Pore-throat structure, fractal characteristics and permeability prediction of tight sandstone: the Yanchang Formation, Southeast Ordos Basin

Pore-throat structure, fractal characteristics and permeability prediction of tight sandstone: the Yanchang Formation, Southeast Ordos Basin | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Pore-throat structure, fractal characteristics and permeability prediction of tight sandstone: the Yanchang Formation, Southeast Ordos Basin Huanmeng Zhang, Ling Guo, Zhiyu Wu, Jiangbo Ma This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4640639/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 13 Nov, 2024 Read the published version in Scientific Reports → Version 1 posted 12 You are reading this latest preprint version Abstract As a typical tight reservoir and an important site for unconventional hydrocarbon accumulation, the Chang 6 member of the Yanchang Formation is characterized by complex pore structures and strong heterogeneity. Analysing and characterizing the pore-throat structure quantitatively holds significant importance in optimizing oil recovery processes. To clarify the nonhomogeneity and structural characteristics of the pore throats in the southeastern Ordos Basin, tight sandstone from the Chang 6 member was selected for analysis. Casting thin section (CTS), scanning electron microscopy (SEM), cathodoluminescence (CL), X-ray diffraction (XRD), and mercury intrusion capillary pressure (MICP) analyses were conducted. According to the results, we found that intergranular pores, feldspar-dissolved pores, intergranular-dissolved pores, and microfractures were the predominant pore types found within the samples. By combining the results of MICP analysis with those of fractal theory, the pore-throat structure of each sample can be categorized into two types: large-scale and small-scale. Fractal theory was employed to quantitatively characterize the complex and irregular pore-throat structure of the reservoir. The average fractal dimension of large pores (D1) was 2.8094, whereas for small pores (D2), it was slightly lower than that of D1, averaging 2.5325. These findings underscore that large-scale pore-throat structures are more complex and exhibit greater heterogeneity. Compared with those of large pores, the pore-throat structure parameters of small pores exhibit a more significant correlation with reservoir properties and fractal dimensions. Therefore, small pores are the primary contributors to the reservoir storage pace and are key factors influencing the pore-throat structure of the Chang 6 tight sandstone. Based on the pore-throat radius and considering the influence of fractal characteristics on the pore structure, a nonlinear permeability prediction model was created using multiple regression analysis. Among these equations, the pore-throat radius corresponding to a mercury saturation of 40% (r40) emerged as the most effective predictor of permeability for tight sandstone. Tight sandstone Pore-throat structure Fractal characteristics Permeability estimation Ordos Basin Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 1. Introduction With advancements in oil and gas exploration and development, the proportion of unconventional oil and gas resources has steadily increased. Tight reservoirs are destined to play a central role in future exploration and development endeavours 1–5 . Tight-sandstone reservoirs represent a vital segment of China’s unconventional oil and gas resources, holding an important position in the nation's energy structure 6–7 . Currently, they are being exploited in large quantities in the Ordos Basin. They play a pivotal role in increasing oil and gas production and ensuring national energy security 8–11 . Moreover, these reservoirs typically exhibit small pore-throat radii and complex structures, resulting in limited connectivity 12–13 . This also poses challenges for the study of reservoir microstructures 14–15 . Tight-oil extraction has shown notable success in North America, especially in certain regions 16 . While research in China is still in its early stages, preliminary exploration indicates promising prospects for tight-oil production 17 . The Ordos Basin is renowned for its substantial reserves of tight oil. The Chang 6 member of the Yanchang Formation in the Ordos Basin is a typical tight reservoir and one of the primary targets for tight-oil exploration and development in this basin 18–20 . The mechanisms of petroleum charging, migration, and accumulation in tight-oil reservoirs differ from those in conventional reservoirs. Therefore, a detailed study of the micropore-throat structure of tight-oil reservoirs is of significant practical importance for understanding the distribution of tight oil and guiding oilfield development. The pore throats of tight sandstone are narrow, and the microstructure of the pore throats is complex and heterogeneous. It is challenging to characterize the morphology of pore throats in tight sandstone using traditional testing methods. Therefore, combining these studies with fractal geometry theory provides a more accurate approach for understanding the complex pore-throat structures in tight sandstone. Fractal theory can relatively accurately describe the homogeneity and complexity of pore-throat structures within tight reservoirs, and it is widely used in petroleum exploration 21–22 . However, the distribution range of pore throats in tight sandstone is large, and the microstructural and fractal features of pores and throats of different radii are bound to differ. Consequently, investigating fractal features across multiple scales becomes imperative. The fractal dimension (D) serves as a pivotal metric for characterizing the heterogeneity of pore-throat structures and has been extensively utilized in prior investigations of such structures. As protuberances and concavities increase, pore-throat surfaces and structures exhibit heightened roughness and complexity, with the fractal dimension providing a quantitative measure of this surface roughness 23–24 . Experimental techniques such as mercury intrusion capillary pressure (MICP), high-pressure mercury intrusion (HPMI), constant-rate mercury injection (CRMI), and nuclear magnetic resonance (NMR) are commonly used to evaluate the pore-throat structures of reservoirs. The fractal dimension of sandstone ranges from 2.0–3.0, which is indicative of the local–whole relationship inherent in sandstone pore-throat structures. This parameter holds substantial significance because it offers a comprehensive representation of the regularity and composite characteristics of pore throats. Fractal dimension analysis has proven to be a proficient method for characterizing pore-throat structures. The closer the fractal dimension (D) is to 3.0, the rougher the pore-throat surface and the more complex the structure 25 . In this study, cast thin section (CTS), scanning electron microscopy (SEM), X-ray diffraction (XRD), and mercury intrusion capillary pressure (MICP) analyses were used to conduct a detailed investigation of the pore-throat types, sizes, and structures in the tight sandstone of the Chang 6 member. The fractal characteristics of the pores and throats of the tight sandstone were studied based on the mercury feed curves of the capillary pressure curve of the Chang 6 member in the Haojiaping area, Ordos Basin. Additionally, this study explored the relationships among fractal characteristics, reservoir properties, and pore-throat structures, and a nonlinear equation was utilized to identify the pore-throat radius that best correlates with permeability. The feasibility of using this radius to predict permeability in tight reservoirs was then verified. 2. Geological Setting The Ordos Basin is a resource-rich, structurally simple, large multirotational cratonic superposition basin. This basin has stable subsidence, gentle tectonics, and migration of depressions (Fig. 1 (a)). Oil reservoirs developed in the Triassic strata of the Ordos Basin. The Upper Triassic Yanchang Formation is the most important tight-oil and gas reservoir for exploration and development. The Ordos Basin experienced a complete inland lake basin evolution, which included the occurrence and development of a lake and intense subsidence, shrinkage, and demise of the lake during the Yanchang period of the Triassic. The Yanchang Formation is divided into the Chang 10 to Chang 1 members from bottom to top 26–28 . During deposition of the Upper Triassic Chang 6 member, the water body experienced shallowing, leading to a reduction in the size of the lake basin. This phase marked the primary period of the formation of lake deltas, with a substantial deposition of deltaic sands. There are extensive opportunities for exploration and prospects in the oil and gas industry (Fig. 1 (b)). The Haojiaping area is located in the middle of the Yishan Slope in the Ordos Basin, which is a west-dipping gently monoclonal tectonic area, and the Chang 6 oil formation group is the main tight-oil target in the study area, with a thickness of 120–150 m. The lithology is dominated by grayish-green fine sandstone, dark mudstone, and delta-front facies. Sandstone mainly formed in channels and channel bars on the delta. 3. Materials and Methods 3.1 Sampling and Processing In this study, a total of 56 core samples were systematically collected from 17 wells situated within the Upper Triassic Yanchang Formation in the Haojiaping area, which is located on the southeastern slope of the Ordos Basin. These samples underwent initial drilling that produced cylindrical specimens measuring approximately 2.5 cm in diameter and 5.0 cm in length. Then, extraction experiments were conducted using alcohol and benzene following sample numbering. After drying at 50 ℃ for 24 hours, the samples were divided into two segments. One segment, measuring 2.5 cm in length, was allocated for helium porosity and nitrogen permeability measurements (36 samples), as well as MICP testing (16 samples). The other segment, measuring 0.5 cm in length, was designated for CTS testing (43 samples), XRD analysis (21 samples) and SEM observation (12 samples). In this study, MICP tests were conducted using an automatic mercury porosimeter (Autopore IV 9505, Micromeritics). CTSs of 43 samples were examined using an Olympus-cx21 polarizing microscope. SEM observations were performed using a Tescan S-3200 N field emission electron microscope 30 . 3.2 Fractal theory Fractal theory is a research theory for structurally complex but self-similar systems in nature, and the geometry of the pore-throat space can be characterized by fractal dimension 31–32 . The fractal dimension of the pore-throat structure can be determined from the MICP results. If the throat structure exhibits fractal characteristics, the number of pore throats with a radius exceeding r can be expressed based on fractal theory as follows: $$\text{N} (>\text{r})={\int }_{\text{r}}^{{\text{r}}_{\text{m}\text{a}\text{x}}}\text{P} \left(\text{r}\right)\text{d}\text{r}={\text{a}\text{r}}^{-\text{D}}$$ 1 where r max represents the maximum pore-throat radius, P(r) denotes the distribution density function of the pore-throat radius, a is a proportionality constant, and D represents the fractal dimension. By taking the derivative with respect to “r”, the distribution density fraction of the pore-throat radius P(r) is derived. $$\text{P}\left(\text{r}\right)=\frac{\text{d}\text{N}(>\text{r})}{\text{d}\text{r}}=\text{a}{\prime }{\text{r}}^{-\text{D}-1}$$ 2 where a \({\prime }\) is a proportionality constant, which is equivalent to -D×a. By transforming Eq. ( 2 ) into Eq. ( 3 ), the total volume V(< r) of pores with a radius less than r can be expressed as follows: $$\text{V}\left(\text{r}\right)={\int }_{{\text{r}}_{\text{s}}}^{\text{r}}\text{P}\left(\text{r}\right)\text{a}{\text{r}}^{3}\text{d}\text{r}=\frac{-{\text{a}}^{2}\text{D}}{3-\text{D}}\left({\text{r}}^{3-\text{D}}-{\text{r}}_{\text{m}\text{i}\text{n}}^{3-\text{D}}\right)$$ 3 The total pore volume (V) can be calculated as follows: $$\text{V}=\frac{{-\text{a}}^{2}\text{D}}{3-\text{D}}\left({\text{r}}_{\text{m}\text{a}\text{x}}^{3-\text{D}}-{\text{r}}_{\text{m}\text{i}\text{n}}^{3-\text{D}}\right)$$ 4 By converting Eqs. ( 3 ) and ( 4 ) into Eq. ( 5 ), one can derive the cumulative volume fraction of pore throats with radii less than r(s). $$\text{s}=\frac{\text{V}(<\text{r})}{\text{V}}=\frac{{\text{r}}^{3-\text{D}}-{\text{r}}_{\text{m}\text{i}\text{n}}^{3-\text{D}}}{{\text{r}}_{\text{m}\text{a}\text{x}}^{3-\text{D}}-{\text{r}}_{\text{m}\text{i}\text{n}}^{3-\text{D}}}$$ 5 Because r min is far less than r max , Eq. ( 5 ) can be simplified as follows: $$\text{s}={\left(\frac{\text{r}}{{\text{r}}_{\text{m}\text{i}\text{n}}}\right)}^{3-\text{D}}$$ 6 Under the assumption that the wetting contact angle is unaffected by the pore-throat size, the fractal formula for the distribution of the pore-throat radius can be derived. $$\text{s}={\left(\frac{{\text{P}}_{\text{c}}}{{\text{P}}_{\text{m}\text{i}\text{n}}}\right)}^{\text{D}-3}$$ 7 Taking the logarithm of both sides of Eq. ( 7 ), the formula is changed as follows: $$\text{l}\text{o}\text{g}\text{S}=\left(\text{D}-3\right)\text{l}\text{o}\text{g}{\text{P}}_{\text{c}}-\left(\text{D}-3\right)\text{l}\text{o}\text{g}{\text{P}}_{\text{m}\text{i}\text{n}}$$ 8 The wetting phase saturation S and capillary pressure P c exhibit a linear relationship. The slope of the linear equation fitted in a log-log coordinate system represents (𝐷−3), from which the fractal dimension D can be calculated. The fractal of the pore-throat structure can be categorized into integral fractal and piecewise fractal based on the presence or absence of turning points in the fractal curve. An integral fractal curve lacks inflection points, indicating similarities in the structures of large and small-pore throats. In contrast, a piecewise fractal curve exhibits distinct turning points. The overall fractal dimension (D) of the pore-throat structure can be determined by employing the weighted average of the porosities of various pore-throat sizes (Eq. ( 9 )). $$\text{D}={\text{D}}_{1}\times \frac{{{\phi }}_{1}}{{{\phi }}_{1}+{{\phi }}_{2}}+{\text{D}}_{2}\times \frac{{{\phi }}_{2}}{{{\phi }}_{1}+{{\phi }}_{2}}$$ 9 4. Results 4.1 Petrophysical characteristics and mineral composition Based on thin-section analysis, scanning electron microscope detection, and X-ray diffraction analysis, the composition of the reservoir rocks in the Chang 6 member in the Haojiaping area primarily consists of quartz, lithic fragments, plagioclase, and potassium feldspar (Fig. 3 (a, b, c)). Statistical analysis using the point-counting method on thin sections of the cast body reveals that in the skeletal grains of the study area, feldspar has the highest proportion (36–69%, with an average of 61.4%), followed by quartz (17–30%, with an average of 26.7%), and then lithic fragments (6–21%, with an average of 11.9%). Therefore, the rock type in the Chang 6 reservoir in the Haojiaping area is predominantly fine-grained feldspar sandstone, with a small amount of lithic feldspar sandstone (Fig. 2 (a)). The results of the XRD experiments show that the mineral components of the reservoir, in descending order of content, are feldspar and quartz, clay minerals (clay, anhydrite, and laumontite), and carbonate (calcite, ankerite, and siderite) (Fig. 2 (b)). The overall average pore-filling material content in the reservoir is approximately 15%, with the main components being siderite, clay, and calcite. The cement content is greater than that of the matrix and is primarily composed of chlorite, illite, calcite, and quartz-cemented materials, along with minor amounts of zeolites, goethite, and asphaltene (Fig. 3 (g,h,l)). The reservoir exhibits strong compaction, a low degree of weathering, good sorting, and poor to moderate roundness. The cement types are mainly pore filling and patchy, with grains exhibiting linear and concavo–convex contacts. The grain-size analysis indicates that the sandstone particles range from 0.03 to 0.32 mm, with an average of 0.28 mm. Sandstone classification can reflect source-rock properties, rock maturity, and physical conditions during deposition. In general, the ratio of plagioclase to lithic fragments (i.e., F/R, referred to as the source index) can reflect the basic characteristics of the source-rock composition 33 . The F/R ratio in the study area is greater than 1, with an average of 5.2, indicating that the predominant source rock in the study area is granite. The relative ratio of stable components (quartz) to unstable components (plagioclase + lithic fragments), or Q/(F + R), is used to represent the transport and abrasion history. Higher component maturity is associated with better abrasion conditions and a longer transport history. The Q/(F + R) ratio in the study area ranges from 0.23 to 0.53, with an average of 0.38, indicating relatively low component maturity. The ratio of grains or clasts to matrix (i.e., G/M, referred to as the flow coefficient) directly reflects the degree of sand–mud mixing and indicates the quality of rock sorting. A small G/M ratio indicates poor sorting, which is typically associated with gravity flow deposits, while a larger ratio indicates traction flow deposits. The average G/M ratio in the study area is 24.7, reflecting good sorting. According to the formula of the rock brittleness index (BI) in China (Eq. ( 10 )), the brittleness index of the target area ranges from 65.31–92.77%, with an average of 82.52%. Meeting the criterion of high brittleness as specified in the national standard “Method for Optimal Selection of Marine Shale Gas Exploration Target: GB/T 35110-20-17” indicates a high content of brittle minerals, providing important prerequisites for the optional selection of exploration sweet spots, reservoir hydraulic fracturing, and the formation of artificial fractures. $$\text{B}\text{I}=\frac{{\text{m}}_{\text{q}\text{u}\text{a}}}{{\text{m}}_{\text{q}\text{u}\text{a}}+{\text{m}}_{\text{c}\text{l}\text{a}}+{\text{m}}_{\text{c}\text{a}\text{r}}}\times 100\text{\%}$$ 10 where BI is the brittleness index (%), is the quartz content (%), is the clay mineral content (%), and is the carbonate content (%). In summary, the reservoirs in the study area exhibit low component maturity, moderate structural maturity, poor erosion conditions, good sorting, poor to moderate roundness, and high brittleness. This suggests that the deposited sediment was not transported over long distances, indicating characteristics of near-source deposition. In addition, the study area is a sweet spot for oil exploration and is conducive to fracture modification. 