| |
Highly gravity-driven flow of a NAPL in water-saturated porous media using the discontinuous Galerkin finite-element method with a generalised Godunov scheme
- 作者:Lauriane Schneider ; Rapha?l di Chiara Roupert ; Gerhard Sch?fer…
- 关键词:Two ; phase flow ; Gravity forces ; Hyperbolic equations ; Godunov scheme ; 58J45
- 刊名:Computational Geosciences
- 出版年:2015
- 出版时间:August 2015
- 年:2015
- 卷:19
- 期:4
- 页码:855-876
- 全文大小:2,703 KB
- 参考文献:1.Amaziane, B., Jurak, M., ?galjic Keko, A.: An existence result for a coupled system modeling a fully equivalent global pressure formulation for immiscible compressible two-phase flow in porous media. J. Differ. Equ. 250, 1685-718 (2011)CrossRef
2.Amaziane, B., Jurak, M., ?galjic Keko, A.: Numerical simulations of water-gas flow in heterogeneous porous media with discontinuous capillary pressures by the concept of global pressure. J. Comput. Appl. Math. 236, 4227-244 (2012)CrossRef 3.Amaziane, B., Jurak, M., ?galjic Keko, A.: Modeling and numerical simulations of immiscible compressible two-phase flow in porous media by the concept of global pressure. Transp. Porous Media 84, 133-52 (2010)CrossRef 4.Andreianov, B., Cancès, C.: Vanishing capillarity solutions of Buckley-Leverett equation with gravity in two-rocks-medium. Comput. Geosci. 17, 551-72 (2013)CrossRef 5.Aris, R.: On the dispersion of a solute in a fluid flowing through a tube. In: Proceedings of The Royal Society A: Mathematical. Physical and Engineering Sciences, p 235 (1956) 6.Binning, P., Celia, M.A.: Practical implementation of the fractional flow approach to multi-phase flow simulation. Adv. Water Resour. 22(5), 461-78 (2010)CrossRef 7.Buckley, S.E., Leverett., M.C.: Mecanism of fluid displacement in sands. Am. Inst. Min. Metall. Pet. Eng. 146, 107-16 (1942) 8.Chavent, G., Jaffré, J.: Mathematical models and finite elements for reservoir simulation. Elsevier Science publishers B.V. (1986) 9.Chavent, G.: A fully equivalent global pressure formulation for three-phases compressible flows. Applicable Analysis. An International Journal 88, 1527-541 (2009)CrossRef 10.Chen, Z., Ewing, R.: Comparison of various formulations of three-phase flow in porous media. J. Comput. Phys. 132, 362-73 (1997)CrossRef 11.Chen, Z.: Finite element methods and their applications. Springer-Verlag, Scientific Computation, Berlin (2005) 12.Cockburn, B., Karniadakis, G.E., Shu, C.-W.: Discontinuous Galerkin methods. Lect. Notes Comput. Sci. Eng., Springer, Berlin 11, 3-0 (2000)CrossRef 13.di Chiara Roupert, R.: Développement d’un code de calcul multiphasique multiconstituants, PhD thesis, Université de Strasbourg (2009) 14.di Chiara Roupert, R., Chavent, G., Sch?fer, G.: Three-phase compressible flow in porous media: total differential compatible interpolation of relative permeabilities. J. Comput. Phys. 229, 4762-780 (2010)CrossRef 15.El Soueidy, C.P.: Eléments finis discontinus multi-domaines en temps pour la modélisation du transport en milieu poreux saturé, PhD thesis, Université de Strasbourg (2008) 16.Ern, A., Mozolevski, I., Schuh, L.: Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures. Comp. Meth. Appl. Mech. Eng. 199(23-4), 1491-501 (2010)CrossRef 17.Ewing, R.: Mathematical modeling and simulation for fluid flow in porous media. Rossiiskaya Akademiya Nauk. Matematicheskoe Modelirovanie 13, 117-27 (2001) 18.Ewing, R., Chen, Z., Espedal, M.: Multiphase Flow Simulation With Various Boundary Conditions. X International Conference on Computational Methods in Water Resources, Heidelberg (1994) 19.Ewing, R.P., Berkowitz, B.: A generalized growth model for simulating initial migration of dense non-aqueous phase liquids. Water Resour. Res., 611-22 (1998) 20.Eymard, R., Gallou?t, T., Ghilani, M., Herbin, R.: Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes. IMA J. Numer. Anal. 18, 563-94 (1998)CrossRef 21.Frette, O.I., M?l?y, K.J., Schmittbuhl, J., Hansen, J.: Immiscible displacement of viscosity-matched fluids in two-dimensional porous media. Phys. Rev. 3, 2969-975 (1997) 22.Godlewski, E., Raviart, P.