**3. Energy conservation schemes in distillation column**

Distillation columns are usually among the major energy-consuming units in the food, chemical, petrochemical and refining industries. According to Danziger (1979), the most effective method of economizing energy in a distillation column is energy recovery of which direct vapour recompression has been regarded as the best solution.

#### **3.1 Heat pumping distillation systems**

Basically, the heat pump can be regarded simply as reverse heat engine. The heat pump requires either work input or external driving thermal energy to remove the heat from a low temperature source and transform it to a higher level.

Over the years, there have been many searches for lower energy alternatives or improved efficiencies in distillation columns. One such search led to the use of heat pumps, the idea which was introduced in the 1950s. Also, Jorapur and Rajvanshi (1991) have used solar energy for alcohol distillation and concluded that it was not economically viable. Heat pumping, however, has been known as an economical energy integration technology for reduction in consumption of primary energy and to minimize negative impact of large cooling and heating demands to the environment. One of the heat pump cycles which have been widely studied is the recompression of the vapours where the reboiler is heated by

Most studies have concluded that heat pumping is an effective means of saving energy and reducing column size without estimating the actual energy consumption and the parameters that are likely to have significant effect on energy consumption. Estimating the actual energy consumption is an important aspect towards the determination of the viability of the

The purpose of this chapter was to study how previously neglected and/or assumed values of different parameters (the pressure increase across the compressor was ignored, column heat loss was assumed to be 10% of the reboiler heat transfer rate, and the overall heat transfer coefcient was determined without considering it as an explicit function of dimensionless numbers, and its dependence on uid viscosity and thermal conductivity neglected) affect the process efficiency, energy consumption and the column size of a

Ethanol distillation, like any other distillation process requires a high amount of thermal energy. Studies carried out by several authors reveal that the distillation process in ethanol distilleries consumes more than half of the total energy used at the distillery (Pfeffer et al. 2007). It has been estimated that distillation takes up about 70-85% of total energy consumed in ethanol production. Pfeffer et al (2007) estimated that distillation consumes half of the

The energy requirements for ethanol production have improved markedly during the past decade due to a variety of technology and plant design improvements. The energy needed to produce a liter of ethanol has decreased nearly 50% over the past decade and that trend is

Distillation columns are usually among the major energy-consuming units in the food, chemical, petrochemical and refining industries. According to Danziger (1979), the most effective method of economizing energy in a distillation column is energy recovery of which

Basically, the heat pump can be regarded simply as reverse heat engine. The heat pump requires either work input or external driving thermal energy to remove the heat from a low

adding a compressor to the column to recover some of the heat lost in the distillate.

system in ethanol–water separation.

vapour recompression heat pump.

**2. Energy requirements in ethanol distillation** 

total production energy 5.6 MJ/Liter out of 11.1 – 12.5 MJ/Liter.

**3. Energy conservation schemes in distillation column** 

direct vapour recompression has been regarded as the best solution.

**3.1 Heat pumping distillation systems** 

temperature source and transform it to a higher level.

likely to continue as process technology improves ( Braisher *et al*, 2006).

The conventional heat pumps are electrically driven vapour recompression types, which work on the principle that a liquid boils at a higher temperature if its pressure is increased. A low-pressure liquid passes into the evaporator, where it takes in heat causing the liquid to boil at low temperature. The low-pressure vapour is passed to the compressor where it is compressed by the application of work to a higher pressure. The resulting high pressure vapour flows to the condenser where it condenses, giving up its latent heat at a high temperature, before expanding back to a low pressure liquid.

The heat pump cycle may be connected to a distillation column in three ways (Fonyo and Benko, 1998) . The simplest alteration is to replace steam and cooling water with refrigerant (closed system). The other two types of heat pump system apply column fluids as refrigerant . When the distillate is a good refrigerant the vapour recompression can be used. If the bottom product is a good refrigerant the bottom flashing can be applied.

In this work, the direct vapour recompression system is studied due to its good economic figures ( Emtir et al, 2003). Also the vapour recompression is the most suitable as the boiling points of both key components (ethanol and water) are close to each other (Danziger, 1979) and the appropriate heat transfer medium (ethanol vapour) is available.

#### **3.2 Use of vapour recompression in distillation columns**

Vapour recompression system has been extensively studied since 1973, the year of drastic rise in energy (Null, 1976). The vapour recompression system is accomplished by using compressor to raise the energy level of vapour that is condensed in reboiler–condenser by exchange of heat with the bottoms. The condensate distillate is passed into reflux drum while the bottom product is vaporised into the column.

Vapour recompression consists of taking the overhead vapour of a column, condensing the vapour to liquid, and using the heat liberated by the condensation to reboil the bottoms liquid from the same column. The temperature driving force needed to force heat to flow from the cooler overhead vapours to the hotter bottoms product liquid is set up by either compressing the overhead vapour so that it condenses at a higher temperature, or lowering the pressure on the reboiler liquid so it boils at a lower temperature, then compressing the bottoms vapour back to the column pressure. While conventional column has a separate condenser and reboiler, each with its own heat transfer fluid such as cooling water and steam, the vapour recompression column has a combined condenser–reboiler, with external heat transfer fluids.

The advantage of vapour recompression lies in its ability to move large quantities of heat between the condenser and reboiler of the column with a small work input. This results from cases where there is only a small difference between the overhead and bottoms temperature. Also, the temperature, and therefore the pressure, at any point may be set where desired to achieve maximum separation. This effect is of particular importance where changing the pressure affects the relative volatility. By operating at more favourable conditions, the reflux requirement can be reduced and therefore the heat duties. These advantages can reduce a large amount of energy.

### **4. Ethanol-water vapour recompression distillation column**

Figure 1 shows a schematic illustration of the distillation column with direct vapour recompression heat pump. An ethanol-water solution in a feed storage tank (FST) at

Energy Conservation in Ethanol-Water

and the fluid flow equations Mori et al (2002).

**4.2 Calculation of the distillation column** 

given (see Enweremadu, 2007).

Distillation Column with Vapour Recompression Heat Pump 39

et al. 2001). The mathematical modeling of the distillation system is derived by applying energy, composition and overall material balances together with vapour-liquid equilibrium under some assumptions (see Muhrer *et al*, 1990 and Enweremadu, 2007). These and other assumptions are aimed at simplifying the otherwise cumbersome heat-and mass-transfer,

In this system, there is a direct coupling between the distillation column and the rest of the system, as the heat pump working fluid is the column's own fluid which, is a binary mixture of ethanol and water at composition XD. Therefore, the set of equations are not solved

The detailed calculation of the overall material and component material balance such as the bottom ow rate, B and distillate ow rate, D; reux ratio, Rr; the molar vapour ow rate which leaves the column top and feeds the condenser, V1; feed vapour ow rate, VF; feed vapour fraction, q; vapour molar ow rate remaining at the bottom of the column, L2 are

The overall (global) energy balance equation applied to a control volume comprising the distillation column and the feed pre-heaters provides the total energy demand in the reboiler:

 Qreb = DhD + BhB + L1hLV, e + Qlosses – FhF – Q1 – Q2 (1) where Qreb is the total heat load added to the reboiler, Qlosses represents the heat losses in the column, which are to be determined; Q1 and Q2 are the heat loads of the pre-heaters; hLV,e is latent heat of vaporisation downstream of throttling valve; hD, is the enthalpy of the distillate; hB is the enthalpy of the bottom product; hF, is the enthalpy of the feed. The details

The first step in the design of a distillation column is the determination of the number of theoretical plates required for the given separation. The theoretical trays are numbered from the top down, and subscripts generally indicate the tray from which a stream originates with n and m standing for rectifying and stripping sections respectively. The design procedure for a tray distillation column consists of determining the liquid and vapour composition or fraction from top to bottom, along the column. In calculating the composition profile of the column two equations relating liquid mole fraction to temperature and vapour mole fraction to the liquid fraction are used. The compositions at the top (XD) and bottom (XB) of the column are previously pre-established data. In this work, the minimum number of theoretical stages (Nmin) is calculated using Fenske's equation:

<sup>1</sup> log . <sup>1</sup>

*X X <sup>N</sup>*

where α is the relative volatility in the column. The actual number of plates is given by:

*<sup>N</sup> <sup>N</sup>* 

log

min *T*

*D B D B X X*

(2)

(3)

separately as in distillation column assisted by an external heat pump.

of the mass balance variables are determined in Enweremadu (2007).

min

Fig. 1. Schematic Diagram of Column with Direct Vapour Recompression Heat Pump

ambient conditions, is preheated with bottom product and condensate in heat exchangers, preheaters PH1 and PH2, and fed to the column. An auxiliary reboiler (AR) is used to start the unit. This reboiler supplies the auxiliary heat duty, which is the heat of vaporization because the main reboiler can work only if there is some compressed vapour already available. The overhead vapours from the top are compressed in the compressor (CP) up to the necessary pressure in such a way that its condensing temperature is greater than the boiling temperature of the column bottom product. The vapour is then condensed by exchanging heat within the tubes of the reboiler-condenser (RC). In a condenser, the inlet temperature is equal to the outlet temperature. Ethanol vapour will only lose its latent heat of condensation. At the same time, the cold fluid (ethanol-water mixture) in the reboiler will absorb this latent heat and its temperature will increase to boil up the mixture to temperature TCEV. The liberated latent heat of condensation provides the boil-up rate to the column while the excess heat extracted from the condensate is exchanged with the feed in preheater PH2. The condensate, which is cooled in the cooler (CL) up to its bubble point at the column operating pressure, expands through the throttling valve (TV) at the same pressure and reaches the flash tank (FT). After expansion, the output phases are a vapour phase in equilibrium with a liquid phase. One part of the product in the liquid phase is removed as distillate and stored in the tank (DST), while the remainder is recycled into the column as reflux L1. The excess of vapour is recycled to the compressor.

#### **4.1 Methodology**

Like this work, nearly all publications in this field are based on modelling and simulation (Brousse et al., 1985; Ferre et al., 1985; Collura and Luyben, 1988; Muhrer *et al*, 1990; Oliveira et al. 2001). The mathematical modeling of the distillation system is derived by applying energy, composition and overall material balances together with vapour-liquid equilibrium under some assumptions (see Muhrer *et al*, 1990 and Enweremadu, 2007). These and other assumptions are aimed at simplifying the otherwise cumbersome heat-and mass-transfer, and the fluid flow equations Mori et al (2002).

#### **4.2 Calculation of the distillation column**

38 Distillation – Advances from Modeling to Applications

Fig. 1. Schematic Diagram of Column with Direct Vapour Recompression Heat Pump

column as reflux L1. The excess of vapour is recycled to the compressor.

Like this work, nearly all publications in this field are based on modelling and simulation (Brousse et al., 1985; Ferre et al., 1985; Collura and Luyben, 1988; Muhrer *et al*, 1990; Oliveira

**4.1 Methodology** 

ambient conditions, is preheated with bottom product and condensate in heat exchangers, preheaters PH1 and PH2, and fed to the column. An auxiliary reboiler (AR) is used to start the unit. This reboiler supplies the auxiliary heat duty, which is the heat of vaporization because the main reboiler can work only if there is some compressed vapour already available. The overhead vapours from the top are compressed in the compressor (CP) up to the necessary pressure in such a way that its condensing temperature is greater than the boiling temperature of the column bottom product. The vapour is then condensed by exchanging heat within the tubes of the reboiler-condenser (RC). In a condenser, the inlet temperature is equal to the outlet temperature. Ethanol vapour will only lose its latent heat of condensation. At the same time, the cold fluid (ethanol-water mixture) in the reboiler will absorb this latent heat and its temperature will increase to boil up the mixture to temperature TCEV. The liberated latent heat of condensation provides the boil-up rate to the column while the excess heat extracted from the condensate is exchanged with the feed in preheater PH2. The condensate, which is cooled in the cooler (CL) up to its bubble point at the column operating pressure, expands through the throttling valve (TV) at the same pressure and reaches the flash tank (FT). After expansion, the output phases are a vapour phase in equilibrium with a liquid phase. One part of the product in the liquid phase is removed as distillate and stored in the tank (DST), while the remainder is recycled into the In this system, there is a direct coupling between the distillation column and the rest of the system, as the heat pump working fluid is the column's own fluid which, is a binary mixture of ethanol and water at composition XD. Therefore, the set of equations are not solved separately as in distillation column assisted by an external heat pump.

