Skip to main content
SpringerLink
Log in

A dynamic network model for two‐phase immiscible flow

  • Published:
Computational Geosciences Aims and scope Submit manuscript

Abstract

A dynamic pore‐scale network model is formulated for two‐phase immiscible flow. Interfaces are tracked through the pore throats using a modified Poiseuille equation, whereas special displacement rules are used at the pore bodies. The model allows interfaces to move over several pore‐lengths within a time step. Initial computational results are presented for a drainage experiment to demonstrate some of the features of the model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Blunt and P. King, Relative permeabilities from two-and three-dimensional pore-scale network modelling, Transport in Porous Media 6 (1991) 407–433.

    Article  Google Scholar 

  2. J.S. Buckley, Multiphase displacements in micromodels, in: Surfactant Science Series, Vol. 36 (Marcel Dekker, New York, 1991) pp. 157–189.

    Google Scholar 

  3. M.A. Celia, P.C. Reeves and L.A. Ferrand, Recent advances in pore-scale models for multiphase flow in porous media, in: Reviews of Geophysics, Supplement, U.S. National Report to International Union of Geodesy and Geophysics 1991–1994 (July 1995) pp. 1049–1057.

  4. M. Chaouche, N. Rakotomalala, D. Salin, B. Xu, and Y. C. Yortsos, Invasion percolation in a hydrostatic or permeability gradient: Experiments and simulations, Phys. Rev. E 49(5) (1994) 4133–4139.

    Article  Google Scholar 

  5. G.N. Constantinides and A.C. Payatakes, Three-dimensional simulation of immiscible displacement of oil ganglia in consolidated porous media, in: Proc. Euro. Symp. Enhanced Oil Recovery (1988) p. 965.

  6. G.N. Constantinides and A.C. Payatakes, A theoretical model of collision coalescence of ganglia in porous media, J. Colloid Interface Sci. 141 (1991).

  7. G.N. Constantinides and A.C. Payatakes, Network simulation of steady-state two-phase flow in consolidated porous media, AIChE J. 42(2) (1996) 365–382.

    Article  Google Scholar 

  8. M.M. Dias and A.C. Payatakes, Network models for two-phase flow in porous media, Part 1. Immiscible microdisplacement of non-wetting fluids, J. Fluid Mechanics 164 (1986) 305–336.

    Article  MATH  Google Scholar 

  9. M.M. Dias and A.C. Payatakes, Network models for two-phase flow in porous media, Part 2. Motion of oil ganglia, J. Fluid Mechanics 164 (1986) 337–358.

    Article  MATH  Google Scholar 

  10. A.F.L. Dullien, Porous Media: Fluid Transport and Pore Structure (Academic Press, New York, 2nd ed., 1992).

    Google Scholar 

  11. E.B. Dussan, Immiscible liquid displacement in a capillary tube: The moving contact line, AIChE J. 23(1) (1977) 131–133.

    Article  Google Scholar 

  12. I. Fatt, The network model of porous media, I. Capillary pressure characteristics, Petroleum Trans. AIME 207 (1956) 144–159.

    Google Scholar 

  13. I. Fatt, The network model of porous media, II. Dynamic properties of a single size tube network, Petroleum Trans. AIME 207 (1956) 160–163.

    Google Scholar 

  14. I. Fatt, The network model of porous media, III. Dynamic properties of networks with tube radius distribution, Petroleum Trans. AIME 207 (1956) 164–181.

    Google Scholar 

  15. W.G. Gray and S.M. Hassanizadeh, Unsaturated flow theory including interfacial phenomena, Water Resour. Res. 27 (1991) 1855–1863.

    Article  Google Scholar 

  16. W.G. Gray and S.M. Hassanizadeh, Macroscale continuum mechanics for multiphase porous-media flow including phases, interfaces contact lines, and common points, Adv. Water Res. 21(4) (1998) 261–281.

