Techno-Economic Optimization of CO2-to-Methanol with Solid-Oxide Electrolyzer

Carbon capture and utilization are promising to tackle fossil-fuel depletion and climate change. CO2 hydrogenation can synthesize various chemicals and fuels, such as methanol, formic acid, urea, and methane. CO2-to-methanol integrated with solid-oxide electrolysis (SOE) process can store renewable power in methanol while recycling recovered CO2, thus achieving the dual purposes of storing excess renewable power and reducing lifetime CO2 emissions. This paper focuses on the techno-economic optimization of CO2 hydrogenation to synthesize green methanol integrated with solid-oxide electrolysis process. Process integration, techno-economic evaluation, and multi-objective optimization are carried out for a case study. Results show that there is a trade-off between energy efficiency and methanol production cost. The annual yield of methanol of the studied case is 100 kton with a purity of 99.7%wt with annual CO2 utilization of 150 kton, representing the annual storage capacity of 800 GWh renewable energy. Although the system efficiency is rather high at around at 70% and varies within a narrow range, methanol production cost reaches 560 $/ton for an electricity price of 73.16 $/MWh, being economically infeasible with a payback time over 13 years. When the electricity price is reduced to 47 $/MWh and further to 24 $/MWh, the methanol production cost becomes 365 and 172 $/ton with an attractive payback time of 4.6 and 2.8 years, respectively. The electricity price has significant impact on project implementation. The electricity price is different in each country, leading to a difference of the payback time in different locations.


Introduction
In the 21st century, the consumption of fossil fuel (oil, natural gas, and coal) and climate change are major problems in the fields of energy, environmental protection, and economic development [1,2]. A large amount of fossil fuel is used to generate electricity with the severe issue of greenhouse gas emissions [3]. Moreover, process industries, such as petrochemical, iron and steel, aluminum, paper and pulp, refineries, and cement, also emit CO 2 as a result of raw material conversion [4,5]. The Paris Agreement seeks to balance sources and sinks after 2050, which effectively calls for new net-zero emissions. To achieve the goals of the Paris Agreement, carbon capture, utilization, and storage (CCUS) is essential to mitigate climate change [5]. Furthermore, carbon capture and utilization (CCU)

Solid-Oxide Electrolysis Process
The SOE processes have been described clearly in the authors' publications, e.g., [33][34][35][36]. The demineralized water (1) is first vaporized and then mixed with the recirculated cooled product (9) from the SOE. The mixed feed (4) is further heated to 750 • C mainly by SOE outlets, waste boiler, or electrical heating if necessary. The steam is then partially decomposed into hydrogen and oxygen in the SOE, and the produced gas mixture (6) is cooled to 40 • C before entering a flash drum, where most of the unreacted water is separated. The obtained hydrogen (17) is transported to the methanol synthesis process, while the oxygen is piped to the oxygen station as a byproduct. The sweep oxygen (11) is cooled or heated to 750 • C and fed into the SOE for the thermal management of the stack. of methanol with a purity of 99.7 wt%, which is the common scale of commercial methanol plants.
The system mainly consists of two blocks: SOE process and methanol synthesis upgrading.