4.2 Porosity and permeability A total of 45 sandstone samples from the Chang 6 member in the study area were analysed. Figure 4 (a) shows that the porosity of the reservoir in the study area ranges from 0.5–10.5%, with the predominant range being 8–10%, and the average porosity is 7.7%. Figure 4 (b) shows that the permeability varies from 0.05 to 0.97 mD, mainly falling between 0.3 and 0.7 mD, with an average of 0.42 mD. These values indicate that the study area is a typical tight reservoir. Figure 4 (c) illustrates a positive correlation between the porosity and permeability, with a coefficient of 0.61. This suggests that the pore-throat structure in the study area is complex and that the pore-throat size significantly impacts the permeability. Conventional thin section, CTS, and SEM analyses indicate that the face porosity of the Chang 6 reservoir in the study area ranges from 1.5–6.25%, with an average of 4.75%. The face porosity is consistently below 10%, confirming that the Chang 6 member is a tight-sandstone reservoir. The predominant storage space is characterized by dissolution pores, with common occurrences of feldspar dissolution pores and cloudy feldspar dissolution pores (Fig. 3 (d, f, i)). The secondary features include micropores and microfractures (Fig. 3 (k)). Intergranular pores make up the majority of the remaining pores and are characterized by polygonal shapes and clearly defined boundaries (Fig. 3 (e, g)), indicating the effects of compaction, cementation, and mixed filling on these pores. Cast thin section (CTS) images reveal secondary enlargement and interstitial authigenic quartz, as well as thin films of chlorite (Fig. 3 (h, j, l)). The presence of chlorite films and quartz is crucial for resisting compaction, contributing to the preservation of pores within the samples. 4.3 Characteristics of the pore throat network Particles are separated by pores, and narrow areas that connect these pores are called throats. A porous medium is composed of pores that serve as reservoirs for fluids and throats that control the flow of fluids through them 34 . According to analyses of cast thin sections and scanning electron microscopy images of the Chang 6 reservoir, the predominant throat types are lamellar (Fig. 3 (d)), necking (Fig. 3 (f)), and sheet-like (Fig. 3 (g)). The primary pore-throat combinations in the Chang 6 reservoir include grain interpores, feldspar dissolution pores, intercrystalline micropores, and microfine throat hybrid combinations. However, these throat types are complex, and their connectivity is relatively weak, thereby restricting fluid flow. Mercury injection capillary pressure (MICP) experiments can be performed on tight-sandstone samples to determine pore-throat structure characteristics and pore-size distributions 35 . Based on the MICP results, pressure‒capillary characteristic curves and throat radius distribution curves are plotted for 16 representative samples (Fig. 5 ). The samples are classified into three types based on their porosity values (Table 1 ): Type I represents samples with porosities greater than 8%, Type II represents samples with porosities between 7% and 8%, and Type III represents samples with porosities less than 7%. Table 1 Porosity, permeability, and parameters from the MICP experiment. Sample Porosity (%) Permeability (mD) Entry pressure (MPa) Maximum pore-throat radius (µm) Median pressure (MPa) Median radius (µm) Sorting coefficient Skewness Maximum mercury saturation (%) Efficiency of mercury withdrawal (%) I H73# 8 0.50 0.17 0.90 3.54 0.07 4.72 2.01 69.19 24.47 H70# 9.2 0.65 0.37 0.90 3.38 0.06 2.89 2.02 71.73 21.40 X5001−9# 8.3 0.73 0.58 1.28 4.25 0.18 0.23 1.74 74.02 31.79 X5001−15# 9.5 0.48 1.73 0.43 11.99 0.06 0.08 1.89 66.05 36.53 H901−13# 8.3 0.55 0.92 0.82 7.60 0.10 0.15 2.04 70.48 33.88 H903−3# 9.9 0.50 0.79 0.94 7.98 0.09 0.19 1.66 68.87 29.65 II X5001−1# 7.2 0.28 6.00 0.13 20.05 0.04 0.02 2.09 63.39 27.37 X5001−3# 7.9 0.48 5.06 0.15 17.92 0.04 0.02 2.01 66.82 30.10 X4008−3# 7.6 0.39 3.87 0.19 13.52 0.06 0.03 1.99 70.49 30.89 H86−4# 7.8 0.26 4.80 0.16 19.26 0.04 0.03 2.15 63.83 39.75 III X5001−5# 5.5 0.09 8.93 0.08 23.51 0.03 0.01 2.03 62.33 28.26 X5001−7# 4.8 0.37 4.31 0.17 19.20 0.04 0.03 2.19 62.04 27.43 X5007−1# 6.7 0.30 6.69 0.11 26.38 0.03 0.02 2.66 57.28 35.36 X5010−6# 4 0.09 6.67 0.11 29.41 0.03 0.02 2.19 52.80 24.08 H4008−4# 6.9 0.53 3.65 0.21 16.50 0.05 0.04 2.16 63.30 32.60 H903−4# 6.6 0.24 2.84 0.26 15.01 0.05 0.05 2.08 66.35 33.09 The capillary pressure curve shows that Type I has a gentle capillary pressure curve (Fig. 5 a). The average porosity for Type I is 8.87%, with an average permeability of 0.53 mD. The entry pressure is relatively low, ranging from 0.17 to 1.73 MPa, with an average of 0.76 MPa. The corresponding maximum throat radius at the entry pressure has an average value of 0.89 µm. At 50% mercury saturation, the median pressure ranges from 3.38 to 11.99 MPa, with an average of 6.46 MPa. The associated average median radius is 0.10 µm. The sorting coefficient ranges from 0.08 to 4.72, with an average of 1.38. The skewness ranges between 1.66 and 2.04, with an average of 1.89. Type I is considered to have poor sorting, is strongly positively skewed, and exhibits coarse skewness. The maximum mercury saturation is a measure of the amount of mercury injected into the pore throat at the maximum pressure. It ranges from 66.05–74.02%, with an average of 70.06%. The average mercury withdrawal efficiency is 29.62%. There is a distinct double peak in the pore-throat distribution of the Type I samples (Fig. 5 b), with peak pore-throat radius values of approximately 0.24 µm and 0.68 µm. Taking Sample X5001-15# as an example, a pore-throat radius larger than 0.1 µm plays a significant role in contributing to permeability (Fig. 5 c), indicating that this type of sample possesses larger throats, facilitating mercury injection into the pore throat. The mercury injection curve for Type II shows a shorter plateau segment than that for Type I (Fig. 5 d). The average porosity for Type II is 7.63%, with an average permeability of 0.35 mD. The entry pressure is higher than that of Type I, with an average of 4.93 MPa. The average maximum throat radius is 0.16 µm, the average median pressure is 17.69 MPa, and the median radius is smaller than that of Type I, with an average of 0.04 µm. The average sorting coefficient is 0.03, indicating excellent sorting. The skewness has an average of 2.06. The maximum mercury saturation for Type II ranges from 63.39–70.49%, with an average of 66.14%. The average mercury withdrawal efficiency is 32.03%. The pore-throat radius distribution of Type II exhibits a weak double peak (Fig. 5 e), with the pore-throat radius primarily distributed in a range of 0.02 to 0.15 µm, peaking at 0.03 µm on the left and 0.07 µm on the right. Taking Sample H4008-3# as an example, the permeability contribution is mainly dominated by throats in a size range of 0.07 to 0.1 µm, indicating that these samples have moderately sized throats. The cumulative permeability contribution curve is slightly shifted to the left compared to that of Type I (Fig. 5 f). The capillary pressure curve for Type III exhibits a steep shape (Fig. 5 g). The average porosity and permeability for Type III are 5.75% and 0.30 mD, respectively. The displacement pressure is high, with an average of 5.52 MPa. The average maximum pore-throat radius is 0.16 µm, the average median pressure is 21.67 MPa, and the median radius is 0.04 µm on average. The sorting coefficient is low, with an average of 0.027, indicating excellent sorting. The skewness has an average of 2.22. The average maximum mercury saturation is 60.70%, and the average mercury withdrawal efficiency is 30.14%. The pore-throat radius distribution of Type III mainly has a distinct single peak (Fig. 5 h), with a radius distributed in a range of 0.02 to 0.10 µm, peaking at 0.03 µm. Taking Sample H903-4# as an example, the radius in a size range of 0.03 to 0.07 µm plays a significant role in contributing to the permeability (Fig. 5 i). 4.4 Fractal features Scatter plots of log(1-S Hg ) versus log(P c ) for each sample are created based on the MICP pore-throat structure parameters, and the slopes of the resulting straight lines are fitted. Examples include Samples H70#, X4008-3#, and X5007-1# (Fig. 6 ). Moreover, due to experimental limitations, the pore parameters obtained via MICP do not accurately reflect the true pore characteristics. Therefore, this paper focuses solely on the fractal characteristics of pore throats. Among the Type Ⅰ, Ⅱ, and Ⅲ samples, small pores are widely distributed. The results indicate that small pores are extensively developed in the sandstone reservoirs in the study area, which is a key factor in the quality of the reservoir. The fractal dimension (D 1 , D 2 ), porosity (Φ 1 , Φ 2 ), and permeability contribution (K 1 , K 2 ) corresponding to large pores and small pores are calculated in Table 2 for further discussion. The fractal dimension D 1 of the large pores ranges between 2.6519 and 2.9934, with an average of 2.8094. In contrast, the fractal dimension D 2 of small pores varies between 2.2307 and 2.7230, with an average of 2.5325. D 1 exceeds D 2 , reflecting the greater structural complexity of the large pores. This complexity can be attributed to the intricate and challenging-to-differentiate shapes of large pores from those of small pores. The total fractal dimension of the Chang 6 tight-sandstone samples is calculated using the weighted average porosity for large pores and small pores, and the mean is 2.5722. These findings suggest that the tight reservoirs in the study area have an extremely complex and heterogeneous pore-throat structure. Fractal dimension values for different pore regions are shown on the graphs. Table 2 Fractal dimension calculation results of the Chang 6 sandstone samples in the Haojiaping area Sample D 1 R 2 Φ 1 (%) K 1 (mD) D 2 R 2 Φ 2 (%) K 2 (mD) D H73# 2.9900 0.9577 0.51 0.03 2.7230 0.9575 7.36 0.47 2.7403 H70# 2.9934 0.9653 0.40 0.28 2.7010 0.9754 8.80 0.37 2.7137 X5001−9# 2.6908 0.9889 1.06 0.29 2.6797 0.9983 7.24 0.44 2.6850 X5001−15# 2.8486 0.8978 0.88 0.08 2.6345 0.9984 8.62 0.40 2.6543 H901−13# 2.7283 0.9742 2.89 0.37 2.6655 0.9962 5.41 0.11 2.6874 H903−3# 2.6515 0.9995 4.16 0.49 2.7114 0.9851 5.74 0.06 2.6862 X5001−1# 2.7512 0.9998 0.95 0.18 2.3893 0.9996 6.25 0.10 2.4371 X5001−3# 2.8192 0.8336 0.42 0.26 2.3568 0.9978 6.78 0.22 2.3838 X4008−3# 2.8478 0.8189 1.47 0.12 2.4285 0.9979 6.13 0.27 2.5096 H86−4# 2.7131 0.9561 1.91 0.15 2.4205 0.9987 5.89 0.11 2.4921 X5001−5# 2.8486 0.8978 0.68 0.04 2.6345 0.9984 4.82 0.05 2.6610 X5001−7# 2.8783 0.8669 0.48 0.05 2.4894 0.9995 4.32 0.32 2.5283 X5007−1# 2.8154 0.9889 0.98 0.09 2.4732 0.9707 5.72 0.21 2.5233 X5010−6# 2.9339 0.9998 0.2 0.02 2.4533 0.998 3.8 0.07 2.4773 H4008−4# 2.7495 0.8966 2.72 0.21 2.5286 0.9988 4.18 0.32 2.6157 H903−4# 2.6900 0.9987 1.86 0.03 2.2307 0.9998 4.74 0.21 2.3601 5. Discussion 5.1 Effects of pore-size distribution on pore-throat structure The porosity of large pores (φ1) has a positive correlation with the sorting coefficient, with a correlation coefficient (R 2 ) of 0.2714 (Fig. 7 e). The sorting coefficient serves as an indicator of reservoir uniformity. A value near zero indicates high uniformity, whereas a higher value signifies lower uniformity. These findings validate Middleton’s assertion in 1962 that as the number of large pores increases, reservoir heterogeneity intensifies 36 . Furthermore, large pores are weakly correlated with other parameters, suggesting that large pores have a limited impact on the pore-throat structure. The porosity of the small pores (φ2) has a negative correlation with the entry pressure and median pressure, 0.2976 and 0.4063, respectively, but no such correlation is found for the large pores (Fig. 7 a and c). These results indicate that the development of small pores strongly affects the entry pressure and median pressure. The maximum pore-throat radius has a weak positive correlation with small pores, with an R 2 value of 0.27 (Fig. 7 b), but does not exhibit a significant correlation with large pores. Similar trends are observed for different pore sizes and median radii (Fig. 7 d). These results suggest that the development of small pores influences both the maximum and median pore-throat radii and is the primary determinant of the effective seepage storage space. Skewness indicates the asymmetry of the pore-throat size distribution. Coarse skewness generally results in good storage and percolation ability 37 . Figure 7 f illustrates a weak negative correlation between skewness and small pores, with a correlation coefficient of 0.1399 (Table 3 ). No significant relationship between skewness and large pores is evident. These findings suggest that skewness is minimally influenced by the pore-throat structure. Figure 7 g illustrates the correlation between the maximum mercury saturation and small pores, with a correlation coefficient (R 2 ) of 0.3713 (Table 3 ). However, there are no significant correlations with large pores, indicating that small pores predominantly contribute to interconnected pores. A higher mercury withdrawal efficiency results in more homogeneous pore and throat sizes. The mercury withdrawal efficiency and large pores exhibit a weak positive correlation (R 2 = 0.1789), suggesting that large pores have a weak effect on mercury withdrawal (Fig. 7 h). The correlation between the total porosity and pore-throat structure is similar to that of small pores. Analysis of the Chang 6 tight reservoirs indicates that small pores dominate the pore-throat structure. As small pores develop, the percolation properties improve, as evidenced by their significant correlations with the entry pressure, maximum pore radius, median pressure, median radius, skewness, and maximum mercury saturation. Table 3 Correlation coefficients between the porosity and parameters of the pore-throat structure Parameters of pore throat structure Correlation coefficients of parameters with φ1 Correlation coefficients of parameters with φ2 Correlation coefficients of parameters with φ Entry pressure(MPa) 0.1156 0.2976 0.5392 Maximum pore throat radius(µm) 0.0678 0.27 0.4303 Median pressure(MPa) 0.0744 0.4064 0.5975 Median radius(µm) 0.0927 0.1294 0.2905 Sorting coefficient 0.2714 0.1224 0.2412 Skewness 0.0999 0.1399 0.3137 Maximum mercury saturation(%) 0.0747 0.3731 0.5607 Efficiency of mercury withdrawal(%) 0.1789 0.0038 0.054 5.2 Relationships between the fractal dimension and reservoir properties A scatter plot is generated using the fractal dimensions D 1 and D 2 , along with porosity and permeability data. D 1 exhibits a clear negative correlation with both porosity and permeability. D 2 has a weak negative correlation with reservoir properties. A larger fractal dimension indicates a more complex pore-throat structure, leading to reduced porosity and permeability in reservoirs. Figure 8 further shows that the porosities of the corresponding pores exhibit hierarchical features, with the permeability converging to a certain point as the fractal dimension increases. Small pores possess the highest porosity, suggesting that they are the primary contributors to the overall porosity of tight reservoirs. The distribution of large pores plays a crucial role in determining reservoir storage and seepage capacities. As previously mentioned, the porosity and permeability of large pores exhibit obvious negative correlations with the fractal dimension (Fig. 8 ). However, interference from small pores diminishes the impact of large-pore porosity and permeability on the fractal dimension. In general, the total fractal dimension exhibits a decreasing trend as the porosity and permeability increase (Fig. 9 ). The analysis reveals that fractal dimensions D 1 , D 2 , and D exhibit distinct correlations with porosity and permeability. The pore-throat structure in the Chang 6 tight-oil sandstone is complex, with pore-throat sizes playing a significant role in the fractal characteristics, homogeneity, and complexity of the pore-throat structure. 