**1. Introduction**

### **1.1 Historical note on using supercritical fluids (SCFs)**

The use of supercritical fluids (SCFs) in various processes is not new and, actually, is not a human invention. Nature has been processing minerals in aqueous solutions at near or above the critical point of water for billions of years. In the late 1800s, scientists started to use this natural process in their labs for creating various crystals. During the last 50–60 years, this process, called hydrothermal processing (operating parameters: water pressure from 20 to 200 MPa and temperatures from 300 to 500°C), has been widely used in the industrial production of high-quality single crystals (mainly gem stones) such as sapphire, tourmaline, quartz, titanium oxide, zircon and others [1].

Also, compressed water, that is, water at a supercritical pressure (SCP), but at a temperature below *T*cr ≈ 374°C, exists in oceans at the depth of 2.2 km and deeper. If at this depth there is an active underwater volcano with the temperature of a magma above *T*cr of water, conditions for existence of supercritical water (SCW) can be reached.

The first works devoted to the problem of heat transfer at supercritical pressures (SCPs) started as early as the 1930s. Schmidt et al. [2] investigated free-convection heat transfer to fluids at a near-critical point with the application to a new effective cooling system for turbine blades in jet engines. They found that the freeconvection heat transfer coefficient (HTC) at the near-critical state was quite high, and decided to use this advantage in single-phase thermosyphons with an intermediate working fluid at the near-critical point [3].

Russia—59%; UK—44%; Italy—42%; and in USA—34%) [4, 5]. More details on

*Typical ranges of thermal efficiencies (gross) of modern thermal and nuclear power plants (NPPs) [4, 5] (for details including schematics and T-s diagrams, see Handbook [6] and Dragunov et al. [7]).*

**No. Power plant Gross thermal**

*Supercritical-Fluids Thermophysical Properties and Heat Transfer in Power-Engineering…*

1 Combined-cycle ThPP (combination of Brayton gas-turbine cycle (fuel natural gas or LNG); combustion-products parameters at gas turbine: *P*in ≈ 2.3 MPa and *T*in ≈ 1650°C) and Rankine cycle steam-turbine parameters: *P*in ≈ 12.5 MPa and *T*in ≈ 585°C (*T*cr = 374°C)

(see **Figure 1**): *<sup>P</sup>*in <sup>≈</sup> 23.5–38 MPa (*P*cr = 22.064 MPa),*T*in <sup>≈</sup> <sup>540</sup>‑625°C (*T*cr = 374°C) and steam reheat at: *<sup>P</sup>* <sup>≈</sup> 0.25*<sup>P</sup>*in and *<sup>T</sup>*reheat <sup>≈</sup> <sup>540</sup>‑625°C)

3 Subcritical-pressure coal-fired ThPP (older plants; Rankine cycle steamturbine parameters (see **Figure 2**): *P*in = 17 MPa (*T*sat = 352°C),*T*in = 540°C (*T*cr = 374°C), and steam reheat at: *P* ≈ 0.25*P*in and *T*reheat = 540°C)

4 Carbon dioxide-cooled reactor (advanced gas-cooled reactor (AGR)) NPP (Generation-III) (reactor coolant (carbon dioxide): *P* = 4 MPa and *T* = 290–650°C; Rankine cycle steam-turbine parameters (see **Figure 2**): *P* = 17 MPa (*T*sat = 352°C); *T*in = 540°C (*T*cr = 374°C), and steam reheat at:

5 Sodium-cooled fast reactor (SFR) (BN-600; BN-800) NPP (reactor coolant (sodium): *P* ≈ 0.1 MPa (above sodium level) and *T*max = 550°C; Rankine cycle steam-turbine parameters (see **Figure 3**): *P* = 14 MPa (*T*sat = 337°C); *T*in = 505°C (*T*cr = 374°C) and steam reheat at: *P* ≈ 0.25*P*in and *T*in = 505°C)

6 Pressurized water reactor (PWR) NPP (Generation-III+, new reactors)

7 Pressurized water reactor (PWR) NPP (Generation-III, current fleet) (reactor coolant: *P* = 15.5 MPa (*T*sat = 345°C) and *T* = 292–329°C; Rankine cycle steam-turbine parameters (see **Figure 4**): *P* = 6.9 MPa and *T*in = *T*sat = 285°C and steam reheat at *P*in ≈ 1 MPa and *T*in ≈ 265°C)

8 Boiling-water-reactor (BWR) or advanced BWR NPP (Generation-III and III+, current fleet) (*P*in = 7.2 MPa and *T*in = *T*sat=288°C (direct cycle) and

