Supercritical CO₂ Mixtures for Advanced Brayton Power Cycles in Line-Focusing Solar Power Plants

Abstract

This work quantifies the impact of using sCO₂-mixtures (s-CO₂/He, s-CO₂/Kr, s-CO₂/H₂S, s-CO₂/CH₄, s-CO₂/C₂H₆, s-CO₂/C₃H₈, s-CO₂/C₄H₈, s-CO₂/C₄H₁₀, s-CO₂/C₅H₁₀, s-CO₂/C₅H₁₂ and s-CO₂/C₆H₆) as the working fluid in the supercritical CO₂ recompression Brayton cycle coupled with line-focusing solar power plants (with parabolic trough collectors (PTC) or linear Fresnel (LF)). Design parameters assessed are the solar plant performance at the design point, heat exchange dimensions, solar field aperture area, and cost variations in relation with admixtures mole fraction. The adopted methodology for the plant performance calculation is setting a constant heat recuperator total conductance (UA_total). The main conclusion of this work is that the power cycle thermodynamic efficiency improves by about 3–4%, on a scale comparable to increasing the turbine inlet temperature when the cycle utilizes the mentioned sCO₂-mixtures as the working fluid. On one hand, the substances He, Kr, CH₄, and C₂H₆ reduce the critical temperature to approximately 273.15 K; in this scenario, the thermal efficiency is improved from 49% to 53% with pure s-CO₂. This solution is very suitable for concentrated solar power plants coupled to s-CO₂ Brayton power cycles (CSP-sCO₂) with night sky cooling. On the other hand, when adopting an air-cooled heat exchanger (dry-cooling) as the ultimate heat sink, the critical temperatures studied at compressor inlet are from 318.15 K to 333.15 K, for this scenario other substances (C₃H₈, C₄H₈, C₄H₁₀, C₅H₁₀, C₅H₁₂ and C₆H₆) were analyzed. Thermodynamic results confirmed that the Brayton cycle efficiency also increased by about 3–4%. Since the ambient temperature variation plays an important role in solar power plants with dry-cooling systems, a CIT sensitivity analysis was also conducted, which constitutes the first approach to defining the optimum working fluid mixture for a given operating condition.

1. Introduction

The need to improve the efficiency of energy power plants emphasizes the importance of optimizing their equipment design and the inlet and operation conditions. For this reason, it is important to analyze how the use of fluid mixtures affects the operating conditions—mainly, plant efficiency [1]. There are different external conditions to the plant (environmental conditions) that mark the need to have a working fluid that adapts to these variable environments, both for low and high temperatures, with the objective that the plant works optimally.

The ever-increasing necessity to reduce the environmental impact of industrial and urban energy conversion processes has led engineers to consider the use of sCO₂-mixtures as working fluid for thermodynamic power and refrigeration cycles [2,3], emphasizing the mitigation of air pollution and the emission of greenhouse gases, and reducing energy production costs [4].

Several configurations of the Brayton cycle are currently under study [5]. One of the very interesting features of this cycle is its ability to achieve high efficiency in a variety of applications operating with intermediate temperature levels: concentrated solar power (CSP) [6,7], waste heat recovery [8,9], coal-fired power plants [10,11,12], and Gen IV nuclear reactors [13,14,15] among others. In this work, the influence of fluid mixtures on the recompression Brayton cycle (cf. Figure 1) has been studied. This power cycle is the evolution of the previous configuration proposed by Angelino [16,17] and has clear connections with Sulzer and Feher’s work [18,19]. The cycle is named after the re-compressor located parallel to the main compressor, which means that the flow is split into two for the compression process. The first amount of stream flows into the cooler, where its temperature is reduced to a value close to the critical temperature. The second stream is not cooled but compressed directly in the re-compressor [5]. In the work of Al-Sulaiman [20], it was determined that the recompression cycle showed the best performance in comparison with other configurations (simple, pre-compression, and divided expansion cycles).

The novelty of this work over the state of the art is new mixtures with mixing ratio and new fluids, in the recompression Brayton cycle. In Section 2, the methodology with which this work was developed is explained. The obtained results of the recompression Brayton cycle using sCO₂-mixtures are discussed in Section 3. Conclusions and future work are discussed in Section 4. An increase in the thermal efficiency of the recompression Brayton power cycle using sCO₂-mixtures is the main conclusion of this manuscript.

