chemicallytechFine Chemical TechnologiesТонкие химические технологии2410-65932686-7575MIREA – Russian Technological University (RTU MIREA).10.32362/2410-6593-2023-18-5-482-497chemicallytech-2001Research ArticleMATHEMATICAL METHODS AND INFORMATION SYSTEMS IN CHEMICAL TECHNOLOGYМАТЕМАТИЧЕСКИЕ МЕТОДЫ И ИНФОРМАЦИОННЫЕ СИСТЕМЫ В ХИМИЧЕСКОЙ ТЕХНОЛОГИИPrinciples of creating a digital twin prototype for the process of alkylation of benzene with propylene based on a neural networkПринципы создания прототипа цифрового двойника процесса алкилирования бензола пропиленом на основе нейронной сетиhttps://orcid.org/0000-0002-5614-3743КичатовК. Г.KichatovK. G.

Кичатов Константин Геннадьевич - кандидат химических наук, доцент, кафедра нефтехимии и химической технологии, Scopus Author ID 54917537800.

450064, Республика Башкортостан, Уфа, ул. Космонавтов, д. 1

Konstantin G. Kichatov - Cand. Sci. (Chem.), Associate Professor, Department of Petrochemistry and Chemical Technology. Scopus Author ID 54917537800.

1, Kosmonavtov ul., Ufa, 450064

kichatov_k@mail.ruhttps://orcid.org/0000-0003-0859-3595ПросочкинаТ. Р.ProsochkinaT. R.

Просочкина Татьяна Рудольфовна - доктор химических наук, профессор, заведующий кафедрой нефтехимии и химической технологии. Scopus Author ID 6508101276.

450064, Республика Башкортостан, Уфа, ул. Космонавтов, д. 1

Tatyana R. Prosochkina - Dr. Sci. (Chem.), Professor, Head of the Department of Petrochemistry and Chemical Technology. Scopus Author ID 6508101276

1, Kosmonavtov ul., Ufa, 450064

agidel@ufanet.ruhttps://orcid.org/0009-0006-8254-1733ВоробьеваИ. С.VorobyovaI. S.

Воробьева Ирина Сергеевна - магистрант, кафедра нефтехимии и химической технологии.

450064, Республика Башкортостан, Уфа, ул. Космонавтов, д. 1

Irina S. Vorobyova - Master Student, Department of Petrochemistry and Chemical Technology.

1, Kosmonavtov ul., Ufa, 450064

isvorobyeva@mail.ruТехнологический факультет, Уфимский государственный нефтяной технический университетРоссияTechnological Faculty, Ufa State Petroleum Technological UniversityRussian Federation202327112023185482497Copyright © Kichatov K.G., Prosochkina T.R., Vorobyova I.S., 20232023Кичатов К.Г., Просочкина Т.Р., Воробьева И.С.Kichatov K.G., Prosochkina T.R., Vorobyova I.S.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.finechem-mirea.ru/jour/article/view/2001Objectives

Objectives. To identify the principles of creating digital twins of an operating technological unit along the example of the process of liquid-phase alkylation of benzene with propylene, and to establish the sequence of stages of formation of a digital twin, which can be applied to optimize oil and gas chemical production.

Methods

Methods. The chemical and technological system consisting of reactor, mixer, heat exchangers, separator, rectification columns, and pump is considered as a complex high-level system. Data was acquired in order to describe the functioning of the isopropylbenzene production unit. The main parameters of the process were calculated by simulation modeling using UniSim® Design software. A neural network model was developed and trained. The influence of various factors of the reaction process of alkylation, separation of reaction products, and evaluation of economic factors providing market interest of the industrial process was also considered. The adequacy of calculations was determined by statistics methods. A microcontroller prototype of the process was created.

Results

Results. A predictive neural network model and its creation algorithm for the process of benzene alkylation was developed. This model can be loaded into a microcontroller to allow for real-time determination of the economic efficiency of plant operation and automated optimization depending on the following factors: composition of incoming raw materials; the technological mode of the plant; the temperature mode of the process; and the pressure in the reactor.

