Predicting the permeability of sandstone from image analysis of pore structure

Abstract

A model is developed that allows accurate prediction of the permeability of a core sample of sedimentary rock, based on two-dimensional image analysis of its pore structure. The pore structure is idealized as consisting of a cubic network of pore tubes, with the tubes having an arbitrary distribution of cross-sectional areas and shapes. The areas and perimeters of the individual pores are estimated from image analysis of scanning electron micrographs of thin sections, with appropriate stereological corrections introduced to account for the angle between axis of the pore tube and plane of the thin section. The individual conductances of each tube are estimated from the measured areas and perimeters, using the hydraulic radius approximation. Variations in the pore diameter along the length of the tube are accounted for with a “constriction factor” whose derivation is based on laminar flow through an irregular tube. Effective-medium theory is used to find the effective single-tube conductance, based on the measured distribution of individual conductances. This procedure is applied to several consolidated North Sea reservoir sandstones, and some outcrop sandstones, with permeabilities ranging from 20 to 1400 mD. The predicted permeabilities are typically within a factor of 2 of the measured values, with an average error in $\log k$ of only 0.168.