We propose a grid-like computational model of tubular reactors. The architecture is inspired by the computations performed by solvers of partial differential equations which describe the dynamics of the chemical process inside a tubular reactor. The proposed model may be entirely based on the known form of the partial differential equations or it may contain generic machine learning components such as multi-layer perceptrons. We show that the proposed model can be trained using limited amounts of data to describe the state of a fixed-bed catalytic reactor. The trained model can reconstruct unmeasured states such as the catalyst activity using the measurements of inlet concentrations and temperatures along the reactor.

Recent studies have provided new information on glycerol hydrochlorination in the presence of carboxylic acids as homogeneous catalysts; particularly interesting is the fact that a part of the carboxylic acid is esterified in some of the steps in the reaction mechanism. Inspired by this observation and the previously proposed mechanism for glycerol hydrochlorination, new kinetic equations were derived. By using the quasi-equilibrium approximation for the reaction intermediates, the rate equations take into account the fraction of catalyst that is present in the form of esters and epoxides. The model explains the initial zero-order kinetics with respect to glycerol. The parameters of the new kinetic equations were fitted by non-linear regression for the set of ordinary differential equations describing the mass balances of the system. Internal control variables were the experimentally recorded temperature inside the reactor and the measured hydrogen chloride concentration in the liquid phase. The kinetic model was fitted to experimental data, and it was confirmed that the rate equations are able to describe the concentration profiles under various conditions. Incorporation of the activity coefficient of hydrogen chloride improved slightly the model predictions. The new kinetic model reduces to the previously proposed kinetic model at carboxylic acid concentrations.