Page 171 - Petrophysics

144 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

This equation is similar to Equation 3.14 for m = 1. Combining
Equations 3.83 and 3.78 gives:

ka = (")? (3.84)
8 z

Assuming z = QFR, where FR is the formation resistivity factor,
Equation 3.59 becomes:

(3.85)

Expressing tortuosity as z = (QFR)~, Equation 3.84 results in:

ka=(%)g 1

and, for z = @(FR)~, Equation 3.84 gives

These equations clearly indicate that no single correlation can be used
to determine the formation permeability from logs alone.
If ka is expressed in mD, rPa in pm, Equation 3.83 becomes:

ka = 126.7rpaQ (3.88)
2
m
Figure 3.30 is a semilog plot of this relationship. The Cartesian axis on
this plot is Qm instead of the conventional +. The importance of including
dimensions of the flow channels in developing k-Q relationships for
carbonates is clearly demonstrated by this plot. FQuation 3.88, which
also is applicable to sandstones, is derived on the basis that the average
pore radius of the flow channels remains constant along the length of the
unit block. As shown in Figure 3.31(A), however, the true pore radius
changes along the flow path length. The effect of changing cross-sectional
area along the flow path can be evaluated by considering the system
of Figure 3.31(B) as two resistors in series. The total conductivity C
of this system is related to the two conductivities C1 and C2 by the
paralIel-conductivity equation:

(3.89)