Shale samples from the upper section of the Lianggaoshan Formation were selected for this study, encompassing a range of lithologies including shell limestone, mudstone-siltstone, siltstone, and fine sandstone, representing the typical lithologies of the Liangshang. Samples were sectioned parallel to bedding planes and prepared according to the specific requirements of each analytical technique. These techniques included total organic carbon (TOC) analysis, Rock-Eval pyrolysis (R _o), X-ray Diffraction (XRD), Field Emission Scanning Electron Microscopy (FE-SEM), CO₂ Gas Adsorption (GO₂GA), Low-Temperature N₂ Adsorption (LTN₂A), Mercury Intrusion Porosimetry (MIP), and NMR.

Based on the T ₂ spectra obtained from one-dimensional NMR experiments, the multifractal dimension of the NMR data under different conditions was calculated using the box-counting method. The core T ₂ spectra were normalized and accumulated, then divided into N equal parts (ε). The entire dataset underwent interpolation, and the probability mass function of the ith segment can be expressed in Equation 6 (Zhang et al., 2024a): P i ε = N i ε ∑ i = 1 N ε N i ε (6) Here, N _i(ε) represents the cumulative porosity or volume of pores within the ith partition, while P _i(ε) denotes the probability mass function.

Within the framework of multifractal theory, the probability mass function P _i(ε) exhibits a power-law relationship with ε, which can be expressed in Equation 7 (Zhang et al., 2021a): P i ε ∝ ε α i (7)

In this equation, α _i represents the Lipschitz-Hölder exponent or singularity strength, indicating the density of data distribution. A smaller α _i value implies a higher degree of data variation or heterogeneity, while a larger α _i value corresponds to greater regularity or uniformity in the data (i.e., higher regularity or orderliness).

It’s possible that different values of (ε) might share the same singularity strength. This can be represented by Equation 8, which denotes the proportion of the total dataset that is occupied by the sum of segmented datasets with singularity strengths clustered around α within a given (ε) range: N α ε ∝ ε − f α (8)

Here, f(α) represents the multifractal spectrum or singularity spectrum. A wider peak in the multifractal spectrum indicates stronger local heterogeneity. A greater right-side skewness reflects greater diversity in singularity exponents, which is associated with sparse pore size distributions. Conversely, greater left-side skewness indicates greater diversity in the smallest singularity exponents, which is linked to higher aggregation probabilities.

The partition function Equation 9 is defined as (Zhang et al., 2022): X q , ε = ∑ i = 1 N ε P i ε q ∝ ε τ q (9)

Here, q represents the order moment or weighting factor, ranging from -∞ to +∞. When q > 1, information from high-density regions (dense areas) is amplified. Conversely, when q < 1, information from low-density regions (sparse areas) is amplified. τ(q) denotes the mass function, which can be expressed by Equation 10: τ q = − lim ε → 0 l g x q , ε lg ⁡ ε = − lim ε → 0 lg ⁡ ∑ i = 1 N ε P i ε q lg ⁡ ε (10)

Different q values correspond to different generalized fractal dimensions D(q), which can be calculated using Equation 11 as follows (Zhao et al., 2017): D q = τ q 1 − q = 1 q − 1 lg ⁡ ∑ i = 1 N ε P i ε q lg ⁡ ε , q ≠ 1 ∑ i = 1 N ε P i ε lg ⁡ P i ε lg ⁡ ε , q = 1 (11)

The relationship between the singularity strength α(q), f(α), and τ(q) corresponding to the order moment q, derived from the Legendre transform, can be expressed by Equations 12, 13 (Liu et al., 2018): α q = d τ q d q (12) f α = q α q − τ q (13)

Within the generalized fractal spectrum q ∼ D(q), the extracted D(q) values reveal the distribution characteristics of the dataset. In the multifractal spectrum α ∼ f(α), extracted values of α(q), f(α), and the spectral width Δα provide insight into the dataset’s distribution. The spectral width Δα can be expressed by Equation 14: ∆ α = α max − α min (14)

Mineralogical analysis, including cast thin sections, SEM with energy-dispersive X-ray spectroscopy (SEM-EDS), and XRD, indicates that quartz and clay minerals are the dominant constituents of the shale samples, averaging 47.26% and 28.56%, respectively. Illite-smectite mixed layers and illite comprise the predominant clay mineral species. Feldspars constitute a significant proportion of the assemblage (0.8%–37.5%, averaging 18.59%), with plagioclase predominating. Carbonate minerals are present in relatively minor amounts (averaging 5.59%), primarily calcite (Figure 2).

