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the mole fraction of the gas in the bed, a concentration shock wave will propagate through the bed (see Figure 3.4). As this is done at constant pressure, the continuity equations (Equations (2.40) and (2.41)) can be integrated analytically to give Equation (3.1) (Knaebel and Hill, 1985, Equation (8)).* This indicates that the mole fraction to the left of the shock wave remains constant at the feed mole fraction, and the mole fraction to the right of the shock wave remains constant at y = 0. Consequently, the velocity of the gas in the bed to the left of the shock wave remains constant and uniform. This is also true of the gas to the right of the shock. Therefore, Equation (3.1) relates the velocity at the entrance of the bed to the velocity at the exit of the bed. Where: ui = velocity at the entrance of the bed {m/s} U2= velocity at the exit of the bed {m/s} yi = mole fraction at the entrance of the bed {-} y2= mole fraction at the exit of the bed {-} "i u2 1 + (B -1)y2 l + (B-l)y1 (3.1) = P = (3A / PB= ratio of the fraction of component A in the gas phase in the bed to the fraction of component B in the gas phase in the bed {-} As yi equals the mole fraction of the feed gas (yo), and y2= 0, this formula simplifies to: u2=Ul[l + (B-l)y0] (32) Where: yo = mole fraction of the feed gas {-} * This equation actually describes the difference in velocities between any two points in an adsorbent bed when the pressure is held constant. 45PDF Image | Energy Efficiency of Gas Separation Pressure Swing Adsorption
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