Thermodynamic and Exergoeconomic Assessment of Environmentally-Benign Zeotropic Mixtures in Organic Rankine Cycle for Sustainable Power Generation

The explosive consumption of fossil energy sources has led to detrimental effects on the environment, leading to a noticeable climate change [1,2]. Notably, a consistent increase in global $CO2$ emissions since the industrial revolution [3]. In the pursuit of net-zero emissions and global sustainability, two concurrent areas of focus are crucial: (i) higher share of renewable energy sources (RES) in the energy mix and (ii) better energy conversion efficiencies, to address both energy demand and the climate change mitigation goals. Typically, renewable energy sources, such as geothermal, biomass, solar, ocean thermal, and waste heat recovery, are considered low-grade thermal energy resources. Organic Rankine cycle (ORC) technology is well suited for converting low-grade thermal energy into power, offering a sustainable pathway for harnessing RES [4–6]. Researchers have investigated the potential of ORC in various RES applications, highlighting its ability to improve conversion efficiency [5,7]. Specifically, ORC has demonstrated success in utilizing low-grade thermal energy sources, which are traditionally challenging and inefficient [8]. However, the choice of working fluids for ORC plays a vital role in the energy conversion process and its impact on the environment.

In most ORC applications, synthetic organic fluids (like HCFC, hydrofluorocarbon (HFC), and hydrofluoroolefin (HFO)) are employed as working fluids owing to their favorable thermophysical properties [9,10]. However, their environmental impact (in terms of global warming potential (GWP)) is much higher than that of natural fluids like hydrocarbons (HC) and $CO2$⁠. Furthermore, to maximize the exergy utilization, zeotropic mixtures, i.e., a mixture of pure fluids exhibiting a non-isothermal phase change phenomena (called temperature glide), as exhibited in Fig. 1, are explored as alternative working fluids in ORC [11].

The temperature glide characteristics enable zeotropic mixtures to have a better temperature profile match with the heat transfer fluid (HTF) (heat source/sink), which in turn, maximizes the exergy utilization [12,13]. Despite the significant progress, finding a sustainable working fluid that can cater to a wide range of applications still remains a challenge. This aspect serves as the motivation and the primary objective of this study. The key objectives of this study are (i) to investigate the potential of $CO2$ utilization in energy harvesting applications; (ii) to investigate the influence of heat source temperatures on the techno-economic aspects of the transcritical organic Rankine cycle (TC-ORC). First, a brief summary of the literature relevant to ORC tested with zeotropic mixtures is presented, followed by the differentiating factors of this study are highlighted.

Braimakis et al. [14,15] performed thermodynamic analysis of pure hydrocarbons and HC-HC binary mixtures in supercritical and subcritical ORC with heat source temperatures ranging from $150∘C$ to $300∘C$ for waste heat recovery applications. Based on their studies, zeotropic mixtures demonstrated higher exergy efficiencies in ORC configurations. Wu et al. [16] studied six synthetic fluid-$CO2$ binary zeotropic mixtures in a TC-ORC with heat source temperatures ranging from $100∘C$ to $150∘C$⁠. In their analysis, the net power maximization was taken as the objective function and achieved a higher exergy efficiency of about 38% when compared to the pure $CO2$-based TC-ORC. Shu et al. [17] thermodynamically analyzed the performance of synthetic fluid-$CO2$ binary zeotropic mixtures for engine waste heat recovery at $466∘C$ by using a regenerative TC-ORC with a preheater. The analysis was performed to understand the influence of mixture fraction and operating parameters on energy and exergy efficiencies. A maximum energy and exergy efficiency of 12% and 39%, respectively, was achieved.

Miao et al. [18] theoretically explored the selection of working fluid for heat source temperatures ranging from $423∘C$ to $623∘C$⁠. With exergy efficiency as the objective function in an ORC, the influence of heat source inlet temperature, critical temperature, and pinch-point temperature difference, were evaluated for different HC-HC binary zeotropic mixtures. They reported that an optimal thermal match in the evaporator and the condenser can increase the efficiency. Kazim et al. [19] numerically compared the performance of supercritical ORC with pure $CO2$ with those of $CO2$-based zeotropic mixtures for temperatures ranging from 400 K to 500 K. Key parameters such as cycle thermal efficiency, volumetric power coefficient, and exergy destruction were evaluated over a range of turbine inlet pressures. Maximum cycle and exergy efficiencies of 15% and 39%, respectively, were achieved with zeotropic mixtures.

