Skip to main content
SpringerLink
Log in

High performance computing of 3D reactive multiphase flow in porous media: application to geological storage of CO2

  • Original Paper
  • Published:
Computational Geosciences Aims and scope Submit manuscript

Abstract

In this paper, we formulate and test numerically a fully coupled fully implicit finite volume (FV) method for solving the nonlinear coupling between two-phase flows and geochemical reactions in porous media on a reservoir scale. The problem is modeled by a highly nonlinear system of degenerate partial differential equations (PDEs governing a compositional two-phase flow model) coupled to ordinary and/or algebraic differential equations (modeling kinetic and equilibrium chemical reactions respectively). The spatial discretization uses a cell-centered FV scheme. After discretizing in time with an implicit Euler scheme, the resulting systems of nonlinear algebraic equations are solved with Newton’s method and the systems of linear equations are solved efficiently and in parallel with an algebraic multigrid method. We discuss two strategies for selecting local time steps. We have developed and implemented this scheme in a new module in the context of the parallel open source platform DuMuX. Parallelization is carried out using the DUNE parallel library package. Two numerical experiments are presented to demonstrate the effectiveness and efficiency of the proposed solver for 3D problems modeling scenarios of CO2 geological storage into a deep saline aquifer. We also report the parallel scalability of the proposed algorithm on a supercomputer with up to 768 processor cores. The proposed method is accurate, numerically robust and exhibits the potential for tackling realistic problems. Lastly, a comparison with a sequential method consisting in decoupling the original problem into a two-phase flow and a reactive transport problem, is performed in term of accuracy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aavatsmark, I.: An introduction to multipoint flux approximations for quadrilateral grids. Comput. Geosci. 6, 405–432 (2002)

    Article  Google Scholar 

  2. Aavatsmark, I., Eigestad, G.T.: Numerical convergence of the MPFA O-method and U-method for general quadrilateral grids. Int. J. Numer. Methods Fluids 51, 939–961 (2006)

    Article  Google Scholar 

  3. Adams, J.J., Bachu, S.: Equations of state for basin geofluids: algorithm review and intercomparison for brines. Geofluids 2, 257–271 (2002)

    Article  Google Scholar 

  4. Ahusborde, E., Amaziane, A., El Ossmani, M.: Improvement of numerical approximation of coupled two-phase multicomponent flow with reactive geochemical transport in porous media. Oil Gas Sci. Technol. - Rev. IFP Energies Nouvelles 73, 73 (2018)

    Article  Google Scholar 

  5. Ahusborde, E., Amaziane, B., El Ossmani, M., Id Moulay, M.: Numerical modeling and simulation of fully coupled processes of reactive multiphase flow in porous media. J. Math. Study 52, 359–377 (2019)

    Article  Google Scholar 

  6. Amir, L., Kern, M.: Preconditioning a coupled model for reactive transport in porous media. Int. J. Numer. Anal. Model. 16, 18–48 (2019)

    Google Scholar 

  7. Alkämper, M., Dedner, A., Klöfkorn, R., Nolte, M.: The DUNE-ALUGrid module. Arch. Numer. Softw. 4, 1–28 (2016)

    Google Scholar 

  8. Barry, D.A., Miller, T., Culligan-Hensley, P.J.: Temporal discretisation errors in non-iterative split-operator approaches to solving chemical reaction/groundwater transport models. J. Contam. Hydrol. 22, 1–17 (1996)

    Article  Google Scholar 

  9. Bethke, C.: Geochemical and Biogeochemicalreaction Modeling, 2nd edn. Cambridge University Press, Cambridge (2007)

    Book  Google Scholar 

  10. Bastian, P., Blatt, M., Dedner, A., Dreier, N.A., Engwer, C., Fritze, R., Gräser, C., Kempf, D., Klöfkorn, R., Ohlberger, M., Sander, O.: The DUNE framework: basic concepts and recent developments. Comput. Math. Appl. 81, 72–112 (2020)

    Google Scholar 

  11. Bastian, P., Blatt, M., Scheichl, R.: Algebraic multigrid for discontinuous galerkin discretizations of heterogeneous elliptic problems. Numer. Linear Algebra Appl. 2, 367–388 (2012)

    Article  Google Scholar 

  12. Brunner, F., Knabner, P.: A global implicit solver for miscible reactive multiphase multicomponent flow in porous media. Comput. Geosci. 23, 127–148 (2019)

    Article  Google Scholar 

  13. Carrayrou, J., Kern, M, Knabner, P.: Reactive transport benchmark of MoMaS. Comput. Geosci. 14, 385–392 (2010)

    Article  Google Scholar 

  14. DuMuX: DUNE for Multi-{Phase, Component, Scale, Physics,...} flow and transport in porous media. http://www.dumux.org(2021)

