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The upscaling process of multicomponent mass transfer and reaction in a rigid and homogeneous porous media was carried out using the method of volume averaging. The first-order reversible reaction which occurs at the solid-fluid interface was considered in this paper. The corresponding macroscopic governing equations were derived from the system dynamics at the pore scale. The effective coefficients were obtained by solving the associated closure problems. This study shows that if the backward reaction rate constant at the microscale is small enough, i.e. k - → 0 , the obtained upscaled model is in accordance with the macroscopic model derived from the first-order irreversible heterogeneous reaction case which was extensively investigated in the literature. The influence of reaction rates on the effective parameters in the macroscopic equations was also investigated. It has been found that both forward and backward reaction rates have significant influence on the effective diffusivities and effective reaction rates in the macroscopic equations. The established equations were successfully verified by the comparison of the direct numerical calculations. [ABSTRACT FROM AUTHOR]

The present paper aims at an upscaled description of solute concentration transport processes in countercurrent dialyzer systems by means of a porous media approach based on the volume averaging theory. In consideration of solute diffusion and ultrafiltration processes, a general set of upscaled solute concentration transport equations has been derived for the three phases in a hollow fiber dialyzer, namely, the blood, membrane and dialysate phases. Moreover, the corresponding closure problems, which can be solved to obtain the effective properties in the upscaled model, are proposed. For the one-dimensional case, analytical expressions of solute concentrations in both blood and dialysate phases are achieved, so as to elucidate the influences of ultrafiltration flow rate and distribution coefficient on both clearance enhancement and solute concentration variations along the length of dialyzer. The results show that both ultrafiltration flow rate and distribution coefficient have no significant effects on solute concentration variations along the length of dialyzer. Nevertheless, the clearance enhancement are found to have linear relationship with both ultrafiltration flow rate and distribution coefficient. [ABSTRACT FROM AUTHOR]