The potential of transcritical cycles based on CO mixtures: An exergy-based analysis

Renewable Energy 199 (2022) 1606–1628 Available online 15 September 2022 0960-1481/© 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/). Contents lists available at ScienceDirect Renewable Energy journal homepage: www.elsevier.com/locate/renene The potential of transcritical cycles based on CO2mixtures: An exergy-based analysis Pablo Rodríguez-deArriba, Francesco Crespi∗, David Sánchez, Antonio Muñoz, Tomás Sánchez Department of Energy Engineering, University of Seville, Camino de los descubrimientos s/n, 41092 Seville, Spain ARTICLE INFO Keywords: CO2cycles CSP applications CO2-blends Exergy analysis ABSTRACT This paper focuses on the thermodynamic comparison between pure supercritical Carbon Dioxide and blended transcritical Carbon Dioxide power cycles by means of a thorough exergy analysis, considering exergy efficiency, exergy destruction and efficiency losses from Carnot cycle as main figures of merit. A reference power plant based on a steam Rankine cycle and representative of the state-of-the-art (SoA) of Concentrated Solar Power (CSP) plants is selected as base-case. Two different temperatures of the energy (heat) source are considered: 575 ◦C (SoA) and 725 ◦C (next generation CSP). Compared to SoA Rankine cycles, CO2blends enable cycle exergy efficiency gains up to 2.7 percentage points at 575 ◦C. At 725 ◦C, they outperform both SoA and pure CO2cycles with exergy efficiencies up to 75.3%. This performance is brought by a significant reduction in the exergy destruction across the compression and heat rejection process rounding 50%. Additionally, it has been found that the internal condensation occurring inside the heat recuperator for those mixtures with a large temperature glide improves recuperator exergy efficiency, supporting the use of simpler layouts without split-compression. Finally, CO2blends exhibit lower cycle exergy efficiency degradation than pure sCO2in the event of an increase in the design ambient temperature. 1. Introduction Concentrated Solar Power (CSP) is widely considered as a very promising contributor towards a complete carbon-free power generation scenario, due to its renewable nature and high dispatchability when coupled with thermal energy storage (TES). However, further investigation is mandatory to reduce CSP levelised cost of electricity (LCoE) in order to make this technology competitive in the energy market. The solar subsystem, composed by solar field, receiver and tower, undoubtedly represents the main contributor to the Overnight Capital Cost (OCC) of Solar Tower technology (ST), closely followed by the TES [1]. Thus, increasing CSP overall performance results to be a mandatory step in the pathway to achieve a reductions in size and cost of these components. Recent studies confirm that the greatest room of improvement lies in the power block, indicating as possible solution the adoption of innovative power cycles, capable of achieving thermal efficiency significantly higher than the one obtained by the state-of-the-art steam-based Rankine [2,3]. In this regard, the potential of supercritical carbon dioxide (sCO2) power cycles has already been recognised by the CSP industry [3] and extensively investigated in ∗Corresponding author. E-mail addresses: [email protected] (P. Rodríguez-deArriba), [email protected] (F. Crespi), [email protected] (D. Sánchez), [email protected] (A. Muñoz), [email protected] (T. Sánchez). the last decade [1,4–8], due to several beneficial aspects inherently enabled by sCO2technology: firstly, a significant reduction in the compression work, achieved by performing compression near the critical point, where the specific volume significantly drops due to real-gas effects (see Fig. 2 in [9]); secondly, the outstanding thermal stability of CO2, which theoretically enables turbine inlet temperature equal or higher rounding 700 ◦C [10], a value widely recognised as a threshold for next-generation solar towers plants and significantly higher than the SoA one (550 ◦C). As a matter of fact, several studies confirm the possibility to achieve power block efficiency equal or higher than 50%, employing sCO2cycles with a turbine inlet temperature rounding 700 ◦C and a minimum cycle temperature in the order of 32– 35 ◦C, a value extremely close to the critical point of carbon dioxide (T𝑐𝑟=31 ◦C) [4]. sCO2technology has been extensively investigated in recent years, and very comprehensive research works can be found in the literature. Should the reader be interested in learning more about these and other aspects of this technology, the authors highly recommend the following readings: the seminal works of Angelino [11– 13] and Feher [14], lately revived by Dostal [15], establishing the https://doi.org/10.1016/j.renene.2022.09.041 Received 17 February 2022; Received in revised form 7 September 2022; Accepted 10 September 2022 Renewable Energy 199 (2022) 1606–1628 1607 P. Rodríguez-deArriba et al. Nomenclature Acronyms C6F6Hexafluorobenzene CSP Concentrated Solar Power D1 CO2–C6F6mixture D2 CO2–TiCl4mixture D3 CO2–SO2mixture E𝐷Exergy destruction [MW] E𝐹Fuel exergy [MW] E𝐿Exergy losses [MW] E𝑃Product exergy [MW] ER𝑇Turbine Expansion Ratio [–] HRU Heat Rejection Unit HTRec High Temperature Heat Recuperator LTRec Low Temperature Heat Recuperator MW Molecular Weight [g/mol] OCC Overnight Capital Cost P𝑚𝑎𝑥 Maximum Cycle Pressure [bar] PC Partial Cooling cycle PHX Primary Heat Exchanger pp percentage point PR𝑀𝐶 Main Compressor Pressure Ratio [–] PR𝑃 𝑟𝑐 Precompressor Pressure Ratio [–] PrC Precompression cycle RC Recompression cycle Rec Heat Recuperator RR Recuperated Rankine cycle sCO2Supercritical Carbon Dioxide SO2Sulfur Dioxide SoA State-of-the-art T𝑚𝑖𝑛 Minimum Cycle Temperature [◦C] TiCl4Titanium Tetrachloride TIT Turbine Inlet Temperature [◦C] W𝑠Specific work [kJ/kg] Greek symbols 𝛼Split-flow factor [–] 𝛥𝜂 Efficiency losses from Carnot Cycle [%] 𝛥𝑃 Pressure drops [%] 𝛥𝑇𝑚𝑖𝑛 Recuperator Minimum Temperature Difference [◦C] 𝛥𝑇𝑃 𝐻𝑋 Temperature Rise in PHX [◦C] 𝜖Exergy efficiency [%] 𝜂Efficiency [%] Subscripts cond condensation cr critical cyc cycle is isentropic k component th thermal thermodynamic fundamentals of sCO2; a thorough overview and categorisation of the different cycle configurations proposed in literature, provided by Crespi et al. [16], and a detailed description of the current state of the technology, presented by Brun et al. [17] and White et al. [9]; finally, cost estimates based on vendor quotes, specific for sCO2technology, can be found in the works of Carlson et al. [18] and Weiland et al. [19]. According to Turchi et al. [20], CSP tower plants currently in construction have an overnight capital cost in the range of 3300– 6200 $/kW, depending on TES capacity (6 h and 13 h respectively). Furthermore, it is worth highlighting that the cost of various subsystems are expected to decrease in the upcoming years. In particular, estimations made in the framework of the SunShot Programme [21] foresee a reduction in the solar field cost from 140$/m2to 50–70$/m2, in the site preparation cost from 16$/m2to 10$/m2, in the tower and receiver cost from 137$/kWth to 100–120$/kWth and in the thermal storage cost from 22$/kWhth to 10–15$/kWhth (based on commercial Solar Salt). Nonetheless, this cost reduction seems not to be sufficient – not even in the most optimistic scenario – to achieve the target LCoE, currently set at 50$/MWh for conventional steam turbines [22]. As previously commented, higher power block efficiency would enable a significant reduction in the size and, expectedly, the cost of both solar field and thermal energy storage. However, it is worth remarking that higher TIT level also entails the need for advanced materials as well as a new technology for the Thermal Energy Storage (commercial Solar Salt cannot exceed 575 ◦C). As a consequence, the specific cost of the TES is prone to rise. Furthermore, supercritical CO2cycles have been proven to lead to a reduction in temperature difference across the solar receiver with respect to steam-based Rankine [6]. This also leads to an increase in the specific costs of TES, brought by the higher volume of salts required for the same amount of stored energy. As a consequence, techno-economic assessments for sCO2technology found in literature still provide unsatisfactory results when compared to SoA CSP, exacerbating the need for further investigation. Amongst others, Thanganadar et al. [8] concluded that OCC for sCO2significantly increases when TIT moves from 600 ◦C to 700 ◦C due to the negative impact on TES cost and, even in the former case, the calculated OCC rounds 5000$/kW (10 h TES), a value comparable to that of SoA Rankine; Crespi et al. estimated an OCC in the order of 5900 $/kW and 6870 $/kW for a Partial Cooling and Recompression cycle respectively (considering a 10 h TES capacity in both cases) [1]; finally, Alfani et al. obtained an OCC rounding 6630 $/kW for a Recompression with Intercooling cycle (15 h TES) [23]. Furthermore, the high ambient temperatures, a characteristic feature of CSP typical locations, are extremely detrimental for sCO2technology, since the compression process is shifted away