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Application of Supercritical Fluids in Power Engineering

Igor Pioro, Sarah Mokry, Wargha Peiman, Eugene Saltanov and Lisa Grande

Faculty of Energy Systems and Nuclear Science, University of Ontario Institute of Technology

2000 Simcoe St. N., Oshawa, Ontario, Canada L1K7H4 E-mail: igor.pioro@uoit.ca

ABSTRACT

In 2001, ten countries initiated the Generation IV International Forum to develop collaboratively the next

generation of nuclear-energy systems, which will provide competitively-priced and reliable energy in a safe and

sustainable manner. Over 100 potential nuclear reactor concepts (or "systems") were reviewed by an

international panel of experts. This panel selected six reactor types that best matched the Generation IV

objectives of sustainability, economics, safety and reliability and proliferation resistance and physical protection.

One of these reactors was the Supercritical Water-cooled Reactor (SCWR). In addition, other reactor concepts

can be linked to the supercritical-“steam” Rankine cycle through heat exchangers.

The supercritical-"steam" cycle was first introduced in coal-fired power plants in 1957, and the extensive

operating experience in this technology will be the cornerstone for SCWR development. The primary objective

for using supercritical water as a coolant in nuclear reactors are: (1) to increase the thermal efficiency of modern

nuclear power plants, which is currently 30 - 35%, to approximately 45% or higher, and (2) to decrease the

operational and capital costs by eliminating the steam generators, steam separators, steam dryers, etc. that are

currently used in modern fossil-fired plants.

Also, some Generation IV reactor concepts can be connected to the supercritical carbon-dioxide Brayton gas-

turbine cycle. Therefore, studies are currently being conducted on heat-transfer at supercritical conditions in

various fluids including water and carbon dioxide.

INTRODUCTION

The use of supercritical fluids in different processes is not new, nor was it a human invention. Mother Nature

has been processing minerals in aqueous solutions at near or above the critical point of water for billions of years

[1]. It was only in the late 1800s when scientists started to use this natural process, called hydrothermal

processing, in their labs for creating various crystals. During the last 50 – 60 years, this process (operating

parameters - water pressures from 20 to 200 MPa and temperatures from 300 to 500ºC) has been widely used in

the industrial production of high-quality single crystals (mainly gem stones) such as quartz, sapphire, titanium

oxide, tourmaline, zircon and others.

The first works devoted to the problem of heat transfer at supercritical pressures started as early as the 1930s.

Schmidt [2] and his associates investigated free-convection heat transfer of fluids at the near-critical point with

the application to a new effective cooling system for turbine blades in jet engines. They found that the free-

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

In the 1950s, the idea of using supercritical water appeared to be rather attractive for steam generators/turbines in

the thermal-power industry. The objective was to increase the total thermal efficiency of coal-fired power

plants. At supercritical pressures there is no liquid-vapour phase transition; therefore, there is no such

phenomenon as Critical Heat Flux (CHF) or dryout. It is only within a certain range of parameters that

deteriorated heat transfer may occur. Work in this area was mainly performed in the former USSR and in the

USA in the 1950s – 1980s.

Therefore, the objective of this paper is a discussion of the applications of supercritical fluids in the power

industry.

SUPERCRITICAL-PRESSURE THERMAL POWER PLANTS

It is well known that electrical-power generation is a key factor for advances in other industries, in agriculture

and contributes to an increased standard of living. For about 100 years, coal was used for generating electrical

energy at coal-fired thermal-power plants worldwide. All coal-fired power plants operate based on the so-called

steam Rankine cycle, which can be grouped at two different levels of pressures: 1) older or smaller capacity

power plants operate at steam pressures no higher than 16 MPa and 2) modern large capacity power plants

(Figure 1) operate at supercritical pressures from 23.5 MPa and up to 38 MPa. Supercritical pressures refers to

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pressures above the critical pressure of water, which is 22.064 MPa. From a thermodynamics perspective, it is

well known that higher thermal efficiencies correspond to higher temperatures and pressures. Therefore, usually

subcritical-pressure plants have thermal efficiencies of about 34 – 38% and modern supercritical-pressure plants

of about 43 – 50%, or even slightly higher. Steam-generators outlet temperatures or steam-turbine inlet

temperatures have reached the level of about 625°C (and even higher) at pressures of 25 – 30 (35 – 38) MPa.