9 Pressurized heavy water reactor (PHWR) NPP (Generation-III, current fleet) (reactor coolant: *P*out = 10 MPa (*T*sat = 311°C) and *T* = 260–310°C; Rankine cycle steam-turbine parameters: *P* = 4.6 MPa and *T*in = *T*sat = 259°C

steam reheat at *P*in ≈ 1 MPa and *T*in ≈ 268°C (see **Figure 4**))

and steam reheat at l *P*in ≈ 1 MPa and *T*in ≈ 240°C)

(reactor coolant (light water): *<sup>P</sup>* = 15.5 MPa (*T*sat = 345°C) and *<sup>T</sup>* = 280‑322°C; Rankine cycle steam-turbine parameters (see **Figure 4**): *P* = 7.8 MPa and *T*in = *T*sat = 293°C and steam reheat at *P*in ≈ 1 MPa and *T*in ≈ 273°C)

2 SCP coal-fired ThPP (Rankine cycle "steam"-turbine parameters

*P* ≈ 0.25*P*in and *T*in = 540°C)

*DOI: http://dx.doi.org/10.5772/intechopen.91474*

**efficiency**

Up to 62%

Up to 55%

Up to 43%

Up to 42%

Up to 40%

Up to 36‑38%

Up to 34‑36%

Up to 34%

Up to 32%

**1.2 Future applications of SCFs in next-generation nuclear-power reactors**

At the end of the 1950s and the beginning of the 1960s, early studies were conducted to investigate a possibility of using SCW in nuclear reactors. Several concepts of nuclear reactors using SCW were developed in Great Britain, France,

Also, at SCPs there is no liquid-vapor-phase transition; therefore, there is no such phenomenon as critical heat flux (CHF) or dryout. It is only within a certain range of parameters a deteriorated heat transfer (DHT) regime may occur. Work in this area was mainly performed in Germany, USA, former USSR, and some other

ThPPs can be found in Pioro and Kirillov [8] and many other sources.

countries in the 1950–1980s [9].

**and NPPs**

**3**

**Table 1.**

In the 1950s, the idea of using SC "steam" (actually, SCW) appeared to be rather attractive for the Rankine power cycle. The objective was to increase a thermal efficiency of coal-fired thermal power plants (ThPPs) (see **Table 1**). This change, that is, substantially higher operating pressures in the Rankine cycle from subcritical ones, and, correspondingly to that, higher inlet-turbine temperature up to 625°C, has allowed increasing of thermal efficiencies from 40–43% to 50–55% (gross) (in total by 7–15%). Currently, SCP coal-fired thermal power plants (world electricity generation with coal 38%—the largest source for electricity generation; in India— 77%; China—65%; Germany—37%; and in USA—30%) are the second ones by thermal efficiencies after gas-fired combined-cycle ThPPs (world electricity generation with natural gas 23%—second largest source for electricity generation; in

*Supercritical-Fluids Thermophysical Properties and Heat Transfer in Power-Engineering… DOI: http://dx.doi.org/10.5772/intechopen.91474*


### **Table 1.**

and Rankine cycles with SC carbon dioxide as a working fluid are being developed, etc. A comparison of thermophysical properties of SCFs with those of subcriticalpressure fluids showed that SCFs as single-phase fluids have unique properties, which are close to "liquid-like" behavior below critical or pseudocritical points and are quite similar to the behavior of "gas-like" substances above these points. A comparison of selected SCW heat transfer correlations has shown that their results may differ from one to another by more than 200%. Based on these comparisons, it became evident that there is a need for reliable, accurate, and wide-range SCW heat transfer correlation(s) to be developed and verified. Therefore, the

objective of this chapter is to summarize in concise form specifics of supercritical-

The use of supercritical fluids (SCFs) in various processes is not new and, actually, is not a human invention. Nature has been processing minerals in aqueous solutions at near or above the critical point of water for billions of years. In the late 1800s, scientists started to use this natural process in their labs for creating various crystals. During the last 50–60 years, this process, called hydrothermal processing (operating parameters: water pressure from 20 to 200 MPa and temperatures from 300 to 500°C), has been widely used in the industrial production of high-quality single crystals (mainly gem stones) such as sapphire, tourmaline, quartz, titanium

Also, compressed water, that is, water at a supercritical pressure (SCP), but at a temperature below *T*cr ≈ 374°C, exists in oceans at the depth of 2.2 km and deeper. If at this depth there is an active underwater volcano with the temperature of a magma above *T*cr of water, conditions for existence of supercritical water (SCW)

