Performance Evaluation of sCO₂–Hydrocarbon Mixtures in SBC-PTES Systems: A Parametric Thermo-Economic Study

Abstract

The development of efficient and economically viable energy storage technologies is key to the integration of renewable energies. This study evaluates the thermo-economic performance of hydrocarbons as working fluids in PTES systems based on a simple Brayton cycle (SBC). Different hydrocarbon mixtures are analyzed to determine their impact on efficiency and costs, identifying optimal operating conditions and combinations that improve system performance and viability. The objective is to identify the optimal candidate and operating conditions for enhanced cost-effectiveness. A multivariable optimization was performed using a validated thermodynamic model, integrated with an economic evaluation framework. Key decision variables included pressure ratios, turbine inlet temperatures, and heat exchanger performance parameters, while several sCO_2–hydrocarbon mixtures were evaluated as working fluids. Energy and exergy analyses were coupled with component-level cost correlations to determine round-trip efficiency, specific investment cost, and levelized cost of storage. The findings indicate that the CO₂/C₂H₆ (60/40) mixture provides the best overall performance, achieving a round-trip efficiency of 54.38% and a levelized cost of storage of 137.1 $/MWh, outperforming pure CO₂. Fluid selection exerts a substantial influence on both thermodynamic and economic indicators, with performance exhibiting a pronounced dependency on critical temperature, molecular complexity, and operating pressure levels. Sensitivity analyses indicate that improvements in heat exchanger effectiveness and turbomachinery efficiency yield substantial reductions in total system cost. The findings indicate that the appropriate alignment of hydrocarbon properties with system design parameters can significantly enhance the feasibility of PTES, offering a technically viable and economically competitive pathway for large-scale energy storage applications.

1. Introduction

Recently, the deployment of electricity storage technologies has insufficiently kept pace with the rapid growth in renewable energy generation [1,2]. The primary constraints on the large-scale implementation of electrical energy storage projects are associated with land requirements, high capital costs and the relatively short operational lifetime of storage equipment [3,4]. Considering these challenges, recent studies have investigated alternative integration pathways employing Pumped Thermal Energy Storage (PTES) systems, highlighting their potential as a complementary solution to conventional battery-based storage technologies, particularly for electricity generated from renewable sources [5,6,7]. Thermal energy storage systems employ heat pump cycles to convert electrical energy into thermal energy, store it in a reservoir, and reconvert it into electricity when required, enabling efficient, flexible, and environmentally benign grid support [8,9,10].

The Brayton cycle has been analyzed and applied in extensive studies due to its operational simplicity, compact layout, with thermal efficiency values typically ranging from 30% to 50% depending on the working fluid and operating conditions [11,12,13]. The literature has proposed multiple configurations of the Brayton cycle [5,8,14], and some of these enhance cycle efficiency through the incorporation of recompression processes and multi-stage regeneration [15]. Other studies have investigated Brayton cycle arrangements featuring both recuperation and recompression, particularly in the context of pumped thermal energy storage (PTES) applications [7,16]. A considerable number of investigations have been conducted which analyze multiple design and operational parameters of energy storage cycles with the objective of optimizing thermodynamic performance, particularly round-trip efficiency. These investigations have also incorporated techno-economic criteria, with emphasis on the levelized cost of storage (LCOS) [3,17,18]. Zhao et al. [12] performed multi-objective optimization of Brayton PTES systems and reported optimal LCOS values ranging from 130 to 230 $/MWh with corresponding round-trip efficiencies of 55–62%, while Shalaby et al. [11] demonstrated that CO₂-based mixtures can enhance cycle performance by up to 8% compared to pure CO₂ at optimal pressure ratios of 2.5–3.5. Furthermore, experimental evidence has demonstrated that recompression variants can achieve efficiencies of approximately 69.38% by increasing charge and discharge temperature levels. This has been shown to outperform basic non-recuperated configurations by up to 33%, with Tafur-Escanta et al. [18] reporting that optimal recompression fractions between 0.07 and 0.25 and compressor inlet pressures of 76–77 bar are critical for achieving this enhanced performance.

Recent studies demonstrate that recompression Brayton cycles using supercritical CO₂ (s-CO₂) offer a competitive solution for long-duration thermal energy storage, with applications reported in nuclear, concentrated solar power systems, photovoltaics and wind power [19,20,21]. Research on s-CO₂-based gas mixtures, such as CO₂/Xe and CO₂/Kr, aims to optimize the efficiency-cost trade-off and system energy density. For instance, CO₂/Kr (75/25) achieves a 61.2% round-trip efficiency, outperforming pure s-CO₂, while CO₂/Xe (20/80) attains the lowest reported LCOS at 133.60 USD/MWh [8]. These results are consistent with the comprehensive study by Yu et al. (2020) [22], which thermodynamically analyzed seven CO₂-based mixtures CO₂/Xe, CO₂/Kr, CO₂/Ar, CO₂/N₂, and CO₂/He under a fixed compressor inlet temperature. These findings are consistent with the study by Yu et al. [22], which demonstrated that the performance of Brayton cycles strongly depends on the critical properties and composition of the working fluid. Hydrocarbons such as methane, ethane, and propane exhibit favourable thermophysical properties, including appropriate critical temperatures, high specific heat capacity, and tunable density, which can enhance thermal matching and reduce irreversibilities within the cycle [21,23]. Moreover, these fluids present environmental advantages, such as negligible ozone depletion potential and relatively low global warming potential compared to synthetic refrigerants [23,24]. Existing studies have mainly addressed thermophysical characterization or alternative applications, leaving a significant gap in their systematic integration into PTES systems. Accordingly, the present study conducts a parametric thermo-economic assessment of sCO₂–hydrocarbon mixtures such as ethane, methane and propane, in simple Brayton cycle PTES systems to evaluate their potential for improving efficiency and reducing storage costs.

