Pore structure and fractal characteristics of transitional shales with different lithofacies from the eastern margin of the Ordos Basin

To better characterize the heterogeneity of transitional shale pore structure and understand its impact on shale gas enrichment, fine characterization of the pore structure of different shale lithofacies was performed by field‐emission scanning electron microscopy, high‐pressure mercury injection, low‐temperature N2 adsorption, and low‐pressure CO2 adsorption. Fractal theory was used to obtain the fractal dimension of the shale pores at different scales and reveal the relationships among the pore structural characteristics, mineral composition, total organic carbon content, and fractal dimension of the shale and their geological significance. The results showed that organic pores, intergranular pores, intragranular pores, and microcracks were generally developed in the transitional shale samples from the study area; elliptic or irregular organic pores were mainly developed in the argillaceous shale lithofacies and siliceous shale lithofacies, and wedge‐shaped or irregular intragranular pores were mainly developed in the calcareous shale lithofacies. The pore size distribution showed a multipeak pattern, and mesopores were the main contributors to the total pore volume (PV), while micropores and macropores contributed little to the total PV. The PV and specific surface area of the siliceous shale were lower than those of the argillaceous shale but higher than those of the calcareous shale, indicating that the change in lithofacies had a significant effect on the shale pores. The common influence of clay minerals, quartz content, and total organic carbon content results in strong heterogeneity and complex pore structure characteristics of shale reservoirs. The pores in the transitional shale from the study area had obvious multiscale fractal characteristics, and the fractal dimension characteristics of different lithofacies and pores at different scales were different, which reflected that the pore structure of the shale had strong heterogeneity. The heterogeneity of the shale pores mainly originated from the macropores and mesopores, while the heterogeneity of micropores was relatively low. The heterogeneity of the pore development and structure at different scales was controlled by the mineral composition matter and organic matter abundance to varying degrees.

heterogeneity of the shale pores mainly originated from the macropores and mesopores, while the heterogeneity of micropores was relatively low.The heterogeneity of the pore development and structure at different scales was controlled by the mineral composition matter and organic matter abundance to varying degrees.

| INTRODUCTION
2][3] From the Precambrian to Neogene, several sets of organic-rich shales developed in continental areas of China, which were formed in three sedimentary environments: marine facies, transitional facies and continental facies. 4In recent years, China has taken the lead in the commercial development of shale gas in the Sichuan Basin.5][6] Among the conventional natural gas reserves discovered in China, more than 50% of the source rocks are marine-continental transitional shale.Marinecontinental transitional shale is mainly distributed in the upper Carboniferous Benxi formation, lower Permian Taiyuan formation, and Shanxi formation in the Ordos Basin, Qinshui Basin, and North China Basin, the upper Permian Longtan Formation in the southern Yangtze area, and the Triassic Xujiahe Formation in the Sichuan Basin. 2,7,8Three sets of transitional shale in the Benxi formation, Taiyuan formation, and Shanxi formation in the Carboniferous-Permian system in the Ordos Basin are largely developed and are favorable for shale gas exploration. 9,10Shale gas is mainly in a free state or an adsorbed state, and adsorbed gas can account for 20%-85% of the total gas content of shale. 11,12Therefore, the form and distribution of natural gas are relatively complex and closely related to the pore structure characteristics of shale reservoirs. 13uch research on the spatial characterization of shale reservoirs has been carried out, and the main technical means used to obtain intuitive two-dimensional (2D) and 3D pore morphology images for analysis include scanning electron microscopy, atomic force microscopy, and helium ion microscopy. 2,14,150][21] The multiscale pore space inside shale reservoirs is described by qualitative description and quantitative characterization. 20,21Different from marine and lacustrine shales, transitional shales have higher total clay mineral contents and fine mineral particles.0][21] In addition, all kinds of minerals in transitional shale reservoirs have undergone multistage mineral transformation throughout geological history, and complex diagenesis affects the development of pore and fracture networks and the occurrence of shale gas. 19,20Therefore, there is an urgent need to use a variety of complementary technical means to characterize the complex pore structure characteristics of transitional shales.
A shale pore network provides not only conventional pore structure parameters but also dimensional information for the quantitative characterization of pore structure complexity.Dimensional information is usually described by fractal theory, which was first proposed by Mandelbrot in 1967. 22Pfeifer and Avnir proposed the fractal theory of porous media based on previous studies. 23Since then, the study of fractal theory has been developed in many fields.5][26][27] Based on the FHH model, it has been found that the pore system of shallow shale gas reservoirs has multiple fractal characteristics and is closely related to the microscopic pore structure of shale, which provides a new way to study the heterogeneity characteristics of shale.
Transitional shale lithofacies are related to geological conditions, petrology, and geochemical characteristics and are identified based on geophysical methods such as petrology, geochemistry, well logging and seismic analysis. 7,17,21Different lithofacies represent different sedimentary environments and processes, resulting in different mineral assemblages, initial organic matter (OM) contents and primary pores.Moreover, the secondary pores formed in different diagenetic periods are also different. 7,19However, the study of pore type and pore size distribution (PSD) is not only important for shale gas resource evaluation but also an important component of shale reservoir evaluation.The gas content of shale gas in different shale rock facies obviously varies, so the comparative analysis of the pore structure of different rock phases has a guiding role for exploration and development.
0][21] Considering the development of the pore structure characteristics of shale at different scales, the complex pore structure of shale will lead to differences in the fractal characteristics at different scales. 28However, there are relatively few studies on the quantitative characterization of the fractal characteristics of pore structures of shale at different scales or the differences in pore heterogeneity characteristics and influencing factors in various pore sizes.In this paper, transitional shale from the eastern margin of the Ordos Basin is selected as the research object.Based on studies of shale petrology and petrogeochemistry, combined with the experimental methods of low-pressure CO 2 adsorption (LPA), low-temperature N 2 adsorption (LTA), high-pressure mercury intrusion (HPMI), and field-emission scanning electron microscopy (FE-SEM), the multiscale pore structure characteristics of shale are comprehensively characterized by qualitative description and quantitative calculation.In addition, fractal models are selected to determine the fractal characteristics of shale pores at different scales according to pore structure differences.Finally, the relationships among the pore structure parameters, petromineral characteristics and fractal dimensions of different shale lithofacies are discussed to provide a reference for favorable area selection and resource potential evaluation of transitional shale reservoirs in the eastern margin of the Ordos Basin, which has important theoretical and practical value.

