Skip to main content
SpringerLink
Log in

Micro-hydrodynamics of immiscible displacement inside two-dimensional porous media

  • Research Paper
  • Published:
Microfluidics and Nanofluidics Aims and scope Submit manuscript

Abstract

In this paper, a Boolean lattice-gas model based on field mediators proposed by Santos and Philippi (Phys Rev E 65:046305, 2002) is used for the simulation of fluid–fluid interface displacement inside two-dimensional simplified porous media. A new procedure is introduced to allow the simulation of different viscosity ratios on the framework of lattice-gas models. The model is verified by simulating the spreading of a liquid drop on a solid surface and by comparing the simulation results with experimental spreading data. Some important basic physical mechanisms occurring at the pore scale are simulated and compared qualitatively with experimental visualizations. The break-off phenomenon of the fluid–fluid interface is observed in bifurcations, when a wetting (or non-wetting) fluid is displacing a non-wetting (or wetting) fluid. The role of break-off is shown to be different in imbibition and drainage processes in agreement with experimental results. Finally, the influence of wettability on the displacement efficiency is investigated in two-dimensional random arrays of disks.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Adler PM, Jacquin CG, Quiblier JA (1990) Flow in simulated porous media. Int J Multiph Flow 16(4):691–712

    Article  MATH  Google Scholar 

  • Anderson WG (1987) Wettability literature survey—Part 6: the effects of wettability on waterflooding. J Pet Technol 39(12):1605–1621

    Google Scholar 

  • Appert C, Zaleski S (1990) Lattice gas with a liquid–gas transition. Phys Rev Lett 64:1–4

    Article  MATH  MathSciNet  Google Scholar 

  • Appoloni CR, Macedo A, Fernandes CP, Philippi PC (2002) Characterization of porous microstructure by X-ray microtomography. Xray Spectrom 31:124–127

    Article  Google Scholar 

  • Bear J (1972) Dynamics of fluids in porous media. Dover Publications, New York

    Google Scholar 

  • Bretherton FP (1961) The motion of long bubbles in tubes. J Fluid Mech 10:166

    Article  MATH  MathSciNet  Google Scholar 

  • Cazabat AM (1987) How does a droplet spread? Contemp Phys 28(4):347–364

    Article  Google Scholar 

  • Chatzis I, Dullien FAL (1983) Dynamic immiscible displacement mechanisms in pore doublets: theory versus experiment. J Colloid Interface Sci 91(1):199–222

    Article  Google Scholar 

  • Chen S, Diemer K, Doolen GD, Eggert K, Fu C, Gutman S, Travis BJ (1991) Lattice gas automata for flow through porous media. Physica D 47:72–84

    Article  Google Scholar 

  • Coninck J, Ruijter MJ, Voue M (2001) Dynamics of wetting. Curr Opin Colloid Interface Sci 6:49–53

    Article  Google Scholar 

  • Cuiec LE (1991) Interfacial phenomena in petroleum recovery, vol 36. Surfactant science series, chap 9. Marcel Dekker, New York, pp 319–375

  • Derjaguin BV (1943) On the thickness of the liquid film adhering to the walls of a vessel after emptying. Acta Physicochim USSR 20:349

    Google Scholar 

  • d’Humières P, Lallemand D, Frisch U (1986) Lattice gas models for 3D hydrodynamics. Europhys Lett 2:291–297

    Article  Google Scholar 

  • dos Santos LOE, Philippi PC (2002) Lattice-gas model based on field mediators for immiscible fluids. Phys Rev E 65:046305

    Article  Google Scholar 

  • dos Santos LOE, Philippi PC, Bertoli SL, Facin PC (2002) Lattice-gas models for single and two-phase flows: application to the up-scaling problem in porous microstructures. Comput Appl Math 21:545–571

    MATH  MathSciNet  Google Scholar 

  • Dupré A (1869) Théorie Mecánique de la Chaleur. Gauthier-Villars, Paris

    Google Scholar 

  • Everett DH, Haynes JM (1972) Model studies of capillary condensation 1. Cylindrical pore model with zero contact angle. J Colloid Interface Sci 38(1):125–137

    Article  Google Scholar 

  • Fernandes CP (1994) Caracterização morfotopológica de espaços porosos: reconstituiçao multiescala e simulação de processos de invasão de fluidos não-molhantes. PhD Thesis, Federal University of Santa Catarina, Florianopolis, Brazil

