Page 173 - Petrophysics 2E

146 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

pore-radius changes on the true permeability k is:

(3.91)

where kR is the ratio of apparent permeability to absolute permeability.
Assuming AP = AP1 + AP2 and AaL = AIL1 + A2L2, Equation 3.88
becomes:

2
r~a m
k = 126.7-$ (3.92)
kR
Letting rpe, the effective pore radius, be equal to rpa/&, Equation 3.92
becomes similar to Equation 3.88:

k = 126.71-:~$~ (3.93)

The value of rpe can vary considerably from the average radius value
E, depending on the texture and heterogeneity present in the system.
Consider two systems with different grain sizes and with no vugs or
fractures (Figure 3.32). Because:

(a) the path of the current represents the true inter-matrix tortuosity,
(b) the tortuosity is a function of grain size and usually decreases with
decrease in the grain size, and
(c) the value of rpe varies with the variation in grain size,
(d) a relationship between z and rpe must exist for a particular formation.
Using experimental data of rpa, m, $, and k, Wafta and Youssef
showed that rpe and z are related as follows [43]:

logrp, = a1& + a2 (3.94)

.- I.... -
"...+

Figure 3.32. Two systems with dqferent grain sizes and pore radii [43J