Applying Fractal Theory to Characterize the Pore Structure of

Article Cite This: Energy Fuels XXXX, XXX, XXX−XXX

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Applying Fractal Theory to Characterize the Pore Structure of Lacustrine Shale from the Zhanhua Depression in Bohai Bay Basin, Eastern China Jianping Yan,*,†,‡ Shaolong Zhang,‡ Jun Wang,§ Qinhong Hu,*,∥ Min Wang,§ and Jing Chao§

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†

State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China ‡ School of Geoscience and Technology, Southwest Petroleum University, Chengdu 610500, China § Institute of Exploration and Development, Shengli Oil Field, SINOPEC, Dongying 257015, China ∥ School of Geosciences in China University of Petroleum (East China), Qingdao 266580, China ABSTRACT: The complexity of the shale pore structure, which can be assessed by the fractal dimension, will affect the percolation and reservoir capability of a shale; thus, the pore structure is important for shale reservoir evaluation. For the pore structure and fractal characteristics of lacustrine shale to be investigated, a combination of X-ray diffraction (XRD), total organic carbon (TOC), scanning electron microscopy (SEM), mercury-injection capillary pressure (MICP), nuclear magnetic resonance (NMR), and Nano-CT experiments were performed on shale samples from the lower submember of the third member of the Eocene Shahejie Formation (Es3L) in the Zhanhua Depression, Bohai Bay Basin. On the basis of fractal theory, the NMR fractal dimensions of the analyzed shale samples were determined by the transversal relaxation time (T2) spectrum from the NMR experiment. The relationships between the NMR fractal dimension and mineral content, TOC, and pore structure parameter were discussed. The results indicate that the pore structure of the lacustrine shale in the study area is complex and exhibits strong heterogeneity. The pore types mainly include intergranular pores, intragranular pores, and some dissolved pores and microfractures. Calcite and clay are the dominant minerals, ranging from 9 to 91% (average 52.23%) and from 1 to 48% (average 18.63%), respectively. The TOC contents are relatively high with values from 0.06 to 9.32%. The calculated NMR fractal dimension (D) values are between 2.2544 and 2.439, which exhibit positive correlations with TOC content, quartz content, and clay mineral content. In contrast, a negative relationship occurs between the NMR fractal dimension and calcite content, indicating that the development of large, dissolved pores in shale samples could reduce the heterogeneity of the pore size distribution. Negative correlations are observed between the NMR fractal dimension and the T2 cutoff value, T2 geometric mean, porosity, and average pore throat radius, whereas the NMR fractal dimension exhibits a positive correlation with the displacement pressure (Pd) and has no obvious relationship with permeability. The different relationships suggest that the NMR fractal dimension is closely related to the pore structure; namely, the smaller the NMR fractal dimension is, the better the pore structure is in the shale samples. Four typical samples were chosen to verify the relationship between the NMR fractal dimensions and the shale pore structure in the logging profile of Well L69. Excellent application results were obtained, suggesting that the NMR fractal dimension can be used to indicate the effectiveness of the reservoir in the study area.

1. INTRODUCTION Shale oil and gas are two new types of unconventional resources with great potential around the world. In recent years, the United States has made great breakthroughs in the exploitation of shale oil, and its production has increased intensively from 2010 to 2015.1 Shale oil is widely distributed in China, and great achievements have been made in the exploration and development of shale oil by drawing on the experience of the United States. Pore structure refers to the geometry, size, distribution, and connectivity of the pores and throats and the characteristic relationships between the pore and throat.2 With shale being a complex and heterogeneous porous medium, its pore structure parameters, such as pore morphology, pore size distribution, pore volume, and specific surface area, are essential for evaluating adsorption,3 storage capacity,4 and flow mechanisms.5 Therefore, it is very important to thoroughly study the pore structure characteristics of shales. © XXXX American Chemical Society

Currently, to elucidate the complex pore structure in shale reservoirs, different methods are applied, including image analysis (e.g., thin section and FE-SEM),6,7 fluid injection (e.g., gas adsorption and mercury injection),7−9 and nonfluid injection (e.g., NMR, Micro-Nano CT, and small-angle neutron scattering)10−13 with some techniques down to a nm-scale resolution. However, each method has advantages and disadvantages in characterizing the pore structure of shale reservoirs, and a selective combination of these methods gives a comprehensive characterization of the reservoir pore structure.14 Previous studies have pointed out the following: (1) shale pores can be divided into intraparticle pores, interparticle pores, and organic-matter pores;15 (2) shale has a wide range of pore sizes, ranging from a few nanometers to a few Received: April 30, 2018 Revised: June 17, 2018 Published: June 18, 2018 A

DOI: 10.1021/acs.energyfuels.8b01501 Energy Fuels XXXX, XXX, XXX−XXX

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Figure 1. (a) Tectonic units and locations of the studied wells in the Zhanhua Depression, Bohai Bay Basin. (b, c) Two different directional cross sections in the study area to show the stratigraphic characteristics in the study area (modified from Jiu et al.37 Q: Quaternary. Nm: Minghuazhen Formation (Pliocene). Ng: Guantao Formation (Miocene). Ed: Dongying Formation (Oligocene). Es4−2: upper fourth member of the Shahejie Formation (Eocene). Es4−1: lower fourth member of the Shahejie Formation (Eocene). Ek: Kongdian Formation (Eocene)).

micrometers;16,17 (3) the porosity of a shale reservoir is jointly controlled by TOC, organic matter maturity, diagenesis, and tectonism;18 and (4) the contributions of different components

to the evolution of shale porosity are different, of which the thermal evolution of organic matter contributes the greatest followed by clay mineral and brittle mineral transformation.19 B


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Figure 2. Generalized Cenozoic stratigraphy of the Zhanhua Depression (modified from Ma et al.38).

of porous rocks can be inferred by the NMR method,25,26 gas adsorption,27−31 MICP,32,33 and image analysis.34,35 Because of factors such as sample size, data interpretation, and measurable pore size range, the fractal dimension obtained from each method could be different. However, the fractal dimension obtained from the same method for different rock samples can effectively reflect the difference in the pore structure. With a combination of XRD analysis, TOC tests, Rock-Eval pyrolysis analysis, MICP tests, NMR experiments, and NanoCT scanning for the Es3L shale samples, the major objectives of this work are as follows: (1) to characterize the pore structure, (2) to calculate the NMR fractal dimension and analyze the influencing factors, and (3) to identify the relationship between

