Thermodynamic Assessment and Optimisation of Supercritical and Transcritical Power Cycles Operating on CO2 Mixtures by Means of Artificial Neural Networks

1 The 7th International Supercritical CO2 Power Cycles Symposium February 21 – 24, 2022, San Antonio, Texas Paper 188 Thermodynamic assessment and optimisation of supercritical and transcritical power cycles operating on CO2 mixtures by means of Artificial Neural Networks Pablo Rodríguez de Arriba PhD Student University of Seville Seville, Spain Francesco Crespi* Lecturer University of Seville Seville, Spain David Sánchez Full Professor University of Seville Seville, Spain Pablo Rodríguez de Arriba is a Ph.D. Student in Energy Engineering at the University of Seville. He obtained a Master’s Degree in Industrial Engineering in 2020 and joined Prof. David Sánchez’s Research Group as Research Assistant since then. His thesis is focused on the techno-economic optimisation and integration of innovative CO2-based technology for Concentrated Solar Power applications, within the framework of the SCARABEUS project. His areas of interest also include thermodynamics, heat transfer, non-conventional working fluids, renewable energies, desalination, WHR and refrigeration. Francesco Crespi is a lecturer in Fluid Mechanics at the University of Seville, where he currently works at the Department of Energy as a postdoctoral research associate. Dr. Crespi started his research activity at the beginning of 2015 after completing a Double Degree in Industrial Engineering from University of Seville and Politecnico of Milan. His research activity at the moment is focused on numerical simulation of sCO2 power cycles, alternative cycle layouts for this technology and analysis of possible dopant candidates for CO2 blends. David Sánchez is a Full Professor in Energy Systems and Fluid Machinery at the University of Seville, where he currently works at the Department of Energy Engineering. He has fifteen years’ experience in the field of stationary power generation using turbomachinery in combination with novel cycle concepts that can introduce step-changes in the Concentrated Solar Power industry, thus enabling higher efficiencies and lower electricity costs. He has conducted research to integrate the sCO2 power cycle into CSP and WHR applications for more than ten years, with both private and public funding at the fundamental and applied levels. ABSTRACT Closed supercritical and transcritical power cycles operating on Carbon Dioxide have proven to be a promising technology for power generation and, as such, they are being researched by numerous international projects today. Despite the advantageous features of these cycles enabling very high efficiencies in intermediate temperature applications, the major shortcoming 2 of the technology is a strong dependence on ambient temperature; in order to perform compression near the CO2 critical point (31ºC), low ambient temperatures are needed. This is particularly challenging in Concentrated Solar Power applications, typically found in hot, semi-arid locations. To overcome this limitation, the SCARABEUS project explores the idea of blending raw carbon dioxide with small amounts of certain dopants in order to shift the critical temperature of the resulting working fluid to higher values, hence enabling gaseous compression near the critical point or even liquid compression regardless of a high ambient temperature. Different dopants have been studied within the project so far (i.e. C6F6, TiCl4 and SO2) but the final selection will have to account for trade-offs between thermodynamic performance, economic metrics and system reliability. Bearing all this in mind, the present paper deals with the development of a non-physics-based model using Artificial Neural Networks (ANN), developed using Matlab’s Deep Learning Toolbox, to enable SCARABEUS system optimisation without running the detailed – and extremely time consuming – thermal models, developed with Thermoflex and Matlab software. In the first part of the paper, the candidate dopants and cycle layouts are presented and discussed, and a thorough description of the ANN training methodology is provided, along with all the main assumptions and hypothesis made. In the second part of the manuscript, results confirms that the ANN is a reliable tool capable of successfully reproducing the detailed Thermoflex model, estimating the cycle thermal efficiency with a Root Mean Square Error lower than 0.2 percentage points. Furthermore, the great advantage of using the Artificial Neural Network proposed is demonstrated by the huge reduction in the computational time needed, up to 99% lower than the one consumed by the detailed model. Finally, the high flexibility and versatility of the ANN is shown, applying this tool in different scenarios and estimating different cycle thermal efficiency for a great variety of boundary conditions. INTRODUCTION sCO2 technology has gained increasing interest among in the scientific community in the last twenty years, and is now the focus of several international research projects for very different applications, such as Concentrated Solar Power (SCARABEUS [1], COMPASSCO2 [2]), fossil fuels (sCO2 flex [3]), heat removal from nuclear plants (sCO2-HeRo [4], sCO2-4-NPP [5]) and Waste Heat Recovery (I-ThERM [6] , CO2OLHEAT [7]). Among the virtues of sCO2 power cycles stand out their high thermal efficiency, low footprint in comparison to conventional steam and gas turbines cycles and operational flexibility [8]. The major drawback of this technology is that low ambient temperatures are needed in order to perform compression near the critical point (31ºC), thus taking advantage of a low compressibility factor. Nevertheless, this is particularly difficult to obtain considering in Concentrated Solar Power (CSP) applications, which are typically situated in