Fractal Analysis of Shale Pore Structure of Continental Gas Shale

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Fractal analysis of shale pore structure of continental shale gas reservoir in the Ordos Basin, NW China Fujie Jiang, Di Chen, Jian Chen, Qianwen Li, Ying Liu, Xinhe Shao, Tao Hu, and Jinxiong Dai Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b00574 • Publication Date (Web): 03 May 2016 Downloaded from http://pubs.acs.org on May 7, 2016

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Fractal analysis of shale pore structure of continental gas shale reservoir in the Ordos Basin, NW China Fujie Jiang a,b,*, Di Chen a,b, Jian Chen a,b, Qianwen Lia,b, Ying Liu a,b, Xinhe Shaoa,b, a,b

Tao Hu , Jinxiong Dai

a,b

a

State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China b College of Geosciences, China University of Petroleum, Beijing 102249, China

Abstract：： Describing the characteristics of shale pore structure is vital for the assessment of shale reservoir, which has significant influence on the storage and seepage mechanisms of gas shale. To profoundly understand the shale pore structure characteristics of continental shale reservoir, fractal analysis was performed on 45 continental shale samples from the Ordos Basin, NW China, via low–pressure N2 adsorption experiments. The characteristics of N2 adsorption isotherms revealed that slit–shaped shale pores are dominant among the geometric shapes of shale pores. During N2 molecules adsorption process, different characteristics were displayed at two regions where relative pressures (P/P0) were 0–0.45 and 0.45–1. The Frenkel–Halsey–Hill (FHH) method was used to calculate fractal dimensions (D) at these two regions. In addition, the fractal exponents “(D − 3)/3” and “(D − 3)” were compared adequately. The results show creditable fractal characteristics for continental shale. Fractal exponent “D − 3” is more suitable for the calculation of the fractal dimension in the study area. The surface fractal dimension (D21) and pore structure fractal dimension (D22) were further investigated. Results indicate that D21, ranging from 2.04 to 2.50, was affected by shale constituents and provided a site for gas shale adsorption. D22 reflects the irregularity and heterogeneity of the shale structure, varying from 2.20 to 2.65, and is higher overall than D21. Furthermore, the value of D22 negatively correlates with the average diameter of the shale. In addition, the comparisons of shale pore structure characteristics between the reservoirs Chang–7 and Chang–9 show that the shale pore structure of Chang–9 reservoir is more irregular and nonhomogeneous, and is favorable for gas shale storage but unfavorable for seepage.

Key words: Fractal analysis; Low–pressure N2 adsorption; Frenkel–Halsey–Hill method; Ordos Basin

1. Introduction Shales are fine–grained sedimentary deposits, the complex and heterogeneous porous media with intricate pore systems, comprising various pore types, multiple pore geometries, and a large range of pore sizes1. Shale reservoirs contain numerous nanopores, which significantly influence the adsorption behavior of gas shale2, 3. Because of the potentially significant gas content in gas shale reservoirs, it is crucial to clarify the pore structure and sorption characteristics of organic– rich shales4-6. Various experimental methods such as microscopic observation, radiation detection, and fluid

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invasion have been used to characterize pore structures1, 3, 7. Focused ion beam scanning electron microscopy, scanning or transmission electron microscopy, and field emission scanning electron microscopy imaging techniques have been used to observe pore type and pore geometries by detailed visualization8-11. Small–angle and ultra–small–angle neutron scattering techniques and nuclear magnetic resonance have been successfully applied to analyze the pore structure of shale reservoirs2, 3, 9, 12, 13. Pore structure can be characterized by experiments such as mercury injection, low–pressure N2 and CO2 adsorption, and helium pycnometry2, 3, 9, 10, 13, 14. Low–pressure N2 adsorption analysis has proven to be an effective method for characterizing the nanopore structure of shales1-3. These experiments were used to investigate pore structure characteristics such as pore type, pore size distribution, pore geometry, and pore volume. However, they could not effectively characterize and quantify the irregularity of shale pore structure. In recent years, fractal theory has been used to investigate the pore structure of coal and shale widely by some researchers15-19. Fractal analysis is useful when describing the geometric and structural properties of fractal surfaces and pore structures20-22. Several experiments such as mercury injection, gas adsorption, discrete, and scattering methods can be used to investigate the irregularity of porous media by fractal theory. Fractal analysis based on nitrogen adsorption isotherms is a promising and widely–used technology to quantitatively characterize the pore structure of shale and coal15, 17, 18, 23, 24. Five methods based on adsorption isotherms have been proposed: the Langmuir model, changing sample size model, the multipoint Brunauer–Emmett– Teller (BET) model, fractal Frenkel–Halsey–Hill (FHH) model, and thermodynamic method20, 25-34. Among these, the fractal FHH method requires only a single adsorption isotherm and can be conducted easily; therefore, it has been proven to be the most effective method. Continental gas shale has been successfully exploited in the Ordos Basin, NW China, reflecting a huge potential of gas shale in China (initial gas production of the Liuping-177 well in the Ordos Basin was 2350 m3/d)35, 36. The geological reserves of gas shale reservoirs are estimated to be approximately 134 × 1012 m3 in China and 19.9 × 1012 m3 in the Ordos Basin37. The basin contains several sets of shales, including the Chang–7 and Chang–9 members of the Upper Triassic Yanchang Formation, which was deposited in a deep–lacustrine and lacustrine sedimentary environment along with abundant organic matter38, 39. The investigation of the shale pore structure is significant to gas storage and flow mechanisms, and it is beneficial for the continental gas shale production in the Ordos Basin. In this study, we performed fractal characteristic analysis of shale samples from the Ordos Basin. Using the fractal FHH method and N2 gas adsorption/desorption isotherms, we obtained pore structure parameters and calculated fractal dimensions, which can be used to quantificationally characterize the irregularity of the shale pore structure. In addition, we discussed the influential factors of fractal dimensions.