For the complexity and heterogeneity of the shale pore structure to be studied, fractal theory has been used to reflect the true properties and conditions of porous materials with no characteristic length scale. Fractals are defined as virtual, selfsimilar objects that appear identical independent of the scale of magnification,20,21 and these self-similar fractal objects could be characterized by the fractal dimension. The fractal dimension is used to describe the irregularity of shale reticular pores, and more complex pore characteristics result in higher fractal dimensions.22 Pfeifer and Avnir indicated that the pores in reservoir rock have fractal characteristics by the adsorption method.23 Shale, as a porous material with complex microstructure and selfsimilarity, satisfies the fractal condition.24 The fractal dimension C


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Energy & Fuels Table 1. Whole-Rock Analysis Results of the Shale Samples from the Es3L Member of Well L69 (Unit: wt %) samples

quartz

potash feldspar

plagioclase

calcite

dolomite

others

clay

illite

kaolinite

chlorite

I/S

7 43 80 112 148 188 228 268 308 402 442 482 522 562 646 688 726 764 806 826 853 870

24 15 30 21 19 17 16 16 19 18 18 14 23 14 19 21 16 11 15 25 5 3

0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0

1 2 3 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0

49 41 30 50 51 59 55 54 57 53 51 59 39 65 61 28 62 72 68 52 90 91

12 22 4 6 6 5 5 5 4 4 5 3 6 2 8 14 4 3 5 3 1 1

2 3 3 4 5 4 2 4 4 4 5 5 6 3 3 6 3 3 2 4 1 1

12 17 30 18 18 14 21 20 15 20 20 18 23 14 8 30 14 10 10 16 3 4

2.88 3.4 8.4 3.6 3.96 2.8 7.98 4 5.85 4.4 4 6.3 8.05 4.62 2.48 12 4.2 3.4 3.1 4.8 0.84 1.08

1.56 1.19 2.7 2.16 2.34 2.24 1.05 1.6 1.5 1.8 1.6 0.18 0 0 0 1.8 0.28 0.1 0.1 0.32 0.27 0.52

1.08 0.51 1.2 1.26 0.9 0.84 0.42 1.2 0.6 0.8 0.6 0.18 0 0 0 0.9 0.14 0.1 0.1 0.16 0.09 0.12

6.48 11.9 17.7 10.98 10.8 8.12 11.55 13.2 7.05 13 13.8 11.34 14.95 9.38 5.52 15.3 9.38 6.4 6.7 10.72 1.8 2.28

heated to 300 °C to release the free hydrocarbon (S1) fraction followed by a temperature ramp of 25 °C/min to 650 °C to release the residual hydrocarbon (S2) and obtain the temperature at which the maximum amount of S2 hydrocarbons (Tmax) is generated. The MICP measurements were carried out on core samples (1 cm × 1 cm × 1 cm) in accordance with the Chinese Oil and Gas Industry Standard SY/T 5346-2005 using a Poremaster 60 type automatic mercury injection instrument made by Quantachrome Instruments. The pressure increases from 0.003 to 30 MPa, and the balance time, interfacial tension, and contact angle are 60 s, 0.48 N/m, and 140°, respectively. The samples were cleaned with ethanol to remove oil, oven-dried at 105 °C, and then equilibrated for 5 h at room temperature before the experiment. The NMR experiment was carried out with an AniMR-150 type fulldiameter core nuclear magnetic resonance analysis system made by Shanghai Niumag Company in the Experimental Teaching Center for Oil and Gas Geology and Exploration at Southwest Petroleum University according to the Chinese Oil and Gas Industry Standard SY/T 6490-2014. The samples were treated by a cleaning, drying, vacuuming, and saturating procedure to achieve a water-saturated state. The echo spacing, number of echoes, number of scans, and test temperature were 0.16 ms, 2048, 256, and 25 °C, respectively. The Nano-CT experiment was carried out by an UltraXRM-L200 CT scanner, and the smallest pixel resolution was 65 nm. In this work, two samples (65 μm in diameter and 65 μm in height) were analyzed in the Nano-CT scanning experiment under the same parameter settings, i.e., the test temperature was 20 °C; the exposure time of a single picture was 120 s, and the total number of pictures collected was 1019. Then, the three-dimensional (3D) digital cores were constructed by Avizo Fire from the FEI company using the Nano-CT scanning images. 2.3. Fractal Theory. Fractal theory was first proposed by French mathematician Mandelbrot in 1975.20 In this work, the fractal dimensions based on the NMR T2 spectrum and Nano-CT images were calculated. 2.3.1. Calculation of the Fractal Dimensions Based on the NMR T2 Spectrum. The fractal dimension calculation method based on nitrogen (N2) adsorption27−31 and mercury injection32,33 has been widely used to characterize the pore structure of porous media. However, the NMR fractal dimension provides more precise insight into the fractal characteristics of the pore structure in shale40 than N2 gas adsorption and mercury injection, and the samples are not damaged in the NMR

pore structure and NMR fractal dimension. The results have some reference values for understanding the pore structure and determining the favorable sections of the lacustrine shale in the Zhanhua Depression, Bohai Bay Basin.

2. GEOLOGICAL SETTINGS, SAMPLES, AND EXPERIMENTAL METHODS 2.1. Geological Settings and Samples. The shale samples were collected from the Es3L member, Well L69, Zhanhua Depression in the Bohai Bay Basin (Figure 1). The burial depth of the Es3L member of the Shahejie Formation ranges from 2910 to 3132 m. The sedimentary environment is a reducing to strongly reducing, semideep to deep lake environment.36 There are Paleozoic, Mesozoic, and Cenozoic strata in the Zhanhua Depression. The Cenozoic strata consist of the Paleogene, Neogene, and Quaternary systems. The Paleogene consists of the Kongdian Formation, Shahejie Formation, and Dongying Formation, and the Neogene consists of the Guantao Formation and Minghuazhen Formation (Figure 2). 2.2. Experimental Methods. A total of 435 samples were collected at depths of 2910−3132 m from Well L69, Zhanhua Depression. A series of measurements were conducted, i.e., XRD analysis, TOC tests, Rock pyrolysis analysis, MICP tests, NMR experiments, and Nano-CT scanning. However, not all samples were subjected to all measurements. Among the samples, 22 were subjected to XRD analysis, 9 to TOC and Rock-Eval pyrolysis, 18 to MICP, 22 to NMR, and 2 to Nano-CT scanning. XRD analysis was performed with X’Pert PRO made by PANalytical B.V. following the Chinese Oil and Gas Industry Standard SY/T51632010. Multiple treatments were carried out before the analysis, including deoiling, desiccation (60 °C), crushing, and grinding to less than 40 μm. TOC is an important index for evaluating the hydrocarbon-generating potential of organic matter in shales.39 The TOC content was measured by a LECO CS230 carbon/sulfur analyzer according to the national standard GB/T 19145-2003 after the samples were crushed to a grain size of 100 mesh and were treated by hydrochloric acid to remove the carbonates at a temperature of 80 °C. Rock-Eval pyrolysis was carried out using Rock-Eval V1 according to national standard GB/T 18602-2012. After being cleaned, crushed, and ground to grain sizes between 0.07 mm and 0.15 mm, the samples were D


