Neural networks based on quantum classical physics solve reservoir penetration equations for oil and gas field development

Predicting fluid flow within underground reservoirs poses a major challenge in optimizing oil and gas extraction, and current methods often struggle with accuracy and computational cost. Xiang Rao of Yangtze River University, Yina Liu of King Abdullah University of Science and Technology, and Yuxuan Shen, also of Yangtze River University, and their colleagues present a new approach that combines the power of quantum-inspired algorithms with established physics-based neural networks. This new technology, called Quantum Classical Physical Information Neural Network (QCPINN), addresses the limitations of existing methods by leveraging quantum principles to improve modeling of complex reservoir behavior. The research team demonstrated that QCPINN accurately simulates fluid flow in various reservoir scenarios such as inhomogeneous single-phase flow, two-phase water flooding, and compositional flow with adsorption, achieving high prediction accuracy with fewer computational resources than traditional techniques, and providing a promising path toward more efficient and reliable reservoir management.

Quantum Machine Learning for Reservoir Simulation

This study explores the application of quantum and hybrid quantum-classical machine learning techniques to reservoir modeling, with a particular focus on solving partial differential equations governing fluid flow in porous media. Traditional reservoir simulations are computationally expensive, especially for complex geometries, heterogeneous formations, and multiphase flows. Quantum computing offers potential speedups and enhanced capabilities to tackle these challenges.

Scientists are investigating quantum-classical hybrid PINNs (QCPINNs), which combine PINNs and quantum layers to improve performance and accuracy, and utilize variational quantum eigensolvers (VQEs) and variational quantum linear solvers (VQLS) to solve linear systems arising in reservoir flow simulations. Researchers are also investigating the application of quantum neural networks to directly predict reservoir properties and flow behavior, as well as hybrid quantum graph neural networks to track flow in porous media. QCPINN integrates classical pre- and post-processing networks with a quantum core, exploiting quantum superposition and entanglement to improve high-dimensional feature mapping, while embedding physical constraints to ensure solution consistency. For the first time, researchers applied QCPINN to three reservoir infiltration models. namely, the pressure-diffusion equation for inhomogeneous single-phase flow, the nonlinear Buckley-Leverette equation for two-phase water flooding, and the convection-diffusion equation for compositional flow considering adsorption. The team systematically tested three different quantum circuit topologies: cascade, crossmesh, and alternate to determine the optimal configuration for different flow scenarios.

Experiments demonstrate that QCPINN achieves higher prediction accuracy with fewer parameters than traditional PINN, with significantly reduced computational complexity and improved efficiency. Specifically, the alternative topology consistently performed better than the other topologies in simulating heterogeneous single-phase flow and two-phase Buckley-Leverette equation scenarios, while the cascade topology was superior in modeling compositional flow with convection-dispersion-adsorption coupling. This study validates the feasibility of QCPINN for reservoir engineering applications, bridging the gap between quantum computing research and real industrial implementation in the oil and gas sector.

Quantum physics improves simulation of reservoir flow

Scientists have developed a new approach to solving the complex equations that arise when modeling fluid flow in oil and gas reservoirs, achieving significant improvements in both accuracy and efficiency. QCPINN integrates classical pre- and post-processing networks with quantum cores and leverages the principles of superposition and entanglement to more effectively map high-dimensional data while ensuring that solutions comply with known physical laws. The experiments simulated three different reservoir flow scenarios: single-phase flow, two-phase water flooding, and compositional flow with adsorption.

The team tested three different quantum circuit topologies: cascade, cross-mesh, and alternate to determine the optimal configuration for each simulation. The results show that the alternating topology consistently outperforms other topologies for modeling single- and two-phase flows, while the cascade topology proves to be most effective for flows with compositions that include convection, dispersion, and adsorption. For a circuit with 3 qubits, the alternative topology achieved a circuit depth of 5 layers and required only 9 trainable parameters, a significant reduction compared to the thousands of parameters typically found in traditional PINNs. Researchers have developed a framework that integrates quantum computing with established physical constraints, allowing for accurate solutions of partial differential equations governing fluid flow in reservoirs while reducing computational demands. Investigation of different quantum circuit topologies has revealed distinct performance characteristics suitable for specific reservoir scenarios. The alternative topology proves to be optimal for modeling inhomogeneous single-phase flows and transient nonlinear two-phase water floods, while the cascade topology excels in simulations involving multiphysics coupled composition flows that incorporate adsorption effects. Quantitative error analysis confirmed the accuracy and stability of all tested topologies, demonstrating low mean absolute and L2 errors and reliable capture of key reservoir flow characteristics. This research represents a significant advance in reservoir simulation, establishing the foundation for industrial applications of quantum computing in oil and gas field development, and providing a path toward more efficient and accurate reservoir simulators and machine learning surrogate models.