Song Zhai

Mehmet Velioglu, Song Zhai, Alexander Mitsos et al.

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.

Mehmet Velioglu, Song Zhai, Sophia Rupprecht et al.

In chemical engineering, process data are expensive to acquire, and complex phenomena are difficult to fully model. We explore the use of physics-informed neural networks (PINNs) for modeling dynamic processes with incomplete mechanistic semi-explicit differential-algebraic equation systems and scarce process data. In particular, we focus on estimating states for which neither direct observational data nor constitutive equations are available. We propose an easy-to-apply heuristic to assess whether estimation of such states may be possible. As numerical examples, we consider a continuously stirred tank reactor and a liquid-liquid separator. We find that PINNs can infer immeasurable states with reasonable accuracy, even if respective constitutive equations are unknown. We thus show that PINNs 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.