UPSCALED MODEL FOR DISPERSIVE MASS TRANSFER IN A TUBULAR POROUS MEMBRANE SEPARATOR
In this work, the steady-state mass transfer of a non-reactive species in a tubular separator involving a porous membrane is studied. This type of equipment has received considerable attention in the literature since it can be used for gas-gas separation processes. In specific, in this work we are interested in studying transport of oxygen from an air current to a pure helium flow. The air is transported in the annular region, whereas the helium is flowing in countercurrent within the inner compartment of the system. The membrane is permeable to gases in different proportions; however, only oxygen is assumed to constitute a dilute solution in both regions of the system. To derive the mathematical model, we averaged the pointwise equations in the system cross-section generating a system of two ordinary differential equations representing non-equilibrium mass transfer in each region of the system. These upscaled equations are written in terms of effective-medium coefficients that capture the essential features from the pointwise transport and are predicted from the solution of the associated closure problem. To evaluate the predictive capabilities of the model, we compared the concentration profiles with those from solving the pointwise equations. The influence of the membrane permeability to oxygen transfer is studied and we found a close correspondence between the pointwise and upscaled models.
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