Article outline

The aim of the work. The Russian helium production potential is concentrated in the territory of Eastern Siberia and the Far East, where more than 30 helium-containing gas fields with a high helium content (0.2-0.8%) have been discovered. The original method of separating gas mixtures based on the selective permeability of the shell of hollow glass microspheres proposed by the authors can be used to separate helium from natural gas. The main objective of this work is to create a basis for a parametric study of a non-stationary gas separation process based on the selective permeability of hollow glass microspheres with respect to helium and other gases.

Methods. Using the approaches of multiphase media mechanics, a mathematical model of the flow of a binary gas mixture through a porous layer of hollow selectively permeable microspheres is developed, taking into account their dispersion distribution by parameters. A quasi-linear system of partial differential equations in a one-dimensional approximation describing the model is examined for characteristics and its type is determined. By non-dimensionalizing the equations, the main dimensionless complexes describing the non-stationary flow of a binary gas mixture through a porous layer of microspheres are obtained. To test the numerical solutions, an analytical solution is found for the stationary one-dimensional problem of binary gas mixture flows through a porous layer. Using the WENO difference scheme, a test calculation is performed for two problems of binary gas mixture flow through an adsorber:

1. the concentration wave propagates in the direction of gas flow (load wave), while the microspheres will be saturated with the target gas, and the mixture will be depleted (microsphere saturation stage);
2. the concentration wave propagates against the direction of gas flow (unload wave), while the adsorbent is already saturated with the target gas and it will be released at an increased rate at the wave front (microsphere regeneration mode).

Results. Based on preliminary studies, a mathematical model of non-stationary gas mixture flow through a porous medium of microspheres with a dispersed distribution of physical and geometric parameters has been developed. The model is single-temperature and single-velocity, and the layer resistance is described by the Forchheimer filtration law. The dependence of the viscosity coefficient and the permeability coefficient of the microsphere shell on temperature is taken into account, and the Wilke formula is used to calculate the viscosity of the mixture.

It is shown that the system of quasi-linear differential equations describing the model is of a hyperbolic type. It is shown that in the case of a developed flow it always has different actual characteristic directions.

Dimensionless criteria responsible for the flow of a gas mixture through a stationary layer of microspheres under conditions of selective gas permeability are obtained and described. Three structural parameters determining the geometry of the backfill were obtained, the existence of four parameters depending only on the physical characteristics of the media was shown, and 11 dimensionless complexes characterizing the gas flow were obtained.

An analytical solution was obtained for the stationary one-dimensional problem of filtration of a binary gas mixture through a layer of microspheres in the general case and in the case of frozen viscosity.

A numerical solution was obtained for two non-stationary problems of air-helium mixture flow through an adsorber filled with silica microspheres, taking into account the selective permeability of helium into the microspheres.

Conclusions. The obtained modeling results show that the process of helium mixture outflow from the adsorber occurs with a constant increase in the helium concentration in the mixture from the value that was established in the adsorber at the beginning of the pumping process. The presented experiment shows that the effect of increasing concentration is observed, however, it is necessary to conduct further parametric research of the cyclic process of filling and pumping out the adsorber to determine possible optimal target values of the mixture separation process in a non-stationary mode.