Three-dimensional characterisation of multi-scale structures of the Silurian Longmaxi shale using focused ion beam-scanning electron microscopy and reconstruction technology

Accepted Manuscript Three-dimensional characterisation of multi-scale structures of the Silurian Longmaxi shale using focused ion beam-scanning electron microscopy and reconstruction technology Yang Ju, Wenbo Gong, Chun Chang, Heping Xie, Lingzhi Xie, Peng Liu PII:

S1875-5100(17)30291-3

DOI:

10.1016/j.jngse.2017.07.015

Reference:

JNGSE 2243

To appear in:

Journal of Natural Gas Science and Engineering

Received Date: 2 May 2017 Revised Date:

19 July 2017

Accepted Date: 27 July 2017

Please cite this article as: Ju, Y., Gong, W., Chang, C., Xie, H., Xie, L., Liu, P., Three-dimensional characterisation of multi-scale structures of the Silurian Longmaxi shale using focused ion beamscanning electron microscopy and reconstruction technology, Journal of Natural Gas Science & Engineering (2017), doi: 10.1016/j.jngse.2017.07.015. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT Revised Manuscript Prepared for Journal of Natural Gas Science and Engineering

Three-dimensional characterisation of multi-scale structures of the Silurian Longmaxi shale using focused ion beam-scanning electron microscopy and reconstruction technology Yang Ju a, b, *, Wenbo Gong c, Chun Chang b, c, Heping Xie d, Lingzhi Xie d, Peng Liu b State Key Laboratory for Geomechanics and Deep Underground Engineering, China University

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a

of Mining and Technology, Xuzhou 221006, China b

State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and

c

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Technology at Beijing, Beijing 100083, China

School of Mechanics and Civil Engineering, China University of Mining and Technology at

d

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Beijing, Beijing 100083, China

Key Laboratory of Energy Engineering Safety and Mechanics on Disasters, The Ministry of

Education, Sichuan University, Chengdu 610065, China

* Corresponding author:

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Yang Ju, State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology at Beijing, D11 Xueyuan Road, Beijing 100083, China

Tel: +86 10 62331490; Fax: +86 10 62331253;

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E-mail: [email protected]

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ABSTRACT China has the largest quantity of technically recoverable shale gas resources in the world. However, the complex, three-dimensional (3D), multi-scale structure of the shale reservoir

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makes it extremely challenging to fully understand the mechanisms that govern shale gas migration and recovery efficiency. In this study, focused ion beam-scanning electron microscopy (FIB-SEM) was applied to identify the nano- and micron-scale 3D structures, including inter-particle pores, organic matter pores, intra-particle pores and fractures, of shale sampled

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from the Longmaxi Formation, Sichuan Basin, China. The 3D structural and physical characteristics, such as morphology, porosity, connectivity, and permeability of multi-scale pores and fractures, were analysed using 3D reconstruction techniques and the lattice Boltzmann method (LBM).

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The results show that the majority of pores in the Longmaxi shale samples varied between 10 and 40 nm in size, although some significantly larger intra-particle pores were also detected. The micro-fractures exhibited higher permeability and gas migration capacity than adjacent nano-pores, and organic matter nano-pores displayed high porosity and good connectivity. This study provides a way to quantitatively characterise the multi-scale structure and its effect on

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shale gas migration and fracturing potential in the Longmaxi formation, as well as in similar shale reservoirs elsewhere around the world.

Keywords: Multi-scale structure; Silurian Longmaxi shale; FIB-SEM; 3D reconstruction;

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Micro-fractures; Lattice Boltzmann method

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1. Introduction Shale gas, a clean, green, fossil energy with minimal environmental pollution at source, is trapped within fine-grained sedimentary rocks composed mainly of organic-rich shale.

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Worldwide, shale gas has received considerable attention owing to its great commercial value in terms of increasing natural gas supply, lowering consumption of petroleum and coal and reducing energy prices (Chen et al., 2011; Clarkson et al., 2016; Maitland, 2000;). China has the largest technically recoverable shale gas reserves, ranking number one with a share of 22.1% in

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the world (EIA, 2011). The safe and efficient exploitation and clean utilisation of shale gas in China has the potential to change the global energy structure and greatly reduce the average energy price, which in turn has substantial value for the economic development of China and

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even the rest of the world. However, the significant differences in the geological and geographical settings of shale reservoirs in China dictate that the mature techniques and valuable experience of reservoir stimulation and shale gas exploration established in the USA cannot be transplanted and applied directly to the resources in China. For instance, the Silurian Longmaxi Formation in the Fuling shale gas field of the Sichuan Basin, i.e., the major shale gas

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reservoir in southern China, has experienced multiple stages of tectonic evolution that have promoted the formation of well-developed faults and diverse and complex microstructures (Chen et al., 2011), which are significantly different from those observed in American shales with stable structures and high effective porosities (Guo, 2016; Hammes et al., 2011;). Although

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the potential of the Sichuan Basin as a principal target for shale gas exploration in China has been proven (National Energy Bureau, 2016), the complex multi-scale structures of shales and

