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This article represents numerical simulation technique for determining effective spectral electromagnetic properties (effective electrical conductivity and relative dielectric permittivity) of saturated porous media. Information about these properties is vastly applied during the interpretation of petrophysical exploration data of boreholes and studying of rock core samples. The main feature of the present paper consists in the fact, that it involves three-dimensional saturated digital rock models, which were constructed based on the combined data considering microscopic structure of the porous media and the information about capillary equilibrium of oil-water mixture in pores. Data considering microscopic structure of the model are obtained by means of X-ray microscopic tomography. Information about distributions of saturating fluids is based on hydrodynamic simulations with density functional technique. In order to determine electromagnetic properties of the numerical model time-domain Fourier transform of Maxwell equations is considered. In low frequency approximation the problem can be reduced to solving elliptic equation for the distribution of complex electric potential. Finite difference approximation is based on discretization of the model with homogeneous isotropic orthogonal grid. This discretization implies that each computational cell contains exclusively one medium: water, oil or rock. In order to obtain suitable numerical model the distributions of saturating components is segmented. Such kind of modification enables avoiding usage of heterogeneous grids and disregards influence on the results of simulations of the additional techniques, required in order to determine properties of cells, filled with mixture of media. Corresponding system of differential equations is solved by means of biconjugate gradient stabilized method with multigrid preconditioner. Based on the results of complex electric potential computations average values of electrical conductivity and relative dielectric permittivity is calculated. For the sake of simplicity, this paper considers exclusively simulations with no spectral dependence of conductivities and permittivities of model components. The results of numerical simulations of spectral dependence of effective characteristics of heterogeneously saturated porous media (electrical conductivity and relative dielectric permittivity) in broad range of frequencies and multiple water saturations are represented in figures and table. Efficiency of the presented approach for determining spectral electrical properties of saturated rocks is discussed in conclusion.

We study an appearance of gravitational convection in a porous medium saturated by the double-diffusive fluid. The rectangle heated from below is considered with anisotropy of media properties. We analyze Darcy – Boussinesq equations for a binary fluid with Soret effect.

Resulting system for the stream function, the deviation of temperature and concentration is cosymmetric under some additional conditions for the parameters of the problem. It means that the quiescent state (mechanical equilibrium) loses its stability and a continuous family of stationary regimes branches off. We derive explicit formulas for the critical values of the Rayleigh numbers both for temperature and concentration under these conditions of the cosymmetry. It allows to analyze monotonic instability of mechanical equilibrium, the results of corresponding computations are presented.

A finite-difference discretization of a second-order accuracy is developed with preserving of the cosymmetry of the underlying system. The derived numerical scheme is applied to analyze the stability of mechanical equilibrium.

The appearance of stationary and nonstationary convective regimes is studied. The neutral stability curves for the mechanical equilibrium are presented. The map for the plane of the Rayleigh numbers (temperature and concentration) are displayed. The impact of the parameters of thermal diffusion on the Rayleigh concentration number is established, at which the oscillating instability precedes the monotonic instability. In the general situation, when the conditions of cosymmetry are not satisfied, the derived formulas of the critical Rayleigh numbers can be used to estimate the thresholds for the convection onset.

New numerical simulation technique to calculate electrical properties of rocks with two-phase “oil– water” saturation is proposed. This technique takes into account surface conductivity of electrical double layers at the contact between solid rock and aqueous solution inside pore space. The numerical simulation technique is based on acquiring of electrical potential distribution in high-resolution three-dimensional digital model of porous medium. The digital model incorporates the spatial geometry of pore channels and contains bulk and surface grid cells. Numerical simulation results demonstrate the importance of surface conductivity effects.