5.3 Relationships between fractal dimension and pore-throat structure A study of the relationship between fractal dimensions and pore-throat structure parameters aims to discover patterns in the variation in fractal dimensions and how fractal features influence pore properties. There is greater complexity in the pore-throat structure with a larger fractal dimension 38 . Using the entry pressure, maximum pore-throat radius, median radius, sorting coefficient, skewness, maximum mercury saturation, and mercury withdrawal efficiency as parameters, a fitting method is applied to the fractal dimension of the tight-sandstone reservoirs to examine the relationship between the pore-throat structure parameters and fractal dimension (Fig. 10 ). Figure 10 shows that D 2 exhibits strong correlations with the parameters of the pore-throat structure, particularly with the entry pressure, maximum pore-throat radius, median pressure, median radius, and sorting coefficient (Fig. 10 a-e). The correlation coefficients are 0.27, 0.55, 0.37, 0.29 and 0.47, respectively. D 1 only has a good correlation with the efficiency of mercury withdrawal (Fig. 10 h). D 2 is negatively correlated with the entry pressure, median pressure, skewness, and mercury withdrawal efficiency (Fig. 10 a, c, f, h). It is positively correlated with the maximum throat radius, median radius, and sorting coefficient (Fig. 10 b, d, e). The maximum throat radius and median radius can be used to measure the pore-throat size of a reservoir. The entry pressure, median pressure, and mercury saturation can reflect the connectivity of the reservoir, while the sorting coefficient and skewness indicate the heterogeneity of the reservoir. The fractal dimension D 2 is generally smaller than D 1 , suggesting that smaller pores in the study area have good uniformity, smooth surfaces, and favourable physical properties. Additionally, the correlation of the total fractal dimension D with the pore-throat structure is similar to that of D 1 . In summary, the findings suggest that the heterogeneity and surface roughness of small pores are predominantly responsible for the pore-throat structure, as well as percolation and storage space. 5.4 Permeability estimation model Although a variety of permeability models based on porosity, mercury pressure parameters, and other parameters have been proposed in previous studies, most of these models do not consider the contribution of pore-throat fractal features to permeability. The fractal dimension and reservoir physical property analyses described in the previous section are combined with the results of previous studies. It is believed that an assessment of reservoir quality may be based on the fractal dimension D, which correlates well with permeability. The current study combines the three most commonly used permeability estimation models: Winland’s r 35 model 39 , Pittman’s r 25 model 40 , and Rezaee’s r 10 model 41 and their equations are as follows: Logr 35 = 0.732 + 0.588Logk − 0.864Logφ ( 10 ) Logk = -1.221 + 1.415Logφ + 1.512Logr 25 ( 11 ) Logk = -1.92 + 0.949Logφ + 2.18Logr 10 ( 12 ) where ri is the pore radius corresponding to mercury saturation i (µm), k is the permeability (mD) and φ is the porosity (%). Table 4 Relationships of permeability with the fractal dimension and pore-throat radius of tight sandstone in the Chang 6 section in the southeastern Ordos Basin Equations R 2 Equations R 2 \(\text{L}\text{o}\text{g}\text{k}=-0.645+\frac{1.367}{\text{D}}-\frac{0.028}{{\text{r}}_{\text{a}\text{p}\text{e}\text{x}}}\) 0.46 \(\text{L}\text{o}\text{g}\text{k}=-1.951+\frac{4.754}{\text{D}}-\frac{0.031}{{\text{r}}_{30}}\) 0.57 \(\text{L}\text{o}\text{g}\text{k}=-2.786+\frac{7.009}{\text{D}}-\frac{0.043}{{\text{r}}_{\text{k}}}\) 0.60 \(\text{L}\text{o}\text{g}\text{k}=-1.689+\frac{4.007}{\text{D}}-\frac{0.023}{{\text{r}}_{35}}\) 0.60 \(\text{L}\text{o}\text{g}\text{k}=-3.076+\frac{7.757}{\text{D}}-\frac{0.66}{{\text{r}}_{5}}\) 0.75 \(\text{L}\text{o}\text{g}\text{k}=-2.211+\frac{5.597}{\text{D}}-\frac{0.025}{{\text{r}}_{40}}\) 0.87 \(\text{L}\text{o}\text{g}\text{k}=-2.298+\frac{5.688}{\text{D}}-\frac{0.053}{{\text{r}}_{10}}\) 0.67 \(\text{L}\text{o}\text{g}\text{k}=-2.086+\frac{5.352}{\text{D}}-\frac{0.024}{{\text{r}}_{45}}\) 0.78 \(\text{L}\text{o}\text{g}\text{k}=-2.560+\frac{6.423}{\text{D}}-\frac{0.052}{{\text{r}}_{15}}\) 0.75 \(\text{L}\text{o}\text{g}\text{k}=-3.094+\frac{8.183}{\text{D}}-\frac{0.024}{{\text{r}}_{50}}\) 0.69 \(\text{L}\text{o}\text{g}\text{k}=-2.561+\frac{6.412}{\text{D}}-\frac{0.043}{{\text{r}}_{20}}\) 0.64 \(\text{L}\text{o}\text{g}\text{k}=-2.576+\frac{6.598}{\text{D}}-\frac{0.017}{{\text{r}}_{55}}\) 0.35 \(\text{L}\text{o}\text{g}\text{k}=-2.201+\frac{5.356}{\text{D}}-\frac{0.035}{{\text{r}}_{25}}\) 0.50 \(\text{L}\text{o}\text{g}\text{k}=-2.241+\frac{5.997}{\text{D}}-\frac{0.016}{{\text{r}}_{60}}\) 0.63 The estimated permeability-measured permeability crossplots calculated from the three models are shown in Fig. 11, which reveals that the three models greatly underestimate the permeability. The outcome arises from the fact that all three models are based on normal sandstone samples, which are less applicable to tight-sandstone reservoirs. As a result, the permeability calculated from the porosity greatly deviates from the measured value. To establish a better relationship between the permeability and fractal dimension as well as between the pore-throat radius, fractal dimension, and permeability corresponding to different mercury saturations, nonlinear multiple regression analyses are used. The equations, along with the correlation coefficients (r 2 ), are shown in Table 4. Among them, the r40 equation achieves the highest value, 0.87. The corresponding equation for using r40 is as follows: $$\text{L}\text{o}\text{g}\text{k}=-2.211+\frac{5.597}{\text{D}}-\frac{0.025}{{\text{r}}_{40}}$$ 13 where k is the permeability (mD), D is the fractal dimension, and r 40 is the pore radius corresponding to 40% mercury saturation (µm). According to Eq. ( 13 ), the pore radius has a positive contribution to the permeability, while the fractal dimension has a negative contribution. As a consequence, these empirical equations are theoretically accurate, in line with fractal theory and previous conclusions. Table 5 Supplementary data for the validation of the permeability estimation model Sample Permeability(mD) D r 40 H904 0.61 2.9735 0.34 X5001-12 0.22 2.8580 0.06 X5010-7 0.87 2.9012 0.05 X5010-8 0.25 2.8878 0.06 H86-7 0.73 2.7012 0.26 H86-18 0.22 2.8580 0.07 H901-17 0.48 2.8824 0.09 X5007-2 0.19 2.8150 0.03 H901-10 0.65 2.8593 0.11 X5012-3 0.96 2.7227 0.12 X5012-2 0.82 2.7006 0.11 The model prediction accuracy is validated using the samples from this study and 11 additional samples from the Chang 6 section in the southeastern Ordos Basin; the details of the additional samples are shown in Table 5 . The crossplot of the estimated permeability versus the measured permeability for the 27 samples shows that the data points have a relatively small deviation from the y = x line (Fig. 12 ). This suggests the applicability of the r 40 model for permeability prediction in the Chang 6 section in the southeastern Ordos Basin. 6. Conclusions In this paper, the pore-throat structure and fractal characteristics of the reservoir were analysed via physical tests, CL, SEM, CTS, XRD, and MICP on tight-oil sandstone samples from the Chang 6 member in the Haojiaping Block, Ordos Basin, China. A reliable permeability estimation model based on the fractal dimension and pore-throat radius was also developed. The conclusions are as follows. The rock types in this study area are predominantly fine-grained feldspar sandstones, with an average porosity of 7.7% and an average permeability of 0.42 mD. The pore types primarily include intergranular pores, feldspar-dissolved pores, intergranular-dissolved pores, and microcracks. The reservoirs in the study area exhibit low component maturity, moderate structural maturity, poor erosional conditions, good sorting, poor to moderate roundness, and high brittleness. This suggests that the deposited sediment was not transported over long distances. In addition, the study area is a sweet spot for oil exploration and is conducive to fracture modification. Small and large pores make up the tight-oil sandstone pore network. The complexity and heterogeneity of the pore-throat structures were quantified using fractal theory, yielding an average total fractal dimension of 2.5722. In addition, the pore throats were divided into two categories, with average fractal dimension values of 2.8094 (D 1 ) for large throats and 2.5325 (D 2 ) for small throats. The heterogeneity and complexity of small-pore structures are greater than those of large-pore structures. Connecting the microscopic pore structure to the macroscopic petrophysical parameters revealed that small pores play a crucial role in determining the pore-throat structure. As small pores develop, the properties of percolation, storage, pore-throat connectivity, and oil recovery improve. To build accurate permeability estimation models for tight sandstone, the widely used Pittman, Winland, and Rezaee models were enhanced through a systematic characterization of pore structures. The fractal dimension–pore-throat radius–permeability prediction model is highly applicable to the tight-sandstone reservoirs of the Chang 6 member in the southeastern Ordos Basin, China. Furthermore, the pore-throat radius corresponding to 40% mercury saturation (r 40 ) is the most effective predictor of permeability for tight sandstone. The use of fractal dimensions to predict permeability in tight-sandstone reservoirs can enhance model credibility. This will be highly significant for predicting reserves and evaluating and developing unconventional oil and gas, geothermal, and groundwater resources. Declarations Data availability All data generated or analysed during this study are included in this published article. Acknowledgments This research was supported by the National Science and Technology Projects of China (42130206). This work was supported by the State Key Laboratory of Continental Dynamics and PetroChina Yanchang Oilfied Company. Finally, we would like to express our thanks to the reviewers of this paper. Author contributions Huanmeng Zhang: Conceptualization, Methodology, Software, Data curation, Writing-Original draft preparation. Ling Guo: Conceptualization, Writing-Reviewing and Editing. Zhiyu Wu: Supervision, Methodology, Funding acquisition. Jiangbo Ma: Resources, Data Curation. Competing interests The author(s) declare no competing interests. References Zou, C. et al. Tight gas sandstone reservoirs in China: characteristics and recognition criteria. Journal of Petroleum Science and Engineering.89(01), 82–91 (2012). Sun, L. et al. Development characteristics and orientation of tight oil and gas in China. Petroleum Exploration and Development. 46(6):1073-1087(2019). Zhu, R.K., Zou, C.N., WU, S.T., Y, Z., Mao, Z.G., 2019. Mechanism for generation and accumulation of continental tight oil in China. Oil & Gas Geology. 40(6): 1168-1184. Li, G,X.et al. Progress, challenges and key issues of unconventional oil and gas development of CNPC. China Petroleum Exploration. 25(2): 1-13(2020). Wu, Z. et al. Advances and challenges in hydraulic fracturing of tight reservoirs: A critical review. Energy Geoscience, 3(4): 427-435(2022). Hu, S,Y. et al. Advances on continental tight oil accumulation and key technologies for exploration and development in China. Natural Gas Geoscience. 30(8): 1083-1093(2019). Li, Y.et al. A brief review of dynamic capillarity effect and its characteristics in low permeability and tight reservoirs. Journal of Petroleum Science and Engineering. 189(1): 1-9(2020). Zou, C. et al. Significance, geologic characteristics. Resource potential and future challenges of tight oil and shale oil. Kuangwu Yanshi Diqiu Huaxue Tongbao. 34(1): 3-17(2012). Zou, C. et al. Progress in China’s unconventional oil & gas exploration and development and theoretical technologies. Acta Geologica Sinica. 89(6): 979-1007(2015). Wei, X. et al. New geological understanding of tight sandstone gas. Lithologic Reservoirs. 29(1): 11-20(2017). He, D. et al. Integrated 3D hydrocarbon exploration in sedimentary basins of China. Oil & Gas Geology. 42(2): 265-284(2021). Gao, H. et al. Pore structure characterization, permeability evaluation and enhanced gas recovery techniques of tight gas sandstones. Journal of Natural Gas Science and Engineering. 28,536–547(2016). Desbois, G. et al. High-resolution 3D fabric and porosity model in a tight gas sandstone reservoir: a new approach to investigate microstructures from mm-to nm-scale combing argon beam cross sectioning and SEM imaging. Journal of Petroleum Science and Engineering. 78, 243–257(2011). Wang, H. et al. Fractal analysis and its impact factors on pore structure of artificial cores based on the images obtained using magnetic resonance imaging. Journal of Applied Geophysics. 86(01), 70–81(2012). Fu S. et al. Transformation of understanding from tight oil to shale oil in the Member 7 of Yanchang Formation in Ordos Basin and its significance of exploration and development . Acta Petrolei Sinica. 42(5)：561-569(2021). Mullen, J. Petrophysical characterization of the eagle ford shale in South Texas. Proceedings of the Canadian Unconventional Resources and International Petroleum Conference. October 19–21, Calgary, Alberta, Canada, SPE138145(2010). Du, J. et al. Discussion on effective development techniques for continental tight oil in China. Petroleum exploration and development. 41(2):217-224(2014). Ren, D. et al. Formation mechanism of the Upper Triassic Yanchang Formation tight sandstone reservoir in Ordos Basin—Take Chang 6 reservoir in Jiyuan oil field as an example. Journal of Petroleum Science and Engineering. 178(1): 497-505(2019). Yang, S. et al. Diagenetic evolution and its impact on reservoir quality of tight sandstones: A case study of the Triassic Chang 6 Member, Ordos Basin, northwest China. Marine and Petroleum Geology. 117(01): 104360(2020). Fu, Y. et al. Implications of lithofacies and diagenetic evolution for reservoir quality: A case study of the Upper Triassic chang 6 tight sandstone, southeastern Ordos Basin, China. Journal of Petroleum Science and Engineering. 218(01): 111051(2022). Geng L. et al. A fractal production prediction model for shale gas reservoirs. Journal of Natural Gas Science and Engineering. 55(01): 354-367(2018). Xia, Y. et al. Fractal dimension, lacunarity and succolarity analyses on CT images of reservoir rocks for permeability prediction. Journal of Hydrology. 579(01): 124-198(2019). Wang, C. et al. Research on Characteristics of Chang 6 Reservoir in Huanxian Area, Ordos Basin. Xi’an Shiyou University. 1-63(2022). Huang, W. et al. Reservoir spaces in tight sandstones: Classification, fractal characters, and heterogeneity. Journal of Natural Gas Science and Engineering. 46(01): 80-92(2017). Rahner, M. et al. Fractal dimensions of pore spaces in unconventional reservoir rocks using X-ray nano- and micro-computed tomography. Journal of Natural Gas Science and Engineering, 55(01): 298-311(2018). Gao, Y. Research on Brittleness Evaluation and Main Controlling Factors of Tight Oil Reservoirs——Acase study from Triassic Yanchang Formation Chang 7 oil formation in Dingbian Dongrengou Oilfield, Ordos Basin. Northwest University. 1-89(2022). Li A. et al. Chemical characteristics of formation water of Chang 2 oil formation of Yanchang Formation in Zhaike area，Ordos Basin and its indication to dense oil reservoir. Natural Gas Geoscience. 33(10): 1637-1647(2022). Wang, L. et al. Lithofacies characteristics and sedimentary environment of Chang 7 black shale in the Yanchang Formation, Ordos Basin. Journal of Palaeography. 25(03): 598-613(2023). Lv, Q. et al. Sedimentary types, characteristics and model of lacustrine fine-grained gravity flow in the Member 7 of Trassic Yanchang Formation in Ningxian area, Ordos Basin. Journal of Palaeogeography. 25(04): 1-18(2023). Alberti, G. et al. 1.6.5 SEM and TEM techniques. World Crop Pests. 6(01): 399-410(1996). Huang, H. et al. A method to probe the pore-throat structure of tight reservoirs based on low-field NMR: Insights from a cylindrical pore model. Marine and Petroleum Geology. 117(01): 104344(2020). Zhong, X. et al. Microscopic pore throat structures and water flooding in heterogeneous low-permeability sandstone reservoirs: A case study of the Jurassic Yan’an Formation in the Huanjiang area, Ordos Basin, Northern China. Journal of Asian Earth Sciences. 219(01): 104903(2021). Jiang, Z. Sedimentary Science . Beijing: Petroleum Industry Press. 1-424(2003). Lala, A. et al. Controls of pore throat radius distribution on permeability. Journal of Petroleum Science and Engineering. 157: 941-950(2017). Qu, Y. et al. Pore–throat structure and fractal characteristics of tight sandstones in Yanchang Formation, Ordos Basin. Marine and Petroleum Geology. 120(01): 104573(2020) Middleton, G. On Sorting, Sorting Coefficients, and the Lognormality of the Grain-Size Distribution of Sandstones: A Discussion. The Journal of Geology. 70(6): 754-756(1962). Blanca, M. et al. Skewness and Kurtosis in Real Data Samples. Methodology. 9(2): 78-84(2013). Cai, J. et al. Fractal Characterization of Spontaneous Co-current Imbibition in Porous Media. Energy & Fuels. 24(3): 1860-1867(2010). Kolodzie Jr.. Analysis of Pore Throat Size and Use of the Waxman-Smits Equation to Determine Ooip in Spindle Field, Colorado. Society of Petroleum Engineers, Dallas, Texas, p. 10(1980). Pittman, E. Relationship of porosity and permeability to various parameters derived from mercury injection-capillary pressure curves for sandstone. AAPG Bulletin. 76 (2): 191–198(1992). Rezaee, R. et al. Tight gas sands permeability estimation from mercury injection capillary pressure and nuclear magnetic resonance data. Journal of Petroleum Science and Engineering. 89, 92–99(2012). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 13 Nov, 2024 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 25 Sep, 2024 Reviews received at journal 22 Sep, 2024 Reviews received at journal 22 Sep, 2024 Reviews received at journal 19 Sep, 2024 Reviewers agreed at journal 12 Sep, 2024 Reviewers agreed at journal 12 Sep, 2024 Reviewers agreed at journal 12 Sep, 2024 Reviewers invited by journal 12 Sep, 2024 Editor assigned by journal 12 Sep, 2024 Editor invited by journal 28 Jun, 2024 Submission checks completed at journal 28 Jun, 2024 First submitted to journal 26 Jun, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4640639","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":327654657,"identity":"271a5327-00fe-4eec-990d-e9be41fba8d6","order_by":0,"name":"Huanmeng Zhang","email":"","orcid":"","institution":"Northwest University","correspondingAuthor":false,"prefix":"","firstName":"Huanmeng","middleName":"","lastName":"Zhang","suffix":""},{"id":327654658,"identity":"eae01883-ff12-4708-9649-3256af8e4aa6","order_by":1,"name":"Ling Guo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2UlEQVRIiWNgGAWjYBACPigtA8SMDxIqaghrYYPSPEDMbPDgzDHStLBJPmxhJkIL/xrDh18qbHj4+deYVSQ2sDHwt3cn4Nci8cbYWOZMGo/kjDdmNxJ3yDBInDm7gYCWM2bSkm2HeQxunAFqOcPGYCCRS4yWfxAtBYltzERo4e8xk/zYANRyvseMgTgtEmzFxgzHQH5hK5ZIOHOMh6Bf+PkPb3z4o8ZGDsT4+KOiRo6/vRe/FgaJBAZmHjAjwwBE8eBXDrbmAAPjDzDj+APCqkfBKBgFo2BEAgCZAUV0vyPemgAAAABJRU5ErkJggg==","orcid":"","institution":"Northwest University","correspondingAuthor":true,"prefix":"","firstName":"Ling","middleName":"","lastName":"Guo","suffix":""},{"id":327654659,"identity":"8bcbe38b-3925-4cb2-92d8-c347fe5456cd","order_by":2,"name":"Zhiyu Wu","email":"","orcid":"","institution":"Northwest University","correspondingAuthor":false,"prefix":"","firstName":"Zhiyu","middleName":"","lastName":"Wu","suffix":""},{"id":327654660,"identity":"e5190446-17b6-4cc9-bc57-69b514f66528","order_by":3,"name":"Jiangbo Ma","email":"","orcid":"","institution":"ShaanxiYanchang Petroleum (China)","correspondingAuthor":false,"prefix":"","firstName":"Jiangbo","middleName":"","lastName":"Ma","suffix":""}],"badges":[],"createdAt":"2024-06-26 07:11:47","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4640639/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4640639/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-024-79203-7","type":"published","date":"2024-11-13T15:57:26+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":60712879,"identity":"1d2b855f-7b8e-4ab7-a4bf-100871a794d9","added_by":"auto","created_at":"2024-07-19 20:28:19","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":685007,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Simplified tectonic units of the Ordos Basin and location of the study area (red rectangle). (b) Stratigraphic column of the sixth member of the Yanchang Formation in the Haojiaping area. (modified by Lv, 2023)\u003csup\u003e29\u003c/sup\u003e\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4640639/v1/5e01638e3757a772bef7a644.png"},{"id":60711767,"identity":"c2abca84-2b17-4799-93e5-840ce37d03d3","added_by":"auto","created_at":"2024-07-19 20:20:18","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":727415,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Triangulation of the extended Long 6 stratigraphic system in the Ordos Basin. The main lithology of the study area is feldspathic fine sandstone. (b) The main mineral component of the Chang 6 reservoir rocks in the study area is feldspar, followed by quartz..\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4640639/v1/9ea29b90418e82dbbfd09d78.png"},{"id":60711818,"identity":"a2ea08d6-8bd2-44b8-b785-c10f811db283","added_by":"auto","created_at":"2024-07-19 20:20:20","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":2644238,"visible":true,"origin":"","legend":"\u003cp\u003eMineral composition and pore-throat types in the Haojiaping area based on CL, CTS, and SEM.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-4640639/v1/dfe4fc57b484af391a2bdb9b.png"},{"id":60711769,"identity":"ec13b7e0-6a1b-4f40-af6f-d468d955cdd0","added_by":"auto","created_at":"2024-07-19 20:20:18","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":346071,"visible":true,"origin":"","legend":"\u003cp\u003ePetrophysical characteristics of the study area.\u003c/p\u003e\n\u003cp\u003e(a) The porosity distribution is mainly in a range of 8%-10%; (b) the permeability distribution ranges mainly from 0.3-0.7 mD; and\u003c/p\u003e\n\u003cp\u003e(c) Porosity–permeability relation (showing an index correlation).\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-4640639/v1/5992ab9b9ccb38a7b7bcfd69.png"},{"id":60711820,"identity":"780f0940-e665-45ca-9d19-49f5779da99d","added_by":"auto","created_at":"2024-07-19 20:20:21","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":867709,"visible":true,"origin":"","legend":"\u003cp\u003eCapillary pressure curves, pore-throat size distribution curves and corresponding contributions to the permeability of the three types of typical samples. The results of the classification are shown in Table 1. (Type I has a porosity greater than 8%, Type II has a porosity ranging from 7% to 8%, and Type III has a porosity less than 7%).\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-4640639/v1/70294a194ae228943421ab4e.png"},{"id":60711817,"identity":"1d16b083-e4ba-4123-93c6-111a38b829dd","added_by":"auto","created_at":"2024-07-19 20:20:20","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":300671,"visible":true,"origin":"","legend":"\u003cp\u003eFractal characteristic curves of typical Samples H70 (a), X4008-3 (b) and X5007-1 (c) with the three types of pore-throat structures.\u003c/p\u003e\n\u003cp\u003eFractal dimension values for different pore regions are shown on the graphs.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-4640639/v1/c967285ec32bd6d1f5f41467.png"},{"id":60711816,"identity":"238b91a5-761e-4bb4-b2cd-1180dcdff2e4","added_by":"auto","created_at":"2024-07-19 20:20:19","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":1026150,"visible":true,"origin":"","legend":"\u003cp\u003eCorrelation analysis of the macroporosity, microporosity and total porosity with the pore-throat structure parameters of the Chang 6 tight-sandstone samples. It is obvious that small pores have a greater effect on pore-size distribution (the formula corresponding to the total fractal dimension D).\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-4640639/v1/9cbb55b44e436b7ccb7ed492.png"},{"id":60711771,"identity":"7d911721-b4dd-4c6e-a2c7-777e22561f32","added_by":"auto","created_at":"2024-07-19 20:20:19","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":217935,"visible":true,"origin":"","legend":"\u003cp\u003eCorrelation of D\u003csub\u003e1\u003c/sub\u003e and D\u003csub\u003e2\u003c/sub\u003e with the porosity and permeability of the corresponding pores in the Chang 6 tight-sandstone sample.\u003c/p\u003e\n\u003cp\u003e(a) Porosity and (b) permeability. It shows that the physical properties of large pores correlate better with the fractal dimension. Therefore, large pores are more affected by the structure of the pore throat (the formula corresponds to the fractal dimension D\u003csub\u003e1\u003c/sub\u003e).\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-4640639/v1/9093a5b2e9a7c4ea9cb62150.png"},{"id":60711781,"identity":"a621661f-92a2-4402-995a-8fba7392be03","added_by":"auto","created_at":"2024-07-19 20:20:19","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":167938,"visible":true,"origin":"","legend":"\u003cp\u003eCorrelation of the total fractal dimension D with the porosity and permeability of the Chang 6 tight-sandstone samples.\u003c/p\u003e\n\u003cp\u003e(a) Porosity and (b) permeability. It has been shown that as D increases, pore structure becomes more complex and porosity and permeability decrease.\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-4640639/v1/ad735b33a979d33f7e27c299.png"},{"id":60711773,"identity":"5f922162-49cf-4365-8eb2-59a55f2d61a4","added_by":"auto","created_at":"2024-07-19 20:20:19","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":1012558,"visible":true,"origin":"","legend":"\u003cp\u003eCorrelation of the fractal dimensions D, D\u003csub\u003e1\u003c/sub\u003e and D\u003csub\u003e2\u003c/sub\u003e versus the pore-throat structure parameters of the Chang 6 tight sandstone samples.\u003c/p\u003e\n\u003cp\u003eIt shows that small pores exhibit strong correlations with the parameters of the pore-throat structure (the formula corresponding to the fractal dimension D\u003csub\u003e2\u003c/sub\u003e).\u003c/p\u003e","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-4640639/v1/06b243ff5fb75138ab6a524e.png"},{"id":60712878,"identity":"f4e08132-39ef-4f9c-887a-d1441caabb39","added_by":"auto","created_at":"2024-07-19 20:28:18","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":234941,"visible":true,"origin":"","legend":"\u003cp\u003eMeasured permeability versus calculated permeability from the Winlan, Pittman and Rezaee models. It is obvious that the predicted values of the three models are lower than the measured values.\u003c/p\u003e","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-4640639/v1/9ac4bf587df6d224c7b48724.png"},{"id":60711823,"identity":"6b343487-2a15-4f8f-98b3-f7d7d15d570f","added_by":"auto","created_at":"2024-07-19 20:20:21","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":214528,"visible":true,"origin":"","legend":"\u003cp\u003eCrossplot of measured versus calculated permeability derived from the new models. The dashed black line indicates where the predicted permeability equals to that measured from experiments.\u003c/p\u003e","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-4640639/v1/640c6ef886f8f44ba793cdaf.png"},{"id":69274987,"identity":"f227e955-8555-4f04-b62f-ba5384cdf23e","added_by":"auto","created_at":"2024-11-18 16:42:45","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":10756235,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4640639/v1/80ee6c69-bd51-4053-b4e2-cac4300884de.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Pore-throat structure, fractal characteristics and permeability prediction of tight sandstone: the Yanchang Formation, Southeast Ordos Basin","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eWith advancements in oil and gas exploration and development, the proportion of unconventional oil and gas resources has steadily increased. Tight reservoirs are destined to play a central role in future exploration and development endeavours\u003csup\u003e1\u0026ndash;5\u003c/sup\u003e. Tight-sandstone reservoirs represent a vital segment of China\u0026rsquo;s unconventional oil and gas resources, holding an important position in the nation's energy structure\u003csup\u003e6\u0026ndash;7\u003c/sup\u003e. Currently, they are being exploited in large quantities in the Ordos Basin. They play a pivotal role in increasing oil and gas production and ensuring national energy security\u003csup\u003e8\u0026ndash;11\u003c/sup\u003e. Moreover, these reservoirs typically exhibit small pore-throat radii and complex structures, resulting in limited connectivity\u003csup\u003e12\u0026ndash;13\u003c/sup\u003e. This also poses challenges for the study of reservoir microstructures\u003csup\u003e14\u0026ndash;15\u003c/sup\u003e. Tight-oil extraction has shown notable success in North America, especially in certain regions\u003csup\u003e16\u003c/sup\u003e. While research in China is still in its early stages, preliminary exploration indicates promising prospects for tight-oil production\u003csup\u003e17\u003c/sup\u003e. The Ordos Basin is renowned for its substantial reserves of tight oil. The Chang 6 member of the Yanchang Formation in the Ordos Basin is a typical tight reservoir and one of the primary targets for tight-oil exploration and development in this basin\u003csup\u003e18\u0026ndash;20\u003c/sup\u003e. The mechanisms of petroleum charging, migration, and accumulation in tight-oil reservoirs differ from those in conventional reservoirs. Therefore, a detailed study of the micropore-throat structure of tight-oil reservoirs is of significant practical importance for understanding the distribution of tight oil and guiding oilfield development.\u003c/p\u003e \u003cp\u003eThe pore throats of tight sandstone are narrow, and the microstructure of the pore throats is complex and heterogeneous. It is challenging to characterize the morphology of pore throats in tight sandstone using traditional testing methods. Therefore, combining these studies with fractal geometry theory provides a more accurate approach for understanding the complex pore-throat structures in tight sandstone. Fractal theory can relatively accurately describe the homogeneity and complexity of pore-throat structures within tight reservoirs, and it is widely used in petroleum exploration\u003csup\u003e21\u0026ndash;22\u003c/sup\u003e. However, the distribution range of pore throats in tight sandstone is large, and the microstructural and fractal features of pores and throats of different radii are bound to differ. Consequently, investigating fractal features across multiple scales becomes imperative. The fractal dimension (D) serves as a pivotal metric for characterizing the heterogeneity of pore-throat structures and has been extensively utilized in prior investigations of such structures. As protuberances and concavities increase, pore-throat surfaces and structures exhibit heightened roughness and complexity, with the fractal dimension providing a quantitative measure of this surface roughness\u003csup\u003e23\u0026ndash;24\u003c/sup\u003e. Experimental techniques such as mercury intrusion capillary pressure (MICP), high-pressure mercury intrusion (HPMI), constant-rate mercury injection (CRMI), and nuclear magnetic resonance (NMR) are commonly used to evaluate the pore-throat structures of reservoirs. The fractal dimension of sandstone ranges from 2.0\u0026ndash;3.0, which is indicative of the local\u0026ndash;whole relationship inherent in sandstone pore-throat structures. This parameter holds substantial significance because it offers a comprehensive representation of the regularity and composite characteristics of pore throats. Fractal dimension analysis has proven to be a proficient method for characterizing pore-throat structures. The closer the fractal dimension (D) is to 3.0, the rougher the pore-throat surface and the more complex the structure\u003csup\u003e25\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn this study, cast thin section (CTS), scanning electron microscopy (SEM), X-ray diffraction (XRD), and mercury intrusion capillary pressure (MICP) analyses were used to conduct a detailed investigation of the pore-throat types, sizes, and structures in the tight sandstone of the Chang 6 member. The fractal characteristics of the pores and throats of the tight sandstone were studied based on the mercury feed curves of the capillary pressure curve of the Chang 6 member in the Haojiaping area, Ordos Basin. Additionally, this study explored the relationships among fractal characteristics, reservoir properties, and pore-throat structures, and a nonlinear equation was utilized to identify the pore-throat radius that best correlates with permeability. The feasibility of using this radius to predict permeability in tight reservoirs was then verified.\u003c/p\u003e"},{"header":"2. Geological Setting","content":"\u003cp\u003eThe Ordos Basin is a resource-rich, structurally simple, large multirotational cratonic superposition basin. This basin has stable subsidence, gentle tectonics, and migration of depressions (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a)). Oil reservoirs developed in the Triassic strata of the Ordos Basin. The Upper Triassic Yanchang Formation is the most important tight-oil and gas reservoir for exploration and development. The Ordos Basin experienced a complete inland lake basin evolution, which included the occurrence and development of a lake and intense subsidence, shrinkage, and demise of the lake during the Yanchang period of the Triassic. The Yanchang Formation is divided into the Chang 10 to Chang 1 members from bottom to top\u003csup\u003e26\u0026ndash;28\u003c/sup\u003e. During deposition of the Upper Triassic Chang 6 member, the water body experienced shallowing, leading to a reduction in the size of the lake basin. This phase marked the primary period of the formation of lake deltas, with a substantial deposition of deltaic sands. There are extensive opportunities for exploration and prospects in the oil and gas industry (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b)).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe Haojiaping area is located in the middle of the Yishan Slope in the Ordos Basin, which is a west-dipping gently monoclonal tectonic area, and the Chang 6 oil formation group is the main tight-oil target in the study area, with a thickness of 120\u0026ndash;150 m. The lithology is dominated by grayish-green fine sandstone, dark mudstone, and delta-front facies. Sandstone mainly formed in channels and channel bars on the delta.\u003c/p\u003e"},{"header":"3. Materials and Methods","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Sampling and Processing\u003c/h2\u003e \u003cp\u003eIn this study, a total of 56 core samples were systematically collected from 17 wells situated within the Upper Triassic Yanchang Formation in the Haojiaping area, which is located on the southeastern slope of the Ordos Basin. These samples underwent initial drilling that produced cylindrical specimens measuring approximately 2.5 cm in diameter and 5.0 cm in length. Then, extraction experiments were conducted using alcohol and benzene following sample numbering. After drying at 50 ℃ for 24 hours, the samples were divided into two segments. One segment, measuring 2.5 cm in length, was allocated for helium porosity and nitrogen permeability measurements (36 samples), as well as MICP testing (16 samples). The other segment, measuring 0.5 cm in length, was designated for CTS testing (43 samples), XRD analysis (21 samples) and SEM observation (12 samples). In this study, MICP tests were conducted using an automatic mercury porosimeter (Autopore IV 9505, Micromeritics). CTSs of 43 samples were examined using an Olympus-cx21 polarizing microscope. SEM observations were performed using a Tescan S-3200 N field emission electron microscope\u003csup\u003e30\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Fractal theory\u003c/h2\u003e \u003cp\u003eFractal theory is a research theory for structurally complex but self-similar systems in nature, and the geometry of the pore-throat space can be characterized by fractal dimension\u003csup\u003e31\u0026ndash;32\u003c/sup\u003e. The fractal dimension of the pore-throat structure can be determined from the MICP results. If the throat structure exhibits fractal characteristics, the number of pore throats with a radius exceeding r can be expressed based on fractal theory as follows:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\text{N} (\u0026gt;\\text{r})={\\int }_{\\text{r}}^{{\\text{r}}_{\\text{m}\\text{a}\\text{x}}}\\text{P} \\left(\\text{r}\\right)\\text{d}\\text{r}={\\text{a}\\text{r}}^{-\\text{D}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere r\u003csub\u003emax\u003c/sub\u003e represents the maximum pore-throat radius, P(r) denotes the distribution density function of the pore-throat radius, a is a proportionality constant, and D represents the fractal dimension.