Skip to main content
SpringerLink
Log in

Influence of Relative Permeability on the Stability Characteristics of Immiscible Flow in Porous Media

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

Relative permeability functions for immiscible displacements in porous media show a wide range of profiles. Although, this behavior is well known, its impact on the stability of the displacement process is unexplored. Our analysis clearly demonstrates for the first time that the viscous instability characteristics of two-phase flows are governed not only by their end point values, but are strongly dependent on the actual profile of relative permeability functions. Linear stability analysis predicts the capacity of the flow to develop large scale fingers which can result in substantial bypassing of the resident fluid. It is observed that relative permeability functions attributed to drainage processes yield a more unstable displacement as compared to functions related to imbibition processes. Moreover, instability is observed to increase for those relative permeability functions which result from increased wettability of the wetting fluid. High accuracy numerical simulations show agreement with these predictions and demonstrate how large amplitude viscous fingers result in significant bypassing for certain relative permeability functions. In the nonlinear regime, the finger amplitude grows at a rate ∝ t1/2 initially, drops to t1/4 at a later time and finally grows ∝ t. The basic mechanisms of finger interaction, however, are not substantially influenced by relative permeability functions.

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

  • Barenblatt, G. I., Entov, V. M., and Ryzhik, V. M.: (1990). Theory of Fluid Flows Through Natural Rocks, Kluwer Academic Publishers.

  • J.T. Bartley D.W.: Ruth (1999) ArticleTitleRelative permeability analysis of tube bundle models Transp. Porous Media 36 161 Occurrence Handle10.1023/A:1006575231732

    Article  Google Scholar 

  • J. Bear (1972) Dynamics of Fluids in Porous Media Wiley New York

    Google Scholar 

  • Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A.: (1986). Spectral Methods in Fluid Dynamics. Springer Series in Computational Dynamics. Springer-Verlag.

  • I.B. Cecilia G.T. Pedro (2004) ArticleTitlePore shape effects on the relative permeability of gas and condensate in three-dimensional pore networks Transp. Porous Media 55 247 Occurrence Handle10.1023/B:TIPM.0000010718.49313.48

    Article  Google Scholar 

  • E.D. Chikhliwala A.B. Huang Y.C. Yortsos (1988) ArticleTitleNumerical study of the linear stability of immiscible displacements in porous media Transp. Porous Media 3 257 Occurrence Handle10.1007/BF00235331

    Article  Google Scholar 

  • Chikhliwala, E. D. and Yortsos, Y. C.: (1988). Investigations on viscous fingering by linear stability and weakly nonlinear stability analysis, SPE J. also SPE paper 14367.

  • A.J. Chorin (1983) ArticleTitleThe instability of fronts in a porous medium Commun. Math. Phys. 91 103 Occurrence Handle10.1007/BF01206054

    Article  Google Scholar 

  • F.J. Fayers (1988) ArticleTitleAn approximate model with physically interpretable parameters for representing miscible viscous fingering SPERE 551 58

    Google Scholar 

  • Fletcher C.A.J. (1991). Computational Techniques for Fluid Dynamics. Springer series in Computational Physics. Vol. 1, 2nd edn. Springer, New York

  • Goda, H. M. and Behrenbruch, P.: (2004). Using a modified Brooks-Corey model to study oil-water relative permeability for diverse pore structures, SPE paper 88538.

  • Hagoort J. (1974). Displacement stability of water drives in water-wet connate-water-bearing reservoirs. SPE J. also SPE paper 4268:63

    Google Scholar 

  • S.M. Hassanizadeh (1986) ArticleTitleDerivation of basic equations of mass-transport in porous-media. 1. Macroscopic balance laws Adv. Water Resour. 9 IssueID4 196 Occurrence Handle10.1016/0309-1708(86)90024-2

    Article  Google Scholar 

  • M. Honarpour L. Koederitz A.H. Harvey (1986) Relative Permeability of Petroleum Reservoirs CRC Press, Inc. Florida

    Google Scholar 

  • P. Jenny S.H. Lee H.A. Tchelepi (2003) ArticleTitleMulti-scale finite-volume method for elliptic problems in subsurface flow simulation J. Comp. Phys. 187 IssueID1 46

    Google Scholar 

  • R. Juanes T. Patzek (2004) ArticleTitleRelative permeabilities for strictly hyperbolic models of three-phase flow in porous media Transp. Porous Media 57 125 Occurrence Handle10.1023/B:TIPM.0000038251.10002.5e

    Article  Google Scholar 

  • M.F. Khaled (1997) ArticleTitleEffects of relative permeability history dependence on two-phase flow in porous media Transp Porous Media 28 181 Occurrence Handle10.1023/A:1006556018950

    Article  Google Scholar 

  • Lake, L. W.: (1989). Enhanced Oil Recovery. 1st edn. Prentice-Hall.

