Mathematical models of dynamics of pressure swing adsorption processes for the separation of synthesis gas (into hydrogen, carbon dioxide and carbon monoxide) and air (into oxygen, nitrogen and argon) have been developed. The models allow calculating the profiles of component concentrations and temperature of gas and solid phases, pressure and velocity of gas mixture along the height of adsorbent in relation to time. The models include the following equations: 1) processes of mass and heat transfer during the adsorption (desorption) of a sorptive (H2, CO2, COandO2, N2, Ar) by granulated zeolite adsorbents 5Aand13Х; 2) kinetics of compound diffusion transport of adsorbate and Langmuir-Freundlich isotherm (for the synthesis gas separation), kinetics of external diffusion and Dubinin-Radushkevich isotherm (for the air separation); 3) the Ergun equation for the calculation of pressure and velocity of gas mixture in adsorbent.The system of partial differential equations was solved by method of lines. The system of ordinary differential equations was solved by the fourth-order Runge-Kutta method with automatic step selection.To analyze the accuracy of mathematical models of the adsorption separation of synthesis-gas for recovery hydrogen, the relative error of the mismatch between the calculated values for the model and the experimental values of the concentration of the product (hydrogen, oxygen) in the 'steady state' (after 15-30 operating cycles of the PSA) was calculated. The maximum value of the relative error did not exceed 11.5%.Numerical studies were carried out in a wide range of changes in the time of the cycle "adsorption-desorption" and the pressure at the stage of adsorption to determine the effect of changes in temperature, composition and pressure of the initial gas mixture on the purity, recovery and temperature of production hydrogen and oxygen, as well as the relationship of the PSA unit capacity with the purity of the resulting product (hydrogen, oxygen). The problem of adaptive optimization of the process of adsorption separation of a gas mixture and obtaining hydrogen and oxygen with a maximum concentration was formulated and solved.The algorithmic and software of the automated adaptive control system was developed.

pressure swing adsorption, zeolite adsorbent, synthesis gas, air, mathematical model, numerical analysis, optimization, controlling

1. Ruthven D.M., Farooq S., Knaebel K.S. Pressure swing adsorption. New York, 1993. 376 p.

2. Akulinin Е.I., Ishin А.А., Skvortsov S.А., Dvoretskiy D.S., Dvoretsky S.I.Mathematical modeling of hydrogen production process by pressure swing adsorption method. Advanced Materials and Technologies. 2017. no. 2. pp. 38–49. doi: 10.17277/amt.2017.01.

3. Akulinin Е.I., Dvoretskiy D.S., Dvoretsky S.I.Dynamics of cyclic adsorption processes for the enrichment of air with oxygen: simulation and optimization. Vestnik Tekhnologicheskogo universiteta [Journal of Technology University] 2016. vol.19. no.  17. pp.108–114. (in Russian)

4. Ko D., Siriwardane R., Biegler L. Optimization of pressure swing adsorption and fractionated vacuum pressure swing adsorption processes for CO2 capture. Industrial & Engineering Chemistry Research. 2005. vol. 44 (21). pp. 8084–8094.

5. Baksh M.S.A., Ackley M.W. Pressure swing adsorption process for the production of hydrogen. Pat. 6340382 USA. 2002.

6. KirillinV.А., Sychev V.V., SheindlinА.Е. Tekhni-cheskaya termodinamika [Technical thermodynamics] Moscow, Publishing house MEI, 2008. 496 p. (in Russian).

7. SumyatskyY.I. [Promyshlennye adsorbtsionnye protsessy] Industrial adsorption processes. Moscow, KolosS, 2009. 183p.(in Russian).

8. Keltsev N.V. Osnovy adsorbtsionnoi tekhnologii [Basics of adsorption technology] Moscow: Chemistry, 1984. 592 p. (in Russian).

9. Shokroo E., Farsani D., Meymandi H., Yadoliahi N. Comparative study of zeolite 5A and zeolite 13X in air separation by pressure swing adsorption. Korean Journal of Chemical Engineering. 2016. vol. 33 (4), pp. 1391–1401.

10. Recleitis G., Reivindrane A., Regsdaile C. Optimization in engineering. Мoscow, World, 1986. 320 p. (in Russian).