Skip to main content
SpringerLink
Log in

Computational simulation for the morphological evolution of nonaqueous phase liquid dissolution fronts in two-dimensional fluid-saturated porous media

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

Abstract

This paper deals with the computational aspects of nonaqueous phase liquid (NAPL) dissolution front instability in two-dimensional fluid-saturated porous media of finite domains. After the governing equations of an NAPL dissolution system are briefly described, a combination of the finite element and finite difference methods is proposed to solve these equations. In the proposed numerical procedure, the finite difference method is used to discretize time, while the finite element method is used to discretize space. Two benchmark problems, for which either analytical results or previous solutions are available, are used to verify the proposed numerical procedure. The related simulation results from these two benchmark problems have demonstrated that the proposed numerical procedure is useful and applicable for simulating the morphological evolution of NAPL dissolution fronts in two-dimensional fluid-saturated porous media of finite domains. As an application, the proposed numerical procedure has been used to simulate morphological evolution processes for three kinds of NAPL dissolution fronts in supercritical NAPL dissolution systems. It has been recognized that: (1) if the Zhao number of an NAPL dissolution system is in the lower range of the supercritical Zhao numbers, the fundamental mode is predominant; (2) if the Zhao number is in the middle range of the supercritical Zhao numbers, the (normal) fingering mode is the predominant pattern of the NAPL dissolution front; and (3) if the Zhao number is in the higher range of the supercritical Zhao numbers, the fractal mode is predominant for the NAPL dissolution front.

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. Alt-Epping, P., Smith, L.: Computing geochemical mass transfer and water/rock ratios in submarine hydrothermal systems: implications for estimating the vigour of convection. Geofluids 1, 163–181 (2001)

    Article  Google Scholar 

  2. Bear, J.: Dynamics of Fluids in Porous Media. Elsevier, Amsterdam (2001)

    Google Scholar 

  3. Chadam, J., Hoff, D., Merino, E., Ortoleva, P., Sen, A.: Reactive infiltration instabilities. IMA J. Appl. Math. 36, 207–221 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  7. Geller, J.T., Hunt, J.R.: Mass transfer from nonaqueous phase organic liquids in water-saturated porous media. Water Resour. Res. 29, 833–845 (1993)

    Article  Google Scholar 

  8. Imhoff, P.T., Jaffe, P.R., Pinder, G.F.: An experimental study of complete dissolution of a nonaqueous phase liquid in saturated porous media. Water Resour. Res. 30, 307–320 (1994)

    Article  Google Scholar 

  9. Imhoff, P.T., Miller, C.T.: Dissolution fingering during the solubilization of nonaqueous phase liquids in saturated porous media: 1. Model predictions. Water Resour. Res. 32, 1919–1928 (1996)

    Article  Google Scholar 

  10. Imhoff, P.T., Thyrum, G.P., Miller, C.T.: Dissolution fingering during the solubilization of nonaqueous phase liquids in saturated porous media: 2. Experimental observations. Water Resour. Res. 32, 1929–1942 (1996)

    Article  Google Scholar 

  11. Imhoff, P.T., Farthing, M.W., Gleyzer, S.N., Miller, C.T.: Evolving interface between clean and nonaqueous phase liquid (NAPL)-contaminated regions in two-dimensional porous media. Water Resour. Res. 38, 1093–1106 (2002)

    Article  Google Scholar 

  12. Imhoff, P.T., Farthing, M.W., Miller, C.T.: Modeling NAPL dissolution fingering with upscaled mass transfer rate coefficients. Adv. Water Resour. 26, 1097–1111 (2003)

    Article  Google Scholar 

  13. Miller, C.T., Poirier-McNeil, M.M., Mayer, A.S.: Dissolution of trapped nonaqueous phase liquids: mass transfer characteristics. Water Resour. Res. 26, 2783–2796 (1990)

    Article  Google Scholar 

  14. Miller, C.T., Gleyzer, S.N., Imhoff, P.T.: Numerical modeling of NAPL dissolution fingering in porous media. In: Selim, H.M., Ma, L. (eds.) Physical Nonequilibrium in Soils: Modeling and Application, pp. 389–415. Ann Arbor Press, Michigan (1998)

    Google Scholar 

  15. Nield, D.A., Bejan, A.: Convection in Porous Media. Springer, New York (1992)

    Google Scholar 

  16. Ormond, A., Ortoleva, P.: Numerical modeling of reaction-induced cavities in a porous rock. J. Geophys. Res. 105, 16737–16747 (2000)

    Article  Google Scholar 

  17. Ortoleva, P., Chadam, J., Merino, E., Sen, A.: Geochemical self-organization II: the reactive-infiltration instability. Am. J. Sci. 287, 1008–1040 (1987)

    Article  Google Scholar 

  18. Powers, S.E., Abriola, L.M., Weber, W.J. Jr.: An experimental investigation of nonaqueous phase liquid dissolution in saturated subsurface systems: transient mass transfer rates. Water Resour. Res. 30, 321–332 (1994)

    Article  Google Scholar 

  19. Raffensperger, J.P., Garven, G.: The formation of unconformity-type uranium ore deposits: coupled hydrochemical modeling. Am. J. Sci. 295, 639–696 (1995)

    Article  Google Scholar 

  20. Renard, F., Gratier, J.P., Ortoleva, P., Brosse, E., Bazin, B.: Self-organization during reactive fluid flow in a porous medium. Geophys. Res. Lett. 25, 385–388 (1998)

    Article  Google Scholar 

  21. Schafer, D., Schafer, W., Kinzelbach, W.: Simulation of reactive processes related to biodegradation in aquifers: 1. Structure of the three-dimensional reactive transport model. J. Contam. Hydrol. 31, 167–186 (1998)

