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.