However, the common level is about 535 – 585°C at pressures of 23.5 – 25 MPa. Using supercritical water-

steam at coal-fired thermal-power plants is the largest application of supercritical fluids in the power industry.

However, in spite of advances in coal-fired power-plant design and operation worldwide, they are still not

considered to be environmental friendly due to the production of carbon-dioxide emissions, as a result of the

combustion process, plus production of ash, slag and even acid rain.

FUTURE APPLICATIONS OF SUPERCRITICAL-PRESSURE FLUIDS IN NUCLEAR POWER

PLANTS

Nuclear power, as coal and other fossil fuels, is a non-renewable resource. However, nuclear resources can be

used for significantly longer time period when compared to some fossil fuels, plus nuclear power does not emit

carbon dioxide into the atmosphere. Currently, this source of energy is considered the most viable option of

electrical generation for the next 50 – 100 years.

Current nuclear reactors, i.e., Generation II and III, consist of water-cooled reactor Nuclear Power Plants (NPPs)

with a thermal efficiency of 30 – 35% (vast majority of reactors); carbon-dioxide-cooled reactor NPPs with a

thermal efficiency up to 42% and liquid-sodium-cooled reactor NPPs with a thermal efficiency up to 40%.

Within the next 5 – 25 years, Generation III+ (2010 – 2025) reactors with improved parameters (water-cooled

NPPs with a thermal efficiency up to 38%) will be implemented. However, these reactors will have only

evolutionary design improvements. Therefore, the next generation or Generation IV (2025 - …) reactors with

new parameters (NPPs with the thermal efficiency of 43 – 50% and even higher for all types of reactors) are

currently under development worldwide.

The supercritical-steam Rankine cycle is very efficient and is the only proven cycle for water-cooled thermal

power plants. Therefore, this cycle can be used in SuperCritical Water-cooled Nuclear Power Plants (SCW

NPPs) (Figure 2). The main objectives of using supercritical water in nuclear reactors are: 1) to increase the

efficiency of modern NPPs, which is currently 30 – 35% to approximately 43 – 50%, and 2) to decrease the

operational and capital costs by eliminating steam generators, steam separators, steam dryers, etc. Currently,

SuperCritical Water-cooled nuclear Reactor (SCWR) concepts are one of six conceptual options included in the

next generation or Generation IV nuclear systems [4]. Moreover, due to various problems with other Generation

IV concepts, this cycle can be connected to any of the Generation IV reactors through their heat exchangers.

In addition, the supercritical carbon-dioxide Brayton gas-turbine cycle is also considered for implementation in

Generation IV nuclear-reactor concepts, such as for Sodium-cooled Fast Reactors (SFRs), Lead-cooled Fast

Reactors (LFRs) (Figure 3) and High Temperature helium-cooled thermal Reactors (HTRs).

Therefore, knowledge of thermophysical-properties specifics at critical and supercritical pressures is very

important for the safe and efficient use of fluids in various industries.

DEFINITIONS OF TERMS AND EXPRESSIONS RELATED TO CRITICAL AND SUPERCRITICAL

REGIONS

Prior to a general discussion on specifics of thermophysical properties and forced-convective heat transfer at

critical and supercritical pressures, it is important to define special terms and expressions used at these

conditions. For a better understanding of these terms and expressions their definitions are listed below together

with corresponding Figures 4 and 5 (for further details, see [4]).

Compressed fluid is a fluid at a pressure above the critical pressure, but at a temperature below the critical

temperature.

Critical point (also called a critical state) is a point in which the distinction between the liquid and gas (or

vapour) phases disappears, i.e., both phases have the same temperature, pressure and volume or density. The

critical point is characterized by the phase-state parameters Tcr, Pcr and Vcr (or ρcr), which have unique values for

each pure substance.

