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3.2.4 Purge Step During the purge step, pure product is throttled to low pressure and used to purge the remaining heavy gas from the adsorbent bed. As with the blowdown step, work is only required if PL < Po; otherwise, the gas is allowed to escape to the atmosphere. During the purge step, a simple wave develops because the mole fraction of the product is less than the mole fraction of the gas in the bed (see Figure 3.7). In this section we develop a mathematical understanding of the purge process in order to calculate the number of moles of pure product necessary to purge the bed (Npu), the number of moles that are purged out of the bed (Nw), and the work required to purge an adsorbent bed. The method of characteristics is used to solve the equations relating to the simple wave. This method is more fully developed by Knaebel and Hill (1985) and states that at constant pressure, the composition is constant along the characteristics. This means that the axial position in the bed with mole fraction y and distance from the product end of the bed z, moves with speed (Equation (10) in Knaebel and Hill, 1985): *= f*u =Constant ^ dt l+ (B-\)y This includes the position at the far right of the simple wave, which has mole fraction zero (point A in Figure 3.7). It is important at this point to note that the velocity of the characteristic (the position with mole fraction y = constant) is related to, but not equal to the velocity of the gas at that axial position in the bed. For this reason, Figure 3.7 makes a distinction between these two velocities; UAis the velocity of the gas through the adsorbent bed at 55PDF Image | Energy Efficiency of Gas Separation Pressure Swing Adsorption
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