An exponential integrator for advection-dominated reactive transport in heterogeneous porous media

  • Authors:

  • A. Tambue;G. J. Lord;S. Geiger

  • Affiliations:

  • Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot Watt University, Edinburgh EH14 4AS, UK;Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot Watt University, Edinburgh EH14 4AS, UK;Institute of Petroleum Engineering and the Edinburgh Collaborative of Subsurface Science and Engineering, Heriot Watt University, Edinburgh EH14 4AS, UK

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2010

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Abstract

We present an exponential time integrator in conjunction with a finite volume discretisation in space for simulating transport by advection and diffusion including chemical reactions in highly heterogeneous porous media representative of geological reservoirs. These numerical integrators are based on the variation of constants solution and solving the linear system exactly. This is at the expense of computing the exponential of the stiff matrix comprising the finite volume discretisation. Using real Leja points or a Krylov subspace technique compared to standard finite difference-based time integrators. We observe for a variety of example applications that numerical solutions with exponential methods are generally more accurate and require less computational cost. They hence comprise an efficient and accurate method for simulating non-linear advection-dominated transport in geological formations.