Transport in Porous Media

, Volume 14, Issue 1, pp 23–32 | Cite as

An investigation into whether the nondiagonal mobility coefficients which arise in coupled, two phase flow are equal

  • Ramon G. Bentsen
Article

Abstract

Recent developments in two-phase flow through porous media show that four mobilities are required to define completely the flow characteristics of a particular porous medium. Because, in idealized porous media, it has been shown that two of these mobilities, the nondiagonal mobilities which represent the viscous coupling exerted between fluid phases, are equal, it has been suggested that they may be equal, as well, in real porous media. It is shown in this paper that these two interactive mobilities cannot be equal in real porous media. Moreover, it is demonstrated that the relative permeabilities which pertain to pure countercurrent flow differ from those which pertain to steady-state, countercurrent flow, and that the pure countercurrent-flow relative permeabilities depend strongly on viscosity ratio. Finally, it is suggested that, because three different experiments give rise to three different sets of relative permeability curves, the conventional description of two-phase flow is inadequate inasmuch as it does not account properly for the viscous coupling exerted between fluid phases.

Key words

Countercurrent flow effective permeability mobility viscous coupling immiscible flow 

Nomenclature

k

absolute permeability, m2

ki

effective permeability of phasei; i=1, 2, m2

kij

generalized effective permeability of phasei; i, j=1, 2, m2

kri

relative permeability of phasei(i.e. (k i /k));i=1, 2

Mr

end point mobility ratio (i.e.k1rΜ2/k2rΜ1)

R12

function relating the flow potential in phase 1 to that in phase 2

Ui

Darcy velocity of phasei;i=1, 2, m/s

Greek Letters

λij

generalized effective mobility of phase i (i.e. kij/Μ j );i j=1, 2, m2/Pa·s

λi

effective mobility of phasei (i.e.k i /Μ i );i=1, 2, m2/Pa·s

Μi

viscosity of phasei, Pa·s

ψi

flow potential of phasei, J/m3

Subscripts and Superscripts

i

irreducible

r

residual

1

wetting phase

2

nonwetting phase

*

countercurrent flow

'

pure countercurrent flow

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bentsen, R. G. and Manai, A. A., 1992, Measurement of cocurrent and countercurrent relative permeability curves using the steady-state method,AOSTRA J. Res. 7, 169–181.Google Scholar
  2. Bentsen, R. G. and Manai, A. A., 1993, On the use of conventional cocurrent and countercurrent effective permabilities to estimate the four generalized permeability coefficients which arise in coupled, two-phase flow,Transport in Porous Media 11, 243–262.Google Scholar
  3. Bourbiaux, B. J. and Kalaydjian, F. J., 1990, Experimental study of cocurrent and countercurrent flows in natural porous media,SPERE 5, 361–368.Google Scholar
  4. de la Cruz, V. and Spanos, T. J. T., 1983, Mobilization of oil ganglia,AIChE J. 29(5), 854–858.Google Scholar
  5. Kalaydjian, F., 1987, A macroscopic description of multiphase flow in porous media involving spacetime evolution of fluid/fluid interface,Transport in Porous Media 2, 537–552.Google Scholar
  6. Kalaydjian, F., 1990, Origin and quantification of coupling between relative permeabilities for two-phase flows in porous media,Transport in Porous Media 5, 215–229.Google Scholar
  7. Leliévre, R. F., 1966, Etude d'écoulements diphasiques permanents à contre-courants en milieu poreux-comparison avec les écoulements de méme sens (in French), PhD thesis, University of Toulouse, France.Google Scholar
  8. Mannseth, T., 1991, Commentary on ‘origin and quantification of coupling between relative permeabilities for two-phase flows in porous media’ by F. Kalaydjian,Transport in Porous Media 6, 469–471.Google Scholar
  9. Rose, W., 1988, Measuring transport coefficients necessary for the description of coupled two-phase flow of immiscible fluids in porous media,Transport in Porous Media 3, 163–171.Google Scholar
  10. Rose, W., 1972, Some problems connected with the use of classical description of fluid/fluid displacement processes,Fundamentals of Transport Phenomena in Porous Media, Elsevier, Amsterdam, pp. 229–240.Google Scholar
  11. Whitaker, S., 1986, Flow in porous media II: The governing equations for immiscible two-phase flow,Transport in Porous Media 1, 105–125.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Ramon G. Bentsen
    • 1
  1. 1.Department of Mining, Metallurgical and Petroleum Engineering EdmontonUniversity of AlbertaAlbertaCanada

Personalised recommendations