Comparative experimental investigation on pore structure and fractal characteristic of marine and continental shales

Abstract

Clarifying the pore structure characteristics of shale reservoirs, which are low porosity, low permeability and high heterogeneity, is an essential prerequisite for the efficient development of shale oil and gas. Fractal theory is especially suited for characterizing the complex pore structures of shales. This work compares the pore structure characteristics between marine shales from the Longmaxi Formation and continental shales from the Shahejie Formation through low-temperature nitrogen adsorption, nuclear magnetic resonance, and scanning electron microscopy. Different fractal scaling models are adopted to determine the fractal dimensions and lacunarities of shales by low-temperature nitrogen adsorption data and scanning electron microscopy images. In addition, the mineral compositions from X-ray diffraction are analyzed to elucidate the mechanisms by which mineral content influences fractal dimensions. Finally, the correlations between total organic carbon content and microscopic structure are discussed. These results indicate that the pore size of marine shale is smaller than that of continental shale. Additionally, the fractal dimensions of marine shales are greater than that of continental shales, suggesting a more complex pore structure. The more quartz and clay content lead to greater complexity in pore space, resulting in higher fractal dimensions. The illite/smectite mixed layer shows a strong positive correlation with fractal dimensions for marine shales, whereas this correlation is less pronounced for continental shales. The presence of microfractures in organic matter leads to a reduction for the pore surface fractal dimension in continental shales.

Graphical abstract

Keywords

shale reservoirs / lithofacies / pore structure / fractal dimension / lacunarity

1 Introduction

Shale, as a key pillar to meet the growing global energy demand, exhibits low porosity, low permeability, and strong heterogeneity. Numerous micro/nanopores are formed within clay minerals and organic matter (Han et al., 2016; Sun et al., 2024a), while micro-fractures are found in the shale matrix, resulting in highly complex pore structures (Ougier-Simonin et al., 2016; Sun et al., 2024b). These factors significantly increase the difficulty of exploring shale oil and gas resources. Additionally, during hydraulic fracturing, interactions between fracturing fluids and minerals frequently occur, leading to mineral dissolution, precipitation, and migration (Khan et al., 2021). These processes alter the pore structure, ultimately limiting the recovery. Therefore, accurately evaluating the pore structure of shale can provides a robust foundation for understanding pore evolution characteristics, describing the multiphase fluid flow mechanisms within shales, and determining the producible limits of shale hydrocarbon resources (Cai et al., 2024).

The fluid injection techniques, imaging approaches, and ray-related methods, are widely applied to characterize the shale pore structures (Wang and Cheng, 2023). The fluid injection method entails introducing mercury into pore spaces or facilitating gas adsorption within them, with changes in fluid pressure and volume being recorded. These data are then combined with suitable theoretical models to determine the characteristics of the pore structure. Mercury intrusion porosimetry (MIP), low-temperature nitrogen adsorption (LTNA), and low-temperature CO₂ adsorption are representative examples of fluid injection techniques. However, fluid injection techniques are limited to characterizing connected pore spaces and cannot evaluate isolated pore structures (Lai et al., 2018; Mou et al., 2021). Moreover, different fluid injection methods differ in their characterization of pore size ranges, requiring the integrated use of various techniques to evaluate the complex pore types present in shale (Clarkson et al., 2013). Imaging methods involve the direct observation of pore structure features in shale samples through images obtained via different imaging techniques. Common methods include X-ray computed tomography, scanning electron microscopy (SEM), and focused ion beam-scanning electron microscopy. Higher resolution reduces the field of view, potentially leading to imaging methods that don’t fully capture the pore structure of shale (Peng et al., 2012). Ray-related techniques, including small angle neutron scattering and nuclear magnetic resonance (NMR), characterize the pore structure of shale by applying radiation or magnetic fields and employing appropriate inversion models (Cheng et al., 2023; Fu et al., 2024). The NMR method can nondestructively and rapidly characterize pore structures, with the ability to assess a wide range of pore sizes. However, paramagnetic mineral can influence the magnetic field distribution within the pore space, potentially causing variations in the magnetic field gradient, which may lead to errors in the inversion of the T₂ spectrum (Livo et al., 2020).

