Abstract
In this paper, we analyzed the mass transfer model with chemical reactions during the absorption of carbon dioxide (CO) 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 CO, 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 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.
Highlights
Carbon dioxide is a generally useful gas made up of a carbon and two oxygen atoms
A novel stochastic technique based on nonlinear autoregressive exogenous (NARX) neural networks with the Levenberg–Marquardt algorithm is utilized to optimize the system of singular nonlinear differential equations for the normalized concentration of CO2 and phenyl glycidyl ether (PGE)
The statistics of approximate solutions obtained by NARX-NM algorithm for steady state concentration profiles of CO2 and PGE are compared with the Adomian decomposition method and Duan–Rach modified (ADM and DRM) [41], Adomian decomposition method (ADM) [10], Residual method [43], and numerical method as shown in Tables 1 and 2
Summary
Carbon dioxide is a generally useful gas made up of a carbon and two oxygen atoms. It is essential in plant photosynthesis, manufacturing carbonated soft drinks, powering pneumatic systems in robots, fire extinguishers, removing caffeine from coffee [1,2], etc. Stochastic computing paradigms based on artificial intelligence have been used extensively to find numerical solutions for different problems arising in various fields, such as fuzzy systems [16,17,18], petroleum engineering [19], carbon capture process [20,21,22], wire coating dynamics [23], biological systems [24,25], civil engineering [26,27], coal-fired power plant retrofitted [28], and electrical and thermal engineering [29,30,31] These contributions motivated the authors to investigate the absorption of carbon dioxide (CO2) into solutions of phenyl glycidyl ether (PGE) by strengthening the computational ability of neural networks. Extensive graphical analysis based on absolute errors, fitting of numerical and approximate solutions, absolute errors, and performance graphs of mean square error are plotted to further validate the worth of the design scheme
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
