Upscaling multicomponent transport in porous media with a linear reversible heterogeneous reaction

Abstract

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.