hot, semi-arid locations. An alternative solution to overcome this limitation is proposed by SCARABEUS project, whose main concept is to investigate the possibility of blending raw carbon dioxide with certain dopants in order to increase the critical temperature of the resulting working fluid, enabling its condensation at high ambient temperature and thus enhancing cycle thermal performance. Three different dopants have been studied in the framework of SCARABEUS project so far – Hexafluorobenzene (C6F6), Titanium tetrachloride (TiCl4) and Sulphur Dioxide (SO2) – and the main outcomes regarding the identification of the best performing cycle layout when each one of these dopants is employed has been already disclosed in the public domain [9], [10]. Nevertheless, the final selection will have to account for trade-offs between thermodynamic performance, economic metrics and system reliability: in other words, a thorough overall system optimization. 3 System Optimization of power plants is a wide task with multiple scopes, ranging from power block thermodynamic Optimization, usually aimed to maximize thermal efficiency, to technoeconomic optimization, with the objective of minimizing the Levelised Cost of Electricity (LCoE) of the entire plant. Moreover, other figures of merits such as environmental or social indicators can be taken into account besides economic metrics in order to perform a multi-objective optimization of the technology (Techno-economic-environmental Optimization). Simulation of power cycles operated near the critical point is highly time-consuming. Convergence is low due to the extreme non-linearity of fluid properties and heat balances [11]. For example, heat exchangers have to be divided in sub-sections in order to account for the high variation of heat capacity [12]. Computational time of such systems are in the order of 101 seconds [13]. An optimization routine to find the set of operational variables maximizing thermal efficiency requires around 100 iterations, therefore, 103 seconds for a single operating point optimization. Annual calculations require 8760 simulations of more complex models that account for off-design performance and operational strategies. This number can be reduced to a few hundred by mapping the cycle off-design performance as a function of the ambient temperature, HTF temperature and HTF mass flow rate, for example, as requested by System Advisor Model. Even if the computational time remains in the order of 101 seconds (although it is very likely to grow due to the increase in the number of nested iteration loops), a single yearly simulation would last 103-104 seconds. What is more, different configurations –in the order of thousands [14]- have to be studied in order to minimize the LCoE. If multiple objective functions were to be considered, generating the Pareto Front would require the use of Metaheuristic Algorithms (e.g., genetic algorithms) and between 5000 and 10000 yearly simulations. In summary, directly optimizing the detailed model leads to prohibitive simulation times. Bearing all this in mind, the present manuscript deals with the creation and development of a surrogate model based on Artificial Neural Networks, which enables to reduce the optimization time by various orders of magnitude [14]–[16]. In this context, it is worth noting the novelty of the proposed approach, which results to be different from other similar investigations published in literature. In [17], [18] the authors studied the Recompression Cycle with sCO2 for nuclear applications. In these studies, a Parametric Optimization is performed, meaning that the system has been first directly optimized by means of a Genetic Algorithm for different conditions and the results of such optimization constitutes the training set provided to the Neural Network. In the present work, the ANN will completely replace the detailed model and the optimization will be performed over the ANN and not on the detailed model. A similar investigation is presented in of [19], where a Neural Network is trained with data obtained with a detailed model for different boundary conditions. Nevertheless, the system thereby studied was a Recuperated Rankine Cycle for low-grade Waste Heat Recovery (TIT < 100ºC) running on different working fluids. Thus, to the authors knowledge, this is the first time that ANNs are used as surrogate models for the optimization of CO2-based power cycles for Concentrated Solar Power applications. The structure of the manuscript is the following: the first part introduces three dopants studied within the SCARABEUS project, namely C6F6, TiCl4 and SO2, along with a brief discussion on the best-performing cycle layout for each working fluid. The second part deals with the development of a comprehensive methodology for the optimization of complex, time-consuming energy models using ANN and applies it to the analysis of sCO2-based power cycles. The computational time invested in generating the training set and training the surrogate model is compensated with extreme flexibility. Finally, the results obtained with the ANN are compared with the ones achieved by the detailed model, developed with the commercial software Thermoflex, showing the reliability of the proposed ANN, which is proven to be capable of reproducing the results of the detailed model with a great accuracy but with an extremely lower computational time needed. 