Besides using various experimental techniques to evaluate pore structures, the fractal theory introduced by Mandelbrot also provides a novel approach to describe the porous media. The pore space of shale follows the self-similarity characteristic (Sakhaee-Pour and Li, 2016; Huang et al., 2021), indicating that pore structure characteristics are independent of the observation scale, which makes fractal theory suitable for the description of shale pore structures (Liu et al., 2023; Wang et al., 2023b; Liu et al., 2024). In fractal theory, the pore structure is evaluated precisely by fractal structural parameters. These parameters include three categories: fractal dimension, lacunarity, and succolarity. The fractal dimension quantifies the complexity of the shale pore structure. Generally, a higher fractal dimension indicates a more complex pore structure. The commonly used fractal dimensions are the pore surface fractal dimension (D_s) and the pore space fractal dimension (D_f), each focusing on different characteristics. The D_s characterizes the roughness of the pore surface (Khalili et al., 2000; Yang et al., 2014), while the complexity of the pore space morphology is typically represented by the D_f (Dathe and Thullner, 2005; Li et al., 2023). For example, the mercury intrusion curve obtained by the MIP method and the transverse relaxation time (T₂) distribution from the NMR method can be used to determine the D_f (Yuan and Rezaee, 2019). The 2D/3D images obtained through imaging methods can be used with the box-counting approach to calculate the corresponding dimensional D_f (Liu et al., 2020). Combining gas adsorption experiments with appropriate fractal scaling models (such as the FHH, Neimark, and Wang-Li models) has been proven to be an effective approach for accessing the D_s (Wood, 2021). Lacunarity describes the clustering and homogeneity of the measured object and can differentiate between pore structures with the same fractal dimension (Plotnick et al., 1996). In general, lacunarity increases with the degree of heterogeneity of the measured object. Succolarity is closely related to the connectivity, tortuosity, and permeability of porous media and is often used to describe the anisotropy of porous materials (Anovitz and Cole, 2015). The shale pore structure is influenced by multiple factors, including lithofacies, mineral compositions, and total organic carbon (TOC) content (Wang et al., 2024), making its fractal features complex and necessitating further investigation. Current research primarily focuses on the fractal characteristics and influencing factors of a specific lithofacies shale (Li et al., 2019b; Tong et al., 2022; Hazra et al., 2024), with less attention given to the differences in fractal features and the underlying mechanisms across different lithofacies types. And the relationship between fractal dimension of shale and mineral content remains unclear.

This work selects typical marine shale samples from the Longmaxi Formation and continental shale samples from the Shahejie Formation. First, a series of experiments, including LTNA, NMR, SEM, mineral composition analysis, and TOC measurement, are conducted to comprehensively investigate the microscopic structure. Next, the fractal dimensions of the samples are determined using the experimental results from LTNA, combined with different fractal scaling equations. Then the fractal dimension and lacunarity from different pores are obtained by SEM images. Subsequently, an analysis is conducted to investigate the relationship between the fractal dimension and pore structure parameters, and the influence mechanism of mineral composition on the fractal dimension is clarified. Finally, the relationship between TOC content and microscopic structure is discussed. These results help reveal the differences in pore structure characteristics with different lithofacies shales and their underlying influencing factors from a fractal theory perspective, providing a foundation for the exploration of shale oil and gas resources.

2 Materials and methodology

2.1 Samples

Twenty-one shale samples are selected for this study, including fifteen samples (Y1−Y15) from the marine Longmaxi Formation (depth: 3744.72−4120.27 m) in the Sichuan Basin and six samples (LY1−LY6) from the continental Shahejie Formation (depth: 3683.00−3920.00 m) in the Jiyang Depression. Samples Y2−Y10 from marine shale are collected from different depths of well L208, with some of the data related to these samples previously published in our earlier work (Cai et al., 2021). Due to the limited number of samples, the porosity and permeability of some shale samples are determined based on Boyle’s law and the transient pulse method, respectively (Table 1).

