The Representative Elementary Volume (REV) concept, a cornerstone in porous system heterogeneity assessment, was initially conceived to determine the minimal domain volume suitable for homogenization and upscaling. However, the definition of REV and usability in continuum-scale models is vague. In this study, we conduct comprehensive REV analyses on multiple samples, encompassing a range of scalar and vector metrics. Our investigation probes the representativity of crucial medium characteristics, including porosity, permeability, and Euler density, alongside descriptors rooted in pore-network statistics, correlation functions, and persistence diagrams. We explore both deterministic and statistical REV sizes (dREV and sREV), facilitating a robust comparative assessment. Crucially, we introduce an novel methodology tailored for harnessing vector metrics, known for their ability to reveal intricate structural insights. Our results underscore the superiority of the sREV approach, particularly for low-content metrics, addressing inherent limitations of dREV in characterizing homogeneities in such cases. Furthermore, the sREV approach incorporates stationarity analysis into REV evaluation, ensuring result consistency between sREV and dREV under stationarity conditions. Encouragingly, our findings suggest that high-information-content metrics, notably correlation functions combined with persistence diagrams, have the potential to establish a universal REV for steady-state physical properties. This proposition warrants further verification through a comprehensive assessment and comparison of REV values across major physical properties. REV analysis plays a pivotal role not only in assessing medium properties but also in scrutinizing different descriptors of 3D images – we note that REV analysis and image/field stationarity analysis are ultimately the same techniques under the hood. The discussion based on obtained results and recent finding by other researchers advances the understanding of REV within porous media, introduces a versatile methodology with broader applications, and is expected to be useful in numerous fields including materials science, cosmology, machine learning, and more. We redefine the classical definition of REV by adding stationarity condition and upper/lower bounds on its volume. While for simplicity, in this work we shall mainly focus on porous media as immediately applicable to digital rock, petrophysics, hydrology and soil physics problems, the developed mythology can be applied to other material types - composites, biological tissues, granular matter, food engineering and numerous other types of matter.

中文翻译：

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在非均质材料中寻找代表性基本体积 （REV）：以多孔介质为例的标量和矢量指标调查


代表性基本体积 （REV） 概念是多孔系统异质性评估的基石，最初旨在确定适合均质化和放大的最小域体积。然而，连续尺度模型中 REV 和可用性的定义是模糊的。在本研究中，我们对多个样本进行了全面的 REV 分析，包括一系列标量和矢量指标。我们的调查探讨了关键介质特性的代表性，包括孔隙率、渗透率和欧拉密度，以及植根于孔隙网络统计、相关函数和持久性图的描述符。我们探索了确定性和统计 REV 大小 （dREV 和 sREV），促进了稳健的比较评估。至关重要的是，我们引入了一种为利用矢量指标量身定制的新方法，该方法以其揭示复杂结构见解的能力而闻名。我们的结果强调了 sREV 方法的优越性，特别是对于低内涵指标，解决了 dREV 在这种情况下表征同质性方面的固有局限性。此外，sREV 方法将平稳性分析纳入 REV 评估，确保平稳性条件下 sREV 和 dREV 之间的结果一致性。令人鼓舞的是，我们的研究结果表明，高信息含量指标，特别是与持久性图相结合的相关函数，有可能为稳态物理属性建立通用的 REV。通过对主要物理特性的 REV 值进行全面评估和比较，可以进一步验证这一主张。 REV 分析不仅在评估介质特性方面起着关键作用，而且在仔细检查 3D 图像的不同描述符方面也起着关键作用——我们注意到 REV 分析和图像/场平稳性分析最终是相同的技术。基于获得的结果和其他研究人员的最新发现的讨论促进了对多孔介质中 REV 的理解，引入了一种具有更广泛应用的多功能方法，并有望在包括材料科学、宇宙学、机器学习等在内的众多领域发挥作用。我们通过在其体积上添加平稳性条件和上限/下限来重新定义 REV 的经典定义。虽然为简单起见，在这项工作中，我们将主要关注多孔介质，因为它直接适用于数字岩石、岩石物理学、水文学和土壤物理学问题，而开发的神话可以应用于其他材料类型——复合材料、生物组织、颗粒物质、食品工程和许多其他类型的物质。