Chord length distribution based modeling and adaptive model predictive control of batch crystallization processes using high fidelity full population balance models

The control of batch crystallizers is an intensively investigated topic as suitable crystallizer operation can reduce considerably the downstream operation costs and produce crystals of desired properties (size, shape, purity, etc.). Nevertheless, the control of crystallizers is still challenging. In this work the development of a fixed batch time full population balance model based adaptive predictive control system for cooling batch crystallizers is presented. The model equations are solved by the high resolution finite volume algorithm involving fine discretization, which provides a high fidelity, accurate solution. A physically relevant crystal size distribution (CSD) to chord length distribution (CLD) transformation is also developed making possible the direct, real-time application of the focused beam reflectance measurement (FBRM) probe in the control system. The measured CLD and concentration values are processed by the growing horizon estimator (GHE), whose roles are to estimate the unmeasurable system states (CSD) and to readjust the kinetic parameters, providing an adaptive feature for the control system. A repeated sequential optimization algorithm is developed for the nonlinear model predictive control (NMPC) optimization, enabling the reduction of sampling time to the order of minutes for the one-day long batch. According to the simulation results, the strategy is highly robust to parametric plant-model mismatch and significant concentration measurement noise, providing very good control of the desired CLD.