from the vicinities of the critical point, compromising its actual potential in terms of thermodynamic gains against SoA Rankine. As a matter of fact, the drop in thermal efficiency can be as high as 4 percentage points (pp) when minimum cycle temperature (𝑇𝑚𝑖𝑛) moves from 35 ◦C (close to critical point) to 50 ◦C (realistic value for CSP typical locations), independently on the cycle layout considered [24]. In order to overcome this weakness whilst still retaining the thermodynamic features enabling potentially higher efficiencies, the use of blended sCO2has been investigated in the very last years. Invernizzi & van der Stelt studied totally supercritical and condensation cycles of CO2mixed with benzene [25]. Later, Invernizzi extended his work to other hydrocarbons, such as toluene [26]. Baik & Lee provided experimental data of the performance of CO2-R32 mixture, concluding that blended CO2working fluids can reduce the efficiency degradation of pure sCO2power cycles in warm environments [27]. Manzolini et al. performed a techno-economic assessment of CO2mixtures with TiCl4 and N2O4as dopants for Concentrated Solar Power applications and estimated a LCoE reduction of 10% in comparison with steam Rankine [28]. Valencia-Chapi et al. explored multiple CO2mixtures for Solar Power Plants applications, achieving an increase in thermal efficiency of 3–4 pp with respect to pure sCO2[29,30]. It is exactly in this scenario where the SCARABEUS project [31] is being developed, with the main idea of increasing the critical temperature of the working fluid through the addition of certain additives to the raw sCO2, enabling its condensation even at very high ambient temperatures, thus producing Renewable Energy 199 (2022) 1606–1628 1608 P. Rodríguez-deArriba et al. higher thermal efficiency than with either (steam) Rankine or sCO2 cycles. Thermal efficiency is a suitable figure of merit to compare power cycles working under similar heat source and sink temperatures. Nevertheless, the comparison between steam Rankine cycles and supercritical CO2cycles is often misleading because different turbine inlet temperatures (TIT) are involved: lower for steam cycles and higher for sCO2 systems. In other words, higher energy efficiencies of the latter cycles can potentially be brought about by the higher temperatures of heat addition to the cycle and not by an inherently more efficient conversion of this energy into useful work. The utilisation of the 2nd Law of Thermodynamics to carry out an exergy analysis, as opposed to the more usual energy analysis, has a twofold benefit. On the one hand, it provides meaningful information about whether or not a cycle is closer to the best thermodynamic performance attainable for given heat source/sink temperatures (Carnot cycle). On the other, it allows the identification of those component where exergy losses are taking place; i.e., where cycle performance is departing from the ideal (reference) Carnot cycle. As a result, it is possible to modify the cycle layout to compensate for these losses, thus yielding a cycle performance closer to the true potential enabled by the temperatures of heat source and sink. Several authors have carried out exergy analyses of sCO2cycles in the past [12,13,32,33], yielding the known conclusion that the main source of irreversibilities in the Simple Recuperated cycle operating on sCO2is the recuperative heat exchanger, due to the dissimilar heat capacity of the high- and lowpressure streams. This conclusion brought about a series of advanced layouts proposed by Angelino [12], featuring split-compression that resulted in the well-known Recompression and Partial Cooling layouts. These cycles largely improved the exergy efficiency of the Simple Recuperated Brayton cycle, redistributing exergy destruction and reducing the losses associated to the recuperative heat exchangers and the heat rejection unit, at the expense of increasing the losses across the compression and expansion processes. Such advanced sCO2cycles exhibit a more uniform loss distribution across the different cycle components, in contrast with that of the steam Rankine cycle which concentrates most of the exergy destruction in the primary heat addition process [13]. These conclusions about the most interesting cycle layouts for given boundary conditions can nevertheless change when the characteristics of the working fluid vary. Such is the case of the SCARABEUS project where the addition of additives brings about modifications of the working fluid properties (most notably the critical pressure and temperature). Previous studies, developed in the context of SCARABEUS by some of the authors, demonstrated that part-flow configurations can be of little interest for some sCO2-based blends, due to poor adaptability to compression in liquid phase [24,34]. This is numerically confirmed for two of the additives currently under investigation in SCARABEUS – Hexafluorobenzene (C6F6) and Titanium Tetrachloride (TiCl4) – and paves the way for the exploration of other cycle layouts. Amongst these, attention was paid by the authors to other cycle configurations that had been disregarded by the sCO2scientific community in the last years, in particular the Recuperated Rankine and Precompression cycles about which, unfortunately, only a few studies analysing the 2nd Law characteristics can be found in literature. On the contrary, the Recompression cycle does exhibit a good performance for the third additive hereby studied, Sulfur Dioxide (SO2), due to a much narrower Pressure–Temperature envelope of the resulting mixture, inherently brought by the use of this dopant [35]. Bearing all this in mind, the present paper aims to analyse the intrinsic 2nd Law performance of sCO2cycles in depth, following the footsteps of Gianfranco Angelino back in the late 1960s, with the aim of exploring the performance enhancement that sCO2blends could potentially bring to the technology. To this end, two different heat source temperatures are considered: 575 ◦C, representative of contemporary CSP plants using state-of-the-art technology, and 725 ◦C, Table 1 Common set of boundary conditions for sCO2-based cycles (pure or blended). Parameter Value Maximum cycle pressure [bar] 250 Minimum cycle temperature [◦C] 50 Turbine inlet temperature [◦C] 550/700 Turbine isentropic efficiency [%] 93 Compressor isentropic efficiency [%] 89 Pump isentropic efficiency [%] 88 Heat exchangers temperature approach [◦C] 5 Primary heat exchanger pressure drops [%] 1.5 Heat rejection unit pressure drops [%] 1.0 Heat recuperator pressure drops [%] 1.0 (low pressure side) 1.5 (high pressure side) representative of next-generation receiver technologies. The work is organised as follows: In the first part of the manuscript a thorough description of the computational environment is provided, followed by a brief introduction to the fundamentals of exergy analysis as used in the paper. In the second part, sCO2cycles, either pure or blended, are optimised and compared between them and against SoA CSP Rankine cycles using steam, and a series of interesting conclusions are drawn. Afterwards, a parametric analysis of the two key optimisation variables – maximum cycle pressure (P𝑚𝑎𝑥) and molar composition of the working fluid – is conducted. Finally, the effects of varying minimum cycle temperature are investigated by means of a sensitivity analysis, comparing both pure and blended CO2-based systems. 2. Computational environment 2.1. Definition of reference case, candidate cycles and blends Three different power cycle technologies are considered in this work: (i) SoA steam-based Rankine cycles, (ii) pure supercritical CO2 cycles and (iii) transcritical cycles using CO2blends. Due to the intrinsic differences between these technologies, in particular between the Rankine and sCO2-based cycles (either pure or blended), it is not possible to define a complete set of common boundary conditions to be employed in the simulations. Rather, the only common specifications are power output, set to 100 MW gross, minimum cycle temperature, set to 50 ◦C to have a representative value applicable to a site with extreme ambient conditions, and the two heat source temperatures, 575 and 725 ◦C respectively. The reference power cycle considered for contemporary CSP plants using steam turbine technology features reheat and feedwater heating. Live steam is produced at 150 bar and 550 ◦C and the extraction pressures for the seven feedwater heaters are set so as to balance peak cycle efficiency and inventory and auxiliary power consumption of the molten salt system. Condensation is enabled by an Air-Cooled Condenser with a design pressure of 0.123 bar (50 ◦C).1 For the cycles based on CO2, either pure or blended, a total of five different cycles are considered: Recuperated Rankine,Precompression and Recompression for CO2mixtures, Recompression and Partial Cooling for pure sCO2. These cycle configurations were originally proposed by Angelino in 1968 [12] and their layouts are shown in Fig. 1, along with the corresponding temperature–entropy diagrams. The first cycle is a mere adaption of a Rankine cycle employing CO2-based blends, whilst the remaining ones are characterised by advanced