Quantitative pore characterization and the relationship between pore distributions and organic matter in shale based on Nano-CT image analysis: A case study for a lacustrine shale reservoir in the Triassic Chang 7 member, Ordos Basin, China

Journal of Natural Gas Science and Engineering 27 (2015) 1630e1640

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Quantitative pore characterization and the relationship between pore distributions and organic matter in shale based on Nano-CT image analysis: A case study for a lacustrine shale reservoir in the Triassic Chang 7 member, Ordos Basin, China Xuejing Guo a, *, Yinghao Shen b, Shunli He a a b

College of Petroleum Engineering, China University of Petroleum, Beijing, 102200, China The Unconventional Natural Gas Institute, China University of Petroleum, Beijing, 102200, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 21 August 2015 Received in revised form 19 October 2015 Accepted 23 October 2015 Available online 28 October 2015

The microstructure of shale has always been of interest in studies associated with shale gas reservoirs. In addition, the influence of the presence of organic matter on the pore distribution is not well-understood. Although considerable attention has been given to the total organic carbon (TOC) content together with the total porosity, concerns regarding investigating the pores in rocks separately according to the different media where the pores are distributed are still rare. This paper presents a comparative study of the pore size distribution (PSD) in organic matter (OM) and the mineral matrix (MM) within the same sample with the OM-hosted pores and MM-hosted pores accurately distinguished and quantitatively analysed. Four shale samples from a shale play in the Ordos Basin are scanned using nano-CT scanning with a resolution of 65 nm. The calculated total organic carbon (TOC) of the samples are 3.48%, 4.47%, 2.76%, and 3.01% with corresponding porosities of 4.30%, 4.97%, 4.50%, and 4.74%, respectively. The results show that more of the large pores exist in the OM with better connectivity and irregular shapes, while the pores in the MM are smaller on average, have less connectivity, and primarily consist of tiny spheres. The pore-medium-ratio (PMR) was introduced to illustrate the pore volume distribution characteristics within each specific medium. The PMR is a ratio between the volume of pores in a specific medium (i.e., MM or OM in this study) and the volume of that medium. According to the PMR curves, the small pores are distributed homogeneously, while the large pores have a heterogeneous distribution and are medium-dependent. It is concluded that the OM affects the pore distribution in three aspects: 1. the OM has a higher PMR; 2. most large pores occur in the OM; and 3. the small pores in the MM tend to appear around the OM. Insights into the various distributions of the pores have been developed. Pores in either medium exhibit an exponential distribution in number. Three sections of the pore volume distribution and surface area distribution are found. Furthermore, the concept is verified that small pores have a large effect on the surface area, while large pores have a large effect on the pore volume. © 2015 Elsevier B.V. All rights reserved.

Keywords: Organic matter Nano-CT Pore size distribution Shale

1. Introduction Shale gas exploitation has received increased attention in recent years. Because shales have a more complex pore structure than conventional reservoir rocks, such as sandstones, studying the internal microstructure of shale is imperative (Xiong et al., 2015; Bai et al., 2013; Chalmers et al., 2012). Shale is a heterogeneous porous

* Corresponding author. E-mail address: fl[email protected] (X. Guo). http://dx.doi.org/10.1016/j.jngse.2015.10.033 1875-5100/© 2015 Elsevier B.V. All rights reserved.

media, and the porosity and pore size distribution (PSD) are important parameters to characterize the pore structure (Barrett et al., 1951; Hao et al., 2013; Meyer and Klobes, 1999). Compared with the micrometre-scale pores in sandstone and carbonate reservoir, the pores in shale are much smaller in size, usually a few to a few hundred nanometres (Groen et al., 2003; Nelson, 2009). A combination of fluid invasion and radiation methods has been used to characterize shale samples. Knowledge of the pore size distribution from the two methods is critical to understanding the mechanism of fluid storage and flow (Liu et al., 2013b). The fluid invasion method, or indirect method, includes the gas adsorption

