Contemporary research in reactive crystallization processes involves a multitude of phenomena spanning various scales. Notably, supersaturation is generated at the micro-scale due to chemical reactions. This heightened supersaturation level directly triggers primary nucleation and molecular growth (molecular processes) and indirectly leads to irreversible agglomeration (a secondary process). Modelling these phenomena requires assuming a functional form (kernel) and tuning the fitting parameters appropriately (eight in this contribution).

The most prevalent methodology for simplified models involves executing a multivariate optimization routine that identifies the optimal parameter set by comparing model predictions with experimental targets (e.g., characteristic sizes from Number Size Distributions). A randomly chosen initial point (or a swarm of initial points) is subjected to a local minimum search through an optimization method (such as conjugate gradient).

However, a simplified eight-parameter model reveals a plethora of local minima, making the optimization problem highly dependent on the initial candidate and, on the other hand, it becomes practically impossible to perform for 3D models. In this contribution, the authors propose an innovative, quick-responsive procedure that provides a data-driven model for computationally expensive 3D models employing Neural Networks. Initially, a Computational Fluid Dynamics (CFD) - Population Balance Model (PBM) describing the precipitation in a T-mixer (Figure 1) was employed to generate the numerical dataset. Solving partial differential equations, the CFD-PBM model associates parameter sets and operational conditions (e.g., initial concentrations of reactants) with corresponding sizes.

Subsequently, a Deep Learning Neural Network (DLNN) was trained using the dataset above, with the input-output order reversed: sizes and concentrations were given as input, and the parameter set was the output. Experimental sizes at five concentrations were then provided to the trained DLNN, and the predicted mean parameter set was tested with the 3D model. The resulting set successfully reproduced the experimental data to infer parameters and predict diameters in a Y-mixer. Furthermore, uncertainty in parameters was quantified and depicted in Figure 2.

This innovative approach attests to the effectiveness of integrating 3D CFD-PBM models and deep learning techniques to precisely and responsively characterize reactive crystallization processes. It paves the way for a deeper understanding and more optimized design of reactive crystallization processes.