jamtJournal of Advanced Materials and TechnologiesJournal of Advanced Materials and Technologies2782-21922782-2206ФГБОУ ВО «ТГТУ»10.17277/jamt-2025-10-04-351-363jamt-82Research ArticleМатериалы для энергетики и охраны окружающей среды, фотовольтаика следующего поколения и зеленые технологииMaterials for energy and environment, next-generation photovoltaics, and green technologiesМоделирование сорбционного равновесия CO2, CO, CH4, H2 с использованием уравнения Дубинина–Астахова на цеолитах NаX, CаA и активном углеModeling CO2, CO, CH4, and H2 sorption equilibrium on NaX and CaA zeolites and activated carbon using the Dubinin–Astakhov equationhttps://orcid.org/0000-0002-4352-810XДворецкийД. С.DvoretskyD. S.

Дворецкий Дмитрий Станиславович, доктор технических наук, профессор

ул. Советская, 106/5, пом. 2, Тамбов, 392000, Российская Федерация

Dmitry S. Dvoretsky, D. Sc. (Eng.), Professor

Bld. 2, 106/5, Sovetskaya St., Tambov, 392000, Russian Federation

dvoretsky@yahoo.comhttps://orcid.org/0000-0002-7571-3748ДворецкийС. И.DvoretskyS. I.

Дворецкий Станислав Иванович, доктор технических наук, профессор

ул. Советская, 106/5, пом. 2, Тамбов, 392000, Российская Федерация

Stanislav I. Dvoretsky, D. Sc. (Eng.), Professor

Bld. 2, 106/5, Sovetskaya St., Tambov, 392000, Russian Federation

sdvoretsky@mail.tstu.ruhttps://orcid.org/0000-0003-0848-4380АкулининЕ. И.AkulininE. I.

Акулинин Евгений Игоревич, доктор технических наук, доцент

ул. Советская, 106/5, пом. 2, Тамбов, 392000, Российская Федерация

Evgeniy I. Akulinin, D. Sc. (Eng.), Associate Professor

Bld. 2, 106/5, Sovetskaya St., Tambov, 392000, Russian Federation

akulinin2006@yandex.ruhttps://orcid.org/0000-0003-1766-3786ТуголуковЕ. Н.TugolukovE. N.

Туголуков Евгений Николаевич, доктор технических наук, профессор

ул. Советская, 106/5, пом. 2, Тамбов, 392000, Российская Федерация

Evgeny N. Tugolukov, D. Sc. (Eng.), Professor

Bld. 2, 106/5, Sovetskaya St., Tambov, 392000, Russian Federation

tugolukov.en@mail.ruВарниковГ. И.VarnikovG. I.

Варников Глеб Игоревич, студент

ул. Советская, 106/5, пом. 2, Тамбов, 392000, Российская Федерация

Gleb I. Varnikov, Student

Bld. 2, 106/5, Sovetskaya St., Tambov, 392000, Russian Federation

glebvarnikov@gmail.comУсачевВ. Б.UsachevV. B.

Усачев Владимир Борисович, директор

ул. Железнодорожная, 5, Протвино, 142281, Российская Федерация

Vladimir B. Usachev, Head

5, Zheleznodorozhnaya St., Protvino, 142281, Russian Federation

npo@sialuch.ruТамбовский государственный технический университетРоссияTambov State Technical UniversityRussian FederationАО НИИ НПО «Луч» Протвинский филиалРоссияJSC Research Institute of Scientific Production Association Luch, Protvino branchRussian Federation202524022026104351363Copyright © Дворецкий Д.С., Дворецкий С.И., Акулинин Е.И., Туголуков Е.Н., Варников Г.И., Усачев В.Б., 20262026Дворецкий Д.С., Дворецкий С.И., Акулинин Е.И., Туголуков Е.Н., Варников Г.И., Усачев В.Б.Dvoretsky D.S., Dvoretsky S.I., Akulinin E.I., Tugolukov E.N., Varnikov G.I., Usachev V.B.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://jamt.elpub.ru/jour/article/view/82