layouts, originally proposed to enhance the performance of the simple recuperative by 1This power block is adapted from the cycle proposed for the Rice Solar Energy Project in California [36]. When the higher heat source temperature is taken into account (725 ◦C), live steam is produced at 180 bar and 600 ◦C, herein considered as the maximum live steam temperature enabled by SoA steam turbine technology. Renewable Energy 199 (2022) 1606–1628 1609 P. Rodríguez-deArriba et al. Table 2 Thermodynamic properties of dopants. MW [kg/kmol] T𝑐𝑟 [◦C] P𝑐𝑟 [bar] Thermal stability CO244.01 31.06 73.83 >700 ◦C [10] SO264.06 157.60 78.84 >700 ◦C [10] C6F6186.06 243.58 32.73 up to 625 ◦Ca TiCl4189.69 364.85 46.61 up to 700 ◦Ca aThreshold temperature currently obtained by University of Brescia and Politecnico di Milano for the SCARABEUS project. Complete set of experimental results to be disclosed in an oncoming publication by these two institutions. Table 3 Additive hazard according to NFPA 704 [37]. Compound Health hazard Flammability Chemical reactivity Special hazard CO22 0 0 Simple Asphyxiant C6F61 3 0 – TiCl43 0 2 React with water SO23 0 0 – means of two different approaches. On the one hand, the Precompression layout is characterised by the addition of a pre-compressor in the low-pressure section of the cycle, between the high and low temperature recuperators, in order to overcome the limitation imposed by condensing pressure on turbine exhaust pressure. This provides an additional degree of freedom for further optimisation, increasing the expansion ratio achievable by the turbine. On the other hand, the Recompression cycle is obtained by dividing the flow of working fluid in two different streams before the heat rejection unit: one is sent to HRU, main compressor (or pump, in transcritical embodiment) and the low temperature recuperator (LTRec), whilst the other is compressed in a re-compressor and mixed with the former stream at LTRec outlet. The final aim of this stratagem, as claimed by Angelino, is to enhance LTRec heat recuperation potential by decreasing the internal irreversibilities of this components, by means of a reduction of the mass flow circulating through the high-pressure/low-temperature side of LTRec. The latter, in fact, is usually characterised by a really high mean specific heat due to the vicinity to the critical point, and a drop in its mass flow is found to be a very effective means to balance the heat capacities of the two sides of the recuperator, improving the exergy efficiency of this heat exchanger. Finally, the Partial Cooling cycle is an evolution of the Recompression, obtained by adding a heat rejection unit and a compressor before the split-flow. Thanks to this particular configuration, the Partial Cooling cycle ensures a very good compromise between thermal efficiency, specific work and temperature rise across primary heat exchanger, standing as one of the most promising alternative for CSP plant applications [1]. A common set of boundary conditions applied to all CO2-based systems is summarised in Table 1, where two Turbine Inlet Temperatures (TIT) are considered, 550 ◦C and 700 ◦C, corresponding to the two different heat source temperatures mentioned above. In the first step of the analysis, the maximum cycle pressure and the minimum cycle temperature are set to 250 bar and 50 ◦C respectively, and the influence of the variations of these parameters is then study at the end of this manuscript by means of sensitivity analysis. In spite of fixing a set of common boundary conditions, it is worth remarking that each different cycle presents a series of specific parameters (i.e. degrees of freedom) that can be varied in order to maximise its thermal efficiency. Considering pure CO2systems, the main compressor pressure ratio (PRMC) can be optimised, for a given maximum cycle pressure, varying the pressure level at compressor inlet (station 1 in both cycle configurations, see Fig. 1a and b). This allows to achieve a compromise between the beneficial and detrimental effects of compressing near the critical point (reduction in compression work, increase in irreversibilities in the heat regeneration). On the contrary, pump inlet pressure is not a degree of freedom in SCARABEUS systems and, for a given blend, cannot be modified without affecting the minimum cycle temperature, due to the condensing nature of these cycles. On the other hand, optimising the molar fraction of dopant – varying the composition of the working fluid and, thus, shifting the critical point itself – results to be a very interesting mean to increase both thermal and exergy efficiency of SCARABEUS systems. Furthermore, the turbine expansion ratio (ERT) can be freely optimised in the Partial Cooling and Precompression cycles, independently on the PRMC, varying the pressure ratio of the precompressor (PRPrC, stations 10–11 and 7–8 for Partial Cooling and Precompression respectively, see Fig. 1b and d). Finally, the split-flow factor 𝛼, defined as the percentage of the working fluid circulating through the recompressor and low-temperature recuperator, is a very interesting optimisation parameter for Recompression and Partial Cooling cycles (stations 1, 2 and 3 for both configurations). The optimum values of all these parameters are further discussed in Section 4.1 and disclosed in Table 6. The main thermodynamic characteristics of the three candidate dopants are provided in Table 2, whilst a brief evaluation of these additives is summarised in Table 3, following NFPA 704 standard. For sake of comparison, the same parameters referring to Carbon Dioxide are added in both tables. Some of these features are currently under evaluation by the SCARABEUS consortium in order to assess how much they compromise the commercial deployment of the technology (high flammability of C6F6, aggressive water reactivity for TiCl4and toxicity of SO2). In particular, it is worth mentioning that the preliminary results obtained by SCARABEUS consortium found that C6F6is expected to present a thermal stability significantly lower than the other chemical compounds in analysis and, more importantly, lower than the TIT level considered as representative for next-generation CSP plant. In spite of this fact, authors decided to investigate the performance of CO2-C6F6blends for the entire set of boundary conditions employed in the present paper, in order to provide a complete comparison with the other dopants in analysis. Nevertheless, if the threshold temperature indicated in Table 2 will be confirmed, this would be a crucial limitation to the adoption of CO2-C6F6mixtures in high-temperature CSP applications. Further information about this and other dopants being screened now will be reported by the corresponding partners in future publications. The thermodynamic properties of the CO2-based mixtures have been obtained with the commercial software Aspen Plus [38] (more information can be found in previous works by the authors [24,35]). The critical loci, the pressure–temperature envelopes and the main thermodynamic properties of the three sCO2mixtures considered in this work are provided in Fig. 2 and Table 4. 2.2. Simulation tools The modelling and simulation of the power cycle has been developed using the commercial software Thermoflex [39], a widely used software for power plant engineering and analysis with builtin data sets of steam and carbon dioxide properties using Refprop database [40]. Unfortunately, Thermoflex does not have a similar database of properties for CO2mixtures of variable composition. These Table 4 Main characteristics of working fluids. 𝑃𝑐𝑜𝑛𝑑 and temperature glide refer to a bubble temperature of 50 ◦C. Mixture Molar comp. [%] MW [kg/kmol] T𝑐𝑟 [◦C] P𝑐𝑟 [bar] P𝑐𝑜𝑛𝑑 [bar] Glide [◦C] D1C15 CO2–C6F6[85–15] 65.32 102.1 121.3 77.52 88.4 D2C17 CO2–TiCl4[83–17] 68.77 116.4 212.6 96.17 181.6 D3C20 CO2–SO2[80–20] 48.03 64.2 91.85 77.41 16.1 Renewable Energy 199 (2022) 1606–1628 1610 P. Rodríguez-deArriba et al. Fig. 1. Cycle layouts considered for pure (a, b) and blended (c, d, e) CO2systems. properties have thus been estimated with Aspen Plus [38] and the resulting data has been incorporated into Thermoflex through a dedicated User-defined General Fluid feature specifically developed by Thermoflow for the SCARABEUS project. Further information regarding the calculation of thermophysical properties can be found in previous papers by the authors [24,35] and by other partners of the SCARABEUS consortium [41]. The models in Thermoflex have been linked to an external optimiser in Matlab, using the surrogateopt function included in Matlab’s ’Global Optimisation Toolbox’. Finally, several in-house Matlab code have been developed to obtain the exergy analysis from the Renewable Energy 199 (2022) 1606–1628 1611 P. Rodríguez-deArriba et al. Fig. 2. Thermodynamic features of the candidate blends: Critical loci (a) and Pressure–Temperature envelopes (b) are provided. Table 5 Definition of fuel exergy, product exergy and exergy losses for each component. Component EFEPELComponent EFEPEL W E2−E1 adiabatic W E2−E1 adiabatic E1−E2 W adiabatic E3−E4 E2−E1 adiabatic Q(1- 𝑇 𝑜 𝑇) E2−E1 adiabatic E1−E2 0 Q(1- 𝑇 𝑜 𝑇) E1 + E2 E3 adiabatic E1 E2+E3 adiabatic Table 6 Cycle optimum specifications for all the CO2-based configurations studied. Two energy source temperatures are considered (575/725 ◦C). Acronym Layout Working fluid PR𝑀𝐶 ER𝑇PR𝑃 𝑟𝐶 𝛼 RC CO2Recompression 100% CO22.37/2.45 2.20/2.27 X 0.29/0.29 PC CO2Partial Cooling 100% CO22.23/2.24 3.18/3.70 1.55/1.80 0.4/0.41 PrC D1 Precompression 85% CO2/15% C6F63.22/3.22 3.91/4.20 1.31/1.41 X RR D2 Rec. Rankine 83% CO2/17% TiCl42.60/2.60 2.47/2.47 X X RC D3 Recompression 80% CO2/20% SO23.16/3.16 2.93/2.93 X 0.38/0.38 heat and mass balances calculated in Thermoflex and to post-process the results. 