Exergy valorization of a water electrolyzer and CO2 hydrogenation tandem system for hydrogen and methane production

In this work, we introduce a water electrolysis and CO2 hydrogenation tandem system which focuses on methane generation. The concept consists of a water electrolyzer thermally coupled to a CO2 hydrogenation reactor, where the power required to generate hydrogen comes from renewable energy. A thermodynamic analysis of the tandem system was carried out. Our analysis exposes that it is possible to increase the exergy efficiency of the water electrolyzer and CO2 hydrogenation system by thermal coupling, where the thermal energy required to split water into H2 and O2 during the electrolysis process is compensated by the heat generated during the CO2 hydrogenation reaction. Here, the conditions at which high exergy efficiency can be achieved were identified.

PEM water electrolysis in combination with a CO 2 hydrogenation reactor is an attractive way for converting electric power coming from renewable sources into CH 4 . Other alternative to generate CH 4 from renewable energy is the co-electrolysis of H 2 O and CO 2 in solid oxide cells (SOECs) 16,17 . However, these cells are operated at very high temperatures, which make their design and operation more complicated than PEM electrolysis cells.
The hydrogenation process to convert CO 2 into CH 4 , also known as the Sabatier reaction, is a highly exothermic process which generates a lot of heat [18][19][20] . This heat has to be removed from the Sabatier reactor in order to maintain a relatively low temperature. Avoiding high operation temperatures of the Sabatier reactor helps to prevent catalyst sintering which decreases the catalyst lifetime 12,[18][19][20][21] .
The efficiency of a water electrolyzer-Sabatier reactor system can be improved by thermally coupling the system. To split water into H 2 and O 2 , the electrolyzer demands electrical and thermal energy. The removed heat from the Sabatier reactor can be supplied to the electrolyzer, which will reduce the thermal energy demand and then the overall efficiency of the system is improved. A schematic illustration of the system concept is shown in Fig. 1a. This PtG system consists of supplying renewable energy to power a water electrolyzer to generate H 2 , and then this H 2 is used to hydrogenate CO 2 and produce CH 4 . The efficiency of the system can be increased by exchanging the heat generated during the hydrogenation process of CO 2 to the water electrolysis process. The thermodynamic concept of the system is shown in Fig. 1b. The theoretical energy required to split liquid H 2 O into gaseous H 2 and O 2 is equal to the enthalpy change (ΔH elec ) of H 2 O, which is the sum of the Gibbs free energy change (ΔG, electrical demand) and entropy change times temperature (TΔS, thermal demand). By exchanging the heat generated by the Sabatier reaction to compensate the water electrolysis thermal demand TΔS, the overall efficiency of the system can be improved. However, it is necessary to identify the conditions at which a maximum efficiency can be achieved. For this, an exergy analysis of the system is required to identify optimal operating conditions. Exergy valorization analysis is a useful technique to quantify the maximum work potential of a system. This thermodynamic analysis is also used to identify the factors or parameters that affect the efficiency of a process 22-24 . In this work, an exergy analysis of a water electrolyzer and CO 2 hydrogenation tandem system is presented. Operating conditions at which high exergy efficiency can be achieved are identified.

