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Article

Theoretical Analysis on Absorption of Carbon Dioxide (CO2) into Solutions of Phenyl Glycidyl Ether (PGE) Using Nonlinear Autoregressive Exogenous Neural Networks

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Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Khyber Pakhtunkhwa, Pakistan
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COMBA R&D Laboratory, Faculty of Engineering, Universidad Santiago de Cali, Cali 76001, Colombia
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Department of Computer and Information Sciences, Imam Mohammad Ibn Saud Islamic University, Alhasa 31982, Saudi Arabia
*
Author to whom correspondence should be addressed.
Academic Editors: Aurora Costales and Fernando Cortés-Guzmán
Molecules 2021, 26(19), 6041; https://doi.org/10.3390/molecules26196041
Received: 5 September 2021 / Revised: 24 September 2021 / Accepted: 27 September 2021 / Published: 5 October 2021
(This article belongs to the Special Issue Advances in the Theoretical and Computational Chemistry)
In this paper, we analyzed the mass transfer model with chemical reactions during the absorption of carbon dioxide (CO2) into phenyl glycidyl ether (PGE) solution. The mathematical model of the phenomenon is governed by a coupled nonlinear differential equation that corresponds to the reaction kinetics and diffusion. The system of differential equations is subjected to Dirichlet boundary conditions and a mixed set of Neumann and Dirichlet boundary conditions. Further, to calculate the concentration of CO2, PGE, and the flux in terms of reaction rate constants, we adopt the supervised learning strategy of a nonlinear autoregressive exogenous (NARX) neural network model with two activation functions (Log-sigmoid and Hyperbolic tangent). The reference data set for the possible outcomes of different scenarios based on variations in normalized parameters (α1, α2, β1, β2, k) are obtained using the MATLAB solver “pdex4”. The dataset is further interpreted by the Levenberg–Marquardt (LM) backpropagation algorithm for validation, testing, and training. The results obtained by the NARX-LM algorithm are compared with the Adomian decomposition method and residual method. The rapid convergence of solutions, smooth implementation, computational complexity, absolute errors, and statistics of the mean square error further validate the design scheme’s worth and efficiency. View Full-Text
Keywords: carbon dioxide; phenyl glycidyl ether; reaction mechanisms; reaction kinetics and diffusion; chemical reactivity concentration of CO2 and PGE; artificial intelligence; machine learning; NARX networks carbon dioxide; phenyl glycidyl ether; reaction mechanisms; reaction kinetics and diffusion; chemical reactivity concentration of CO2 and PGE; artificial intelligence; machine learning; NARX networks
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MDPI and ACS Style

Khan, N.A.; Sulaiman, M.; Tavera Romero, C.A.; Alarfaj, F.K. Theoretical Analysis on Absorption of Carbon Dioxide (CO2) into Solutions of Phenyl Glycidyl Ether (PGE) Using Nonlinear Autoregressive Exogenous Neural Networks. Molecules 2021, 26, 6041. https://doi.org/10.3390/molecules26196041

AMA Style

Khan NA, Sulaiman M, Tavera Romero CA, Alarfaj FK. Theoretical Analysis on Absorption of Carbon Dioxide (CO2) into Solutions of Phenyl Glycidyl Ether (PGE) Using Nonlinear Autoregressive Exogenous Neural Networks. Molecules. 2021; 26(19):6041. https://doi.org/10.3390/molecules26196041

Chicago/Turabian Style

Khan, Naveed Ahmad, Muhammad Sulaiman, Carlos Andrés Tavera Romero, and Fawaz Khaled Alarfaj. 2021. "Theoretical Analysis on Absorption of Carbon Dioxide (CO2) into Solutions of Phenyl Glycidyl Ether (PGE) Using Nonlinear Autoregressive Exogenous Neural Networks" Molecules 26, no. 19: 6041. https://doi.org/10.3390/molecules26196041

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