Page 303 - Reservoir Formation Damage

Cake Filtration: Mechanism, Parameters and Modeling 283

5 = 0 according to Eq. 12-13. Consequently, substituting B = 0 and
Eq. 12-63, Eq. 12-65 can be expressed in the following linear form:

(12-80)
= [\n(A/C)-2CK f/q 0]

3
Thus, a straightline plot of ln[-g dq/dt\ versus (l/q] yields the values
of (2C) and [ln(A/C)-2C£y/<7 0] as the slope and intercept of this line,
respectively. This allows for determination of the A and C coefficients
only. The determination of a full set of A, B, C, and D from Eqs. 12-49
and 12-65 requires both the filtrate flow rate (or volume) and the cake
thickness versus the filtration time data. Once these coefficients are
determined, then their values can be used in Eqs. 12-50, 12-13, 12-63,
and 12-64 to determine the values of the deposition and erosion rate
constants k d and k e. The discussion of the linear filtration about the
determination of i cr by Eq. 12-6 is valid also in the radial filtration case.
At dynamic equilibrium, the filter cake thickness and the filtrate
flow rate attain certain limiting values 8^ and q x. Then, substituting Eq.
12-46 into Eqs. 12-49 and 62 yields the following relationships, respectively:

Aq_=B(l-SJr w) (12-81)

+ D) (12-82)

The filter cake permeability is determined by Eq. 12-64 as:

= DK f/\n(r e/r w) (12-83)
K c
The equations and the linear plotting schemes developed in this section
allow for determination of the parameters of the filtration models, mentioned
at the beginning of this section, from experimental filtrate flow rate (or
volume) and/or filter cake thickness data. The remaining parameters
should be either directly measured or estimated. In the following appli-
cations, the best estimates of the missing data have been determined by
adjusting their values to fit the experimental data. This is an exercise
similar to several other studies, including Liu and Civan (1996) and Tien
et al. (1997). They have resorted to a model assisted estimation of the
parameters because there is no direct method of measurement for some
of these parameters.