High-Order Adaptive Scheme for Reactive Transport in Heterogeneous Porous Media

Abstract

Subsurface sequestration of carbon dioxide, contaminant transport, and enhanced oil recovery processes often involve complex reaction dynamics. The rock-fluid interactions span a very wide range of length and time scales, and it is important for the numerical solutions to resolve these scales properly. To address these challenges, we extend the adaptive transport scheme for the simulation of reactive transport in heterogeneous porous media developed previously (Deucher and Tchelepi, 2021) to account for (a) higher-order approximation of the convective fluxes and (b) coupling with a chemical solver connected to geochemical databases. The numerical results demonstrate that adaptivity is more effective when a higher-order approximation of the fluxes is used. This is because of lower levels of numerical dispersion compared with low-order approximations, which helps resolve the displacement fronts more accurately. As a result, the regions that experience significant concentration and saturation gradients are more confined, and that leads to improvements in the computational efficiency of the adaptive scheme. The robustness of the approach is demonstrated using a highly heterogeneous two-phase case with multiple wells and a variable total liquid-rate. Due to the modularity of the adaptive scheme, coupling with a chemical solver module is straightforward. The scheme is tested for a three-dimensional case that considers injection of carbonated water in a reservoir matrix of calcite. The results show that the adaptive scheme leads to an accurate representation of the reference concentration distributions of the six reactive components throughout the simulation and leads to a large reduction in the number of cell updates required to achieve the solution.