Transport in Porous Media

, Volume 11, Issue 3, pp 201–218 | Cite as

Viscous coupling in two-phase flow in porous media and its effect on relative permeabilities

  • R. Ehrlich


An idealized model of a porous rock consisting of a bundle of capillary tubes whose cross-sections are regular polygons is used to assess the importance of viscous coupling or lubrication during simultaneous oil-water flow. Fluids are nonuniformly distributed over tubes of different characteristic dimension because of the requirements of capillary equilibrium and the effect of interfacial viscosity at oil-water interfaces is considered. With these assumptions, we find that the importance of viscous coupling depends on the rheology of the oil-water interface. Where the interfacial shear viscosity is zero, viscous coupling leading to a dependence of oil relative permeability on oil-water viscosity ratio for viscosity ratios greater than one is important for a range of pore cross-section shapes and pore size distributions. For nonzero interfacial shear viscosity, viscous coupling is reduced. Using values reported in the literature for crude oil-brine systems, we find no viscous coupling.

Key words

Porous medium model two-phase flow Darcy's law relative permeabilities 


Lower Case

a, b, c

Undertermined parameter sets in velocity distribution function




Unit normal vector too-w interface


Coordinate in cylindrical system


Number of sides of polygon tube cross section


Fluid velocity


Coordinate in cylindrical system

Upper Case

F, Fo, Fw

Coefficients in tube flow equation


Pressure Gradient


Interface mean curvature


Integrals defined by (A3) and (A11)–(A13)


Number of tube sizes


Defines number of undetermined parameter in velocity distribution


Capillary number


Dimensionless interfacial shear viscosity




Volume flow rate


Characteristic tube dimension (Figure A1)

So, Sw

Oil and water saturations

St, Si

Tube wall and oil-water interface area

V (m)

Pore volume of tubes of dimensionR(m) in bundle

Greek Letters


Interfacial shear viscosity




Interfacial tension


Coordinate in cylindrical system


Coordinate in second cylindrical system


Stress tensor



Oil phase quantity


Water phase quantity


r-component of vector


θ-component of vector


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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • R. Ehrlich
    • 1
  1. 1.Chevron Oil Field ResearchLa HabraUSA

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