The detailed calculation of the overall material and component material balance such as the bottom ow rate, B and distillate ow rate, D; reux ratio, Rr; the molar vapour ow rate which leaves the column top and feeds the condenser, V1; feed vapour ow rate, VF; feed vapour fraction, q; vapour molar ow rate remaining at the bottom of the column, L2 are given (see Enweremadu, 2007).

The overall (global) energy balance equation applied to a control volume comprising the distillation column and the feed pre-heaters provides the total energy demand in the reboiler:

$$\mathbf{Q\_{reb}} = \mathbf{D}\mathbf{h\_D} + \mathbf{B}\mathbf{h\_B} + \mathbf{L\_I}\mathbf{h\_{LV,e}} + \mathbf{Q\_{losses}} - \mathbf{F}\mathbf{h\_F} - \mathbf{Q\_1} - \mathbf{Q\_2} \tag{1}$$

where Qreb is the total heat load added to the reboiler, Qlosses represents the heat losses in the column, which are to be determined; Q1 and Q2 are the heat loads of the pre-heaters; hLV,e is latent heat of vaporisation downstream of throttling valve; hD, is the enthalpy of the distillate; hB is the enthalpy of the bottom product; hF, is the enthalpy of the feed. The details of the mass balance variables are determined in Enweremadu (2007).

The first step in the design of a distillation column is the determination of the number of theoretical plates required for the given separation. The theoretical trays are numbered from the top down, and subscripts generally indicate the tray from which a stream originates with n and m standing for rectifying and stripping sections respectively. The design procedure for a tray distillation column consists of determining the liquid and vapour composition or fraction from top to bottom, along the column. In calculating the composition profile of the column two equations relating liquid mole fraction to temperature and vapour mole fraction to the liquid fraction are used. The compositions at the top (XD) and bottom (XB) of the column are previously pre-established data. In this work, the minimum number of theoretical stages (Nmin) is calculated using Fenske's equation:

$$N\_{N\text{ min}} = \frac{\log\left(\frac{X\_D}{1 - X\_D}, \frac{1 - X\_{\text{s}}}{X\_{\text{s}}}\right)}{\log a} \tag{2}$$

where α is the relative volatility in the column. The actual number of plates is given by:

$$N = \frac{N\_{\text{min}}}{\eta\_{\text{r}}} \tag{3}$$

Energy Conservation in Ethanol-Water

From dimensional analysis,

Rajput (2002) as: For laminar flow,

For turbulent flow,

(5) reduces to:

surrounding; Tp – plate temperature.

given as

Distillation Column with Vapour Recompression Heat Pump 41

Also, from geometry of the insulated cylinder (Fig.2), the external diameter of insulation is

 dins = do + 2tins (8) Details of how the logarithmic mean diameter of the insulating layer (dins,m), external area of heat exchange (Ao) and the logarithmic mean area (A*m*) can be found in Enweremadu (2007).

2

Kwal

(9)

*o ins K Nu <sup>h</sup> d t*

where, tins is the thickness of insulation; Kins – thermal conductivity of the insulation materials; Nu – Nusselt number; do – external diameter of column; Tamb – temperature of the

*ins <sup>o</sup>*

Fig. 2. Hypotethical Section of the Distillation Column with Insulation

Cold fluid (air)

QLo

where Gr is the Grashof number and Pr is Prandtl.

For vertical cylinders, the commonly used correlations for free convection are adapted from

ri row rins

hot fluid

hi

Tp

ho

Based on the assumptions of neglecting hi, Ai and the effect of thermal resistance, equation

1/4 Nu 0.59 Gr.Pr for (104<Gr.Pr<109) (10)

Ti

Tsurf Kins

> Tins To

1/3 *Nu* 0.10 Gr.Pr for (109<Gr.Pr<1012) (11)

where *<sup>T</sup>* is the tray efficiency.

#### **4.2.1 Heat losses from distillation column**

The heat loss from the distillation column is the main factor that affects heat added and removed at the reboiler and condenser respectively. Most distillation columns operate above ambient temperature, and heat losses along the column are inevitable since insulating materials have a finite thermal conductivity. Heat loss along the distillation column increase condensation and reduces evaporation. Thus, the amount of vapour diminishes in the upward part of the column, where the flow of liquid is also less than at the bottom.

To prevent loss of heat, the distillation column should be well insulated. Insulation of columns using vapour recompression varies with the situation. Where the column is hot and extra reboiler duty is used, the column should be insulated (Sloley, 2001). The imperfect insulation of the column causes some heat output.

In determining the heat loss from the distillation column, it is assumed that the temperature is uniform in the space between two plates. The heat transfer between the column wall and the surrounding is then determined from the well-known relationship for overall heat transfer coefficient:

$$Q\_{Loss} = \mathcal{U}\_P A\_0 \Delta T\_P \tag{4}$$

where Up, the overall heat transfer coefficient is given by Gani, Ruiz and Cameron (1986), as

$$\mathbf{U}\_p = f\left(\mathbf{h}\_{o'}\mathbf{h}\_{i'}\mathbf{K}\_{p'}\mathbf{A}\_{o'}\mathbf{A}\_{1'}\mathbf{A}\_{m'}\mathbf{t}\_{\rm{ins}}\right) \tag{5}$$

where the temperature difference, *Tp* , is given as *<sup>p</sup> amb T TT <sup>p</sup>*

ho, the heat transfer coefficient between the surroundings and the column external surface, is given as

$$\mathbf{h}\_{\rm o} = \mathbf{f}(\mathbf{N}\mathbf{u}\_{\prime}\,\,\mathbf{K}\_{\rm irs}\,\,\mathbf{d}\_{\rm o}\,\,\mathbf{t}\_{\rm irs}) \tag{6}$$

hi is the heat transfer coefficient inside the column; *K*p is the thermal conductivity of the tray material; Ao is the external area of heat exchange; Ai is the internal area of heat exchange; A*m* is the logarithmic mean area; tins is the thickness of insulation.

The heat output is calculated with the general expression for convection around cylindrical objects.

$$Q\_{loss} = \frac{T\_p - T\_{amb}}{\left\{h\_i A\_i + \frac{\ln\left(r\_{\text{ball}} / \, r\_{\text{ball}}\right)}{K\_{\text{wall}} \cdot A\_{\text{wall}}} + \frac{\ln\left(r\_{\text{ins}} / r\_{\text{ball}}\right)}{K\_{\text{ins}} \cdot A\_{\text{m}}} + \right\}\_{h\_o A\_o}}\tag{7}$$

The column inner surface heat transfer resistance is neglected as the heat transfer coefficient for condensing vapor is large and therefore will have little effect on the overall heat transfer.

Based on the assumptions in Enweremadu (2007), the heat transfer due to free convection between the surroundings and the external column wall and due to conduction through the insulation materials is predicted.

Also, from geometry of the insulated cylinder (Fig.2), the external diameter of insulation is given as

$$\mathbf{d}\_{\rm{irs}} = \mathbf{d}\_{\rm{o}} + 2\mathbf{t}\_{\rm{irs}} \tag{8}$$

Details of how the logarithmic mean diameter of the insulating layer (dins,m), external area of heat exchange (Ao) and the logarithmic mean area (A*m*) can be found in Enweremadu (2007).

From dimensional analysis,

40 Distillation – Advances from Modeling to Applications

The heat loss from the distillation column is the main factor that affects heat added and removed at the reboiler and condenser respectively. Most distillation columns operate above ambient temperature, and heat losses along the column are inevitable since insulating materials have a finite thermal conductivity. Heat loss along the distillation column increase condensation and reduces evaporation. Thus, the amount of vapour diminishes in the

To prevent loss of heat, the distillation column should be well insulated. Insulation of columns using vapour recompression varies with the situation. Where the column is hot and extra reboiler duty is used, the column should be insulated (Sloley, 2001). The imperfect

In determining the heat loss from the distillation column, it is assumed that the temperature is uniform in the space between two plates. The heat transfer between the column wall and the surrounding is then determined from the well-known relationship for overall heat

where Up, the overall heat transfer coefficient is given by Gani, Ruiz and Cameron (1986), as

ho, the heat transfer coefficient between the surroundings and the column external surface,

 ho = f(Nu, *K*ins, do, tins) (6) hi is the heat transfer coefficient inside the column; *K*p is the thermal conductivity of the tray material; Ao is the external area of heat exchange; Ai is the internal area of heat exchange;

The heat output is calculated with the general expression for convection around cylindrical

ln / ln / 1 1 *wall wall ins wall*

The column inner surface heat transfer resistance is neglected as the heat transfer coefficient for condensing vapor is large and therefore will have little effect on the overall heat transfer. Based on the assumptions in Enweremadu (2007), the heat transfer due to free convection between the surroundings and the external column wall and due to conduction through the

*o i o i i wall wall o o ins m*

*r r rr h A K A KA h A*

*Losses <sup>o</sup> Q UA T P P* (4)

(7)

*U fhhK A A A t <sup>p</sup> o i o m ins* ,, , , , , *<sup>p</sup>* <sup>1</sup> (5)

upward part of the column, where the flow of liquid is also less than at the bottom.

where 

transfer coefficient:

is given as

objects.

insulation materials is predicted.

*<sup>T</sup>* is the tray efficiency.

**4.2.1 Heat losses from distillation column** 

insulation of the column causes some heat output.

where the temperature difference, *Tp* , is given as *<sup>p</sup> amb T TT <sup>p</sup>*

A*m* is the logarithmic mean area; tins is the thickness of insulation.

*amb <sup>P</sup> loss*

*T T <sup>Q</sup>*

$$\hbar h\_o = \frac{K\_{ins} \cdot N\mu}{d\_o + 2t\_{ins}} \tag{9}$$

where, tins is the thickness of insulation; Kins – thermal conductivity of the insulation materials; Nu – Nusselt number; do – external diameter of column; Tamb – temperature of the surrounding; Tp – plate temperature.

Fig. 2. Hypotethical Section of the Distillation Column with Insulation

For vertical cylinders, the commonly used correlations for free convection are adapted from Rajput (2002) as:

For laminar flow,

$$\text{Nu} = 0.59 \text{(Gr.Pr)}^{1/4} \text{ for (104°Gr.Pr} \text{<10°)} \tag{10}$$

For turbulent flow,

$$\text{Nu} = 0.10 \text{(Gr.Pr)}^{1/3} \text{ for (10°°Gr.Pr} \text{<10°2)} \tag{11}$$

where Gr is the Grashof number and Pr is Prandtl.

Based on the assumptions of neglecting hi, Ai and the effect of thermal resistance, equation (5) reduces to:

Energy Conservation in Ethanol-Water

condensation temperature as

temperature; *A and B* are constants.

volume is determined by:

(Ackland, 1990):

PTOP:

TTOP.

fluid. These are obtained from thermodynamic correlations.

while the condensation pressure is determined from ideal gas equation.

