Page 100 - Reservoir Formation Damage

Permeability Relationships 83

Bourbie et al. (1986) determined that n = 1 for ()><0.05 and n = 3 for 0.08
<(j)<0.25. In view of this evidence and Eq. 5-14, the Carman-Kozeny
equation appears to be valid for the 0.08 < <)) < 0.25 fractional porosity
range. Reis and Acock (1994) warn that these exponents may be low
"because the permeabilities were not corrected for the Klinkenberg effect."

The Modified Carman-Kozeny Equation
Incorporating the Flow Units Concept
The derivation of the Carman-Kozeny equation presented in the pre-
ceding section inherently assumed uniform diameter cyclindrical flow
tubes analogy. Therefore, for applications to nonuniform diameter flow
tubes, the Carman-Kozeny equation has been modified by inserting a
geometric shape factor, F s (Amaefule et al., 1993), as:

(5-16)

Hearn et al. (1984, 1986) introduced the "flow units" concept and Amaefule
et al. (1993) defined a lumped parameter as following, called the "flow
zone indicator" to combine the three unknown parameters, F s, i and Z g ,
into one unknown parameter:

1
FZI =
(5-17)

Therefore, a plot of experimental data based on the logarithmic form of
Eq. 5-16 (Amaefule et al., 1993)

(5-18)
.-4>

should yield a straightline with a slope of two. Hence, the FZI 2 value
can be obtained as the value of K/§ at the (|) = 0.5 value.
Implicit in Eq. 5-18 is the assumption that formations with similar flow
characteristics can be represented by the same characteristic flow zone
indicator parameter values. Consequently, formations having distinct flow
zone parameters can be identified as different flow units.