Mathematical Investigations of a Kinetic Model for Glycerol Hydrogenolysis Via Heterogeneous Catalysis

In this paper we report on some mathematical investigations of the chemical process for the hydrogenolysis of glycerol over a heterogeneous metal catalyst. The main interest of this process is related to the fact that glycerol is produced as a by-product in the production of biodiesel in huge amounts that are expected to exceed the projected demands. This makes the sustainability of biodiesel production depend on the conversion of the glycerol into useful products hence it is a desirable goal to have effective conversion methods. A reaction model from literature is used to derive a system of ordinary differential equations (ODE) which is then analysed using methods from qualitative analysis of ODEs. Numerical solutions of the system are simulated to try and find out the solution's behaviour in the chemistry point of view. It was found that all solutions of the model converge to some stable limit point in a 2-dimensional plane in the positive cone of the R 5 phase space, and the limit point depends on the values of rate constants k i as well as on the hydrogen to glycerol initial ratios. Even though the results are based on a specific kinetic model, it is hoped that they may help in providing tools for better understanding and description of the reaction.

Automated summary

This paper reports on mathematical investigations of the chemical process for the hydrogenolysis of glycerol over a heterogeneous metal catalyst. The main goal is to develop effective conversion methods to enhance the sustainability of biodiesel production. The analysis of ordinary differential equations and numerical simulations reveal that all solutions converge to a stable limit point, depending on the initial ratios and rate constants. These findings contribute to a better understanding and description of the reaction.