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where Fair and Fair are the molar flow rates of dry air in the tube and shell, respec- ts tively, which we assume to remain constant along the length of the membrane. We adopt a three resistance model to describe the water flux from the tube- side bulk fluid to the corresponding membrane interface, through the membrane, and from the opposite membrane interface to the corresponding shell fluid for each position as given by J1 = −kt (ctmtymtw − cttytw) axial (6.3) (6.4) (6.5) with 1 Pmsw lm Pmtw ∂cw D dPw J2 = − J3 = −ks (ctmsymsw − ctsysw) where ymtw and ymsw are the mole fractions of water in the tube and shell-side respectively, and ctt, ctmt, ctms, and cts are the total molar concentrations in the bulk fluid of the tube, the tube-side film, the shell-side film, and the bulk fluid in the shell, respectively. The limits of integration of the flux through the membrane, J2, are the partial pressures of water in the shell and tube-sides, i.e., Pmsw and Pmtw. The values for the shell and tube convective mass transfer coefficients, kt and ks, were obtained using the correlations Shah and London6 developed for laminar fluid flow across tube bundles and inside the tubes, or those developed by Gnielinski2 for transitional fluid flow given by Sh = (ζ/8) (Re − 1000) Sc (1 + 12.7 (ζ/8))1/2 ζ = 0.316 Re1/4 Sc2/3 − 1 (6.6) (6.7) where Sh is the Sherwood number, Sc is the Schmidt number, and Re is the Reynolds number. Ye and LeVan8 provide a relationship for the diffusion coefficient of a single tube module written D= Pem (6.8) Vstd × 104 (∂cw/∂Pw) ∂Pw films 109PDF Image | TEMPERATURE SWING ADSORPTION COMPRESSION AND MEMBRANE SEPARATIONS
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