Abstract Pores with sizes ranging from nanometers to micrometers are widely distributed in shale gas and shale oil formations. These pores are the sites for hydrocarbon accumulation and provide the flow paths for hydrocarbons during production. The Middle Bakken member is the main production zone of the Bakken Formation in North Dakota. In order to reveal the pore structures of the Middle Bakken, we employed field emission scanning electron microscopy (FE-SEM). After segmentation of the SEM images, we calculated the surface area and shape of the pores using image analysis and then quantified the complexity and heterogeneity of the pore structures by applying both fractal and multifractal analyses. Finally, we employed the fractal permeability model to estimate the permeability of the samples. The results showed that different pore types, such as interparticle and intraparticle pores exist in the Middle Bakken samples. Even under the same scale of the same sample, the pore parameters could be different. Sample 2 has the largest average porosity, followed by Sample 1 and Sample 3. The mean pore size of these samples is less than 31 nm indicating that the pores in Middle Bakken samples are very small. The pore structures in the Middle Bakken exhibited fractal and multifractal behavior. The fractal dimension from the entire size range of pores is the largest compared with the fractal dimension of the subdivided groups. The pore size distribution in Sample 2 is the most heterogeneous.

中文翻译：

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孔隙结构的图像分析：Middle Bakken 的深入研究

摘要 页岩气和页岩油地层中广泛分布着纳米级到微米级的孔隙。这些孔隙是油气聚集的场所，并在生产过程中为油气提供流动路径。中巴肯段是北达科他州巴肯组的主要产区。为了揭示中巴肯的孔隙结构，我们采用了场发射扫描电子显微镜（FE-SEM）。在对 SEM 图像进行分割后，我们使用图像分析计算了孔隙的表面积和形状，然后通过应用分形和多重分形分析来量化孔隙结构的复杂性和异质性。最后，我们采用分形渗透率模型来估计样品的渗透率。结果表明，不同的孔隙类型，Middle Bakken 样品中存在粒间孔和粒内孔等。即使在同一样品的同一尺度下，孔隙参数也可能不同。样品 2 的平均孔隙率最大，其次是样品 1 和样品 3。这些样品的平均孔径小于 31 nm，表明 Middle Bakken 样品的孔隙非常小。巴肯中部的孔隙结构表现出分形和多重分形行为。与细分组的分形维数相比，整个孔隙尺寸范围的分形维数最大。样品 2 中的孔径分布最不均匀。其次是样品 1 和样品 3。这些样品的平均孔径小于 31 nm，表明 Middle Bakken 样品中的孔非常小。巴肯中部的孔隙结构表现出分形和多重分形行为。与细分组的分形维数相比，整个孔隙尺寸范围的分形维数最大。样品 2 中的孔径分布最不均匀。其次是样品 1 和样品 3。这些样品的平均孔径小于 31 nm，表明 Middle Bakken 样品中的孔非常小。巴肯中部的孔隙结构表现出分形和多重分形行为。与细分组的分形维数相比，整个孔隙尺寸范围的分形维数最大。样品 2 中的孔径分布最不均匀。