| GEOLOGICAL SETTING
The Ordos Basin is a large multicycle craton basin with a superimposed Paleozoic platform, platform margin depression and Meso-Cenozoic intraplatform depression.0][31] The Daning-Jixian area is located at the southern end of the Jinxi flexural fold belt and the southeastern edge of the Yishan slope in the eastern margin of the Ordos Basin (Figure 1). 29The marine and continental transitional shales of the Shanxi Formation are relatively developed, with considerable longitudinal cumulative thickness but many interlayers.The shales of the Shanxi Formation have a high OM abundance, and kerogen is dominated by Type II-III kerogen and is in the highly mature to overmature stage, with a high shale gas yield and great hydrocarbon generation potential.
The Shanxi formation in the Daning-Jixian area is a typical marine and continental transitional stratum, which is divided into the Shan 1 member and Shan 2 member from top to bottom. 31The Shan 1 member is a lacustrine-delta facies, which mainly develops sandstone, shale and other lithologies. 31The shale thickness is 40-60 m, and its top is in contact with the sandstone of the lower Shihezi formation.The Shan 2 member is a delta facies-onshore facies, mainly developed with coal, sandstone, shale and other lithologies. 31It is characterized by the interposition of thin shale with coal and sandstone in the longitudinal direction.The thickness of the Shan 2 shale is 40-80 m, and the maximum thickness of a single layer is 50 m.The Shan 2 member is further divided into the Shan 2 1 submember, Shan 2 2 submember, and Shan 2 3 submember, among which the Shan 2 3 submember has the most stable shale distribution and the greatest thickness, mainly distributed between 20 and 50 m (Figure 1), and is the key target horizon for the exploration and development of marine and continental transitional shale gas in the eastern margin of the Ordos Basin.

| Samples
Core samples were collected from the DJ3-4 Well in the eastern margin of the Ordos Basin.Information on the sample depth, horizon and rock equality is shown in Table 1.
The relevant experiments on the shale samples mainly included total organic carbon (TOC) content experiments, Xray diffraction (XRD) experiments on whole rock mineral components, FE-SEM, LPA, LTA, and HPMI experiments.
To ensure the representativeness of the samples, core samples with obvious differences, such as differences in lithofacies, TOC content and stratigraphy, were taken into account in the selection of the samples.Therefore, the research results can reflect the characteristics of shale reservoirs in the target strata in the study area to a certain extent.

| TOC, mineral components, and shale lithofacies
The TOC content of transitional shale samples in the study area was determined by a LECO CS-200 carbon and sulfur analyzer.Powder samples of 0.1-0.5 g (particle size greater than 200 mesh) were used for testing.Before the experiment, the powder sample was treated with dilute hydrochloric acid at a volume ratio of 1:7 to remove the inorganic carbon in the sample, and then the dissolved sample was washed with distilled water until neutral.After the treatment, the sample was dried at 60-80°C.Finally, the sample was burned in oxygen flow at a high temperature (930°C).The whole-rock mineral components of the samples were quantitatively analyzed by a BRUKER D8ADVANCE X-ray diffractometer according to SY/T6201-1996 standards.Testing and analysis were conducted with a 200 mesh powder sample in a tube at a voltage of 35 kV, a tube current of 30 mA, a Cu target radiation source (λ = 1.54 A), a scanning range of 2θ = 5-80°, and a scanning speed of 2°/ min under the conditions of testing.By observing the characteristic diffraction peak intensity of different mineral crystals in the XRD patterns, the contents of various minerals in the sample were determined.