4 CANDIDATE DOPANTS As previously commented in the introduction, three different candidate dopants are considered in this work - C6F6, TiCl4 and SO2 – and their main thermophysical properties are provided in Table 1. It can be easily noticed that the critical temperatures of these compounds are considerably higher than the one of pure CO2 (186ºC for C6F6, 190ºC for TiCl4 and 64ºC for SO2), being this the key feature that enables condensation of the resulting mixtures at temperatures equal or higher than 50ºC. A discussion regarding the safety issues related to these dopants, based on the NFPA 704 standards, can be found in previous papers by the same authors [9]. A special comment must be made on dopant thermal stability, currently being investigated by other partners of SCARABEUS consortium (University of Brescia and Politecnico di Milano). The complete set of results of this research activity will be disclosed in the near future by these institutions and cannot be hereby discussed due to confidentiality issue, but the main conclusions are presented in Table 1. On one hand, very promising results have been obtained for TiCL4, for which thermal degradation is observed only for temperatures above 700ºC. Almost no preliminary results have been obtained for CO2 and SO2, which are currently being tested, but different references from literature depict a very promising scenario, with foreseen thermal stability for temperatures higher than 700ºC [20]. On the other hand, the same cannot be said for C6F6, which shows some signs of thermal degradation for temperatures above 600/625ºC. Nevertheless, it is worth noting that this is merely a preliminary results and this threshold value needs further investigation to be confirmed. For this reason, in the present paper TIT values higher than 625ºC are taken into account, in order not to limit the analysis and compare the ANN reliability when employed to foresee the thermal performance obtained with the three dopants with the same set of boundary conditions. Nonetheless, if C6F6 thermal stability will be confirmed to be limited to 625ºC, this would be the maximum TIT level to be considered for technoeconomic optimization, and this would undoubtedly be an important drawback for this dopant. Table 1. Thermo-physical properties of pure CO2, C6F6, TiCl4 and SO2 CO2 C6F6 TiCl4 SO2 MW [kg/kmol] 44.01 186.06 189.69 64.06 Tcr [ºC] 31.06 243.58 364.85 157.60 Pcr [bar] 73.83 32.73 46.61 78.84 Thermal stability Up to 700ºC Up to 625ºC >700ºC >700ºC BIP - 0.16297 - 0.0003951·T 0.0704 0.0242 Thermo-physical properties of the mixtures have been obtained with Aspen v11 [21], employing Peng-Robinson’s Equation of State with Van der Walls mixing rule. The binary interaction parameters (BIP, see last row in Table 1). have been calibrated on experimental data available in Aspen library. Further information regarding properties estimation can be found in previous papers by SCARABEUS Consortium [9], [22], [23] . The critical loci of the three mixtures are presented in Figure 1, highlighting the range of molar fraction of dopant employed in the present study: 10%-20% for C6F6, 15%-25% for TiCl4 and 20-40% for SO2. These candidate ranges of dopant molar fraction were identified in previous works by the authors, and are based on a twofold criterion: i) maximize cycle thermal efficiency, ii) guarantee a gap in the order of 30ºC between minimum cycle temperature and mixture critical temperature, in order not to operate compression in the extreme vicinity of the critical point. 5 Figure 1. Critical Loci of SCARABEUS mixtures. Candidate ranges of dopant molar fraction are indicated by markers. CANDIDATE CYCLE LAYOUTS Three different candidate cycles are considered for SCARABEUS mixtures, previously identified in a work by the authors by means of a thorough screening of sCO2 cycle layout proposed in literature [10]: the simple recuperated (hereby called Recuperated Rankine), the Precompression and the Recompression cycle, whose layouts are presented in Figure 2. For the three dopants considered, the optimum combinations of cycle layout and working fluid, as identified in previous works for a minimum cycle temperature of 50ºC (SCARABEUS reference case), are: Precompression with 15% molar fraction of C6F6, Recuperated Rankine with 15% of TiCl4 and Recompression with 30% of SO2. Interestingly, these three configurations were originally proposed by Gianfranco Angelino in its seminal work [24]–[26], in a very similar transcritical embodiment as the one considered in the present work. The transcritical nature of SCARABEUS cycles, to which from now on we will add the adjective "transcritical" to differentiate them from the typical supercritical embodiment of pure CO2 cycles, is due to the fact that the addition of certain dopants enables the condensation of the working fluid for temperature levels higher than 31ºC (critical temperature of CO2). This fact, besides the obvious need for a main pump and a condenser instead of a main compressor and cooler, leads to an extremely interesting side-effect: in transcritical cycles, the main pump inlet pressure is no longer a free/optimizable parameter, but it is constrained by the minimum cycle temperature through the bubble point (condensation process). Actually, the condensing pressure can indeed be changed by means of an innovative degree of freedom - the molar fraction of dopant – but at the expense of considering different thermodynamic behavior of the mixture and, from a practical point of view, changing the working fluid. On the contrary, for supercritical cycles, that pressure level is a further degree of freedom for optimization, which allows to change the heat capacity of the low pressure stream – in order to balance the heat capacities in the heat regeneration - at the expense of penalizing specific work. 6 Figure 2. Candidate cycles for SCARABEUS concept Bearing this in mind, the same cycle layout can behave in a very dissimilar way depending if it is considered in a transcritical or supercritical embodiment. In order to fully appreciate these different behaviors, a series of crucial cycle parameters which plays a fundamental role in its thermodynamic optimization are hereby identified and discussed, and their effects are resumed in Table 2. It is worth remarking the fact that