Transport in Porous Media

, Volume 10, Issue 3, pp 285–291 | Cite as

Onset of viscous fingering for miscible liquid-liquid displacements in porous media

  • Gökhan Coskuner
Short Communication
Received:
Revised:

Abstract

The displacement of one fluid by another miscible fluid in porous media is an important phenomenon that occurs in petroleum engineering, in groundwater movement, and in the chemical industry. This paper presents a recently developed stability criterion which applies to the most general miscible displacement. Under special conditions, different expressions for the onset of fingering given in the literature can be obtained from the universally applicable criterion. In particular, it is shown that the commonly used equation to predict the stable velocity ignores the effects of dispersion on viscous fingering.

Key words

Miscible displacement stability length effect critical velocity 

Nomenclature

C

Solvent concentration

\(\bar C\)

Unperturbed solvent concentration

DL

Longitudinal dispersion coefficient [m2/s]

DT

Transverse dispersion coefficient [m2/s]

g

Gravitational acceleration [m/s2]

Isr

Instability number

k

Permeability [m2]

K

Ratio of transverse to longitudinal dispersion coefficient

L

Length of the porous medium [m]

Lx

Width of the porous medium [m]

Ly

Height of the porous medium [m]

M

Mobility ratio

V

Superficial velocity [m/s]

Vc

Critical velocity [m/s]

Vs

Velocity at the onset of instability [m/s]

µ

Viscosity [Pa/s]

\(\bar \mu \)

Unperturbed viscosity [Pa/s]

µ0,µs

Viscosities of oil and solvent, respectively [Pa/s]

ρ

Density [kg/m3]

ρ0,ρs

Densities of oil and solvent, respectively [kg/m3]

Φ

Porosity

Ω

Dimensionless length

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Blackwell, R. J., Rayne, J. R., and Terry, W. M., 1959: Factors influencing the efficiency of miscible displacements,Trans. AIME 216, 1.Google Scholar
  2. Chang, S. H. and Slattery, J. C., 1986: A linear stability analysis for miscible displacements,Transport in Porous Media 1, 179.Google Scholar
  3. Chang, S. H. and Slattery, J. C., 1988: Stability of vertical miscible displacements with developing density viscosity gradients,Transport in Porous Media 3, 277.Google Scholar
  4. Coskuner, G. and Bentsen, R. G., 1987a: A new stability theory for designing graded viscosity banks,J. Canad. Petrol. Technol. 26(6), 26.Google Scholar
  5. Coskuner, G. and Bentsen, R. G., 1987b: Prediction of instability for miscible displacements in a Hele-Shaw cell,Rev. L'Institut Francais du Petrole 42(2), 151.Google Scholar
  6. Coskuner, G. and Bentsen, R. G., 1989: Effect of length on unstable miscible displacements,J. Canad. Petrol. Technol. 28(4), 34.Google Scholar
  7. Coskuner, G. and Bentsen, R. G., 1990a: A scaling criterion for miscible displacements,J. Canad. Petrol. Technol. 29(1), 86.Google Scholar
  8. Coskuner, G. and Bentsen, R. G., 1990b: An extended theory to predict the onset of viscous instabilities for miscible displacements in porous media,Transport in Porous Media 5(5), 473.Google Scholar
  9. Dumore, J. M., 1964: Stability considerations in downward miscible displacements,Trans. AIME 231, 356.Google Scholar
  10. Gardner, J. W. and Ypma, J. G. J., 1984: An investigation of phase behavior — microscopic bypassing interaction of CO2 flooding,Soc. Petrol. Eng. J. 25(5), 508.Google Scholar
  11. Hill, S., 1952: Channeling in packed columns,Chem. Eng. Sci. 1, 247.Google Scholar
  12. Hoyt, D. L., 1986: Miscible flooding at controlled velocities,U.S. Patent, No. 4,593,761.Google Scholar
  13. Offeringa, J. and van der Poel, C. 1954: Displacement of oil from porous media by miscible liquids,Trans. AIME 201, 311.Google Scholar
  14. Perrine, R. L., 1961a: Stability theory and its use to optimize recovery,Trans. AIME 222, 9.Google Scholar
  15. Perrine, R. L., 1961b: The development of stability theory for miscible liquid-liquid displacements,Trans. AIME 222, 17.Google Scholar
  16. Peters, E. J., Broman, W. H., and Broman, J. A., 1984: A stability theory for miscible displacement, SPE 13167, Society of Petroleum Engineers, PO Box 833836, Richardson, TX 75083-3836.Google Scholar
  17. Slobod, R. L. and Thomas, R. A., 1963: Effect of transverse diffusion on fingering in miscible displacements,Trans. AIME 228, 9.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Gökhan Coskuner
    • 1
  1. 1.Calgary Research CentreShell Canada LimitedCalgaryCanada

Personalised recommendations