Dynamic Characteristics of the Pore Heterogeneity of Longmaxi Shale Based on High-Pressure Triaxial Creep Testing

Abstract

The dynamic changes in shale pore structure due to tectonic uplift are crucial for understanding the processes of shale gas enrichment and accumulation, particularly in complex tectonic regions. To explore the heterogeneous changes in pore structure and their influencing factors during the last tectonic uplift of Longmaxi shale, triaxial creep experiments were performed under varying confining pressure conditions. In addition, FE-SEM, MIP, LN2GA, and LCO2GA experiments were employed to both qualitatively and quantitatively characterize the pore structure of three distinct groups of Longmaxi shale samples. To further investigate pore heterogeneity, the multifractal dimension was applied to examine the evolution of the shale pore structure under the influence of the last tectonic uplift. The results revealed that the primary pore types in Longmaxi shale include organic matter pores, microfractures, intergranular pores, and intragranular pores. The shale’s mechanical properties and mineral content have a significant impact on the heterogeneity of these pores. Notably, the shale pores exhibit distinct multifractal characteristics, highlighting the complex nature of pore heterogeneity. The singular index (α₀) and ten other multifractal dimension parameters provide valuable insights into the heterogeneity characteristics of shale pores from various perspectives. Additionally, dynamic changes in pore heterogeneity are primarily controlled by the mineral composition. Under identical creep pressure variation conditions, significant differences are observed in the pore rebound behavior of Longmaxi shale with different mineral compositions. Under high-pressure conditions, the content of TOC and quartz plays a dominant role in controlling pore heterogeneity, with their influence initially decreasing and then increasing as pressure decreases. The reduction in creep pressure emphasizes the controlling effect of TOC, quartz, and feldspar content on pore connectivity. This study introduces high-pressure triaxial creep experiments to simulate the stress response behavior of pore structures during tectonic uplift, offering a more comprehensive reflection of pore evolution in organic-rich shale under realistic geological conditions.

1. Introduction

After more than a decade of exploration and development, China has achieved large-scale, high-efficiency shale gas development in the Sichuan Basin and its surrounding areas, with notable examples including the Fuling and Weiyuan regions [1,2,3]. However, significant breakthroughs in Longmaxi shale gas exploration have yet to be made in structurally complex areas, such as the northeastern Chongqing–western Hubei tectonic belt and the southwestern Sichuan–northeastern Yunnan region of the Sichuan Basin [4,5,6]. Previous studies on the Longmaxi shale in the Sichuan Basin and its surrounding areas have shown that black shales, both inside and outside the basin, exhibit high consistency in sedimentary environment, material composition, and sedimentary thickness. However, during actual exploration, significant differences are observed in the burial depth of shale and shale gas content across different sections [7,8,9,10,11]. Several local scholars have pointed out that the fundamental reason for the differences in shale gas development effectiveness in structurally complex areas is related to late-stage tectonic activities, particularly the large-scale differential tectonic uplift processes during the Yanshanian to Himalayan periods. This process not only determines the subsequent adjustment path of the shale gas reservoir but also serves as a key geological event for the enrichment and preservation of Longmaxi shale gas [12,13]. Therefore, it is essential to systematically study the changes in shale gas storage space, from deposition and burial to tectonic uplift.

Key elements for the efficient development of shale gas resources in complicated tectonic settings are pores and fractures, which operate as gas storage and flow spaces and display dynamic heterogeneity that regulates the storage and migration of shale gas. Current research methods for shale pore structure primarily include high-pressure mercury intrusion (MIP), low-temperature nitrogen adsorption (LN₂GA) and carbon dioxide adsorption (LCO₂GA), small-angle X-ray scattering (SAXS), field emission scanning electron microscopy (FE-SEM), and nuclear magnetic resonance (NMR), among other techniques. These methods span scales from the nanoscale to the micrometer and can systematically reveal the geometric morphology, spatial distribution, and evolutionary properties of shale pores from multiple dimensions, thus achieving both quantitative and qualitative characterization of pore structures. This provides a crucial basis for understanding the heterogeneity of shale reservoirs [14,15,16,17]. The fractal dimension, as a key parameter reflecting the geometry and spatial distribution characteristics of complex pore systems, offers unique advantages in revealing the evolution patterns and heterogeneity of shale pore structures. It has been widely applied in multi-scale analyses of reservoir microstructures [18,19,20,21]. Existing studies on pore heterogeneity have primarily focused on the controlling effects of temperature and material composition [22,23,24]. However, the current understanding of the dynamic evolution of pore heterogeneity in overmature shales under decompression conditions remains insufficient. For instance, Xiang et al. [25] conducted a comparative study of overmature shale samples under different structural units and burial depth conditions. They found that tectonic uplift and erosion (i.e., depressurization) led to pore collapse and closure, significantly influencing the evolution of shale reservoir porosity. In contrast, Gou et al. [26] used the fluid inclusion homogenization temperature analysis method to study the effect of strata uplift. They proposed that strong tectonic uplift and the accompanying rapid depressurization might promote the rapid opening of shale fractures, thereby improving the storage and permeability of shale reservoirs. Although the above research findings appear contradictory, they highlight the significant impact of the depressurization process on the complexity of the dynamic evolution mechanism of overmature shale pores, further emphasizing the need for in-depth research in this field.

