3D characterization and quantitative evaluation of

International Journal of Coal Geology 174 (2017) 41–54

Contents lists available at ScienceDirect

International Journal of Coal Geology journal homepage: www.elsevier.com/locate/coal

3D characterization and quantitative evaluation of pore-fracture networks of two Chinese coals using FIB-SEM tomography

MARK

Sandong Zhou, Dameng Liu⁎, Yidong Cai, Yanbin Yao, Zhentao Li Coal Reservoir Laboratory of National Engineering Research Center of CBM Development & Utilization, School of Energy Resources, China University of Geosciences, Beijing 100083, China

A R T I C L E I N F O

A B S T R A C T

Keywords: Coalbed methane Pore connectivity Permeability FIB-SEM Pore network model

To more finely describe the physical basis of coalbed methane (CBM) accumulation and flow mechanisms, two different rank coals (Ro,m of 0.4% and 0.85%) from the southern Junggar Basin of northwest China were systematically investigated to characterize pore-fracture spaces and their nanoscale connectivity in three dimensions (3D) using focused ion beam scanning electron microscopy (FIB-SEM) tomography. We reconstructed the 3D pore morphology of two different rank coals, quantify the pore size/volumes distribution and developed a novel pore network extraction (PNE) model. Samples of subbituminous coal (SC) and high-volatile bituminous coal (HBC) presented significant pore spaces for CBM adsorption, with total voxel numbers of 28,944 and 83,866, respectively; both samples predominantly consisted of closed-pore diameters of 10–50 nm. The numbers, volumes, and areas of pores (< 100 nm) were less in SC than in HBC, revealing that the SC adsorption capability was weaker than HBC. The porosities acquired by FIB-SEM were 26.06 and 42.85% for the samples SC and HBC, respectively, which could indicate the storage capability of the SC reservoir was lower than that of the HBC reservoir. The SC and HBC samples revealed a significant connectivity for CBM seepage, with a connected pores proportion of ~100% in pores > 300 nm. The SC sample allowed pore space connections throughout, whereas the HBC sample partially displayed pore space connections in a 3D pore network. It was found that a throat size of 400–500 nm could possibly dominate coal permeability in the SC sample; the numbers of throats (fractures) decreased with rising throat size. These results show that the gas accumulation capacity of the SC reservoir are lower than that of the HBC, whereas the fluid flow capability of the SC reservoir is higher than that of the HBC reservoir. These findings may be scientifically significant for lucubrating nanoscale pores to affect CBM storage and seepage. This paper comments on the reduction of the gas sorption capability and mass transport rate in CBM development, and we provide recommendations for relevant future work.

1. Introduction

bodies; Hemes et al., 2015); this classification has been used to gain insight into the effects of pore/fracture geometry and morphology on gas sorption and flow capability (Cai et al., 2013). CBM is concentrated on adsorbing pore surfaces of 2–10 nm and 10–50 nm size (Zhou et al., 2016a, 2016b, 2016c), and gas transport properties are significantly influenced by the mesoporosity and macroporosity (Zhao et al., 2016). The two-dimensional (2D) pore geometry characteristics of SC and HBC samples have been extensively investigated, resulting only in knowledge of pore morphology and size. Three-dimensional (3D) pore/ fracture connectivity in SC and HBC remains lacking in systematic research and needs further study (Wang et al., 2016a). Therefore, the 3D microscopic structure characteristics of fluid adsorption and flow in SC and HBC are relevant. Tahmasebi et al. (2016) proposed a new approach for permeability with 3D multi-scale structures. Pore structure characterization has been

The exploration and development of coalbed methane (CBM) have been rapidly growing in Australia, Poland and China (Kang et al., 2016; Kędzior, 2015; Saurabh et al., 2016), especially in subbituminous coals (SC) and high-volatile bituminous coals (HBC) (Connell et al., 2016; Li et al., 2016a). However, modified theoretical rationalizations, such as gas adsorptive/flow capacity and storage/transport mechanisms, remain essential in understanding the CBM commercial development of SC and HBC (Li et al., 2016a, 2016b). The following bonding pore/ fracture size ranges from IUPAC and Hodot were used in the research reported in this paper: super micropores (< 2 nm), micropores (2–10 nm), transition pores (10–102 nm), mesopores (102–103 nm), macropores (> 103 nm) and throats/fractures (irregular shape, sphericality < 0.3 and restriction of serially smaller spheres, linking two pore

⁎

Corresponding author. E-mail address: [email protected] (D. Liu).

http://dx.doi.org/10.1016/j.coal.2017.03.008 Received 27 November 2016; Received in revised form 19 March 2017; Accepted 21 March 2017 Available online 24 March 2017 0166-5162/ © 2017 Elsevier B.V. All rights reserved.


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Table 1 Petrographic and proximate analysis results for two Chinese coals. Sample no.

SC HBC

Ro,m (%)

0.40 0.85

Coal rank classes*

Subbituminous High-volatile bituminous

Coal composition (wt%)

Proximate analysis (%)

Vitrinite

Inertinite

Liptinite

Mineral

Mad

Ad

Vdaf

FCad

58.6 68.6

39.9 24.9

0.4 0.5

1.1 6.0

11.1 6.7

6.0 2.8

31.2 23.9

51.7 66.6

Ro, m = maximum vitrinite reflectance under oil immersion; *: after Flores (2014); Mad = moisture content (wt%, air-dried basis); Ad = ash yield (wt%, dry basis); Vdaf = volatile matter content (wt%, dry, air free basis); FCad = fixed carbon content (wt%, air-dried basis).

Fig. 1. The BSE images by sequential FIB-SEM showing the anisotropy of the microstructure from sample SC. a) - 1st, b) - 300th, c) - 500th, d) - 770th.

present, many researchers have combined two or more methods to characterize 2D and 3D pore geometry and connectivity (Gaboreau et al., 2016; Keller et al., 2013a). However, the experimental conditions of different methods generally cannot consistently match, which may result in a relatively high error. Although X-CT can accurately present coal cleats, seepage-pores and 3D spatial distribution, it cannot show coal nanopores or adsorption-space characteristics because of image resolution (> 150 nm; Wang et al., 2016a). Little research has been reported on coal 3D pore morphology by FIB-SEM measurement, especially for pore diameters < 100 nm, which are numerous and significant for CBM adsorption, desorption and diffusion. In this work, the 3D pore networks of typical pore structures, including primary and secondary pores of SC and HBC samples from the Xishanyao Formation of the southern Junggar Basin, were determined by FIB-SEM. We developed a novel 3D model for intuitively presenting the spatial distributions of pore-fractures. Additionally, we quantified the area and volume proportions of closed (isolated) and connected

researched by many experts using three categories of analysis techniques (Deng et al., 2016): (1) microscopic imaging, such as scanning electron microscopy (SEM) (Curtis et al., 2012), broad ion beam scanning electron microscopy (BIB-SEM) (Giffin et al., 2013), focused ion beam scanning electron microscopy (FIB-SEM) (Hemes et al., 2015), field emission SEM (Chalmers et al., 2012), atomic force microscopy (Pan et al., 2015), helium ion microscopy (Gastel et al., 2015), transmission electron microscopy (Mathews and Sharma, 2012) and X-ray computed microtomography (X-CT) (Karacan and Okandan, 2001; Karacan et al., 2003; Zhang et al., 2016); (2) penetration fluids, including mercury porosimetry (Clarkson et al., 2012), helium pycnometry (Zhao et al., 2014) and N2/CO2 adsorption (Abunowara et al., 2016; Nie et al., 2015; Zhao et al., 2016); and (3) nondestructive physical techniques, including Fourier Transform infrared spectroscopy (Baysal et al., 2016), nuclear magnetic resonance (Genetti et al., 1999; Zhou et al., 2017), Raman spectroscopy (Wu et al., 2014) and synchrotron small angle X-ray scattering (Clarkson et al., 2013). At 42


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Fig. 2. 2D micro-pores structure of sample SC from the southern Junggar Basin, NW China.

ash yields of 6.0 and 2.8% (dry basis), volatile matter contents of 31.2 and 23.9% (dry ash-free basis) and fixed carbon contents of 51.7 and 66.6% (air dried basis) for the SC and HBC samples, respectively (Table 1). Drying is obligatory for electron microscopy (Keller et al., 2011; Song et al., 2015, 2016). We used high-pressure freezing and subsequent freeze-drying rather than conventional drying or freezedrying. These special techniques can minimize the evolution of drying artifacts, including drying shrinkage and ice formation (Keller et al., 2013b). A detailed introduction to high-pressure freezing methods was elaborated by Bachmann and Mayer (1987), and the drying procedures were the same as those of Keller et al. (2013b).

pores. In particular, quantitative information about pore size (down to 4 nm voxel size)/volume distribution (PS/VD, which is significant for CBM adsorbability and diffusion), porosity, connectivity, and transport capability were calculated. These discoveries and their implications for the storage and flow of fluids in coals are also discussed. 2. Materials and methods 2.1. Sample preparation and petrological characteristics Two different rank coal samples (SC and HBC) originating from the Xishanyao Formation in the southern Junggar Basin of northwest China were used in this study. The SC and HBC samples had a maximum vitrinite reflectance of 0.4% and 0.85%, respectively. The samples were carefully wrapped and immediately sent to the laboratory for petrological analysis. The maximum vitrinite reflectance, maceral compositions and proximate analyses followed the standards ISO 7404.3-1994, ISO 7404.5-1994 and ISO 17246-2010, respectively; analyses were performed in the Beijing Key Laboratory of Unconventional Natural Gas Geology Evaluation and Development Engineering. Details of the experimental apparatus and procedures were reported in our previous research (Zhou et al., 2016a). Table 1 shows the vitrinite, inertinite, liptinite and mineral contents of the two samples. The proximate analyses produced moisture contents of 11.1 and 6.7% (air-dried basis),

2.2. FIB-SEM tomography Prior to samples drying, cuboidal-shaped 0.5 × 1 × 1 cm3 coal samples suitable for FIB-SEM were polished with dry emery paper and then ground by argon ion. Subsequently, the coal samples were glued onto a sample holder for FIB-SEM measurements. The resulting single FIB-SEM slices were obtained following the procedure of Hemes et al. (2015), so that an area within the coal sample was selected for FIB-SEM tomography. The SEM and FIB landing voltage ranges were an electron beam of 20 V–30 kV and an ion beam of 500 V–30 kV, respectively, with a magnification of 300×–500k ×. The configuration consisted of the detectors (secondary electron (SE) detector, E-T SE 43


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Fig. 3. 2D micro-fractures structure of sample HBC from the southern Junggar Basin, NW China.

3D visualization, was presented in Hemes et al. (2015). Single FIB-SEM images were realigned with the software Fiji/ImageJ (http://imagej. nih.gov/ij/) plugins ‘StackReg’ or ‘TurboReg’ (Abràmoff and Viergever, 2002), and volumes of interest were handled in Fiji/ImageJ by the plugin ‘VolumeJ’ (Münch et al., 2009). Münch et al. (2009) used a destriping filter (‘xStripes.jar’) to exclude perpendicular curtaining irregularities arising during the ion-beam milling of anisotropic mediums. Additionally, we used enhancing image filters (background equalization, noise reduction and sharpening of pore boundaries) in Adobe Photoshop CS6 to increase the quality of subsequent semiautomatic porosity segmentation. Pore volume reconstruction and pore space segmentation were performed by 3D visualization using the FEI Avizo® Fire 8.1.1 imaging software. Subsequently, the quantitative pore surface area/volume and fracture length/area determinations were performed on the rendered volumes by dispatching grayscale values to microstructural features and setting thresholds on the grayscale to segment features (Hemes et al., 2015). Biswal et al. (1998) and Hilfer and Helmig (2004) applied covariance analysis to investigate the spatial anisotropy of performance at the scale of surveillance (Keller et al., 2013a) and to evaluate the relative error of the property calculation (Kanit et al., 2003). The detailed estimates of volumes in the present research were determined by covariance functions (Hemes et al., 2015; Kanit et al., 2003).

detector and ESB backscattered electrons (BSE) detector), the X-ray spectrometer and the gas injection systems (up to 5 units for heightened etch or deposition). Each sample was imaged using FEI's exclusive Helios NanoLab™ 650 DualBeam™ FIB-SEM technologies, following the procedure detailed in Holzer et al. (2006) and Münch et al. (2006). In this system, the through-the-lens detector has high efficiency for collecting secondary electrons and on-axis backscattered electrons and is supplemented by a progressive detection suite that contains three detectors: two multi-segment solid state detectors for low kV SE/ BSE and scanning transmission electron mode (S/TEM) equipment and a third dedicated to optimized FIB-SE and FIB-SI (secondary ion) imaging. The SEM images of the freshly ground coal surfaces in situ were obtained at a high resolution of 2.5 nm, with an acceleration voltage of 2 kV and a working distance of 4 mm, which resulted in a pixel-size of 14.8 × 14.8 nm. The angle between the electron and ion columns was set at 52° and ~800 SEM images of FIB slices were obtained. Each FIB-SEM imaging had an angle of 52° to the ion beam, which was perpendicular to the surveyed sample surface (Holzer et al., 2004). This allowed the y-axis of the total images to be sloped by y/sin (52°) for practical scale performance (Song et al., 2015, 2016). 2.3. Pre-processing of FIB-SEM and evaluation of representative volumes The entire 2D imaging procedure, including volume rendering and 44


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Fig. 4. 3D pore-fractures network reconstruction (a1 and b1), identification (a2 and b2) and extraction (a3 and b3). Each color signals a pore not connected to the others in a2 and b2. a1), a2), a3) - sample SC; b1), b2), b3) - sample HBC. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

the area analyzed, Si is the plot against the centers of the respective bin and C is a constant of equilibrium. The power-law exponent (D) should be acquired by the slope of a linear fitting to the log-log pore areas distribution. Each pore volume is evaluated with respect to its typicality for the coal matrix pore microstructures. We used two complementary methods, the Box Counting method and local porosity distribution, to determine the varied porosity in any subset of the stack (Song et al., 2016). The former method exists in displacing a box of given size L throughout entire probable locations of every binary image (Houben et al., 2013). The local porosity distribution is stated as in (Keller et al., 2013a; Song et al., 2015) by:

