The Formation Factor

Part 6, Chapter 6: Resistivity Logs and Invasion Profiles

Learning objectives

Define the formation factor F = Ro/Rw = a/phi^m
Read the cementation exponent m as the slope on a log-log F-vs-phi plot
Relate m to pore geometry (clean versus vuggy)
Compute the wet-rock resistivity Ro = F*Rw

Geometry Amplifies Resistivity

Before any hydrocarbon enters, the rock geometry already raises the resistivity above that of the brine itself, because the current must wind through the tortuous pore network instead of a straight tube of salt water. The formation factor measures that amplification:

F = \frac{R_o}{R_w} = \frac{a}{\phi^{\,m}}.

It is the ratio of the wet-rock resistivity $R_o$ to the water resistivity $R_w$ , and it grows as porosity falls.

The Cementation Exponent

Plot F against porosity on log-log axes and the relation is a straight line whose slope is the cementation exponent $m$ . For clean, intergranular rock $m$ is close to 2; in vuggy or fractured carbonates, where the current path is longer and more broken, it climbs toward 2.3 or higher. The coefficient $a$ shifts the whole line up or down: Archie used $a=1$ , the Humble equation $a=0.62$ . Because $m$ carries straight into the saturation, choosing it wrong, a sandstone $m$ in a vuggy carbonate, biases the pay.

From F to Ro

The formation factor is the bridge from the easy measurement to the one Archie needs. Multiply it by the water resistivity and you have the wet-rock resistivity $R_o = F,R_w$ , the resistivity the rock would show if it were fully water-bearing. That is the baseline the true resistivity is compared against to find the water saturation, the very next chapter. Read together with the deep Rt, the formation factor closes the resistivity half of Archie.

References

Archie, G. E. (1942). The electrical resistivity log as an aid in determining some reservoir characteristics. Transactions of the AIME, 146(1).
Asquith, G. and Krygowski, D. (2004). Basic Well Log Analysis, 2nd ed. AAPG Methods in Exploration 16.