3. Fundamentals of exergy analysis Exergy can be defined as the maximum work that can be extracted from a thermodynamic system from its current state until a final state of equilibrium with the environment – the dead state – is reached, assuming that the system interacts with the environment only [42]. Flow exergy of the working fluid can be calculated using Eq. (1), where 𝐻0and 𝑆0are the enthalpy and entropy at the pressure and temperature of the environment 𝑃0and 𝑇0, here set to 40 ◦C and 1 bar. Other forms of exergy such as kinetic, potential and chemical exergy have not been considered in the analysis, and the cycles are assumed to operate in steady-state. 𝐸𝑓𝑙𝑜𝑤 = (𝐻−𝐻0) − 𝑇0(𝑆−𝑆0)(1) The approach to exergy analysis employed in this work is inspired by the work by Penkuhn and Tsatsaronis [33]. Thermodynamic irreversibility is a consequence of the generation of entropy over a thermodynamic transformation, also called ‘‘exergy destruction’’ (E𝐷), and this can be applied to both the individual components (Eq. (2)) and overall power cycle (Eq. (3)); these are identified with the subindex kand cyc respectively. Regarding heat rejection and addition, constant cold and hot reservoir temperatures are considered, set to 40 ◦C and 575/725 ◦C (depending on TIT) respectively. The definition of this parameter makes use of the concept of product exergy (E𝑃), fuel (or educt) exergy (E𝐹)2and Exergy losses (E𝐿), explained in detail 2Following the definition provided in [43], the authors have considered the fuel or educt exergy to be representative of all the resources expended to provide the product exergy, not only the one characterised by higher exergy. Despite the possible dual denomination (i.e. fuel or educt), the authors have decided to employ only the former in the remainder of the manuscript for the sake of simplicity. Renewable Energy 199 (2022) 1606–1628 1612 P. Rodríguez-deArriba et al. in [43,44]Table 5 includes fuel exergy, product exergy and exergy losses definition for all the components considered in this work [45]. 𝐸𝐷,𝑘 =𝑇0𝛥𝑆𝑔𝑒𝑛,𝑘 =𝐸𝐹 ,𝑘 −𝐸𝑃 ,𝑘 −𝐸𝐿,𝑘 (2) 𝐸𝐷,𝑐𝑦𝑐 =𝐸𝐹 ,𝑘 −𝐸𝑃 ,𝑐𝑦𝑐 −𝐸𝐿,𝑐𝑦𝑐 (3) In addition to these parameters, the following two figures of merits are added to the analysis: exergy efficiency (𝜖) and Efficiency losses from Carnot Cycle (𝛥𝜂𝑘). The first index is well-known and defined as the ratio between product exergy and fuel exergy, applicable to both individual components (Eq. (4)) and global system (Eq. (5)). The second metric, though, deserves a more thorough explanation. 𝛥𝜂𝑘is a means to translate the irreversibility taking place in each individual component (typical of 2nd Law analysis) into an actual thermal efficiency loss (1st Law), employing Carnot cycle efficiency as a reference case [46]. With this in mind, the thermal efficiency loss brought about by a component is defined as the ratio between the exergy destruction that takes place in that particular component and the heat provided to the cycle (𝑄𝑖𝑛). The correlation employed to calculate this parameter is provided in Eq. (6). 𝜖𝑘=𝐸𝑃 ,𝑘 𝐸𝐹 ,𝑘 = 1 − 𝐸𝐷,𝑘 +𝐸𝐿,𝑘 𝐸𝐹 ,𝑘 (4) 𝜖𝑐𝑦𝑐 =𝐸𝑃 ,𝑐𝑦𝑐𝑙𝑒 𝐸𝐹 ,𝑐𝑦𝑐𝑙𝑒 = 1 − ∑𝑘(𝐸𝐷,𝑘 +𝐸𝐿,𝑘) 𝐸𝐹 ,𝑐𝑦𝑐 (5) 𝛥𝜂𝑘=𝑇0𝛥𝑆𝑔𝑒𝑛,𝑘 𝑄𝑖𝑛 (6) 4. Results and discussion In this section the complete set of results obtained with Thermoflex software are presented and discussed. Firstly, a justification of the optimum cycle configuration (e.g. layout synthesis) for each different dopant is provided from an exergy perspective, confirming the potential of SCARABEUS concept to reduce cycle internal irreversibilities. Secondly, the optimised blended cycles – Precompression with C6F6, Recuperated Rankine with TiCl4and Recompression with SO2– are compared against pure CO2technology and SoA Rankine cycle by means of a combined 1st and 2nd law analysis. Afterwards, a parametric analysing varying cycle maximum pressure, molar fraction of dopant and ambient temperature is undertaken, studying the dependence of exergy efficiency on these three parameters. 4.1. Optimum specification and layout synthesis for the CO2-based power cycles Before assessing the optimum cycle configurations for the different dopants taken into account in the present study, a preamble discussing the main implications of employing these novel working fluids results to be mandatory. CO2-based mixtures can be studied under either supercritical (pressure and temperature of any cycle stations higher than the corresponding critical values) or transcritical embodiments (subcritical conditions at pump and/or HRU inlet). If a fully supercritical set-up is adopted, the main compressor inlet pressure can be optimised in order to maximise thermal efficiency, achieving the perfect compromise between the advantages and disadvantages of operating the compression near the critical point: on the one hand, a low compression work, brought by the low specific volume of the working fluid at those conditions; on the other hand, high exergy destruction in the recuperator, due to the vast increase in the heat capacity of the cold stream inside this component, which directly affects to cycle heat regeneration potential [13]. On the contrary, if transcritical embodiments are taken into account, pump inlet pressure cannot be freely optimised, since it is fixed by cycle minimum temperature (𝑇𝑚𝑖𝑛) due to the condensing nature of the cycle. For a given dopant, the transition from supercritical to transcritical embodiment theoretically depends on the molar composition of the working fluid, since as long as the critical temperature of the mixture is below the minimum cycle temperature, the cycle remains supercritical. There exits, therefore, a value of dopant molar fraction at which the critical temperature equals 𝑇𝑚𝑖𝑛. As a consequence, if a suitable amount of dopant is added, condensation even at high ambient temperatures can be enabled. If a simple recuperative cycle is taken into account with a 𝑇𝑚𝑖𝑛 set at 50 ◦C, this threshold value corresponds to 4% for C6F6, 7% for TiCl4and 12% for SO2, as can be observed in Fig. 3. Whether or not this strategy (i.e., SCARABEUS concept) can actually bring about an enhancement of the thermodynamic performance of pure sCO2cycles will depend on the specific dopant selected, its molar content and the cycle layout employed. In this context, an exergy analysis can reveal how the irreversibilities within different cycle configurations are altered when C6F6, TiCl4or SO2are added to CO2. Fig. 3 shows the breakdown of exergy destruction as a function of dopant molar fraction, obtained considering the different components of a simple recuperative cycle – Turbine, Pump/Compressor, Primary Heat Exchanger (PHX), Heat Recuperator (Rec) and Heat Rejection Unit (HRU) – operated with the three CO2-based mixtures considered in the present study. The transition from a supercritical embodiment (hereby called Simple Recuperated) to transcritical one (Recuperated Rankine) has been emphasised with a dashed line. A first observation is that an optimum composition capable of minimising the total exergy destruction (stack value of all five areas) can be identified, and it results to be in the order of 15%–20% for C6F6, and approximately 17% and 8% for TiCl4and SO2respectively. Interestingly, the optimum composition for the two first dopants lies inside the transcritical zone, achieving an important reduction (23.3% and 37%, respectively) in the total exergy destruction with respect to the reference CO2cycle (0% molar fraction of dopant); on the contrary, the lowest overall exergy destruction observed for SO2mixtures corresponds to a fully supercritical embodiment, and it results to be only 5% lower than the one obtained considering pure CO2. This circumstance can be explained by comparing the exergy destruction breakdown of each dopant. It is observed that the adoption of transcritical configurations enables a significant reduction (>50%) of the exergy destroyed in the Heat Rejection Unit (HRU), independently on the dopant. This is an indirect consequence of the lower temperature rise produced by the compression process, brought by operating the latter in liquid phase [25], which reduces the duty of the HRU [24]. For the three cases, the exergy destroyed in the turbomachinery decreases with a rise in dopant molar fraction, mainly due to the increasing molar mass of the mixture [46]. On the contrary, the exergy destruction in the PHX (slightly) diminishes continuously with the molar fraction for C6F6and TiCl4, whilst it rises significantly when the molar fraction of SO2is increased. This indicates that the addition of C6F6and TiCl4potentially reduces the heat duty of the PHX, thanks to a higher heat