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distinct styles of shale accumulation and migration continue to make the clean, safe, efficient, and sustainable exploitation of shale gas in China extremely challenging. The intrinsic feature of a shale gas reservoir that distinguishes it from conventional petroleum reservoirs is the presence of widespread, randomly distributed pores of various sizes that have low connectivity and permeability (Nelson, 2009). Shale gas molecules occupy these natural pores and fractures in the form of free gas (micro-porosity), and cover the organic matter and mineral surfaces as adsorbed gas (nano-porosity) (Javadpour, 2009). The multi-scale structure (pores and fractures) of shale determines the dynamic mechanism and migration capacity of

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shale gas. It is essential to obtain an accurate description and understanding of the multi-scale structures in shale, in order to determine the gas-transport mechanism. Moreover, in fracturing stimulation of shale reservoirs, the 3D morphological and distribution characteristics of the

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shale microstructure have significant influence directly on the fracturing potential, involving fracture initiation, propagation and coalescence. The existence of natural fractures causes fracturing deviation due to changes in the stress field around its region (Taheri-Shakib et al., 2016; Wang et al., 2016b). The mutual influence of pre-existing fractures and the propagated

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fractures contributes to a complex and connected fracture network that has a positive fracturing effect (Curtis, 2002; Gale et al., 2007). In addition to the natural fracture geometry, the existence of pore structure induces a leak-off of the fracking fluid that contributes to an

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increase in pore pressure and a decrease in cracking pressure in fracture initiation (Taheri-Shakib et al., 2016), which compromises the hydraulic fracturing efficiency. Therefore, to date, considerable attention has been given to the nano- and micron-scale pore structures of shales (Becker et al., 2011; Wells et al., 2014; Zhang et al., 2017) and their correlation with gas-bearing prediction through sample experiments employing pore

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characterisation methods. These include small-angle and ultra-small-angle neutron scattering, low-pressure gas adsorption, high-pressure mercury intrusion porosimetry and nuclear magnetic resonance (Clarkson et al., 2013; Ross and Bustin, 2009; Washburn and Birdwell, 2013; Xin et al., 2015; Xu et al., 2015); as well as digital imaging methods, including polarised light

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microscopy, field emission-scanning electron microscopy, transmission electron microscopy and atomic force microscopy (Bernard et al., 2013; Fu et al., 2015; Tian et al., 2016; Zou et al., 2011).

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It should be noted that pore characterisation methods can provide quantitative information about connected pores in large-scale samples, however, they do not permit direct and comprehensive observation of complete pore morphologies, in particular of the non-connected pore structures. Digital imaging methods allow visualisation of the interior structure of shale in microscopic regions, even down to nano-scale resolution. In terms of sample size, however, these methods appear to be insufficient owing to the incompatibility of high resolution with a large imaging field in each imaging process. Moreover, the majority of studies have focused predominantly on pores rather than on multi-scale fractures in shale. The few existing studies,

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however, have shown that natural micro-fractures widen the zone of fracturing stimulation greatly and maximise gas transport pathways as weak planes that reactivate and connect adjacent pores during fracturing treatment (Curtis, 2002; Gale et al., 2007). Characterisation of

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the multi-scale fractures is highly desirable in order to improve the efficiency of hydraulic fracturing, and thereby also the accuracy of gas production prediction (Dieterich et al., 2016). Overall, however, there is a significant lack of systematic studies of this problem using experimental or numerical methods.

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In terms of the Silurian Longmaxi shale, a number of investigations have been conducted to date to probe the pore structure and the contribution of organic matter to pore growth (Cao et al., 2015, 2016; Ma et al., 2016; Shi et al., 2015; Tang et al., 2015, 2016b; Wang et al., 2016a).

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Numerous 2D images of shale microstructures in the Longmaxi Formation have visually confirmed the existence of few micron-sized fractures and abundant nano-pores (Cao et al., 2016; Gai et al., 2016; Liang et al., 2014; Shi et al., 2015; Wang et al., 2016a). In these studies, the Loucks classification method (Loucks et al., 2012) was adopted to classify pores in terms of their genesis into (i) inter-particle (Inter-P) pores present between grains and crystals; (ii)

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intra-particle (Intra-P) pores located within mineral particles; and finally (iii) organic matter (OM) pores. However, these previous studies predominantly analysed the planar characteristics of pore structures present in the Longmaxi shale. Only a small number of studies have dealt with 3D pore structures of the Longmaxi shale (Jiang et al., 2017; Jiao et al., 2014; Tang et al., 2016b;

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Zhou et al., 2016). Nevertheless, the existing studies have shown that an accurate 3D model of shale represents not only the 3D distribution of areas and sizes of organic matter and minerals

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(Passey et al., 2010), but also describes quantitatively its micron- and nano-scale pore-throat system (Zou et al., 2015). A high-resolution reconstructed 3D model of the microstructure of a tight rock can be used to determine the influence of the microstructure on the migration properties of hydrocarbons, and thus to evaluate the producibility of shale formations (Porter and Wildenschild, 2010; Tomutsa et al., 2007; Wang et al., 2016c). Moreover, the 3D morphological and distribution characteristics of the shale microstructure provide the knowledge essential for understanding the impact of material heterogeneity on fracturing stimulation of shale reservoirs (Tang et al., 2000; Wong et al., 2006; Xie et al., 2016). However,

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quantitative characterisation of the spatial connectivity of multi-scale pores and micro-fractures, and analysis of their impact on gas migration in the Longmaxi shale remain significantly underexplored.

