½ � =fuel ktoe ½ � (1)

Installed capacity (MW) Electricity (GWh/a) Share of electricity (%) Electricity (GWh/a)

fuel cost [EGP/toe] was 181.84 according to the following equation [22].

below 8 cent/kWh is achieved.

3.2. A strategy for CSP finance in Egypt

Table 1. Installing CSP model parameters for capacity.

152 Thermal Power Plants - New Trends and Recent Developments

per capita as shown in Table 2 [22].

3.2.2. Cost of fuel (CoF)

Study [23] Egypt

Table 2. Electricity output/capita in Egypt.

3.2.1.1. Assuming the electricity output per capita

3.2.1. Calculating levelized cost parameter of electricity (LCOE)

The fixed O&M costs vary between the different types of generation, as Combined Cycle Charge around 2 US/kW, Gas about 13 USD/kW while the most expensive ones are the Steam energy plants with 28 USD/kW. Using the weighted average according to the, respectively, installed capacity about 7178, 1641 and 11,458 MW, the average fixed operation and maintenance cost could be calculated as 17.58 USD/kW/year [23].

### 3.3. LCOE for conventional power in Egypt

Figure 13 shows the levelized cost of electricity (LCOE) calculated as in Annex 5 for the peak load, medium load and base load segments as well as for the resulting weighted average cost of electricity.


Table 3. Weighted average for the CSP plant investment cost.

Figure 13. LCOE for conventional power in Egypt.

For rising economies with high demand rise rates, the fuel cost escalation and fuel consumption of installed power capacity are greatly relevant, as it will directly affect economic development negatively. For the Egypt model case, we have assumed a rather moderate 3.6% growth of electricity demand, while growth rates of over 7% yearly.

Egypt has a technical potential exceeding 2800 kWh/m<sup>2</sup> /y, while the newly identified project location of Kom Ombo in Egypt has DNI average of about 2500 kWh/m<sup>2</sup> /y [24]. Therefore, this DNI value could be used as an indicator for DNI in Egypt in this model and this indicator compared with Spain with only a DNI level of 2090 kWh/m<sup>2</sup> /y [7, 8, 11]. These data could be used for calculating C0 [11].

$$\mathbf{C\_{o}}\_{\mathbf{Gypt}} = (\mathbf{CSP})\_{\mathbf{ain}^\*} \xrightarrow[DNI \to \mathbf{ypt}]{DNIspain} \* \mathbf{\mathfrak{F}/\mathbf{\mathfrak{C}}} \tag{4}$$

More concern should be devoted to solar energy, especially CSP, by establishing a special subauthority to support solar energy field. The responsibility of this entity is to measure DNI and also to identify a specific location for solar energy plant project and stand by feasibility studies. They would also assign and acquire land for solar energy plant projects, provide technical

/y] 2500

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CSP progress ratio [22] 0.88

LCOE for CSP in Egypt in 2010 [ct\$/kWh] 26.86

The major objective of this chapter is to create a continuous flow of the required data to be used as a base for taking decisions and to provide sufficient information about project needs. Project specifications, the other similar project in a different site, accurate information market and cost changes help the decision maker to determine and achieve the right target with minimum cost. The aim is to facilitate the creation in the highest level of decision makers' community to serve the scientific project and to maximize scientific findings and overcome existing barriers of perspective, culture, geography and time. There is a need for scientists, as individuals or as groups, to develop a diversity of data analysis strategies, to clearly identify key target audi-

Payback period is the minimum time it takes to recover investment costs. The payback method is often used as a rough evidence to cost performance. The payback period for the

support and set a part business partners.

Figure 14. EgyptLCOE (CSP) vs. conventional power.

Egypt DNI [kWh/m<sup>2</sup>

Annex

Annex 1

ences, and to learn how to execute an effective project.

Table 4. Levelized cost of electricity (LCOE) for CSP in Egypt parameters.

Assuming a USD–EUR exchange rate of 1.19, C0 Egypt is equal to 26.86 ct\$/kWh (Annex 6) (C0Egypt = 26.86 ct\$/kWh), which is in the lower half of estimated CSP costs worldwide by the IEA of (20–30) ct\$/kWh in 2010 [8]. The cost which is shown in Figure 14 depends on the yearly solar radiation, and Egypt has high direct normal irradiance. Applying equation to the following data (Table 4), Figure 14 shows the results for Egypt CSP cost curve, which decreases from 26.88 to 7.56 ct\$/kWh from 2010 to 2050, respectively.