-A.: Hyperbolic systems of conservation laws (3/4), Ellipses. Paris (1991) 23.Helmig, R.: Multiphase Flow and transport Processes in the subsurface. Springer (1997) 24.Hoteit, H., Firoozabadi, A.: Multicomponent fluid flow by discontinuous Galerkin and mixed methods in unfractured and fratured media. Resources Research, p 41 (2005) 25.Hoteit, H., Firoozabadi, A.: Numerical modeling of two-phase flow in heterogeneous permeable media with different capillarity pressures, Advances in Water Resources, p 31 (2008) 26.Huber, R., Helmig, R.: Multiphase flow in heterogeneous porous media: a classical finite element method versus an implicit pressure–explicit saturation-based mixed finite element–finite volume approach. Int. J. Numer. Methods Fluids 29, 899-20 (1999)CrossRef 27.Kaasschieter, E.F.: Solving the Buckley-Leverett equation with gravity in a heterogeneous porous medium. Comput. Geosci. 3, 23-8 (1999)CrossRef 28.Kru?kov, S.N.: First order quasilinear equations with several independent variables. Mat. Sb. (N.S.) 81(123), 228-55 (1970) 29.Langtangen, H.P., Tveiko, A.: Instability of Buckley-Leverett Flow in a Hetegogeneous Med - 作者单位:Lauriane Schneider (1)
Rapha?l di Chiara Roupert (1) Gerhard Sch?fer (1) Philippe Helluy (2)
1. Laboratoire d’Hydrolgie et de Géochimie de Strasbourg, UMR 7517 CNRS-Université de Strasbourg-ENGEES, 1, rue Blessig, 67084, Strasbourg Cedex, France 2. Institut de Recherche Mathématique Avancée, UMR 7501 CNRS-Université de Strasbourg, 7 rue René-Descartes, 67084, Strasbourg Cedex, France
- 刊物类别:Mathematics and Statistics
- 刊物主题:Mathematics
Mathematical Modeling and IndustrialMathematics Geotechnical Engineering Hydrogeology Soil Science and Conservation
- 出版者:Springer Netherlands
- ISSN:1573-1499
文摘
In this paper, we develop an implementation of gravity effects within a Global Pressure formulation in a numerical scheme based on the implicit pressure explicit saturation (IMPES) approach. We use the Discontinuous Galerkin Finite-Element Method (DGFEM) combined with a generalised Godunov scheme to model an immiscible two-phase flow with predominant gravity effects. The saturation profile of a displacing non-aqueous phase liquid (NAPL) in an initially water-saturated porous medium depends strongly on the ratio between the total specific discharge and the density difference between the NAPL and water. We discuss the solution of the nonlinear Buckley-Leverett equation for the general case in which the flux function is non-monotonic. Using a detailed functional analysis of the characteristics of the given hyperbolic equation, three limit cases are identified as significant for modelling the shock and rarefaction regions. The derived maximum (or entry) and front saturations of NAPL are functions of the viscosity ratio M and the gravity number G. We first test the developed numerical model in the case of a one-dimensional highly gravity-driven flow of NAPL within a homogeneous porous medium. The numerically calculated NAPL entry and front saturations of NAPL agree well with the theoretical values. Furthermore, the numerical diffusion of the shock front is lower than that of the calculated using a first-order Finite Volume method, which is generally used in reservoir engineering because of its robustness. Finally, we apply the developed DGFEM scheme to a 2D heterogeneous porous medium and analyse its capability of modelling the non-uniform saturation field using spatial moment analysis. Keywords Two-phase flow Gravity forces Hyperbolic equations Godunov scheme
| |
NGLC 2004-2010.National Geological Library of China All Rights Reserved.
Add:29 Xueyuan Rd,Haidian District,Beijing,PRC. Mail Add: 8324 mailbox 100083
For exchange or info please contact us via email.
| |