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In this study, FIB-SEM was applied to the identification of multiple structural morphologies of shale sampled from the Longmaxi Formation in the Fuling shale gas field, Sichuan Basin, China. The 2D FIB-SEM images were used to construct 3D digital models of representative volume elements (RVEs), comprising nano- and micro-scale pores and micro-fractures, utilising

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a reconstruction method developed by ourselves in-house. The 3D structural characteristics of the Longmaxi shale, in terms of the pore size distribution and connectivity of micron– nanometre sized pores, natural micro-fractures, and adjacent nano-pores, were quantitatively

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characterised based on the 3D-reconstructed models. Additionally, the LBM was employed to analyse the influence of the multi-scale structure on shale gas migration in the Longmaxi shale. The results provide experimental foundations for understanding the multi-scale structure and its effect on shale gas migration in the Longmaxi shale reservoir, as well as for evaluating gas

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production and fracturing potential in similar shale reservoirs elsewhere in China.

2. Sample preparation and methods

The shale samples used in this study, were characterized by high total organic carbon (TOC) contents of 2.28 % and relatively high thermal maturity (Ro = 2.11 %), and were cut-out from an

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outcrop of the Silurian Longmaxi Formation in the Fuling shale gas field, Sichuan Basin, China (Fig. 1). During specimen preparation, shale samples from the same area were machine-cut into

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cakes (15 mm in diameter and 5 mm thick). Each cake sample was subsequently polished using mechanical and argon-ion treatments to produce a flawless shale surface. Finally, an FEI Helios NanoLab 650 FIB-SEM was used to mill the sample surface and image each polished section. For imaging, the exposed surface of a prepared sample was oriented normally with respect to the ion beam and a target observation area of dozens of square microns in size was milled using the focused ion beam in order to obtain a clear nano-resolution image. Then electron signals, generated from the interaction between high energy electrons and various mineral surfaces, were captured by separate detectors. Signal processing of the feedback information from back

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scattered electrons was used to produce each image (Kelly et al., 2015), and allow acquisition of sequential SEM images. Thus, sequential, micro-area, cross-sectional images with a specific thickness were obtained to describe the 2D structure of the shale. Currently, FIB-SEM is

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considered to be a powerful high-resolution tool for identifying and analysing pore structures present in micro-areas of shale (Bai et al., 2013; Lin et al., 2016; Yoon and Dewers, 2013; Yu et al., 2016). The milling damage potentially induced to the sample surface is negligible for most rock materials, since it affects only a few dozens of atoms; i.e., an area that is an order of

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magnitude smaller than the size of the milling area in each cross-section of the material. For this reason, such damage has generally been regarded as insignificant in nano-structure imaging (Giannuzzi and Stevie, 2005; Kelly et al., 2015). In summary, each milling operation in a

image.

Avizo

image

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micro-area formed a new planar morphology of shale, which was then represented by a frame processing

software

(https://www.fei.com/

software/avizo-for-materials-science) integrated with the 3D reconstruction program developed in-house (Ju et al., 2014a, 2014b, 2017a) was employed for the 3D reconstruction of the sequential, cross-sectional, planar images, and analysis of the multi-scale structures of the shale

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microscopic structures).

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(including image segmentation, pore network extraction, and petrophysical parameters of the

Fig. 1. Location map showing structural subdivisions of the Sichuan Basin, China, and sampling location (red square). Figure was modified from Yang et al. (2016).

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Previous studies showed that a structural model of a specific scale is often used to handle the particular physical and mechanical behaviours of interest at a distinctive scale (Clarkson et al., 2016; Javadpour et al., 2007; Ning et al., 2016). It is difficult to solve the diverse physical

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properties of shales using just one structural model. Nevertheless, Chen’s study has confirmed that the pore-scale imaging and simulation can be used to determine the shale parameters, such as micro-structural geometry and its local-scale permeability, which are physically meaningful and useful for predictions at the field scale (Chen et al., 2016). Using the FIB-SEM

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technique, it is sufficient to select a representative field of 10 to 33 μm in size at nano-scale resolution to analyse the typical characteristics of the pore structure of the Longmaxi shale (Lin et al., 2016). Kelly and co-workers investigated shale properties through FIB-SEM images and

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found that a suitable representative volume for shale permeability and pore-scale networks should be approximately 5,000 μm3 (Kelly et al., 2015). Therefore, in order to identify and characterise the nano- and micro-scale structure of the Longmaxi shale, we selected an area of about 20 × 20 μm2 as a representative field at a high-resolution nano-scale. To represent the microstructural heterogeneity in the shale, four representative volume elements (RVEs), in

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which each microstructure has various impacts on shale gas storage and transport, referred to as S1, S2, S3, and S4 (Fig. 2), were selected to investigate the multi-scale structural characteristics. These RVEs were cut out from the representative field of the shale outcrop and imaged at different nano-scale spatial resolutions, focusing on different types of structures. In

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more detail, S1 contained Inter-P pores and was imaged at a spatial resolution of 15 nm/pixel, S2 contained OM pores and was imaged at a higher resolution of 7 nm/pixel, S3 was

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characterised by Intra-P pores and had a lower image resolution of 20 nm/pixel and finally, S4 incorporated micro-fractures at the lowest resolution of 22 nm/pixel. The observed surface was defined as the X–Y plane, and the sample thickness, or distance interval, as increments on the Z plane. A sample thickness of 20 nm was selected for S1, S3, and S4, while S2 was divided into 10 nm slices. The actual volumes of the observed elements S1, S2, S3, and S4 were 15 × 13.2 × 9.2 μm3, 11 × 9 × 9 μm3, 20 × 12 × 12 μm3 and 21 × 14 × 12.6 μm3, respectively (see Table 1). The sequential 2D images were used to produce 3D digital models of these RVEs. Then, Avizo image processing software and the in-house developed reconstruction program were used to

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quantitatively analyse morphological characteristics, such as pore size, mineral distribution, pore-throat network, and connectivity in the micro-areas. Figs. 3–6 show the 3D-reconstructed models of the RVEs obtained from the Longmaxi shale samples. For more information about the

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(S1)

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3D reconstruction methods, please refer to the literature (Ju et al., 2014a, 2014b, 2017a).

(S3)

(S2)

(S4)

Fig. 2. SEM images illustrating typical pore structures in different RVEs of the Longmaxi

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Formation shale samples: (S1) Inter-P pores; (S2) organic matter (OM) pores; (S3) Intra-P pores;

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and (S4) micro-fractures (P = particle).

3. Results and discussion 3.1. 2D imaging

Two-dimensional observation of the shale structure at nano-scale resolution is relatively easy to carry out and costs less than 3D visualisation. Moreover, the reconstruction of a 3D model to provide a representation of the real microstructure of shale without information about the 2D structure is impractical. Two-dimensional imaging plays a guiding role in determining the region of interest for subsequent 3D rendering of particular structures by

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providing a morphological distribution map. Fig. 2 shows 2D SEM images of the typical structures observed in the selected RVEs S1, S2, S3, and S4. The image acquired for S1 shows that Inter-P pores are typically well connected and concentrate around grains. Many Inter-P

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pores extend between organic matter (OM) and clay aggregates, and are similar to the pores observed in clay minerals (Tang et al., 2015). While isolated ellipsoidal OM pores were observed in S2, the imaging revealed a notable absence of developmental pathways for shale gas migration in a view of the organic matter cross-section. The 2D bubble-like pore arrangement

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has also been demonstrated in core samples from the Longmaxi Shale examined by Jiao and co-workers (Jiao et al., 2014). Imaging of S3 revealed that Intra-P pores occur in the mineral grains with irregular forms such as that of an approximate ellipse with sharp corners and

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protrusions. The image obtained for S4 showed that micro-fractures are generated at various mineral interfaces, and in comparison to the micro-fractures observed within clay clasts, are less abundant, but at the same time more integrated and larger, with an average size of 6.768 × 0.502 μm2 in 2D images. Previously, micro-fractures have been observed between the OM and minerals in 2D sections of Longmaxi shale cores using SEM (Zhou et al., 2016) and

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micro-computed tomography (CT) (Ma et al., 2016). These micro-fractures can act as potential fissures and induce crack propagation during fracturing (Gale et al., 2007). The SEM images in Fig. 2 demonstrate the Intra-P pores found in mineral grains, while the Inter-P pores range from 2.04 μm to 20 nm in size, and the OM pores mainly range from 7 to 90.5 nm. The relatively good

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connectivity of the Inter-P pores in the scanned regions suggests that they facilitate transportation of free gas. Nevertheless, the 2D SEM images shown in Fig. 2 reveal only the

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superficial structures of the 3D pores present in shale samples, and thus fail to provide information about the actual 3D interior pore structure and spatial interconnectivity. 3.2. 3D-reconstructed pore structure Three-dimensional modelling using FIB-SEM can be used to visualise the internal structure of shale, which in turn has the potential to enhance fracturing stimulation and recovery efficiency of shale reservoirs. Moreover, the 3D-reconstructed models of shale provide more comprehensive spatial information in terms of structural morphology, e.g., the spatial distribution and interconnectivity of nano-scale pores and the spatial connectivity between

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micro-fractures and adjacent pores. Such information is essential for the assessment of potential shale gas migration and gas recovery rate. Figs. 3–6 display the 3D appearance and structure of the four RVEs of the Longmaxi shale determined from the sequential FIB-SEM

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images using a 3D reconstruction program developed in-house and the Avizo image-processing software. In terms of the coarse-grained representation of the digital model, the 3D reconstructions shown in Figs. 3–6 lack some small sub-structures within voxels as a result of the limited instrumental detection resolution, as well as the layer with finite thickness between

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adjacent sections milled in FIB-SEM imaging process. These sub-structures were excluded from the subsequent statistical analysis. In this study, the fixed milling thickness was set at 20 nm for S1, S3, and S4, and 10 nm for S2, i.e., values close to the pixel size of the corresponding SEM

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image in order to ensure consistency in terms of resolution.