The above literature analysis clearly shows the growing interest in $CO2$-based zeotropic mixtures for sustainably harnessing RES. It is important to note that most of the work reported primarily focused only on the thermodynamic performance to assess the feasibility of the zeotropic mixtures. However, a comprehensive analysis covering all aspects, i.e., energy, exergy, system sizing, and exergoeconomics of zeotropic mixtures is essential to meet the sustainable development goals. To the best of the authors’ knowledge, such comprehensive analysis focusing on eco-friendly zeotropic mixtures has hitherto been reported. This study addresses the knowledge gap in the scientific literature through a comprehensive approach.

In this study, the energy, exergy, and exergoeconomic (3E) analysis is employed to assess the merits of natural zeotropic mixtures and derive new figures of merit by considering the technical and economic factors in a TC-ORC system. Furthermore, among the ORC configurations, the TC-ORC configuration is chosen as it yields better thermal performance than subcritical and supercritical ORC configurations. Thus, the operational metrics (thermal and exergy efficiencies), system compactness (heat transfer area), and exergoeconomics are investigated as a function of $CO2$ concentration and heat source inlet temperatures in a TC-ORC configuration. The results are also compared with those of synthetic zeotropic mixtures. The results presented will be a novel addition to the scientific knowledge by offering three perspectives based on (i) maximizing power generation, (ii) maximizing system compactness, and (iii) minimizing the system cost, to highlight the potential of natural zeotropic mixtures.

The techno-economic analysis of the influence of natural- and synthetic-zeotropic mixtures on the performance of a TC-ORC configuration was performed using an in-house matlab program and the REFPROP v10.0 [20] thermodynamic properties database. In all the binary zeotropic mixtures, $CO2$ was taken as the secondary mixture component to promote the $CO2$ utilization. In this section, the description of the thermodynamic cycle and the methodologies adopted for the energy, exergy, and economic analysis are presented. For this purpose, the standard TC-ORC configuration is investigated. The selection of zeotropic mixtures for this study is also discussed alongside their key thermophysical properties and environmental metrics.

Figure 2 shows the TC-ORC configuration, which comprises a pump, evaporator, turbine, and condenser, along with the heat source and heat sink. The working fluid (i.e., zeotropic mixture) enters the pump (at state 1) at lower (subcritical) pressure and exits at supercritical pressure (state 2). In the evaporator, thermal energy exchange (i.e., heat addition) occurs between the zeotropic mixture and the air (heat source). Then, the zeotropic mixture undergoes an expansion process in the turbine (between states 3 and 4) to generate power. After the expansion process, the low-pressure zeotropic mixture exchanges thermal energy with water (i.e., heat rejection) in the condenser. This thermal energy exchange is accompanied by the phase change of the zeotropic mixture. Then, the zeotropic mixture enters the pump to start the next cycle. It is assumed that the zeotropic mixture leaves the condenser as a saturated liquid (state 1) to prevent the possibility of cavitation in the pump. The techno-economic analysis was performed assuming steady-state operating conditions and by employing the conservation of mass and energy principles that are typically used in the field of energy harvesting [21]. Other relevant assumptions made in this study are as follows:

• Negligible heat and frictional losses in the system.

• The quality of the zeotropic mixture at the turbine exit was restricted to a minimum of 90%.

• The isentropic efficiencies of the turbine (⁠$ηisen,turb$⁠) and pump (⁠$ηisen,pump$⁠) were considered as 65% and 85%, respectively, in line with the literature [22,23].

• Both heat source (air at 150, 250, and $350∘C$⁠) and heat sink (water at $24∘C$⁠) were assumed to enter the evaporator and condenser, respectively, at a pressure of 100 kPa.

• Both the heat exchangers are considered as a counter-flow, shell and tube type heat exchanger configuration for the purpose of thermal energy exchange between the zeotropic mixture and the heat transfer fluid.