По результатам экспериментальных исследований получены адсорбционные изотермы для газов: диоксида углерода, оксида углерода, метана и водорода на промышленных адсорбентах. Предложен подход для расчета коэффициентов уравнения Дубинина–Астахова на основе экспериментальных изотерм, позволяющий определять величину равновесной адсорбции компонентов водородсодержащей газовой смеси с высокой точностью. Подход включает: расчет значений предельного адсорбционного объема данного адсорбента и характеристической энергии адсорбции стандартного газа (азота) для заданного адсорбента с использованием экспериментальных изотерм адсорбции азота, полученных при температуре 77,3 K в диапазоне относительных давлений адсорбции от 0 до 1 на каждом из исследуемых адсорбентов, а именно: NaX, CaA, СКТ-4; нахождение расчетных значений коэффициентов аффинности, показателя степени, термического коэффициента предельной адсорбции уравнения Дубинина–Астахова (для температур и давлений, при которых получены экспериментальные изотермы сорбции исследуемых газов), обеспечивающих минимальное значение невязки между расчетными и экспериментальными изотермами; усреднение найденных значений коэффициентов аффинности и показателя степени. Эффективность предложенного подхода продемонстрирована на примере расчета параметров уравнения Дубинина–Астахова для CO2, CO, CH4 при использовании цеолитов NaX, CaA, активного угля СКТ-4. Среднеквадратическое отклонение между расчётными и экспериментальными данными не превышает 6,6 % в широком диапазоне давлений (до 3,0 МПа) и температур (293…353 K) для изученных сорбентов (цеолиты NaX, CaA, активный уголь СКТ-4). 

In light of the findings from experimental studies, adsorption isotherms were obtained for carbon dioxide, carbon monoxide, methane, and hydrogen gases on industrial adsorbents. A methodology has been put forth for calculating the coefficients of the Dubinin–Astakhov equation based on experimental isotherms. This approach enables the determination of the equilibrium adsorption of components of a hydrogen-containing gas mixture with a high degree of accuracy. The approach includes: calculating the limiting adsorption volume of a given adsorbent and the characteristic adsorption energy of a standard gas (nitrogen) for the specified adsorbent using experimental nitrogen adsorption isotherms obtained at a temperature of 77.3 K in the relative pressure range from 0 to 1 for each of the studied adsorbents, namely: NaX, CaA, SKT-4; determining the calculated values of the affinity coefficients, the exponent, and the thermal coefficient of limiting adsorption in the Dubinin–Astakhov equation (for the temperatures and pressures at which the experimental sorption isotherms of the studied gases were obtained), which minimize the residual between the calculated and experimental isotherms; averaging the obtained values of the affinity coefficients and the exponent. The efficacy of the proposed approach is substantiated by the calculation of the parameters of the Dubinin–Astakhov equation for CO2, CO, and CH4 using NaX and CaA zeolites and SKT-4 activated carbon. The root mean square deviation between the calculated and experimental data does not exceed 6.6 % over a wide range of pressures (up to 3.0 MPa) and temperatures (293–353 K) for the studied sorbents (zeolites NaX, CaA, and activated carbon SKT-4). 