2. Samples and methods In this study, totally 45 shale samples from eight wells were cut from fresh cores, of which 32 samples were from the Chang–7 member and 13 were from the Chang–9 member. To comprehensively analyze the shale pore structure, geochemical, mineralogical, and low–pressure N2 adsorption tests were performed. All samples were cleaned with distilled water, ground to 80–100 mesh powder (150–187 mm particles in size), and dried at 383.15 K for 24 h before testing. The total organic carbon contents


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(TOC, wt%) of the 45 samples were measured using a LECO CS230 carbon–sulfur analyzer. Vitrinite reflectance (Ro, %) values of the 45 samples were determined using a MPV–SP microphotometer. The TOC and Ro tests were performed at 295.15 K and 35% humidity. X–ray diffraction and clay mineral analysis were conducted on the samples using a D8 Discover X–ray diffractometer. Low–pressure N2 adsorption experiments were performed for the 45 samples using a Quantachrome Quadrasorb SI Surface Area Analyzer. All samples were dried at 378.15 K for 24 h in a vacuum oven to remove water before experiments. N2 adsorption isotherms at 77 K were obtained with the relative pressure (P/P0) ranging from 0.004 to 0.995. The specific surface area (SSA) was calculated using BET method with data from N2 adsorption under the relative pressures (P/P0) ranging from 0.05 to 0.35. The pore size distribution (PSD) and pore volume (PV) were determined by using the Barrett–Joyner–Halenda (BJH) model. Table 1 lists the basic properties and N2 adsorption results of 45 samples, including the core well name, member name, TOC, thermal maturity, and mineral composition.

3. Geological setting The Ordos Basin, located in the west of North China Platform (Fig. 1), is the oldest craton in China, which has gone through four important geologic periods including early Paleozoic marine platform, late Paleozoic marine and terrestrial alteration, Mesozoic foreland basin and Cenozoic basin margin faulting and subsidence40, 41. The geologic structure of Ordos Basin is gentle with eastward upwarp and westward pitch, lacking anticlines and faults. The Ordos Basin can be divided into six structural units: the Yimeng uplift zone in the north, the Weibei uplift zone in the south, the Jinxi flexural fold zone in the east, the Xiyuan obduction zone, and the Tianhuan depression in the west, the Yishan slope in the midsection which has the largest area42. Yishan slope forming in Early–Cretaceous, is a gentle westward tilt monocline, the dip angle of which is less than 1°. The study area is located in the south of Yishan slope (Fig. 1). The basement of Ordos Basin is crystalline rock in Archean Eonothem and Palaeoproterozoic, which has have undergone five tectonic evolutionary stages: Meso–Neoproterozoic aulacogen, Early Paleozoic shallow marine platform, Late Paleozoic strand plain, Mesozoic inland depression, and Cenozoic fault depression43, 44. Starting from the Early–Triassic, Ordos massif uplifted in east and sink in west, forming the basin prototype. The tectonic activities from Late–Triassic to Late– Cretaceous have significant influence on the generation and aggregation of hydrocarbon in the Ordos Basin45. In Late–Triassic, the inward of Ordos Basin came into being large–scale freshwater lake, and deposited the Chang–10 to Chang–1 members44. The Chang–9 and Chang–7 members are the main source rock in the study area, which are the target layers (Fig. 2)46. The Chang–9 member deposited in semi–deep lacustrine environment (Fig. 2), the Kerogen types of which are sapropelic and hybrid types. The top of Chang–9 member deposited a suit of Lijiapan shales47. The thickness of Chang–7 member is relative large, which broadly distribute in the Ordos Basin (Fig. 2). The Chang–7 member was deposited in deep lacustrine environment with humic– sapropelic Kerogen, the bottom of which deposited a suit of Zhangjiatan shales43, 44. In the early period of Late– Jurassic, an intense tectonic–hot incident occurred in the Ordos Basin and its surrounding, forming the present tectonic framework, and the organic matter of Yanchang Formation started to mature42, 48 .


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4. Results 4.1 Mineral composition and geochemistry According to previous studies, shale composition, including minerals and organic matter, strongly influences the pore structure1, 49. Mineral composition affects petrophysical properties and flow characteristics of shales; thus, mineral characterization is critical to the evaluation of shales50. The XRD mineral composition of 45 samples are given in Figure 3 and Table 1. The XRD data showed a wide range in inorganic fraction compositions. The dominant components were clay minerals, with an average value of 48.75 wt% (34–65 wt%) in Chang–7 and 49.23 wt% (41–64 wt%) in Chang–9, followed by quartz and feldspar; content feeble carbonate minerals was also present (Fig. 3). Pyrite was observed in 45 samples with the highest concentration of up to 22 wt% (Chang–7 sample yy33–8) and 4 wt% (in Chang–9 samples yy13–22, yy4–6, and yy8–16). Siderite was also observed in the highest content of up to 31 wt% (yy33–1) in the Chang–7 sample and 3 wt% in Chang–9 (Fig. 3). Mixed–layer illite/smectite (I/S) takes the dominant proportion in clay mineral content, with a mean value of 60.59 wt% (45–79 wt%) in Chang–7 and 65.38 wt% (44–88 wt%) in Chang–9, followed by illite and chlorite, but no smectite (Fig. 3, Table 1). Table 1 and Figure 3 show the results of the geochemical analysis performed on 45 samples. TOC is an important index for evaluating the hydrocarbon–generating potential of organic matter in shales. The TOC ranged from 1.46% to 11.44% with an average value of 4.96% in Chang–7 and significantly varied from 0.50% to 6.26% with a mean value of 3.16% in Chang–9, both demonstrating that there is abundant organic matter in the study area. Figure 3 and Table 1 show that Ro varies slightly from 0.84% to 1.10% with an average value of 0.84% in Chang–7 and an average value of 1.04% (0.88%–1.10%) in Chang–9, indicating that organic matter is at a mature hydrocarbon generation stage.