Results and Discussion
thermodynamic analysis of Co 2 hydrogenation process. The equilibrium composition of the CO 2 hydrogenation process was computed following the Gibbs energy minimization method, see Methods for more details. The main reaction to convert CO 2 into methane is the Sabatier reaction: To analyze the influence of temperature, pressure and feed H 2 /CO 2 molar ratio on the CO 2 hydrogenation products, equilibrium compositions were obtained at different conditions. Figure 2a shows the equilibrium composition of the CO 2 hydrogenation process at H 2 /CO 2 = 4, 0.1 MPa and different temperatures. It is observed that the largest mole fraction of CH 4 and H 2 O products are obtained at low temperatures (100-300 °C), indicating that the Sabatier reaction is favored at low temperatures, where a high conversion of CO 2 into CH 4 can be achieved. At high temperatures, CH 4 generation decreases and CO appears which means that the water gas shift reaction is favored. Figure 2b shows the thermodynamic conversion of CO 2 at 0.1, 0.5 and 1.0 MPa, H 2 /CO 2 = 4 and different temperatures. A high conversion is observed at low temperatures, it is also noticed that a high conversion can be maintained at higher temperatures by increasing the pressure. The effect of H 2 /CO 2 molar ratio on the CO 2 hydrogenation products and CO 2 conversion is shown in Fig. 2c,d. Under these conditions, the CO 2 conversion decreases with temperature and the generation of solid carbon (C) is favored. The presence of solid carbon affects the performance of catalyst, since the catalyst can be deactivated when solid carbon is deposited on it. To prevent the deactivation of catalysts, it is important to identify the conditions at which solid carbon can be generated. Figure 2e shows the carbon generation at 4 and 2 H 2 /CO 2 molar ratios, and at different temperatures and pressures. It is observed that when the H 2 /CO 2 molar ratio of 4 is not maintained, solid carbon is generated, while at a temperature above 590 °C this carbon generation is not observed under any conditions. This temperature coincides with the operating temperature of the Sabatier reactor used on the International Space Station 11 , probably as a measure to prevent the generation of carbon when the H 2 /CO 2 ratio of 4 cannot be maintained. exergy analysis of the sabatier process. The exergy efficiency of the Sabatier process is defined by is the Sabatier exergy efficiency, Ex CH 4 and Ex H 2 are the exergy of CH 4 and H 2 , respectively. Details of the exergy calculations are described in the methods section. Figure 3 shows the exergy efficiency of the Sabatier process for H 2 /CO 2 molar ratio of 4 (a) and 2 (b) at 0.1, 0.5 and 1.0 MPa as a function of temperature. In the case of the H 2 /CO 2 molar ratio of 4 (Fig. 3a), the highest efficiency is observed in the temperature range of 100-150 °C and starts decreasing with temperature. In the case of the H 2 /CO 2 molar ratio of 2 (Fig. 3b), the highest efficiency is observed at 340 °C for 0.1 MPa, while for 0.5 and 1.0 MPa it is observed at 400 °C and 420 °C, respectively. The exergy efficiency of the Sabatier process is proportional to the CH 4 generation flow rate, and this rate has a high dependency on temperature and H 2 /CO 2 molar ratio as can be observed in Fig. 2a,c. exergy analysis of the system. The overall exergy efficiency of the system is defined by the following equation: overall ex out in where η overall ex is the overall exergy efficiency, Ex out is the exergy output and Ex in is the exergy input. Here, Ex out is equal to ( ) , while Ex in corresponds to the electrical energy required to generate hydrogen from water electrolysis, more details on the calculations are given in the methods section. Figure 4 shows the overall exergy efficiency of the system for H 2 /CO 2 molar ratio of 4 (a) and 2 (b) as a function of Sabatier temperature. In the case of the H 2 /CO 2 molar ratio of 4 (Fig. 4a), the overall exergy efficiency has a maximum at 200 °C. While in the case of the H 2 /CO 2 molar ratio of 2 (Fig. 4b), the maximum is found at 340 °C. The maximum overall exergy efficiency is achieved when the thermal exchange between the water electrolyzer and CO 2 hydrogenation reactor reaches its optimal point. This indicates that the thermal coupling within the system increases the exergy efficiency.
Our exergy valorization analysis identifies the three main parameters that contribute to achieve high exergy efficiencies for the water electrolyzer -CO 2 hydrogenation system. The first parameter is the H 2 /CO 2 feed gas molar ratio. When this molar ratio is lower than 4, the methane generation rate decreases and solid carbon is generated, Fig. 2c,e. The second parameter is the Sabatier reaction temperature. CH 4 generation is favored in the temperature range of 100-300 °C, while at higher temperatures the water gas shift reaction takes, affecting the CH 4 generation, Fig. 2a. The third parameter that contributes to the enhancement of the system is the thermal coupling of the water electrolyzer and Sabatier reactor. The heat generated by the Sabatier reaction compensates the water electrolysis thermal demand (TΔS), which contributes to increase the overall exergy efficiency of the system, Fig. 4a. In the case of co-electrolysis of CO 2 in H 2 O, it has been shown that this system is also able to achieve high exergy efficiencies to generate H 2 and CH 4 . However, the water gas shift reaction has a significant effect on the system efficiency 16,17 . As mentioned above, this reaction is favored at high temperatures and this type of CO 2 co-electrolysis is carried out at high temperatures. In order to mitigate the effect of the water gas shift reaction and increase the efficiency of the system, CH 4 has to be fed through the cell anode.
Since the focus of the present work is the exergy valorization of the water electrolysis-CO 2 hydrogenation tandem system, a detailed cost analysis is not included. However, a few remarks can be made on the operating www.nature.com/scientificreports www.nature.com/scientificreports/ conditions that can have an impact on the system running costs. As mentioned above, maintaining a feed gas rate H 2 /CO 2 of 4 avoids the generation of solid carbon. The generation of solid carbon affects the catalyst activity and decreases its lifetime, which directly impact the running cost of the system. Another factor that can impact the system running costs is high temperatures. Catalyst sintering is favored at high temperatures and this causes a www.nature.com/scientificreports www.nature.com/scientificreports/ loss in the catalyst activity 12,[18][19][20][21] . So that, by operating the system at a relative low temperature (100-300 °C) helps to avoid catalyst sintering.
In summary, our thermodynamic analysis of the water electrolyzer-CO 2 hydrogenation tandem system exposes the conditions at which high exergy efficiency can be achieved. The results also show that the thermal coupling within the CO 2 hydrogenation and water electrolysis processes contributes to increase the overall exergy efficiency of the system.