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The box-counting fractal dimension is calculated by the expression

Table 2. Organic Geochemical Analysis Results of the Shale Samples from the Es3L Member of Well L69 samples

depth (m)

TOC (wt %)

Tmax (°C)

S1 (mg/g)

S2 (mg/g)

43 80 112 148 188 268 308 688 764

2924.22 2941.60 2949.65 2958.57 2968.56 2988.98 2999.11 3094.41 3113.40

0.82 5.07 7.67 3.84 2.87 3.24 2.69 2.87 1.24

437 443 443 438 438 443 440 440 434

0.43 2.95 2.63 2.62 1.95 2.77 4.04 2.09 1.19

2.35 35.15 53.15 25.03 17.27 20.01 14.11 13.83 3.73

N (s) = B ·s−D

where s is the side length of each square box (pixel), B is a constant, N(s) is the number of boxes with side length s required to cover the image, and D is the box-counting fractal dimension. The procedure of the box-counting approach is as follows:43 first, a series of grids with a side length of s covers the binary Nano-CT scanning image. Second, the number of grids needed to cover the object, which is pores in this work, is completely counted. Finally, the box-counting fractal dimension is obtained from the slope of the data pair (log(s), log(N(s))). Usually, the increasing sequence of s uses a set of powers of 2, i.e., {2, 4, 8, 16, 32, ...}. The binarization of the Nano-CT scanning image is important for calculating the box-counting fractal dimension, so the threshold must be determined. In this work, the method to determine the threshold is as follows: (1) select 20 Nano-CT images using a sequence of image numbers, i.e., {50, 100, 150, 200, ...}; (2) obtain the thresholds for each Nano-CT image by adjusting the pore ratio until achieving the sample porosity, and (3) obtain the optimum threshold of the sample by averaging the values after removing the maximum and minimum values.

method. In this work, the fractal dimensions of 22 typical shale samples were calculated using the NMR T2 spectrum. The formula for calculating the NMR fractal dimension is41

log(Sv) = (3 − D)log(T2) + (D − 3)log(T2max )

(2)

(1)

where T2 is the transverse relaxation time (ms), Sv is the proportion of the pore volume below the corresponding T2 in the total pore volume, D is the NMR fractal dimension, and T2max is the maximum of the transverse relaxation time (ms). According to eq 1, the NMR fractal dimension, which is the threedimensional representation of the pore structure of a rock, can be calculated by the slope of the fitting equation by drawing the double logarithmic coordinate diagram of T2 and Sv. The fractal dimension that is substantially affected by the geometric irregularity and roughness of the surface is generally in the range of 2−3.42 When the fractal dimension is 3, it corresponds to a completely irregular or rough surface; when the fractal dimension is 2, it corresponds to a completely smooth surface. 2.3.2. Calculation of the Fractal Dimensions Based on Nano-CT Scanning Images. The fractal dimension of the Nano-CT scanning images, which could describe the fractal characteristics of the pore structure, can be calculated by the box-counting approach. The boxcounting fractal dimension reflects the two-dimensional information on the pore structure and is widely used because of its computational simplicity on the basis of image binarization.35

3. RESULTS 3.1. Rock and Geochemical Characteristics. The XRD analysis results show that the mineral components are dominated by calcite and clay and contain minor quartz, plagioclase, and potassium feldspar. The calcite content ranges from 9 to 91% with an average of 52.2%. The average clay content is 18.6% with a range between 1 and 48%. The quartz content varies between 3 and 48% with an average of 18.04%. The clay minerals are mainly the Illite-smectite mixed layer (I/S) with an average content of 61.37% followed by Illite with an average content of 29.65% (Table 1). The TOC contents are from 0.06 to 9.32% with an average of 2.89%, suggesting that the shales are organic-rich. The distribution range of S1 is from 0.01 to 32.63 mg/g with an average of 2.97 mg/g, which is substantially smaller than the

Figure 3. Longitudinal distribution characteristics of minerals in Well L69. E


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Figure 4. SEM images of the different pore types in the mud shale from Well L69. (a) Distribution of strawberry pyrite between the I/S layer. (b) Distribution of spheroidal pyrite between the I/S layer. (c) Distribution of regular octahedral pyrite between the I/S layer. (d) Intercrystalline pores along the clay layer.47 (e) Intracrystalline pores developed in the calcite. (f) Distribution of dolomites in the pores. (g) Distribution of calcite in the pores. (h) Feldspar dissolved pore. (i) Calcite dissolved pore. (j) Slit-shaped organic matter pore.47 (k) Structural microfracture. (l) Bedding microfracture.