  • Frisch U, Hasslacher B, Pomeau Y (1986) Lattice-gas automata for the Navier–Stokes equations. Phys Rev Lett 56(14):1505–1508

    Article  Google Scholar 

  • de Gennes PG (1985) Wetting: statics and dynamics. Rev Modern Phys 57(3):827–863

    Article  Google Scholar 

  • Hardy J, Pomeau Y, Pazzis O (1973a) Time evolution of a two-dimensional classical lattice system. Phys Rev Lett 31(5):276–279

    Article  Google Scholar 

  • Hardy J, Pomeau Y, Pazzis O (1973b) Time evolution of a two-dimensional model system. I. Invariant states and time correlation functions. J Math Phys 14(12):1746–1759

    Article  Google Scholar 

  • Hazlett RD (1995) Simulation of capillary-dominated displacements in microtomographic images of reservoir rocks. Transp Porous Media 20:21–35

    Article  Google Scholar 

  • Joshi MY (1974) A class of stochastic models for porous media. PhD Thesis, University of Kansas, Lawrence, USA

  • Koplik J, Banavar JR, Willemsen JF (1988) Molecular dynamics of Poiseuille flow and moving contact lines. Phys Rev Lett 60(13):1282–1285

    Article  Google Scholar 

  • Landau L, Levich B (1942) Dragging of a liquid by a moving plate. Acta Physicochimi USSR 17:42

    Google Scholar 

  • Liang ZR, Fernandes CP, Magnani FS, Philippi PC (1998) A reconstruction technique for three-dimensional porous media using image analysis and Fourier transforms. J Pet Sci Eng 21:273–283

    Article  Google Scholar 

  • Marmur A (1983) Equilibrium and spreading of liquids on solids surfaces. Adv Colloid Interface Sci 19(19):75–102

    Article  Google Scholar 

  • Maruyama S, Kimura T, Lu M (2002) Molecular scale aspects of liquid droplet on a solid surface. Therm Sci Eng 10(6):23–29

    Google Scholar 

  • Mungan N (1966) Interfacial effects in immiscible liquid–liquid displacement in porous media. Soc Pet Eng J, pp 247–253

  • Perez E, Schaffer E, Steiner U (2001) Spreading dynamics of polydimethylsiloxane drops: crossover from Laplace to Van der Waals spreading. J Colloid Interface Sci 234:178–193

    Article  Google Scholar 

  • Quiblier JA (1984) A new three-dimensional modeling technique for studying porous media. J Colloid Interface Sci 98:84–102

    Google Scholar 

  • Rothman DH, Zaleski S (1997) Lattice-gas cellular automata—simple models of complex hydrodynamics. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Santos LOE, Facin PC, Philippi PC (2003) Lattice-Boltzmann model based on field mediators for immiscible fluids. Phys Rev E 68:056302

    Article  Google Scholar 

  • Sorbie KS, Wu YZ, McDougall SR (1995) The extended Washburn equation and its application to the oil/water pore doublet problem. J Colloid Interface Sci 174:289–301

    Article  Google Scholar 

  • Tanner LH (1979) The spreading of silicone oil drops on horizontal surfaces. J Phys D 12:1473–1484

    Article  Google Scholar 

  • Thompson PA, Robbins MO (1989) Simulation of contact line motion: slip and the dynamic contact angle. Phys Rev Lett 63(7):766–769

    Article  Google Scholar 

  • Young T (1805) An essay on the cohesion of fluids. Philos Trans R Soc Lond 95:65–87

    Article  Google Scholar 

Download references

Acknowledgments

Financial support was given by National Agency of Petroleum (PRH09-ANP/MME/MCT), Financial Supporter of Studies and Projects (Finep) and National Council for Scientific and Technological Development (CNPq).

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Porous Media and Thermophysical Properties Laboratory, Federal University of Santa Catarina, P. O. Box 476, Florianópolis, Santa Catarina, 88040-900, Brazil

    Fabiano G. Wolf, Luís O. E. dos Santos & Paulo C. Philippi

Authors
  1. Fabiano G. Wolf
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Luís O. E. dos Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paulo C. Philippi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fabiano G. Wolf.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wolf, F.G., dos Santos, L.O.E. & Philippi, P.C. Micro-hydrodynamics of immiscible displacement inside two-dimensional porous media. Microfluid Nanofluid 4, 307–319 (2008). https://doi.org/10.1007/s10404-007-0183-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10404-007-0183-2

Keywords

Search

Navigation