Spatio-temporal Upscaling of Reactive Transport in Porous Media for Ultra-long Time Predictions: Theory and Numerical Experiments

Abstract:

Transport of a solute in the subsurface can be described on a variety of scales ranging from the pore-scale to the continuum-scale. Despite physiochemical processes are well understood at the pore level, in most practical applications it is satisfactory to know the macroscopic (averaged in space and/or time) values of the state variables. Predictions of subsurface transport behavior under time dependent boundary conditions over ultra-long times require the formulation of continuum scale models for time-averages. In the current study, we employ homogenization method to perform spatio-temporal upscaling of a pore-scale advection-diffusion equation in a periodic porous medium with nonlinear heterogeneous reaction on the solid-liquid interface to (i) obtain macro-time continuum-scale equations and (ii) identify their applicability regimes in terms of relevant dimensionless groups. In addition, the applicability conditions obtained by homogenization are verified by numerical simulations of transport in a planar fracture with reacting walls and time-varying boundary conditions at the inlet. Our analysis shows a good match between numerical simulations and theoretical predictions.