The Es3L can be divided into two sequences and six system tracts;44 thus, the fluctuation of the paleo-water depth could account for the decrease or increase in different minerals. 3.2. Pore Types. For effectively describing the different pores in shale, several pore type classifications have been

S2 values (0.01−78.59 mg/g) with an average of 14.64 mg/g (Table 2). With increasing depth, the contents of both the detrital minerals (quartz and feldspar) and clay minerals decrease, whereas carbonate minerals (calcite and dolomite) increase (Figure 3). F


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(1) Intragranular pores: Two types of intragranular pores (inter- and intracrystalline pores) are observed in the samples. Intercrystalline pores are developed among pyrite and clay minerals. The pyrite in the study area often appears in the forms of strawberry druse, spherulitic shapes, and regular octahedral shapes (Figures 4a−c). The pyrite intercrystalline pores affected by the morphology and distribution of pyrite grains are mainly triangular and polygonal with a pore size range from 0.77 to 0.99 μm. Intercrystalline pores along the clay layers mostly occur as triangular and slit-shaped (Figure 4d), and they have small pore sizes with a minimum of 17 nm.47 In contrast, the intracrystalline pores, developed in the calcite, are often round or oblate in shape with nanoscale pore sizes (Figure 4e). (2) Intergranular pores: The geometry of the intergranular pores is controlled by the original pores and diagenesis and is influenced by compaction and cementation. Panels f−g in Figure 4 show the intergranular pores developed around inorganic mineral grains. They often have large pore sizes and good connectivity, which could have a large influence on the reservoir and percolation of shale oil and gas. (3) Dissolved pores: Organic acids play a very important role in the formation of pores in shale,48 and the pores formed during hydrocarbon generation evolution, which could provide hydrogen ions to cause the dissolution of unstable minerals such as calcite and feldspar and then result in dissolution pores.49,50 The pore size and morphology of dissolved pores are affected by the dissolution intensity, and the pore boundaries are often irregular. Figure 4h shows the small, dotlike dissolution pores of feldspar, and Figure 4i shows the calcite-dissolved pores, which were easily observed within calcite and were often isolated with a pore size of ∼2.34 μm. (4) Organic-matter pores: These are formed in the process of oil and gas generation; however, they are poorly developed in the Es3L member.51 At the boundaries between organic matter and inorganic minerals, slit-shaped pores measuring 29−406 nm

Table 3. Mercury Injection Pore Structure Parameters of the Shale Samples from the Es3L Member of Well L69 samples

porosity (%)

displacement pressure (Mpa)

av pore throat radius (μm)

maximum mercury saturation (%)

7 43 80 112 148 188 228 268 308 402 442 482 522 562 726 764 806 826

4.61 3.42 8.6 5.11 4.75 2.09 3.35 3.62 3.65 6.55 8.08 5.36 6.03 4.21 4.75 5.43 5.59 7.15

0.29959 2.00087 0.01336 0.01308 0.07329 0.01319 0.0087 0.00865 0.00856 0.21563 0.0131 0.02376 0.16065 0.04331 0.30483 0.51911 0.53655 0.07437

0.4749 0.1026 12.4538 9.6687 2.1487 14.0716 27.9138 15.8793 31.0997 0.8282 10.0906 6.2019 1.1875 3.0079 0.5063 0.3556 0.3225 2.1341

16.99 8.72 19.81 22.26 17.56 25.03 39.41 41.16 48.76 14.74 11.55 42.23 12.47 34.7 12.03 8.03 11.66 12.55

proposed in the literature. Slatt and O’Brien divided the shale pore types into six types: interparticle pores produced by flocculation, organic pores, fecal pellet pores, fossil clastic pores, and intraparticle pores with mineral grains and microfractures.45 Loucks et al. divided the shale reservoir space into intraparticle pores, interparticle pores, and organic-matter pores.15 Huang et al. divided the shale reservoir space into three types: inorganic mineral pores, organic-matter pores, and microfractures according to the pore types of shale.46 The pore types of the mud shale in Well L69 mainly include intragranular pores, intergranular pores, dissolved pores, microfractures, and small amounts of organic-matter pores.

Figure 5. Mercury injection curves and pore size distributions of the mud shale samples from Well L69. (a) Mercury injection curves of 18 samples. (b) Mercury injection curves of sample 43. (c) Mercury injection curves of sample 308. (d) Pore size distribution curves of 18 samples. (e) Pore size distribution curves of sample 43. (f) Pore size distribution curves of sample 308. G


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Figure 6. Shape of the NMR curve of the mud shale samples from Well L69. (a) Nuclear magnetic T2 spectra of 22 samples. (b) First, (c) second, (d) third, and (e) fourth type of nuclear magnetic T2 spectra.

in diameter are developed with a high length-width ratio similar to microfractures (Figure 4j).47 Liu et al. also found that Bakken shales have interparticle pores along the edge of the organic matter and grain.52 (5) Microfractures: In the study area, these can be divided into structural and bedding microfractures. Structural microfractures, mainly caused by tectonic stress, are long and wide. The length and width of the microfracture shown in Figure 4k are approximately 44.64 and 1.12 μm, respectively. Bedding fractures (Figure 4l) are microfractures that formed between

lamina under low stress, and they are parallel to the bedding planes. Bedding microfractures are rarely filled with other minerals (Figure 4l); thus, they can have better horizontal connectivity. 3.3. Characteristics of Mercury Intrusion Curves and NMR T2 Spectrum. The MICP test is an effective method to study pore structure. The pore structure information is not only qualitatively obtained by the shape of the MICP curves but also quantitatively described by the mercury injection pore structure parameters.53 Table 3 shows these parameters for the samples subjected to MICP testing. Figures 5a and 5d show the obviously H


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Figure 7. CT scanning and pseudocolor image of samples T55 and T77 from Well L69. (a) CT scanning image of sample T55. (b) CT scanning image of sample T77. (c) Pseudocolor image of sample T55. (d) Pseudocolor image of sample T77.

Table 4. Calculation results of the fractal dimension based on NMR samples

fitting equation

R2

D

samples

fitting equation

R2

D

7 80 148 228 308 442 522 646 726 806 853

y = 0.5610x − 1.2418 y = 0.5769x − 1.2834 y = 0.5788x − 1.2846 y = 0.5765x − 1.2700 y = 0.6043x − 1.3521 y = 0.6267x − 1.4122 y = 0.6418x − 1.4343 y = 0.6178x − 1.3811 y = 0.6480x − 1.4686 y = 0.6174x − 1.4030 y = 0.6410x − 1.4318

0.3934 0.4076 0.4024 0.3983 0.4228 0.4443 0.4434 0.4342 0.454 0.442 0.4421

2.4390 2.4231 2.4212 2.4235 2.3957 2.3733 2.3582 2.3822 2.3520 2.3826 2.3590

43 112 188 268 402 482 562 688 764 826 870

y = 0.6323x − 1.4082 y = 0.6132x − 1.3723 y = 0.6354x − 1.4153 y = 0.5739x − 1.2641 y = 0.6420x − 1.4384 y = 0.6528x − 1.5008 y = 0.6621x − 1.5259 y = 0.6156x − 1.3887 y = 0.7456x − 1.7287 y = 0.6491x − 1.4700 y = 0.6557x − 1.4818