The first works devoted to the problem of heat transfer at supercritical pressures (SCPs) started as early as the 1930s. Schmidt et al. [2] investigated free-convection heat transfer to fluids at a near-critical point with the application to a new effective

convection heat transfer coefficient (HTC) at the near-critical state was quite high, and decided to use this advantage in single-phase thermosyphons with an interme-

attractive for the Rankine power cycle. The objective was to increase a thermal efficiency of coal-fired thermal power plants (ThPPs) (see **Table 1**). This change, that is, substantially higher operating pressures in the Rankine cycle from subcritical ones, and, correspondingly to that, higher inlet-turbine temperature up to 625°C, has allowed increasing of thermal efficiencies from 40–43% to 50–55% (gross) (in total by 7–15%). Currently, SCP coal-fired thermal power plants (world electricity generation with coal 38%—the largest source for electricity generation; in India— 77%; China—65%; Germany—37%; and in USA—30%) are the second ones by thermal efficiencies after gas-fired combined-cycle ThPPs (world electricity

generation with natural gas 23%—second largest source for electricity generation; in

In the 1950s, the idea of using SC "steam" (actually, SCW) appeared to be rather

cooling system for turbine blades in jet engines. They found that the free-

diate working fluid at the near-critical point [3].

fluids thermophysical properties and heat transfer in power-engineering

**Keywords:** supercritical water, carbon dioxide, refrigerant,

**1.1 Historical note on using supercritical fluids (SCFs)**

applications.

**1. Introduction**

forced convective heat transfer

*Advanced Supercritical Fluids Technologies*

oxide, zircon and others [1].

can be reached.

**2**

*Typical ranges of thermal efficiencies (gross) of modern thermal and nuclear power plants (NPPs) [4, 5] (for details including schematics and T-s diagrams, see Handbook [6] and Dragunov et al. [7]).*

Russia—59%; UK—44%; Italy—42%; and in USA—34%) [4, 5]. More details on ThPPs can be found in Pioro and Kirillov [8] and many other sources.

Also, at SCPs there is no liquid-vapor-phase transition; therefore, there is no such phenomenon as critical heat flux (CHF) or dryout. It is only within a certain range of parameters a deteriorated heat transfer (DHT) regime may occur. Work in this area was mainly performed in Germany, USA, former USSR, and some other countries in the 1950–1980s [9].

### **1.2 Future applications of SCFs in next-generation nuclear-power reactors and NPPs**

At the end of the 1950s and the beginning of the 1960s, early studies were conducted to investigate a possibility of using SCW in nuclear reactors. Several concepts of nuclear reactors using SCW were developed in Great Britain, France, USA, and former USSR. However, this idea was abandoned for almost 30 years with the emergence of light water reactors (LWRs), but regained interest in the 1990s following LWRs maturation ([6, 9–13]).

299 units or 68% from the total number of 441 units; (2) BWRs—65 units or 15%; (3) PHWRs—48 units or 11%; (4) light water, graphite-moderated reactors

*Supercritical-Fluids Thermophysical Properties and Heat Transfer in Power-Engineering…*

Therefore, six concepts of nuclear-power reactors/NPPs of next generation, Generation-IV, were proposed (see **Table 2**), which will have thermal efficiencies comparable with those of modern thermal power plants. Supercritical water-cooled reactor (SCWR) is one of these six concepts under development in a number of countries [6, 17]. Analysis of Generation-IV concepts listed in **Table 2** shows that SCFs, such as helium and water, will be used as reactor coolants, and SCFs such as helium, nitrogen (or mixture of nitrogen (80%) and helium (20%)), carbon dioxide, and water will be used as working fluids (WFs) in power Brayton and Rankine cycles (critical parameters of selected SCFs are listed in **Table 3**). However, it should be mentioned that helium as the reactor coolant and as the working fluid in Brayton power cycle will be at supercritical conditions, which are far above by pressure and temperature critical parameters, that is, helium will behave as

Nowadays, the most widely used SCFs are water, carbon dioxide, and refrigerants [9]. Quite often, carbon dioxide and refrigerants are considered as modeling fluids and used instead of SCW due to significantly lower critical pressures and temperatures, which decreases the complexity and costs of thermalhydraulic experiments. However, they can be/will be used as working fluids in new SCP

Also, other applications of SCFs will be discussed in the following chapters and

*T***cr** *P***cr** *ρ***cr Application in power engineering at**

44.01 30.978 7.3773 467.6 WF in Brayton and Rankine power

**SCPs**

cycles (see **Figures 5** and **6**)

**Figure 7**); WF in Brayton power cycle (see **Figure 7**)

N2 (80%) & He (20%) is proposed (see **Figures 8** and **9**))

tests

tests

ThPP; reactor coolant in SCWR; WF in Rankine power cycle (see **Figure 1**)

power cycles: Brayton and Rankine ones [6] (for details, see **Table 3**).