A total number of 460 FIB-SEM images were used to reconstruct the 3D digital models for S1, as shown in Fig. 3. The organic matter fragments shown in Fig. 3A exhibited a dendritic distribution, whereas pyrites occurred as isolated bright grains with a size range of 0.5–2 μm. Further, irregular pores were observed at junctions of different mineral particles. To highlight

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the various shale components, the 3D greyscale model was differentiated into four components in Fig. 3B, defined by adjusting the thresholds for the greyscale levels associated with each voxel. The pore structure extracted from the multi-phase model is shown in Fig. 3C. It is important to note that organic matter in shale, i.e., the hydrocarbon compound kerogen, can produce

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abundant oil and gas after thermal cracking. This means that the levels of original pore space available for shale gas storage are usually affected by the presence of kerogen (Tang et al.,

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2016a). The RVE S1 was found to have a porosity of 0.4 % in the 3D digital model analysis. The Inter-P pores in S1 displayed a sheet-like distribution, which is consistent with the orientation of mineral edges. In order to highlight the pore volume distribution and evaluate pore connectivity, the pores were split into four quartiles in terms of their quantity per unit of volume (Fig. 3D). This volume distribution shows that the pores in the top quartile (red) had the smallest volume for the same number of pores, whereas the largest pores (blue) displayed a more clustered distribution and better connectivity. These results suggest that Inter-P pores most likely have a fairly good connectivity and can therefore generate joints, which may develop into effective

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space for storage of shale gas diffused from organic matter and matrix minerals. A total number of 900 FIB-SEM images were used to digitally represent S2, as shown in Fig. 4. The multi-phase model (Fig. 4B) clearly showed that organic matter (yellow) comprises the

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main part of S2 and contains numerous isolated/connected pores (red), with different minerals (green) and quartz (white) occupying the remaining space. The structure of OM pores exhibited a spherical to ellipsoidal geometry, with an average radius of 25.8 nm (Fig. 4C). The porosity of OM pores in S2 was determined as 1.83 %, which is consistent with previously published

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analysis of Longmaxi shale samples (Yang et al., 2016; Zhou et al., 2016). Zhou and co-workers (Zhou et al., 2016) presented the dense 3D nano-pore structure of kerogen in Longmaxi shale cores by FIB-SEM, which displayed a pore morphology similar to that observed for the OM pores

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in S2. The authors have not, however, reflected the pore connectivity quantitatively in the 3D digital model. Connectivity analysis of OM pores afforded a maximum coordination number of 11 and an average number of 1.71 for the pore-network model shown in Fig. 4D. In contrast to the other shale components reported in the present study, the organic matter exhibited a

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higher quantity of pores potentially available for shale gas transportation.

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Fig. 3. 3D digital reconstructions for a volume of 15 × 13.2 × 9.2 μm3 in size observed in RVE S1. (A) Greyscale model. (B) Multi-phase model showing the basic mineral matrix (green), pyrite (white), organic matter (yellow), and pores (red). (C) Pore model extracted from (B), showing

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of pores per unit of volume). Fractures are shown in pink.

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Inter-P pores and micro-fractures. (D) Pore volume distribution (quartiles represent the quantity

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Fig. 4. 3D digital reconstructions for a volume of approximately 11 × 9 × 9 μm3 in size observed

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in RVE S2. (A) Greyscale model. (B) Multi-phase model showing the basic mineral matrix (green), quartz (white), organic matter/kerogen (yellow), and pores (red). (C) Pore model extracted from (B). (D) Pore-throat network showing the connectivity of organic matter (OM) pores.

The reconstructed 3D model for S3 was prepared using 600 sequential 2D slices, as shown in Fig. 5. The greyscale model showed clearly the presence of a complex and heterogeneous micro-texture of Intra-P pores, ranging from nanometre to micron size and varying from near spherical to irregular polyhedron in shape (Fig. 5A). The multi-phase model shown in Fig. 5B

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exhibited three main components, namely carbonate (green), quartz (pink), and pores (red). Of particular note is that the white region surrounding the pores in Fig. 5A reflects their boundaries, shown in Fig. 5B, which is typical in FIB-SEM-based digital representations (Sun et

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al., 2016). The 3D pore structure observed in S3 showed a concentrated distribution of pores with good connectivity (Fig. 5C) rather than the more dispersed distribution determined in other Longmaxi shale samples (Cao et al., 2016; Tang et al., 2016b; Wang et al., 2016a). In this case, the presence of micro-pores might result in a close connection between pores of various

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sizes. To investigate the relationship between pore size and connectivity, the distribution of pore volume was examined (Fig. 5D), which showed that small pores (red and green) are scattered roughly in the areas surrounding the large pores (blue and yellow). The large pores were

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separated by a relatively shorter spatial distance and were more likely to connect with each other than the small pores. In addition, the Intra-P pores in S3 possessed an irregular architecture with a curved pore wall, which was difficult to capture using 2D sectional images. This type of pore is usually generated by burial dissolution of carbonate and feldspar grains (Yang et al., 2014). In fact, heavy dissolution can even lead to larger micro-sized pores. Although

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the amount of micro-scale pores in the shale was not high, the impact of these larger pores on

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the connectivity distribution is essential for this shale RVE.

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(D)

Fig. 5. 3D digital reconstructions for a volume of 20 × 12 × 12 μm in size observed in RVE S3. (A) 3

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Greyscale model. (B) Multi-phase model showing carbonate (green), quartz (pink), and pores

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quantity of pores per unit of volume).

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(red). (C) Pore model extracted from (B). (D) Pore volume distribution (quartiles represent the

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Fig. 6. 3D digital reconstructions for a volume of 21 × 14 × 12.6 μm3 in size observed in RVE S4. (A) Greyscale model. (B) Multi-phase model showing fractures (blue) and pores (red). Non-voids were removed for clarity. (C) Pore volume distribution (quartiles represent the quantity of pores per unit of volume). (D) Morphology of micro-fracture.

