A kinetic model is required for upset scenarios with runaway chemical reactions that are analyzed dynamically through SuperChems™. Kinetic parameters for these chemical reactions are usually determined by trial and error, one variable at a time. The simplest case requires two parameters, the pre-exponential factor and the activation energy. Even this unpretentious condition presents obstacles. When fixing the pre-exponential factor to determine the activation energy or vice-versa, one is optimized for the fixed value of the other, which most likely is not the real optimum. Neither parameter is optimized in this manner.
It is virtually impossible to optimize kinetic parameters by trial and error when two or more factors are present, so it makes sense to consider an alternative technique. One effective method is Experimental Design, a statistical technique that simultaneously identifies the optimum of all model factors under consideration. An experimental design organizes, conducts, and interprets the results for the best outcome based on the smallest number of trials.
The word trial usually refers to experiments. When developing a kinetic model, a trial represents a SuperChems™ run with kinetic parameters that are part of the design. The typical experimental design works with squares, cubes, or hypercubes, depending on the number of input variables or predictors. A multi-dimensional cubic design is much better than trial and error. However, a superior experimental design technique can be applied to establish kinetic parameters. It is known as Response Surface Methodology (RSM) [1], carried out with a Central Composite Design (CCD) [2].
RSM is a collection of mathematical and statistical techniques for modeling and analyzing complex relationships between kinetic parameters (predictors) and kinetic rates (responses or control variables).
This white paper employs a known chemical reaction to provide the background for kinetic development with RSM. It is the exothermic reaction of di-tert-butyl peroxide decomposition in toluene. The goal is to generate kinetic parameters for SuperChems™ dynamic simulations involving runaway reactions.
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