\u003c/p\u003e \u003cp\u003eBy taking the derivative with respect to \u0026ldquo;r\u0026rdquo;, the distribution density fraction of the pore-throat radius P(r) is derived.\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\text{P}\\left(\\text{r}\\right)=\\frac{\\text{d}\\text{N}(\u0026gt;\\text{r})}{\\text{d}\\text{r}}=\\text{a}{\\prime }{\\text{r}}^{-\\text{D}-1}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere a\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\prime }\\)\u003c/span\u003e\u003c/span\u003e is a proportionality constant, which is equivalent to -D\u0026times;a.\u003c/p\u003e \u003cp\u003eBy transforming Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) into Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), the total volume V(\u0026lt;\u0026thinsp;r) of pores with a radius less than r can be expressed as follows:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\text{V}\\left(\\text{r}\\right)={\\int }_{{\\text{r}}_{\\text{s}}}^{\\text{r}}\\text{P}\\left(\\text{r}\\right)\\text{a}{\\text{r}}^{3}\\text{d}\\text{r}=\\frac{-{\\text{a}}^{2}\\text{D}}{3-\\text{D}}\\left({\\text{r}}^{3-\\text{D}}-{\\text{r}}_{\\text{m}\\text{i}\\text{n}}^{3-\\text{D}}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe total pore volume (V) can be calculated as follows:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\text{V}=\\frac{{-\\text{a}}^{2}\\text{D}}{3-\\text{D}}\\left({\\text{r}}_{\\text{m}\\text{a}\\text{x}}^{3-\\text{D}}-{\\text{r}}_{\\text{m}\\text{i}\\text{n}}^{3-\\text{D}}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eBy converting Eqs.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) and (\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) into Eq.\u0026nbsp;(\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e5\u003c/span\u003e), one can derive the cumulative volume fraction of pore throats with radii less than r(s).\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\text{s}=\\frac{\\text{V}(\u0026lt;\\text{r})}{\\text{V}}=\\frac{{\\text{r}}^{3-\\text{D}}-{\\text{r}}_{\\text{m}\\text{i}\\text{n}}^{3-\\text{D}}}{{\\text{r}}_{\\text{m}\\text{a}\\text{x}}^{3-\\text{D}}-{\\text{r}}_{\\text{m}\\text{i}\\text{n}}^{3-\\text{D}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eBecause r\u003csub\u003emin\u003c/sub\u003e is far less than r\u003csub\u003emax\u003c/sub\u003e, Eq.\u0026nbsp;(\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e5\u003c/span\u003e) can be simplified as follows:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\text{s}={\\left(\\frac{\\text{r}}{{\\text{r}}_{\\text{m}\\text{i}\\text{n}}}\\right)}^{3-\\text{D}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eUnder the assumption that the wetting contact angle is unaffected by the pore-throat size, the fractal formula for the distribution of the pore-throat radius can be derived.\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\text{s}={\\left(\\frac{{\\text{P}}_{\\text{c}}}{{\\text{P}}_{\\text{m}\\text{i}\\text{n}}}\\right)}^{\\text{D}-3}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eTaking the logarithm of both sides of Eq.\u0026nbsp;(\u003cspan refid=\"Equ7\" class=\"InternalRef\"\u003e7\u003c/span\u003e), the formula is changed as follows:\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\text{l}\\text{o}\\text{g}\\text{S}=\\left(\\text{D}-3\\right)\\text{l}\\text{o}\\text{g}{\\text{P}}_{\\text{c}}-\\left(\\text{D}-3\\right)\\text{l}\\text{o}\\text{g}{\\text{P}}_{\\text{m}\\text{i}\\text{n}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe wetting phase saturation S and capillary pressure P\u003csub\u003ec\u003c/sub\u003e exhibit a linear relationship. The slope of the linear equation fitted in a log-log coordinate system represents (\u0026#119863;\u0026minus;3), from which the fractal dimension D can be calculated.\u003c/p\u003e \u003cp\u003eThe fractal of the pore-throat structure can be categorized into integral fractal and piecewise fractal based on the presence or absence of turning points in the fractal curve. An integral fractal curve lacks inflection points, indicating similarities in the structures of large and small-pore throats. In contrast, a piecewise fractal curve exhibits distinct turning points. The overall fractal dimension (D) of the pore-throat structure can be determined by employing the weighted average of the porosities of various pore-throat sizes (Eq.\u0026nbsp;(\u003cspan refid=\"Equ9\" class=\"InternalRef\"\u003e9\u003c/span\u003e)).\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$$\\text{D}={\\text{D}}_{1}\\times \\frac{{{\\phi }}_{1}}{{{\\phi }}_{1}+{{\\phi }}_{2}}+{\\text{D}}_{2}\\times \\frac{{{\\phi }}_{2}}{{{\\phi }}_{1}+{{\\phi }}_{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Results","content":"\u003cdiv id=\"Sec7\"\u003e\n \u003ch2\u003e4.1 Petrophysical characteristics and mineral composition\u003c/h2\u003e\n \u003cp\u003eBased on thin-section analysis, scanning electron microscope detection, and X-ray diffraction analysis, the composition of the reservoir rocks in the Chang 6 member in the Haojiaping area primarily consists of quartz, lithic fragments, plagioclase, and potassium feldspar (Fig. \u003cspan\u003e3\u003c/span\u003e(a, b, c)). Statistical analysis using the point-counting method on thin sections of the cast body reveals that in the skeletal grains of the study area, feldspar has the highest proportion (36\u0026ndash;69%, with an average of 61.4%), followed by quartz (17\u0026ndash;30%, with an average of 26.7%), and then lithic fragments (6\u0026ndash;21%, with an average of 11.9%). Therefore, the rock type in the Chang 6 reservoir in the Haojiaping area is predominantly fine-grained feldspar sandstone, with a small amount of lithic feldspar sandstone (Fig. \u003cspan\u003e2\u003c/span\u003e(a)). The results of the XRD experiments show that the mineral components of the reservoir, in descending order of content, are feldspar and quartz, clay minerals (clay, anhydrite, and laumontite), and carbonate (calcite, ankerite, and siderite) (Fig. \u003cspan\u003e2\u003c/span\u003e(b)). The overall average pore-filling material content in the reservoir is approximately 15%, with the main components being siderite, clay, and calcite. The cement content is greater than that of the matrix and is primarily composed of chlorite, illite, calcite, and quartz-cemented materials, along with minor amounts of zeolites, goethite, and asphaltene (Fig. \u003cspan\u003e3\u003c/span\u003e(g,h,l)). The reservoir exhibits strong compaction, a low degree of weathering, good sorting, and poor to moderate roundness. The cement types are mainly pore filling and patchy, with grains exhibiting linear and concavo\u0026ndash;convex contacts. The grain-size analysis indicates that the sandstone particles range from 0.03 to 0.32 mm, with an average of 0.28 mm.\u003c/p\u003e\n \u003cp\u003eSandstone classification can reflect source-rock properties, rock maturity, and physical conditions during deposition. In general, the ratio of plagioclase to lithic fragments (i.e., F/R, referred to as the source index) can reflect the basic characteristics of the source-rock composition\u003csup\u003e33\u003c/sup\u003e. The F/R ratio in the study area is greater than 1, with an average of 5.2, indicating that the predominant source rock in the study area is granite. The relative ratio of stable components (quartz) to unstable components (plagioclase\u0026thinsp;+\u0026thinsp;lithic fragments), or Q/(F\u0026thinsp;+\u0026thinsp;R), is used to represent the transport and abrasion history. Higher component maturity is associated with better abrasion conditions and a longer transport history. The Q/(F\u0026thinsp;+\u0026thinsp;R) ratio in the study area ranges from 0.23 to 0.53, with an average of 0.38, indicating relatively low component maturity. The ratio of grains or clasts to matrix (i.e., G/M, referred to as the flow coefficient) directly reflects the degree of sand\u0026ndash;mud mixing and indicates the quality of rock sorting. A small G/M ratio indicates poor sorting, which is typically associated with gravity flow deposits, while a larger ratio indicates traction flow deposits. The average G/M ratio in the study area is 24.7, reflecting good sorting. According to the formula of the rock brittleness index (BI) in China (Eq.\u0026nbsp;(\u003cspan\u003e10\u003c/span\u003e)), the brittleness index of the target area ranges from 65.31\u0026ndash;92.77%, with an average of 82.52%. Meeting the criterion of high brittleness as specified in the national standard \u0026ldquo;Method for Optimal Selection of Marine Shale Gas Exploration Target: GB/T 35110-20-17\u0026rdquo; indicates a high content of brittle minerals, providing important prerequisites for the optional selection of exploration sweet spots, reservoir hydraulic fracturing, and the formation of artificial fractures.\u003c/p\u003e\n \u003cdiv id=\"Equ10\"\u003e\n \u003cdiv id=\"FileID_Equ10\" name=\"EquationSource\"\u003e$$\\text{B}\\text{I}=\\frac{{\\text{m}}_{\\text{q}\\text{u}\\text{a}}}{{\\text{m}}_{\\text{q}\\text{u}\\text{a}}+{\\text{m}}_{\\text{c}\\text{l}\\text{a}}+{\\text{m}}_{\\text{c}\\text{a}\\text{r}}}\\times 100\\text{\\%}$$\u003c/div\u003e\n \u003cdiv\u003e10\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003ewhere BI is the brittleness index (%), is the quartz content (%), is the clay mineral content (%), and is the carbonate content (%).\u003c/p\u003e\n \u003cp\u003eIn summary, the reservoirs in the study area exhibit low component maturity, moderate structural maturity, poor erosion conditions, good sorting, poor to moderate roundness, and high brittleness. This suggests that the deposited sediment was not transported over long distances, indicating characteristics of near-source deposition. In addition, the study area is a sweet spot for oil exploration and is conducive to fracture modification.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\"\u003e\n \u003ch2\u003e4.2 Porosity and permeability\u003c/h2\u003e\n \u003cp\u003eA total of 45 sandstone samples from the Chang 6 member in the study area were analysed. Figure \u003cspan\u003e4\u003c/span\u003e(a) shows that the porosity of the reservoir in the study area ranges from 0.5\u0026ndash;10.5%, with the predominant range being 8\u0026ndash;10%, and the average porosity is 7.7%. Figure \u003cspan\u003e4\u003c/span\u003e(b) shows that the permeability varies from 0.05 to 0.97 mD, mainly falling between 0.3 and 0.7 mD, with an average of 0.42 mD. These values indicate that the study area is a typical tight reservoir. Figure \u003cspan\u003e4\u003c/span\u003e(c) illustrates a positive correlation between the porosity and permeability, with a coefficient of 0.61. This suggests that the pore-throat structure in the study area is complex and that the pore-throat size significantly impacts the permeability. Conventional thin section, CTS, and SEM analyses indicate that the face porosity of the Chang 6 reservoir in the study area ranges from 1.5\u0026ndash;6.25%, with an average of 4.75%. The face porosity is consistently below 10%, confirming that the Chang 6 member is a tight-sandstone reservoir. The predominant storage space is characterized by dissolution pores, with common occurrences of feldspar dissolution pores and cloudy feldspar dissolution pores (Fig. \u003cspan\u003e3\u003c/span\u003e(d, f, i)). The secondary features include micropores and microfractures (Fig. \u003cspan\u003e3\u003c/span\u003e (k)). Intergranular pores make up the majority of the remaining pores and are characterized by polygonal shapes and clearly defined boundaries (Fig. \u003cspan\u003e3\u003c/span\u003e(e, g)), indicating the effects of compaction, cementation, and mixed filling on these pores. Cast thin section (CTS) images reveal secondary enlargement and interstitial authigenic quartz, as well as thin films of chlorite (Fig. \u003cspan\u003e3\u003c/span\u003e(h, j, l)). The presence of chlorite films and quartz is crucial for resisting compaction, contributing to the preservation of pores within the samples.\u003cspan\u003e\u003c/span\u003e\u003c/p\u003e\n\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\"\u003e\n \u003ch2\u003e4.3 Characteristics of the pore throat network\u003c/h2\u003e\n \u003cp\u003eParticles are separated by pores, and narrow areas that connect these pores are called throats. A porous medium is composed of pores that serve as reservoirs for fluids and throats that control the flow of fluids through them\u003csup\u003e34\u003c/sup\u003e.\u003c/p\u003e\n \u003cp\u003eAccording to analyses of cast thin sections and scanning electron microscopy images of the Chang 6 reservoir, the predominant throat types are lamellar (Fig. \u003cspan\u003e3\u003c/span\u003e(d)), necking (Fig. \u003cspan\u003e3\u003c/span\u003e(f)), and sheet-like (Fig. \u003cspan\u003e3\u003c/span\u003e(g)). The primary pore-throat combinations in the Chang 6 reservoir include grain interpores, feldspar dissolution pores, intercrystalline micropores, and microfine throat hybrid combinations. However, these throat types are complex, and their connectivity is relatively weak, thereby restricting fluid flow. Mercury injection capillary pressure (MICP) experiments can be performed on tight-sandstone samples to determine pore-throat structure characteristics and pore-size distributions\u003csup\u003e35\u003c/sup\u003e. Based on the MICP results, pressure‒capillary characteristic curves and throat radius distribution curves are plotted for 16 representative samples (Fig. \u003cspan\u003e5\u003c/span\u003e). The samples are classified into three types based on their porosity values (Table \u003cspan\u003e1\u003c/span\u003e): Type I represents samples with porosities greater than 8%, Type II represents samples with porosities between 7% and 8%, and Type III represents samples with porosities less than 7%.\u003c/p\u003e\n \u003cdiv\u003e\u0026nbsp;\u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 1\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003ePorosity, permeability, and parameters from the MICP experiment.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eSample\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePorosity\u003c/p\u003e\n \u003cp\u003e(%)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePermeability\u003c/p\u003e\n \u003cp\u003e(mD)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eEntry pressure\u003c/p\u003e\n \u003cp\u003e(MPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMaximum pore-throat radius\u003c/p\u003e\n \u003cp\u003e(\u0026micro;m)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMedian pressure\u003c/p\u003e\n \u003cp\u003e(MPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMedian radius\u003c/p\u003e\n \u003cp\u003e(\u0026micro;m)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSorting coefficient\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSkewness\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMaximum mercury saturation\u003c/p\u003e\n \u003cp\u003e(%)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eEfficiency of mercury withdrawal\u003c/p\u003e\n \u003cp\u003e(%)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003eI\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH73#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e69.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e24.47\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH70#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.89\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e71.73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e21.40\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5001\u0026minus;9#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e74.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e31.79\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5001\u0026minus;15#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e11.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.89\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e66.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e36.53\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH901\u0026minus;13#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e70.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e33.88\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH903\u0026minus;3#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e68.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e29.65\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"4\"\u003e\n \u003cp\u003eII\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5001\u0026minus;1#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e20.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e63.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e27.37\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5001\u0026minus;3#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e17.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e66.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e30.10\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX4008\u0026minus;3#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e13.