The results for group A and group B of the binary mixtures are calculated for a total heat exchanger conductance (UAtotal) of 5000, 10,000, and 15,000 kW/K (combining low and high temperature heat exchangers, i.e., UAtotal is the sum of UALT and UAHT).
3.1. Results of ‘Group A’ Mixtures (Substances for Reducing the Critical Temperature)
For ‘group A’ mixtures, the maximum molar fractions for the s-CO
2/He, s-CO
2/Kr and s-CO
2/CH
4 mixtures have been fixed at 90.0/10.0, 68.0/32.0 and 67.0/33.0 respectively because in these conditions their critical temperatures are close to 273.15 K. The molar fraction span for the s-CO
2/C
2H
6 was 100.0/0.0 to 0.0/100.0 because its critical temperature range is approximately 304.13 K to 290.21 K. This means that the CIT’s range studied is approximately 304.13 K to 273.15 K, except for the s-CO
2/C
2H
6. The power cycle diagrams for pressure with respect to the enthalpy are shown in
Figure 4, where it is possible to see the cycle has a different behavior when it uses sCO
2-mixture as working fluid.
For the study of the Brayton cycle performance, optimal values of CIT and CIP at the main compressor and recompressor inlet has been considered; it has been observed that the sCO
2-mixtures produce a gain in cycle efficiency over pure s-CO
2 cycles of approximately 4%. Also, a linear trend is observed for s-CO
2/Kr and s-CO
2/CH
4 (cf.
Figure 5).
Table 2 shows the results summary (cycle thermal efficiency and working fluid properties using group A sCO
2-mixtures) for the Brayton cycle working with UA
total = 15,000 kW/K, CIT and CIP optimized. To summarize the results obtained, some working fluid properties which have a direct impact on the cycle performance and on the power cycle equipment detail design are shown in this table.
The turbomachine dimensions are constrained to the working fluid density [
33,
34]. If the density is increased, the compressor and turbine sizes will be minimized. The addition of krypton provides higher density values; hence, the turbomachines would have a minimized size. However, the isobaric heat capacity (Cp), kinetic viscosity and thermal conductivity must also be considered in the heat exchangers design. The heat exchanger’s heat transfer coefficients are closely related to the viscosity (dynamic and kinetic), thermal conductivity, density and isobaric heat capacity [
35]. The highest Cp and density values and the lowest kinetic viscosity value minimize the recuperator (low-temperature recuperator (LTR) and high-temperature recuperator (HTR)) dimensions. The ethane mixture is the solution for maximizing the isobaric heat capacity. Moreover, the helium mixture and krypton mixture are the solution for minimizing the kinetic viscosity.
Another important issue to be considered is the Ultimate Heat Sink (UHS) thermal storage system, this system design depends on the mixture critical temperature. Here, two possible technical solutions are going to be studied. The night cooling radiative panels could be proposed as the first technical solution, and this proposal has been discussed by Ana Dyreson [
36]. The cooling fluid’s lowest temperature for this proposal could be between 278.15 and 298.15 K; for this scenario, the ethane mixture, with a critical temperature around 290.82 K, is the optimal solution, as stated by J. Muñoz-Antón [
37] and Steven A. Wright [
38].
In the future, alternative refrigerants could also be utilized to vary the UHS temperature range. Cooling with cold storage system based on water ice could be proposed as the second technical solution. In this case, the helium mixture, with a critical temperature around 274.24 K, is the most suitable option.
In conclusion, maximizing the working fluid density in turbomachines minimizes the equipment dimensions, but also has to be warrantied the equipment manufacturability. Maximizing the Cp and density values and minimizing the kinetic viscosity value reduce the heat exchangers size, and finally, selecting a mixture with a critical temperature compatible with the UHS storage system. The optimum s-CO2 mixtures could be obtained with helium or ethane. However, another constraint, which was not cited before, is the added substance’s maximum operating temperature. Helium has a maximum working temperature of around 2000 K, and the maximum working temperature of ethane is around 675 K. Accordingly, for the purposes in this work, the optimum mixture is s-CO2/He (90.0/10.0). However, for future works, it would be advisable to continue researching on a mixture based on adding both helium and ethane, as this last fluid has a very beneficial impact on the heat exchanger and also simplifies the UHS storage system’s economical and technical design, opening future research paths for studying diverse refrigeration thermodynamic cycles coupled with the main s-CO2 Brayton power cycle.
