为何二维模型无法捕捉三维非均质介质中的流动特性：连通性视角
Why 2D Models Fail to Capture Flow Properties in 3D Heterogeneous Media: A Connectivity Perspective
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中文总结 AI 辅助
本文从连通性视角分析二维与三维非均质介质中等效水力传导系数随粗化尺度的变化，发现连通性导致二维与三维宏观流动特性显著不同，揭示二维模型的严重局限。
中文摘要 AI 辅助
我们分析了在二维和三维非均质介质中，等效水力传导系数 $K_{eq}$ 随粗化尺度 $\lambda/I$ 的变化情况。在所有情况下，局部水力传导系数 $k({\bf r})$ 均服从对数正态分布，而 $k({\bf r})$ 的空间连通性从高（HCS）、经中间或多高斯（ICS）和低（LCS）、到无结构（NS）不等。采用随机方法，我们刻画了 $P[\log(K_{eq})]$ 的完整分布及其矩：均值 $\langle K_{eq}\rangle$、对数方差 $\sigma_{\log(K_{eq})}^{2}$ 和对数偏度 $\gamma_{\log(K_{eq})}$，作为 $\lambda/I$ 的函数。二维与三维之间出现显著差异，我们将其归因于与空间维度相关的两个关键因素。我们观察到，与ICS相比，LCS和HCS表现出两个显著特征：多高斯介质中 $k({\bf r})$ 粗化的现有解析表达式不适用，且 $P[\log(K_{eq})]$ 在所有尺度 $\lambda/I$ 下均偏离高斯分布。随后采用临界路径分析来量化样本的连通性，并表明 $K_{eq}$ 对其呈幂律依赖。我们的结果表明，即使地质统计参数相同，连通性也可导致二维与三维宏观流动特性出现显著差异，凸显了使用二维模型表征三维流动的严重局限性。
英文摘要
We analyze how the equivalent hydraulic conductivity, $K_{eq}$, varies with the coarsening scale $λ/I$ in 2D and 3D heterogeneous media. Their local hydraulic conductivity, $k({\bf r})$, follows a lognormal distribution in all cases, while spatial connectivity of $k({\bf r})$ ranges from high (HCS), through intermediate or multi-Gaussian (ICS) and low (LCS), to unstructured (NS). Using a stochastic approach, we characterize the full distribution $P[\log(K_{eq})]$, and its moments: mean $\langle K_{eq}\rangle$, log-variance $σ_{\log(K_{eq})}^{2}$, and log-skewness $γ_{\log(K_{eq})}$, as a function of $λ/I$. Significant contrasts appear between 2D and 3D, which we interpret in terms of two key factors associated with spatial dimensionality. We observe that, compared with ICS, LCS and HCS exhibit two distinct features: existing analytical expressions for coarse-graining of $k({\bf r})$ in multi-Gaussian media do not apply, while $P[\log(K_{eq})]$ deviates from Gaussian at all scales $λ/I$. Critical path analysis is then used to quantify the connectivity of our samples, and show that $K_{eq}$ exhibits a power-law dependence on it. Our results reveal that connectivity can lead to substantial differences between 2D and 3D macroscopic flow properties, even for the same geostatistical parameters, highlighting the severe limitations of using 2D models to represent 3D flows.
发表机构
- Universidad de Buenos Aires（布宜诺斯艾利斯大学）
- IFP Energies Nouvelles（法国石油研究院）
- CONICET（阿根廷国家科学研究委员会）
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