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A total number of 630 FIB-SEM images were used to represent the micro-fracture structure of S4. Fig. 6 displays both the micro-fractures and nano-pores observed in the shale in 3D. Two

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different types of microstructures were characterised by image-processing methods. The properties of these microstructures determined through statistical analysis are listed in Table 2. It should be noted that the micro-fractures in the Longmaxi Formation shale have been characterised using 2D sectional images in previous work (Liang et al., 2014; Shi et al., 2015;

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Tang et al., 2015). However, only a few studies have reported the characterisation of connectivity between micro-fractures and their nano-pores in three dimensions owing to the lack of accurate 3D representation of shale structure (Cao et al., 2016; Jiao et al., 2014; Ma et al.,

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2016). Our results indicate that the porosity of micro-fractures was over five times higher than that of nano-pores in this RVE, although the number of nano-pores was about 200 times greater than that of micro-fractures. In contrast, the average specific surface area (i.e., the surface area of rock per unit of volume) of nano-pores was much larger relative to that of micro-fractures. These results indicate that the micro-fractures have a greater total storage space and better

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connectivity for gas migration, but at the same time a lower capacity for adsorbed gas than the nano-pores. Meanwhile, the co-existence of nano-pores and micro-fractures gives rise to the heterogeneity of structure and petrophysical properties of the Longmaxi shale. Both nano-pores

RVE.

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and micro-fractures have a significant influence on the petrophysical properties of the shale

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Table 1 Morphological parameters of 3D-reconstructed models in shale samples. Samples

S1

S2

S3

S4

15×13.2×9.2

11×9×9

20×12×12

21×14×12.6

The number of SEM images

460

900

600

630

Porosity (%)

0.20

1.83

6.38

0.54

SSA (S/V, 1/μm) *

735.5

63.6

8.9

37.5

Pixel size for X and Y (nm)

15

7

20

22

Maximum pore radius (nm)

216

90.5

2043

95.4

Model volume (μm3)

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1.5

8.6

51.7

22.1

Average pore radius (nm)

19.0

25.8

112.7

23.0

Standard deviation of pore radius

11.3

10.6

119.1

13.7

Average coordination number

3.54

1.17

2.71

2.57

Total No. of pores

5322

17202

6421

2711

Average radius of throats (nm)

12.1

14.8

77.6

15.1

Average length of throats (nm)

42.3

40.5

175

48

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* SSA: specific surface area; S/V: surface to volume ratio

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Minimum pore radius (nm)

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The pore volume distribution, shown in Fig. 6C, suggests that pores in the lowest quartile in terms of total volume (red) are more abundant than larger pores (blue). Furthermore, as shown in Fig. 6D, the reconstructed model produced for S4 contained 13 micro-fractures ranging in width from 0.50 to 6.29 μm. Other parameters of micro-fractures, such as length (Euclidean distance between extreme points), volume, and porosity, are listed in Table 2. The

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findings confirm that micro-fractures promote shale gas accumulation and migration significantly as reservoir space and flow channels, while adjacent nano-pores contribute mainly to shale structural heterogeneity. This heterogeneity in turn affects the fluid transfer processes and the connectivity between artificial fractures and original micro-fractures. These results are

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in agreement with those reported previously by Haggerty and Gorelick (1995). Table 2 Statistically determined properties of nano-pores and micro-fractures in S4. Volume (μm3)

SSA (1/μm)

Porosity (%)

Number

Fracture

18.43

33.1

0.46

13

Pore

2.50

61.8

0.08

2712

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Void type

3.3. Porosity and pore-size distributions

The pore network module of the Avizo image-processing software was used to characterise the 3D microstructure of the shale. The pore network model was extracted from micro-porous

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voxels of the 3D digital model using a maximal ball algorithm (Dong and Blunt, 2009). The pore spaces in this pore network model were displayed as spheres and channels as cylinders. Table 1 lists the morphological parameters of the reconstructed shale models. The porosity of the

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samples, namely the proportion of void voxels in the 3D digital models, was approximately 0.20, 1.83, 6.38, and 0.54 % for S1, S2, S3, and S4, respectively, while the corresponding specific surface area (SSA) was 735.5, 63.6, 8.9, and 37.5 μm-1. The porosity of S2 was greater than those of S1 and S4, which suggests that organic matter provides more pore space per unit of

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volume for shale gas storage than other shale components. The relatively larger SSA of S2, namely significant pore surface in OM pores, also indicates that organic matter has greater potential for gas adsorption capacity. It is significant to note that the porosity of S3, with Intra-P

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pores, was much greater than those of the other samples. This anomalous result can be explained by the presence of a single large pore with a radius of 2.043 μm. Table 1 shows that the average shale pore size was 19.0, 25.8, 112.7, and 23.0 nm for S1, S2, S3, and S4, respectively. Obviously, the pores with larger size contribute more to the pore volume, while the smaller pores determine the specific surface area. This pore size order follows the same trend

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as porosity, and also shows that the distribution of pore size in shale is mainly on the nanometre scale. Our findings are consistent with previously reported results. For instance, Liang et al. (2014) found that the porosity of the Longmaxi shale ranged from 0.77 to 8.7 %. Applying 3D nano-pore structure models, Zhou et al. (2016) showed that 75 % of pores ranged

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from 5 to 50 nm, with an average value of 32 nm, while the porosity ranged from 1.32 to 3.25 %, closely matching our results.

