Page 292 - Reservoir Formation Damage

272 Reservoir Formation Damage

The relationships between filtrate flow rate and cumulative filtrate
volume are given by

= \qdt (12-27)

= dQ/dt (12-28)

Note that Eqs. 12-24 and 25 simplify to Eqs. 12-29 and 12-33 (Civan,
1998a), respectively, when the inertial effects are neglected, that is, for
P C = P / = 0 .

(12-29)

where

(12-30)

(12-31)
D=L fK c/K f

= q/a (12-32)
u c
and

2
= -(l/C)q (Aq-B) (12-33)

subject to

(12-34)

Then, the analytical solutions for the filtrate flow rate and cumulative
volume as well as the filter cake thickness can be derived as demonstrated
by Civan (1998a, 1999a).
The analytical solution of Eqs. 12-33 and 34 is (Civan, 1998a)

' A 1 "
c A B q + i i
ln i
B B A i q (j (12-35)
B q 0 _