Finite Volume Scheme for Coupling Two–Phase Flow with Reactive Transport in Porous Media

  • E. Ahusborde
  • B. Amaziane
  • M. El Ossmani
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 200)


In this work the numerical solution of a system of coupled partial differential and differential algebraic equations describing two-phase multicomponent flow, transport and chemical reactions is considered. An implicit finite volume scheme is used to descretize a two-phase two-component flow problem, which is then sequentially coupled to a reactive transport problem solved by a direct substitution approach (DSA). More precisely, we used firstly the module 2p2c implemented in the parallel open-source simulator DuMu\(^X\) to solve a two-phase two-component flow with two dominant species without chemistry. Secondly, the reactive transport is described by advection dispersion equations coupled to differential algebraic equations to deal with the minor species. Again an implicit finite volume method is used to discretize this subsystem using a DSA. In this context, we have developed and integrated a reactive transport module \(1pNc-react\) in the DuMu\(^X\) framework. Finally, numerical results for a highly complex geochemistry problem are presented to demonstrate the ability of our method to approximate solutions of two-phase flows with reactive transport in heterogeneous porous media.


Cell centred Porous media Reactive transport Two-phase flow Kinetic reactions Code coupling DuMu\(^X\) 

MSC (2010):

76S05 74S10 74F25 76T10 



This work was partially supported by the Carnot Institute, ISIFoR project (Institute for the sus-tainable engineering of fossil resources) and CDAPP (Agglomeration Community of Pau-Pyrenees). Their supports are gratefully acknowledged. We also thank the DuMu\(^X\) and DUNE teams for their help during the development of our reactive transport module.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.CNRS/Univ Pau & Pays Adour, Laboratoire de Mathematiques Et de Leurs Applications de Pau, Fédération IPRA, UMR5142PauFrance
  2. 2.University Moulay Ismaïl, EMMACS-ENSAM, Marjane IIMeknèsMorocco

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