Solid-Oxide Electrolysis Process
The SOE processes have been described clearly in the authors' publications, e.g., [33][34][35][36]. The demineralized water (1) is first vaporized and then mixed with the recirculated cooled product (9) from the SOE. The mixed feed (4) is further heated to 750 °C mainly by SOE outlets, waste boiler, or electrical heating if necessary. The steam is then partially decomposed into hydrogen and oxygen in the SOE, and the produced gas mixture (6) is cooled to 40 °C before entering a flash drum, where most of the unreacted water is separated. The obtained hydrogen (17) is transported to the methanol synthesis process, while the oxygen is piped to the oxygen station as a byproduct. The sweep oxygen (11) is cooled or heated to 750 °C and fed into the SOE for the thermal management of the stack.
For the SOE modeling, a quasi-2D model developed and experimentally validated in [33][34][35] is employed. The SOE operates adiabatically with an inlet temperature of 750 °C and a maximum temperature gradient of 120 °C. The other key parameters are shown in Table 1. Under the adiabatic conditions, if the stack operates with a properly large current density (overpotential), the stack outlet temperature will be higher than the inlet temperature [33], which offers additional freedom and benefits for system design since electrical heating can be reduced. Figure 1. Schematic of the CO2-to-methanol system integrated with solid-oxide electrolyzer (SOE). Heat exchanger network is not explicitly designed, but its performance is estimated with classical chemical engineering method in, e.g., [37].  Heat exchanger network is not explicitly designed, but its performance is estimated with classical chemical engineering method in, e.g., [37].
For the SOE modeling, a quasi-2D model developed and experimentally validated in [33][34][35] is employed. The SOE operates adiabatically with an inlet temperature of 750 • C and a maximum temperature gradient of 120 • C. The other key parameters are shown in Table 1. Under the adiabatic conditions, if the stack operates with a properly large current density (overpotential), the stack outlet temperature will be higher than the inlet temperature [33], which offers additional freedom and benefits for system design since electrical heating can be reduced.
The CO 2 -to-methanol model is mainly built on the basis of the work of References [4,19]. The commercial catalyst CuO-ZnO-Al 2 O 3 is employed for a feed ratio of H 2 /CO 2 being 3 at 290 • C and 78 bar with a recirculation ratio of 5.2, achieving a single-pass CO 2 -to-methanol conversion of 21% and a crude methanol content of 4.4 vol.%. In line with the capacity of commercial methanol plants, the annual yield of methanol of the proposed system is set as 100 kton with a purity of 99.7 wt%. Assuming annual operation hours of 7200, the CO 2 stream fed into the system is around 21 ton/hr. A CO 2 capture unit was assumed to be located near the methanol plant supplying carbon dioxide at 2 bar and ambient temperature. We assumed to use captured CO 2 because we wanted to fix a cost of carbon dioxide to be used in the economic analysis. Solutions such as the one described in [38] are too dependent on the location of the plant and cannot be generalized. It is mixed with 2.9 ton/h of H 2 (17) and then enters the methanol synthesis process. The reactant is pressurized to 78 bar and heated up to 230 • C before entering the reactor, which is modeled as an isothermal reactor at 290 • C. The resulting gas (22) from the methanol reactor is cooled to 40 • C with vapor-liquid separation at 74 bar. The gas stream (33) of unreacted H 2 and CO 2 is recycled to the reactor after purging around 1.3% of it to avoid the accumulation of inert gases. The liquid stream (24) is relieved to 1.2 bar and fed to the crude methanol flash drum. The residue gas (32), mainly H 2 and CO 2 , is burnt in a waste boiler together with the purge gas to achieve heat recovery. The liquid, the crude methanol of 63 wt% methanol and 37 wt% water, out of the crude methanol flash drum is gas-free. The crude methanol (26) is pressurized to 3 bar and further upgraded in a distillation column (modeled with RadFrac column) to reach a purity of 99.7 wt%.

Heat Exchanger Network and Steam Turbine Network
The performance of the heat exchanger network is estimated by mathematically-formulated heat cascade calculation, described elsewhere [33,39]. The steam turbine network (steam cycle) is employed for heat recovery, which is formulated as described in [40,41].

Methodology
The optimal system design is investigated regarding the overall energy efficiency and methanol product cost, as described below.

Thermodynamic Performance Indicators
The thermodynamic performance is evaluated with energy efficiency (η) in the following Equation (3).
where · M MeOH is mass flow of the produced methanol, LHV MeOH is the LHV of methanol, ∆ · E is electric power input.

Economic Performance Indicators
Cost evaluation considers both capital expenditure (CAPEX) and operational expenditure (OPEX). The investment cost (CAPEX) is estimated based on [37], with the uncertainty range up to ±30% [37,42,43]. The OPEX includes depreciation costs and variable costs, related to labor, electricity, catalysts, oxygen, and carbon dioxide, etc.

