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Transport in Porous Media

, Volume 29, Issue 1, pp 99–125 | Cite as

A Similarity Solution for Oil Lens Redistribution Including Capillary Forces and Oil Entrapment

  • M. I. J. van Dijke
  • S. E. A. T. M. van der Zee
Article

Abstract

Redistribution of a LNAPL lens (oil) at the phreatic surface is described using a multi-phase flow model, with emphasis on the effect of oil entrapment by water. The flow process is analyzed under the assumption that the vertical capillary and gravitational forces balance. Vertical integration leads to explicit functions which approximate the relations between the free oil volume per unit lateral area and the vertically averaged oil relative permeability on the one hand and the vertical position of the interface between zones with either two or three phases on the other hand. A linear relation between the trapped and free oil volume per unit lateral area approximates the vertically integrated nonlinear expression for the trapped oil saturation. The resulting differential equation admits a similarity solution describing the lateral spreading of free oil and the amount and location of trapped oil. Comparison with illustrative numerical computations, which are based on the nonreduced flow model in a two-dimensional planar or axisymmetric domain, shows that the analytical solution provides a good approximation of the free oil distribution at all later times.

multi-phase flow LNAPL lens redistribution oil entrapment vertical equilibrium similarity solution numerical simulations 

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References

  1. 1.
    Barenblatt, G. I.: 1952, On some unsteady motions of a liquid or a gas in a porous medium, Prikl. Mat. Mekh. 16, 67-78 (in Russian).Google Scholar
  2. 2.
    Barenblatt, G. I., Entov, V. M. and Ryzhik, V. M.: 1990, Theory of Fluid Flows in Natural Rocks, Kluwer Acad. Publ., Dordrecht.Google Scholar
  3. 3.
    Bear, J.: 1972, Dynamics of Fluids in Porous Media, Elsevier, New York.Google Scholar
  4. 4.
    Bear, J., Ryzhik, V., Breaster, C. and Entov, V.: 1996, On the movement of an LNAPL lens on the water table, Transport in Porous Media 25, 283-311.Google Scholar
  5. 5.
    Blunt, M., Zhou, D. and Fenwick, D.: 1995, Three-phase flow and gravity drainage in porous media, Transport in Porous Media 20, 77-103.Google Scholar
  6. 6.
    Celia, M. A., Bouloutas, E. T. and Zarba, R. L.: 1990, A general mass-conservative numerical solution for the unsaturated flow equation, Water Resour. Res. 26, 1483-1496.Google Scholar
  7. 7.
    Corapcioglu, M. Y., Tuncay, K. and Ceylan, B. K.: 1996, Oil mound spreading and migration with ambient groundwater flow in coarse porous media, Water Resour. Res. 32, 1299-1308.Google Scholar
  8. 8.
    Craven, A. H. and Peletier, L. A.: 1972, Similarity solutions for degenerate quasilinear parabolic equations, J. Math. Anal. Appl. 38, 73-81.Google Scholar
  9. 9.
    Dracos, T.: 1978, Theoretical considerations and practical implications on the infiltration of hydrocarbons in aquifers. In: Proc. IAH Int. Symp. on Ground Water Pollution by Oil Hydrocarbons, 5-9 June, Prague, pp. 127-137.Google Scholar
  10. 10.
    El-Kadi, A. I.: 1994, Applicability of sharp-interface models for NAPL transport: 2. Spreading of LNAPL, Ground Water 32, 784-793.Google Scholar
  11. 11.
    Hulshof, J. and Vazquez, J. L.: 1994, Self-similar solution of the second kind for the modified porous medium equation, Eur. J. Appl. Math. 5, 391-403.Google Scholar
  12. 12.
    Huyakorn, P. S., Wu, Y. S. and Park, N. S.: 1994, An improved sharp-interface model for assessing NAPL contamination and remediation of groundwater systems, J. Contam. Hydrol. 16, 203-234.Google Scholar
  13. 13.
    Kaluarachchi, J. J. and Parker, J. C.: 1992, Multiphase flow with a simplified model for oil entrapment, Transport in Porous Media 7, 1-14.Google Scholar
  14. 14.
    Land, C. S.: 1968, Calculation of imbibition relative permeability for two-and three-phase flow from rock properties, Trans. Am. Inst. Min. Metal. Pet. Eng. 243, 149-156.Google Scholar
  15. 15.
    Lenhard, R. J. and Parker, J. C.: 1987, A model for hysteretic constitutive relations governing multiphase flow, 2. permeability-saturation relations, Water Resour. Res. 23, 2197-2206.Google Scholar
  16. 16.
    Lenhard, R. J. and Parker, J. C.: 1990, Estimation of free hydrocarbon volume from fluid levels in monitoring wells, Ground Water 28, 57-67.Google Scholar
  17. 17.
    Miller, C. A. and Van Duijn, C. J.: 1995, Similarity solutions for gravity-dominated spreading of a lens of organic contaminant. In: M. F. Wheeler. (ed.), Environmental Studies: Math. Computational and Statistical Analysis, IMA Vol. Math. Appl. 79, Springer-Verlag, New York.Google Scholar
  18. 18.
    Parker, J. C. and Lenhard, R. J.: 1987, A model for hysteretic constitutive relations governing multiphase flow, 1. saturation-pressure relations, Water Resour. Res. 23, 2187-2196.Google Scholar
  19. 19.
    Parker, J. C. and Lenhard, R. J.: 1989, Vertical integration of three-phase flow equations for analysis of light hydrocarbon plume movement, Transport in Porous Media 5, 187-206.Google Scholar
  20. 20.
    Pattle, R. E.: 1959, Diffusion from an instanteneous point source with a concentrationdependent coefficient, Quart. J. Mech. Appl. Math. 12, 407-409.Google Scholar
  21. 21.
    Van Dijke, M. I. J., Van der Zee, S. E. A. T. M. and Van Duijn, C. J.: 1995, Multi-phase flow modeling of air sparging, Adv. Water Resour. 18, 319-333.Google Scholar
  22. 22.
    Wu, Y.-S., Huyakorn, P. S. and Park, N. S.: 1994, A vertical equilibrium model for assessing nonaqueous phase liquid contamination and remediation of groundwater systems, Water Resour. Res. 30, 903-912.Google Scholar
  23. 23.
    Yortsos, Y. C.: 1995, A theoretical analysis of vertical flow equilibrium, Transport in Porous Media, 18, 107-129.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • M. I. J. van Dijke
    • 1
  • S. E. A. T. M. van der Zee
    • 1
  1. 1.Department of Soil Science and Plant NutritionWageningen Agricultural UniversityWageningenThe Netherlands

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