0.4342 0.4267 0.4357 0.3975 0.4442 0.4628 0.4668 0.4376 0.5167 0.4546 0.4560

2.3677 2.3868 2.3646 2.4261 2.3580 2.3472 2.3379 2.3844 2.2544 2.3509 2.3443

mercury saturation is smaller (average 14.877%) than that for the type I curve (average 41.252%) under the same experimental conditions, indicating the well-developed micropores of the type I curve. Moreover, the type II curve is very steep and lacks a horizontal stage in the initial stage of mercury intrusion, and the porethroat radius mainly ranges from 102 nm to 103 nm (Figure 5e). The shape, magnitude, and width of the T2 distribution can qualitatively reflect the connectivity and size distribution of a sample’s pores.10 The NMR T2 distributions of the samples in a water-saturated state are shown in Figure 6a with relaxation time distributions ranging from 10−2 to 104 ms. As observed in this figure, the NMR T2 spectrum curves are messy, also suggesting the complexity of the pore structure and the strong heterogeneity of the shale sample. According to the different characteristics of the T2 spectrum, four categories have been proposed in this work. The first type of

different shape of the MICP curves and the wide range of porethroat size distributions in the samples, respectively, indicating the different qualities and the strong microscopic heterogeneities in the samples. Two types of MICP curves can be identified based on the characteristics of the mercury intrusion curves (Figure 5a) and the pore throat radius distribution curves (Figure 5b). Type I curves (samples 562, 482, 268, 228 and 308) exhibit a low displacement pressure (average 0.0186 MPa) and a relatively horizontal stage in the initial stage of mercury intrusion (Figure 5c), reflecting the development of large pore-throats and well-sorted throats. The pore size distribution of sample 308 is shown in Figure 5f, and the pore-throat radius mainly ranges from 104 nm to 105 nm. The type II curve (e.g., sample 43) have a displacement pressure typically larger than 0.326 MPa, suggesting the prevalence of small pore throats in the pore networks that make it difficult for mercury to enter. In addition, the maximum I


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Figure 8. Fractal calculation results of samples 80 and 308 from Well L69.

Figure 9. Box fractal dimension calculation results of Nano-CT scanning image 500, sample T55, and Nano-CT scanning image 250, sample 250.

T2 spectrum (e.g., sample 43) has continuous bimodal distributions, which feature higher magnitudes of short T2 peaks (higher left peak but lower right peak) (Figure 6b) corresponding to the relative development of micropores and poor pore connectivity.54 The second type of T2 spectrum (e.g., sample 764) is shown in Figure 6c with similar continuous bimodal distributions to the first type. However, there is a higher signal amplitude of the T2 peak in the range of 10−100 ms (lower left

peak but higher right peak), indicating the relative abundance of macropores. Three peaks were observed in the third type (sample 112) and the fourth type (sample 522) of T2 spectrum, indicating the development of micropores, macropores, and microfractures. However, the difference is that sample 522 has a smaller magnitude difference between the first peak and second peak than that of sample 112, suggesting that sample 522 has larger pores and better pore connectivity than sample 112. J


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Energy & Fuels Table 5. Calculation Results of the Box-Counting Fractal Dimension Based on the Nano-CT Imagesa T55 (por: 5%)

T77 (por: 8%)

CT image no.

fitting equation

box fractal dimension

R2

CT image no.

fitting equation

box fractal dimension

R2

50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

y = −1.3992x + 4.4253 y = −1.4225x + 4.4691 y = −1.3606x + 4.3174

1.3992 1.4225 1.3606

0.9916 0.9942 0.9943

50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

y = −1.4940x + 4.6241 y = −1.2839x + 4.1117

1.4940 1.2839

0.9977 0.9962

y = −1.2724x + 4.0928 y = −1.4174x + 4.4401 y = −1.2873x + 4.0772 y = −1.5337x + 4.7201 y = −1.5665x + 4.7907

1.2724 1.4174 1.2873 1.5337 1.5665

0.9959 0.9974 0.9988 0.9975 0.9981

y = −1.5486x + 4.7489 y = −1.1653x + 3.8046 y = −1.4758x + 4.5861 y = −1.6460x + 4.9657 y = −1.4675x + 4.5690 y = −0.9669x + 3.3165 y = −1.6222x + 4.9224 y = −1.6294x + 4.9396 y = −1.5199x + 4.6912 y = −1.3761x + 4.3406 y = −0.8004x + 2.7269

1.5486 1.1653 1.4758 1.6460 1.4675 0.9669 1.6222 1.6294 1.5199 1.3761 0.8004

0.9979 0.9960 0.9969 0.9979 0.9965 0.9912 0.9980 0.9979 0.9970 0.9973 0.9922

y = −1.4634x + 4.5611 y = −1.4273x + 4.4714 y = −1.3268x + 4.2467 y = −1.3625x + 4.304 y = −1.4148x + 4.4448 y = −1.3869x + 4.3927 y = −1.3815x + 4.3737 y = −1.3045x + 4.1984 y = −1.3291x + 4.2558 y = −1.2710x + 4.1178 y = −1.2867x + 4.1636 y = −1.4246x + 4.4651 y = −1.3464x + 4.2973 y = −1.4469x + 4.5354 y = −1.4793x + 4.6070

1.4634 1.4273 1.3268 1.3625 1.4148 1.3869 1.3815 1.3045 1.3291 1.2710 1.2867 1.4246 1.3464 1.4469 1.4793

0.9960 0.9965 0.9925 0.9974 0.9958 0.9926 0.9935 0.9901 0.9916 0.9899 0.9876 0.9962 0.9913 0.9927 0.9942

a

Note: Images 200 and 250 of sample T55 have the minimum and maximum threshold value, respectively, when adjusting the pore ratio to be close to the sample porosity. The same applies to images 150 and 450 of sample T77.