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e70.49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e30.89\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH86\u0026minus;4#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e19.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e63.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e39.75\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003eIII\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5001\u0026minus;5#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e23.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e62.33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e28.26\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5001\u0026minus;7#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e19.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e62.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e27.43\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5007\u0026minus;1#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e26.38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e57.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e35.36\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5010\u0026minus;6#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e29.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e52.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e24.08\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH4008\u0026minus;4#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e16.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e63.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e32.60\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH903\u0026minus;4#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e15.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e66.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e33.09\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eThe capillary pressure curve shows that Type I has a gentle capillary pressure curve (Fig. \u003cspan\u003e5\u003c/span\u003ea). The average porosity for Type I is 8.87%, with an average permeability of 0.53 mD. The entry pressure is relatively low, ranging from 0.17 to 1.73 MPa, with an average of 0.76 MPa. The corresponding maximum throat radius at the entry pressure has an average value of 0.89 \u0026micro;m. At 50% mercury saturation, the median pressure ranges from 3.38 to 11.99 MPa, with an average of 6.46 MPa. The associated average median radius is 0.10 \u0026micro;m. The sorting coefficient ranges from 0.08 to 4.72, with an average of 1.38. The skewness ranges between 1.66 and 2.04, with an average of 1.89. Type I is considered to have poor sorting, is strongly positively skewed, and exhibits coarse skewness. The maximum mercury saturation is a measure of the amount of mercury injected into the pore throat at the maximum pressure. It ranges from 66.05\u0026ndash;74.02%, with an average of 70.06%. The average mercury withdrawal efficiency is 29.62%. There is a distinct double peak in the pore-throat distribution of the Type I samples (Fig. \u003cspan\u003e5\u003c/span\u003eb), with peak pore-throat radius values of approximately 0.24 \u0026micro;m and 0.68 \u0026micro;m. Taking Sample X5001-15# as an example, a pore-throat radius larger than 0.1 \u0026micro;m plays a significant role in contributing to permeability (Fig. \u003cspan\u003e5\u003c/span\u003ec), indicating that this type of sample possesses larger throats, facilitating mercury injection into the pore throat.\u003c/p\u003e\n \u003cp\u003eThe mercury injection curve for Type II shows a shorter plateau segment than that for Type I (Fig. \u003cspan\u003e5\u003c/span\u003ed). The average porosity for Type II is 7.63%, with an average permeability of 0.35 mD. The entry pressure is higher than that of Type I, with an average of 4.93 MPa. The average maximum throat radius is 0.16 \u0026micro;m, the average median pressure is 17.69 MPa, and the median radius is smaller than that of Type I, with an average of 0.04 \u0026micro;m. The average sorting coefficient is 0.03, indicating excellent sorting. The skewness has an average of 2.06. The maximum mercury saturation for Type II ranges from 63.39\u0026ndash;70.49%, with an average of 66.14%. The average mercury withdrawal efficiency is 32.03%. The pore-throat radius distribution of Type II exhibits a weak double peak (Fig. \u003cspan\u003e5\u003c/span\u003ee), with the pore-throat radius primarily distributed in a range of 0.02 to 0.15 \u0026micro;m, peaking at 0.03 \u0026micro;m on the left and 0.07 \u0026micro;m on the right. Taking Sample H4008-3# as an example, the permeability contribution is mainly dominated by throats in a size range of 0.07 to 0.1 \u0026micro;m, indicating that these samples have moderately sized throats. The cumulative permeability contribution curve is slightly shifted to the left compared to that of Type I (Fig. \u003cspan\u003e5\u003c/span\u003ef).\u003c/p\u003e\n \u003cp\u003eThe capillary pressure curve for Type III exhibits a steep shape (Fig. \u003cspan\u003e5\u003c/span\u003eg). The average porosity and permeability for Type III are 5.75% and 0.30 mD, respectively. The displacement pressure is high, with an average of 5.52 MPa. The average maximum pore-throat radius is 0.16 \u0026micro;m, the average median pressure is 21.67 MPa, and the median radius is 0.04 \u0026micro;m on average. The sorting coefficient is low, with an average of 0.027, indicating excellent sorting. The skewness has an average of 2.22. The average maximum mercury saturation is 60.70%, and the average mercury withdrawal efficiency is 30.14%. The pore-throat radius distribution of Type III mainly has a distinct single peak (Fig. \u003cspan\u003e5\u003c/span\u003eh), with a radius distributed in a range of 0.02 to 0.10 \u0026micro;m, peaking at 0.03 \u0026micro;m. Taking Sample H903-4# as an example, the radius in a size range of 0.03 to 0.07 \u0026micro;m plays a significant role in contributing to the permeability (Fig. \u003cspan\u003e5\u003c/span\u003ei).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\"\u003e\n \u003ch2\u003e4.4 Fractal features\u003c/h2\u003e\n \u003cp\u003eScatter plots of log(1-S\u003csub\u003eHg\u003c/sub\u003e) versus log(P\u003csub\u003ec\u003c/sub\u003e) for each sample are created based on the MICP pore-throat structure parameters, and the slopes of the resulting straight lines are fitted. Examples include Samples H70#, X4008-3#, and X5007-1# (Fig. \u003cspan\u003e6\u003c/span\u003e). Moreover, due to experimental limitations, the pore parameters obtained via MICP do not accurately reflect the true pore characteristics. Therefore, this paper focuses solely on the fractal characteristics of pore throats. Among the Type Ⅰ, Ⅱ, and Ⅲ samples, small pores are widely distributed. The results indicate that small pores are extensively developed in the sandstone reservoirs in the study area, which is a key factor in the quality of the reservoir.\u003c/p\u003e\n \u003cp\u003eThe fractal dimension (D\u003csub\u003e1\u003c/sub\u003e, D\u003csub\u003e2\u003c/sub\u003e), porosity (\u0026Phi;\u003csub\u003e1\u003c/sub\u003e, \u0026Phi;\u003csub\u003e2\u003c/sub\u003e), and permeability contribution (K\u003csub\u003e1\u003c/sub\u003e, K\u003csub\u003e2\u003c/sub\u003e) corresponding to large pores and small pores are calculated in Table \u003cspan\u003e2\u003c/span\u003e for further discussion. The fractal dimension D\u003csub\u003e1\u003c/sub\u003e of the large pores ranges between 2.6519 and 2.9934, with an average of 2.8094. In contrast, the fractal dimension D\u003csub\u003e2\u003c/sub\u003e of small pores varies between 2.2307 and 2.7230, with an average of 2.5325. D\u003csub\u003e1\u003c/sub\u003e exceeds D\u003csub\u003e2\u003c/sub\u003e, reflecting the greater structural complexity of the large pores. This complexity can be attributed to the intricate and challenging-to-differentiate shapes of large pores from those of small pores.\u003c/p\u003e\n \u003cp\u003eThe total fractal dimension of the Chang 6 tight-sandstone samples is calculated using the weighted average porosity for large pores and small pores, and the mean is 2.5722. These findings suggest that the tight reservoirs in the study area have an extremely complex and heterogeneous pore-throat structure.\u003c/p\u003e\n \u003cp\u003eFractal dimension values for different pore regions are shown on the graphs.\u003c/p\u003e\n \u003cdiv\u003e\u0026nbsp;\u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 2\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003eFractal dimension calculation results of the Chang 6 sandstone samples in the Haojiaping area\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSample\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eD\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u0026Phi;\u003csub\u003e1\u003c/sub\u003e (%)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eK\u003csub\u003e1\u003c/sub\u003e (mD)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eD\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u0026Phi;\u003csub\u003e2\u003c/sub\u003e (%)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eK\u003csub\u003e2\u003c/sub\u003e (mD)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eD\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH73#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.9900\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9577\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.7230\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9575\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.7403\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH70#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.9934\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9653\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.7010\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9754\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.7137\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5001\u0026minus;9#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.6908\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9889\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.6797\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9983\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.6850\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5001\u0026minus;15#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.8486\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8978\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.6345\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9984\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.6543\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH901\u0026minus;13#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.7283\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9742\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.89\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.6655\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9962\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.6874\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH903\u0026minus;3#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.6515\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9995\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.7114\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9851\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.6862\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5001\u0026minus;1#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.7512\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9998\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.3893\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9996\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.4371\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5001\u0026minus;3#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.8192\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8336\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.3568\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9978\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.3838\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX4008\u0026minus;3#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.8478\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8189\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.4285\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9979\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.5096\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH86\u0026minus;4#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.7131\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9561\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.4205\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9987\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.89\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.4921\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5001\u0026minus;5#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.8486\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8978\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.6345\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9984\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.6610\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5001\u0026minus;7#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.8783\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8669\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.4894\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9995\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.5283\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5007\u0026minus;1#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.8154\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9889\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.4732\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9707\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.5233\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5010\u0026minus;6#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.9339\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9998\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.4533\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.998\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.4773\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH4008\u0026minus;4#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.7495\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8966\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.5286\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9988\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.6157\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH903\u0026minus;4#\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.6900\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9987\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.2307\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9998\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.3601\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"5. Discussion","content":"\u003cdiv id=\"Sec12\"\u003e\n \u003ch2\u003e5.1 Effects of pore-size distribution on pore-throat structure\u003c/h2\u003e\n \u003cp\u003eThe porosity of large pores (\u0026phi;1) has a positive correlation with the sorting coefficient, with a correlation coefficient (R\u003csub\u003e2\u003c/sub\u003e) of 0.2714 (Fig. \u003cspan\u003e7\u003c/span\u003ee). The sorting coefficient serves as an indicator of reservoir uniformity. A value near zero indicates high uniformity, whereas a higher value signifies lower uniformity. These findings validate Middleton\u0026rsquo;s assertion in 1962 that as the number of large pores increases, reservoir heterogeneity intensifies\u003csup\u003e36\u003c/sup\u003e. Furthermore, large pores are weakly correlated with other parameters, suggesting that large pores have a limited impact on the pore-throat structure.\u003c/p\u003e\n \u003cp\u003eThe porosity of the small pores (\u0026phi;2) has a negative correlation with the entry pressure and median pressure, 0.2976 and 0.4063, respectively, but no such correlation is found for the large pores (Fig. \u003cspan\u003e7\u003c/span\u003ea and c). These results indicate that the development of small pores strongly affects the entry pressure and median pressure.\u003c/p\u003e\n \u003cp\u003eThe maximum pore-throat radius has a weak positive correlation with small pores, with an R\u003csub\u003e2\u003c/sub\u003e value of 0.27 (Fig. \u003cspan\u003e7\u003c/span\u003eb), but does not exhibit a significant correlation with large pores. Similar trends are observed for different pore sizes and median radii (Fig. \u003cspan\u003e7\u003c/span\u003ed). These results suggest that the development of small pores influences both the maximum and median pore-throat radii and is the primary determinant of the effective seepage storage space.\u003c/p\u003e\n \u003cp\u003eSkewness indicates the asymmetry of the pore-throat size distribution. Coarse skewness generally results in good storage and percolation ability\u003csup\u003e37\u003c/sup\u003e. Figure \u003cspan\u003e7\u003c/span\u003ef illustrates a weak negative correlation between skewness and small pores, with a correlation coefficient of 0.1399 (Table \u003cspan\u003e3\u003c/span\u003e). No significant relationship between skewness and large pores is evident. These findings suggest that skewness is minimally influenced by the pore-throat structure.