    Article  Google Scholar 

  17. S.M. Hassanizadeh, Dynamic effects in the capillary pressure-saturation relationship, in: Proc. of 4th Int. Conf. on Civ. Eng., Vol. IV: Water Resources and Environmental Engineering, Sharif U. of Tech., Iran (1997) pp. 141–149.

    Google Scholar 

  18. S.M. Hassanizadeh and W.G. Gray, General conservation equations for multi-phase systems: 1. Averaging procedure, Adv. Water Res. 2(3) (1979) 131–144.

    Article  Google Scholar 

  19. S.M. Hassanizadeh and W.G. Gray, Mechanics and thermodynamics of multiphase flow in porous media including interface boundaries, Adv. Water Res. 13(4) (1990) 169–186.

    Article  Google Scholar 

  20. S.M. Hassanizadeh and W.G. Gray, Thermodynamic basis of capillary pressure in porous media, Water Resour. Res. 29 (1993) 3389–3405.

    Article  Google Scholar 

  21. C. Huh and L.E. Scriven, Hydrodynamic model of steady movement of a solid/liquid/fluid contact line, J. Colloid Sci. 35 (1971) 85–101.

    Article  Google Scholar 

  22. J. Koplik, Creeping flow in two-dimensional networks, J. Fluid Mech. 119 (1982) 219–247.

    Article  MATH  Google Scholar 

  23. J. Koplik and T.J. Lasseter, Two-phase flow in random network models of porous media, Soc. Petroleum Engrg. J. 2 (1985) 89–100. Also appeared as Soc. Petroleum Engrg. Paper 11014 (1982).

    Google Scholar 

  24. N.R. Morrow, ed., Interfacial Phenomena in Petroleum Recovery, Surfactant Science Series, Vol. 36 (Marcel Dekker, New York, 1991).

  25. R.A. Novy, P.G. Toledo, H.T. Davis and L.E. Scriven, Capillary dispersion in porous media at low wetting phase saturations, Chem. Engrg. Sci. 44(9) (1989) 1785–1797.

    Article  Google Scholar 

  26. P.C. Reeves, The development of pore-scale network models for the simulation of capillary pressuresaturation-interfacial area — relative permeability relationships in multi-fluid porous media, Ph.D. thesis, Princeton University (1997).

  27. P.C. Reeves and M.A. Celia, A functional relationship between capillary pressure, saturation, and interfacial area as revealed by a pore-scale network model, Water Resour. Res. 32 (1996) 2345–2358.

    Article  Google Scholar 

  28. M. Sahimi, Flow and Transport in Porous Media and Fractured Rock (VCH, Weinheim, Germany, 1995).

    Google Scholar 

  29. D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor & Francis, London, 2nd ed., 1992).

    Google Scholar 

  30. J. van Brakel, Pore space models for transport phenomena in porous media: Review and evaluation with special emphasis on capillary liquid transport, Powder Technology 11 (1975) 205–236.

    Article  Google Scholar 

  31. S.C. van der Marck and J. Glas, Pressure measurements during forced imbibition experiments in micro-models, European J. Mech. B Fluids 16 (1997) 681–692.

    Google Scholar 

  32. S.C. van der Marck, T. Matsuura and J. Glas, Viscous and capillary pressures during drainage: Network simulations and experiments, Phys. Rev. E 56 (1997) 5675–5687.

    Article  Google Scholar 

  33. E.W. Washburn, The dynamics of capillary flow, Phys. Rev. 17 (1921) 273–283.

    Article  Google Scholar 

  34. C. Zarcone, R. Lenormand and E. Touboul, Numerical models and experiments on immiscible displacement in porous media, J. Fluid Mech. 189 (1988) 165–187.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Bergen, N‐5008, Bergen, Norway E-mail:

    Helge K. Dahle

  2. Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ, 08544, USA E-mail:

    Michael A. Celia

Authors
  1. Helge K. Dahle
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael A. Celia
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dahle, H.K., Celia, M.A. A dynamic network model for two‐phase immiscible flow. Computational Geosciences 3, 1–22 (1999). https://doi.org/10.1023/A:1011522808132

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1011522808132

Search

Navigation