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Now we can calculate the number of moles of purge, using the perfect gas law withP=PL andV=VPU. = 1^^_B_ RT B A Where: Npu = number of moles of pure light product used to purge the bed {mol} This is Knaebel and Hill's Equation (35). (3.32) N PU In order to calculate the volume of the withdrawal piston (the imaginary piston that contains all of the gas that is purged from the bed) and the work to extract the purged gas, we integrate the flow out the end of the bed.* From Figure 3.7, we find that the gas leaving the left of the bed and entering the withdrawal piston has changing velocity ui(t) and mole fraction yi(t). W e must develop an equation that describes the velocity ui(t) as a function of yi(t). Once we know ui(t) we can integrate the flow from t = 0 to t = tpu to find the final volume of the imaginary withdrawal piston, Vwi, that contains all of the purged gas. Once we have Vwi we can calculate the work required for the purge step. * This can also be done by mass balance, knowing the moles of pure purge Npu, the initial conditions (P = PL, y = yB), and the final conditions (P = PL, y = 0). of the bed. We perform the integration, as it reveals the purge process. 58PDF Image | Energy Efficiency of Gas Separation Pressure Swing Adsorption
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