The physical properties of shale oil reservoirs under overburden pressure are of great significance for reservoir prediction and evaluation during exploration and development. Based on core, thin section, and SEM observations, as well as test data such as XRD, TOC, and porosity and permeability under pressure conditions, this study systematically analyzes the variation of physical properties of different lithofacies shales in the Jiyang depression and the influence of rock fabric on the physical variation under pressure. The porosity and permeability of shale samples significantly decrease under pressure. According to the phased reduction in porosity and permeability, the pressurization process is divided into three pressure stages: low pressure (<8 MPa), medium pressure (8–15 MPa), and high pressure (>15 MPa). The reduction of porosity is fastest in the low-pressure stage and slowest in the medium-pressure stage. The reduction of permeability is fastest in the low-pressure stage and the slowest in the high-pressure stage. The rock fabric has a significant impact on porosity and permeability under pressure conditions. The permeability of laminated shale and bedded shale is higher than that of massive shale under pressure, and the permeability loss rate is lower than that of massive shales. Especially under lower pressure, the difference can be 10–20 times. In addition, the reduction rate of porosity and permeability under pressure is negatively correlated with felsic minerals content, which is positively correlated with carbonate minerals content and clay minerals content. The contribution of clay minerals to the porosity reduction rate is dominant, followed by carbonate minerals. The contribution of carbonate minerals to the permeability reduction rate is dominant, followed by clay minerals. The TOC content has no significant impact on the porosity and permeability of shales under pressure in the study due to the low maturity.

With the change in global energy structure, shale oil and gas has become the core growth point of China’s oil and gas resources [1-4]. In the past decade, a series of important progresses have been made in the exploration and development of shale oil and gas in China, including breakthroughs in the exploration of shale oil in Junggar Basin, Ordos Basin, Jianghan Basin, Songliao Basin, and Bohai Bay Basin [5-8]. However, due to the heterogeneity of shales and the complexity of geological conditions in China, the prediction and evaluation of shale oil reservoirs still face many challenges [3, 9, 10].

Many studies have shown that rock fabric, such as laminated structure and mineral composition, has a significant influence on the pore development and physical properties of shale oil reservoirs [10-14]. However, most of these studies were conducted under unpressurized conditions, and there are some errors with the formation conditions, which affect the prediction and evaluation of shale oil desserts. To recover the real physical parameters under formation conditions, some scholars carried out pressure experiments and found that both porosity and permeability of shale decreased gradually with the increase of effective pressure, and proposed exponential function, binomial, and other functional models to describe the change of porosity and permeability with pressure during pressurization [15-22]. However, for individual shale samples, the differences in porosity and permeability between different samples under the same pressure conditions are large [17-19], and the reasons for these differences are still unclear and need to be further explored. In this study, the Es3x-Es4s shales from the Jiyang depression were selected. Through petrology, mineralogy, porosity and permeability experiments under effective pressure, and FE-SEM observation, the physical characteristics of the shale reservoirs under effective pressure and the influence of rock fabric on porosity and permeability were discussed to provide a basis for the prediction and evaluation of the shale oil desserts in the Paleocene shale of the Jiyang depression.

2.1. Sample Collection and Processing

The Jiyang depression is located in the southeast of the Bohai Bay Basin, China, with four sub-depressions from south to north, Dongying, Huimin, Zhanhua, and Chezhen (Figure 1(a)) [23]. It has made great breakthroughs in multiple layers and types of shale oil in Dongying, Zhanhua, and other sags during the past ten years of exploration, showing a good exploration prospect of shale oil in Jiyang depression [24-26]. Currently, Es4s, Es3x, and Es1 are the main exploration intervals for shale oil in Jiyang depression (Figure 1(b)), characterized by high carbonate content, with an average content of more than 50% [23, 27, 28]. In addition, the laminae are well developed with alternating light laminae and dark laminae [23, 29, 30].

As the main exploration intervals for shale oil in Jiyang depression, there are many industrial oil flow wells and sampling wells in Es4s-Es3x. The samples in this study were collected from Well BYP5, F201, and FYP1 (Figure 1(a)), and the basic information is shown in Table 1.

