Fourier-Feature Physics-Informed Neural Networks for Thermo-Hydro-Mechanical Modelling of Oil–Water Flow in Fractured Porous Media
Abstract
Flow in fractured porous reservoirs is coupled to rock deformation and heat transfer through pressure-dependent properties, temperature-dependent viscosity, and fluid exchange between the matrix and fractures. These interactions produce contrasting spatial and temporal scales that can complicate neural approximation of the governing equations. This study investigates a Fourier-feature physics-informed neural network (Fourier-PINN) for thermo-hydro-mechanical (THM) modelling of two-phase oil-water flow in a dual-continuum system. The formulation includes phase mass balances, quasi-static mechanical equilibrium, thermal constitutive relations, stress-sensitive permeability, and pressure-driven and imbibition-related exchange. An established Fourier feature map is combined with a weighted data-and-physics loss to approximate matrix pressure, fracture pressure, oil saturation in each continuum, and temperature. The assessment includes a comparison with a baseline PINN, residual diagnostics, field visualisation, and a parameter study. The reported comparisons show improved agreement with the reference data for matrix pressure, matrix oil saturation, and temperature, with R2 values of 0.923, 0.923, and 0.947, respectively. The reported extrapolation error decreases from 14.7% for the baseline PINN to 4.2% for the Fourier-PINN. Scenario comparisons suggest that fracture permeability and matrix-fracture exchange influence pressure communication and matrix oil mobilisation under the…
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