Population Balance Model-Based Multiobjective Optimization of a Multisegment Multiaddition (MSMA) Continuous Plug-Flow Antisolvent Crystallizer

Crystallization is a major separation process in the pharmaceutical industry. Most crystallizations are performed batchwise, but there is great incentive for converting them to continuous operations. This paper investigates the modeling, simulation, and optimization of a special antisolvent plug-flow crystallizer: the multisegmented, multiaddition plug-flow crystallizer (MSMA-PFC). The MSMA-PFC accepts multiple antisolvent flows along its length, permitting finer control of supersaturation. A steady-state population balance equation was applied for tracking the crystal size distribution, and a mass balance equation was used to track the depletion of dissolved solute (flufenamic acid). A multiobjective optimization framework was applied to determine the antisolvent flow rates into each segment that simultaneously maximize the average crystal size, and minimize the coefficient of variation. The set of coupled differential equations was solved, depending on circumstance, with either the method-of-moments (MOM), or the high-resolution finite-volume (FV) method. The significant nonconvexity in the objective functions motivated the use of the nondominated sorting genetic algorithm (NSGA-II) to calculate the Pareto frontiers for the two competing objectives. It was found that the optimal antisolvent profile provides better product crystals, compared to the cases with equal additions of antisolvent in 1-4 injection points by keeping the total amount of antisolvent the same. The sensitivity of the Pareto frontier to variation in the growth and nucleation kinetic parameters was investigated. In addition, a novel simultaneous design and control (SDC) approach was proposed, based on the optimization of the full crystallizer design, over not only antisolvent profile, but also the number of injections and total crystallizer length, providing the best crystallization design that can allow optimal product performance in conjunction with the multiaddition control approach.