Lithofacies, defined by rock characteristics (composition, geochemistry, and sedimentary structures) and depositional environment (He et al., 2024), were classified within the Lianggaoshan Formation using a “four-component, three-end-member” scheme that incorporates TOC, rock fabric, and inorganic mineral composition (Figure 3A) (Feng et al., 2024). Given the limited range of organic matter abundance in the Lianggaoshan Formation (TOC generally <2%), thresholds of 0.6% and 1.5% TOC were selected to delineate organic matter content (Wang et al., 2024; Yin et al., 2024). This classification scheme identified four dominant lithofacies: high-organic matter laminated felsic shale, medium-organic bedded felsic shale, low-organic massive argillaceous siltstone, and massive fine-silt sandstone (Figure 3B).

Organic geochemical analysis of Lianggaoshan Formation shales in the northeastern Sichuan Basin reveals favorable hydrocarbon generation potential. The relationship between TOC content and hydrocarbon generation potential (S ₁ + S ₂) reveals the varying hydrocarbon-generating capacities of different lithofacies (Xue et al., 2024). TOC values range from 0.15% to 2.95% (average 1.09%), indicating overall promising hydrocarbon generation potential. High-organic laminated felsic shales exhibit higher TOC and stronger hydrocarbon generation capacity, largely concentrated within the “Good” range, suggesting significant potential (Figure 4A). Conversely, medium-organic bedded felsic shale, low-organic massive argillaceous siltstone, and massive fine-silt sandstone exhibit a comparatively lower hydrocarbon-generating capacity, falling within thre “Poor” to “Fair” egions. The relationship between hydrogen index (HI) and pyrolytic peak temperature (T_max) further clarifies the type and maturity of organic matter in these shales (Hu et al., 2024a). The T_max of the shales in study area ranges from 336°C to 494°C, with an average of 468.15°C, indicating that the organic matter is mature to highly mature. R _o values (1.06%–1.68%, average 1.46%) corroborate these findings, confirming the high maturity. The organic matter primarily comprises Type II₁ and Type II₂ kerogen, with a high proportion (67%–78%) of sapropelic organic matter (Figure 4B), further supporting significant oil generation potential.

Analysis of Jurassic Lianggaoshan Formation shales in the northeastern Sichuan Basin reveals significant lithofacies-dependent variations in pore type and development (Wang et al., 2024). Based on SEM observations and the shale pore classification scheme proposed by Loucks et al. (2012), the main pore types in the study area identified include clay mineral interparticle pores, organic pores, quartz dissolution pores, intergranular pores, pyrite interparticle pores, and microfractures. High-organic laminated felsic shales exhibit abundant organic pores, predominantly irregular in shape and ranging from 100 to 500 nm in size (Figure 5A). Inorganic porosity is represented by intragranular dissolution pores and pyrite interparticle pores. Additionally, intergranular pores formed by mineral edge dissolution are also relatively well developed, with pore sizes generally exceeding 1 μm. This lithofacies exhibits a diverse array of pore types, with localized areas displaying honeycomb-like organic pores, indicating a high potential for reservoir space development (Figures 5B, C).

Medium-organic bedded felsic shale is characterized by intergranular pores between inorganic rigid grains as the main pore type. While organic pores are also present, their volume proportion is relatively low, mainly concentrated within dissolution pores on the surface of feldspars (Figure 5D). Intergranular pores are well developed in this lithofacies, and quartz dissolution pores also constitute a significant proportion, demonstrating a certain degree of storage capacity (Figure 5E).

Low-organic massive argillaceous siltstone and massive fine-silt sandstone exhibit a relatively simple pore type. Poorly developed organic pores, primarily irregular shapes filling interparticle spaces between quartz grains and clay minerals, are observed (Figures 5F, G). Inorganic pore development is limited in this lithofacies, with relatively few pyrite interparticle pores and microfractures (Figures 5H, I). Consequently, these lithofacies exhibit limited reservoir potential.