In Egypt, CSP potential is about 73,000 TWh/year. Egypt is the highest one in the region. Other promising characteristics are a high DNI which is around 19,870–3200 kWh/m<sup>2</sup> /year, few cloudy days, high sun duration hours (9–11 h), huge expanses of vacant desert land, and an outstretch national electric grid. All of these elements make Egypt a perfect location for CSP projects.

The chapter aims to obtain a range of data for economic CSP energy. The chapter explains international CSP economic methods with financial analyses on the basis of expectations for the increase of solar energy in Egypt.

Figure 14. EgyptLCOE (CSP) vs. conventional power.


Table 4. Levelized cost of electricity (LCOE) for CSP in Egypt parameters.

More concern should be devoted to solar energy, especially CSP, by establishing a special subauthority to support solar energy field. The responsibility of this entity is to measure DNI and also to identify a specific location for solar energy plant project and stand by feasibility studies. They would also assign and acquire land for solar energy plant projects, provide technical support and set a part business partners.

The major objective of this chapter is to create a continuous flow of the required data to be used as a base for taking decisions and to provide sufficient information about project needs. Project specifications, the other similar project in a different site, accurate information market and cost changes help the decision maker to determine and achieve the right target with minimum cost.

The aim is to facilitate the creation in the highest level of decision makers' community to serve the scientific project and to maximize scientific findings and overcome existing barriers of perspective, culture, geography and time. There is a need for scientists, as individuals or as groups, to develop a diversity of data analysis strategies, to clearly identify key target audiences, and to learn how to execute an effective project.

#### Annex

For rising economies with high demand rise rates, the fuel cost escalation and fuel consumption of installed power capacity are greatly relevant, as it will directly affect economic development negatively. For the Egypt model case, we have assumed a rather moderate 3.6%

DNI value could be used as an indicator for DNI in Egypt in this model and this indicator

Assuming a USD–EUR exchange rate of 1.19, C0 Egypt is equal to 26.86 ct\$/kWh (Annex 6) (C0Egypt = 26.86 ct\$/kWh), which is in the lower half of estimated CSP costs worldwide by the IEA of (20–30) ct\$/kWh in 2010 [8]. The cost which is shown in Figure 14 depends on the yearly solar radiation, and Egypt has high direct normal irradiance. Applying equation to the following data (Table 4), Figure 14 shows the results for Egypt CSP cost curve, which decreases from

In Egypt, CSP potential is about 73,000 TWh/year. Egypt is the highest one in the region. Other promising characteristics are a high DNI which is around 19,870–3200 kWh/m<sup>2</sup>

few cloudy days, high sun duration hours (9–11 h), huge expanses of vacant desert land, and an outstretch national electric grid. All of these elements make Egypt a perfect location for

The chapter aims to obtain a range of data for economic CSP energy. The chapter explains international CSP economic methods with financial analyses on the basis of expectations for

DNIspain

/y, while the newly identified project

DNIEgypt <sup>∗</sup> \$=€ (4)

/y [7, 8, 11]. These data could be

/y [24]. Therefore, this

/year,

growth of electricity demand, while growth rates of over 7% yearly.

location of Kom Ombo in Egypt has DNI average of about 2500 kWh/m<sup>2</sup>

Co Egypt ¼ ð Þ CSP ain<sup>∗</sup>

Egypt has a technical potential exceeding 2800 kWh/m<sup>2</sup>

Figure 13. LCOE for conventional power in Egypt.

154 Thermal Power Plants - New Trends and Recent Developments

26.88 to 7.56 ct\$/kWh from 2010 to 2050, respectively.

the increase of solar energy in Egypt.

used for calculating C0 [11].

CSP projects.

compared with Spain with only a DNI level of 2090 kWh/m<sup>2</sup>

#### Annex 1

Payback period is the minimum time it takes to recover investment costs. The payback method is often used as a rough evidence to cost performance. The payback period for the solar energy project is calculated as the total cost of investment divided by the income of the first year from the energy produced. If the payback period analysis is less than the expected power system life, the projects of the power system are potential to be cost-effective evidence. Projects of power system with short payback periods are considered to have lower risks. Table 5 shows the equation for payback calculation indicated by Enas R. Shouman et al. [1, 18].

If the life cycle cost analysis is lower than that for the base case and in other aspects is equal, then the life cycle cost meets the objectives of investor and budget constraints. It is considered as cost-effective and the preferred investment. Table 7 shows the equation to calculate

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LCC general formulas present value sum of costs and benefits of power system over lifetime which is (LCC = P1�S1 + M1 + R1 + E1) for evaluation criteria to compare LCC among

where P1 is the purchase and installation cost; S1 the salvage value; M1 the maintenance and

Adjusted internal rate of return (AIRR) is a discounted cash flow technique that measures the yearly yield from a solar energy project, taking into account the reinvestment of tentative receipts at a specified rate. The cost-effectiveness of power project estimating adjusted internal rate of return (AIRR) includes comparisons between the projects calculated AIRR and the investor's minimum acceptable rate of return (MARR). Table 8 represents the cost-

PVI the present value of investment, c the costs, and 1/n the nth root of the ratio of TV/PVI.