| FE-SEM observation
FE-SEM was used to qualitatively describe the pore morphology of shale samples and obtain the pore structure characteristics of the shale. 32Before the experiment, the sample was prepared into cubes with dimensions of 1.5 cm × 1 cm × 0.5 cm, and then the surface of the sample was polished by a HITACHI IM 4000 argon ion polishing instrument.The experiments were performed with a Zeiss Gemini SEM 500 FE-SEM.The maximum resolution was

| HPMI measurements
An AUTOPORE 9505 mercury injection instrument was used for the HPMI measurements.During the test phase, the instrument provided a mercury injection pressure of up to 60,000 psi, corresponding to the lower limit of the test aperture of approximately 3 nm.Before the test, the sample was shaped into a cube with a size of 1 cm × 1 cm × 1 cm, and the surface of the cube was smoothed to reduce the influence of the pockmark effect during the test. 32At the same time, the sample was continuously dried at 60°C for 48 h to ensure that the original pores of the sample were not damaged by the high temperature and that the internal gas impurities were effectively removed.The vacuum inside the instrument was maintained during the test.Based on the mercury intake and removal process data automatically recorded by the instrument, pore structure parameters, such as pore volume (PV) and PSD, were obtained by combining the Washburn equation. 33

| CO 2 and N 2 gas adsorption experiments
LTA and LPA experiments were carried out by an Autosorb-iQ-MP-C automatic physicochemical adsorption instrument, and the particle size of the tested samples was 60-80 mesh (0.25-0.18 mm).Before performing the N 2 adsorption experiment at a low temperature, the samples were placed into the degassing station and degassed at 110°C for 12 h to remove the moisture and volatile substances in the samples.Then, the degassed samples were moved to the analysis station, and adsorption and desorption tests were carried out at 77 K with high purity N 2 as the adsorbent.BET and nonlocal density functional theory (NLDFT) models were used to obtain pore structure parameters, including specific surface area (SSA), PV and PSD.The sample pretreatment of the LPA experiment was similar to that of the LTA experiment.Briefly, 1-2 g (60-80 mesh) powder samples were weighed and degassed for 16 h, and the adsorption test was carried out at 273 K with highpurity CO 2 as the adsorbent.The pore structure parameters, including the PV, SSA, and PSD, were obtained based on the NLDFT theoretical model.

| Fractal method
5][36][37] Previous studies have shown that the adsorbate molecules in micropores are usually filled with micropores.Jaroniec et al. conducted micropore-activated carbon adsorption experiments and concluded that the PSD of micropores is the core factor affecting their heterogeneity. 36A micropore fractal model based on the PSD function J x ( ) and pore size x was proposed, and the calculation formula is: where J x ( ) is the distribution density function of the pores, x is the size of the pores (nm), and D1 is the fractal dimension of the micropores.The fractal FHH model based on the LTA experiment is also widely used to calculate the fractal dimension of the pore structure in porous solid media, 15,17,[35][36][37][38] and the corresponding calculation formula is: where V is the gas adsorption amount at the equilibrium pressure p (cm 3 ), p 0 is the gas saturated vapor pressure (MPa), p is the equilibrium pressure (MPa), C is a constant, and D2 is the mesoporous fractal dimension which is obtained from the slope of the fitted curve from the linear regression between V ln( ) and p p ln[ln( / )] 0 .HPMI data can be used to better characterize macropores in shale samples, so the fractal dimension of the macropores was mainly calculated by HPMI data.The previous thermodynamic fractal dimension calculation model based on the mercury injection method was calculated by the following formulae 39 : where W n is the surface energy of the hole (J), Q n is the incremental mercury intake (mL), and r n is the radius corresponding to the amount of mercury at time n (μm).C is a constant, and D3 is the macropore fractal dimension, which is obtained from the slope of the fitted curve from the linear regression between W r ln ( / ) n n 2 and Q ln( ) n .Based on the geometric definition of fractals, the fractal dimension of three-dimensional porous media is generally between 2 and 3. 23 In particular, the closer the fractal dimension is to 2, the smoother the pore surface, and the more regular the pore structure.The closer the fractal dimension is to 3, the rougher the pore surface, and the more complex the pore structure.1][42] Therefore, with the help of the fractal theory of porous media, the pore structure characteristics of shale reservoirs can be better analyzed, and the shale gas adsorption capacity and reservoir heterogeneity can be more thoroughly understood.

| Geochemical and lithofacies characteristics
The TOC content of marine-continental transitional shale samples in the eastern margin of the Ordos Basin ranges from 0.43% to 10.50%, with an average value of 3.19%.The TOC contents of shale samples from the Shanxi formation are relatively high, ranging from 0.71% to 10.50%, with an average value of 4.43%.The TOC contents of the Taiyuan and Benxi shale samples are lower, ranging from 0.43%-1.24%(mean 0.88%) and 2.65%-2.96%(mean 2.81%), respectively.The TOC contents of the Shanxi formation samples are higher than those of the Taiyuan and Benxi formation samples, which is basically consistent with previous studies on transitional shale in the Ordos Basin. 9,10,29he typical classification scheme is based on the mineral composition of siliceous minerals (quartz and feldspar), carbonate minerals (calcite and dolomite), and clay minerals.Therefore, shales are divided into 4 types: siliceous shale lithofacies (SL), calcareous shale lithofacies (CL), mixed shale lithofacies (ML), and argillaceous shale lithofacies (AL). 6,43As shown in Table 1, 5 samples were classified as AL, another five samples as SL, and four samples as CL (Figure 2; Table 1).No samples in this study were classified as ML.As shown in Figure 2, siliceous shales (SL) are rich in quartz with quartz contents ranging from 39.04% to 75.49%.Calcite and dolomite are predominant in calcareous shale (CL), with average contents of 60.01% and 13.06%, respectively.AL is mainly clay, and the content of AL ranges from 50.80% to 74.05%.Different lithofacies have obvious differences.The TOC contents of the AL and siliceous shale (SL) are high, with average contents of 4.68% and 3.33%, respectively.The TOC content of the CL is the lowest, with an average content of 1.14%.In addition, the vitrinite reflectance of transitional shale in the study area ranges from 2.11% to 2.61%, with an average of 2.31%, indicating that transitional shale is in the overmature gas generation stage, which provides a good foundation for the development of the transitional shale reservoir pore structure.

| FE-SEM image analysis
FE-SEM was used to qualitatively describe the pore morphology of shale samples and obtain the pore structure characteristics of the shale. 32According to the research of Loucks et al., 41 the pores in shale can be divided into OM pores, inorganic pores and microfractures, among which inorganic pores can be further divided into intraparticle (intraP) pores and interparticle (interP) pores.The pore structure of transitional shale in the eastern margin of the Ordos Basin is characterized by complex OM pores, interP pores, intraP pores and microfractures.The location of OM pores in the study area is controlled by the content and distribution of OM in shale.OM pores are the pores developed in OM and are the most important reservoir space of shale gas.As shown in Figure 3, the shape of the organic pores is oval-or bubble-shaped with irregular boundaries.

(A) (B)
F I G U R E 2 (A) Lithofacies of transitional shale samples.The QFM includes quartz, feldspar, mica, and pyrite minerals: siliceous lithofacies (SL), mixed lithofacies (ML), argillaceous lithofacies (AL), and calcareous lithofacies (CL).(B) Lithofacies of transitional shale samples based on the classification by Gamero et al. 43 Among them, oval or irregular organic pores in soil and siliceous shale are well developed, mainly with pore radii of hundreds of nanometers (Figure 3A,B), which are mainly formed by mass gas production in asphalt and have good pore connectivity.These findings indicate that OM pores have strong heterogeneity.At the same time, OM pores in the CL shale are poorly developed, angular and irregular in shape, dominated by pore radii of tens of nanometers, and have poor connectivity (Figure 3C).The inorganic pores in transitional shales in the study area are relatively developed, among which the interP pores are mainly developed between pyrite crystals with triangular or irregular shapes (Figure 3F).In addition, the inter-P pores are related to clay minerals and form triangles or slits in the laminar clay cleavage (Figure 3E).In addition, brittle minerals have strong compressive resistance, which is conducive to the formation and preservation of pores.IntraP pores are mainly developed in brittle minerals, clay minerals, and strawberry pyrite.Due to their isolation and poor connectivity, these pores are triangular and ellipsoidal with smooth edges (Figure 3D,H,I,L).Since the study area was in a reductive sedimentary environment, a certain amount of pyrite framboid angular interP pores developed (Figure 3G,J), and the pore size is generally less than 300 nm.Microfractures are beneficial for increasing the reservoir space of shale reservoirs and allow the accumulation of shale gas. 44icrofracture networks usually have good connectivity and enhance the seepage capacity of shale reservoirs.Microfractures are also developed in some samples in the study area, mainly distributed around rigid mineral particles or in the shrinkage joints of clay minerals (Figure 3I,K).The opening degree and extension length of microcracks vary, but the extension direction is generally consistent with the direction of mineral particle edges and clay mineral lamella layers.

| Quantitative analyses of pore structure
The pore structure distribution of shale can be quantitatively characterized by LPA, LTA, and HPMI experiments.Due to the different molecular diameters of CO 2 and N 2 (0.33 and 0.36 nm, respectively), the minimum pore sizes of shale pores that can be detected by gas adsorption experiments using CO 2 and N 2 as molecular probes are different. 42Generally, LPA experiments are used to characterize micropores (<2 nm), LTA experiments are used to characterize mesopores (2-50 nm), and HPMI experiments are used to characterize macropores (>50 nm). 26,45Then, the quantitative characterization of pore structure within the full pore size range of shale can be achieved by combining the results of these three technical means.

