A global method for coupling transport with chemistry in heterogeneous porous media

TL;DR

This paper introduces a global Newton-Krylov method for reactive transport modeling in porous media that maintains separate transport and chemistry codes, improving efficiency and flexibility in solving coupled systems.

Contribution

It presents a novel global solution approach using Newton-Krylov methods that treats transport and chemistry separately, applicable to operator splitting frameworks.

Findings

Successfully applied to MoMaS benchmark

Reduces computational complexity of coupled systems

Maintains modularity of transport and chemistry codes

Abstract

Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection-diffusion PDE's coupled with algebraic equations. When solving this coupled system, the algebraic equations have to be solved at each grid point for each chemical species and at each time step. This leads to a coupled non-linear system. In this paper a global solution approach that enables to keep the software codes for transport and chemistry distinct is proposed. The method applies the Newton-Krylov framework to the formulation for reactive transport used in operator splitting. The method is formulated in terms of total mobile and total fixed concentrations and uses the chemical solver as a black box, as it only requires that on be able to solve chemical equilibrium problems (and compute derivatives), without having to know the solution method. An additional advantage of the Newton-Krylov method is that the Jacobian is only needed as an operator in a Jacobian matrix times vector product. The proposed method is tested on the MoMaS reactive transport benchmark.