Significance of dynamic effect in capillarity during drainage experiments in layered porous media

Vadose Zone Journal

Volumn 9, Issue 3, 2010, Pages 697-708

  Fučík, Radek ^a   Mikyška, Jiří ^a   Sakaki, Toshihiro ^b   Beneš, Michal ^a   Illangasekare, Tissa H ^b  

^a CZECH TECHNICAL UNIVERSITY IN PRAGUE   (Czech Republic)

^b Department of Metallurgical and Materials Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACCUMULATION TIME; CAPILLARY BARRIER EFFECT; CAPILLARY PRESSURE-SATURATION RELATIONSHIP; CAPILLARY PRESSURES; DRAINAGE EXPERIMENTS; DYNAMIC EFFECTS; EXPERIMENTAL SETUP; FLUID PROPERTY; LABORATORY EXPERIMENTS; LAYERED POROUS MEDIA; MATERIAL INTERFACES; NUMERICAL SCHEME; POROUS MEDIUM; PRESSURE VALUES; SEMI-ANALYTICAL SOLUTION; STATIC MODEL;

CAPILLARITY; CAPILLARY TUBES; EXPERIMENTS; INTERFACES (MATERIALS); INVESTMENTS; MULTIPHASE FLOW; POROUS MATERIALS;

PRESSURE EFFECTS;

CAPILLARITY; DRAINAGE; EXPERIMENTAL STUDY; GEOACCUMULATION; HETEROGENEITY; HOMOGENEITY; MATHEMATICAL ANALYSIS; NUMERICAL MODEL; ONE-DIMENSIONAL MODELING; POROUS MEDIUM; PRESSURE EFFECT; SATURATION; TWO PHASE FLOW;

EID: 79960240066     PISSN: None     EISSN: 15391663     Source Type: Journal    
DOI: 10.2136/vzj2009.0106     Document Type: Article

References (38)

