Space-time upscaling of reactive transport in porous media

TL;DR

This paper develops a space-time upscaling method for reactive transport in porous media using coarse-grained averages and global random walk simulations, enabling better modeling of biodegradation processes.

Contribution

It introduces a novel space-time upscaling approach based on CGST averages verified through microscopic simulations, applicable to complex biodegradation scenarios.

Findings

CGST averages closely match classical volume averages in slow-varying processes.

Significant differences between averages occur in fast, time-dependent biodegradation simulations.

The method improves modeling accuracy for reactive transport in heterogeneous porous media.

Abstract

Reactive transport in saturated/unsaturated porous media is numerically upscaled to the space-time scale of a hypothetical measurement through coarse-grained space-time (CGST) averages. The reactive transport is modeled at the fine-grained Darcy scale by the actual number of molecules involved in reactions which undergo advective and diffusive movements described by global random walk (GRW) simulations. The CGST averages verify identities similar to a local balance equation which allow us to derive expressions for the flow velocity and the intrinsic diffusion coefficient in terms of averaged microscopic quantities. The latter are further used to verify the CGST-GRW numerical approach. The upscaling approach is applied to biodegradation processes in saturated aquifers and variably saturated soils and the CGST averages are compared to classical volume averages. One finds that if the process is characterized by slow variations in time, as in homogeneous reaction systems, the differences between the two averages are negligible. Instead, the differences are significant and can be extremely large in simulations of time-dependent biodegradation processes in both soils and saturated aquifers.