Conclusions

Conclusions. The model of a complex chemicotechnological system of cumene production, created and calibrated on the basis of long-term industrial data and the results of calculations of the output parameters, enables the parameters of the technological process of alkylation to be calculated (yield of reaction products, energy costs, conditional profit at the output of finished products). During the development of a hardware-software prototype, adapted to the operation of the real plant, the principles and stages of creating a digital twin of the operating systems of chemical technology industries were identified and formulated.

Цели

Цели. Выявление принципов создания цифровых двойников реально действующей технологической установки на примере процесса жидкофазного алкилирования бензола пропиленом и установление последовательности этапов формирования цифрового двойника, которая может быть применима для оптимизации работы нефтегазохимического производства.

Методы

Методы. Рассмотрена в целом химико-технологическая система, состоящая из реактора, смесителя, теплообменников, сепаратора, ректификационных колонн и насоса, как система высокого уровня. Выполнен сбор данных, описывающих функционирование установки получения изопропилбензола алкилированием бензола пропиленом путем расчета основных параметров процесса с помощью имитационного моделирования с применением специализированного программного обеспечения UniSim® Design. Разработана и обучена нейросетевая модель, учитывающая влияние различных факторов реакционного процесса алкилирования, разделения продуктов реакции и оценки экономических факторов, обеспечивающих рыночную привлекательность рассматриваемого промышленного процесса. Определена адекватность результатов расчетов оптимальных параметров процесса методами математической статистики. Создан прототип цифрового двойника процесса, реализованной на микроконтроллере.

Результаты

Результаты. Создана прогностическая нейросетевая модель и алгоритм ее построения для процесса алкилирования бензола пропиленом, позволяющая при загрузке ее в микроконтроллер обеспечить в режиме реального времени определение экономической эффективности работы установки и автоматическую оптимизацию работы установки в зависимости от состава поступающего сырья технологического режима системы, температурного режима проведения процесса и давления в реакторе.

Выводы

Выводы. Созданная модель сложной химико-технологической системы производства кумола, откалиброванная на основании промышленных данных длительного пробега технологической установки и результатов расчетов выходных параметров процесса при помощи нейронной сети, реализованной на микроконтроллере, позволяет рассчитать параметры технологического процесса алкилирования (выход продуктов реакции, энергетические затраты, условную прибыль при выпуске готовой продукции). В процессе разработки прототипа программно-аппаратного комплекса управления установкой алкилирования бензола пропиленом на основе данных, адаптированных к работе реальной установки, были выявлены и сформулированы принципы и этапы создания цифрового двойника производственных систем отраслей химической технологии.

цифровой двойниккумолпромышленная установканейронные сетимашинное обучениеESP8266digital twincumeneindustrial plantneural networksmachine learningESP8266ReferencesPopov N.A. Business process optimization in the digitalization era of production. Strategic Decisions and Risk Management. 2019;10(1):28–35. https://doi.org/10.17747/2618-947X-2019-1-28-35Popov N.A. Business process optimization in the digitalization era of production. Strategic Decisions and Risk Management. 2019;10(1):28–35. https://doi.org/10.17747/2618-947X-2019-1-28-35Geng Z., Zhang Y., Li C., Han Y., Cui Y., Yu B. Energy optimization and prediction modeling of petrochemical industries: An improved convolutional neural network based on cross-feature. Energy. 2020;194(4)116851. https://doi.org/10.1016/j.energy.2019.116851Geng Z., Zhang Y., Li C., Han Y., Cui Y., Yu B. Energy optimization and prediction modeling of petrochemical industries: An improved convolutional neural network based on cross-feature. Energy. 2020;194(4)116851. https://doi.org/10.1016/j.energy.2019.116851Cozmiuc D., Petrisor I. Industrie 4.0 by Siemens. J. Cases Inf. Technol. 2018;20(2):30–48. https://doi.org/10.4018/JCIT.2018040103Cozmiuc D., Petrisor I. Industrie 4.0 by Siemens. J. Cases Inf. Technol. 2018;20(2):30–48. https://doi.org/10.4018/JCIT.2018040103Ardito L., Petruzzelli A.M., Panniello U., Garavelli A.C. Towards Industry 4.0: Mapping digital technologies for supply chain management-marketing integration. Bus. Process Manag. J. 2019;25(2):323–346. https://doi.org/10.1108/BPMJ-04-2017-0088Ardito L., Petruzzelli A.M., Panniello U., Garavelli A.C. Towards Industry 4.0: Mapping digital technologies for supply chain management-marketing integration. Bus. Process Manag. J. 2019;25(2):323–346. https://doi.org/10.1108/BPMJ-04-2017-0088Rindfleisch A., O’Hern M., Sachdev V. The Digital Revolution, 3D Printing, and Innovation as Data. J. Product Innov. Manag. 2017;34(5):681–690. https://doi.org/10.1111/jpim.12402Rindfleisch A., O’Hern M., Sachdev V. The Digital Revolution, 3D Printing, and Innovation as Data. J. Product Innov. Manag. 2017;34(5):681–690. https://doi.org/10.1111/jpim.12402D’Ippolito B., Messeni Petruzzelli A., Panniello U. Archetypes of incumbents’ strategic responses to digital innovation. J. Intellectual Capital. 2019;20(5):662–679. https://doi.org/10.1108/JIC-04-2019-0065D’Ippolito B., Messeni Petruzzelli A., Panniello U. Archetypes of incumbents’ strategic responses to digital innovation. J. Intellectual Capital. 2019;20(5):662–679. https://doi.org/10.1108/JIC-04-2019-0065Theorin A., Bengtsson K., Provost J., Lieder M., Johnsson C., Lundholm T., et al. An event-driven manufacturing information system architecture for Industry 4.0. Int. J. Prod. Res. 2017;55(5):1297–1311. https://doi.org/10.1080/00207543.2016.1201604Theorin A., Bengtsson K., Provost J., Lieder M., Johnsson C., Lundholm T., et al. An event-driven manufacturing information system architecture for Industry 4.0. Int. J. Prod. Res. 2017;55(5):1297–1311. https://doi.org/10.1080/00207543.2016.1201604Broekhuizen T.L.J., Broekhuis M., Gijsenberg M.J., Wieringa J.E. Introduction to the special issue – Digital business models: A multi-disciplinary and multi-stakeholder perspective. J. Bus. Res. 2021;122:847–852. https://doi.org/10.1016/j.jbusres.2020.04.014Broekhuizen T.L.J., Broekhuis M., Gijsenberg M.J., Wieringa J.E. Introduction to the special issue – Digital business models: A multi-disciplinary and multi-stakeholder perspective. J. Bus. Res. 2021;122:847–852. https://doi.org/10.1016/j.jbusres.2020.04.014Appio F.P., Frattini F., Petruzzelli A.M., Neirotti P. Digital Transformation and Innovation Management: A Synthesis of Existing Research and an Agenda for Future Studies. J. Product Innov. Manag. 2021;38(1):4–20. https://doi.org/10.1111/jpim.12562Appio F.P., Frattini F., Petruzzelli A.M., Neirotti P. Digital Transformation and Innovation Management: A Synthesis of Existing Research and an Agenda for Future Studies. J. Product Innov. Manag. 2021;38(1):4–20. https://doi.org/10.1111/jpim.12562Kholopov V.A., Antonov S.V., Kurnasov E.V., Kashirskaya E.N. Digital Twins in Manufacturing. Russ. Engin. Res. 2019;39(12):1014–1020. https://doi.org/10.3103/s1068798X19120104Kholopov V.A., Antonov S.V., Kurnasov E.V., Kashirskaya E.N. Digital Twins in Manufacturing. Russ. Engin. Res. 2019;39(12):1014–1020. https://doi.org/10.3103/s1068798X19120104Agrawal A., Gans J., Goldfarb A. Prediction Machines: The Simple Economics of Artificial Intelligence. Boston, Massachusetts: Harvard Business Review Press; 2018. 272 p.Agrawal A., Gans J., Goldfarb A. Prediction Machines: The Simple Economics of Artificial Intelligence. Boston, Massachusetts: Harvard Business Review Press; 2018. 272 p.Ceipek R., Hautz J., Petruzzelli A.M., De Massis A., Matzler K. A motivation and ability perspective on engagement in emerging digital technologies: The case of Internet of Things solutions. Long Range Plann. 2021;54(5):101991. https://doi.org/10.1016/j.lrp.2020.101991Ceipek R., Hautz J., Petruzzelli A.M., De Massis A., Matzler K. A motivation and ability perspective on engagement in emerging digital technologies: The case of Internet of Things solutions. Long Range Plann. 2021;54(5):101991. https://doi.org/10.1016/j.lrp.2020.101991Eggers J.P., Kaul A. Motivation and Ability? A Behavioral Perspective on the Pursuit of Radical Invention in Multi-Technology Incumbents. Acad. Manage. J. (AMJ). 2018;61(1):67–93. https://doi.org/10.5465/amj.2015.1123Eggers J.P., Kaul A. Motivation and Ability? A Behavioral Perspective on the Pursuit of Radical Invention in Multi-Technology Incumbents. Acad. Manage. J. (AMJ). 2018;61(1):67–93. https://doi.org/10.5465/amj.2015.1123Libert B., Beck M., Wind Y. (Jerry). 7 Questions to Ask before Your Next Digital Transformation. Harvard Bus. Rev. 2016;12(7):11–13. URL: https://hbr.org/2016/07/7questions-to-ask-before-your-next-digital-transformation. Accessed January 5, 2022.Libert B., Beck M., Wind Y. (Jerry). 7 Questions to Ask before Your Next Digital Transformation. Harvard Bus. Rev. 2016;12(7):11–13. URL: https://hbr.org/2016/07/7questions-to-ask-before-your-next-digital-transformation. Accessed January 5, 2022.Correani A., De Massis A., Frattini F., Petruzzelli A.M., Natalicchio A. Implementing a Digital Strategy: Learning from the Experience of Three Digital Transformation Projects. Calif. Manag. Rev. 2020;62(4):37–56. https://doi.org/10.1177/0008125620934864Correani A., De Massis A., Frattini F., Petruzzelli A.M., Natalicchio A. Implementing a Digital Strategy: Learning from the Experience of Three Digital Transformation Projects. Calif. Manag. Rev. 2020;62(4):37–56. https://doi.org/10.1177/0008125620934864Grieves M., Vickers J. Digital Twin: Mitigating Unpredictable, Undesirable Emergent Behavior in Complex Systems. In: Kahlen J., Flumerfelt S., Alves A. (Eds.). Transdisciplinary Perspectives on Complex Systems. Cham.: Springer; 2017. P. 85–113. https://doi.org/10.1007/978-3-31938756-7_4Grieves M., Vickers J. Digital Twin: Mitigating Unpredictable, Undesirable Emergent Behavior in Complex Systems. In: Kahlen J., Flumerfelt S., Alves A. (Eds.). Transdisciplinary Perspectives on Complex Systems. Cham.: Springer; 2017. P. 85–113. https://doi.org/10.1007/978-3-31938756-7_4Negri E., Fumagalli L., Macchi M. A Review of the Roles of Digital Twin in CPS-based Production Systems. Procedia Manuf. 2017;11:939–948. https://doi.org/10.1016/j.promfg.2017.07.198Negri E., Fumagalli L., Macchi M. A Review of the Roles of Digital Twin in CPS-based Production Systems. Procedia Manuf. 2017;11:939–948. https://doi.org/10.1016/j.promfg.2017.07.198Zhou X., Eibeck A., Lim M.Q., Krdzavac N.B., Kraft M. An agent composition framework for the J-Park Simulator – A knowledge graph for the process industry. Comput. Chem. Eng. 2019;130(2):106577. https://doi.org/10.1016/j.compchemeng.2019.106577Zhou X., Eibeck A., Lim M.Q., Krdzavac N.B., Kraft M. An agent composition framework for the J-Park Simulator – A knowledge graph for the process industry. Comput. Chem. Eng. 2019;130(2):106577. https://doi.org/10.1016/j.compchemeng.2019.106577Kockmann N. Digital methods and tools for chemical equipment and plants. React. Chem. Eng. 2019;4(9):1522–1529. https://doi.org/10.1039/C9RE00017HKockmann N. Digital methods and tools for chemical equipment and plants. React. Chem. Eng. 2019;4(9):1522–1529. https://doi.org/10.1039/C9RE00017HPerno M., Hvam L., Haug A. Implementation of digital twins in the process industry: A systematic literature review of enablers and barriers. Comput. Ind. 2022;134:103558. https://doi.org/10.1016/j.compind.2021.103558Perno M., Hvam L., Haug A. Implementation of digital twins in the process industry: A systematic literature review of enablers and barriers. Comput. Ind. 2022;134:103558. https://doi.org/10.1016/j.compind.2021.103558Hsu Y., Chiu J.M., Liu J.S. Digital Twins for Industry 4.0 and Beyond. In: 2019 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM). IEEE; 2019. P. 526–530. https://doi.org/10.1109/IEEM44572.2019.8978614Hsu Y., Chiu J.M., Liu J.S. Digital Twins for Industry 4.0 and Beyond. In: 2019 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM). IEEE; 2019. P. 526–530. https://doi.org/10.1109/IEEM44572.2019.8978614Lu Y., Liu C., Wang K.I.K., Huang H., Xu X. Digital Twin-driven smart manufacturing: Connotation, reference model, applications and research issues. Robot. Comput. Integr. Manuf. 2020;61:101837. https://doi.org/10.1016/j.rcim.2019.101837Lu Y., Liu C., Wang K.I.K., Huang H., Xu X. Digital Twin-driven smart manufacturing: Connotation, reference model, applications and research issues. Robot. Comput. Integr. Manuf. 2020;61:101837. https://doi.org/10.1016/j.rcim.2019.101837Durão L.F.C.S., Haag S., Anderl R., Schützer K., Zancul E. Digital Twin Requirements in the Context of Industry 4.0. In: Chiabert P., Boura A., Noë F., Ríos J. (Eds.). Product Lifecycle Management to Support Industry 4.0. PLM 2018. IFIP Advances in Information and Communication Technology. Cham.: Springer; 2018. V. 540. P. 204–214. https://doi.org/10.1007/978-3-030-01614-2_19Durão L.F.C.S., Haag S., Anderl R., Schützer K., Zancul E. Digital Twin Requirements in the Context of Industry 4.0. In: Chiabert P., Boura A., Noë F., Ríos J. (Eds.). Product Lifecycle Management to Support Industry 4.0. PLM 2018. IFIP Advances in Information and Communication Technology. Cham.: Springer; 2018. V. 540. P. 204–214. https://doi.org/10.1007/978-3-030-01614-2_19Kuehner K.J., Scheer R., Strassburger S. Digital Twin: Finding Common Ground – A Meta-Review. Procedia CIRP. 2021;104(11):1227–1232. https://doi.org/10.1016/j.procir.2021.11.206Kuehner K.J., Scheer R., Strassburger S. Digital Twin: Finding Common Ground – A Meta-Review. Procedia CIRP. 2021;104(11):1227–1232. https://doi.org/10.1016/j.procir.2021.11.206Adamenko D., Kunnen S., Pluhnau R., Loibl A., Nagarajah A. Review and comparison of the methods of designing the Digital Twin. Procedia CIRP. 2020;91:27–32. https://doi.org/10.1016/j.procir.2020.02.146Adamenko D., Kunnen S., Pluhnau R., Loibl A., Nagarajah A. Review and comparison of the methods of designing the Digital Twin. Procedia CIRP. 2020;91:27–32. https://doi.org/10.1016/j.procir.2020.02.146Zweber J.V., Kolonay R.M., Kobryn P., Tuegel E.J. Digital Thread and Twin for Systems Engineering: Requirements to Design. In: 55th AIAA Aerospace Sciences Meeting. Reston, Virginia: American Institute of Aeronautics and Astronautics; 2017. https://doi.org/10.2514/6.2017-0875Zweber J.V., Kolonay R.M., Kobryn P., Tuegel E.J. Digital Thread and Twin for Systems Engineering: Requirements to Design. In: 55th AIAA Aerospace Sciences Meeting. Reston, Virginia: American Institute of Aeronautics and Astronautics; 2017. https://doi.org/10.2514/6.2017-0875Schleich B., Anwer N., Mathieu L., Wartzack S. Shaping the digital twin for design and production engineering. CIRP Annals. 2017;66(1):141–144. https://doi.org/10.1016/j.cirp.2017.04.040Schleich B., Anwer N., Mathieu L., Wartzack S. Shaping the digital twin for design and production engineering. CIRP Annals. 2017;66(1):141–144. https://doi.org/10.1016/j.cirp.2017.04.040Zhou G., Zhang C., Li Z., Ding K., Wang C. Knowledge-driven digital twin manufacturing cell towards intelligent manufacturing. Int. J. Prod. Res. 2020;58(4):1034–1051. https://doi.org/10.1080/00207543.2019.1607978Zhou G., Zhang C., Li Z., Ding K., Wang C. Knowledge-driven digital twin manufacturing cell towards intelligent manufacturing. Int. J. Prod. Res. 2020;58(4):1034–1051. https://doi.org/10.1080/00207543.2019.1607978Melesse T.Y., Di Pasquale V., Riemma S. Digital Twin Models in Industrial Operations: A Systematic Literature Review. Procedia Manuf. 2020;42:267–272. https://doi.org/10.1016/j.promfg.2020.02.084Melesse T.Y., Di Pasquale V., Riemma S. Digital Twin Models in Industrial Operations: A Systematic Literature Review. Procedia Manuf. 2020;42:267–272. https://doi.org/10.1016/j.promfg.2020.02.084Aghayarzadeh M., Alizadeh R., Shafiei S. Simulation and Optimization of Styrene Monomer Production Using Neural Network. Iranian Journal of Chemical Engineering (IJChE). 2014;11(1-Serial Number 1, January):30–41. https://dorl.net/dor/20.1001.1.17355397.2014.11.1.3.2Aghayarzadeh M., Alizadeh R., Shafiei S. Simulation and Optimization of Styrene Monomer Production Using Neural Network. Iranian Journal of Chemical Engineering (IJChE). 2014;11(1-Serial Number 1, January):30–41. https://dorl.net/dor/20.1001.1.17355397.2014.11.1.3.2Alizadeh M., Sadrameli S.M. Modeling of Thermal Cracking Furnaces Via Exergy Analysis Using Hybrid Artificial Neural Network–Genetic Algorithm. J. Heat Transfer. 20161;138(4):042801. https://doi.org/10.1115/1.4032171Alizadeh M., Sadrameli S.M. Modeling of Thermal Cracking Furnaces Via Exergy Analysis Using Hybrid Artificial Neural Network–Genetic Algorithm. J. Heat Transfer. 