Among thermo-mechanical concepts, Pumped Thermal Energy Storage (PTES) systems based on Brayton cycles have emerged as a promising solution for large-scale energy storage due to their geographical flexibility and projected round-trip efficiencies in the range of 50–75% [25,26]. Two main configurations have been extensively investigated [27]. Brayton PTES systems typically operate with inert gases such as argon or nitrogen and can be integrated with packed-bed or liquid-tank thermal storage, achieving theoretical efficiencies up to 67% at temperatures between 600 and 1000 °C [28,29]. In contrast, transcritical CO₂ PTES systems configurations have demonstrated round-trip efficiencies of up to 65% in large-scale systems, while advanced multi-tank layouts improve thermal matching with the variable specific heat of CO₂ and reduce irreversibilities [16,30]. In this context, the sCO₂–hydrocarbon mixtures represent an alternative in Brayton-based PTES systems configurations to tailor thermophysical properties, reduce irreversibilities, and enhance thermo-economic performance.

A parametric assessment of pumped thermal energy storage (PTES) systems based on Brayton cycles requires the systematic evaluation of thermodynamic and design parameters [7]. In the context of simple Brayton cycle layouts, the fundamental variables to be considered are the compression/expansion ratio, the maximum and minimum cycle temperatures, the selected working fluid, and, most crucially, the isentropic and polytropic efficiencies of compressors and expanders. These considerations are particularly relevant considering the high back work ratio inherent to these systems [5]. In recompression Brayton cycle (RBC) configurations, the analysis is extended to include the recompressed mass flow fractions during charge and discharge (${\gamma }_{chg}$, ${\gamma }_{dis}$), which effectively reduce net compression work and enhance thermal matching with the storage subsystem. In this context, supercritical CO₂ is commonly adopted as the working fluid due to its favourable thermophysical properties [3,16]. Recent multi-objective optimization studies of supercritical CO₂ RBC-PTES systems highlight a clear trade-off between round-trip efficiency (${\eta }_{RT}$) and levelized cost of storage (LCOS). Minimum LCOS values of 148.72 USD/MWh are obtained at ${\eta }_{RT}\approx 57.1\%$, whereas efficiency-oriented designs achieve ${\eta }_{RT}$ up to 61.5% at an LCOS of 158.40 USD/MWh, under optimal compressor inlet pressures of 76–77 bar, turbine inlet temperatures of 953–993 K, and charge fractions ranging from 0.07 to 0.25 [18]. The resulting increase in effective energy density is primarily associated with reduced thermodynamic irreversibility and improved integration with sensible thermal energy storage.

This study presents a thermo-economic evaluation of a pumped thermal energy storage (PTES) system based on a simple Brayton cycle (SBC), employing supercritical CO₂ (s-CO₂)–hydrocarbon mixtures (ethane, methane, and propane) as working fluids. The main contributions of this work are three-fold: (i) the assessment of s-CO₂–hydrocarbon mixtures as alternative working fluids for SBC-PTES systems; (ii) a comprehensive thermo-economic analysis based on key performance indicators, including round-trip efficiency and levelized cost of storage (LCOS); and (iii) a sensitivity analysis to quantify the influence of critical design parameters, such as pinch point temperature and heat exchanger effectiveness, on system performance.

The remainder of this paper is organized as follows. Section 2 describes the materials and methods, including system configuration, working fluid selection, operating conditions, and the optimization framework. Section 3 presents and discusses the results, while Section 4 summarizes the main conclusions and outlines directions for future work.

2. Materials and Methods

2.1. System Description

The present work analyses a pumped thermal energy storage configuration operating on a simple Brayton cycle, as illustrated in Figure 1. During the charging mode (see Figure 1a), the system functions through an enhanced Brayton arrangement that improves overall efficiency by recovering and reusing thermal energy from available waste-heat sources. A fundamental element of the cycle under discussion is the recuperator, whose function is to recover heat internally by means of the transfer of energy from the turbine exhaust (hot stream) to the compressed working fluid leaving the compressor (cold stream). The thermodynamic interactions associated with this internal heat exchange are further detailed in states 6 → 6r and 8 → 8r of the discharging configuration shown in Figure 1b. It is imperative to elucidate that the precooler functions exclusively during the discharging stage; consequently, it is depicted with dashed lines in the charging diagram. In the process of discharging, the working fluid must be able to reject heat before entering the main compressor. This requirement is achieved through a water-based crossflow heat exchange process within the precooler. This thermal management strategy is pivotal in ensuring the stability and efficiency of the cycle operation. In essence, the performance of the Brayton-based PTES system is governed by a reduced number of key operating variables, primarily the compressor inlet temperature and the pressure ratio. These require coordinated optimization to maximize energy recovery efficiency.

The system reaches a maximum operating temperature of 760 °C in the hot storage tank, a condition met under the operating regime considered in this study, characterized by a turbine inlet temperature of 700 °C during the discharge stage. To ensure compliance with this thermal condition, a molten salt mixture composed of ZnCl₂/NaCl/KCl is used as the heat transfer fluid, with mass proportions of 44.3%, 13.8%, and 41.9%, respectively. This selection guarantees adequate thermal stability and efficient performance within the system’s operating temperature range. The operating interval (approximately 10–11 h of charging and discharging) is consistent with the use of sensible thermal storage using molten salts, which allows operation on extended hourly scales due to its high heat capacity and thermal stability at high temperatures, thus justifying the sizing adopted for the PTES system. The main design parameters of the thermal storage system (TES) are presented in

Table 1. TES system design parameters.

