Physics-informed neural networks (PINNs) have emerged as a promising alternative to purely data-driven neural networks (NNs) for surrogate modeling, particularly in data-scarce scenarios. This study evaluates the performance of hybrid-PINNs against traditional NNs for modeling the adsorption step of a Direct Air Capture (DAC) process. As the complexity of the modeled system increases, larger datasets and longer computational times are required for numerical methods. Therefore, the study aims to develop approaches that minimize data requirements while maintaining accuracy, which is crucial for efficient modeling of complex physical systems. While both AI models can achieve high accuracy with abundant data, the advantages of hybrid-PINNs become more evident as data becomes scarce. In the intermediate and low-data regimes, the physics constraints embedded in hybrid-PINNs significantly improve generalization and predictive accuracy. For extreme low-data conditions, a curriculum learning strategy is implemented, progressively enforcing physics constraints to mitigate underfitting and enhance model stability. Despite these benefits, hybrid-PINNs exhibit a computational cost approximately one order of magnitude higher than traditional NNs as enforcing physics constraints increases training complexity. The results suggest that PINNs hold potential for modeling complex multi-physics problems in DAC and beyond, provided challenges related to gradient balancing and computational efficiency are addressed.

Geothermal installations often face operational challenges related to scaling which can lead to loss in production, downtime, and an increase in operational costs. To accurately assess and minimize the risks associated with scaling, it is crucial to understand the interplay between geothermal brine composition, operating conditions, and pipe materials. The accuracy of scaling predictive models can be impacted by uncertainties in the brine composition, stemming from sub-optimal sampling of geothermal fluid, inhibitor addition, or measurement imprecision. These uncertainties can be further increased for fluid at extreme conditions especially high salinity and temperature. This paper describes a comprehensive method to determine operational control strategies to minimize the scaling considering brine composition uncertainties. The proposed modelling framework to demonstrate the optimization under uncertainty workflow consists of a multiphase flow solver coupled with a geochemistry model and an uncertainty quantification workflow to locally estimate the probability of precipitation potential, including its impact on the hydraulic efficiency of the geothermal plant by increasing the roughness and/or decreasing the diameter of the casings and pipelines. For plant operation optimization, a robust control problem is formulated with scenarios which are generated based on uncertainties in brine composition using an exhaustive search method. The modelling and optimization workflow was demonstrated in a geothermal case study dealing with barite and celestite scaling in a heat exchanger. The results showed the additional insights in the potential impact of brine composition uncertainties (aleatoric uncertainties) in scaling potential and precipitation location. Comparing the outcome of optimization problem for the deterministic and fluid composition uncertainties, a change of up to 2.5% in the temperature control settings was observed to achieve the optimal coefficient of performance.

Physics-Informed Neural Networks (PINNs) have emerged as a promising alternative to purely data-driven neural networks (NNs) for surrogate modeling, particularly in data-scarce scenarios. This study evaluates the performance of hybrid-PINNs against traditional NNs for modeling the adsorption step of a Direct Air Capture (DAC) process. As the complexity of the modeled system increases, larger datasets and longer computational times are required for numerical methods. Therefore, the study aims to develop approaches that minimize data requirements while maintaining accuracy, which is crucial for efficient modeling of complex physical systems. While both AI models can achieve high accuracy with abundant data, the advantages of hybrid-PINNs become more evident as data becomes scarce. In the intermediate and low-data regimes, the physics constraints embedded in hybrid-PINNs significantly improves generalization and predictive accuracy. For extreme low-data conditions, a curriculum learning strategy is implemented, progressively enforcing physics constraints to mitigate underfitting and enhance model stability. Despite these benefits, hybrid-PINNs exhibit a computational cost approximately one order of magnitude higher than traditional NNs, as enforcing physics constraints increases training complexity. The results suggest that PINNs hold potential for modeling complex multi-physics problems in DAC and beyond, provided challenges related to gradient balancing and computational efficiency are addressed.

The prediction of the gas production from mature gas wells, due to their complex end-of-life behavior, is challenging and crucial for operational decision making. In this paper, we apply a modified deep LSTM model for prediction of the gas flow rates in mature gas wells, including the uncertainties in input parameters. Additionally, due to changes in the system in time and in order to increase the accuracy and robustness of the prediction, the Ensemble Kalman Filter (EnKF) is used to update the flow rate predictions based on new observations. The developed approach was tested on the data from two mature gas production wells in which their production is highly dynamic and suffering from salt deposition. The results show that the flow predictions using the EnKF updated model leads to better Jeffreys' J-divergences than the predictions without the EnKF model updating scheme.