Unlike traditional shale pore evolution studies, the innovation of this research lies in excluding the influence of non-pressure factors on pore heterogeneity evolution and, for the first time, revealing the intrinsic connection between pore heterogeneity and pore rebound recovery. The shale samples used in this study were obtained through shale creep deformation experiments and are all freshly extracted outcrop samples, ensuring identical initial pore structure and organic geochemical features before the experiment. Therefore, changes in pore structure before and after the creep experiment can be attributed to adjustments in the pore rebound recovery process. Additionally, this study quantitatively describes the dynamic evolution process of pore system heterogeneity and spatial distribution in shale under tectonic uplift, based on multifractal theory. This theoretical framework not only reveals the regulatory mechanism of the last tectonic uplift on pore structure but also provides scientific evidence for understanding shale pore structure evolution under tectonic stress field influence. The research findings provide theoretical support for shale gas reservoir characteristics and recoverability assessments. Moreover, the revelation of pore structure heterogeneity under tectonic uplift helps guide the optimization of fracturing technology and fracture network design, thus having significant application value in improving shale gas productivity and development efficiency.

In order to thoroughly examine how tectonic uplift affects the heterogeneity of the pore structure of Longmaxi shale in the Sichuan Basin, this study used a high-pressure geotechnical triaxial testing equipment to perform compression recovery under various confining pressure circumstances, depending on the physical properties of Longmaxi shale. In combination with the FE-SEM, MIP, LN₂GA, and LCO₂GA experiments, this study revealed the evolutionary patterns of pore heterogeneity in Longmaxi shale under the influence of the last tectonic uplift from the perspective of multifractal theory. This research is of great significance in revealing how late-stage tectonic uplift activities affect the dynamic changes in the heterogeneity of shale pore structures.

2. Regional Geological Background

The Sichuan Basin has experienced multiple stages of tectonic activity and reworking since the Paleozoic, including the passive continental margin phase, formed by differential subsidence from the Ediacaran to the Middle Triassic; the foreland basin phase, formed by compressional forces after the Late Triassic; and the strong uplift phase, following the Cenozoic [27,28,29,30]. Influenced by Cenozoic uplift, the Longmaxi Formation has experienced overall uplift, resulting in a relatively shallow burial depth today. There are two main portions to the Longmaxi Formation’s layers. The lower section, Long I, includes siliceous shale and black carbonaceous shale that is rich in organic matter, distinguished by a thickness of between 30 and 120 m and a high quantity of organic materials. The upper section, Long II, is composed of gray or yellow-green shale interbedded with sandstone or mudstone and has a lower content of graptolite. Based on the contour map of the organic-rich shale thickness in the Longmaxi Formation in the Upper Yangtze region (Figure 1), compiled by previous researchers, the Longmaxi shale is widely distributed and has considerable thickness. Overall, it extends outward from the two central high-value areas: South Sichuan, Luzhou, and East Sichuan, Shizhu. In the vicinity of these high-value areas, black shale is more than 100 m thick, providing a material foundation for shale gas enrichment and accumulation.

3. Sample Information and Experimental Methods

3.1. Samples and Experimental Plan

Three sizable, recently formed outcrop samples from the Longmaxi Formation were gathered for this investigation from the eastern and southern Sichuan Basin (Figure 1). The specific locations were as follows: an open stone pile site at the Dafengao Tunnel in Shizhu County, Chongqing (East Chongqing), a profile at Tianba in Wuxi County, Chongqing (situated in the low-steep fold belt of East Chongqing, within a tectonically stable area), and an open quarry at Shuanghe Town, Changning County, Yibin City (South Sichuan, located in the high-steep fold belt, also a tectonically stable area). Due to tunnel expansion and quarry excavation, numerous intact and fresh shale samples were gathered from both sites. (Figure 1). The shale samples collected for this study were all from the LM 1 biozone of the Lower Silurian Longmaxi Formation. The selected samples underwent total organic carbon (TOC) measurement, X-ray diffraction (XRD) mineral analysis, laser Raman spectroscopy (Raman), FE-SEM, LN₂GA, LCO₂GA, and MIP testing to analyze the geochemical features, mineral features, and the samples’ pore structure (Figure 2).

This study aimed to identify the patterns of pore heterogeneity evolution at various sizes in shale as a result of the last tectonic uplift. First, a high-pressure geotechnical triaxial testing system was employed to perform compression–recovery tests on shale under varying confining pressure conditions. MIP, LN₂GA, and LCO₂GA experiments, as well as argon ion beam polishing followed by scanning electron microscopy observations, were employed. The pore structure at different scales in the creep-deformed shale samples was quantitatively characterized. Additionally, the evolution patterns of the shale pore structure were investigated using multifractal theory, revealing the heterogeneity evolution of pores in the Longmaxi Formation shale under the influence of the last tectonic uplift.

3.2. Experimental Methods

3.2.1. High-Pressure Testing System

This study utilized the high-pressure geotechnical triaxial testing system (GDS-DYNTTS) from the School of Resources and Earth Sciences at China University of Mining and Technology. Triaxial creep experiments on shale were performed under various confining pressure conditions. To maintain the same initial pore structure in the samples, which is essential for studying the heterogeneity and dynamic spatial distribution changes of the shale pore system under tectonic uplift, a low-speed, dry, diamond-wire cutting method was employed to prepare 50 × 100 mm standard cylindrical shale core samples from the same fresh outcrop. The samples were grouped into univariate control sets. The GDS-DYNTTS system operates under temperature conditions ranging from −20 °C to 800 °C, confining pressures from 0 to 30 MPa, and axial stress conditions from 0 to 1.6 GPa. The shale triaxial creep experiment comprises three main stages: the synchronous pre-loading confining pressure stage (simulating burial) at a loading rate of 5000 kPa/h, the confining pressure holding stage (simulating underground storage) with a creep duration of 72 h, and the rapid unloading confining pressure stage. This setup effectively simulates the in-situ conditions of the strata.

