Page 299 - Reservoir Formation Damage

Cake Filtration: Mechanism, Parameters and Modeling 279

The wall shear-stress is calculated by Eq. 12-47 for the varying cake
radius, r c=r c(t}. The filter cake thickness is calculated by means of
Eqs. 12-46 and 62. Equations 12-65 and 66 can be solved numerically
using an appropriate method such as the Runge-Kutta method. How-
ever, for thin cakes, it is reasonable to assume that the wall-shear stress
is approximately constant, because r c=r w. Then, Eq. 12-65 can be
integrated as (Civan, 1998a):

q

For constant rate filtration, Eq. 12-49 subject to Eq. 12-51 can be
integrated numerically for varying shear-stress i s. When the filter cake
is thin, the variation of the shear-stress i s by the cake radius r c can be
neglected and an analytical solution can be obtained as for dynamic
filtration conditions (fi*0) (Civan, 1999a):

8 Aq.
t = + —f-ln (12-68)
2
B B
T -
B
The solution for static filtration conditions (B = 0) is obtained as (Civan,
1999a):

s
1*2 2
t = r w 5--8
w (12-69)
2
Eq. 12-68 and 12-69 apply irrespective of whether the flow is Darcy or
non-Darcy.

Determination of Model Parameters
and Diagnostic Charts

The majority of the reported filtration studies have not made attempts
at measuring a full set of measurable parameters. The filtration models
presented in this chapter may provide some guidance for the types of
parameters needed for simulation.
As listed in Table 12-1, Civan's (1998a, 1999a) filtration models
require the values of 20 parameters for simulation. Only five of these
parameters may not be directly or conveniently measurable with the