Parameter	Values Range
HTF type	ZnCl2/NaCl/KCl Molten Salt
Salt maximum bulk operating temperature [°C]	>1073.15 K
Salt melting or liquidus point [°C]	423.15 K
Storage duration [h]	11
Hot Tank temperature	765.97 → 1012.71 K
Cold Tank Temperature	341.34 → 378.92 K

.

2.2. Input Assumptions

The main modelling assumptions are summarized in Table 2. This table presents a compendium of the principal inputs and the constraints employed in the thermodynamic simulations of the SBC-PTES system.

The discharge stage was defined as a net electrical power output of 25 MW. During the charging and discharging stage, the temperatures of the compressor inlet and the turbine inlet were found to be optimal. The compressor outlet pressure was set at a maximum of 30 MPa. The efficiencies of the components were assumed to be constant at 0.80 for the compressors and 0.85 for the turbines, a value consistent with the literature [14,31,32,33,34,35].

It was hypothesized that pressure drops would amount to 1% of the inlet pressure across recuperators and precoolers [36,37]. A sensitivity analysis was conducted for the purpose of evaluating the influence of the pinch point on the performance of the SBC-PTES system.

Table 2. Input assumptions.

	Parameter	Value	Units
Net power discharge	${\dot{W}}_{\mathrm{n}\mathrm{e}\mathrm{t}}^{\mathrm{d}\mathrm{i}\mathrm{s}}$	25	MW
Compressor inlet pressure (charging and discharging stage)	$P_1 \& P_5$	Optimized	MPa
Compressor outlet pressure (charging and discharging stage)	$P_2 \& P_6$	30	MPa
Compressor inlet temperature (charging and discharging stage)	${\mathrm{T}}_1 \& {\mathrm{T}}_5$	Optimized	K
Turbine inlet temperature (charging and discharging stage)	$T_3 \& {\mathrm{T}}_7$	Optimized	K
Compressor efficiency [14,32,33,34,35]	${\eta }_{\mathrm{c}}$	0.80	-
Turbine efficiency [14,32,33,35]	${\eta }_{\mathrm{t}}$	0.85	-
Compression ratio (charging and discharging stage)	${r_{\mathrm{p}}}^{\mathrm{c}\mathrm{h}\mathrm{g}} \& {r_{\mathrm{p}}}^{\mathrm{d}\mathrm{i}\mathrm{s}}$	Optimized	-
Pressure drops for recuperator [36,37]	$\Delta P/P_{\mathrm{R}}$	1	%
Pressure drops for precooler [36,37]	$\Delta P/P_{\mathrm{P}\mathrm{C}}$	1	%
Pinch point	$\Delta T_{\mathrm{m}\mathrm{i}\mathrm{n}}$	2–25	K

Table 2. Input assumptions.

	Parameter	Value	Units
Net power discharge	${\dot{W}}_{\mathrm{n}\mathrm{e}\mathrm{t}}^{\mathrm{d}\mathrm{i}\mathrm{s}}$	25	MW
Compressor inlet pressure (charging and discharging stage)	$P_1 \& P_5$	Optimized	MPa
Compressor outlet pressure (charging and discharging stage)	$P_2 \& P_6$	30	MPa
Compressor inlet temperature (charging and discharging stage)	${\mathrm{T}}_1 \& {\mathrm{T}}_5$	Optimized	K
Turbine inlet temperature (charging and discharging stage)	$T_3 \& {\mathrm{T}}_7$	Optimized	K
Compressor efficiency [14,32,33,34,35]	${\eta }_{\mathrm{c}}$	0.80	-
Turbine efficiency [14,32,33,35]	${\eta }_{\mathrm{t}}$	0.85	-
Compression ratio (charging and discharging stage)	${r_{\mathrm{p}}}^{\mathrm{c}\mathrm{h}\mathrm{g}} \& {r_{\mathrm{p}}}^{\mathrm{d}\mathrm{i}\mathrm{s}}$	Optimized	-
Pressure drops for recuperator [36,37]	$\Delta P/P_{\mathrm{R}}$	1	%
Pressure drops for precooler [36,37]	$\Delta P/P_{\mathrm{P}\mathrm{C}}$	1	%
Pinch point	$\Delta T_{\mathrm{m}\mathrm{i}\mathrm{n}}$	2–25	K

The system was conceptualized with a design objective of a discharge power output of 25 MW, accompanied by a charging duration of 11 h. The duration of the discharge process was not predetermined but instead exhibited variation based on the accumulated energy storage capacity inherent to each design configuration. The model is operational in steady-state conditions; however, it does not consider thermal or standby losses incurred by storage tanks.

In order to achieve the objective of this work, it was hypothesized that the maximum turbine inlet temperature recorded was 973.15 K during the discharging stage. To ensure that the required operating temperature of the turbine inlet is satisfied, it has been determined that the ZnCl₂/NaCl/KCl molten salt (a mixture of 44.3% ZnCl₂, 13.8% NaCl, and 41.9% KCl) should be used as the heat transfer fluid in the thermal energy storage system. The maximum operating temperature of this salt is greater than 1073.15 K [38,39].

