Are self-consistent models capable of jointly modeling elastic velocity and electrical conductivity of reservoir sandstones?

Self-consistent (SC) models are commonly used for simulating elastic and electrical properties of reservoir rocks. We have developed a technique to test the capability of SC models to jointly model elastic velocity and electrical conductivity of porous media using a database of measurements of these properties on reservoir sandstones. The pores were represented by randomly oriented spheroidal shapes with a spectrum distribution of aspect ratios, and elasticity theory was used to compute the variation of aspect ratios and volume fractions of the pores subject to varying differential pressures. Using this method, the pore aspect ratio spectra of a reservoir sandstone were obtained separately from the measured elastic (P- and S-waves) velocity and electrical conductivity under loading. We have determined that when the SC formalism is used, there is a systematic discrepancy in the estimated pore structure predicted by the two measurements. Despite the supposed applicability of the SC method to this class of problem, the pore aspect ratio spectrum inverted from one physical property (e.g., velocity or conductivity) failed in practice to predict the other physical property (e.g., conductivity or velocity), at least for porous sandstones. Our results suggested the requirement of a new model to link the elastic and electrical properties to a unified pore aspect ratio spectrum of rocks.