A comparative study of permeability prediction for Eocene sandstones - Part 2: Application and modification of the Schlumberger-Doll Research equation

Nuclear magnetic resonance (NMR) relaxometry provides insight into the pore radius distribution (PRD) of rocks. Several permeability (k) of prediction models are based on the knowledge of the PRD. The Schlumberger-Doll Research (SDR) equation relates the weighted geometric mean of the transverse relaxation time (T-2) and porosity to k. In the common form of SDR equation, porosity is raised to the fourth power. This exponent is not in agreement with theoretical models of permeability prediction. Modified versions of the SDR equation have been tested with varying exponents for porosity and other characteristic relaxation times or pore radii determined from NMR relaxometry. We have evaluated the quality of various k-prediction models using a sample set of Eocene sandstones with known values of measured permeability. A porosity exponent of five provides the best quality permeability prediction using the weighted geometric mean of T-2. The replacement of the weighted geometric mean of T-2 by the weighted arithmetic or harmonic mean in combination with a porosity exponent of six indicates a slightly lower predictive quality. The use of average pore radii instead of average T-2 enables a better permeability prediction. The porosity exponents become smaller in these equations. This finding is confirmed by multivariate regression that provides noninteger exponents for porosity, relaxation time, or characteristic pore radii.

Automated summary

NMR relaxometry provides a method to study the pore characteristics of rocks, and can be used to predict permeability. Modifying the equations with different exponents can improve the quality of permeability prediction.