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If we now pass an electrical current between the two faces, the resistance of
the block is Rwl,/A, or, substituting eq. 6.4, Rwli/fAl. The resistivity of the
block is therefore:

Substituting this result into the definition of F (eq. 6.3), we obtain:

The Formation Resistivity Factor is a dimensionless material constant
that is proportional to the square of the tortuosity and inversely proportional
to the porosity of the material. It is independent of the resistivity, and so
also of the salinity of the pore fluid. Not all rocks with, say, 20% porosity
will have the same formation factor because their tortuosities will normally
differ. Note that the tortuosity of a rock, which is also important for fluid
now, can be obtained from (but see Winsauer et a)., 1952: they mea-
sured the tortuosity by an independent electrical method and concluded that
Ff =
Archie (1942) also inferred from experimental data that:

F = af-“ (6.6)
where the factor a is close to unity, and the exponent rn varies between 1.4
for unconsolidated sands and about 2.3 for indurated sandstones (it is unity
for straight pores). This empirical result seems to bear little relationship to
eq. 6.5, but it is intuitively reasonable to suppose that tortuosity is an
inverse function of porosity - the greater the porosity, the smaller the tor-
tuosity. Winsauer et al.’s tabulation (1952, p. 266, table 11) may be used to
obtain an empirical relationship between porosity and tortuosity. If we take
their measured tortuosity, it is closely approximated by f-2’3: if we take
mas the measure of tortuosity, it is closely approximated by 0.9 f-” . Sub-
stituting these results into eq. 6.5, the first suggests that F = f-2.3, while the
second suggests F = 0.8 f-’. If the aberrant (third) data point is omitted, the
second suggests F = 0.6 f-’.’. These data are plotted on Fig. 6-2.
In addition to Archie’s formula, as eq. 6.6 is called, the following are also
in common use, and there is no significant practical difference between
them :
F = 0.81 f-2 for sand

F= f-2 for hard sandstone
F = 0.62 f-’.” “Humble Formula”

These results, amply justified by decades of use, suggest that JFf is a better
measure of tortuosity than the direct measurement used by Winsauer and his