Before experiments, the samples were treated in different ways as illustrated in Figure 2. First, a plug sample (diameter of 25 mm and length of 60 mm) was drilled parallel to the bedding from the core sample. Then, a 2 cm high micro plug was cut from one side of the plug, which was used for thin section and scanning electron microscopy observations. The remaining plug sample was used for the measurement of porosity and permeability under effective pressure. After completing the measurement of porosity and permeability, the plug sample was crushed for TOC and mineral composition analysis.

2.2. Experimental Methods and Instruments

2.2.1. Microscopy and Scanning Electron Microscopy Observations

A Zeiss microscope was used to observe the thin sections of rocks with a thickness of 30 μm to clarify the development characteristics and mineral distribution of the laminae. A high-resolution field emission scanning electron microscope (Zeiss Sigma 500) was used to observe the morphology, size, and distribution of pores. The surface of the samples (10 × 10 μm) was polished by hand grinding and argon ion polishing (Leica EM 3X) to achieve better image quality.

2.2.2. Organic Petrology and X-ray Diffraction

Vitrinite reflectance (Ro%) measurements were undertaken using a Zeiss microscope equipped with a J&M MSP200 microphotometer. The total organic carbon (TOC) contents were determined using a Vario MICRO cube elemental analyzer. Before testing, the shale samples were ground to less than 200 mesh and reacted with dilute HCL for 72 hours to remove carbonate minerals. The X-ray diffraction (XRD) analysis was conducted using a Dmax IIIa diffractometer with a Cu x-ray tube (40 kV, 30 mA). The separation and XRD tests of clay minerals were carried out according to the Chinese petroleum industry standard (SY/T 5163–2018). The above experiments were carried out in the Key Laboratory of Surficial Geochemistry (KLSG), Ministry of Education, Nanjing University.

2.2.3. Measurement of Porosity and Permeability Under Effective Pressure

The porosity and permeability under effective pressure conditions were measured by PoroPerm-200 automatic porosity-permeability instrument. The realization of overpressure conditions mainly relies on a core holding system, which uses gas as the pressurized medium to mimic the pressurization of hydraulic fracturing, thus realizing the online testing of porosity permeability under overpressure conditions. During the experiment, high-pressure air was used for the pressurized gas source and high-purity helium was used for the test. To avoid the influence of slip effect on the permeability of shale samples, the driving pressure was kept constant during the pressurization process. The effective pressure points set in this experiment were kept constant during the pressurization process. The effective pressure points set in this experiment were 2.41, 4.48, 6.55, 8.62, 10.69, 12.07, 20, 30, and 50 MPa, respectively. The measurements were kept at each pressure point for 30 minutes, and then the porosity and permeability under the corresponding pressures were measured after stabilization. Before the overpressure experiments, the shale samples need to be extracted (72 hours) with dichloromethane and methanol (93:7) to remove the residual oil in the samples.

3.1. Laminae Types and Characteristics

The shale is characterized by laminations in the Jiyang depression [29-31]. According to the thickness of the lamination, the shale samples were divided into laminated shale (<2 mm), bedded shale (2 mm to 2 cm), and massive shale (>2 cm) by combing core and thin section observations. Except for massive shales, the laminations of laminated shale and bedded shale are well-developed, showing as alternating light lamination and dark lamination (Figure 3).

In addition, there is a significant difference in the mineral composition between light lamination and dark lamination. The main mineral of the light lamination is calcite, with small amounts of quartz, feldspar, and dolomite floating between mud crystalline calcite and sparry calcite; the mineral composition of dark lamination is more complex, and is dominated by clay minerals, also contains some calcite, dolomite, quartz, feldspar, and organic matter (OM). The difference in the mineral composition of lamination results in strong heterogeneity in the distribution of minerals in laminated shales and bedded shales. In contrast, massive shales lack laminae and thus have a relatively homogeneous distribution of minerals.

3.2. TOC Content, Ro, and Mineral Composition

The mean vitrinite reflectance (Ro%), TOC content, and mineral composition of shale samples are presented in Table 2. The shale samples in this study have lower thermal maturity (0.78% Ro to 1.12% Ro) and moderate TOC content (2.85 to 6.26 wt%, avg. 3.51 wt%). The minerals include calcite (7 to 69 wt%, avg. 37 wt%), clay minerals (4 to 30 wt%, avg. 22%), quartz (10 to 34 wt%, avg. 19 wt%), feldspar (4 to 22 wt%, avg. 11 wt%), dolomite (3 to 22 wt%, avg. 10 wt%) and a small amount of pyrite (1 to 3 wt%, average <2 wt%). Among clay minerals, illite/smectite mixed layer (20 to 66 wt%, avg. 51 wt%) is dominated, followed by illite (25 to 72 wt%, avg. 46 wt%), with a small amount of kaolinite and chlorite.