• The pinch point temperature difference in the heat exchanger was restricted to $5∘C$⁠.

• The mass flowrate of the zeotropic mixture was taken as $1kg/s$⁠.

Various performance metrics, such as maximum net power generated (⁠$W˙net,max$⁠), first- (⁠$ηI$⁠) and second-law (⁠$ηII$⁠) efficiencies, exergy destruction at the individual components, heat transfer aspects, and exergoeconomics were analyzed. These parameters were determined as a function of operating conditions, such as the turbine inlet pressure (varying from 5 MPa to 25 MPa), the heat source inlet temperature (ranging from $150∘C$ to $350∘C$⁠), and $CO2$ concentration varying from 5% to 95% in the zeotropic mixture. The heat source temperatures considered here will cover a wide range of potential thermal energy sources such as geothermal, ocean thermal, and waste heat from industrial processes, etc. It is worth mentioning here that the pure fluid scenarios (i.e., $CO2$ concentration of 0% and 100%) are not considered as they are extensively reported in the literature. The main objective of this study is to evaluate the potential of natural zeotropic mixtures in energy harvesting applications and compare their performance with those of synthetic zeotropic mixtures.

A total of six fluids comprising natural and synthetic fluids were selected from an initial large list of fluids from the REFPROP database based on their thermophysical properties (critical properties) and environmental attributes (GWP, 100 years), encompassing various categories. The fluid categories included hydrocarbons (HC), HFC, and HFO. The key thermophysical and environmental characteristics of the identified fluids are presented in Table 1.

In this study, two natural zeotropic mixtures (DME-$CO2$⁠, propylene-$CO2$⁠) and four synthetic zeotropic mixtures (R32-$CO2$⁠, R41-$CO2$⁠, R152a-$CO2$⁠, and R1234ze-$CO2$⁠) were investigated. Unlike pure fluids, zeotropic mixtures exhibit temperature glide characteristics. Therefore, the temperature glide phenomena of all the zeotropic mixtures were determined as a function of $CO2$ concentration, and the maximum temperature glide goes up to $35∘C$ for some of the mixtures. The graphical representation of the temperature glide phenomenon is presented in the later section. Although the temperature glide phenomenon is beneficial in terms of achieving a better temperature profile match between the zeotropic mixture and the heat transfer fluid, excessive temperature glide could potentially lead to a significant fractionation of the mixture components [24] and could detrimentally affect the overall performance.

Here the heat lost by the source is equivalent to the heat gained by the zeotropic mixture.

The total exergy destruction was determined as the sum of exergy destruction at the components. The results obtained by employing the above methodology were compared between this study and the literature findings [25] to gain confidence in the methodology employed. The maximum net power (⁠$W˙net,max$⁠) attained for R32, considering the heat source at the turbine inlet of $210∘C$ and 100 kPa pressure is depicted in Fig. 3. The results obtained under these conditions demonstrated a divergence of less than 1% from the literature data, affirming the reliability and rigorousness of the thermodynamic analysis.

In addition to the first-law (⁠$ηI$⁠) and second-law (⁠$ηII$⁠) efficiencies, the heat transfer characteristics of the zeotropic mixtures were also analyzed. The parameter “$UA$” indicates the compactness of the heat exchanger, which is typically determined by applying the logarithmic mean temperature difference method between the inlet and outlet temperatures of the heat exchanger. However, the logarithmic mean temperature difference (LMTD) method relies on the assumption of constant fluid properties, which could lead to inaccurate findings when dealing with supercritical fluids. Consequently, the application of the LMTD method under such conditions requires a comprehensive approach, as detailed in the Supplemental Sec. 5.1 available in the Supplemental Materials on the ASME Digital Collection. Furthermore, a detailed analysis to calculate the $UA$ value for the condenser, as detailed in the Supplemental Sec. 5.2 available in the Supplemental Materials, was employed. The most commonly used shell and tube type heat exchanger was considered for the thermal energy exchangers, namely, evaporator and condenser. The heat transfer coefficients for both the shell and the tube sides were calculated individually.

