Coupled simulation of pressure and saturation in water flooding using a quantum linear system solver
Abstract
Sequential water flood simulation alternates implicit pressure solves with explicit saturation updates. This study examines, under ideal statevector access, how a solution state produced by the Harrow‑Hassidim‑Lloyd quantum linear system algorithm can be inserted into that sequential workflow for a two‑phase model in one dimension. The evolving pressure systems are preconditioned from the left using rebuilt sparse approximate inverses, converted by Hermitian block dilation, and treated with signed phase estimation at finite resolution. The formulation also identifies the classical normalization, sign recovery, and complete field readout operations required before a solution state can drive the transport update. Steady and transient component tests precede coupled calculations on three successively refined grids. Across these grids, the statevector and direct pressure solutions remain closely aligned in direction, while the finest grid saturation trajectories show the largest difference and the statevector branch reaches the imposed upper saturation bound. Each plotted statevector pressure is aligned by a global scalar with the exact solution of its current dilated system, so the results assess algebraic data exchange rather than an independent reconstruction of physical pressure. A separate pilot covering five steps finds similar directional agreement between pressure solutions when a right sparse approximate inverse is rebuilt or updated using a sparse approximate map, but the combined setup problem. The results show that close directional agreement between pressure solutions does not by itself guarantee accurate saturation transport and thus provide a reference point for assessing such solvers in sequential reservoir simulation. All calculations use ideal statevectors; no quantum hardware, speedup of the complete workflow, or hardware advantage is demonstrated.
Document Type: Original article
Cited as:
Xu, L., Xiang, Y., Li, M., Zhang, L., Jia, C. Coupled simulation of pressure and saturation in water flooding using a quantum linear system solver. Advances in Geo‑Energy Research, 2026, 21(3): 220‑237. https://doi.org/10.46690/ager.2026.09.03
DOI:
https://doi.org/10.46690/ager.2026.09.03Keywords:
Reservoir simulation, water flooding, implicit pressure explicit saturation, quantum linear solver, Harrow‑Hassidim‑Lloyd algorithm, statevector simulationReferences
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Copyright (c) 2026 Li Xu, Yahong Xiang, Ming Li, Lei Zhang, Cunqi Jia
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