Cayer, Galanis. Analysis of a CO2 transcritical power cycle using a low
temperature source; Applied Energy 86 (2009): 1055–1063
Abstract
 Methodology: 4 steps
o Energy analysis
o Exergy analysis
o Finite size thermodynamics
o HX surface
 Fixed parameters:
o Tin and mass flow rate heat source
o Tmin and Tmax cycle
o Sink temperature
 Variables
o pmax cycle
o Net power output
 Results
o Optimum pressure in each of the 4 steps
o Step 1 and 2: optimum pmax maximizes thermal and exergetic efficiency (similar
pressure)
o Step 3 and 4: optimim pmax minimises UA and A (nearly identical), but much lower
pmax than for step 1 and 2.
Results
 Actually, coal fired transcritical power plants at high temperatures (above 500°C) constitute a
mature technology and are among the best performing heat engines with a thermal
efficiency as high as 49%1. Studies on nuclear plants using CO2 or helium have been
published2 and showed that standard gas turbines can be used with CO23. On the other hand,
studies of low temperature transcritical cycles are rare. The geothermal area was the first to
consider it with several fluids such as propane, isobutane and pentane4, CO25, R125 and
R134a6.
 To the present, none of the published studies on transcritical cycles with CO2 have presented
results other than those obtained by applying the first law of thermodynamics. For limited
capacity heat sources as is the case with thermal wastes, a more detailed study is necessary.
In the present article, a methodology is exposed and applied to the study of a CO2
transcritical cycle supplied by a steady stream of low temperature process gases.
1
Tsiklauri G, Talbert R, Schmitt B, Filippov G, Bogoyavlensky R, Grishanin E. Supercritical steam cycles for nuclear power plant. Nucl Eng Des
2005;235(15):1651–64.
2
Dostal V, Driscoll MJ, Hejzlar P, Todreas NE. A supercritical CO2 gas turbine power cycle for next-generation nuclear reactors. In:
Proceedings of ICONE 10, 10th international conference on nuclear engineering, Arlington, Virginia: 14–18 April, 2002.
3 Kato Y, Nitawaki T, Muto Y. Medium temperature carbon dioxide gas turbine reactor. Nucl Eng Des 2004;230:195–207.
4 Goldsberry FL. The variable pressure supercritical Rankine cycle for integrated natural gas and power production from the geopressured
geothermal resource. Houston Texas: Geopressure Projects Office; 1982.
5 Maghiar T, Antal C. Power generation from low-enthalpy geothermal resources. GHC Bull 2001. June.
6 Gu Z, Sato H. Performance of supercritical cycles for geothermal binary design. Energy Convers Manage 2002;43(7):961–71.
System description and modeling
 2 configurations: with and without IHE


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Heat source: industrial gas, 314.5 kg/s, Tinlet = 100°C.
Coolant condenser: water at 10°C.
CO2 as working fluid  reasons
o critical properties of 7.4 MPa and 31°C are well suited for the external conditions
mentioned above,
o environment-friendly with an ozone depletion potential (ODP) of zero and a global
warming potential (GWP) of 1 over 100 years7,
o it is abundant, non-flammable, non-toxic and its cost is fairly low,
o it is compatible with standard materials and lubricants and is not harmful to the
environment,
o it has potentially favourable thermodynamics and transports properties,
o its thermophysical properties are well known even in the supercritical area.
General assumptions are applied: each component is considered as a steady-state steadyflow system, the kinetic and potential energies as well as the heat and friction losses are
neglected, the pump and the turbine isentropic efficiencies are set to 0.8, saturated liquid is
supposed at the condenser exit, regenerator effectiveness is 0.9 and the minimum cycle
temperature (T1) is set to 15°C which fixes the minimum pressure (p1 = p4) of the working
fluid, the maximum temperature is set to 95°C. A minimum temperature difference of 3°C is
applied in the condenser at the point where the working fluid is saturated vapour.
Hxs: S&T, counterflow, one pass each stream.
Methodology
7
Calm JM, Hourahan GC. Refrigerant data summary. Eng Syst 2001;18(11): 74–88.

