Abstract
A mathematical model is developed and designed for the cumene reactor in cumene production process in Hindustan Organic Chemicals Limited (HOCL), Kochi with improved operating conditions. High purity cumene is produced by the alkylation of benzene with propylene in this catalytic condensation process where solid phosphoric acid (SPA) is used as the catalyst. The mathematical model has been derived from mass and energy balance equations considering the reactor as fixed packed bed reactor and two different numerical methods are presented here to solve the modelling equations. The explicit finite difference method (FDM) involves the approximation of derivatives into finite differences, and in the other one, orthogonal collocation (OC), Ordinary Diffeential Equations (ODEs) are formed at the collocation points and are solved using Runge–Kutta fourth order numerical scheme. Here the analysis shows that the predictions from the model are in good alignment with the plant data. The combined feed has the optimum value of 1:2:8 for propylene, propane and benzene and the profiles of temperature and concentration can be obtained along the reactor. The model has been implemented in COMSOL Multiphysics as a packed bed reactor using the same parameters collected from the plant of study. It has been found that the reaction occurs at a satisfactory level even with a low temperature than the reactor temperature at the plant by changing the catalytic particle size. The reaction performance is also analysed for the physical properties like porosity and catalyst size.
Acknowledgement
The writers place their gratitude to the HOCL, Kochi, Kerala for providing their timely support for the completion of the work. Authors express their sincere thanks to Mr. K. K. Kunjumon, Chief General Manager (Production & Engineering), Mr. T. P. Sachidandan, General Manager (Production) and their team, HOCL, for their valuable advice and suggestion. Authors would like to thank the anonymous referees for several suggestions for the improvement of this paper.
-
Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
-
Research funding: None declared.
-
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
Afshar Ebrahimi, A., H. A. Ebrahim, and E. Jamshidi. 2008. “Solving Partial Differential Equations of Gas-Solid Reactions by Orthogonal Collocation.” Computers & Chemical Engineering 32 (8): 1746–59, https://doi.org/10.1016/j.compchemeng.2007.08.017.Search in Google Scholar
Amodio, P., and G. Settanni. 2015. “Variable-Step Finite Difference Schemes for the Solution of Sturm-Liouville Problems.” Communications in Nonlinear Science and Numerical Simulation 20 (3): 641–9, https://doi.org/10.1016/j.cnsns.2014.05.032.Search in Google Scholar
Arora, S., S. S. Dhaliwal, and V. K. Kukreja. 2006. “Simulation of Washing of Packed Bed of Porous Particles by Orthogonal Collocation on Finite Elements.” Computers & Chemical Engineering 30 (6–7): 1054–60, https://doi.org/10.1016/j.compchemeng.2006.02.002.Search in Google Scholar
Arora, S., and I. Kaur. 2015. “Numerical Solution of Heat Conduction Problems Using Orthogonal Collocation on Finite Elements.” Journal of the Nigerian Mathematical Society 34 (3): 286–302, https://doi.org/10.1016/j.jnnms.2015.10.001.Search in Google Scholar
Assous, F., P. Degond, E. Heintze, A. Raviart, and J. Segre. 1993. “On a Finite-Element Method for Solving the Three-Dimensional Maxwell Equations.” Journal of Computational Physics 109 (2): 222–37, doi:https://doi.org/10.1006/jcph.1993.1214.Search in Google Scholar
Babolian, E., S. Bazm, and P. Lima. 2011. “Numerical Solution of Nonlinear Two-Dimensional Integral Equations Using Rationalized Haar Functions.” Communications in Nonlinear Science and Numerical Simulation 16 (3): 1164–75, https://doi.org/10.1016/j.cnsns.2010.05.029.Search in Google Scholar
Bayliss, A., and E. Turkel. 1980. “Radiation Boundary Conditions for Wave‐Like Equations.” Communications on Pure and Applied Mathematics 33 (6): 707–25, https://doi.org/10.1002/cpa.3160330603.Search in Google Scholar
