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A stochastic formulation for the description of cooling-antisolvent mediated crystal growth processes based on the Fokker-Planck equation is discussed. Previous results are further extended to include not only the additional degree of freedom (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 crystallization 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. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2843-2851, 2013 [ABSTRACT FROM AUTHOR]

A new formulation of the recent stochastic approach for the description of the particle-size distribution (PSD) time evolution in antisolvent crystal-growth processes is presented. In this new approach, the crystals size is modeled as a random variable driven by a Gompertz growth term and the corresponding Fokker-Planck equation is carried out. This proposed formulation, allows an analytical solution to describe the time evolution of the PSD as a function of the model parameters. The analytical solution is obtained by exploiting the typical properties of linear partial differential equations with linear coefficients, and using the analogy with Kalman filter, in terms of the first two stochastic moments: mean and variance of the PSD. Furthermore, an alternative way for the parameters estimation based on the maximum likelihood estimation is also introduced. Validations against experimental data are provided for the NaCl-water-ethanol antisolvent crystallization system. © 2012 American Institute of Chemical Engineers AIChE J, 2012 [ABSTRACT FROM AUTHOR]