3.3. Pore Types and Characteristics

Based on scanning electron microscopy observations and previous studies [32, 33], four types of pores are found in the Jiyang depression: interparticle (InterP) pores, intraparticle (IntraP) pores, fracture pores, and a few OM pores.

Fracture pores, a major pore type in the Es3x-Es4s shales, mainly include interlayer fractures, tectonic fractures, and irregular fractures. The interlayer fractures are mostly developed at the interface of the laminae in laminated shales and bedded shales. The main body of the interlayer fractures is nearly horizontal and relatively stable in extension (Figure 4(a–c)). Tectonic fractures usually form an angle with the direction of the laminae and span multiple layers. Irregular fractures are mostly related to shrinkage by hydrocarbon generation and the dehydration of clay minerals [34], and usually extend around rigid particles (Figure 4(d)), with poor continuity.

IntraP pores occur inside mineral particles/crystals and are controlled by mineral types, including the pores in clay aggregates (Figure 4(e–f)), dissolution pores in calcite and dolomite (Figure 4(e–f)), pores in feldspar cleavages, and pores in pyrite aggregates (Figure 4(g)). IntraP pores are mostly isolated and have poor connectivity. InterP pores occur between mineral particles/crystals or at the edges of mineral particles/crystals and mainly include the pores between calcite granules (Figure 4(i–j)), between clay minerals (Figure 4(h)), and between calcite and dolomite, quartz, feldspar (Figure 4(k)) in the research area. Compared with IntraP pores, the InterP pores generally have good connectivity. Most of the InterP pores are wedge-shaped (5–10 μm) or slit-shaped in calcite laminae of laminated shales and bedded shales (Figure 4(i–j)), which are related to calcite recrystallization and have reformed by late dissolution [35]. The shape of InterP pores is irregular in massive shales and argillaceous laminae of laminated shales and bedded shales, with diameters ranging from 500 nm to 2 μm. OM pores are not developed in this study, and only a small amount of elongated slit-shaped OM pores were observed inside or at the edges of the OM (Figure 4(l)).

3.4. Porosity and Permeability Under Effective Pressure Influence

3.4.1. Reduction of Porosity Permeability at Effective Pressure

The porosity and permeability of shale samples at different effective pressures are shown in online Supplementary Material Tables S1 and S2. It can be seen that the porosity and permeability of shale samples under effective pressure are significantly lower than the initial porosity and initial permeability. During the pressurization process, the porosity and permeability of the samples decreased with the increase of the effective pressure, and the corresponding porosity loss and permeability loss continued to increase (Figure 5). When the effective pressure reaches the maximum value (50 MPa) of this experiment, the porosity and permeability of the samples are the lowest, and the corresponding loss rate also reaches the maximum value. At this time, the porosity loss rate of shale samples was 9.48%–54.32%, and the permeability loss rate was 95.18% to 99.5%. Compared with porosity, the permeability loss of shale samples is generally greater.

3.4.2. Phased Changes in Porosity Permeability During Pressurization Process

From the viewpoint of the whole pressurization process, the decrease in porosity and permeability shows an obvious stage with increasing effective pressure. This phasing is specifically manifested in the permeability as follows: at lower pressure, the permeability decreases rapidly, and the permeability loss rate increases rapidly; at medium pressure, the decrease in permeability slows down, and the increase in the permeability loss rate slows down; and at high pressure, the decrease in permeability is very slow, and the increase in the permeability loss rate is also very slow. Thus, based on the differential decrease in porosity and permeability during pressurization process, the pressurization process can be divided into three stages: low-pressure stage (<8 MPa), medium-pressure stage (8–15 MPa), and high-pressure stage (>15 MPa).

