Page 290 - Reservoir Formation Damage

270 Reservoir Formation Damage

1
where P is the inertial flow coefficient in cm" , K is the permeability
in Darcy, and T is the tortuosity (dimensionless). Substituting Eq. 12-4
into Eq. 12-15 yields

pp
(12-17)

As explained by Civan (1998a,b), the instantaneous carrier fluid filtration
flow rate q is the same everywhere in the cake and filter irrespective of
whether the process is undergoing a constant pressure or a constant rate
filtration. In the following, the formulations for variable and constant rate
filtration processes are derived.
For variable rate filtration occurring under an applied pressure dif-
ference, integrating Eq. 12-17 for conditions existing prior to and during
the process of formation of a filter cake leads to, respectively:

loV-Lf ,
• Pe e = + (12-18)
aK f

and

| (12-19)
p/ a
K cL faK f
Consequently, eliminating (p c -p e) between Eqs. 12-18 and 19, and then
solving for q, yields for Darcy flow m^ =p c =0)

(12-20a)

and for non-Darcy flow:

(12-20b)
2a

in which

(12-21)