Parameter Identification in Population Balance Models Using Uncertainty and Sensitivity Analysis

The accurate estimation of sensitive parameters in a mathematical model predicting the outcome of a real experiment is of great importance in studying a complex physical phenomenon. A systematic methodology based on the uncertainty and sensitivity analysis framework is proposed for precise estimation of model parameters. The nonintrusive polynomial chaos expansion and the Sobol'-based sensitivity indices are used to quantify the uncertainties in the model prediction due to parameter uncertainties, and the Monte Carlo method is used for the validation of uncertainty quantification results. A population balance model for an unseeded batch cooling crystallization of L-asparagine monohydrate with two different sets of kinetic models for nucleation and crystal growth is selected to demonstrate the methodology. The results clearly demonstrate the effectiveness of the proposed strategy in improving the predictive ability of the population balance model. For models involving many uncertain parameters, the proposed strategy can be adopted to rank parameters by decreasing importance and then achieve precise estimation of the more significant parameters using a suitable optimization algorithm and experimental data set.