Numerical modeling of the benzene reaction with ozone in gas phase using differential neural networks

In the present paper a mathematical model of a gas–gas reaction between ozone and benzene in a tubular reactor is considered. Usually, mathematical models of chemical process are governed by a set of ordinary differential equations assuming that the corresponding concentration dynamics depends only on time. On the other hand, the spatial distribution of the mass, energy and concentrations may be observed in the case of a more complex model structure that demands the use of models described by partial differential equations. The example of such complex model describing, the reaction between benzene and ozone in the gas phase, is considered here. The approach suggested in this study is based on the differential neural network (DNN) technique which permits to convert the task of mathematical modeling of a tubular reactor containing an uncertain (not well-defined) dynamics to a non-parametric identification problem. The asymptotic convergence of the obtained identification error to an ellipsoidal zone containing the origin is shown using the Lyapunov-like analysis. The coincidence between the benzene and ozone concentrations variation calculated by the suggested DNN-algorithm and those generated by a kinetic model is shown to be good enough.