Optimal seeding in batch crystallization

Abstract

This is the first comprehensive study on the optimization of seed distribution in a crystallization process. For a batch crystallizer, a dynamic programming formulation optimizes a property of the product crystals over the supersaturation profile and the seed characteristics, namely the mean size of the seed crystals, the seed mass, and the width of the seed distribution. Three optimization objectives are considered: ( I ) weight mean size, (2) coefficient of variation, and (3) the ratio of the nucleated crystal mass to seed crystal mass. Different objectives lead to substantially different optimal seed distributions. It is shown that optimizing over the seed distribution can have a larger effect on the product crystal size distribution than optimizing over the supersaturation profile.C'est la premikre Ctude complkte sur I'optimisation de la distribution des semences dans un prockdk de cristallisation. Pour un cristalliseur discontinu, une formulation de programmation dynamique optimise une propriktk des cristaux du produit en fonction du profil de sursaturation et des caractkristiques des semences, B savoir la taille moyenne des cristaux de semences, la masse des semences et la largeur de la distribution des semences. Trois objectifs d'optimisation sont considkrks : ( I ) le poids moyen, ( 2 ) le coefficient de variation et (3) le rapport entre la masse de cristaux nuclkCdgerminks et la masse de cristaux de semences. Diffkrents objectifs conduisent B des distributions de semences optimales substantiellement diffkrentes. On montre que I'otpimisation de la distribution de semences peut avoir un effet plus important sur la distribution de taille des cristaux de produit que I'optimisation en fonction du profil de sursaturation.Keywords: crystallization, optimal control, dynamic programming, batch control rystallization from solution is an industrially important C unit operation due to its ability to provide high purity separations. The crystal size distribution (CSD) is a critically important factor in the production of high quality products and for determining the efficiency of downstream operations, such as filtration and washing. Batch crystallizers are heavily used in industry, and a large proportion of these crystallizers are seeded. While it is well-known that the optimal supersaturation profile and the seed characteristics have a strong influence on the crystal size distribution in batch crystallizers (Chianese et al., 1984; Bohlin & Rasmuson, 1992; Rawlings et al., 1993), optimal control studies have only optimized over the supersaturation profile (Ajinkya & Ray, 1974; Chang & Epstein, 1982;Jones, 1974; Jones & Mullin,, 1974; Morari, 1980; Miller & Rawlings, 1994; Mullin & N'yvlt, 1971).This study is the first comprehensive investigation of the effect of the seed distribution on the final CSD properties for a crystallization process. The model equations are based on the moment equations. The seed distribution is parameterized in terms of its width, the mean size, and the seed mass. A dynamic programming f...

A new framework and a simpler method for the development of batch crystallization recipes

“…Several authors have published reports that optimizing seed properties can improve the outcome dramatically and may be more important than optimizing the supersaturation trajectory. [7][8][9] However, these results are reported for specific case study systems and it is not clear to what extent they are valid in the general case.…”

Optimal seed recipe design for crystal size distribution control for batch cooling crystallisation processes

“…The prediction and estimation of the shape of the distribution at the end of the batch can provide useful information for monitoring or designing the operating curve for the supersaturation controller. Model-based approaches can be used for better predictive control (Chung et al, 1999;Fujiwara et al, 2005;Larsen et al, 2006;Rawlings et al, 1993;Ward et al, 2006;Worlitschek and Mazzotti, 2004;Zhang andRohani, 2003, Grosso et al, 2009) but also for product design by reverse engineering the process to achieve the desired CSD (Hounslow and Reynolds, 2006). Although these approaches have been proved to produce high quality crystals, in the vast majority of cases they do not take into account the characteristics of the seed.…”

“…In seeded crystallisation, ideally the supersaturation is maintained at the desired constant value throughout the entire batch by the application of properly designed control algorithms (Chung et al, 1999;Nagy and Braatz, 2003;Xie et al, 2001;Zhang and Rohani, 2003;Simon et al, 2009a). Supersaturation, generated by cooling, can be consumed by the growth of seeds added, and hence, it can be kept relatively low throughout the batch if enough seeds are loaded.…”

“…Although it is recognized that the most important manipulated variables for the optimisation of crystallisation processes are supersaturation trajectories as well as the seed characteristics (Bohlin and Rasmuson, 1996;Heffels and Kind, 1999;Kalbasenka et al, 2007;Ruf et al, 2000, Yannick et al, 2009, the number of approaches focusing on temperature or anti-solvent addition trajectory optimisations is disproportionally higher than contributions considering seed recipe optimisations. The approaches proposed so far, mainly consider the optimisation of the width and amount of a particular monomodal seed distribution (Chung et al, 1999;Kalbasenka et al, 2007).…”

Stereo imaging camera model for 3D shape reconstruction of complex crystals and estimation of facet growth kinetics

“…Next, the solution was cooled down to 28 o C at a slow cooling rate of 0.05 o C/min. At the temperature of 28 o C, 0.6 g of seeds (2% of the solute (Chung et al, 1999;Kubota et al, 2001)) were added to the supersaturated solution. After that, the solution was cooled down at a cooling rate of 0.05 o C/min for one hour.…”