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The equations used for modeling displacement in the present study are the incompressible forms of the displacement equations derived by Moore et al. (2016) and are listed in Equations (2.14) through (2.16), where the total pressure drop in the channel is calculated as the sum of pressure drops across liquid- and gas-filled regions. The interface location, which marks the boundary between the two phases during displacement, is tracked through the variable z in Equation (2.14). The interface velocity defined by Equation (2.17) shows the velocity of the fluids during the displacement stage and is used in the energy and species conservation equations. P dP z dP Lz tot dz IF dz IF (2.14) (2.15) (2.16) (2.17) L G dP u2 fL du L dt G h u dzIF dt dz L 2D L h dP u2 fG du dz G 2D G dt With modifications incorporated for the decoupled momentum approach, the species equation for the microchannel during the displacement stage is given by Equation (2.18). A similar approach is followed for all other governing equations illustrated previously. This modeling approach is applicable for both displacement scenarios (gas by liquid and liquid by gas.) The clean displacement approach adopted for the displacement of gas is justified by the experimental findings of Moore (2012), who observed a liquid slug cleanly displacing residual gas present in the microchannel. 29PDF Image | TEMPERATURE SWING ADSORPTION PROCESSES FOR GAS SEPARATION
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