Page 103 - Reservoir Formation Damage

86 Reservoir Formation Damage

The lower and upper bounds of the pore throat size range are estimated
by a simultaneous solution of the non-linear integral equations given by:

(5-27)

a
h
\yf(y)dy =
(5-28)

for which the mean pore throat size is estimated by solving the follow-
ing equation which relates the pore throat size variation to the rate
of deposition:

, t>0 (5-29)

where k 6 is a rate constant and e p is the volume of deposition per unit bulk
volume, subject to the initial mean pore throat diameter, either determined
from the initial pore throat size distribution using Eq. 5-28, or estimated as
a fraction of the mean pore diameter using:

(5-30)

Note that r\ is not a fraction because it is a lumped coefficient including
the mentioned fraction, some unit conversion factors, and the shape factor.
Chang and Civan (1991, 1992, 1997) considered that the pore throat
and particle diameters can be better represented by bimodal distribution
functions over finite diameter ranges, given by Popplewell et al. (1989) as:

(5-31)

where w is an adjustable weighting factor in the range of 0 < w < 1, and
./i(y) and/ 2 (j) denote the distribution functions for the fine and coarse
fractions, each of which are described by:

(5-32)