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan\u003e7\u003c/span\u003eg illustrates the correlation between the maximum mercury saturation and small pores, with a correlation coefficient (R\u003csub\u003e2\u003c/sub\u003e) of 0.3713 (Table \u003cspan\u003e3\u003c/span\u003e). However, there are no significant correlations with large pores, indicating that small pores predominantly contribute to interconnected pores. A higher mercury withdrawal efficiency results in more homogeneous pore and throat sizes. The mercury withdrawal efficiency and large pores exhibit a weak positive correlation (R\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.1789), suggesting that large pores have a weak effect on mercury withdrawal (Fig. \u003cspan\u003e7\u003c/span\u003eh).\u003c/p\u003e\n \u003cp\u003eThe correlation between the total porosity and pore-throat structure is similar to that of small pores. Analysis of the Chang 6 tight reservoirs indicates that small pores dominate the pore-throat structure. As small pores develop, the percolation properties improve, as evidenced by their significant correlations with the entry pressure, maximum pore radius, median pressure, median radius, skewness, and maximum mercury saturation.\u003c/p\u003e\n \u003cdiv\u003e\n \u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 3\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003eCorrelation coefficients between the porosity and parameters of the pore-throat structure\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"4\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eParameters of pore throat structure\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCorrelation coefficients of parameters with \u0026phi;1\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCorrelation coefficients of parameters with \u0026phi;2\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCorrelation coefficients of parameters with \u0026phi;\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eEntry pressure(MPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1156\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2976\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5392\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMaximum pore throat radius(\u0026micro;m)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0678\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4303\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMedian pressure(MPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0744\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4064\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5975\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMedian radius(\u0026micro;m)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0927\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1294\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2905\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSorting coefficient\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2714\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1224\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2412\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSkewness\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0999\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1399\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3137\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMaximum mercury saturation(%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0747\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3731\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5607\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eEfficiency of mercury withdrawal(%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1789\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0038\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.054\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\"\u003e\n \u003ch2\u003e5.2 Relationships between the fractal dimension and reservoir properties\u003c/h2\u003e\n \u003cp\u003eA scatter plot is generated using the fractal dimensions D\u003csub\u003e1\u003c/sub\u003e and D\u003csub\u003e2\u003c/sub\u003e, along with porosity and permeability data. D\u003csub\u003e1\u003c/sub\u003e exhibits a clear negative correlation with both porosity and permeability. D\u003csub\u003e2\u003c/sub\u003e has a weak negative correlation with reservoir properties. A larger fractal dimension indicates a more complex pore-throat structure, leading to reduced porosity and permeability in reservoirs. Figure \u003cspan\u003e8\u003c/span\u003e further shows that the porosities of the corresponding pores exhibit hierarchical features, with the permeability converging to a certain point as the fractal dimension increases. Small pores possess the highest porosity, suggesting that they are the primary contributors to the overall porosity of tight reservoirs. The distribution of large pores plays a crucial role in determining reservoir storage and seepage capacities.\u003c/p\u003e\n \u003cp\u003eAs previously mentioned, the porosity and permeability of large pores exhibit obvious negative correlations with the fractal dimension (Fig. \u003cspan\u003e8\u003c/span\u003e). However, interference from small pores diminishes the impact of large-pore porosity and permeability on the fractal dimension. In general, the total fractal dimension exhibits a decreasing trend as the porosity and permeability increase (Fig. \u003cspan\u003e9\u003c/span\u003e). The analysis reveals that fractal dimensions D\u003csub\u003e1\u003c/sub\u003e, D\u003csub\u003e2\u003c/sub\u003e, and D exhibit distinct correlations with porosity and permeability. The pore-throat structure in the Chang 6 tight-oil sandstone is complex, with pore-throat sizes playing a significant role in the fractal characteristics, homogeneity, and complexity of the pore-throat structure.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec14\"\u003e\n \u003ch2\u003e5.3 Relationships between fractal dimension and pore-throat structure\u003c/h2\u003e\n \u003cp\u003eA study of the relationship between fractal dimensions and pore-throat structure parameters aims to discover patterns in the variation in fractal dimensions and how fractal features influence pore properties. There is greater complexity in the pore-throat structure with a larger fractal dimension\u003csup\u003e38\u003c/sup\u003e. Using the entry pressure, maximum pore-throat radius, median radius, sorting coefficient, skewness, maximum mercury saturation, and mercury withdrawal efficiency as parameters, a fitting method is applied to the fractal dimension of the tight-sandstone reservoirs to examine the relationship between the pore-throat structure parameters and fractal dimension (Fig. \u003cspan\u003e10\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan\u003e10\u003c/span\u003e shows that D\u003csub\u003e2\u003c/sub\u003e exhibits strong correlations with the parameters of the pore-throat structure, particularly with the entry pressure, maximum pore-throat radius, median pressure, median radius, and sorting coefficient (Fig. \u003cspan\u003e10\u003c/span\u003ea-e). The correlation coefficients are 0.27, 0.55, 0.37, 0.29 and 0.47, respectively. D\u003csub\u003e1\u003c/sub\u003e only has a good correlation with the efficiency of mercury withdrawal (Fig. \u003cspan\u003e10\u003c/span\u003eh). D\u003csub\u003e2\u003c/sub\u003e is negatively correlated with the entry pressure, median pressure, skewness, and mercury withdrawal efficiency (Fig. \u003cspan\u003e10\u003c/span\u003ea, c, f, h). It is positively correlated with the maximum throat radius, median radius, and sorting coefficient (Fig. \u003cspan\u003e10\u003c/span\u003eb, d, e). The maximum throat radius and median radius can be used to measure the pore-throat size of a reservoir. The entry pressure, median pressure, and mercury saturation can reflect the connectivity of the reservoir, while the sorting coefficient and skewness indicate the heterogeneity of the reservoir. The fractal dimension D\u003csub\u003e2\u003c/sub\u003e is generally smaller than D\u003csub\u003e1\u003c/sub\u003e, suggesting that smaller pores in the study area have good uniformity, smooth surfaces, and favourable physical properties. Additionally, the correlation of the total fractal dimension D with the pore-throat structure is similar to that of D\u003csub\u003e1\u003c/sub\u003e. In summary, the findings suggest that the heterogeneity and surface roughness of small pores are predominantly responsible for the pore-throat structure, as well as percolation and storage space.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec15\"\u003e\n \u003ch2\u003e5.4 Permeability estimation model\u003c/h2\u003e\n \u003cp\u003eAlthough a variety of permeability models based on porosity, mercury pressure parameters, and other parameters have been proposed in previous studies, most of these models do not consider the contribution of pore-throat fractal features to permeability. The fractal dimension and reservoir physical property analyses described in the previous section are combined with the results of previous studies. It is believed that an assessment of reservoir quality may be based on the fractal dimension D, which correlates well with permeability. The current study combines the three most commonly used permeability estimation models: Winland\u0026rsquo;s r\u003csub\u003e35\u003c/sub\u003e model\u003csup\u003e39\u003c/sup\u003e, Pittman\u0026rsquo;s r\u003csub\u003e25\u003c/sub\u003e model\u003csup\u003e40\u003c/sup\u003e, and Rezaee\u0026rsquo;s r\u003csub\u003e10\u003c/sub\u003e model\u003csup\u003e41\u003c/sup\u003e and their equations are as follows:\u003c/p\u003e\n \u003cp\u003eLogr\u003csub\u003e35\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.732\u0026thinsp;+\u0026thinsp;0.588Logk \u0026minus;\u0026thinsp;0.864Log\u0026phi; (\u003cspan\u003e10\u003c/span\u003e)\u003c/p\u003e\n \u003cp\u003eLogk = -1.221\u0026thinsp;+\u0026thinsp;1.415Log\u0026phi;\u0026thinsp;+\u0026thinsp;1.512Logr\u003csub\u003e25\u003c/sub\u003e (\u003cspan\u003e11\u003c/span\u003e)\u003c/p\u003e\n \u003cp\u003eLogk = -1.92\u0026thinsp;+\u0026thinsp;0.949Log\u0026phi;\u0026thinsp;+\u0026thinsp;2.18Logr\u003csub\u003e10\u003c/sub\u003e (\u003cspan\u003e12\u003c/span\u003e)\u003c/p\u003e\n \u003cp\u003ewhere ri is the pore radius corresponding to mercury saturation i (\u0026micro;m), k is the permeability (mD) and \u0026phi; is the porosity (%).\u003c/p\u003e\n \u003cdiv\u003e\n \u003ctable id=\"Tab4\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 4\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003eRelationships of permeability with the fractal dimension and pore-throat radius of tight sandstone in the Chang 6 section in the southeastern Ordos Basin\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"4\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eEquations\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eEquations\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan\u003e\u003cspan\u003e\\(\\text{L}\\text{o}\\text{g}\\text{k}=-0.645+\\frac{1.367}{\\text{D}}-\\frac{0.028}{{\\text{r}}_{\\text{a}\\text{p}\\text{e}\\text{x}}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan\u003e\u003cspan\u003e\\(\\text{L}\\text{o}\\text{g}\\text{k}=-1.951+\\frac{4.754}{\\text{D}}-\\frac{0.031}{{\\text{r}}_{30}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.57\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan\u003e\u003cspan\u003e\\(\\text{L}\\text{o}\\text{g}\\text{k}=-2.786+\\frac{7.009}{\\text{D}}-\\frac{0.043}{{\\text{r}}_{\\text{k}}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan\u003e\u003cspan\u003e\\(\\text{L}\\text{o}\\text{g}\\text{k}=-1.689+\\frac{4.007}{\\text{D}}-\\frac{0.023}{{\\text{r}}_{35}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.60\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan\u003e\u003cspan\u003e\\(\\text{L}\\text{o}\\text{g}\\text{k}=-3.076+\\frac{7.757}{\\text{D}}-\\frac{0.66}{{\\text{r}}_{5}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan\u003e\u003cspan\u003e\\(\\text{L}\\text{o}\\text{g}\\text{k}=-2.211+\\frac{5.597}{\\text{D}}-\\frac{0.025}{{\\text{r}}_{40}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.87\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan\u003e\u003cspan\u003e\\(\\text{L}\\text{o}\\text{g}\\text{k}=-2.298+\\frac{5.688}{\\text{D}}-\\frac{0.053}{{\\text{r}}_{10}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan\u003e\u003cspan\u003e\\(\\text{L}\\text{o}\\text{g}\\text{k}=-2.086+\\frac{5.352}{\\text{D}}-\\frac{0.024}{{\\text{r}}_{45}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.78\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan\u003e\u003cspan\u003e\\(\\text{L}\\text{o}\\text{g}\\text{k}=-2.560+\\frac{6.423}{\\text{D}}-\\frac{0.052}{{\\text{r}}_{15}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan\u003e\u003cspan\u003e\\(\\text{L}\\text{o}\\text{g}\\text{k}=-3.094+\\frac{8.183}{\\text{D}}-\\frac{0.024}{{\\text{r}}_{50}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.69\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan\u003e\u003cspan\u003e\\(\\text{L}\\text{o}\\text{g}\\text{k}=-2.561+\\frac{6.412}{\\text{D}}-\\frac{0.043}{{\\text{r}}_{20}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan\u003e\u003cspan\u003e\\(\\text{L}\\text{o}\\text{g}\\text{k}=-2.576+\\frac{6.598}{\\text{D}}-\\frac{0.017}{{\\text{r}}_{55}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.35\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan\u003e\u003cspan\u003e\\(\\text{L}\\text{o}\\text{g}\\text{k}=-2.201+\\frac{5.356}{\\text{D}}-\\frac{0.035}{{\\text{r}}_{25}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan\u003e\u003cspan\u003e\\(\\text{L}\\text{o}\\text{g}\\text{k}=-2.241+\\frac{5.997}{\\text{D}}-\\frac{0.016}{{\\text{r}}_{60}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.63\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Equ11\"\u003e\n \u003cp\u003eThe estimated permeability-measured permeability crossplots calculated from the three models are shown in Fig. 11, which reveals that the three models greatly underestimate the permeability. The outcome arises from the fact that all three models are based on normal sandstone samples, which are less applicable to tight-sandstone reservoirs. As a result, the permeability calculated from the porosity greatly deviates from the measured value. To establish a better relationship between the permeability and fractal dimension as well as between the pore-throat radius, fractal dimension, and permeability corresponding to different mercury saturations, nonlinear multiple regression analyses are used. The equations, along with the correlation coefficients (r\u003csub\u003e2\u003c/sub\u003e), are shown in Table 4. Among them, the r40 equation achieves the highest value, 0.87. The corresponding equation for using r40 is as follows:\u003c/p\u003e\n \u003cdiv id=\"FileID_Equ11\" name=\"EquationSource\"\u003e$$\\text{L}\\text{o}\\text{g}\\text{k}=-2.211+\\frac{5.597}{\\text{D}}-\\frac{0.025}{{\\text{r}}_{40}}$$\u003c/div\u003e\n \u003cdiv\u003e13\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003ewhere k is the permeability (mD), D is the fractal dimension, and r\u003csub\u003e40\u003c/sub\u003e is the pore radius corresponding to 40% mercury saturation (\u0026micro;m). According to Eq. (\u003cspan\u003e13\u003c/span\u003e), the pore radius has a positive contribution to the permeability, while the fractal dimension has a negative contribution. As a consequence, these empirical equations are theoretically accurate, in line with fractal theory and previous conclusions.\u003c/p\u003e\n \u003cdiv\u003e\n \u003ctable id=\"Tab5\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 5\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003eSupplementary data for the validation of the permeability estimation model\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"4\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSample\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePermeability(mD)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eD\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003er\u003csub\u003e40\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH904\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.9735\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.34\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5001-12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.8580\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.06\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5010-7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.9012\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5010-8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.8878\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.06\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH86-7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.7012\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.26\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH86-18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.8580\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.07\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH901-17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.8824\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5007-2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.8150\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eH901-10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.8593\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.11\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5012-3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.7227\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.12\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX5012-2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.7006\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.11\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eThe model prediction accuracy is validated using the samples from this study and 11 additional samples from the Chang 6 section in the southeastern Ordos Basin; the details of the additional samples are shown in Table \u003cspan\u003e5\u003c/span\u003e. The crossplot of the estimated permeability versus the measured permeability for the 27 samples shows that the data points have a relatively small deviation from the y\u0026thinsp;=\u0026thinsp;x line (Fig. \u003cspan\u003e12\u003c/span\u003e). This suggests the applicability of the r\u003csub\u003e40\u003c/sub\u003e model for permeability prediction in the Chang 6 section in the southeastern Ordos Basin.