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and mercury injection methods. The gas adsorption method takes CO2 or N2 as the operational medium and is used to measure the specific surface area (SSA) and pore size (Mastalerz et al., 2012; Schull, 1948). However, isolated pores cannot be measured using this method. Moreover, a large error would occur when measuring a tight rock with a small SSA (Clarkson et al., 2013). Low pressure adsorption (LPA) of CO2 (Clarkson et al., 2013) is used for characterization of micropores (diameter < 2 nm). N2 LPA (Yang et al., 2014; Liu et al., 2015; Kuila and Prasad, 2011; Ross and Bustin, 2009; Scherdel et al., 2010) is used for characterization of mesopores (2 nm < diameter < 50 nm) and macropores (diameter > 50 nm). Unfortunately, LPA has a maximum pore diameter limit of 300 nm (Scherdel et al., 2010). The mercury intrusion porosimetry (MIP) method can be used to quickly and accurately determine the porosity of rocks, pore diameter, etc., but its application is limited to interconnected pores that range from 3.6 nm to 1 mm (Clarkson et al., 2012c; Münch and Holzer, 2008; Mastalerz et al., 2013). These techniques (MIP þ LPA) provide quantitative and reproducible porosity data but cannot provide direct information of the actual pore geometry and their connectivity. Direct approaches, such as field emission scanning electron microscopy/transmission electron microscopy (FE-SEM/TEM) (Sondergeld et al., 2010; Loucks et al., 2009), focused ion beam scanning electron microscopy (FIB-SEM) (Curtis et al. 2012b; Ma et al., 2015; Dewers et al., 2012; Keller et al., 2011) and smallangle neutron scattering (SANS) and ultra-small-angle neutron scattering (USANS) (Mastalerz et al., 2012; Clarkson et al., 2012a) have been successfully used to observe the shapes, sizes and distributions of pores in shale, and the anisotropy of the microstructure. These methods are intuitive and clear, but the sample heterogeneity and regional differences are ignored because the scanned area is usually tiny (Liu et al., 2011). Source rock consists of two different media: inorganic mineral matrix (MM) and organic matter (OM) (Zou et al., 2010). The main features of the MM are mineral composition and reaction to stress, while the feature of OM is the maturity of kerogen (Huang et al., 2012). Due to the difference in surface energy, distinguishing and quantifying the pore volume in OM is important for gas adsorption and desorption process modelling, which can be used as guidance for actual production (Zhang et al., 2012). However, opinions vary on how OM affects PSD, and clear descriptions are rare (Bernard et al., 2010b). Some studies suggest that the existence of OM is positively related to the large pores or even all pores (Ambrose et al., 2012; Milliken et al., 2013), while other studies have found correlation between OM and small pores (Tian et al., 2013; Jiao et al., 2014). For pores in OM and MM, the qualitative evaluations are basically made through intuitive observations (Kuila et al., 2014), but there is little published quantitative data of comparisons of pores within the two media (Milliken et al., 2013). The objective of this study is to obtain quantitative pore structure parameters, both inside and outside of the OM to explore the relationship between OM and PSD. In this study, samples from a shale reservoir in the Ordos basin are scanned using Nano-CT scanning and then reconstructed. The pore structures are compared for the pores in the sample, pores in the OM, and pores in the MM, and the distribution laws are presented. 2. Samples and methods 2.1. Samples The research samples are from the Upper Triassic Chang-7 member shale of the Ordos basin. The upper Triassic Yanchang Formation is the main target for petroleum exploration and development in the Ordos Basin; the formation of the Chang-7

