Physics-Informed Model For H2-brine Interfacial Tension Prediction Outside the Development Range: Hydrogen Storage Implications

• PINN models enhance IFT prediction accuracy by integrating PR-EoS and LGT. • Achieved superior validation with R² = 0.91, surpassing traditional ML limitations. • Optimized 54% physics weight improves PINN adherence to physical laws and data fit. • Combines ML and physics, advancing predictive modeling for hydrogen applications. Underground hydrogen storage (UHS) in saline aquifers is increasingly recognized as a strategic option for large-scale energy storage, where the interfacial tension (IFT) between hydrogen (H₂) and brine directly controls capillary entry pressure, residual trapping, injectivity, and long-term containment security. However, accurate IFT prediction under reservoir pressure–temperature–salinity conditions remains challenging because laboratory measurements are costly and difficult to perform for volatile hydrogen systems, while conventional predictive correlations and purely data-driven machine-learning models often lack reliability when extrapolated beyond their calibration ranges. Consequently, a critical gap persists between the engineering need for physically consistent, wide-range IFT prediction and the limited availability of representative experimental datasets. In this study, this gap is addressed by developing a physics-informed predictive framework designed to enhance extrapolation robustness while preserving thermodynamic consistency. A curated database comprising 400 experimental H₂–brine IFT data points was assembled and partitioned into development (training/testing) and independent validation sets, the latter extending beyond the development range to explicitly assess extrapolation capability. A Physics-Informed Neural Network (PINN) was constructed in which the total loss function was formulated as a weighted combination of data mismatch and physics residuals. Unlike conventional black-box regressors, derivative-based physical constraints with respect to pressure, temperature, and salinity were incorporated directly into the loss function via automatic differentiation, thereby enforcing physically meaningful sensitivities during training based on the Peng–Robinson Equation of State (PR-EoS) and Linear Gradient Theory (LGT). Furthermore, selected thermodynamic constants associated with the embedded physics formulation were treated as learnable parameters rather than fixed coefficients, enabling physics-consistent calibration to experimental data while maintaining adherence to governing principles. This dual strategy—physics-residual enforcement and adaptive physical parameters—enabled empirical flexibility without sacrificing mechanistic interpretability. Within the development range, high predictive accuracy was achieved, with R² = 0.98 and corresponding RMSE values of 1.34 mN/m (training) and 2.07 mN/m (testing). More importantly, strong performance was maintained on the out-of-range validation dataset (R² = 0.91, RMSE = 2.30 mN/m), demonstrating stable, physically consistent extrapolation behavior. In contrast, the purely data-driven neural network exhibited significant degradation in validation performance (R² = 0.587, RMSE = 4.544 mN/m), despite comparable in-range accuracy. An optimal balance between physics enforcement and data fitting was observed when the physics contribution represented 54% of the total loss (λ = 1.2), confirming that controlled physics weighting was essential for maximizing generalization. A robust, physically grounded predictive tool is therefore provided for UHS feasibility screening, reservoir-simulation support, and sensitivity analysis. The principal novelty lies in embedding derivative-based physics constraints and treating selected physical constants as learnable parameters within the training process, thereby improving extrapolation reliability relative to conventional data-driven models while preserving engineering interpretability.