2.4. Pore space analyses The pore space analyses consisted of volume rendering and connected component analysis, modeling pore network extraction (PNE) and analysis of pore-size distributions, especially the area/volume percentage of closed pores in the total pores (Hemes et al., 2015; Holzer et al., 2006; Zhou et al., 2016a). We used the Avizo plugin ‘connected component analysis’ to quantify the porosity volumes, which were considered to be connected in 3D. Dong and Blunt (2009) coded a version of network extraction, called PNE, which was built on the ‘maximum ball approach’ of Silin and Patzek (2006). Many papers (Houben et al., 2013, 2014; Klaver et al., 2012, 2016) have used the following equation to obtain pore size distribution:

log(Ni (bi (Sarea )) = −D log(Si ) + log C

μ (ϕ, L ) =

(1)

where Ni is the pore size frequency, bi is the bin-size, Sarea is the size of

1 m

m

∑ δ (ϕ − ϕ (x i , L ) ) i =1

(2)

where m is the number of positions of L and δ(t) is the Dirac delta

45


29.5–2763.7 27.3–2515.8

3.1. 2D pore-fracture morphology

74.362 67.640

19.770 23.212

Fig. 1 shows the anisotropic microstructure of the SC sample by four single FIB-SEM images. The pore space morphology and connectivity distinctly varied from the 1st to the 770th image (Fig. 1a–d), which indicates that gas adsorption and flow capabilities could significantly vary in micro-areas. Fig. 2b–f shows the representative pore geometry of coal sample SC magnified from Fig. 2a. Generally, the primary pore types in samples SC and HBC were intraplatelet (IntraP) pores (Fig. 2b), organic matter (OM) pores (Fig. 2c and e), interparticle (InterP) pores (Fig. 2d), and intercrystalline (InterC) pores (Fig. 2f), which is in agreement with our previous work (Zhou et al., 2016c). Fig. 3a–f shows that the HBC sample developed multi-scale and different morphology micro-fractures in single FIB-SEM images. In contrast to the SC sample (Figs. 2 and 3), the HBC sample had more micro-fractures because of the first coalification jump that could cause huge micro-fractures in vitrinite (Bustin and Guo, 1999). Fig. 3b and c shows distinctly wellconnected micro-fractures with lengths of 1 μm–50 μm and a maximum width of 3.5 μm, except for those filled with a certain mineral. Nanoscale fracture characteristics, including the aperture, length and connectivity, are quantitatively presented in Fig. 3d–f. These microfractures may provide significant CBM migration pathways.

5.826 4.838 516 715

477.804 374.93

3.2. 3D reconstructed structures

14.105 12.407 28,944 83,866 SC HBC

Min. (nm)

579.458 901.164

18.409 14.452

24.528 27.167

667.600 723.139

26.06 42.85

FIB-SEM tomography was applied to survey the 3D-space porefracture reconstructed structure to determine detailed information about the typical pore-fracture network structures (Holzer et al., 2006; Liu et al., 2016; Münch et al., 2006). The reconstructed structure was determined using the three procedures of reconstruction, identification and extraction (Fig. 4). The sub-volumes of the SC and HBC samples were 5.609 × 3.08 × 5.446 μm and 4.679 × 3.2 × 4.24 μm, respectively. The samples were segmented into either coal matrix (black) or fluid space (other color) for each FIB-SEM slice (Fig. 4a2 and b2). The extracted fluid space in the SC sample was more capacious than that of the HBC sample (Fig. 4a3 and b3), which indicated that the SC sample may have contained high fluid space. However, it is unclear which types of coal rank adsorption and seepage capabilities were relatively stronger. Table 3 presents the detailed numerical porefracture structural parameters. Both the SC and HBC samples had pore voxel numbers of 28,944 and 83,866, average pores of 18.409 and 14.452 nm, pore volumes of 24.528 and 27.167 μm3 and areas of 667.6 and 723.139 μm2, respectively (Table 3). Additionally, Table 4 shows the detailed pore (< 50 nm) distribution; this scale of pores dominated the total pore voxel numbers (pore numbers proportion > 95%). These results show that SC and HBC could supply enormous gas adsorption spaces. Meanwhile, samples SC and HBC contained hundreds of throats (fractures) with average apertures of 74.362 and 67.64 nm, maximum apertures adjacent to 500 nm and varying channel lengths of 29.5–2763.7 nm and 27.3–2515.8 nm, respectively (Table 2). These throats may also be an effective channel for CBM migration and can also provide space for CBM storage.

KKT = liquid permeability predictions with Katz-Thompson model.

Channel length (nm) Area (μm2) Avg. (nm) Min. (nm) Total no.

Max. (nm)

3. Results and discussions

Total no.

Max. (nm)

Avg. (nm)

Volume (μm3)

Area (μm2)

Volume fraction (%)

Throat (fracture) Pore Sample no.

Table 2 Structural parameters of two Chinese coals pore-throats from FIB-SEM.

function. μ(ϕ,L) has the potential to obtain the local porosity value ϕ in a box of size L, localized on a pixel of coordinates xi. The porosity distribution at a given box size is acquired by the Mean filter tool, and the stack histogram furnishes values of average porosity and standard deviation (Robinet and Gaboreau, 2013). This is recognized as illustrating a representative essential volume of porosity.

4.804 1.989

KKT (10− 3 mD)

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3.3. Pore interconnectivity and geometry 3.3.1. 3D visualization connectivity and prediction of fluid permeability Fig. 5 shows the rotated 3D visualization of pore connectivity and 46


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Fig. 5. 3D visualization of pores connectivity and PNE modeling. a1), a2) - sample SC; b1), b2) - sample HBC. a1), b1) - individual pore components sectionalized from Otsu thresholding (Gaboreau et al., 2016). Each color represents a pore not connected to the others. a2), b2) – Skeleton representation of the pore space. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

model and dc is the critical or breakthrough aperture, which is commonly considered to be the peak of pore size distribution from mercury porosimetry. dc is the equivalent of throat diameter; it chains successively smaller spheres, linking two pore bodies from PNE. F is the formation factor, ϕ is the coal porosity and τ is taken to be equal to the geometrical tortuosity obtained by FIB-SEM. Note that this simulated permeability does not take liquid/solid surface interactions into account. Table 2 presents the liquid permeabilities KKT for the two rank coals; the value for SC was 4.8 × 10− 3 mD and that for HBC was 1.9 × 10− 3 mD. Compared with experimental fluid permeability, KKT values were smaller by several orders of magnitude, probably because of the following reasons. First, significant interactions of gas, water and nanoparticles (i.e., pulverized coal) exist in mass transport that can influence the coal permeability (Abdelfatah et al., 2017; Zang and Wang, 2017). Second, macroscopic fissures (longer than tens of microns) occur in coals (Connell et al., 2016); these cannot be captured by skeletonizations of the percolating pore network from FIB-SEM because of small sample sizes. However, it is still concluded that the simulation of fluid transport (permeability) in SC was higher than that

establishes the PNE model. The 3D visualization of pore-fractures in the SC sample showed a relatively scattered distribution with six colors of independent multi-pores (Fig. 5a1), whereas the HBC sample had concentrations in two parts (Fig. 5b1). These results confirmed that the connectivity of the SC sample was better than that of the HBC sample; this result had also been shown by the coal permeability (SC of 15.58 mD and HBC of 0.14 mD) in previous work (Zhou et al., 2016a). Moreover, the PNE models could directly determine the pore-fracture significant connectivity (Fig. 5a2 and b2). Therefore, both samples were favorable for CBM transport because of good connectivity in SC and HBC. Based on previous research (Song et al., 2015, 2016), the KatzThompson model (Katz and Thompson, 1987) can predict fluid transport along the shortest pore path in porous media such as shale and claystone. The Katz-Thompson model is given by:

