Study of the pore space heterogeneity effect on the absolute permeability tensors calculated under different boundary conditions and driving forces using a “Computational Rock Physics” technology

Abstract

In this paper, we study the effect of pore space heterogeneity on off-diagonal permeability tensors calculated for four possible combinations between external boundary conditions (non-flow and periodic) and the driving force inducing the fluid flow (pressure drop and body force). The results were obtained using “Computational Rock Physics” technology, which involves numerical experiments in digital models of porous media. As a mathematical model describing a single-phase flow in porous media, the lattice Boltzmann equations in combination with the multi-relaxation time scheme are used. Porous structures with various heterogeneities are generated using a combination of the Monte-Carlo movement algorithm and the Quartet Structure Generation Set method. The results show that for non-flow boundary conditions (BC), the diagonal components calculated for the body force exceed the corresponding values calculated for the pressure drop, but for the periodic BC, the opposite trend was revealed. It has been established that the heterogeneity significantly affects the sensitivity of the permeability components to the type of driving force as follows: an increase in heterogeneity promotes an increase in differences between the permeability components calculated under pressure drop and body force. The sensitivity of the diagonal components to the driving force is higher in the case of non-flow BC. The paper also considers the issue of the asymmetry of the permeability tensor and the influence of heterogeneity, types of boundary conditions, and driving forces on it. It was found that the permeability tensor is absolutely symmetrical only for periodic BC and body force, while for the other three combinations this is not the case. The power of tensor asymmetry increases with increasing pore space heterogeneity. Differences in the permeability components, as well as the power of tensor asymmetry, decrease with the increasing scale of the sample.