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member is the most important source rock in this basin. The Chang-7 shale is a continental shale 100e120 m thick with a low density that is normally <2.48 g/cm3 and is composed of ash black mudstone and shale with a small amount of a thin layer of siltstone and fine sandstone interlayers. Shale in this area has poor physical properties, generally cannot be penetrated, and has a porosity of 0.16%e5.12% (average 2.11%) and permeability of 0.0043  103 mm2 ~ 0.239  103 mm2 (average 0.0133  103 mm2). Four samples were taken from a burial depth of 1369.6e1453.4 m with a TOC of 3.48%, Ro of 0.92%, and Type IIA kerogen from this region. 2.2. Experiment set-up and conditions A Nano-CT from ZEISS Xradia Company is used in this research. Through X-ray microscopic imaging with optical lens, ultra-high resolution non-destructive 3D imaging is obtained and then reconstructed. Using a lens to focus the optical magnification, the Nano-CT can achieve high resolution and high contrast with a maximum resolution of 50 nm. In this research, four samples are scanned under the same parameter settings, i.e., test temperature is 20  C; exposure time of a single picture is 120 s; total number of pictures collected is 1016; and cumulative scanning time of one specimen is approximately 54 h. 2.3. Image segmentation method The image segmentation method mentioned below is a new approach for obtaining the PSD in OM and MM at the same time based on image sequences. The meaning of this is quite obvious: when the PSD in the OM and MM are analysed separately, insights into the distribution law are gained through comparison and combination; when the PSD in the OM and MM are analysed simultaneously, errors that might occur in the intermediate process are limited to a minimum range. This method has a wide range of applications. It can be included in all image processing analyses and used on all continuous medium. After the 2D slices are obtained and the 3D core template reconstructed, the areas of the OM/MM and the pores within the OM/MM/sample are segmented on the basis of the 3D template shown in Fig. 3 using Avizo Fire® from the FEI Company. The process is as follows: (1) Determine the OM and the pores in the sample based on grey-scale segmentation. Assume the grey-scale range of the OM is a: [a1, a2], and the grey-scale range of the pore is b: [b1, b2]. A grey value of b2 < a1 indicates that there is no overlap between the OM and pores. (2) Select an area SOM in the 3D template as the OM according to the grey-scale a and area Ptotal as total pore area according to the grey-scale b. (3) Considering the continuity of the OM, the area of the OM needs to be closed. A closing fills the holes inside the particles, eliminates the small details by smoothing the boundary from the outside and connects the close particles (Fig. 1). The closed area is SOM-closed. (4) Taking the enclosed area SOM-closed as the template, determine the POM as the pores in the OM based on grey-scale segmentation in this area according to grey-scale b. (5) Subtract SOM-closed from the overall sample area Ssample; the resulting area is SMM for the MM. Taking SMM area as a template, determine PMM as the pores in the OM based on grey-scale segmentation in this area according to grey-scale b. It is verified that Ptotal ¼ POM þ PMM.

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Fig. 1. Diagram of closing an area.

Fig. 2. 2D Nano-CT scanning images of the four shale samples.

3. Results 3.1. 2D sample texture features Through the Nano-CT scanning, 1016 slices of 2D images are obtained with a resolution of 65 nm and image size of 1008  1024 pixels. The valid scanned sample areas form a cylinder with a diameter of 62,920 nm and height of 66,040 nm. Because of the difference between the overall grey level of the centre area and the surrounding area, the darker surrounding area may influence the

segmentation result if not removed. Therefore, a cube with a side of 500 pixels (32,500 nm in length) from the central area is used as the research object to avoid errors. The texture constituents of the rock are easy to recognize in Fig. 2: dark grey for organic matter, bright colour for pyrite, and pure black for pores. Visible in the current resolution, the distribution of the OM and pores is obviously heterogeneous, and the quantity, size, shape, and development degree are different at different positions. Microcracks appear around the pyrite and other high density rock particles with widths of 200e350 nm, and 2D

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pores in the MM are smaller on average, have worse connectivity and are predominately tiny spheres (Fig. 4c). OM pores dominate the gas shale pore system and control the distribution of the accumulated absorbed gas (Fig. 4d; Milliken et al., 2013).

3.3. Quantitative nano-CT image analysis

Fig. 3. 3D Nano-CT scanning image of sample 5e1.

lengths of 1450e11,270 nm. Apparently the pore distribution is more concentrated and better connected in the OM. The 2D diameter of a large macropore could be up to a few microns.

