Inferring and Propagating Kinetic Parameter Uncertainty for Condensed Phase Burning Models

Abstract

Kinetic parameters for serial pyrolysis reactions were calibrated from thermogravimetric analysis (TGA) data using Bayesian inference via Markov Chain Monte Carlo (MCMC) simulations assuming a serial reaction mechanism. Calibrations were performed for high-impact polystyrene (HIPS), bisphenol-A polycarbonate (PC), and poly(vinyl chloride) (PVC) at heating rates of 3 K/min and 10 K/min. The resulting parameter inferences are probabilistic as opposed to the point estimates calibrated in previous studies and are visualized using posterior probability density functions (PDFs) generated by kernel density estimation (KDE). Correlations between the parameters are identified and discussed. In particular, it is clear that pre-exponential constants and activation energies for a given reaction have a strong positive correlation. It is hypothesized that the degree of overlap in the posterior PDFs might be a measure of model adequacy. Point-estimates of the kinetic parameters were made by finding the mode of the posterior PDFs. For HIPS, it was determined that a one-reaction pyrolysis model is most appropriate, and that the posterior modes for $\log \left( A_1\right)$ and $E_1$ are $19.5\,\log (1/s)$ and 292 kJ/mol, respectively, for the 3 K/min data. To evaluate the effect of kinetic parameter uncertainty on predictions of burning rate, samples from the posterior PDF were used to simulate gasification and cone calorimetry experiments using the fire dynamics simulator (FDS). In some cases, it was found that models with fewer parameters provided better predictions due to over-fitting associated with greater model complexity. Another important observation is that for the predictions of PVC cone calorimetry, the time to peak heat release rate can range from around 40 s to 180 s for a number of different kinetic parameter combinations that all fit the TGA data fairly well. It is argued that the proposed methodology is necessary for progress in modeling of condensed phase physics for fire problems as it supports both model validation and engineering predictions.