The Timur and Tixier Estimators

Permeability from Porosity and Swi

If permeability cannot be read from a log, the oldest workaround is to estimate it from two things logs do give: the porosity and the irreducible water saturation. Timur and Tixier are both empirical power laws of that pair:

Both say the same thing in slightly different constants: permeability climbs steeply with porosity and falls as the irreducible water drops.

Why Irreducible Water Works

The clever part is the $S_{wi}$. Irreducible water is the film capillarity holds on grain surfaces, so a rock that holds little irreducible water has large grains, wide throats, and little surface area, exactly the rock that flows well. A rock that holds a lot of irreducible water is fine-grained and tight. So the irreducible water is a stand-in for the throat size that ordinary logs miss, which is the whole reason these estimators work. It connects straight back to the bulk-volume water of Chapter 7: at irreducible conditions, $S_{wi}$ is what the saturation analysis already gives.

Calibrate, or Beware

Two cautions. First, the form is robust but the constants are local: Timur and Tixier can disagree by a factor of several, as the widget shows, so the estimator must be tuned to core for the field before its numbers are trusted. Second, both assume the rock is at irreducible water; in a transition zone, where some water is movable, $S_{wi}$ is overstated and the permeability comes out too low. Used with those caveats, they remain the quickest permeability estimate in the toolbox.

References

• Timur, A. (1968). An investigation of permeability, porosity, and residual water saturation relationships. SPWLA 9th Annual Logging Symposium.
• Tixier, M. P. (1949). Evaluation of permeability from electric-log resistivity gradients. Oil and Gas Journal, 48.