Iranian Journal of Mathematical Chemistry

Iranian Journal of Mathematical Chemistry

Concentration of Ethanol and Acetaldehyde Inside the Catalyst Particle and in the Reaction Stream: Theoretical and Numerical Approach

Document Type : Research Paper

Authors
Baskaran Yamuna 1
Athimoolam Meena 1
Lakshmanan Rajendran 2
Mohammad Izadi 3
1 Department of Mathematics‎, ‎Saraswathi Narayanan College‎, ‎Madurai-625022‎, ‎India
2 Department of Mathematics‎, ‎AMET Deemed to be University‎, ‎Kanathur‎, ‎Chennai‎- ‎603112‎, ‎India
3 Department of Applied Mathematics‎, ‎Faculty of Mathematics and Computer‎, ‎Shahid Bahonar University of Kerman‎, ‎Kerman 76169-14111‎, ‎Iran,\\Department of Mathematics‎, ‎Saveetha School of Engineering‎, ‎SIMATS‎, ‎Saveetha University‎, ‎Chennai 602105‎, ‎Tamil Nadu‎, ‎India
10.22052/ijmc.2026.257981.2091
Abstract
‎The current research investigates the nonlinear behaviour of dimensionless ethanol and acetaldehyde concentrations in a fixed-bed laboratory reactor operating with a ${Mn}_9{Cu}_1$ catalyst for catalytic combustion‎. ‎The main objective is to obtain accurate analytical solutions of the coupled nonlinear governing equations and evaluate their usefulness for reactor analysis‎. ‎A semi-analytical hyperbolic function method is applied to derive rapidly convergent solutions‎, ‎which are validated through MATLAB (version 7.8.0‎, ‎R2009a) numerical simulations‎. ‎Excellent agreement between analytical and numerical results confirms the reliability of the method‎. ‎The findings show that the approach efficiently captures reactive transport and catalytic kinetics while reducing computational iteration time‎. ‎The solutions provide insight into catalyst performance and ethanol oxidation efficiency‎, ‎supporting optimization of reactor operating conditions‎. ‎Overall‎, ‎the study demonstrates that the hyperbolic function method is a simple‎, ‎computationally efficient tool for modelling complex nonlinear catalytic combustion systems‎.
Keywords
Catalytic combustion
Nonlinear reaction kinetics
Fixed-bed reactor modelling
Hyperbolic function method
Mathematical chemistry
Subjects
[1] J. Mittal, Recent progress in the synthesis of layered double hydroxides and their application for the adsorptive removal of dyes: a review, J. Environ. Manage. 295 (2021)#113017, https://doi.org/10.1016/j.jenvman.2021.113017.
[2] R. Okabe, A. Miura, M. Fukushima, M. Terashima, M. Sasaki, S. Fukuchi and T. Sato, Characterization of an adsorbed humin-like substance on an allophanic soil formed via catalytic polycondensation between catechol and glycine and its adsorption capability toward pentachlorophenol, Chemosphere 83 (2011) 1502-1506, https://doi.org/10.1016/j.chemosphere.2011.01.053.
[3] J. -Y. Chin and S. A. Batterman, VOC composition of current motor vehicle fuels and vapors and collinearity analyses for receptor modeling, Chemosphere 86 (2012) 951–958, https://doi.org/10.1016/j.chemosphere.2011.11.017.
[4] G. Rochard, L. Olivet, M. Tannous, C. Poupin, S. Siffert and R. Cousin, Recent advances in the catalytic treatment of volatile organic compounds: a review based on the mixture effect, Catalysts 11 (2021) #1218, https://doi.org/10.3390/catal11101218.
[5] M. J. M. Figueredo, C. Cocuzza, S. Bensaid, D. Fino, M. Piumetti and N. Russo, Catalytic abatement of volatile organic compounds and soot over manganese oxide catalysts, Materials 14 (2021) #4534, https://doi.org/10.3390/ma14164534.
[6] E. Loccufier, G. Watson, Y. Zhao, M. Meledina, R. Denis, P. G. Derakhshandeh, P. V. D. Voort, K. Leus, D. P. Debecker, K. D. Buysser and K. D. Clerck, CO2 methanation with Ru@MIL-101 nanoparticles fixated on silica nanofibrous veils as standalone structured catalytic carriers, Appl. Catal. B: Environ. 320 (2023) #121972, https://doi.org/10.1016/j.apcatb.2022.121972.
[7] C. He, J. Cheng, X. Zhang, M. Douthwaite, S. Pattisson and Z. Hao, Recent advances in the catalytic oxidation of volatile organic compounds: a review based on pollutant sorts and sources, Chem. Rev. 119 (2019) 4471–4568, https://doi.org/10.1021/acs.chemrev.8b00408.