2.2 Experiments

2.2.1 LTNA

The shales are ground into a 60−80 mesh powder and placed in glass tubes, which are then connected to a vacuum system. Under vacuum environment, these powders are dried at 130°C for 12 h to remove any residual moisture and impurities. After drying, the glass tubes containing shale powder are connected to the Micromeritics ASAP 2020 instrument. Following a second vacuum treatment, the LTNA experiment is initiated. At 77.3 K, as the relative pressure varied, nitrogen molecules undergo a physical adsorption/desorption process within the pore spaces. The nitrogen adsorption/desorption curves are constructed based on the amounts of nitrogen adsorbed/desorbed. From the adsorption/desorption curves, the pore surface area (PSA), pore size distribution (PSD), pore volume (PV), and average pore size (APS) are derived using the Brunauer-Emmett-Teller model and the Barrett-Joyner-Halenda method.

2.2.2 NMR and SEM

After being prepared into a cylinder with a diameter of 2.5 cm and a length of 3 cm, the samples are saturated with a 4% KCl solution at 25 MPa for 3 days. NMR experiments are conducted on the saturated shale samples by the NIUMAG 12 MHz core analyzer. The T₂ spectrums of the saturated shales are obtained using the Carr-Purcell-Meiboom-Gill sequence. The echo space is set to 100 µs, the echo number is chosen to 6000, the repetition time is 3 s, and each NMR test contains 64 scans.

The representative samples are selected from both marine and continental shale, which are first cut into appropriate size thin sections and mechanically polished. The surfaces of thin sections are then further smoothed using argon ion polishing. After argon ion polishing treatment, the ZEISS Merlin field emission SEM instrument is utilized to characterize the microscopic structure of samples.

2.2.3 Analysis of TOC content and mineral

The TOC content reflects the hydrocarbon generation potential of source rocks and is a key indicator for evaluating reservoir quality. The shale samples are crushed and ground into powder, followed by the addition of hydrochloric acid to remove inorganic minerals. The powder is then rinsed with deionized water for 2−3 days. Afterward, the powder is placed in an oven for drying. Finally, the processed powder samples are analyzed for TOC using a carbon-sulfur analyzer, and the TOC values are recorded.

The mineral composition strongly influences the pore types and structure of shale. The dried shale samples are crushed to be 200 mesh powder and then used to determine the mineral composition by X-ray diffraction (XRD) analysis.

2.3 Fractal theory

2.3.1 Pore surface fractal dimension

Using fractal theory, gas adsorbed by porous media can be utilized to evaluate the complexity of the pore surface. The Frenkel-Halsey-Hill (FHH) model has been proven to be one of the most effective methods for calculating the D_s (Pfeifer and Avnir, 1983; Pfeifer et al., 1989). In LTNA experiments, the nitrogen adsorption volume, saturation vapor pressure, and equilibrium adsorption pressure can be obtained. The D_s of shale can be determined using the FHH model expressed in the following form:

(1)\ln V=k\ln \left(\ln \frac{P_0}{P}\right)+C,

where V is the volume of nitrogen adsorbed by the shale powder at 77.3 K, P₀ denotes the saturation vapor pressure at 77.3 K, P is the equilibrium pressure during the adsorption process, k represents the fitting slope of the lnV versus ln(ln(P₀/P)), and C is the intercept of the regression line between lnV and ln(ln(P₀/P)). The D_s can be calculated using k, as expressed by the following equation:

(2)D_s=3+k.

2.3.2 Pore space fractal dimension

Based on the fractal theory proposed by Mandelbrot, the quantities of pores and the pore size obeys the following fractal scaling relationship (Mandelbrot, 1982):

(3)N\propto r^{-D_{\mathrm{f}}},

where N represents the cumulative number of pores with a radius greater than or equal to r (r represents a certain pore radius), and 2 < D_f < 3 (Three dimension). By taking the logarithm on both sides of Eq. (3), the following expression is obtained:

(4)\ln N\propto (-D_{\mathrm{f}})\ln r,

where the D_f can be determined by fitting the slope of data points of lnN versus lnr. The PSD of shale samples is obtained by the LTNA method. The PSD allows for the determination of the cumulative pore volume corresponding to different pore radius. Then, by applying Eq. (4), the D_f of the shale samples can be determined. For simplicity, the pore space fractal dimension derived from PSD of LTNA is denoted as D_f1 in this study.