recuperation. As a consequence, it could be expected that the exergy destruction in the recuperator (grey area in Fig. 3) would increase for mixtures based on C6F6or TiCl4and decrease for SO2, accordingly to the higher and lower fuel exergy involved in this equipment. Nevertheless, when SO2is added to the raw CO2, the use of a transcritical embodiment always produces a significant rise in the exergy destroyed in the recuperator (E𝐷,𝑅𝑒𝑐 ) with respect to the pure CO2case, contrarily to what can be observed for C6F6and TiCl4. These circumstance can be explained taking a step back and focusing on the definition of exergy efficiency of a single equipment 𝜖𝑘: according to Eq. (4), E𝐷,𝑅𝑒𝑐 is equal to the product of the fuel exergy and (1-𝜖𝑅𝑒𝑐). In this regard, Fig. 4(a) depicts both fuel exergy and exergy efficiency of the recuperator as a function of the dopant molar fraction for the three candidate blends. As expected, the fuel exergy increases with the molar content of C6F6and TiCl4and is reduced when adding SO2. Whereas the exergy efficiency is inversely proportional to the molar fraction in the SO2case, there exists a minimum value for C6F6and TiCl4from which the exergy efficiency of the recuperator Renewable Energy 199 (2022) 1606–1628 1613 P. Rodríguez-deArriba et al. Fig. 3. Breakdown of exergy destruction for Recuperated Rankine layout as function of dopant molar fraction. Different blends are considered. starts increasing. This is due to the internal condensation of the mixture taking place inside the recuperator, which leads to an abrupt rise in hot stream specific heat capacity near the cold end of this heat exchanger. At the same time, and approximately in the same region of the recuperator, the cold stream heat capacity rises due to the proximity to the critical point. Fig. 4(b) provides a graphical representation of this circumstance for a 85%CO2-15%C6F6mixture. As a consequence, the internal condensation acts as a natural mechanism to balance the heat capacity of both streams, producing an increase in the exergy efficiency and a reduction of the exergy destruction. As a matter of fact, this effect is responsible of the good performance of CO2-C6F6and CO2- TiCl4mixtures in the Recuperated Rankine layout, whilst exacerbates the increase in total exergy destruction in the CO2-SO2case. Interestingly, this circumstance explains, from an exergetic standpoint, a conclusion obtained in previous works by the authors, i.e. the poor performance achieved by CO2-SO2mixtures when combined with a simple recuperative cycle, and their great adaptability to a Recompression layout [35], as it will be discussed in the next paragraph of the present section. In fact, the narrow pressure–temperature envelope of these mixtures, as afore-commented in this manuscript, results to be the main driver for their poor and good performance with Recuperated Rankine and Recompression cycle, respectively, both effects brought by the lack of internal condensation in the recuperator. Bearing all this in mind, the optimum cycle layouts for each mixture, identified in previous works by the authors, can be confirmed from a 2nd law standpoint. With this aim, Precompression layout is hereby taken into account for both CO2-C6F6and CO2-TiCl4mixtures, whilst the Recompression is considered for CO2-SO2.Fig. 5 shows the breakdown of exergy destruction as a function of dopant molar fraction for these three cases. It can be observed that the optimum composition for CO2-C6F6and CO2-TiCl4blends rounds 15% and 17% of dopant respectively, values extremely similar to the ones previously obtained in Fig. 3. Interestingly, a clear reduction of the exergy destroyed in the HTRec when passing from a supercritical to a transcritical embodiment can be observed in both cases (more information on this is provided later in this section). On the contrary, the optimum molar fraction of SO2employed in Recompression cycle results to be significantly different than the one obtained in Fig. 3(c) for a simple recuperative layout, and corresponds to a transcritical layout (see Fig. 5(b)). This circumstance is due to the fact that this cycle modification (i.e. split-compression) helps alleviating the large exergy destruction in the heat recuperator, which is the main drawback of increasing the molar fraction of SO2, thus taking advantage of the vast reduction in the exergy destroyed in the HRU for molar content of SO2higher than 12%, brought by the condensing nature of the cycle. Even if the actual optimum corresponds to a 15% of SO2, a higher molar fraction of dopant has been chosen in order to Renewable Energy 199 (2022) 1606–1628 1614 P. Rodríguez-deArriba et al. Fig. 4. (a) Recuperator fuel exergy (solid lines) and exergy efficiency (dashed lines) as a function of the molar fraction for C6F6, TiCl4and SO2, (b) Specific heat capacity [kJ/(kg K)] of cold and hot streams inside the recuperator, considering a 85%CO2-15%C6F6mixture. guarantee a minimum temperature difference of roughly 15 ◦C between minimum cycle temperature and the resulting critical temperature of the blend [35]. This assumption, made for sake of security, ensures working fluid condensation even at minimum cycle temperatures up to 60 ◦C, corresponding to extreme ambient conditions. Fig. 6 presents the exergy destruction breakdown for these three advanced layouts, as a function of the pressure ratio of the precompressor (PR𝑃 𝑟𝐶 ) and the split-flow factor 𝛼, for Precompression and Recompression cycles respectively. This figure can be employed as a suitable tool to compare these advanced layouts against the simple recuperative configuration: if PR𝑃 𝑟𝐶 is equal to 1, in fact, the Precompression cycles converges to the Recuperated Rankine cycle; on the other hand, if 𝛼is set to 0, Recompression cycle is practically transformed into a Recuperated Rankine one. In this regards, several interesting observations can be made. Firstly, Precompression cycle is hereby confirmed to be able to improve the performance achieved by CO2-C6F6mixtures with respect to the Recuperated Rankine (PR𝑃 𝑟𝐶 =1), enabling a drop in the overall exergy destruction in the order of 14.6%, when PR𝑃 𝑟𝐶 is set to 1.41. On the contrary, the thermal performance enhancement obtained by using Precompression layout instead of Recuperated Rankine is very limited if CO2-TiCl4mixtures are taken into account, with a maximum E𝐷 reduction rounding 8%. This marginal gain in exergy efficiency, which corresponds as well to a slight increase in cycle thermal efficiency [24], does not seem to be sufficient to justify the use of the Precompression layout. For this reason, Recuperated Rankine is hence selected for CO2-TiCl4blends, due to its expected better operability and lower capital cost, both features brought by its significantly simpler layout. Finally, for CO2-SO2blends, the adoption of a Recompression cycle is clearly beneficial for cycle thermodynamic performance, as demonstrated by the impressive reduction in E𝐷>43%, obtained for 𝛼=38%. These circumstances confirm, from a exergy standpoint, the results obtained in previous works by the authors, which identified the following combination of best-performing cycle layouts and working fluid compositions: Precompression with 85%CO2–15%C6F6,Recuperated Rankine with 83%CO2–17%TiCl4and Recompression with 80%CO2–20%SO2. It is worth noting that the improvement in cycle exergetic performance achieved by Precompression with CO2-C6F6and Recompression with CO2-SO2is mainly caused, in both cases, by a significant reduction in the exergy destruction in heat recuperation process. Interestingly, these similar results are obtained by means of significantly different thermodynamic behaviours of these two cycle configurations. The Precompression cycle provokes a twofold effect: on the one hand, it increases the specific work, overcoming the constraint imposed on turbine exhaust pressure by the pump inlet one, which is fixed, for a given minimum cycle temperature, due to the condensing nature of the cycle; on the other hand, the turbine outlet temperature diminishes, with a consequent reduction in heat recuperation potential of this cycle. The reduction of the circulating mass flow affects, from an exergy perspective, all exergy flows equally, but only translates into an overall reduction of the exergy destruction in the pump and the HRU. In the turbine, the higher expansion ratio of the cycle leads to a grow in the specific exergy destruction (kJ/kg) which completely counterbalances the reduction in the mass flow, leading to a larger exergy destruction as net effect. Similarly, the lower turbine outlet temperature results in a higher temperature rise in the PHX, increasing its exergy destruction. Obviously, the inclusion of the precompressor adds a new source of irreversibility, associated to the compression of the fluid in gas phase. In the recuperators, opposing trends for the exergy destruction can be observed for the LTRec and HTRec, an increasing one in the former and a decreasing one in the latter. This is due to a redistribution of the heat recovered in these two components, which is progressively shifted towards the LTRec, as can be seen by looking at the trends of fuel exergy in Fig. 7(a), represented in solid