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sume that axial diffusion is negligible compared to the bulk flow, gases may be treated as ideal, the membrane apparatus is isothermal, and end effects may be neglected. We write a tube side material balance in which the rate of water lost inside the tubes is set equal to the surface integral of the rate at which water is transported to the membrane interface given by j1dA1 where j1 is the mass flux of water to the membrane interface. We convert equation 5.1 from a mass to a molar perspective to yield ωtinxtwin − ωtoutxtwout = − (5.1) (5.2) where Fair is the total molar flow rate of dry air which is related to the total molar flow rate by Fair =1−y Ftot (5.3) t tw(i) t(i) which we assume to remain constant through the length of the membrane. We then introduce a two resistance model to account for the transport of water from the tube-side fluid to the tube-side membrane interface and for the transport of water through the membrane itself. These are given by J1 = −kt (ctmtymtw − cttytw) (5.4) y y air tw tw Ft − =− J1dA1 A t 1 − ytw z=L 1 − ytw z=0 A J2 = − 1 Psw lm Pmtw D dcw dPw dPw (5.5) where J1 and J2 are the local mass transfer rates , ysw and ytw are the mole fractions of water in the shell and tube, and Pmtw and Psw are the partial pressures of water at the tube-side membrane interface and in the shell, respectively. The convective mass transfer coefficient of water for the tube side interfacial resistance, kt, is determined from correlations Shah and London5 developed for laminar flow in tubes. 80PDF Image | TEMPERATURE SWING ADSORPTION COMPRESSION AND MEMBRANE SEPARATIONS
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