Effective reaction at a fluid–solid interface: Applications to biotransformation in porous media

Abstract

In this work we develop, via volume averaging, the macroscale transport equation for a reactive chemical species undergoing a heterogeneous reaction with Michaelis–Menton type kinetics. We describe the closure problem required to predict the effective macroscale reaction rate from the microscale geometry and the chemical, physical, and microbial properties. The effective rate of reaction predicted from the closure problem is compared with the reaction rate that is obtained by direct numerical simulation at the microscale. This comparison shows that the macroscale description of the reaction process is generally valid when the coefficient of variation of the concentration field is small compared with unity. Our results are subsequently used to interpret laboratory data for the enzymatic transformation of p-nitrophenyl phosphate hexahydrate. In particular, we provide some interpretation of the observed effect of porewater velocity on the effective reaction rate.