Modeling and inversion of elastic wave velocities and electrical conductivity in clastic formations with structural and dispersed shales

Abstract

This paper presents a new approach for simulating P- and S-wave velocities, and electrical conductivity in shaly-sand rocks and determining the shale spatial distribution (dispersed and/or structural shales). In this approach, we used the effective medium method and hierarchical model for clastic formations. We treat shaly-sand formations as porous natural-composite materials containing: solid grains (such as quartz, feldspars and structural shale) and pores completely filled with a mixture of hydrocarbon, water and dispersed shale. For calculating the effective elastic properties and electrical conductivity of this composite, we have applied the multi-component self-consistent effective media approximation (EMA) method. We simulate the elastic velocities and electrical conductivity for clastic formations in two steps. Firstly, we calculate the effective properties of mixture (combination of water, hydrocarbon and dispersed shale) filling the pores. Then we find the effective elastic and electrical conductivity properties of formation constituted of solid grains (quartz and structural shale) and pores with the effective properties determined in the previous step. We considered that all components are represented by ellipsoids. The aspect ratios (shapes) of grains and pores; are defined as a porosity function obtained for the model of clean sand formations. Modeling results have demonstrated that the shapes of both shale components (dispersed and structural) weakly affect the effective elastic velocities and electrical conductivity of shaly-sand formation and can be approximated by flatted ellipsoids. The model proposed has been used to determine the volumes of dispersed and structural shales for two sets of published experimental data obtained from the cores. For determining the shale distribution, we have performed the joint inversion of the following physical properties: P-, S-wave velocities, total porosity, and total shale volume. Additionally, we have predicted the effective electrical conductivity for the second set of data, taking into account the shale distribution obtained by the inversion process. A good agreement between the simulated effective conductivity and measured data confirms the determination of shale spatial distribution, and allows us to validate the proposed model and calculation technique.