  15. DUNE: The distributed and unified numerics environment. http://www.dune-project.org (2021)

  16. Erhel, J., Sabit, S.: Analysis of a global reactive transport model and results for the MoMaS benchmark. Math. Comput. Simul. 137, 286–298 (2017)

    Article  Google Scholar 

  17. Eymard, R., Gallouët, T., Guichard, C., Herbin, R., Masson, R.: TP or not TP, that is the question. Comput. Geosci. 18, 285–296 (2014)

    Article  Google Scholar 

  18. Fan, Y., Durlofsky, L.J., Tchelepi, H.A.: A fully-coupled flow-reactive-transport formulation based on element conservation, with application to CO2 storage simulations. Adv. Water Resour. 42, 47–61 (2012)

    Article  Google Scholar 

  19. Fenghour, A., Wakeham, W.A., Vesovic, V.: The viscosity of carbon dioxide. J. Phys. Chem. Ref. Data 27, 31–44 (1998)

    Article  Google Scholar 

  20. Hammond, G.E., Valocchi, A.J., Lichtner, P.C.: Modeling multicomponent reactive transport on parallel computers using Jacobian-Free Newton Krylov with operator-split preconditioning. Dev. Water Sci. Elsevier 47, 727–734 (2002)

    Google Scholar 

  21. Hoffmann, J., Kräutle, J., Knabner, P.: A parallel global-implicit 2-D solver for reactive transport problems in porous media based on a reduction scheme and its application to the MoMaS benchmark problem. Comput. Geosci. 14, 421–433 (2010)

    Article  Google Scholar 

  22. Kala, K., Voskov, D., Huzefa Ammiwala, M.: Parameterization of element balance formulation in reactive compositional flow and transport. Soc. Petroleum Eng. https://doi.org/10.2118/193898-MShttps://doi.org/10.2118/193898-MS (2019)

  23. Kirkham, D.H., Helgeson, H.C., Flowers, G.C.: Theoretical prediction of the thermodynamic behavior of aqueous electrolytes by high pressures and temperatures: IV. Calculation of activity coefficients, osmotic coefficients, and apparent molal and standard and relative partial molal properties to 600oC and 5 KB. Am. J. Sci. 281, 1249–1516 (1981)

    Article  Google Scholar 

  24. Koch, T., Gläser, D., Weishaupt, K., Ackermann, S., Beck, M., Becker, B., Burbulla, S., Class, H., Coltman, E., Emmert, S., Fetzer, T., Grüninger, C., Heck, K., Hommel, J., Kurz, T., Lipp, M., Mohammadi, F., Scherrer, S., Schneider, M., Seitz, G., Stadler, L., Utz, M., Weinhardt, F., Flemisch, B.: DuMuX 3 - an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling. Comput. Math. Appl. 8, 423–443 (2020)

    Google Scholar 

  25. Kräutle, S., Knabner, P.: A new numerical reduction scheme for fully coupled multicomponent transport-reaction problems in porous media. Water Resour. Res. 41, W09414 (2005)

    Article  Google Scholar 

  26. Linga, G., Møyner, O., Nilsen, H.M., Moncorgé, A., Lie, K.A.: An implicit local time stepping method based on cell reordering for multiphase flow in porous media. J. Comput. Phy. X 6 (2020)

  27. Mayer, K.U., Frind, E.O., Blowes, D.W.: Multicomponent reactive transport modeling in variably saturated porous media using a generalized formulation for kinetically controlled reactions. Water Resour. Res. 38, 1–21 (2002)

    Article  Google Scholar 

  28. Mayer, K.U., MacQuarrie, K.T.B.: Solution of the MoMaS reactive transport benchmark with MIN3P-model formulation and simulation results. Comput. Geosci. 14, 405–419 (2010)

    Article  Google Scholar 

  29. Nghiem, L., Sammon, P., Grabenstetter, J., Ohkuma, H.: Modeling CO2 storage in aquifers with a fully-coupled geochemical EOS compositional simulator. Soc. Pet. Eng. SPE-89474-MS (2004)

  30. Niemi, A., Bear, J., Bensabat, J.: Geological Storage of CO2 in Deep Saline Formations. Springer, Berlin (2017)

    Book  Google Scholar 

  31. Saad, Y.: Iterative Methods for Sparse Linear Systems, 2nd edn. Society for Industrial and Applied Mathematics, Philadelphia (2003)