Berger, R. J., E. H. Stitt, G. B. Marin, F. Kapteijn, and J. A. Moulijn. 2001. “Chemical Reaction Kinetics in Practice.” Cattech 5 (1): 30–60.Search in Google Scholar
Bokade, V. V., and U. K. Kharul. 2009. “Selective Synthesis of Cumene by Isopropylation of Benzene Using Catalytic Membrane Reactor.” Chemical Engineering Journal 147 (2–3): 97–101, https://doi.org/10.1016/j.cej.2008.06.035.Search in Google Scholar
Botte, G. G., J. A. Ritter, and R. E. White. 2000. “Comparison of Finite Difference and Control Volume Methods for Solving Differential Equations.” Computers & Chemical Engineering 24 (12): 2633–54, https://doi.org/10.1016/S0098-1354(00)00619-0.Search in Google Scholar
Carey, G. F., and B. A. Finlayson. 1975. “Orthogonal Collocation on Finite Elements.” Chemical Engineering Science 30 (5–6): 587–96.10.1016/0009-2509(75)80031-5Search in Google Scholar
Chudinova, A., A. Salischeva, E. Ivashkina, O. Moizes, and A. Gavrikov. 2015. “Application of Cumene Technology Mathematical Model.” Procedia Chemistry 15: 326–34, https://doi.org/10.1016/j.proche.2015.10.052.Search in Google Scholar
Coulson, J. M. 1966. “Chemical Reactors.” Nature 212 (5059): 236–7, https://doi.org/10.1038/212236b0.Search in Google Scholar
Dawson, C. N., Q. Du, and T. F. Dupont. 1991. “A Finite Difference Domain Decomposition Algorithm for Numerical Solution of the Heat Equation.” Mathematics of Computation 57 (195): 63–71.10.1090/S0025-5718-1991-1079011-4Search in Google Scholar
Feng, L., F. Liu, and I. Turner. 2019. “Finite Difference/Finite Element Method for a Novel 2D Multi-Term Time-Fractional Mixed Sub-diffusion and Diffusion-Wave Equation on Convex Domains.” Communications in Nonlinear Science and Numerical Simulation 70: 354–71, https://doi.org/10.1016/j.cnsns.2018.10.016.Search in Google Scholar
Flegiel, F., S. Sharma, and G. P. Rangaiah. 2015. “Development and Multiobjective Optimization of Improved Cumene Production Processes.” Materials and Manufacturing Processes 30 (4): 444–57, https://doi.org/10.1080/10426914.2014.967355.Search in Google Scholar
Gardinii, L., A. Servida, M. Morbidelli, and S. Carra. 1986. “A Unified Collocation Algorithm for Packed-Bed Chemical Reactor Simulation.” Chemical Engineering Communications 43 (1–3): 85–105, https://doi.org/10.1080/00986448608911324.Search in Google Scholar
Gera, V., M. Panahi, S. Skogestad, and N. Kaistha. 2013. “Economic Plantwide Control of the Cumene Process.” Industrial & Engineering Chemistry Research 52 (2): 830–46, https://doi.org/10.1021/ie301386h.Search in Google Scholar
Ghodoosi, F., M. R. Khosravi-Nikou, and A. Shariati. 2017. “Mathematical Modeling of Reverse Water-Gas Shift Reaction in a Fixed-Bed reactor.” Chemical Engineering & Technology 40 (3): 598–607, https://doi.org/10.1002/ceat.201600220.Search in Google Scholar
Han, M., X. Li, and S. Lin. 2001. “Intrinsic Kinetics of the Alkylation of Benzene with Propylele over β Zeolite Catalyst.” Kinetics and Catalysis 42 (4): 533–8, https://doi.org/10.1023/A:1010581708069.10.1023/A:1010581708069Search in Google Scholar
Jinasena, A., G.-O. Kaasa, and R. Sharma. 2017. “Use of Orthogonal Collocation Method for a Dynamic Model of the Flow in a Prismatic Open Channel: For Estimation Purposes.” In Proceedings of the 58th Conference on Simulation and Modelling (SIMS 58) Reykjavik, Iceland, September 25th – 27th, 2017, Vol. 138, 90–6. Linkopings University, Linkoping: Linkoping University Electronic Press.10.3384/ecp1713890Search in Google Scholar
Junqueira, P. G., P. V. Mangili, R. O. Santos, L. S. Santos, and D. M. Prata. 2018. “Economic and Environmental Analysis of the Cumene Production Process Using Computational Simulation.” Chemical Engineering and Processing: Process Intensification 130 (June): 309–25, https://doi.org/10.1016/j.cep.2018.06.010.Search in Google Scholar