| HPMI measurements
Figure 4 shows the mercury withdrawal curve of the sample in the study area.The shape of the curve can reflect the distribution characteristics of each pore throat and the quality of pore connectivity.The mercury intrusion and extrusion curve has the characteristics of steep ends and a broad middle.In the initial stage Low-pressure CO 2 adsorption (LPA), low-temperature N 2 adsorption (LTA), and high-pressure mercury intrusion (HPMI) curves for transitional shales in the eastern margin of the Ordos Basin.
(<0.5 MPa), with increasing pressure, mercury in the nonwetting phase enters large pores or microfractures, resulting in a rapid increase in mercury saturation in the nonwetting phase.The moderate increase in the middle section represents a small increase in mercury saturation, indicating that the pores in this section are relatively undeveloped.With the continuous increase in pressure (>200 MPa), the mercury intake into shale increases rapidly, reflecting the development of many nanoscale pores in the shale.
Based on the Washburn equation, the PSD curve and pore structure parameters of shale samples in the pore size range of approximately 7 nm to 10 µm were obtained by calculating the HPMI experimental data (Table 2).The PSD curves of all shale samples are shown in Figures 5 and 6.Among them, the PV of the AL shale varies from 0.0004 to 0.0025 cm 3 /g, with an average of 0.013 cm 3 /g, and the SSA varies from 0.0117 to 0.3762 m 2 /g, with an average of 0.1539 m 2 /g.The PV of the SL shale varies from 0.0008 to 0.0031 cm 3 /g, with an average of 0.0019 cm 3 /g, and the SSA varies from 0.0089 to 0.6003 m 2 /g, with an average of 0.1941 m 2 /g.The PV of the CL shale varies from 0.0003 to 0.0012 cm 3 /g, with an average of 0.006 cm 3 /g, and the SSA varies from 0.0015 to 0.0398 m 2 /g, with an average of 0.0128 m 2 /g.

| Low-temperature N 2 adsorption
Due to the strong heterogeneity of shale, the pore structure is complex, and the pore-type changes significantly. 46,47The N 2 adsorption-desorption isotherm is shown in Figure 4. Based on the classification scheme of isothermal adsorption curves proposed by International Union of Pure and Applied Chemistry, it is considered that the N 2 isothermal adsorption curves of all transitional shale in this study are Type IV, which indicates that there are certain mesopores and macropores in the shale samples.Moreover, the hysteresis curves also show H3 or H4 characteristics, indicating that wedge-shaped, ink bottle-shaped and cylindrical pores are developed in the transitional shale in the study area.
According to the fluctuation trend of the N 2 isothermal adsorption curve, the adsorption process can be roughly divided into three stages: (1) when p/p 0 = 0-0.3, the adsorption curve rises slowly and presents a slightly convex shape.When p/p 0 = 0.3, the adsorption of the monomolecular layer on the pore surface is basically saturated and gradually transitions to multimolecular layer adsorption with increasing relative pressure. 48(2) When p/ p 0 = 0.3-0.9, the gas adsorption capacity increases steadily with increasing relative pressure.(3) When p/p 0 = 0.9-1.0, the adsorption curve rapidly becomes steeper and does not reach saturation when p/p 0 is close to 1, which is mainly due to the condensation of gas, indicating that there is a certain number of macropores or microfractures in the shale.When p/p 0 = 0.45-1.0, the adsorption curve and desorption curve are separated, and a hysteresis loop is formed between the two curves.This is because capillary condensation occurs during this relative pressure interval, and the adsorption process and desorption process are not completely reversible.
Based on the NLDFT theoretical model, the LTA experimental data were calculated to obtain the PSD curve and pore structure parameters of shale samples in the pore size range of 1.06-78 nm (Table 2).The PSD curves of all shale samples show a bimodal distribution, with two main peaks at 1.6 and 4.0 nm, as shown in Figures 5 and 6, indicating that these pores are essential in terms of PV and SSA contributions.The density functional theory (DFT) PV and SSA of the AL shales are large, with average values of 0.027 cm 3 /g and 11.567 m 2 / g, respectively.Second, the average DFT PV and SSA values of the SL shale are 0.014 cm 3 /g and 6.380 m 2 /g, respectively.The PV and SSA of the CL shale are small, with average values of 0.007 cm 3 /g and 3.255 m 2 /g, respectively.

| Low-pressure CO 2 adsorption
The CO 2 adsorption isothermal curve is shown in Figure 4.The CO 2 isothermal adsorption curves of all shale samples are Type I, reflecting the micropore-filling phenomenon of the shale samples, indicating that a certain number of micropores are developed in the shale. 49The maximum CO 2 adsorption capacity of all shale samples ranges from 0.24 to 3.59 cm 3 /g.The maximum adsorption volumes of the AL shale and SL shale are 1.18-3.59and 0.42-2.87cm 3 /g, respectively.The maximum adsorption capacity of the CL shale is the lowest among the three types, ranging from 0.24 to 0.66 cm 3 /g.
Based on the NLDFT theoretical model, the PSD curve and pore structure parameters of shale samples in the pore size range of 0.3-1.5 nm were calculated based on the experimental LPA data (Table 2).The PSD characteristics of all shale samples are similar, with three distinct peaks at 0.4, 0.5, and 0.85 nm, as shown in Figure 5, indicating that these pores account for the majority of the PV.The micropore PVs of the argillaceous shales and siliceous shales are larger, 0.005 and 0.005 cm 3 /g, respectively.Calcareous shale has the smallest micropore PVs of 0.001-0.002cm 3 /g, with an average of 0.001 cm 3 /g.As shown in Figure 6, the distribution characteristics of the micropore SSA are similar to those of the micropore PVs, revealing that the pores with peaks at 0.4, 0.5, and 0.85 nm have relatively large surface areas.