<sup>C</sup> LV,CHP

vap

Distillation Column with Vapour Recompression Heat Pump 43

where TCEV is the column vapourization (reboiler) temperature and ΔTCHP, a pre-established mean temperature difference across the heat exchangers (temperature drop in reboilercondenser). Next is the estimation of the relevant thermodynamic properties of the working

The thermodynamic properties are determined as functions of temperature. The relationships used for calculating the working fluid density, viscosity, thermal conductivity and heat capacity for input at various locations are presented in Enweremadu (2007). The condensation pressure, PCHP is expressed as a function of

PCHP = f(TCHP) (19)

The latent heat of condensation from column to heat pump is numerically exactly equal to the latent heat of vaporisation, but has the opposite sign: latent heat of vaporisation is always positive (heat is absorbed by the substance), whereas latent heat of condensation is always negative (heat is released by the substance). Latent heat of condensation is expressed as a function of condensation temperature and is determined from the relationship

> bp C

where Hvap is the heat of vapourisation at the boiling point of ethanol; TC is the critical

The vapour specific volume at location "**a"** (entrance to the compressor) is expressed as a function of column condensation temperature, TCC and pressure at the top of the column,

T R cc

*TOP x*

1

*P <sup>n</sup>*

Since compression is polytropic, at location **"b"** (compressor discharge), the vapour specific

*P P v*

The vapour specific enthalpy at "a" is a function of top pressure,PTOP and top temperature,

ha=f(TTOP, PTOP) (23)

*a*

v *TOP <sup>a</sup> CHP*

where n is the polytropic index and ΔP is the pressure increase across the compressor.

*v*

b

<sup>T</sup> A B 1- <sup>T</sup> <sup>T</sup> 1- <sup>T</sup> h H <sup>T</sup>

 

1- <sup>T</sup>

CHP

*<sup>P</sup>* (21)

(22)

(20)

 

CHP C

$$\mathbf{U}\_{\mathcal{P}} = \mathbf{f}(\mathbf{h}\_{\mathbf{0}\prime} \mathbf{K}\_{\mathcal{P}\prime} \mathbf{A}\_{\mathbf{0}\prime} \mathbf{A}\_{m\prime} \mathbf{t}\_{\mathrm{inv}}) \tag{12}$$

while equation (7) is given as

$$Q\_{\text{losses}} = \frac{(T\_p - T\_{amb})\pi P\_s N}{\ln\left(r\_{in} \mid r\_{Ouml}\right)} + \frac{1}{h\_o A\_o} \tag{13}$$

where 1 ln *wall* <sup>1</sup> *<sup>P</sup> <sup>o</sup> ins p m oo U r r K A hA* 

The heat loss from the column trays is given by

$$\mathbf{Q}\_{\text{loss from rays}} = \frac{(T\_P - T\_{amb})\Delta\pi P\_s \mathbf{N}}{\frac{\ln\left(r\_{ins}/r\_o\right)}{K\_p \cdot \frac{\Delta\pi P\_s.t\_{ins}}{\ln\left(1 + \frac{\Delta t\_{ins}}{d\_o}\right)}} + \frac{1}{\frac{K\_{ins} \cdot \text{Nu}}{d\_o + 2t\_{ins}} \cdot (\pi d\_{ins,m} P\_s)}\tag{14}$$

The total heat loss from the column is expressed as

$$\mathbf{Q}\_{\text{loss}} = \mathbf{Q}\_{\text{loss from tuny}} + \text{Heat loss from the two cylinder heads} \tag{15}$$

Based on the assumptions made, heat loss through the cylinder heads is given by

$$\mathbf{Q}\_{\text{loss at cylinder heads}} = \frac{\mathbf{2(T\_P - T\_{\text{amb}})} \pi r\_\alpha^2}{\frac{\text{tins}}{\text{K}\_P} + \frac{1}{\text{ho}}} \tag{16}$$

Therefore,

$$Q\_{\rm loss} = \frac{(T\_P - T\_{\rm amb})\Delta\pi P\_{\rm SN}}{\frac{1\,\mathrm{m}\,(r\_{\rm ins}/r\_o)}{\mathrm{K}\_P \cdot \frac{2\,\mathrm{m}\,P\_s\,\mathrm{at}\_{\rm ins}}{\mathrm{In}\,(1 + \frac{\Delta t\_{\rm ins}}{d\_o})}} + \frac{2\{\mathrm{TP}\,-\mathrm{T}\_{\rm amb}\}\pi r\_o^2}{\frac{\mathrm{K}\_{\rm ins}\,\mathrm{s}\,\mathrm{Nu}}{\mathrm{d}\_o + 2\,\mathrm{t}\_{\rm ins}} \cdot (\pi\,\mathrm{d}\boldsymbol{\pi}\_{\rm ins}\,\mathrm{m}\,P\_s)}}\tag{17}$$

#### **4.3 Calculation of heat pump and compressor parameters**

The heat pump is thermodynamically linked to the column through the heat load from the pump to the column QHPC and from the column to the pump QCHP, and reboiler–condenser temperature. These parameters provide the basis for the heat pump calculation.

The calculation of the heat pump parameters begins with the estimation of the working fluid condensation temperature obtained from the reboiler temperature and temperature drop across the heat exchangers.

$$\mathbf{T}\_{\rm CHF} = \mathbf{T}\_{\rm CEV} + \Delta \mathbf{T}\_{\rm CHP} \tag{18}$$

U*P* = f(ho, Kp, Ao, A*m*, tins) (12)

 ( ) ln / *ins wall* 1 *p amb s*

*T T PN <sup>Q</sup> r r*

*p m oo*

(13)

(14)

(16)

*o*

(17)

*r*

<sup>2</sup> P amb

*o*

*h*

ins p

2(T - T ) t 1 K

, .

*K A hA*

( )2 ln 1

*s ins ins <sup>p</sup> ins m <sup>s</sup> ins o ins <sup>o</sup>*

 

*amb s P*

*P t K Nu <sup>K</sup> d P t d t*

2 . ( ) <sup>2</sup> <sup>2</sup> ln 1

loss from trays Q Q Heat loss from the two c loss ylinder heads (15)

p

 

K *ho*

*losses <sup>o</sup>*

Based on the assumptions made, heat loss through the cylinder heads is given by

, .

2 . ( ) <sup>2</sup> <sup>2</sup> ln 1

The heat pump is thermodynamically linked to the column through the heat load from the pump to the column QHPC and from the column to the pump QCHP, and reboiler–condenser

The calculation of the heat pump parameters begins with the estimation of the working fluid condensation temperature obtained from the reboiler temperature and temperature drop

TCHP = TCEV + ∆TCHP (18)

( )2 ln 1

*s ins ins P s ins m ins o ins <sup>o</sup>*

 

*amb S P*

*P t K Nu <sup>K</sup> d P t d t*

temperature. These parameters provide the basis for the heat pump calculation.

*T T PN <sup>Q</sup> r r*

*o ins*

*d*

<sup>2</sup> p amb <sup>o</sup> loss at cylinder heads ins

2(T - T ) r Q t 1

while equation (7) is given as

where

*U*

Therefore,

across the heat exchangers.

1 ln *wall* <sup>1</sup> *<sup>P</sup> <sup>o</sup> ins*

*r r*

*p m oo*

The heat loss from the column trays is given by

loss from trays

The total heat loss from the column is expressed as

*T T PN <sup>Q</sup> r r*

*d*

**4.3 Calculation of heat pump and compressor parameters** 

*loss <sup>o</sup> ins*

*K A hA*

where TCEV is the column vapourization (reboiler) temperature and ΔTCHP, a pre-established mean temperature difference across the heat exchangers (temperature drop in reboilercondenser). Next is the estimation of the relevant thermodynamic properties of the working fluid. These are obtained from thermodynamic correlations.

The thermodynamic properties are determined as functions of temperature. The relationships used for calculating the working fluid density, viscosity, thermal conductivity and heat capacity for input at various locations are presented in Enweremadu (2007). The condensation pressure, PCHP is expressed as a function of condensation temperature as

$$\mathbf{P}\_{\rm CHP} = \mathbf{f}(\mathbf{T}\_{\rm CHP}) \tag{19}$$

while the condensation pressure is determined from ideal gas equation.

The latent heat of condensation from column to heat pump is numerically exactly equal to the latent heat of vaporisation, but has the opposite sign: latent heat of vaporisation is always positive (heat is absorbed by the substance), whereas latent heat of condensation is always negative (heat is released by the substance). Latent heat of condensation is expressed as a function of condensation temperature and is determined from the relationship (Ackland, 1990):

CHP CHP C <sup>C</sup> LV,CHP bp C vap <sup>T</sup> A B 1- <sup>T</sup> <sup>T</sup> 1- <sup>T</sup> h H <sup>T</sup> 1- <sup>T</sup> (20)

where Hvap is the heat of vapourisation at the boiling point of ethanol; TC is the critical temperature; *A and B* are constants.

The vapour specific volume at location "**a"** (entrance to the compressor) is expressed as a function of column condensation temperature, TCC and pressure at the top of the column, PTOP:

$$w\_{\!\!\!\!-} = \frac{\mathbf{T}\_{\text{ev}} \propto \mathbf{R}}{P\_{\text{TOP}}} \tag{21}$$

Since compression is polytropic, at location **"b"** (compressor discharge), the vapour specific volume is determined by:

$$\mathbf{V}\_{\text{b}} = \mathcal{U}\_{\text{s}} \left( \frac{P\_{\text{T}\text{op}}}{P\_{\text{CHP}} + \Delta P} \right)^{\frac{1}{n}} \tag{22}$$

where n is the polytropic index and ΔP is the pressure increase across the compressor.

The vapour specific enthalpy at "a" is a function of top pressure,PTOP and top temperature, TTOP.

$$\mathbf{h}\_{\mathbf{a}} \mathbf{=} \mathbf{f} (\mathbf{T}\_{\text{TCP}}, \mathbf{P}\_{\text{TCP}}) \tag{23}$$

Energy Conservation in Ethanol-Water

determined from

efficiency.

Distillation Column with Vapour Recompression Heat Pump 45

while the liquid specific enthalpy at location e (at the exit of the throttling valve) is

 hL,e=f(TCC) (29) The temperature at compressor discharge is determined from the knowledge of the compressor efficiency. The ideal discharge temperature (the temperature that gives an overall change in entropy equal to zero) is calculated before correcting with the compressor

TOP

*e*

b TOP

T T

The dryness fraction after the isenthalpic expansion is given by

*bp*

Therefore, the molar flow rate across the compressor is expressed as

*c*

CpL is the molar specific heat of the working fluid in the liquid phase.

While the dryness fraction at condenser exit is determined by

Since this is a throttling process, Td = Te and hd = he

compressor is calculated by

exchange at the condenser, as follows:

CHP

0.263 P P T -1 P

> *pol*

, , *L LV e e*

*e*

*h h h*

where the molar latent heat of vaporization at location "e" is adapted from Ackland (1990):

*LV* , \*1 1 1

The molar vapour flow rate which is recycled in the flash tank and conveyed to the

1 1 *<sup>e</sup> <sup>R</sup>*

,

*Q MC T T h*

where Q23 is the distribution of excess heat between the pre-heater Q2 and the cooler Q3 and

The energy balance, applied to the heat pump working fluid, yields the available energy for

, *<sup>v</sup>* 1 *Q M Cp T T cd b CHP c LV CHP*

*LV CHP*

23 *<sup>L</sup>*

 

*<sup>V</sup> <sup>V</sup>*

*e*

*<sup>h</sup>* (36)

*P CHP d*

*e d <sup>d</sup> vap C bp C <sup>C</sup> h H TT T T A B TT*

TOP

(32)

(30)

(31)

(33)

*<sup>M</sup> V V* <sup>1</sup> *<sup>R</sup>* (34)

(35)

The vapour specific enthalpy at "b" may be determined as a function of compressor discharge temperature Tb and condensation pressure PCHP but in this study, it is determined by the development of numerical computation with calculations utilizing the Redlich – Kwong equation of state. The Redlich – Kwong equation of state is given as

$$P = \frac{RT}{V - b} - \frac{a}{T^{\frac{\nu}{2}}V\left(V + b\right)}\tag{24}$$

Where

$$\begin{aligned} \mathbf{a} &= 0.42747 \left( \frac{R^2 T\_c^{\frac{54}{\zeta}}}{P\_c} \right) \\\\ \mathbf{b} &= 0.08664 \left( \frac{RT\_c}{P\_c} \right) \end{aligned}$$

and P = pressure (atm); V = molar volume (liters/g-mol); T = temperature (K); R = gas constant (atm. Liter/g-mol.K); Pc = critical pressure (atm).

