Modeling and analysis of MSMPR cascades involving nucleation, growth and agglomeration mechanisms with slurry recycling

•MSMPR crystallizer cascade is modelled with detailed agglomeration description.•The product agglomeration degree is inversely proportional with the mean size.•Recirculation (roughly) halved the start-up time under optimal conditions.•Recirculation improves the rise time but leads to more complex dynamics. The batch-production dominated pharmaceutical industries started to evaluate various continuous production platforms recently. With this wave, transitions from batch to continuous crystallization and continuous crystallization design became research topics of interest in the pharma industry. Mixed suspension mixed product removal (MSMPR) crystallizers are intensively investigated due to their relatively simple operation procedure and available experience from other industries. This paper aims to provide a comprehensive population balance model based evaluation of MSMPR cascades with slurry recirculation. Beyond secondary nucleation and crystal growth, a multi-level agglomeration mechanism governing the agglomeration of particles at different turbulence length scales is employed. The dynamic model-equations are transformed and solved using the quadrature method of moments, which paves the way for numerical experimentation and optimal design. An important aim of this paper is to analyze the effects of slurry recycling on system start-up, attainable particle property domains as well as the robustness of the system with respect to kinetic parameter uncertainties and operating condition disturbances. It is shown that the mean product size is generally inversely proportional with the agglomeration degree in a broad operating condition domain for 2,3 and 4-stage MSMPR cascades. The boundaries of the attainable property space are determined numerically by solving appropriate optimization problems. The results suggest that recirculation shrinks the attainable particle size region. The quantification of effects of kinetic parameter uncertainties is approached probabilistically, indicating that the recirculation strategy has weak effects on the robustness in steady-state and transient, too. Finally, simple start-up strategies are compared with the optimal start-up, which revealed that optimization may bring over two-fold start-up time improvement in recirculation enabled systems. However, recirculation results in more complex dynamics, requiring more sophisticated control strategies.