Computers and Chemical Engineering 52 (2013) 216–229 Contents lists available at SciVerse ScienceDirect Computers and Chemical Engineering jou rn al h om epa ge: w ww.elsevier.com/locate/compchemeng Modeling induced nucleation processes during batch cooling crystallization: A sequential parameter determination procedure Kerstin Wohlgemuth ∗ , Gerhard Schembecker Laboratory of Plant and Process Design, Department of Biochemical and Chemical Engineering, Technische Universitaet Dortmund, Emil-Figge-Str. 70, 44227 Dortmund, Germany a r t i c l e i n f o Article history: Received 1 August 2012 Received in revised form 26 November 2012 Accepted 10 December 2012 Available online 23 January 2013 Keywords: Crystallization Induced nucleation Mathematical modeling Population balance Simulation a b s t r a c t An existing model is extended to simulate batch cooling crystallizations with induced nucleation pro- cesses like ultrasound or gassing. All important phenomena such as nucleation, growth, agglomeration and breakage are taken into account. A differentiation between ultrasound and gassing is necessary. Induced nucleation processes also require a modification of crystal growth mechanism. In general, the model parameters required for the kinetics are determined simultaneously by fitting them to experimental data. Mostly a correlation model results without physical basis. Here, the model parameters are sequentially determined by decoupling the mechanisms, saving effort and time, and make it possible to reduce the number of parameters also. The model and the model parameter determination procedure are validated using three different organic solute/solvent systems. The number of simulation runs for parameter fitting was reduced to less than 100 instead of simultaneous parameter determination, which requires several hundreds of thousands runs, resulting in physically reasonable solutions. © 2012 Elsevier Ltd. All rights reserved. 1. Introduction Batch crystallization processes are difficult to control. A possi- bility to improve reproducibility and crystal product quality, such as the mean crystal size and width of crystal size distribution, is the control of nucleation. One possibility is the addition of seed crystals to the supersaturated solution to prevent spontaneous nucleation and maintain supersaturation within the metastable zone, so that the seed crystals will grow only. A second oppor- tunity is the controlled initiation of nucleation by ultrasound or gassing (Wohlgemuth, Kordylla, Ruether, & Schembecker, 2009; Wohlgemuth, Ruether, & Schembecker, 2010). Whereas the success of the first approach is strongly influenced by the quality of the seed crystals, the latter depends on process parameters for initiation only: insonation/gassing period, insonation/gassing temperature (initial supersaturation), ultrasonic power, ultrasonic frequency and gas flow. Furthermore, induced nucleation processes do not involve the risk of contamination. Modeling of such processes is essential, since an out-of-spec product leads to high resource consumption and thus profit loss. A prediction of the crystal size distribution at the end of a batch run in dependence of process parameters is required. In case of cooling crystallization these process parameters are cooling rate, saturation concentration, overheating and stirring rate. Combining ∗ Corresponding author. Tel.: +49 231 755 3020; fax: +49 231 755 2341. E-mail address: kerstin.wohlgemuth@bci.tu-dortmund.de (K. Wohlgemuth). it with induced nucleation processes the process parameters for initiation mentioned above have to be taken into account, too. In general, the determination of model parameters is done by fit- ting the values of all used ones to experimental data simultaneously using the least squares method (e.g., Hu, Rohani, & Jutan, 2005; Puel, Fevotte, & Klein, 2003). A high number of model parameters make it nearly possible to adjust everything. The challenge is to get param- eter values which are physically sensible. The overall result is just a correlation model without physical basis. Moreover, as the number of model parameters and their variation range increases, the num- ber of simulation runs increases exponentially. This is accompanied with high computing times and several thousands of simulation runs. Therefore a need of fast and decoupled model parameter determination is obvious. Therefore, a sequential parameter deter- mination procedure is presented. The paper is organized as follows: Section 2 introduces the model developed, which is implemented in MATLAB (Version R2010b, MathWorks). Besides normal cooling crystallizations induced nucleation processes like gassing and sonocrystallization can be simulated. All important phenomena during crystalliza- tion processes are taken into account. A differentiation between gassing and sonocrystallization is required and subject of Section 3. In Section 4 the approach of model parameter determination for cooling crystallizations is presented. A step-by-step example of parameter fitting for cooling crystallization of paracetamol from acetonitrile is given for demonstration purposes. The simulation of induced nucleation processes is topic of Section 5. In Section 6 the sequential parameter determination approach is validated 0098-1354/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compchemeng.2012.12.001