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4.3 Conclusions A generalized perturbation solution has been developed for a constant pattern profile of the nonplug-flow fixed-bed adsorption continuity equation. The velocity pro- file is described by an axisymmetric function, and the adsorbed-phase concentration is expressed by a slightly favorable isotherm. The evaluation performed in this paper extends to the first and second order terms considering both axial and transverse gradients in the fluid-phase concentration. As such, the fluid-phase concentration is described by a plug-flow model with a radial correction term. For the condition considered, the radial variations of concentration are small compared to those in the axial direction, making the cross-sectionally averaged con- centration indiscernible from the solution to the plug-flow model. However, the mixing-cup concentration moves ahead of and behind what the plug-flow model pre- dicts based on the magnitude of the perturbation parameter in the velocity profile and of the first order correction term. The solution for the constant pattern profile of the nonplug-flow fixed-bed adsorption continuity equation shows that a radial gradient of the fluid-phase con- centration will form based on the shape of the velocity profile. This in turn influences the breakthrough behavior at the bed outlet, causing breakthrough to occur nonuni- formly across the bed outlet, but with transverse dispersion attenuating the effect in comparison with the extent of the deviations from plug flow in the velocity profile. The magnitude of this outcome is important in designing adsorption-based systems where it is necessary to have low breakthrough concentrations and high utilization of the adsorbent. By being able to describe the impacts any deviations from plug flow will have on the fluid-phase concentration and thus the breakthrough behavior, it is possible to improve designs of fixed-bed adsorbers and chromatographic processes. 69PDF Image | TEMPERATURE SWING ADSORPTION COMPRESSION AND MEMBRANE SEPARATIONS
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