Lei, Z., C. Li, J. Li, and B. Chen. 2004. “Suspension Catalytic Distillation of Simultaneous Alkylation and Transalkylation for Producing Cumene.” Separation and Purification Technology 34 (1–3): 265–71, https://doi.org/10.1016/S1383-5866(03)00199-0.Search in Google Scholar
Luyben, W. L. 2003. “Design and Control of the.” Principles and Case Studies of Simultaneous Design 2 (1): 107–33, https://doi.org/10.1021/ie9011535.Search in Google Scholar
Luyben, W. L. 2014. “Effect of Peak Temperature Limitations on the Design of Processes with Cooled Tubular reactors.” International Journal of Chemical reactor Engineering 12 (1): 191–203, doi:https://doi.org/10.1515/ijcre-2013-0138.Search in Google Scholar
Ma, Z., and G. Guiochon. 1991. “Application of Orthogonal Collocation on Finite Elements in the Simulation of Non-Linear Chromatography.” Computers & Chemical Engineering 15 (6): 415–26, https://doi.org/10.1016/0098-1354(91)87019-6.Search in Google Scholar
Maity, D., R. Jagtap, and N. Kaistha. 2013. “Systematic Top-Down Economic Plantwide Control of the Cumene Process.” Journal of Process Control 23 (10): 1426–40, https://doi.org/10.1016/j.jprocont.2013.09.005.Search in Google Scholar
Mehra, M., and N. K. R. Kevlahan. 2008. “An Adaptive Wavelet Collocation Method for the Solution of Partial Differential Equations on the Sphere.” Journal of Computational Physics 227 (11): 5610–32, https://doi.org/10.1016/j.jcp.2008.02.004.Search in Google Scholar
Nugraha, M. G., H. Saptoadi, M. Hidayat, B. Andersson, and R. Andersson. 2019. “Particle Modelling in Biomass Combustion Using Orthogonal Collocation.” Applied Energy 255 (August): 113868, https://doi.org/10.1016/j.apenergy.2019.113868.Search in Google Scholar
Park, H. M. 2018. “A Multiscale Modeling of Fixed Bed Catalytic Reactors.” International Journal of Heat and Mass Transfer 116: 520–31, https://doi.org/10.1016/j.ijheatmasstransfer.2017.09.035.Search in Google Scholar
Pathak, A. S., S. Agarwal, V. Gera, and N. Kaistha. 2011. “Design and Control of a Vapor-Phase Conventional Process and Reactive Distillation Process for Cumene Production.” Industrial & Engineering Chemistry Research 50 (6): 3312–26, https://doi.org/10.1021/ie100779k.Search in Google Scholar
Rajendran, V. M. P. L. 2012. Mathematical Modelling of Steady-State Concentration in Immobilized Glucose Isomerase of Packed-Bed Reactors, https://doi.org/10.1007/s10910-011-9973-6.13331346.Search in Google Scholar
Sreekumar, S., A. Kallingal, and V. Mundakkal Lakshmanan. 2021. “Adaptive Neuro-Fuzzy Approach to Sodium Chlorate Cell Modeling to Predict Cell pH for Energy-Efficient Chlorate Production.” Chemical Engineering Communications 208 (2): 256–70, https://doi.org/10.1080/00986445.2019.1708740.Search in Google Scholar
Torabi, A., M. Kazemeini, and M. Fattahi. 2016. “Developing a Mathematical Model for the Oxidative Dehydrogenation of Propane in a Fluidized Bed Reactor.” Asia-Pacific Journal of Chemical Engineering 11 (3): 448–59.10.1002/apj.1966Search in Google Scholar
Walas, S.M. 1988. Chemical Process Equipment: Selection and Design, Vol. 1. Boston: Butterworths.Search in Google Scholar
Yadav, O. P., and R. Jiwari. 2019. “A Finite Element Approach to Capture Turing Patterns of Autocatalytic Brusselator Model.” Journal of Mathematical Chemistry 57 (3): 769–89, https://doi.org/10.1007/s10910-018-0982-6.Search in Google Scholar
Yang, X., S. Wang, B. Li, Y. He, and H. Liu. 2020. “Performance of Ethanol Steam Reforming in a Membrane-Assisted Packed Bed Reactor Using Multiscale Modelling.” Fuel 274 (April): 117829, https://doi.org/10.1016/j.fuel.2020.117829.Search in Google Scholar
Zhai, J., Y. Liu, L. Li, Y. Zhu, W. Zhong, and L. Sun. 2015. “Applications of Dividing Wall Column Technology to Industrial-Scale Cumene Production.” Chemical Engineering Research and Design 102: 138–49, https://doi.org/10.1016/j.cherd.2015.06.020.Search in Google Scholar
Supplementary Material
The online version of this article offers supplementary material (https://doi.org/10.1515/ijcre-2021-0177).
© 2021 Walter de Gruyter GmbH, Berlin/Boston