2. Assumptions and Methods

This work proposes a comparison between the performance of the cycles operating with pure s-CO₂ and the cycles of admixtures of s-CO₂ with He, Kr, H₂S, CH₄, C₂H₆, C₃H₈, C₄H₈, C₄H₁₀, C₅H₁₀, C₅H₁₂, and C₆H₆. These mixtures have been used because their physical properties stimulate the better behavior of the plant cycle.

The computer program SCSP (Supercritical Concentrated Solar Power Plant) is used for the simulations of the performance of the recompression Brayton cycle using pure s-CO₂ and sCO₂-mixtures. This program has been developed by members of the Energy Engineering Department at the Technical University of Madrid [21] and it is based on the software core developed by Dyreby in his doctoral thesis [22]. SCSP sets a constant heat recuperator total conductance for the performance calculation methodology and uses optimization algorithms (SUBPLEX [23], NEWUOA [24] and BOBYQA [25]) to calculate the optimal cycle performance. Figure 2 illustrates the iteration process for the cycle models integrated into the SCSP software.

The fluid properties were obtained from the REFPROP (Reference fluid Properties) database developed by NIST (National Institute of Standards and Technology) in the USA [26]. Figure 3a,b show, respectively, the critical pressure and temperature of the mixture when the mole fraction of the additive fluid changes. Figure 3a specifies that the tendency of the pressure lines is very different among the different binary mixtures based on s-CO₂, as there a non-linearity between the critical pressure and the mole fraction. Figure 3b shows that the critical temperature distributions of mixtures follow a monotonous, nearly linear trend. The critical temperatures of s-CO₂/He, s-CO₂/Kr, s-CO₂/CH₄, and s-CO₂/C₂H₆ have a downward slope, while the critical temperatures of s-CO₂/H₂S, s-CO₂/C₃H₈, s-CO₂/C₄H₁₀, s-CO₂/C₅H₁₀, s-CO₂/C₅H₁₂, s-CO₂/C₄H₈, and s-CO₂/C₆H₆ have an upward slope. Therefore, based on the critical temperature distribution trends, the s-CO₂ binary mixtures can be divided into two groups: ‘group A’ mixtures (substances for reducing the critical temperature) and ‘group B’ mixtures (substances for increasing the critical temperature).

The performances of the pure s-CO₂ and sCO₂-mixtures’ recompression Brayton cycle have been analyzed. The input parameters for the simulation are shown in

Table 1. Main assumptions for the power cycles calculations.

	Nomenclature	Value	Unit
Net power output	W	50.00	MW
Compressor inlet temperature	T1	Optimized 1//[318.15//323.15//328.15//333.15] 2	K
Compressor inlet pressure	P1	Optimized 3//critical pressure 4	MPa
Turbine inlet temperature	T6	823.15	K
Turbine inlet pressure	P6	25.00	MPa
Main compressor efficiency [31,32]	ηmc	0.89	-
Re-compressor efficiency [31,32]	ηrc	0.89	-
Turbine efficiency [31,32]	ηt	0.93	-
Heat exchanger conductance for low temperature recuperator	UALT	2500//5000//7500	kW/K
Heat exchanger conductance for high temperature recuperator	UAHT	2500//5000//7500	kW/K
Split fraction	γ	Optimized	-

¹ CIT optimized for group A mixtures. ² CIT’s range for group B mixtures. ³ CIP optimized for group A mixtures. ⁴ CIP just above the critical pressure for group B mixtures.

. The results obtained were validated with the Thermoflex 27 software [27], UniSim Design R451 software [28] (UniSim uses Peng-Robinson equation of state for thermodynamic property estimations), and scientific articles about the effect of gaseous admixtures on cycles with s-CO₂ [1,29,30].

3. Results and Discussion

The results for group A and group B of the binary mixtures are calculated for a total heat exchanger conductance (UA_total) of 5000, 10,000, and 15,000 kW/K (combining low and high temperature heat exchangers, i.e., UA_total is the sum of UA_LT and UA_HT).

