Page 176 - Reservoir Formation Damage

158 Reservoir Formation Damage

Based on Eqs. 8-35 and 8-36, the excess shear stress can be correlated
for one-dimensional horizontal flow:

•-T, (8-39)

The previous studies are mostly limited to one-dimensional Newtonian
fluid flow and they typically used (Civan et al., 1989; Khilar and Folger,
1987; Gruesbeck and Collins, 1982; Cernansky and Siroky, 1985; Ohen
and Civan, 1989, 1990):

(8-40)

In general, for multi-dimensional flow (Civan, 1996)

(8-41)

where if/ is the flow potential and D is the hydraulic tube diameter tensor
for anisotropic media. 5 is a unit vector.

Particle Transfer Across Fluid-Fluid Interfaces
The driving force for particle transfer between two fluid phases is the
wettability of the fluid phases relative to the wettability of the particles.
Particles prefer to be in the phase that wets them (Muecke, 1979) (see
Figure 8-9 by Civan, 1994). But, mixed-wet particles tend to remain on
the interface where they are most stable (Ivanov et al., 1986) (see Figure
8-10). In the region involving the interface between wetting and non-
wetting phases, it can be postulated that particles A in a weaker wettability
phase-1 first move to the interface and then migrate from the interface
to a stronger wettability phase-2 according to the following consecutive
processes (Civan, 1996):

Nonwetting phase - 1 —» Interface —> Wetting phase - 2 (8-42)

Therefore, the following power-law rate expressions can be proposed: