Internal Fines Removal Using Population Balance Model Based Control of Crystal Size Distribution under Dissolution, Growth and Nucleation Mechanisms

Abstract

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.

Ultrasonic crystallization monitoring technique for simultaneous in-line measurement of liquid and solid phase

“…The counts, however, indicate the increase in the particle number during the crystallization, which is caused by the abrasion of crystals [37]. As shown in Fig Fig.…”

“…Generally, the data obtained by the laser backscattering technique scatters more as can be seen e.g. in [16,37]. The fluctuation of the data result, on the one hand, from the multi-scattering of the detected particles.…”

“…Therefore, it is only possible to point out that the in-line measured crystal size increases and both techniques are able to detect these changes caused by the temperature profile. The course of the crystal sizes, however, scatters much more in case of 3D ORM, which is a known topic [16,37]. In Table 2 the calculated results for j and d 50 are also listed.…”

Advanced control approaches for combined cooling/antisolvent crystallization in continuous mixed suspension mixed product removal cascade crystallizers

“…D G and D B are dissolution rates. When S o 1, the negative values of nucleation rate and growth rate are used to approximate dissolution rates (Qamar et al, 2010;Nagy et al, 2011). k G1 , k G2 , k G3 , k B1 , k B2 , k B3 are empirical parameters from literature (Lindenberg et al, 2009).…”

Application of Model Predictive Control to a Continuous Multiple‐Effect Crystallizer

“…Many efforts have been made to develop strategies to control particulate processes. For batch processes, it is common to control parameters such as temperature or pressure trajectory or to add antisolvents to achieve the desired degree of supersaturation during inherent transiency of the process , , , as well as the agitation speed or the rate of fines removal to improve the crystal size . In continuous crystallization, depending on the strategy and the available measuring techniques, the selected controlled variables are usually the operating pressure or temperature, the slurry level, the slurry density or the heat added or removed .…”