The optimal efficiency of the s-CO₂ recompression Brayton cycle using pure s-CO₂ is for a CIT (Compressor Inlet Temperature) equal to the critical temperature and a CIP (Compressor Inlet Pressure) above the critical pressure [22]. These values are 45.4% (CIP = 7.41 MPa and UA_total = 5000 kW/K), 48.4% (CIP = 7.43 MPa and UA_total = 10,000 kW/K), and 49.4% (CIP = 7.44 MPa and UA_total = 15,000 kW/K).

As mentioned above, the s-CO₂ binary mixtures are divided into two groups: substances for reducing the critical temperature, group A, which include s-CO₂/He, s-CO₂/Kr, s-CO₂/CH₄, and s-CO₂/C₂H₆; and substances for increasing the critical temperature, group B, which include s-CO₂/H₂S, s-CO₂/C₃H₈, s-CO₂/C₄H₁₀, s-CO₂/C₅H₁₀, s-CO₂/C₅H₁₂, s-CO₂/C₄H₈ and s-CO₂/C₆H₆.

In the case of group A, sCO₂-mixtures, the recompression Brayton cycle efficiency is maximum when the cycle works with a CIT and CIP nearly the critical point. To avoid the phase changing zone, the condition of working just above the critical point was appointed.

In the case of group B sCO₂-mixture, a CIT range of 318.15 to 333.15 K and CIP just above critical pressure were considered in this study.

3.1. Results of ‘Group A’ Mixtures (Substances for Reducing the Critical Temperature)

For ‘group A’ mixtures, the maximum molar fractions for the s-CO₂/He, s-CO₂/Kr and s-CO₂/CH₄ 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-CO₂/C₂H₆ 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-CO₂/C₂H₆. 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 sCO₂-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 sCO₂-mixtures produce a gain in cycle efficiency over pure s-CO₂ cycles of approximately 4%. Also, a linear trend is observed for s-CO₂/Kr and s-CO₂/CH₄ (cf. Figure 5).

Table 2. Results summary for ‘group A’ mixtures with UA_total = 15,000 kW/K, CIT and CIP optimized.

	Molar Mass (kg/kmol)	Density (kg/m3)	Isobaric Heat Capacity (kJ/kg*K)	Kinetic Viscosity (cm2/s)	Thermal Conductivity (W/m*K)	Prandtl Number	Plant Efficiency
s-CO2 pure	44.01	565.43	49.62	7.19 × 10−4	1.03 × 10−1	19.61	0.49
s-CO2/He (90.0/10.0)	40.01	386.23	378.95	6.68 × 10−4	5.52 × 10−2	177.08	0.53
s-CO2/Kr (68.0/32.0)	56.74	740.15	7.95	6.20 × 10−4	5.94 × 10−2	6.13	0.53
s-CO2/CH4 (67.0/33.0)	34.78	414.49	6.59	7.42 × 10−4	6.52 × 10−2	3.11	0.52
s-CO2/C2H6 (68.0/32.0)	39.55	371.85	1830.20	7.91 × 10−4	9.13 × 10−2	597.86	0.52

shows the results summary (cycle thermal efficiency and working fluid properties using group A sCO₂-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-CO₂ Recompression Brayton cycle is shown in Figure 6, this cycle works with CIP and CIT optimal values, pure s-CO₂ 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 w_mc, the specific work of the recompressor is w_rc, the specific work of the turbine is w_t, the maximum achievable temperature in the high-pressure side from the low-pressure side is T_t, 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

$${\eta }_{th}=\frac{1 -\left(1-\gamma \right)·\frac{w_{mc}}{w_t}-\gamma ·\frac{w_{rc}}{w_t} }{1+ \frac{{\mathsf{\Delta }\mathrm{h}}_{rg}}{w_t}}$$

(1)

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, w_mc/w_t, the dimensionless recompression work, w_rc/w_t, and the dimensionless additional enthalpy supplied due to real gas conditions, Δh_rg/w_t. 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:

$${\mathsf{\Delta }}_{{\mathrm{h}}_{rg}}={\mathsf{\Delta }\mathrm{h}}_a+{\mathsf{\Delta }\mathrm{h}}_{Tt}$$