3.2. 3D sample texture features A 3D template is reconstructed based on the 2D CT scanning images at the nanoscale (Fig. 3 shows the 3D template for sample 5e1 as an example). Morphology analysis of the pores is discussed below through observation of the 3D template. By using the image segmentation method described in Section 2.3, the pores and OM are segmented out; then, the 3D templates of the OM and pores are reconstructed as shown in Fig. 4. The 3D template of sample 5e1 (Fig. 3), together with those of the OM and pores in the OM/MM/sample (Fig. 4) demonstrate the following 3D pore texture features at the nano-scale: (1) Nano-CT images of the sample show abundant nanopores and few micron-scale pores. The pores are distributed in the organic matter and within or around mineral particles and have large differences in size. Shapes vary from nearly spherical (Fig. 4c) to irregularly polygonal (Fig. 4b, d), with slightly irregular ellipsoids being the most common shape. While a majority of pores are nano-scale pores, the microscale pores (including semi-micro-scale pores) dominate the volume (Fig. 4b, c, d). The large micro-scale pores act as main pathways to connect other large pores, while the most isolated sphere nano-pores act as storage space because of their poor connectivity. (2) The OM is distributed with a natural heterogeneity throughout the sample (Fig. 4a). Accordingly, the distribution of pores in the OM has stronger heterogeneity (Fig. 4b). Although the distribution of pores in the MM has slight heterogeneity, the pores in the MM are obviously more homogeneous in spatial distribution than those in the OM (Fig. 4c, d). Moreover, the pores in the MM have a certain degree of aggregation around the OM (Fig. 4d). OM pores are the most abundant pore type in the sample. The small OM pores with elliptical cross-sections are generally distributed independently within the OM, but a few large pores with irregular cross-sections combined with each other and resulted in complex shapes such as grape-shaped forms (Fig. 4b). (3) Most of the large pores exist in the OM with better connectivity and irregular shapes (Fig. 4b). On the contrary, the

Based on the 3D template, parameters such as porosity and OM content are calculated (Table 1). The sample size is 34,328.125  109 nm3 with the pore radius of the four samples ranging from 32.5 nm (when the minimum diameter reaches 65 nm, which is the resolution value, the radius is 32.5 nm) to approximately 5000 nm. Large pores tend to have more complex cross-sections than small pores. The pores are assumed to be equivalent spheres when measured. Note that the equivalent spherical radius might be quite different from the actual pore radius because of the complex shapes of the pores. Also note that the values of the Max Pore Radius shown in Table 1 should be viewed as a maximum values (see the explanation in Section 4.3). Based on the classification scheme proposed by the International Union of Pure and Applied Chemistry (IUPAC, 1994), pores are divided into three groups based on size: macropores (>50 nm), mesopores (2e50 nm), and micropores (<2 nm) (Loucks et al., 2012; Furmann et al., 2014). Therefore, the pores observed in this study are all macropores due to the resolution limit. As is shown in Table 1, the TOC values of the four samples agree well with the common value (3.48%) of this area, and the porosities are within the range (0.16%e5.12%) of this area, which indicate that the data measured are reliable. Tian et al. (2013) discovered that the OM content has a positive correlation with the total porosity, which was confirmed in further research (Tian et al., 2015). Milliken et al. (2013) also reported that shales with TOC < 5.5 wt.% display a positive correlation between TOC and porosity. The result from the Nano-CT image analysis in this study, however, does support this trend. The possible reasons might be the difference in samples from different reservoirs, and the difference in resolution. Additionally, the dilution of the pore volume and influence of the MM pores might be alternative explanations as stated in Section 4.2. 4. Discussion 4.1. Comparison of the PSDs for 4 samples It is calculated from the pore data that the volumes of the pores with diameters <1 mm account for 33.29%, 31.60%, 45.99%, and 47.85% of the total pore volumes for samples 1e1, 1e2, 5e1, and 5e2, respectively, with the corresponding SSA of 62.83%, 62.80%, 73.75%, and 74.09% of the total SSA of the pores. Obviously, the bigger pores contribute more to the pore volume, while the smaller pores contribute more to the specific surface area. Based on this observation, the influence of the lost small pores due to the limit of the experiment resolution on total porosity is tiny but the influence on the SSA is large. Xiong et al. (2015) discovered that the micropores and fine mesopores (pore size between 2 and 6 nm) of shales significantly contribute to the SSA, whereas large mesopores (pore size between 20 and 50 nm) and macropores of shales significantly contribute to the pore volume. This conclusion is consistent with our study, though for different ranges of pore sizes. The percentages of the pore volumes in the OM with diameters >1 mm to the total pore volumes in the OM for the four samples are 84.58%, 87.18%, 78.63%, and 76.85%, respectively, indicating a large

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Fig. 4. 3D nanoscale OM and pore distributions in shale sample 5e1 (from the same angle with Fig. 3): (a) OM distribution in sample 5e1; (b) distribution of the pores within the OM in sample 5e1; (c) distribution of the pores within the MM in sample 5e1; and (d) distribution of all the pores in sample 5e1.

