Stochastic Approach for the Prediction of PSD in Nonisothermal Antisolvent Crystallization Processes Giuseppe Cogoni, Stefania Tronci, Giuseppe Mistretta, and Roberto Baratti Dipartimento di Ingegneria Meccanica, Chimica e dei Materiali, Universit a degli Studi di Cagliari, Piazza D’Armi, I-09123, Cagliari, Italy Jose A. Romagnoli Dept. of Chemical Engineering, Louisiana State University, South Stadium Road, Baton Rouge, LA 70803 DOI 10.1002/aic.14089 Published online March 26, 2013 in Wiley Online Library (wileyonlinelibrary.com) A stochastic formulation for the description of cooling-antisolvent mediated crystal growth processes based on the Fok- ker-Planck equation is discussed. Previous results are further extended to include not only the additional degree of free- dom (temperature) in the approach, but also to formulate the model parameters dependencies with the input manipulated variables (antisolvent flow rate and temperature) toward a global model to be used within all possible operating regimes. The obtained global models are used to define, for the first time, an operating map of the crystalliza- tion process, where asymptotic isomean and isovariance curves are reported in an antisolvent flow-rate-temperature plane. Input multiplicities are identified and validated both numerically and experimentally for the NaCl-water-ethanol nonisothermal antisolvent crystallization system. V C 2013 American Institute of Chemical Engineers AIChE J, 59: 2843– 2851, 2013 Keywords: antisolvent crystallization, nonisothermal crystallization, global model, Fokker-Planck equation Introduction Antisolvent aided crystallization is an advantageous sepa- ration technique when the solute is highly soluble or heat sensitive. The driving force in crystal formation is the super- saturation that establishes the thermodynamic equilibrium for the solid–liquid separation. The main technologies used to obtain the super-saturation are cooling of the solution and antisolvent addition, and a proper combination of them could improve the quality of the product, as recently demonstrated for few systems. 1,2 The organic systems, paracetamol and acetyl-salicylic acid, used in the aforementioned two articles have solubilities that change significantly with temperature, therefore, to incorporate cooling with antisolvent crystalliza- tion can significantly increase crystallization yield. It has also been shown recently 3 that even for systems with solubil- ity weakly dependent on temperature; it is possible to impart significantly improved control over both the distribution mean size and coefficient of variation by manipulating tem- perature together with antisolvent feed rate. This strategy would allow us to add a second degree of freedom (cooling) to be used to control the crystallization process. The control of the crystal size and the crystal size distribu- tion is an important and challenging problem and several factors can affect the size and the widening of the size distri- bution. The development of effective mathematical models describing the crystal growth dynamics is, therefore, a crucial issue toward finding the optimal process performance and to control the crystal size and distribution. Antisolvent crystallization has been modeled for many systems using the traditional population balance modeling approach. 4–9 As an alternative, it was recently shown 10,11 that it is possible to describe a crystallization process by means of a stochastic approach, which allows the obtainment of the crystal size distribution (CSD) evolution with respect to time using the Fokker-Planck equation. Furthermore, this type of represen- tation leads to simpler models and allow for the analytical solution to describe the CSD over time in antisolvent crystal- lization operations in the case of linear growth term 11 and in asymptotic CSD for nonlinear growth term. 12 However, the Fokker-Planck-based model does not have an explicit dependency of the control input (i.e., antisolvent flow rate), and/or the temperature, although these variables do affect the process parameters. In order to use the model over the whole operating range, linear piece-wise interpolation approaches have been so far exploited 10–12 as a function of a single input (antisolvent flow rate). Even though effective results were obtained, the use of linear interpolation can be difficult to use when a continuous input-output relationship is required, as in case of model-based control algorithms. Fur- thermore, when temperature dependency is incorporated, a typical experimental campaign with three temperature levels and three antisolvent flow rate values requires the implicit estimation of 27 different parameter values. In order to use the model over the whole operational range proper relationships between the parameters of the model and the two process variables, namely antisolvent flow rate and temperature, has to be developed. Consequently, in this Correspondence concerning this article should be addressed to R. Baratti roberto.baratti@dimcm.unica.it. V C 2013 American Institute of Chemical Engineers AIChE Journal 2843 August 2013 Vol. 59, No. 8