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nitrogen (if applicable) have already been determined from specification of the cold inlet flow rates of all components and from Equations (13 – 17). The inlet flow rate of the sweep gas (e.g., air or steam) on the anode side must also be specified. At this point, the total electrolyzer-inlet enthalpy given by the second summation on the right-hand side of Eqn. (14) can be evaluated. The current density, active cell area, and number of cells are then specified, yielding the total ionic current, Ie. Care must be taken to insure that the specified inlet gas flow rates and total ionic current are compatible. The minimum required inlet steam and CO2 molar flow rates must satisfy the constraint represented by Equation (22) to avoid starvation. (22) The oxygen contribution from the CO2 is only counted once, since we want to avoid creation of carbon soot, which could foul the cells. Evaluation of the electrolyzer-outlet total enthalpy, the first summation in Eqn. (14), requires the product temperature, but the product temperature is generally unknown and is determined from solution of the energy equation, so an iterative solution must be applied. The iterative solution process proceeds as follows. Based on a guessed value of electrolyzer outlet temperature, TP, and the specified current, the electrolyzer outlet composition can be determined as described previously, allowing for evaluation of the total enthalpy of the products. The remaining term in the energy equation is the electrical work, which is the product of the per-cell operating voltage and the total ionic current. The operating voltage corresponding to the specified current density is obtained from Equation (23). (23) The stack area-specific resistance, ASR(T), quantifies the loss mechanisms in the operating cell. It must be estimated, based on experimental data or an appropriate model, and specified as a function of temperature. The operating-cell mean Nernst potential, , accounting for the variation of gas composition and temperature across the operating cell, can be obtained from an integrated form of the steam-hydrogen-based (or the CO2-CO-based) Nernst equation, as per Equation (24). (24) The variable in this Equation is the unknown product temperature, TP, which appears both explicitly and implicitly in the upper integration limits. The steam mole fraction has been expressed in the integrand numerator in terms of the hydrogen mole fraction. The mole-fraction subscripts 0, 1, 2 again refer to the cold inlet, hot electrolyzer inlet, and the hot electrolyzer outlet states, respectively. Mole fractions at states 0 and 1 are fully defined. The state-2 mole fractions are based on the specified current density and the guessed value for TP. Once the mean Nernst potential is evaluated based on a guessed value for TP, the operating voltage can be determined and the energy equation can be evaluated. The final converged solution for TP must simultaneously satisfy the chemical balance Equations (13, 14, and 18), the equilibrium constant Equation (13), and the energy Equation (21), subject to Equations (23 through 24). The solution methodology described above can be applied to any specified electrolyzer heat loss or gain. For adiabatic operation, Q = 0. Alternately, if the heat loss or gain from the operating electrolyzer is known from a separate heat transfer analysis for a given operating point, the value of that heat loss or gain would be used. For isothermal electrolyzer operation, once the inlet flow rates, current density, and operating temperature are specified, an iterative solution is not necessary and the triple integral of Equation (17) reduces to a double integral 12 American Institute of Aeronautics and AstronauticsPDF Image | CO2 and Steam Co-Electrolysis for Resource Utilization in Space
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