Evaluation criteria

Compare LCC among mutually exclusive Alternatives. Minimum LCC

Evaluation criteria

AIRR must be equal to or greater than the investor's minimum rate of return

LCC1 < LCC2

as present value

P1, S1, M1, R1, E1

LCC = P1�S1 + M1 + R1 + E1

AIRR = Find the nth root of the ratio of the terminal value of all cash flows (except investment costs) to the present value of investment costs and subtract 1 AIRR = (TV/PVI)1/n � 1

exclusive alternatives. Minimum LCC and LCC1 < LCC2.

R1 the replacement costs; and E1 the electricity costs.

effectiveness if the AIRR is greater than the MARR.

Table 7. Life Cycle Cost guidelines are to define cost-effectiveness.

where TV is terminal value of all cash flows except investment costs,

Method financial analysis General formulas: All costs expressed

Method of financial analysis General formulas: All costs expressed as

Table 8. General formulas and evaluation criteria for adjusted internal rate of return.

present value

LCC [18].

repair costs;

Annex 4

Life cycle cost (LCC)

life of a system

Present value sum of costs and benefits over

Adjusted internal rate of return (AIRR) measures annual yield from a project assuming reinvestment of interim

proceeds at the MARR

where Y = summation from years 1 to Y; E = reduction in electricity costs in year j;

M = differential maintenance and repair costs in year j; S = differential salvage value in year j;

R = differential replacement costs; and P = differential purchase and installation costs.

## Annex 2

Savings-to-investment ratio (SIR) can be used to compare savings to costs of one energy system relative to an alternative power system. For a good result for net savings, the savingto-investment ratio (SIR) should be greater than one. The higher the ratio, the greater the savings realized relative to the investment. Table 6 represents the SIR methods in financial analysis by Enas R. Shouman et al. [1, 18].

#### Annex 3

Life-cycle cost analysis (LCC) shows a summation of all relevant present and future costs to build the system for CSP energy system. These costs include energy, installation, acquisition, operations and maintenance, repair, inflation, replacement (less salvage value) and the discount rate for the life of the investment.


Table 5. Payback period general formulas.


Table 6. Savings-to-investment ratio general formulas and evaluation criteria.

If the life cycle cost analysis is lower than that for the base case and in other aspects is equal, then the life cycle cost meets the objectives of investor and budget constraints. It is considered as cost-effective and the preferred investment. Table 7 shows the equation to calculate LCC [18].

LCC general formulas present value sum of costs and benefits of power system over lifetime which is (LCC = P1�S1 + M1 + R1 + E1) for evaluation criteria to compare LCC among exclusive alternatives. Minimum LCC and LCC1 < LCC2.

where P1 is the purchase and installation cost; S1 the salvage value; M1 the maintenance and repair costs;

R1 the replacement costs; and E1 the electricity costs.

## Annex 4

solar energy project is calculated as the total cost of investment divided by the income of the first year from the energy produced. If the payback period analysis is less than the expected power system life, the projects of the power system are potential to be cost-effective evidence. Projects of power system with short payback periods are considered to have lower risks. Table 5 shows the equation for payback calculation indicated by Enas R. Shouman

M = differential maintenance and repair costs in year j; S = differential salvage value in

Savings-to-investment ratio (SIR) can be used to compare savings to costs of one energy system relative to an alternative power system. For a good result for net savings, the savingto-investment ratio (SIR) should be greater than one. The higher the ratio, the greater the savings realized relative to the investment. Table 6 represents the SIR methods in financial

Life-cycle cost analysis (LCC) shows a summation of all relevant present and future costs to build the system for CSP energy system. These costs include energy, installation, acquisition, operations and maintenance, repair, inflation, replacement (less salvage value) and the dis-

Evaluation criteria

system project life time

present value

SIR = (E-M) (P�S + R)

Payback period is less than the power

Criteria evaluation

SIR>1

where Y = summation from years 1 to Y; E = reduction in electricity costs in year j;

R = differential replacement costs; and P = differential purchase and installation costs.

et al. [1, 18].

year j;

Annex 2

Annex 3

(DPB)

analysis by Enas R. Shouman et al. [1, 18].

