(712f) Embedding Data-Driven Classifier Surrogates in Solvent Mixture Design Optimisation Problems

Solvent mixtures are important and widely used in chemical engineering, especially in separation processes, such as extraction, absorption and crystallization.¹ The suitability of a solvent or solvent mixture depends on the specific process of interest and is tightly linked to operating conditions. This makes the design of solvents/solvent mixtures especially challenging. Over the last few decades, the Computer-Aided Mixture/blend Design (CAM^bD) framework has been developed as a systematic methodology for solvent mixture design, for example, the crystallization of active pharmaceutical ingredients.² A recurring feature of solvent mixture design is the need to include constraints that describe phase equilibrium and phase stability, because the performance of the process units is linked to a particular type of phase behaviour, e.g., the presence of a solid phase and a homogeneous liquid phase in a crystallizer. The rigorous modelling of such constraints results in a bilevel optimization problem ³ but even reformulation as a single-level problem a highly nonconvex problem .^4,5 This is compounded by the fact that the mixtures of interest are invariably described by nonlinear thermodynamic equations. There is therefore a need to develop more tractable formulations of the problem to address these numerical challenges.

In this work, we investigate the use of surrogate models to replace the nonlinear thermodynamic constraints with a focus on the reliability and tractability of the resulting optimization problem. We examine two types of machine learning models, support vector machines (SVMs) and artificial neural networks (ANNs), with the aim to train models that are valid over a range of solvent mixtures and thermodynamic conditions. Instead of training regression models, we train classifier models to predict the phase behaviour of the mixtures of interest, specifically the phase stability of the mixture and the solubility of the target product. The surrogate models are trained based on phase equilibrium data generated using the UNIFAC group contribution method.⁶ This provides an alternative framework to define the optimisation problem. Given certain candidate solvents and a target product, the van der Waals surface area, van der Waals volume, composition of the solvent mixture and temperature are selected as the features of the surrogate models. We consider different kernel function formulations of SVMs and activation functions for ANNs. For the phase stability, the Matthews correlation coefficient (MCC) is applied as the metric while for the solubility, the deviation between the true and predicted solubility by fixing composition of certain solvent is used to evaluate the classifier performance.

We apply the proposed approach to two case studies. Given as set of 9 candidate solvents, Case 1 aims to find the optimal binary solvent mixture that yields the highest solubility of ibuprofen at a fixed temperature. Case 2 considers a more challenging cooling / anti-solvent crystallisation process, with variable initial temperature. In Case 1, the results show that the problem can be solved more efficiently with some surrogate models than with the .⁷ Using ANNs, the problem can be solved within 10 seconds, which is much faster than with any other approach tested. Although BARON⁸ can solve the models in case 1 within shorter runtimes, numerical difficulties sometime appears which makes it unreliable. This also happens with the solver GUROBI. ⁹ In Case 2, better (local) solutions are obtained from the surrogate-based models than with the model based on thermodynamic equations with sBB solver.¹⁰ However, this case remains intractable for global solvers within a limited runtime. These results reveal the potential and benefits of implementing machine learning classifier models in the solvent design problem, as an alternative to the standard thermodynamics-based models.

Reference

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