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(4) Genetic algorithm is employed to iterate the steps 1–3 with a systematic generation of decision variables and comparison of the evaluated solutions and to finally obtain a cluster of Pareto- optimal solutions (or Pareto front) revealing the trade-offs between the conflicting objective functions. system-level heat cascade, as well as cost breakdown. A sensitivity analysis is conducted to identify gas constrains the minimum system efficiency (Figure 3b). The factor of limiting the maximum efficiency is, ho4w.1e. vTerra,dde-uOefftboetwheesnyEsftfeicmie-nlceyvaenl dheCaotstintegration, as discussed below. Ensertgrioesn2g0l1y8,e1x1o, xthFeOrRmPiEcEmR RoEdVeIEwWith the stack outlet temperature hitting the upper bound of 870 °C7 offor15an inlet temperature of 750 °C. A further increase in the current density will require additional sweep gas to cool the stack, thus the upper bound of the sweep gas constrains the minimum system efficiency (Figure 3b). The factor of limiting the maximum efficiency is, however, due to the system- Filgevuerelh2e.aTtriandteg-orffatiboentw,aesednismcuetshseadnobleplorwod.uctioncostandenergyefficiency(MCP—minimumcost Figure 2. Trade-off between methanol production cost and energy efficiency (MCP—minimum cost point, MEP—maximum efficiency point). point, MEP—maximum efficiency point). There is only a slight trade-off between the cost and efficiency, as shown in Figure 2: The methanol production cost increases with the increasing system efficiency. However, the ranges of both objective functions are limited, which indicates that the operating window of the SOE stack is rather narrow to realize a system efficiency as high as possible. This can be explained by the variation of the key decision variables with respect to the system efficiency as shown in Figure 3. The efficiency increase is mainly due to a decrease in current density, which results in a reduced overpotential (voltage), as shown in Figure 3a. The current density remains at a high level between 0.9 and 1.1 A/cm2 with the voltage slightly over 1.42 V, which indicates that the stacks are operated under Figure 3. Variation of key variables with respect to the system efficiency: (a) current density and Figure 3. Variation of key variables with respect to the system efficiency: (a) current density and voltage and (b) pressure and sweep-gas feed. For all designs, the utilization factor is settled at the voltage and (b) pressure and sweep-gas feed. For all designs, the utilization factor is settled at the upper bound (80%), and the stack’s outlet temperature is at 870 °C◦. upper bound (80%), and the stack’s outlet temperature is at 870 C. 4. Results and Discussion Energies 2019, 12, 3742 The techno-economic feasibility of the proposed system is investigated via the Pareto fronts, 7 of 15 the current density will require additional sweep gas to cool the stack, thus the upper bound of the sweep the major factors enhancing its economic performance. The SOE is preferred to operate under high pressure over 20 bar (Figure 3b), due to the high The SOE is preferred to operate under high pressure over 20 bar (Figure 3b), due to the high pressure of the methanol synthesis process. This allows for reducing significantly the work required pressure of the methanol synthesis process. This allows for reducing significantly the work required for hydrogen compression, which can take up to 1/4 and even 1/3 of the total power consumption. for hydrogen compression, which can take up to 1/4 and even 1/3 of the total power consumption. The The highest SOE pressure is approaching 78 bar, which indicates the avoidance of hydrogen highest SOE pressure is approaching 78 bar, which indicates the avoidance of hydrogen compression. compression. 4.2. Heat Integration 4.3. Heat Integration Two design points, i.e., minimum cost design point (MCP) and maximum efficiency design point Two design points, i.e., minimum cost design point (MCP) and maximum efficiency design point (MEP(M),EaPre),saerleescetledctfeodrfdoretdaeitlaeidleidnivnevsetsitgiagtaitoionnoontthesystemlleevveellhheaetaitnitnetgergartiaotnio,ans,sahsoswhonwinnFinguFriegure4. 4. It is built from a summation of hot and cold streams in the same temperature intervals. The segment It is built from a summation of hot and cold streams in the same temperature intervals. The segment from left to right means excess of heat that needs to be extracted from the system, whereas the system from left to right means excess of heat that needs to be extracted from the system, whereas the system needs to absorb heat. It provides the following straightforward conclusions from Figure 4a. Below needs to absorb heat. It provides the following straightforward conclusions from Figure 4a. Below 400 °C, there is a significant heat requirement for water vaporization and distillation column, which 400 ◦C, there is a significant heat requirement for water vaporization and distillation column, which leads to the pinch point of the heat exchange. The steam generation between 200 and 300 °C is ◦ leads to the pinch point of the heat exchange. The steam generation between 200 and 300 C is supported mainly by the high-temperature heat available from the waste boiler and the SOE outlet, supported mainly by the high-temperature heat available from the waste boiler and the SOE outlet, which is not rational for the heat cascade utilization. The SOE outlet contributes a significant amount which is not rational for the heat cascade utilization. The SOE outlet contributes a significant amount of heat, indicating the importance of the exothermic operation of the SOE for the system-level heat of heat, indicating the importance of the exothermic operation of the SOE for the system-level heat management. The heat for distillation column can be more or less covered by the heat released from manmageethmaennolt.syTnhtehehseisaptrfocredssi.sTtihlleaMtioCnPcoalsuemrunscatnsblieghmtlyorheigohrelrecsusrcroenvtedrednsbitythaenhtehaetMreElPeacsaesde from under the same reactant utilization, indicating slightly more water input and thus heat for steam methanol synthesis process. The MCP case runs at slightly higher current density than the MEP case generation. This difference is also shown in the integrated grand composite curves of the SOE in under the same reactant utilization, indicating slightly more water input and thus heat for steam Figure 4b,c, where the composite curves without SOE are very similar to each other, while the heat generation. This difference is also shown in the integrated grand composite curves of the SOE in supply and uptake by the SOE are slightly different with different operating points. Figure 4b,c, where the composite curves without SOE are very similar to each other, while the heat In general, by choosing proper operating point of the SOE, the SOE integrated CO2-to-methanol supply and uptake by the SOE are slightly different with different operating points. can realize the self-sufficient heat management, so that it only needs a small or even no electrical heating.PDF Image | Optimization of CO2-to-Methanol with Solid-Oxide Electrolyzer
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