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"6. Conclusions","content":"\u003cp\u003eIn this paper, the pore-throat structure and fractal characteristics of the reservoir were analysed via physical tests, CL, SEM, CTS, XRD, and MICP on tight-oil sandstone samples from the Chang 6 member in the Haojiaping Block, Ordos Basin, China. A reliable permeability estimation model based on the fractal dimension and pore-throat radius was also developed. The conclusions are as follows.\u003c/p\u003e \u003cp\u003eThe rock types in this study area are predominantly fine-grained feldspar sandstones, with an average porosity of 7.7% and an average permeability of 0.42 mD. The pore types primarily include intergranular pores, feldspar-dissolved pores, intergranular-dissolved pores, and microcracks. The reservoirs in the study area exhibit low component maturity, moderate structural maturity, poor erosional conditions, good sorting, poor to moderate roundness, and high brittleness. This suggests that the deposited sediment was not transported over long distances. In addition, the study area is a sweet spot for oil exploration and is conducive to fracture modification.\u003c/p\u003e \u003cp\u003eSmall and large pores make up the tight-oil sandstone pore network. The complexity and heterogeneity of the pore-throat structures were quantified using fractal theory, yielding an average total fractal dimension of 2.5722. In addition, the pore throats were divided into two categories, with average fractal dimension values of 2.8094 (D\u003csub\u003e1\u003c/sub\u003e) for large throats and 2.5325 (D\u003csub\u003e2\u003c/sub\u003e) for small throats. The heterogeneity and complexity of small-pore structures are greater than those of large-pore structures. Connecting the microscopic pore structure to the macroscopic petrophysical parameters revealed that small pores play a crucial role in determining the pore-throat structure. As small pores develop, the properties of percolation, storage, pore-throat connectivity, and oil recovery improve.\u003c/p\u003e \u003cp\u003eTo build accurate permeability estimation models for tight sandstone, the widely used Pittman, Winland, and Rezaee models were enhanced through a systematic characterization of pore structures. The fractal dimension\u0026ndash;pore-throat radius\u0026ndash;permeability prediction model is highly applicable to the tight-sandstone reservoirs of the Chang 6 member in the southeastern Ordos Basin, China. Furthermore, the pore-throat radius corresponding to 40% mercury saturation (r\u003csub\u003e40\u003c/sub\u003e) is the most effective predictor of permeability for tight sandstone. The use of fractal dimensions to predict permeability in tight-sandstone reservoirs can enhance model credibility. This will be highly significant for predicting reserves and evaluating and developing unconventional oil and gas, geothermal, and groundwater resources.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eData availability\u003c/p\u003e\n\u003cp\u003eAll data generated or analysed during this study are included in this published article.\u003c/p\u003e\n\u003ch2\u003eAcknowledgments\u003c/h2\u003e\n\u003cp\u003eThis research was supported by the National Science and Technology Projects of China (42130206). This work was supported by the State Key Laboratory of Continental Dynamics and PetroChina Yanchang Oilfied Company. Finally, we would like to express our thanks to the reviewers of this paper.\u003c/p\u003e\n\u003ch2\u003eAuthor contributions\u003c/h2\u003e\n\u003cp\u003eHuanmeng Zhang: Conceptualization, Methodology, Software, Data curation, Writing-Original draft preparation. Ling Guo: Conceptualization, Writing-Reviewing and Editing. Zhiyu Wu: Supervision, Methodology, Funding acquisition. Jiangbo Ma: Resources, Data Curation.\u003c/p\u003e\n\u003ch2\u003eCompeting interests\u003c/h2\u003e\n\u003cp\u003eThe author(s) declare no competing interests.\u003c/p\u003e\n"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eZou, C. et al. Tight gas sandstone reservoirs in China: characteristics and recognition criteria. Journal of Petroleum Science and Engineering.89(01), 82\u0026ndash;91 (2012).\u003c/li\u003e\n\u003cli\u003eSun, L. et al. Development characteristics and orientation of tight oil and gas in China. Petroleum Exploration and Development. 46(6):1073-1087(2019).\u003c/li\u003e\n\u003cli\u003eZhu, R.K., Zou, C.N., WU, S.T., Y, Z., Mao, Z.G., 2019. Mechanism for generation and accumulation of continental tight oil in China. Oil \u0026amp; Gas Geology. 40(6): 1168-1184.\u003c/li\u003e\n\u003cli\u003eLi, G,X.et al. Progress, challenges and key issues of unconventional oil and gas development of CNPC. China Petroleum Exploration. 25(2): 1-13(2020).\u003c/li\u003e\n\u003cli\u003eWu, Z. et al. Advances and challenges in hydraulic fracturing of tight reservoirs: A critical review. Energy Geoscience, 3(4): 427-435(2022).\u003c/li\u003e\n\u003cli\u003eHu, S,Y. et al. Advances on continental tight oil accumulation and key technologies for exploration and development in China. Natural Gas Geoscience. 30(8): 1083-1093(2019).\u003c/li\u003e\n\u003cli\u003eLi, Y.et al. A brief review of dynamic capillarity effect and its characteristics in low permeability and tight reservoirs. Journal of Petroleum Science and Engineering. 189(1): 1-9(2020).\u003c/li\u003e\n\u003cli\u003eZou, C. et al. Significance, geologic characteristics. Resource potential and future challenges of tight oil and shale oil. Kuangwu Yanshi Diqiu Huaxue Tongbao. 34(1): 3-17(2012).\u003c/li\u003e\n\u003cli\u003eZou, C. et al. Progress in China\u0026rsquo;s unconventional oil \u0026amp; gas exploration and development and theoretical technologies. Acta Geologica Sinica. 89(6): 979-1007(2015). \u003c/li\u003e\n\u003cli\u003eWei, X. et al. New geological understanding of tight sandstone gas. Lithologic Reservoirs. 29(1): 11-20(2017).\u003c/li\u003e\n\u003cli\u003eHe, D. et al. Integrated 3D hydrocarbon exploration in sedimentary basins of China. Oil \u0026amp; Gas Geology. 42(2): 265-284(2021).\u003c/li\u003e\n\u003cli\u003eGao, H. et al. Pore structure characterization, permeability evaluation and enhanced gas recovery techniques of tight gas sandstones. Journal of Natural Gas Science and Engineering. 28,536\u0026ndash;547(2016).\u003c/li\u003e\n\u003cli\u003eDesbois, G. et al. High-resolution 3D fabric and porosity model in a tight gas sandstone reservoir: a new approach to investigate microstructures from mm-to nm-scale combing argon beam cross sectioning and SEM imaging. Journal of Petroleum Science and Engineering. 78, 243\u0026ndash;257(2011).\u003c/li\u003e\n\u003cli\u003eWang, H. et al. Fractal analysis and its impact factors on pore structure of artificial cores based on the images obtained using magnetic resonance imaging. Journal of Applied Geophysics. 86(01), 70\u0026ndash;81(2012).\u003c/li\u003e\n\u003cli\u003eFu S. et al. Transformation of understanding from tight oil to shale oil in the Member 7 of Yanchang Formation in Ordos Basin and its significance of exploration and development . Acta Petrolei Sinica. 42(5)：561-569(2021).\u003c/li\u003e\n\u003cli\u003eMullen, J. Petrophysical characterization of the eagle ford shale in South Texas. Proceedings of the Canadian Unconventional Resources and International Petroleum Conference. October 19\u0026ndash;21, Calgary, Alberta, Canada, SPE138145(2010).\u003c/li\u003e\n\u003cli\u003eDu, J. et al. Discussion on effective development techniques for continental tight oil in China. Petroleum exploration and development. 41(2):217-224(2014).\u003c/li\u003e\n\u003cli\u003eRen, D. et al. Formation mechanism of the Upper Triassic Yanchang Formation tight sandstone reservoir in Ordos Basin\u0026mdash;Take Chang 6 reservoir in Jiyuan oil field as an example. Journal of Petroleum Science and Engineering. 178(1): 497-505(2019). \u003c/li\u003e\n\u003cli\u003eYang, S. et al. Diagenetic evolution and its impact on reservoir quality of tight sandstones: A case study of the Triassic Chang 6 Member, Ordos Basin, northwest China. Marine and Petroleum Geology. 117(01): 104360(2020).\u003c/li\u003e\n\u003cli\u003eFu, Y. et al. Implications of lithofacies and diagenetic evolution for reservoir quality: A case study of the Upper Triassic chang 6 tight sandstone, southeastern Ordos Basin, China. Journal of Petroleum Science and Engineering. 218(01): 111051(2022).\u003c/li\u003e\n\u003cli\u003eGeng L. et al. A fractal production prediction model for shale gas reservoirs. Journal of Natural Gas Science and Engineering. 55(01): 354-367(2018).\u003c/li\u003e\n\u003cli\u003eXia, Y. et al. Fractal dimension, lacunarity and succolarity analyses on CT images of reservoir rocks for permeability prediction. Journal of Hydrology. 579(01): 124-198(2019).\u003c/li\u003e\n\u003cli\u003eWang, C. et al. Research on Characteristics of Chang 6 Reservoir in Huanxian Area, Ordos Basin. Xi\u0026rsquo;an Shiyou University. 1-63(2022).\u003c/li\u003e\n\u003cli\u003eHuang, W. et al. Reservoir spaces in tight sandstones: Classification, fractal characters, and heterogeneity. Journal of Natural Gas Science and Engineering. 46(01): 80-92(2017).\u003c/li\u003e\n\u003cli\u003eRahner, M. et al. Fractal dimensions of pore spaces in unconventional reservoir rocks using X-ray nano- and micro-computed tomography. Journal of Natural Gas Science and Engineering, 55(01): 298-311(2018).\u003c/li\u003e\n\u003cli\u003eGao, Y. Research on Brittleness Evaluation and Main Controlling Factors of Tight Oil Reservoirs\u0026mdash;\u0026mdash;Acase study from Triassic Yanchang Formation Chang 7 oil formation in Dingbian Dongrengou Oilfield, Ordos Basin. Northwest University. 1-89(2022).\u003c/li\u003e\n\u003cli\u003eLi A. et al. Chemical characteristics of formation water of Chang 2 oil formation of Yanchang Formation in Zhaike area，Ordos Basin and its indication to dense oil reservoir. Natural Gas Geoscience. 33(10): 1637-1647(2022).\u003c/li\u003e\n\u003cli\u003eWang, L. et al. Lithofacies characteristics and sedimentary environment of Chang 7 black shale in the Yanchang Formation, Ordos Basin. Journal of Palaeography. 25(03): 598-613(2023).\u003c/li\u003e\n\u003cli\u003eLv, Q. et al. Sedimentary types, characteristics and model of lacustrine fine-grained gravity flow in the Member 7 of Trassic Yanchang Formation in Ningxian area, Ordos Basin. Journal of Palaeogeography. 25(04): 1-18(2023).\u003c/li\u003e\n\u003cli\u003eAlberti, G. et al. 1.6.5 SEM and TEM techniques. World Crop Pests. 6(01): 399-410(1996).\u003c/li\u003e\n\u003cli\u003eHuang, H. et al. A method to probe the pore-throat structure of tight reservoirs based on low-field NMR: Insights from a cylindrical pore model. Marine and Petroleum Geology. 117(01): 104344(2020).\u003c/li\u003e\n\u003cli\u003eZhong, X. et al. Microscopic pore throat structures and water flooding in heterogeneous low-permeability sandstone reservoirs: A case study of the Jurassic Yan\u0026rsquo;an Formation in the Huanjiang area, Ordos Basin, Northern China. Journal of Asian Earth Sciences. 219(01): 104903(2021).\u003c/li\u003e\n\u003cli\u003eJiang, Z. Sedimentary Science . Beijing: Petroleum Industry Press. 1-424(2003).\u003c/li\u003e\n\u003cli\u003eLala, A. et al. Controls of pore throat radius distribution on permeability. Journal of Petroleum Science and Engineering. 157: 941-950(2017).\u003c/li\u003e\n\u003cli\u003eQu, Y. et al. Pore\u0026ndash;throat structure and fractal characteristics of tight sandstones in Yanchang Formation, Ordos Basin. Marine and Petroleum Geology. 120(01): 104573(2020)\u003c/li\u003e\n\u003cli\u003eMiddleton, G. On Sorting, Sorting Coefficients, and the Lognormality of the Grain-Size Distribution of Sandstones: A Discussion. The Journal of Geology. 70(6): 754-756(1962).\u003c/li\u003e\n\u003cli\u003eBlanca, M. et al. Skewness and Kurtosis in Real Data Samples. Methodology. 9(2): 78-84(2013).\u003c/li\u003e\n\u003cli\u003eCai, J. et al. Fractal Characterization of Spontaneous Co-current Imbibition in Porous Media. Energy \u0026amp; Fuels. 24(3): 1860-1867(2010).\u003c/li\u003e\n\u003cli\u003eKolodzie Jr.. Analysis of Pore Throat Size and Use of the Waxman-Smits Equation to Determine Ooip in Spindle Field, Colorado. Society of Petroleum Engineers, Dallas, Texas, p. 10(1980). \u003c/li\u003e\n\u003cli\u003ePittman, E. Relationship of porosity and permeability to various parameters derived from mercury injection-capillary pressure curves for sandstone. AAPG Bulletin. 76 (2): 191\u0026ndash;198(1992).\u003c/li\u003e\n\u003cli\u003eRezaee, R. et al. Tight gas sands permeability estimation from mercury injection capillary pressure and nuclear magnetic resonance data. Journal of Petroleum Science and Engineering. 89, 92\u0026ndash;99(2012). \u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Tight sandstone, Pore-throat structure, Fractal characteristics, Permeability estimation, Ordos Basin","lastPublishedDoi":"10.21203/rs.3.rs-4640639/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4640639/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"As a typical tight reservoir and an important site for unconventional hydrocarbon accumulation, the Chang 6 member of the Yanchang Formation is characterized by complex pore structures and strong heterogeneity. Analysing and characterizing the pore-throat structure quantitatively holds significant importance in optimizing oil recovery processes. To clarify the nonhomogeneity and structural characteristics of the pore throats in the southeastern Ordos Basin, tight sandstone from the Chang 6 member was selected for analysis. Casting thin section (CTS), scanning electron microscopy (SEM), cathodoluminescence (CL), X-ray diffraction (XRD), and mercury intrusion capillary pressure (MICP) analyses were conducted.\nAccording to the results, we found that intergranular pores, feldspar-dissolved pores, intergranular-dissolved pores, and microfractures were the predominant pore types found within the samples. By combining the results of MICP analysis with those of fractal theory, the pore-throat structure of each sample can be categorized into two types: large-scale and small-scale. Fractal theory was employed to quantitatively characterize the complex and irregular pore-throat structure of the reservoir. The average fractal dimension of large pores (D1) was 2.8094, whereas for small pores (D2), it was slightly lower than that of D1, averaging 2.5325. These findings underscore that large-scale pore-throat structures are more complex and exhibit greater heterogeneity. Compared with those of large pores, the pore-throat structure parameters of small pores exhibit a more significant correlation with reservoir properties and fractal dimensions. Therefore, small pores are the primary contributors to the reservoir storage pace and are key factors influencing the pore-throat structure of the Chang 6 tight sandstone. Based on the pore-throat radius and considering the influence of fractal characteristics on the pore structure, a nonlinear permeability prediction model was created using multiple regression analysis. Among these equations, the pore-throat radius corresponding to a mercury saturation of 40% (r40) emerged as the most effective predictor of permeability for tight sandstone.","manuscriptTitle":"Pore-throat structure, fractal characteristics and permeability prediction of tight sandstone: the Yanchang Formation, Southeast Ordos Basin","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-19 20:20:10","doi":"10.21203/rs.3.rs-4640639/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-09-25T21:14:40+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-09-23T01:12:30+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-09-22T09:29:43+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-09-19T14:17:36+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"299000449815739418065192830586927984494","date":"2024-09-13T00:52:24+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"238750641857947457331134733055394681428","date":"2024-09-12T11:00:31+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"220109924826421469004989162584852265964","date":"2024-09-12T10:53:22+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-09-12T10:32:07+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-09-12T10:30:03+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-06-28T04:08:19+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-06-28T04:05:21+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-06-26T07:10:23+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"395807ab-28d6-401a-b247-6521816eec49","owner":[],"postedDate":"July 19th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-11-18T16:01:51+00:00","versionOfRecord":{"articleIdentity":"rs-4640639","link":"https://doi.org/10.1038/s41598-024-79203-7","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2024-11-13 15:57:26","publishedOnDateReadable":"November 13th, 2024"},"versionCreatedAt":"2024-07-19 20:20:10","video":"","vorDoi":"10.1038/s41598-024-79203-7","vorDoiUrl":"https://doi.org/10.1038/s41598-024-79203-7","workflowStages":[]},"version":"v1","identity":"rs-4640639","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4640639","identity":"rs-4640639","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}