Energy analysis
o See next paper
o Regenerator: heat exchanged between the two streams in the regenerator is:
In an ideal heat exchanger, one of the following two situations can occur depending
on which of the two streams in the regenerator has the smaller heat capacity: either
T5 tends towards T1 or T2 tends towards T4. In this way, the maximum heat
exchange Qmax is given by the smaller of the following two quantities:
The regenerator effectiveness IHX is then expressed as:
Utilisation of variable properties in the regenerator by applying Eqs. 9, 10a, 10b
(instead of the traditional ones obtained by replacing the enthalpy differences by the
product of temperature differences and a constant specific heat) has a very
significant effect on the cycle thermal efficiency. As an example, for a cycle with a
high pressure of 7.5 MPa and the previously specified maximum and minimum cycle
temperatures (95°C and 15°C, respectively) the thermal efficiency obtained with the
traditional method is 25.8% versus 6.3% when considering variable properties. Since
the corresponding Carnot efficiency is 21.7%, it is obvious that the traditional
definition of the effectiveness leads to unacceptable results. By extension, the LMTD
and e–NTU methods, which are also based on the assumption of constant properties,
should not be used in an analysis such as the present one.

Exergy analysis
o
o
o

One limitation of the energy analysis is that it does not consider the quality of the
heat exchange in the vapour generator and in the condenser. To achieve this, a
second law analysis is required. The final results of this section are the exergetic
efficiency of the cycle and the relative exergy destruction in each component of the
system.
The exergy analysis requires the mass flow rates of the working fluid and the coolant
in order to characterize the heat transfer processes.
Rest see next paper
Finite size thermodynamics analysis
o A widely used method [20] of finding UA is by applying the logarithmic mean
temperature difference (LMTD) between the inlet and outlet of the heat exchanger.
However, the LMTD method is based on constant properties, an assumption leading
to incorrect results in the case of supercritical fluids, as mentioned before. An
alternative solution consists in discretising the heat exchangers so that the
properties variation in each step is small and an average constant value, different for
each step, can be assigned to each of them. The discretisation is performed by
dividing the overall enthalpy change for one of the streams in N equal differences
h.
o The corresponding temperatures and other properties at each intermediate state are
then determined from the known enthalpy and pressure. The heat transfer for each
step i as well as the corresponding properties of the other stream (air in the
evaporator, low pressure CO2 in the regenerator, water in the condenser) and the
fractional UAi values are calculated from the following equations modeling the
assumed counter-flow configuration:
o
A numerical study demonstrated that a discretisation with N = 20 is sufficient to
reach step-size independent results for all the three heat exchangers. For that
number of steps, Eq. (20a) can be simplified by replacing the LMTD by the difference
between the mean temperatures of each step, expressed by Eq. (20b), without
affecting the results:
o
This last equation has the advantage of decreasing significantly the calculation time
and guarantees numerical convergence without the need of very good initial guess
o

values, in opposition to the LMTD-method for which the logarithm complicates the
numerical resolution.
The condenser requires a more detailed analysis for the calculation of the UA value.
As mentioned before, two situations are conceivable depending on the state of the
working fluid at the turbine outlet. First, when the carbon dioxide is superheated
vapour, the condenser is divided into a single-phase region and a two-phase region.
Each region is then subdivided in 20 steps with equal enthalpy differences for the
carbon dioxide. Second, when the state of CO2 at the exit of the turbine falls in the
two-phase region, this region is subdivided in 20 steps with equal enthalpy
differences and the first one ignored.
Calculation of HXs surface
o Vapour generator
 The high pressure working fluid flows inside the tubes and the air flows in
the shell. Because of the poor heat transfer coefficient of air, longitudinal
fins are added on the outside of each tube. The number of tubes and the
shell diameter are obtained from the mass balance equations by fixing the
minimum velocity at 0.5 m/s for the liquid carbon dioxide and the maximum
velocity at 30 m/s for the hot entering air.
 As mentioned before, the vapour generator is discretised in 20 steps and the
properties necessary for the calculation of the corresponding heat transfer
coefficients (i.e. the isobaric specific heats, the dynamic viscosities, the
thermal conductivities and the densities) are evaluated with EES at the
prevailing local conditions and are used to determine the Prandtl and
Reynolds numbers as well as the Darcy friction factor.
 Heat transfer coefficients

This correlation is similar to the one developed by Petukhov, but includes
corrections to take into account the differences between the bulk and the
wall properties.