Apart from the PSD obtained from LTNA, the D_f can also be determined using images of porous media. For SEM images of shale samples, the box-counting method is a commonly used approach to calculate the D_f (Xia et al., 2019). When using the box-counting method, square boxes of varying sizes are moved by a distance equal to their side length to cover the entire 2D image. And the quantities of boxes that cover the measured object is recorded. Therefore, by performing a linear fit of boxes numbers and box sizes on a logarithmic scale, the slope S can be obtained, and D_f2 (represents the fractal dimension of the micropore space in SEM images) is equal to −S.

2.3.3 Lacunarity

The fractal dimension can evaluate the complexity of pores but is unable to measure heterogeneity. Therefore, the lacunarity is introduced to represent the heterogeneity of shale, compensating for the limitations of the fractal dimension. A larger lacunarity indicates a more pronounced heterogeneity in the pore structure. The lacunarity is obtained using the gliding box-counting method, where the step size for each box movement is the length of pixel of image. The lacunarity (Λ) corresponding to a box size λ can be defined by the ratio of the statistical moment function at q = 2 to the square of the statistical moment function at q = 1, as demonstrated below (Allain and Cloitre, 1991):

(5)\mathrm{\Lambda }(\lambda )=\frac{Z_Q^{(q=2)}(\lambda )}{{\left[Z_Q^{(q=1)}(\lambda )\right]}^2}.

The lacunarity varies with the box size λ and the quantities of studied objects. For the SEM images (L × L pixels), the maximum lacunarity is given by Λ_max = Λ(1) = 1/ϕ (ϕ is the porosity), and the minimum lacunarity is described by Λ_min = Λ(L) = 1. The porosity of the sample has a significant impact on the lacunarity calculation, requiring normalization of the lacunarity. The normalized lacunarity (Λ*) is defined as (Roy et al., 2010)

(6){\mathrm{\Lambda }}^{\ast }(\lambda )=\frac{\mathrm{\Lambda }(\lambda )-{\mathrm{\Lambda }}_{min}}{{\mathrm{\Lambda }}_{max}-{\mathrm{\Lambda }}_{min}}=\varphi \frac{\mathrm{\Lambda }(\lambda )-1}{1-\varphi }.

3 Results and discussion

3.1 Pore structure characteristics

3.1.1 Nitrogen adsorption isotherms

The LTNA experiment provides the nitrogen adsorption/desorption curves and PSD of the shale samples (Fig. 1). The maximum adsorption capacity of the marine shale samples is greater than 10.00 cm³/g, with sample Y2 exhibiting the highest maximum adsorption capacity (29.02 cm³/g) (Fig. 1(a)). For the continental samples, as depicted in Fig. 1(b), LY1 has the lowest maximum nitrogen adsorption capacity (4.68 cm³/g), while LY3 has the highest maximum nitrogen adsorption capacity (9.63 cm³/g). Compared to marine shale, the continental shale exhibits lower adsorption capacity at the same relative pressure, indicating that marine shale contains a greater quantity of pores with stronger adsorption capacity. Due to the capillary condensation effect, the adsorption and desorption curves exhibit branching at P/P₀ = 0.45, resulting in the formation of hysteresis loops. Different hysteresis loop patterns correspond to different types of pores (Thommes et al., 2015), the hysteresis loop of shale samples corresponds to the type H3, suggesting that the samples are primarily composed of slit-shaped pores. Except for Y1 and Y13, the PSD of the remaining samples ranges from 1 nm to 116.15 nm (Fig. 1(c)). Most pores fall within the 10 nm to 100 nm range. The PSD of the continental samples in Fig. 1(d) is similar to that of the samples from Fig. 1(c), with pores ranging from 1 nm to 112.01 nm. The highest pore frequency is observed at a pore size of 30 nm. The average pore radius of marine shale is 18.89 nm, while that of continental shale is 22.12 nm, indicating that the pores in marine shales are more compact and its pore structure is relatively more complex. Based on the PSD, the pore types of shales are classified into micropores (< 2 nm), mesopores (2−50 nm), and macropores (> 50 nm) (Figs. 1(e) and 1(f)). The marine shale is predominantly composed of mesopores and micropores, with a higher quantity of micropores compared to continental shale. In contrast, the continental shale is mainly characterized by mesopores and macropores.

