Physics-Informed Neural Networks for Energy-Based Modeling of Non-Newtonian Fluid Flow and Fracture Propagation in Subsurface Formations

This study presents a Physics-Informed Neural Network (PINN) approach for modeling the energy balance of non-Newtonian fluid flow and fracture propagation in hydraulic fracturing. Conventional solvers, such as finite difference and finite element methods, often require extensive mesh refinement, struggle with steep viscosity gradients, and face limitations when coupled thermo-hydro-mechanical processes. To address these issues, a synthetic dataset of 3000 samples was generated, with 1000 cases each for 1D, 2D, and 3D fracture domains. The dataset included fracture geometry, pressure (1-50 MPa), shear rate (1 to 1000 s-1), and viscosity (0.003-0.1 Pa·s), enabling the PINN to incorporate the governing laws of mass, momentum, energy, and damage evolution directly into its training. Advanced strategies, such as adaptive sampling and staged training, were applied to capture shear-dependent viscosity and strong gradients near fracture tips. The PINN achieved significantly higher accuracy than the finite difference method (FDM) across all domains. In 1D, the tip error reduction was about 90%, whereas in 2D, reductions were above 85%. In 3D, reductions were around 85%. The approach produced smooth fracture profiles, maintained thermodynamic consistency, and remained stable under Gaussian noise up to 15%, reflecting robustness under field uncertainty. Scalability tests showed a 76.5% reduction in runtime and a 53.1% reduction in memory use in 3D domains, confirming efficiency at larger scales. This study advances PINN-based energy formulations for hydraulic fracturing in ways not addressed by previous works by embedding shear-rate-dependent viscosity into the loss function, providing a mesh-free and efficient tool with potential extensions to proppant transport and multiphase flow.