Multi-objective optimization of temperature profile using reinforcement learning in batch crystallization process

Crystal size distribution (CSD) is an essential criterion for determining the production of high-quality crystals since it influences the efficiency of the crystallization process. Producing specified CSD in the crystallization process represents a main challenge as it depends on temperature control, which indirectly regulates the solution’s concentration and affects the crystal’s evolution. Different temperature profiles may influence the distribution of crystal products, and a suitable optimization algorithm is required to produce an optimum temperature trajectory that produces the desired CSD. Thus, this study aims to maximize the CSD of the grown seed crystals while minimizing the nucleus-grown crystals by employing the best optimization algorithm for the potash alum crystallization process. The crystallization process was developed and simulated in Matlab software using a potash alum in the water system. Four optimization algorithms were proposed with different objective functions, such as maximizing mean crystal size (I), minimizing coefficient of variation (II), minimizing nucleus-grown crystals (III), and maximizing CSD (IV). Based on the simulation results, optimization IV, which maximizes CSD, performs best with a large mean crystal size of 490 µm. Furthermore, the number of fine crystals was among the lowest at a volume distribution of 0.00071 m3/m compared to the linear profile at 0.00191 m3/m. Optimization IV employs a dissolution strategy, which manipulates two quality specifications in one algorithm (size of crystals and number of fines), which is considered the best optimal cooling profile for seeded batch crystallization by maximizing CSD and minimizing the generation of nucleus-grown crystals.

The development of robust and effective control strategies for crystallization processes is challenging due to the complexity of the underlying phenomena. The main objective is to control crystal mean size, crystal size distribution, purity and crystal shape. A novel trajectory tracking control strategy based on Reinforcement Learning (RL) was developed to control the batch cooling crystallization of paracetamol in water, used here as a case study. More specifically, a model-based reinforcement learning technique was designed to achieve effective tracking of three reference trajectories namely: process temperature, supersaturation and mean particle size to ensure the attainment of the targeted final product quality and dynamic process performance. An off-policy RL method based on a deep deterministic policy gradient (DDPG) algorithm was used. The performance of the RL control was compared and validated against MPC. To address the tracking control problem in the case of noisy measurements and model uncertainties, the RL approach was combined with a Kalman filter. Finally, Transfer Learning (TL) was implemented to investigate optimal and cost-effective training strategies of the RL agent.

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

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

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.

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

Introducing uncertainty analysis of nucleation and crystal growth models in Process Analytical Technology (PAT) system design of crystallization processes

The quality of a crystalline product is defined by its crystal size distribution, purity, morphology, and kind of solid state. It is highly influenced by the nucleation behavior during the crystallization process. A convenient and often used experimental method for determining nucleation behavior is by measuring metastable zone widths (MSZW) in relatively small volumes. However, to what extent these can be related to nucleation behavior on larger (industrial) scales is not known. Two major reasons for this are the lack of experimental data for MSZW measurements on different scales and the incomplete understanding of the complexity of processes determining the MSZW. In order to investigate the relationship between the nucleation behavior for paracetamol in water at the 1 mL and 1 L scales, MSZW measurements were performed. Well controlled MSZW measurements at 1 mL displayed large variations. This implies that at this scale a large number of experiments have to be performed to achieve a statistically sound experimental description of the MSZW. In contrast to the 1 mL experiments, the MSZW measurements performed at 1 L scale showed hardly any variations. The measured MSZW values at the 1 L scale corresponded to the onset of the MSZW distribution at the 1 mL scale, implying a simple scale up rule for laboratory MSZW data to larger scales. Careful in situ observation during several cooling crystallization experiments of paracetamol in water on a 3 mL scale showed the presence of a single crystal preceding the outburst of nuclei. This would imply that initially a single nucleus forms which, after growth to a considerable size, undergoes secondary nucleation. An abundance of fragments originate from this single crystal after secondary nucleation. This observation implies that the crystals produced in an industrial crystallizer originate all from one single crystal and are formed by secondary nucleation. Visualization experiments with other model systems showed that the mechanism is not limited to paracetamol but seems to occur more generally.

Development of a new crystal growth process using a semiconductor powder and reducing the thermal stresses

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

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.

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.

The sizes of crystals on aluminium oxide films formed by exposing commercial aluminium (2S) and two nickel‐ and iron‐containing alloys to pure water at high temperature were determined by measuring and counting crystals on electron micrographs of surface replicas. The mean crystal size was determined for eight different times at five temperatures over the range 150–350°. The increase in crystal size followed a law of the type D = Ain and the values of n found were in the range 0.18–0.26. The size distributions for various times at 300° and for various temperatures after 7 h. of exposure are discussed.