Deteriorated Heat Transfer (DHT) is characterized with lower values of the wall heat transfer coefficient

compared to those for normal heat transfer; and hence, has higher values of wall temperature within some part of

a test section or within the entire test section.

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Figure 1. Single-reheat-regenerative cycle 600-MWel Tom’-Usinsk thermal-power plant (Russia) layout [5]: CP – Circulation Pump; Cond P – Condensate Pump; Cyl

– Cylinder; GCLP – Gas Cooler of Low Pressure; GCHP – Gas Cooler of High Pressure; H – Heat exchanger (feedwater heater); HP – High Pressure; LP – Low

Pressure; IP – Intermediate Pressure and TDr – Turbine Drive.

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Figure 2. SCWR schematic: USA pressure-vessel

concept (courtesy of U.S. DOE).

Figure 3. Lead-cooled Fast Reactor with supercritical

carbon dioxide Brayton cycle (courtesy of U.S. DOE).

Improved Heat Transfer (IHT) is characterized with higher values of the wall heat transfer coefficient compared

to those for normal heat transfer; and hence, lower values of wall temperature within some part of a test section

or within the entire test section. In our opinion, the improved heat-transfer regime or mode includes peaks or

“humps” in the heat transfer coefficient near the critical or pseudocritical points.

Near-critical point is actually a narrow region around the critical point, where all thermophysical properties of a

pure fluid exhibit rapid variations.

Normal Heat Transfer (NHT) can be characterized in general with wall heat transfer coefficients similar to

those of subcritical convective heat transfer far from the critical or pseudocritical regions, when they are

calculated according to the conventional single-phase Dittus-Boelter-type correlations: Nu = 0.0023 Re0.8

Pr0.4

.

Pseudocritical line is a line, which consists of pseudocritical points.

Pseudocritical point (characterized with Ppc and Tpc) is a point at a pressure above the critical pressure and at a

temperature (Tpc > Tcr) corresponding to the maximum value of the specific heat at this particular pressure.

Supercritical fluid is a fluid at pressures and temperatures that are higher than the critical pressure and critical

temperature. However, in the present paper, the term supercritical fluid includes both terms – a supercritical

fluid and compressed fluid.

Supercritical “steam” is actually supercritical water, because at supercritical pressures fluid is considered as a

single-phase substance. However, this term is widely (and incorrectly) used in the literature in relation to

supercritical “steam” generators and turbines.

Superheated steam is a steam at pressures below the critical pressure, but at temperatures above the critical

temperature.

THERMOPHYSICAL PROPERTIES AT CRITICAL AND SUPERCRITICAL PRESSURES

The general trends of various properties near the critical and pseudocritical points [4], [6] can be illustrated on a

basis of those of water and carbon dioxide (Figs. 6 - 9). Properties of supercritical helium and R-134a are shown

in [4].

Figures 6 through 9 show variations in the basic thermophysical properties of water at the critical (Pcr = 22.064

MPa) and three supercritical pressures (P = 25.0, 30.0, and 35.0 MPa) and those of carbon dioxide at the

equivalent pressures to those of water (the conversion is based on (

)

(

)

). Thermophysical

properties of 105 pure fluids including water, carbon dioxide, helium, refrigerants, etc., 5 pseudo-pure fluids

(such as air) and mixtures with up to 20 components at different pressures and temperatures, including critical

and supercritical regions, can be calculated using the NIST REFPROP software [7]. Critical parameters of

selected fluids are listed in Table 1.

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(a) (b)

Figure 4. Pressure-Temperature diagram for water (a) and carbon dioxide (b).