| Fractal dimension analysis
Based on high-resolution scanning electron microscopy, the transitional shale reservoirs in the eastern margin of the Ordos Basin are rich in micropores and nanopores.The pores developed in this shale are different in not only size but also morphology. 26,50ince the surface micromorphology and spatial structure of pores have an important impact on the migration and accumulation of shale gas, to better characterize the pore structure characteristics of shale and clarify the complexity of pores at different scales, the fractal characteristics of pores in the transitional shale at different scales were characterized and analyzed. 23,51,52n this study, the fractal dimension of micropores (D1) was obtained by using LPA data, the fractal dimension of mesopores (D21 and D22) was obtained by using the fractal FHH model based on LTA data, and the fractal dimension of macropores was determined by  3. The fitting degree (R 2 > 0.9) of the fractal fitting results based on different experimental data and fractal models is good (Figure 7), indicating that the pores at different scales of shale have fractal characteristics.In the transitional shales in the study area, the D1 of the CL shale is the smallest (between 2.091 and 2.354, with an average value of 2.171) and that of the AL shale is the largest (between 2.314 and 2.314, with an average value of 2.337).The D21 of the CL shale is also the smallest (between 2.273 and 2.440, with an average of 2.351), while that of the AL shale is the largest (between 2.415 and 2.525, with an average of 2.484).However, the D22 of the AL shale is the smallest (2.534-2.740,mean 2.666), while that of the CL shale is the largest (2.717-2.830,mean 2.774).The CL shale has the lowest D3 (between 2.512 and 2.789, with an average of 2.631), and the AL shale has the highest D3 (between 2.387 and 2.627, with an average of 2.476).The differences in the fractal dimension of the lithofacies and the pore scale of the transitional shales in the study area indicate that the complexity of the micropore, mesopore, and macropore structures developed in the shales varies significantly among shales with different lithofacies.

| Relationships between pore structure characteristics and lithofacies
Based on the NLDFT theoretical model and Washburn equation, the experimental data of LPA, LTA, and HPMI were processed to obtain the PSD curves of transitional shale with different pore size ranges from the study area.The PSD curves of different pore size ranges were spliced.4][55] As shown in Figures 8 and 9, although there are some differences in the curve morphology of different lithofacies samples, they are similar in the distribution range of the pore diameter peak value of various lithofacies samples.
There are significant differences in the pore structure parameters of the transitional shale with different lithofacies from the study area (Table 4), indicating that the pore structure development characteristics of transitional shale are controlled by the lithofacies.The total PV and total SSA of the argillaceous shale are the largest (mean values of 0.034 cm 3 /g and 30.869 m 2 /g, respectively).The PV and SSA of the SL shale are slightly different from those of the AL shale, with average values of 0.020 cm 3 /g and 22.179 m 2 /g, respectively.The CL shale has the smallest total PV and total T A B L E 3 Fractal dimension values for transitional shale.SSA (mean 0.008 cm 3 /g and 7.519 m 2 /g, respectively).The total PV and total SSA of the SL shale are lower than those of the AL shale but higher than those of the CL shale, indicating that the change in lithofacies has a significant effect on the shale pores.

Sample ID Formation
The PV distribution characteristics of shale with different lithofacies also vary greatly (Figure 10A).In general, mesopores still account for the majority of the PV (mean value of 66%), followed by micropores (mean 19%), and macropores account for the minority of the PV (mean value of 16%).The CL shale has the smallest micropore, mesopore and macropore volumes (mean values of 0.001, 0.006, and 0.001 cm 3 /g, respectively).The micropore, mesopore and macropore volumes of the AL are the largest (0.004-0.011, 0.018-0.031,and 0.003-0.0071cm 3 /g, respectively, with average values of 0.007, 0.022, and 0.005 cm 3 /g).The  micropore, mesopore and macropore volumes of the SL shale are between those of the CL shale and AL shale, with average values of 0.005, 0.012, and 0.003 cm 3 /g, respectively.
The distribution characteristics of the SSA of the shales with different lithofacies also vary greatly (Figure 10B).In general, micropores still account for the majority of the SSA (mean 68%), followed by mesopores (mean 31%), and macropores account for the minority of the SSA (mean 1% This study shows that the pore structure of transitional shale is controlled by the lithofacies.

