Scale dependence of reaction rates in porous media

Elemental turnover in porous media depends on substrate concentrations at the pore-scale. In this study, the effect of small scale variability in concentration fields on reaction rate estimates and the validity of the continuum approximation in reactive transport models are investigated via a pore-scale numerical model. Artificial porous media are generated using an identical overlapping sphere algorithm. By comparison between explicit pore-scale simulations and macroscopic continuum approximations, it is shown that inhomogeneous solute distribution within the pores can affect estimates of elemental turnover rates. The error associated with large scale rate estimates depends on the type of reaction, pore geometry, reaction kinetics and macroscopic concentration gradient. A correction term that involves a phenomenological parameter which can be evaluated numerically and macroscopic concentration gradients is introduced to improve the accuracy of upscaled homogeneous reaction rates. Implications for macroscopic descriptions of surface processes and surface attached microbial populations are discussed and it is shown that pore-scale heterogeneity can substantially affect estimates of heterogeneous reactions, while for homogeneous reactions, the error amounts to only a couple of percents.