Table 1 Measurements of the investigated samples. Samples

Well

Depth

FTotal %

TOC Wt. %*

OM% BV %*

Max pore radius* nm

1e1 1e2 5e1 5e2

1 1 5 5

1426.5 1453.4 1369.6 1383.2

4.30 4.97 4.50 4.74

3.48 4.47 2.76 3.01

5.17 6.58 4.10 4.45

5252.75 4457.04 4391.50 3385.74

*TOC (wt. %) ¼ total organic carbon (wt. %), TOC is a measure of the organic richness of a rock, i.e., it is the quantity of organic carbon (both kerogen and bitumen) in a rock sample (Jarvie, 1991); OM% (BV %) ¼ total organic carbon (bulk volume percent); Max Pore Radius ¼ largest pore radius, measured as the equivalent spherical radius.

proportion of large micron-sized pores in the OM. The pore quantity distribution and pore volume distributions are shown in Fig. 5. The pores with a radius >1100 nm are not shown in Fig. 5 because they only account for 10e20 pores in total and are distributed randomly over a large radius range of 1100e5000 þ nm with most of the average radius intervals vacant. Another reason is that the super large pores might be a combination of several large pores together with a bundle of small pores inferred from the 3D observation (Fig. 4d), so they are useless in determining the PSD law. However, it is noted that these large pores account for approximately half of the total volume. As seen in Fig. 5a, the number of pores for a given pore size dramatically decreases as the pore size increases. When the radius is greater than 600 nm, the number decreases to less than 10 for every radius interval, and the curves fluctuate strongly, which indicates an irregular distribution. In Fig. 5b, the curves of the total

pore volumes of the four samples share a peak at the average radius values of approximately 103 nm. The accumulated pore volume curves of the four samples have similar trends. After rapid growth, the curves grow gently when the radius >200 nm. Again, when the radius is greater than 600 nm, the curves of the total pore volume and accumulated pore volume fluctuate strongly because of the limitation of the sample size because there are not enough large pores to accurately depict the distribution. In other words, for the pores with radius >600 nm, there is no longer any statistical significance in the number related to the sample size in this research. Therefore, to distinguish the relationships between the curves more, an average radius range of 32.5e600 nm is chosen when drawing the curves (Figs. 6, 8e10). 4.2. Quantification of the OM hosted and MM hosted pores The number, volume, and average radius of pores in the sample/

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Fig. 5. Pore size distributions (PSDs) of the four samples: (a) pore quantity distributions and (b) pore volume distributions including total pore volume (Vpore) distributions and accumulated pore volume (Accu Vpore) distributions.

OM/MM are calculated (Table 2). The MM pores are the smallest pores observed (Table 2) and have the lowest shape complexity (Fig. 4c). The OM pores are approximately three times larger than the MM pores based on the average pore size (Table 2). In summary, the MM pores are dominant in quantity, while the OM pores dominate the total volume and average radius (Table 2), which coincides well with the conclusions from the 3D image (Fig. 4d). The OM pores have good extensibility and high connectivity. However, because the OM accounts for only 4.10%e6.58% of the total volume of the sample, the distribution of the OM pores are strongly affected by the distribution of the OM itself. Therefore, although the OM contributes most of the large pores that dominate the pore volume, as indicated in Figs. 6, 8 and 9, the total volume of the OM pores is diluted in the sample area. On the contrary, the MM pores within the scope of observation have a larger distribution space, but have poorer extensibility and lower connectivity. A large proportion of the MM pores lie in the relatively small radius range of 100e200 nm. While the porosity is determined by the combination of the OM pore volume and MM pore volume, it is reasonable that the OM, affected by the dilution effect of the sample and the influence of the MM pores, seemingly has no direct relationship with total porosity (Table 1). The distributions of the pores in the sample/OM/MM are