| Relationships among TOC content, mineral composition, and pore structure characteristics
Shale reservoirs are characterized by low porosity and ultralow permeability, diverse pore types and wide PSDs, resulting in extremely complex pore mechanisms. 56The influence of the TOC content on the PV and SSA of the transitional shale from the study area is shown in Figure 11A,B, indicating that TOC is the main factor controlling the pore development of different shale lithofacies in the study area, which is completely consistent with previous research results on the transitional shale in the eastern margin of the Ordos Basin. 10,29,39The TOC content is positively correlated with the total PV, micropore PV and mesopore PV (R 2 = 0.69, 0.86, and 0.58, respectively), indicating that the pores of transitional shale are mainly developed in OM and contribute many micropores and mesopores to the total number of pores.The TOC content has a weak positive correlation with the macropore PV (R 2 = 0.44), which might indicate that there are a considerable number of inorganic macropores.The TOC content is also positively correlated with the total SSA and the micropore and mesopore SSAs (R 2 = 0.86, 0.86, and 0.66, respectively), indicating that micropores and mesopores developed in OM can provide a large amount of space for adsorbed gas.The TOC has a weak positive correlation with the macropore SSA (R 2 = 0.37), which may indicate that the macropores developed in shale OM cannot provide a large SSA for adsorbed gas.
In addition to the TOC content, the contents of mineral components affect the pore structure of transitional shale in the study area.Quartz is the main mineral component of the transitional shale in the study area, and studying the relationship of quartz content with PV and SSA is of great significance for understanding the main controlling factors of the pore structure. 10,29,57The influence of the quartz content on the PV and SSA of the transitional shale in the study area is shown in Figure 11B,E, indicating that the quartz content is not the key factor controlling the pore development of the transitional shale in the study area.There is no significant correlation between the quartz content and the PV and SSA of the total pores, micropores, mesopores, and macropores.With increasing clay mineral content, the total PV and the micropore, mesopore, and macropore PVs and SSAs of transitional shale increase.For transitional shales in the study area, due to the dominant role of clay mineral-related pores in the pore system, many clay mineral-related pores caused by a high clay mineral content compensate for the effect of the reduced compaction resistance of the reservoir.Therefore, the clay mineral content is positively correlated with the PV and SSA (Figure 11C,F).At the same time, clay minerals have a more obvious control effect on the PV and SSA, indicating that many clay mineral-related pores can provide considerable PV and SSA for shale reservoirs.

| Relationships among TOC content, mineral composition, and fractal dimension
To explore the influence of the main mineral components and TOC on the fractal dimension of transitional shale pores, experimental data were plotted as shown in Figure 12.D1 tends to increase with increasing TOC content and clay mineral content but has no obvious relationship with the action of various organic and inorganic components.OM in shale accumulates, is buried, and matures to generate hydrocarbons during geological history.The higher the content of OM is, the more micro-and nano-OM pores are generated during the process of thermally mature hydrocarbon generation and expulsion.As a result, the microporescale pore network of shale tends to be complicated, and the pore space morphology becomes more disordered, which is reflected in the increase in the fractal dimension D1 of micropores.The correlation between mesoporous scale pores D21 and D22 and TOC content is not strong mainly because the formation of mesopores in shale is more complex.It is speculated that the heterogeneity of mesopores is controlled by other factors in addition to TOC content.With the sedimentary and diagenetic evolution of transitional shale, the structure of nanoscale macropores tends to become complicated, and the heterogeneity of pores increases.Quartz mainly functions as a skeleton mineral for structural support. 21However, in the late evolution of diagenesis, the skeleton pores experience a series of complex filling and evolution processes, resulting in no obvious correlations among the quartz content, pore development and pore structure.Clay minerals include a variety of clay minerals.Different clay minerals vary greatly in terms of morphology and structure and have different influences on the development and structure of pores at different scales. 10,58Generally, many micro-and nanopores are generated in the maturation thermal evolution process.A variety of micropores complicate the structure of micropores in the pore network system of shale, which leads to an increase in D1 and D22.With increasing clay content, more interlamellar pores and fractures in clay minerals are developed in shale, and plastic clay minerals easily deform, which makes the interlamellar fracture network configuration of clay minerals more complex and thus leads to an increase in D3.

