Effective medium modeling of pressure effects on the joint elastic and electrical properties of sandstones

Abstract

Subsurface rocks are subjected to different stress states, and as such, physical properties of rocks including elastic modulus and electrical resistivity are stress-dependent. Joint modeling of the stress-dependence of elastic and electrical properties is important for interpreting coincident elastic and electrical measurements. We present a modeling approach for the pressure-dependence of the joint elastic and electrical properties in brine-saturated sandstones, that links both properties to the same microstructure. This approach combines the differential effective medium (DEM) and the self-consistent approximation (SCA) with the dual-porosity concept to model the pressure-dependence of P-wave velocity and electrical resistivity simultaneously measured in four sandstone samples. There is good agreement between model results and laboratory experimental results for both the elastic and electrical properties. The model parameters optimized to fit the data are: constant stiff and “soft” (or compliant) aspect ratios; a fixed critical porosity; and pressure-dependent stiff and soft porosities. These model-derived pressure-dependent porosities correlate with the observed velocity and resistivity pressure-sensitivity of the rocks, for example, the higher the initial volume fraction of compliant pores, the higher the P-wave velocity pressure sensitivity. The results show that the pressure-dependence of the P-wave velocity and electrical resistivity can be jointly modeled satisfactorily using the dual-porosity concept, where the pore space is simplified to contain a single set of stiff and soft pores.