KKT =

dc2 d 2ϕ = c 226F 226τ

(3)

where KKT is the fluid permeability predicted by the Katz-Thompson

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Table 3 The connected/closed pore subsection distribution, computed by 3D digital core based on FIB-SEM. Pore size (nm)

Sample SC

Sample HBC

0–50 50–100 100–150 150–200 200–250 250–300 300–350 350–400 400–450 450–500 500–550 550–600 0–50 50–100 100–150 150–200 200–250 250–300 300–350 350–400 400–500 500–600 600–910

Connected pores

Closed pores

Total pores

CPP (%)

Voxels count

V (μm3)

A (μm2)

VF (%)

Voxels count

V (μm3)

A (μm2)

VF (%)

Voxels count

V (μm3)

A (μm2)

VF (%)

V

A

276 106 40 31 37 31 25 7 7 8 6 3 496 106 42 45 45 22 11 9 9 10 4

0.0403 0.161 0.315 0.718 1.774 2.710 3.569 1.606 2.229 3.490 3.430 2.320 0.049 0.163 0.331 1.029 2.171 1.930 1.582 2.041 3.369 6.463 6.444

3.97 11.08 15.35 27.73 58.40 80.69 94.27 35.79 42.54 61.54 59.56 30.75 5.45 12.63 15.35 37.39 75.49 52.98 41.67 43.57 68.51 119.08 69.96

0.043 0.171 0.335 0.763 1.886 2.880 3.793 1.707 2.369 3.709 3.646 2.466 0.077 0.257 0.521 1.621 3.420 3.040 2.492 3.215 5.307 10.18 10.15

28,117 204 26 7 6 6 1 0 0 0 0 0 82,934 114 11 5 2 1 0 0 0 0 0

0.626 0.265 0.184 0.141 0.290 0.516 0.138 0 0 0 0 0 1.077 0.141 0.094 0.099 0.088 0.132 0 0 0 0 0

76.09 19.38 10.96 6.05 10.69 19.54 3.23 0 0 0 0 0 151.91 11.87 4.51 4.31 3.08 3.68 0 0 0 0 0

0.665 0.282 0.196 0.150 0.308 0.548 0.147 0 0 0 0 0 1.696 0.222 0.148 0.156 0.139 0.208 0 0 0 0 0

28,393 310 66 38 43 37 26 7 7 8 6 3 83,430 220 53 50 47 23 11 9 9 10 4

0.666 0.426 0.499 0.859 2.064 3.226 3.707 1.606 2.229 3.490 3.430 2.320 1.126 0.304 0.425 1.128 2.259 2.062 1.582 2.041 3.369 6.463 6.444

80.05 30.46 26.30 33.79 69.09 100.23 97.50 35.79 42.54 61.54 59.56 30.75 157.36 24.49 19.86 41.70 78.57 56.66 41.67 43.57 68.51 119.08 69.96

0.708 0.453 0.530 0.913 2.194 3.429 3.940 1.707 2.369 3.709 3.646 2.466 1.774 0.479 0.669 1.777 3.558 3.248 2.492 3.215 5.307 10.18 10.15

6.05 37.84 63.09 83.63 85.96 84.02 96.27 100 100 100 100 100 4.35 53.62 77.91 91.23 96.12 93.60 100 100 100 100 100

4.95 36.38 58.34 82.08 84.53 80.50 96.69 100 100 100 100 100 3.46 51.55 77.31 89.67 96.08 93.50 100 100 100 100 100

Note: V = volumes; A = areas; CPP = connected pores proportion; VF = volume fraction.

(Table 3). The percentage of connected pores generally increased with increasing pore size both in SC and HBC (Fig. 6). The connected pores and throat characteristics control the permeability, which in turn affects the producibility of CBM in SC and HBC reservoirs. Fig. 7 shows the total adsorption-pores (< 100 nm) and seepagepores (> 100 nm) size distribution, volumes and areas. In adsorptionpores, most pores (> 95%) were < 30 nm (Fig. 7a1 and b1), which can likely be attributed to pore volumes and areas. The cumulative pore volumes and areas vs. pore size displayed generally prove the logarithmic function. Therefore, these pores (< 30 nm) can provide tremendous space for methane reserves, especially adsorbed at pore-specific surfaces. In seepage-pores, both the pore volumes and areas increased with rising pore diameters, and pore areas had a strong exponential relationship with pore size (Fig. 7a2 and b2). The cumulative pore volumes and areas vs. pore sizes mainly displayed an exponential relationship, showing that larger pores can provide larger volumes for methane transport.

in HBC. 3.3.2. Pore geometry Table 3 and Fig. 6 show the quantified connected/closed pore size distribution, volume and area proportions of multi-scale pores from FIB-SEM. For pores of 0–50 nm in the SC sample, connected and closed pores voxel were numbered at 276 and 28,117, volumes were 0.0403 and 0.626 μm3, and areas were 3.97 and 76.09 μm2, respectively (Table 3). For pores of 0–50 nm in the HBC sample, connected and closed pores voxel numbers were 496 and 82,934, volumes were 0.049 and 1.077 μm3, and areas were 5.45 and 151.91 μm2, respectively (Table 3). It has been found that closed pore (< 50 nm) areas could be significant positions for gas adsorption (Cai et al., 2013; Zhou et al., 2016c). The connected pore (< 50 nm) volume and area proportions in sample SC were 6.05% and 4.95%, respectively, and the respective proportions of 4.35% and 3.46% were found in sample HBC (Table 3 and Fig. 6). Tens of thousands of closed pores can offer significant space for CBM adsorption. For pores of 50–100 nm in sample SC, connected and closed pore voxel numbers were 106 and 204, volumes were 0.161 and 0.265 μm3 and areas were 11.08 and 19.38 μm2, respectively (Table 3). The connected pore volume and area percentages varied between 30 and 40%, which reflect that pore structures can be parallelplate like and be favorable for CBM desorption and diffusion. For pores of 50–100 nm in sample HBC, connected and closed pore voxel numbers were 106 and 114, volumes were 0.163 and 0.141 μm3 and areas were 12.63 and 24.49 μm2, respectively (Table 3), which indicates that half of the pores could provide fluid migration pathways. For pores of 100–350 nm in samples SC and HBC, the primary pores were connected pores with voxel numbers of 164 and 165, volumes of 9.086 and 7.044 μm3 and areas of 276.43 and 222.88 μm2, respectively (Table 3). For pores > 350 nm in samples SC and HBC, all pores were connected pores with voxel number of 31 and 32, volumes of 13.074 and 18.318 μm3, and areas of 230.17 and 301.13 μm2, respectively

3.4. CBM accumulation and transport capabilities related to pore-fracture structures 3.4.1. CBM accumulation capabilities of SC and HBC In the SC and HBC, methane storage has mainly been classified by accumulation via the following: (i) free methane that tends to focus on larger micro-pores and -fractures and (ii) adsorption methane that is more towards the center in smaller nanometer pores (Colosimo et al., 2016; Li et al., 2016a, 2016b). Previous research has demonstrated that adsorbed methane is concentrated at pore diameters of < 50 nm (Cai et al., 2013; Zhou et al., 2016c). Therefore, we quantified pore size (< 50 nm), volume distribution and connected-pore amounts in Table 4 and Fig. 8. In contrast to the SC sample, the HBC sample consisted of larger voxel numbers, volumes and areas of pores (< 50 nm), especially for pore diameters < 30 nm. The volume and

