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Keywords:
two-phase flow; non-aqueous phase liquids (NAPL); control volume finite elements; capillary pressure parameters; Brooks–Corey model; plume sensitivity
Summary:
We have developed a multiphase flow code that has been applied to study the behavior of non-aqueous phase liquids (NAPL) in the subsurface. We describe model formulation, discretization, and use the model for numerical investigation of sensitivity of the NAPL plume with respect to capillary parameters of the soil. In this paper the soil is assumed to be spatially homogeneous. A 2-D reference problem has been chosen and has been recomputed repeatedly with modified parameters of the Brooks–Corey capillary pressure model. In this paper we present selected figures showing the resulting plumes as well as quantitative information regarding position of the center of mass of the plume and variances (spreads) of the plume in both axes. These data allow us to evaluate influence of the capillary pressure parameters on the plume morphology in a way that has already been used for characterization of the plume distribution in laboratory experiments. Results confirm the hypothesis that capillary pressure parameters are the key quantities that determine the fate of organic contaminants in the subsurface, and emphasize the significance of the residual NAPL saturation for correct modeling of the NAPL contamination.
References:
[1] http, UG homepage.//: sit. iwr.uni-heidelberg.de/$\tilde{\ }$ug/
[2] Bastian P., Birken K., Lang S., Johannsen K., Neuß N., Rentz-Reichert, H., Wieners C.: UG: A flexible software toolbox for solving partial differential equations. Comput. and Visualization in Science 1 (1997), 27–40 Zbl 0970.65129
[3] Bastian P., Johannsen, K., Reichenberger V.: UG Tutorial, 199.
[4] Beneš M., Fučík R., Mikyška, J., Illangasekare T. H.: Generalization of the benchmark solution for the two-phase flow. In: FEM_MODFLOW 2004 (K. Kovář, Z. Hrkal, and J. Bruthans, eds.), Karlovy Vary 2004, pp. 181–184
[5] Beneš M., Fučík R., Mikyška, J., Illangasekare T. H.: An improved semi-analytical solution for validation of numerical models of two-phase flow in porous media. Vadoze Zone Journal 6 (2007), 93–104 . ISSN 1539-1663
[6] Beneš M., Illangasekare T. H., Mikyška J.: On the numerical treatment of sharp texture transitions in two-phase flow. In: Czech–Japanese Seminar in Applied Mathematics 2005 (M. Beneš, M. Kimura, and T. Nakaki, eds.), COE Lecture Note Vol. 3, Hakozaki 6-10-1, Higashi-ku, Fukuoka, 812-8581, Japan 2006, pp. 106–116. Available on-line at http://www.math.kyushu-u.ac.jp/ masato/cj/proceedings-CJ05.html MR 2279051
[7] Beneš M., Stýblo M., Maryška, J., Mužák J.: The application of mathematical models of the transport of chemical substances in the remediation of consequences of the uranium mining. In: Proc. 3rd Workshop on Modelling of Chemical Reaction Systems, Heidelberg 1996, ISBN 3-932217-00-4
[8] Brooks R. H., Corey A. T.: Hydraulic properties of porous media. Colorado State University Hydrology Paper 3, Colorado State University 1964
[9] Buckley S. E., Leverett M. C.: Mechanism of fluid displacements in sands. Trans. AIME 146 (1942), 107–116
[10] Burdine N. T.: Relative Permeability Calculations from Pore-size Distribution Data. Technical Report, Petroleum Transaction, AIME, 1953
[11] Chen Z. X., Bodvarson G. S., Witherspoon P. A.: Comment on “exact integral solution for two-phase flow” by David B. McWhorter and Daniel K. Sunada. Water Resources Research 28 (1992), 5, 1477–1478 DOI 10.1029/92WR00473
[12] Forsyth P. A.: A control volume finite element approach to NAPL groundwater contamination. SIAM J. Sci. Statist. Comput. 12 (1991), 5, 1029–1057 DOI 10.1137/0912055 | MR 1114973 | Zbl 0725.76087
[13] Helmig R.: Multiphase Flow and Transport Processes in the Subsurface: A Contribution to the Modeling of Hydrosystems. Springer Verlag, Berlin 1997
[14] Huyakorn P. S., Pinder G. F.: Computational Methods in Subsurface Flow. Academic Press, New York 1983 Zbl 0577.76001
[15] McWhorter D. B., Sunada D. K.: Exact integral solutions for two-phase flow. Water Resources Research 26 (1990), 3, 399–413 DOI 10.1029/WR026i003p00399
[16] McWhorter D. B., Sunada D. K.: Reply. Water Resources Research 28 (1992), 5, 1479 DOI 10.1029/92WR00474
[17] Mikyška J.: Numerical Model for Simulation of Behaviour of Non-Aqueous Phase Liquids in Heterogeneous Porous Media Containing Sharp Texture Transitions. PhD Thesis, Faculty of Nuclear Science and Physical Engineering, Czech Technical University in Prague, Prague 2005
[18] Straka R.: Numerical simulation of reaction-diffusion dynamics. In: Proc. Czech Japanese Seminar in Applied Mathematics (M. Beneš, J. Mikyška, and T. Oberhuber, eds.), Czech Technical University in Prague 2005
[19] Turner A. D.: Behavior of Dense Non-aqueous Phase Liquids at Soil Interfaces of Heterogeneous Formations: Experimental Methods and Physical Model Testing. Master’s Thesis, Colorado School of Mines, Golden, Colorado 2004
[20] Vorst H. A. van der: Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems. SIAM J. Sci. Statist. Comput. 13 (1992), 631–644 DOI 10.1137/0913035 | MR 1149111
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