4.2 N2 adsorption–desorption isotherms Nitrogen molecules (inert molecules) can be attracted onto a solid particle to form a liquid film by Van der Waals (VDW) force20, 51. The thickness of the liquid film grows with increasing pressure, meanwhile the vapor interface becomes smoother than the adsorbing surface20, 21. When the nitrogen molecule adsorption takes place in nanopores, abundant in shale and with a large specific surface area, the vapor interface diminishes due to the action of surface tension31. The liquid film collapses at some critical pressure and fills the entire pore. Due to the influence of VDW forces and surface tension, the N2 adsorption isotherms generally form hysteresis loops. As shown in Figure 4, the N2 adsorption isotherms of the shale samples belong to the type IV isotherm, according to the classification of the International Union of Pure and Applied Chemistry (IUPAC)51, 52. A hysteresis loop can also be seen obviously in all 45 samples (Fig. 4), no plateaus are observed at higher pressures covering region, implying that these samples contain both mesopores and macropores53. The adsorption/desorption isotherms are steep in the relatively high pressure zone (0.9–1). This phenomenon may suggest that pores of these samples are dominated by mesopores (diameter, d50 nm) are relatively few. The adsorption amount ranges from 9.28 to 35.60ml/g at a P/P0 of 0.99, showing a week positive relationship with Ro (Fig. 5). However, the adsorption amount is low at relatively low pressure region (P/P0 < 0.01), which indicates the presence of micropores. When capillary condensation


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occurs within the mesopores, there is an obvious “forced closure” phenomenon of desorption branch at P/P0 ≈0.45 (especially in samples yy5–3 and yy12–23) (Fig. 4), known as the Tensile Strength Effect (TSE). 51, 54. According to the IUPAC hysteresis loop classification, the hysteresis loops of all the shale samples are similar to the Type H3 loop. This phenomenon indicates that plate–like and slit–shaped pores dominate in the shale reservoir. The pore structure parameters including specific surface area (SSA), pore volume (PV), and average pore diameter can be acquired from N2 physisorption experiments. In this study, SSA was calculated by the multipoint BET method using N2 adsorption data under relative pressures (P/P0) ranging from 0.05 to 0.351. PV was calculated by using BJH model from adsorption branch under a P/P0 range of 0.06–0.991, 3. According to Table 1, the value of BET–SSA is between 2.78 and 15 m2/g with a mean value of 5.96 for Chang–7 samples, and an average value of 9.43 m2/g (6.11– 14.7 m2/g) for Chang–9 samples. The BJH–PV value ranges from 15.5 to 56.4µl/g (average 27.4µl/g) for Chang–7 samples, with an average value of 40.7µl/g (25.2–56.2µl/g) for Chang–9 samples. Average pore diameters between 10.4nm and 42.1nm with mean value of 19.22nm were found in Chang–7 samples, and an average of 16.95nm (12.2–20.7nm) was obtained for Chang–9 samples. Hysteresis loops predicted the types of shale pore preferably, but could not quantitatively describe the degree of irregular pore geometry. However, fractal analysis may make up for this deficiency by calculating the fractal dimensions, detailed descriptions follow.

4.3 Fractal isotherms equation Shale pores with a non–uniform structure and irregular surface geometry are formed naturally during the sedimentation process18, 54. Fractal geometry has great potential for characterizing and simulating the geometry of complex non–Euclidean shapes, especially the complex shapes of many objects found in nature, providing that the requirement of self–similarity is satisfied; the geometry of rock pores is a typical example of such shapes55, 56. Fractal dimension (D) ranging from 2 to 3, is used as an important parameter to quantitatively evaluate the surface roughness or structural irregularity of a solid. For a regular and smooth surface, D = 2 and higher indicates a more irregular and space–filling surface. The Fractal Frankel–Halsey–Hill method based on N2 adsorption isotherms has proven to be the most effective method for describing the non–uniform and irregular geometric and structural properties of porous solids, such as coal and shale57. Fractal FHH theory is based on Van der Waals (VDW) adsorption on planar surfaces and capillary condensation on nanopores in N2 adsorption experiments. The fractal dimension (D) can be measured independently by using the fractal version of the FHH equation combined with N2 adsorption isotherm data. Under the assumption that the surface has self–similar fractal characteristics, based on the modified FHH theory of multilayer gas adsorption, D can be determined using the following equation20, 21: ே

ே௠

∝ ሾܴܶ ln(ܲ଴ /ܲ)ሿ௄

(1),

where R is the gas constant; T the absolute temperature when the isotherm was obtained, 77.3 K; N is the number of molecules adsorbed at equilibrium pressure P; Nm is the number of gas molecules in a monolayer; P0 is the saturated vapor pressure of nitrogen at temperature T, and K is the power law exponent dependent on the fractal dimension (D) and mechanism of adsorption. The process of N2 adsorption follows Avogadro's law, and the value of Vm is 34.64×10–4 m3 at


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77.3K. An additional constant, Const, may be included in Eq. (1) to account for the amount of adsorbed volume when the fractal regime is first reached, namely, the data may be described by ௉

ln ܸ = ‫ ݐݏ݊݋ܥ‬+ ‫ ܭ‬ln ቂln ቀ ௉బቁቃ

(2),

where V is the volume of N2 adsorbed at each equilibrium pressure P, ml/g. The detailed process has been described in the literature15, 20, 31, 32, 58-61. K is a key parameter to acquire D, and can be obtained from the slope of the plot of ln(V) versus ln(ln (P0/P)). At the early stage of N2 adsorption, liquid nitrogen molecules are absorbed onto the monolayer shale surface. At this stage, VDW adsorption on the planar surface between the solid and adsorbed film is dominant, which tends to make the gas–film interface replicate the surface roughness. Considering the VDW effect alone, the relationship between K and D is written as: K=ቀ

஽భ ିଷ ଷ

ቁ

(3),

for higher coverage in the range of capillary condensation, liquid nitrogen achieves multi– molecular layer adsorption onto the shale pores. Controlled by the surface tension between liquid and gas, the interface tends to move away from the surface and smooths out the liquid/vapor meniscus to reduce the interface area. In this situation, considering surface tension only, the relationship between K and D changes to the following expression: K = (‫ܦ‬ଶ − 3) (4). It has been proposed that the curvature of the lnV vs ln(ln(P0/P)) plot may be effective for determining the coexistence of the surface tension and Van der Waals force effects15, 54, 62, 63. For the convenience of description, we used D1 in Eq. (3) and D2 in Eq. (4) to analyze the two mechanism of adsorption. The former is derived from the area surrounding the monolayer region and the latter from the multilayer region.