calculated statistically and mapped in Figs. 6 and 8e10. Both the OM and MM pore distributions follow an exponential law. The total pore number distribution is close to the MM pore number distribution with a small radius and is consistent with the OM pore number distribution with a large radius (Fig. 6). The intersection abscissas of the trend lines of the OM pore distribution and MM pore distribution of the four samples are 149.81 nm, 154.38 nm, 185.13 nm, and 164.02 nm, respectively. The whole rock is assumed to be composed of dual media, namely OM and MM, with the pores within either single medium distributed following an exponential distribution. The density difference is reflected as a grey-scale difference in the sample image. Although the MM actually contains a variety of minerals, the densities of the minerals could be viewed as a high density group compared with the low density of the OM. As for the pyrite, although there is a large difference between the density of pyrite and other minerals and despite its porous characteristic, it is still classified in the MM group in this research. This is because the pores in pyrite could not be obtained due to the resolution limit, which makes the pyrite appear as solid particles even though the pores around pyrite particles are actually interparticle pores in the MM. Because the OM pores and MM pores follow an exponential distribution, further analysis has been performed between the

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Fig. 6. Pore amount distributions of the four samples: (a) pore amount distribution of sample 1e1; (b) pore amount distribution of sample 1e2; (c) pore amount distribution of sample 5e1; and (d) pore amount distribution of sample 5e2.

Fig. 7. Correlation between the coefficient a of the trend line function of the pore quantity distribution and content of the corresponding medium.

indices of the coefficient of the trend line function and the content of the corresponding medium (Fig. 7). The exponential function of the pore number and pore radius can be assumed to be:

Npore in b ¼ qear

(1)

A positive correlation relationship has been found between the coefficient a and the volume fractions of the OM/MM. Klaver et al. (2012) believe that PSD can be described by a power-law for shale rocks and dual-power-law for carbonate fossils. One possible explanation for the contradiction between the two different trends of pore distributions from their study and this research is that the distribution curve of the pores in the sample seems to be in line with the power-law distribution on the whole when the OM and MM were not analysed separately (Fig. 6a), whereas the distribution of the pores in the sample could actually be the combination of two exponential functions. The pore volume distributions of the samples are shown in Fig. 8. The Vpore-in-core curve and Vpore-in-MM curve share a peak at the average radius value of approximately 103 nm, beyond which the MM pore volume decreases dramatically. The Vpore-in-OM curve rapidly increases as the radius increases up to 134 nm, after which the value of the curve decreases gently. The Vpore-in-core curve is close to the Vpore-in-MM curve when the radius <160 nm and is consistent with Vpore-in-OM curve when the radius >260 nm. Based on this observation, more large pores are in the OM, while most small pores are in the MM, which confirms the conclusion from direct image observations (Fig. 4). Moreover, the Accu-Vpore-in-MM curves end at radius values approximately 300 nm, which indicates no large pores with radii greater than 300 nm exist in the MM. To clarify the pore distribution pattern, the pore-medium-ratio (PMR) was introduced and the PMR curves were drawn (Fig. 9), in which

in which: r ¼ pore radius; b ¼ specific medium, namely OM/MM/core; a ¼ coefficient; and Npore in b ¼ amount of the pores within medium b.

P PMRd;b ¼ in which:

r2d Vpore in b

Vb

(2)

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Fig. 8. Pore volume distributions of the four samples: (a) pore volume distribution of sample 1e1; (b) pore volume distribution of sample 1e2; (c) pore volume distribution of sample 5e1; and (d) pore volume distribution of sample 5e2.

Fig. 9. Pore-medium-ratio (PMR) distributions of the four samples: (a) PMR distribution of sample 1-1; (b) PMR distribution of sample 1e2; (c) PMR distribution of sample 5e1; and (d) PMR distribution of sample 5e2.

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Fig. 10. Total surface area (TSA) distributions of the four samples: (a) total surface area distribution of sample 1e1; (b) total surface area distribution of sample 1e2; (c) total surface area distribution of sample 5e1; and (d) total surface area distribution of sample 5e2.

