The dielectric permittivity of carbonate formations from the unified microstructure model

Abstract

Abstract In this paper we study the influence of pore microstructure and saturation of pore systems on the dielectric permittivity of double-porosity formations. The dielectric permittivity calculations were fulfilled using the unified model approach. This approach is based on the calculation of different physical properties from the single microstructure model applying the symmetric variant of the effective medium approximation (EMA). Porous rock is considered as a composed material that consists of solid grains and fluid filled pores of a small scale (primary porosity) that form a homogeneous isotropic matrix. Secondary pores of a large scale are represented by inclusions of different shapes placed in this matrix. Each component of rock (grains, primary and secondary pores) is approximated by a three-axial ellipsoid. The aspect ratios of grain and primary-pore ellipsoids are introduced as a function of porosity. The shapes of secondary pores such as a crack, vug, and channel are modeled by varying ellipsoidal aspect ratios. The distribution of saturating immiscible fluids in pore space is described by two models: (1) water (the wetting component) is concentrated in a film attached to the pore walls while oil or gas (the non-wetting component) occupies the central part of a pore; in this model a pore is considered as a layered ellipsoid with the wetting component in the outer layer; (2) the saturating fluid contains spherical drops of oil placed in the water. The dielectric permittivity obtained by using the unified microstructure model with variable aspect ratios of matrix grains and pores demonstrates a good agreement with the experimental data. The influence of secondary pores on the dielectric permittivity depends on pore shape and decreases with oil saturation.