3.4. CT Characteristics. Sample T55 has a porosity of 5%, whereas the porosity of sample T77 is 7%, and their Nano-CT scanning images are shown in Figure 7a and b. The gray value of the pixels in the CT images is typically connected with the rock sample density.55 Shale is composed of a variety of complex minerals, which result in varying gray values in the CT images.56 In general, the gray value of voids (pores and fractures) is low, as represented by dark black, whereas that of high-density mineral parts is high, as represented by bright white.57 To clearly observe the morphology of the components in the CT scanning image, pseudocolor processing was carried out using Matlab software. After processing, the voids (pores and fractures) were dark blue, and the mineral parts were dark red (Figures 7c, d). Figure 7 shows that the distribution of the pores in the two samples is obviously heterogeneous, and the shape, size, and development degree are different at different positions. Intergranular pores and pyrite can also be recognized in the image. The dark blue area of sample T77 is larger than that of sample T55, indicating the pore structure of sample T77 is better than that of sample T55. 3.5. Fractal Dimension. 3.5.1. Fractal Dimension of NMR. The calculated fractal dimension values based on the NMR T2 spectrum of the shale samples are listed in Table 4. The fractal dimension values range from 2.2544 to 2.439 with an average of 2.3742, indicating the complex pore structure of shale samples. Figure 8 is a double logarithmic curve of Sv and T2 for samples 228 and 482. The fractal dimensions obtained by eq 1 are 2.4235 and 2.3472. 3.5.2. Fractal Dimension of the Nano-CT Scanning Images. The threshold values of samples T55 and T77 are 154 and 208, respectively, and the calculations of the fractal dimensions of Nano-CT scanning image 500 for sample T55 and Nano-CT scanning image 250 for sample T77 are shown in Figure 9. Table 5 lists the calculation results of the box-counting fractal dimension based on 20 Nano-CT scanning images of samples T55 and T77.

4. DISCUSSION 4.1. Pore Types and Their Influencing Factors. Dissolved pores are mainly formed by the dissolution of unstable minerals (e.g., feldspar and carbonate minerals) by acidic fluid caused by the hydrocarbon generation of organic matter.48−50 High carbonate mineral contents and the suitable thermal maturity of organic matter in the study area are beneficial to the development of calcite dissolved pores, which is confirmed by the SEM images (Figure 4i). In addition, feldspar-dissolved pores can also be observed (Figure 4h) because kaolinite can be transformed into Illite, which will consume potassium ions and promote the dissolution of potassium feldspar.58 Organic-matter pores (Figure 4j) are not developed in Well L69. The reason for this is because the organic-matter pores develop as obvious features when organic matter develops to a certain extent. Crutis et al. proposed that there is no secondary organic porosity when the vitrinite reflectivity (Ro) < 0.9% in the Woodford shale.59 Reed et al. held that it is 0.8%.60 Wu et al. proved that a large number of organic-matter pores in the lacustrine shale of the Ordos Basin begin to appear when Ro > 1.2%.19 Therefore, the reason for this phenomenon is that the Ro values of the shale samples in the Es3L member of Well L69 in the Zhanhua Depression mainly range from 0.74 to 0.87%.51 The SEM images show that there are pores developed in the clay mineral (Figures 4d, f, g), but the relationship between the clay mineral content and porosity is complex. It is very likely that the clay minerals easily fill the macropores and cracks, which have a negative effect on porosity, but they also develop intercrystalline and intergranular pores (Figures 4d, f, g). The superposition of the two effects may result in the complex contribution of clay minerals to porosity.61 The development of fractures in rocks is closely related to the content of brittle minerals (e.g., quartz and calcite).62 With the increase in brittle mineral contents, more fractures are likely to develop. It is noted that the development of fractures is also K


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Figure 10. (a) Analysis position of sample T55. (b) Analysis position of sample T77. (c) Three-dimensional digital cores of sample T55. (d) Threedimensional digital cores of sample T77. (e) Pore connectivity of sample T55. (f) Pore connectivity of sample T77.

however, there are also many isolated pores that have poor connectivity, and the pore connectivity in sample T77 is better than that in sample T55. The studies of Guo et al.11 and Milliken et al.17 showed that a large number of organic pores can guarantee the good connectivity of shale micropores. Under the condition of poor organic-matter pores in the study area, the pore connectivity may be related to the development and pore size of inorganic pores. In addition, the calculated box-counting fractal dimensions from the Nano-CT scanning images of sample T55 are smaller than those of sample T77 on average, which shows that the boxcounting fractal dimension of the pore structure increases with the increase in the pore ratio. Therefore, the box-counting fractal dimension is closely related to the pore structure, and better pore structure results in larger box-counting fractal dimension. 4.3. Relationships between the NMR Fractal Dimension and the Compositions and TOC Content of Shale. Figure 11 shows that the NMR fractal dimensions of the shale samples from the Es3L member in Well L69 have positive

affected by other factors, such as tectonic stress, sedimentary microfacies, and TOC content.62,63 Microfractures developed in the shale of the Es3L member in the Zhanhua Depression (Figures 4k, l). 4.2. CT and Pore Structure. Panels c and d in Figure 10 show the three-dimensional digital cores of samples T55 and T77 based on the Nano-CT scanning images (the position of the analysis is shown in Figure 10a, b). Panels c and d in Figure 10 exhibit a random distribution of voids (red part) and organic matter (blue part) in shale, indicating their strong heterogeneity. The void development in sample T77 is higher than that in sample T55, which is consistent with the results of the core physical analysis. The micropore distribution of the shale reservoir has obvious heterogeneity. In other words, there are differences in the size, shape, and abundance of micropores in different positions. This microscopic difference will affect the connectivity of the tight reservoir space and the permeability of the reservoir.64 Panels e and f in Figure 10 show the pore connectivity in the two samples. Some pores can be interconnected by the throats; L


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Figure 11. Relationships between the NMR fractal dimension and (a) TOC, (b) quartz content, (c) calcite content, and (d) clay content.

