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 calculation 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), carried out with a Central Composite Design (CCD).
RSM is a collection of mathematical and statistical techniques for modeling and analyzing complex relationships between predictors (input variables) and responses (output variables).
This white paper employs the same chemical reaction of Part 2 of this series to provide the background for kinetic development with RSM: the exothermic di-tert-butyl peroxide decomposition in toluene. Part 2 of this series determined the kinetic parameters based on the conventional inferred self-heating rate vs. measured temperature approach. Part 3 will develop kinetic parameters based on all-measured temperature vs. time calorimetric output.
“We cannot effectively develop kinetic parameters for a runaway chemical reaction by trial and error.”
Sometimes, the adiabatic calorimetry output may not include self-rates, but Process Safety Office® SuperChems™ calculates the self-rate derivatives for temperature and pressure. The temperature and pressure versus time data may look smooth, but occasionally their time derivatives are uneven, thus compromising kinetic development.
Figure 1: Inputs for kinetic development. a: The conventional self-heating rate vs. temperature method; b: The alternative temperature vs. time approach
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