Page 135 - Petroleum Geology

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proportional to the number of ions, each of which can conduct a specific
amount of electrical charge. Ground water contains many different ions, the
common ones being Na’, Ca2+, Mg” (cations); C1-, SO:-, C0:- and HCOS
(anions). Each of these ions has a different conduction capacity, so a valuable
simplification is to consider an equivalent NaCl solution that would have the
same electrical properties as the more complex reality. In general, the more
saline the solution, the more conductive and less resistant it is.
The resistivity of a material is a measure of the difficulty with which an
electrical current flows through the material. It is the inverse of conduc-
tivity. Some electrical logging devices measure conductivity, but most
measure (directly or indirectly) resistivity.
Ohm’s law states (with certain limits on the magnitude of the quantities)
that for a given conductive material, the ratio of the voltage (potential)
across the ends and the current in the conductor is constant* :

v (volts)
-~ constant = resistance r (ohms).
=
I (amps)
If the cross-sectional area A of the conductor is uniform, the resistance is
proportional to the length I and inversely proportional to A. Thus, the
resistivity R is related to resistance by:
r = RE/A. (6.2)
If the resistance is measured in ohms (52 ) and the unit of length is the metre,
then the unit of resistivity is ohm * m2 m-’, or ohm-metre (ohm-m). Resistivity
is numerically equal to the resistance of a metre cube of the conductive
material.
Consider a cube of non-conductive material, 1 X 1 X 1 m. The resistivity of
this cube is infinite. If a straight hole of 1 cm2 cross-sectional area is drilled
through the cube normal to the two faces between which the current will be
passed, and this hole is filled with water of resistivity (R,) one ohm-metre,
the resistance of this water in the hole will be:
Rw - length 1 . 1
~ ~ _ - _ _ - 10,000 52
_
_
area 0.0001
and the resistivity of the cube will be 10,000 ohm-m. If a second hole of the
same size is drilled parallel to the first, and both holes are filled with water
of resistivity R, = 1 ohm-m, the resistivity of the cube will be 5000 ohm-m. If
there are 2000 such holes, the resistivity of the cube will be 5 ohm-m, and the
“porosity” will be 20%. The resistivity of the cube is thus inversely propor-

* The notation R for resistance and p for resistivity is not usually followed in well-log
analysis.