these parameters will be part of the complete set of input variables considered in the ANN (see next sections of the paper). The Main Compressor Inlet Pressure allows to change the proximity to the critical point in supercritical power cycles. This allows to balance the benefits (low compressibility factor, higher Pressure Ratio) and disadvantages (irreversibilities in the heat regeneration) of working near the critical point. In transcritical cycles, this pressure level is fixed by the cycle temperature through the bubble point. The molar composition has a similar but conceptually different impact: instead of varying main pump inlet conditions, it allows to shift the critical point itself. Additionally, different composition of the same dopant has different condensing pressure for the same bubble temperature, thus having an effect on the Pressure Ratio. The split-compression works similarly in both transcritical and supercritical cycles: at the expense of a lower specific work, the heat regeneration is improved by reducing the heat capacity of the high pressure stream. The addition of a Pre-compressor in transcritical configurations permits to overcome the limitation imposed by pump inlet pressure on turbine exhaust, hence increasing cycle specific work. On the contrary, in supercritical configurations, this cycle modification causes a rise in main compressor inlet pressure, resulting in an enhanced heat recuperation process (balancing heat capacities, reducing internal irreversibilities). This leads to a rise in cycle thermal efficiency, but with an overall detrimental effect in terms of specific work. In fact, the direct consequence is that main compressor inlet is shifted away from the critical point, resulting in a significant rise in compression power. Finally, the effect of Maximum Cycle Pressure is very similar for both transcritical and supercritical embodiments, and can be optimized in order to maximize either thermal efficiency or specific work. 7 Table 2. Comparison between the degrees of freedom of transcritical and supercritical power cycles Transcritical Supercritical Main Compressor (Pump) Inlet pressure Set by Minimum Cycle Temperature through the bubble point (condensation process). Further degree of freedom: compromise between cycle specific work and recuperator performance Molar Composition Shift in critical point of mixture: affects to both thermo-dynamic props and pump inlet pressure Only pure fluids are considered for supercritical cycles. Split compression factor Improves internal heat recovery and harms specific work. Improves internal heat recovery and harms specific work. Precompressor pressure ratio Overcomes the limitation on turbine exhaust pressure, increasing both thermal efficiency and specific work. Beneficial effect on thermal efficiency, detrimental for specific work Maximum Cycle Pressure Affects specific work and available energy for regeneration at turbine exhaust Affects specific work and available energy for regeneration at turbine exhaust COMPUTATIONAL ENVIRONMENT In order to allow an easier combination with the ANN, cycle simulations have been completed with various in-house codes written in Matlab R2021a [27], thoroughly validated with the results obtained with Thermoflex [28] and already presented in previous works by the same authors [9], [10]. As afore-commented, the layouts considered for transcritical power cycles (i.e., SCARABEUS working fluids) are the Recuperated Rankine Cycle, Transcritical Precompression Cycle and the Transcritical Recompression Cycle. Moreover, two well-known pure sCO2 cycles have also been studied for sake of comparison: Recompression Cycle and Partial Cooling Cycle, considered as representative for pure sCO2 technology. The same set of boundary conditions has been employed for both pure and blended configurations, and it is hereby provided in Table 3. On the other hand, different values of Turbine Inlet Temperature, Minimum Cycle Temperature and Maximum Cycle Pressure are taken into account, as specified in Table 4. Table 3. Complete set of fixed boundary conditions Gross Output [MW] ηis,T [%] ηis,C [%] ηis,P [%] 100 93 89 88 ΔTmin [ºC] ΔPPHX [%] ΔPHRU [%] ΔPREC [%] low/high P side 5 1.5 1.0 1.0/1.5 Thermodynamic properties of the candidate blends, previously obtained with Aspen software, have been introduced in Matlab codes by means of look-up tables for fixed molar compositions: 8 for C6F6, dopant molar fractions from 10-20% with a step of 1%; for TiCl4, from 15-25% with 1% step; and for SO2 from 20-40% with 2% step. ARTIFICIAL NEURAL NETWORK Artificial Neural Networks have been modelled using Matlab’s Deep Learning Toolbox [29]. The training set have been generated using the Matlab codes. The ranges of the various parameters sampled for the generation of the training sets are shown in Table 4. Minimum Cycle Temperature accounts for different locations (ambient temperature) from mild (35ºC, lower bound) to hot (60ºC, upper bound) climates. Turbine Inlet Temperature refers to both state-of- the-art of CSP plant (550ºC, lower bound) as well as advanced CSP receiver temperatures (700ºC, upper bound). Maximum Cycle Pressure stands as a technological boundary condition for current materials (250 bar, lower bound) and advanced material constraints (350 bar, upper bound). The remaining ANN training set limitations (e.g. Precompressor pressure ratio, split flow factor 1 etc.) have been fixed considering the results obtained in previous research activities by the authors [9]. Table 4. Ranges of the various parameters sampled during the generation of the ANN training sets Lower bound Upper bound System Minimum Cycle Temperature [ºC] 35 60 All Turbine Inlet Temperature [ºC] 550 800 All Maximum Cycle Pressure [bar] 250 350 All Molar fraction C6F6 [%] 10 20 Transcritical Precompression with CO2-C6F6 Molar fraction TiCl4 [%] 15 25 Recuperated Rankine with CO2-TiCl4 Molar fraction SO2 [%] 20 40 Transcritical Recompression with CO2-SO2 Precompressor PR [-] 1.0 1.6 Transcritical Precompression with CO2-C6F6 Split-flow factor [-] 0 0.6 Transcritical Recompression with CO2-SO2 Main Compressor PR [-] 1.5 4 sCO2 Recompression / Partial Cooling Precompressor PR [-] 1.0 2.5 sCO2 Partial Cooling Split-flow factor [-] 0 0.6 sCO2 Recompression 1 Note that split-flow factor of a Recompression cycle (either transcritical or supercritical) refers to the fraction of working fluid that flows through the re-compressor. Thus, if this value is set to zero, the Recompression cycle is practically transformed into a Simple recuperated cycle. 