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Fig. 6. The plots of pore size, areas, volume and volume fraction segmented distributions. a) - sample SC; b) - sample HBC.

and HBC samples (Table 2), respectively, values similar to those from previous work (Zhou et al., 2016b). The results demonstrate that the porosity of the HBC sample was extremely higher than that of the SC sample, meaning that the HBC sample pore structure supplied much more space for gas storage. These results could have been caused by the pores that were newly formed during the first coalification jump.

area proportions of closed pores (< 50 nm) dominated in both samples (SC and HBC), especially the pore diameters of 10–30 nm (~ 100% are closed pores) (Table 4 and Fig. 8). The connected pores could probably provide CBM pathways for flow from smaller pores to larger pores. Moreover, the 44.5–48.7 nm pores in the SC sample, which had an average connected-pore volume proportion of 24.56% and an area proportion of 24.50%, may be significant for CBM desorption and free gas storage. The same phenomenon was found in the HBC sample for pore sizes of 48.84–49.63 nm (Table 4). The amount, volumes, and areas of adsorption pores in SC were less than in HBC (Figs. 6 and 7; Table 3), which indicates that the SC adsorption ability was weaker than that of HBC. The connected pores (50–100 nm) of sample HBC were higher in amount and proportion than those of sample SC (Table 3; Fig. 6). Additionally, the volume fractions of the pores in the SC and HBC samples, which represent the probable pore porosity of the samples (Wang et al., 2016b), were 26.06% and 42.85% for the SC

3.4.2. CBM flow capabilities of SC and HBC Connected-pore and throat (fracture) physical properties (e.g., diameter, count proportion, throat length) determine the porous media permeability (Chen et al., 2016; Giffin et al., 2013; Huang et al., 2016; Kelly et al., 2015; Klaver et al., 2015; Lubelli et al., 2013). Fig. 9 reveals the connected-pore diameter, area and volume distributions for the SC and HBC samples. Both had hundreds of 0–50 nm and 50–100 nm pores, medium amounts of 100–150, 150–200, 200–250, 250–300 and 300–350 nm pores, and a small amount of > 350 nm pores (Table 3;

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Fig. 7. Pores diameter, area and volume distribution. a1), a2), - sample SC; b1), b2) - sample HBC.

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Table 4 (continued)

Table 4 The detailed pore (< 50 nm) distribution, computed by 3D digital core based on FIBSEM. Pore size (nm)

Voxels count

APCP (%)

VPCP (%)

Sample SC 14.0105 17.6522 20.2067 22.2403 23.9577 25.4588 26.8012 28.0211 29.1431 30.1848 31.1591 32.0761 32.9435 33.7674 34.5529 35.3043 36.025 36.718 37.3857 38.0304 38.654 39.2581 39.8441 40.4134 40.967 41.5061 42.0316 42.5442 43.0448 43.534 44.0124 44.4807 44.9393 45.3887 45.8294 46.2618 46.6862 47.1031 47.5127 47.9154 48.3114 48.701 49.0845 49.4621 49.834

21,056 3578 1240 635 399 256 167 138 112 89 66 66 52 44 29 37 28 27 20 27 29 28 24 20 16 14 16 22 13 18 14 7 19 9 15 9 12 7 9 13 8 9 7 5 13

0.094 0.68 2.15 3.79 3.81 2.59 7.55 6.15 11.49 4.38 9.87 12.68 16.68 10.51 6.70 4.92 27.84 14.45 34.64 3.31 16.42 7.11 13.03 10.48 18.65 29.06 18.30 9.17 17.92 29.57 29.30 0 39.44 25.59 27.57 39.63 7.69 16.19 39.23 23.42 15.01 11.92 0 0 26.08

0.094 0.64 2.34 4.41 4.51 3.12 7.78 6.52 13.39 5.62 15.15 21.21 25.49 13.64 6.89 5.41 28.57 18.52 36.84 3.85 17.86 7.41 13.04 10.53 20.00 23.08 20.00 9.52 16.67 29.41 30.77 0 38.89 25.00 28.57 37.50 9.09 16.67 37.50 25.00 14.29 12.50 0 0 25.00

Sample HBC 12.407 15.6319 17.894 19.6949 21.2157 22.545 23.7338 24.814 25.8076 26.7301 27.5929 28.405 29.173 29.9027 30.5983 31.2637 31.9019 32.5156 33.1069 33.6778 34.23 34.7649 35.2839 35.788 36.2783

64,581 10,542 3390 1507 907 538 351 237 194 127 126 97 80 61 62 42 59 37 38 36 21 23 25 23 26

0.0247 0.655 1.652 2.787 4.189 4.461 6.553 6.329 11.340 15.748 11.111 10.309 16.25 14.754 13.115 14.286 5.085 16.216 10.526 25 9.524 8.696 36 26.087 30

0.0253 0.654 1.628 2.677 3.995 4.06 6.342 6.097 10.336 10.069 10.66 10.102 16.07 14.54 12.258 15.905 4.995 15.155 10.443 24.484 9.019 8.18 37.765 26.249 29.799

Pore size (nm)

Voxels count

APCP (%)

VPCP (%)

36.7557 37.221 37.675 38.1183 38.5515 38.9751 39.3898 39.7959 40.1939 40.5842 40.967 41.3429 41.7121 42.0748 42.4314 42.7821 43.1271 43.4667 43.8011 44.1304 44.4549 44.7747 45.0901 45.401 45.7078 46.0105 46.3093 46.6043 46.8956 47.1833 47.4675 47.7484 48.026 48.3005 48.5718 48.8402 49.1056 49.3682 49.628 49.8852

18 17 24 9 18 14 8 15 12 10 9 9 8 8 10 7 4 4 6 8 9 8 3 6 4 5 8 2 3 3 3 3 4 3 7 3 3 7 3 1

16.67 11.765 20.833 11.11 22.22 14.286 12.5 33.33 25 20 0 44.44 50 0 40 28.571 25 25 33.33 12.5 22.22 25 0 16.67 50 0 37.5 100 0 0 33.33 66.67 0 0 14.286 33.333 33.333 57.143 33.333 0

17.083 10.465 20.151 9.618 23.671 14.367 12.463 32.815 23.529 17.905 0 40.855 51.147 0 36.729 27.758 22.549 29.295 36.385 11.167 20.77 27.46 0 13.684 48.932 0 40.425 100 0 0 31.54 65.677 0 0 11.307 33.427 24.238 59.676 33.977 0

Note: APCP = the area proportion of connected pores; VPCP = the volume proportion of connected pores.

Fig. 8. The proportion of connected pores (< 50 nm) in samples SC and HBC. APCP = the area proportion of connected pores; VPCP = the volume proportion of connected pores.

