Abstract

In porous media theory, upscaling techniques are fundamental to deriving rigorous Darcy-scale models for flow and reactive transport in subsurface systems. Due to limitations in classical upscaling methods, a number of ad hoc techniques have been proposed to address physical regimes of higher reactivity, such as moderately reactive regimes where diffusive and reactive mass transport are of the same order of magnitude. In Part 1 of this two part series, we present a strategy for expanding the applicability of classical homogenization theory by generalizing the assumed closure form. We detail the implementation of this strategy on two reactive mass transport problems with moderately reactive physics. The strategy produces nontrivial homogenized models with effective parameters that couple reactive, diffusive, and advective transport. Numerical validation is provided for each problem to justify the implemented strategy.