The thermodynamic and heat transfer analysis will provide valuable insights into assessing the feasibility of natural zeotropic mixtures for sustainable energy harvesting. However, practical implementation is frequently impeded by economic constraints. Thus, achieving an optimized design requires striking a balance between operational performance and economic feasibility. This holistic approach ensures that technical improvements align with economic considerations, leading to the most efficient and cost-effective solutions. The exergoeconomic analysis in this study was based on the specific exergy costing (SPECO) method [26]. The SPECO method employed in this study is detailed along with the cost equations in the Supplemental Sec. 5.3 available in the Supplemental Materials. The techno-economic assessment employed in this study is summarized as a flowchart in Fig. 4.

In this section, the influence of the $CO2$ fraction and thermal energy reservoir, i.e., heat source, temperatures on the ORC performance metrics such as maximum power generated, thermal and exergy efficiencies, and exergy destruction at the components, heat transfer characteristics (i.e., system compactness), and exergoeconomics are analyzed. For this purpose, several binary zeotropic mixtures, natural (HC-$CO2$⁠) and synthetic (HFC-$CO2$⁠, HFO-$CO2$⁠), are considered as working fluids with $CO2$ as the secondary mixture component in a TC-ORC configuration. Three heat source temperatures, namely, 150, 250, and $350∘C$⁠, are investigated as the temperature range will cover a wide range of thermal energy sources for sustainable energy harvesting.

The role of $CO2$ fraction in the zeotropic mixture on the critical properties, pressure and temperature indicated two major trends that could be beneficial from an application perspective, (i) the critical pressure of the zeotropic mixtures vary non-linearly with the $CO2$ fraction, and thus, widening the operating range of the transcritical cycle, (ii) the critical temperature decreases gradually with the increase of $CO2$ fraction in the zeotropic mixture as shown in Fig. 5. Furthermore, the temperature glide phenomenon, i.e., non-isothermal phase change process at a given pressure, is a characteristic feature of zeotropic mixtures. For the zeotropic mixtures considered in this study, the temperature glide varies from $5∘C$ to $35∘C$ with varying $CO2$ fractions, as shown in Fig. 6. The underlying trends are showcased using a polynomial fit in all the results presented here.

When assessing the performance of ORC, the maximum net power generated has been widely used as an objective function as it is directly correlated to the thermophysical properties and the heat source temperature. In this study, the net power generated is determined for all the zeotropic mixtures by varying the turbine inlet pressure at each $CO2$ fraction. However, in Fig. 7, only the maximum net power output achieved at a given $CO2$ concentration is shown and compared across the heat source temperatures. As a result, the turbine inlet pressures may not necessarily be the same across mixtures. As expected, the maximum power generated increases with the increase in the heat source temperature.

Interestingly, for the zeotropic mixtures considered, the augmentation of maximum power generated with an increase in heat source temperature is significant only for $CO2$ fractions less than 65%, beyond which the increase is moderate. Among the zeotropic mixtures, the natural zeotropic mixtures (DME-$CO2$⁠, propylene-$CO2$⁠) exhibited a substantial improvement in performance with increasing $THS$⁠. Least performance enhancement is observed for the HFO-$CO2$ zeotropic mixtures at all fractions of $CO2$⁠, showing a maximum deviation from other mixtures at $THS=350∘C$⁠, indicating that they may not be suitable for high source temperature applications. The maximum power generated displays an inverse correlation with $CO2$ concentration in all cases.

