Numerical simulation of two-phase multicomponent flow with reactive transport in porous media: application to geological sequestration of CO₂^*

¹ LMA Pau UMR 5142, Bâtiment IPRA - UPPA, Avenue de l’Université - BP 1155, 64013 Pau Cedex
² INRIA, CRI Paris–Rocquencourt, BP 105, 78153 Le Chesnay Cedex & Maison de la Simulation, Digiteo Labs, CEA Saclay, 91191 Gif-sur-Yvette Cedex
³ LMA Pau UMR 5142, Bâtiment IPRA - UPPA, Avenue de l’Université - BP 1155, 64013 Pau Cedex & Maison de la Simulation, Digiteo Labs, CEA Saclay, 91191 Gif-sur-Yvette Cedex

Abstract

In this work, we consider two-phase multicomponent flow in heterogeneous porous media with chemical reactions. Equations governing the system are the mass conservation law for each species, together with Darcy’s law and complementary equations such as the capillary pressure law. Coupling with chemistry occurs through reactions rates. These rates can either be given non-linear functions of concentrations in the case of kinetic chemical reactions or are unknown in the case of equilibrium chemical reactions (such as reactions in aqueous phase). In this latter case, each reaction gives rise to a mass action law, an algebraic relation that relates the activities of the implied species. The resulting system will couple partial differential equations with algebraic equations. The aim of this paper is to develop a numerical method for the simulation of this system. We consider a sequential approach that consists in splitting the initial problem into two sub-systems. The first subsystem is a two-phase two-component flow, while the second subsystem is devoted to a reactive transport problem. For the two-phase two-component flow part, we have used an already existing module of the open-source parallel multiphase flow simulator DuMu^X. To solve the reactive transport problem, we have implemented a new module in the DuMu^X framework that solves a single phase multicomponent transport problem, and we have coupled it with a locally developed code for chemical equilibrium, called ChemEqLib, through a sequential iterative approach. Then, both modules have been coupled to propose a simple, but mathematically consistent, iterative method that handles two-phase flow with reactive transport. The approach is validated on a 2D example from the literature representative of a model for the long-term fate of sequestered CO₂.