156 Thermal Power Plants - New Trends and Recent Developments

count rate for the life of the investment.

Table 5. Payback period general formulas.

recompensing for the time value of money.

Savings-to-investment ratio (SIR)

Discounted payback period

Minimum time it takes to recover an investment

Financial analysis General formulas: All costs expressed as present value

j = 1

The ratio represents how many times savings exceed costs and

Table 6. Savings-to-investment ratio general formulas and evaluation criteria.

DPB = Find Y, such that <sup>Y</sup> <sup>P</sup>ð Þ EJ � MJ � RJ <sup>þ</sup> SJ =P

Payback Period <sup>¼</sup> Overalcostofthepowersystem

Financial analysis General formulas: Costs of

Totalcostofthefuelgeneratoratfristyear

Adjusted internal rate of return (AIRR) is a discounted cash flow technique that measures the yearly yield from a solar energy project, taking into account the reinvestment of tentative receipts at a specified rate. The cost-effectiveness of power project estimating adjusted internal rate of return (AIRR) includes comparisons between the projects calculated AIRR and the investor's minimum acceptable rate of return (MARR). Table 8 represents the costeffectiveness if the AIRR is greater than the MARR.

where TV is terminal value of all cash flows except investment costs,

PVI the present value of investment, c the costs, and 1/n the nth root of the ratio of TV/PVI.


Table 7. Life Cycle Cost guidelines are to define cost-effectiveness.


Table 8. General formulas and evaluation criteria for adjusted internal rate of return.

#### Annex 5

#### Levelized cost of electricity (LCOE) estimation follows the following calculations.

$$\textbf{LCOE} = \frac{\sum\_{t=1}^{n} \frac{I\_t + M\_t + F\_t}{\left(1 + r\right)^t}}{\sum\_{t}^{n} 1 \frac{E\_t}{\left(1 + r\right)^t}}$$

[4] Trieb F et al. Concentrating Solar Power for the Mediterranean Region, MED (CSP). BMU, Germany: German Aerospace Center (DLR); 2005. http://www.dlr.de/tt/med-Concentrating

Economic Future of Concentrating Solar Power for Electricity Generation

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159

[5] Kearney AT, ESTELA. Solar Thermal Electricity 2025. Brussels: ESTELA; 2010. http:// www.estelasolar.eu/index.php?id=22 and EASAC 2011, "Concentrating Solar Power" [6] NREL Solar Paces database (http://www.nrel.gov/Concentrating Solar Power (CSP)/ solarpaces/by\_project.cfm). BNEF Database. Protermosolar (http://www.protermosolar.

[7] OECD/IEA, International Energy Agency Technology Roadmap Concentrating Solar

[8] Shouman ER, Khattab NM. Future economic of concentrating solar power (CSP) for electricity generation in Egypt. Renewable and Sustainable Energy Reviews. 2015;41:

[9] Technology Roadmap Concentrating Solar Power. Paris: International Energy Agency;

[10] http://www.seda-eg.com/content/advantages-egypts-geographical-position-global-sun-belt [11] CSIR, ESKOM, DME. 2004. http://www.watersafe.co.za/2010/08/20/why-solar-energy-in-

[12] International Energy Agency (IEA). Technology Roadmap Concentrating Solar Power

[14] EIA. Annual Energy Outlook Online. 2006. Available at: www.eia.doe.gov/oiaf/aeo

2885/4422\_read-6575 Includes data from: Algeria, Libya, Morocco, Tunisia

[15] German Aerospace Center (DLR). Concentrating Solar Power for the Mediterranean Region. [Online]. 2005. Available at: http://www.dlr.de/tt/en/desktopdefault.aspx/tabid-

[17] Trieb F et al. Combined Solar and Desalination Plants: Techno-Economic Potential in Medi-

[18] Shouman ER, El Shenawy T, Khattab NM. Market financial analysis and cost performance for photovoltaic technology through international and national perspective with case study for Egypt. Journal of Renewable and Sustainable Energy Reviews. 2016;57:

[19] Kearney AT, ESTELA. Solar Thermal Electricity 2025. Brussels: ESTELA; 2010. http://www.

[20] IEA. Technology Roadmap Concentrating Solar Power. International Energy Agency,

[13] http://newenergynews.blogspot.com/search?q=(CSP)+economic+

[16] Renewable Energy Sector in egypt. Final Report, IMC; 2006

terranean Partner Countries. MED CSD. Final Report; 2010. p.21

Solar Power (CSP)

com/)

Power; 2010

1119-1127

south-africa

540-549

estelasolar.eu/index.php?id=22

Paris. 2010, 2010. www.iea.org

2010. www.iea.org

where LCOE is the average lifetime levelized cost of electricity.

generation; It the investment expenditures in the year t; Mt. the operation and maintenance expenditures in the year t; Ft the fuel expenditures in the year t; Et the electricity generation in the year t; r the discount rate; and n the life of the system.

