Model of sand formations for joint simulation of elastic moduli and electrical conductivity

Abstract

This paper presents an approach for the joint simulation of elastic-wave velocities (compressional and shear waves) and electrical conductivity for clastic rocks using a unified microstructural model. We treat clastic formations as porous composite materials containing two components: solid grains and pores completely saturated with fluids (gas-water-oil mixture). The effective shapes of both components correspond to triaxial ellipsoids. For calculating the effective properties of such a composite, we apply the self-consistent effective media approximation (EMA) method. This method treats all components equally without introducing any host and requires having knowledge of their shapes. To determine the pore and grain effective aspect ratios, we have used a set of experimental data that included the empirical regression equations published for the elastic-wave velocities in clean sandstone formations and Archie's law for the electrical conductivity. By applying the inversion procedure that consists of minimizing the difference between the experimental and EMA-predicted data, the aspect ratios of grains and pores as a porosity function have been obtained. Based on this relation and knowing individual property components (elastic and electrical conductivity) for grains and conductivity for pore saturating fluids, we can calculate effective properties of the clean sandstone formations. We demonstrate that to simplify the simulation of effective properties, grains and pores can be approximated by spheroids. However, in this case, the relative errors that the inversion process yields are higher in comparison with those of the three-axis ellipsoids. Additionally, we have determined the aspect ratios of components for several velocity equations (including different confinement pressures) and various cementation factors 'm' in Archie's law. We have modelled electrical conductivity for clastic formations with different water mineralization and oil saturation. The effective conductivity obtained by using our approach reflects a good fit with the published experimental data.