Within each stage, the decrease in porosity and permeability with effective pressure can be fitted with a linear function (Figure 6), which exhibits a higher fitting degree than overall fitting. The absolute values of the slopes of the porosity-effective pressure and permeability-effective pressure fitting curves are defined as the porosity reduction rate and permeability reduction rate under effective pressure, respectively. According to the fitting results (Figure 6), the porosity reduction rate (%/MPa) of shale samples is 0.0093–0.2620 at the low-pressure stage, which is 0.0027–0.0562 at the medium-pressure stage, and 0.0045–0.0564 at the high-pressure stage. In other words, the porosity reduction rate is the highest at the low-pressure stage, and lowest at the medium-pressure stage, with a difference ranging 2–15 times. The reduction of permeability with effective pressure exhibits similar phased characteristics (Figure 6). The permeability reduction rate (mD/MPa) of shale samples is 0.0002–16.1060 at the low-pressure stage, which is 0.000003–1.9931 at the medium-pressure stage, and 0.0000004–0.0912 at the high-pressure stage. Thus, the permeability reduction rate is the highest in the low-pressure stage, and lowest in the high-pressure stage, with a difference of two orders of magnitude. In conclusion, with the increase of effective pressure, the reduction of porosity goes through three stages of rapid-slow-rapid changes in sequence, and the reduction of permeability goes through three stages of rapid–slow–basically stable changes in sequence.

4.1. Effect of Lithofacies on Porosity Permeability at Effective Pressure

Previous studies have shown that the permeability of laminated shales and bedded shales is generally higher than that of massive shales [36, 37]. The shale samples in this study exhibit the same characteristics: the permeability (mD) of the laminated samples ranges from 0.0156 to 5.1990, and that of the bedded samples ranges from 0.0026 to 110.7375, which is much higher than that of the massive sample (0.0014 mD). This may be related to the differential development of fractures in different lithofacies. As mentioned in section 3.3, the interface of laminae in laminated shales and bedded shales is prone to the development of interlayer fractures, while only a small number of small-scale irregular fractures are present in massive shales. Fractures can greatly improve the permeability of shale reservoirs [38], thus the permeability of laminated shales and bedded shales is generally higher than that of massive shales.

The permeability of laminated shales and bedded shales remains higher than that of massive shales under effective pressure, while the permeability loss of massive shale isgreater, especially under lower effective pressure (online Supplementary Material Tables S3 and S4). When the effective pressure is 2.41 MPa, the permeability of the massive shale sample decreases by 85.17%, compared to a decrease of 2.79%–4.48% for the laminated samples and 1.42% ~ 7.50% for the bedded samples. As the effective pressure increases, the difference in permeability loss rate gradually decreases, and the permeability loss rate of laminated shales and bedded shales is always lower than that of massive shales. When the effective pressure reaches 4.48 MPa, the permeability of the massive shale decreases by 91.31%, compared to a decrease of 52.75% ~ 69.92% for the laminated samples and 32.82%–73.48% for the bedded samples. When the effective pressure reaches 20 MPa, the permeability loss of shale samples is more than 96%.

The reduction of permeability can be attributed to the following factors: (1) compression and closure of fractures, (2) the reduction of pores’ size and closure of matrix pores, and (3) loss of connectivity between pores [15, 16, 39]. For laminated shales and bedded shales containing a large number of interlayer fractures, the reduction of permeability is mainly attributed to the closure of fractures, followed by the compression and closure of matrix pores. For massive shales dominated by matrix pores, the reduction of permeability is mainly related to matrix pores (Figure 7). Massive shales have small pore size and poor connectivity, so the reduction of pores’ size and closure of pores lead to higher permeability reduction at lower pressure. The fractures in laminated shales and bedded shales are also compressed but not completely closed, so the permeability reduction is relatively low. In addition, the relatively low permeability reduction of laminated shales and bedded shales may also be related to uneven compression. The distribution of pores is relatively uniform in massive shales, while it varies significantly due to mineral composition in laminated shales and bedded shale. Argillaceous laminae are rich in clay minerals which are plastic, and have strong compressibility. However, the compressibility of slit-shaped and wedge-shaped intergranular pores in calcite laminae is weaker than pores in argillaceous laminae due to the support of rigid calcite particles. This is also the main reason why the porosity of laminated samples and bedded samples is generally higher than that of massive samples in this study.

4.2. Effect of Minerals Content on Porosity-Permeability Reduction

As mentioned in 3.3, mineral composition affects the type and development of pores [40, 41]. In addition, researches have shown that mineral composition also affects the compressive capacity of rocks to some extent [1, 42]. Felsic minerals have high hardness and strong anticompression ability, clay minerals have strong plasticity and are easy to be compressed under pressure, while carbonate minerals are in between [1, 42]. Therefore, the correlation coefficient method was adopted to analyze the contribution of individual mineral components to the porosity-permeability reduction at effective pressure in this study.