Figs. 6 and 9). The connected-pore areas and volumes display bimodal distributions, with the first peak at 200–300 nm and the second peak at > 450 nm (Fig. 8). The connected-pore percentage was > 50% at a pore size of 100–300 nm and 100% at a pore size > 300 nm (Table 3; Fig. 6). These phenomena also showed that both SC and HBC reservoirs 51


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permeability was lower than that of the SC sample. This phenomenon may result from coal reservoir physical properties with high anisotropism. Therefore, it is important to be able to establish the 3D porefracture network characteristics for an accurate evaluation of the physical properties of the SC and HBC reservoirs when looking for a high permeability zone. However, FIB-SEM tomography can precisely characterize SC and HBC pore-fracture networks down to a 4-nm voxel size. Remaining for further study are investigations into the extracted 3D visualization of the cleats (> 104 nm) by X-ray μ-CT and nanopores (< 4 nm) by helium ion scanning microscopy and, ultimately, exploration into the applications of this technology as an investment for the modeling of single and multi-phase fluid transport in different rank coal and shale reservoirs.

4. Conclusions The originality of this work rests with a progressive imaging technique (FIB-SEM tomography) to quantify the pore-fracture space geometry and build upon the 3D pore network extraction modeling of two different rank coals (SC and HBC), with the following preliminary conclusions: 1. PNE modeling aims to simplify the complicacy of 3D pore space to quantify CBM storage and flow space connectivity analyses by identifying pores and throats. We presented a conceptual model of 3D pore networks by reconstruction, identification and extraction in SC and HBC. The SC sample showed entire pore space connects, whereas the HBC sample displayed typical pore space connects in a 3D pore network. The methods allow for furnishing a realistic and forthright presentation of pore space and its connectivity in 3D. 2. Both SC and HBC samples presented significant pore space for CBM storage, with total voxel numbers of 28,944 and 83,866, average diameters of 18.409 and 14.452 μm, volumes of 24.528 and 27.167 μm3 and areas of 667.6 and 723.139 μm2, respectively. Porosity, resolvable by FIB-SEM, was 26.06 and 42.85% for the SC and HBC samples, respectively, which indicates that the former reservoir accumulation capacity is lower than the latter. This method can figure out pores down to ~ 4 nm voxel diameter and allows qualitative and quantitative research into coal porosity. 3. The SC and HBC samples showed significant connectivity to CBM transport, with connected pore proportions of ~100% in pores > 300 nm. The number of throats (fractures) decreased with increasing throat size, with total numbers of 516 and 715, average sizes of 74.36 and 67.64 nm and channel lengths of 29.5–2763.7 nm and 27.3–2515.8 nm for the SC and HBC samples, respectively. The SC reservoir fluid transport capability is higher than that of the HBC reservoir due to the former developing the throat size of 400–500 nm that may dominate the coal permeability.

Fig. 9. Histograms depicting the diameter, area and volume distribution of the connected-pores. a) - sample SC; b) - sample HBC.

have significant flow capability for CBM migration, which is attributed to relatively high permeability. Although the HBC sample had a larger number of connected-pore voxels than that of the SC sample for size 0–50 nm (Tables 3 and 4; Figs. 6 and 9), which may have little influence on methane flow capability, we could not deduce that the methane flow capability of the HBC sample was higher than that of the SC sample. Fig. 10 and Table 5 show the throats (fractures) distribution calculated from the 3D digital core. Throat size varied from 5.826 to 477.804 nm for the SC sample and from 4.838 to 374.93 nm for the HBC sample (Table 2; Fig. 10), with the main pores in the range of 4–100 nm (Table 5). The voxel numbers of throats decreased with increasing throat size; the throat areas were mainly distributed at a throat size of > 50 nm (Fig. 10), and average throat length was randomly distributed (Table 5). The number of throats of size > 300 nm in the SC sample was higher than in the HBC sample (Table 5), which may indicate that the permeability of the SC sample was higher than that of the HBC sample. The throat size of 400–500 nm dominated the coal permeability in the SC sample. The SC pore-fractures were connected globally, whereas the HBC sample reservoirs were connected locally, as shown in Fig. 5, which indicates that the percolation capability of SC coal is higher than that of HBC coal. Contrasting the SC sample (Figs. 2, 5a1) with the HBC sample (Figs. 3, 5b1), HBC's pore-fracture characterization had higher connectivity and larger diameters in a plane observation, whereas its

Acknowledgements This study was funded by the National Major Research Program for Science and Technology of China (2016ZX05043-001), the Fundamental Research Funds for the Central Universities (35732016129), the National Natural Science Foundation of China (41602170) and the Key Project of Coal-based Science and Technology in Shanxi Province-CBM accumulation model and reservoir evaluation in Shanxi province (MQ2014-01). Special thanks are given to the editor Dr. C. Özgen Karacan and reviewers for their valuable advice and constructive comments on the manuscript.

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Fig. 10. Throats size, area distributions and channel length. a) - sample SC; b) - sample HBC.

References

Table 5 The throat (fracture) subsection distribution, computed by 3D digital core based on FIBSEM. Throat size (nm)

Voxels count

Area (μm2)

Average length (μm)

Total length (μm)

Sample SC 0–10 10–20 20–30 30–40 40–50 50–100 100–150 150–200 200–250 250–300 300–350 350–400 400–500

87 85 55 32 22 86 72 38 16 14 4 5 2

0.0145 0.0611 0.1021 0.1221 0.1398 1.3351 3.6486 3.5661 2.4803 3.414 1.2932 2.242 1.3504

0.1802 0.2707 0.4487 0.5978 0.6617 0.7863 0.8481 0.7807 0.9793 0.6653 0.8159 0.8411 0.6315

15.6759 23.0079 24.6769 19.1311 14.5566 67.618 61.0654 29.6671 15.668 9.3139 3.2635 4.2056 1.2629

Sample HBC 0–10 10–20 20–30 30–40 40–50 50–100 100–150 150–200 200–250 250–300 300–350 350–400

199 110 65 18 16 112 79 62 32 14 6 2

0.288 0.0709 0.1242 0.0669 0.1083 2.1078 3.7845 5.991 4.9471 3.2675 1.84 0.875

0.1118 0.2189 0.3862 0.5008 0.5866 0.8257 0.8221 0.8466 1.0257 0.8664 0.7920 1.9415

22.2579 24.0747 25.1018 9.0148 9.3854 92.4732 64.9481 52.4871 32.8229 12.1294 4.7518 3.8829

