Borehole Environment

G. E. Archie of Shell was making electrical measurements on core samples, with the aim of relating them to permeability

His measurements consisted of completely saturating core samples with saltwater of known resistivity Rw and relating the measured resistivity Ro of the fully saturated core to the resistivity of the water.

He found that, regardless of the resistivity of the saturating water, the resultant resistivity of a given core sample was always

related to the water resistivity by a constant factor F

(1)

Formation Factor

The formation factor is a function of porosity and can be expressed as a power law of the form:

(2)

where the exponent m is very nearly 2.

This empirical observation can be used to describe the variation in formation resistivity for a fixed water resistivity when the porosity changes.

The lower the porosity, the higher the resistivity will be.

The exponent m is the cementation exponent, as it was observed to increase with the cementation of the grains. In general, it was recognized that m increased with the tortuosity of the electric path through the pore space

Formation Factor

The exponent n, called the saturation exponent, is very nearly 2 for the data considered.

An approximate expression for the water saturation is

(4)

On loglog paper, the data of water saturation versus relative resistivity plotted as a straight line, suggesting a relationship of the form (3)

(5)

However, the fully saturated resistivity Ro can be related to the water resistivity using the previously discovered Archie relationship. So the expression becomes

(6)

However, a more general form, is

(7)

where the constants a, m, and n need to be determined for the particular field or formation being evaluated.