Capital Investment
The pressure-and-material-factored method and the capacity-factored method are employed to calculate the investment cost. The capacity-factored method given in Equation (4) is used for the components listed in Table 2.
where C 0 p,re f and A 0 re f refer to the base cost and size or capacity of equipment taken from literature while α is cost exponent, which is assumed to be 0.65-0.85. I index and I ref_index are Marshall and Swift index of the desired and reference year (2017).  [43] a The SOE stack is taken as around 2000 $/stack [45], with its lifetime being around 48,000 hours [28].
The pressure-and-material-factored method is for standard series equipment and process vessels, such as pump, compressor, heat exchanger, flash drum, waste boiler and distillation column. The related factors refer to the paper by Turton et al. [37].

Operational Cost
The OPEX calculation is based on literature [46]. The depreciation cost is calculated by dividing the total investment cost by the present worth of annuity as shown in Equation (5).
where C dep is the depreciation cost ($/year), C inv is the total investment cost ($/year), i is the annual interest rate and n is the plant lifetime (year).

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: where C opt is the operating cost ($/year), C MeOH rev is the methanol revenue ($/year), and C byp rev is the revenue of byproduct from the exported electricity and the sold oxygen ($/year).
where P MeOH is methanol production (ton/year).

Optimization Methodology and Problem Definition
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][48][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][34][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.

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.

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/cm 2 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 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-level heat integration, as discussed below.
(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 Paretooptimal solutions (or Pareto front) revealing the trade-offs between the conflicting objective functions.

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. 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/cm 2 with the voltage slightly over 1.42 V, which indicates that the stacks are operated under  (Figure 3b). The factor of limiting the maximum efficiency is, however, due to the systemlevel heat integration, as discussed below. 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 for hydrogen compression, which can take up to 1/4 and even 1/3 of the total power consumption. The highest SOE pressure is approaching 78 bar, which indicates the avoidance of hydrogen compression.

Heat Integration
Two design points, i.e., minimum cost design point (MCP) and maximum efficiency design point (MEP), are selected for detailed investigation on the system level heat integration, as shown in Figure  4. 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 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 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, 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 management. The heat for distillation column can be more or less covered by the heat released from methanol synthesis process. The MCP case runs at slightly higher current density than the MEP case under the same reactant utilization, indicating slightly more water input and thus heat for steam generation. This difference is also shown in the integrated grand composite curves of the SOE in Figure 4b,c, where the composite curves without SOE are very similar to each other, while the heat supply and uptake by the SOE are slightly different with different operating points.
In general, by choosing proper operating point of the SOE, the SOE integrated CO2-to-methanol can realize the self-sufficient heat management, so that it only needs a small or even no electrical heating. 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 for hydrogen compression, which can take up to 1/4 and even 1/3 of the total power consumption. The highest SOE pressure is approaching 78 bar, which indicates the avoidance of hydrogen compression.

Heat Integration
Two design points, i.e., minimum cost design point (MCP) and maximum efficiency design point (MEP), are selected for detailed investigation on the system level heat integration, as shown in Figure 4. 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 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 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, 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 management. The heat for distillation column can be more or less covered by the heat released from methanol synthesis process. The MCP case runs at slightly higher current density than the MEP case under the same reactant utilization, indicating slightly more water input and thus heat for steam generation. This difference is also shown in the integrated grand composite curves of the SOE in Figure 4b,c, where the composite curves without SOE are very similar to each other, while the heat supply and uptake by the SOE are slightly different with different operating points.    In general, by choosing proper operating point of the SOE, the SOE integrated CO 2 -to-methanol can realize the self-sufficient heat management, so that it only needs a small or even no electrical heating.