водородсодержащая газовая смесьадсорбентадсорбционное разделениеадсорбционное равновесиеизотерма адсорбцииуравнение Дубинина–Астаховацеолитактивный угольсреднеквадратическая ошибкамаксимальное отклонениеhydrogen-containing gas mixtureadsorbentadsorption separationadsorption equilibriumadsorption isothermDubinin–Astakhov equationzeoliteactivated carbonroot mean square errormaximum deviationReferencesKel'tsev NV. Fundamentals of adsorption technology. Moscow: Khimiya; 1976. 512 p. (In Russ.)Kel'tsev NV. Fundamentals of adsorption technology. Moscow: Khimiya; 1976. 512 p. (In Russ.)Ruthven DM, Farooq S, Knaebel KS. Pressure swing adsorption. New York: VCH Publishers; 1993. 189 p.Ruthven DM, Farooq S, Knaebel KS. Pressure swing adsorption. New York: VCH Publishers; 1993. 189 p.Shumyatsky YI. Industrial Adsorption Processes. Moscow: KolosS; 2009. 183 p. (In Russ.)Shumyatsky YI. Industrial Adsorption Processes. Moscow: KolosS; 2009. 183 p. (In Russ.)Dvoretskii SI, Dvoretskii DS, Akulinin EI, Meronyuk KI, et al. Modern approaches to development of flexible pressure swing adsorption units for separation of hydrogen-containing gaseous mixtures. Theoretical Foundations of Chemical Engineering. 2024;58(6):1957-1979. DOI:10.1134/S0040579525601013Dvoretskii SI, Dvoretskii DS, Akulinin EI, Meronyuk KI, et al. Modern approaches to development of flexible pressure swing adsorption units for separation of hydrogen-containing gaseous mixtures. Theoretical Foundations of Chemical Engineering. 2024;58(6):1957-1979. DOI:10.1134/S0040579525601013Akulinin EI, Ishin AN, Skvortsov SA, Dvoretskiy DS, Dvoretskiy SI. Numerical study of the dynamics of the adsorption separation of a gas mixture and hydrogen concentration. Khimicheskaya tekhnologiya = Theoretical Foundations of Chemical Engineering. 2018;19(8):368-375. (In Russ.)Akulinin EI, Ishin AN, Skvortsov SA, Dvoretskiy DS, Dvoretskiy SI. Numerical study of the dynamics of the adsorption separation of a gas mixture and hydrogen concentration. Khimicheskaya tekhnologiya = Theoretical Foundations of Chemical Engineering. 2018;19(8):368-375. (In Russ.)Akulinin E, Golubyatnikov O, Dvoretsky D, Dvoretsky S. Methodology for creating and studying units for adsorption separation and purification of gas mixtures. Journal of Advanced Materials and Technologies. 2021;6(3):179-203. DOI:10.17277/jamt.2021.03.pp.179-203Akulinin E, Golubyatnikov O, Dvoretsky D, Dvoretsky S. Methodology for creating and studying units for adsorption separation and purification of gas mixtures. Journal of Advanced Materials and Technologies. 2021;6(3):179-203. DOI:10.17277/jamt.2021.03.pp.179-203Akulinin EI, Golubyatnikov OO, Dvoretsky DS, Dvoretsky SI. A numerical study of heat and mass exchange processes in swing adsorption device for oxygenenriched air. Advanced Materials & Technologies. 2019; (3(15)):056-065. DOI:10.17277/amt.2019.03.pp.056-065Akulinin EI, Golubyatnikov OO, Dvoretsky DS, Dvoretsky SI. A numerical study of heat and mass exchange processes in swing adsorption device for oxygenenriched air. Advanced Materials & Technologies. 2019; (3(15)):056-065. DOI:10.17277/amt.2019.03.pp.056-065Delgado JA, Agueda VI, Uguina MA, Sotelo JL, Brea P. Hydrogen recovery from off-gases with nitrogenrich impurity by pressure swing adsorption using CaX and 5A zeolites. Adsorption. 2015;21(1-2):107-123. DOI:10.1007/s10450-015-9654-zDelgado JA, Agueda VI, Uguina MA, Sotelo JL, Brea P. Hydrogen recovery from off-gases with nitrogenrich impurity by pressure swing adsorption using CaX and 5A zeolites. Adsorption. 