Advertisement

Computational Geosciences

, Volume 17, Issue 1, pp 151–166 | Cite as

Computational modeling of moving interfaces between fluid and porous medium domains

  • Chongbin Zhao
  • Thomas Poulet
  • Klaus Regenauer-Lieb
  • B. E. Hobbs
Original Paper

Abstract

This paper presents a numerical procedure for computational modeling of moving interfaces between fluid and porous medium domains. To avoid the direct description of the interface boundary conditions at the interface between the fluid and porous medium domains, Darcy’s law is used to simulate fluid flows in both the fluid and porous medium domains. For the purpose of effectively simulating the fluid flow using Darcy’s law, the artificial permeability of the fluid domain is used to establish a permeability ratio between the artificial permeability in the fluid domain and the real permeability in the porous medium domain. Using the proposed permeability ratio, the ratio of fluid pressure gradient in the porous medium domain to that in the fluid domain can be appropriately simulated. To verify the proposed numerical procedure, analytical solutions have been derived for a benchmark problem, which can be simulated using the proposed numerical procedure. Comparison of the numerical solutions with the derived analytical solutions has demonstrated the correctness and accuracy of the proposed numerical procedure. Through applying the proposed numerical procedure to several examples associated with the fluid–porous medium interface propagation problems, the related numerical solutions have demonstrated that: (1) the proposed numerical procedure is capable of simulating the morphological instability of the fluid–porous medium interface in a coupled fluid flow–chemical dissolution system when the system is in a supercritical state; and (2) the permeability ratio can have a considerable effect on the evolved morphologies of the fluid–porous medium interface in the coupled fluid flow–chemical dissolution system.

