Estimating Dense-Packed Zone Height in Liquid-Liquid Separation: A Physics-Informed Neural Network Approach

Separating liquid-liquid dispersions in gravity settlers is critical in chemical, pharmaceutical, and recycling processes. The dense-packed zone height is an important performance and safety indicator but it is often expensive and impractical to measure due to optical limitations. We propose to estimate phase heights using only inexpensive volume flow measurements. To this end, a physics-informed neural network (PINN) is first pretrained on synthetic data and physics equations derived from a low-fidelity (approximate) mechanistic model to reduce the need for extensive experimental data. While the mechanistic model is used to generate synthetic training data, only volume balance equations are used in the PINN, since the integration of submodels describing droplet coalescence and sedimentation into the PINN would be computationally prohibitive. The pretrained PINN is then fine-tuned with scarce experimental data to capture the actual dynamics of the separator. We then employ the differentiable PINN as a predictive model in an Extended Kalman Filter inspired state estimation framework, enabling the phase heights to be tracked and updated from flow-rate measurements. We first test the two-stage trained PINN by forward simulation from a known initial state against the mechanistic model and a non-pretrained PINN. We then evaluate phase height estimation performance with the filter, comparing the two-stage trained PINN with a two-stage trained purely data-driven neural network. All model types are trained and evaluated using ensembles to account for model parameter uncertainty. In all evaluations, the two-stage trained PINN yields the most accurate phase-height estimates.

Physics-Informed Neural Networks for Dynamic Process Operations with Limited Physical Knowledge and Data

In chemical engineering, process data is often expensive to acquire, and complex phenomena are difficult to model rigorously, rendering both entirely data-driven and purely mechanistic modeling approaches impractical. We explore using physics-informed neural networks (PINNs) for modeling dynamic processes governed by differential-algebraic equation systems when process data is scarce and complete mechanistic knowledge is missing. In particular, we focus on estimating states for which neither direct observational data nor constitutive equations are available. For demonstration purposes, we study a continuously stirred tank reactor and a liquid-liquid separator. We find that PINNs can infer unmeasured states with reasonable accuracy, and they generalize better in low-data scenarios than purely data-driven models. We thus show that PINNs, similar to hybrid mechanistic/data-driven models, are capable of modeling processes when relatively few experimental data and only partially known mechanistic descriptions are available, and conclude that they constitute a promising avenue that warrants further investigation.