Transport in Porous Media

, Volume 101, Issue 2, pp 191–213 | Cite as

Numerical Modelling of Sub-pore Scale Events in Two-Phase Flow Through Porous Media

  • Ali Q. Raeini
  • Branko Bijeljic
  • Martin J. Blunt
Article

Abstract

We use a new volume-of-fluid based finite-volume method to model two-phase flow through simple pore geometries and study the mechanisms controlling two-phase flow at the pore scale. The numerical model is used to study layer flow and snap-off, and investigate the effect of geometry and flow rate on trapping and mobilization of the disconnected ganglia. Furthermore, a new variable, the capillary field, is introduced to characterize the capillary force under dynamic situations, and a force-balance concept is presented to relate flow rates to pore-scale forces—dynamic pressure gradient and the capillary field. This description of the flow has the potential to be used in pore-network models to study the effect of pore-scale structures on the flow at larger scales. As an illustration of the applicability of this concept, we use the relations obtained from the numerical simulations to predict the threshold capillary number for blob mobilization during imbibition and show that this information can be used to reproduce the direct numerical simulation results accurately.

Keywords

Pore-scale modelling Capillary field Snap-off  Layer flow  Capillary trapping 

References

  1. Al-Gharbi, M.S., Blunt, M.J.: Dynamic network modeling of two-phase drainage in porous media. Phys. Rev. E 71(1), 016308 (2005)CrossRefGoogle Scholar
  2. Berg, S., Ott, H., Klapp, S.A., Schwing, A., Neiteler, R., Brussee, N., Makurat, A., Leu, L., Enzmann, F., Schwarz, J.O., Kersten, M., Irvine, S., Stampanoni, M.: Real-time 3D imaging of Haines jumps in porous media flow. Proc. Natl. Acad. Sci. U.S.A. 110, 3755–3759 (2013)CrossRefGoogle Scholar
  3. Blunt, M.J., Bijeljic, B., Dong, H., Gharbi, O., Iglauer, S., Mostaghimi, P., Paluszny, A., Pentland, C.: Pore-scale imaging and modelling. Adv. Water Resour. 51, 197–216 (2013)CrossRefGoogle Scholar
  4. Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface tension. J. Comput. Phys. 100(2), 335–354 (1992)CrossRefGoogle Scholar
  5. Bryant, S., Blunt, M.: Prediction of relative permeability in simple porous media. Phys. Rev. A 46(4), 2004–2011 (1992)CrossRefGoogle Scholar
  6. Dullien, F.A.L.: Porous Media: Fluid Transport and Pore Structure. Academic Press, San Diego (1979)Google Scholar
  7. He, W., Yi, J.S., Van Nguyen, T.: Two-phase flow model of the cathode of PEM fuel cells using interdigitated flow fields. AIChE J. 46(10), 2053–2064 (2000)CrossRefGoogle Scholar
  8. Issa, R.I.: Solution of the implicitly discretized fluid flow equations by operator-splitting. J. Comput. Phys. 62(1), 40–65 (1986)CrossRefGoogle Scholar
  9. Kanner, B., Glass, J.E.: Surface viscosity and elasticity—significant parameters in industrial processes. Ind. Eng. Chem. 61(5), 31–41 (1969)CrossRefGoogle Scholar
  10. Lake, L.W.: Enhanced Oil Recovery. Prentice Hall, Englewood Cliffs (1989)Google Scholar
  11. Lenormand, R., Zarcone, C., Sarr, A.: Mechanisms of the displacement of one fluid by another in a network of capillary ducts. J. Fluid Mech. 135, 337–353 (1983)CrossRefGoogle Scholar
  12. Mayer, R.P., Stowe, R.A.: Mercury porosimetry-breakthrough pressure for penetration between packed spheres. J. Colloid Sci. 20(8), 893–911 (1965)CrossRefGoogle Scholar
  13. Meakin, P., Tartakovsky, A.M.: Modeling and simulation of pore-scale multiphase fluid flow and reactive transport in fractured and porous media. Rev. Geophys. 47, RG3002 (2009)Google Scholar
