Modeling and control of crystal shape in continuous protein crystallization

Abstract

In this work, a continuous crystallization process with a fines trap is modeled in an effort to produce tetragonal hen-egg-white (HEW) lysozyme crystals with a desired shape distribution. The crystal shape of tetragonal lysozyme crystals is defined by the aspect ratio of the crystal heights in the direction of the (110) and (101) faces. A kinetic Monte Carlo (kMC) simulation is used to model the crystal nucleation, growth, and dissolution through a fines trap in a continuous crystallization process. Specifically, the crystal growth processes are simulated through adsorption, desorption, and migration mechanisms, and the crystal growth rates are calibrated through experimental data (Durbin and Feher, 1986). Additionally, a nucleation rate expression is developed based on the results from an experimental work (Galkin and Vekilov, 2001) to simulate the crystals nucleated at different times. Then, the method of moments is used to approximate the dominant behavior of a population balance equation (PBE) describing the evolution of the crystal volume distribution through the three leading moments. The moment model is used, along with solute mass and energy balance equations, to design a model predictive controller (MPC), which allows for the crystallizer to produce crystals with a desired shape distribution. In the proposed MPC, the jacket temperature is manipulated to appropriately suppress the influence of undesired effects such as process disturbances and measurement noise, while handling significant changes in the set-point value. Furthermore, it is demonstrated that a continuous process with a fines trap can produce crystals with a low polydispersity.