2.3. Working Fluid

In this work, the simple Brayton cycle employs supercritical CO₂ and sCO_2–hydrocarbon mixtures as the working fluid. As demonstrated in Figure 2, the variation in the substance’s thermophysical properties is exhibited, particularly about the critical temperature, critical pressure, and critical density, which are contingent on the additive’s mole fraction. These thermophysical properties were obtained from the REFPROP thermodynamic database [39], ensuring the accuracy and consistency of the data used in the analysis. Figure 2a demonstrates the critical pressure in relation to critical temperature for the binary mixtures CO₂/CH₄, CO₂/C₂H₆, and CO₂/C₃H₈ across the complete composition range. The three curves converge at a single point corresponding to pure CO₂; from this common state, the mole fraction of each hydrocarbon increases along its respective curve until reaching the critical point of the pure hydrocarbon at the end of each trajectory. As the hydrocarbon fraction increases, the CO₂/CH₄ mixture initially exhibits a significant rise in critical pressure, reaching a maximum at intermediate compositions, followed by a decline toward the lower critical pressure characteristic of pure methane. The CO₂/C₂H₆ system displays a smoother, moderately non-linear trend, with a slight pressure increase near the CO₂-rich region and a subsequent decrease as the composition approaches pure ethane. Conversely, the CO₂/C₃H₈ mixture exhibits a comparatively extensive pressure plateau at intermediate temperatures prior to a marked reduction in critical pressure as the system approaches the critical conditions of pure propane. The figure provides a comprehensive representation of the non-linear evolution of the critical locus as the hydrocarbon mole fraction increases from the CO₂-rich limit to the pure hydrocarbon limit for each binary mixture. For the compositions that are highlighted, the CO₂/C₂H₆ (60/40) ratio is found in the intermediate region, with a moderate critical temperature (270–280 K) and pressure (5.5–6 MPa), indicating balanced component effects. The CO₂/CH₄ (90/10) mixture, which is closer to the CO₂-rich region, shows relatively low critical temperatures (210–220 K) but elevated pressures (5.5 MPa). This reflects strong pressure sensitivity to the methane addition. In contrast, CO₂/C₃H₈ (90/10) exhibits higher critical temperatures (300–310 K) and pressures (7–7.5 MPa), indicative of the influence of propane. It is evident from the points that the critical point of the mixture is subject to variation depending on the composition and hydrocarbon type.

As illustrated in Figure 2b, the critical density of binary mixtures of CO₂ with CH₄, C₂H₆, and C₃H₈ is shown as a function of the hydrocarbon mole fraction. In all cases, the critical density decreases monotonically as the concentration of the hydrocarbon increases from 0 (pure CO₂, ≈460–470 kg·m⁻³) to 1 (pure hydrocarbon). However, the magnitude and curvature of this reduction are dependent upon the specific additive. The CO₂/CH₄ mixture demonstrates the most significant overall decrease, particularly at high methane fractions (x > 0.6), reaching the lowest critical density values among the mixtures. The CO₂/C₂H₆ mixture displays an intermediate and relatively smooth decline across the entire composition range, while the CO₂/C₃H₈ mixture shows a sharper initial drop at low propane fractions followed by a more moderate decrease at higher compositions. These trends underscore the profound compositional dependence of the critical density and the consequential influence of the molecular nature of the hydrocarbon on the mixture’s critical behaviour. For the selected compositions, the CO₂/C₂H₆ (60/40) mixture exhibits an intermediate critical density of approximately 270–280 kg/m³, consistent with its smooth and gradual decline across composition. The CO₂/CH₄ (90/10) mixture, which remains in the proximity of the CO₂-rich region, exhibits a comparatively elevated critical density (440–450 kg/m³), suggesting a marginal impact of methane at low fractions. Conversely, the CO₂/C₃H₈ (90/10) mixture exhibited a more pronounced reduction, with critical density values ranging from approximately 380 to 400 kg/m³. This observation is indicative of the more substantial influence of propane, even at low concentrations. The representative points highlight the differing sensitivities of each mixture to composition changes.

2.4. Thermodynamic Analysis

The concept of “exergetic efficiency of the cycle” is delineated as the ratio of the coefficient of performance (COP) of the heat pump to the equivalent Carnot COP of the cycle for the charge stage [8,40]. The formulation presented in Equation (1) is defined by the following parameters.

$${{\eta }_{ex}}^{chg}={\displaystyle \frac{{COP}_{HP}^{chg}}{{COP}_{Eq-Carnot}^{chg}}}$$

(1)

In the present context, the term ${COP}_{Eq-Carnot}^{chg}$ is employed to signify the equivalent Carnot COP of the cycle for the charge stage [8,21,40,41]. This quantity is calculated using Equation (2).

$${COP}_{Eq-Carnot}^{chg}={\displaystyle \frac{1}{1-\frac{T_{abs}^{chg}}{T_{rej}^{chg}}}}$$

(2)

In the framework of the charging stage, the temperature at which heat is absorbed and the temperature at which heat is rejected can be represented by the following parameters: $T_{abs}^{chg}$, while $T_{rej}^{chg}$ respectively. To utilize the previously mentioned formula, it is necessary to determine $T_{abs}^{chg}$ and $T_{rej}^{chg}$ using Equations (3) and (4).

$$T_{abs}^{chg}={\displaystyle \frac{{\int }_4^{1r}T·ds}{s_{1r}-s_4}}$$

(3)

$$T_{rej}^{chg}={\displaystyle \frac{{\int }_2^{3r}T·ds}{s_{3r}-s_2}}$$

(4)

The exergy destruction rate of the components of the cycle under examination is represented by the following Equations (5)–(9).

$${{\dot{E}}_D}_{hot tank}^{chg}={\dot{m}}_{ms}^{chg}·\left(e_{ms in}^{chg}-e_{ms out}^{chg}\right)+{\dot{m}}_{mix}^{chg}·\left(e_2-e_{3r}\right)$$

(5)

$${{\dot{E}}_D}_{cold tank}^{chg}={\dot{m}}_w^{chg}·\left(e_{w in}^{chg}-e_{w out}^{chg}\right)+{\dot{m}}_{mix}^{chg}·\left(e_4-e_{1r}\right)$$

(6)

$${{\dot{E}}_D}_{tur}^{chg}={\dot{m}}_{mix}^{chg}·\left(e_3-e_4\right)-{\dot{W}}_{tur}^{chg}$$