(2)

where Δh_Tt is the enthalpy variation of the isothermal T_t; this variable tends to zero when the turbine works at high temperatures. Thus, in these cases, Equation (1) can be approximated to:

$${\eta }_{th}=\frac{1 -\left(1-\gamma \right)·\frac{w_{mc}}{w_t}-\gamma ·\frac{w_{rc}}{w_t} }{1+ \frac{{\mathsf{\Delta }\mathrm{h}}_a}{w_t}}$$

(3)

The dimensionless variables w_mc/w_t, w_rc/w_t and Δh_a/w_t play an important role in the cycle efficiency. For this reason, the fluctuation of w_mc/w_t, w_rc/w_t and Δh_a/w_t of the s-CO₂ mixtures with respect to the pure s-CO₂ have been obtained using the next equations:

$${\delta }_{w_{mc}/w_t} =\frac{(w_{mc}/w_t{)}_{sCO{2}_{pure}}- (w_{mc}/w_t{)}_{sCO{2}_{mixture}}}{(w_{mc}/w_t{)}_{sCO{2}_{pure}}}$$

(4)

$${\delta }_{w_{rc}/w_t} =\frac{(w_{rc}/w_t{)}_{sCO{2}_{pure}}- (w_{rc}/w_t{)}_{sCO{2}_{mixture}}}{(w_{rc}/w_t{)}_{sCO{2}_{pure}}}$$

(5)

$${\delta }_{{\mathsf{\Delta }\mathrm{h}}_a/w_t} =\frac{({\mathsf{\Delta }\mathrm{h}}_a/w_t{)}_{sCO{2}_{pure}}- ({\mathsf{\Delta }\mathrm{h}}_a/w_t{)}_{sCO{2}_{mixture}}}{({\mathsf{\Delta }\mathrm{h}}_a/w_t{)}_{sCO{2}_{pure}}}$$

(6)

$${\delta }_{total}= {\displaystyle \sum }_i{\delta }_i= {\delta }_{w_{mc}/w_t}+{\delta }_{w_{rc}/w_t}+{\delta }_{{\mathsf{\Delta }\mathrm{h}}_a/w_t}$$

(7)

where ${\delta }_{w_{mc}/w_t}$ is the variation of the dimensionless main compression work of the sCO₂-mixtures respect to the pure s-CO₂, ${\delta }_{w_{rc}/w_t}$ is the variation of the dimensionless recompression work of the sCO₂-mixtures respect to the pure s-CO₂, ${\delta }_{{\mathsf{\Delta }\mathrm{h}}_a/w_t}$ is the variation of the dimensionless additional enthalpy of the sCO₂-mixtures respect to the pure s-CO₂, and ${\delta }_{total}$ is the total variation of the dimensionless cycle work of the sCO₂-mixtures respect to the pure s-CO₂. It has been observed that the cycle efficiency increases when ${\delta }_{total}$ increases [40]. Therefore, the influence of the dimensionless variables w_mc/w_t, w_rc/w_t and Δh_a/w_t on the cycle efficiency can be displayed in Figure 7.

The adoption of s-CO₂ cycles is particularly promising for large-scale, high-temperature CSP plants [2]. Four factors are important for incorporating s-CO₂ 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-CO₂ 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]:

$${\mathrm{SF}}_{COST}={\mathrm{SF}}_{EA}·{\mathrm{C}}_{UC}·CF$$

(8)

where ${\mathrm{SF}}_{COST}$ is the cost of the solar field, ${\mathrm{SF}}_{EA}$ is the effective area of the solar field, ${\mathrm{C}}_{UC}$ is the linear collector unitary costs, and $CF$ is the construction factor of the solar field. The linear collector unitary costs and construction factor (cf.

Table 3. Linear collector unitary costs. PTC: parabolic trough collector; LF: linear Fresnel; HTF: Heat Transfer Fluid.

	Value	Unit
PTC with AISI 347 stainless steel receiver for Solar Salt as HTF	432	$/m2
LF with AISI 347 stainless steel receiver for Solar Salt as HTF	300	$/m2
Construction factor	1.16	-

) 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-CO₂/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-CO₂ mixtures, could reach 6 million USD compared to using pure s-CO₂ (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-CO₂ 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-CO₂/H₂S, s-CO₂/C₃H₈, s-CO₂/C₄H₁₀, s-CO₂/C₅H₁₀, s-CO₂/C₅H₁₂, s-CO₂/C₄H₈ and s-CO₂/C₆H₆ 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 sCO₂-mixture as working fluid.