Taking the reference state for the enthalpy of liquid ethanol *<sup>o</sup> <sup>L</sup> h* , temperature, To and the enthalpy of vaporisation Δ *<sup>o</sup> Hvap* , then the enthalpy of ethanol vapour as an ideal gas at temperature T can be calculated from

$$\mathbf{h}\_{\mathbf{h}}\stackrel{\circ}{\mathbf{h}} = \mathbf{h}\_{L}^{\circ} + \Delta H\_{\text{vup}}^{\circ} + \int\_{T\_{\sigma}}^{T} \mathbf{C}\_{P}^{\circ} dT \tag{25}$$

Using the isothermal enthalpy departure and the Redlich-Kwong equation of state, the enthalpy of ethanol vapour at T and P can be calculated from

$$h\nu = h\_L^o + \Delta H\_{vap}^o + \int\_{T\_o}^{T} \mathbf{C}\_P^o dT + RT \left[ Z - 1 - \frac{1.5a}{bRT^{1.5}} \ln\left(1 + \frac{b}{V}\right) \right] \tag{26}$$

where Z is the compressibility factor, Cpo is the molar specific heat capacities of gases at zero pressure given as a polynomial in temperature.

Equations 24–26 are then solved with POLYMATH(R) Simultaneous Algebraic Equation Solver (See Enweremadu, 2007).

The vapour specific heat at location "e" is calculated thus **(**Oliveira *et al*, 2002):

$$\mathbf{h} = h \mathbf{\iota}, \mathbf{c} - \mathbf{C}p \iota \Delta T \mathbf{s} \mathbf{c} \tag{27}$$

The specific liquid enthalpies have been assumed to be simple functions of temperature.

The liquid specific enthalpy at location "c" is determined from EZChemDB Thermodynamic Properties Table for Ethanol (AM Cola LLC, 2005) using the expression

$$\mathbf{h}\mathbf{h}\_{,\mathbf{c}} = \mathbf{f}\mathbf{(T\_{CHP})}\tag{28}$$

The vapour specific enthalpy at "b" may be determined as a function of compressor discharge temperature Tb and condensation pressure PCHP but in this study, it is determined by the development of numerical computation with calculations utilizing the Redlich –

> *RT a <sup>P</sup> V b T VV b*

a = 0.42747

constant (atm. Liter/g-mol.K); Pc = critical pressure (atm).

temperature T can be calculated from

Solver (See Enweremadu, 2007).

Taking the reference state for the enthalpy of liquid ethanol *<sup>o</sup>*

enthalpy of ethanol vapour at T and P can be calculated from

*<sup>T</sup> oo o <sup>b</sup> L vap <sup>T</sup>*

zero pressure given as a polynomial in temperature.

o o

*o*

The vapour specific heat at location "e" is calculated thus **(**Oliveira *et al*, 2002):

Properties Table for Ethanol (AM Cola LLC, 2005) using the expression

b = 0.08664 *<sup>c</sup>*

and P = pressure (atm); V = molar volume (liters/g-mol); T = temperature (K); R = gas

enthalpy of vaporisation Δ *<sup>o</sup> Hvap* , then the enthalpy of ethanol vapour as an ideal gas at

*<sup>L</sup> vap <sup>T</sup>*

Using the isothermal enthalpy departure and the Redlich-Kwong equation of state, the

*a b h h H C dT RT Z <sup>p</sup> bRT <sup>V</sup>*

where Z is the compressibility factor, Cpo is the molar specific heat capacities of gases at

Equations 24–26 are then solved with POLYMATH(R) Simultaneous Algebraic Equation

The specific liquid enthalpies have been assumed to be simple functions of temperature.

The liquid specific enthalpy at location "c" is determined from EZChemDB Thermodynamic

*T o o*

*H C dT <sup>p</sup>* (25)

1.5 1.5 1 ln 1

he , *h Cp T L c SC <sup>L</sup>* (27)

h f(T ) L,c CHP (28)

(26)

h h <sup>b</sup> *<sup>o</sup>*

 <sup>1</sup> <sup>2</sup> )

5 <sup>2</sup> 2 *c c R T P* 

> *c RT P*

(24)

*<sup>L</sup> h* , temperature, To and the

Kwong equation of state. The Redlich – Kwong equation of state is given as

Where

while the liquid specific enthalpy at location e (at the exit of the throttling valve) is determined from

hL,e=f(TCC) (29)

The temperature at compressor discharge is determined from the knowledge of the compressor efficiency. The ideal discharge temperature (the temperature that gives an overall change in entropy equal to zero) is calculated before correcting with the compressor efficiency.

$$\mathrm{T\_{TOP}} = \mathrm{T\_{TOP}} + \frac{\left[\mathrm{P\_{CH^{+}}} + \Delta\mathrm{P}\right]^{0.263}}{\mathrm{Pr\_{core}}} \right] \tag{30}$$

$$\mathrm{T\_{TOP}} = \frac{\mathrm{T\_{TOP}} + \Delta\mathrm{T\_{TOP}}}{\eta\_{\mathrm{rel}}} \tag{31}$$

The dryness fraction after the isenthalpic expansion is given by

$$
\beta\_e = \frac{h\_e - h\_{\perp,e}}{h\_{\perp\nu,e}} \tag{31}
$$

where the molar latent heat of vaporization at location "e" is adapted from Ackland (1990):

$$\Delta H\_{\text{V},\varepsilon} = \Delta H\_{\text{vup}\_{\text{t}\text{p}}} \, \mathrm{\*} \left( \left( \mathbf{1} - T \mathrm{d} / T\_{\text{C}} \right) \Big| \left( \mathbf{1} - T\_{\text{b} \text{p}} / T\_{\text{C}} \right) \right)^{\wedge} A + B \Big( \left( \mathbf{1} - T \mathrm{d} / T\_{\text{C}} \right) \Big) \tag{32}$$

Since this is a throttling process, Td = Te and hd = he

The molar vapour flow rate which is recycled in the flash tank and conveyed to the compressor is calculated by

$$V\_R = \frac{V\_1 \mathcal{B}\_e}{1 - \mathcal{B}\_e} \tag{33}$$

Therefore, the molar flow rate across the compressor is expressed as

$$
\dot{M} = V\_1 + V\_R \tag{34}
$$

While the dryness fraction at condenser exit is determined by

$$\mathcal{B}\_c = \frac{Q\_{23} \int \dot{M} - \mathbb{C}\_{P\_L} \left( T\_{\rm CHP} - T\_d \right)}{h\_{1V, \rm CHP}} \tag{35}$$

where Q23 is the distribution of excess heat between the pre-heater Q2 and the cooler Q3 and CpL is the molar specific heat of the working fluid in the liquid phase.

The energy balance, applied to the heat pump working fluid, yields the available energy for exchange at the condenser, as follows:

$$Q\_{cd} = \dot{M} \left[ \mathbb{C} p v \left( T\_b - T\_{\rm{CHP}} \right) + \left( 1 - \mathcal{J}\_c \right) h\_{LV, \rm{CHP}} \right] \tag{36}$$

Energy Conservation in Ethanol-Water

Equation (43) shows that the pressure ratio *<sup>b</sup>*

Pressure drop across the column, ∆P*cl*.

Temperature difference in the reboiler, ∆PCHP.

viscosity of the fluid and ξ is the resistance coefficient.

difference in boiling points.

Distillation Column with Vapour Recompression Heat Pump 47

1

*pol a*

*n P* 

*a P*

ratio or the pressure increase to be provided by the compressor of a column with vapour

Pressure drops in the vapour ducts may be caused by frictional loss, ∆Pf; static pressure difference, due to the density and elevation of the fluid, ∆Ps; and changes in the kinetic energy, ∆Pk. Since, there are elbows, valves and other fittings along the pipes then the pressure drop is calculated with resistance coefficients specifically for the elements. Therefore, the pressure drop along a circular pipe with valves and fittings is given by

> 2 1 2

and u is the fluid velocity; d*p* is the pipe diameter and ρ is the fluid density; is the Fanning friction factor which is a function of Reynolds number; l*p* is the pipe length; is the dynamic

The pressure drop over the entire distillation column, ∆Pcl is caused by losses due to vapour flowing through the connecting pipes and through pressure drop over the stages in rectifying and stripping section. This depends mainly on the column internals, number of stages, gas load and operating conditions. ΔPcl =0, if zero vapour boil up is assumed. But constant pressure drop is assumed in this work. The pressure drop over a stage consists of dry and wet pressure drop. The dry pressure is caused by vapour passing through the perforation of the sieve tray. The aerated liquid (static head) on the tray causes the wet pressure drop. Constant pressure drop per tray have been estimated from several authors to be equal to 5.3mmHg per tray (Muhrer, Collura and Luyben 1990). The total column

 0.13332 5.3 0.707 *P x xN N cl* (45) The top and bottom products have different compositions and boiling points. For a fixed bottom temperature of the column, there is a vapour – pressure difference, ∆Pb due to the

*u l*

*p P*

Pb *P P TOP BOTTOM* (46)

(44)

*d*

 

*cp a a*

recompression is influenced by the following (Meili, 1990; Han et al, 2003): Pressure drop in vapour ducts (pipes) and over valves and fittings, ∆P*p*.

**4.3.1 Determination of the pressure increase over the compressor** 

*P PP P PsfK*

pressure drop has been found by summing plate pressure drops ΔPcl

The difference in boiling points between the top and bottom products, ∆P*b*.

*M n <sup>P</sup> W P*

1 1

(43)

*P* is crucial to the power requirement. This

*n n b*

A comparison is made between this energy available at the condenser, Qcd, with the energy required by the column reboiler, Qreb. This brings about the following heat load control.

i. If the rate of energy available at the heat pump condenser, Qcd, is greater than the rate of energy required by the reboiler Qreb, then the condenser gives up Qreb to the reboiler and the remaining energy is conveyed to the preheaters (Q2) and cooler (Q3)

$$\text{if } Q\_{\text{il}} > Q\_{\text{re}\theta} \text{ then } Q\_{\text{l}\text{rc}} = Q\_{\text{re}\theta} \tag{37}$$

ii. But if Qcd is smaller than or equal to Qreb, then all energy available is transferred to the reboiler and the auxiliary reboiler will provide the "extra" Qreb i.e.

$$\text{if } Q\_{\text{cl}} \le Q\_{\text{rl}} \text{ then } \ Q\_{\text{fl}^{\text{IC}}} = Q\_{\text{cl}} \tag{38}$$

where QHPC is the energy yield by the heat pump to the distillation column. The factor by which the heat pump contributes to the heat load of the reboiler is given as

$$f = \frac{Q\_{\text{MPC}}}{Q\_{r\text{cb}}} \tag{39}$$

For a distillation column with vapour recompression, driving the compressor uses the most energy. Thus, the power consumption must be known so as to assess the feasibility of such a system. For a perfect gas, that is, a gas having a constant specific heat, Cp = Cpo, then the specific enthalpy rise between the compressor inlet and outlet is

$$
\Delta \mathbf{l} = \mathbf{h}\_b - \mathbf{h}\_a = \mathbf{C}\_{\mathcal{P}}^o \left( T\_b - T\_a \right) \tag{40}
$$

And if the change of state is isentropic,

$$
\Delta h = \int\_{a}^{b} v \, dp = \frac{\mathcal{V}}{\mathcal{V} - \mathbf{1}} \cdot \frac{\mathbf{R}u \cdot \mathbf{T}}{\dot{M}} \left[ \left( \frac{P\_b}{P\_a} \right)^{\frac{r-1}{r}} - \mathbf{1} \right] \tag{41}
$$

In reality, ideal gases do not exist and therefore improvements are made on equation (41).

