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- Mathematical investigations of a kinetic model for glycerol hydrogenolysis via heterogeneous catalysisPublication . Costa, Fernando Pestana da; Ndlovu, Thandokuhle Quinton; Shozi, MzamoIn 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 R5 phase space, and the limit point depends on the values of rate constants ki 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.
- Hydrogenolysis of Xylitol to value added products: a mathematical approachPublication . Ndlovu, Thandokuhle Quinton; Costa, Fernando Pestana da; Magagula, Vusi; Shozi, MzamoIn this paper we mathematically investigate the kinetics underlying the hydrogenolysis of xylitol over a metal based catalyst by using ordinary differential equations. The primary motivation for mathematically investigating this reaction lies on the fact that some of the value added products from this reaction are sourced from fossil fuels, which are not environmentally friendly. They have been reported by different researchers that they are the primary drive of global warming which leads to climate change, which causes severe disturbances in the Earth´s natural systems and economies. Xylitol, on the other hand, which is readily available from biomass have been reported as an alternative raw material for some of the value added products. A reaction mechanism proposed from experimental data is used to formulate a system of ordinary differential equations which is then analyzed using some qualitative analysis tools from mathematics. Numerical simulations are performed to try and ascertain the long time behavior of the system's solutions. Results showed that the solutions to the system approaches a lower dimensional invariant set with X_k=0 for k=1,...,8 and X_k>0 for k=9, 10, 11. These numerical results were found to be in agreement with the experimental results from the chemistry point of view. Therefore, it is believed that this model can be extended for use in other sugar alcohols higher than xylitol, like sorbitol as means to maximize the yields of the desired products.