Focusing only on maximizing the net power generated may not necessarily lead to the best choice of working mixtures. The heat transfer parameter, $UA$⁠, signifies the compactness of the energy-exchanging systems. Therefore, normalizing the maximum net power by the system compactness (i.e., power generated per unit heat transfer area) may offer a different perspective in assessing the performance of zeotropic mixtures, as the system size has a direct influence on the system economics. For instance, although the natural zeotropic mixtures (DME-$CO2$⁠) exhibited superior performance in terms of power generated, in the context of normalized power (Fig. 8), their beneficial role is significant only up to 50% of $CO2$ fraction, beyond which they are comparable to other synthetic zeotropic mixtures (except R32-$CO2$ and R41-$CO2$⁠). This exemplifies that the DME-$CO2$ mixtures could be potential alternatives to synthetic zeotropic mixtures with comparable performance and system size, if not better. The synthetic zeotropic mixtures (R32-$CO2$ and R41-$CO2$⁠) demonstrated better outcomes in terms of performance and system sizing, especially at higher $THS$ of 250 and $350∘C$⁠. This could be attributed to the combined influence of their thermophysical properties and lower temperature glide with the $CO2$ fraction. The most noticeable change is observed for the HFO-$CO2$ (R1234ze-$CO2$⁠) zeotropic mixtures. Although the R1234ze-$CO2$ mixtures yielded a sub-optimal power at all $THS$ considered, their performance is comparable to other zeotropic mixtures in terms of the normalized metric. Interestingly, the trends of R1234ze-$CO2$ and propylene-$CO2$ are comparable, with the latter exhibiting better performance at lower $CO2$ fractions and the former at higher $CO2$ fractions. The trends are further supported by the variation of the total heat exchanger area determined for these mixtures at different $THS$ and $CO2$ fractions, as shown in Supplemental Fig. 1 available in the Supplemental Materials.

Thermal efficiency emerges as a critical parameter due to its direct impact on the system’s economic performance. Therefore, in Fig. 9, the thermal efficiencies of the zeotropic mixtures in a TC-ORC are compared at different $CO2$ fractions and heat source temperatures. The thermal efficiencies obtained at the maximum power conditions are shown in Fig. 9, as this would exemplify the best-case scenario. The trends demonstrate that as the $CO2$ fraction increases up to 50% (i.e., $XCO2=0.5$⁠), the thermal efficiencies of all mixtures, except R41-$CO2$ and R32-$CO2$⁠, exhibit a steep decrease, beyond which, the influence of $CO2$ fraction on the thermal efficiency is marginal. This trend corroborates well with their temperature glide exhibited at similar $CO2$ fractions (Fig. 6) and indicates that the turbine inlet enthalpies are affected by the temperature profile match between the heat source and zeotropic mixtures during the heat addition process in the evaporator.

At the heat source temperature of $150∘C$⁠, DME-$CO2$ mixtures exhibit better performance than all the synthetic zeotropic mixtures for $CO2$ fractions up to 35%. For $THS>150∘C$⁠, the R32-$CO2$ mixtures demonstrate thermal efficiencies higher than DME-$CO2$ mixtures. Nevertheless, at $THS=350∘C$⁠, the thermal efficiencies of DME-$CO2$ are comparable to those R41-$CO2$ mixtures and higher than all other zeotropic mixtures considered. Interestingly, for $THS$ up to $250∘C$⁠, the thermal efficiencies of propylene-$CO2$ mixtures are comparable to those of R152a-$CO2$ mixtures. However, with the increase in $THS$ to $350∘C$⁠, propylene-$CO2$ mixtures yield lower thermal efficiencies than R152a-$CO2$⁠, albeit following the same trend. These trends indicate that the natural zeotropic mixture, propylene-$CO2$⁠, may not be an optimal choice for energy harvesting applications with higher source temperatures. The thermal efficiency trends highlight a few takeaways, (i) at lower $THS$⁠, the influence of $CO2$ fraction on system performance is significant only up to 50%, beyond which the influence is marginal. However, at higher $THS$⁠, this $CO2$ fraction threshold increases up to 75%. This is significant as higher $CO2$ fractions could be beneficial from safety [27] and $CO2$ utilization standpoints; (ii) at lower $THS$⁠, the natural zeotropic mixtures could be an effective alternative to synthetic zeotropic mixtures without a significant compromise on performance.

Thermal efficiency primarily quantifies the amount of energy converted into useful work but does not reflect the maximum possible under given conditions. Therefore, assessing the second-law (exergy) efficiency becomes crucial to gauge the quality of energy exchange. Figure 10 illustrates the exergy efficiencies achieved by zeotropic mixtures in TC-ORC as a function of $CO2$ fraction and $THS$⁠. For all the zeotropic mixtures, the exergy efficiency decreases with the increase in the $CO2$ fraction, indicating that higher fractions of $CO2$ in the zeotropic mixture could be detrimental to the system performance. In other words, these trends highlight that while employing the TC-ORC configuration for energy harvesting applications with heat source temperatures considered here, $CO2$-based zeotropic mixtures have the potential to deliver an effective energy conversion process than by employing pure $CO2$ as a working fluid. This could be attributed to the lower critical temperature of pure $CO2$ and the beneficial effect of temperature glide associated with zeotropic mixtures.