(7)

$${{\dot{E}}_D}_{com}^{chg}={\dot{m}}_{mix}^{chg}·\left(e_1-e_2\right)-{\dot{W}}_{com}^{chg}$$

(8)

$${{\dot{E}}_D}_{rec}^{chg}={\dot{m}}_{mix}^{chg}·\left(\left(e_{1r}-e_1\right)+\left(e_{3r}-e_3\right)\right)$$

(9)

$${{\eta }_{ex}}^{dis}={\displaystyle \frac{{\eta }_{th}^{dis}}{{\eta }_{Eq-Carnot}^{dis}}}$$

(10)

In accordance with the findings outlined in the extant literature [40,42], the exergy efficiency of the cycle in the discharge stage is delineated by the following Equation (10). This equation stipulates the relationship between the thermal efficiency and the equivalent Carnot efficiency, thereby defining the exergy efficiency of the cycle in the discharge stage.

The value of ${\eta }_{Eq-Carnot}^{dis}$ denotes the equivalent Carnot efficiency of the cycle during its discharge stage [40,42]. The efficiency of the process can be measured using the following Equation (11).

$${\eta }_{Eq-Carnot}^{dis}=1-{\displaystyle \frac{T_{rej}^{dis}}{T_{abs}^{dis}}}$$

(11)

As illustrated in Equations (12) and (13), the term $T_{abd}^{dis}$ serves to indicate the specific temperature at which heat is absorbed, whereas $T_{rej}^{dis}$ is employed to denote the temperature at which heat is rejected, and both of these temperatures are defined within the context of the discharge stage. The values of these temperatures are determined through the utilization of the following equations:

$$T_{abs}^{dis}={\displaystyle \frac{{\int }_{6r}^{7}T·ds}{s_7-s_{6r}}}$$

(12)

$$T_{rej}^{dis}={\displaystyle \frac{{\int }_{8r}^{5}T·ds}{s_5-s_{8r}}}$$

(13)

2.5. Costs Analysis

The estimation of costs was conducted utilizing power-law correlations that have been validated in preceding studies [8,43]. The calculation of the costs associated with the heat recuperators, turbine, compressors, gearbox and generator was performed by utilizing Equations (14) and (15).

$$C=a·S{P}^b·f_T$$

(14)

In this context, “$a$” and “$b$” are known as the adjustment coefficients. “$SP$” is the abbreviation for “scaling parameter”. $f_T$ is the component of the scaling parameter that is determined by Equation (10). The “$C$” in this equation is the component cost.

$$f_T=\left\{\begin{array}{c}1 if T_{max}<T_{bp}\\ 1+c·\left(T_{max}-T_{bp}\right)+d·{\left(T_{max}-T_{bp}\right)}^2 if T_{max}\ge T_{bp}\end{array}\right.$$

(15)

The temperature breakpoint, denoted by $T_{bp}$, is conventionally established at 550 °C. The fit coefficients, $a$ and $b$, are utilized to ascertain the maximum temperature rating of the component, $T_{max}$.

As demonstrated in the reference [8,43], the fitting coefficients $a, b, c$ and $d$ are provided for the various components of the power cycle.

The financial outlay required for the acquisition of hot and cold storage tanks is determined by utilizing Equations (16) and (17), respectively [44].

$${C_{tank}}^{hot}=510·V_{ms}$$

(16)

$${C_{tank}}^{cold}=204·V_w$$

(17)

where $V_{ms}$ and $V_w$ represents the volume of molten salt in the hot tank and the volume of water in the cold tank, respectively.

The levelized cost of electricity (LCOE) method was devised to enable the facilitation of a meaningful financial comparison between the financial costs associated with electricity generation using renewable sources and those associated with conventional technologies. It is evident that the framework under discussion gave rise to the concept of LCOS, which adapts the LCOE methodology for the evaluation of energy storage systems [8,45]. The calculation of LCOS may be facilitated by utilizing the following Equation (18), the validity of which has been substantiated in the extant scientific literature [46,47]:

$$LCOS={\displaystyle \frac{CAPEX}{{\dot{E}}_{dis}·{\sum }_n^N\frac{1}{{\left(1+r\right)}^n}}}+{\displaystyle \frac{OPEX}{{\dot{E}}_{dis}}}+{\displaystyle \frac{C_{elec}}{{\eta }_{rt}}}$$

(18)

The discount rate ($r$), the specific year of operation ($n$), and the lifetime of technology ($N$) are the key variables to consider [48,49]. The initial financial outlay required for the acquisition of the necessary equipment is referred to as the capital expenditure (CAPEX). In accordance with the financial limits delineated in the referenced material [48,49], the operating and maintenance costs (OPEX) have been determined to be equivalent to 2.2% of the capital expenditure. Equation (19) is utilized to determine the energy produced over the course of a year, which is denoted by ${\dot{E}}_{dis}$.

$${\dot{E}}_{dis}={\dot{W}}_{net}^{dis}·y_{dis}·H_{dis}·{\eta }_g$$

(19)

where $y_{dis}$ are the yearly discharge cycles, $H_{dis}$ are the discharge hours of the plant and ${\eta }_g$ is the generator efficiency due to the energy production.

The round-trip efficiency denoted here as ${\eta }_{rt}$, can be calculated from the total electrical power consumed and produced during the discharge and charge stages, respectively [8,48,50,51], as illustrated in Equation (20).

$${\eta }_{rt}={\displaystyle \frac{{\dot{W}}_{net}^{dis}·H_{dis}}{{\dot{W}}_{net}^{chg}·H_{chg}}}$$

(20)

In accordance with this investigation, the charging hours of the installation ($H_{chg}$) are assumed to be constant [48,52]. It is recommended that further research in this field should focus on the optimization of this parameter. Additionally, the impact of $H_{chg}$ on the LCOS of the plants should be the subject of further investigation. To calculate the LCOS, there are coefficients and parameters that must be entered. Kindly direct your attention to

Table 3. Coefficients and parameters for LCOS calculation [8].

