Determination of unit parameters with selective membranes

About the authors:

Alexander Ya. Gilmanov, Cand. Sci. (Phys.-Math.), Senior Lecturer, Department of Modeling of Physical Processes and Systems, School of Natural Sciences, University of Tyumen, Tyumen, Russia; a.y.gilmanov@utmn.ru; ORCID: 0000-0002-7115-1629

Maria A. Demenchuk, Engineer Researcher, Department of Modeling of Physical Processes and Systems, Institute of Physics and Technology, University of Tyumen; m.a.demenchuk@utmn.ru

Alexander P. Shevelev, Cand. Sci. (Phys.-Math.), Associate Professor, Professor, Department of Modeling of Physical Processes and Systems, School of Natural Sciences, University of Tyumen, Tyumen, Russia; a.p.shevelev@utmn.ru; ORCID: 0000-0003-0017-4871

Abstract:

The energy complex of Russia is largely based on oil and gas potential. One of the ways to maintain the rate of hydrocarbon production is the use of gas methods. In this regard, inexpensive methods of obtaining pure gases are relevant. One of such approaches is the use of installations with selective membranes, the use of which is ineffective without preliminary modeling. There are currently no models that provide accurate quantitative results. Therefore, the main goal of this article is to develop a detailed mathematical model of the gas separation process in an installation with selective membranes and to determine the technological parameters with its help. The paper deals with the division of air in a membrane unit into pure gases: nitrogen and oxygen. The membrane consists of fibers, their sizes are comparable to the sizes of gas molecules, due to which the gas separation process takes place, since the transmission rate of the components is different. Filtering rate is a function of spatial coordinate and time. The basic system of the mechanics equations of multiphase systems is used for modeling. The developed mathematical model is based for the first time on the most detailed approach, in which the process is considered both inside and outside the membrane. To describe the processes outside the membrane, a system of equations for component fluxes is used, and inside the membrane, the conservation laws of mass and momentum are used. The model is reduced to a dimensionless form in order to get away from dimensional physical quantities and to carry out a criterion analysis to assess the contribution of parameters affecting the gas separation process. The data used for the evaluation correspond to a real membrane plant. By numerically solving the model equations, the distribution of nitrogen concentration inside and outside the membrane tubes is obtained. Analysis of the model in a dimensionless form shows that all factors make a comparable order of magnitude contribution to the final distribution of gas concentration.

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