Quantum-classical Physics-Informed Neural Networks Solve Reservoir Seepage Equations for Oil and Gas Field Development

Predicting fluid flow within underground reservoirs presents a significant challenge in optimising oil and gas extraction, and current methods often struggle with accuracy and computational cost. Xiang Rao from Yangtze University, Yina Liu from King Abdullah University of Technology, and Yuxuan Shen, also from Yangtze University, and their colleagues introduce a novel approach that combines the power of quantum-inspired algorithms with established physics-informed neural networks. This new technique, termed Quantum-Classical Physics-Informed Neural Network, or QCPINN, tackles the limitations of existing methods by leveraging quantum principles to improve the modelling of complex reservoir behaviour. The team demonstrates that QCPINN accurately simulates fluid flow in various reservoir scenarios, including heterogeneous single-phase flow, two-phase waterflooding, and compositional flow with adsorption, achieving high prediction accuracy with fewer computational resources than conventional techniques and offering a promising pathway towards more efficient and reliable reservoir management.

Quantum Machine Learning for Reservoir Simulation

This research explores the application of quantum and hybrid quantum-classical machine learning techniques to reservoir modeling, specifically focusing on solving the partial differential equations that govern fluid flow in porous media. Traditional reservoir simulation is computationally expensive, particularly for complex geometries, heterogeneous formations, and multi-phase flow. Quantum computing offers potential speedups and enhanced capabilities for tackling these challenges.

Scientists are investigating Quantum-Classical Hybrid PINNs, or QCPINNs, which combine PINNs with quantum layers to improve performance and accuracy, and utilizing the Variational Quantum Eigensolver, or VQE, and Variational Quantum Linear Solver, or VQLS, for solving linear systems arising in reservoir flow simulations. Researchers are also exploring Quantum Neural Networks for directly predicting reservoir properties and flow behavior, and applying Hybrid Quantum Graph Neural Networks to trace flow in porous media. The QCPINN integrates classical preprocessing and postprocessing networks with a quantum core, harnessing quantum superposition and entanglement to improve high-dimensional feature mapping while embedding physical constraints to ensure solution consistency. Researchers applied the QCPINN to three reservoir seepage models for the first time: the pressure diffusion equation for heterogeneous single-phase flow, the nonlinear Buckley-Leverett equation for two-phase waterflooding, and the convection-diffusion equation for compositional flow considering adsorption. The team systematically tested three distinct quantum circuit topologies, Cascade, Cross-mesh, and Alternate, to determine optimal configurations for different flow scenarios.

Experiments demonstrate that QCPINNs achieve high prediction accuracy with fewer parameters than classical PINNs, significantly reducing computational demands and improving efficiency. Specifically, the Alternate topology consistently outperformed others in simulations of heterogeneous single-phase flow and two-phase Buckley-Leverett equation scenarios, while the Cascade topology excelled in modeling compositional flow with convection-dispersion-adsorption coupling. This research verifies the feasibility of QCPINN for reservoir engineering applications, bridging the gap between quantum computing research and practical industrial implementation in the oil and gas sector.

Quantum Physics Improves Reservoir Flow Simulations

Scientists developed a novel approach to solving complex equations that arise when modeling fluid flow within oil and gas reservoirs, achieving significant improvements in both accuracy and efficiency. The QCPINN integrates classical pre- and post-processing networks with a quantum core, leveraging the principles of superposition and entanglement to map high-dimensional data more effectively while ensuring solutions adhere to known physical laws. Experiments involved simulating three distinct reservoir flow scenarios: single-phase flow, two-phase waterflooding, 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. Results demonstrate that the Alternate topology consistently outperformed others in modeling single-phase and two-phase flow, while the Cascade topology proved most effective for compositional flow involving convection, dispersion, and adsorption. For a circuit with three qubits, the Alternate topology achieved a circuit depth of 5 layers and required only 9 trainable parameters, a substantial reduction compared to the thousands of parameters typically found in classical PINNs. Researchers developed a framework integrating quantum computing with established physical constraints, enabling accurate solutions to partial differential equations governing fluid flow in reservoirs with reduced computational demands. Investigations into different quantum circuit topologies revealed distinct performance characteristics suited to specific reservoir scenarios. The Alternate topology proved optimal for modeling heterogeneous single-phase flow and transient nonlinear two-phase waterflooding, while the Cascade topology excelled in simulations involving multi-physics coupled compositional flow, which incorporates adsorption effects. Quantitative error analysis confirmed the accuracy and stability of all tested topologies, with low mean absolute and L2 errors demonstrating reliable capture of key reservoir flow characteristics. This work represents a significant advancement in reservoir simulation, establishing a foundation for the industrial application of quantum computing in oil and gas field development and offering a pathway towards more efficient and accurate reservoir simulators and machine learning surrogate models.