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

TL;DR

This paper introduces a quantum-classical physics-informed neural network (QCPINN) that leverages quantum computing principles to improve the accuracy of reservoir seepage modeling across various flow equations.

Contribution

It adapts the DV-Circuit QCPINN architecture for reservoir seepage models, demonstrating enhanced prediction accuracy over classical PINNs in multiple scenarios.

Findings

QCPINN achieves higher accuracy than classical PINNs.

Different quantum circuit topologies perform optimally in different flow scenarios.

QCPINN demonstrates feasibility for reservoir engineering applications.

Abstract

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.