Optimizing Crystal Size Distribution Based on Different Cooling Strategies in Batch Crystallization Process

The temperature profile is a critical parameter in industrial batch cooling crystallization processes which directly impacts the crystal size distribution (CSD) and subsequent down streaming operations. Conventional cooling approaches, including natural and linear cooling, often fail to achieve optimal results. Linear cooling may trigger excessive primary nucleation by crossing metastable limits, while natural cooling leads to inconsistent nucleation and growth, resulting in smaller and non-uniform crystals. Hence, optimized cooling profiles are used to achieve the desired target CSD. This study employs reinforcement learning (RL) to optimize the temperature profile for batch cooling crystallization for two systems: paracetamol in water and potassium dihydrogen phosphate (KDP) in aqueous solution. RL dynamically adjusts the cooling trajectory by iteratively interacting with a process model, aiming to maximize mean crystal size while minimizing the coefficient of variation. A comprehensive mathematical model incorporating population balance equations, mass balance, and energy balance is developed to simulate the crystallization process. For the paracetamol system, the RL-optimization strategy resulted in a 107.5 % increase in mean crystal size compared to the natural cooling profile. In the case of the KDP system, a 12 % increase in mean crystal length is achieved relative to a linear cooling profile, along with a significant reduction in the coefficient of variation, indicating improved crystal size uniformity. The optimization results obtained using RL are also compared with that from a genetic algorithm for both cases, and RL demonstrated superior performance. This work underscores the potential of RL in advancing broader applications in chemical process optimization.

Solubility phase diagram which consists of information on solute concentration, metastable and saturation limits against temperature, provides helpful insights in designing crystallization process to achieve desired crystal size distribution (CSD). Usually, the design of cooling crystallization process involves high supersaturation level at the beginning of the process in the metastable zone that is bounded by metastable and saturation limits. However, this high level of supersaturation causes an increment in both nucleation and crystal growth rates which induce the growth of the seed crystals as well as unwanted secondary nucleation that produce excessive fine crystals. Mitigation by employing proper temperature trajectory or policy along metastable zone to avoid unnecessary long operational time and fine crystals is needed. Thus, the purpose of this paper is to develop and simulate mathematical model of seeded batch crystallization process for the case of potash alum which is mainly used for purification in water treatment. Dynamic response of such process under open-loop operation for three cooling policies which are natural, linear and cubic is performed for evaluating the effect of different cooling policies on CSD. Simulation results based on the dynamic behaviour for all three cooling policies show cubic cooling policy obtained the best performance by achieving mean crystal size of 420 µm from the targeted CSD at 430 µm, and the mean crystal size for fine crystals is the lowest which is 35 µm compared to linear and natural cooling policies, at 40 µm and 55 µm, respectively. This information is prominent in deciding proper temperature trajectory of optimal cooling policy for potash alum crystallization process.

Experimental implementation of a Quality-by-Control (QbC) framework using a mechanistic PBM-based nonlinear model predictive control involving chord length distribution measurement for the batch cooling crystallization of l-ascorbic acid

The ideal requirements for highly efficient evaporative crystallization in batch or semi-batch type operations are a high crystal growth rate, a high density of suspended crystalline particles in a slurry and a sharp crystal size distribution. On the other hand, the initial seed crystal conditions are also very important because they affect the crystal size and distribution during the entire period of operation. In the present study, the influence of seeding conditions (average diameter and mass) and heating rate on both the crystal growth rate of sodium chloride (NaCl) and the crystal size distribution were investigated in an optimal design draft-tube stirred vessel containing high suspension density slurries of sodium chloride particles up to 30 vol%. In order to determine the optimal seeding conditions to simultaneously achieve a high crystal growth rate and narrow size distribution, an optimal operation index Iop has been defined based on a comparison of the experimental data and a model calculation with the assumption of ideal crystal growth. The results show that Iop correlate with the particle number of seed crystals and have a maximum value. With Iop correlation, the appropriate seeding conditions for achieving a high crystal growth rate and sharp size distribution have been determined.

New perspectives for the on-line monitoring of pharmaceutical crystallization processes using in situ infrared spectroscopy

Study of batch maltitol (4- O-α- d-glucopyranosyl- d-glucitol) crystallization by cooling and water evaporation

Characterization of tectono-metamorphic events using crystal size distribution (CSD) diagrams. A case study from the Acebuches metabasites (SW Spain)

On-line dynamic optimization integrated with generic model control of a batch crystallizer

Kinetic parameter estimation for most batch crystallization processes is necessary because nucleation and crystal growth kinetic parameters are often not available. The existing identification methods are generally based on simplified population balance models such as moment equations, which contain insufficient information on the crystal size distribution (CSD). To deal with these problems, a new optimization‐based identification approach for general batch cooling seeded crystallization is proposed in this study. The final‐time CSD is directly used for identification. A novel effective method for solving the population balance equation is developed and used to identify nucleation and growth kinetic parameters. Cooling crystallization of ammonium sulfate in water was experimentally investigated, where the concentration was measured by an on‐line density meter and the final‐time CSD was analyzed by a Malvern Mastersizer 2000. Kinetics for ammonium sulfate are determined based on cooling crystallization experiments. Applying these kinetics in simulation provides a good prediction of the product CSD. © 2004 American Institute of Chemical Engineers AIChE J, 50: 1786–1794, 2004

In this paper, a data-driven modeling and optimization method is proposed for batch operation of the cooling crystallization process based on the design of experiments (DoE) in the operation ranges of cooling rate and initial solution supersaturation. The proposed model reflecting a mapping relationship between the manipulated variables of operating conditions and the product crystal size distribution (CSD) is established by two classes of basis functions, one is the wavelet basis function for reshaping the CSD and the other is the polynomial basis function for weighting the chosen wavelet basis functions to reflect the nonlinear relationship between the manipulated variables and the size distribution of product crystals. Meanwhile, a fractional factorial design of DoE is presented to reduce the number of experiments for the above modeling, in comparison with the classical full factorial design. The optimal operating conditions are designed by introducing a comprehensive objective function that combines the information entropy of the product CSD and the ratio of desired product yield with respect to the target crystal size. A particle swarm optimization algorithm with guaranteed convergence is given to solve the nonconvex optimization problem based on the established CSD prediction model. Simulation studies and experiments on the batch seeded β-form L-glutamic acid (LGA) crystallization process are conducted to demonstrate the effectiveness and advantage of the proposed method.

