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In order to simplify the analysis, the piston areas are sized such that the velocity at the entrance of the bed (ui) is the same as the velocity of the left piston, and the velocity of the gas at the exit of the bed (u2) is the same as the velocity of the right piston. This is done by equating the piston area to the open cross-sectional area of the bed. The actual cross section of the bed is A,but the void fraction of the bed is e; the product of these values gives the open cross-sectional area. This implies that any velocities inside the bed are interstitial velocities. Now we must calculate the time it takes for the shock wave to travel through the bed. As the bed is initially clean, the time is takes is just the length of the bed divided by the velocity of the shock wave. At constant pressure, the velocity of a shock wave can be found by using Equation (3.1) and the criteria that there is no accumulation in the shock wave. This results in the following equation (Equation (17) from Knaebel and Hill, 1985). Where: U 5 _ PAU\ l +(/?-l)y2 _ PAUI l + (/?-l)y i (3.3) PA= fraction of species A in the bed that is in the gas phase {-} ui = velocity immediately on the high side of the shock wave {m/s} u2 = velocity immediately on the low side of the shock wave {m/ s} yi = mole fraction immediately on the high side of the shock wave {-} y2 = mole fraction immediately on the low side of the shock wave {-} 46PDF Image | Energy Efficiency of Gas Separation Pressure Swing Adsorption
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