Resistivity Logs Revisited

L. Dunham
Consulting Petrophysicist ([email protected])

The primary test of any log designed to measure resistivity is that it must be sensitive only to changes in formation resistivity. This paper will prove that resistivity logs respond to changes in the resistivity, shape and dimensions of material within the pore space and are resistance logs. Consider a clean water sand with the following properties:
1. ф = 35%
2. R(t) = .2 ohm meters
3. R(w) = .03 ohm meters Theoretically, the resistivity log is responding to a quartz matrix filled with water of .03 ohm meter resistivity. However, quartz may be replaced with other minerals [limestone, dolomite, granite, etc.] of different resistivity and R(t) would remain unaffected. Ignoring matrix resistivity is equivalent to ignoring the resistivity and thickness of insulation that surrounds an electrical circuit. In this example, measured resistivity is sensitive only to changes in water resistivity and is not affected by matrix resistivity, provided matrix resistivity is sufficiently large to be an effective insulator.

Next consider the change to R(t) when porosity of this clean sand is reduced to 3% by quartz overgrowths, while water resistivity remains constant. Because R(t) will increase when porosity is decreased proves resistivity logs are not primarily sensitive to changes in formation resistivity and proves resistivity logs respond to equation 1. Resistivity logs are cumulative pore space resistance [matrix R(t)] logs.
R = p L/A (1)
R = resistance of pore space, X, p = water resistivity, X-M²/M;
A = cross-sectional area of pore space, M²; L = length of pore space, M.

AAPG Search and Discovery Article #90903©2001 AAPG Mid-Continent Meeting, Amarillo, Texas