Estimating pore volume compressibility by spheroidal pore modeling of digital rocks

Abstract

The real pores in digital cores were simplified into three abstractive types, including prolate ellipsoids, oblate ellipsoids and spheroids. The three-dimensional spheroidal-pore model of digital core was established based on mesoscopic mechanical theory. The constitutive relationship of different types of pore microstructure deformation was studied with Eshelby equivalent medium theory, and the effects of pore microstructure on pore volume compressibility under elastic deformation conditions of single and multiple pores of a single type and mixed types of pores were investigated. The results showed that the pore volume compressibility coefficient of digital core is closely related with porosity, pore aspect ratio and volumetric proportions of different types of pores. (1) The compressibility coefficient of prolate ellipsoidal pore is positively correlated with the pore aspect ratio, while that of oblate ellipsoidal pore is negatively correlated with the pore aspect ratio. (2) At the same mean value of pore aspect ratio satisfying Gaussian distribution, the more concentrated the range of pore aspect ratio, the higher the compressibility coefficient of both prolate and oblate ellipsoidal pores will be, and the larger the deformation under the same stress condition. (3) The pore compressibility coefficient increases with porosity. (4) At a constant porosity value, the higher the proportion of oblate ellipsoidal and spherical pores in the rock, the more easier for the rock to deform, and the higher the compressibility coefficient of the rock is, while the higher the proportion of prolate ellipsoidal pores in the rock, the more difficult it is for rock to deform, and the lower the compressibility coefficient of the rock is. By calculating pore compressibility coefficient of ten classical digital rock samples, the presented analytical elliptical-pore model based on real pore structure of digital rocks can be applied to calculation of pore volume compressibility coefficient of digital rock sample.