Except for the R32-$CO2$ and R41-$CO2$ mixtures, the exergy efficiency decreases non-linearly with the increase in $CO2$ fraction at a given $THS$⁠. This corroborates well with the mixture temperature glide variation with $CO2$ fraction, wherein the mixtures with high-temperature glide exhibit a high degree of nonlinearity. This further indicates that zeotropic mixtures with excessive temperature glide could result in higher exergy destruction during the energy harvesting process and, in turn, detrimental to the overall performance of the system. Interestingly, the influence of the $CO2$ fraction on the degree of nonlinearity decreases with the increase in heat source temperature.

The most notable variations are exhibited by the DME-$CO2$ and R152a-$CO2$ mixtures. It is worth highlighting that although DME-$CO2$ mixtures exhibit sub-optimal exergy conversion at $THS=150∘C$⁠, at higher $THS$⁠, DME-$CO2$ mixtures demonstrate superior performance when compared to other zeotropic mixtures. Furthermore, the difference in performance between R32-$CO2$ and DME-$CO2$ mixtures narrows with the increase in $THS$⁠. On the other hand, Propylene-$CO2$ mixtures perform well at lower $THS$⁠. These findings underscore the complexities of optimizing energy conversion in ORC systems while using zeotropic mixtures and highlight the need for a comprehensive assessment of exergy destruction at the components level to gain further insights. Here, the TC-ORC components that are investigated include the condenser, pump, evaporator, and turbine. In addition, the exergy destruction associated with the thermal energy reservoirs (heat source and heat sink) is also included to understand the extent of energy potential leaving the evaporator and condenser, respectively. Such detailed analysis will provide valuable information to develop strategies to mitigate the exergy destruction, and they are compared across zeotropic mixtures at the maximum power conditions.

In Fig. 11, the exergy destruction for a pair of zeotropic mixtures having similar trends is compared. At $THS=150∘C$⁠, a majority of the exergy destruction is associated with the heat source, indicating that a lot of work potential is leaving the system at lower fractions of $CO2$⁠. With the increase in $CO2$ fraction, the temperature glide increases, and that seems to play a beneficial role in reducing this exergy loss in the case of DME-$CO2$ zeotropic mixtures. For $CO2$ fractions between 30% and 80%, most of the exergy destruction is associated with the heat sink, highlighting the magnitude of work potential leaving the system. At higher $THS$⁠, although the exergy efficiencies of DME-$CO2$ mixtures are comparable to those of R32-$CO2$ mixtures, a significant portion of exergy is lost in the heat sink. This trend further highlights that at higher $THS$⁠, the performance of DME-$CO2$ can be further augmented by deploying a regenerator at the exit of the turbine to reuse this lower-grade thermal for preheating the mixtures entering the evaporator. In the case of R32-$CO2$ mixtures, the exergy loss associated with the thermal energy reservoirs is not significant when compared to DME-$CO2$ mixtures at all $THS$⁠, albeit a lower temperature glide when compared to DME-$CO2$ mixtures. This could be due to their thermophysical characteristics favoring the exergy exchange process between the zeotropic mixture and the heat source and sink. Nonetheless, in both DME-$CO2$ and R32-$CO2$ mixtures, the exergy destruction in the component turbine contributes up to 25% in the case of the former and up to 40% in the case of the latter mixtures.

