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At steady state the molar rate of transfer of water for each film and through the membrane are equal at any axial position, i.e., J1dA1 = J2dA2 = J3dA3 (6.15) where dA1 and dA3 are the differential cross-sectional areas inside and outside a tube, respectively and dA2 is the logarithmic mean of the two. We relate the rate at which the tube-side mass changes to the mass flux to the membrane interface by equating a tube-side mass balance with an area integral of the tube-side interfacial resistance given by tions. Heat Transfer air Ft ytw(i+1) 1 − ytw(i+1) ytw(i) 1 − ytw(i) − where Aid is the surface area required for a membrane under ideal operating condi- The overall energy balance for the system is written ωt|z=L Cpt|z=L (Tt|z=L − Tref ) − ωt|z=0 Cpt|z=0 (Tt|z=0 − Tref ) = ωs|z=0 Cps|z=0 (Ts|z=0 − Tref ) − ωs|z=L Cps|z=L (Ts|z=L − Tref ) where Cpt and Cps are the mean specific heats of the tube and shell-side fluids, Tt and Ts are the temperatures of the tube and shell-side fluids, and ωt and ωs are the mass flow rates of the process and purge gas streams, respectively. We assume that temperature changes throughout the membrane module are small enough that the corresponding variations in specific heats are negligible. We then write the specific heat in terms of the molar fraction of water C =C My pt pw w tw(i) C =C M y ps pw w sw(i) +CM1−y p a tw(i) +C M 1−y pa a sw(i) (6.18) (6.19) 111 = − J1 dAid (6.16) Aid (6.17)PDF Image | TEMPERATURE SWING ADSORPTION COMPRESSION AND MEMBRANE SEPARATIONS
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