#### Annex 6

#### The cost experience curve function is

$$c\_x = c\_0 \left(\frac{P\_x}{P\_0}\right)^{\frac{\log \mu\_0}{\log 2}}$$

where PR is the progress ratio, Cx is the specific investment at point x, C0 is the specific investment at reference point 0, Px is the cumulated capacity at point x, and P0 is the cumulated capacity at reference point 0 [11, 16, 17].

### Author details

Enas Raafat Maamoun Shouman

Address all correspondence to: shouman@hotmail.com

Information Systems Department, Engineering Division, National Research Centre, Giza, Egypt

#### References


[4] Trieb F et al. Concentrating Solar Power for the Mediterranean Region, MED (CSP). BMU, Germany: German Aerospace Center (DLR); 2005. http://www.dlr.de/tt/med-Concentrating Solar Power (CSP)

Annex 5

Annex 6

Author details

Egypt

References

Enas Raafat Maamoun Shouman

Levelized cost of electricity (LCOE) estimation follows the following calculations.

Pn t¼1

Pn t 1 Et ð Þ <sup>1</sup>þ<sup>r</sup> <sup>t</sup>

generation; It the investment expenditures in the year t; Mt. the operation and maintenance expenditures in the year t; Ft the fuel expenditures in the year t; Et the electricity generation in

ItþMtþFt ð Þ <sup>1</sup>þ<sup>r</sup> <sup>t</sup>

LCOE ¼

cx ¼ c0

Px P0 � �logPR log2

where PR is the progress ratio, Cx is the specific investment at point x, C0 is the specific investment at reference point 0, Px is the cumulated capacity at point x, and P0 is the cumu-

Information Systems Department, Engineering Division, National Research Centre, Giza,

[1] Shouman ER, Hesham Ezz. Forecasting transition electricity solar energy from MENA to

[3] http://meteonorm.com/images/uploads/demo\_uploads/ghi\_world\_mn71.png. March 2015

Europe. Journal of Engineering and Applied Sciences. March 2016;11(5)

where LCOE is the average lifetime levelized cost of electricity.

the year t; r the discount rate; and n the life of the system.

The cost experience curve function is

158 Thermal Power Plants - New Trends and Recent Developments

lated capacity at reference point 0 [11, 16, 17].

Address all correspondence to: shouman@hotmail.com

[2] Burn, Energy Journal. http://burnanenergyjournal.com/


[21] Neij L et al. Experience Curves: A Tool for Energy Policy Assessment: Lund University, European Commission, Lund; 2003. http://www.iset.unikassel.de/extool/Extool\_

[22] Egyptian Electricity Holding Company: 2008/2009. Arab Republic of Egypt: Ministry of

[23] Trieb F, Müller-Steinhagen H, Kern J. Financing concentrating solar power in the Middle

[24] Loosen A et al. Pre-Feasibility Study Report- KomOmbo. EMPower Program, Phase II; United Nations Environment Program; German Ministry of Economic Cooperation and

final\_report.pdf

Electricity & Energy

East and North Africa. Elsevier; 2011

160 Thermal Power Plants - New Trends and Recent Developments

Development (BMZ) represented by KfW. 2010

## *Edited by Paweł Madejski*

The demand for electricity and heat production is still largely covered by conventional thermal power plants based on fossil fuel combustion. Thermal power stations face a big challenge to meet the environmental requirements constantly keeping high process efficiency and avoiding lifetime shortening of critical components. In recent years, many activities have been observed to reduce pollutant emissions and optimize performance in thermal power plants.

Increased share of renewable sources of energy in domestic markets enforces flexible operation and fast adjustment to actual demand. Gas power plants start to play a very important role in this process, allowing for rapid change of load and emission reduction. Operation under changing load together with keeping emissions at the accurate level requires constantly introducing new solutions and technologies as well as carrying out many research and development activities for optimization of the electricity and heat production process.

The edited book is aimed to present new technologies, innovative solutions, measurement techniques, tools and computational methods dedicated to thermal power plants in the light of new trends and challenges.

Published in London, UK © 2018 IntechOpen © imbeatstudio / iStock

Thermal Power Plants - New Trends and Recent Developments

Thermal Power Plants

New Trends and Recent Developments

*Edited by Paweł Madejski*