    Article  Google Scholar 

  22. Schafer, D., Schafer, W., Kinzelbach, W.: Simulation of reactive processes related to biodegradation in aquifers: 2. Model application to a column study on organic carbon degradation. J. Contam. Hydrol. 31, 187–209 (1998)

    Article  Google Scholar 

  23. Seyedabbasi, M.A., Farthing, M.W., Imhoff, P.T., Miller, C.T.: The influence of wettability on NAPL dissolution fingering. Adv. Water Resour. 31, 1687–1696 (2008)

    Article  Google Scholar 

  24. Soerens, T.S., Sabatini, D.A., Harwell, J.H.: Effects of flow bypassing and nonuniform NAPL distribution on the mass transfer characteristics of NAPL dissolution. Water Resour. Res. 34, 1657–1673 (1998)

    Article  Google Scholar 

  25. Steefel, C.I., Lasaga, A.C.: Evolution of dissolution patterns: permeability change due to coupled flow and reaction. In: Melchior, D.C., Basset, R.L. (eds.) Chemical Modeling in Aqueous Systems II. Am. Chem. Soc. Symp. Ser., vol. 416, pp. 213–225 (1990)

  26. Steefel, C.I., Lasaga, A.C.: 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. 294, 529–592 (1994)

    Article  Google Scholar 

  27. Willson, C.S., Hall, J.L., Miller, C.T., Imhoff, P.T.: Factors affecting bank formation during surfactant-enhanced mobilization of residual NAPL. Environ. Sci. Technol. 33, 2440–2446 (1999)

    Article  Google Scholar 

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

    Article  Google Scholar 

  29. Zhao, C., Xu, T.P., Valliappan, S.: Numerical modeling of mass transport problems in porous media: a review. Comput. Struct. 53, 849–860 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  30. Zhao, C., Hobbs, B.E., Mühlhaus, H.B.: Finite element modelling of temperature gradient driven rock alteration and mineralization in porous rock masses. Comput. Methods Appl. Mech. Eng. 165, 175–186 (1998)

    Article  MATH  Google Scholar 

  31. Zhao, C., Hobbs, B.E., Mühlhaus, H.B., Ord, A.: Finite element modelling of rock alteration and metamorphic process in hydrothermal systems. Commun. Numer. Methods Eng. 17, 833–843 (2001)

    Article  MATH  Google Scholar 

  32. Zhao, C., Hobbs, B.E., Mühlhaus, H.B., Ord, A., Lin, G.: Finite element modeling of three-dimensional steady-state convection and lead/zinc mineralization in fluid-saturated rocks. J. Comput. Methods Sci. Eng. 3, 73–89 (2003)

    MATH  Google Scholar 

  33. Zhao, C., Hobbs, B.E., Ord, A., Peng, S., Mühlhaus, H.B., Liu, L.: Numerical modeling of chemical effects of magma solidification problems in porous rocks. Int. J. Numer. Methods Eng. 64, 709–728 (2005)

    Article  MATH  Google Scholar 

  34. Zhao, C., Hobbs, B.E., Hornby, P., Ord, A., Peng, S.: Numerical modelling of fluids mixing, heat transfer and non-equilibrium redox chemical reactions in fluid-saturated porous rocks. Int. J. Numer. Methods Eng. 66, 1061–1078 (2006)

    Article  MATH  Google Scholar 

  35. Zhao, C., Hobbs, B.E., Ord, A., Hornby, P., Peng, S.: Effect of reactive surface areas associated with different particle shapes on chemical-dissolution front instability in fluid-saturated porous rocks. Transp. Porous Media 73, 75-94 (2008)

    Article  MathSciNet  Google Scholar 

  36. 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)

    Article  Google Scholar 

  37. Zhao, C., Hobbs, B.E., Ord, A.: Convective and Advective Heat Transfer in Geological Systems. Springer, Berlin (2008)

    MATH  Google Scholar 

  38. Zhao, C., Hobbs, B.E., Ord, A.: Fundamentals of Computational Geoscience: Numerical Methods and Algorithms. Springer, Berlin (2009)

    MATH  Google Scholar 

  39. Zhao, C., Hobbs, B.E., Ord, A.: Theoretical analyses of nonaqueous-phase-liquid dissolution induced instability in two-dimensional fluid-saturated porous media. Int. J. Numer. Anal. Methods Geomech. (2009). doi:10.1002/nag.880

    Google Scholar 

  40. Zhao, C., Hobbs, B.E., Ord, A., Peng, S.: Effects of mineral dissolution ratios on chemical-dissolution front instability in fluid-saturated porous media. Transp. Porous Media 82, 317–335 (2010)

    Article  Google Scholar 

  41. Zienkiewicz, O.C.: The Finite Element Method. McGraw-Hill, London (1977)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computational Geosciences Research Centre, Central South University, Changsha, 410083, China

    Chongbin Zhao

  2. School of Earth and Environment, The University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia

    B. E. Hobbs, K. Regenauer-Lieb & A. Ord

  3. CSIRO Division of Earth Science and Resource Engineering, P. O. Box 1130, Bentley, WA, 6102, Australia

    K. Regenauer-Lieb

Authors
  1. Chongbin Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. E. Hobbs
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. Regenauer-Lieb
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Ord
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chongbin Zhao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhao, C., Hobbs, B.E., Regenauer-Lieb, K. et al. 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). https://doi.org/10.1007/s10596-010-9206-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10596-010-9206-2

Keywords

Search

Navigation