Component	Parameter	Value	Units
Discount rate [48,53]	$r$	8	%
Electricity price [48,54]	$C_{ele}$	55	$/MWh
Generator efficiency [47,48]	${\eta }_g$	0.98	-
Plant life [48,49]	$N$	30	years
Storage time [48,52]	$H_{chg}$	11	h
Yearly discharge cycles [48,49,53]	$y_{dis}$	350	1/year

for further information.

2.6. Simulation Methodology

The purpose of this study is to optimize the main design variables of the simple Brayton cycle-based PTES system (SBC-PTES). This study will allow for a comprehensive exploration of the impact of these variables on the system’s thermodynamic behaviour and techno-economic indicators. In order to perform the required simulations, custom code was implemented in MATLAB R2022a. In addition, the thermophysical properties of the working fluid (pure CO₂ and binary mixtures) were obtained using REFPROP v10 [39], accessed via a Python 3.9.12 wrapper. A comprehensive overview of the computational procedure is provided in the flowchart presented in Figure 3.

2.7. Benchmarking and Validation

Ensuring the accuracy of the models is of the utmost importance in guaranteeing the reliability of the simulation outcomes and subsequent analyses. The preliminary components of the systems under scrutiny in the present study bear a strong resemblance to those delineated in [8,55]. Accordingly, the models are validated using data from Wang et al. [56]. The results of the validation process are presented in

Table 4. Results of model validation.

Parameter	Unit	Reference [56]	This Work	Error [%]
$CI{P}^{\mathrm{d}\mathrm{i}\mathrm{s}}$	MPa	1.20	1.20	0.00
$CI{T}^{\mathrm{d}\mathrm{i}\mathrm{s}}$	K	573	573	0.00
${r_{\mathrm{p}}}^{\mathrm{c}\mathrm{h}\mathrm{g}}$	-	7.25	7.25	0.00
${r_{\mathrm{p}}}^{\mathrm{d}\mathrm{i}\mathrm{s}}$	-	7.25	7.25	0.00
${\eta }_{\mathrm{c}}$	%	90	90	0.00
${\eta }_{\mathrm{t}}$	%	92	92	0.00
${\eta }_{\mathrm{r}\mathrm{t}}$	%	62.83	63.53	1.12

. This demonstrates a satisfactory alignment between the simulation outcomes and existing data from the literature sources. This finding lends further credence to the reliability of the models developed in this study.

3. Results and Discussion

This section presents an analysis of the results obtained for the SBC-PTES system operating with pure CO₂ and with different supercritical binary mixtures of CO₂ and hydrocarbons. The study includes an evaluation of the thermodynamic performance during the charge states, the exergy efficiency, the distribution of irreversibilities per component, and the thermo-economics behaviour in terms of LCOS and round-trip efficiency, as well as a sensitivity analysis to variations in the pinch point temperature. Environmental considerations related to the use of CO₂ and hydrocarbon mixtures as working fluids are also considered.

3.1. Thermodynamic Performance of the SBC-PTES System with CO₂-Hydrocarbon Mixtures

Figure 4 shows the comparison of the performance parameters of the SBC-PTES system during the charge (coefficient of performance, COP) and discharge (thermal efficiency) phases, using as working fluids both pure carbon dioxide and binary mixtures of CO₂ with hydrocarbons (C₂H₆, CH₄ and C₃H₈) in different proportions in a supercritical state. Figure 4a shows that the system exhibits a real COP of between 1.19 and 1.22, depending on the working fluid. The CO₂/C₃H₈ (90/10) mixture showed the best performance, with a COP of approximately 1.21, followed by the CO₂/CH₄ (90/10) mixture. Pure CO₂ also maintains competitive performance, with a COP of 1.22. On the other hand, the mixture with ethane (CO₂/C₂H₆, 60/40) presented the lowest real COP value (1.19), attributable to the higher fluid density and the thermophysical behaviour during the compression process.

In all cases, the actual COP values are approximately 20–22% lower than the equivalent Carnot COP, suggesting that internal system losses in isentropic compression processes remain a significant limiting factor, although hydrocarbon mixtures allow the system to approach the ideal limit.

Figure 4b shows the actual thermal efficiency achieved by the system during discharge mode. The CO₂/C₂H₆ mixture reported the highest actual thermal efficiency value (0.46), surpassing pure CO₂ (0.43), while the mixtures with methane and propane (90/10) showed similar values (0.44 and 0.43), respectively. This behaviour is associated with the combined effect of the specific heat capacity of the fluid and the effective pressure ratio reached during expansion. The equivalent Carnot efficiency for all working fluids ranged from 0.59 to 0.61, implying that the system operates within a range of 70 to 75% of the theoretical maximum possible.

Figure 5 presents a comparison of the exergy efficiency during the charging and discharging stages of the SBC-PTES system for the four working fluids. In all cases, the exergy efficiency is higher during the charging stage due to the lower number of irreversibilities associated with this phase of the process. Among the mixtures studied, the system that works with C₂H₆ as the working fluid maintains the highest exergetic efficiency in discharge state (0.75), surpassing even pure CO₂ (0.73), which suggests a greater adaptability of ethane to controlled expansion conditions in the electricity generation stage. The results shown in Figure 1 and Figure 2 indicate that, while pure CO₂ remains competitive as a working fluid in terms of overall efficiency, hydrocarbon mixtures, especially those with ethane, offer a viable alternative that deserves attention in scenarios where the objective is to optimize both the storage and energy conversion systems of the SBC-PTES.

