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Ye and LeVan9 provide a relationship for the diffusion coefficient of a single tube module in the form DYL = Pem (5.6) Vstd (dcw/dPw) where Vstd is the molar volume of gas at a standard state, and P em is the permeability of water through the membrane for a single tube as a function of the partial pressure of water given by Pem = Patm The diffusion coefficient in equation 5.6, DY L, is inversely proportional to the slope of the water adsorption curve, dcw/dPw, determined from the partial derivative of the ratio of the moles of water to the sulfonic acid sites, λ, with respect to the partial pressure of water 2.8 × 10−6P3/2 sat sat sat 1.1 × 10−6P3/2 w (5.10) Substituting equation 5.10 into equation 5.6 yields (5.11) Pem = w (5.7) and yields MNaf dcw = dλ ρNaf dPw dPw 17.81 79.2 108 P −P2 Pw+P3 Pw2 (5.8) (5.9) dcw ρN af dP =M w Naf where ρNaf and MNaf are the density and molecular weight of Nafion⃝R , respectively, and Psat is the saturated vapor pressure for water. In their second paper, Ye and LeVan10 discuss the impact that the membrane thickness has on the permeability of the membrane concluding that a simple propor- tionality relationship does not adequately consider interfacial skin effects. Instead, they develop a permeability for a multi-tube membrane module determined empiri- cally as Patm PatmVstd (∂cw/∂Pw) DY L in equation 5.11 is evaluated for partial pressures ranging from 0 to 3 kPa and shown in Figure 5.3. 1.1 × 10−6P3/2 DYL = w 81PDF Image | TEMPERATURE SWING ADSORPTION COMPRESSION AND MEMBRANE SEPARATIONS
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