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4.3.4 BSF Model Rezaei and Webley44 previously developed a relationship between productivity and cycle time that accounts for various non-idealities: where K is an equilibrium constant (i.e. Henry constant for a linear system), ΔP is column pressure drop, WCideal is isothermal working capacity, L is column length, LMTZ is the mass transfer zone (MTZ) length, and U is gas velocity. Although their application was comparing structured and non-structured adsorbents, the relationship also helps explain why a minimum BSF exists in small scale PSA as well. The expression relates working capacity to productivity (or BSF) and U through a proportionality constant k’. ΔP and LMTZ both increase as a function of gas velocity (U ∝ 1/cycle time) and reduce isothermal working capacity. Pressure drop reduces working capacity because the adsorbent at one end of the column no longer experiences the same swing in pressure as the other end. A longer MTZ increases the unused column length, which also limits available working capacity. Equation 4.5 exhibits a minimum BSF as gas velocity increases. The velocity and absolute value of the minimum BSF depends on the extent to which pressure drop and MTZ spreading contribute to working capacity reduction. At the limit of isothermal operation and local equilibrium, the MTZ length is not a function of velocity and pressure drop determines the velocity and depth of the minimum BSF. When mass and heat transfer limitations are significant, the MTZ length is a function of velocity and a minimum may develop even if pressure drop is negligible. 64PDF Image | LIMITS OF SMALL SCALE PRESSURE SWING ADSORPTION
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