Figure 6 presents a breakdown of each exergy destruction component for the SBC-PTES system during the charging stage. In all cases, the heat recuperator was the component with the greatest exergy destruction, accounting for between 34.9% and 39.5% of the total exergy. This trend is consistent with the irreversible nature of heat transfer processes with a finite temperature difference. The second largest contributor was the compressor, with values between 28.8% and 29.3%, reflecting the losses associated with non-ideal adiabatic compression and its impact on the overall cycle efficiency.

Among the mixtures evaluated, the system using CO₂/C₂H₆ showed the greatest exergy destruction in the recuperator (39.5%) and the least in the turbine (6.1%), suggesting greater thermodynamic compatibility between this fluid and the cycle architecture. Conversely, the CO₂/CH₄ mixture showed a level of exergetic destruction (17.3%) and a higher exergetic destruction in the hot tank (7.2%), possibly attributed to the less favourable thermal properties of methane.

These results clearly identify critical points of irreversibility within the system, prioritizing the optimization of the recuperator and compressor design and operation to improve overall performance. Furthermore, they reinforce the importance of selecting the working fluid, as it directly influences the exergy destruction pattern of each component.

Figure 7 shows the comparison between the Levelized Storage Cost (LCOS) and the round-trip efficiency (RTE) for the different working mixtures evaluated in the SBC-PTES system. The analysis reveals a clear sensitivity of both indicators to the type of fluid, highlighting the significant thermo-economic trade-offs when selecting hydrocarbon mixtures. Pure CO₂ base fluid has an LCOS of approximately 141.1 $/MWh, with a round-trip efficiency of 52.33%. However, by incorporating ethane in a mole fraction (60/40), the system achieves the highest round-trip efficiency (54.38%), accompanied by a significant reduction in LCOS to 137.1 $/MWh, representing a performance improvement of around 2% and a cost improvement of 3% compared to pure CO₂. This behaviour suggests that the CO₂/C₂H₆ mixture allows for more efficient use of sensible heat and less irreversibility in the charging/discharging processes. Conversely, CO₂/CH₄ mixtures with a mole fraction of 90/10 show a slight increase in round-trip efficiency (52.69%), with an increase in the LCOS to 147.1 $/MWh. Meanwhile, the CO₂/C₃H₈ mixture with a mole fraction of 90/10 shows a slight decrease in round-trip efficiency (52.29%), with an increase in the LCOS to approximately 142.5 $/MWh. These results indicate that, despite maintaining good thermodynamic properties, the inclusion of methane or propane does not offer substantial economic or operational benefits in the SBC-PTES system.

Figure 8 shows the T-s diagram of the charging and discharging stages for pure CO₂ and the CO₂/C₂H₆ mixture, where differences in the PTES system morphology can be observed, explaining the better performance of the mixture. In particular, the CO₂/C₂H₆ mixture exhibits a more favourable slope in the compression and expansion processes, which reduces irreversibilities in the heat exchangers. Furthermore, improved thermal adaptation is observed in the heat exchangers, with smaller temperature differences during the exchange processes, which increases internal heat recovery within the system. As a result, the mixture reduces overall entropy generation and improves the utilization of stored energy, leading to greater round-trip efficiency of the system compared to pure CO₂.

Compared to previous studies based on mixtures with noble gases (CO₂/Kr, CO₂/Xe) [8], the use of CO₂/C₂H₆ mixtures shows a more favourable performance under equivalent conditions. For a power output of 50 MW and turbomachine efficiencies of 0.80/0.85, the mixture with Kr exhibits an LCOS of 125.8 $/MWh and an RTE of 0.535, while the mixture with C₂H₆ achieves an LCOS of 120.7 $/MWh and an RTE of 0.601, demonstrating a simultaneous improvement in both cost and system efficiency.

Furthermore, C₂H₆ offers a significant advantage over Kr due to its greater availability and lower cost, as it is a hydrocarbon widely accessible on an industrial scale. This aspect reinforces the technical and economic viability of CO₂ and hydrocarbon mixtures as a competitive alternative in PTES systems.

3.2. Pinch Point Sensitivity Analysis

Figure 9 presents the sensitivity of the levelized storage cost and the round-trip efficiency of the SBC-PTES system as a function of the point temperature, comparing the performance of pure CO₂ against the mixtures CO₂/C₂H₆, CO₂/CH₄ and CO₂/C₃H₈.

In all cases, an inverse relationship is observed between the pinch point temperature and the round-trip efficiency. As the pinch point temperature increases from 2 °C to 25 °C, the RTE of the CO₂/C₂H₆ mixture decreases from 55.55 to 47.12 (∆RTE ≈ 8.4%), while the RTE of pure CO₂ decreases from 53.26 to 46.54 (∆RTE ≈ 6.7%), see Figure 9a. This greater thermal sensitivity of the mixture indicates greater susceptibility to thermal irreversibilities when the temperature differential across the heat recuperators increases.

In contrast, the LCOS shows a relationship with the increase in the pinch point temperature. In the case of the CO₂/C₂H₆ mixture, the LCOS increases from 136.5 to 152.9 $/MWh (∆LCOS ≈ 12%), while for pure CO₂, the values increase from 140.7 to 154.0 $/MWh (∆LCOS ≈ 9.5%). This trend confirms that reducing the efficiency of heat recuperators decreases the overall efficiency of the system and increases the cost of energy storage.

Figure 9b shows a similar trend; however, when approaching temperatures between 2 °C and 10 °C, the mixture with CH₄ exhibits a lower LCOS and higher RTE compared to pure CO₂. Nevertheless, this advantage diminishes as the pinch point temperature increases, suggesting that the use of mixtures with hydrocarbons is more favourable in designs that prioritize high heat recovery using heat exchangers with narrow temperature margins.