Cost Distribution
Based on the economic assumptions given in Table 3, the two chosen designs are economically evaluated with the key indicator given in Table 4. It shows that, for the given economic assumptions, both designs are not economically feasible with a payback time over 13 years. However, it is still interesting to understand the cost breakdown and identify the key contributors to the levelized methanol cost. The cost distribution is analyzed based on MCP. Figure 5 shows the investment distribution of the proposed case at MCP. The total investment is 133.8 M$, with the highest contribution from the SOE (79%). All other components contribute less than 10%, respectively. Figure  main influence factors of methanol production cost and payback time will be the prices of the SOE stack, the imported electricity, and CO 2 .

Cost Distribution
Based on the economic assumptions given in Table 3, the two chosen designs are economically evaluated with the key indicator given in Table 4. It shows that, for the given economic assumptions, both designs are not economically feasible with a payback time over 13 years. However, it is still interesting to understand the cost breakdown and identify the key contributors to the levelized methanol cost. The cost distribution is analyzed based on MCP. Figure 5 shows the investment distribution of the proposed case at MCP. The total investment is 133.8 M$, with the highest contribution from the SOE (79%). All other components contribute less than 10%, respectively. Figure  6 shows the distribution of operating cost (positive value) and revenue (negative value) of the proposed case at MCP. The total operating cost (70 M$/year) is mostly contributed by the electricity consumption, about 50 M$/year, followed by the CO2 purchase, about 10 M$/year. The revenue comes from the sale of methanol and byproduct oxygen, about 50 M$/year and 29 M$/year, respectively. Therefore, it can be seen that the main influence factors of methanol production cost and payback time will be the prices of the SOE stack, the imported electricity, and CO2.    Table 4. Summary of the two optimal solutions with MeOH capacity of 100 kton/year and the economic assumptions given in Table 3.

Cost Distribution
Based on the economic assumptions given in Table 3, the two chosen designs are economically evaluated with the key indicator given in Table 4. It shows that, for the given economic assumptions, both designs are not economically feasible with a payback time over 13 years. However, it is still interesting to understand the cost breakdown and identify the key contributors to the levelized methanol cost. The cost distribution is analyzed based on MCP. Figure 5 shows the investment distribution of the proposed case at MCP. The total investment is 133.8 M$, with the highest contribution from the SOE (79%). All other components contribute less than 10%, respectively. Figure  6 shows the distribution of operating cost (positive value) and revenue (negative value) of the proposed case at MCP. The total operating cost (70 M$/year) is mostly contributed by the electricity consumption, about 50 M$/year, followed by the CO2 purchase, about 10 M$/year. The revenue comes from the sale of methanol and byproduct oxygen, about 50 M$/year and 29 M$/year, respectively. Therefore, it can be seen that the main influence factors of methanol production cost and payback time will be the prices of the SOE stack, the imported electricity, and CO2.

Sensitivity Analysis
A sensitivity analysis is further performed to the key influential factors, the prices of the imported electricity and carbon dioxide, and the SOE stack to identify the economic conditions making such integrated system economically attractive. The wholesale electricity price differs from country to country. For example, the prices in the 4th quarter of 2017 are within 57-62 €/MWh in Italy, Portugal, Greece, Switzerland, and France, but the range becomes 30-31 €/MWh in Denmark, Sweden, and Norway [51]. The imported price of CO 2 is assumed to be 55 €/ton according to the literature [53]. With the progress of CO 2 capture and sequestration technology and governments' concern with environmental protection, the price of imported CO 2 may be reduced.
In this study, the purchase price of SOE stack is assumed to be 2000 $/stack [45], with its lifetime being 48,000 hours [28]. At present, the SOE is still at the demonstration stage with high investment costs. Mass production towards commercialization will significantly reduce the cost of SOE stack and related equipment. The stack lifetime (48,000 hours) is below the lower bound (60,000 to 90,000 hours [28]) put forward by industry experts. Therefore, SOE stacks need to be replaced for three times when the project lifetime is 25 years and operates for 7200 hours per year. In the future, with the development of materials and design of the SOE stack, the lifetime of SOE stack is expected to be significantly improved. if the lifetime of SOE stack is doubled to 96,000 hours, SOE stacks will only need to be replaced once, which significantly reduces the investment cost into SOE.
For the sensitivity analysis, the stack price varies from 2000 $/stack to 1000 $/stack, the electricity price varies from 60 to 20 €/MWh, the CO 2 varies from 50 to 30 €/ton, and the lifetime of SOE stack from 48,000 to 96,000. The results are summed up in Figure 7. When the SOE stack price reduces from 2000 $/stack to 1000 $/stack (Figure 7a), the payback time decreases almost by half from 14 years to 8.4 years. When the lifetime of SOE stack extends from 48,000 to 96,000 hours, (Figure 7d), the payback time decreases almost by 30% from 14 years to 10 years. When the price of the imported electricity changes from 60 €/MWh to 20 €/MWh (Figure 7b), the payback time is reduced down to 2.8 years, which indicates great economic competitiveness. When the price of the imported CO 2 varies from 50 €/ton to 30 €/ton (Figure 7c), the payback time is shortened to 10 years.

