The First Application of Quantum Computing Algorithm in Streamline-Based Simulation of Water-Flooding Reservoirs

Abstract Though generic quantum computers are not yet available, we have access to the Noisy Intermediate-Scale Quantum (NISQ) era. The advent of variational quantum algorithms has opened doors for quantum computing in science and engineering during the NISQ era. This study integrates the quantum algorithm with classical streamline methods for efficient, high-precision simulation of two-phase flows, aiming to inform future quantum computing-based reservoir simulation technologies. We employ the variational quantum algorithm to solve the linearized finite volume discrete pressure equations. This process involves decomposing the coefficient matrix of the linear equations using the Pauli basis and preparing the quantum state of the coefficient vector through a unitary operation. A parameterized hardware-efficient ansatz is then constructed, and the quantum circuit’s output (i.e., the cost function value) is obtained via the Hadamard Test. Classical optimizer minimizes the cost function, updating the ansatz parameters to solve the pressure equations. Streamline distribution across the computational domain and time of flight distribution along each streamline are rapidly derived, with water saturation distribution calculated using a high order weighted essentially non-oscillatory (WENO) scheme on each streamline. This results in an integrated workflow combining quantum computing, streamline tracking, and high-order numerical methods. We tested three cases, including homogeneous reservoirs, heterogeneous reservoirs, and multi-well injection and production scenarios. Xanadu’s Pennylane open-source library was used to implement the variational quantum algorithm for computing pressure distribution. The results show that this variational quantum algorithm can achieve high-precision calculation of pressure distribution within fewer optimization steps, with relative computational errors all within 1%. Based on the streamline distribution obtained from tracking, the WENO scheme on the streamlines reduces the numerical dispersion error of the calculated saturation distribution compared to the upwind finite difference scheme, thereby further improving the computational resolution of the waterflooding front. This work pioneers a hybrid quantum-classical workflow for streamline-based reservoir simulation, showcasing its potential for accuracy, efficiency, and robustness in two-phase flow simulations across various reservoir types, paving the way for future quantum computing-based general-purpose reservoir simulators.