9 An Artificial Neural Network (also called Neural Network, ANN) is a mathematical model inspired by the working of a biological brain. A brain is built form a massive number (more than 1011) of interconnected units called neurons. The resulting structure is both capable of storing and processing information. To that end, the brain modified the arrangement of the neurons (connections can grow) and the strength of these links (called synapses). ANN cannot achieve such complexity but it resembles some of its key operating principles: (1) they are formed by a large number of simple units, (2) they can learn from the environment, and (3) the knowledge can be stored inside the network by modifying the weights of the connections. Artificial Neural Networks can be used in a broad range of applications fields from engineering to finance or even literature [30]. In this work, ANN are used to replicate the behavior of a physical model. This problem is called function approximation, meaning that the ANN is asked to create a mapping between the inputs and the targets, identifying the hidden dynamics underlying between them [31]. The fundamental unit of an ANN is the neuron (Figure 3). It is a mathematical element that receives, processes and transfers information. More specifically, it collects a vector of I inputs (x) and transforms it into the scalar y. To do so, neurons count on three elements. The synaptic connections collect all inputs and assign a weight to each one of them; the Adder sums up the weighted inputs and then add a threshold value called bias; and, finally, a Transfer (activation) function that transforms the output from the adder into the output of the neuron. The transfer function is chosen depending on the problem that wants to be solved, it can either be linear/nonlinear or discrete/continuous. The most important types are Threshold Functions (not used in function approximation but for pattern recognition), Linear Functions (the output is equal to the input) and Sigmoid Functions (S-shaped functions with two horizontal asymptotes). Figure 3. Neuron scheme Neural Network consists of multiple neurons connected between them. Neurons are organized in parallel forming a layer, while layers are arranged in series giving place to the network. Three types of layers are identified: Input layer, which does not transform the information in any way but distributes into the network; the Output layer, which produces the output of the network; and the Hidden layer(s), which are found between the Input and Output layers and are actually responsible of the computational power of ANN. The type of Neural Network studied for function approximation problems is the Multilayer Feedforwards Network. In this configuration, the information flows only in one direction, from the input layer to the output layer through the hidden layer(s). Moreover, the network will be fully-connected, meaning that the output from all the 16 Figure 7. Selection maps for Transcritical Recompression Cycle on CO2-SO2 at 250 bar (Pmax). Left figure refers to SO2 molar fraction; Right figure to Split flow factor. The Precompressor Pressure Ratio that maximizes thermal efficiency in the PrC CO2-C6F6 system increases with TIT and is inversely proportional to Tmin, with values from 1.25 to 1.55 (Figure 5 right). The split flow factor for the RC CO2-SO2 (see Figure 7 right) presents more indented borders, but this is mainly due to the small variation of this parameter in the whole range of boundary conditions considered (<0.02), meaning that its optimum value is barely affected by cycle operating conditions. To properly quantify the accuracy of the ANN predictions in these maps, two validations were performed. The first one (RMSE 1 in Table 8) refers to the RMSE of the predicted thermal efficiency with respect to the value obtained by the detailed model when simulated at the optimum design conditions predicted by the ANN (i.e., the values from the previous figures). Afterwards, the detailed models have been directly optimized for three levels of Turbine Inlet Temperature -550ºC, 625ºC and 700ºC- and multiple Minimum Cycle Temperatures –from 35ºC to 60ºC with a 2.5ºC step. The RMSE of the optimum thermal efficiency obtained by the detailed models and the thermal efficiency obtained by the ANNs were calculated (RMSE 2 in Table 8). Table 8. Validation with the detailed model of the optimum design points. RMSE in [%] System Architecture RMSE test RMSE 1 RMSE 2 PrC CO2-C6F6 [5] 0.122 0.05 0.04 RR CO2-TiCl4 [5] 0.171 0.14 0.12 RC CO2-SO2 [20] 0.12 0.18 0.2 RC sCO2 [30] 0.123 0.22 0.24 PC sCO2 [30] 0.119 0.23 0.3 A twofold conclusion can be drawn observing the trends of RMSE1 and RMSE2: firstly, both RMSE1 and RMSE2 result to be of the same order of magnitude, indicating that the optimum cases predicted by the ANN are in good accordance with the one obtained with the detailed 17 model (“real” optimum values); secondly, the error is extremely low for the three SCARABEUS systems – always below 0.2 percentage points (pp), and equal or below 0.05 pp for PrC CO2- C6F6 – and slightly higher for the sCO2 systems (0.2-0.3 p.p.). This circumstance