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Once steady state is reached, the rates at which mass is transfered to the membrane interface and is transported through the membrane satisfy J1dA1 = J2dA2 (5.12) where dA1 is the differential area based on the outside diameter of the tube and dA2 is the logarithmic mean of the cross-sectional areas of the tube and shell. We recognize that the relationship used in our model to calculate the diffusion coefficient of water in the membrane was determined for a shell and tube membrane module operating with a purge gas on the shell side. Also, data used by Ye and LeVan9 in establishing the diffusion coefficient shown in equation 5.11 considered relative humidity values in the tube and shell ranging from 6.5% to 94%. To account for any differences in water transport through the membrane between normal operation employing a purge stream and vacuum operation we introduce a membrane diffusion efficiency, η, of the form ηDY L = D (5.13) where DY L is the diffusion coefficient determined from the relationship Ye and LeVan9 developed which we modify for use in our system as described by equation 5.11. Substituting equation 5.13 into 5.5 and integrating yields J =−η 1.1×10−6 2P5/2 −P5/2 (5.14) 2 PatmVstd × 104 lm 5 sw mtw 5.4 Results We examine the dehydration performance of a multi-tube Nafion⃝R membrane module via a numerical solution of the coupled tube-side material balance and rate equations. We model the membrane in Figure 5.2 as a set of differential segments in series and solve the material balances for each segment simultaneously using a nonlinear equation solver that implements a modified Powell method.2 The estimated errors associated with measuring the water concentration for the tube and shell side outlets were determined by taking the average of the difference 83PDF Image | TEMPERATURE SWING ADSORPTION COMPRESSION AND MEMBRANE SEPARATIONS
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