4.4 Fractal dimension calculation According to the above analysis, N2 adsorption isotherms form hysteresis loops under the effect of VDW force and surface tension. The force–closed phenomenon of desorption branch at P/P0≈0.45 was obvious in most of the samples (Fig. 4), as well as the obvious hysteresis loops when P/P0 was over 0.45. The plots of lnV vs ln[ln(P0/P)] for most samples divide into two linear segments at P/P0 =0.45 (Fig. 6), in addition, adsorption isotherms represent anomalous adsorption characteristics between isotherms at relative pressures of 0–0.45 and 0.45–1. These phenomena indicate that the two regions display different fractal characteristics. In view of the above analysis, we set P/P0 =0.45 as a boundary between region 1 (P/P0, 0–0.45; slope K1) and region 2 (P/P0, 0.45–1; slope K2), and calculated the fractal dimension D at region1 (D1) and region 2 (D2). The calculated results are listed in Table 2. According to Table 2, all correlation coefficients are very high (about 0.98) for most of the samples, demonstrating that the FHH model could be used to analyze shale pore structure characteristics adaptively in this study area and there are commendable fractal characteristics for shales in Chang–7 and Chang–9. The values of D1 in both region 1 and 2 calculated with Eq. (3) for the 45 samples are all considerably low, less than 2 (Table 2), and deviate from the definition of the fractal dimension of pore surfaces and structures59. The research results demonstrate that Eq. (3) is invalid to the continental shale of Chang–7 and Chang–9 member in the Ordos Basin, and that VDW force is weak in the N2 adsorption process. As a contrast, Eq. (4) is more reliable for


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calculating D in both regions 1 and 2. The values of D2 in regions 1 and 2 calculated by Eq. (4), are between 2 and 3 (except sample yy12–17 in region 1, Table 2), which is logical. This phenomenon reveals that VDW forces and surface tension do not function alone in the N2 molecules adsorption, in fact they always work together to affect the fractal characteristics of shale pores. As a consequence, D2 calculated by Eq. (4) could be used to analyze the fractal characteristics of shale pores. The correlation between D2 in region 1 (simplified as D21) and D2 in region 2 (simplified as D22) is weak (Fig. 7), indicating that the fractal dimensions in the two regions are different. According to Table 2, D21 ranges from 2.04 to 2.50 with an average value of 2.29, and D22 varies from 2.20 to 2.66 with a mean of 2.52, showing the heterogeneity of the pore surfaces of these shale samples.

5. Discussion To some extent, the components and degree of thermal evolution of organic–rich shales influence the fractal dimensions, as well as the shale pore structure parameters. To comprehensively characterize the fractal characteristics, the relationships between them, as well as that between D21 and D22, are discussed below.

5.1 The correlations between fractal dimension and shale constituent The relationships between fractal dimensions versus TOC of continental shales in the Ordos Basin are shown in Figure 8. Figure 8(a) shows a slightly negative correlation between TOC and the value of D21, and the relationship between TOC and the value of D22 is vague with scattered plots in Figure 8 (b). The results observed in this study are contrary to those obtained by Liu et al.64. In the above analysis, the organic matter is at the hydrocarbon generation stage, in which micropore volumes would decrease owing to the filling of pores by low volatile hydrocarbons65, and the available micropores of shales may decrease with the increase of TOC content. In addition, shale samples with a higher TOC content probably produce more homogeneous mesopores due to the hydrocarbon generation effect. Therefore, the shale reservoir would become relatively homogeneous, and the value of D21 decreases with increasing TOC. Yang et al.18 proposed that crystallites in the organic matter affects the value of fractal dimensions. Nitrogen physisorption is relatively accurate for the mesopores, but unreliable for micropores. Hence, the analysis of fractal dimensions using micropores measured by nitrogen physisorption is unreliable. The relationship between D21 and clay content is equivocal (Fig. 9), but D21 is moderately positively correlated with the I/S content (Fig. 10). The value of D22 has a chaotic relationship with I/S or clay content. Smectite is scarce in the study area (Table 1), and the burial depth of the samples ranges from 1212.53 to 1754.43m. Smectite simply transformed to an I/S mixed–layer at this depth, which lead to low smectite content but highest I/S content66-68. In addition, fractal dimensions have a chaotic relationship with the quartz and feldspar content (Fig. 11), which indicated that quartz and feldspar had little effect on pores.


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5.2 The correlations between fractal dimensions and shale pore structure parameters The relationship between fractal dimensions and shale pore structure parameters are shown in Figures 12–14. As shown in Figure 12, fractal dimensions and SSA show a slightly positive correlation. The BET-SSA increase with increasing fractal dimensions, indicating D21 and D22 could reflect the complexity of pores or surface roughness. The specific surface area of smectite, illite and chlorite are 800ml/g, 30ml/g, and 15ml/g, respectively69-71, and the SSA of I/S falls between smectite and illite. As a consequence, shale samples with higher I/S content always have a greater D21 value (Fig. 10a). The fractal dimensions show a scattered relationship with PV (Fig. 13), indicating that pore volume has little influence on fractal dimensions. An obviously negative correlation can be observed in Figure 14a between D22 and the average pore diameter, which is consistent with marine gas shale studied by Yang et al. (2014)18..Shale samples with higher value of D22 have more complicated pore structure, which may be caused by that shale samples with smaller average pore diameters will also contain more micropores18. In contrast, no obvious relationship has been observed between D21 and the average pore diameters (Fig. 14b), which indicated that D22 may be more suitable for describing the pore structure. The average pore diameter varies from 10.4 nm to 42.1nm, with an average of 18.56nm, belong to mesopores (2– 50nm). The phenomenon indicates that mesopores or even micropores are abundant in the samples. Generally speaking, the pore structure becomes more heterogeneous as the number of nanopores increase, which probably causes the reduction in the fractal dimension value. D22 increased as the pore diameter decreased, demonstrating an irregular and complicated pore structure in the shale pores.

