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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
Article

Abstract

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 

Nomenclature

Lower Case

a, b, c

Undertermined parameter sets in velocity distribution function

k

Permeability

n

Unit normal vector too-w interface

r

Coordinate in cylindrical system

s

Number of sides of polygon tube cross section

v

Fluid velocity

z

Coordinate in cylindrical system

Upper Case

F, Fo, Fw

Coefficients in tube flow equation

Gp

Pressure Gradient

H

Interface mean curvature

J,J1,J2,J3

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

M

Number of tube sizes

N

Defines number of undetermined parameter in velocity distribution

Nca

Capillary number

Nε

Dimensionless interfacial shear viscosity

P

Pressure

Q

Volume flow rate

R

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

ε

Interfacial shear viscosity

Μ

Viscosity

σ

Interfacial tension

θ

Coordinate in cylindrical system

Φ

Coordinate in second cylindrical system

Τ

Stress tensor

Subscripts

o

Oil phase quantity

w

Water phase quantity

r

r-component of vector

θ

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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