Page 208 - Reservoir Formation Damage

Single-Phase Formation Damage by Fines Migration and Clay Swelling 189

+ \
^ L
i L
r L c *^ m H

Filter
Cake
Region

Figure 10-4. Pore filling and internal filter cake formation in a core (after Civan,
1994; reprinted by permission of the U.S. Department of Energy; after Civan 1992
SPE; reprinted by permission of the Society of Petroleum Engineers).

R c(t) and R m are the resistances of the pore filling and uninvaded regions
defined by

R c(t) = \lK c(t) (10-18)

R m = l/K m (10-19)
The rate of increase of the filtration resistance of the pore filling particles
is assumed proportional to the particle mass flux of the flowing phase
according to:

dR c/dt = (k c/L c)(q/A)p pf (10-20)

subject to the initial condition
(10-21)

Then, solving Eqs. 10-20 and 21 yields:

(10-22)

is the pore filling particles resistance rate constant.
k c