AI 中文总结
研究针对油藏压力和饱和度稀疏监测问题，提出基于张量的模态分解与稀疏重建框架，通过QR排序和张量压缩感知实现，在布鲁日基准测试中增加仪器井数量可提升相关指标，验证了该方法用于耦合油藏场的可行性。
AI 中文摘要
油藏压力和饱和度的稀疏监测需要在从少量观测值重建全场时保留网格结构的数值方法。我们提出了一种用于耦合压力-饱和度场的基于四维张量的模态分解（TBMD）和稀疏重建框架。该方法使用显式属性模式、网格范围内空间属性纤维的模式4枢轴正交三角（QR）排序以及基于张量的压缩感知用于网格范围和现有井测量算子。使用10个具有固定地质的井控实现对布鲁日基准进行评估。在联合压力-饱和度仅井研究中，增加仪器井数量可降低相对弗罗贝尼乌斯误差、提高结构相似性指数测量值和峰值信噪比。结果支持了张量结构稀疏重建用于耦合油藏场的可行性，并为与替代降阶和稀疏传感方法的受控比较提供了基础。
英文摘要
Sparse monitoring of reservoir pressure and saturation requires numerical methods that retain gridded structure while reconstructing full fields from few observations. We present a four-dimensional tensor-based modal decomposition (TBMD) and sparse reconstruction framework for coupled pressure-saturation fields. The approach uses an explicit property mode, mode-4 pivoted orthogonal-triangular (QR) ranking of grid-wide spatial-property fibers, and tensor-based compressive sensing for both grid-wide and existing-well measurement operators. The Brugge benchmark is evaluated using 10 well-control realizations with fixed geology. Each realization is processed independently as a tensor of size 139 x 48 x 2 x 134 under an 80/20 temporal split with training-fitted property-wise min-max normalization. In the joint pressure-saturation well-only study, increasing the number of instrumented wells from 1 to 10 reduces the relative Frobenius error from about 0.57 to 0.20, increases the Structural Similarity Index Measure from about 0.47 to 0.88, and raises the peak signal-to-noise ratio from about 33.8 to 37 dB. By 20 wells, the relative error drops to about 0.11. The results support the feasibility of tensor-structured sparse reconstruction for coupled reservoir fields and provide a basis for controlled comparisons with alternative reduced-order and sparse-sensing methods.
Comments63 pages, 12 figures