20161;138(4):042801. https://doi.org/10.1115/1.4032171Xin S., Yingya W., Huajian P., Jinsen G., Xinguing L. Prediction of Coke Yield of FCC Unit Using Different Artificial Neural Network Models. China Petroleum Processing and Petrochemical Technology. 2016;18(3):102–109. URL: http://www.chinarefining.com/EN/Y2016/V18/I3/102Xin S., Yingya W., Huajian P., Jinsen G., Xinguing L. Prediction of Coke Yield of FCC Unit Using Different Artificial Neural Network Models. China Petroleum Processing and Petrochemical Technology. 2016;18(3):102–109. URL: http://www.chinarefining.com/EN/Y2016/V18/I3/102Meyers R.A. Handbook of Petrochemicals Production Processes. 1st ed. New York, Chicago, San Francisco, Athens, London, Madrid, Mexico City, Milan, New Delhi, Singapore, Sydney, Toronto: McGraw-Hill Education; 2005. 744 p.Meyers R.A. Handbook of Petrochemicals Production Processes. 1st ed. New York, Chicago, San Francisco, Athens, London, Madrid, Mexico City, Milan, New Delhi, Singapore, Sydney, Toronto: McGraw-Hill Education; 2005. 744 p.Ananieva E.A., Egorova E.V., Larin L.B. Current status and future tends of combined process producing acetone and phenol. 1. The market review and modern state phenol preparation processes. Fine Chem. Technol. 2007;2(2):27–43 (in Russ.).Ananieva E.A., Egorova E.V., Larin L.B. Current status and future tends of combined process producing acetone and phenol. 1. The market review and modern state phenol preparation processes. Fine Chem. Technol. 2007;2(2):27–43 (in Russ.).Larin L.B., Egorova E.V., Ananieva E.A. Current status and future tends of combined process for producing acetone and phenol. II. Intensification methods of cumene oxidation process. Fine Chem. Technol. 2008;3(3):53–60 (in Russ.).Larin L.B., Egorova E.V., Ananieva E.A. Current status and future tends of combined process for producing acetone and phenol. II. Intensification methods of cumene oxidation process. Fine Chem. Technol. 2008;3(3):53–60 (in Russ.).Pathak A.S., Agarwal S., Gera V., Kaistha N. Design and Control of a Vapor-Phase Conventional Process and Reactive Distillation Process for Cumene Production. Ind. Eng. Chem. Res. 2011;50(6):3312–3326. https://doi.org/10.1021/ie100779kPathak A.S., Agarwal S., Gera V., Kaistha N. Design and Control of a Vapor-Phase Conventional Process and Reactive Distillation Process for Cumene Production. Ind. Eng. Chem. Res. 2011;50(6):3312–3326. https://doi.org/10.1021/ie100779kZhai J., Liu Y., Li L., Zhu Y., Zhong W., Sun L. Applications of dividing wall column technology to industrialscale cumene production. Chem. Eng. Res. Des. 2015;102:138–149. https://doi.org/10.1016/j.cherd.2015.06.020Zhai J., Liu Y., Li L., Zhu Y., Zhong W., Sun L. Applications of dividing wall column technology to industrialscale cumene production. Chem. Eng. Res. Des. 2015;102:138–149. https://doi.org/10.1016/j.cherd.2015.06.020Chudinova A., Salischeva A., Ivashkina E., Moizes O., Gavrikov A. Application of Cumene Technology Mathematical Model. Procedia Chem. 2015;15:326–334. https://doi.org/10.1016/j.proche.2015.10.052Chudinova A., Salischeva A., Ivashkina E., Moizes O., Gavrikov A. Application of Cumene Technology Mathematical Model. Procedia Chem. 2015;15:326–334. https://doi.org/10.1016/j.proche.2015.10.052Zarutskii S.A., Kichatov K.G., Nikitina A.P., Prosochkina T.P., Samoilov N.A. Simulation of the Process for Cumene