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Transport in Porous Media

, Volume 19, Issue 1, pp 67–77 | Cite as

Macroscopic capillary pressure

  • V. De La Cruz
  • T. J. T. Spanos
  • D. Yang
Article

Abstract

The macroscopic pressure difference between two immiscible, incompressible fluid phases flowing through homogeneous porous media is considered. Starting with the quasi-static motions of two compressible fluids, with zero surface tension, it is possible to construct a complete system of equations in which all parameters are clearly defined by physical experiments. The effect of surface tension is then formally included in the definition of the specific process under consideration. Incorporating these effects into the pressure equations and taking the limit as compressibilities go to zero, the independent pressure equations are shown to yield indeterminate forms. However, the difference of the two pressure equations is found to yield a new process-dependent dynamical equation.

Key words

Capillary pressure multiphase flow pressure equations 

List of Symbols

J

LeverettJ function

Ki

bulk modulus of fluidi (i=1, 2)

Ks

bulk modulus of solid

K

permeability

P

fractional porosity of the wetting phase (in LeverettJ function)

pi

macroscopic pressure of fluidi (i=1, 2)

Qij

Mobilities (i, j=1, 2) (cf. de la Cruz and Spanos, 1983)

Vi

macroscopic velocity vector of fluidi (i=1, 2)

Greek Letters

α

surface tension

αi

compliance factor for fluidi (i=1, 2) for incompressible flow defined in equations (29) and (30) (process-dependent)

Β

compliance factor for the flow of two incompressible fluid (cf. eqns. (32) and (33) for relation toαi)

δi

compliance factor for a compressible fluid (i=1, 2) (process-dependent) (cf. de la Cruzet al., 1989, 1993)

δiα

modification to static compliance factor for fluidi (i=1, 2) as a result of quasi-static flow

ηi

fraction of space occupied by fluidi (i=1, 2) measured dynamically

ηio

fraction of space occupied by fluidi (i=1, 2) measured statically

Μi

shear viscosity of fluidi (i=1, 2)

ξi

bulk viscosity of fluidi (i=1, 2)

ρi

density of fluidi (i=1, 2)

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References

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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • V. De La Cruz
    • 1
  • T. J. T. Spanos
    • 1
  • D. Yang
    • 1
  1. 1.Department of PhysicsUniversity of AlbertaEdmontonCanada

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