Skip to main content
SpringerLink
Log in

Modelling subsurface coupled chemical reactions and fluid flow over long time periods

  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

Simulation of coupled chemical reactions and fluid flow in porous sedimentary basins over long time periods is a numerical challenge. Most models representing such a physical problem are solved as PDEs where efficient timestepping with controlled error is difficult. We use the differential algebraic equation system approach where robust adaptive timestepping algorithms are available in the solvers, e.g., RADAU5 and DASSL. Mathematical and numerical models for coupled chemical reactions and fluid flow are derived. The models have several interesting properties, e.g., strong nonlinearities and stiffness, which are discussed. We test the performance of our code.

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. C.M. Bethke, Geochemical Reaction Modelling - Concepts and Applications (Oxford University Press, Oxford, 1996).

    Google Scholar 

  2. K.E. Brenan, S.L. Campbell and L.R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations (Elsevier, Amsterdam, 1989).

    MATH  Google Scholar 

  3. G. Dahlquist, L. Edsberg, G. Sköllermo and G. Söderlind, Are the numerical methods and software satisfactory for chemical kinetics?, in: Numerical Integration of Differential Equations and Large Linear Systems: Proc. Bielefeld, ed. J. Hinze, Lecture Notes in Mathematics 968 (Springer, Berlin, 1980) pp. 149-164.

    Google Scholar 

  4. R.W. Freund, A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems, SIAM J. Sci. Comput. 14 (1993) 470-482.

    Article  MATH  MathSciNet  Google Scholar 

  5. R.M. Garrels and M.E. Thompson, A chemical model for sea water at 25°C and one atmosphere total pressure, Amer. J. Sci. 260 (1962) 57-66.

    Article  Google Scholar 

  6. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems (Springer, Berlin, 1991).

    MATH  Google Scholar 

  7. H.C. Helgeson, Evaluation of irreversible reactions in geochemical processes involving minerals and aqueous solutions, I. Thermodynamic relations, Geochim. Cosmochim. Acta 32 (1968) 853-877.

    Article  Google Scholar 

  8. P.C. Lichtner, Continuum model for simultaneous chemical reactions and mass transport in hydrothermal systems, Geochim. Cosmochim. Acta 49 (1985) 779-800.

    Article  Google Scholar 

  9. P.C. Lichtner, The quasi-stationary state approximation to coupled mass transport and fluid-rock interaction in a porous media, Geochim. Cosmochim. Acta 52 (1988) 143-165.

    Article  Google Scholar 

  10. P.C. Lichtner, The quasi-stationary state approximation to fluid/rock reaction: Local equilibrium revisited, in: Diffusion, Atomic Ordering, and Mass Transport, ed. J. Gangly, Adv. Phys. Geochem. 8 (Springer, Berlin, 1991) pp. 453-559.

    Google Scholar 

  11. D.C. Mangold and C.-F. Tsang, A summary of subsurface hydrological and hydrochemical models, Rev. Geophys. 29 (1991) 51-79.

    Google Scholar 

  12. P.J. Ortoleva, Geochemical Self-Organization (Oxford University Press, Oxford, 1994).

    Google Scholar 

  13. P. Ortoleva, J. Chadam, E. Merino and A. Sen, Geochemical self-organization, II. The reactive-infiltration instability, Amer. J. Sci. 287 (1987) 1008-1040.

    Article  Google Scholar 

  14. P. Ortoleva, E. Merino, C. Moore and J. Chadam, Geochemical self-organization, I. Reaction-transport feedbacks and modeling approach, Amer. J. Sci. 287 (1987) 979-1007.

    Article  Google Scholar 

  15. C.I. Steefel and A.C. Lasaga, Evolution of dissolution patterns: Permeability change due to coupled flow and reaction, Chemical Modelling of Aqueous Systems II, eds. D.C. Melchior and R.L. Bassett, ACS Symp. series 416 (1990) pp. 212-225.

  16. C.I. Steefel and A.C. Lasaga, Putting transport into water-rock interaction models, Geology 20 (1992) 680-684.

    Article  Google Scholar 

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

    Article  Google Scholar 

  18. J.G. Verwer and M. van Loon, An evaluation of explicit pseudo-steady-state approximation schemes for stiff ODE systems from chemical kinetics, J. Comput. Phys. 113 (1994) 347-352.

    Article  MATH  MathSciNet  Google Scholar 

  19. G.T. Yeh and V.S. Tripathi, A critical evaluation of recent developments in hydrogeochemical transport models of reactive multichemical components, Water Resources Res. 25 (1989) 93-108.

    Article  Google Scholar 

  20. G.T. Yeh and V.S. Tripathi, A model for simulating transport of reactive multispecies components: Model development and demonstration, Water Resources Res. 27 (1991) 3075-3094.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Energy Technology, Postbox 40, N-20007, Kjeller, Norway

    Astrid Holstad

Authors
  1. Astrid Holstad
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Holstad, A. Modelling subsurface coupled chemical reactions and fluid flow over long time periods. Numerical Algorithms 19, 95–110 (1998). https://doi.org/10.1023/A:1019102406258

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1019102406258

Keywords

Search

Navigation