    Book  Google Scholar 

  32. Seigneur, N., Lagneau, V., Corvisier, J., Dauzères, A: Recoupling flow and chemistry in variably saturated reactive transport modelling - an algorithm to accurately couple the feedback of chemistry on water consumption, variable porosity and flow. Adv. Water Resour. 122, 355–366 (2018)

    Article  Google Scholar 

  33. Sin, I., Corvisier, J.: Multiphase multicomponent reactive transport and flow modeling. Rev. Mineral. Geochem. 85, 143–195 (2019)

    Google Scholar 

  34. Spycher, N., Pruess, K.: CO2-H2O mixtures in the geological sequestration of CO2. II. Partitioning in chloride brines at 12–100∘C and up to 600 Bar. Geochim. Cosmochim. Acta 69, 3309–3320 (2005)

    Article  Google Scholar 

  35. Steefel, C.I., Appelo, C.A.J., Arora, B., Jacques, D., Kalbacher, T., Kolditz, O., Lagneau, V., Lichtner, P.C., Mayer, K.U., Meeussen, J.C.L., Molins, S., Moulton, D., Shao, H., S̆imůnek, J., Spycher, N., Yabusaki, S.B., Yeh, G.T.: Reactive transport codes for subsurface environmental simulation. Comput. Geosci. 19, 445–478 (2015)

    Article  Google Scholar 

  36. Steefel, C.I., Lasaga, A.I.: A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution reactions with application to reactive flow in single phase hydrothermal systems. Am. J. Sci. May 294, 529–592 (1994)

    Article  Google Scholar 

  37. Steefel, C.I., MacQuarrie, K.T.B.: Approaches to modeling of reactive transport in porous media. Rev. Mineral. 34, 82–129 (1996)

    Google Scholar 

  38. Span, R., Wagner, W.: A new equation of state for carbon dioxide covering the fluid region from the triple-point temperature to 1100 K at pressures up to 800 MPa. J. Phys. Chem. Ref. Data 25, 1–88 (1996)

    Article  Google Scholar 

  39. Vohralik, M., Wheeler, M.F.: A posteriori error estimates, stopping criteria, and adaptivity for two-phase flows. Comput. Geosci. 17, 789–812 (2013)

    Article  Google Scholar 

  40. Wolery, T.J.: EQ3/6 software package for geochemical modeling of aqueous systems: Package overview and instal- lation guide (version 8.0) Lawrence Livermore National Laboratory Report UCRL-MA-110662 PT I (1992)

  41. Xiao, Y., Whitaker, F., Xu, T., Steefel, C. (eds.): Reactive Transport Modeling: Applications in Subsurface Energy and Environmental Problems. Wiley, Hoboken (2018)

    Google Scholar 

  42. Xu, B., Nagashima, K., DeSimone, J.M., Johnson, C.S.: Diffusion of water in liquid and supercritical carbon dioxide: an NMR study. J. Phys. Chem. A 107, 1–3 (2003)

    Article  Google Scholar 

  43. Zhang, F., Yeh, G.T., Parker, J.C.: Groundwater Reactive Transport Models. Bentham e–books, Sharjah (2012)

    Book  Google Scholar 

Download references

Acknowledgements

This research has been partly supported by the Carnot Institute ISIFoR project (Institute for the sustainable engineering of fossil resources). This support is gratefully acknowledged. The authors gratefully thank the anonymous referees for their insightful comments and suggestions. We also thank Mustapha El Ossmani for his help during the development of our reactive transport module in DuMuX and the CINES (National Computing Center for Higher Education) to give us access to their computing resources facility. This work was granted access to the HPC resources of CINES under the allocations A0060610019 and A0080610019 made by GENCI. Computer time for a part of this study was also provided by the computing facilities MCIA (Mésocentre de Calcul Intensif Aquitain) of the Université de Bordeaux and of the Université de Pau et des Pays de l’Adour.

Author information

Authors and Affiliations

  1. Universite de Pau et des Pays de l’Adour, E2S UPPA, CNRS, LMAP, Pau, France

    Etienne Ahusborde & Brahim Amaziane

  2. Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS-INPT-UPS, Toulouse, France

    Mohamed Id Moulay

Authors
  1. Etienne Ahusborde
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Brahim Amaziane
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohamed Id Moulay
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Brahim Amaziane.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ahusborde, E., Amaziane, B. & Moulay, M.I. High performance computing of 3D reactive multiphase flow in porous media: application to geological storage of CO2. Comput Geosci 25, 2131–2147 (2021). https://doi.org/10.1007/s10596-021-10082-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10596-021-10082-x

Keywords

Search

Navigation