3.2.2. Geochemical Analyzers

This study determined the total organic carbon (TOC) content using the HCS-0A high-frequency infrared carbon–sulfur analyzer (Shanghai Baoying Optoelectronic Technology Co., Ltd., Shanghai, China), following the China Petroleum and Natural Gas Industry Standard GB/T19145-2003 [31]. Full-rock analysis was conducted using the Rigaku Ultima IV X-ray diffractometer (Rigaku Company, Tokyo, Japan) at the Jiangsu Institute of Geology and Mineral Resources, according to the National Standard SY/T5163-2018 [32], to determine the content of inorganic minerals such as clay minerals, quartz, and pyrite. The organic matter aggregation points in the shale samples were analyzed using the Bruker SENTERRA laser confocal Raman spectrometer (Bruker Corporation, Billerica, MA, USA) at the Modern Analysis and Testing Center of China University of Mining and Technology. The organic matter maturity of the different shale samples was calculated based on the equivalent vitrinite reflectance formula.

3.2.3. Field Emission Scanning Electron Microscopy (FE-SEM) Experiment

The FE-SEM experiment was carried out using the HITACHI SU8010 model from Hitachi Corporation (Tokyo, Japan). This device has an acceleration voltage range of 0.1 to 30 kV and a magnification range from 30 to 200,000 times, making it suitable for identifying macropores larger than 5 nm. Furthermore, the integrated energy dispersive spectrometer allows for mineral type analysis. The experimental procedure is as follows: First, a surface of the shale samples, both before and after deformation, is cut. Then, the surface is polished using argon ion polishing technology to achieve a smooth, flat finish. To improve the sample’s conductivity, a gold coating is applied to the polished surface. Finally, a scanning electron microscope is employed to observe and analyze the pore morphology of the sample.

3.3. Multifractal Model

Compared to a single fractal, the multifractal model uses continuous functions to represent multifractal characteristics. The multifractal features of the samples’ complete pore-size distribution curve were calculated and analyzed in this study using the box-counting method with the following calculation formula [33,34]:

A logarithmic transformation was applied to the measurement interval I = [0.2, 2000], converting it into a dimensionless interval I′ = [0, 4], consisting of 100 equidistant subintervals.

$$y_i=\mathrm{l}\mathrm{g}({\displaystyle \frac{{\phi }_i}{{\phi }_1}}),i=1,2,3\dots$$

(1)

In the equation, $y_i$ is the dimensionless value of the transformed interval, ${\phi }_{1 }$ = 0.2 nm; ${\phi }_i$ is the pore diameter at the experimental measurement point, in nm.

In the interval I′, there are $H\left(\epsilon \right)$ = 2^k subintervals of size ε = 4 × 2^−k, and each subinterval must contain at least one measurement point. Therefore, the value of k in this study falls between 1 and 4.

$$P_i(\epsilon )={\displaystyle \frac{N_i\left(\epsilon \right)}{N_T}}$$

(2)

$P_i\left(\epsilon \right)$ is the pore volume probability (percentage content) for each subinterval, dimensionless; $N_i\left(\epsilon \right)$ is the pore volume for each subinterval, in cm³/g; $N_T$ is the sample’s total pore volume, in cm³/g.

The q-th moment weighted sum of the pore volume probability $P_i\left(\epsilon \right)$ for each interval is denoted as $u(q,\epsilon )$.

$$u\left(q,\epsilon \right)={\displaystyle \sum _{i=1}^{H\left(\epsilon \right)}}{p}_i^q$$

(3)

The relationship between $u(q,\epsilon )$ and $\epsilon$ is as follows:

$$u(q,\epsilon )\propto {\epsilon }^{\tau \left(q\right)}$$

(4)

$$\tau \left(q\right)=\underset{\epsilon \to 0}{\lim }{\displaystyle \frac{\lg u(q,\epsilon )}{\lg \epsilon }}$$

(5)

where τ(q) is the q-th order mass exponent, obtained by applying least squares fitting to the double logarithmic curve of $\lg u(q,\epsilon )$–$\mathit{lg}\epsilon$. The slope of this curve is τ(q). The generalized multifractal dimension spectrum D(q) and τ(q) have the following relationship:

$$D\left(q\right)={\displaystyle \frac{\tau \left(q\right)}{q-1}},q\ne 1$$

(6)

$$\tau D\left(q\right)=\underset{\epsilon \to 0}{\mathrm{l}\mathrm{i}\mathrm{m}}{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^{2^k}}\left[p_i\left(\epsilon \right)lg{p}_i\left(\epsilon \right)\right]}{lg\epsilon }},q=1$$

(7)

When q = 0, 1 and 2, they correspond to the capacity dimension D(0), the information entropy dimension D(1), and the correlation dimension D(2), respectively.

The relationship between the multifractal singularity exponent α(q) and τ(q) is as follows:

$$\alpha \left(q\right)={\displaystyle \frac{d\tau \left(q\right)}{dq}}$$

(8)

The calculation formula for the multifractal spectrum function $f\left[\alpha \left(q\right)\right]$ is as follows:

$$f\left[\alpha \left(q\right)\right]=\mathrm{q}\alpha \left(q\right)-\tau \left(q\right)$$

(9)

Using Equations (6)–(9), the multifractal generalized dimension spectrum (D(q)), multifractal singularity exponent (α(q)), and multifractal spectrum function (f[α(q)]) of the sample’s entire pore size distribution were computed within the range of −10 ≤ q ≤ 10, with a step size of 1 [35]. A step size of 1 represents a compromise between efficiency, by reducing computational load, and maintaining adequate resolution. The range of −10 ≤ q ≤ 10 is chosen to prevent extreme q values from amplifying computational errors, although expanding the range could make certain features more pronounced.