A schematic diagram of the pressure vs. enthalpy for the s-CO
2 Recompression Brayton cycle is shown in
Figure 6, this cycle works with CIP and CIT optimal values, pure s-CO
2 as working fluid and UA
total = 15,000 kW/K. The specific heat contributing to the cycle through the primary heat exchanger is represented by q
PHX. The specific work of the main compressor is
wmc, the specific work of the recompressor is
wrc, the specific work of the turbine is
wt, the maximum achievable temperature in the high-pressure side from the low-pressure side is
Tt, and Δh
a is the specific enthalpy increment between the entrance of the primary heat exchanger and the exit of the turbine.
The thermal efficiency of the recompression Brayton cycle is properly defined as the net specific work divided by the net supply of heat [
19]. The thermal efficiency can be expressed as
where
γ is the split fraction of the flow of the plant. The thermal efficiency depends on three dimensionless variables: the dimensionless main compression work,
wmc/
wt, the dimensionless recompression work,
wrc/
wt, and the dimensionless additional enthalpy supplied due to real gas conditions, Δh
rg/
wt. These terms depend on the thermodynamic properties of the working fluid in the recompression cycle. Further, Δh
rg is the difference between the heat needed in a cycle working at real gas conditions and the heat needed in an ideal cycle [
39]. It can be expressed by:
where Δh
Tt is the enthalpy variation of the isothermal
Tt; this variable tends to zero when the turbine works at high temperatures. Thus, in these cases, Equation (1) can be approximated to:
The dimensionless variables
wmc/
wt,
wrc/
wt and Δh
a/
wt play an important role in the cycle efficiency. For this reason, the fluctuation of
wmc/
wt,
wrc/
wt and Δh
a/
wt of the s-CO
2 mixtures with respect to the pure s-CO
2 have been obtained using the next equations:
where
is the variation of the dimensionless main compression work of the sCO
2-mixtures respect to the pure s-CO
2,
is the variation of the dimensionless recompression work of the sCO
2-mixtures respect to the pure s-CO
2,
is the variation of the dimensionless additional enthalpy of the sCO
2-mixtures respect to the pure s-CO
2, and
is the total variation of the dimensionless cycle work of the sCO
2-mixtures respect to the pure s-CO
2. It has been observed that the cycle efficiency increases when
increases [
40]. Therefore, the influence of the dimensionless variables
wmc/
wt,
wrc/
wt and Δh
a/
wt on the cycle efficiency can be displayed in
Figure 7.
The adoption of s-CO
2 cycles is particularly promising for large-scale, high-temperature CSP plants [
2]. Four factors are important for incorporating s-CO
2 into CSP plants: superior performance vs. steam Rankine cycles, the ability to integrate thermal energy storage, ultimate heat sink thermal energy storage [
36,
37,
38], and dry cooling [
41]. This work presents air-cooled s-CO
2 cycle configurations specifically selected for a CSP application. The estimated cost calculation of the PTC (parabolic trough collector) and LF (linear Fresnel) systems were developed with the following equation [
42]:
where
is the cost of the solar field,
is the effective area of the solar field,
is the linear collector unitary costs, and
is the construction factor of the solar field. The linear collector unitary costs and construction factor (cf.
Table 3) have been obtained from Thermoflex 27 software [
27].
The better performance of the plant implies a smaller solar field effective area; this, in turn, reduces the cost of the 50 MW plant. In view of this,
Figure 8 shows that the savings with the installation of PTC could reach up to 8 million USD for the mixture of s-CO
2/He with a 10% molar fraction.