2015;21(1-2):107-123. DOI:10.1007/s10450-015-9654-zOreggioni GD, Brandani S, Luberti M, Baykan Y, et al. CO2 capture from syngas by an adsorption process at a biomass gasification CHP plant: Its comparison with amine-based CO2 capture. International Journal of Greenhouse Gas Control. 2015;35:71-81. DOI:10.1016/j.ijggc.2015.01.008Oreggioni GD, Brandani S, Luberti M, Baykan Y, et al. CO2 capture from syngas by an adsorption process at a biomass gasification CHP plant: Its comparison with amine-based CO2 capture. International Journal of Greenhouse Gas Control. 2015;35:71-81. DOI:10.1016/j.ijggc.2015.01.008Shi W, Yang H, Shen Y, Fu Q et al. Two-stage PSA/VSA to produce H2 with CO2 capture via steam methane reforming (SMR). International Journal of Hydrogen Energy. 2018;43(41):19057-19074. DOI:10.1016/j.ijhydene.2018.08.077Shi W, Yang H, Shen Y, Fu Q et al. Two-stage PSA/VSA to produce H2 with CO2 capture via steam methane reforming (SMR). International Journal of Hydrogen Energy. 2018;43(41):19057-19074. DOI:10.1016/j.ijhydene.2018.08.077Dubinin MM. Adsorption and Porosity. Moscow: VAKhZ; 1972. 124 p. (In Russ.)Dubinin MM. Adsorption and Porosity. Moscow: VAKhZ; 1972. 124 p. (In Russ.)Dubinin MM. Fundamentals of the theory of adsorption in micropores of carbon adsorbents: characteristics of their adsorption properties and microporous structures. Carbon. 1989;27(3):457-467. DOI:10.1016/0008-6223(89)90078-XDubinin MM. Fundamentals of the theory of adsorption in micropores of carbon adsorbents: characteristics of their adsorption properties and microporous structures. Carbon. 1989;27(3):457-467. DOI:10.1016/0008-6223(89)90078-XQuayle OR. The parachors of organic compounds. An interpretation and catalogue. Chemical Reviews. 1953;53(3):439-589. DOI:10.1021/cr60166a003Quayle OR. The parachors of organic compounds. An interpretation and catalogue. Chemical Reviews. 1953;53(3):439-589. DOI:10.1021/cr60166a003McGowan JC, Mellors A. Molecular volumes and the parachor. In: McGowan JC, Phillips GT. (eds.), Molecular volumes in chemistry and biology: Applications including partitioning and toxicity. Halsted Press; 1986. p. 1-20.McGowan JC, Mellors A. Molecular volumes and the parachor. In: McGowan JC, Phillips GT. (eds.), Molecular volumes in chemistry and biology: Applications including partitioning and toxicity. Halsted Press; 1986. p. 1-20.Park J, Beum H, Han S, Cho D, Cho K. Pressure swing adsorption process and pressure swing adsorption apparatus. United States patent 10,933,366. 02 March 2021.Park J, Beum H, Han S, Cho D, Cho K. Pressure swing adsorption process and pressure swing adsorption apparatus. United States patent 10,933,366. 02 March 2021.Park Y, Kang JH, Moon DK, Jo YS, Lee CH. Parallel and series multi-bed pressure swing adsorption processes for H2 recovery from a lean hydrogen mixture. Chemical Engineering Journal. 2021;408:127299. DOI:10.1016/j.cej.2020.127299Park Y, Kang JH, Moon DK, Jo YS, Lee CH. Parallel and series multi-bed pressure swing adsorption processes for H2 recovery from a lean hydrogen mixture. Chemical Engineering Journal. 2021;408:127299. DOI:10.1016/j.cej.2020.127299Zhang N, Bénard P, Chahine R, Yang T, Xiao J. Optimization of pressure swing adsorption for hydrogen purification based on Box-Behnken design method. International Journal of Hydrogen Energy. 