Page 324 - Reservoir Formation Damage

304 Reservoir Formation Damage

Thickness-Averaged Fluid Pressure and Cake Porosity

The average fluid pressure in the filter cake for linear filtration can
be expressed similar to Dake (1978) as:

x
x w l w
p = J ptydx J tydx (12-144)
*c I x c
The average cake porosity is given by:

X / X
$=J<M*/ /<** (12-145)
x c I x c
The following expression can be derived from Eqs. 12-144 and 12-145:

=\ Ptydx/ J dx (12-146)

Note x w is a constant, but x c = x c(t) varies by time.
Similarly, the following three expressions can be written for radial flow:

w / w
p = j /?()) rdr I j <|) rdr
(12-147)

rdr
(12-148)

w w
= \ /?()) rdr \ rdr
(12-149)

Eq. 12-147 is given by Dake (1978). Note that r w is a constant, but
r c = r c(t) varies by time.
Eqs. 12-146 and 149 define the average fluid pressure, but they cannot
be used directly because the pressure distribution over the cake thickness
is not a priori known. Civan (1998b, 1999b) circumvented this problem
by applying a procedure similar to Jones and Roszelle (1978) to express
a local function value in terms of its average.