Comparing the recompression Brayton cycle using pure s-CO₂ and the same cycle using ‘group B’ sCO₂-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 sCO₂-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-CO₂/H₂S and s-CO₂/C₃H₈. The cycle efficiency improves by about 3 to 4%, when the cycle works with group B sCO₂-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 ${\delta }_{total}$ increases. Therefore, the influence of the parameters w_mc/w_t, w_rc/w_t and Δh_a/w_t 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-CO₂/H₂S mixture (66.0/34.0), and the minimum saving was obtained with s-CO₂/C₅H₁₂ 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-CO₂/H₂S mixture (66.0/34.0).

There are different issues to be considered when selecting the optimum sCO₂-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. Results summary for ‘group B’ mixtures with CIT = 318.15 K, CIP = critical pressure ¹ and UA_total = 15,000 kW/K.

	Molar Mass (kg/kmol)	Density (kg/m3)	Isobaric Heat Capacity (kJ/kg*K)	Kinetic Viscosity (cm2/s)	Thermal Conductivity (W/m*K)	Prandtl Number	Plant Efficiency
s-CO2 pure	44.01	202.44	2.45	9.62 × 10−4	3.17 × 10−2	1.50	0.42
s-CO2/H2S (64.0/34.0)	40.78	323.24	17.12	7.95 × 10−4	9.23 × 10−2	14.20	0.46
s-CO2/C3H8 (92.5/7.5)	44.02	195.79	2.64	9.71 × 10−4	3.29 × 10−2	1.52	0.46
s-CO2/C4H8 (92.5/7.5)	44.92	368.04	12.54	7.49 × 10−4	6.34 × 10−2	5.46	0.46
s-CO2/C5H10 (97.5/2.5)	44.66	311.47	6.46	7.64 × 10−4	5.06 × 10−2	3.04	0.45
s-CO2/C6H6 (92.5/7.5)	46.57	613.85	7.30	8.28 × 10−4	7.26 × 10−2	5.11	0.46
s-CO2/C4H10 (90.0/10.0)	45.42	401.36	12.98	7.50 × 10−4	6.64 × 10−2	5.61	0.46
s-CO2/C5H12 (97.5/2.5)	44.71	287.34	5.27	8.30 × 10−4	4.06 × 10−2	2.16	0.45

¹ Just above the critical pressure of the working fluid.

). 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-CO₂/H₂S and s-CO₂/C₄H₁₀ mixtures have higher Cp values, and the s-CO₂/C₆H₆ mixture has a higher density value. The s-CO₂/C₄H₈ and s-CO₂/C₄H₁₀ 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-CO₂/H₂S, s-CO₂/C₃H₈, s-CO₂/C₄H₁₀, s-CO₂/C₅H₁₀, s-CO₂/C₅H₁₂, s-CO₂/C₄H₈ and s-CO₂/C₆H₆ mixtures are shown in

Table 5. Results summary for group B mixtures with CIP = critical pressure ¹ and UA_total = 15,000 kW/K.

