On the Design of Optimally Informative Experiments for Dynamic Crystallization Process Modeling

Abstract

In this paper, we present the challenging application of now well-established general and systematic procedures for model development, statistical discrimination, and validation to a published large-scale dynamic crystallization process model. Because of the model's size, this represents, to our knowledge, the first application of such statistical methods to such a largescale dynamic model. For completeness, a brief review of both the model development procedures and the dynamic model are included in the paper. In reviewing the model development procedures, we cover such methods as parametric identifiability testing (to determine whether the parameters, as they appear in the model, can in fact be identified), as well as optimal design of dynamic experiments for both model discrimination among three crystallization models (differing in their kinetics only) and parameter precision improvement within the single "best" dynamic model. Because of the relatively large scale of the model, an optimization-based approach is used for testing of model parameter identifiability that involves semi-infinite programming (SIP) to ensure that the entire control (or input) space has been explored. The problem of designing dynamic experiments is cast as an optimal control problem that enables the calculation of optimal sampling points, experiment durations, fixed and variable external control profiles, and initial conditions of a dynamic experiment subject to general constraints on inputs and outputs. Within this framework, methods are presented to provide experiment design robustness, accounting for parametric uncertainty and subsequently model prediction uncertainty. The paper details the progression of the three crystallization models through the model development procedures and shows the Gahn and Mersmann model (Chem. Eng. Sci. 1999, 54, 1273 to be superior to its competitors.

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