Joint modeling of acoustic velocities and electrical conductivity from unified microstructure of rocks

Abstract

[1] A technique for the joint modeling of the electrical conductivity and acoustic velocities in porous rocks is proposed. The technique is based on the model of twocomponent media, composed by grains, which constitute a solid frame and pores saturated by a fluid. For this model we used symmetrical effective medium approximation method that provides the simulation of the acoustic and electrical parameters for multicomponent systems with equally treated constituents. The individual element of each component as a pore or grain was approximated by an ellipsoid. The aspect ratios for grain and pore ellipsoids are introduced as a function of porosity. By applying this technique we performed the calculation of acoustic velocities and electrical conductivity for carbonate formations with a primary pore system. For such formations the experimentally determined acoustic and electrical parameters are described by the empirical regression equations for the P and S wave velocities versus porosity and Archie's law. The ellipsoid aspect ratios were obtained by minimizing the differences of both predicted P wave velocity and conductivity with experimental data. The results obtained demonstrate that electrical conductivity is more sensitive to the pore and grain geometry than acoustic velocities. To ensure the conductivity for the low porosities, the form of pores tends to a needle shape. The simulation technique developed is the base for the petrophysical inversion of well log data to reconstruct the microstructure of porous rocks.

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

“…However, the elastic and electrical properties were calculated for spherical inclusions which represent only one secondary porosity type (vuggy porosity). A technique for the joint simulation of acoustic and electrical parameters proceeding from a unified microstructural model of porous media was proposed by Kazatchenko et al (2004a). However, this work was only focusing in the model for carbonate porous matrix.…”

“…The another approach to modeling double porosity media consists in a development of the unified model that permit different physical properties to be simulated (Brie et al, 1985;Endres and Knight, 1991;Sheng, 1991;Kazatchenko et al, 2004a). Endres and Knight (1991) using the Kuster-Toksö z approach (Kuster and Toksoz, 1974) calculated the elastic wave velocities and dielectric constant for spheroidal inclusions with a wide range distribution of aspect ratios (from spheres to oblate spheroids).…”

“…We have applied the approach proposed by Kazatchenko et al (2004a) for determining the matrix effective parameters of carbonate formations. The matrix thermal conductivity was given by empirical expressions presented by Pribnow and Sass (1995) and Schoen (1996).…”

“…The matrix thermal conductivity was given by empirical expressions presented by Pribnow and Sass (1995) and Schoen (1996). Based on this unified model (Kazatchenko et al, 2004a) and by applying the EMA method we have simulated effective acousticwave velocities, electrical and thermal conductivities as functions of the primary and secondary porosity, and shapes of secondary pores (aspect ratios).…”

Fluid substitution in rocks saturated with viscoelastic fluids

“…As mentioned, the effect of a Newtonian pore fluid on the elastic moduli of a rock can be predicted from the properties of dry rock and fluid compressibility using the Gassmann/Biot theory. An alternative approach, which addresses the problem of estimating elastic moduli from knowledge of rock constituents and microstructure, is based on effective-medium theories ͑e.g., Hashin and Shtrikman, 1963;Budiansky, 1965;Hill, 1965;Mukerji et al, 1995;Kazatchenko et al, 2004͒. These theories allow one to compute equivalent elastic properties of a mixture of two or more elastic constituents.…”