Application of method of lines in chemical engineering problems

Abstract

In this work, two problems in chemical engineering are studied and solved. Estimation of an important parameter of dust explosions, the deflagration index kST , and a study of unsteady state with axial diffusion Plug Flow Reactors are presented. Both problems are approached by characterizing the physical phenomena involved with suitable transport equations. Such equations have been developed with the synergy of both consolidated theoretical models and ad hoc assumptions and semi-empiric approaches, according to the specific problem analyzed. The final equation systems result in a system of non-linear Partial Differential Equations. The numerical solution of such equations has been performed by implementing the Method of Lines, a numerical method based on the discretization of spatial derivative operators, transforming a system of PDEs into a system of ODEs or DAEs. The resulting ODEs/DAEs systems have been implemented and solved inside MAT LABTMenvironment. The Method of Lines is presented for uniform and non-uniform grids, generalized with the use of spatial derivatives discretization stencils of several orders of accuracy. For the estimation of kST , we validated the model with 8 organic dust: Aspirin, Cork, Corn starch, Niacin, Polyethylene, Polystyrene, Sugar and Wheat flour. Results showed an interesting match between experimental and simulated data: predictions for the deflagration index were good, while the evolution of process variables (such as the temperature of the gas phase), still leaves room for improvements. For the PFR study, we propose 1-D models, taking in account the reactor start-up, thermal and material axial diffusion, and the presence of a heating/cooling system. In order to judge the quality of the results, we took as case study a reaction well studied in the literature over the years: the oxidation of Naphthalene. We developed the so-called Runaway Boundaries for the reaction considered. Our results found good matches with the available literature data and analysis. We also noticed a shifting of the Runaway Boundaries when considering a more realistic heating/cooling system