Tensor Representation of Capillary Model of a Porous Medium (Theory and Experiment)

Generalization is given for the case of anisotropic porous media represented by a simple model of capillary porous medium. It is an idealized model in which the porous medium is a periodic lattice formed by mutually perpendicular cylindrical capillaries. It is assumed that each capillary system is characterized by its parameter da and stacking period aa (a = 1, 2, 3). It is shown that for anisotropic porous media, the functions of pore density distribution by radius and the values of the equivalent pore diameter depend on the direction and are set by symmetric tensor of the second rank. Scalar values of equivalent pore diameter are calculated, as is customary in crystal physics, in the form of the tensor properties along a predetermined direction. In the article an idea is given of the permeability coefficients tensor for simple capillary model of porous media and showed that the direction permeability value is determined by the tensor composition of luminal factor and pore distribution density by radii. The proposed theoretical representations of pore distribution density by radii; equivalent pore diameter and permeability coefficients are tested on the experimental data obtained in the laboratory experiment on a real core material. The main directions of the permeability tensor are determined from the extreme values of the transmission velocity of ultrasonic waves through the lateral surface of the core. Measurements on the control sample confirmed the tensor nature of the permeability. Pore distribution curves by radii are obtained by tomographic studies of core samples (device SkyScan 1172). A good agreement between theoretical and experimental results is obtained.