4.2.1. Carbonate Minerals

As shown in Figure 8, there is a positive correlation between carbonate minerals content and porosity-permeability reduction rate. This positive correlation indicates that carbonate-related pores have compressibility to some extent. The correlation coefficient (R2) between carbonate minerals content and average porosity reduction rate is only 0.07, which is basically not correlated, while the R2 between carbonate minerals content and stage porosity reduction rate is 0.58, 0.35, and 0.29, respectively, indicating a good correlation (Figure 8). Permeability also shows similar characteristics (Figure 8). In other words, the correlation between carbonate minerals content and stage permeability reduction rates (R2=0.69, 0.88, 0.82) is higher than that between carbonate minerals content and average permeability reduction rate (R2=0.62). This indicates that the influence of carbonate minerals on porosity-permeability reduction rate has obvious stage characteristics under effective pressure.

In addition, the correlation between carbonate minerals and permeability reduction rate is significantly better than that of porosity. This implies that the contribution of carbonate minerals to the permeability reduction rate is greater than that to porosity reduction rate. This may be related to the pore structure of shales. In terms of pore structure, porosity is related to the total volume of all pores, while permeability depends on the connectivity between pores. As mentioned in 3.3, the shales develop carbonate-related pores, clay-related pores, and felsic-related pores in this study. Intergranular pores between carbonate minerals and felsic minerals have good connectivity, while clay-related pores have poor connectivity. Therefore, carbonate minerals have a greater influence on permeability, which is consistent with Su et al [43].

4.2.2. Clay Minerals

There is a weak negative correlation between clay minerals and porosity-permeability reduction rate (Figure 9). Obviously, this is inconsistent with the conventional understanding of the compressibility of clay minerals [42, 44]. Further analysis shows that two samples (F201-2 and FYP1-6) with low clay minerals content (<10%) interfere with the changing characteristics of the whole curve. After removing the two samples with low clay minerals content, there is a positive correlation between the clay minerals content and porosity-permeability reduction rate, which shows that the porosity-permeability reduction rate increases with the increase of clay minerals content (Figure 9). Consistent with carbonate minerals, the correlation between the content of clay minerals and stage porosity-permeability reduction rate is better than the average porosity-permeability reduction rate.

In contrast to carbonate minerals, the correlation between clay minerals content and permeability reduction rate is lower than its correlation with porosity reduction rate. This means that the contribution of clay minerals content to porosity reduction rate is higher than its contribution to permeability reduction rate. This is consistent with the pore development characteristics of shales. In this study, the shale samples are widely developed with clay mineral-related pores, which are numerous but poorly connected to each other (Figure 7).

4.2.3. Felsic Minerals

Under effective pressure conditions, there is a negative correlation between felsic minerals content and porosity-permeability reduction rate to a certain extent (Figure 10), which is consistent with the conventional understanding of the strong anticompression ability of felsic minerals. As shown in Figure 10, the correlation between felsic minerals content and stage porosity-permeability reduction rate is significantly better than that between felsic minerals content and average porosity-permeability reduction rate, which is similar to carbonate minerals and clay minerals. In addition, the contribution of felsic minerals content to the stage permeability reduction rate (R2>0.87) is higher than to the stage porosity reduction rate (R2=0.34), which is consistent with carbonate minerals. As described in 3.2 and 3.3, felsic minerals are low in content and dispersed in carbonate minerals and clay minerals. As a result, felsic minerals-related pores have a low contribution to the total porosity. Compared with other minerals, felsic minerals have a stronger anticompression ability at effective pressure, thus greatly protecting the connectivity of the pore-fracture system. Therefore, the permeability reduction rate shows a trend of increasing with the increase of felsic minerals content.

