(27d) Optimization Toolbox for Modeling of Multiple Runaway Reaction Systems

The classical approach to modeling a runaway reaction using adiabatic calorimeter data involves a plot of the pseudo rate constant, which is expected to be a straight line if the order of reaction is correctly chosen. The Arrhenius pre-exponential factor and activation energy of the reaction are evaluated from the intercept and slope respectively. In the event of multiple reaction systems, it is observed that the model predictions for the reaction self-heat rate are often inaccurate although the pseudo rate constant plot is linear for a chosen reaction order. This can be attributed to the fact that the heat liberated during the course of a runaway reaction, as measured by an adiabatic calorimeter, is the cumulative effect due to one or more singular reactions, which could be either exothermic or endothermic in nature. An algorithm has been developed to model the behavior of such systems by using an optimization procedure that minimizes the error between the experimental data and predictions based on multiple Arrhenius kinetic equations. The adiabatic decomposition of di-tert-butyl peroxide (DTBP) has been chosen as an example to illustrate the essential concepts of the algorithm and its software implementation. The methodology will find useful applications like:- (1) Identifying the stage-wise progress of a runaway reaction that can provide necessary inputs to the chemist who can formulate an appropriate reaction mechanism. (2) Thermal inertia effects of the adiabatic bomb calorimeter can be well accounted in the case of complex reactions that undergo change in mechanism. (3) Developing accurate models for predicting self-heat rate data, which is the key information required for simulating venting behavior through emergency relief systems. (4) Design of mitigation systems such as quenching and inhibition.