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Spent Oxidant Effluent Calculation mol percent Gas FC inlet CO2 30.00 H2O 0.70 N2 54.70 O2 14.6 Total 100.00 FC inlet 83.13 1.94 151.71 40.33 277.11 lb mol/hr FC reaction FC outlet -57.61 25.52 1.94 151.71 -28.81 11.52 -86.42 190.69 Mol percent FC outlet 13.38 1.02 79.56 6.04 100.00 Example 9-5 MCFC Effluent Composition - Accounting for the Water Gas Shift Reaction For the above example, determine the composition of the effluent (spent) fuel stream in mol percent including the effect of the water gas shift reaction. Assume an effluent temperature of 1200 oF and that the water gas shift reaction proceeds to equilibrium. Solution: For convenience, the water gas shift reaction is presented below: CO+H2O⇔CO2 +H2 The double headed arrow is used to indicate that the reaction is in equilibrium. That is, the reaction does not proceed completely to the left or to the right. Instead, the reaction proceeds to an equilibrium point, where both “products” and “reactants” remain. The equilibrium composition depends on the initial composition and final temperature and pressure. Fortunately, the equilibrium concentrations can be determined by a temperature dependent equilibrium constant, K, and the following equation: K= [CO2][H2] [CO][H 2 O] The quantities in brackets represent the thermodynamic activities of the reacting species. Because the reaction is equimolar, the quantities in brackets are also equal to the mole fractions of the respective components. At 1200 oF, the equilibrium constant is 1.96758. A check of the compositions from the preceding example shows that those concentration levels are not in equilibrium. [CO2][H2]= [0.50][0.125]=∞ ≠ 1.967 [CO][H 2 O] [0.0][0.375] 58 Equilibrium constants can be calculated from fundamental chemical data such as Gibbs free energy, or can be determined from temperature dependent tables or charts for common reactions. One such table has been published by Girdler Catalysts (1). The following algorithm fits this temperature dependent data to within 5% for 800 to 1800 oF, or within 1% for 1000 to 1450 oF: Kp= e(4,276/T -3.961). Kp(1200 oF or 922K) equals 1.967. 9-8PDF Image | Fuel Cell Handbook (Seventh Edition)
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