Crystal shape and size control using a plug flow crystallization configuration

Abstract

This work focuses on modeling and control of a continuous plug flow crystallizer (PFC) used to produce tetragonal hen-egg-white (HEW) lysozyme crystals and proposes an optimization-based control scheme to produce crystals with desired size and shape distributions in the presence of disturbances. Initially, a kinetic Monte Carlo (kMC) model is developed to simulate the crystal growth in a seeded PFC, which consists of five distinct segments. The crystal growth rate equations taken from (Durbin and Feher, 1986) are used in the kMC simulations for the modeling of the crystal growth in the direction of (110) and (101) faces. Then, a population balance equation (PBE) is presented to describe the spatio-temporal evolution of the crystal volume distribution of the entire crystal population, and the method of moments is applied to derive a reduced-order moment model. Along with the mass and energy balance equations, the leading moments that describe the dominant dynamic behavior of the crystal volume distribution are used in the optimization-based controller to compute optimal jacket temperatures for each segment of the PFC and the optimal superficial velocity, in order to minimize the squared deviation of the average crystal size and shape from the set-points throughout the PFC. Furthermore, a feed-forward control (FFC) strategy is proposed to deal with feed flow disturbances that occur during the operation of the PFC. Using the proposed optimization and control schemes, crystals with desired size and shape distributions are produced in the presence of significant disturbances in the inflow solute concentration and size distribution of seed crystals.