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.