The heat exchange surfaces of each side are then calculated using the
following equation and the fins global efficiency:

In this equation the thermal resistance of the tubes wall is neglected and
fouling is not considered
o
Condenser
 Similar to vapour generator, but few exceptions.
 However, this time the longitudinal fins are positioned inside the tubes
because of the good transfer properties of water and the risk of fouling if fins
are installed on the water side.
 The number of tubes and the shell diameter are obtained by assuming a
minimum velocity of 1.5 m/s for the saturated liquid carbon dioxide and a
maximum velocity of 3 m/s for the water.
 Petukhov’s correlation (Eq. (21)) is employed on the water side and for the
single-phase carbon dioxide. For the two-phase region of the CO2, Cavallini’s
correlation [23] is used
o
Regenerator
 Modeling of the regenerator follows the same methodology as the two
preceding heat exchangers. The higher pressure working fluid from the pump
circulates inside the tubes and the lower pressure one from the turbine in
the shell.
 The fins are located inside the tubes to reduce the regenerator size and
facilitate assembly.
 The minimum velocity of the cold stream of carbon dioxide is set to 1.5 m/s
and the maximum velocity of the supersaturated CO2 at 10 m/s.
 Petukhov’s correlation (Eq. (21)) is used for the low pressure carbon dioxide
and Krasnoshchekov–Protopopov’s correlation (Eq. (22)) for the supercritical
CO2 coming from the pump.
Simulation results
 Energy results

Exergy results
o The regenerator has a beneficial effect on the optimizing high pressure but its effect
on the thermal and exergetic efficiency is not significant.
o Fig. 8 also shows that as a increases the exergetic efficiency decreases. In other
words, when the net power output extracted from a fixed and limited heat source
increases the total exergy destruction increases as well. This effect is due to the
increase of the working fluid mass flow rate with a, which in turn increases the
exergy destruction in the heat exchangers. Moreover, the high pressure which
maximises gex remains relatively constant for the two values of a under
consideration.
o
An exergy destruction distribution analysis showed that around 50% of the
irreversibility takes place in the vapour generator, 27% in the turbine, 11% in the
condenser, 7% in the pump and less than 5% in the regenerator. This distribution is
essentially the same for all values of the high pressure and a. In view of these results,

efforts should be made to improve the temperature matching between the heat
source and the working fluid in the evaporator!!
Finite size thermodynamics results
o With the regenerator, the UA is significantly higher which means that the new UA
added by the regenerator is not fully compensated by a reduction at the vapour
generator. The observed drastic drop between 12.5 and 13 MPa happens when the
high pressure is important enough to induce a turbine outlet temperature higher
than the one at the pump outlet. The regenerator is then omitted and the UA values
are those for a system without regenerator.
o

Other observations are that the total UA increases with a and that the optimum
value of the high pressure is essentially independent of . Furthermore, the
optimum value of the high pressure without regenerator is approximately 2 MPa
lower than the value of P3 which maximises the thermal and exergetic efficiencies
but quite close to the one which maximises the specific net output.
o It is also important to notice that each of the four curves presents an
augmentationof UA at low and high pressures. This phenomenon is explained by Fig.
7, which shows that the specific net output tends to zero at low and high pressures.
In order to achieve the fixed net power output, the mass flow rate of the working
fluid must therefore increase and this in turn increases significantly the UA.
o It must also be noted that as  and the mass flow rate of the working fluid increase,
the temperature of the air at the exit of the vapour generator decreases and
approaches the entrance temperature T2 of the CO2. Since the former cannot
become lower than T2, this condition implies the existence of an upper bound for a
value of . For the present conditions, the maximum value of  is near 0.28
Heat transfer surface
o
o
o
These results are similar to those for UA (see Fig. 9). Again, the total A increases with
 and each curve without regenerator presents a minimum.
With the regenerator, the total heat exchange surfaces are significantly higher and
again, an important drop occurs at the pressure where this component is withdrawn.
Thus, in all cases, the variation of  does not have a significant effect on the
optimizing high pressure for the values of  under consideration. These values of the
high pressure are comparable to the ones optimizing the total UA.
Conclusion
Main results
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The value of a does not influence the specific net power output and the thermal efficiency
but it affects the exergetic efficiency, the UA and the total surface of the system’s heat
exchangers.
A pressure of approximately 13.5 MPa maximises the thermal and exergetic efficiencies
without regenerator while a value of 11.5 MPa maximises the specific net power output. It is
to be noted here that in a context of a free heat source like industrial waste gases, the focus
should be on maximising the specific net output instead of the thermal efficiency.
The inclusion of a regenerator improves marginally the two efficiencies but has no effect on
the specific net power output; however the regenerator lowers the pressures for which the
two efficiencies reach their maximum values. On the other hand, this component increased
significantly the minimum UA and total heat exchange surface. Based on these conflicting
influences alone, it is difficult to decide on the appropriateness of incorporating a
regenerator in the system.
The exergetic efficiency decreases with the increase of the net power output extracted from
the fixed and limited heat source.
For systems not including a regenerator, similar values of the pressure minimise the product
UA and the total surface of the heat exchangers; these pressures are significantly lower than

