(298c) Crystallization Process Optimization Using Derivative-Free Optimization Algorithms

Polymorphism is of key importance in the pharmaceutical and fine-chemicals industry.  Modeling of polymorphism phenomena is based on Population Balance Equations (PBEs), which are sets of partial differential equations whose analytical solution is not always available [1].  Moreover, when optimization is to be done over a simulator, it is often difficult to calculate derivatives of variables of PBEs either analytically or numerically.  This renders most derivative-based optimization methods of little or no use.  Derivative-free optimization (DFO) algorithms are specifically designed for this kind of problem [2]. In this work, we use g-CRYSTAL as a black box simulator to perform simulation-based optimization of crystallization processes.  DFO is used to optimize one particular polymorph and minimize the time of producing a desired particle size distribution.  This goal is achieved by optimizing process variables, including temperature and cooling profile of reactor, super saturation of seed molecule, flow rates, and concentrations of species.  We present extensive computational results, where we compare the results of 28 DFO algorithms on several case studies.

References

[1] Rudiyanto Gunawan, Irene Fusman, and Richard D. Braatz. High resolution algorithms for multidimensional population balance equations. AIChE Journal, 50(11):2738{2749, 2004.

[2] Luis Miguels Rios and Nikolaos V.Sahinidis. Derivative-free optimization: A review of algorithms and comparison of software implementations. Journal of Global Optimization, DOI 10.1007/s10898-012-9951-y, 2012.