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

Abstract

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.

Mathematical Modeling, Design, and Optimization of a Multisegment Multiaddition Plug-Flow Crystallizer for Antisolvent Crystallizations

“…(8) and (9). In such a way, less-expensive function evaluations are possible for the optimization algorithms 24 . Identical results were obtained with MOM and FVM when a suitably fine level of discretization was employed 29,30 .…”

“…to observe the Pareto front among several key performance indices, such as the volume-based mean crystal size, coefficient of variation (CV), yield, or the ratio of seeded crystals over nucleated crystals 24,31,32 . In the current application, the residence time distribution is narrow in a plug-flow crystallizer and should not contribute to a broadening of the CSD through back-mixing effects.…”

“…Vetter et al 23 recently investigated the attainable regions of particle sizes for a single-stage ideal plug-flow crystallizer, which assumed continuous addition of anti-solvent along the tube; they compared the achievable product qualities to those manufactured in MSMPR and batch crystallizers. Ridder et al 24 proposed a simultaneous design and control (SDC) approach to optimize the number of segments and anti-solvent distributions along a MSMA-PFC for an anti-solvent crystallization processes. More specifically, recent studies by Kwon et al 25 also focused on the multi-segment plug-flow crystallizer to control the crystal shape and size distribution by optimizing jacket temperature for each segment.…”

“…This is an important consideration for the design of a continuous manufacturing process 26 . For example, 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 8 varying lengths of tube and longer mean residence times can be obtained by assembling a greater number of PFC segments and the distribution of anti-solvent additions along the segments can be optimized to create different supersaturation profiles along the tube 24 , as indicated schematically in Figure 1.…”

“…Dynamic and steady-state mathematical models of a general plug-flow crystallizer are presented, followed by their extensions to a multi-segment multi-addition design for anti-solvent crystallization. Unlike the equally-spaced anti-solvent addition proposed by Ridder et al 24 , the configuration studied here allows for optimization of 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9…”