Steady-State Two-Phase Flow Modeling Using Physics-Informed Neural Networks

This work presents a Physics-Informed Neural Network (PINN) framework for steady-state modeling of two-phase flow in pipelines, addressing the strong nonlinear coupling of mass, momentum, and energy conservation equations. The proposed PINN is trained directly from these governing equations, without requiring experimental data. The network outputs pressure and temperature profiles, from which thermophysical properties are obtained using PVT tables. This formulation enables the construction of a physics-governed loss function that enforces the conservation laws throughout the spatial domain. Validation against a marching-method reference demonstrates excellent agreement in pressure, temperature, gas holdup, and solution gas ratio profiles for different fluid compositions. The model accurately captures the pressure losses dominated by hydrostatic effects and the thermal cooling caused by heat exchange along the water column and with the seabed—conditions typical of subsea flowlines and risers. The framework also supports inverse analysis, enabling real-time monitoring, virtual sensing, and flow optimization.