Geology Reference
In-Depth Information
l
Fig. 3.5
Equivalent channel model for permeability
In the Archie relation, m
¼
1
:
3 for sand-like granular media and m
¼
2 for a
wide range of rocks with porosities 0.001-0.1 (Brace et al.
1965
; Gonten and
Whiting
1967
).
The equivalent channel model on which (
3.45
)to(
3.49
) are based is obviously
oversimplified and does not take fully into account the variations in cross-section
of the pore space along the fluid paths or branching or any lack of connectivity in
these paths, and the electrical analog may not be an exact one. However, the
relations (
3.48
) and (
3.49
) can be useful for practical purposes. Thus, they are
found to give a reasonably good fit to observations on fairly porous rocks (see
Paterson
1983
for a reappraisal of earlier observations). They probably also apply
at least approximately to microcracked rocks such as granite; thus, analysis of
measurements by Brace et al. (
1968
) and Brace (
1977
) in these terms indicates that
increase in confining pressure produces a decrease in hydraulic radius, presumably
reflecting a decrease in the mean crack opening width (Paterson
1983
). Also, the
empirical observation that k
/
F
1
:
5
(Brace et al.
1968
) indicates that R
/
1
=
F
p
for granite under varying confining pressure. In the case of granular media, it has
been found empirically that the permeability is well described by k
¼
0
:
0006d
2
