Page 298 - Reservoir Formation Damage
P. 298
278 Reservoir Formation Damage
(12-59)
2nhK
(12-60)
Substituting Eq. 12-57 and considering the initial condition given by
Eq. 12-51, Eq. 12-49 can be solved using a numerical scheme, such as
the Runge-Kutta-Fehlberg four (five) method (Fehlberg, 1969).
The cumulative filtrate volume is given by Eq. 12-27. The pressure
difference (P c~P e}, or the slurry injection pressure p c when the back
pressure p e is prescribed, can be calculated by Eq. 12-56.
When the inertial flow terms are negligible, equating Eqs. 12-55 and
12-56 and rearranging leads to (Civan, 1998a):
(12-61)
Equation 12-61 can be written as:
(12-62)
where
= q 0D/K f (12-63)
where q 0 is the injection rate given by Eq. 12-55 for $ f = 0 before the
filter cake buildup and
(12-64)
Thus, substituting Eqs. 12-46 and 12-62 into Eq. 12-49 and rearranging
yield the filtration flow rate equation as (Civan, 1998a):
2
= (-\/C)q [Aqexp(C/q-D)-B]exp(C/q-D) (12-65)
subject to the initial condition given by:
(12-66)