5.3 Discussion of fractal dimension D21 and D22 The fractal dimension can quantify geometric and structural properties of fractal surfaces and pore structures effectively, and two descriptive forms are often used, the surface fractal dimension and pore structure dimension72. As discussed above, the fractal dimension D21 seems to be influenced by shale constituents, such as the quantity (TOC) and the content of I/S, and the D21 values could represent the surface fractal dimension. Whereas, the fractal dimension D22 has good relationship with the pore structure parameters, especially with SSA and the average pore diameter, and indicated that the D22 values are more significantly related to pore structure fractal dimension. The logical fractal dimension, calculated by Eq. (4) at two regions of relative pressure 0–0.45 and 0.45–1, demonstrates the coexistence of VDW forces and surface tension. At a relative pressure of 0–0.45, the nitrogen molecules behave as monolayer adsorption, and micropore filling occurs under the effect of VDW forces. In the monolayer region, the gas interface is dimensional, which may only react to the pore surface of shale. In this study, the fractal dimension (D21) relates to this region, corresponding to the surface fractal dimension. As a contrast, nitrogen molecules undergo multilayer adsorption, with the mesopores and macropores filling at relative pressures of 0.45–1 where surface tension dominates. In the multilayer region, the nitrogen molecules film fill the pore space, which lead to that the film interface may reflect the pore structure. Therefore, the fractal dimension (D22), corresponding to the pore structure dimension, relates to this region. The surface fractal dimension D21 and pore structure dimension D22 reflect the different surface behaviors at the liquid/vapor interface, and do not display good correlation (Fig. 7), which


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is inconsistent with the research results of Wang et al. 54 and Liu et al.64. This phenomenon shows that D21 and D22 are comparatively independent. D21 represents the pore surface irregularity. The values of surface fractal dimension 2 and 3 indicate a perfectly flat and very rough pore surface, respectively15. The higher the value, the more irregular and rougher the pore surface. In contrast, the pore structure fractal dimension (D22) describes the pore structure irregularity. The higher the pore structure fractal dimension value, the complex the pore size. The values 2 and 3 of D22 represent porous media with homogeneous pore–size distribution and inhomogeneous pores, respectively.

5.4 The comparison between Chang–7 and Chang–9 Overall, both fractal dimensions D21 and D22 in Chang–9 are higher than those in Chang–7 (Fig. 7, Table 2), suggesting more irregular and nonhomogeneous pores in the reservoir shale in Chang–9. Ro increased as the depth increased (Table 1), leading to more hydrocarbon generation breaking brittle minerals to form microfractures, which makes the shale reservoir more irregular. In addition, more smectite converted into I/S mixed–layer as the depth increased, causing a higher SSA and greater gas adsorption capacity in Chang–9 (Table 1). The N2 adsorption volume at a relative pressure of 0.99 under the standard state for Chang–9, ranged from 15.77 to 35.38ml/g with an average of 25.52ml/g, greater than that in Chang–7 which had a mean of 17.02ml/g (9.28– 35.60ml/g) (Table 1). The phenomenon demonstrates that the gas shale adsorption space in Chang–9 is bigger than that in Chang–7. According to the analysis above, the shale reservoir in Chang–9 is favorable for gas shale storage because of its space, but it is unfavorable for gas flow ascribing to the more irregular shale pores. More fracturing will be needed to obtain a high gas yield from Chang–9.

6. Conclusions and suggestions In this study, 45 samples of continental shales from the Chang–7 and Chang–9 members of the Upper Triassic Yanchang Formation in the Ordos Basin, NW China, were subjected to geochemical and mineralogical tests, and low–pressure N2 adsorption experiments. The FHH method was used to investigate the fractal characteristics of these shales by combining the data from N2 adsorption isotherms. In addition, the relationships between the shale composition, shale structure parameters, and fractal dimensions are discussed in this paper. The key conclusions are summarized as follows: (1). Geochemical analysis shows that organic matter in the shale samples is abundant, with an average TOC value of 4.44% (0.51–11.44%), and is at a mature hydrocarbon generation stage. XRD test results reveal that clay minerals are dominant, followed by quartz. Pyrite and siderite was also observed in some samples, showing a non–uniform mineralogical composition in this area. (2). The shale pores show obvious fractal characteristics. Comparing the results calculated from Eqs. (3) and (4), the fractal dimension calculated using Eq. (4), namely K = (‫ ܦ‬− 3), is more realistic in this study area. (3). The adsorption characteristics at the relative pressures of 0–0.45 and 0.45–1 are different. Two types of fractal dimension have been obtained from the two regions in this study, namely, the surface fractal dimension and the pore structure dimension.


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(4). The surface fractal dimension D21 ranging from 2.04 to 2.50, was affected by shale constituents and provided sites for gas shale adsorption. The pore structure dimension D22 reflected the irregularity and heterogeneity of the shale structure. It varied from 2.20 to 2.65 and was higher than D21 overall. In addition, the value of D22 negatively correlated to the average diameter of the shale. (5). Comparison between the Chang–7 and Chang–9 members reveal that the shale reservoir of Chang–9 is more irregular and nonhomogeneous, and favorable for gas shale storage while unfavorable for seepage. As a result of the above analysis, we propose the following: low–pressure N2 adsorption is suitable for mesopores but unreliable for micropores and macropores as shale has a very complicated nanopore structure system, one method is insufficient for the analysis of shale fractal characteristics. To comprehensively characterize the fractal characteristics of continental shale more diverse experiments and further detailed investigations are necessary.