3.1.2 T₂ distribution

The T₂ distribution spectra of all saturated shales are shown in Fig. 2, with the horizontal axis representing the transverse relaxation time and the vertical axis indicating the water mass within the samples. Fig. 2(a) illustrates the T₂ distribution of marine shale samples. It can be observed that the T₂ spectra exhibit a distinct bimodal characteristic, indicating the complexity of the pore types in the shale. The left peaks of samples Y1, Y11, and Y13 are all located around 0.6 ms, with the right peaks around 30 ms. For Y12, the left peak occurs near 0.3 ms, and the right peak is approximately at 14 ms. However, the T₂ distribution spectrum of Y10 has three peaks, indicating a more complex pore structure. Compared to the other samples, the T₂ spectrum of Y12 is distinctly shifted to the left (toward shorter T₂), indicating the existence of a greater number of smaller pores. Fig. 2(b) displays the T₂ distribution characteristics of continental shale samples. It can be found that the T₂ distribution of LY6 shows a unimodal distribution, with the peak located at 0.4 ms. The T₂ spectra of the remaining continental shale samples demonstrate a bimodal characteristic, with the left peak at approximately 0.3 ms and the right peak around 20 ms. Compared to marine shales, the T₂ spectrum amplitude of continental shales in the 10−100 ms range is higher, indicating a greater quantity of macropores in continental shales.

The logarithmic mean of the T₂ can reflect the differences in the average pore size of different shale samples, as shown:

(7)T_{2\mathrm{L}\mathrm{M}}=\mathrm{e}\mathrm{x}\mathrm{p}\left(\sum _{T_{2\mathrm{m}\mathrm{i}\mathrm{n}}}^{T_{2\mathrm{m}\mathrm{a}\mathrm{x}}}\frac{A_i}{A_{\mathrm{T}}}\ln T_{2i}\right),

where T_2LM represents the logarithmic mean of the transverse relaxation time, T_2min and T_2max denote the minimum and maximum transverse relaxation times respectively, T_2i is the ith T₂ value within the range from T_2min to T_2max, A_i is the amplitude corresponding to T_2i, and A_T indicates the total amplitude of the shale sample. The calculated T_2LM of all samples are displayed in Fig. 3. The average T_2LM for the marine shale samples is 0.5781 ms. For the continental shale samples, the average T_2LM is 0.6131 ms.

3.1.3 Microscopic pore types, mineral composition and TOC content

The 2D images of shale samples (marine: Y15; continental: LY3) obtained using the SEM are utilized to visually analyze the microscopic structure characteristics. The SEM images of Y15 at different resolutions are depicted in Figs. 4(a), 4(b), and 4(c). The pyrite and dark organic matter are dispersed in Fig. 4(a). The organic matter is characterized by a specific number of pores developed within its structure. In addition to the presence of organic matter, the shale also contains inorganic minerals, within which intragranular pores are developed. The clay minerals in the shale are arranged in a platy structure, with intragranular pores of the clay minerals developed in a slit-like pattern (Fig. 4(b)). Figs. 4(d), 4(e), and 4(f) represent the microscopic pore structure and mineral types of the LY3. Microfractures and dissolved pores are present within the inorganic minerals (Fig. 4(f)). SEM images reveal that the continental shale samples contain a higher proportion of carbonate minerals, which are more prone to the formation of dissolved pores. In comparison to the LY3, the marine shale Y15 contains a higher amount of organic matter and clay mineral, leading to a more complex pore structure.

The mineral composition of all shale samples is provided in Table 2. Marine shale samples contain a higher proportion of quartz and clay minerals, while continental shale samples are richer in carbonate minerals. Different depositional environments result in variations in the mineral types, which in turn leads to differences in pore structure characteristics. An increase in the clay and silicate minerals promotes the development of micropores, whereas a higher content of carbonate minerals facilitates the formation of mesopores and macropores. This is consistent with the results shown in Figs. 1(e) and 1(f). According to the Table 2, the average TOC of marine shales is 2.36%, whereas the average TOC of continental shales is 2.11%.

3.2 Fractal dimension

3.2.1 Fractal dimension from LTNA

Based on the different fractal dimension calculation method described in Section 2.3, the D_s and the D_f1 can be obtained using LTNA experiments. The calculation schematics for each method are displayed in Fig. 5, with the data derived from Y2.

