Computational Geosciences

, Volume 14, Issue 3, pp 465–481 | Cite as

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

  • Laila Amir
  • Michel KernEmail author
Original paper


Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection–diffusion PDEs 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 one 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.


Geochemistry Transport in porous media Newton–Krylov methods Advection-diffusion-reaction equations 

Mathematics Subject Classifications (2000)

76V05 65M99 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.INRIA Paris-RocquencourtLe Chesnay CedexFrance
  2. 2.ITASCA Consultants, S.A.EcullyFrance

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