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ΔnO is the relative molar rate of monatomic oxygen removal from the CO2/steam mixture given by Equation (19). (19) In this Equation, Ie is the total ionic current, Ie = i·Acell·Ncells,. is the total molar flow rate on the CO2 and steam side, including any inert gas flows, and F is the Faraday number. Finally, using the modified oxygen balance equation, the post-electrolyzer equilibrium composition (state 2) can be determined as a function of temperature from simultaneous solution of three chemical balance equations and the equilibrium constant equation. In general, the electrolyzer outlet temperature is unknown. The magnitude of any temperature change associated with electrolyzer operation depends both on the operating conditions (operating voltage, inlet composition, gas flow rates, etc.) and on the thermal boundary condition. If the electrolyzer operating voltage is below the thermal neutral voltage, the endothermic reaction heat requirement dominates and the stack will tend to cool off. If the operating voltage is above thermal neutral, ohmic heating dominates and the stack tends to heat up. If adiabatic electrolyzer operation is assumed, the outlet temperature can be determined as a function of operating voltage from simultaneous solution of the energy equation and the chemical balance and equilibrium constant equations. Alternately, if isothermal operation is assumed, the outlet composition can be determined independently of the energy equation and the heat required to maintain isothermal operation can be calculated as a function of operating voltage. For pure-steam or pure-CO2 electrolysis, the thermal neutral voltage is given by Equation (20). (20) ΔHR,,j(T) is the enthalpy of reaction for electrolysis of pure component j (H2O or CO2) at temperature T. At 800°C, Vtn,H2O = 1.29 V and Vtn,CO2 = 1.46 V. For co-electrolysis, the thermal neutral voltage can range anywhere between the respective pure-component values, depending on inlet composition, oxygen utilization, and temperature (via the equilibrium constant, Keq(T)). There is no simple explicit relation for the multi-component thermal neutral voltage. In general, the thermal neutral voltage for coelectrolysis will be closer to the pure-steam value if the inlet composition is dominated by steam and hydrogen. Conversely, if the inlet composition is dominated by CO2 and CO, the coelectrolysis thermal neutral voltage will be closer to the pure-CO2 value. At an operating temperature of 800°C, with syngas-production-relevant inlet compositions for coelectrolysis (i.e., ~2-to-1 steam/hydrogen vs CO2), a thermal neutral voltage value of ~1.34 V is typical. The energy equation for the coelectrolysis process is represented by Equation (21). (21) is the external heat transfer rate to or from the electrolyzer, is the rate of electrical work supplied to the electrolyzer, is the molar flow rate of each reactant or product, is the standard-state enthalpy of formation of each reactant or product and is the sensible enthalpy for each reactant or product. Applying the energy equation in this form, all reacting and non-reacting species in the inlet and outlet streams are accounted for, including inert gases, process steam, hydrogen (introduced to maintain reducing conditions on the steam/hydrogen electrode), CO2, and any excess un-reacted process gases. In general, determination of the outlet temperature from Equation (21) is an iterative process. The heat transferred during the process must first be specified (e.g., zero for the adiabatic case). The temperature-dependent enthalpy values of all species must be available from curve fits or some other database. The cathode-side hot electrolyzer-inlet molar composition and flow rates of steam, hydrogen, CO2, CO, and any inert carrier gases such as 11 American Institute of Aeronautics and AstronauticsPDF Image | CO2 and Steam Co-Electrolysis for Resource Utilization in Space
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