The calculated results of the D_s and the D_f1 for all shales are presented in Table 3. The D_s ranges from 2.4283 to 2.7468. The average D_s for marine shale samples is 2.6643. And the average D_s for the continental shale samples is 2.5225. The average D_s of the marine shale is greater than that of the continental shale, indicating that the pore surface morphology of marine shale is more complex. This difference can be attributed to the varying diagenetic processes associated with different types of shale (Zhang et al., 2018). The D_f1 values for marine samples range from 2.2988 to 2.5104, with an average value of 2.4303. For continental samples, the D_f1 values vary from 2.1386 to 2.3168, with an average of 2.2267.

3.2.2 Fractal dimension and lacunarity from image method

The grayscale images of shale samples obtained from SEM are processed using Avizo software. First, median filtering is applied to remove environmental noise. Subsequently, the grayscale images undergo an appropriate threshold segmentation. Through the threshold segmentation algorithm, the pore distribution characteristics of shales with different lithofacies are extracted. Then, based on the binary image, the fractal dimension and lacunarity are calculated using the box-counting method (Fig. 6(a)) and the gliding box-counting method (Fig. 6(b)), respectively. The normalized lacunarity (Λ*(λ)) for gliding boxes of different sizes (λ) typically ranges from 0 to 1. As λ increases, the Λ*(λ) gradually decreases and eventually approaches 0. Generally, the Λ*(λ) corresponding to the median box size on a log₂λ scale is selected to quantitatively characterize the heterogeneity of the pore.

The fractal dimension and normalized lacunarity of different pores are determined by the above methods (Fig. 7). For Y15, the D_f2 of inorganic pores ranges from 1.4203 to 1.5591, with an average value of 1.4882. The D_f2 of organic matter pores varies from 1.3001 to 1.4735, with an average value of 1.4033. For LY3, the fractal dimension of inorganic pores spans from 1.1271 to 1.4642, with an average value of 1.2823. The fractal dimension of organic pores fluctuates between 1.1776 and 1.3719, with an average value of 1.2954. For both inorganic and organic pores, the D_f2 of marine shale is larger than that of continental shale, which is consistent with the conclusion of D_f1. The average Λ*(r) of inorganic pores for Y15 is 0.1441, while that of organic pores is 0.1465. For LY3, the average Λ*(r) of inorganic pores is 0.0807, whereas that of organic pores is 0.1601. Compared to marine shale, the organic matter in continental shale is more concentrated in its distribution.

3.3 Correlations between pore structure and fractal dimension

LTNA can directly provide PV, PSA, APS, and other pore structure parameters of shale samples. These parameters could quantitatively describe the complex pore structure characteristics within the samples. The relationship between different pore structure parameters and D_s is illustrated by Fig. 8. To simplify subsequent descriptions for the marine shale samples, “marine A” refers to the shale samples not associated with well L208, while “marine B” represents the samples obtained from well L208. A positive correlation is observed between the PSA and D_s for all shale samples (Fig. 8(a)). As the PSA increases, the D_s also increases, indicating a more complex pore surface. Comparing the PSA of shales with different lithofacies, the PSA of marine shale ranges from 6.2629 to 29.2234 m²/g, with an average value of 21.1754 m²/g. The PSA of continental shale are distributed between 1.4068 and 8.2531 m²/g, with an average value being 3.1596 m²/g, which is significantly lower than that of marine shale. When the PV increases, suggesting a more complex pore structure, the value of D_s rises accordingly (Fig. 8(b)). The PV of marine shale spans from 0.0143 to 0.0437 cm³/g (average value: 0.0313 cm³/g). In contrast, the PV of continental shale ranges from 0.0057 to 0.0150 cm³/g (average value: 0.0109 cm³/g).

