Simulation of acoustic velocities, electrical and thermal conductivities using unified pore-structure model of double-porosity carbonate rocks

Abstract

This paper studies the influence of a pore-space microstructure on the physical properties of double-porosity carbonate rocks. Starting from a unified microstructure model for double porosity media and applying the self-consistent method of the Effective Medium Approximation, we have calculated the elastic-wave velocities, electrical and thermal conductivities as functions of primary and secondary porosities, and secondary pore shapes. The double porosity medium is treated as a heterogeneous material composed of a homogeneous isotropic matrix that corresponds to a solid frame with primary small-scale pores and secondary pores represented by large-scale inclusions. Both pore-systems are completely saturated with water. Pores are arbitrarily orientated, and randomly distributed in the matrix. The shapes of secondary pores are approximated by three-axial ellipsoids. By varying the ellipsoid aspect ratios we model different secondary porosity types. The simulations performed demonstrate the different character of the dependences of the acoustic-wave velocities and electrical conductivity upon the inclusion shapes, matrix and secondary porosity values. The thermal conductivity has low sensitivity to the secondary pores for all considered shapes. Based on the responses of the acoustic and electrical parameters to the shapes of the secondary pores, we propose a new geophysical classification of the secondary porosity into four types: vugs (quasi-spherical inclusions), quasi vugs (oblate ellipsoids), channels (prolate ellipsoids), and cracks (strongly flatted inclusions). Additionally, we have calculated the rock physical properties for mixture of two types of the secondary pores. We show that in this case the joint analysis of acoustic-wave velocities and electrical conductivity allows each secondary-porosity type to be identified.