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T Tw TFS k w k rrout (A.7) (A.8) For the simulation of the 2-D axisymmetric model, the adsorbent layer and the microchannel are assumed to be filled with CH4-CO2 mixture (99:1) at the start of the adsorption stage, while the temperature for all the calculation points is assumed to be 25°C. As in the case with the radially lumped model, CH4:CO2 (70:30) mixture enters the microchannel and saturates the adsorbent layer. The microchannel species, energy and momentum balance equations are the same as those used for the development of the radially lumped model. The adsorbent layer response predicted by the lumped model is compared with that predicted by the 2-D model to justify the use of lumped model. The assumed values of hydraulic diameter Dh and adsorbent layer thickness th for the microchannel are 200 μm and 100 μm, with a length of 1 m. Figure A.1 shows the variation of the adsorbed CO2 concentration along thickness of the adsorbent layer and that along the axis of the microchannel at different time instances. As CO2 enters the microchannel, it enters the adsorbent layer after overcoming the convection resistance and then gradually diffuses outward in the adsorbent layer. Due the effective diffusion coefficient being of the order of 10-8 m2 s-1 at 5500 kPa (≈ 10-6 m2 s-1 at 100 kPa), a slightly inclined CO2 concentration front is seen in Figure A.1. The effect of such a pattern is marginal underutilization of the adsorbent layer (in the upper right corner, at the contour at 1.2 s), as the feed wave front reaches the microchannel outlet. After this instant in the process, the product purity starts to drop regardless of wr FSth rr FS out 2 kw hTT g,i w,i T w r T rrin rrin 169PDF Image | TEMPERATURE SWING ADSORPTION PROCESSES FOR GAS SEPARATION
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