**kg/kmol °C MPa kg/m3**

2 Ethanol, C2H6O 46.068 241.56 6.268 273.19 N/A

4 Methanol, CH3OH 32.042 239.45 8.1035 275.56 N/A

3 Helium,<sup>2</sup> He 4.0026 Reactor coolant in VHTR & GFR (see

5 Nitrogen, N2 28.013 ‑146.96 3.3958 313.3 WF in Brayton cycle (also, mixture of

6 R-12, CCl2F2 120.91 111.97 4.1361 565.0 Modeling fluid in thermalhydraulic

7 R-134a, CF3CH2F 102.03 101.06 4.0593 511.9 Modeling fluid in thermalhydraulic

, H2O 18.015 373.95 22.064 322.0 WF in Rankine cycle of coal-fired

(LGRs)—13 units of 3%.

*DOI: http://dx.doi.org/10.5772/intechopen.91474*

compressed gas.

are listed in Pioro and Duffey [9].

**No. Fluid Molar**

1 Carbon dioxide,<sup>1</sup> CO2

8 Water<sup>3</sup>

**Table 3.**

**5**

**mass**

*1,2,3Thermodynamics diagrams: P-T and T-s can be found in Handbook [6]. <sup>3</sup> Thermodynamics diagrams: P-T and T-s are shown in* **Figure 10***.*

*Critical parameters of selected fluids and gases (based on NIST [25]).*

This interest was triggered by economical considerations, because nuclear power plants (NPPs) with LWRs (and, especially, with PHWRs) have relatively low thermal efficiencies within the range of 30–36% for Generation-III reactors and up to 37% (38%) for advanced reactors of Generation-III+ (see **Table 1**) compared to those of modern ThPPs (up to 62% for combined-cycle plants and up to 55% for SCP Rankine cycle plants (see **Table 1**)) [6]. Therefore, NPPs with various designs of water-cooled reactors at subcritical pressures cannot compete with modern advanced ThPPs. Also, it should be noted that currently, water-cooled reactors are the vast majority of nuclear-power reactors in the world [14, 15]: (1) PWRs—


**Table 2.**

*Estimated ranges of thermal efficiencies (gross) of Generation-IV NPP concepts (Generation-IV concepts are listed according to thermal-efficiency decrease) [6, 16].*

*Supercritical-Fluids Thermophysical Properties and Heat Transfer in Power-Engineering… DOI: http://dx.doi.org/10.5772/intechopen.91474*

299 units or 68% from the total number of 441 units; (2) BWRs—65 units or 15%; (3) PHWRs—48 units or 11%; (4) light water, graphite-moderated reactors (LGRs)—13 units of 3%.

Therefore, six concepts of nuclear-power reactors/NPPs of next generation, Generation-IV, were proposed (see **Table 2**), which will have thermal efficiencies comparable with those of modern thermal power plants. Supercritical water-cooled reactor (SCWR) is one of these six concepts under development in a number of countries [6, 17]. Analysis of Generation-IV concepts listed in **Table 2** shows that SCFs, such as helium and water, will be used as reactor coolants, and SCFs such as helium, nitrogen (or mixture of nitrogen (80%) and helium (20%)), carbon dioxide, and water will be used as working fluids (WFs) in power Brayton and Rankine cycles (critical parameters of selected SCFs are listed in **Table 3**). However, it should be mentioned that helium as the reactor coolant and as the working fluid in Brayton power cycle will be at supercritical conditions, which are far above by pressure and temperature critical parameters, that is, helium will behave as compressed gas.

Nowadays, the most widely used SCFs are water, carbon dioxide, and refrigerants [9]. Quite often, carbon dioxide and refrigerants are considered as modeling fluids and used instead of SCW due to significantly lower critical pressures and temperatures, which decreases the complexity and costs of thermalhydraulic experiments. However, they can be/will be used as working fluids in new SCP power cycles: Brayton and Rankine ones [6] (for details, see **Table 3**).

Also, other applications of SCFs will be discussed in the following chapters and are listed in Pioro and Duffey [9].