Therefore, compression is polytropic and the isentropic index γ, is replaced by the polytropic index, n (see Enweremadu, 2007). The compressor polytropic efficiency *pol* = 0.7 - 0.8 is used.

Also, because a saturated vapour, especially at higher pressures, shows deviations from the ideal gas behaviour, the compressibility factor, Z is used. Hence equation (41) becomes

$$
\Delta \mathbf{l}\_{eff} = \frac{n}{n-1} \cdot \frac{Z \cdot R\_u \cdot T\_a}{\eta\_{pol} \cdot \dot{M}} \left[ \left( \frac{P\_b}{P\_a} \right)^{\frac{n-1}{n}} - 1 \right] \tag{42}
$$

Therefore, the power input for driving the compressor is the energy that increase the enthalpy of the gas

A comparison is made between this energy available at the condenser, Qcd, with the energy required by the column reboiler, Qreb. This brings about the following heat load

i. If the rate of energy available at the heat pump condenser, Qcd, is greater than the rate of energy required by the reboiler Qreb, then the condenser gives up Qreb to the reboiler

if *Q Q cd reb* then *Q Q HPC reb* (37)

ii. But if Qcd is smaller than or equal to Qreb, then all energy available is transferred to the

if *Q Q cd reb* then *Q Q HPC cd* (38)

where QHPC is the energy yield by the heat pump to the distillation column. The factor by

For a distillation column with vapour recompression, driving the compressor uses the most energy. Thus, the power consumption must be known so as to assess the feasibility of such a system. For a perfect gas, that is, a gas having a constant specific heat, Cp = Cpo, then the

> 1 *<sup>b</sup> <sup>b</sup> <sup>a</sup> <sup>a</sup> Ru T <sup>P</sup> h vdp M P*

In reality, ideal gases do not exist and therefore improvements are made on equation (41). Therefore, compression is polytropic and the isentropic index γ, is replaced by the polytropic index, n (see Enweremadu, 2007). The compressor polytropic efficiency

Also, because a saturated vapour, especially at higher pressures, shows deviations from the ideal gas behaviour, the compressibility factor, Z is used. Hence equation (41) becomes

Therefore, the power input for driving the compressor is the energy that increase the

*ua b*

*pol a*

1

*<sup>n</sup> ZR T P <sup>h</sup> n MP* 

*eff*

*HPC reb*

*<sup>o</sup>*

*<sup>Q</sup> <sup>f</sup> Q* (39)

*ba ba hh h CT T p* (40)

1

(41)

1

1 1

(42)

*n n*

and the remaining energy is conveyed to the preheaters (Q2) and cooler (Q3)

reboiler and the auxiliary reboiler will provide the "extra" Qreb i.e.

which the heat pump contributes to the heat load of the reboiler is given as

specific enthalpy rise between the compressor inlet and outlet is

And if the change of state is isentropic,

control.

*pol* = 0.7 - 0.8 is used.

enthalpy of the gas

$$\dot{\mathcal{W}}\_{cp} = \frac{\dot{M}}{\eta\_{pol}} \frac{n}{n-1} P\_a \nu\_a \left[ \left( \frac{P\_b}{P\_a} \right)^{\frac{n}{n-1}} - 1 \right] \tag{43}$$

Equation (43) shows that the pressure ratio *<sup>b</sup> a P P* is crucial to the power requirement. This

ratio or the pressure increase to be provided by the compressor of a column with vapour recompression is influenced by the following (Meili, 1990; Han et al, 2003):


#### **4.3.1 Determination of the pressure increase over the compressor**

Pressure drops in the vapour ducts may be caused by frictional loss, ∆Pf; static pressure difference, due to the density and elevation of the fluid, ∆Ps; and changes in the kinetic energy, ∆Pk. Since, there are elbows, valves and other fittings along the pipes then the pressure drop is calculated with resistance coefficients specifically for the elements. Therefore, the pressure drop along a circular pipe with valves and fittings is given by

$$
\Delta P\_P = \Delta P\_s + \Delta P\_f + \Delta P\_K = \frac{\rho u^2}{2} \left( 1 + \frac{\lambda l\_P}{d\_P} + \sum \xi \right) \tag{44}
$$

and u is the fluid velocity; d*p* is the pipe diameter and ρ is the fluid density; is the Fanning friction factor which is a function of Reynolds number; l*p* is the pipe length; is the dynamic viscosity of the fluid and ξ is the resistance coefficient.

The pressure drop over the entire distillation column, ∆Pcl is caused by losses due to vapour flowing through the connecting pipes and through pressure drop over the stages in rectifying and stripping section. This depends mainly on the column internals, number of stages, gas load and operating conditions. ΔPcl =0, if zero vapour boil up is assumed. But constant pressure drop is assumed in this work. The pressure drop over a stage consists of dry and wet pressure drop. The dry pressure is caused by vapour passing through the perforation of the sieve tray. The aerated liquid (static head) on the tray causes the wet pressure drop. Constant pressure drop per tray have been estimated from several authors to be equal to 5.3mmHg per tray (Muhrer, Collura and Luyben 1990). The total column pressure drop has been found by summing plate pressure drops ΔPcl

$$
\Delta P \, d = 0.13332 \,\text{x} \mathbf{5}.3 \mathbf{x} \,\text{N} = 0.707 \,\text{N} \,\tag{45}
$$

The top and bottom products have different compositions and boiling points. For a fixed bottom temperature of the column, there is a vapour – pressure difference, ∆Pb due to the difference in boiling points.

$$
\Delta \mathbf{P} \mathbf{b} = P\_{\text{TOP}} - P\_{\text{ROTTOM}} \tag{46}
$$

Energy Conservation in Ethanol-Water

inner surface is given by

Then

2005).

where fg fg p CHP <sup>L</sup>

h h 0.375C (T -T ) wall

'

Distillation Column with Vapour Recompression Heat Pump 49

 *HPC HPC*

However, a careful analysis reveals that the overall heat transfer coefficient U is an explicit function of Prandtl, Reynolds and Nusselt numbers, and depends on other properties such as viscosity and thermal conductivity. The overall heat transfer coefficient referenced to

1 1 1 ln( / ) (/) U 2

As thermal resistance of the wall is negligible, (Kwall is large and ln(ro/ri)) ≈ 0, it is then

11 1 *ex ex Uh h i o*

0.023 0.8 0.4 0.14 (Re ) (Pr ) ( ) *ex*

0.25 3 ' ( ) 0.555

*CHP ex*

*L i wall*

*dT T*

*ll v*

where KL is thermal conductivity of the liquid, diex is the inside diameter of the reboiler-

0.023 ( ) 0.555

*UA K ud C K gh*

*HPC m m L L v L fg pm wall ex m mm L CHP ex*

 

*o i wall ex*

*d K dT T*

 

*<sup>L</sup> fg <sup>i</sup>*

*K gh <sup>h</sup>*

11 1

 

( )

0.8 0.4 0.14 3 '

*m wall o m <sup>m</sup> o m*

where μ*m* is the mean bulk fluid viscosity and μw all is the viscosity of the liquid at the wall. The expression for condensation at low velocities inside tubes is adapted from **(**Holman,

*ex*

*<sup>K</sup> <sup>h</sup> d*

*ex*

condenser tubes and μL is the density of the condensate (liquid).

*o*

Assuming adiabatic expansion at the throttling valve, then

Therefore, the overall heat transfer coefficient may be determined from

*i o wall*

*i o*

*r r h hK*

*<sup>Q</sup> UA*

*CHP*

*i oi*

(59)

(57)

(58)

(60)

( )

(61)

 

*r rr*

*<sup>T</sup>* (56)

where Vc is compressor displacement volume (m3) and ω is angular velocity (rad s–1).

The overall heat transfer coefficient between condenser and reboiler is given by

**4.3.2 Determination of the reboiler-condenser parameters** 

compared with the inner tube diameter (ri/ro ≈1)

where,

$$P\_{\rm rco} = 10 \left[ \text{Arro-} \frac{\text{Brro}}{\text{Tror+Clro}} \right] \tag{47}$$

$$\mathbf{P\_{BOTOM}} = \mathbf{10} \left[ \mathbf{A\_{BOTOM}} \mathbf{+} \frac{\mathbf{B\_{BOTOM}}}{\mathbf{T\_{BOTOM}} + \mathbf{C\_{BOTOM}}} \right] \tag{48}$$

The temperature difference in the reboiler- condenser is expressed by means of the vapour – pressure equation as a pressure difference, ∆PCHP. Temperature differences of 8 – 17oC are quite common for ethanol-water distillation (Gopichand et al, 1988; Canales and Marquez, 1992). Using the Clausius – Clapeyron equation for a two- point fit,

$$
\Delta P\_{C\bar{H}^p} = \mathbf{e}^r \frac{\Delta Hvap}{\mathbf{R}} \left(\frac{-\Delta T\_{C\bar{H}P}}{T\_{C\bar{H}P}T\_{C\bar{E}V}}\right) \tag{49}
$$

Therefore the total pressure increase over the compressor becomes

$$
\Delta \mathbf{P}^\* = \Delta \mathbf{P} \mathbf{b} + \Delta \mathbf{P} \mathbf{d} + \Delta \mathbf{P} \mathbf{C} \mathbf{H} \mathbf{p} + \Delta \mathbf{P}\_{\mathbf{P}} \tag{50}
$$

For this distillation system, the compression (pressure) ratio is

$$\frac{P\_b}{P\_a} = \frac{P\_{\text{CHP}} + \Delta P}{P\_{\text{TOP}}} \tag{51}$$

where PTOP is inlet pressure (vapour pressure at top temperature).

Other compressor parameters are calculated by the following equations:

i. Compressor power input is determined from equation (43) and (51)

$$\dot{\mathcal{W}}\_{cp} = \frac{\dot{\mathcal{M}}}{\eta\_{pol}} \frac{n}{n-1} P\_{\text{root}} \cdot \nu\_a \left[ \left( \frac{P\_{\text{cpt}} + \Delta P}{P\_{\text{Tot}}} \right)^{\frac{n-1}{n}} - 1 \right] \tag{52}$$

ii. Compressor heat load rate (energy balance)

$$Q\_{cp} = \eta\_{pol}\dot{\mathcal{W}}\_{cp} - \dot{M}(h\_b - h\_a) \tag{53}$$

iii. Compressor volumetric efficiency

$$\eta\_{v} = \mathbf{C}\_{\circ} \left\{ \mathbf{1} - r \left[ \left( \frac{P\_{\rm{CHP}} + \Delta P}{P\_{\rm{TOP}}} \right)^{\frac{1}{w}} - \mathbf{1} \right] \right\} \tag{54}$$

where Cv is empirical volumetric coefficient and r is the compressor clearance ratio.

iv. Compressor nominal capacity or compressor displacement rate

$$V\_{\text{-}}\rho = \frac{\dot{M}\nu\_a}{\eta\_v} \tag{55}$$

where Vc is compressor displacement volume (m3) and ω is angular velocity (rad s–1).