Conclusions
In this study, the techno-economic optimization of the solid-oxide electrolyzer integrated CO2to-methanol is carried out. Firstly, the system is designed in detail with the models developed using ASPEN Plus and calibrated with the manufacturer or experimental data. Then, multi-objective optimization and system-level heat integration are employed to compare the performances of the optimal conceptual designs in terms of energy efficiency and methanol production cost. A sensitivity analysis is performed to identify the key influential parameters for high economic competitiveness. Therefore, the economic performance of such a system is very sensitive to the price of imported electricity. Take the European electricity prices in the 4th quarter of 2017 as an example, the proposed project is not feasible to be invested in some countries with higher electricity prices, such as Italy, Portugal, Greece, Switzerland, or France, but it is worth investing in Denmark, Sweden and Norway because of the lower imported electricity prices. The SOE stack price and lifetime are also highly sensitive to the investment feasibility of the project. With a 25% reduction in its price, the payback time can be reduced by about 20%. With the lifetime of SOE stack doubled to 96,000 hours, the payback time can be reduced by about 30%. It reflects the significant impact of SOE commercialization on economic feasibility. The price of the imported CO 2 has a smaller impact on the investment than the two factors mentioned above.
The payback time of commercial methanol production plants is usually less than 5 years. The payback time of proposed process is over 13 years in this study. We assumed that such a long payback time, which is almost three times the normal payback time for such plants, is not acceptable. The sensitivity analysis, however, shows that the payback time can be shorter than 5 years with a reduction in stack cost and the electricity purchase price and with an extended stack lifetime.

Conclusions
In this study, the techno-economic optimization of the solid-oxide electrolyzer integrated CO 2 -to-methanol is carried out. Firstly, the system is designed in detail with the models developed using ASPEN Plus and calibrated with the manufacturer or experimental data. Then, multi-objective optimization and system-level heat integration are employed to compare the performances of the optimal conceptual designs in terms of energy efficiency and methanol production cost. A sensitivity analysis is performed to identify the key influential parameters for high economic competitiveness. The major conclusions are

•
There is a trade-off between the system efficiency and methanol production cost. Increasing system efficiency will slightly increase the cost. The operating window of solid-oxide stack is rather narrow due to the high heat requirement of steam generation and methanol upgrading.
The optimized system is with a system efficiency of above 68% with annual utilization of carbon dioxide 150 kton.

•
The bottleneck of the heat integration comes from steam generation and distillation column. The SOE needs to operate at highly exothermic mode to drive the whole system and avoid heat transfer from/to the stack. High-pressure operation of the SOE stack is also preferred to avoid the work by hydrogen compression. The steam generation is driven mainly by the heat from the SOE outlet and the waste boiler. Almost no electrical heating is required for all designs.

•
The economic performance is dominated by SOE stack, the electricity price, and the product sale revenue. Given the current market assumptions on these factors, the concept is not economically feasible with a payback time over 13 years. However, if reducing the stack to 1000 $/stack and electricity price down to 20 €/MWh, which is available in some countries, the payback time can be reduced to even less than 3 years, indicating its competitiveness for specific economic conditions.