the ones maximising the thermal and exergetic efficiencies but close to the one maximising
the specific net power output.
The high pressures minimising the product UA and the surface of the heat exchangers are
essentially independent of the net power output.
SHORT

Methodology: 4 steps
o Energy analysis
o Exergy analysis
o Finite size thermodynamics: the discretization is performed by dividing the overall
enthalpy change for one of the streams in N equal differences h.
o HX surface:
 Vapour generator
 Working fluid inside the tubes, because of higher pressure
 Hot air in the shell
 Longitudinal fins on OUTside of tubes because of poor HTC of air.
 # tubes and shell diameter obtained by assuming:
o Minimum velocity working fluid = 0.5 m/s
o Maximum velocity hot air = 30 m/s
 Prandtl and Reynolds numbers + Darcy friction factor  EES
 Heat transfer coefficient HTC:
o Air side the Petukhov correlation.
o CO2 side, the Krasnoshchekov–Protopopov correlation
o Thermal resistance tubes wall neglected
o Fouling not considered
 Condenser
 Working fluid inside the tubes, because of higher pressure
 Water in the shell
 Longitudinal fins on INside of tubes because of good HTC of water +
fouling risk in water
 # tubes and shell diameter obtained by assuming:
o Minimum velocity saturated liquid CO2 = 1.5 m/s
o Maximum velocity water = 3 m/s
 Heat transfer coefficient HTC:
o Water side + single-phase CO2 the Petukhov correlation.
o Two-phase CO2 side, the Cavallini’s correlation
 Regenerator
 High pressure working fluid from pump inside the tubes
 Low pressure from turbine in the shell
 Longitudinal fins on INside of tubes to reduce regenerator size and
facility assembly
 # tubes and shell diameter obtained by assuming:
o Minimum velocity cold stream CO2 = 1.5 m/s
o Maximum velocity supersaturated CO2 = 10 m/s
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Heat transfer coefficient HTC:
o Low pressure CO2 the Petukhov correlation.
Supercritical CO2 pump side, the Krasnoshchekov–Protopopov
correlation
Fixed parameters:
o Heat source: Hot air at 100°C
o Mass flow rate heat source = 314.5 kg/s
o Tmin and Tmax cycle
o Sink temperature = 10°C
General assumptions
o Each component steady-state steady-flow system
o Kinematic and potential energies neglected
o Heat and friction losses neglected
o Pump and turbine isentropic efficiencies = 0.8
o Regenerator effectiveness = 0.9
o Saturated liquid at condenser outlet
o Minimum cycle temperature (T1) is set to 15°C which fixes the minimum pressure
(p1 = p4) of the working fluid
o The maximum temperature is set to 95°C.
o A minimum temperature difference of 3°C is applied in the condenser at the point
where the working fluid is saturated vapour.
o Hxs: S&T, counterflow, one pass each stream.
Variables
o pmax cycle between 90 and 150bar
o Net power output   = 0.15 or 0.2
Results
o Optimum maximum pressure in each of the 4 steps.
o Step 1 and 2: optimum pmax maximizes thermal and exergetic efficiency (± similar
pressure).
o Step 3 and 4: optimim pmax minimises UA and A (nearly identical), but much lower
pmax than for step 1 and 2.
o Augmentation of the net power output has no influence on results of energy
analysis, decreases exergetic efficiency and increases HX surface. No significant
effect on optimizing pmax.