  14. Mogensen, K., Stenby, E.H.: A dynamic two-phase pore-scale model of imbibition. Transp. Porous Med. 32(3), 299–327 (1998)CrossRefGoogle Scholar
  15. OpenFOAM. The open source CFD toolbox. http://www.openfoam.org (2010). Accessed 25 June 2010
  16. Oren, P.E., Bakke, S., Arntzen, O.J.: Extending predictive capabilities to network models. SPE J. 3(4), 324–336 (1998)Google Scholar
  17. Payatakes, A.C.: Dynamics of oil ganglia during immiscible displacement in water-wet porous media. Annu. Rev. Fluid Mech. 14(1), 365–393 (1982)CrossRefGoogle Scholar
  18. Princen, H.M.: Capillary phenomena in assemblies of parallel cylinders: I. Capillary rise between two cylinders. J. Colloid Interface Sci. 30(1), 69–75 (1969)CrossRefGoogle Scholar
  19. Prodanović, M., Bryant, S.L.: A level set method for determining critical curvatures for drainage and imbibition. J. Colloid Interface Sci. 304(2), 442–458 (2006)CrossRefGoogle Scholar
  20. Raeini, A.Q., Blunt, M.J., Bijeljic, B.: Modelling two-phase flow in porous media at the pore scale using the volume-of-fluid method. J. Comput. Phys. 231(17), 5653–5668 (2012)CrossRefGoogle Scholar
  21. Ransohoff, T.C., Radke, C.J.: Laminar flow of a wetting liquid along the corners of a predominantly gas-occupied noncircular pore. J. Colloid Interface Sci. 121(2), 392–401 (1988)CrossRefGoogle Scholar
  22. Roof, J.G.: Snap-off of oil droplets in water-wet pores. SPE J. 10(1), 85–90 (1970)Google Scholar
  23. Rubin, E., Meyer, L., de Coninck, H.: IPCC special report on carbon dioxide capture and storage. Prepared by working group III of the intergovernmental panel on climate change Intergovernmental Panel on Climate Change. Cambridge, UK (2005)Google Scholar
  24. Rusche, H.: Computational fluid dynamics of dispersed two-phase flows at high phase fractions. PhD thesis, Imperial College London (2002)Google Scholar
  25. Ryazanov, A.V., van Dijke, M.I.J., Sorbie, K.S.: Two-phase pore-network modelling: existence of oil layers during water invasion. Transp. Porous Med. 80(1), 79–99 (2009)CrossRefGoogle Scholar
  26. Stegmeier, G.L.: Mechanisms of entrapment and mobilization of oil in porous media. In: Shah, D.O., Schechter, R.S. (eds.) Improved Oil Recovery by Surfactant and Polymer Flooding. Academic Press, New York (1977)Google Scholar
  27. Ubbink, O.: Numerical prediction of two fluid systems with sharp interfaces. PhD thesis, Imperial College London (1997)Google Scholar
  28. Unsal, E., Mason, G., Ruth, D.W., Morrow, N.R.: Co- and counter-current spontaneous imbibition into groups of capillary tubes with lateral connections permitting cross-flow. J. Colloid Interface Sci. 315(1), 200–209 (2007)CrossRefGoogle Scholar
  29. Valvatne, P.H., Blunt, M.J.: Predictive pore-scale modeling of two-phase flow in mixed wet media. Water Resour. Res. 40(7), W07406 (2004)Google Scholar
  30. Wang, Z.H., Wang, C.Y., Chen, K.S.: Two-phase flow and transport in the air cathode of proton exchange membrane fuel cells. J. Power Sources 94(1), 40–50 (2001)CrossRefGoogle Scholar
  31. Williams, M.W., Kothe, D.B., Puckett, E.G.: Accuracy and convergence of continuum surface tension models. In: Proceedings of Fluid Dynamics at Interfaces, pp. 294–305. Cambridge University Press, Cambridge (1998)Google Scholar
  32. Yamasaki, A.: An overview of CO\(_2\) mitigation options for global warming-emphasizing CO\(_2\) sequestration options. J. Chem. Eng. Japan 36(4), 361–375 (2003)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Ali Q. Raeini
    • 1
  • Branko Bijeljic
    • 1
  • Martin J. Blunt
    • 1
  1. 1.Imperial College LondonLondonUK

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