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Global implicit solver for multiphase multicomponent flow in porous media with multiple gas components and general reactions
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  • Original Paper
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  • Published: 18 April 2022

Global implicit solver for multiphase multicomponent flow in porous media with multiple gas components and general reactions

Global implicit solver for multiple gas components

  • Markus M. Knodel  ORCID: orcid.org/0000-0001-8739-08031,
  • Serge Kräutle2 &
  • Peter Knabner2 

Computational Geosciences volume 26, pages 697–724 (2022)Cite this article

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Abstract

In order to study the efficiency of the various forms of trapping including mineral trapping scenarios for CO2 storage behavior in deep layers of porous media, highly nonlinear coupled diffusion-advection-reaction partial differential equations (PDEs) including kinetic and equilibrium reactions modeling the miscible multiphase multicomponent flow have to be solved. We apply the globally fully implicit PDE reduction method (PRM) developed 2007 by Kräutle and Knabner for one-phase flow, which was extended 2019 to the case of two-phase flow with a pure gas in the study of Brunner and Knabner. We extend the method to the case of an arbitrary number of gases in gaseous phase, because CO2 is not the only gas that threats the climate, and usually is accompanied by other climate killing gases. The application of the PRM leads to an equation system consisting of PDEs, ordinary differential equations, and algebraic equations. The Finite Element discretized / Finite Volume stabilized equations are separated into a local and a global system but nevertheless coupled by the resolution function and evaluated with the aid of a nested Newton solver, so our solver is fully global implicit. For the phase disappearance, we use persistent variables which lead to a semismooth formulation that is solved with a semismooth Newton method. We present scenarios of the injection of a mixture of various gases into deep layers, we investigate phase change effects in the context of various gases, and study the mineral trapping effects of the storage technique. The technical framework also applies to other fields such as nuclear waste storage or oil recovery.

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Acknowledgements

M.M.K. thanks Florian Frank (AM1 Universität Erlangen) for very stimulating discussions on the subject, Tobias Elbinger (AM1) and Ernesto Monaco (AM1) for various hints concerning the basic program code of F. Brunner, and Olaf Ippisch (TU Claustal-Zellerfeld) for very useful hints concerning the Modified Newton method.

M.M.K. thanks Erlangen University for the kind funding, and the RRZE of Erlangen University for the supplied computing time at the Emmy cluster, and Thomas Zeiser and Markus Wittmann from the RRZE for their kind help.

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Open Access funding enabled and organized by Projekt DEAL.

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Authors and Affiliations

  1. Goethe Center for Scientific Computing (GCSC), Goethe Universität Frankfurt, Kettenhofweg 139, 60325, Frankfurt am Main, Germany

    Markus M. Knodel

  2. Applied Mathematics 1, Universität Erlangen-Nürnberg, Cauerstr. 11, 91058, Erlangen, Germany

    Serge Kräutle & Peter Knabner

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Correspondence to Markus M. Knodel.

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Knodel, M.M., Kräutle, S. & Knabner, P. Global implicit solver for multiphase multicomponent flow in porous media with multiple gas components and general reactions. Comput Geosci 26, 697–724 (2022). https://doi.org/10.1007/s10596-022-10140-y

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  • Received: 17 August 2021

  • Accepted: 09 February 2022

  • Published: 18 April 2022

  • Issue Date: June 2022

  • DOI: https://doi.org/10.1007/s10596-022-10140-y

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Keywords

  • Globally implicit solver
  • PDE reduction method
  • Nested Newton
  • Equilibrium reactions
  • CO2
  • Injection of various gases
  • Porous media
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