Two-Phase Flow in Heterogeneous Porous Media with Non-Wetting Phase Trapping
- 583 Downloads
This article presents a mathematical model describing flow of two fluid phases in a heterogeneous porous medium. The medium contains disconnected inclusions embedded in the background material. The background material is characterized by higher value of the non-wetting-phase entry pressure than the inclusions, which causes non-standard behavior of the medium at the macroscopic scale. During the displacement of the non-wetting fluid by the wetting one, some portions of the non-wetting fluid become trapped in the inclusions. On the other hand, if the medium is initially saturated with the wetting phase, it starts to drain only after the capillary pressure exceeds the entry pressure of the background material. These effects cannot be represented by standard upscaling approaches based on the assumption of local equilibrium of the capillary pressure. We propose a relevant modification of the upscaled model obtained by asymptotic homogenization. The modification concerns the form of flow equations and the calculation of the effective hydraulic functions. This approach is illustrated with two numerical examples concerning oil–water and CO2–brine flow, respectively.
KeywordsTwo-phase flow modeling Capillary trapping Upscaling Homogenization
The author A.S. would like to thank the German Research Foundation (DFG) for providing the financial support for the project within the Cluster of Excellence in Simulation Technology (EXC 310/1) at the University of Stuttgart. In addition, support from the International Research Training Group “Nonlinearities and Upscaling in Porous Media” (NUPUS) for the same author is kindly acknowledged here. The authors would like to thank Andreas Lauser for help in numerical implementation of the model, and two anonymous reviewers for their helpful suggestions.
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
- Amaziane B., Bourgeat A., Koebbe J.: Numerical simulation and homogenization of two-phase flow in heterogeneous porous media. Transport Porous Med. 6(5–6), 519–547 (1991)Google Scholar
- Barker J., Thibeau S.: A critical review of the use of pseudo relative permeabilities for upscaling. SPE Reservoir Eng. 12(2), 138–143 (1997)Google Scholar
- Brooks, R., Corey, A.: Hydraulic Properties of Porous Media. Hydrology Paper 3. Colorado State University, Fort Collins, COGoogle Scholar
- Burdine N.: Relative permeability calculations from pore size distribution data. Trans. Am. Inst. Min. Metall. Petrol. Eng. 198, 71–77 (1953)Google Scholar
- Flemisch, B., Fritz, J., Helmig, R., Niessner, J., Wohlmuth, B.: DUMUX: a multiscale multi-physics toolbox for flow and transport processes in porous media. In: Ibrahimbegovic, A., Dias, F., Matthies, H., Wriggers, P. (eds.) ECCOMAS Thematic Conference on Multi-scale Computational Methods for Solids and Fluids. Cachan, France, November 28–30 (2007)Google Scholar
- Helmig R.: Multiphase Flow and Transport Processes in the Subsurface: A Contribution to the Modeling of the Hydrosystems. Springer, Berlin (1997)Google Scholar
- Saadatpoor, E., Bryant, S., Sepehrnoori, K.: New trapping mechanism in carbon sequestration. Transport Porous Med. (2009b). doi: 10.1007/s11242-009-9446-6
- Szymkiewicz A.: Calculating effective conductivity of heterogeneous soils by homogenization. Arch. Hydro-eng. Environ. Mech. 52(2), 111–130 (2005)Google Scholar
- van Duijn C., Mikelic A., Pop I.: Effective equations for two phase flow with trapping on the micro scale. SIAM J. Appl. Math. 62, 531–1568 (2002)Google Scholar