Methods
In the analysis a steady state and steady flow are assumed. Chemical kinetics effects are not considered in the calculations. All values of enthalpy, Gibbs free energy and entropy for all the species were computed using Aspen Plus V8.8, Aspen Tech TM .
Water electrolysis. The theoretical energy required to split liquid H 2 O into gaseous H 2 and O 2 is equal to the enthalpy change (ΔH elec ) of H 2 O, which is a function of temperature and pressure and can be calculated with the following equation: where ΔG is the Gibbs free energy change and ΔS is the entropy change. These thermodynamic parameters are a function of the operative temperature (T) and pressure (P). The theoretical energy ΔH corresponds to the sum of electrical energy demand ΔG and thermal energy demand TΔS (Q demand ). ΔH, ΔG and ΔS were calculated using the following equations:  www.nature.com/scientificreports www.nature.com/scientificreports/ Co 2 hydrogenation process. The equilibrium composition of the reactions was calculated using the Gibbs free energy minimization method, which is a widely used method to perform thermodynamic analysis of reacting systems 20,21,25 . The equilibrium composition and the enthalpy of reaction (ΔH r ) for the CO 2 hydrogenation possible products were computed using Aspen Plus V8.8, Aspen Tech TM . The species considered in the analysis are: CH 4 , CO, CO 2 , H 2 O, H 2 and C (solid carbon). All the species were considered in gas phase, with the exception of C, which was considered in solid phase. The computations were carried out in the temperature range of 100 °C-800 °C and at different pressures. The thermodynamic conversion of CO 2 , CH 4 generation and carbon generation were calculated from the equilibrium composition results using the following equations: ( 100) (14) in Where CO 2,in and CO 2,out are the molar flow rate of CO 2 at inlet and outlet, respectively. CH 4,out is the molar flow rate of CH 4 at outlet. C out is the molar flow rate of solid carbon at outlet. exergy calculation. The exergy coming out (Ex out ) of the system is calculated based on the CH 4 generation molar rate: The exergy of a specific gas (Ex i ) is equal to the sum of physical exergy (Ex i Ph ) and chemical exergy (Ex i Ch ): The physical exergy is calculated according the following equation: where m i is the molar flow rate of the gas, h i is the enthalpy of the gas at the Sabatier reaction conditions, and h 0 is the enthalpy at the gas at the dead state. T 0 is the temperature at the dead state. S i is the entropy of the gas at the Sabatier conditions and S 0 is the gas entropy at the dead state. The dead state conditions are assumed to be 298.15 K and 1 atm. The chemical exergy is calculated using the following equation: i Ch i i 0,

= ⋅
where Ex i 0, is the standard chemical exergy of the gas. For the heat flow from the Sabatier reactor (Q sab ) to the water electrolysis system, the exergy is calculated as follows: www.nature.com/scientificreports www.nature.com/scientificreports/