The paper presents a novel methodology for the estimation of the shape of the crystal size distribution (CSD) during a crystallization process. The approach, based on a combination of the quadrature method of moments (QMOM) and the method of characteristics (MOCH), provides a computationally efficient solution of the population balance equation (PBE) and hence a fast prediction of the dynamic evolution of the CSD for an entire batch. Furthermore, under the assumption that for supersaturation-controlled crystallization the main phenomenon is growth, an analytical CSD estimator is derived for generic size-dependent growth kinetics. These approaches are evaluated for the crystallization of potassium alum in water. The model parameters are identified on the basis of industrial experimental data, obtained using an efficient implementation of supersaturation control. The proposed methods are able to predict and reconstruct the dynamic evolution of the CSD during the batch. The QMOM-MOCH solution approach is evaluated in a model-based dynamic optimization study, which aims to obtain the optimal temperature profiles required to achieve desired target CSDs. The technique can serve as a soft sensor for predicting the CSD, or as a computationally efficient algorithm for off-line design or online adaptation of operating policies based on knowledge of the full CSD data.

The paper presents a methodology for the dynamic optimization of the crystal size distribution (CSD) considering growth, nucleation, and dissolution mechanisms for batch cooling crystallization processes. The optimal temperature trajectories are obtained by solving the population balance model (PBM) using the quadrature method of moments in conjunction with the method of characteristics. The coupled algorithm allows a computational efficient approach for the estimation of the shape of the CSD during crystallization processes with generic apparent size-dependent growth (caused by the actual mechanism or growth rate dispersion) and dissolution and secondary nucleation mechanisms. The approach is evaluated for the crystallization of potassium alum in water. The model parameters for growth and dissolution are identified based on pilot scale industrial and laboratory experimental data, respectively, and are used to design the optimal dynamic temperature trajectories to obtain the desired monomodal target shape of the CSD at the end of the batch. Simulation results illustrate that the incorporation of the dissolution mechanism in the model allows development of optimal in situ fine removal policies, which programmatically drive the process in the undersaturated region offering more flexibility in shaping the CSD. The online application of the controlled dissolution-based optimal control method can adapt the operating policy in the case of accidental seeding, which is a common disturbance in industrial crystallization processes and can eliminate the need for additional equipment used for external fines removal loop.

The paper presents a novel quality-by-design framework for the design of optimal seed recipes for batch cooling crystallisation systems with the aim to produce a desired target crystal size distribution (CSD)

This paper provides an experimental and simulation based analysis of the effect of seed quality on the shape of the product crystal size distribution of a seeded batch cooling crystallization process. Various seeds were prepared using different protocols, involving milling, washing, and sieving. The cooling batch crystallization processes of potassium dichromate in water with the different seeds were monitored using process analytical technologies (PAT), such as attenuated total reflectance (ATR) UV/vis spectroscopy, focused beam reflectance measurement (FBRM), and online laser diffraction for real-time crystal size distribution measurement. A population balance model with apparent size-dependent growth, which incorporates the effect of growth rate dispersion, is used to simulate the evolution of the crystal size distribution (CSD) using the different seed distributions as initial conditions. The simulation results were in good agreement with the experimental product CSD, when the good quality crystalline seed was used with no fines. However, the mean crystal size of the product was overpredicted by the growth-only model, when milled seeds were used with different fine contents. This was caused mainly by the excessive initial breeding, due to the different surface properties resulting from the preparation method, the Ostwald ripening promoted by the fines, and the pronounced agglomeration observed in these cases during the experiments. The simulation and experimental results provide evidence of the importance of consistent and well-defined seed quality and suitable preparation procedures for high quality crystalline products.

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