  • S.K. Lele (1992) ArticleTitleCompact finite differences with spectral-like resolution J. Comput. Phys. 103 16 Occurrence Handle10.1016/0021-9991(92)90324-R

    Article  Google Scholar 

  • Pavone, D.: (1992). Observations and correlations for immscible viscous-fingering experiments, SPE Res. Eng. May also SPE paper 19670, 187.

  • Peaceman, D. W.: (1977). Fundamentals of Numerical Reservoir Simulation, Elsevier Scientific Pub. Co.

  • Peters, E. J. and Flock, D. L.: (1981). The onset of instability during two-phase immsicible displacements in porous media, SPE J. April also SPE paper 8371, 249.

  • L.A. Rapoport W.J. Leas (1953) ArticleTitleProperties of linear water food Petrol. Trans. AIME 198 139

    Google Scholar 

  • A. Riaz E. Meiburg (2003) ArticleTitleThree-dimensional miscible displacement simulations in homogeneous porous media with gravity override J. Fluid Mech. 494 95 Occurrence Handle10.1017/S0022112003005974

    Article  Google Scholar 

  • A. Riaz E. Meiburg (2004) ArticleTitleVorticity interaction mechanisms in variable-viscosity heterogeneous miscible displacements with and without density contrast J. Fluid Mech. 517 1 Occurrence Handle10.1017/S0022112004000448

    Article  Google Scholar 

  • A. Riaz H.A. Tchelepi (2004) ArticleTitleLinear stability analysis of immiscible two-phase flow in porous media with capillary dispersion and density variation Phys. Fluids 16 IssueID12 4727 Occurrence Handle10.1063/1.1812511

    Article  Google Scholar 

  • Riaz, A. and Tchelepi, H. A.: (2005). Numerical simulation of immiscible two-phase flow in porous media, To appear in Phys. Fluids.

  • W. Rose D. Rose (2005) ArticleTitleAn upgraded porous medium coupled transport process algorithm Transp. Porous Media 59 IssueID3 357 Occurrence Handle10.1007/s11242-004-1524-1

    Article  Google Scholar 

  • M. Ruith E. Meiburg (2000) ArticleTitleMiscible rectilinear displacements with gravity override. Part 1. Homogeneous porous medium J. Fluid Mech. 420 225 Occurrence Handle10.1017/S0022112000001543

    Article  Google Scholar 

  • A.E. Scheidegger (1974) The Physics of Flow Through Porous Media, 3rd edn University of Toronto Press Toronto

    Google Scholar 

  • C.T. Tan G.M.: Homsy (1988) ArticleTitleSimulation of nonlinear viscous fingering in miscible displacement Phys. Fluids 31 IssueID6 1330 Occurrence Handle10.1063/1.866726

    Article  Google Scholar 

  • G.-Q. Tang A. Firoozabadi (2002) ArticleTitleRelative permeability modification in gas/liquid systems through wettability alteration to intermediate gas wetting SPE Res. Eval. Eng. 5 IssueID6 427

    Google Scholar 

  • G.Q. Tang A.R. Kovscek (2004) ArticleTitleAn experimental investigation of the effect of temperature on recovery of heavy oil from diatomite SPE J. 9 IssueID2 163

    Google Scholar 

  • H.A. Tchelepi L.J. Durlofsky W.H. Chen A. Bernath M.C.H. Chien (1999) ArticleTitlePractical use of scale up and parallel reservoir simulation technologies in field studies SPE Res. Eval. Eng. 2 IssueID4 368

    Google Scholar 

  • Tchelepi, H. A. and Orr, F. M. J.: (1994). Interaction of viscous fingering, permeability inhomogeneity and gravity segregation in three dimensions, SPE Res. Eng. p. 266.

  • Y.C. Yortsos (1987) ArticleTitleStability of certain class of miscible displacement processes in porous media IMA J. Appl. Math. 38 167

    Google Scholar 

  • Y.C. Yortsos F.J. Hickernell (1989) ArticleTitleLinear stability of immiscible displacement in porous media SIAM J. 49 IssueID3 730

    Google Scholar 

  • Yortsos, Y. C. and Huang, A. B.: (1986). Linear stability analysis of Immiscible displacement: Part 1 – Simple basic flow profiles, SPE J. also SPE paper 12692.

  • W.B. Zimmerman G.M. Homsy (1991) ArticleTitleNonlinear viscous fingering in miscible displacement with anisotropic dispersion Phys. Fluids 3 IssueID8 1859 Occurrence Handle10.1063/1.857916

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Petroleum Engineering, Stanford University, Stanford, CA, 94305, USA

    Amir Riaz & Hamdi A. Tchelepi

Authors
  1. Amir Riaz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hamdi A. Tchelepi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hamdi A. Tchelepi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Riaz, A., Tchelepi, H.A. Influence of Relative Permeability on the Stability Characteristics of Immiscible Flow in Porous Media. Transp Porous Med 64, 315–338 (2006). https://doi.org/10.1007/s11242-005-4312-7

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-005-4312-7

Keywords

Search

Navigation