Page 263 - Reservoir Formation Damage

Two-Phase Formation Damage by Fines Migration 243

in which Re } is the phase J Reynolds number given by (Ucan and Civan,
1996):

(11-10)

where (3 is the inertial flow coefficient given by a suitable correlation,
such as by Liu et al. (1995).

Determination of Fluid Saturations and Pressures

Two alternative convenient formulations can be taken for solution of
the equations of continuity and motion given by Eqs. 11-3 and 8 for
pressures and saturations of the various phases flowing through porous
media. In the first approach, Eq. 11-8 is substituted into Eq. 11-3 to obtain:

a* \*-J ; J=W > N

The capillary pressure is defined as the difference between the nonwetting
and wetting phase pressures according to:

PCNW ~ PN Pw (11-12)

The phase / volume fraction is given by:

(11-13)

where (() is porosity and S } is the saturation of phase J.
Thus, substituting Eqs. 11-12 and 11-13 into Eq. 11-11 yields the
following equations for the wetting and nonwetting phases, respectively:

(11-14)
a* \i w i

a* a* ds a* ™*

(11-15)