Fig. 6. Statistics on the angles between fracture plane and three coordinate axes (a) Sample YP10, (b) Sample YP30 (islands removed), (c) Sample YP40.
The histograms of the isotropy index of Samples YP10, YP30 and YP40 are shown in Fig. 7. The isotropy index of the most clusters in both Samples YP30 and YP40 is less than 0.2, characteristic of the shapes of cracks. Comparatively, Sample YP10 has more cracks which are not ideal fracture morphology, i.e., unlike Griffith cracks. Sample YP40 has the probability of 80% for the isotropy index between 0.0 and 0.15, which can be interpreted that the cracks in Sample YP40 are closer to ideal fracture morphology than in other samples.
Fig. 7. Statistics of isotropy index of core samples. (a) Sample YP10, (b) Sample YP30 (islands removed), (c) Sample YP40.
For better understanding of the shape of cracks, we use Mayavi2 software package to display the orientation matrix of clusters by ellipsoidal glyphs in Sample YP10 (Fig. 8). Fig. 8(a) displays 110 largest clusters (with≥10000 voxels) and Fig. 8(b) displays 164 small clusters (with less than 1000 and more than 700 voxels). To obtain the best visualization of the shapes of the cracks, the magnitude factor of ellipsoids used is 3 for large cracks (Fig. 8(a)) and 125 for small cracks (Fig. 8(b)), respectively.
It is clear that the relatively large clusters are very thin, showing typical crack morphology, while the small clusters have blade-like, rod-like and spherical morphological shapes. The visualization well explains the results in Fig. 7(a), in which a large number of small clusters with high isotropy index in the sample. Thus it causes that a high percentage of clusters do not have typical crack morphology.
Fig. 8. Visualization of clustered equivalent ellipsoid of Sample YP10. (a) 110 largest clusters, the magnitude factor of ellipsoids is 3; (b) 164 smallest clusters, the magnitude factor of ellipsoids is 125.
The Zingg Diagram (Zingg, 1935; Voigt and Twala, 2012) is a versatile shape classification scheme that plots intermediate/long axis versus short/intermediate axis to identify if the grains are spheroids, discoids, rods or blades. We use the modified Zingg Diagram to further describe the crack shapes of the shale samples. The classified characters of clusters (cracks) are shown with (τ1/τ3)1/2 as the horizontal-axis versus (τ2/τ3)1/2 as the vertical-axis. Fig. 9 shows the statistical results of Samples YP10, YP30 and YP40.
All the points are located above the diagonal because of τ1<τ2<τ3. It can be seen that the points are mainly distributed in the range adjacent to the vertical axis and particularly large cracks concentrate in the range of (τ1/τ3)1/2<0.2 or even 0.1, indicating that most of the large cracks are close to ideal fracture morphology. Those clusters with the isotropy index greater than 0.2 may be caused by the bending of the cracks. The (τ2/τ3)1/2 values of the cracks are relatively distributed over a wide range, implying that the width of cracks change greatly.
Fig. 9. Statistics of fracture morphological characteristics. (a) Sample YP10, (b) Sample YP30 (islands removed), (c) Sample YP40.
Finally, the fitting of the fractal dimension of three samples are given below. Fig. 10 shows the graph of LN(N(δ)) against LN(δ) with box length δ from 2, 4, 8, 16, 32, 64 to 128 voxels. The plots show a very good linear relationship between LN(δ) and LN(N(δ)), and the absolute values of the slope is the fractal dimension. The correlation coefficients R are all above 0.98, which confirms that the fitted results are reliable and the characteristics of cracks do show fractal character. Fig. 10(b) compares the fittings of the fractal dimension before and after removing islands, which shows that the small pores in the sample have little effect on the fractal dimension, but only causes lower correlation coefficient.
Fig. 10. Fitting results of fracture fractal dimensions. (a) Sample YP10, (b) Sample YP30 (before and after islands being removed), (c) Sample YP40.
Table 2 lists the fractal dimensions of all 6 analyzed samples. For these 5 samples of isothermal experiments, the fractal dimensions trend to decrease with increasing fluid pressure. This can be interpreted as some of the holes and micro-fractures in shale are closed with increasing pressure. The original Sample YS (the last row of Table 2) is not subject to any temperature or pressure, and its fractal dimension is different from that the other 5 samples.
Although all these samples are taken from the same specimen, the heterogeneity of the natural rocks may cause structural differences between the 6 samples. Thus, the results are insufficient to derive the relationship between the fractal dimension of the cracks and the pressure. To obtain the reliable law of the fractal dimensions of cracks with temperature or pressure, it is required the observation of real-time scanning of the evolution of cracks in the identical sample under high-pressure and high-temperature.
Table 2. Comparison in sample fractal dimensions.
(1) We come to the conclusion that to effectively characterize fractures in 3D space, there are three basic requirements: 1) high-resolution 3D images; 2) individual fractures can be separated if they are intersected and form a network; 3) The scheme of fracture characterization.
(2) Micro-tomography provides high-resolution 3D images of samples at micro-scale. We demonstrate that in this study, 6 samples with natural and artificial fractures can be effectively separated manually in spite of heavy workload. Our in-house code CTSTA is proven to be a very effective tool in characterizing fractures.
(3) With all these prerequisites met, we fulfill a detailed characterization of micro-fractures in shale reservoir rocks from the Permian Lucaogou Formation, Junggar Basin. Our work provides detailed information of fractures including porosity, specific surface area, percolation, the shape, orientation and dimensions of individual fractures.
(4) In addition, the fractal dimensions of fractures are extracted. The fractal dimension is the most commonly used scaling parameter that describes the characteristics of cracks across scales. Our results show that fractures in the shale samples analyzed are characteristic of fractal distribution. Furthermore, five out of the six samples that experience isothermal variable-pressure action show that the fractal dimension decreases with increasing pressure.
This work was financially supported by the National Basic Research Program of China (973 Project) “Formation mechanism and enrichment law of China’s terrestrial tight oil (shale oil)” (2014CB239004). We would like to acknowledge the support of Professor Zou Caineng, the chief scientist of the project.
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* Corresponding author. School of Earth Sciences and Engineering, Sun Yat-sen
University, Guangdong, 510275, China.
2096-2495/© 2018 Chinese Petroleum Society. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).