Table 2 Comparison of the pores in different media. Samples

Npore-sample

Npore-OM

Npore-MM

Vpore-sample 109 nm3

Vpore-OM 109 nm3

Vpore-MM 109 nm3

Avg Rsample nm

Avg ROM nm

Avg RMM nm

1e1 1e2 5e1 5e2

2,26,224 2,62,956 2,81,314 3,05,763

17,999 19,535 33,708 37,438

2,08,225 2,43,421 2,47,606 2,68,325

1475.91 1705.93 1544.78 1627.63

1163.99 1338.47 1061.07 1104.45

311.91 367.46 483.71 523.18

115.94 115.72 109.46 108.33

249.04 253.89 195.91 191.71

70.99 71.18 77.56 77.51

Npore-sample: number of pores in the sample; Npore-OM: number of pores in the OM; Npore-MM: number of pores in the MM; Vpore-sample: total volume of the pores in the sample; Vpore-OM: total volume of the pores in the OM; Vpore-MM: total volume of the pores in the MM; Avg Rsample: average pore radius in the sample; Avg ROM: average pore radius in the OM; Avg RMM: average pore radius in the MM.

r ¼ pore radius; b ¼ specific medium, namely OM/MM/core; d ¼ specific radius range; Vpore in b ¼ volume of the pores within medium b; and Vb ¼ volume of the medium b. The PMR reveals the pore volume distribution characteristics within each specific medium as well as allowing more obvious comparisons among different media. A higher PMR value means a larger value of pore volume per unit volume of the medium and lower density of the specific medium. As is shown in Fig. 8, the PMROM is significantly higher than the PMRMM for almost the whole radius range, which indicates that the OM is the greater contributor to pore space. Pores with a radius approximately 134 nm contribute most of the pore space in the OM; the PMROM curve decreases smoothly for pores further away from 134 nm. Moreover, there is a dramatic increase in the difference between PMROM and PMRMM from zero or nearly zero as the radius increases. This indicates that small pores tend to distribute homogeneously in all the different media, while the larger pores tend to have a more heterogeneous distribution and depend more on the OM.

The total surface area (TSA) distributed among the average radius intervals is shown in Fig. 10. It is quite obvious that the MM pores have a significant contribution to the TSAsample, especially within the radius range of 32.5e160 nm. The TSA distribution curve of pores-in-core could be divided into three sections: average radius <160 nm, when the TSAsample curve is relatively consistent with the TSAMM curve, which indicates that the TSA is dominated by the small MM pores; the average radius >260 nm, when the TSAsample curve is consistent with the TSAOM curve; 160 nm < average radius <260 nm, when the TSAsample is determined by the combination of the TSAMM and TSAOM. 4.3. Validation and limitations of nanopore quantitative analysis 4.3.1. Nano-CT scanning images Ambrose et al. (2012) reported that nearly all of the porosity is associated with the kerogen network. Jiao et al. (2014) also believed that the OM pores are the most abundant for smaller pore sizes. However, it is the MM, instead of the OM, that contains most of the relatively smaller sized pores in this study (Table 2 Column NporeMM). The reasons for this contradiction might be:

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1. The samples are from different reservoirs with different sedimentation mechanisms and different OM maturity, which may result in differences in the PSD. 2. Different experiments with different resolutions and different sample sizes result in different analysis results. The most frequently used experiment measurements when exploring the nano-to-micro sized PSD in shale is the combination of SEM and LPA, with resolutions of approximately 2 nm. Using that method, the PSD with pores ranging from several to several hundred nanometres could be obtained. However, the scanning area of a SEM is too small for the investigation of a valid distribution of larger micro-sized pores, which are also important because they are the main pore volume contributor and act as a flow channel. The Nano-CT scanning used in this study, with a resolution of 65 nm, could accommodate a much larger 3D sample; therefore, the valid PSD range is extended to include much larger micro-sized pores. However, because the minimum pore size was defined by image resolution, not by actual pore sizes that were below resolution, the porosities obtained by Nano-CT scanning may be low and should be viewed as minimum values. This also provides an explanation for the contradiction between the different peaks of the PSD curves reported, i.e., a peak of the PSD at 4e5 nm as reported by Cao et al. (2015), a peak at 3 nm by Kuila et al. (2014), and 103 nm in this study. Overall, the SEM method and the Nano-CT method address the PSDs at different scales with some overlap. 3. There are technical problems with image processing. For example, it is possible to treat a bundle of interconnected small pores as a single large pore automatically when doing pore labelling. Thus, fewer small pores are identified, while super large pores may be artificially identified. In dealing with this problem, the upper limit of the radius range is narrowed down to a valid value (1100 nm in this study as discussed in Section 4.1) to avoid the influence of the irregular distribution of abnormally large pores on the total distribution law. Another problem is grey scale control when doing image segmentation. The grey scale range defines the segmented area for further analysis. Even a slight variation in grey scale would result in a significant change of the selected area. Therefore, to obtain a valid grey scale value, lots of grey scale experiments and referential parameters are required. In this study, grey scale ranges were considered valid when the porosities of the four samples in this case were all in the normal range of the reservoir, while at the same time, the TOC values were all close to the reference value of the research area.