Axial Location, m

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Te

mp

era

ture

, oC

300

350

400

450

600

550

500

Bulk Fluid Enthalpy, kJ/kg

1400 1600 1800 2000 2200 2400 2600 2800

HT

C,

kW

/m2K

2

4

8

12

1620

28

36

Heated length

Bulk fluid temperature

tin

tout

Inside wall temperature

Heat transfer coefficient

pin=24.0 MPa

G=503 kg/m2s

Q=54 kW

qave

= 432 kW/m2

C381.1t o

pc

Hpc

Dittus - Boelter correlation

DHT Improved HT

Normal HTNormal HT

(a) (b)

Figure 5. Temperature and HTC profiles along heated length of vertical circular tubes with upward flow [4]: (a)

Water, ID 10 mm; and (b) Carbon Dioxide, ID 8 mm.

Table 1. Critical parameters of selected fluids [7].

Fluid Pcr, MPa Tcr, ºC cr, kg/m3

Carbon dioxide (CO2) 7.3773 30.98 467.6

Freon-134a (1,1,1,2-tetrafluoroethane, CH2FCF3) 4.0593 101.06 511.9

Helium (He) 0.2276 -267.95 72.567

Water (H2O) 22.064 373.95 322.0

At critical and supercritical pressures a fluid is considered as a single-phase substance in spite of the fact that all

thermophysical properties undergo significant changes within the critical and pseudocritical regions. Near the

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critical point, these changes are dramatic. In the vicinity of pseudocritical points, with an increase in pressure,

these changes become less pronounced (see Figs. 6 - 9).

Also, it can be seen that properties such as density and dynamic viscosity undergo a significant drop (near the

critical point this drop is almost vertical) within a very narrow temperature range (see Figs. 6a,b and 7a,b), while

the kinematic viscosity and specific enthalpy undergo a sharp increase (for details see [4]). The volume

expansivity, specific heat, thermal conductivity and Prandtl number have peaks near the critical and

pseudocritical points (see Figs. 8a,b and 9a,b). The magnitude of these peaks decreases very quickly with an

increase in pressure. Also, “peaks” transform into “humps” profiles at pressures beyond the critical pressure. It

should be noted that the dynamic viscosity, kinematic viscosity and thermal conductivity undergo through their

minimum right after the critical and pseudocritical points.

Specifics of forced-convection heat transfer at supercritical pressures can be found in [4] and [8-12]

Figure 6a. Density vs. Temperature: Water. Figure 6b. Density vs. Temperature:

Carbon Dioxide.

Figure 7a. Dynamic viscosity vs. Temperature: Water. Figure 7b. Dynamic viscosity vs. Temperature:

Carbon Dioxide.

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Figure 8a. Specific heat vs. Temperature: Water. Figure 8b. Specific heat vs. Temperature: Carbon

Dioxide.

Figure 9a. Thermal conductivity vs. Temperature:

Water.

Figure 9b. Thermal conductivity vs. Temperature:

Carbon Dioxide.

CONCLUSIONS

Supercritical fluids are used quite intensively in various industries. The application of supercritical

water/”steam” in the power industry has significantly increased the thermal efficiency of power plants. Based on

this experience, the next-generation of nuclear power plants have planned to use supercritical-fluid power cycles

such as the Rankine “steam” cycle and the supercritical carbon-dioxide Brayton gas-turbine cycle.

NOMENCLATURE

A flow area, m2

cp specific heat at constant pressure, J/kg K

D inside diameter, m

G mass flux, kg/m2s;

flA

m

H specific enthalpy, J/kg

h heat transfer coefficient, W/m2K

k thermal conductivity, W/m K

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m mass-flow rate, kg/s; V

P, p pressure, MPa

Q heat-transfer rate, W

q heat flux, W/m2;

hA

Q

T, t temperature, ºC

u axial velocity, m/s

V volume-flow rate, m3/kg or volume, m

3

Greek Letters

α thermal diffusivity, m2/s;

pc

k

dynamic viscosity, Pa·s

density, kg/m3

kinematic viscosity, m2/s

Non-dimensional Numbers

Nu Nusselt number;

k

Dh

Pr Prandtl number;

k

c p

Re Reynolds number;