[8] D. F. de Waard, P. D. Kouris, M. D. Boot and E. J. M. Hensen, Mixed Cu–Mn oxide catalysts for solvolysis of technical lignin, ACS Sustainable Chem. Eng. 13 (2025) 3269–3279, https://doi.org/10.1021/acssuschemeng.4c09666.
[9] X. Zha, C. Yang, X. Huang, J. Ding and Z. Ding, Recent progress and perspectives on metal oxide catalysts for thermocatalytic and photocatalytic oxidation of VOCs: a review, Environ. Pollut. Bioavailab. 36 (2024) #2376827, https://doi.org/10.1080/26395940.2024.2376827.
[10] M. K. Zamisa, T. W. Seadira and S. J. Baloyi, Transforming wastewater treatment: Recent advancements in catalytic wet air oxidation with pillared clay catalysts for phenol remediation, Environ. Pollut. 361 (2024) #124842, https://doi.org/10.1016/j.envpol.2024.124842.
[11] M. L. Rodriguez and L. E. Cadus, Mass transfer limitations in a monolithic reactor for the catalytic oxidation of ethanol, Chem. Eng. Sci. 143 (2016) 305-313,https://doi.org/10.1016/j.ces.2015.12.010.
[12] P. O. Larsson and A. Andersson, Oxides of copper, ceria-promoted copper, manganese, and copper–manganese on Al2O3 for the combustion of CO, ethyl acetate, and ethanol, Appl. Catal. B: Environ. 24 (2000) 175–192, https://doi.org/10.1016/S0926-3373(99)00104-6.
[13] D. Z. Khater, R. S. Amin, M. Mahmoud and K. M. El-Khatib, Evaluation of mixed transition-metal (Co, Mn, and Cu) oxide electrocatalysts anchored on different carbon supports for robust oxygen reduction reaction in neutral media, RSC Adv. 12 (2022) 2207–2218, https://doi.org/10.1039/d1ra07721j.
[14] D. Delimaris and T. Ioannides, VOC oxidation over MnOx􀀀CeO2 catalysts prepared by a combustion method, Appl. Catal. B: Environ. 84 (2008) 303–312, https://doi.org/10.1016/ j.apcatb.2008.04.006.
[15] T. Liu, Y. Yao, L. Wei, Z. Shi, L. Han, H. Yuan, B. Li, L. Dong, F. Wang and C. Sun, Preparation and evaluation of copper–manganese oxide as a high-efficiency catalyst for CO oxidation and NO reduction by CO, J. Phys. Chem. C 121 (2017) 12757–12770, https://doi.org/10.1021/acs.jpcc.7b02052.
[16] M. Dehghan and J. Manafian, The solution of variable-coefficient fourth-order parabolic partial differential equations by the homotopy perturbation method, Z. Naturforsch. A 64  (2009) 420–430.
[17] M. Dehghan, J. Manafian and A. Saadatmandi, Solving nonlinear fractional partial differential equations using the homotopy analysis method, Numer. Methods Partial Differential Equations 26 (2010) 448–479.
[18] M. Izadi, S. K. Yadav and G. Methi, Two efficient numerical techniques for solutions of fractional shallow water equation, Partial Differ. Equ. Appl. Math. 9 (2024) #100619, https://doi.org/10.1016/j.padiff.2024.100619.
[19] M. Dehghan, J. Manafian and A. Saadatmandi, Application of semi-analytical methods for solving the Rosenau-Hyman equation arising in the pattern formation in liquid drops, Internat. J. Numer. Methods Heat Fluid Flow 22 (2012) 777–790, https://doi.org/10.1108/09615531211244916.
[20] R. Rajalakshmi, A. Marimuthu, S. Naganathan, L. Rajendran and M. Izadi, Mathematical modeling and sensitivity analysis of enzymatic biofuel cells with various electrode geometries, J. Appl. Comput. Mech. (2025) In Press, https://doi.org/10.22055/jacm.2025.48646.5391.
[21] Y. Qian, J. Manafian, S. Y. Mohyaldeen, L. S. Esmail, S. A. Gorovoy and G. Singh, Multiple-order line rogue wave, lump and its interaction, periodic, and cross-kink solutions for the generalized CHKP equation, Propuls. Power Res. 10 (2021) 277–293, https://doi.org/10.1016/j.jppr.2021.09.002.
[22] Y. F. Patel and M. Izadi, Dynamic modeling and parameter sensitivity in singular nonisothermal reaction-diffusion systems: A DTM-Padé solution for spherical catalysts, J. Nonlinear Math. Phys. 32 (2025) #71, https://doi.org/10.1007/s44198-025-00332-2.