4.3.2. Radius range As mentioned above, the radius range is reduced (in this case from 5000 þ nm of the upper limit to 1100 nm) to avoid the influence of abnormally large pores that actually might be combinations of bundles of interconnected small pores. However, the range should be reduced further before it is valid because of the sample size limitation. Limited by the sample size, it is unlikely to capture enough large pores to fully reveal the full-range PSD for the entire reservoir. Thus, some of the large pores, although obtained in the sample, have to be ignored when drawing the PSD curves in quest of the distribution rules. In this case, the valid radius range is 32.5 nme600 nm based on Fig. 5. 4.3.3. Implications on gas occurrence The isothermal adsorption capacity of OM for methane is almost double that of MM. Due to the difference in surface energy, differentiating and quantifying the pore volume in the OM and MM have critical significance in estimating the storage and production

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properties of unconventional reservoirs (Ross and Bustin, 2009). Various experimental methods have been performed to investigate the PSD in OM and MM separately. Milliken et al. (2013) explored the PSD of OM pores using SEM. Kuila et al. (2014) presented the relative contribution of OM-hosted pores to the total pore volume by OM removal and subcritical gas-adsorption (SGA) analysis. The Nano-CT scanning that has been used in this study helped capture OM pores and MM pores simultaneously for a larger scale. Although all the experiments have limitations, these experiments complement and verify each other, and reveal the PSD law over a wider range than a single study. According to Ambrose et al. (2012), a significant portion of the total gas in place appears to be associated with the interconnected large nanopores within the OM. Therefore, if the gas in place could be investigated separately in the OM/MM by using the research methods in this study to separate the PSD for the OM/MM, the total gas occurrence could be calculated more accurately. 5. Conclusions Four samples from the Ordos basin are scanned using Nano-CT scanning and are analysed. The organic matter-hosted pores and the mineral matrix-hosted pores are considered separately. The results reveal important information on how the presence of organic matter in shale influences the pore distribution. Significant conclusions of this study are as follows: (1) The idea of investigating the pores in rocks separately according to the different media where the pores are located is a creative idea and has large advantages. Most previous studies on pore size distribution tend to investigate the overall distribution of pores in a sample. In this research, efforts were made to investigate the pore distribution law of organic matter pores and mineral matrix pores quantitatively; these efforts resulted in impressive results; (2) The 3D pore texture features are observed at the nanoscale and characterised by statistics. The TOC seemingly has no direct relationship with total porosity in this study. In fact, the organic matter affects the pore distribution in three aspects: 1. the organic matter has a higher pore medium ratio (PMR, ratio of pore volume per medium volume); 2. most large pores occur in the organic matter; and 3. the small pores in the mineral matrix tend to appear around the organic matter; (3) The pore-medium-ratio (PMR) was introduced. This analysis reveals the pore volume distribution characteristics within each specific medium and allows for more obvious comparisons among different media. It is concluded from the PMR curves that the small pores tend to distribute homogeneously in all different media, while the larger pores tend to have a more heterogeneous distribution and depend more on the OM. (4) Both the OM pores and MM pores follow exponential distribution laws for quantity versus pore size; a positive correlation was found between the coefficient a and the volume fractions of OM/MM. (5) The valid pore radius range in this study is 32.5 nme600 nm. The lower limit was determined by the resolution and the upper limit by the sample size. Three sections of the pore volume curve of the pores in a sample are found based on the contribution of the medium: organic matter or mineral matrix. The same three sections are also found in the surface area distribution graphs. Thus, the concept that small pores have a large effect on the surface area while large pores have a large effect on the pore volume is verified.

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