The solar field’s effective area with linear Fresnel is larger than the solar field’s effective area with the parabolic trough collector (approximately 12%). Nevertheless, the estimated cost of the solar field with LF is lower than the solar field with PTC, because the price per square meter of the solar field with LF is lower than that of the PTC. Thermodynamic results show that savings, when the Brayton cycle coupled with LF’s solar field uses s-CO
2 mixtures, could reach 6 million USD compared to using pure s-CO
2 (cf.
Figure 9).
3.2. Results of Group B Mixtures (Substances for Increasing the Critical Temperature)
For group B mixtures, the cycle works with a CIP just above critical pressure and a CIT’s range from 318.15 K to 333.15 K. This CIT’s range has been studied in this work because most of CSPs are located in sites where the ambient temperature is above the s-CO
2 critical temperature, i.e., CIT = 318.15, 323.15, 328.15, and 333.15 K [
43,
44].
In the case of CIT equal to 318.15 K and UA
total = 15,000 kW/K, the maximum molar fractions for the s-CO
2/H
2S, s-CO
2/C
3H
8, s-CO
2/C
4H
10, s-CO
2/C
5H
10, s-CO
2/C
5H
12, s-CO
2/C
4H
8 and s-CO
2/C
6H
6 mixtures have been fixed at 66.0/34.0, 72.5/27.5, 90.0/10.0, 97.5/2.5, 97.5/2.5, 92.5/7.5, and 92.5/7.5 respectively, because the critical temperatures in these conditions are just below to 318.15 K. The power cycle diagrams for pressure with respect to the enthalpy are shown in
Figure 10, where it is possible to see the cycle has a different behavior when it uses sCO
2-mixture as working fluid.
Comparing the recompression Brayton cycle using pure s-CO
2 and the same cycle using ‘group B’ sCO
2-mixtures, it can be observed that the cycle efficiency with group B mixtures decreases when it works with CIT and CIP just above the critical point. In contrast, a better efficiency has been obtained if the cycle works with sCO
2-mixtures and higher compressor inlet temperatures, i.e., 318.15, 323.15, 328.15 and 333.15 K. Most series of cycle efficiency versus molar fraction have a linear trend, with a minority of lines following an exponential trend, such as the mixtures s-CO
2/H
2S and s-CO
2/C
3H
8. The cycle efficiency improves by about 3 to 4%, when the cycle works with group B sCO
2-mixtures, CIP just above critical pressure and CIT = 318.15 K, as shown in
Figure 11.
The same analysis of ‘group A’ mixtures (substances added for decreasing the critical temperature) has been developed with ‘group B’ mixtures (substances added for increasing the critical temperature). As a result of this analysis, it has been observed that the cycle efficiency increases when
increases. Therefore, the influence of the parameters
wmc/
wt,
wrc/
wt and Δh
a/
wt on the cycle efficiency that works with UA
total = 15,000 kW/K and CIT = 318.15 K can be seen in
Figure 12.
Due to the mixtures used in the recompression Brayton cycle, savings in PTC installations could reach up to 7 million USD for CIT = 318.15 K (cf.
Figure 13). The maximum saving was obtained with the s-CO
2/H
2S mixture (66.0/34.0), and the minimum saving was obtained with s-CO
2/C
5H
12 mixture (97.5/2.5).
Alternatively, in the case of linear Fresnel installations, savings could reach 6 million USD for CIT = 318.15 K (cf.
Figure 14). In the same way as for the PTC installations, the maximum saving for LF installations was obtained with the s-CO
2/H
2S mixture (66.0/34.0).
There are different issues to be considered when selecting the optimum sCO
2-mixture. The first one is the mixture density; as already explained in this work, the density has a direct impact on the turbomachine’s final dimension. It has been seen benzene mixtures provide the maximum density at the compressor inlet (
Table 4). Other important considerations to be assessed are related to the isobaric heat capacity and kinetic viscosity. As mentioned before in this study, the highest Cp and density values and the lowest kinetic viscosity value minimize the recuperator (low-temperature recuperator (LTR) and high-temperature recuperator (HTR)) dimensions. The s-CO
2/H
2S and s-CO
2/C
4H
10 mixtures have higher Cp values, and the s-CO
2/C
6H
6 mixture has a higher density value. The s-CO
2/C
4H
8 and s-CO
2/C
4H
10 mixtures have lower kinetic viscosity value.