#### **4.3.2 Determination of the reboiler-condenser parameters**

The overall heat transfer coefficient between condenser and reboiler is given by

$$\left(\text{ULA}\right)\_{\text{H^{\text{C}}}} = \frac{Q\_{\text{H^{\text{C}}}}}{\Delta T\_{\text{CH^{\text{-}}}}} \tag{56}$$

However, a careful analysis reveals that the overall heat transfer coefficient U is an explicit function of Prandtl, Reynolds and Nusselt numbers, and depends on other properties such as viscosity and thermal conductivity. The overall heat transfer coefficient referenced to inner surface is given by

$$\frac{1}{\mathbf{U}} = \frac{1}{h i} + (ri \;/\; r \circ) \frac{1}{h o} + \frac{r i \ln(r \circ /\; r)}{2 \,\mathrm{K} \,\mathrm{wall}} \tag{57}$$

As thermal resistance of the wall is negligible, (Kwall is large and ln(ro/ri)) ≈ 0, it is then compared with the inner tube diameter (ri/ro ≈1)

Then

48 Distillation – Advances from Modeling to Applications

TOP TOP TOP TOP - <sup>B</sup>

BOTTOM BOTTOM BOTTOM BOTTOM - <sup>B</sup>

The temperature difference in the reboiler- condenser is expressed by means of the vapour – pressure equation as a pressure difference, ∆PCHP. Temperature differences of 8 – 17oC are quite common for ethanol-water distillation (Gopichand et al, 1988; Canales and Marquez,


*CHP CHP CEV Hvap T*

> *CHP TOP*

*P P P P P*

*b a*

*P T T*

<sup>P</sup> <sup>A</sup> <sup>10</sup> T C

<sup>P</sup> <sup>A</sup> <sup>10</sup> T C

1992). Using the Clausius – Clapeyron equation for a two- point fit,

Therefore the total pressure increase over the compressor becomes

For this distillation system, the compression (pressure) ratio is

where PTOP is inlet pressure (vapour pressure at top temperature).

iv. Compressor nominal capacity or compressor displacement rate

ii. Compressor heat load rate (energy balance)

iii. Compressor volumetric efficiency

Other compressor parameters are calculated by the following equations: i. Compressor power input is determined from equation (43) and (51)

1

*CHP v v*

*cp <sup>a</sup> pol*

*TOP*

*Q W Mh h cp*

*P P C r*

*c*

*Mn P P W P n P* 

TOP

BOTTOM

*CHP*

(49)

P P P P P b cl CHP p (50)

1 1

*pol cp b a* (53)

(55)

(54)

*n n*

(52)

*CHP*

1 1

*P*

where Cv is empirical volumetric coefficient and r is the compressor clearance ratio.

*<sup>M</sup> <sup>a</sup> <sup>V</sup>* 

*TOP*

*v*

*TOP*

1

*m*

(51)

 

(47)

(48)

where,

$$\frac{1}{M} = \frac{1}{h i\_{\rm ex}} + \frac{1}{h o\_{\rm ex}}\tag{58}$$

$$h\_{\theta\_{cr}} = \frac{0.023 K\_m}{d\_{o\_{cr}}} (\text{Re}\,\text{m})^{0.8} (\text{Pr}\,\text{m})^{0.4} (\frac{\mu\text{u}\,\text{u}}{\mu\text{m}})^{0.14} \tag{59}$$

where μ*m* is the mean bulk fluid viscosity and μw all is the viscosity of the liquid at the wall.

The expression for condensation at low velocities inside tubes is adapted from **(**Holman, 2005).

$$\mu\_{\rm li} = 0.555 \left[ \frac{\rho (\rho\_l - \rho\_v) \text{K} \text{s}^3 \text{g} \text{h}\_{fg}^{'}}{\mu \mu \text{d}\_{\rm cr} (T\_{\rm CH} - T\_{\rm wall})} \right]^{0.25} \tag{60}$$

where fg fg p CHP <sup>L</sup> 'h h 0.375C (T -T ) wall

where KL is thermal conductivity of the liquid, diex is the inside diameter of the reboilercondenser tubes and μL is the density of the condensate (liquid).

Therefore, the overall heat transfer coefficient may be determined from

$$\frac{1}{\mu\text{L}\_{\text{e}\pi}} = \frac{1}{\frac{0.023\,\text{K}\_{\text{m}}\left(\frac{\rho\_{\text{r}}\,\mu\text{d}\phi\_{\text{e}\pi}}{\mu\_{\text{m}}}\right)^{0.8}\left(\frac{\text{C}\_{\text{r}\pi}}{\text{K}\_{\text{m}}}\right)^{0.4}\left(\frac{\mu\_{\text{w}\text{l}}}{\mu\_{\text{w}}}\right)^{0.14}} + \frac{1}{0.555\left[\frac{\rho\_{\text{r}}(\rho\_{\text{r}}-\rho\_{\text{r}})\text{K}\_{\text{g}\text{h}\text{}}^{3}\text{g}\text{h}^{'}\_{\text{f}\text{s}}\right]}}\tag{61}$$

Assuming adiabatic expansion at the throttling valve, then

Energy Conservation in Ethanol-Water

pre-heater Q2, will be determined as

**4.5 Thermodynamic analysis** 

compressor power input, .

W cp

Then the thermodynamic efficiency is expressed as:

**4.6 Solution method and error analysis** 

as follows:

Distillation Column with Vapour Recompression Heat Pump 51

It is important to verify whether Q1 alone is capable of pre-heating the feed to reach the desired condition, otherwise the amount of heat that should be withdrawn from the second

The value of heat at the second pre-heater Q2 should be, at the most equal to Qwithdrawn to prevent the feed reaching 50% dry. Therefore, a convenient heat load control could be made

If Q Q , 23 withdrawn then Q Q , 2 23 Q 0 <sup>3</sup>

Since vapour recompression uses a refrigeration cycle rather than a Carnot cycle, the

*Q Q COP*

The thermodynamic efficiency of a separation process is the ratio of the minimum amount of thermodynamic work required for separation to the minimum energy required for the separation (Olujic *et al,* 2003). For a vapour recompression distillation column, the energy required for separation process is composed of the reboiler heat load, Qreb, and the

For the separation of a binary mixture by distillation the minimum thermodynamic energy

*HPC* 23

*cp*

.

T Wmin Q

The equations that model the system components were grouped together in one single system. The analyses of the status of the variables were carried out to identify those that were the input data and those which were the unknowns. The equations were then grouped

*W*

performance of the heat pump is defined according to the following relation;

*h*

T

required to achieve complete separation is given by (Liu and Quian, 2000):

Q Q FSV FSL *FhLV F*, (68)

(71)

Q W *Qreb cp* (72)

*VRC* (74)

*W RT X X X X* min *TOP F F* ln( ) (1 )ln(1 ) *<sup>F</sup> <sup>F</sup>* (73)

, , . ( ) 0.5 *<sup>p</sup> Q F C T T Fh withdrawn <sup>F</sup> sat F F LV F* (69)

If Q Q <sup>23</sup> withdrawn , then Q Q <sup>2</sup> withdrawn Q Q -Q 3 23 2 (70)

$$\mathbf{h}\_{\rm e} = \mathbf{h}\_{\rm d} = \mathbf{h}\_{\rm l,c} - \mathbf{C}\_{\rm l} \mathbf{n}\_{\rm L} \Delta \mathbf{T}\_{\rm SC} \tag{62}$$

From the condenser prescribed degree of sub-cooling, the temperature of the working fluid after cooling and before throttling is given by

$$\mathbf{T}\_d = \mathbf{T}\_{\rm CHF} - \Delta \mathbf{T}\_{\rm SC} \tag{63}$$

where TSC is the degree of sub-cooling (K)

The corresponding latent heat (enthalpy) is given as

$$\mathbf{h}\_d = \mathbf{h}\_{L,c} - \mathbf{C}\_{\mathbf{P}\_L} \Delta T\_{\mathbf{SC}} \tag{64}$$

#### **4.4 Analysis of distribution of excess heat rate**

The distillation system uses the column's working fluid as refrigerant and does not execute a closed cycle. Therefore the excess heat which may occur is not assessed by an overall energy balance but by the method of Oliveira *et al* (2001). When the energy available at the condenser Qcd, is greater than the energy required by the reboiler Qreb, the column receives the amount Qcd and the energy left over corresponds to the excess. But if Qcd is smaller than or equal to Qreb, then all the energy available is transferred to the reboiler, i.e. there will be no excess. Thus,

$$\text{if } Q\_{cd} > Q\_{rb} \text{ then } \quad Q\_{23} = Q\_{cd} - Q\_{rb} \tag{65}$$

$$\text{if } Q\_{cd} \le Q\_{rb} \quad \text{then} \quad Q\_{23} = 0$$

where Q23 is the excess heat due to energy interactions between the heat pump and the reboiler.

The distribution of the excess heat rate, Q23 , between the pre-heater (Q2) and cooler (Q3) is accomplished by controlling the feed condition pre-heated by Q2. In other words, the value of Q2 should be such that the feed reaches a prescribed condition. The pre-heating of the feed is carried out by Q1 (heat exchanged between the bottom product and the feed) and Q2 (heat exchange between the heat pump working fluid and the feed), in the heat exchangers. The heat provided by the bottom product is determined as follows:

$$Q\_1 = B.C\_{\mathcal{V}\_B} \left( T\_{\text{CF}} - T\_{\text{RE}} \right) \tag{66}$$

where, TCEV is the column evaporation temperature. CpB is the specific heat of the bottom product. TBE is the temperature at the bottom product flow exit.

The best feed condition is that of saturated liquid (Halvorsen, 2001). The energy required to pre-heat the feed to reach saturated condition is expressed as

$$Q\_{\rm F^{\rm SL}} = F.C\_{\rm PF}(T\_{\rm sat,F} - T\_{\rm F})\tag{67}$$

where, Tsat,F and TF are the saturation temperature of the feed source and the temperature of the feed source respectively. CpF is the specific heat of the feed source.

To make the feed a saturated vapour, the energy required is given as

$$\mathbf{Q\_{\text{FSV}}} = \mathbf{Q\_{\text{FSL}}} + F \mathbf{h\_{LV,F}} \tag{68}$$

It is important to verify whether Q1 alone is capable of pre-heating the feed to reach the desired condition, otherwise the amount of heat that should be withdrawn from the second pre-heater Q2, will be determined as

$$Q\_{withdranun} = F.C\_{"\tau\_F}(T\_{sat,F} - T\_F) + 0.5Fh\_{LV,F} \tag{69}$$

The value of heat at the second pre-heater Q2 should be, at the most equal to Qwithdrawn to prevent the feed reaching 50% dry. Therefore, a convenient heat load control could be made as follows:

$$\begin{array}{ccccc}\text{If} & \mathbf{Q}\_{2} > \mathbf{Q}\_{\text{with drawn}} & \text{then} & \mathbf{Q}\_{2} = \mathbf{Q}\_{\text{with drawn}} & \mathbf{Q}\_{2} = \mathbf{Q}\_{2}\mathbf{-}\mathbf{Q}\_{2} \\\\ \text{If} & \mathbf{Q}\_{2} < \mathbf{Q}\_{\text{with drawn}} & \text{then} & \mathbf{Q}\_{2} = \mathbf{Q}\_{2} & \mathbf{Q}\_{2} = \mathbf{0} \end{array}$$

#### **4.5 Thermodynamic analysis**

50 Distillation – Advances from Modeling to Applications

 he = hd = hL,c – CpL.ΔTSC (62) From the condenser prescribed degree of sub-cooling, the temperature of the working fluid

Td = TCHP – TSC (63)

The distillation system uses the column's working fluid as refrigerant and does not execute a closed cycle. Therefore the excess heat which may occur is not assessed by an overall energy balance but by the method of Oliveira *et al* (2001). When the energy available at the condenser Qcd, is greater than the energy required by the reboiler Qreb, the column receives the amount Qcd and the energy left over corresponds to the excess. But if Qcd is smaller than or equal to Qreb, then all the energy available is transferred to the reboiler, i.e. there will be

if *Q Q cd reb* then *Q QQ* <sup>23</sup> *cd reb* (65)

if *Q Q cd reb* then 23 *Q* 0

where Q23 is the excess heat due to energy interactions between the heat pump and the

The distribution of the excess heat rate, Q23 , between the pre-heater (Q2) and cooler (Q3) is accomplished by controlling the feed condition pre-heated by Q2. In other words, the value of Q2 should be such that the feed reaches a prescribed condition. The pre-heating of the feed is carried out by Q1 (heat exchanged between the bottom product and the feed) and Q2 (heat exchange between the heat pump working fluid and the feed), in the heat exchangers.

where, TCEV is the column evaporation temperature. CpB is the specific heat of the bottom

The best feed condition is that of saturated liquid (Halvorsen, 2001). The energy required to

where, Tsat,F and TF are the saturation temperature of the feed source and the temperature

The heat provided by the bottom product is determined as follows:

product. TBE is the temperature at the bottom product flow exit.

pre-heat the feed to reach saturated condition is expressed as

of the feed source respectively. CpF is the specific heat of the feed source.