4. Results and Discussion

4.1. Physical Properties of Shale Reservoirs

The experimental results indicate significant differences in TOC, organic matter equivalent vitrinite reflectance (VRequ), and mineral content among Longmaxi shale samples from the Sichuan Basin. The TOC content of the shale accurately reflects the abundance of organic matter in the shale. The mean TOC content of the shale samples is 5.62%. According to the organic matter classification and evaluation standards for source rocks, shales with a TOC > 2% are considered organic-rich. All Longmaxi shale samples selected for this study are organic-rich shales. The Longmaxi shale contains minerals such as quartz, feldspar, clay, carbonate, and pyrite, according to the XRD analysis. Quartz, feldspar, and clay are present in all three samples. The average quartz content in the samples is 57.6%, making it the primary mineral component. The average feldspar content is 6.6%. The average clay mineral content is 24.5% (

Table 1. Physical property parameters of Longmaxi shale samples.

Sample	TOC (%)	Average VRequ (%)	vG-vD	Content of Inorganic Minerals %
				Quartz	Feldspar	Clay	Carbonate	Pyrite
TB-1	7.8	3.04	265.35	79.2	4.1	16.7	0	0
SH-1	2.79	3.53	273.68	27.7	9	40.1	22.6	0
DFA-1	6.29	3.49	274.42	66.0	6.7	16.6	5.6	5.1

), and clay minerals can influence the porosity and permeability of shale. The TB-1 sample lacks carbonate minerals, suggesting a different sedimentary environment or diagenetic history compared to the other samples. Pyrite is present only in the DFA-1 sample, likely indicating an anoxic depositional environment, as pyrite typically forms under such conditions. These variations in mineral composition may reflect different sedimentary environments within the study area, which, in turn, influence the reservoir characteristics and source rock potential of the shale.

4.2. Pore Structure

4.2.1. Pore Types

(1)

Organic Matter Pores

In this study, scanning electron microscopy observations of shale samples under different pressure gradients revealed that the organic matter in the samples can be roughly divided into two categories: organic matter occurring between rigid mineral particles and organic matter occurring within clay minerals. The first type of organic matter is primarily distributed between rigid minerals such as quartz, feldspar, and pyrite (Figure 3a,c–f,h,i). Rigid minerals such as feldspar and quartz have a high compressive strength, which allows them to withstand formation pressure and create a robust, rigid structure; the organic matter pores between these minerals are primarily sponge-like, with pore shapes that are elliptical, nearly circular, or slit-like. The pore sizes are relatively uniform, with organic matter pore diameters mostly less than one hundred nanometers (Figure 3a,c–f). The second type of organic matter combines with clay minerals to form “organic-clay composites.” Due to the high plasticity and weak compressive strength of clay minerals, the organic matter pores tend to be slit-like or irregular in shape, with a large variation in pore sizes, ranging from tens of nanometers to over one hundred nanometers (Figure 3b,e,g) [36,37].

(2)

Intergranular Pores and Intragranular Pores

Scanning electron microscopy observations reveal intergranular and intragranular pores developed between different minerals and within the minerals of shale. When quartz, feldspar, and clay mineral particles come into touch with one another, intergranular pores frequently form, primarily due to the mutual support between mineral particles, and they are mostly primary pores (Figure 4a–e,g–h). The pore shapes of intergranular pores are diverse, including irregular polygonal, wedge-shaped, elongated, angular, and slit-like. Significant differences exist in the morphology and size of intergranular pores developed between rigid minerals and those developed between plastic minerals. Intergranular pores between rigid minerals are more irregular, with pore sizes reaching several hundred nanometers (Figure 4a,d,g) [38], while those between clay minerals have more uniform shapes and sizes, with pore dimensions mostly in the tens of nanometers. Pressure also affects the size of intergranular pores. At 20 MPa, intergranular pores are mainly in the range of tens of nanometers, with a few reaching several hundred nanometers (Figure 4a–c). In contrast, pore sizes of shale samples at 10 MPa and 0 MPa range from a few micrometers to tens of nanometers (Figure 4d–e,g–h). The intergranular pores are interconnected, easily forming locally dense pore networks that provide channels and space for shale gas storage and diffusion.

Intragranular pores primarily form within minerals such as quartz and pyrite, with quartz dissolution pores being the most common, followed by mold pores, formed after the complete dissolution of pyrite. The shapes of these pores are primarily polygonal, circular, and elliptical (Figure 4f,i). The size variation of these pores is not significant, with the majority of pores having sizes between a few micrometers and tens of nanometers. Compared to intergranular pores, intragranular pores have poorer connectivity, mostly forming isolated pores that are not favorable for shale gas migration and development [36].

(3)

Characteristics of Microfracture Development

Scanning electron microscopy observations revealed numerous microfractures in the samples. These microfractures fall into two general categories: intercrystalline fractures (Figure 5g,i) and intragranular fractures (Figure 5a–i). Intercrystalline fractures are mostly serrated, with angular edges, characterized by longer fracture lengths and wider fracture widths compared to intragranular microfractures. It is speculated that differences in the physical properties of the minerals on either side of the fracture cause varying degrees of deformation under stress, leading to easier rupture and the formation of wider and longer fractures. Intragranular fractures include microfractures generated by the compression and rupture of brittle minerals, microfractures formed by the dissolution of brittle minerals, and interlayer microfractures in clay minerals. Among them, microfractures generated by the compression and rupture of brittle minerals are characterized by long fracture lengths (tens of micrometers) and narrow fracture widths; these fractures are mostly long, straight, and linear. The interlayer microfractures in clay minerals are mostly oval or irregular in shape, with short fracture lengths (a few micrometers) and fracture widths primarily concentrated in the tens of nanometers. Observations showed that for the same series of shale samples under different triaxial creep pressure conditions, as pressure decreased, the fracture length changed little, the fracture width gradually increased, and the microfractures became more developed, with stronger connectivity. It is speculated that, with tectonic uplift and the release of pressure in the formation, the original pressure balance of tectonic microfractures is disrupted, resulting in internal pressure release that causes the microfractures to expand and form a new pressure balance (Figure 5j–k). Additionally, shale gas seepage and storage are significantly aided by microfractures, and their development is also beneficial for shale gas fracturing.

