Page 102 - Reservoir Formation Damage

Permeability Relationships 85

This approach is particularly useful in porous media undergoing alteration
during formation damage. Frequently, the Carman-Kozeny equation fails
to represent the cases where the pore throats are plugged without sig-
nificant porosity reduction.
This problem can be alleviated by introducing a flow efficiency factor,
y, in view of Eq. 5-19 (Ohen and Civan, 1993; Chang and Civan, 1991,
1992, 1997). Hence, the permeability variation can be expressed by
(Chang and Civan, 1997):

K
(5-24)

where a, b, and c are some empirically determined parameters and K 0
and § 0 denote the permeability and porosity at some initial or reference
state. The flow efficiency factor, y, can be interpreted as a measure of
the fraction of the open pore throats allowing fluid flow. Thus, when the
pore throats are plugged, then y = 0, and therefore K = 0, even if <|) * 0.
This phenomenon is referred to as the "gate or valve effect" of the pore
throats (Chang and Civan, 1997; Ochi and Vernoux, 1998).
In order to estimate the flow efficiency factor, Ohen and Civan (1993)
assumed that, although the pore throat sizes vary with time, they always
remain log-normally distributed:

f ( y ) = (5-25)

in the range of d l<y<d h, where s d is the standard deviation and d t is
the mean pore throat diameter.
Then, assuming that the pore throats smaller than the size, d p, of the
suspended particles will be plugged, the flow efficiency factor is estimated
by the fraction of pores remaining open at a given time:

d
"I l \
= l-E pjf(y)dynf(y)dy
(5-26)

where E p is the plugging efficiency factor. Particles that are sticky and
deformable can mold into the shape of pore throats and seal them. Then,
the plugging is highly efficient and E p is close to unity. Particles that are
rigid and nonsticky cannot seal the pore throats effectively and still allow
for some fluid flow. Thus, E < 1 for such plugs.