To make the feed a saturated vapour, the energy required is given as

, *<sup>L</sup> d Lc SC hh C T <sup>P</sup>* (64)

*Q*<sup>1</sup> *BC T T* . *pB CEV BE* (66)

*Q FC T T FSL PF F F* .( ) *sat*, (67)

after cooling and before throttling is given by

where TSC is the degree of sub-cooling (K)

The corresponding latent heat (enthalpy) is given as

**4.4 Analysis of distribution of excess heat rate** 

no excess. Thus,

reboiler.

Since vapour recompression uses a refrigeration cycle rather than a Carnot cycle, the performance of the heat pump is defined according to the following relation;

$$\text{COP}\_h = \frac{Q\_{\text{HPC}} + Q\_{\text{23}}}{\dot{W}\_{\text{cp}}} \tag{71}$$

The thermodynamic efficiency of a separation process is the ratio of the minimum amount of thermodynamic work required for separation to the minimum energy required for the separation (Olujic *et al,* 2003). For a vapour recompression distillation column, the energy required for separation process is composed of the reboiler heat load, Qreb, and the

compressor power input, . W cp

$$\mathbf{Q}\_{\mathbf{i}} = \mathbf{Q}\_{r\theta\theta} + \dot{\mathbf{W}}\_{c\theta} \tag{72}$$

For the separation of a binary mixture by distillation the minimum thermodynamic energy required to achieve complete separation is given by (Liu and Quian, 2000):

$$\mathcal{W}\_{\text{min}} = -RT\_{\text{TOP}} \left( X\_{\text{F}} \ln(X\_{\text{F}}) + (1 - X\_{\text{F}}) \ln(1 - X\_{\text{F}}) \right) \tag{73}$$

Then the thermodynamic efficiency is expressed as:

$$
\eta\_{\rm N\%} = \frac{\mathbf{W\_{\rm min}}}{\mathbf{Q\_{\rm r}}} \tag{74}
$$

#### **4.6 Solution method and error analysis**

The equations that model the system components were grouped together in one single system. The analyses of the status of the variables were carried out to identify those that were the input data and those which were the unknowns. The equations were then grouped

Energy Conservation in Ethanol-Water

**Compressor volumetric efficiency**

0.72 0.725 0.73 0.735 0.74 0.745 0.75 0.755

pressure increase across compressor

ΔP increases the total energy consumption.

9.24

9.26

9.28

**Total energy consumption (kW)**

across compressor

9.3

9.32

9.34

large displacement rate.

Distillation Column with Vapour Recompression Heat Pump 53

0 20 40 60 80 100

**Pressure increase across compressor (kPa)**

variables indicates that the compressor displacement rate is directly proportional to ΔP. A reduction in compressor volumetric efficiency caused by increase in ΔP, increases the compressor displacement rate. This implies an increase in the displacement volume required although this cannot be observed in the figures. The compressor displacement required for a given speed is related to compressor size. For the large specific volume obtained, 9.74m3 kg-1 ethanol as the heat pump working fluid will require a compressor of greater capacity i.e

It can be observed from Figure 5 that an increase in pressure increase across the compressor,

0 20 40 60 80 100

Energy Heat load

**Pressure increase across compressor (kPa)**

Fig. 5. The variation of total energy consumption and heat load rate with pressure increase

For a given reboiler heat transfer rate, Qreb, it is obvious that as ΔP increases, the total energy consumption increases. The total energy consumption and hence the energy

Fig. 4. The variation of compressor volumetric efficiency and volume flow rate with

0.00374

0.114

0.134

0.154

**Heat load rate (kW)**

0.174

0.00378

0.00382

**Compressor volume flow rate** 

**(m³/s)**

0.00386

Vol efficiency Vol flow rate

0.0039

together, resulting in a set of non-linear algebraic equations, which were solved iteratively based on the step by step use of the successive substitution method. Solution was obtained when convergence was attained. The convergence was checked by using the criterion:

$$
\boldsymbol{\varepsilon}\_{\rm a} = \frac{\mathbf{X}\_{i \leftrightarrow 1} \cdot \mathbf{X}\_{i}}{\mathbf{X}\_{i \leftrightarrow 1}} \times 100\% \tag{75}
$$

The model is coded in MATLAB environment and used to evaluate the unknowns. A control programme for column VRC was written to compare the actual column (column in which the parameters studied were considered, VRCΔP).

#### **5. Discussion of results**

#### **5.1 Effects of pressure increase over the compressor**

Figure 3 shows how the compressor power input, . *Wcp* varies with the pressure increase over the compressor, ΔP. It is obvious from the plots that an increase in pressure over the compressor increases the compression (pressure) ratio leading to increase in compressor power input. The curve in Figure 3 shows the effect of pressure increase over the compressor on coefficient of performance. As the pressure increase over the compressor, ΔP increases, the compression ratio increases and the coefficient of performance, COP decreases due to increase in compressor power input.

Fig. 3. The variation of coefficient of performance and compressor power input with pressure increase across compressor

In Figure 4, a negative non-linear relationship exists between the compressor volumetric efficiency and pressure increase over the compressor. For a given compressor nominal capacity, when the pressure increase across the compressor, ΔP increases, the pressure ratio also increases resulting in the reduction in volumetric efficiency.

The influence of pressure increase over the compressor, ΔP on the required compressor displacement rate (Vcω) is shown in Figure 4. The linear relationship that exists between the

together, resulting in a set of non-linear algebraic equations, which were solved iteratively based on the step by step use of the successive substitution method. Solution was obtained when convergence was attained. The convergence was checked by using the criterion:

X - X x 100%

(75)

*Wcp* varies with the pressure increase

0.5

0.52

0.54

**Compressor power input (kW)**

0.56

COP Power 0.58

0.6

i 1 i 1 <sup>i</sup> <sup>a</sup>

which the parameters studied were considered, VRCΔP).

**5.1 Effects of pressure increase over the compressor**  Figure 3 shows how the compressor power input, .

due to increase in compressor power input.

6

5

pressure increase across compressor

5.2

5.4

5.6

**Coefficient of performance**

5.8

**5. Discussion of results** 

X

The model is coded in MATLAB environment and used to evaluate the unknowns. A control programme for column VRC was written to compare the actual column (column in

over the compressor, ΔP. It is obvious from the plots that an increase in pressure over the compressor increases the compression (pressure) ratio leading to increase in compressor power input. The curve in Figure 3 shows the effect of pressure increase over the compressor on coefficient of performance. As the pressure increase over the compressor, ΔP increases, the compression ratio increases and the coefficient of performance, COP decreases

0 20 40 60 80 100

In Figure 4, a negative non-linear relationship exists between the compressor volumetric efficiency and pressure increase over the compressor. For a given compressor nominal capacity, when the pressure increase across the compressor, ΔP increases, the pressure ratio

The influence of pressure increase over the compressor, ΔP on the required compressor displacement rate (Vcω) is shown in Figure 4. The linear relationship that exists between the

**Pressure increase across compressor (kPa)**

Fig. 3. The variation of coefficient of performance and compressor power input with

also increases resulting in the reduction in volumetric efficiency.

Fig. 4. The variation of compressor volumetric efficiency and volume flow rate with pressure increase across compressor

variables indicates that the compressor displacement rate is directly proportional to ΔP. A reduction in compressor volumetric efficiency caused by increase in ΔP, increases the compressor displacement rate. This implies an increase in the displacement volume required although this cannot be observed in the figures. The compressor displacement required for a given speed is related to compressor size. For the large specific volume obtained, 9.74m3 kg-1 ethanol as the heat pump working fluid will require a compressor of greater capacity i.e large displacement rate.

It can be observed from Figure 5 that an increase in pressure increase across the compressor, ΔP increases the total energy consumption.

Fig. 5. The variation of total energy consumption and heat load rate with pressure increase across compressor

For a given reboiler heat transfer rate, Qreb, it is obvious that as ΔP increases, the total energy consumption increases. The total energy consumption and hence the energy

Energy Conservation in Ethanol-Water

1.2

0

2007; Enweremadu et al, 2009).

compressor power input respectively.

0.2

0.4

0.6

**Thermal conductance (kW/K)**

factor

0.8

1

Distillation Column with Vapour Recompression Heat Pump 55

0 0.2 0.4 0.6 0.8 1 1.2

**Condenser distribution factor** Fig. 6. Variation of Reboiler-condenser thermal conductance with condenser distribution

Table 1 summarises the comparison of some parameters of the two vapour recompression columns studied, the control (VRC) and the actual (VRCΔP). Both systems operate at 101.2 kPa and the effect of pressure drop effect is considered to account properly for variations in heat duty. A pressure drop of 0.707kPa per tray is assumed here as a reasonable estimate for the purposes of this study. The pressure ratio as used throughout this work is the ratio of the condensation pressure, PCHP to the top pressure, PTOP, for the VRC system and sum of the condensation pressure, PCHP and pressure increase over the compressor, ΔP, to the top pressure, PTOP for the VRCΔP system. Since the energy consumption changes linearly with the feed flow rate, and as the present work makes a comparison of the relative performances, the base case flow rate was taken to be 1.098x10-4kmol s-1 . Also the column heat loss and the effect of such parameters as pressure increase across the compressor, the overall heat transfer coefcient of reboiler–condenser as an explicit function of Prandtl, Reynolds and Nusselt numbers which in turn depend on uid properties are considered to account properly for variations in heat duty (Enweremadu,

Table 1 shows that the VRC enables some energy savings when compared with VRCΔP. The VRC has a slightly lower compression ratio and consumes less energy than VRCΔP system. Although there was a marginal increase in ΔP, which increased the compressor power input slightly, the performances of the two systems differ greatly by 27.5%. However, in addition to the pressure increase, the energy consumption appears to depend more on the rate of heat transfer in the reboiler. Hence the total energy consumption is indirectly related to column heat loss and pressure increase across the compressor through reboiler heat transfer and

Also from Table 1, the heat transfer duties of the reboiler-condenser in terms of the overall heat transfer coefficient for the two systems show that the VRCΔP has a higher value when compared with the VRC system. This implies that the VRCΔP will require a smaller heat

**5.3 Comparison of the vapour recompression distillation systems** 

savings from the work of Oliveira *et al* (2001) in heat pump distillation gave lower values. This could be attributed to non-consideration of the effect of pressure increase over the compressor and the subsequent increase in compression ratio and in compression power input respectively.