Keywords

Computational modeling Fluid domain Porous medium domain Moving interface Coupled system Chemical dissolution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Beavers, G.S., Joseph, D.D.: Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207 (1967)CrossRefGoogle Scholar
  2. 2.
    Brinkman, H.C.: A calculation of the viscous force exerted by a flowing fluid on dense swarm of particles. Appl. Sci. Res. A1, 27–34 (1947)Google Scholar
  3. 3.
    Chadam, J., Hoff, D., Merino, E., Ortoleva, P., Sen, A.: Reactive infiltration instabilities. IMA J. Appl. Math. 36, 207–221 (1986)CrossRefGoogle Scholar
  4. 4.
    Chadam, J., Ortoleva, P., Sen, A.: A weekly nonlinear stability analysis of the reactive infiltration interface. IMA J. Appl. Math. 48, 1362–1378 (1988)Google Scholar
  5. 5.
    Chen, J.S., Liu, C.W.: Numerical simulation of the evolution of aquifer porosity and species concentrations during reactive transport. Comput. Geosci. 28, 485–499 (2002)CrossRefGoogle Scholar
  6. 6.
    Chen, J.S., Liu, C.W., Lai, G.X., Ni, C.F.: Effects of mechanical dispersion on the morphological evolution of a chemical dissolution front in a fluid-saturated porous medium. J. Hydrol. 373, 96–102 (2009)CrossRefGoogle Scholar
  7. 7.
    Cohen, C.E., Ding, D., Quintard, M., Bazin, B.: From pore scale to wellbore scale: impact of geometry on wormhole growth in carbonate acidization. Chem. Eng. Sci. 63, 3088–3099 (2008)CrossRefGoogle Scholar
  8. 8.
    Daus, A.D., Frid, E.O., Sudicky, E.A.: Comparative error analysis in finite element formulations of the advection-dispersion equation. Adv. Water Resour. 8, 86–95 (1985)CrossRefGoogle Scholar
  9. 9.
    Detournay, E., Cheng, A.H.D.: Fundamentals of poroelasticity. In: Hudson, J.A., Fairhurst, C. (eds.) Comprehensive Rock Engineering, vol. 2. Analysis and Design Methods, Pergamon, New York (1993)Google Scholar
  10. 10.
    Fredd, C.N., Fogler, H.S.: Influence of transport and reaction on wormhole formation in porous media. AIChE J. 44, 1933–1949 (1998)CrossRefGoogle Scholar
  11. 11.
    Golfier, F., Zarcone, C., Bazin, B., Lenormand, R., Lasseux, D., Quintard, M.: On the ability of a Darcy-scale model to capture wormhole formation during the dissolution of a porous medium. J. Fluid Mech. 457, 213–254 (2002)CrossRefGoogle Scholar
  12. 12.
    Kalia, N., Balakotaiah, V.: Modeling and analysis of wormhole formation in reactive dissolution in carbonate rocks. Chem. Eng. Sci. 62, 919–928 (2007)CrossRefGoogle Scholar
  13. 13.
    Kalia, N., Balakotaiah, V.: Effect of medium heterogeneities on reactive dissolution of carbonates. Chem. Eng. Sci. 64, 376–390 (2009)CrossRefGoogle Scholar
  14. 14.
    Nield, D.A., Bejan, A.: Convection in Porous Media. Springer, New York (1992)Google Scholar
  15. 15.
    Ormond, A., Ortoleva, P.: Numerical modeling of reaction-induced cavities in a porous rock. J. Geophys. Res. 105, 16737–16747 (2000)CrossRefGoogle Scholar
  16. 16.
    Ortoleva, P., Chadam, J., Merino, E., Sen, A.: Geochemical self-organization II: the reactive-infiltration instability. Am. J. Sci. 287, 1008–1040 (1987)CrossRefGoogle Scholar
  17. 17.
    Panga, M.K.R., Ziauddin, M., Balakotaiah, V.: Two-scale continuum model for simulation of wormholes in carbonate acidization. AIChE J. 51, 3231–3248 (2005)CrossRefGoogle Scholar
  18. 18.
    Rubinstein, J.: Effective equations for flow in random porous media with a large number of scales. J. Fluid Mech. 170, 379–383 (1986)CrossRefGoogle Scholar
  19. 19.
    Scheidegger, A.E.: The Physics of Flow through Porous Media. University of Toronto Press, Toronto (1974)Google Scholar
  20. 20.
    Tam, C.T.: The drag on a cloud of spherical particles in low Raynolds number flows. J. Fluid Mech. 38, 537–546 (1969)CrossRefGoogle Scholar
  21. 21.
    Turcotte, D.L., Schubert, G.: Geodynamics: Applications of Continuum Physics to Geological Problems. Wiley, New York (1982)Google Scholar
  22. 22.
    Vafai, K., Thiyagaraja, R.: Analysis of flow and heat transfer at the interface region of a porous medium. Int. J. Heat Mass Transfer 25, 1183–1190 (1987)CrossRefGoogle Scholar
  23. 23.
    Zhao, C., Hobbs, B.E., Hornby, P., Ord, A., Peng, S., Liu, L.: Theoretical and numerical analyses of chemical-dissolution front instability in fluid-saturated porous rocks. Int. J. Numer. Anal. Methods Geomech. 32, 1107–1130 (2008)CrossRefGoogle Scholar
  24. 24.
    Zhao, C., Hobbs, B.E., Ord, A.: Fundamentals of Computational Geoscience: Numerical Methods and Algorithms. Springer, Berlin (2009)Google Scholar
  25. 25.
    Zhao, C., Hobbs, B.E., Regenauer-Lieb, K., Ord, A.: Computational simulation for the morphological evolution of nonaqueous-phase-liquid dissolution fronts in two-dimensional fluid-saturated porous media. Comput. Geosci. 15, 167–183 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Chongbin Zhao
    • 1
  • Thomas Poulet
    • 2
  • Klaus Regenauer-Lieb
    • 2
    • 3
  • B. E. Hobbs
    • 3
  1. 1.Computational Geosciences Research CentreCentral South UniversityChangshaChina
  2. 2.CSIRO, Division of Earth Science and Resource EngineeringBentleyAustralia
  3. 3.School of Earth and EnvironmentThe University of Western AustraliaCrawleyAustralia

Personalised recommendations