Abdelfatah, E., Pournik, M., Shiau, B.J.B., Harwell, J., 2017. Mathematical modeling and simulation of nanoparticles transport in heterogeneous porous media. J. Nat. Gas Sci. Eng. http://dx.doi.org/10.1016/j.jngse.2017.01.028. Abràmoff, M.D., Viergever, M.A., 2002. Computation and visualization of threedimensional soft tissue motion in the orbit. IEEE Trans. Med. Imaging 21 (4), 296–304. Abunowara, M., Bustam, M.A., Sufian, S., Eldemerdash, U., 2016. Description of carbon dioxide adsorption and desorption onto Malaysian coals under subcritical condition. Procedia Eng. 148, 600–608. Bachmann, L., Mayer, E., 1987. In: Steinbrecht, R.A., Zierold, K. (Eds.), Cryotechniques in Biological Electron Microscopy. Springer, Berlin, pp. 3–31. Baysal, M., Yürüm, A., Yıldız, B., Yürüm, Y., 2016. Structure of some western Anatolia coals investigated by FTIR, Raman, 13C solid state NMR spectroscopy and X-ray diffraction. Int. J. Coal Geol. 163, 166–176. Biswal, B., Manwart, C., Hilfer, R., 1998. Three-dimensional local porosity analysis of porous media. Phys. A Stat. Mech. Appl. 255 (3–4), 221–241. Bustin, R.M., Guo, Y., 1999. Abrupt changes (jumps) in reflectance values and chemical compositions of artificial charcoals and inertinite in coals. Int. J. Coal Geol. 38 (3–4), 237–260. Cai, Y., Liu, D., Pan, Z., Yao, Y., Li, J., Qiu, Y., 2013. Pore structure and its impact on CH4 adsorption capacity and flow capability of bituminous and subbituminous coals from Northeast China. Fuel 103, 258–268. Chalmers, G.R., Bustin, R.M., Power, I.M., 2012. Characterization of gas shale pore systems by porosimetry, pycnometry, surface area, and field emission scanning electron microscopy/transmission electron microscopy mage analyses: examples from the Barnett, Woodford, Haynesville, Marcellus, and Doig units. AAPG Bull. 96, 1099–1119. Chen, D., Pan, Z., Shi, J.-Q., Si, G., Ye, Z., Zhang, J., 2016. A novel approach for modelling coal permeability during transition from elastic to post-failure state using a modified logistic growth function. Int. J. Coal Geol. 163, 132–139. Clarkson, C., Wood, J., Burgis, S., 2012. Nanopore-structure analysis and permeability predictions for a tight gas siltstone reservoir by use of low-pressure adsorption and mercury-intrusion techniques. SPE Reserv. Eval. Eng. 15, 648–661. Clarkson, C.R., Solano, N., Bustin, R.M., Bustin, A.M.M., Chalmers, G.R.L., He, L., Melnichenko, Y.B., Radlinski, A.P., Blach, T.P., 2013. Pore structure characterization of North American shale gas reservoirs using USANS/SANS, gas adsorption, and mercury intrusion. Fuel 103, 606–616. Colosimo, F., Thomas, R., Lloyd, J.R., Taylor, K.G., Boothman, C., Smith, A.D., Lord, R.,

53


S. Zhou et al.

morphology and distribution in postmature to overmature samples from the Haynesville and Bossier Shales. Mar. Pet. Geol. 59, 451–466. Klaver, J., Desbois, G., Urai, J.L., Littke, R., Urai, J.L., 2016. BIB-SEM pore characterization of mature and post mature Posidonia Shale samples from the Hils area, Germany. Int. J. Coal Geol. 158, 78–89. Li, H., Lin, B., Yang, W., Zheng, C., Hong, Y., Gao, Y., Liu, T., Wu, S., 2016a. Experimental study on the petrophysical variation of different rank coals with microwave treatment. Int. J. Coal Geol. 154–155, 82–91. Li, X., Fu, X., Liu, A., An, H., Wang, G., Yang, X., Wang, L., Wang, H., 2016b. Methane adsorption characteristics and adsorbed gas content of low-rank coal in China. Energy Fuel 30, 3840–3848. Liu, S., Sang, S., Wang, G., Ma, J., Wang, X., Wang, W., Du, Y., Wang, T., 2016. FIB-SEM and X-ray CT characterization of interconnected pores in high-rank coal formed from regional metamorphism. J. Pet. Sci. Eng. http://dx.doi.org/10.1016/j.petrol.2016. 10.006. Lubelli, B., de Winter, D.A.M., Post, J.A., van Hees, R.P.J., Drury, M.R., 2013. CryoFIB–SEM and MIP study of porosity and pore size distribution of bentonite and kaolin at different moisture contents. Appl. Clay Sci. 80–81, 358–365. Mathews, J.P., Sharma, A., 2012. The structural alignment of coal and the analogous case of Argonne Upper Freeport coal. Fuel 95, 19–24. Münch, B., Gasser, P., Holzer, L., Flatt, R., 2006. FIB-nanotomography of particulate systems-part II: particle recognition and effect of boundary truncation. J. Am. Ceram. Soc. 89 (8), 2586–2595. Münch, B., Trtik, P., Marone, F., Stampanoni, M., 2009. Stripe and ring artifact removal with combined wavelet-Fourier filtering. Opt. Express 17 (10), 8567–8591. Nie, B., Liu, X., Yang, L., Meng, J., Li, X., 2015. Pore structure characterization of different rank coals using gas adsorption and scanning electron microscopy. Fuel 158, 908–917. Pan, J., Zhu, H., Hou, Q., Wang, H., Wang, S., 2015. Macromolecular and pore structures of chinese tectonically deformed coal studied by atomic force microscopy. Fuel 139, 94–101. Robinet, J., Gaboreau, S., 2013. 2D and 3D high-resolution imaging to reconstruct the microstructure of clay media. In: 11th European Congress of Stereology and Image Analysis, July 9 12, Kaiserslautern, Germany, . Saurabh, S., Harpalani, S., Singh, V.K., 2016. Implications of stress re-distribution and rock failure with continued gas depletion in coalbed methane reservoirs. Int. J. Coal Geol. 162, 183–192. Silin, D., Patzek, T., 2006. Pore space morphology analysis using maximal inscribed spheres. Phys. A Stat. Mech. Appl. 371 (2), 336–360. Song, Y., Davy, C.A., Troadec, D., Blanchenet, A.M., Skoczylas, F., Talandier, J., et al., 2015. Multi-scale pore structure of cox claystone: towards the prediction of fluid transport. Mar. Pet. Geol. 65, 63–82. Song, Y., Davy, C.A., Bertier, P., Troadec, D., 2016. Understanding fluid transport through claystones from their 3d nanoscopic pore network. Microporous Mesoporous Mater. 228, 64–85. Tahmasebi, P., Javadpour, F., Sahimi, M., 2016. Stochastic shale permeability matching: three-dimensional characterization and modeling. Int. J. Coal Geol. http://dx.doi. org/10.1016/j.coal.2016.08.024. Wang, Y., Pu, J., Wang, L., Wang, J., Jiang, Z., Song, Y.F., Wang, C.C., Wang, Y., Jin, C., 2016a. Characterization of typical 3D pore networks of Jiulaodong formation shale using nano-transmission X-ray microscopy. Fuel 170, 84–91. Wang, Y., Zhu, Y., Liu, S., Zhang, R., 2016b. Pore characterization and its impact on methane adsorption capacity for organic-rich marine shales. Fuel 181, 227–237. Wu, D., Liu, G.J., Sun, R.Y., Chen, S.C., 2014. Influences of magmatic intrusion on the macromolecular and pore structures of coal: evidences from Raman spectroscopy and atomic force microscopy. Fuel 119, 191–201. Zang, J., Wang, K., 2017. Gas sorption-induced coal swelling kinetics and its effects on coal permeability evolution: model development and analysis. Fuel 189, 164–177. Zhang, Y.H., Xu, X.M., Lebedev, M., Sarmadivaleh, M., Barifcani, A., Iglauer, S., 2016. Multi-scale X-ray computed tomography analysis of coal microstructure and permeability changes as a function of effective stress. Int. J. Coal Geol. 165, 149–156. Zhao, Y., Liu, S., Elsworth, D., Jiang, Y., Zhu, J., 2014. Pore structure characterization of coal by synchrotron small-angle X-ray scattering and transmission electron microscopy. Energy Fuel 28, 3704–3711. Zhao, J., Xu, H., Tang, D., Mathews, J.P., Li, S., Tao, S., 2016. A comparative evaluation of coal specific surface area by CO2 and N2 adsorption and its influence on CH4 adsorption capacity at different pore sizes. Fuel 183, 420–431. Zhou, S., Yan, G., Xue, H., Guo, W., Li, X., 2016a. 2D and 3D nanopore characterization of gas shale in Longmaxi formation based on FIB-SEM. Mar. Pet. Geol. 73, 174–180. Zhou, S., Liu, D., Cai, Y., Yao, Y., 2016b. Fractal characterization of pore–fracture in lowrank coals using a low-field NMR relaxation method. Fuel 181, 218–226. Zhou, S., Liu, D., Cai, Y., Yao, Y., 2016c. Gas sorption and flow capabilities of lignite, subbituminous and high-volatile bituminous coals in the Southern Junggar Basin, NW China. J. Nat. Gas Sci. Eng. 34, 6–21. Zhou, S., Liu, D., Cai, Y., Yao, Y., 2017. Effects of the coalification jump on the petrophysical properties of lignite, subbituminous and high-volatile bituminous coals. Fuel 199, 219–228.

