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Numerical simulation of two-phase flow in deformable porous media: Application to carbon dioxide storage in the subsurface

Author

Listed:
  • Kolditz, O.
  • Bauer, S.
  • Böttcher, N.
  • Elsworth, D.
  • Görke, U.-J.
  • McDermott, C.-I.
  • Park, C.-H.
  • Singh, A.K.
  • Taron, J.
  • Wang, W.

Abstract

In this paper, conceptual modeling as well as numerical simulation of two-phase flow in deep, deformable geological formations induced by CO2 injection are presented. The conceptual approach is based on balance equations for mass, momentum and energy completed by appropriate constitutive relations for the fluid phases as well as the solid matrix. Within the context of the primary effects under consideration, the fluid motion will be expressed by the extended Darcy's law for two phase flow. Additionally, constraint conditions for the partial saturations and the pressure fractions of carbon dioxide and brine are defined. To characterize the stress state in the solid matrix, the effective stress principle is applied. Furthermore, the interaction of fluid and solid phases is illustrated by constitutive models for capillary pressure, porosity and permeability as functions of saturation. Based on this conceptual model, a coupled system of nonlinear differential equations for two-phase flow in a deformable porous matrix (H2M model) is formulated. As the displacement vector acts as primary variable for the solid matrix, multiphase flow is simulated using both pressure/pressure or pressure/saturation formulations. An object-oriented finite element method is used to solve the multi-field problem numerically. The capabilities of the model and the numerical tools to treat complex processes during CO2 sequestration are demonstrated on three benchmark examples: (1) a 1-D case to investigate the influence of variable fluid properties, (2) 2-D vertical axi-symmetric cross-section to study the interaction between hydraulic and deformation processes, and (3) 3-D to test the stability and computational costs of the H2M model for real applications.

Suggested Citation

  • Kolditz, O. & Bauer, S. & Böttcher, N. & Elsworth, D. & Görke, U.-J. & McDermott, C.-I. & Park, C.-H. & Singh, A.K. & Taron, J. & Wang, W., 2012. "Numerical simulation of two-phase flow in deformable porous media: Application to carbon dioxide storage in the subsurface," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(10), pages 1919-1935.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:10:p:1919-1935
    DOI: 10.1016/j.matcom.2012.06.010
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    References listed on IDEAS

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    1. Arts, R. & Eiken, O. & Chadwick, A. & Zweigel, P. & van der Meer, L. & Zinszner, B., 2004. "Monitoring of CO2 injected at Sleipner using time-lapse seismic data," Energy, Elsevier, vol. 29(9), pages 1383-1392.
    2. Singh, A.K. & Goerke, U.-J. & Kolditz, O., 2011. "Numerical simulation of non-isothermal compositional gas flow: Application to carbon dioxide injection into gas reservoirs," Energy, Elsevier, vol. 36(5), pages 3446-3458.
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    1. Grunwald, Norbert & Maßmann, Jobst & Kolditz, Olaf & Nagel, Thomas, 2020. "Non-iterative phase-equilibrium model of the H2O-CO2-NaCl-system for large-scale numerical simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 46-61.

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