DG

Subscripts or superscripts ave average

b bulk

cal calculated

cr critical

ext external

fl flow

h heated

in inlet

mixer mixer (chamber)

out outlet or outside

pc pseudocritical

w wall

Abbreviations and acronyms widely used in the

text and list of references

CHF Critical Heat Flux

DHT Deteriorated Heat Transfer

DOE Department Of Energy (USA)

HT Heat Transfer

HTC Heat Transfer Coefficient

HTR High Temperature Reactor

(helium cooled)

ID Inside Diameter

IHT Improved Heat Transfer

LFR Lead-cooled Fast Reactor

NHT Normal Heat Transfer

NIST National Institute of Standards

and Technology (USA)

NPP Nuclear Power Plant

REFPROP REFerence PROPerties

SCW SuperCritical Water

SCWR SuperCritical Water-cooled

Reactor

SFR Sodium-cooled Fast Reactor

USA United States of America

USSR Union of Soviet Socialist

Republics

REFERENCES

[1] Levelt Sengers, J.M.H.L., Supercritical fluids: Their properties and applications, Chapter 1, in book:

Supercritical Fluids, editors: E. Kiran et al., NATO Advanced Study Institute on Supercritical Fluids –

Fundamentals and Application, NATO Science Series, Series E, Applied Sciences, Kluwer Academic

Publishers, Netherlands, Vol. 366, 2000, p. 1.

[2] Schmidt, E., Eckert, E. and Grigull, V., Heat transfer by liquids near the critical state, AFF Translation, No.

527, Air Materials Command, Wright Field, Dayton, OH, USA, April, 1946.

[3] Pioro, L.S. and Pioro, I.L., Industrial Two-Phase Thermosyphons, Begell House, New York, NY, USA,

1997, 288 pages.

[4] Pioro, I.L. and Duffey, R.B., Heat Transfer and Hydraulic Resistance at Supercritical Pressures in Power

Engineering Applications, ASME Press, New York, NY, USA, 2007, 328 pages.

[5] Kruglikov, P.A., Smolkin, Yu.V. and Sokolov, K.V., Development of engineering solutions for thermal

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Int. Workshop "Supercritical Water and Steam in Nuclear Power Engineering: Problems and Solutions”,

Moscow, Russia, October 22–23, 2009, 6 pages.

[6] Pioro, I.L., Thermophysical properties at critical and supercritical pressures, Section 5.5.16 in Heat

Exchanger Design Handbook, Begell House, New York, NY, USA, 2008, 14 pages.

[7] Lemmon, E.W., Huber, M.L. and McLinden, M.O. NIST Standard Reference Database 23: Reference Fluid

Thermodynamic and Transport Properties-REFPROP, Version 9.0, National Institute of Standards and

Technology, Standard Reference Data Program, Gaithersburg, 2010.

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[8] Pioro, I., The Potential Use of Supercritical Water-Cooling in Nuclear Reactors. Chapter in Nuclear Energy

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[9] Pioro, I. and Mokry, S., Thermophysical Properties at Critical and Supercritical Conditions, Chapter in

book “Heat Transfer. Theoretical Analysis, Experimental Investigations and Industrial Systems”, Editor: A.

Belmiloudi, INTECH, Rijeka, Croatia, 2011, p. 573.

[10] Pioro, I. and Mokry, S., Heat Transfer to Fluids at Supercritical Pressures, Chapter in book “Heat Transfer.

Theoretical Analysis, Experimental Investigations and Industrial Systems”, Editor: A. Belmiloudi,

INTECH, Rijeka, Croatia, 2011, p. 481.

[11] Pioro, I., Mokry, S. and Draper, Sh., Specifics of Thermophysical Properties and Forced-Convective Heat

Transfer at Critical and Supercritical Pressures, Reviews in Chemical Engineering, Vol. 27, Issue 3-4,

2011, p. 191.

[12] Mokry, S., Pioro, I.L., Farah, A., King, K., Gupta, S., Peiman, W. and Kirillov, P., Development of

Supercritical Water Heat-Transfer Correlation for Vertical Bare Tubes, Nuclear Engineering and Design,

Vol. 241, 2011, p. 1126.