Kalin, R.M., 2016. Biogenic methane in shale gas and coal bed methane: a review of current knowledge and gaps. Int. J. Coal Geol. 165, 106–120. Connell, L.D., Mazumder, S., Sander, R., Camilleri, M., Pan, Z.J., Heryanto, D., 2016. Laboratory characterisation of coal matrix shrinkage, cleat compressibility and the geomechanical properties determining reservoir permeability. Fuel 165, 499–512. Curtis, M.E., Sondergeld, C.H., Ambrose, R.J., Rai, C.S., 2012. Microstructural investigation of gas shales in two and three dimensions using nanometer scale resolution imaging. AAPG Bull. 96, 665–677. Deng, H., Hu, X., Li, H., Luo, B., Wang, W., 2016. Improved pore-structure characterization in shale formations with FESEM technique. J. Nat. Gas Sci. Eng. 35, 309–319. Flores, R.M., 2014. Coal and Coalbed Gas: Fueling the Future: Chapter 4- Coalification, Gasification, and Gas Storage. Elsevier, Waltham, MA, pp. 167–233. http://dx.doi. org/10.1016/B978-0-12-396972-9.00004-5. Dong, H., Blunt, M.J., 2009. Pore-network extraction from micro-computerized tomography images. Phys. Rev. E 80 (2), 1957–1974. Gaboreau, S., Robinet, J.-C., Prêt, D., 2016. Optimization of pore-network characterization of a compacted clay material by TEM and FIB/SEM imaging. Microporous Mesoporous Mater. 224, 116–128. Gastel, R.V., Hlawacek, G., Dutta, S., Poelsema, B., 2015. Backscattered helium spectroscopy in the helium ion microscope: principles, resolution and applications. Nucl. Inst. Methods 344 (344), 44–49. Genetti, D., Fletcher, T.H., Pugmire, R.J., 1999. Development and application of a correlation of 13C NMR chemical structural analyses of coal based on elemental composition and volatile matter content. Energy Fuel 13, 60–68. Giffin, S., Littke, R., Klaver, J., Urai, J.L., 2013. Application of BIB-SEM technology to characterize macropore morphology in coal. Int. J. Coal Geol. 114 (4), 85–95. Hemes, S., Desbois, G., Urai, J.L., Schröppel, B., Schwarz, J.O., 2015. Multi-scale characterization of porosity in boom clay (HADES-level, Mol, Belgium) using a combination of X-ray μ-CT, 2D BIB-SEM and FIB-SEM tomography. Microporous Mesoporous Mater. 208, 1–20. Hilfer, R., Helmig, R., 2004. Dimensional analysis and upscaling of two-phase flow in porous media with piecewise constant heterogeneities. Adv. Water Resour. 27 (10), 1033–1040. Holzer, L., Indutnyi, F., Gasser, P., Münch, B., Wegmann, M., 2004. Three-dimensional analysis of porous BaTiO3 ceramics using FIB nanotomography. J. Microsc. 216 (1), 84–95. Holzer, L., Muench, B., Wegmann, M., Gasser, P., Flatt, R.J., 2006. FIB-nanotomography of particulate systems-part I: particle shape and topology of interfaces. J. Am. Ceram. Soc. 89 (8), 2577–2585. Houben, M.E., Urai, J.L., Desbois, G., 2013. Pore morphology and distribution in the Shaly facies of opalinus clay (Mont Terri, Switzerland): insights from representative 2D BIB-SEM investigations on mm to nm scale. Appl. Clay Sci. 71 (1), 82–97. Houben, M.E., Desbois, G., Urai, J.L., 2014. A comparative study of representative 2D microstructures in Shaly and Sandy facies of opalinus clay (Mont Terri, Switzerland) inferred form BIB-SEM and MIP methods. Mar. Pet. Geol. 49 (1), 143–161. Huang, N., Jiang, Y., Li, B., Liu, R., 2016. A numerical method for simulating fluid flow through 3-D fracture networks. J. Nat. Gas Sci. Eng. 33, 1271–1281. Kang, Y., Huang, F., You, L., Li, X., Gao, B., 2016. Impact of fracturing fluid on multi-scale mass transport in coalbed methane reservoirs. Int. J. Coal Geol. 154–155, 123–135. Kanit, T., Forest, S., Galliet, I., Mounoury, V., Jeulin, D., 2003. Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int. J. Solids Struct. 40 (13–14), 3647–3679. Karacan, C.Ö., Okandan, E., 2001. Adsorption and gas transport in coal microstructure: investigation and evaluation by quantitative X-ray CT imaging. Fuel 80 (4), 509–520. Karacan, C.Ö., Grader, A.S., Halleck, P.M., 2003. Evaluation of local porosity changes in limestone samples under triaxial stress field by using X-ray computed tomography. Geol. Soc. Lond. Spec. Publ. 215 (1), 177–189. Katz, A.J., Thompson, A., 1987. Prediction of rock electrical conductivity from mercury injection measurements. J. Geophys. Res. Solid Earth 92 (B1), 599–607. Kędzior, S., 2015. Methane contents and coal-rank variability in the Upper Silesian Coal Basin, Poland. Int. J. Coal Geol. 139, 152–164. Keller, L.M., Holzer, L., Wepf, R., Gasser, P., 2011. 3D geometry and topology of pore pathways in opalinus clay: implications for mass transport. Appl. Clay Sci. 52 (1–2), 85–95. Keller, L.M., Holzer, L., Schuetz, P., Gasser, P., 2013a. Pore space relevant for gas permeability in opalinus clay: statistical analysis of homogeneity, percolation, and representative volume element. J. Geophys. Res. Solid Earth 118, 2799–2812. Keller, L.M., Schuetz, P., Erni, R., Rossell, M.D., Lucas, F., Gasser, P., et al., 2013b. Characterization of multi-scale microstructural features in opalinus clay. Microporous Mesoporous Mater. 170 (4), 83–94. Kelly, S., El-Sobky, H., Torres-Verdín, C., Balhoff, M.T., 2015. Assessing the utility of FIBSEM images for shale digital rock physics. Adv. Water Resour. 1–15. Klaver, J., Desbois, G., Urai, J.L., Littke, R., 2012. BIB-SEM study of the pore space morphology in early mature Posidonia Shale from the Hils area. Germany. Int. J. Coal Geol. 103, 12–25. Klaver, J., Desbois, G., Littke, R., Urai, J.L., 2015. BIB-SEM characterization of pore space

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