Comparison of the effective pressure law for permeability and resistivity formation factor in Chelmsford granite

Abstract

Permeability, resistivity formation factor, and pore volume change were simultaneously measured on samples of Chelmsford granite subjected to confining pressure and pore pressure cycles. Using a technique described in a previous paper, the tangent coefficients of the effective pressure law for permeability α _k and for formation factor α _F were determined. α _k and α _F did not differ significantly from one another. They showed a strong stress history dependence as has already been observed for α _k in several crystalline rocks. According to the definition of the effective pressure law used here, two physical properties with identical α's must be related through a one-to-one functional relationship. Hence, the observation above suggests that such a relationship may be empirically found between permeability and formation factor. Indeed, analysis of the data revealed that, to a good approximation, permeability was inversely proportional to the formation factor. The same relation has previously been observed in other crystalline rocks. This relationship was included in a recent version of the so-called equivalent channel model. Using this model, the specific surface area of the cracksA _c/V_S, the standard deviation of the distribution of asperities heightsh and the hydraulic radiusm _o were evaluated. The following values were respectively found: 850 cm⁻¹, 0.008 μm and 0.14 μm. The specific surface area of the cracks was independently estimated on micrographs of polished sections using a standard quantitative stereology method. The result was in good agreement with the values estimated from the transport properties data.