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However, the average pore size is not sufficient in itself to comprehensively describe the pore structure of Longmaxi shale samples. Instead, information on the radius and volume distribution is also required. Fig. 7 shows the radius and volume distributions determined for the modelled pore structure. The count percentage of pores between 10–40 nm in S1 was over 75 % and the relevant volume percentage was established to be 70 %, as shown in Fig. 7A. Similarly, the count and volume percentages of pores between 10–40 nm in size were about 86 % and 64 %, respectively for S2 (Fig. 7B), and 69 % and 56 %, respectively for S4 (Fig. 7D). These results indicate that the pore volume in S1, S2, and S4 should be sufficient for storing

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considerable quantities of gas, even though a large proportion of the pore radii are finer than 40 nm. In addition, micropores and fine mesopores affect the SSA value of pores, which represents the gas adsorption capacity of shale structures (Xiong et al., 2015). This is no different than in

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our study, where the SSA values of S1, S2, and S4 are larger than that of S3, namely greater adsorption potentials in shale. However, almost 65 % of all pores in S3 had a radius of about 80 nm, and in fact, the main fraction in terms of pore volume was supplied by pores with a radius > 0.95 μm (Fig. 7C).

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The results of our quantitative analysis show that pores with a radius of less than 40 nm dominate the pore structure of shale samples—an observation that is consistent with the reconstructed pore structure (Figs. 3–6). The agreement in the structure of the different

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nano-pores means that FIB-SEM images can provide information on the key petrophysical properties of RVEs during up-scaling (Ning et al., 2016). However, micro-scale pores distort the regular distribution of pore quantities and volumes in FIB-SEM images, and their effect needs to be taken into account in the up-scaling of the shale structure model in future work. 3.4. Pore connectivity and permeability

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Pore connectivity and permeability are important parameters for evaluating the probability of shale gas accumulation and migration. Pore connectivity mirrors the interrelationship between the target pore and its adjacent pores, and is described by the coordination number (the number of pores connected to the target pore) in the pore network model (Dong and Blunt,

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2009; Yu et al., 2016). Fig. 8 shows the coordination number distributions associated with the pore structures in the different outcrop samples from the Longmaxi Shale Formation, which

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exhibit a consistent trend with over 60 % of total pores displaying a coordination number lower than 3. The percentage of pores with a coordination number of 1 is about 52.7 % in the organic matter of S2, while the average coordination number was 3.54, 1.71, 2.71, and 2.57 for S1, S2, S3, and S4, respectively.

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(B)

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(A)

(C)

(D)

Fig. 7. Pore size and volume distributions determined for the different shale samples, showing the relationship between pore dimensions and shale structure: (A), (B), (C) and (D) represent

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RVEs S1, S2, S3, and S4, respectively. Note the different scale in (C).

Fig. 8. The connectivity of the pore system as represented by the distributions of coordination number associated with RVEs S1, S2, S3, and S4. The coordination number represents the number of pores connected to the target pore.

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Fig. 9. D3Q19 model for discretizing the velocity of particle

It has been shown that the 3D-reconstructed pore structures of S1, S2, and S3 have an

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extremely low permeability, and cannot therefore form effective flow paths for fluids. In contrast, S4 shale RVE displayed improved path integrity. To quantitatively evaluate the fluid spatial transport capability in S4, we applied the LBM to simulate fluid migration in S4 and determine the permeability of the micro-fracture model. It is well known that LBM has been

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developed into an effective and powerful tool for simulating unsteady non-Darcy seepage processes at microscopic scales, exhibiting excellent numerical stability and constitutive

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versatility (Ju et al., 2014a, 2017b; Kelly et al., 2015; Ren et al., 2015; Sun et al., 2017). On the basis of molecular dynamics and statistical theory, the LBM assumes a fluid system consisting of numerous discrete particles with prescriptive velocity vectors, and computes the density distribution function at each lattice point. Conserving the mass and momentum of the fluid system, the density and velocity of fluid particles are determined by calculating the distribution function (Ju et al., 2014a, 2017b). To enhance the precision of the LBM simulation, the D3Q19 velocity model (Ju et al., 2014a, 2017b; Qian et al., 1992) was adopted to discretise lattice velocity (see Fig. 9), and the LBM single-relaxation-time-BGK (Bhatnagar–Gross–Krook)

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equation was applied to display the evolution of single flow pathways driven by pressure. Simulating single-phase gas flow at the nano-scale must take into account multiple physical processes, including gas desorption, diffusion (Fickian and Knudsen diffusions), thin wetting

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films, slippage and boundary layer effects. The LBM simulation provides information about the geometric permeability, i.e., the fluid flow capability that changes as a function of pore space geometry, and the Knudsen value, which is limited in the theoretically continuous regime for the pore-scale modelling under shale reservoir-like conditions (Kelly et al., 2015). For more details

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about the principles and equations employed in LBM simulations, please refer to the literature (Ju et al., 2014a, 2017b; Qian et al., 1992). In terms of the pore structure of S4, the LBM simulation revealed that the permeability of the micro-fracture model (S4) is 0.394 μD, which is

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close to the experimental results for Longmaxi shale reported previously by Liang et al. (2014). Fig. 10 presents the 3D velocity distribution of fluid flow within the micro-fracture model (S4) and 2D velocity distributions at the inlet and halfway plane, which directly reflect the high permeation capacity of micro-fractures in shale micro-areas. The result clearly shows that micro-fractures are the primary pathways for fluid flow, connecting the microscopic pore

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structure with macro-channels during hydrofracturing of Longmaxi shale reservoirs.

