(60b) A New Hybrid Approach to Designing of New Multiphase Contactors for the Circular Economy

Today, new low-carbon technologies rely on metals whose extraction poses significant environmental challenges. To integrate these metals into a circular economy, recycling is essential to minimize waste and maximize resource utilization. One effective method for achieving this is through a hydro-metallurgical process, which can be simplified into three main stages: dissolving the various metals, selective separation, and recovery in solid form.

This paper focuses on the selective separation stage, specifically using liquid-liquid extraction. Typically, this stage is conducted in multiphase flow contactors. To apply the principles of a circular economy in the design of liquid-liquid extraction equipment—namely minimizing material and energy losses while maximizing recycling process efficiency—it is crucial to predict the evolution of the exchange surface between the two liquids as a function of the physico-chemical parameters of the fluids.

To achieve this, a coupling between single-phase computational fluid dynamics (CFD) and the population balance equation (PBE) is employed. The CFD determines turbulent kinetic energy dissipation, while the PBE, an integro-differential equation, provides the evolution of drop size distributions (DSDs) within the multiphase flow contactors when solved.

This evolution is governed by the breakup and coalescence phenomena of the dispersed phase. These phenomena determine the DSD, and hence the residence time of the mixture and the efficiency of mass transfer in solvent extraction processes. Numerous kernels, such as those proposed by Coulaloglou and Tavlarides in 1977, describe these breakup and coalescence events. These kernels aim to model the physical processes occurring inside the multiphase flow contactors.

As they are complex functions of the flow and the physico-chemical properties of the fluids, existing models rely on empirical parameters. In this work, these parameters are estimated by inverse methods from experimental DSDs, determined either by in situ image acquisition and processing or by off-line characterization from a laboratory reactor.

However, this approach has limitations. When fluid properties change or when working with a different scale or process conditions, these parameters must be re-identified, which can be challenging. The models obtained are only predictive within a specific range and lose accuracy when the viscosity of the continuous phase increases. Additionally, due to an incomplete understanding of breakup physics, the breakup frequency provided by different models can be inconsistent, as noted by Liao et al., 2009.

To overcome these challenges, a new method based on machine learning, specifically Physically Informed Neural Networks (PINNs) has been developed (Raissi et al., 2019). Unlike traditional neural networks, PINNs integrate knowledge of the physical laws governing the data into the learning process. This integration ensures that their predictions respect the fundamental laws of physics.

PINNs are particularly effective for solving problems described by physical equations. By integrating these equations during learning, PINNs can identify empirical parameters within the equations, resulting in a predictive model. This approach has been successfully applied to find unknown parameters in the PBE (Chen et al., 2021). Using PINNs, it is possible to model complex processes in contactors, such as breakup, and predict their behavior with high accuracy.

The developed network takes the measured DSDs as input and can predict quantities of interest in the kernels, such as the breakage frequency. During training, the network was informed of the PBE structure to ensure it adhered to the physics present in the multiphase contactors.

A comparison of the new approach was made with conventional fundamental modelling with parameter identification (Castellano S et al., 2018). Evaluation was first conducted on numerical data by simulation using breakage vectors with different shapes and intensities of breakage frequencies. In all cases, the PINN successfully retrieved the breakage vectors used to generate the DSDs.

Then, a large number of oil-in-water emulsion experiments were carried out with varying oil viscosities, surface tensions, agitation rate, and volume fractions. For each experiment, the PINN was applied to retrieve the breakage vectors. The results were remarkable; the retrieved breakage vectors aligned well with physical expectations. For instance, as the viscosity of the dispersed phase increased, the breakage frequency decreased, and as the stirring speed increased, the breakage frequency increased. In perspective, the PINN results can be used to develop new physical droplet breakage kernels. Also, a generalization for other daughter size distribution functions would be interesting to investigate.

REFERENCE

Castellano, S., Sheibat-Othman, N., Marchisio, D., Buffo, A., Charton, S., 2018. Description of droplet coalescence and breakup in emulsions through a homogeneous population balance model. Chemical Engineering Journal 354, 1197–1207. https://doi.org/10.1016/j.cej.2018.07.176

Chen, X., Wang, L.G., Meng, F., Luo, Z.-H., 2021. Physics-informed deep learning for modelling particle aggregation and breakage processes. Chem. Eng. J. 426, 131220. https://doi.org/10.1016/j.cej.2021.131220

Coulaloglou, C.A., Tavlarides, L.L., 1977. Description of interaction processes in agitated liquid-liquid dispersions. Chemical Engineering Science 32, 1289–1297. https://doi.org/10.1016/0009-2509(77)85023-9

Raissi, M., Perdikaris, P., Karniadakis, G.E., 2019. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707. https://doi.org/10.1016/j.jcp.2018.10.045

Yixiang Liao, Dirk Lucas, 2009. A literature review of theoretical models for drop and bubble breakup in turbulent dispersions. Chemical Engineering Science, Volume 64, Issue 15, 3389-3406, https://doi.org/10.1016/j.ces.2009.04.026.