Another important factor impacting in the power cycle performance is the mixture maximum operating temperature. At an operating temperature of around 823.15 K at the turbine inlet, hydrocarbons pyrolysis or chemical decomposition could occur. Also, air infiltration in the power cycle working fluid due to leakages could provoke added substance auto-ignition. The mixture substances which are more stable in these scenarios are the cyclic hydrocarbons, short-string hydrocarbons, and hydrocarbons with double links. Based on the REFPROP fluid property library information [
26], the maximum operating temperature for benzene and hydrogen sulfide is 725 K and 760 K, respectively. The advantage of benzene is that it has a lower mole fraction than hydrogen sulfide.
This study paves the way for future works which should achieve a detailed equipment design and cost assessments. The final recommendation extracted from this analysis is to compare the cycle performance and detailed equipment design with benzene and hydrogen sulfide mixtures. Subsequent analyses should be focused on comparing the results with the other mixtures in
Table 4.
Another complementary power cycle design work will be focused on adding two or more substances to the sCO2-mixtures, considering the benefits provided by each individual substance, and balancing the required critical temperature according to the CSP-sCO2 location ambient conditions.
For the case where CIT equal to 323.15, 328.15 and 333.15 K, the maximum molar fractions for the s-CO
2/H
2S, s-CO
2/C
3H
8, s-CO
2/C
4H
10, s-CO
2/C
5H
10, s-CO
2/C
5H
12, s-CO
2/C
4H
8 and s-CO
2/C
6H
6 mixtures are shown in
Table 5. Bearing in mind that in these conditions the critical temperatures are below to CIT’s range studied, i.e., if the additives molar fraction exceeds these values, the mixture critical temperature will be greater than CIT’s range studied. A power cycle efficiency improvement from 3% to 4% has been obtained for group B sCO
2-mixtures.
Thermodynamic results show savings in PTC’s installations could reach up to 11 million USD for CIT = 323.15 K, 9 million USD for CIT = 328.15 K, and 10 million USD for CIT = 333.15 K. Alternatively, in the case LF’s installations, the savings could reach 8 million USD for CIT = 323.15 K, 7 million USD for CIT = 328.15 K, and 7 million USD for CIT = 333.15 K.
As discussed previously for
Table 4, there are several factors when selecting the optimum s-CO
2 mixture, namely power cycle efficiency impact, critical temperature, the plant location’s ambient temperature, equipment, performance, and cost, etc. When increasing the CIT (cf.
Table 5), the first conclusion is the requirement to increase the substance’s mole fraction to reach critical temperature values just below of the CIT’s range (323.15, 328.15 and 333.15 K).
The substance’s addition influences in the sCO
2-mixtures properties. The higher impact on the plant’s equipment design has been gained by density, isobaric heat capacity and kinetic viscosity, similar to working with CIT = 318.15 K. Therefore, the recommendations for the power cycle detail design are the same as cited in
Table 4.
The dry-cooling technical solution is usually adopted in deserts, where water is a scarce resource and the ambient temperature is high. A typical temperature selected for CSP design is 318.15 K, hence, the CIT = 333.15 K is a solution in these places because the difference between the plant location’s ambient temperature and CIT is around 15.00 K.
To summarize the conclusions obtained from
Table 5, it is important to highlight that the substance addition mole fraction has an important impact on sCO
2-mixture decomposition. The target should be aligned with the mole fraction minimization. For example, the benzene mole fraction is 12.50%, which is much lower than hydrogen sulfide at 50.00% when the cycle works with CIT = 333.15 K.
Finally, it is important to remark that the plant results showed in
Table 4 and
Table 5 were obtained with a CIP just above the critical pressures. A future study will focus on optimizing the CIP in order to make a comparison with the work developed by J. Dyreby [
22] wherein plant efficiency improvement has been demonstrated to increase the CIP above the critical pressure.