CO₂GA, LTN₂A and MIP experiments were conducted to characterize the pore morphology of different lithofacies within the Jurassic Lianggaoshan Formation shales of the northeast Sichuan Basin. High-organic laminated felsic shale exhibits a distinct co-existence of micropores, mesopores, and macropores (Figures 6A–C). CO₂ adsorption experiments demonstrate well-developed mesopores, primarily exhibiting irregular shapes below 100 nm (Figure 6A). These micropores often exhibit fine, crack-like, or intergranular forms. N₂ adsorption experiments further revealed mesopores, predominantly exhibiting ink-bottle-like and parallel plate-like pores morphologies (Figure 6B). Hysteresis in the adsorption-desorption isotherms indicates pore connectivity and complex morphology. MIP porosimetry revealed well-developed macropores and microfractures, exhibiting predominantly slit-shaped and near-circular morphologies in the nanometer to micrometer rang (Figure 6C).

Medium-organic bedded felsic shale exhibits a simpler pore morphology (Figures 6D–F). CO₂ adsorption experiments indicate that the micropores primarily comprised irregular intergranular pore spaces (Figure 6D), but their development was less pronounced than in high-organic laminated felsic shale. N₂ adsorption experiments showed that mesopores were mainly slit-shaped and plate-shaped (Figure 6E), but their hysteresis loop characteristics are less pronounced compared to high-organic matter lithofacies, indicating lower complexity of these mesopores. MIP experiments reveal the limited development of macropores and microfractures, with the pore morphology primarily characterized by simple intergranular pores (Figure 6F), resulting in a relatively simple overall pore structure and limited reservoir potential.

Low-organic matter massive argillaceous siltstone exhibits a more simplified and limited pore morphology (Figures 6G–I). CO₂ adsorption experiments show limited micropore development, with the pore morphology primarily characterized by a small number of irregular and tiny intergranular pores (Figure 6G). N₂ adsorption experiments reveal a limited number of mesopores, with the pore morphology primarily characterized by ink-bottle-like and slit-shaped (Figure 6H). The hysteresis loop characteristics suggest poor connectivity of these pores. MIP experiments indicated very limited macropore and microfracture development (Figure 6I), with the pore structure consisting primarily of simple linear or point-like features, thus limiting the storage capacity of this lithofacies.

Massive fine-silt sandstone exhibits a slightly improved pore morphology (Figures 6J–L). CO₂ adsorption experiments revealed a limited development of micropores, primarily exhibiting irregular intergranular spaces (Figure 6J). N₂ adsorption experiments show a more developed mesoporous and macroporous morphology, with hysteresis loop characteristics suggesting that these pores are mainly wedge-shaped, ink-bottle-like, and plate-shaped (Figure 6K). MIP experiments further indicated relatively well-developed macropores and microfractures (Figure 6L), characterized by near-circular or linear morphologies and a wide pore size distribution.

By integrating low-temperature gas adsorption (CO₂ and N₂) with high-pressure mercury intrusion data, the pore volume distribution characteristics of different lithofacies of the Jurassic Lianggaoshan Formation shales in Northeast Sichuan Basin were systematically analyzed. Analysis of pore volume distribution in high-organic laminated felsic shale revealed a significant dominance of mesopores (Figures 7A, B). The pore size distribution peaked between 10 and 100 nm, with mesopores comprising 68.3%, micropores 28.7%, and macropores only 3.0% of the total pore volume. This indicates that mesopores constitute the primary reservoir space within this lithofacies.

The pore volume distribution of medium-organic bedded felsic shale similarly exhibits a predominance of mesopores (Figures 7D, E). The pore size distribution peak between 10 nm and 50 nm, with mesopores comprising 64.2%, micropores 32.5%, and macropores only 3.3% of the total pore volume. Compared to high-organic matter laminated felsic shale, the relative proportion of mesopores is slightly lower, but they still constitute the primary reservoir space.