(A)

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(B)

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Revised Manuscript Prepared for Journal of Natural Gas Science and Engineering

(C)

Fig. 10. (A) 3D distribution of flow velocity within a micro-fracture model (RVE S4) with a

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porosity of 0.54 %. The fluid flows in the direction of the X-axis, perpendicular to the Y–Z plane. The point x = 0 refers to the flow inlet, and x = 315 is the halfway point into the flow. (B) Inlet

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plane. (C) Halfway plane.

4. Conclusions

The Silurian Longmaxi Formation in the Sichuan Basin, i.e., the major shale gas reservoir in China, has experienced multiple stages of tectonic evolution that have promoted the formation of diverse, well-developed and multi-scale structures, which make accurate evaluation of

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fracturing stimulation efficiency of the reservoir and recovery rate of shale gas in this area challenging. In our study, shale outcrop samples were obtained from the Longmaxi Formation and FIB-SEM technology was used to identify the microscopic pores and fractures of shale at multiple scales. Series of sequential high-resolution 2D FIB-SEM images were used to

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reconstruct 3D digital models for the shale RVEs, S1, S2, S3, and S4, and to analyse actual 3D structures (Inter-P pores, OM pores, Intra-P pores, and micro-fractures) in shale using Avizo

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image-processing software and a reconstruction method developed in-house. The 3D structural characteristics of the Longmaxi shale in terms of pore size distribution and connectivity of micron–nanometre pores and natural micro-fractures and adjacent nano-pores were quantitatively characterised on the basis of the 3D-reconstructed models. Additionally, the LBM was employed to evaluate the gas transport capability in the multi-scale structure of the Longmaxi shale. The analysis showed that the micro-fractures with higher connectivity and porosity, and lower gas adsorption capacity (SSA value) than those of adjacent nano-pores in the same area, as well as large Intra-P pores, distort the pore structure characteristics, such that

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nano-pores ranging from 10 to 40 nm in size are the dominant structural species in FIB-SEM images. The LBM simulation of gas flow in shale microstructure indicated that micro-fractures are associated with higher gas permeation capacity than nano-pores. These micro-fractures

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should be taken into account when using the RVE model to predict the petrophysical properties of the Longmaxi shale. In contrast, the adjacent nano-pores possess larger gas monolayer adsorption capacity owing to their greater specific surface area. The relationship between micro-fractures and adjacent nano-pores is important for the understanding of the cross-scale

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transport mechanism (i.e., desorption, diffusion and flow from kerogen into fractures). In this work, the characterisation of the 2D and 3D shale structure at the nano- and micron-scale enhanced our understanding of the features that contribute to shale gas storage and migration

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in the Longmaxi Formation in the Sichuan Basin. Our preliminary study provides an experimental reference for the accurate evaluation of the multi-scale structure and the fracturing potential of strata in shale formations with similar geological and geographical conditions elsewhere in the world.

It is believed that during hydraulic fracturing, a large amount of adsorbed gas is desorbed

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from the organic matrix that contains numerous nano-scale pores. It migrates within the connected micro-scale fractures in the vicinity of nano-scale pores and is transported to the macro-scale hydrofracturing cracks. The hydrofracturing cracks bridge the isolated nano-scale pores, the existing micro-scale fractures, and the macro-scale cracks, forming a complex fracture

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network through which the shale gas migrates from the nano-scale pores to the gas wells. Understanding the relationship between the pore connection and gas permeability is of great

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significance to evaluating the efficiency of a hydrofracturing model in which the isolated pores are connected to the hydrofracturing crack network (Sun et al., 2017). The present work aims to provide a quantitative approach to digitally represent the naturally complex structure of the Longmaxi shale, which consists of nano-pores and micro-fractures; thus, the connection between the nano-scale pores and the hydrofracturing crack network was not considered in our 3D reconstruction model. We have carried out a series of real triaxial hydrofracturing tests and CT image analysis to disclose the connection between the nano-scale pores and the generated fracture network. The multiscale models, consisting of connected pores and fractures at various

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scales, were reconstructed, and the percolation method was used to elucidate the mechanisms via which the shale gas diffuses within the organic matrix consisting of nano-scale pores and flows within the fracture network. Considering the main objective of this study and the length

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limit of the manuscript, we will provide a detailed analysis of this issue in our subsequent study.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos.

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51374213 and 51674251), the State Key Research Development Program of China (Grant No. 2016YFC0600705), the National Natural Science Foundation for Distinguished Young Scholars of China (Grant No. 51125017), the Science Fund for Creative Research Groups of the National

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Natural Science Foundation of China (Grant No. 51421003), the Fund for Creative Research and Development Group Program of Jiangsu Province (Grant No. 201427), the Priority Academic Program Development of Jiangsu Higher Education Institutions (Grant No. PAPD2014), and the China Postdoctoral Science Foundation.

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Highlights FIB-SEM was used to identify the 3D multi-scale structure of the Longmaxi shale.

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Shale structures were characterised using 3D reconstructed models.

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Shale gas transport and permeability were analysed by lattice Boltzmann method.

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Pores with 10–40 nm in size predominate in the Longmaxi shale samples.

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Micro-fractures in shale show high porosity and good connectivity.

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