Production by Alkylation of Benzene in Equilibrium Reactor. Pet. Chem. 2018;58(8):681–686. https://doi.org/10.1134/S0965544118080212Zarutskii S.A., Kichatov K.G., Nikitina A.P., Prosochkina T.P., Samoilov N.A. Simulation of the Process for Cumene Production by Alkylation of Benzene in Equilibrium Reactor. Pet. Chem. 2018;58(8):681–686. https://doi.org/10.1134/S0965544118080212Mahmoudian F., Moghaddam A.H., Davachi S.M. Genetic‐based multi‐objective optimization of alkylation process by a hybrid model of statistical and artificial intelligence approaches. Can. J. Chem. Eng. 2022;100(1):90–102. https://doi.org/10.1002/cjce.24072Mahmoudian F., Moghaddam A.H., Davachi S.M. Genetic‐based multi‐objective optimization of alkylation process by a hybrid model of statistical and artificial intelligence approaches. Can. J. Chem. Eng. 2022;100(1):90–102. https://doi.org/10.1002/cjce.24072Sun X.Y., Xiang S.G. Product Distributions of Benzene Alkylation with Propylene Estimation Using Artificial Neural Network (ANN). Adv. Mat. Res. 2013;772:227–232. https://doi.org/10.4028/www.scientific.net/AMR.772.227Sun X.Y., Xiang S.G. Product Distributions of Benzene Alkylation with Propylene Estimation Using Artificial Neural Network (ANN). Adv. Mat. Res. 2013;772:227–232. https://doi.org/10.4028/www.scientific.net/AMR.772.227Tikhonenkov A.S., Peresypkin A.V., Toporskaya A.S., Suloeva E.S. Modeling of measuring systems based on programmable debugging circuits Arduino. In: 2017 XX IEEE International Conference on Soft Computing and Measurements (SCM). IEEE; 2017. P. 519–521. https://doi.org/10.1109/sCM.2017.7970636Tikhonenkov A.S., Peresypkin A.V., Toporskaya A.S., Suloeva E.S. Modeling of measuring systems based on programmable debugging circuits Arduino. In: 2017 XX IEEE International Conference on Soft Computing and Measurements (SCM). IEEE; 2017. P. 519–521. https://doi.org/10.1109/sCM.2017.7970636Vorobyova I.S., Kichatov K.G., Prosochkina T.R. Neural network for determining the optimal parameters of the alkylation of benzene with propylene. Computer program registration certificate RU 2020612986, 03.06.2020. Application № 2020612093 dated February 26, 2020 (in Russ.).Vorobyova I.S., Kichatov K.G., Prosochkina T.R. Neural network for determining the optimal parameters of the alkylation of benzene with propylene. Computer program registration certificate RU 2020612986, 03.06.2020. Application № 2020612093 dated February 26, 2020 (in Russ.).Prokhorov A., Lysachev M. Digital Twin. Analysis, Trends, Global Experience. 1st ed. Borovkov A. (Ed.). Moscow: AliancePrint; 2020. 401 р. (in Russ.). URL: https://datafinder.ru/files/new4/digital_twin_book.pdfProkhorov A., Lysachev M. Digital Twin. Analysis, Trends, Global Experience. 1st ed. Borovkov A. (Ed.). Moscow: AliancePrint; 2020. 401 р. (in Russ.). URL: https://datafinder.ru/files/new4/digital_twin_book.pdfMandolla C., Petruzzelli A.M., Percoco G., Urbinati A. Building a digital twin for additive manufacturing through the exploitation of blockchain: A case analysis of the aircraft industry. Comput. Ind. 2019;109:134–152. https://doi.org/10.1016/j.compind.2019.04.011Mandolla C., Petruzzelli A.M., Percoco G., Urbinati A. Building a digital twin for additive manufacturing through the exploitation of blockchain: A case analysis of the aircraft industry. Comput. Ind. 2019;109:134–152. https://doi.org/10.1016/j.compind.2019.04.011

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