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...

Many of the crystals in the pharmaceuticals, photographic, and other industries are multidimensional; that is, their growth is associated with the change of multiple internal coordinates. The main governing equation for such systems is a highly nonlinear multidimensional population balance equation that must be solved for a wide range of length scales. For population balance equations, it is well-known that the standard first-order schemes give diffusive solutions while the commonly used second-order schemes give spurious oscillations. This paper presents a highresolution simulation algorithm that provides short computation times and high accuracy. The high-resolution algorithm is compared to the upwind difference and Lax-Wendroff methods through simulations of potassium dihydrogen phosphate (KDP, KH 2 PO 4 ) crystal nucleation and growth. No spurious oscillations or numerical diffusion occurred, in contrast to the upwind method and Lax-Wendroff methods. The numerical stability of the algorithm is assessed using the Courant-Friedrichs-Lewy condition.

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Advances in sensor technology and increased competition in the pharmaceutical industry have generated significant interest in the identification of models for the solution formation of crystals with multiple characteristic dimensions. A procedure is proposed that uses a small number of batch experiments to identify the kinetic parameters for multidimensional crystallization processes. The parameters are estimated simultaneously from the on-line measurement of infrared spectra and from cross-moments of the crystal size distribution. The identification procedure maximizes the informativeness of the data produced by each experiment, produces an estimate of the accuracy of the kinetic parameters, and allows the consideration of competing hypotheses for characterizing the crystallization kinetics. The parameter identification strategy is applied to the batch crystallization of potassium dihydrogen phosphate, which forms two-dimensional crystal from solution. To the best of the author's knowledge, this is the first time that the kinetic parameters for a multidimensional crystallization process are identified from a small number of batch experiments.

Copper electrodeposition in submicron trenches