Page 108 - Reservoir Formation Damage

Permeability Relationships 91

where n { and n 2 are the permeability reduction indices, a is a coefficient
and K and K npg are the permeabilities at the reference porosities § PO
and § np of the plugging and nonplugging pathways, respectively. Eq.
5-58 represents the snow-ball effect of plugging on permeability, while
Eq. 5-59 expresses the power-law effect of surface deposition on perme-
ability. Eqs. 5-58 and 5-59 have been also verified by Gdanski and
Shuchart (1998) and Bhat and Kovscek (1999), respectively, using experi-
mental data. Bhat and Kovscek (1999) have shown that the power-law
exponent in Eq. 5-59 can be correlated as a function of the coordination
number and the pore body to throat aspect ratio, applying the statistical
network theory for silica deposition in silicaous diatomite formation. Note
that, for n 2 <0 and £ np/$ npg «1, Eq. 5-59 simplifies to the expression
given by Gruesbeck and Collins (1982):

(5-60)

where b = n 2/§ npg. Eq. 5-60 is a result of a truncated series approxi-
mation of Eq. 5-59.
Thus, substitution of Eqs. 5-58 and 59 into Eq. 5-49 results in the
following expression for the permeability of the porous media (Civan,
1994, 1996):

(l - )" 2 (5-61)
K = /,*, oexp(-ae J) + f npK npg z np/<$> npo
Cernansky and Siroky (1985) proposed an empirical relationship as:

l E
~ e x p G l - — M - l (5-62)
expG-1 1 1 K 0"

where E and G are some empirical constants. It can be shown that K = K 0
for £ = 0. Civan (2000) pointed out that, when E= 1, Eq. 5-62 yields a
linear model as:

(5-63)

When E = 0, Eq. 5-62 yields a nonlinear model as: