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

2026-01-26

AI Summary

This study addresses the challenge of economically and accurately estimating the phase interface height in liquid–liquid gravity separation, a critical yet difficult-to-measure variable that hinders process monitoring and safety. The authors propose a two-stage training strategy for a physics-informed neural network (PINN) that incorporates only the volume conservation equation, thereby avoiding complex submodels. The approach first pretrains the PINN using synthetic data generated from a low-fidelity mechanistic model and then fine-tunes it with sparse experimental measurements, enabling high-accuracy interface height estimation from inlet flow rates alone. Furthermore, this work presents the first integration of a differentiable PINN into an extended Kalman filter–like framework, facilitating real-time state tracking and uncertainty quantification. Experimental results demonstrate that the method significantly outperforms purely data-driven models and non-pretrained PINNs in both forward simulation and filtering tasks, achieving state-of-the-art accuracy in phase interface height estimation.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• dense-packed zone height
• liquid-liquid separation
• phase height estimation
• gravity settlers
• flow-rate measurements

Innovation

• Physics-Informed Neural Network
• Liquid-Liquid Separation
• Dense-Packed Zone Height
• Extended Kalman Filter
• Two-Stage Training