We present a new statistical variance approach for characterizing heterogeneities related to pore spaces in reservoir rocks. Laboratory-based computer microtomography data for reservoir sandstone samples were acquired and processed using advanced image segmentation techniques. The samples were processed using a method based on the digital rock physics concept using the high-performance Navier–Stokes flow solver in the GeoDict commercial software package. The digitized structures were subjected to computational fluid dynamic simulations. The effects of structural matrix modifications caused by the precipitation of minerals on the porosity–permeability relationship and the characterization of the representative elementary volume were assessed. The variances of the digital flow fields were compared at the pore scale (6 µm). The algorithm for analysing variance was benchmarked using a synthetic dataset that provided artificial repetitive structural patterns at both low and high resolutions. This gave an estimate of the sensitivity of the proposed algorithm to minor inhomogeneities. Representative elementary volume variance analysis was performed by comparing the correlation coefficients for various pore–grain composition patterns with the variances of simulated mean flow velocities. Probability density functions indicate that the flow velocities and pore space geometries differed greatly for different samples. The normalized probability density functions of the mean flows shifted to higher velocities as the resolution decreased. We found that a representative elementary volume analysis was more reliably achieved by analysing the mean flow velocity variance than by analysing the pore microstructure alone.

中文翻译：

---

孔隙尺度孔隙度方差和渗透率非均质性分析

我们提出了一种新的统计方差方法来表征与储层岩石孔隙空间相关的非均质性。使用先进的图像分割技术获取和处理储层砂岩样品的基于实验室的计算机显微断层扫描数据。使用基于数字岩石物理概念的方法处理样品，使用 GeoDict 商业软件包中的高性能 Navier-Stokes 流求解器。对数字化结构进行计算流体动力学模拟。评估了由矿物沉淀引起的结构基体改性对孔隙度-渗透率关系和代表性单元体积特征的影响。在孔隙尺度 (6 µm) 上比较了数字流场的差异。分析方差的算法使用合成数据集进行基准测试，该数据集提供低分辨率和高分辨率的人工重复结构模式。这给出了所提出的算法对轻微不均匀性的敏感性的估计。通过比较各种孔-颗粒组成模式的相关系数与模拟平均流速的方差，进行代表性的基本体积方差分析。概率密度函数表明，不同样品的流速和孔隙空间几何形状差异很大。随着分辨率的降低，平均流量的归一化概率密度函数向更高的速度移动。