4.2.2. Pore-Size Distribution Patterns

The principles of different testing methods vary significantly, leading to considerable differences in the accuracy of the pore size ranges they measure and characterize. Previous studies have shown that MIP, LN2GA, and LCO2GA exhibit higher detection accuracy for macropores, mesopores, and micropores, respectively. In this study, to accurately and realistically reflect and describe the shale’s full-scale pore structure, the results of MIP, LN2GA, and LCO2GA were integrated. This comprehensive approach established the distribution of pores at full scale curves for different shale series under varying triaxial creep pressures (Figure 6). The joint characterization results show that at 2 nm (the micro-mesopore boundary), the pore-size curve shows a smooth connection, while at 50 nm (the meso-macropore boundary), a distinct discontinuity appears in the pore-size curve. This may be due to inherent differences between high-pressure mercury injection and nitrogen adsorption tests, resulting in a significant difference in the curve at the meso-macropore boundary [38].

According to the joint characterization graph (Figure 6), the changes in pore diameter and stage pore volume across different shale series exhibit similarities, with the change curves showing three peaks (two highs and one low). The pore sizes fall within the ranges of 0.50–0.95 nm, 2.45–4.00 nm, and 10.00–50.00 nm. In the TB and SH series samples (Figure 6a–c), the number of micropores decreases as pressure decreases, while the number of mesopores and macropores gradually increases. As the formation undergoes uplift, micropores converted by pressure gradually rebound into mesopores and macropores. In the DFA series samples (Figure 6g–i), the number of micropores first decreases sharply and then slowly increases as pressure decreases, forming a “U”-shaped curve. The number of mesopores and macropores first increases and then remains relatively unchanged.

Based on MIP, LN₂GA, LCO₂GA, and other experiments, the structural parameters of shale pores before and after deformation were determined (

Table 2. Pore structure parameters of shale under different triaxial pressure gradients.

Sample Number	Pressure	High-Pressure Mercury Injection Experiment (50–20,000 nm)		N2 Adsorption Experiment (2–50 nm)		CO2 Adsorption Experiment (0–2 nm)
		Macropore Volume (cm3/g)	Macroporous Specific Surface Area (m2/g)	Mesoporous Volume (cm3/g)	Mesoporous Specific Surface Area (m2/g)	Micropore Volume (cm3/g)	Specific Surface Area of Micropores (m2/g)
TB-1	20 MPa	0.00150	0.01740	0.0247	13.052	0.00950	32.49
	10 MPa	0.00211	0.04462	0.0212	8.8348	0.00731	27.07
	0 MPa	0.00191	0.03856	0.0239	11.761	0.01091	36.13
SH-1	20 MPa	0.00254	0.04804	0.0113	6.4531	0.00722	19.26
	10 MPa	0.00186	0.03669	0.0107	6.1393	0.00675	18.37
	0 MPa	0.00165	0.02577	0.0115	6.6592	0.00517	14.24
DFA-1	20 MPa	0.00164	0.01293	0.0104	5.7819	0.00726	22.38
	10 MPa	0.00198	0.02279	0.0156	9.611	0.00469	14.60
	0 MPa	0.00116	0.00767	0.0146	8.603	0.01286	37.99

). In terms of total pore volume contribution, mesopores dominate, contributing 51.02% to 70.03%, with an average of 61.14%. Macropores contribute the least, accounting for 4.05% to 12.06%, with an average of 7.61% (Figure 7). The contribution of different pore types to the total specific surface area also varies significantly. Micropores contribute the most to the total pore specific surface area, averaging 73.43%, while macropores contribute the least, with an average of only 0.10% (Figure 7). Previous studies and experimental results on the Longmaxi Formation and its adjacent strata have consistently shown that the pore structure of this shale type exhibits distinct distribution characteristics: mesopores usually account for the largest share of the total pore volume, often exceeding 50%, whereas micropores dominate the total specific surface area, generally contributing no less than 80% [8,39]. Overall, the proportion of total mesopore volume and micropore specific surface area in the samples of this study demonstrates strong consistency with previous research results, further supporting the conclusions on pore structure characteristics. In summary, mesopores control the total pore volume of shale, whereas micropores control its total specific surface area. Micropores and mesopores serve as the primary sites for shale gas storage [16,40].

4.3. Computational and Heterogeneity Analysis of Multifractals

4.3.1. Calculation of Multifractal Parameters

Figure 8 presents the double logarithmic plot of the partition function versus measurement scale for three series of shale samples under different creep pressures. The partition function spectra of the three shale sample series exhibit strong linear correlations, with R² values between 0.892 and 0.999. This suggests that there are distinct multifractal features in the samples’ pore size distribution [41,42,43].

The corresponding parameters are calculated by Formulas (6) to (9), as shown in

Table 3. Multifractal singular spectral parameters and generalized dimension spectral parameters of nano-pore size in shale samples.