confirms another observation previously made in this section, i.e. that the SCARABEUS transcritical systems seems to be easier to reproduce with the ANN than pure CO2 supercritical ones. Once again, it is worth noting that the RMSE of the test set alone is not representative of the real prediction capability of the network, and that a more complete and thorough analysis, considering different figures of merit (not only thermal efficiency) and/or alternative data division in set, should be addressed in the future to confirm these results. In spite of this fact, the extremely low RMSE obtained confirm the fact that the maps provided in Figure 5 to Figure 7 can be used to obtain the specifications required for the design of the different components of the cycle with an acceptable precision. In fact, the deviation in the prediction of the thermal efficiency can be considered as acceptable for real-case design scenarios, where a subsequent selection of standardized equipment would affect the optimum design point adding a higher uncertainty than that of the network. What is more, the interest in the ANN is further demonstrated if the computational time spent in the two cases is compared. Table 9 shows a comparison between the detailed and surrogate (ANN) models of the time spent during the optimization of SCARABEUS reference case (TIT 700ºC, Tmin 50ºC and Pmax 250 bar) for the five systems studied. The fast-speed evaluation of ANN enables to perform an optimization in less than five seconds, independently of the system considered. On the contrary, the computational time required for the optimization by means of the detailed model strongly depends on the system considered due to a twofold reason: on one hand, due the numerical complexity of the model (the Precompression Cycle is the harder); on the other hand, due to the method employed for the calculation of fluid properties (look-up tables employed for the CO2 mixtures are more time consuming that pure CO2 properties obtained by Refprop). Moreover, the quantitative values shown in the second column of Table 9 depends on the tolerance required for the energy balances or, in the case of the SCARABEUS working fluid, the size of the look-up table. In any case, the reduction in computational time brought by the use of the ANN is extremely clear, and ranges from 78% for Recuperated Rankine - the simplest layout - up to outstanding value of 99.8%, for the Transcritical Precompression with CO2-C6F6. Table 9. Time requirements [s] for the optimization of the reference SCARABEUS case (TIT 700ºC, Tmin 50ºC, Pmax 250 bar) for the detailed and surrogate (ANN) models. Detailed model ANN Time savings [%] PrC CO2-C6F6 1810.5 4.3 99.8 RR CO2-TiCl4 18.4 4.1 77.7 RC CO2-SO2 464.9 4.4 99.1 RC sCO2 148.9 4.4 97.0 PC sCO2 141.5 4.8 96.6 Moreover, further studies are performed over the trained ANN, proving the flexibility and reliability of this tool. Given that the ANN for the PrC CO2-C6F6 system was trained for Precompressor Pressure Ratio (PRPrC) from 1 to 1.6, the ANN of this system is a superstructure including the Recuperated Rankine cycle (when PRPrC = 1). In other words, the ANN originally 18 trained for a Transcritical Precompression cycle can be satisfactorily 2 employed to estimate, for a given dopant, the performance of a Recuperated Rankine. Similarly, considering the ANN trained for the Transcritical Recompression with CO2-SO2 mixture, this can be employed to reproduce a Recuperated Rankine if the split-flow factor is fixed to 0. Bearing this in mind, the thermal efficiency contour maps for this Recuperated-Rankine-simulator ANN have been obtained for the same boundary conditions of Figure 5 and Figure 7, and the thermal efficiency gains enabled by the advanced layouts with respect to the Recuperated Rankine are estimated. Figure 8 (left) illustrates the thermal efficiency gain brought by the use of a Transcritical Precompression instead of a Recuperated Rankine with CO2-C6F6 mixtures: it is perfectly observable that it is always higher than 1.4 pp, and it reaches a maximum for high TIT and Tmin, confirming the superiority of the advanced layout and the results obtained in previous works by the authors [10]. On the other hand, the improvement for the CO2-SO2 system is even more evident (see Figure 8 (right)), with thermal efficiency gains ranging 6 to 9 pp. Figure 8. Thermal efficiency gains for the PrC CO2-C6F6 (left) and RC CO2-SO2 (right) with respect to the Recuperated Rankine Cycle. Colorbars represent the gain in thermal efficiency expressed in percentage points. Finally, a study on the optimum cycle maximum pressure is provided, repeating the optimization process considering this parameter as a free variable, and not fixing it at 250 bar (reference case for SCARABEUS project). Results in Figure 9 indicates that the thermal efficiency improvement is quite limited for the PrC CO2-C6F6 and RR CO2-TiCl4, and below 1 pp for the RC CO2-SO2 case, confirming 250 bar as a reasonable pressure level for the SCARABEUS technology. 2 A slight error is hereby introduced by the fact that Precompression cycle presents two recuperators instead of one (RR case): the ANN would consider a double pressure loss for this component. The results would therefore provide a conservative estimation of the thermal efficiency of the Recuperated Rankine cycle. The deviation is lesser than a relative 1%, a value of the same order of magnitude of the uncertainty brought by calculation tools. The same rationale can be applied for the Recompression. 