Acknowledgments This investigation is financially supported by the Natural Science Foundation of China (NSFC) (41572106), the PetroChina Innovation Foundation (2014D–5006–0106), and the Beijing Higher Education Young Elite Teacher Project (YETP0668). The insightful reviews by the reviewers significantly improve the manuscript, for which we are grateful.

References (1) Bustin, R.M.; Bustin, A.M.M.; Cui, X.; Ross, D.J.K.; Murthy, P.V.S. Impact of shale properties on pore structure and storage characteristics. In: SPE 119892 Presented at the Society of Petroleum Engineers Gas shale Production Conference. Fort Worth, Texas, 2008. (2) Clarkson, C.R.; Wood, J.M.; Burgis, S.E.; Aquino, S.D.; Freeman, M. Nanopore structure analysis and permeability predictions for a tight gas siltstone reservoir by use of low pressure adsorption and mercury intrusion techniques. SPE Res. Eval. Eng. 2012, 15, 648-661. (3) Clarkson, C.R.; Solano, N.; Bustin, R.M.; Bustin, A.M.M.; Chalmers, G.R.L; He L.; Melnichenko, Y.B.; Radlin, A.P.; Blach, T.P. Pore structure characterization of North American gas shale reservoirs using USANS/SANS, gas adsorption, and mercury intrusion. Fuel 2013, 103, 606-616. (4) Montgomery, S.L.; Jarvie, D.M.; Bowker, K.A.; Pollastro, R.M. Mississippian Barnett Shale, Fort Worth basin, north-central Texas: Gas-shale play with multi–trillion cubic foot potential. AAPG bulletin 2005, 89(2), 155-175. (5) Pollastro, R.M. Total petroleum system assessment of undiscovered resources in the giant Barnett Shale continuous (unconventional) gas accumulation, Fort Worth Basin, Texas. AAPG bulletin 2007, 91(4), 551-578. (6) Ross, D.J.K; Bustin, R.M. Impact of mass balance calculations on adsorption capacities in microporous gas shale reservoirs. Fuel 2007, 86(17), 2696 -2706. (7) Wang, G.; Ju, Y.; Yan, Z.; Li, Q. Pore structure characteristics of coal-bearing shale using fluid invasion methods: A case study in the Huainan-Huaibei Coalfield in China, Marine and Petroleum Geology 2015, 62, 1-13. (8) Bernard, S.; Horsfield, B.; Schulz, H.M.; Wirth, R.; Schreiber, A.; Sherwood, N.


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Figures

Figure 1. Location of the sampling wells and regional tectonic profile in the Ordos Basin, NW China.


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Figure 2. Stratigraphic column and depositional environment of upper Triassic Yanchang Formation in the Ordos Basin, NW China (modified after Ding et al., 2013)73.


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Figure 3. Mineral and geochemical properties of continental shale samples in the Ordos Basin. Upper-section shows the information for 32 samples in Chang-7, and the lower-part for 13 samples in Chang-9.


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Figure 4. Nitrogen adsorption/desorption isotherms of continental shale samples yy5-3 (a) and yy12-23 (b) in the Ordos Basin, NW China.

Figure 5. Correlations between the adsorbed volume at STP and Ro for continental shale samples in the Ordos Basin. STP is the standard temperature and pressure.


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Figure 6. Plots of lnV VS ln(ln(P0/P)) from the nitrogen adsorption isotherms for yy5-3 sample (a) and yy12-23 sample (b).


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Figure 7. The comparison of fractal dimension D2 calculated by Eq. (4) at relative pressure 0-0.45 and 0.45-1. The red dotted line is where D21 is equal to D22.


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Figure 8. The correlations between TOC and fractal dimensions D21 (a) and D22 (b) for continental shale samples in the Ordos Basin.


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Figure 9. The correlations between Clay content and fractal dimensions D21 (a) and D22 (b) for continental shale samples in the Ordos Basin.


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Figure 10. The correlations between I/S content and fractal dimensions D21 (a) and D22 (b) for continental shale samples in the Ordos Basin. I/S is simplified Illite- Smectite mixed-layer.

Figure 11. Variations of quartz content as a function of fractal dimensions D21 (a) and D22 (b), and variations of feldspar content as a function of fractal dimensions D21 (c) and D22 (d) for continental shale samples in the Ordos Basin.


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Figure 12. The correlations between the special surface area and fractal dimensions D21 (a) and D22 (b) for continental shale samples in the Ordos Basin. The SSA was calculated by the multipoint Brunauer-Emmett-Teller (BET) method using the N2 adsorption data.


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Figure 13. Variations of pore volume as a function of fractal dimensions D21 (a) and D22 (b) for continental shale samples in the Ordos Basin. The PV is calculated using Barrett-Joyner-Halenda (BJH) model from N2 adsorption branch.


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Figure 14. The correlations between the average diameter and fractal dimensions D21 (a) and D22 (b) for continental shale samples in the Ordos Basin.


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Tables Table 1 Basic properties and N2 adsorption results of the continental shale samples in the Ordos Basin, NW China (TOC: Total Organic Carbon; Ro: thermal maturity; Ill.: Illite; Kln.: Kaolinite; Chl.: Chlorite; I/S.: Illite-Smectite mixed-layer; STP: standard temperature and pressure. Volume @ STP is obtained at relative pressure about 0.98.) Sample

Depth

Layer

TOC

Ro

ID

(m)

No.

(wt%)

(%)

yy13-19

1212.53

Chang-7

4.798

0.864

Clay mineral composition

Volume

(wt%)

@ STP

Ill.

Kln.

BET-SSA

BJH-PV

（m2/g）

(ml/g)

Average Diameter

Chl.

I/S.

