Streamlining crystallization process scale-up using statistical modeling of experiments and complementary CFD flow fields

Abstract

Our paper presents a simple method that bridges computational fluid dynamics (CFD) simulations with systematic experimentation using multivariable statistics, which was developed in the spirit of rapid applicability, quick transferability, and practical simplicity in the process development and scale-up stage. This applies to technologies that have already been developed on a small scale, and it applies when the focal point of scale-up is the stirring conditions, rather than heat transfer or other issues. We propose identifying the predictive CFD variables on the measured CQAs and then training a predictive model that allows us to estimate the CQAs from the simulated flow fields in a technology transfer. The case study of cooling crystallization of L-glutamic acid demonstrates the workflow. Small-scale experiments (0.5 L) are performed with varied active volume and agitation rates, and the particle size distributions (PSD) of the products are measured. The corresponding quasi-steady-state CFD simulations were executed to obtain the flow field using the $k-\varepsilon$ turbulence model. A partial least squares (PLS)–based recursive feature selection identified the predictive mixing parameters from the plethora of available CFD variables and simultaneously built a predictive model for the product CQA-s. Five critical CFD variables were identified in this case study, all related to the shear-rate distributions. The calibrated optimal PLS model had two components, and allowed the prediction of the mean sizes of the product, that is, $D_{v10}$, $D_{v50}$, and $D_{v90}$ on a 5 L scale with 0.2, 16.4, and $1.2\mu m$ deviation from the measured values. This data-driven method simplifies and accelerates the CFD-based scale-up under certain conditions (moderate nonlinearities, flow-centric problem) but does not aim to replace the meticulously identified nonlinear first-principles models.