Combined mathematical and artificial intelligence modeling of catalytic bio-methanol conversion to dimethyl ether

This study is devoted to developing a combined mathematical and artificial intelligence modeling for simulating the conversion of bio-methanol into dimethyl ether. This methodology couples a precise mathematical model with single-layer perceptron artificial neural networks formulated by several combinations of training and transfer functions, to constitute a machine learning that overcomes the computational tools with the capability of learning without being explicitly programmed, so that it may be used to teach these tools to handle the data with high efficiency in order to predict the upcoming unseen ones precisely. Hence, the novelty of this study deals with the development of a machine learning modeling combined with artificial neural networks, benefitting from an extended mathematical-model-driven dataset, applied for the first time in the conversion of bio-methanol into dimethyl ether in large-scale catalytic dehydration reactors, assessing two process schemes, namely adiabatic and water-cooled operations. To this scope, datasets have been generated by an accurate mathematical model validated experimentally by reference pilot data, adopting the best equilibrium and kinetic expressions, and the simulated numerical data have been then employed as the source of the machine learning models. Extended databanks for the sensitivity analyses of the two process schemes have been then generated by the model (2688 data points in each case), 70% of which has been employed for the artificial neural networks training with mean squared error as the performance function. A single-layer perceptron network yielded the best performances in the adiabatic and water-cooled process schemes, revealing less than 0.5% deviations for the input variables (feed temperature, pressure, flow rate, and concentration) and outputs (temperature, pressure, and flow rates of methanol, dimethyl ether, and water). The simulations revealed that, as the best result of this work, methanol may be converted into dimethyl ether up to similar to 80% at 498 K, depending on the validated equilibrium constant adopted, with a maximum error of 0.11%. As a further relevant result, this study demonstrated that analyzing the methanol conversion into dimethyl ether reaction as a function of several variables such as feed flow rate, feed methanol concentration, and input temperature, the accuracy of the neural network with a small number of neurons (5) did not provide accurate output results, whereas 15 neurons in the hidden layer intensify their precision, with the interesting feature that a single-layer perceptron network may detect even small changes to the operating variables.