line. The overall reduction of the exergy destruction in the heat recuperation (sum of the contribution of LTRec and HTRec) cannot be only attributed to the reduction of the mass flow, but to an enhancement of the exergy efficiency in the recuperation. In Fig. 7(a), the impact of the PR𝑃 𝑟𝐶 on the exergy efficiency of LTRec and HTRec is depicted with dashed lines. It can be seen that both exergy efficiencies grow with PR𝑃 𝑟𝐶 , concluding that the addition of a compressor in the low-pressure side of the cycle, besides enhancing specific work, also contributes to a reduction of the irreversibility in the heat recuperation. On the contrary, the split-flow stratagem employed in the Recompression happens to penalise specific work. From an exergy perspective, the larger mass flow provokes the growth in the exergy destruction in the turbomachinery (pump, turbine and recompressor). On the other hand, the reduction in the exergy destruction experimented by the PHX and, more importantly, by the HRU, leads to a higher internal heat recuperation, which reduces the heat duty in both equipment. Nevertheless, the larger amount of recuperated heat does not translate into a rise in the exergy destroyed in the recuperators (sum of LTRec and HTRec) but, conversely, to its Renewable Energy 199 (2022) 1606–1628 1621 P. Rodríguez-deArriba et al. Fig. 12. Breakdown of exergy destruction as function of maximum cycle pressure. Different combinations of blend and cycle layout are considered. Fig. 13. Recuperator exergy efficiency as a function of maximum cycle pressure. Different combinations of blend and cycle layout are considered. Solid lines for LTRec and dashed lines for HTRec, when applicable. SCARABEUS concept, similarly to pure sCO2technology, is prone to be extrapolated to other application fields, characterised by a wide range of ambient temperatures. Therefore, a sensitivity analysis varying minimum cycle temperature is undertaken, in order to analyse the capability of SCARABEUS systems to maintain their good thermal performance with difference ambient conditions, comparing it against pure sCO2 technology. To this aim, minimum cycle temperatures from 35 ◦C to 60 ◦C are hereby taken into account, and the exergy efficiencies of the different systems are then calculated considering a 10 ◦C lower cold source temperature (25 ◦C–50 ◦C). A hot source temperature of 725 ◦C is taken into account, and the remaining boundary conditions are the ones previously indicated in Table 1. For each minimum cycle temperature, the entire set of CO2-based systems have been duly optimised, following the same rationale discussed in Section 4.1. The results of this sensitivity analysis are provided in Fig. 14 as a function of minimum cycle temperature, showing that the three SCARABEUS systems present a significantly less steep trend with respect to pure CO2ones. In particular, Precompression cycle with D1, Recuperated Rankine cycle with D2 and Recompression cycle with D3 show an exergy efficiency reduction rounding 2.4, 3.5, 3.2 percentage points respectively, against the 5.2 and 4.1 pp drop observed in Recompression and Partial Cooling operated with pure CO2. These results utterly confirm the stronger adaptability to high ambient temperatures that characterises SCARABEUS systems, which enable exergy efficiency gains up to 3 percentage points with Renewable Energy 199 (2022) 1606–1628 1622 P. Rodríguez-deArriba et al. Fig. 14. Cycle exergy efficiency as a function of minimum cycle temperature. Five different combinations of working fluid and cycle layout are considered. Fig. 15. Relative difference in main cycle indicators when minimum cycle temperature increases from 35 ◦C to 60 ◦C. Five different combinations of working fluid and cycle layout are considered. respect to the pure CO2cycles if a minimum cycle temperature of 60 ◦C is considered. On the contrary, the interest in CO2-blend seems not to be justified at low temperature levels, where the performance of pure CO2 systems are extremely enhanced (compression process can be operated in the extreme vicinity of the critical point). As a matter of fact, the exergy efficiency gains achieved by SCARABEUS systems is reduced to (roughly) 1 percentage point at 35 ◦C, and in some cases the pure CO2 performs even better than the blended solution (see RC CO2and PrC D1, Fig. 14). The trends shown in Fig. 14 can be explained by reasoning about the optimisation rationale specific to each system, observing how the corresponding optimisable parameters are adapted when the minimum temperature of the design cycle is increased. In this regard, Fig. 15 depicts the relative variation of some relevant cycle parameters, namely mean compressibility factor  𝑍(i.e., arithmetic average between main compressor inlet and outlet conditions), specific work (Ws), main compressor/pump pressure ratio (PRcompr), turbine expansion ratio (ERturb), temperature rise in the compression process (𝛥𝑇𝑐𝑜𝑚𝑝𝑟) and temperature rise across Primary Heat Exchanger (𝛥𝑇𝑃 𝐻𝑋 ). This last parameter results to be particularly, since it is an indicator of the heat recuperation potential of a cycle (the greater the amount of heat internally recovered, the lower the 𝛥𝑇𝑃 𝐻𝑋 ), as well as the size and cost of the TES (the lower the 𝛥𝑇𝑃 𝐻𝑋 , the bigger the TES). As already commented in Section 2, two main differences can be identified between pure and blended CO2-based systems: on the one hand, the pressure at the inlet of the main compressor/pump (cycle station 1 in Fig. 1) can be optimised independently in pure CO2systems, whereas this parameter is completely bound to the pump inlet temperature in SCARABEUS ones, due to the condensing nature of these cycles; on the other hand, the latter present an added degree of freedom, which is the possibility to optimise the composition of the blend, hence directly modifying the critical conditions of the working fluid, enabling its condensation even at high ambient temperatures. This happens to be of uttermost importance, since one of the key-factors of the outstanding thermal performance presented by sCO2technology is its extremely low compression work, enabled by a low compressibility factor. Nevertheless, this is only valid if the compression process is operated in the extreme vicinity of the critical point, since the compressibility factor significantly increases as long as the main compressor inlet is shifted away from this particular condition. Bearing all this in mind, it is clear that pure CO2cycles do not present any means to avoid the strong rise in  𝑍in high ambient temperature scenarios, and the consequent increase in compression work. As a consequence, cycle thermal performance is maximised reducing the main compressor pressure ratio – increasing main compressor inlet pressure, even at the cost of decreasing cycle specific work – with the purpose of increasing turbine outlet temperature in order to enhance the heat recuperation potential of the cycle. This can be better understood observing the relative deviations of  𝑍, W𝑠and 𝛥𝑇𝑃 𝐻𝑋 in Fig. 15. Furthermore, it can be noticed that the difference between the exergy efficiency of RC CO2and PC CO2decreases significantly with the minimum cycle temperature (see Fig. 14, passing from 1.5pp at 35 ◦C to less than 0.2pp at 60 ◦C). This is brought by the different strategies employed by this configurations to maximise their thermal performance, and it can also be inferred from Fig. 15: PC CO2exhibits a reduction in the main compressor pressure ratio higher than the one of RC CO2, but a lower reduction in the turbine expansion ratio. This is due to the fact that PC Renewable Energy 199 (2022) 1606–1628 1623 P. Rodríguez-deArriba et al. Fig. 16. Exergy destruction breakdown as a function of design minimum cycle temperature. Recompression cycle with pure CO2(a) and CO2-SO2blend (b). CO2cycle overcomes the constraint imposed by the main compressor inlet pressure on the turbine exhaust – thanks to the addition of a precompressor (see Section 2) – and ER𝑡𝑢𝑟𝑏 can be optimised to face the rise in T𝑚𝑖𝑛. As a consequence, PC CO2achieves exergy efficiency similar to the one obtained by RC CO2, but with greater specific work (i.e. lower circulating mass flow, smaller footprint) and higher 𝛥𝑇𝑃 𝐻𝑋 (smaller size and, expectedly, cost of the TES). This fact results to be of utmost importance, as it affirms the Partial Cooling as the most promising pure CO2cycle configuration for high ambient temperatures, also from a techno-economic standpoint. With regards to the blended systems, the main reason behind the superiority of SCARABEUS concept at high T𝑚𝑖𝑛 (see Fig. 14) is the condensing nature of these cycles, which allows the pump to operate with a low mean compressibility factor even at extreme ambient conditions. As it can be observed in Fig. 15, SCARABEUS systems show a limited rise in  𝑍, in the order of 15%, whilst this parameter grows by more than 35% in RC CO2and PC CO2. In spite of this, the three SCARABEUS systems present relative reductions of specific work ranging 25%–40%, values comparable to, or even higher than, the ones observed for pure sCO2cycles. This leads to a scenario in which cycle pressure ratio is also decreasing, due to two counteracting effects: