Page 136 - Petroleum Geology

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tional to the “porosity” when the resistivity of the contained water is con-
stant.
If the holes are now filled with water of a different resistivity, the result-
ing resistivity of the cube will be different. Other things being equal, the
larger the resistivity of the water, the larger the resistivity of the cube.
In nature, the pore passages through rocks are neither straight nor of con-
stant diameter; and almost all are interconnected in a permeable rock. (We
are concerned only with effective porosity because pores that are completely
enclosed in non-conductive material do not contribute to the flow of elec-
tricity - or, of course, the flow of fluid.) Electrical current passes only
through the electrolyte saturating the pore spaces, so the paths are tortuous
and longer than the direct path. The mean path length between opposing
faces of a metre cube is greater than one metre. The ratio of the mean ef-
fective length (It) and the macroscopic length (1) is known as tortuosity” and
is a dimensionless geometrical property of the rock. On account of tortuos-
ity, a metre cube of rock with 20% porosity, the pores being saturated with
water of one ohm-m resistivity, would have a resistivity greater than 5 ohm-m.
It will be convenient to consider at this point a fundamental dimension-
less material constant that is used in electrical-log interpretation : the ratio
of the resistivity of a porous rock that is saturated with an electrolyte and
the resistivity of the electrolyte. This is called the Formation Resistivity
Factor (F) or Formation Factor, which was defined by Archie (1942):

R, = FR, (6.3)
where R, is the resistivity of a rock saturated with an electrolyte of resis-
tivity R,. Experiment showed that the Formation Resistivity Factor is a
measure of porosity ; but its significance is perhaps clearer when considered
in the following manner.
Consider a rectangular block of porous and permeable sandstone through
which an electrical current will be passed between opposing faces of area A
separated by the length 1. The fractional porosity, f, of this block is the
volume of the pores divided by the volume of the block, and the volume of
the pores is given equally by fA1 and A&,, where A, is the true area normal
to the tortuous electrical flow paths and 1, is the true mean length of these
paths. So:
fAl = A
and:
A, = fA1/lt - (6.4)

* Some authors define tortuosity as the square of this ratio, but the simple ratio is pre-
ferred here.