	Mole Fraction (%)	CIT (K)	Plant Efficiency	PTC Cost (Million USD)	LF Cost (Million USD)
s-CO2 pure	100.0	323.15	0.42	97.23	76.65
s-CO2/H2S	60.0/40.0	323.15	0.45	86.66	68.37
s-CO2/C3H8	65.0/35.0	323.15	0.45	89.80	70.56
s-CO2/C4H8	90.0/10.0	323.15	0.45	90.00	70.81
s-CO2/C5H10	95.0/5.0	323.15	0.45	89.13	70.12
s-CO2/C6H6	90.0/10.0	323.15	0.44	90.28	71.72
s-CO2/C4H10	87.5/12.5	323.15	0.45	90.12	70.87
s-CO2/C5H12	95.0/5.0	323.15	0.45	90.32	71.05
s-CO2 pure	100.0	328.15	0.40	99.91	78.76
s-CO2/H2S	55.0/45.0	328.15	0.44	90.77	71.56
s-CO2/C3H8	60.0/40.0	328.15	0.44	91.88	72.15
s-CO2/C4H8	87.5/12.5	328.15	0.44	92.10	72.41
s-CO2/C5H10	95.0/5.0	328.15	0.44	92.70	72.90
s-CO2/C6H6	90.0/10.0	328.15	0.43	92.87	73.09
s-CO2/C4H10	85.0/15.0	328.15	0.44	92.47	72.67
s-CO2/C5H12	82.5/7.5	328.15	0.44	91.75	72.12
s-CO2 pure	100.0	333.15	0.39	102.59	80.87
s-CO2/H2S	50.0/50.0	333.15	0.43	92.73	73.09
s-CO2/C3H8	55.0/45.0	333.15	0.43	93.90	73.72
s-CO2/C4H8	85.0/15.0	333.15	0.43	94.22	74.04
s-CO2/C5H10	92.5/7.5	333.15	0.43	93.97	73.85
s-CO2/C6H6	87.5/12.5	333.15	0.42	95.21	74.87
s-CO2/C4H10	82.5/17.5	333.15	0.43	94.75	74.43
s-CO2/C5H12	92.5/7.5	333.15	0.43	94.91	74.58

¹ Just above the critical pressure of the working fluid.

. 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 sCO₂-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-CO₂ 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 sCO₂-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 sCO₂-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.

4. Conclusions

This study was mainly focused on quantifying the impact of CSP-sCO₂ thermal efficiency due to the mixing of the substances (He, Kr, CH₄ C₂H₆, C₃H₈, C₄H₈, C₄H₁₀, C₅H₁₀, C₅H₁₂, and C₆H₆) with pure s-CO₂. The obtained results confirmed that the variations in working fluid properties directly impact in the cycle thermodynamic efficiency.

On one hand, it is confirmed that He, Kr, CH₄ and C₂H₆ addition reduces the critical temperature, and hence it increases the power cycle thermal efficiency. Detailed results are summarized in Table 2. The working fluids mixtures s-CO₂/He (90.0/10.0) and s-CO₂/Kr (68.0/32.0) increase the power cycle efficiency from 49.0% to 53.0%. Further, krypton and helium are inert gases and the addition of them to the pure s-CO₂ is very beneficial for avoiding the equipment materials corrosion. The group sCO₂-mixtures, for reducing the sCO₂ critical temperature, are very suitable for the CSP-sCO₂ night sky cooling technology.

On the other hand, another CSP ultimate heat sink technical solution is the dry-cooling system with air-cooled heat exchangers. Most CSPs are located in sites where the ambient temperature is above the s-CO₂ critical temperature (CIT = 318.15, 323.15, 328.15, and 333.15 K). In this scenario, the target is setting the CIT near the working fluid’s critical temperature, hence, it is required to increase the working fluid critical temperature by adding H₂S, C₃H₈, C₄H₈, C₄H₁₀, C₅H₁₀, C₅H₁₂ or C₆H₆ to the cycle’s working fluid. In Table 4 and Table 5 the results obtained for the CSP with dry-cooling scenario are summarized. As a result of this work, it is concluded that the solar power plant design-point efficiency is improved by about 3–4% when adding the mentioned substances in comparison with the reference pure s-CO₂.

In works developed by Dyreby [22] and Marchionni [45], it was observed that an increase in the turbine inlet temperature (TIT) implies an improvement in the performance of the recompression Brayton cycle. As a result of this study, it is concluded that this effect of increasing the TIT is equivalent to the use of mixtures of supercritical fluids in the Brayton cycles.

Future works should align with the working fluid chemical composition customization according to the ambient conditions where the solar power plant will be located. The environmental impact should also play an important role, and the substances added should be environmentally friendly. For this reason, inert gases in combination with other substances are advisable in future CSP-sCO₂ conceptual designs.

Additional simulations are required to analyze more complex Brayton cycle configurations: the recompression with partial cooling cycle (RCPC) and recompression with main compressor intercooling cycle (RCMCI), both with reheating.

In addition, it will be necessary to analyze the variation of increasing the CIP for compensating the CIT increment in hot locations.

Also, detailed experimental analysis is required to verify that the possible reactions and chemical decomposition of mixtures do not affect the plant’s performance.