The pore volume distribution of low-organic matter massive argillaceous siltstone is dominated by micropores, with the pore size distribution primarily concentrated within the range of 1 nm–10 nm, with micropores accounting for 58.7% of the total pore volume, mesopores contributing 35.4%, and macropores accounting for only 5.9% (Figures 7G, H). This indicates that micropores comprise the primary reservoir space in this lithofacies.

Massive fine-silt sandstone exhibits a more balanced pore size distribution, concentrated between 10 and 50 nm (Figures 7J, K). Mesopores comprise 59.8%, micropores 29.1%, and macropores 11.1% of the total pore volume. Compared to other lithofacies, this lithofacies shows a slightly higher proportion of macropores; however, mesopores remain the primary reservoir space.

By converting the NMR T₂ spectra to specific pore sizes (Figures 7C, F, I, L), the results indicate that the nuclear magnetic conversion pores are consistent with the pore size distribution morphology obtained from experiments. Furthermore, after conversion, the T₂ spectral distribution peaks of the four rock cores show a high degree of overlap with the peaks of the combined pore size distributions obtained from CO₂ adsorption, low-temperature N₂ adsorption, and MIP.

Multifractal theory, through D(q) and f(α) indices, quantifies the spatial distribution and heterogeneity of pore structures, clarifying pore complexity and heterogeneity at various microscopic scales, which is crucial for predicting hydrocarbon accumulation space and flow paths. By analyzing the multifractal characteristics of high-organic-content lamellar feldspathic shale, medium-organic-content lamellar feldspathic shale, low-organic-content blocky argillaceous siltstone, and silty sandstone from the Jurassic Lianggaoshan Formation in Northeast Sichuan, we uncover the complexity and heterogeneity of pore structures across different lithofacies (Figure 8). The pore size distribution and multifractal analysis of the high-organic-content lamellar feldspathic shale (Figures 8A–C) indicate that its generalized fractal dimension D(q) decreases with increasing q. The D(q) curve in Figure 8B shows thatΔD increases with q, reflecting significant heterogeneity in this lithofacies; the multifractal spectrum f(α) in Figure 8C shows a broad distribution of Δα and αmax, further indicating that this heterogeneity is concentrated in low-probability regions. Similarly, the medium-organic-content lamellar feldspathic shale (Figures 8D–F) shows high heterogeneity, albeit slightly lower than that of the high-organic-content lithofacies, and its f(α) analysis suggests that the heterogeneity mainly arises from low-probability regions. The multifractal characteristics of the low-organic-content blocky argillaceous siltstone (Figures 8G–I) and the silty sandstone (Figures 8J–L) reveal lower heterogeneity. The D(q) curve of the low-organic-content lithofacies exhibits a smaller increment, indicating relatively homogeneous pore structures; its f(α) analysis further confirms that the heterogeneity is concentrated in medium-probability regions.

In high-organic matter laminated felsic shale, macropore pore volume exhibits a positive correlation with TOC content (R ² = 0.59) (Figures 9A), suggesting that higher organic matter content promotes macropore development, consistent with the hydrocarbon generation process during organic matter thermal evolution (Hu et al., 2024b). This observation aligns with findings in other basins, such as the Bakken Formation, where high TOC content also correlates with macropore development, facilitating oil accumulation (Jiang et al., 2023a; Liu et al., 2024). Meanwhile, quartz content positively influences the development of meso- and micropores (R ² = 0.71, R ² = 0.32). Similar trends have been reported by Su et al. (2023) in the Permian Basin, where quartz enrichment enhances pore connectivity and supports hydrocarbon migration. Medium-organic bedded felsic shale shows a negative correlation between micro- and mesoporous volumes and TOC content (R ² = −0.13, R ² = −0.27), indicating that the development of micropores and mesopores is restricted under moderate organic matter content, potentially the generation of residual asphalt by the organic matter that blockage the pore space (Guo et al., 2020). Quartz content still promotes mesoporous formation (R ² = 0.83), while clay minerals also exhibit a tendency to promote pore development. Micro- and macropores show positive correlations with clay mineral content, respectively, indicating that pore structure development in this lithofacies is also significantly influenced by clay minerals (Figure 9B). Despite a positive correlation between macropore volume and TOC content in low-organic matter massive argillaceous siltstone (R ² = 0.31), suggesting some promotion of macropore development by organic matter, the negative correlation between micro- and mesoporous volumes and TOC content (R ² = −0.37, R ² = −0.61) reflects the inhibition of smaller pore space development in low-organic matter shales. Additionally, quartz content exhibits a degree of negative correlation with mesoporous volume in this lithofacies (R ² = −0.057), suggesting that an increase in quartz content might lead to a reduction in pore space, particularly mesopores. The positive correlation of clay minerals (R ² = 0.96) further confirms their positive impact on pore development (Figure 9C). In contrast to other lithofacies, micropore, mesopore and macropore volumes in massive fine-silt sandstone exhibit a negative correlation with TOC content (Figure 9D), indicating that an increase in TOC content might lead to a decrease in pore volume. Simultaneously, quartz content exhibits a significant positive impact on the formation of meso- and macropores (R ² = 0.98), consistent with the trend observed in high-organic matter shales.