| Relationships between pore structure characteristics and fractal dimensions
As shown in Figure 13, the relationships among the fractal dimensions of micropores (D1), mesopores (D21 and D22), and macropores (D3) in transitional shale and their corresponding pore parameters are quite different.D1, D21, and D3 are positively correlated with PV and SSA.D21 is negatively correlated with PV and SSA.In shales with the same lithofacies, there are abundant micropores and mesopores and relatively few macropores.Moreover, most of the micropores and mesopores in shales are OM pores, with various pore-throat combinations.Under the superposition of multiscale pore-throat systems, pore heterogeneity is greatly improved, and the PV and SSA are also large.In addition, the extrusion deformation of OM pores during the evolution of OM and the transformation of geological history aggravates the complexity of the pore configuration of shale, resulting in the strong heterogeneity of the micropore and mesopore distributions of shale. 59However, with the increase in PV and SSA, macropores are also relatively more developed.The pore shape of macropores is relatively simple, mainly composed of inorganic pores and microfractures, such as inter-P pores and clay mineral interlayer pores.
The pore structure of transitional shale in the Ordos Basin has obvious heterogeneity, which is manifested in not only the significant differences in pore type, development degree and pore size proportion among different shale lithofacies but also the obvious differences in the fractal characteristics of the multiscale pores of shale.The degree of pore heterogeneity of shale is comprehensively controlled by sedimentary diagenesis, thermal evolution, shale mineral composition, organic carbon content, late pore transformation deformation, and other factors.In this study, the fractal characteristics of the pore space of transitional shales with different lithofacies reflect the differential development of pore heterogeneity.Transitional shales in the study area have obvious multiscale fractal characteristics.Moreover, the fractal dimensions of pores at different scales (D1, D21, D22, and D3) of various shale lithofacies have certain correlations with various formation parameters (TOC content, quartz and clay mineral content, pore structure parameters, etc.).Therefore, the comprehensive analysis of shale quality characteristics and the calculation of the fractal dimension of shale pores can provide an important reference for the optimization of favorable reservoir segments.

| CONCLUSIONS
1. OM pores, interP pores, intraP pores, and microfractures are generally developed in transitional shale.The pore morphology is mainly wedge-shaped, ink bottle-shaped, and oval-shaped.Elliptic or irregular OM pores are mainly developed in the AL and SL shales, and wedge-shaped or irregular intraP pores are mainly developed in the CL shales.2. The PSD in transitional shale shows a multipeak pattern, with mesopores as the major contributors to the total volume (mean value of 66%), while micropores and macropores contribute little to the total volume (mean values of 19% and 15%, respectively).
The total PV and total SSA of the SL shale are lower than those of the AL shale but higher than those of the CL shale, indicating that lithofacies changes have a significant impact on shale pores.3. OM is beneficial for the development of shale pores overall, especially for the development of micropores and mesopores.The influence of mineral composition on pore development in shale reservoirs is complex, and brittle minerals dominated by quartz have no obvious relationship with pore development.Clay minerals can promote the development of pores at all scales.4. The fractal dimensions of micro-, meso-, and macropores reflect the complexity of pores at different scales; the heterogeneity of mesopores and macropores is the strongest, while the heterogeneity of micropores is relatively weak.The heterogeneity of pores at different scales is mainly affected by TOC content and clay mineral content.Based on the above discussion, the fractal dimension of transitional shale in the eastern margin of the Ordos Basin has a good correlation with the pore structure parameters.The comprehensive analysis of shale quality characteristics and the calculation of shale pore fractal dimensions can provide an important reference for the optimization of favorable reservoir segments.
Field-emission scanning electron microscopy images of various pores in the eastern margin of the Ordos Basin.(A, D, G, J) Typical pore photographs in AL. (B, E, H, K) Typical pore photographs in SL. (C, F, I, L) Typical pore photographs in CL.

5
Pore volume distribution curve of transitional shale with pore size.

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Specific surface area (SSA) distribution curve of transitional shale with pore size.using HPMI data and the thermodynamic fractal model (D3).The research results are shown in Table

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Fractal fitting for different lithofacies of transitional shale.Pore volume distribution characteristics of transitional shale.F I G U R E 9 Distribution characteristics of the specific surface area of transitional shale.

F
I G U R E 10 Distributions of different scales of pores acquired from low-pressure CO 2 adsorption (LPA), low-temperature N 2 adsorption (LTA), and high-pressure mercury intrusion (HPMI).(A) Percentage of pore volume (PV); (B) percentage of specific surface area (SSA).

F
I G U R E 11 Relationships between total organic carbon (TOC) content, mineral composition, and pore structure parameters of transitional shales.(A, D) TOC versus pore volume (PV) and specific surface area (SSA); (B, E) quartz content versus PV and SSA; and (C, F) clay content versus PV and SSA.

1
Comprehensive histogram of the regional geological setting and stratigraphy in the eastern margin of the Ordos Basin.Transitional shale sample information from the eastern margin of the Ordos Basin..8nm, the magnification was 20-200 million times, and the accelerated voltage adjustment range was 0.02-30 kV.During the secondary electron (SE) imaging observation of the polished surface of shale samples, a clearer image was obtained by optimizing the acceleration voltage and scanning speed of the working state.
Abbreviation: TOC, total organic carbon.0 Pore structure parameters of transitional shale.
T A B L E 4 Distribution of PV and SSA in transitional shale.
12Relationships between total organic carbon (TOC) contents, mineral composition, and fractal dimension of transitional shales.(A) TOC versus fractal dimension; (B) quartz content versus fractal dimension; and (C) clay content versus fractal dimension.
quartz content.There is no obvious correlation between D21 and TOC and the quartz and clay mineral contents, while D22 tends to decrease with increasing TOC and clay mineral contents.D3 tends to increase with increasing TOC content and clay mineral content but has no obvious relationship with the quartz content.Because shale reservoirs are geological bodies with complex makeups, complex, and diverse pore structure networks are formed under the joint