*Thermodynamics diagrams: P-T and T-s are shown in* **Figure 10***.*

### **Table 3.**

*Critical parameters of selected fluids and gases (based on NIST [25]).*

USA, and former USSR. However, this idea was abandoned for almost 30 years with the emergence of light water reactors (LWRs), but regained interest in the 1990s

This interest was triggered by economical considerations, because nuclear power plants (NPPs) with LWRs (and, especially, with PHWRs) have relatively low thermal efficiencies within the range of 30–36% for Generation-III reactors and up to 37% (38%) for advanced reactors of Generation-III+ (see **Table 1**) compared to those of modern ThPPs (up to 62% for combined-cycle plants and up to 55% for SCP Rankine cycle plants (see **Table 1**)) [6]. Therefore, NPPs with various designs of water-cooled reactors at subcritical pressures cannot compete with modern advanced ThPPs. Also, it should be noted that currently, water-cooled reactors are the vast majority of nuclear-power reactors in the world [14, 15]: (1) PWRs—

**No. Nuclear power plant Gross**

**1** Very high-temperature reactor (VHTR) NPP (reactor coolant—helium (SCF): *P* = 7 MPa and *T*in/*T*out = 640/1000°C; primary power cycle—direct SCP Brayton helium-gas-turbine cycle; possible back-up—indirect Brayton or combined cycles

**2** Gas-cooled fast reactor (GFR) or high-temperature reactor (HTR) NPP (reactor coolant—helium (SCF): *P* = 9 MPa and *T*in/*T*out = 490/850°C; primary power cycle—direct SCP Brayton helium-gas-turbine cycle (see **Figure 7**); possible back-up—indirect SCP Brayton or combined cycles (see **Figures 8** and **9**))

**3** Supercritical water-cooled reactor (SCWR) NPP (one of Canadian concepts; reactor coolant—SC light water: *P* = 25 MPa and *T*in/*T*out = 350/625°C (*T*cr = 374°C); direct cycle; SCP Rankine cycle with high-temperature secondary-steam superheat: *T*out = 625°C; possible back-up–indirect SCP Rankine "steam"-turbine cycle with high-temperature secondary-steam superheat) (for details of SCP Rankine cycle, see

dissolved uranium fuel: *T*in/*T*out = 700/800°C; primary power cycle—indirect SCP carbon dioxide Brayton gas-turbine cycle; possible back-up—indirect Rankine

coolant—liquid lead: *P* ≈ 0.1 MPa and *T*in/*T*out = 420/540°C; primary power cycle—indirect subcritical-pressure Rankine steam cycle: *Pin* ≈ 17 MPa (*P*cr = 22.064 MPa) and *T*in/*T*out = 340/505°C (*T*cr = 374°C); high-temperature secondary-steam superheat (in one of the previous designs of BREST-300 NPP primary power cycle was indirect SCP Rankine "steam" cycle: *Pin* ≈ 24.5 MPa (*P*cr = 22.064 MPa) and *T*in/*T*out = 340/520°C (*T*cr = 374°C); also, note that powerconversion cycle in a different LFR designs from other countries is based on SCP

**6** Sodium-cooled fast reactor (SFR) NPP (Russian design BN-600: reactor coolant liquid sodium (primary circuit): *P* ≈ 0.1 MPa and *T*in/*T*out = 380/550°C; liquid sodium (secondary circuit): *T*in/*T*out = 320/520°C; primary power cycle—indirect Rankine steam-turbine cycle: *Pin* ≈ 14.2 MPa (*T*sat ≈ 337°C) and *T*in max = 505°C (*T*cr = 374°C); secondary-steam superheat: *P* ≈ 2.45 MPa and *T*in/*T*out = 246/505°C; possible back-up in some other countries—indirect SCP carbon dioxide Brayton gas-turbine cycle)

*BREST-OD-300 is Fast Reactor with "NATural safety"-Test-Demonstration in Russian abbreviations (БРЕСТ-OD-300—Быстрый Реактор с ЕСТественной безопасностью—Опытно –Демонстрационный).*

*Estimated ranges of thermal efficiencies (gross) of Generation-IV NPP concepts (Generation-IV concepts are*

**4** Molten salt reactor (MSR) NPP (reactor coolant—sodium-fluoride salt with

**5** Lead-cooled fast reactor (LFR) NPP (Russian design BREST-OD-300\*

**eff., %**

≥55

≥50

45–50

50

41–43

40

: reactor

following LWRs maturation ([6, 9–13]).

*Advanced Supercritical Fluids Technologies*

(see **Figures 5** and **6**))

**Table 1** Item No. 2 and **Figure 1**)

carbon dioxide Brayton gas-turbine cycle

*listed according to thermal-efficiency decrease) [6, 16].*

steam-turbine cycle)

*\**

**4**

**Table 2.**
