Page 302 - Reservoir Formation Damage

282 Reservoir Formation Damage

Equation 12-33 can be rearranged in a linear form as:

d(\\ 1 dq A B
n H
— = i = q + (12-76)
dt(q dt
Thus, the intercept (B/C) and slope (-A/C) of the straight-line plot of
Eq. 12-76 can be used with Eqs. 12-30, 12-31, 12-12, and 12-13 to
obtain the following expressions:

(B/C),
(12-77)
(A/C)(t-T c>
k d

, _
d~ (12-78)

Comparing Eqs. 12-75 and 12-77 yields an alternative expression for
determination of the limit filtrate rate as:

q x=(B/C)/(A/C) (12-79)

Eq. 12-79 can be used to check the value of q x obtained by Eq. 12-72.
Equation 12-74 can be used to determine the filter cake permeability, K c.
Equations 12-70 and 12-75 or 12-77 and 12-78 can be used to calculate
the particle deposition and erosion rates k d and k e, if the cake porosity <J) C
and the critical shear stress i cr are known. ty c can be measured. i cr can be
estimated by Eq. 12-6, but the ideal theory may not yield a correct value as
explained previously by Ravi et al. (1992) and in this chapter. Therefore,
Ravi et al. (1992) suggested that i cr should be measured directly.

Radial Filtration

Given the filter cake thickness 8, the progressing surface cake radius
can be calculated by Eq. 12-46. Then a straight line plot of ln(r c /r w )
r c
vs. (l/q) data according to Eq. 12-62 yields the values of C and D as
the slope and intercept of this line, respectively. A straightline plot of
[d8/df] versus \q/(r w -8)] data according to Eq. 12-49 yields the values
of A and B as the slope and intercept of this line, respectively. At static
filtration conditions, v = 0 and T = 0 according to Eq. 12-47. Therefore,