Effective parameters for biogeochemical reaction rates in heterogeneous porous media

Abstract

Biogeochemical reactions are the key processes that control the cycle and transformation of subsurface materials. However, biogeochemical reaction rates vary with observation scales. Such scaling effect are usually addressed with effective parameters, but it remains unclear how to estimate these effective parameters. In this work, we summarized those main factors that may affect the estimation of effective parameters, and discussed the variation of effective parameters under different combinations of factors in numerical simulations. The results indicate that the substrate sources strongly affect the estimation of the effective parameters. In scenarios with identical substrate sources, the effective parameters differ little from the intrinsic parameters, and thus the macroscopic effective biogeochemical reaction rate can be directly estimated from the volume-averaged concentrations of reactants. However, in scenarios with different substrate sources, the mean-field rates usually overestimate the macroscopic effective rates, and the extent of such overestimation diminishes with increasing flow velocity (or with decreasing Da). The above results provide meaningful insights into the estimation of macroscopic effective biogeochemical reaction rates in a variety of natural or artificial scenarios. We also decomposed the effective parameters to explain the above results. It is suggested that the homogeneous distribution of electron donors, electron acceptors and microorganisms, as well as their positive spatial correlation with each other, are the main reasons for the diminished scaling effect of biogeochemical reactions.