As in the previous cases, a lower pinch point value significantly increases system efficiency and reduces the LCOS. However, the CO₂/C₃H₈ mixture exhibits greater sensitivity to increases in the pinch point temperature compared to pure CO₂, with a more pronounced loss of RTE, see Figure 9c. This suggests that, although this mixture can operate with high efficiency under optimal thermal design conditions, its performance is more severely affected under thermal constraints, compromising its economic competitiveness compared to the other fluids studied.

3.3. Environmental Considerations of CO₂-Hydrocarbon Mixtures in SBC-PTES Systems

The utilization of hydrocarbons as additives in CO₂ mixtures has been demonstrated to enhance thermodynamic and economic performance, while concurrently ensuring environmental acceptability. Compared to fluorinated refrigerants, these compounds have moderate global warming potential (GWP) values: Methane (CH₄) ≈ 27.2, Ethane (C₂H₆) ≈ 12.4, and Propane (C₃H₈) ≈ 4.3 [55]. In closed SBC-PTES systems, direct emissions can be minimized through airtight designs and maintenance protocols, substantially reducing their climate impact compared to other high-GWP industrial refrigerants. Therefore, these blends can represent a viable alternative from a sustainability perspective, combining energy efficiency with a smaller direct climate footprint, in line with the principles of energy transition and climate change mitigation. Furthermore, SBC-PTES systems that use hydrocarbons as CO₂ additives as working fluids offer a more environmentally sustainable alternative to electrochemical technologies, such as lithium-ion or redox flow batteries. By not requiring critical metals like lithium, cobalt, or nickel, they eliminate the ecological and social impacts associated with their extraction, thus reducing dependence on geopolitically sensitive resources.

Life cycle assessment (LCA) studies have identified that battery-based technologies, especially lithium-ion batteries, have significant environmental impacts associated with the extraction of critical metals and intensive manufacturing stages [57,58,59]. In contrast, thermal storage systems tend to have lower overall impacts in categories such as global warming potential, eutrophication, and water consumption, primarily because they avoid the use of critical materials and intensive manufacturing processes. These environmental indicators, including eutrophication potential, are based on LCA studies published in the literature [59,60], which employ standardized methodologies such as ReCiPe and CML for benchmarking energy storage technologies (see Figure 10). This comparison is interpreted as a qualitative and comparative evaluation between energy storage technologies, whose objective is to contextualize the environmental potential of PTES systems.

4. Conclusions

Comparative analysis of the SBC-PTES system using pure CO₂ and binary mixtures with hydrocarbons (C₂H₆, CH₄ and C₃H₈) as working fluids has revealed that the thermo-economic performance of the system is influenced by the fluid composition and the thermal operating conditions.

The combined analysis of COP and thermal efficiency suggests that blends with CH₄ and C₂H₆ offer a favourable compromise between charging and discharging efficiency, allowing for a more balanced system performance. This is especially relevant for stationary applications with cyclic operating regimes. In general, while the CO₂/C₂H₆ mixture exhibits higher round-trip efficiency at low pressure point temperatures, its performance degrades more rapidly under thermally irreversible conditions. This improvement occurs even with a slightly lower turbine inlet temperature (TIT) compared to pure CO₂ and the other mixtures (see Table 3), suggesting that the higher specific heat and lower viscosity of the mixture allow for better energy recovery without compromising the performance of the SBC-PTES system. Therefore, proper selection of the thermal approach temperature is crucial for optimizing the balance between thermodynamic performance and economic viability, especially when using binary mixtures as the working fluid. From an economic perspective, the lowest LCOS was obtained for the CO₂/C₂H₆ mixture, reaching 137.1 $/MWh, while configurations with CH₄ and C₃H₈ have higher levelized costs of storage due to their lower overall thermal efficiency, see

Table 5. Multiparameter optimization results of SBC-PTES system to minimize LCOS.

	CO2 Pure	CO2/C2H6 (60/40)	CO2/CH4 (90/10)	CO2/C3H8 (90/10)	Units
CIP	74	59	81	70	bar
CIT	307.1	292.1	302.1	308.1	K
TIT	973.2	953.2	973.2	963.2	K
$r_p^{chg}$	4.054	5.084	3.703	4.285	-
$r_p^{dis}$	4.054	5.084	3.703	4.285	-
$H_{chg}$	11	11	11	11	h
$H_{dis}$	10.1	10.21	10.08	9.93	h
LCOS	141.1	137.1	141.8	142.5	$/MWh
${\eta }_{rt}$	52.33	54.38	52.69	52.29	%

.

Taken together, these findings demonstrate the importance of thermal design and working fluid selection in SBC-PTES systems, suggesting that specific blends of CO₂ with low viscosity, high specific heat hydrocarbons can offer a competitive balance between energy performance and economic viability, especially when operating with a low pinch point and optimizing heat recovery.

Regarding limitations, the analysis developed is based on a thermodynamic and techno-economic approach under idealized conditions. Therefore, transient dynamic phenomena and the experimental validation of the working fluid properties have not been considered. Furthermore, the behaviour of materials in contact with CO₂ mixtures under supercritical conditions has not been evaluated, an aspect that can significantly influence the design, performance, and service life of turbomachines.

In this context, the following future lines of research are proposed: (i) the development and analysis of more complex dynamic cycles applied to PTES systems, (ii) the experimental validation of the thermophysical properties of CO₂ mixtures as working fluids, and (iii) the study of the impact of using supercritical CO₂ on the materials employed in turbomachine design. These lines of research will allow progress toward a more comprehensive and realistic evaluation of the performance of this technology.