19 Figure 9. Thermal efficiency gains achieved optimizing maximum cycle pressure for different cycles and working fluids, with respect to their corresponding 250 bar reference case. Colorbars are expressed in percentage points. CONCLUSIONS The present manuscript, developed in the framework of SCARABEUS project, investigated the thermodynamic assessment and optimization by means of an Artificial Neural Network of different CO2-based power cycles. Three dopants were studied, namely C6F6, TiCl4 and SO2, combined with candidate cycle layouts identified in previous works by the authors: Transcritical Precompression for CO2-C6F6, Recuperated Rankine for CO2-TiCl4 and the Transcritical Recompression for CO2-SO2. In the first part of the manuscript, the candidate dopants and cycle layouts were thoroughly presented and discussed, along with the main assumptions made and a brief description of the computational environment employed: Aspen v11 for the estimation of thermophysical properties of the mixtures, Thermoflex and Matlab for the cycle simulations and modeling (detailed models). The second part of the manuscript dealt with the development of a comprehensive methodology to design and train Artificial Neural Networks capable of behaving as surrogate models of the detailed ones. The methodology is then applied to the three aforementioned SCARABEUS cycles and the two most promising pure sCO2 ones, the Recompression and the Partial Cooling. Results shows that Feedforward Neural Network with one hidden layer are a very promising and 20 reliable tool, capable of predicting the optimum thermal efficiency with a Root Mean Square Error below 0.2 percentage points. An optimization routine conducted using the ANN models takes around 4-5 seconds, a value 99% lower than the one needed for a direct optimization over the detailed model. Furthermore, it was demonstrated that the trained Neural Networks can be used with extreme flexibility. In this work, they have been employed for (1) generation of selection maps for different TIT and Tmin levels, (2) calculation of thermal efficiency gains enabled by advanced layouts with respect to the Recuperated Rankine Cycle and (3) quantification of the thermal efficiency that could be achieved if maximum cycle pressure were optimized instead of fixed at 250 bar. The key aspects having the largest impact on the design of ANN were found to be the sampling of the detailed model and the measure of the error during training. Bearing this in mind, future works will compare different sampling methods in order to guarantee that the different datasets employed during training are statistically representative of the design space and, at the same time, have the lowest size (computational burden). Additionally, future works will couple ANN with Genetic Algorithms (GA) in order to perform multi-objective optimization problems. To that end, additional ANNs will have to be trained for each system, accounting for different Key Performance Indicators such as specific work or specific CAPEX. 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, 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). Nomenclature ANN Artificial Neural Network BIP Binary Interaction Parameter CSP Concentrated Solar Power LCoE Levelised Cost of Electricity [€/MWh] TIT Turbine Inlet Temperature [ºC] Tmin Minimum Cycle Temperature [ºC] PC Partial Cooling Cycle PrC Precompression Cycle Pmax Maximum Cycle Pressure [bar] RC Recompression Cycle RMSE Root Mean Square Error [p.p.] RR Recuperated Rankine Cycle ΔTmin Minimum Temperature Difference [ºC] ΔP Relative Pressure losses [%] 21 ηis,T Turbine isentropic efficiency [%] ηis,C Compressor isentropic efficiency [%] ηis,P Pump isentropic efficiency [%] ηth Thermal efficiency [%] REFERENCES [1] “SCARABEUS Project: Supercritical CARbon dioxide/Alternative fluid Blends for Efficiency Upgrade of Solar power plants. GrantID: 814985.” https://cordis.europa.eu/project/id/814985 (accessed Oct. 26, 2021). [2] “COMPASsCO2 Project: COMponents’ and Materials’ Performance for Advanced Solar supercritical CO2 power plants. Grant ID:958418.” https://cordis.europa.eu/project/id/958418 (accessed Oct. 26, 2021). [3] “sCO2-Flex Project: Supercritical CO2 cycle for flexible and sustainable support to the electricity system. Grant ID:764690.” https://cordis.europa.eu/project/id/764690 (accessed Oct. 26, 2021). [4] “sCO2-Hero Project: The supercritical CO2 Heat Removal System. Grandt ID: 662116.” https://cordis.europa.eu/project/id/662116 (accessed Oct. 26, 2021). [5] “sCO2-4-NPP Project: Innovative sCO2-based heat removal technology for an increased level of safety of nuclear power plants.Grant ID: 847606.” https://cordis.europa.eu/project/id/847606 (accessed Oct. 26, 2021). [6] “I-ThERM Project: Industrial Thermal Energy Recovery Conversion and Management. Grandt ID: 680599.” https://cordis.europa.eu/project/id/680599 (accessed Oct. 26, 2021). [7] “CO2OLHEAT Project: Supercritical CO2 power cycles demonstration in Operational environment Locally valorising industrialWaste Heat. Grandt ID: 10102283.” https://cordis.europa.eu/project/id/101022831 (accessed Oct. 26, 2021). [8] M. T. White, G. Bianchi, L. Chai, S. A. Tassou, and A. I. Sayma, “Review of supercritical CO 2 technologies and systems for power generation,” Applied Thermal Engineering, vol. 185, p. 116447, Feb. 2021, doi: 10.1016/j.applthermaleng.2020.116447. [9] F. Crespi et al., “Thermal efficiency gains enabled by using CO2 mixtures in supercritical power cycles,” Energy, vol. 238, p. 121899, Jan. 2022, doi: 10.1016/j.energy.2021.121899. [10] F. Crespi, G. S. Martínez, P. Rodriguez de Arriba, D. Sánchez, and F. Jiménez-Espadafor, “Influence of Working Fluid Composition on the Optimum Characteristics of Blended Supercritical Carbon Dioxide Cycles,” in Volume 10: Supercritical CO2, Virtual, Online, Jun. 2021, p. V010T30A030. doi: 10.1115/GT2021-60293. [11] L. Wang et al., “A Review of Evaluation, Optimization and Synthesis of Energy Systems: Methodology and Application to Thermal Power Plants,” Energies, vol. 12, no. 1, p. 73, Dec. 2018, doi: 10.3390/en12010073. [12] J. A. Bennett, A. Moisseytsev, and J. J. Sienicki, “Modeling and cycle optimization,” in Fundamentals and Applications of Supercritical Carbon Dioxide (SCO2) Based Power Cycles, Elsevier, 2017, pp. 105–125. doi: 10.1016/B978-0-08-100804-1.00005-0. [13] J. J. Dyreby, “Modeling the Supercritical Carbon Dioxide Brayton Cycle with Recompression,” Wisconsin-Madison, 2014. [14] P. Richter, E. Ábrahám, and G. Morin, “Optimisation of Concentrating Solar Thermal Power Plants with Neural Networks,” in Adaptive and Natural Computing Algorithms, vol. 6593, A. Dobnikar, U. Lotrič, and B. Šter, Eds. