Page 140 - Petroleum Geology

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resistivity it would have if the oil saturation were zero (that is, if the pores
were saturated with the water that occurs in the reservoir), and n is a
saturation exponent with a value about 2. Inserting this value of n and sub-
stituting eq. 6.3 into 6.7, we get:

sW = (FR,/R#~ (6.8a)
or :
R, = FR,/s;. (6.8b)
As mentioned before, the theoretical validity of these formulae is dubious.
Resistance of adsorbed water films to lateral electrical flow is almost cer-
tainly involved. The saturation exponent n is probably also a function of
saturation because the true area available for flow, and the tortuosity
through the water, are also involved. With these reservations, the formulae
can be put to practical use.
The true resistivity of a petroleum-bearing rock is only relatively higher
than that of the same rock saturated with the same water. The true resistivity
may be quite low when the Formation Factor is small (large porosity) and
the resistivity of the connate water is low (large salinity, high temperature).
The resistivity index, Rt/Ro, is used as a guide to possible production (it
is approximately equal to the inverse square of the water saturation). Local
experience will be the guide, but many reservoirs with 30% water saturation
produce oil with no appreciable water, so resistivity ratios > 10 may well
produce clean oil.
The determination of the true resistivity of formations (Rt) is one of the
main goals of electrical logging. It is not simple. Its determination is in the
realm of the specialist well-log analyst or petrophysicist.

Resistivity in the subsurface.
Resistance and, by calibration or measurement, resistivity are measured
by systems of four electrodes. A known current is passed between two of
them (Fig. 6-4) and a potential is developed as a consequence between the
other two. This can be measured. For example, a current is passed between
electrodes 1 and 4 in Fig. 6-4, and a voltmeter reads the potential between
electrodes 2 and 3.
It has also been found that if the role of the electrodes is interchanged,
and the same current passed between electrodes 2 and 3, the potential be-
tween electrodes 1 and 4 is identical to that originally found between 2 and
3. This interchangeability of electrodes, known as reciprocity, is used in sub-
surface devices so that one electrode can fulfil more than one function.
If a current is passed between two electrodes in a very large volume of
homogeneous conductive material, as in Fig. 6-5, a potential field is generated
throughout the material and current flows down paths from high potential
to low potential. These current paths form a three-dimensional pattern such