It is worth highlighting that these trends demonstrate that a staged work extraction process (i.e., multi-stage turbine) could assist in tapping the unutilized exergy and converting them into power. Interestingly, at $THS=350∘C$⁠, in R32-$CO2$ mixtures, the exergy destruction in the condenser increases significantly with the increase in $CO2$ fraction, much higher than in the turbine. This emphasizes that for R32-$CO2$ mixtures with higher $CO2$ fractions employing a regenerator would be more beneficial than employing a staged turbine at higher $THS$⁠. The absolute values of exergy destruction in each component at different $CO2$ fractions and $THS$ for the DME-$CO2$ and R32-$CO2$ mixtures are provided in Supplemental Tables 3 and 4 available in the Supplemental Materials, respectively. A similar analysis for other mixtures is presented in Supplemental Sec. 5.4 available in the Supplemental Materials.

While analyzing the performance based on thermodynamic parameters such as efficiencies, exergy destruction, or heat transfer parameters is desirable, it must also be evaluated within the context of economic feasibility. A system cannot be considered viable even if it achieves higher efficiency when the associated cost outweighs the benefits. Therefore, it is essential to analyze and compare the system performance in the context of economic feasibility for making informed decisions. Here, exergoeconomics is employed using the SPECO approach to determine the cost associated with the system performance based on exergy principles. The cost of exergy destruction is analyzed and presented for two different scenarios: (1) system achieving maximum net power output (Fig. 12), and (2) system achieving maximum compactness (Supplemental Fig. 2 available in the Supplemental Materials). Unlike the earlier discussions, here, the cost of exergy destruction accounts only for the exergy destruction at the system components (i.e., pump, evaporator, turbine, and condenser) and does not include the exergy lost through the heat source and heat sink.

In scenario 1, the cost of exergy destruction for R41-$CO2$ mixtures is the highest and remains almost constant across all $CO2$ fractions at $THS=150∘C$⁠, as shown in Fig. 12. However, at higher $THS$⁠, the increase in $CO2$ fraction results in a moderate decrease in cost. Although the exergy destruction (quantified through exergy efficiency in Fig. 10) associated with R41-$CO2$ mixtures is comparable to other zeotropic mixtures, their cost is higher owing to high specific cost (estimated using Supplemental Eq. (16) available in the Supplemental Materials) when compared to other zeotropic mixtures. At $THS=150∘C$⁠, the natural zeotropic mixtures (DME-$CO2$ and propylene-$CO2$⁠) are comparable up to 50% of $CO2$ fraction but higher than those of other zeotropic mixtures. However, for $CO2$ fractions higher than 50%, DME-$CO2$ mixtures yield the best economic outcomes. This point of cost inflection with $CO2$ fraction for DME-$CO2$ increases to 75% with the increase in $THS$⁠. The cost associated with exergy destruction for all mixtures increases with an increase in $THS$⁠, in line with the steep decrease in their exergy efficiencies. Furthermore, the cost difference between the zeotropic mixtures increases with an increase in $THS$⁠. In scenario 1, the cost analysis indicates that the natural zeotropic mixtures (DME-$CO2$⁠) are beneficial only when the $CO2$ fraction is above 60% at all $THS$ investigated. Additionally, the other natural zeotropic mixture, propylene-$CO2$⁠, is not cost-effective for energy harvesting applications with high heat source temperatures. A similar comparison is presented based on system compactness (scenario 2) in Supplemental Sec. 5.3 available in the Supplemental Materials, as both maximization of net power and system compactness as objective functions yield similar economic outcomes for the TC-ORC configuration investigated.

In this study, new figures of merit for the eco-friendly, natural zeotropic binary mixtures comprising hydrocarbons and $CO2$ were derived in the context of sustainable energy harvesting. The techno-economic assessments presented evaluate $CO2$ utilization in natural zeotropic mixtures and compare their performance with those of the synthetic zeotropic mixtures in a transcritical-organic Rankine cycle. To this end, the thermodynamic performance (energy and exergy efficiencies, exergy destruction), system compactness, and exergoeconomics were analyzed under varying heat source temperatures and $CO2$ fractions. The main findings of this study are summarized as follows:

• Under the conditions studied, the maximum power achieved with natural zeotropic mixtures (⁠$DME−CO2>$$propylene−CO2$⁠) is higher than those of synthetic zeotropic mixtures by up to 50% at $CO2$ fractions below 65%.

• The normalized power generated offered a different perspective. Notably, the normalized trends of natural zeotropic mixtures are comparable to synthetic zeotropic mixtures under the conditions studied.

