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Energies 2019, 12, 3742 6 of 15 3.2.3. Payback Time and Levelized Methanol Production Cost The payback time τ is calculated by dividing the total investment cost with the annual profit of the methanol plant in Equation (6) with the annual profit being the difference between revenue and operation cost: τ= Cinv (6) Cmeth + Cbyp − C rev rev opt where C is the operating cost ($/year), CMeOH is the methanol revenue ($/year), and Cbyp is the opt rev rev revenue of byproduct from the exported electricity and the sold oxygen ($/year). The methanol production cost ($/ton) is defined in Equation (7). C +C −Cbyp CMeOH = opt dep rev PMeOH where PMeOH is methanol production (ton/year). 3.3. Optimization Methodology and Problem Definition (7) Multi-objective techno-economic optimization is carried out with an inhouse optimization platform developed by the Group of Industrial Process and Energy Systems Engineering at École Polytechnique Fédérale de Lausanne [47–49], Switzerland. The methodology has been described in detail in [33,47,49] and applied to deal with various energy systems and industrial processes [33–35]. The iterative optimization is implemented as follows with the decision variables and their bounds considered listed in Table 1. (1) For specific values of the decision variables, Aspen Plus is employed to obtain the mass and energy flows of the considered process and also each equipment. (2) Heat cascade calculation is performed mathematically with the selection and sizing of hot and cold utilities to close the energy balance. Classical hot-cold and grand composite curves are obtained for the interpretation of thermal integration as well as the calculation of heat exchanger numbers and area [37,49]. (3) The objective functions, i.e., the system efficiency, methanol production cost (payback time), are then calculated with the estimation of investment and operating costs, following Section 3.2. (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. 4. Results and Discussion The techno-economic feasibility of the proposed system is investigated via the Pareto fronts, system-level heat cascade, as well as cost breakdown. A sensitivity analysis is conducted to identify the major factors enhancing its economic performance. 4.1. Trade-Off between Efficiency and Cost 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 strongly exothermic mode with the stack outlet temperature hitting the upper bound of 870 ◦C for an inlet temperature of 750 ◦C. A further increase inPDF Image | Optimization of CO2-to-Methanol with Solid-Oxide Electrolyzer
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