[23] P. Zhou, J. Manafian, M. Lakestani, O. A. Ilhan, N. J. angi Bahador, A. A. Fattah, K. H. Mahmoud, R. Nuray and N. Nagiyeva, Analytical evaluations using a neural-networkbased method for wave solutions of the combined Kairat-II-X differential equation in fluid mechanics, Sci. Rep. 16 (2026) #7753, https://doi.org/10.1038/s41598-026-38761-8.
[24] M. S. Dahaghin and H. Hassani, A new optimization method for a class of time-fractional convection–diffusion–wave equations with variable coefficients, Eur. Phys. J. Plus. 132 (2017) #130, https://doi.org/10.1140/epjp/i2017-11407-y.
[25] H. Hassani, Z. Avazzadeh, P. Agarwal, M. J. Ebadi and A. Bayati Eshkaftaki, Generalized Bernoulli–Laguerre polynomials: Applications in coupled nonlinear systems of variable-order fractional PDEs, J. Optim. Theory Appl. 200 (2024) 371–393, https://doi.org/10.1007/s10957-023-02346-6.
[26] S. Sabermahani, Y. Ordokhani and H. Hassani, General Lagrange scaling functions: Application in a general model of variable-order fractional partial differential equations, Comput. Appl. Math. 40 (2021) #269.
[27] Z. Avazzadeh and H. Hassani, Transcendental Bernstein series for solving reaction–diffusion equations with nonlocal boundary conditions through an optimization technique, Numer. Methods Partial Differential Equations 35 (2019) 2258–2274, https://doi.org/10.1002/num.22411.
[28] A. Ghasemi and A. Saadatmandi, A Bernoulli-reproducing kernel method for a class of nonlinear singular boundary value problems, J. Appl. Anal. Comput. 14 (2024) 3260–3281, https://doi.org/10.11948/20230508.
[29] M. Izadi, H. Ahmad and H. M. Srivastava, Numerical computations of time-dependent auto-catalytic glycolysis chemical reaction-diffusion system, MATCH Commun. Math. Comput. Chem. 93 (2025) 69–97, https://doi.org/10.46793/match.93-1.069I.
[30] R. Nalini, A. Meena, L. Rajendran and M. Izadi, Approximate solutions of transient reaction-diffusion equations for second-order regeneration at spherical microelectrodes via HPM, Edelweiss Appl. Sci. Technol. 9 (2025) 1471–1483, https://doi.org/10.55214/2576-8484.v9i9.10155.
[31] M. Agustina Campesi, N. J. Mariani, M. C. Pramparo, B. P. Barbero, L. E. Cadús, O. M. Martínez and G. F. Barreto, Combustion of volatile organic compounds on a MnCu catalyst: A kinetic study, Catal. Today 176 (2011) 225–228, https://doi.org/10.1016/j.cattod.2011.01.009.
[32] M. L. Clarance Mary, M. Chitra Devi, A. Meena, L. Rajendran and M. Abukhaled, A reliable Taylor series solution to the nonlinear reaction–diffusion model representing the steady-state behavior of a cationic glucose-sensitive membrane, J. Math. Comput. Sci. 11 (2021) 8354–8381, https://doi.org/10.28919/jmcs/6799.
[33] M. Chitra Devi, P. Pirabaharan, L. Rajendran and M. Abukhaled, An efficient method for finding analytical expressions of substrate concentrations for different particles in an immobilized enzyme system, Reac. Kinet. Mech. Cat. 130 (2020) 35–53, https://doi.org/10.1007/s11144-020-01757-0.
[34] M. Chitra Devi, P. Pirabaharan, M. Abukhaled and L. Rajendran, Analysis of the steadystate behavior of a pseudo-first-order EC-catalytic mechanism at a rotating disk electrode, Electrochim. Acta 345 (2020) #136175, https://doi.org/10.1016/j.electacta.2020.136175.
[35] K. M. Dharmalingam, M. Veeramuni and K. Valli, Ethanol and acetaldehyde in a fixedbed laboratory reactor by the Adomian decomposition method, Malaya J. Mat. 8 (2020) 886-892, https://doi.org/10.26637/MJM0803/0026.
[36] K. M. Dharmalingam, M. Veeramuni, H. Rezazadeh, C. Tunç, Variational iteration method for solving ethanol and acetaldehyde concentrations in a fixed-bed laboratory reactor, Appl. Appl. Math. 16 (2021) 383–398.
Iranian Journal of Mathematical Chemistry
Volume 17, Issue 3
In Progress
Summer 2026
Pages 233-254