Page 150 - Reservoir Formation Damage

132 Reservoir Formation Damage

(7-21)

Several other relationships, which may be convenient to use in the for-
mulation of the transport phenomena in porous media, are given in
the following:
The volume flux , My, and the velocity , Vy, of a phase j are related by:

(7-22)

where e jr is the volume fraction of the irreducible phase j in porous
media. When an irreducible residual fluid saturation, S jr exists in porous
media, Eq. 7-22 should be substituted into Eq. 7-15 for the flowing phase
volume flux as:

(7-23)

In deforming porous media, the volumetric flux of the solid phase can
be expressed in terms of the velocity according to the following equation:

«,=6,v, (7-24)

where e 5 and v s denote the solid phase volume fraction and velocity,
respectively.
Substituting Eq. 7-14, Eq. 7-24 becomes:

",=(l-4>)v, (7-25)

Accounting for the immobile fluid fraction, e jr, in deforming porous
media, the volumetric flux of the fluid relative to the deforming solid
phase is given by Civan (1994, 1996):

(7-26)

The volume fraction of species i of phase j in the bulk system is
given by:

(7-27)