Helium enrichment of natural gas in non-steady diffusion-sorption processes in the bed of glass microspheres

A numerical study of the dynamics of filling a column containing a packed bed of hollow glass microspheres with a methane-helium mixture is carried out for cases of stepwise and smooth pressure rise at the column entrance. The quartz glass shells of microspheres are permeable to helium and impermeable to methane. Computations are performed in one-dimensional isothermal approximation for different values of the microsphere radius, shell thickness and temperature. The equations governing the gas mixture dynamics and helium sorption by microspheres are solved numerically. The relation between the rate of column filling with a gas and the rate of helium sorption by individual microspheres defines the regime of the process. In the case of the slow movement of a pressure wave (low rate of column filling), an equilibrium (wave) regime takes place. In the case of rapid column filling when the characteristic time of column filling with the mixture and the time of microsphere saturation with helium are considerably different, the operation regime of the column appears to be non-equilibrium. The results obtained are supposed to be used for the development of non-cryogenic methods of natural gas enrichment with helium and separation of mixtures.