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To simplify this we will look at a specific position in the bed and then generalize the equations to any position in the bed. We look then at position C in Figure 3.7, which always has mole fraction yc. The gas at position C is moving at velocity uc, while position C itself is moving at constant velocity: dz dt The relation between the velocities and mole fractions of any two points in an adsorbent bed is given in Equation (3.1). Therefore, uc and yc are related to U2and y2 (which is equal to zero) by the following expression. «c= /'\ l + (/?-l)yc Substimting Equation (3.34) into Equation (3.33) yields: (334> (3.35) BAUC (3.33) i+G*-i)yc dz Itc [l+(/?-l)y]2 c _ PAu2 At time t = 0, position C is at the right end of the bed, as are the positions of all values of y, and when t > 0, position C travels with velocity described by Equation (3.35). We can now calculate the time it takes for position C to reach the other end of the bed. time = distance / velocity f = - ^ [ l (/?-l)y ]2 0.36; c+c PAU2 59PDF Image | Energy Efficiency of Gas Separation Pressure Swing Adsorption
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