[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.

A B S T R A C TAn approach to determining the effective elastic moduli of rocks with double porosity is presented. The double-porosity medium is considered to be a heterogeneous material composed of a homogeneous matrix with primary pores and inclusions that represent secondary pores. Fluid flows in the primary-pore system and between primary and secondary pores are neglected because of the low permeability of the primary porosity. The prediction of the effective elastic moduli consists of two steps. Firstly, we calculate the effective elastic properties of the matrix with the primary small-scale pores (matrix homogenization). The porous matrix is then treated as a homogeneous isotropic host in which the large-scale secondary pores are embedded. To calculate the effective elastic moduli at each step, we use the differential effective medium (DEM) approach. The constituents of this composite medium -primary pores and secondary poresare approximated by ellipsoidal or spheroidal inclusions with corresponding aspect ratios.We have applied this technique in order to compute the effective elastic properties for a model with randomly orientated inclusions (an isotropic medium) and aligned inclusions (a transversely isotropic medium). Using the special tensor basis, the solution of the one-particle problem with transversely isotropic host was obtained in explicit form.The direct application of the DEM method for fluid-saturated pores does not account for fluid displacement in pore systems, and corresponds to a model with isolated pores or the high-frequency range of acoustic waves. For the interconnected secondary pores, we have calculated the elastic moduli for the dry inclusions and then applied Gassmann's tensor relationships. The simulation of the effective elastic characteristic demonstrated that the fluid flow between the connected secondary pores has a significant influence only in porous rocks containing cracks (flattened ellipsoids). For pore shapes that are close to spherical, the relative difference between the elastic velocities determined by the DEM method and by the DEM method with Gassmann's corrections does not exceed 2%. Examples of the calculation of elastic moduli for water-saturated dolomite with both isolated and interconnected secondary pores are presented. The simulations were verified by comparison with published experimental

In this article, we propose an approach to obtain the equivalent permeability of the fluid-filled inclusions embedded into a porous host in which a fluid flow obeys Darcy's law. The approach consists in the comparison of the solutions for one-particle problem describing the flow inside the inclusion, firstly, by the Stokes equations and then by using Darcy's law. The results obtained for spheres (3D) and circles (2D) demonstrate that the inclusion equivalent permeability is a function of its radius and, additionally, depends on the host permeability. Based on this definition of inclusion permeability and using effective medium method, we have calculated the effective permeability of the double-porosity medium composed of the permeable matrix (with small scale pores) and large scale secondary spherical pores.

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S U M M A R YMost natural porous rocks have heterogeneities at nearly all scales. Heterogeneities of mesoscopic scale-that is, much larger than the pore size but much smaller than wavelength-can cause significant attenuation and dispersion of elastic waves due to wave-induced flow between more compliant and less compliant areas. Analysis of this phenomenon for a saturated porous medium with a small volume concentration of randomly distributed spherical inclusions is performed using Waterman-Truell multiple scattering theorem, which relates attenuation and dispersion to the amplitude of the wavefield scattered by a single inclusion. This scattering amplitude is computed using recently published asymptotic analytical expressions and numerical results for elastic wave scattering by a single mesoscopic poroelastic sphere in a porous medium.This analysis reveals that attenuation and dispersion exhibit a typical relaxation-type behaviour with the maximum attenuation and dispersion corresponding to a frequency where fluid diffusion length (or Biot's slow wavelength) is of the order of the inclusion diameter. In the limit of low volume concentration of inclusions the effective velocity is asymptotically consistent with the Gassmann theory in the low-frequency limit, and with the solution for an elastic medium with equivalent elastic inclusions (no-flow solution) in the low-frequency limit. Attenuation (expressed through inverse quality factor 1/Q) scales with frequency ω in the lowfrequency limit and with ω −1/2 in the high-frequency limit. These asymptotes are consistent with recent results on attenuation in a medium with a periodic distribution of poroelastic inclusions, and in continuous random porous media.Seismic attenuation and dispersion are wavefield characteristics that can provide important information about the structure and composition of a medium. It is well known that Biot's (1962) theory of elastic wave propagation in homogeneous porous media underestimates the observed attenuation and dispersion by at least one order of magnitude. One possible cause of the larger than predicted attenuation is associated with the presence of spatial heterogeneities . When a porous medium contains regions of variable compliance, the passing compressional wave can cause pore fluid to flow from more compliant to less compliant areas and vice versa. Analysis of this phenomenon requires a theoretical model of wave propagation in an inhomogeneous porous medium.Theoretical studies of elastic wave attenuation and dispersion in saturated porous media due to the presence of small-scale heterogeneities were initiated in the 1970s, when J.E. White and his colleagues introduced two theoretical models of this phenomenon. They developed a 1-D model of a finely layered porous medium (White et al. 1976) consisting of alternating layers of gas and liquid saturation, and a 3-D model of an array of spherical gas patches embedded in a homogeneous liquid-saturated porous background (White 1975). The results of these studies were later rederived...