#### **5.2 Effects of column heat loss**

The direct effect of column heat loss could be seen from equation (17). From the equation, it follows that, for a given reboiler heat load or heat expenditure, fewer trays are required for a given separation if heat losses are reduced. Where heat loss occurs, more vapour has to be produced in the reboiler, since the reboiler must provide not only the heat removed in the condenser but also the heat loss. The effect of this is a decrease in process and energy efficiency. Indirectly, heat loss affects the column size in terms of number of plates. In the control system, the reflux ratio was as high as 7.5 compared with 5.033 obtained for the actual system. Therefore, if heat losses are properly accounted for, there may not be any need for downward review of the number of plates in order to reduce the reflux ratio (Enweremadu and Rutto, 2010). Therefore, pressure drop across the column, ΔPcl and the difference in boiling points between the top and bottom products, ΔPb which have the most profound effects on the pressure increase across the compressor, ΔP will be properly predicted. The overall implication of this is that the column size would be determined properly.

#### **5.2.1 Overall heat transfer coefficient**

Analysis of the overall heat transfer coefficient, U of the heat pump reboiler-condenser revealed an increase in the value of U. This was expected as the value of U in boiling and condensation processes are high. Also, the value of the heat transfer coefficient of the condensing ethanol is dominated the relationship used in determining U. A low value of overall heat transfer coefficient U will result in an increase in the heat exchanger surface area which may be a disadvantage to ethanol-water system. But the results from this work showed an increase in the value of U with the implication of a reduction in the reboilercondenser heat transfer area.

The variation of the reboiler-condenser thermal conductance (UA) with the heat pump distribution factor, f, is shown in Figure 6. The plots show that the greater the heat load taken by the heat pump i.e. larger f's, the larger the thermal conductance, UA, and the larger the heat exchanger area. However, for better performance of any heat transfer system, the thermal resistance (Rth) which is the inverse of thermal conductance (Rth = 1/UA), should be as low as possible. Therefore the value of the heat transfer area for the VRCΔP system will be smaller compared to the VRC system. Hence, the reboiler-condenser studied has a better performance.

The relationship between the thermal conductance, UA and the reboiler-condenser temperature difference, ΔTCHP shows that the higher the reboiler-condenser temperature difference, the lower the thermal conductance. The implication of this is that a higher ΔTCHP causes a reduction of the necessary heat transfer area. However, beyond a certain limit of the thermal driving force, the heat transfer area and the performance of the heat pump reboiler-condenser reduces. This is expected as higher ΔTCHP leads to higher compression ratio, higher compressor power input and higher energy consumption.

savings from the work of Oliveira *et al* (2001) in heat pump distillation gave lower values. This could be attributed to non-consideration of the effect of pressure increase over the compressor and the subsequent increase in compression ratio and in compression power

The direct effect of column heat loss could be seen from equation (17). From the equation, it follows that, for a given reboiler heat load or heat expenditure, fewer trays are required for a given separation if heat losses are reduced. Where heat loss occurs, more vapour has to be produced in the reboiler, since the reboiler must provide not only the heat removed in the condenser but also the heat loss. The effect of this is a decrease in process and energy efficiency. Indirectly, heat loss affects the column size in terms of number of plates. In the control system, the reflux ratio was as high as 7.5 compared with 5.033 obtained for the actual system. Therefore, if heat losses are properly accounted for, there may not be any need for downward review of the number of plates in order to reduce the reflux ratio (Enweremadu and Rutto, 2010). Therefore, pressure drop across the column, ΔPcl and the difference in boiling points between the top and bottom products, ΔPb which have the most profound effects on the pressure increase across the compressor, ΔP will be properly predicted. The overall

Analysis of the overall heat transfer coefficient, U of the heat pump reboiler-condenser revealed an increase in the value of U. This was expected as the value of U in boiling and condensation processes are high. Also, the value of the heat transfer coefficient of the condensing ethanol is dominated the relationship used in determining U. A low value of overall heat transfer coefficient U will result in an increase in the heat exchanger surface area which may be a disadvantage to ethanol-water system. But the results from this work showed an increase in the value of U with the implication of a reduction in the reboiler-

The variation of the reboiler-condenser thermal conductance (UA) with the heat pump distribution factor, f, is shown in Figure 6. The plots show that the greater the heat load taken by the heat pump i.e. larger f's, the larger the thermal conductance, UA, and the larger the heat exchanger area. However, for better performance of any heat transfer system, the thermal resistance (Rth) which is the inverse of thermal conductance (Rth = 1/UA), should be as low as possible. Therefore the value of the heat transfer area for the VRCΔP system will be smaller compared to the VRC system. Hence, the reboiler-condenser studied has a better

The relationship between the thermal conductance, UA and the reboiler-condenser temperature difference, ΔTCHP shows that the higher the reboiler-condenser temperature difference, the lower the thermal conductance. The implication of this is that a higher ΔTCHP causes a reduction of the necessary heat transfer area. However, beyond a certain limit of the thermal driving force, the heat transfer area and the performance of the heat pump reboiler-condenser reduces. This is expected as higher ΔTCHP leads to higher compression

ratio, higher compressor power input and higher energy consumption.

implication of this is that the column size would be determined properly.

input respectively.

**5.2 Effects of column heat loss** 

**5.2.1 Overall heat transfer coefficient** 

condenser heat transfer area.

performance.

Fig. 6. Variation of Reboiler-condenser thermal conductance with condenser distribution factor

#### **5.3 Comparison of the vapour recompression distillation systems**

Table 1 summarises the comparison of some parameters of the two vapour recompression columns studied, the control (VRC) and the actual (VRCΔP). Both systems operate at 101.2 kPa and the effect of pressure drop effect is considered to account properly for variations in heat duty. A pressure drop of 0.707kPa per tray is assumed here as a reasonable estimate for the purposes of this study. The pressure ratio as used throughout this work is the ratio of the condensation pressure, PCHP to the top pressure, PTOP, for the VRC system and sum of the condensation pressure, PCHP and pressure increase over the compressor, ΔP, to the top pressure, PTOP for the VRCΔP system. Since the energy consumption changes linearly with the feed flow rate, and as the present work makes a comparison of the relative performances, the base case flow rate was taken to be 1.098x10-4kmol s-1 . Also the column heat loss and the effect of such parameters as pressure increase across the compressor, the overall heat transfer coefcient of reboiler–condenser as an explicit function of Prandtl, Reynolds and Nusselt numbers which in turn depend on uid properties are considered to account properly for variations in heat duty (Enweremadu, 2007; Enweremadu et al, 2009).

Table 1 shows that the VRC enables some energy savings when compared with VRCΔP. The VRC has a slightly lower compression ratio and consumes less energy than VRCΔP system. Although there was a marginal increase in ΔP, which increased the compressor power input slightly, the performances of the two systems differ greatly by 27.5%. However, in addition to the pressure increase, the energy consumption appears to depend more on the rate of heat transfer in the reboiler. Hence the total energy consumption is indirectly related to column heat loss and pressure increase across the compressor through reboiler heat transfer and compressor power input respectively.

Also from Table 1, the heat transfer duties of the reboiler-condenser in terms of the overall heat transfer coefficient for the two systems show that the VRCΔP has a higher value when compared with the VRC system. This implies that the VRCΔP will require a smaller heat

Energy Conservation in Ethanol-Water

VRC<sup>Δ</sup>**<sup>P</sup>** will have a better performance.

difference between the two systems.

is higher than in the VRC system.

increase in heat transfer area.

performance.

**6. Conclusions** 

capacity.

substantial.

Distillation Column with Vapour Recompression Heat Pump 57

transfer area which is economical in terms of material conservation. Also, with higher U, the

The column heat losses for the two vapour recompression distillation columns are shown in Table 1. The heat losses in distillation columns with heat pumps have been assumed to correspond to around 3% of the energy supplied to the reboiler (Danziger, 1979). Oliveira, Marques and Parise (2002) assumed it to be as high as 10%. However, in this study, the heat exchanged by the distillation column with the surroundings is considered and its effect included in the balance equation (1). The results obtained for the VRCΔP showed a marked

A comparison of the main reboiler heat transfer rate for the two systems is presented in Table 1. It is evident that neglecting and /or assuming a value for column heat loss instead of determining it had a significant effect on the values of Qreb in both systems. The heat pump distribution factor, f, for the VRCΔP system is 0.346 which is slightly less than that for the VRC system (0.451). Since low value of heat load taken by the heat pump, f implies lower thermal conductance, then the value of the heat transfer area for the VRCΔP system is smaller when compared to the VRC system. However, lower value of thermal conductance, UA, for the VRCΔP system indicates that the VRC system will have a better

The simulation results also show that the coefficient of performance and the thermodynamic efficiency of the VRCΔP system is lower when compared to the VRC system. Fonyo and Benko (1998) have shown that the electrically-driven compression heat pump should work with a COP not lower than 3-5. The value of 5.85 obtained from this study has shown that although there is a decrease in the effectiveness of the VRCΔP system when compared with the VRC system with COP of 6.15, it is within the acceptable range. This may be due to the fact that the compressor power input and the total energy consumption in the VRCΔP system

1. Pressure increase across the compressor, ΔP increases the compression ratio, the compressor power input, temperature in the heat pump reboiler-condenser while the compressor volumetric efficiency decreases. The effect of these is the reduction in the heat pump coefficient of performance and the use of a compressor of greater

2. Neglecting the effects of pressure increase across the compressor, ΔP reduces the compression ratio and hence maximizes the energy efficiency. However, this leads to a substantial decrease in temperature in the heat pump reboiler-condenser. The overall effect of this is a decrease in the overall heat transfer coefficient, U resulting in an

3. From the comparison between the VRCΔP and VRC systems, there was a profound difference in the overall heat transfer coefficient while the column heat loss was

The increase in the total energy consumption, reboiler heat transfer rate and the thermodynamic efficiency were appreciable, while there was only a marginal increase

From the outcome of the study, the following conclusions may be drawn:


Table 1. Model results of the actual column and control column (Enweremadu, 2007; Enweremadu et al, 2008 & 2009)

transfer area which is economical in terms of material conservation. Also, with higher U, the VRC<sup>Δ</sup>**<sup>P</sup>** will have a better performance.

The column heat losses for the two vapour recompression distillation columns are shown in Table 1. The heat losses in distillation columns with heat pumps have been assumed to correspond to around 3% of the energy supplied to the reboiler (Danziger, 1979). Oliveira, Marques and Parise (2002) assumed it to be as high as 10%. However, in this study, the heat exchanged by the distillation column with the surroundings is considered and its effect included in the balance equation (1). The results obtained for the VRCΔP showed a marked difference between the two systems.

A comparison of the main reboiler heat transfer rate for the two systems is presented in Table 1. It is evident that neglecting and /or assuming a value for column heat loss instead of determining it had a significant effect on the values of Qreb in both systems. The heat pump distribution factor, f, for the VRCΔP system is 0.346 which is slightly less than that for the VRC system (0.451). Since low value of heat load taken by the heat pump, f implies lower thermal conductance, then the value of the heat transfer area for the VRCΔP system is smaller when compared to the VRC system. However, lower value of thermal conductance, UA, for the VRCΔP system indicates that the VRC system will have a better performance.

The simulation results also show that the coefficient of performance and the thermodynamic efficiency of the VRCΔP system is lower when compared to the VRC system. Fonyo and Benko (1998) have shown that the electrically-driven compression heat pump should work with a COP not lower than 3-5. The value of 5.85 obtained from this study has shown that although there is a decrease in the effectiveness of the VRCΔP system when compared with the VRC system with COP of 6.15, it is within the acceptable range. This may be due to the fact that the compressor power input and the total energy consumption in the VRCΔP system is higher than in the VRC system.
