Page 296 - Reservoir Formation Damage

276 Reservoir Formation Damage

Reservoir
formation

Filter
cake

Mud :•*
slurry

Figure 12-4. Radial filter cake over a wellbore sandface (after Civan, ©1999
SPE; reprinted by permission of the Society of Petroleum Engineers).

Substituting Eqs. 12-2, 12-9, 12-46, and 12-48 into Eq. 12-45 results
in (1999a)

(12-49)
dt r w -8 '
where

^yp^ (12 ~ 50)

and B is given by Eq. 12-13. The initial condition for Eq. 12-49 is

S = 0,f = 0 (12-51)

Forchheimer's (1901) equation for radial flow of the carrier fluid reads as

(12-52)
K
The radial volumetric flux of the carrier fluid is given by