Modeling, simulation and kinetic parameter estimation in batch crystallization processes

Abstract

IntroductionThe onset of instability in industrial continuous crystallization processes in response to small disturbances has previously been shown to be determined primarily by the strong nonlinear dependence of nucleation rates on the relative supersaturation driving force (Buyevich et al., 1991;Jager et al., 1991). Consequently, accurate kinetic modeling of crystallization kinetics, especially nucleation, is a prerequisite to the optimal design and control of crystallization processes. Seeded batch experiments provide a convenient means of obtaining kinetic data, since batch runs permit investigations over wider ranges of supersaturations and are less time-consuming than MSMPR studies (Tavare and Garside, 1986). Using the batch data, nonlinear optimization can be used to fit kinetic parameters to the data (Eaton and Rawlings, 1990; Witkowsky et al., 1989;Stewart et al., 1992). As formulated using SimuSolv (Steiner et al., 1990), the procedure involves: (1) constructing a differentiaValgebraic process model for batch crystallization;(2) sequentially solving the model for parameter sets until a logarithmic likelihood objective function constructed from the measured response function and model-generated response and covariance is maximized. In practice, however, the identification of reaction rate models will present problems whenever limitations to the operating range of experimental apparatus d o not permit the identification of a full mechanistic model (Box and Hill, 1967).For limited sample sizes, reparameterizing the model in a close-to-linear form can improve results as well as speed convergence Watts, 1981, 1988). Ratkowsky (1985) has Correspondence concerning this article should be addressed 10 R. J . Farrell discussed applications of reparameterization to solid-phase catalytic reactions. Recently, Edgar and Wright (1992) used reparameterization to obtain preexponential and activation energy parameters for the water gas shift reaction in a fixed-bed catalytic reactor using a data set involving a narrow temperature range. Chen and Aris (1992) also used reparameterization and rescaling to obtain Arrhenius parameters. For complex models, there is little guidance regarding the proper choice for the reparameterization function. Usually, it is necessary to experiment with several transformations (Bates and Watts, 1988). In fact, suitable reparameterizations for a particular process model may change for different data sets (Ratkowsky, 1983).For batch crystallization, difficulties with CSD measurements below 4 micron can limit the information content of the data. The relative success of previous experimental studies may be explained by the relative importance of small particle measurements to the identification of a process model. Qui and Rasmunson (1 991) have successfully identified nucleation and growth kinetics for succinic acid in a batch cooling crystallizer. This system is easily identifiable since it is characterized by low nucleation rates and high growth. On the other hand, Rawlings and coworkers hav...

Overview of Secondary Nucleation: From Fundamentals to Application

“…Secondary nucleation rates in power law models are generally assumed to be the result of the energy transfer to the crystal, the efficiency of contact, and the survival of the fine particles formed. − Anisi and Kramer discussed the general simple power law model and described the secondary nucleation with a power law function from the aspects of saturation, crystal mass fraction, and turbulence in the mold, as shown in eq where, ε is the dissipated power, φ T the volumetric holdup, σ the degree of supersaturation, and K SN , n 1 , and a are the fitting parameters.…”

Mouse strain‐specific patterns of mammary epithelial ductal side branching are elicited by stromal factors

“…The overall effects of death and birth of crystals may be accounted as experimental deviations from an ideal batch operation The initial and boundary conditions for solving Eq. 1, as described by Farrell and Tsai (1994), are The nucleation rate and the independent‐size growth rate equations, expressed as power‐law functions, include a power‐law term to account for the effect of agitation, as recommended by Qiu and Rasmunson (1994): The total mass of crystals formed is calculated as a function of the third moment in which the third moment is calculated as The overall mass balance and its initial condition become …”

Simulation of solids processes accounting for particle‐size distribution

“…19 and 20, it is important to note the range of applicability of these predictions. For crystallization, Farrell and Tsai (1994) discussed the importance and difficulty of accurately determining kinetic parameters for various process conditions. Hill and Ng (1996b) showed that empirical data for multiple particle breakage can be represented by various breakage function parameters.…”