Sample	Pressure	α0	α0–α10	α−10–α0	α−10–α10	Rd	Hurst	D0	D1	D2	D0–D10	D−10–D0	D−10–D10
TB-1	20 MPa	1.362	0.732	0.712	1.443	0.020	0.911	1	0.866	0.821	0.320	0.898	1.218
	10 MPa	1.540	1.056	1.026	2.082	0.029	0.819	1	0.696	0.639	0.477	1.337	1.814
	0 MPa	1.234	0.603	0.645	1.248	−0.043	0.907	1	0.865	0.814	0.323	0.712	1.035
SH-1	20 MPa	1.046	0.194	0.204	0.398	−0.009	0.974	1	0.969	0.947	0.118	0.178	0.295
	10 MPa	1.116	0.254	0.563	0.817	−0.308	0.975	1	0.970	0.949	0.112	0.537	0.649
	0 MPa	1.391	0.768	0.996	1.764	−0.227	0.875	1	0.784	0.750	0.341	1.183	1.523
DFA-1	20 MPa	1.252	0.453	0.742	1.195	−0.289	0.961	1	0.943	0.922	0.160	0.814	0.974
	10 MPa	1.041	0.313	0.165	0.477	0.148	0.946	1	0.940	0.891	0.233	0.148	0.381
	0 MPa	1.452	0.702	0.831	1.533	−0.128	0.890	1	0.783	0.780	0.241	1.079	1.319

. It is evident that for the three shale sample series, D₀ > D₁ > D₂, which also indicates that the pore size distribution of the shale samples exhibits multifractal characteristics. The main parameters of the singular spectrum include the singular index (α₀), the width of the singular spectrum (α₋₁₀–α₁₀), the right spectrum width (α₋₁₀–α₀), the left spectrum width (α₀–α₁₀), and the difference between the left and right spectrum widths (R_d). The value of α₀ ranges from 1.041 to 1.540, with an average of 1.270; α₋₁₀-α₁₀ ranges from 0.398 to 2.082, with an average of 1.217; Rd ranges from −0.308 to 0.148, with an average of −0.089 [44]. Hurst, D₀, D₁, D₂, generalized dimension spectrum width (D₋₁₀–D₁₀), right spectrum width (D₋₁₀–D₀) and left spectrum width (D₀–D₁₀) are the primary parameters of the generalized dimension spectrum. Hurst is a key parameter for characterizing pore connectivity [18], with an average value of 0.917; D₋₁₀–D₁₀ ranges from 0.295 to 1.814, with an average of 1.023.

4.3.2. Heterogeneity Analysis of Multifractals

The singularity index (α₀) reflects the concentration of the pore size distribution. The α₀ value of TB-1 (10 MPa) is the largest, indicating large fluctuations in its local distribution, a narrow distribution range, and strong heterogeneity. This suggests that the sample at 10 MPa has a complex pore network with significant pore size variation, which may enhance permeability. The singular spectrum’s α₀–α₁₀ and α₋₁₀–α₀ represent distinct information about the pore size distribution. The pore distribution features of high/low probability density zones are highlighted by α₀–α₁₀ and α₋₁₀–α₀, offering insight into the impact of these regions on reservoir capacity and gas migration pathways. Specifically, pores in high-probability regions are beneficial for gas storage, while pores in low-probability regions favor gas migration. The difference between the left and right spectrum widths, R_d[R_d = (α₀–α₁₀) − (α₋₁₀–α₀)], shows the amount of variation in the singular spectrum distribution center. When R_d > 0, the pore distribution is greatly impacted by the high probability density region; when R_d < 0, the opposite is true. The closer R_d is to 0, the more uniform the pore size distribution in the high/low probability density regions [18,45]. In this study, only TB-1(20 MPa),TB-1(10 MPa), and DFA-1(10 MPa) have R_d > 0, indicating that the pore size distribution of these three samples is dominated by the high-probability region. The R_d value of SH-1(20 MPa) is closest to zero, indicating the most uniform pore size distribution. The larger the value of Δα[Δα = α₋₁₀–α₁₀], the greater the heterogeneity of the pore structure. SH-1(20 MPa) has the lowest Δα, exhibiting the weakest multifractality and heterogeneity, which is consistent with the conclusion from R_d, while TB-1(10 MPa) has the highest Δα, showing the strongest heterogeneity, which is consistent with the conclusion from α₀. Δf [Δf = f (α_min) − f (α_max)] represents the multifractal spectrum’s form features. When Δf > 0, f (α) exhibits a left-hook shape; when Δf < 0, f (α) exhibits a right-hook shape [18]. In this study, only the DFA-1(10 MPa) sample shows a left hook shape, indicating that its high-probability subset dominates (Figure 9).

