TEMPERATURE SWING ADSORPTION COMPRESSION AND MEMBRANE SEPARATIONS

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TEMPERATURE SWING ADSORPTION COMPRESSION AND MEMBRANE SEPARATIONS ( temperature-swing-adsorption-compression-and-membrane-separa )

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small deviations from plug flow, dispersion in the axial and transverse directions, and with adsorption equilibrium described by a slightly favorable isotherm. We begin by first assuming that the adsorbent bed is sufficiently long for a constant pattern adsorption wave to develop. Then, we decompose the continuity equation into a series of differential equations similar to Aris.1 We use a perturbation analysis to obtain an approximate solution for the fluid-phase concentration. The results are general in the sense that the solution applies to perturbations of any axisymmetrical velocity profile and slightly favorable isotherm. We believe this to be the first analytical treatment of constant pattern behavior for a fixed-bed adsorber described by a nonplug-flow differential equation with axial and radial dispersion. 4.2 Theory We examine mass transfer for axisymmetrical flow of fluid through a deep bed of packed adsorbent particles, so that the fluid-phase concentration c is a function of radius, time, and axial position only. The material balance for this system may be written ∂n ′∂c ∂c 1∂􏱴∂c􏱵 ∂2c ρb∂t+ε∂t+ε⃗v∂z=εDrr∂r r∂r +εDz∂z2 with boundary conditions in the radial direction of ∂ c 􏱱􏱱 ∂ c 􏱱􏱱 ∂r􏱱􏱱=0 ∂r􏱱􏱱 =0 (4.1) 􏱱r=0 􏱱r=Rbed where ⃗v is the local velocity which may vary across the cross section of the bed but not axially, Rbed is the radius of the bed, and the adsorbed-phase concentration n is described by a slightly favorable (i.e., concave downward) adsorption isotherm. Dr and Dz in equation 4.1 are molecular diffusion or dispersion coefficients in the radial 52

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