the fractal dimensions of N2 adsorption.30 Our results show that there is a positive correlation between the content of quartz and the NMR fractal dimensions of lacustrine shale. On the one hand, the continental clastic quartz in this study area could be small due to a long transportation distance and easily fill in the pore, resulting in irregular pore shapes. On the other hand, quartz is not the main mineral component in the study area, and a high quartz content means a high clay mineral content and low calcite content (Figure 3). Therefore, the NMR fractal dimension increases with increasing quartz content. Figure 11c shows that there is a negative correlation between the calcite content and NMR fractal dimensions. This may be due to unstable minerals (e.g., calcite and feldspar) reacting with the acidic fluid to generate some dissolved pores, which in turn results in the development of dissolved pores, especially in the case of high carbonate mineral contents in the study area. Therefore, the average pore size increases, the complexity of the pore structure decreases, and the fractal dimension decreases. A positive correlation occurs between the content of clay minerals and the NMR fractal dimensions (Figure 11d). The main reason is clay minerals have a relatively high specific surface area of pores because of the layer structure and flocculent structure, thus enhancing the complexity of the pore surface.22 In addition, the development of intracrystalline and intergranular pores in clay minerals can further complicate the pore structure (Figures 4d, e).

correlations with the contents of quartz, clay minerals, and TOC while showing a negative correlation with the calcite content. Previous studies have pointed out that there is a positive correlation between the fractal dimensions calculated by N2 adsorption and TOC content.22,24,65 The reason is that a high content of TOC in shale will develop a large number of organicmatter pores, which increases the number of micropores, resulting in a large specific surface area and high fractal dimension. In this study, the relationship between the NMR fractal dimension of the shale samples and the content of TOC is also positively correlated (Figure 11a), but the reason is different. The development of organic pores in shale is mainly affected by the content, type, and maturity of organic matter, especially the maturity.66 As mentioned before, the organic matter maturity is relatively low in the study area. In addition, clay minerals play an important role in enriching the organic matter in lacustrine shale.67 Therefore, the high content of organic matter, which means a high content of TOC, occurring as the shale matrix is not beneficial to the development of shale porosity (Figure 10c), and it will increase the heterogeneity of the pore structure, resulting in an increasing NMR fractal dimension. The relationship between quartz and the NMR fractal dimensions is shown in Figure 11b. Quartz from different sources (continental or biogenic) has different constructive effects on a shale reservoir. Hu et al. reported that the quartz in marine shale derived from siliceous organisms has a positive relationship with M


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Figure 12. Relationship between the NMR fractal dimension and (a) T2 cutoff value, (b) T2 geometric mean value, (c) porosity, and (d) displacement pressure.

4.4. Relationships between the NMR Fractal Dimension and Pore Structure Parameters. The NMR fractal dimension has a negative correlation with the T2 cutoff value, T2 geometric mean value, porosity, and average pore throat radius and a positive correlation with the displacement pressure with no obvious relationship with permeability. Among them, the negative relationship with the T2 geometric mean value is the strongest. Therefore, the pore structure is closely related to the NMR fractal dimension, and better pore structure results in smaller fractal dimensions.26 However, panels a and c in Figure 12 do not show strong negative correlations between the NMR fractal dimensions and

the T2 cutoff value and porosity, indicating that the T2 cutoff value and porosity only reflect the quality of the pore structure to some extent. In other words, the weight of the T2 cutoff value and porosity for pore structure evaluation is small. The strongest negative relationship is between the NMR fractal dimension and T2 geometric mean value (Figure 12b), suggesting that the T2 geometric mean value has the largest weight in the evaluation of pore structure. The NMR fractal dimension is weakly related to the displacement pressure (Figure 12d). On one hand, smaller displacement pressure results in larger pore throats, indicating a better pore structure. As mentioned above, the weight of the displacement N


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Figure 13. (a) Well logging profile in Well L69. (b) Trend of the fractal dimension of four typical samples. (c) Characteristics of the mercury injection curves and NMR T2 spectra of four samples (Note: Full hole microresistivity imaging (FMI) measuring the formation of microresistivity includes 192 electrodes and a vertical resolution of 0.2 in with the dark color representing high conductivity and the light color representing high resistivity; it is indicated that the core sample developed a fracture when there is a black line in the fracture track; SAB: the length of the gentle part of the capillary pressure curve of the total mercury volume; a: the tilt angle of the gentle part of the capillary pressure curve).

between the NMR fractal dimension and pore structure to be verified, the relationship between the effectiveness of the reservoir and the NMR fractal dimension was observed and analyzed on the basis of log interpretation and dividing the favorable sections of the Es3L member Well L69 (Figure 13a). Samples 482 and 562 were obtained from favorable sections (3042−3081.1 m), and their NMR fractal dimensions are 2.3427 and 2.3379, respectively, which are smaller than those of samples 442 and 806 from unfavorable sections with NMR fractal dimensions of 2.3733 and 2.3826, respectively. The characteristics of the mercury injection curves and NMR T2 spectra of four typical samples are shown in Figure 13c. As the NMR fractal dimension increases, the corresponding maximum mercury saturation gradually decreases, the displacement pressure increases, and the length of the gentle segment of the mercury-injection curve becomes shorter, which indicates

pressure in the pore structure evaluation is small. On the other hand, conventional mercury injection cannot express all the pore structure information in shale. Therefore, the pore structure parameters obtained from conventional mercury injection could be limited in the evaluation of pore structure. These two reasons cause a weak positive correlation trend between the NMR fractal dimension and displacement pressure. Figure 12e shows the negative correlation between the average pore throat radius and NMR fractal dimension. A smaller average pore throat radius means more micropores in the shale sample, reflecting the complexity of the pore structure.24,68 There is no obvious relationship between the NMR fractal dimension and permeability (Figure 12f), which may be because fractures have a large influence on permeability in shale reservoirs.62 4.5. Verification of the Relationship between the Fractal Dimension and Pore Structure. For the relationship O


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Energy & Fuels that the pore structure tends to be worse. The NMR T2 spectrum curves show that the peak number of the NMR T2 spectra changes from three to two and that the amplitude of the left peak tends to be higher, reflecting the deteriorating pore structure with the increasing NMR fractal dimension. Therefore, the fractal dimension can be used to indicate the effectiveness of shale reservoirs when the conventional logging curves cannot reflect it well.

Science and Technology Major Project of China (Grant No. 2017ZX05049-004).

