Page 168 - Petrophysics 2E

PERMEABILITY-POROSITY RELATIONSHIPS 141

in the outer layers of curved beds. Murray applied this approach to the
Spanish pool in McKenzie County, North Dakota, and demonstrated a
good coincidence between areas of maximum curvature and areas of
best productivity.
The flow of fluid through porous media is directly analogous to the
flow of electricity. McGuire and Sikora used this analogy and showed
that the width of artificial fractures is much more important than their
length in affecting communication among natural fractures [41]. Stearns
and Friedman summarized that the permeability of a naturally fractured
formation can be expected to be greatest where the reservoir bed
contains wide, closely spaced, smooth fractures oriented parallel to the
fluid pressure gradient [42].
Fracture permeability cannot be estimated directly from well logs.
The modern trend is to combine core-derived parameters with
computer-processed log data to establish a statistical relationship
between the permeability of the matrix-fracture system and various
parameters, such as porosity and irreducible water saturation. With such
a relationship established, the formation’s petrophysical parameters,
including permeability distribution, can be deduced from log data alone
in wells or zones without core data. In carbonate formations, however,
where structural heterogeneity and textural changes are common, and
only a small number of wells are cored because of the difficulty and
cost of the coring, the application of statistically derived correlations
is extremely limited. Watfa and Youssef developed a sound theoretical
model that relates directly to the flow of path length (tortuosity), pore
radius changes, porosity, and cementation factor m [43]. This model
assumes that:

(1) a porous medium can be represented by a bundle of tubes, as shown
in Figure 3.29;

Cube Length = L
k J

Figure 3.29. A bundle-oftubes model [43J.