first and foremost, for a given blend composition, working fluid condensing pressure (i.e. pump inlet pressure) always increases with bubble temperature (i.e. minimum cycle temperature, see Fig. 2); secondly, and to a smaller extent, a rise in dopant molar fraction leads to a decrease in the condensing pressure, for a given bubble temperature [24,35]. As a consequence, increasing the molar fraction of dopant (i.e. tailor the working fluid composition) appears to be a possible means of mitigating the drop in the cycle pressure ratio caused by the increase in minimum cycle temperature, hence increasing cycle performance. This tailorability can be defined as the ability to adjust the properties of the fluid to variations in the design T𝑚𝑖𝑛 in order to best exploit the characteristics of the thermodynamic cycle employed. In this regard, the optimum dopant molar fraction for each SCARABEUS system is shown in Fig. 14 by means of different colour scales, being a darker colour representative of a higher molar fraction (for a given dopant). Furthermore, the value of the resulting optimum molar fraction is also indicated by labels, in order to improve figure readability. It can be observed that the dopant molar fraction increases with T𝑚𝑖𝑛 when Hexafluorobenze (PrC D1) and Sulfur Dioxide (RC D3) are considered (from 12% to 17% and from 16% to 28% respectively), whereas for it presents a very slight reduction if Titanium Tetrachloride is taken into account (RR D2). This indicates a somehow better working fluid tailorability for PrC D1 and RC D3 systems in comparison with RR D2 one, which is also consistent with the less steep trends exhibited by the former cycle configurations (see Fig. 14). Bearing all this in mind, the significant reduction in W𝑠experimented by RR D2 (observed in Fig. 15) can be explained by its low tailorability, together with the extremely recuperative nature of this system, already discussed in Section 4.1. In this regard, the tendency towards lower molar fraction follows a rationale similar to the one previously discussed for pure CO2systems: in order to optimise thermal efficiency, the heat recuperation potential is significantly enhanced (see the vast reduction in 𝛥𝑇𝑃 𝐻𝑋 in Fig. 15), at the expense of its specific work. On the contrary, the advanced layout configurations of PrC D1 and RC D3, together with their good tailorability, allows a better compromise between heat recuperation and specific work. This fact results to be more accentuated for the Precompression cycle with C6F6, due to the possibility of optimise the expansion ratio of the turbine independently, brought by the addition of a precompressor between the low and high temperature recuperators (see Sections 2and 4.1). Finally, Fig. 16 compares the exergy destruction breakdown of the Recompression cycle working on pure CO2(a) and on CO2-SO2mixture (b), in order to better describe the effects of the change in working fluid for a given layout. The major difference is found in the growth of exergy destruction of the HRU with T𝑚𝑖𝑛. For the RC CO2, it changes from 6.22 to 11.09 MW (+78%) whereas for RC D3 5.20 to 6.53 MW (+26%). This larger irreversibilities in the sCO2case is brought by a higher temperature rise in the compression process (see 𝛥𝑇𝑐𝑜𝑚𝑝𝑟 in Fig. 15) which ultimately lead to an increase in the HRU inlet temperature. The remaining components are just responsible of a 4.9 MW (+19%) and 4.3 MW (+17%) increment, respectively. 5. Conclusions The aim of this work is to explore the 2nd Law performance of transcritical power cycles working on blended Carbon Dioxide in order to assess their actual potential and the reasons for the expected performance gains with respect to either contemporary steam turbine technology or pure supercritical CO2cycles. To this end, the paper has presented a thorough comparison of three CSP power cycle technologies (steam Rankine, pure sCO2and blended sCO2) based on exergy analysis for two different turbine inlet temperatures (550 and 700 ◦C) and one single minimum cycle temperature (50 ◦C). Three different candidate additive has been considered, namely Hexafluorobenzene (C6F6), Titanium Tetrachloride (TiCl4) and Sulfur Dioxide (SO2). A series of interesting conclusions can be drawn, putting this technology forward as a very promising alternative for mid-term future of CSP plant: Renewable Energy 199 (2022) 1606–1628 1624 P. Rodríguez-deArriba et al. •The large temperature glide of CO2-C6F6and, especially, CO2- TiCl4mixtures leads to working fluid condensation inside the recuperator, being this feature the main driver of the large cycle efficiency achieved by these two fluids with a Recuperated Rankine cycle. •On the contrary, the lack of internal condensation observed with CO2-SO2mixtures results to be extremely beneficial for the adoption of a Recompression layout. •sCO2blends are a promising working fluid even at turbine inlet temperatures as low as 550 ◦C, enabling better energy and exergy efficiencies than state-of-the-art steam Rankine (1.8 and 2.7 pp higher 1st and 2nd Law efficiencies, respectively); •At 700 ◦C, sCO2mixtures clearly outperform both state-of-the-art (steam) Rankine cycles and pure sCO2cycles, achieving thermal and exergy efficiencies as high as 51.6 and 75.3%. This confirms that the technology is a firm candidate for next generations CSP plants; •Compared to pure sCO2cycles, using sCO2mixtures leads to a significant drop in the amount of exergy destroyed across the compression and heat rejection processes, rounding 50% for a given cycle output. This is enabled by the possibility to condense the working fluid. On the other hand, a larger (relative) E𝐷is experienced in the recuperators, even if this is still comparable to pure sCO2cycles from a quantitative standpoint. This sets a focus area for future research of CO2mixtures, where solutions to tackle the larger irreversibilities of these components will have to be devised; •The interest in considering maximum cycle pressures higher that 250 bar is extremely scarce, due to the very limited gains achieved in thermal performance. For a Precompression cycle operated with CO2-C6F6blends, this threshold value can be reduced to 200 bar; •At high ambient temperatures, CO2mixtures behave significantly better than pure CO2. The gain, in terms of exergy efficiency, can be as high as 3 percentage points, for a minimum cycle temperature of 60 ◦C; •This enhanced performance achieved by CO2mixtures is brought by the condensing nature of the cycle, together with the tailorability of the working fluid (i.e. possibility to optimise the molar fraction of dopant as a function of minimum cycle temperature, in order to maximise cycle thermal efficiency). Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The SCARABEUS project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement Nº814985. The University of Seville is also gratefully acknowledged for supporting this research through its Internal Research Programme (Plan Propio de Investigación), under contract No 2019/00000359. Last but not least, the regional government of Andalusia (Junta de Andalucía) is gratefully acknowledged for sponsoring the contract of Pablo Rodríguez de Arriba under the Programme for Youth Employment 2014–2020 (Phase 4). Appendix. Complete heat & mass balances and resume of exergy balances by components This annex presents the complete heat & mass balances and a resume of exergy balances by components for all the CO2-based systems considered in the present paper (see Tables A.8–A.17). The entire set of cycles have been optimised following the methodology discussed in Section 4.1. The results refer to two different turbine inlet temperature levels, 550 ◦C and 700 ◦C. The flow exergy of each cycle station (𝐸) have been expressed taking as reference the exergy at cycle station 1 (𝐸1=0), for each combination of cycle layout/TIT. In this regard, cycle stations refers to Fig. 1. Renewable Energy 199 (2022) 1606–1628 1625 P. Rodríguez-deArriba et al. Table A.8 Heat & mass balance of Recompression cycle with pure CO2. Two temperature levels are considered, cycle stations refers to Fig. 1a. Cycle stations T [◦C] P [bar] 𝑚 [kg/s] h [kJ/kg] s [kJ/kg K] E [kJ/kg] 𝜌[kg/m3] Z [-] TIT=550 ◦C 1 50.0 105.3 999.1 367.0 1.52 0.0 450.0 0.38 2 96.7 250.0 999.1 397.0 1.53 27.0 604.0 0.59 3 182.9 246.3 999.1 558.0 1.93 64.0 346.0 0.83 4 182.9 246.3 1407.2 558.0 1.93 64.0 346.0 0.83 5 417.1 242.7 1407.2 867.0 2.48 200.0 183.0 1.02 6 550.0 239.1 1407.2 1032.0 2.70 296.0 147.0 1.04 7 451.1 108.5 1407.2 923.0 2.71 183.0 79.0 1.01 8 187.9 107.5 1407.2 615.0 2.19 40.0 137.0 0.90 9 101.7 106.4 1407.2 502.0 1.91 12.0 203.0 0.74 10 182.9 246.3 408.1 558.0 1.93 64.0 346.0 0.83 TIT=700 ◦C 1 50.0 102.2 752.1 377.0 1.55 0.0 412.0 0.41 2 102.3 250.0 752.1 409.0 1.56 29.6 578.0 0.61 3 193.4 246.3 752.1 574.0 1.96 69.8 330.0 0.85 4 193.4 246.3 1059.3 574.0 1.96 69.8 330.0 0.85 5 549.5 242.7 1059.3 1032.0 2.70 296.7 150.0 1.04 6 700.0 239.1 1059.3 1222.0 2.91 419.6 123.0 1.05 7 586.1 105.3 1059.3 1086.0 2.93 280.3 64.0 1.02 8 198.4 104.3 1059.3 629.0 2.22 43.5 128.0 0.91 9 107.3 103.3 1059.3 513.0 1.95 12.8 188.0 0.77 10 193.3 246.3 307.2 574.0 1.96 69.8 330.0 0.85 Table A.9 Resume of exergy balance by