A sequential approach for numerical simulation of two-phase multicomponent flow with reactive transport in porous media

We develop a new scheme for numerical solution of immiscible compressible two-phase flow in porous media with geochemistry. The problem is modelled by the mass balance law for each phase, Darcy-Muskat's law, and the capillary pressure law. Coupling with chemistry occurs through reactions rates. These rates can be either given nonlinear functions of concentrations in the case of kinetic chemical reactions or unknown for equilibrium chemical reactions. Each kinetic reaction produces an ordinary differential equation while each equilibrium reaction gives rise to a mass action law that is an algebraic relation that links the activities of concerned species. An implicit finite volume scheme is applied to solve the two-phase flow equations, which is then sequentially coupled to a method for solving the reactive transport problem. More precisely, we used firstly the module 2p2c implemented in the parallel open-source simulator DuMuX to solve a simplified two-phase two-component flow with two dominant species without chemistry. Secondly, we have developed and integrated a reactive transport module in the DuMuX framework to deal with the other species using a sequential iterative approach (SIA) where transport, equilibrium chemical reactions and kinetic chemical reactions are solved sequentially. A new module for transport and a code using the GSL library for the chemical problem have been coupled. Finally, our approach has been validated by solving several test cases. Here we will present two benchmark tests to demonstrate the ability of our method to approximate solutions of single and two-phase flows with reactive transport in heterogeneous porous media.