In summary, the development extent of pore structures in different lithofacies of shales in the study area is closely related to TOC content, quartz, and clay mineral content. TOC content generally exhibits a positive correlation with the development of micro- and mesopores, although its increase may inhibit pore development in certain lithofacies. Quartz content generally contributes to the formation of meso- and macropores, while an increase in clay mineral content leads to the formation of numerous intercrystalline pores, also playing a positive role in shale pore development.

The diverse composition of shales is a key factor driving the variability in pore structures. Compared to conventional reservoirs, shale reservoirs not only exhibit complex mineral assemblages but also contain organic matter and abundant organic pores (Wang et al., 2023). The application of multifractal theory provides a quantitative evaluation of pore structure heterogeneity across various lithofacies, addressing a notable gap in current research. For instance, Zhang et al. (2024a) primarily investigated the effects of TOC and quartz content but did not incorporate multifractal metrics such as ΔD and Δα, which are crucial for understanding heterogeneity at multiple scales. In high-organic matter laminated felsic shale, ΔD shows a significant positive correlation with quartz content (R ² = 0.55), while clay mineral content exhibits a negative correlation (R ² = −0.37) (Figure 10A). This suggests that quartz enrichment enhances shale compaction resistance, reducing pore structure heterogeneity, whereas clay minerals contribute to increased heterogeneity due to compaction. The correlation between TOC content and ΔD and Δα is weak, indicating a limited influence of TOC on pore heterogeneity in this lithofacies. In medium-organic bedded felsic shale, ΔD shows a weak correlation with TOC content, while a positive correlation with clay mineral content is observed (R ² = 0.14) (Figure 10B). This indicates that clay minerals play a more prominent role in enhancing pore heterogeneity in this lithofacies, while quartz, although exhibiting a certain degree of heterogeneity reduction, has a relatively minor impact. In low-organic matter massive argillaceous siltstone, quartz content is positively correlated with ΔD (R ² = 0.24) (Figure 10C), indicating that quartz continues to contribute to pore structure homogeneity even under low-organic matter conditions. However, the negative correlation between clay mineral content and ΔD and Δα (R ² = −0.85 and −0.9) suggests that clay minerals are more prone to induce pore structure complexity and enhanced heterogeneity in low-organic matter shales. Massive fine-silt sandstone exhibits a strong positive correlation between TOC content and ΔD (R ² = 0.83) (Figure 10D), reflecting that organic matter enrichment can lead to a significant increase in pore heterogeneity. The negative correlation between quartz and ΔD (R ² = −0.96) suggests that quartz helps maintain pore structure homogeneity in this lithofacies, while clay minerals continue to enhance pore structure heterogeneity.

In summary, the controlling mechanisms of quartz and clay minerals on pore structure heterogeneity in different lithofacies exhibit significant differences. An increase in quartz content typically contributes to reduced heterogeneity, while an increase in clay mineral content often leads to enhanced heterogeneity. The influence of TOC varies among different lithofacies, with a particularly prominent effect in massive fine-silt sandstone.