(ml/g)

(nm)

29

13

58

21.212

5.39

0.034

24.4

yy13-22

1362.17

Chang-9

5.136

0.893

35

18

47

15.773

7.05

0.025

13.9

yy13-24

1364.02

Chang-9

0.508

0.88

18

15

67

29.441

11.3

0.047

16.1

yy4-3

1378.52

Chang-7

2.045

0.899

24

7

69

35.601

9.8

0.056

22.5

yy34-3

1388.2

Chang-7

5.45

0.843

23

7

70

14.629

15

0.023

19.3

yy34-4

1392.02

Chang-7

4.76

0.861

24

5

71

12.167

4.17

0.02

18.1

yy34-5

1392.46

Chang-7

9.66

0.876

24

6

70

11.817

4.92

0.019

14.9

yy34-6

1399.05

Chang-7

4.2

0.914

22

7

71

13.701

5.25

0.022

16.2

yy34-8

1399.37

Chang-7

4.74

0.906

22

7

71

9.275

5.54

0.016

10.4

yy8-1

1441.9

Chang-7

1.461

0.949

19

24

57

12.306

6.53

0.02

11.7

yy8-3

1443.77

Chang-7

2.144

0.976

26

17

57

20.157

6.3

0.033

19.8

yy8-7

1446.15

Chang-7

7.658

0.913

27

16

57

17.243

8.13

0.029

13.1

yy8-11

1448.42

Chang-7

3.83

0.924

28

11

51

25.61

9.31

0.041

17

yy5-1

1450.2

Chang-7

5.519

0.923

29

17

54

22.497

6.2

0.036

22.5

yy5-2

1450.63

Chang-7

3.911

0.94

33

5

10

52

11.404

4.22

0.019

16.7

yy8-15

1451.04

Chang-7

5.154

0.931

29

10

9

52

16.708

7.16

0.027

14.5

yy5-3

1451.1

Chang-7

4.826

0.923

25

10

16

49

24.424

7.68

0.039

19.7

yy5-4

1451.23

Chang-7

3.544

0.924

27

11

15

47

22.763

8.29

0.036

17

yy5-8

1453.4

Chang-7

4.274

0.92

25

9

13

53

24.522

6.59

0.039

23

yy5-10

1454.42

Chang-7

4.471

0.93

26

9

10

55

20.773

7.48

0.033

17.2

yy9-9

1518.62

Chang-7

4.617

1.017

25

25

50

23.543

7.11

0.038

20.5

yy9-10

1519.55

Chang-7

6.788

1.019

23

25

52

15.957

6.56

0.026

15.1

10

yy4-6

1533.21

Chang-9

6.261

1.03

22

7

67

35.377

10.6

0.056

20.7

yy8-16

1597.2

Chang-9

4.769

1.046

32

4

24

44

27.057

8.9

0.044

18.8

yy8-20

1601.04

Chang-9

0.521

16

2

82

27.499

9.03

0.044

18.8

yy8-21

1602.1

Chang-9

0.799

1.062

17

11

72

24.416

11.2

0.038

13.5

yy8-22

1603.12

Chang-9

0.904

1.094

16

7

77

28.925

14.7

0.046

12.2

yy5-20

1603.73

Chang-9

2.924

1.042

25

7

68

27.499

9.03

0.044

18.8

yy8-24

1604.98

Chang-9

2.063

1.062

17

32

51

16.659

6.11

0.027

16.9

yy33-1

1608.98

Chang-7

6.27

0.857

21

9

2

68

13.467

3.86

0.022

21.6

yy33-2

1609.18

Chang-7

5.15

0.857

22

9

4

65

9.576

3.26

0.016

18.2

yy33-3

1611.1

Chang-7

5.3

0.86

20

6

7

67

16.762

5.63

0.027

18.4

yy33-6

1613.08

Chang-7

3.81

0.881

23

4

5

68

10.586

2.9

0.017

22.6

yy12-17

1613.1

Chang-7

4.573

0.984

24

31

45

20.641

4.83

0.034

26.5

yy33-7

1613.68

Chang-7

5.16

0.883

22

10

68

9.578

2.99

0.016

19.8


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

17

Page 28 of 29

yy12-5

1618.15

Chang-7

4.999

0.975

32

yy33-8

1619.02

Chang-7

5.26

0.889

18

yy33-9

1620.38

Chang-7

1.52

0.902

21

yy33-10

1621.45

Chang-7

3.66

0.911

21

2

yy12-23

1624.29

Chang-7

7.809

1.097

28

0

9

63

12.073

4.57

0.019

16.3

yy12-21

1625.24

Chang-7

11.44

1.012

32

16

52

18.919

2.78

0.031

42.1

yy9-11

1663.39

Chang-9

5.419

1.09

25

19

56

23.094

9.08

0.038

15.7

1

51

21.047

5.93

0.034

22

2

79

14.018

4.48

0.023

19.4

5

74

9.982

4.23

0.016

14.6

4

73

11.599

3.62

0.019

19.8

yy9-20

1671.39

Chang-9

5.287

1.102

21

10

69

25.655

8.93

0.041

17.8

yy12-10

1750.3

Chang-9

5.419

1.09

27

11

62

22.955

7.92

0.037

17.9

yy12-7

1754.43

Chang-9

1.076

1.097

10

1

88

27.435

8.8

0.044

19.3

1

Table 2 Fractal dimensions calculated by fractal FHH model using N2 adsorption Sample

Depth

Layer

Region 1 (at relative pressure 0-0-45)

Region 2 (at relative pressure 0.45-1)

ID

(m)

No.

