Page 253 - Petrophysics 2E

226 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

Equation 4.44 can be expressed as:

(4.45)

The value of fG for most porous rocks is close to unity. Hence, fG/qrn >>

(1 - fc) and Equation 4.45 can be approximated by:
fG
om
FR = - (4.46)

This expression is the Humble formula (Equation 4.40) where fG = a.
Thus Archie formula and Humble formula are special cases of Rosales
general formula. Rosales showed experimentally that, for sandstones,
Equation 4.46 can be written as follows [ 111

(4.47)

This expression was compared graphically with the Humble formula,
Equation 4.34, and the Timur et al. formula [12]:
1.13
FR = - (4.48)
$1.73

Figure 4.16 is a log-log plot of Equations 4.39 (line A), 4.42 (line B),
and 4.48 (line C). The three formulas give approximate results within
the region practical interest, i.e., 10 5 @ 5 40. As $ approaches unity,
however, Equation 4.42 gives a curved line that satisfies the condition
FR = 1 when @ = 1, whereas the Humble formula (Equation 4.39) and
the Timur et al. formula (Equation 4.48) are straight lines for all values
of @, which does not satisfy that condition. From Equation 4.35, the
tortuosity is:

t = @FR (4.49)

Substituting Equation 4.44 into Equation 4.49 yields a general expression
for calculating tortuosity:

(4.50)

Inasmuch as the value of fG is approximately equal to unity for most
porous rocks, Equation 4.50 can be written as follows:

1
z=- (4.51)
Om- 1