• The thermal and exergy efficiencies of DME-$CO2$ mixtures are on par, if not better, with the best performing synthetic zeotropic mixture, R32-$CO2$ at higher heat source temperatures. However, the performance of DME-$CO2$ suffered significantly at the lowest heat source temperature investigated, indicating a sub-optimal performance.

• A closer examination of the exergy destruction revealed that a major portion of the energy potential is lost in the energy exchange process at lower pressure with the increase in heat source temperature and highlighted that advanced ORC configurations like a regenerative cycle in conjunction with a multi-stage turbine would be beneficial.

• The natural zeotropic mixtures (DME-$CO2$ and propylene-$CO2$⁠) can achieve cost parity, if not better, with those of the synthetic zeotropic mixtures under the conditions investigated.

The authors would like to thank GTIIT for providing all the needed resources to perform this study.

Kumaran Kannaiyan: Conceptualization, Methodology, Data curation, Draft writing and review, Funding resources; Bhawandeep Sharma: Formal analysis, Data Curation; Chengzhi Ye: Data curation.

This article does not include research in which human participants were involved. Informed consent was obtained for all individuals. Documentation provided upon request. This article does not include any research in which animal participants were involved. There are no competing financial interests or personal relationships between the authors that could influence the work reported here.

The authors attest that all data for this study are included in the paper.

$c$ =

specific exergy cost (⁠$$/kJ$⁠)

$d$ =

diameter (m)

$f$ =

friction factor

$h$ =

specific enthalpy (⁠$kJ/kg$⁠)

$s$ =

specific entropy (⁠$kJ/kg/K$⁠)

$x$ =

quality of the zeotropic mixture

$A$ =

heat transfer surface area (⁠$m2$⁠)

$H$ =

heat transfer coefficient (⁠$W/m2/K$⁠)

$K$ =

thermal conductivity (⁠$W/m/K$⁠)

$P$ =

pressure (⁠$kPa$⁠)

$T$ =

temperature (⁠$K$⁠)

$U$ =

overall heat transfer coefficient (⁠$W/m2/K$⁠)

$m˙$ =

mass flowrate (⁠$kg/s$⁠)

$C˙$ =

cost rate (⁠$$/h$⁠)

$Q˙$ =

heat rate (⁠$kW$⁠)

$W˙$ =

power (⁠$kW$⁠)

$XCO2$ =

mass fraction of $CO2$

$Ex˙$ =

exergy rate (⁠$kW$⁠)

$XD˙$ =

exergy destruction (⁠$kW$⁠)

$Zk˙$ =

cost rate associated with components (⁠$$/h$⁠)

$ex$ =

specific exergy (⁠$kJ/kg$⁠)

Pr =

Prandtl number

Re =

Reynolds number

$ηII$ =

exergy (second law) efficiency

$ηI$ =

thermal (first law) efficiency

$ϕ$ =

ratio of mass flowrates of zeotropic mixture and HTF

$ρ$ =

density (⁠$kg/m3$⁠)

$c$ =

critical

$i$ =

inner

$k$ =

component k of ORC

$l$ =

liquid

$o$ =

outer

$v$ =

vapor

$D$ =

destruction

$F$ =

fuel

$P$ =

product

$sh$ =

shell

$zm$ =

zeotropic mixture

$HS$ =

heat source

$in$ =

input

$0$ =

dead state

$CO2$ =

carbon dioxide

R1234ze =

(1E)-1,3,3,3-tetrafluoro-1-propene

R1270 =

propylene

R152a =

1-chloro-1,1-difluoroethane

R32 =

difluoromethane

R41 =

fluoromethane

RE170 =

dimethyl Ether

DME =

dimethyl ether

GWP =

global warming potential

HC =

hydrocarbon

HCFC =

hydrochlorofluorocarbon

HFC =

hydrofluorocarbon

HFO =

hydrofluoroolefin

HTF =

heat transfer fluid

LMTD =

logarithmic mean temperature difference

ODP =

ozone depletion potential

ORC =

organic Ranking cycle

RES =

renewable energy sources

TC-ORC =

transcritical ORC

TG =

temperature glide