A population balance incorporating nucleation, growth, and agglomeration, solved using quadrature method of moments, was coupled with a parameter estimation procedure. The seeded antisolvent crystallization of paracetamol from methanol and water was chosen as the model system. All parameters concerned were regressed from moments calculated using the measured square weighted chord length distribution (CLD) generated by focused beam reflectance measurements (FBRM). The FBRM and the concentration data are utilized together to obtain experimental moments that reflect the mass of solids in the tank. Using the estimated kinetic parameters, the crystallization model was validated using an additional experiment with a new nonlinear addition rate. Experimental crystal size distributions (CSDs) measured by laser diffraction were compared to CSDs calculated by the model and were found to be in good agreement. No such work exists in the literature using FBRM to model an antisolvent system which considers agglomeration. On the basis of the kinetic parameters estimated using the above method, the solution to the optimal antisolvent addition rate profiles was obtained by applying nonlinear constrained multiobjective free final time formulation optimization on the validated model. These profiles were experimentally tested and CSD were compared with experiments used in the parameter estimation procedure. A 73.3% reduction in batch time was achieved with little impact on the CSD. Analyses of the various conflictions are presented with the aid of a pareto optimal plot to provide the practitioner with increased flexibility.
Growth kinetics, growth mechanisms, and the effect of solvent composition for the antisolvent crystallization of paracetamol in methanol−water mixtures have been determined by means of isothermal seeded batch experiments at constant solvent composition. A numerical model incorporating the population balance equation based on antisolvent free solubility was fitted to the desupersaturation data, and growth rate parameters are evaluated. An attenuated total reflectance−Fourier transform infrared (ATR-FTIR) probe was employed to measure online solute concentration and focused beam reflectance measurement (FBRM) was utilized to ensure negligible nucleation occurred. The model is validated by the final particle size distributions (PSDs) and online solute concentration measurements. Crystal growth rate was found to decrease with increasing water mass fractions up to a mass fraction of 0.68 where an increase is observed. A method has been introduced linking the effect of solvent composition with the growth mechanism and the growth rates. Utilizing the growth mechanism it has been postulated that a combination of the solubility gradient, viscosity, selective adsorption, and surface roughening are responsible for the reduction in growth rates with solvent composition. Furthermore, the effects of seed mass, size and initial supersaturation on the crystal growth rates were investigated to demonstrate the efficacy of the model at predicting these various phenomena.
The novel technique presented in this paper involves the pre-calculation of the moments of a pre-defined 2-parameter Probability Density Function (PDF) for a range of values of each parameter. This pre-calculation results in moment surfaces where the surfaces are a function of the two defining parameters. The intersection of constant moment contour lines (termed moment iso-lines) on these surfaces using simulation moment outputs results in the recovery of the defining parameters. Knowledge of the PDF and the total particle count or solids loading allows for the reconstruction of the full PSD. This technique proves to be very efficient which makes it ideal for the reconstruction of large numbers of distributions, for example in transient population balance models or model-based control algorithms, without the need for repeated application of optimisation algorithms.
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