1. Bastian, P. 1999. Numerical computation of multiphase flows in porous media. Habilitation thesis. Kiel Univ., Kiel, Germany.
2. Bear, J., and A. Verruijt. 1990. Modeling groundwater flow and pollution. D. Reidel, Dordrecht, the Netherlands.
3. Brooks, R.H., and A.T. Corey. 1964. Hydraulic properties of porous media. Hy-drol. Pap. 3. Colorado State Univ., Fort Collins.
4. Burdine, N.T. 1953. Relative permeability calculations from pore-size distribution data. Trans. Am. Inst. Min. Eng. 198:71-78.
5. Camps-Roach, G., D.M. O'Carroll, T.A. Newson, T. Sakaki, and T.H. Illangasek-are. 2010. Experimental investigation of dynamic effects in capillary pressure: Grain size dependency and upscaling. Water Resour. Res. (in press), doi:10.1029/2009WR008792.
6. Dahle, H.K., M.A. Celia, and M.S. Hassanizadeh. 2005. Bundle-of-tubes model for calculati ng dynamic effects in the capillary-pressure-saturation relationship. Transp. Porous Media 58:5-22.
7. de Neef, M.I., and J. Molenaar. 1997. Analysis of DNAPL Infiltration in a medium with a low-permeable lens. Comput. Geosci. 1:191-214.
8. Fučík, R., M. Beneš, J. Mikyška, and T.H. Illangasekare. 2004. Generalization of the benchmark solution for the two-phase porous-media flow. p. 181-184. In K. Kovar et al. (ed.) Int. Conf. on Finite-Element Models, MODFLOW, and More: Solving Groundwater Problems, Carlsbad, Czech Republic. 13-16 Sept. 2004.
9. Fučík, R., J. Mikyška, and T.H. Illangasekare. 2005. Evaluation of saturation-dependent flux on two-phase flow using generalized semi-analytic solution. p. 23-35. In M. Benes et al. (ed.) Proc. Czech-Japanese Seminar in Applied Mathematics. Faculty of Nucl. Sci. and Phys. Eng., Czech Tech. Univ., Prague.
10. Fučík, R., J. Mikyška, M. Beneš, and T.H. Illangasekare. 2007. An improved semi-analytical solution for verification of numerical models of two-phase flow in porous media. Vadose Zone J. 6:93-104.
11. Fučík, R., J. Mikyška, M. Beneš, and T.H. Illangasekare. 2008. Semianalytical solution for two-phase flow in porous media with a discontinuity. Vadose Zone J. 7:1001-1007.
12. Fučík, R., J. Mikyška, T. Sakaki, and T.H. Illangasekare. 2009. Numerical study of the effect of dynamic capillary pressure in porous medium. p. 14-30. In M. Benes et al. (ed.) Proc. Czech-Japanese Seminar in Applied Mathematics 2008. COE Lecture Note, Vol. 14. Faculty of Math., Kyushu Univ., Fukuoka, Japan.
13. Gray, W.G., and S.M. Hassanizadeh. 1991a. Paradoxes and realities in unsaturated flow theory. Water Resour. Res. 27:1847-1854.
14. Gray, W.G., and S.M. Hassanizadeh. 1991b. Unsaturated flow theory including interfacial phenomena. Water Resour. Res. 27:1855-1863.
15. Hassanizadeh, S.M., M.A. Celia, and H.K. Dahle. 2002. Dynamic effect in the capillary pressure-saturation relationship and its impacts on unsaturated flow. Vadose Zone J. 1:38-57.
16. Hassanizadeh, S.M., and W.G. Gray. 1993. Thermodynamic basis of capillary pressure in porous media. Water Resour. Res. 29:3389-3406.
17. Helmig, R. 1997. Multiphase flow and transport processes in the subsurface: A contribution to the modeling of hydrosystems. Springer-Verlag, Berlin.
18. Helmig, R., A. Weiss, and B.I. Wohlmuth. 2007. Dynamic capillary effects in heterogeneous porous media. Comput. Geosci. 11:261-274.
19. Helmig, R., A. Weiss, and B.I. Wohlmuth. 2009. Variational inequalities for modeling flow in heterogeneous porous media with entry pressure. Com-put. Geosci. 13:1-17.
20. Illangasekare, T.H., E.J. Armbruster III, and D.N. Yates. 1995. Non-aqueous-phase fluids in heterogeneous aquifers: Experimental study. J. Environ. Eng. 121:571-579.
21. Ippisch, O., H.J. Vogel, and P. Bastian. 2006. Validity limits for the van Genu-chten-Mualem model and implications for parameter estimation and numerical simulation. Adv. Water Resour. 29:1780-1789.
22. LeVeque, R.J. 2002. Finite volume methods for hyperbolic problems. Cambridge Univ. Press, Cambridge, UK.
23. Leverett, M.C. 1941. Capillary behavior in porous solids. Trans. Am. Inst. Min. Eng. 142:152-169.
24. Manthey, S. 2006. Two-phase flow processes with dynamic effects in porous media: Parameter estimation and simulation. Inst. fur Wasserbau der Uni-versitat Stuttgart, Stuttgart, Germany.
25. Manthey, S., M.S. Hassanizadeh, and R. Helmig. 2005. Macro-scale dynamic effects in homogeneous and heterogeneous porous media. Transp. Porous Media 58:121-145.
26. McWhorter, D.B., and D.K. Sunada. 1990. Exact integral solutions for two-phase flow. Water Resour. Res. 26:399-413.
27. Mikyska, J., M. Benes, and T.H. Illangasekare. 2009. Numerical investigation of non-aqueous phase liquid behavior at heterogeneous sand layers using VODA multiphase flow code. J. Porous Media 12:685-694.
28. Nieber, J.L., R.Z. Dautov, A.G. Egorov, and A.Y. Sheshukov. 2005. Dynamic capillary pressure mechanism for instability in gravity-driven flows: Review and extension to very dry conditions. Transp. Porous Media 58:147-172.
29. Nordbotten, J.M., M.A. Celia, H.K. Dahle, and S.M. Hassanizadeh. 2007. Interpretation of macroscale variables in Darcy's law. Water Resour. Res. 43:W08430, doi:10.1029/2006WR005018.
30. Nordbotten, J.M., M.A. Celia, H.K. Dahle, and S.M. Hassanizadeh. 2008. On the definition of macroscale pressure for multiphase flow in porous media. Water Resour. Res. 44:W06S02, doi:10.1029/2006WR005715.
31. O'Carroll, D.M., T.J. Phelan, and L.M. Abriola. 2005. Exploring dynamic effects in capillary pressure in multistep outflow experiments. Water Resour. Res. 41:W11419, doi:10.1029/2005WR004010.
32. Peszynska, M., and S.Y. Yi. 2008. Numerical methods for unsaturated flow with dynamic capillary pressure in heterogeneous porous media. Int. J. Numer. Anal. Model. 5:126-149.
33. Sakaki, T., D.M. O'Carroll, and T.H. Illangasekare. 2010. Direct quantification of dynamic effects in capillary pressure for drainage and wetting cycles. Vadose Zone J. 9:424-437.
34. Stauffer, F. 1978. Time dependence of the relations between capillary pressure, water content and conductivity during drainage of porous media. p. 3.35-3.52. In IAHR Symp. on Scale Effects in Porous Media, Thessaloniki, Greece. 28 Aug.-1 Sept. 1978. Int. Assoc. Hydro-Environ. Eng. Res., Madrid.
35. van Duijn, C.J., and M.J. de Neef. 1998. Self-similar profiles for capillary diffusion driven flow in heterogeneous porous media. Adv. Water Resour. 21:451-461.
36. van Duijn, C.J., J. Molenaar, and M.J. de Neef. 1995. The effect of capillary forces on immiscible two-phase flow in heterogeneous porous media. Transp. Porous Media 21:71-93.
37. van Duijn, C.J., L.A. Peletier, and I.S. Pop. 2007. A new class of entropy solutions of the Buckley-Leverett equation. SIAM J. Math. Anal. 39:507-536.
38. van Genuchten, M.Th. 1980. A closed-form equation for predicting the hydraulic conducti vity of unsaturated soils. Soil Sci. Soc. Am. J. 44:892-898.