Permeability prediction in anisotropic shaly formations

We present a unified model for simulating the permeability and electrical conductivity of anisotropic shaly formations. The model is based on Willis' formulae and the concept of a host medium, the selection of which is crucial in predicting these transport properties. Different rock components, including shales and mudrocks, are characterized by parameters typifying their pore geometry, namely the aspect ratio, size and orientation distribution of the pores. In this regard the model is an extension of the elastic model of Xu & White for predicting P- and S-wave velocities in siliciclastic rocks. The electrochemical effect of clay minerals on electrical conductivity is simulated by Waxman & Smits' model. A novel feature of the permeability model is that its percolation factor is estimated by a nonlinear transformation of the percolation factor found from conductivity measurements. The model was tested on the laboratory measurements published by Waxman & Smits. Comparison of the results with those from the Waxman & Smits, Dual-Water, and Kozeny-Carman models, and with multilinear and non-linear regression techniques, demonstrated that the unified model predicted conductivity and permeability more accurately than any of these models from the same number or fewer parameters. The improved prediction was most noticeable in samples containing a significant clay mineral fraction. Apart from Waxman & Smits' data, we have found no published dataset that is comprehensive enough to test physical predictions of both conductivity and permeability.