Page 316 - Reservoir Formation Damage

296 Reservoir Formation Damage

(12-100)

Eqs. 12-97 through 100 can be solved numerically subject to the initial
conditions given by:

(12-101)

Linear Filtration Formulation

The radial filter cake equations derived above can be readily converted
to linear filter cake equations by means of the transformation given by:

T
A,
ri
i
A,
= — T i , h = Jt ~w — \.. — r 2 — i 'c c 2 (12-102)
"C
'w
Thus, application of Eq. 12-102 to Eqs. 12-87 through 90 yields,
respectively, the following thickness-averaged mass balance equations for
the linear cake formation (Civan, 1998b):
(12-103)

(12-104)
dt

— (h (12-105)

dh

(12-106)
fitter

Similarly, Eqs. 12-97 through 100, respectively, become (Civan, 1999b):

(12-107)
= N° ps + (x w -x c)N p2s