Comparison of methods for upscaling permeability from the pore scale to the core scale

Several methods are compared for estimating the core-scale permeability of a rock whose pore space is idealized as consisting of a cubic network of pore tubes having a distribution of pore-scale hydraulic conductances. The conductance distribution of the pores is estimated from image analysis of scanning electron micrographs of rock sections. An explicit solution of the network equations is used as a benchmark to establish the exact macroscopic permeability. The other three upscaling methods used are Kirkpatrick's isotropic effective medium approximation, Bernasconi's anisotropic effective medium approximation, and the generalized perturbation ansatz (GPA) proposed by Gelhar and Axness. The analysis is carried out on a suite of petroleum reservoir sandstones from the North Sea, with measured core-scale permeabilities ranging from 20 to 500 mD. The log-variances of the pore-scale hydraulic conductance distribution were in the range of 2-3. The predictions of both the Kirkpatrick equation and the GPA are in each case within 10% of those computed by explicit network calculation, and all permeability predictions are generally within a factor of two of the core-scale values measured in the laboratory.