2021;46(7): 5403-5417. DOI:10.1016/j.ijhydene.2020.11.045Zhang N, Bénard P, Chahine R, Yang T, Xiao J. Optimization of pressure swing adsorption for hydrogen purification based on Box-Behnken design method. International Journal of Hydrogen Energy. 2021;46(7): 5403-5417. DOI:10.1016/j.ijhydene.2020.11.045Brea P, Delgado JA, Águeda VI, Gutiérrez P, Uguina MA. Multicomponent adsorption of H2, CH4, CO and CO2 in zeolites NaX, CaX and MgX. Evaluation of performance in PSA cycles for hydrogen purification. Microporous and Mesoporous Materials. 2019;286:187-198. DOI:10.1016/j.micromeso.2019.05.021Brea P, Delgado JA, Águeda VI, Gutiérrez P, Uguina MA. Multicomponent adsorption of H2, CH4, CO and CO2 in zeolites NaX, CaX and MgX. Evaluation of performance in PSA cycles for hydrogen purification. Microporous and Mesoporous Materials. 2019;286:187-198. DOI:10.1016/j.micromeso.2019.05.021Luberti M, Brown A, Balsamo M, Capocelli M. Numerical analysis of VPSA technology retrofitted to steam reforming hydrogen plants to capture CO2 and produce blue H2. Energies. 2022;15(3). DOI:10.3390/en15031091Luberti M, Brown A, Balsamo M, Capocelli M. Numerical analysis of VPSA technology retrofitted to steam reforming hydrogen plants to capture CO2 and produce blue H2. Energies. 2022;15(3). DOI:10.3390/en15031091Yang SI, Park JY, Choi DK, Kim SH. Effects of the residence time in four-bed pressure swing adsorption process. Separation Science and Technology. 2009;44(5): 1023-1044. DOI:10.1080/01496390902729122Yang SI, Park JY, Choi DK, Kim SH. Effects of the residence time in four-bed pressure swing adsorption process. Separation Science and Technology. 2009;44(5): 1023-1044. DOI:10.1080/01496390902729122Abdeljaoued A, Relvas F, Mendes A, Chahbani MH. Simulation and experimental results of a PSA process for production of hydrogen used in fuel cells. Journal of Environmental Chemical Engineering. 2018;6(1):338-355. DOI:10.1016/j.jece.2017.12.010Abdeljaoued A, Relvas F, Mendes A, Chahbani MH. Simulation and experimental results of a PSA process for production of hydrogen used in fuel cells. Journal of Environmental Chemical Engineering. 2018;6(1):338-355. DOI:10.1016/j.jece.2017.12.010Li H, Liao Z, Sun J, Jiang, B et al. Modelling and simulation of two-bed PSA process for separating H2 from methane steam reforming. Chinese Journal of Chemical Engineering. 2019;27(8):1870-1878. DOI:10.1016/j.cjche.2018.11.022Li H, Liao Z, Sun J, Jiang, B et al. Modelling and simulation of two-bed PSA process for separating H2 from methane steam reforming. Chinese Journal of Chemical Engineering. 2019;27(8):1870-1878. DOI:10.1016/j.cjche.2018.11.022KNT group production of sorbents and catalysts. [Website]. Available from: https://www.kntgroup.ru/ru/main [Accessed 03 February 2025].KNT group production of sorbents and catalysts. [Website]. Available from: https://www.kntgroup.ru/ru/main [Accessed 03 February 2025].JSC "Experimental Chemical Plant". [Website]. URL: https://лидеркарбон.рф/ [Accessed 03 February 2025].JSC "Experimental Chemical Plant". [Website]. URL: https://лидеркарбон.рф/ [Accessed 03 February 2025].D'yakonov VP, Kruglov VA. Matlab extension packs: A special reference book. Saint Petersburg: Piter; 2001. 475 p. (In Russ.)D'yakonov VP, Kruglov VA. Matlab extension packs: A special reference book. Saint Petersburg: Piter; 2001. 475 p. (In Russ.)

The authors declare that there are no conflicts of interest present.