Page 291 - Reservoir Formation Damage

Cake Filtration: Mechanism, Parameters and Modeling 271

(12-22)
K cL f)aK f

(12-23)
aK

Alternatively, eliminating (p c-p e] between Eqs. 12-18 and 12-19 and
then solving for 8 yields:

i-
aK t
5 =
(12-24)
aK,

Notice that Eq. 12-24 yields 8 = 0 when q = q 0. Differentiating Eq. 12-
24 with respect to time and then substituting into Eq. 12-11 yields

\LL c
~r

(12-25)

a dt aK a 2 ^ '

The initial condition for Eq. 12-25 is

(12-26)

Substituting Eq. 12-20 and considering the initial condition given
by Eq. 12-14, Eq. 12-11 can be solved using a numerical scheme, such
as the Runge-Kutta-Fehlberg four (five) method (Fehlberg, 1969). Eqs.
12-25 and 12-26 can also be solved numerically using the same method.