Hurst[Hurst = (D₂ + 1)/2] is a common expression for the correlation dimension D₂, typically ranging from 0.5 to 1. In this study, all samples have Hurst values greater than 0.8, indicating that the variation in porosity across different pore size intervals exhibits positive autocorrelation. The Hurst value of SH-1(10 MPa) reaches 0.975, indicating excellent pore connectivity. The larger D₀ is, the broader the pore-size distribution range. In this study, D₀ is 1 for all samples. D₁ is the information entropy dimension, where a smaller D₁ indicates a greater fluctuation in the local pore volume distribution and higher pore concentration. The difference between D₀ and D₁ can be used to characterize the local concentration and pore size spacing in the pore size distribution. The smaller the difference, the more uniform the pore size distribution. Among the samples, the D₁ values of the SH-1 and DFA-1 series samples show similar changes with decreasing pressure, which is quite different from the TB-1 series samples. The consistent changes in the first two series of samples may be due to the presence of carbonate minerals. The dissolution pores in the carbonate minerals fracture under compressive stress, and as the pressure decreases, the fractured pores cannot rebound and recover, while other pores expand, ultimately leading to an increase in pore heterogeneity. Among them, the D₁ value of TB-1(10 MPa) is the smallest, at 0.696, indicating that the pore size is concentrated within a narrow range, with strong heterogeneity. This result aligns with the examination of the singular spectrum parameter. D₋₁₀–D₀ can more accurately evaluate the pore structure in low-probability density regions and is generally considered a representative parameter for the heterogeneity of macropores (>50 nm) [46]. D₀–D₁₀ evaluates the pore structure in high probability density regions and is generally considered a representative parameter for the heterogeneity of micropores (0–50 nm). When D₋₁₀–D₀ > D₀–D₁₀, it indicates that the heterogeneity of macropores in the sample is greater than that of micropores. The opposite is true when D₋₁₀–D₀ < D₀–D₁₀. The difference in D₋₁₀–D₁₀ can indicate the uneven distribution characteristics of pores. When D₋₁₀–D₁₀ is small, it suggests a more uniform pore distribution, and the curve of the generalized dimension spectrum is relatively flat. For example, the curve of SH-1(20 MPa) is nearly a straight line, indicating that under high confining pressure, The SH sample’s pore shape is comparatively consistent (Figure 10) [44,47].

4.4. Dynamic Variations in Pore Heterogeneity in Shale

Figure 11 shows significant differences in pore size heterogeneity across different shale series under varying creep pressure gradients. For the TB-1 sample, as pressure decreases, heterogeneity first increases and then decreases, while pore connectivity initially decreases and subsequently increases. The analysis suggests that, under high pressure, the organic matter pores in the TB-1 sample are compressed, and the pores between quartz minerals are supported and protected, leading to minimal deformation. As pressure decreases, microfractures open, and the pores gradually begin to rebound. However, due to the presence of creep pressure, the rebound time, rebound rate, and extent of rebound vary, causing pore morphology to become more diverse and complex, which results in an increase in the fractal dimension of the pores. Secondly, during the rebound of clay minerals, expansion and migration block the pore throats or microfractures, leading to increased heterogeneity and decreased connectivity. As pressure decreases further, the degree of pore rebound reaches its maximum, and the originally compressed pores expand and recover. Shale pores and microfractures connect with each other, forming a well-connected network of microfractures; this causes pore heterogeneity to diminish and connectivity to increase (Figure 12a–c). For the SH-1 samples, as pressure decreases, heterogeneity continuously increases, while pore connectivity almost consistently decreases. SH-1 contains a significant amount of carbonate and clay minerals. Under high-pressure creep conditions, intergranular pores formed by the minerals are compressed and fractured, resulting in pores with similar morphology and uniform size, thereby leading to lower pore structure heterogeneity. As creep pressure decreases, the crushed intergranular pores no longer rebound and recover, while other pores gradually rebound and expand under reduced pressure conditions. Additionally, because the shale samples had a high concentration of clay minerals, the rearrangement of mineral particles increases the roughness of pore edges, causing a rise in the fractal dimension, an increase in the tortuosity of pore flow paths, and possibly the formation of heterogeneous flow barriers locally, thus weakening connectivity (Figure 12d–f). For the DFA-1 samples, heterogeneity first decreases and then increases as pressure decreases, while pore connectivity continuously decreases. DFA-1 contains a significant amount of brittle minerals. As pressure decreases, the pores in brittle minerals rebound less due to support protection, while the rebound of organic matter pores is more significant. During this process, two types of pores with similar sizes emerge, leading to a decrease in heterogeneity. As pressure continues to decrease, the fractured mineral pores cannot rebound and recover, and the difference in morphology between the highly rebounded pores becomes greater, resulting in increased heterogeneity. Additionally, the debris from the fractured intergranular pore walls, along with clay, fills the pore throats and fractures, reducing pore connectivity (Figure 12g–i). This indicates that under the same creep pressure variation conditions, Longmaxi shale with different mineral compositions exhibits distinct pore rebound behaviors [30,36].

4.5. Influencing Factors of Dynamic Changes in Pore Heterogeneity

As mentioned earlier, different shale series exhibit significant differences in pore size heterogeneity under varying creep pressure gradients. To identify the main controlling factors, the following correlation analysis diagrams (Figure 13 and Figure 14) were created. In this study, Δα was used as an indicator of shale pore heterogeneity. According to the correlation diagrams, Δαat 20 MPa shows a strong positive correlation with quartz and TOC. As pressure decreases, the correlation between the two first decreases and then increases. In contrast, clay minerals and feldspar minerals exhibit a strong negative correlation (Figure 13a–d). This indicates that under higher pressures, the amount of clay and quartz minerals, as well as the TOC content, primarily regulate the heterogeneity of pore size. As pressure decreases, the influence of TOC content and the content of quartz and clay minerals on pore size heterogeneity first decreases. When TOC content is high, organic matter is distributed at various microscopic locations, including filling pores between quartz mineral particles, occurring between quartz and clay minerals, forming organic–clay composites with clay, and forming organic matter aggregates. When the shale is under 20 MPa pressure, the organic matter pores between quartz and feldspar mineral particles, supported and protected by quartz, experience less deformation, while organic matter pores between plastic minerals undergo more deformation, leading to greater pore heterogeneity in the shale. When there is a large concentration of quartz minerals, the probability of mutual compression between brittle minerals increases, potentially forming new microfractures and pores, which leads to an increase in shale pore heterogeneity. Therefore, under higher pressures, pore size heterogeneity is primarily controlled by TOC and quartz mineral content. As the formation undergoes uplift and pressure decreases, the shale pores begin to rebound. Due to the different pore types and their locations, the extent of rebound varies. Pores between plastic minerals rebound more quickly, while pores between brittle minerals rebound more slowly due to the supporting and protective effect. This is primarily related to pore type and location, with the control exerted by TOC and quartz mineral content on pore size heterogeneity weakening. As pressure continues to decrease, the control exerted by TOC content and the content of quartz and feldspar minerals on pore size heterogeneity strengthens. In the later stages of pressure release, microfractures in organic matter and quartz minerals continue to expand, further intensifying pore heterogeneity. The enhanced control exerted by feldspar is primarily due to its plastic deformation characteristics—pores that have been fractured cannot rebound, creating significant morphological differences between them and the pores that have rebounded, thus amplifying heterogeneity [30,36].