Considering the difference in D_s among all samples, the correlation between the APS and D_s is analyzed separately (Fig. 8(c)). In comparison to the other samples, the relationship between the APS and D_s for the marine A is weaker (R² = 0.4349). As the pore size increases, the pore surface becomes smoother, resulting in a decrease in D_s. The APS of three types samples is 7.8764 nm (marine A), 9.1464 nm (marine B), and 18.2035 nm (continental), respectively. The APS of continental shale is larger than that of marine shale, which is consistent with the results reflected by the average T_2LM of the shale samples. By combining the PSA and PV, the ratio of surface area and volume (S/V) is determined, and the relationship between the S/V and D_s is analyzed, as shown in Fig. 8(d). There is a strong positive relationship between the S/V and D_s for all shales. A higher S/V represents a more complex pore surface morphology, which leads to a larger D_s. Due to the smaller pore size of marine shale, it results in a higher S/V. When compared to the other five continental shale samples, LY5 has the highest D_s (2.7233). The lower amplitude of the T₂ spectrum at longer transverse relaxation times and the smaller T_2LM of LY5 indicate smaller pore sizes compared to the other continental shale samples, which in turn results in a higher D_s.

The relationship between D_f1 and pore structure parameters are described by Fig. 9. Similar to the trend observed for D_s, PSA, PV, and S/V all show a positive correlation with D_f1. As the PSA, PV, and S/V increase, indicating a more complex pore space structure, a larger D_f1 is found. There is a negative correlation between pore size and D_f1. With pore size rising, the pore structure becomes more homogeneous and D_f1 decreases.

3.4 Effect of mineral composition on pore structure and fractal dimension

Essentially, different mineral types and contents induce variations in pore surface morphology, which in turn cause changes in PSA, ultimately leading to alterations in the D_s (Li et al., 2019a). For marine shale, the D_s decreases with increasing quartz content, showing a negative correlation (Fig. 10(a)). This is consistent with the results of Li et al. (2024) and Cao et al. (2016). The relatively smooth surface of quartz minerals reduces the heterogeneity of the pore structure, which means that a higher quartz content is associated with a smaller PSA (Shan et al., 2020). For the marine shale, the quartz content spans from 34.80% to 48.0%, with an average quartz content being 40.35%. In contrast, for the continental shale, the quartz content varies within the range of 12.90% to 25.20%, and the average quartz content is 20.03%. As the continental shale contain relatively low amounts of quartz, there is no significant relationship between quartz content and PSA (Fig. 11(a)), which explains the lack of a clear correlation between quartz content and D_s in Fig. 10(a).

Shale contains abundant clay minerals, which predominantly form micropores. These micropores, with their high S/V, significantly influence the pore structure characteristics of the shale (Chen et al., 2016). The clay mineral content of the marine shale spans from 22.10% to 40.10%, attaining an average clay content of 31.63%. By contrast, the continental shale samples have a clay mineral content fluctuating between 16.00% and 33.10%, with an average clay content being 23.78%. Marine shales exhibit a higher clay mineral content compared to continental samples. Clay minerals, which have low compressive strength, tend to undergo a flake-like, ordered arrangement under prolonged compaction. This results in complex surface morphologies of the clay mineral pores (Wilson et al., 2016). With an increase in clay content, the PSA also rises, demonstrating a positive correlation (Fig. 11(b)). Consequently, a noticeable positive correlation exists between clay mineral content and D_s, indicating that higher clay content is associated with a higher D_s (Fig. 10(b)).

According to the Table 2, the predominant clay mineral types present in the marine shale are illite, chlorite, and illite/smectite mixed layer (I/S). In contrast, the I/S is the predominant clay mineral type for the continental shale, with a smaller proportion of illite. For the marine shale, a positive correlation is observed between I/S and D_s (Fig. 10(c)). I/S represents an intermediate product in the transformation of smectite to illite. During the dehydration and transformation process of smectite, a certain quantity of micropores will be generated (Chang et al., 2022). An increase in the I/S content (with its rough surface) leads to a rise in micropore surface area (Fig. 11(c)), thereby enhancing the complexity of the pore surface. The average I/S content of marine shale is 7.18%, while the average I/S content for continental shale is 19.86%. Due to the high and relatively uniform distribution of I/S for continental shale, there is no significant correlation between I/S content and D_s in these samples. With an increase in illite content, D_s also rises, showing a relatively strong positive correlation between illite content and D_s (Fig. 10(d)). As the final transformation product of smectite, illite fills larger pores and divides them into smaller pores, which increases the PSA and roughness (Wang et al., 2023a), as shown in Fig. 11(d), resulting in a higher D_s. The average illite content for marine shale is 17.89%, while it is 3.37% for continental shale. The lower illite content for continental shale indicates a relatively low conversion rate of smectite to illite.

