Physics-informed neural networks for modeling two-phase steady state flow with capillary heterogeneity at varying flow conditions

Multi-phase flow simulations in heterogeneous porous media are essential in many applications, for example, CO₂ sequestration, enhanced oil and gas recovery, groundwater contaminant treatment, soil aeration, and energy security. Modeling such complex systems is significantly changeling considering flow with capillary heterogeneity (hydraulic discontinuities). Traditional modeling methods have several limitations, particularly the requirement for separate two-phase flow simulations for each change of a parameter. Physics-informed neural networks (PINNs) allows the integration of physical constraints in the training process of Deep Neural Networks (DNNs). In this work, we utilized the PINNs approach to simulate 1D, steady-state, two-phase flow with capillary heterogeneity. The PINNs system was trained with high variability in the input parameters, including boundary conditions, phase flow rates, permeability values, and the hydraulic state equations. A single DNN was trained to produce saturation and capillary pressure profiles for a homogeneous core slice. The trained DNN was utilized to construct different heterogeneous structures. Numerical simulations and data from coreflooding experiments of two-phase flow were used to examine the accuracy of the suggested approach. Results showed high accuracy of the trained PINNs system predictions, with deviations from the numerical solutions of less than 3%, and less than 1% with the experimental data. A single training of the PINNs system was required and provided many solutions for different permeability structures, phase flow rates, hydraulic parameters, and boundary conditions in less than 1 s.