Release:2016, Vol. 2. №3
About the authors:Dmitry E. Igoshin, Cand. Sci. (Phys-Math.), Senior Researcher, Tyumen Branch of the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences; Associate Professor, Department of Fundamental Mathematics and Mechanics, Department of Applied and Technical Physics, University of Tyumen; firstname.lastname@example.org
In the previous works the authors considered two-parameter models of periodic porous media. The unit cell size and a dimensionless parameter — the degree of the intersection of spheres — act as model parameters. In such models the porosity of the material is connected one-to-one with the permeability for a fixed unit cell size, i. e. graphically many points of the medium in the axes “porosity-permeability” are located on the curve. However, in real earth material the experimental values of porosity and permeability are located in these axes in a “cloud” even for a single lithology type material taken from a single well. In this regard, it is essential to develop a three-parameter model porous medium, for which the region values of the permeability will match better the experimental data. The aim of this article is the development of the previously reviewed models in the event of a broadcast angle different from a right angle. The model periodic structure based on the rhombohedral lattice system is considered as an example. For the described structure exact porosity and minimal luminal are obtained analytically. Permeability estimation is obtained taking into account the sinuous channels. It is shown that when θ = 90° permeability value agrees well with the corresponding value for the cubic simple structure, and at θ = 60° — with the appropriate value for the face-centered cubic structure.