The mineral composition can also influence the pore volume, thereby affecting the D_f. The variation trend between the D_f1 and the mineral content is illustrated by Fig. 12. Similar to the effect of mineral content on D_s, there is a negative correlation between quartz content and D_f1 (Fig. 12(a)). This is attributable to the fact that quartz particles exhibit good sorting and roundness, resulting in relatively homogeneous pore structure (Zhang et al., 2024). As depicted in Fig. 13(a), it is evident that the higher quartz content, the smaller the pore volume. As previously mentioned, no obvious correlation exists between the quartz and D_s for continental shale. However, the quartz content of continental shale exhibits a higher correlation with D_f1 (R² = 0.6269). This indicates that D_f1 is more sensitive to the variations within the pore space. The relatively large number of micropores developed within the clay minerals contributes to an increase in pore volume (Fig. 13(b)), augmenting the complexity and heterogeneity of the pore space. Hence, a pronounced positive correlation exists between the clay and D_f1 (Fig. 12(b)), with higher the clay content corresponding to a larger D_f1.

In contrast to a relatively strong positive correlation between the I/S and D_s (R² = 0.7658) for marine shale, the correlation between I/S and D_f is weaker (R² = 0.4541) (Fig. 12(c)). From Fig. 11(c), it is evident that there is a relatively weaker positive correlation between the PSA and the I/S (R² = 0.5591). However, the positive correlation between the PV and the I/S is relatively strong (R² = 0.8017). This indicates that the alterations in PV and PSA are not solely determined by I/S, but are influenced by multiple factors in concert. An increase in illite content is accompanied by a rise in D_f1 (R² = 0.6755, Fig. 12(d)). This implies that rocks with a high illite content have a larger PV (Fig. 13(d)), which in turn enhances the complexity of the pore space.

3.5 Correlations between TOC and microscopic structure

For marine shale, with the TOC content increases, the S/V rises correspondingly, with a weak positive correlation (R² = 0.3715, Fig. 14(a)). The organic matter pores are typically small (Wang et al., 2021), leading to the number of small pores rising with high organic matter content. This results in a reduction of the overall APS and an increase in the S/V. In Fig. 14(b), a weak positive correlation exists between TOC and D_s, indicating that organic matter slightly increases the roughness of the pore surface. A higher TOC content suggests that the shale samples contain more organic matter (Li et al., 2016), which possesses complex pore structures and surfaces (Liu et al., 2015), leading to an increase in fractal dimension. However, compared to Fig. 14(a), the relationship of TOC and S/V for continental shale shows a distinct difference. The interconnected microfractures are present within the organic matter of continental shale. The presence of these microfractures reduces the S/V, which leads to a negative correlation between the D_s and TOC content (Fig. 14(d)).

4 Conclusions

In this study, the pore structure characteristics, pore surface fractal dimensions, pore space fractal dimensions, and lacunarities of shales from different lithofacies are evaluated by multiscale pore structure characterization methods. In combination with the mineral composition, the influence patterns of mineral types and their respective contents on the fractal dimensions have been clarified. The relationships between the TOC content from different lithofacies and microscopic structure are also discussed. The following conclusions are derived.

1) Compared to the Shahejie continental shales, the Longmaxi marine shales exhibit smaller average pore sizes. A comparison of the fractal dimensions between shales of different lithofacies reveals that both the pore surface fractal dimension and the pore space fractal dimension for marine shales are higher than those for continental shales. These results reveal that marine shales have more complex pore surfaces and pore spaces.

2) Quartz with the smoother surface reduces the heterogeneity of the pore space and induces a lower fractal dimension. The clay enhances the complexity of the pore space, resulting in a strong positive correlation between clay and fractal dimension.

3) The illite/smectite mixed layer exhibits a strong positive correlation with fractal dimensions for marine shales, while this correlation is weaker for continental shales. Illite fills larger pores, contributing to both greater pore surface roughness and increased pore complexity. A higher illite content is associated with a higher fractal dimension.

4) For marine shales, a weak positive correlation exists between TOC content and pore surface fractal dimension. However, the presence of microfractures within the organic matter results in a negative correlation between TOC content and pore surface fractal dimension for continental shales.

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