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011, pp. 190–199. doi: 10.1007/978-3-642-20282-7_20. [15] M. V. J. J. Suresh, K. S. Reddy, and A. K. Kolar, “ANN-GA based optimization of a high ash coal-fired supercritical power plant,” Applied Energy, vol. 88, no. 12, pp. 4867–4873, 22 Dec. 2011, doi: 10.1016/j.apenergy.2011.06.029. [16] Y. Xu, C. Mao, Y. Huang, X. Shen, X. Xu, and G. Chen, “Performance evaluation and multi-objective optimization of a low-temperature CO2 heat pump water heater based on artificial neural network and new economic analysis,” Energy, vol. 216, p. 119232, Feb. 2021, doi: 10.1016/j.energy.2020.119232. [17] Q. H. Deng, D. Wang, H. Zhao, W. T. Huang, S. Shao, and Z. P. Feng, “Study on performances of supercritical CO2 recompression Brayton cycles with multi-objective optimization,” Applied Thermal Engineering, vol. 114, pp. 1335–1342, Mar. 2017, doi: 10.1016/j.applthermaleng.2016.11.055. [18] H. Zhao, Q. Deng, W. Huang, D. Wang, and Z. Feng, “Thermodynamic and Economic Analysis and Multi-objective Optimization of Supercritical CO2 Brayton Cycles,” Journal of Engineering for Gas Turbines and Power, vol. 138, no. 8, p. 081602, Aug. 2016, doi: 10.1115/1.4032666. [19] M. M. Rashidi, O. A. Bég, A. B. Parsa, and F. Nazari, “Analysis and optimization of a transcritical power cycle with regenerator using artificial neural networks and genetic algorithms,” Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, vol. 225, no. 6, pp. 701–717, Sep. 2011, doi: 10.1177/0957650911407700. [20] R. E. Kirk and D. F. Othmer, Encyclopedia of chemical technology. 2003. Accessed: Nov. 09, 2021. [Online]. Available: http://www.mrw.interscience.wiley.com/emrw/9780471238966/home [21] Aspen Plus v11 (2021). Aspentech. [22] G. Manzolini, M. Binotti, D. Bonalumi, C. Invernizzi, and P. Iora, “CO2 mixtures as innovative working fluid in power cycles applied to solar plants. Techno-economic assessment,” Solar Energy, vol. 181, pp. 530–544, Mar. 2019, doi: 10.1016/j.solener.2019.01.015. [23] G. Di Marcoberardino, E. Morosini, and G. Manzolini, “Preliminary investigation of the influence of equations of state on the performance of CO2 + C6F6 as innovative working fluid in transcritical cycles,” Energy, vol. 238, p. 121815, Jan. 2022, doi: 10.1016/j.energy.2021.121815. [24] G. Angelino, “Perspectives for the Liquid Phase Compression Gas Turbine,” Journal of Engineering for Power, vol. 89, no. 2, pp. 229–236, Apr. 1967, doi: 10.1115/1.3616657. [25] G. Angelino, “Carbon Dioxide Condensation Cycles For Power Production,” Journal of Engineering for Power, vol. 90, no. 3, pp. 287–295, Jul. 1968, doi: 10.1115/1.3609190. [26] G. Angelino, “Real Gas Effects in Carbon Dioxide Cycles,” in ASME 1969 Gas Turbine Conference and Products Show, Cleveland, Ohio, USA, Mar. 1969, p. V001T01A071. doi: 10.1115/69-GT-102. [27] Matlab v2021a (2021). MathWorks. [28] Thermoflex v29 (2021). Thermoflow. [29] “Deep Learning Toolbox. MathWorks.,” 2021. https://es.mathworks.com/products/deeplearning.html (accessed Nov. 09, 2021). [30] S. S. Haykin, Neural networks: a comprehensive foundation, 2nd ed. Upper Saddle River, N.J: Prentice Hall, 1999. [31] M. T. Hagan, H. B. Demuth, M. H. Beale, and O. De Jésus, Neural network design, 2nd edition. s.L: Martin T. Hagan, 2014. [32] M. Stein, “Large Sample Properties of Simulations Using Latin Hypercube Sampling,” Technometrics, vol. 29, no. 2, pp. 143–151, May 1987, doi: 10.1080/00401706.1987.10488205. [33] D. Palomo Guerrero, “Aportaciones al mantenimiento predictivo de plantas de potencia: aplicación a motores diesel lentos de 2 tiempos,” Sevilla, 2017. [Online]. Available: https://idus.us.es/handle/11441/70480 23 [34] L. Tong, P. Bénard, Y. Zong, R. Chahine, K. Liu, and J. Xiao, “Artificial neural network based optimization of a six-step two-bed pressure swing adsorption system for hydrogen purification,” Energy and AI, vol. 5, p. 100075, Sep. 2021, doi: 10.1016/j.egyai.2021.100075. [35] Y. Li, M. Jia, X. Han, and X.-S. Bai, “Towards a comprehensive optimization of engine efficiency and emissions by coupling artificial neural network (ANN) with genetic algorithm (GA),” Energy, vol. 225, p. 120331, Jun. 2021, doi: 10.1016/j.energy.2021.120331. [36] A. Gharehghani, H. R. Abbasi, and P. Alizadeh, “Application of machine learning tools for constrained multi-objective optimization of an HCCI engine,” Energy, vol. 233, p. 121106, Oct. 2021, doi: 10.1016/j.energy.2021.121106. [37] A. Naserbegi and M. Aghaie, “Multi-objective optimization of hybrid nuclear power plant coupled with multiple effect distillation using gravitational search algorithm based on artificial neural network,” Thermal Science and Engineering Progress, vol. 19, p. 100645, Oct. 2020, doi: 10.1016/j.tsep.2020.100645. [38] B. Chegari, M. Tabaa, E. Simeu, F. Moutaouakkil, and H. Medromi, “Multi-objective optimization of building energy performance and indoor thermal comfort by combining artificial neural networks and metaheuristic algorithms,” Energy and Buildings, vol. 239, p. 110839, May 2021, doi: 10.1016/j.enbuild.2021.110839. [39] G. C. Cawley and N. L. C. Talbot, “On Over-fitting in Model Selection and Subsequent Selection Bias in Performance Evaluation,” p. 29. [40] “Global Optimization Toolbox. Mathworks,” 2021. https://es.mathworks.com/products/global-optimization.html (accessed Nov. 10, 2021).