Figure 11A reveals that the ΔD values for micropores are concentrated between 1.3 and 1.5, with a smaller pore volume, suggesting a relatively uniform micropore structure and low heterogeneity. The ΔD values for mesopores exhibit a wider range, reaching 1.5 to 1.9, with a larger variation in pore volume, reflecting a more complex mesoporous structure and stronger heterogeneity. The ΔD values for macropores are relatively scattered, with larger pore volumes, but the correlation between ΔD and pore volume is not pronounced, implying that the formation of macropores is influenced by multiple geological factors, resulting in a higher level of structural complexity and heterogeneity. Figure 11B illustrates the relationship between pore volume and roughness Δα. The Δα values for micropores are smaller, concentrated between 0.5 and 0.6, indicating smooth and uniform micropore surfaces. The Δα values for mesopores and macropores have a wider distribution, particularly for mesopores, which can reach 1.0, reflecting a rougher surface and higher heterogeneity in mesopores and macropores (Zhang et al., 2021b).

In high-organic matter laminated felsic shale, micropores exhibit lower fractal dimensions (ΔD) and roughness (Δα), indicating a simpler and more uniform pore structure. This observation aligns with the development characteristics of organic pores in high-organic matter shales. Micropores primarily form during the thermal evolution of organic matter, resulting in regular pore morphology, stable structure, and low heterogeneity (Zhu et al., 2023; Liang et al., 2024). These micropores play a crucial role in shale oil enrichment by providing stable reservoir space. In medium-organic bedded felsic shale, mesopores exhibit higher ΔD and Δα values, reflecting a complex and heterogeneous pore structure in this lithofacies. Mesopores dominate this lithofacies, controlled by the enrichment and distribution of siliceous minerals. High silica content contributes to the formation of complex pore networks, increasing pore connectivity and complexity, thereby enhancing shale oil mobility. However, this complexity introduces uncertainty in exploration and development. Macropores in low-organic matter massive argillaceous siltstone exhibit high ΔD values and a wide distribution of Δα values, indicating a high degree of pore structure heterogeneity. Macropores are predominantly composed of interlayer and intergranular pores in clay minerals. Clay minerals are prone to deformation during diagenesis and compaction, leading to complex macropore structures and increased surface roughness (Jiang et al., 2023b; Liang et al., 2024). While the presence of macropores provides pathways for fluid flow, their high heterogeneity may restrict effective fluid migration and recovery (Chang et al., 2024b; Chen et al., 2024b). In massive fine-silt sandstone, the ΔD and Δα values of all pore types exhibit significant variations, reflecting an exceptionally complex and heterogeneous pore structure in this lithofacies. This high heterogeneity is likely controlled by the combined effect of quartz and clay minerals in the rock, particularly when quartz content is high, complex pore networks develop, while the plastic deformation of clay minerals further exacerbates surface roughness and structural irregularity.

Therefore, the pore structures and multifractal characteristics of different lithofacies within the Lianggaoshan Formation display significant variations, providing an in-depth understanding of reservoir flow capacity and hydrocarbon enrichment potential. Compared to conventional porosity-permeability models used in previous studies, the application of multifractal dimensions provides a more nuanced characterization of pore heterogeneity and its influence on reservoir quality. The micropore structure of high-organic-matter shale is simple and uniform; this low heterogeneity and narrow pore size distribution favor the accumulation and retention of shale oil. In contrast, the mesopore structure of medium-organic-matter lithofacies is relatively complex. Although its pore structure is conducive to hydrocarbon accumulation, its high heterogeneity poses challenges to development, such as uneven flow paths and increased seepage resistance. Conversely, the low-organic-matter lithofacies exhibits prominent macropore structures and high heterogeneity, which may reduce effective hydrocarbon recovery rates. Additionally, the pore structure of blocky fine-silty sandstone lithofacies shows extreme complexity and heterogeneity, reflecting the influence of quartz-clay mineral interactions on pore development. Multifractal analysis, using generalized fractal dimensions D(q) and multifractal spectra f(α), provides quantitative insights into the pore heterogeneity of different lithofacies and their distribution across probability regions, enabling us to reveal shale reservoir structural characteristics at a microscopic scale. This analytical approach offers scientific support for predicting reservoir flow paths and optimizing “sweet spot” zones, thereby providing critical backing for the exploration and development of shale oil resources within the Lianggaoshan Formation in the Sichuan Basin.