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(1) Monge, M.; Gil-Alana, L. A.; de Gracia, F. P. U.S. shale oil production and WTI prices behaviour. Energy 2017, 141, 12−19. (2) Fu, H.; Wang, X.; Zhang, L.; Gao, R.; Li, Z.; Xu, T.; Zhu, X.; Xu, W.; Li, Q. Investigation of the factors that control the development of pore structure in lacustrine shale: A case study of block X in the Ordos Basin, China. J. Nat. Gas Sci. Eng. 2015, 26, 1422−1432. (3) Cai, Y.; Liu, D.; Pan, Z.; Yao, Y.; Li, J.; Qiu, Y. Pore structure and its impact on CH4, adsorption capacity and flow capability of bituminous and subbituminous coals from Northeast China. Fuel 2013, 103, 258−268. (4) Ross, D. J. K.; Bustin, R. M. The importance of shale composition and pore structure upon gas storage potential of shale gas reservoirs. Mar. Pet. Geol. 2009, 26 (6), 916−927. (5) Vafaie, A.; Habibnia, B.; Moallemi, S. A. Experimental investigation of the pore structure characteristics of the Garau gas shale formation in the Lurestan Basin, Iran. J. Nat. Gas Sci. Eng. 2015, 27 (10), 432−442. (6) Klaver, J.; Desbois, G.; Littke, R.; Urai, J. L. BIB-SEM pore characterization of mature and post mature Posidonia Shale samples from the Hils area, Germany. Int. J. Coal Geol. 2016, 158, 78−89. (7) Tian, H.; Pan, L.; Xiao, X.; Wilkins, R. W. T.; Meng, Z.; Huang, B. A preliminary study on the pore characterization of Lower Silurian black shales in the Chuandong Thrust Fold Belt, southwestern China using low pressure N2, adsorption and FE-SEM methods. Mar. Pet. Geol. 2013, 48, 8−19. (8) Chen, Y.; Wei, L.; Mastalerz, M.; Schimmelmann, A. The effect of analytical particle size on gas adsorption porosimetry of shale. Int. J. Coal Geol. 2015, 138, 103−112. (9) Hu, Q.; Zhang, Y.; Meng, X.; Li, Z.; Xie, Z.; Li, M. Characterization of micro-nano pore networks in shale oil reservoirs of Paleogene Shahejie Formation in Dongying Sag of Bohai Bay Basin, East China. Petroleum Exploration and Development 2017, 44 (5), 720− 730. (10) Kewen, W.; Ning, L. Numerical simulation of rock pore-throat structure effects on NMR T2 distribution. Applied Geophysics 2008, 5 (2), 86−91. (11) Guo, X.; Shen, Y.; He, S. Quantitative pore characterization and the relationship between pore distributions and organic matter in shale based on Nano-CT image analysis: A case study for a lacustrine shale reservoir in the Triassic Chang 7 member, Ordos Basin, China. J. Nat. Gas Sci. Eng. 2015, 27, 1630−1640. (12) Clarkson, C. R.; Solano, N.; Bustin, R. M.; Bustin, A. M. M.; Chalmers, G. R. L.; He, L.; Melnichenko, Y. B.; Radliński, A. P.; Blach, T. P. Pore structure characterization of North American shale gas reservoirs using USANS/SANS, gas adsorption, and mercury intrusion. Fuel 2013, 103, 606−616. (13) Yang, R.; He, S.; Hu, Q.; Sun, M.; Hu, D.; Yi, J. Applying SANS technique to characterize nano-scale pore structure of Longmaxi shale, Sichuan Basin (China). Fuel 2017, 197, 91−99. (14) Lai, J.; Wang, G.; Wang, Z.; Chen, J.; Pang, X.; Wang, S.; Zhou, Z.; He, Z.; Qin, Z.; Fan, X. A review on pore structure characterization in tight sandstones. Earth-Sci. Rev. 2018, 177, 436−457. (15) Loucks, R. G.; Reed, R. M.; Ruppel, S. C.; Hammes, U. Spectrum of pore types and networks in mudrocks and a descriptive classification for matrix-related mudrock pores. AAPG Bull. 2012, 96 (6), 1071− 1098. (16) Nelson, P. H. Pore-throat sizes in sandstones, tight sandstones, and shales. AAPG Bull. 2009, 93 (3), 329−340. (17) Milliken, K. L.; Rudnicki, M.; Awwiller, D. N.; Zhang, T. Organic matter−hosted pore system, Marcellus Formation (Devonian), Pennsylvania. AAPG Bull. 2013, 97 (2), 177−200. (18) Liu, W.; Liu, J.; Cai, M.; Luo, C.; Shi, X.; Zhang, J. Pore evolution characteristic of shale in the Longmaxi Formation, Sichuan Basin. Petroleum Research. 2017, 2, 291−300.

5. CONCLUSIONS In this work, 22 lacustrine shale samples from the Es3L member, Zhanhua Depression, Bohai Bay Basin, are investigated by X-ray diffraction, organic geochemistry analysis, conventional mercury injection, nuclear magnetic field, and Nano-CT analysis, and their fractal characteristics are determined based on NMR T2 spectrum. According to the physical significance of the fractal dimension, the relationship between the mineral content, TOC and pore structure parameters, and the NMR fractal dimension is discussed. The following conclusions can be made: (1) The main mineral component of the shale samples from the Shahejie formation, Zhanhua Depression, Bohai Bay Basin are calcite, clay minerals, and quartz. The pore types are mainly intercrystalline pores in clay minerals, intercrystalline pores in pyrite, dissolved pores, and microfractures. (2) The analysis of mercury injection and nuclear magnetic field data shows that the pore throat distribution in the shale samples has a wide range, indicating the poor sorting property. The pore structure of the shale samples is complex and shows a strong pore heterogeneity. (3) The fractal dimension of the shale samples calculated by NMR ranges from 2.2544 to 2.439 with an average of 2.3742. The NMR fractal dimension is positively correlated with the TOC content, quartz content, and clay mineral content. There is a negative correlation between the calcite content and NMR fractal dimension. (4) The NMR fractal dimension of the shale samples is negatively correlated with the T2 cutoff value, the mean value of the T2 geometry, porosity, and average pore throat radius, whereas there is a positive relationship between the NMR fractal dimension and the displacement pressure and no obvious correlation with permeability. There is a close relationship between the NMR fractal dimension and pore structure; thus, the NMR fractal dimension can be used to indicate the effectiveness of the shale reservoirs when the conventional logging curves cannot reflect it well.

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Shaolong Zhang: 0000-0002-0670-9825 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Open Fund of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Southwest Petroleum University) (Grant No. PLN201702), National Natural Science Foundation of China (Grant No. 41202110, 51674211), Applied Basic Research Projects in Sichuan Province (Grant No. 2015JY0200), and National P


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