Why Permeability Is Hard

Part 9, Chapter 9: Permeability Estimation

Learning objectives

Distinguish porosity (a volume) from permeability (a flow rate)
State Kozeny-Carman and the d-squared throat-size control
Explain why same-porosity rocks can differ in k by orders of magnitude
Recognize that log permeability is fundamentally an estimate

Volume Versus Rate

Every property so far has been a kind of volume or fraction, and logs read those well. Permeability is different. It is a rate, a measure of how fast fluid moves through the connected pore network, and it is governed not by how much pore there is but by the size of the throats that link the pores. Flow through a tube goes as the radius squared, by Poiseuille, and Kozeny-Carman carries that law into rock:

k = c\,\frac{\phi^{3}}{(1-\phi)^{2}}\,d^{2}.

The grain size $d$ , which sets the throat size, enters squared. Porosity enters too, but over the narrow range real rocks span it is the minor term.

The d-Squared Problem

The widget makes the difficulty plain. Hold the porosity fixed and sweep the grain size, and the permeability climbs a straight log-log line of slope two, from a fraction of a millidarcy in silt to darcies in clean coarse sand, a swing of thousands. Now nudge the porosity: the line barely shifts. Two rocks at the same porosity, one coarse and one fine, log identically and yet flow worlds apart.

Why Logs Struggle

Here is the consequence. Logs pin the porosity but say almost nothing about the grain and throat size, the very thing that controls permeability. So permeability cannot be read off a log the way porosity or saturation can; it must come from a transform, a porosity-permeability relation calibrated against core, and it carries real uncertainty. The rest of this chapter is the toolkit for building and trusting that estimate: the Timur and Tixier equations, the poro-perm crossplot, flow units, and the NMR permeability that gets closest to measuring the throats directly.

References

Kozeny, J. (1927). Uber kapillare Leitung des Wassers im Boden. Sitzungsberichte der Akademie der Wissenschaften in Wien, 136.
Amaefule, J. O. et al. (1993). Enhanced reservoir description: using core and log data to identify hydraulic flow units. SPE 26436.