Quantum-Classical Physics-Informed Neural Networks for Solving Reservoir Seepage Equations

In this paper, we adapt the Discrete Variable (DV)-Circuit Quantum-Classical Physics-Informed Neural Network (QCPINN) and apply it for the first time to four typical reservoir seepage models. These include the pressure diffusion equation for heterogeneous single-phase flow, the nonlinear Buckley-Leverett (BL) equation for simplified two-phase waterflooding, the convection-diffusion equation for compositional flow considering adsorption, and the fully coupled pressure-saturation two-phase oil-water seepage equation for heterogeneous reservoirs with exponential permeability distribution. The QCPINN integrates classical preprocessing/postprocessing networks with a DV quantum core, leveraging quantum superposition and entanglement to enhance high-dimensional feature mapping while embedding physical constraints to ensure solution consistency. We test three quantum circuit topologies (Cascade, Cross-mesh, Alternate) and demonstrate through four numerical experiments that QCPINNs achieve higher prediction accuracy than classical PINNs. Specifically, the Alternate topology outperforms others in heterogeneous single-phase flow, BL equation simulations and heterogeneous fully coupled pressure-saturation two-phase flow, while the Cascade topology excels in compositional flow with convection-dispersion-adsorption coupling. The Cross-mesh topology shows competitive early-stage convergence and accuracy across scenarios with balanced performance in coupled two-phase flow. Our work verifies the feasibility of QCPINN for reservoir engineering applications, bridging the gap between quantum computing research and industrial practice in oil and gas engineering.