components. The results, expressed in MW, refers to Recompression cycle with pure CO2. Two temperature levels are considered, cycle stations refers to Fig. 1a. Cycle components Cycle stations TIT = 550 ◦C TIT = 700 ◦C 𝐸𝐹𝐸𝑃𝐸𝐿𝐸𝐷𝜖𝑘[%] 𝐸𝐹𝐸𝑃𝐸𝐿𝐸𝐷𝜖𝑘[%] Compressor 1–2 30.06 27.26 0.00 2.81 90.67 24.55 22.29 0.00 2.26 90.80 Recompressor 9–10 23.17 21.41 0.00 1.76 92.41 18.91 17.50 0.00 1.40 92.58 Turbine 6–7 158.43 153.41 0.00 5.02 96.83 147.51 143.55 0.00 3.96 97.32 Low temp. recuperator 2–3/8–9 39.87 37.02 0.00 2.85 92.85 32.50 30.20 0.00 2.30 92.91 Mixer 3–4–10 90.52 90.52 0.00 0.00 100.00 73.91 73.91 0.00 0.00 100.00 High temp. recuperator 4–5/7–8 201.50 190.63 0.00 10.87 94.61 250.90 240.38 0.00 10.51 95.81 Primary heat exchanger 5–6 147.25 135.31 0.00 11.94 91.89 138.35 130.16 0.00 8.19 94.08 Heat rejection unit 9–1 11.84 0.00 0.00 11.84 – 9.62 0.00 0.00 9.62 – Table A.10 Heat & mass balance of Partial Cooling cycle with pure CO2. Two temperature levels are considered, cycle stations refers to Fig. 1b. Cycle stations T [◦C] P [bar] 𝑚 [kg/s] h [kJ/kg] s [kJ/kg K] E [kJ/kg] 𝜌[kg/m3] Z [-] TIT=550 ◦C 1 50.0 112.2 604.8 349.0 1.46 0.0 524.0 0.35 2 87.0 250.0 604.8 375.0 1.47 23.4 651.0 0.56 3 156.2 246.3 604.8 515.0 1.83 51.0 395.0 0.77 4 156.2 246.3 1008.0 515.0 1.83 50.9 395.0 0.77 5 360.9 242.7 1008.0 797.0 2.37 162.0 203.0 1.00 6 550.0 239.1 1008.0 1032.0 2.70 295.1 147.0 1.04 7 409.2 75.3 1008.0 879.0 2.72 136.1 58.0 1.00 8 161.2 74.5 1008.0 598.0 2.21 14.6 100.0 0.90 9 92.0 73.8 1008.0 514.0 2.00 −3.8 133.0 0.80 10 50.0 73.0 1008.0 449.0 1.81 −9.7 185.0 0.65 11 86.9 113.3 1008.0 470.0 1.82 9.0 251.0 0.66 12 156.2 246.3 403.2 515.0 1.83 50.9 395.0 0.77 TIT=700 ◦C 1 50.0 111.5 423.7 351.0 1.47 0.0 518.0 0.35 2 87.7 250.0 423.7 377.0 1.48 23.7 647.0 0.57 3 175.6 246.3 423.7 547.0 1.90 60.1 358.0 0.81 4 175.6 246.3 718.2 547.0 1.90 60.1 358.0 0.81 5 474.9 242.7 718.2 938.0 2.58 239.6 166.0 1.03 6 700.0 239.1 718.2 1222.0 2.91 418.4 123.0 1.05 7 524.5 64.7 718.2 1016.0 2.93 205.9 43.0 1.01 8 180.6 64.0 718.2 624.0 2.30 14.1 80.0 0.93 9 92.7 63.4 718.2 523.0 2.05 −9.7 110.0 0.83 10 50.0 62.8 718.2 465.0 1.88 −15.3 145.0 0.71 11 101.1 112.7 718.2 495.0 1.89 12.6 220.0 0.72 12 175.6 246.3 294.4 547.0 1.90 60.1 358.0 0.81 Renewable Energy 199 (2022) 1606–1628 1626 P. Rodríguez-deArriba et al. Table A.11 Resume of exergy balance by components. The results, expressed in MW, refers to Partial Cooling cycle with pure CO2. Two temperature levels are considered, cycle stations refers to Fig. 1b. Cycle components Cycle stations TIT = 550 ◦C TIT = 700 ◦C 𝐸𝐹𝐸𝑃𝐸𝐿𝐸𝐷𝜖𝑘[%] 𝐸𝐹𝐸𝑃𝐸𝐿𝐸𝐷𝜖𝑘[%] Compressor 1–2 15.63 14.13 0.00 1.50 90.42 11.09 10.03 0.00 1.06 90.44 Recompressor 11–12 18.40 16.92 0.00 1.48 91.95 15.15 13.98 0.00 1.17 92.29 Precompressor 10–11 20.85 18.85 0.00 2.00 90.42 22.05 20.01 0.00 2.03 90.77 Turbine 6–7 160.34 154.95 0.00 5.39 96.64 152.65 148.23 0.00 4.42 97.11 Low temp. recuperator 2–3/8–9 18.46 16.68 0.00 1.77 90.39 17.13 15.43 0.00 1.70 90.08 Mixer 3–4–12 51.36 51.36 0.00 0.00 100.00 43.15 43.15 0.00 0.00 100.00 High temp. recuperator 4–5/7–8 122.47 111.98 0.00 10.49 91.44 137.71 128.93 0.00 8.78 93.62 Primary heat exchanger 5–6 150.05 134.15 0.00 15.90 89.40 139.70 128.44 0.00 11.26 91.94 Heat rejection unit ♯1 9–10 6.02 0.00 0.00 6.02 – 4.00 0.00 0.00 4.00 – Heat rejection unit ♯2 11–1 5.43 0.00 – 5.43 0.00 5.34 0.00 0.00 5.34 – Table A.12 Heat & mass balance of Precompression cycle with 85%CO2–15%C6F6. Two temperature levels are considered, cycle stations refers to Fig. 1d. Cycle stations T [◦C] P [bar] 𝑚 [kg/s] h [kJ/kg] s [kJ/kg K] E [kJ/kg] 𝜌[kg/m3] Z [-] TIT=550 ◦C 1 50.0 77.8 1152.8 −7488.0 −1.48 0.0 894.0 0.21 2 71.1 250.0 1152.8 −7468.0 −1.47 18.0 1004.0 0.57 3 211.0 246.3 1152.8 −7238.0 −0.91 72.0 495.0 0.81 4 401.5 242.7 1152.8 −6973.0 −0.44 191.0 281.0 1.00 5 550.0 239.1 1152.8 −6774.0 −0.17 306.0 217.0 1.05 6 437.7 61.1 1152.8 −6898.0 −0.16 178.0 68.0 0.99 7 215.9 60.5 1152.8 −7163.0 −0.60 52.0 108.0 0.90 8 237.3 79.3 1152.8 −7146.0 −0.60 68.0 136.0 0.89 9 87.2 78.5 1152.8 −7376.0 −1.15 8.0 309.0 0.55 TIT=700 ◦C 1 50.0 77.8 878.5 −7488.0 −1.48 0.0 894.0 0.21 2 71.1 250.0 878.5 −7468.0 −1.47 18.2 1004.0 0.57 3 237.9 246.3 878.5 −7198.0 −0.83 86.8 444.0 0.85 4 534.0 242.7 878.5 −6796.0 −0.20 293.4 225.0 1.05 5 700.0 239.1 878.5 −6570.0 0.06 439.0 180.0 1.07 6 572.3 56.9 878.5 −6728.0 0.07 276.3 52.0 1.01 7 242.9 56.3 878.5 −7130.0 −0.53 61.7 93.0 0.92 8 270.4 79.3 878.5 −7106.0 −0.53 84.2 124.0 0.92 9 87.1 78.5 878.5 −7376.0 −1.15 8.4 309.0 0.55 Table A.13 Resume of exergy balance by components. The results, expressed in MW, refers to Precompression cycle with pure 85%CO2–15%C6F6. Two temperature levels are considered, cycle stations refers to Fig. 1d. Cycle components Cycle stations TIT = 550 ◦C TIT = 700 ◦C 𝐸𝐹𝐸𝑃𝐸𝐿𝐸𝐷𝜖𝑘[%] 𝐸𝐹𝐸𝑃𝐸𝐿𝐸𝐷𝜖𝑘[%] Pump 1–2 23.59 21.01 0.00 2.57 89.09 17.98 16.02 0.00 1.96 89.09 Precompressor 7–8 19.93 18.58 0.00 1.34 93.25 21.02 19.69 0.00 1.34 93.64 Turbine 4–5 148.30 143.52 0.00 4.79 96.77 142.90 139.00 0.00 3.90 97.27 Low temp. recuperator 2–3/8–9 68.72 61.95 0.00 6.77 90.14 66.59 60.21 0.00 6.38 90.41 High temp. recuperator 3–4/6–7 144.87 137.62 0.00 7.25 95.00 188.52 181.53 0.00 6.98 96.30 Primary heat exchanger 4–5 144.59 132.37 0.00 12.23 91.54 136.19 127.91 0.00 8.28 93.92 Heat rejection unit 9–1 9.64 0.00 0.00 9.64 – 7.34 0.00 0.00 7.34 – Table A.14 Heat & mass balance of Recuperated Rankine cycle with 83%CO2–17%TiCl4. Two temperature levels are considered, cycle stations refers to Fig. 1c. Cycle stations T [◦C] P [bar] 𝑚 [kg/s] h [kJ/kg] s [kJ/kg K] E [kJ/kg] 𝜌[kg/m3] Z [-] TIT=550 ◦C 1 50.0 96.2 1575.3 −6837.0 −1.22 0.0 1129.0 0.22 2 63.4 250.0 1575.3 −6822.0 −1.22 13.0 1189.0 0.52 3 411.7 246.3 1575.3 −6376.0 −0.28 167.0 303.0 0.98 4 550.0 242.7 1575.3 −6237.0 −0.10 247.0 236.0 1.04 5 449.6 98.1 1575.3 −6316.0 −0.09 166.0 114.0 0.98 6 71.9 97.1 1575.3 −6762.0 −1.00 4.0 490.0 0.48 TIT=700 ◦C 1 50.0 96.2 1239.9 −6837.0 −1.22 0.0 1129.0 0.22 2 63.4 250.0 1239.9 −6822.0 −1.22 13.4 1189.0 0.52 3 541.3 246.3 1239.9 −6246.0 −0.11 242.2 242.0 1.03 4 700.0 242.7 1239.9 −6090.0 0.07 343.0 195.0 1.06 5 589.3 98.1 1239.9 −6185.0 0.08 244.6 93.0 1.01 6 71.9 97.1 1239.9 −6762.0 −1.00 4.2 490.0 0.48 Renewable Energy 199 (2022) 1606–1628 1627 P. Rodríguez-deArriba et al. Table A.15 Resume of exergy balance by components. The results, expressed in MW, refers to Recuperated Rankine cycle with pure 83%CO2–17%TiCl4. Two temperature levels are considered, cycle stations refers to Fig. 1c. Cycle components Cycle stations TIT = 550 ◦C TIT = 700 ◦C 𝐸𝐹𝐸𝑃𝐸𝐿𝐸𝐷𝜖𝑘[%] 𝐸𝐹𝐸𝑃𝐸𝐿𝐸𝐷𝜖𝑘[%] Pump 1–2 23.76 21.14 0.00 2.62 88.97 18.70 16.64 0.00 2.06 88.97 Turbine 4–5 127.82 123.76 0.00 4.06 96.83 121.97 118.70 0.00 3.26 97.32 Heat recuperator 2-3/5–6 254.95 241.44 0.00 13.50 94.70 298.10 283.72 0.00 14.39 95.17 Primary heat exchanger 3–4 138.08 126.77 0.00 11.31 91.81 132.93 124.91 0.00 8.02 93.97 Heat rejection unit 6–1 6.59 0.00 0.00 6.59 – 5.20 0.00 0.00 5.20 – Table A.16 Heat & mass balance of Recompression cycle with 80%CO2–20%SO2. Two temperature levels are considered, cycle stations refers to Fig. 1e. Cycle stations T [◦C] P [bar] 𝑚 [kg/s] h [kJ/kg] s [kJ/kg K] E [kJ/kg] 𝜌[kg/m3] Z [-] TIT=550 ◦C 1 50.0 79.1 665.3 −8008.0 −1.15 0.0 781.0 0.18 2 74.3 250.0 665.3 −7984.0 −1.14 21.0 846.0 0.49 3 187.3 246.3 665.3 −7763.0 −0.58 67.0 398.0 0.78 4 187.4 246.3 1073.0 −7763.0 −0.58 67.0 398.0 0.78 5 372.8 242.7 1073.0 −7524.0 −0.14 168.0 221.0 0.98 6 550.0 239.1 1073.0 −7316.0 0.15 286.0 161.0 1.04 7 415.4 81.5 1073.0 −7447.0 0.16 151.0 69.0 0.99 8 192.3 80.7 1073.0 −7686.0 −0.26 43.0 113.0 0.89 9 81.1 79.9 1073.0 −7824.0 −0.60 11.0 204.0 0.64 10 187.4 246.3 407.8 −7763.0 −0.58 68.0 398.0 0.78 TIT=700 ◦C 1 50.0 79.1 512.8 −8008.0 −1.15 0.0 781.0 0.18 2 74.3 250.0 512.8 −7984.0 −1.14 21.1 846.0 0.49 3 187.3 246.3 512.8 −7763.0 −0.58 67.5 398.0 0.78 4 187.3 246.3 827.1 −7763.0 −0.58 67.5 398.0 0.78 5 499.3 242.7 827.1 −7376.0 0.07 250.9 176.0 1.03 6 700.0 239.1 827.1 −7140.0 0.34 400.7 134.0 1.06 7 550.6 81.5 827.1 −7299.0 0.36 237.6 57.0 1.01 8 192.3 80.7 827.1 −7686.0 −0.26 42.6 113.0 0.89 9 81.1 79.9 827.1 −7824.0 −0.60 11.3 204.0 0.64 10 187.4 246.3 314.3 −7763.0 −0.58 67.5 398.0 0.78 Table A.17 Resume of exergy balance by components. The results, expressed in MW, refers to Recompression cycle with pure 80%CO2–20%SO2. Two temperature levels are considered, cycle stations refers to Fig. 1e. Cycle components Cycle stations TIT = 550 ◦C TIT = 700 ◦C 𝐸𝐹𝐸𝑃𝐸𝐿𝐸𝐷𝜖𝑘[%] 𝐸𝐹𝐸𝑃𝐸𝐿𝐸𝐷𝜖𝑘[%] Pump 1–2 15.78 14.07 0.00 1.71 89.15 12.16 10.85 0.00 1.32 89.15 Recompressor 9–10 24.76 22.90 0.00 1.86 92.49 19.08 17.64 0.00 1.43 92.49 Turbine 6–7 145.30 140.46 0.00 4.84 96.67 134.95 131.17 0.00 3.78 97.20 Low temp. recuperator 2–3/8–9 33.56 30.82 0.00 2.74 91.84 25.87 23.76 0.00 2.12 91.82 Mixer 3–4–10 72.42 72.41 0.00 0.00 100.00 55.81 55.81 0.00 0.00 100.00 High temp. recuperator 4–5/7–8 116.07 108.18 0.00 7.90 93.20 161.22 151.73 0.00 9.49 94.12 Primary heat exchanger 5–6 140.63 126.52 0.00 14.11 89.97 133.65 123.88 0.00 9.77 92.69 Heat rejection unit 9–1 7.55 0.00 0.00 7.55 – 5.82 0.00 0.00 5.82 – References [1] F. Crespi, D. Sánchez, G.S. Martínez, T. Sánchez-Lencero, F. 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