Effective equations for two-phase flow in porous media: The effect of trapping on the microscale

Transport in Porous Media

Volumn 69, Issue 3, 2007, Pages 411-428

  Johannes van Duijn, Cornelis ^a   Eichel, Hartmut ^b   Helmig, Rainer ^b   Pop, Iuliu Sorin ^a  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Homogenization; Porous media; Two phase flow; Upscaling

Indexed keywords

CAPILLARITY; FLOW PATTERNS; HOMOGENIZATION METHOD; INTERFACES (MATERIALS); NUMERICAL METHODS; POROUS MATERIALS; SURFACE TENSION;

CAPILLARY EFFECT; FLOW DIRECTION;

TWO PHASE FLOW;

CAPILLARITY; FLOW PATTERNS; HOMOGENIZATION METHOD; INTERFACES (MATERIALS); NUMERICAL METHODS; POROUS MATERIALS; SURFACE TENSION; TWO PHASE FLOW;

CAPILLARITY; EQUATION; HETEROGENEOUS MEDIUM; POROUS MEDIUM; TWO PHASE FLOW; UPSCALING; VISCOUS FLOW;

EID: 38149024039     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-006-9089-9     Document Type: Article

References (19)

1. Bastian P., Helmig R. (1999) Efficient fully-coupled solution techniques for two-phase flow in porous media. Adv. Water Resour. 23: 199-216
2. Bertsch M., Dal Passo R., van Duijn C.J. (2003) Analysis of oil trapping in porous media flow. SIAM J. Math. Anal. 35: 245-267
3. Brooks R.H., Corey A.T. (1966) Properties of porous media affecting fluid flow. J. Irrig. Drain. Div. Proc. ASCE 92: 61-88
4. Darman N.H., Pickup G.E., Sorbie K.S. (2002) A comparison of two-phase flow dynamic upscaling methods based on fluid potentials. Comp. Geosci. 6: 5-27
5. van Duijn C.J., Mikelic A., Pop I.S. (2002a) Effective equations for two-phase flow with trapping on the micro scale. SIAM J. Appl. Math. 62(5): 1531-1568
6. van Duijn C.J., Mikelic A., Pop I.S. (2002b) Effective Buckley-Leverett equations by homogenization. In: Anile M., Capasso V., Greco A. (eds). Progress in Industrial Mathematics at ECMI 2000: Mathematics in Industry, vol. 1. Springer-Verlag, Heidelberg, pp. 42-51
7. van Duijn C.J., Molenaar J., de Neef M.J. (1995) The effect of capillary forces on immiscible two-phase flow in heterogeneous porous media. Transp. Porous Media 21: 71-93
8. van Genuchten M.Th. (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44: 892-898
9. Helmig R. (1997) Multiphase Flow and Transport Processes in the Subsurface. Springer-Verlag, Heidelberg
10. Hornung U. (1997) Homogenization and Porous Media. Interdisciplinary Applied Mathematics, vol. 6. Springer Verlag, New York
11. Illangasekare T.H., Ramsay J.L., Jensen K.H., Butts M.B. (1995) Experimental study of movement and distribution of dense organic contaminants in heterogeneous aquifers. J. Contam. Hydrol. 20(1-2): 1-25
12. Kueper B.H., Abbott W., Farquhar G. (1989) Experimental observations of multiphase flow in heterogeneous porous media. J. Contam. Hydrol. 5: 83-95
13. Kueper B.H., Frind E.O. (1991) Two-phase flow in heterogeneous porous media. 1. Model development. Water Resour. Res. 27, 1049-1057
14. Leverett M.C. (1941) Capillary behavior in porous solids. Trans. AIME Petr. Eng. Div. 142: 152-169
15. Lewandowska J., Szymkiewicz A., Burzyński K., Vauclin M. (2004) Modeling of unsaturated water flow in double porosity soils by the homogenization approach. Adv. Water Resour. 27(3): 321-345
16. van Lingen, P.: Quantification and reduction of capillary entrapment in cross-laminated oil reservoirs, PhD Thesis. Sub-Faculty of Applied Earth Sciences, Delft University of Technology (1998)
17. Neuweiler, I., Cirpka, O.A.: Homogenization of Richards equation in permeability fields with different connectivities. Water Resour. Res. 41, W02009, doi:10.1029/2004WR003329 (2005)
18. Schweizer, B.: Homogenization of degenerate two-phase flow equations with oil-trapping. Preprint 2006-04, Department of Mathematics, University of Basel (submitted) (2006)
19. Wen X.H., Gómez-Hernández J.J.: Upscaling hydraulic conductivities in heterogeneous media: An overview. J. Hydrol. 183, ix-xxxii (1996)