Continuous processing gains importance in the fine chemical and pharmaceutical industries where crystallization is an important downstream operation. Seeded cooling crystallization of the l-alanine/water system was investigated under similar conditions, i.e., temperature interval, cooling rate, and seed material, both in a stirred batch vessel and in a continuous plug flow crystallizer in the coiled flow inverter (CFI) design with horizontal helical tube coils (ID = 4 mm) and frequent 90° bends of the coils. Short-cut calculations based on characteristic time scales and the Damköhler number allow for comparing the batch and continuous crystallization processes. The experimental results reveal crystal growth and growth rate dispersion to be dominating on the product crystal size distribution (CSD). However, at low flow rates of approximately 31 g min–1, a moving sediment flow of the slurry was present in the CFI crystallizer, resulting in further size dispersion effects. Elevated flow rates of approximately 40 g min–1 resulted in a more homogeneous suspension flow and a product CSD comparable to batch quality. Simulation studies based on a population balance equation model strengthen the hypothesis of the solid phase residence time distribution (RTDS) to be more spread in the moving sediment flow regime, leading to a wider product CSD.

Characterization of the anti-solvent batch, plug flow and MSMPR crystallization of benzoic acid

Managing a crystallization process adequately, it is possible to obtain a crystalline product having the desired crystal size distribution. Recommendations for selecting crystallization parameters that are needed to achieve this goal are given basing of a theoretical analysis in which special attention is paid to the growth of crystals from solutions with a preset concentration. Mathematical equations which enable calculation of the theoretical yield for the crystallization process have been elaborated. New formula giving the crystal nuclei number per unit volume as a function of both supersaturation and nucleation time has been devised based on the logistic kinetics of crystal nucleation proceeding under constant supersaturation. The quantitative relation between number density and mean size of crystals growing in batch crystallization is calculated. The calculation shows that the mean size of crystals reached at any time of their growth is inversely proportional to root third of the crystal number density.

The textures of plagioclase crystals within large olivine oikocrysts preserve the sequence of the formation of anorthosite. Such textures have been quantified in a troctolite‐anorthosite from the Proterozoic Lac-St-Jean anorthosite complex, Canada. Crystal size distributions (CSDs) indicate that initially plagioclase nucleated and grew in an INTRODUCTION environment of linearly increasing undercooling, producing a straight- The textures of plutonic rocks are one of their most line CSD. During this phase, latent heat of crystallization was striking aspects, but they have been little used to elucidate largely removed by circulation of magma through the porous crystal petrological processes as compared with chemical and mush. By about 25% solidification the crystallinity was such that isotopic methods. Where used, discussion has tended it reduced, but did not eliminate, the circulation of magma, resulting to be qualitative, in contrast to quantitative chemical in the retention of more latent heat within the crystal pile. The methods, hence reducing the weight of this approach. temperature rose until it was buVered by the solution of plagioclase Indeed, it is not possible to verify physical models if close to the liquidus temperature of plagioclase. Nucleation of quantitative data are not available. Quantitative textural plagioclase was inhibited and conditions were suitable for textural studies of volcanic rocks are becoming more common coarsening of both plagioclase and olivine to occur (Ostwald and these methods are applied here to the development ripening). In this process small crystals were resorbed, whereas of anorthosite. larger crystals grew from both material recycled by the resorption of Quantitative textural studies of plutonic rocks really crystals smaller than the critical size and new material brought in started with Jackson’s studies of the Stillwater complex by the circulating magmatic fluid. The results of this process resemble in 1961 ( Jackson, 1961). He measured crystal size disthose of high-temperature metasomatism but there is no necessity for tributions, but did not record the area that he measured, a magmatic fluid with a diVerent composition. The shapes of the hence his data cannot be completely compared with plagioclase CSDs fit better the communicating neighbours equation of modern data. His pioneering work was not really followed textural coarsening, rather than the classic Lifshitz‐Slyozov‐Wagner up, and since then most studies have looked only at equation, as do other examples drawn from the literature. If olivine ‘average’ or ‘typical’ crystal sizes. These data are much started to nucleate at a higher temperature than plagioclase, then less revealing of petrological processes than crystal size during the textural coarsening phase olivine would have been more distributions, partly because they only give one parameter undercooled than plagioclase, and would have had a higher maximum for each sample. The few existing studies of crystal size growth rate. In these conditions olivine would coarsen more rapidly distributions in plutonic rocks have not treated than plagioclase and engulf it. Hence the order of crystallization plagioclase. determined from the textures would be the reverse of the order of One problem especially pertinent to quantitative texfirst nucleation of the two phases, from equilibrium phase diagrams. tural studies is the way that many igneous petrologists Maintenance of the temperature near the plagioclase liquidus may look at rocks: they commonly try to reconstruct how a rock has formed by examining the final, fully crystallized also inhibit the nucleation and growth of other phases.

Comparative evaluations of bulk seeded protein crystallization in batch versus continuous slug flow crystallizers