Implementation of an Eulerian Method with a TVD Scheme for Solving Reactive Transport Problems in Porous Media with High Heterogeneity

Abstract

The solution to transport problems in porous media with high conductivity heterogeneity is commonly carried out using Lagrangian methods. These methods are suitable for purely advective problems, however, when diffusive effects are considered, the number of particles needed to describe the system can be very high, which increases the computational demand. They also present significant computational overheads when representing processes that involve interaction with non-mobile phases. On the other hand, Eulerian methods present advantages for solving problems that involve the interaction between mobile and non-mobile phases, such as the dissolution or precipitation of minerals, and when combined with high-resolution schemes, such as TVD, they can be applied to solve advective-diffusive problems. This work presents a GPU implementation of an Eulerian method with a TVD scheme for solving reactive transport problems in porous media with high heterogeneity, considering an equilibrium dissolution/precipitation reaction between two dissolved species and an immobile species which affects the porosity.