K1

R1

D1

D2

K2

R2

D1

D2

yy13-19

1212.53

Chang-7

-0.7569

0.9961

0.7293

2.2431

-0.5212

0.9898

1.4364

2.4788

yy13-22

1362.17

Chang-9

-0.6239

0.9974

1.1283

2.3761

-0.3903

0.9827

1.8291

2.6097

yy13-24

1364.02

Chang-9

-0.7025

0.9979

0.8925

2.2975

-0.4085

0.9712

1.7745

2.5915

yy4-3

1378.52

Chang-7

-0.6356

0.9972

1.0932

2.3644

-0.5223

0.9983

1.4331

2.4777

yy34-3

1388.2

Chang-7

-0.6817

0.9959

0.9549

2.3183

-0.54

0.9988

1.38

2.46

yy34-4

1392.02

Chang-7

-0.7113

0.9931

0.8661

2.2887

-0.4682

0.9938

1.5954

2.5318

yy34-5

1392.46

Chang-7

-0.7448

0.9955

0.7656

2.2552

-0.4401

0.9942

1.6797

2.5599

yy34-6

1399.05

Chang-7

-0.6968

0.9908

0.9096

2.3032

-0.4686

0.9863

1.5942

2.5314

yy34-8

1399.37

Chang-7

-0.7478

0.9867

0.7566

2.2522

-0.3408

0.9516

1.9776

2.6592

yy8-1

1441.9

Chang-7

-0.6137

0.9999

1.1589

2.3863

-0.3435

0.9579

1.9695

2.6565

yy8-3

1443.77

Chang-7

-0.7928

0.9966

0.6216

2.2072

-0.4646

0.9828

1.6062

2.5354

yy8-7

1446.15

Chang-7

-0.8239

0.9987

0.5283

2.1761

-0.3492

0.9872

1.9524

2.6508

yy8-11

1448.42

Chang-7

-0.5951

0.9981

1.2147

2.4049

-0.46

0.9979

1.62

2.54

yy5-1

1450.2

Chang-7

-0.7986

0.7794

0.6042

2.2014

-0.5288

0.9932

1.4136

2.4712

yy5-2

1450.63

Chang-7

-0.6939

0.9837

0.9183

2.3061

-0.4188

0.9739

1.7436

2.5812

yy8-15

1451.04

Chang-7

-0.6666

0.9958

1.0002

2.3334

-0.4166

0.986

1.7502

2.5834

yy5-3

1451.1

Chang-7

-0.7294

0.9944

0.8118

2.2706

-0.4809

0.9983

1.5573

2.5191

yy5-4

1451.23

Chang-7

-0.6484

0.9987

1.0548

2.3516

-0.4587

0.9923

1.6239

2.5413

yy5-8

1453.4

Chang-7

-0.6768

0.9888

0.9696

2.3232

-0.5236

0.9989

1.4292

2.4764

yy5-10

1454.42

Chang-7

-0.5305

0.9951

1.4085

2.4695

-0.4762

0.9952

1.5714

2.5238

yy9-9

1518.62

Chang-7

-0.7442

0.9993

0.7674

2.2558

-0.4763

0.9888

1.5711

2.5237

yy9-10

1519.55

Chang-7

-0.6519

0.9984

1.0443

2.3481

-0.4346

0.9887

1.6962

2.5654

yy4-6

1533.21

Chang-9

-0.6377

0.9958

1.0869

2.3623

-0.5155

0.9962

1.4535

2.4845

yy8-16

1597.2

Chang-9

-0.7429

0.9977

0.7713

2.2571

-0.4626

0.9863

1.6122

2.5374

yy8-20

1601.04

Chang-9

-0.6411

0.9994

1.0767

2.3589

-0.4734

0.9881

1.5798

2.5266

yy8-21

1602.1

Chang-9

-0.593

0.9988

1.221

2.407

-0.3779

0.9818

1.8663

2.6221

yy8-22

1603.12

Chang-9

-0.6162

0.9994

1.1514

2.3838

-0.3508

0.9962

1.9476

2.6492

yy5-20

1603.73

Chang-9

-0.6411

0.9994

1.0767

2.3589

-0.4734

0.9881

1.5798

2.5266

yy8-24

1604.98

Chang-9

-0.675

0.9982

0.975

2.325

-0.4102

0.9844

1.7694

2.5898

yy33-1

1608.98

Chang-7

-0.7034

0.9882

0.8898

2.2966

-0.5427

0.9976

1.3719

2.4573


Page 29 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

yy33-2

1609.18

Chang-7

-0.8169

0.9936

0.5493

2.1831

-0.4848

0.9925

yy33-3

1611.1

Chang-7

-0.7498

0.9909

0.7506

yy33-6

1613.08

Chang-7

-0.7633

0.9883

0.7101

yy12-17

1613.1

Chang-7

-1.0208

0.9964

yy33-7

1613.68

Chang-7

-0.7758

yy12-5

1618.15

Chang-7

-0.8228

yy33-8

1619.02

Chang-7

1.5456

2.5152

2.2502

-0.5119

0.9995

1.4643

2.4881

2.2367

-0.5583

0.999

1.3251

2.4417

-0.062

1.9792

-0.5127

0.9783

1.4619

2.4873

0.9858

0.6726

2.2242

-0.5293

0.9967

1.4121

2.4707

0.9992

0.5316

2.1772

-0.4665

0.9906

1.6005

2.5335

-0.5019

0.9901

1.4943

2.4981

-0.8036

0.9982

0.5892

2.1964

yy33-9

1620.38

Chang-7

-0.6799

0.9958

0.9603

2.3201

-0.466

0.9966

1.602

2.534

yy33-10

1621.45

Chang-7

-0.6647

0.9815

1.0059

2.3353

-0.5074

0.9968

1.4778

2.4926

yy12-23

1624.29

Chang-7

-0.7155

0.9968

0.8535

2.2845

-0.4197

0.9964

1.7409

2.5803

yy12-21

1625.24

Chang-7

-0.9643

0.9895

0.1071

2.0357

-0.6078

0.9831

1.1766

2.3922

yy9-11

1663.39

Chang-9

-0.7709

0.9999

0.6873

2.2291

-0.3909

0.9777

1.8273

2.6091

yy9-20

1671.39

Chang-9

-0.7171

0.9985

0.8487

2.2829

-0.4664

0.9828

1.6008

2.5336

yy12-10

1750.3

Chang-9

-0.6617

0.9993

1.0149

2.3383

-0.4509

0.9947

1.6473

2.5491

yy12-7

1754.43

Chang-9

-0.656

0.9999

1.032

2.344

-0.4791

0.9964

1.5627

2.5209


Fractal Analysis of Shale Pore Structure of Continental Gas Shale

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