In summary, carbonate minerals, clay minerals, and felsic minerals all affect the reduction of porosity and permeability at effective pressure to varying degrees. Carbonate minerals content and clay minerals content are positively correlated with porosity-permeability reduction rate, while felsic minerals content is negatively correlated with porosity-permeability reduction rate. Consistent with the phased changes in porosity-permeability reduction rate, this correlation is also presented with phased characteristics (Figures 8 and 9, Figure 10). In other words, the contribution of minerals to the porosity-permeability reduction rate is different in different pressure stages. Overall, porosity reduction rate is mainly related to clay minerals content (R2=0.74, 0.51, 0.52), followed by carbonate minerals content (R2=0.58, 0.35, 0.29); permeability reduction rate is mainly affected by carbonate minerals content (R2=0.69, 0.88, 0.82), followed by clay minerals content (R2=0.27, 0.46, 0.30).

4.3. Effect of TOC Content on Porosity Permeability Under Effective Pressure

Previous studies have shown that the TOC content (%) has significant effects on the development of pores in organic-rich shales [32, 45-47]. Compared to minerals, OM has stronger ductility and is easier to compress [50]. In this study, there is no significant correlation between TOC content and porosity-permeability reduction rate (Figure 11). This may be attributed to the lower maturity of the shale samples.

A large number of OM pores are developed in medium-high maturity shales, and thus the higher the TOC content, the more developed the OM pores and the larger the total pore volume [47]. In contrast, the maturity of the shale samples in this study is relatively low, with vitrinite reflectance ranging from 0.82% to 1.12%. The lower maturity corresponds to undeveloped OM pores. As described in 3.3, the pore types of shales in the study area are dominated by fractures and inorganic mineral pores, and OM pores are not developed, thus making the effect of TOC content on porosity permeability under effective pressure insignificant.

Under the effective pressure influence, the porosity and permeability of shale decrease with the increase of effective pressure, and the reduction rate is characterized by an obvious stage change. According to the stage changes of porosity-permeability reduction rate, the pressurization process can be divided into three pressure stages: low pressure (<8 MPa), medium pressure (8–15 MPa) and high pressure (>15 MPa). Porosity reduction rate is highest in the low-pressure stage and lowest in the medium-pressure stage, with a difference of 2–15 times. Permeability reduction rate is highest at low-pressure stage and lowest at high-pressure stage, with a difference of 2 orders of magnitude.

Under the effective pressure influence, the rock fabric affects porosity and permeability by influencing mineral distribution, pore development, and differential compaction. The laminae and interlayer fractures are poorly developed, and the distribution of minerals and pores is relatively homogeneous in massive shales. The presence of laminae is accompanied by well-developed interlayer fractures and the differential distribution of minerals and pores in laminated shale and layered shale. the minerals are dominated by calcite in calcite laminae where the pores mainly occur between calcite crystals and at the edges of calcite crystals, with better connectivity; the minerals are dominated by clay minerals in argillaceous laminae where the pores are mainly in clay minerals, with poorer connectivity. The compressibility of clay minerals is stronger than calcite. As a result, the clay mineral-related pores in the argillaceous laminae are more likely to be damaged and lose connectivity under effective pressure conditions, while the calcite-related pores in calcite laminae are less compressed and retain a certain permeability. In addition, interlayer fractures have not been completely closed at lower pressure, thus still able to maintain a certain connectivity. Therefore, compared with massive shale, laminated shale, and bedded shale generally have lower permeability loss and relatively higher permeability under effective pressure.

During pressurization process, the porosity and permeability reduction rates are negatively correlated with felsic minerals content and positively correlated with carbonate minerals content and clay minerals content. Porosity reduction rate is mainly related to clay minerals content (R2=0.74, 0.51, 0.52), followed by carbonate minerals content (R2=0.58, 0.35, 0.29). Permeability reduction rate is primarily related to carbonate minerals content (R2=0.69, 0.88, 0.82), followed by clay minerals content (R2=0.27, 0.46, 0.30). The TOC content has no significant effect on the porosity and permeability of the shale in the study area due to lower maturity.

All relevant data are within the manuscript and supplementary materials.

The authors declared that they have no conflicts of interest to this work.

This study was financially supported by the National Natural Science Foundation of China (Grant No.42072152).

Table S1: Measured porosity of shale samples at different pressures.

Table S2: Measured permeability of shale samples at different pressures.

Table S3: Porosity loss rate calculated based on the values of measured porosity and pressure.

Table S4: Permeability loss rate calculated based on the values of measured permeability and pressure.

Table S5: Porosity-permeability reduction rate at different pressure stages based on the results of segmentation fitting.

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Supplementary data