(356b) Model Identification Using in-Line Estimates of Crystal Size

Application of population balance models (PBM) to crystallization depends on the ability to identify the correct crystal formation mechanism and the corresponding parameters. This is accomplished by solving an optimization problem that reduces the error between a model’s prediction and the experimental values derived from crystallization experiments. Another approach for estimating the correct mechanism and parameters is by maximizing the likelihood function, or probability of observing these phenomena, using Bayesian theory. Industrial applications of this workstream are limited by the data available, which in most cases consists of a solution concentration as a function of time, and initial and final crystal size distributions (CSD). In many cases, this may lead to several mechanisms (and/or parameter sets) capable of explaining the same set of data. In this work we use numerical experiments to address the issue of the amount of data needed to correctly identify the correct mechanism and parameters. In particular, we study the use of in-line estimators of crystal size like the ones introduced in [1,2], which allows for an estimation of the inline CSD as a function of time. We study the applicability of this methodology with actual experimental data.

[1] Irizarry R, Chen A, Crawford R, Codan L, Schoell J. Data-driven model and model paradigm to predict 1D and 2D particle size distribution from measured Chord-length distribution. Chem Eng Sci. 2017; 164: 202-218.

[2] Schoell J, Irizarry R , Sirota E, Mengel C, Codan L, Cote A. Determining particle size distributions from chord length measurements for different particle morphologies. AIChE J. Vol 65.