Hurst can be used to specify the connectivity between pore networks. From Figure 14a–d, it can be seen that at 0 MPa, the correlation between Hurst and the TOC content, quartz, and feldspar content is strong, with the highest correlation being with feldspar, reaching 1. As pressure increases, the correlation weakens, but the correlation with feldspar remains high. At 20 MPa, natural microfractures close, and the organic matter pores and intergranular pores become the main factors influencing pore connectivity. Under high pressure, organic matter pores are compressed and reorganized, increasing their tortuosity. Although intergranular pores benefit from the support and protection of quartz minerals, adjacent clay minerals may fill the pore throats. Therefore, pore connectivity is influenced by a combination of different minerals, resulting in a lower correlation. As the formation uplifts and pressure decreases, microfractures within the quartz minerals re-expand and extend, organic matter pores begin to rebound and return to their original state, and connectivity changes. This process is primarily controlled by TOC and quartz, which is why the correlation is high. The correlation between feldspar content and pore connectivity remains strong, likely due to the presence of numerous dissolution pores in feldspar. Under high pressure, the pore walls of adjacent dissolution pores fracture, allowing isolated pores to connect. As pressure decreases, the microfractures within feldspar expand, further connecting the pores and maintaining a high correlation.

In summary, under high-pressure conditions, TOC and quartz content play a dominant role in pore heterogeneity, and with decreasing pressure, their influence initially weakens before strengthening again. Regarding pore connectivity, decreasing pressure highlights the controlling effects of TOC, quartz, and feldspar content, with feldspar content exhibiting a significant—often decisive—impact on shale pore connectivity. This effect ultimately depends on the mineral composition, diagenetic evolution history, and the scale and extent of feldspar dissolution. It should be noted that these conclusions primarily apply to overmature marine shales similar to the Longmaxi Formation, and caution is warranted when extending them to other lithological types or geological settings.

According to the correlation heatmap of the 11 multifractal dimension parameters (Figure 15), the higher the correlation between two sets of parameters, the more similar they are in characterizing pore size heterogeneity [18]. Except for the weak correlation between R_d and other parameters, the multifractal dimension parameters exhibit strong correlations among themselves. α₀ and D₁ exhibit a strong negative correlation: larger α₀ values and smaller D₁ values indicate stronger pore heterogeneity, consistent with the previous conclusion. The correlation between D₋₁₀–D₀ and D₋₁₀–D₁₀ is higher than that between D₀–D₁₀ and D₋₁₀–D₁₀, indicating that pore-size distribution unevenness is primarily driven by the heterogeneity of large pores. Large pores are typically connected to network pores such as microfractures, providing low-resistance flow channels for shale gas. However, because large pores have low specific surface areas, their gas storage capacity is limited. Therefore, the magnitude of these correlations can indirectly reflect the shale’s gas storage and permeability capacity. In practical production, this implies that early gas production may be dominated by seepage from large pores and fractures, whereas maintaining production in later stages requires a continuous gas supply from micropores and mesopores. This finding provides direct reference value for fracturing design and productivity prediction.

5. Conclusions

This study conducted compression–recovery tests of shale under different confining pressure conditions using triaxial creep experiments. Using scanning electron microscopy observations, pore structure joint characterization, and multifractal dimension analysis, the changes in the pores of different series of Longmaxi shale samples under pressure were systematically studied. The following conclusions were drawn:

(1)

The pore types in Longmaxi shale mainly include organic matter pores, microfractures, intergranular pores, and intragranular pores. The heterogeneity of the pores is significantly controlled by the mechanical properties of the minerals in which they occur: organic matter pores occurring between rigid minerals can effectively resist tectonic stress and are homogeneous, while organic matter pores between plastic minerals have weaker compressive strength and significant size variation. The size distribution of intergranular pores is the opposite of that of organic matter pores. Intragranular pores are mainly quartz dissolution pores, and their morphology and size are relatively uniform. Microfractures within mineral particles typically appear narrow and long, while intercrystalline fractures are characterized by wide and long dimensions.

(2)

The pores in Longmaxi shale mainly consist of mesopores and micropores, with mesopores dominating the total pore volume and micropores controlling the total specific surface area. Together, they form the storage space in Longmaxi shale.

(3)

The pores in Longmaxi shale exhibit distinct multifractal characteristics, and the singular index(α₀) and other 11 multifractal dimension parameters can reflect the heterogeneity of shale pores from different perspectives. Moreover, except for R_d, the remaining 10 parameters show good correlations with each other.

(4)

The dynamic changes in pore heterogeneity are mainly controlled by the mineral composition. Under the same creep pressure variation conditions, there are significant differences in the rebound behavior of pores in Longmaxi shale with different mineral compositions. Under high-pressure conditions, TOC content and quartz mineral content have a dominant influence on pore heterogeneity, and their control ability decreases first and then increases as pressure decreases. As pressure decreases, the control of TOC, quartz, and feldspar content on pore connectivity becomes evident, with feldspar content having a decisive effect on the connectivity of shale pores.