Modification of the SDR equation for permeability prediction

Abstract

We evaluate the potential of permeability prediction of the original and modified versions of the Schlumberger-Doll Research (SDR) equation that is applied to data of nuclear magnetic resonance (NMR) relaxometry. Different definitions of characteristic relaxation time are considered. In a further modification, pore radius replaces the characteristic relaxation time in the original SDR equation. Only a good estimate of the surface relaxivity enables a reliable transformation from the relaxation time distribution (RTD) into the pore radius distribution (PRD). A recently published approach considers the specific surface area per unit pore volume (Spor) and the weighted harmonic mean (T2hm) of the RTD for the determination of an individual value of surface relaxivity for each sample. The evaluation is performed for three sample sets originating from different sandstone formations. The good predictive quality of the original SDR equation is confirmed. However, the prefactors have to be adjusted by calibrating with core data. We demonstrate that the use of average pore radii instead of average relaxation times enables a better permeability prediction. The weighted harmonic mean of the PRD, which proves to be a reliable proxy for the effective hydraulic radius, provides a high quality permeability prediction.