Introduction

Tight sandstone oil and gas represent significant unconventional hydrocarbon resources1,2. Reservoirs with permeabilities below 0.1 mD and porosities under 10% are typically defined as tight sandstone reservoirs3,4,5,6. These reservoirs are characterized by small pore spaces, complex pore structures, significant diagenetic evolution, low permeability, and pronounced heterogeneity7,8,9,10,11. Tight sandstones are globally distributed, found in regions such as in the San Juan Basin in the United States, the Perth Basin in Western Australia, and the East Irish Sea Basin12,13,14. In China, these reservoirs are located in the Ordos Basin, Tarim Basin, Sichuan Basin, Junggar Basin, and Bohai Bay Basin15,16,17,18,19, with a total proven reserve of 210 × 1012 m312. Therefore, studying tight sandstone reservoirs are crucial for the advancement of the petroleum industry.

The size of the pore throats is a critical microscopic factor determining porosity and permeability in reservoirs20. Various experimental methods are currently employed to study the micro pore-throat structures of tight sandstone. Liu et al. (2022) suggest that the pore-throat structures in tight sandstone primarily consist of micron and nanopores21. Wang et al. (2024) employed constant-rate mercury intrusion (CRMI) and high-pressure mercury injection (HPMI) to characterize the pore-throat sizes in tight sandstones from the Yanchang Formation in the Longdong area, Ordos Basin20. Their results indicated that permeability improves as the proportion of small pore throats declines. Bai et al. (2013) used multi-scale CT imaging technology to characterize the micro pore-throat structures of tight sandstone, revealing that nano-sized micropores have poor connectivity and primarily serve as hydrocarbon storage spaces, whereas micron-sized micropores possess some connectivity and function in both storage and fluid flow22. Wang et al. (2020) utilized nuclear magnetic resonance (NMR) and nitrogen adsorption (N2 − GA) to characterize the multifractal characteristics of tight sandstone pore structures, investigating the relationship between multifractal features and the specific surface area of the pores23. Xin et al. (2022) quantitatively characterized the pore structure of ultra-deep tight sandstone reservoirs using NMR transverse relaxation time (T2), analyzing the relationship between NMR parameters and fractal dimensions in ultra-deep tight sandstones24. In summary, previous scholars research has primarily focused on two-dimensional pore-throat analysis and evaluation of pore-throat structures, lacking detailed characterization of the three-dimensional morphology and their combinational features. And it difficult the application of theoretical research to practical production.

The primary aim of this paper is to systematically analyze the pore-throat structure of tight sandstone reservoirs and the influencing factors, explaining the relationship between reservoir pore-throat structure and oil and gas resources. The discussion is organized into five main sections: (1) A brief overview of the types, sizes, and connectivity of reservoir pores; (2) Classification of the reservoir using HPMI and analysis of the pore-throat structure parameters for each type of reservoir; (3) Examination of fractal dimensions of various reservoir pore structures through fractal theory; (4) Analysis of the correlation between fractal dimensions, reservoir properties, and pore-throat structure parameters; (5) Discussion of the impact of pore-throat structure on reservoir oil saturation.

Geological setting

The Ordos Basin, China’s second-largest sedimentary basin25, is located in the western part of the North China Plate, covering a total area of approximately 32 × 104 km226. Structurally, the basin is divided into six primary tectonic units: the Yishan Slope, Western Thrust Belt, Yimeng Uplift, Jinxi Fault-Fold Belt, Tianhuan Depression, and Weibei Uplift (Fig. 1a). The main body of the basin, the Yishan Slope, is characterized by a westward-dipping monocline with a dip angle of 1°, lacking significant secondary structures, and developing only some nose-like uplifts as tertiary structures27.

The Yanchang Formation comprises a sequence of river-delta-lake-delta-river facies, with a total thickness ranging from 1000 to 1300 m. This sequence records the complete evolution of Yanchang Lake, from its formation and development to its peak, decline, and eventual disappearance (Fig. 1b). The Yanchang Formation is subdivided into ten oil-bearing members, from top to bottom, (Chang 1 to Chang 10). The Chang 4 + 5 members are characterized by delta front sedimentary subfacies and have a thickness of approximately 100 m (Fig. 1b).

Fig. 1
figure 1

Location of the Dingbian area in the Ordos Basin (a) and comprehensive stratigraphic column (b).

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Samples, experiments and methods

Samples

The samples for this study were collected from four wells (G189, G115, C205, and Y142) in the Dingbian area. Two hundred core samples with a diameter of 2.5 cm were drilled from the Chang 4 + 5 reservoir, followed by hydrocarbon remove and drying. The tests conducted in this study include casting thin sections, SEM, micro-CT, and HPMI.

Experimental and testing

Casting thin sections were used to study the petrological characteristics of the reservoir, including mineral composition and pore-throat features. Under vacuum conditions, blue epoxy resin was injected into 150 casting thin sections, covered with cover glasses, and stained with a mixture of alizarin red and potassium ferricyanide. Observations were made using an Olympus CX21 optical microscope at the Analysis and Testing Center of the Changqing Oilfield Branch.

SEM was used to observe the mineral composition, clay minerals, and pore morphology of the rock fragments. Small cubic samples (1 cm3) were mounted onto stubs and coated with gold. The experiments were conducted using a Quanta 400 FEG environmental scanning electron microscope (manufactured by Field Electron and Ion Company, USA) at an acceleration voltage of 30 kV to observe 200 samples.

Thirty-three cylindrical rock samples (diameter: 2.5 cm, length: 2.5 cm) with intact surfaces were selected for HPMI testing (Table 1). The experiments were conducted using a Micromeritics 9220II mercury porosimeter (Micromeritics Instrument Corporation, USA), with a maximum pressure of 117 MPa during testing. The rock surface tension was set at 485 mN/m, and the contact angle was set to 130°, covering a pore diameter range of 6 nm to 63 μm. The tests were performed at the Analysis and Testing Center of the Changqing Oilfield Branch.

For micro-CT scanning, samples were collected from the Chang 4 + 5 tight sandstone of well G149. Cylindrical samples (diameter: 2 mm, length: 2 mm) were mounted on carbon fiber stubs and positioned between the X-ray source and detector for scanning. The experiments utilized an UltraXRM-L200 nano 3D X-ray microscope (Carl Zeiss Corporation, Germany) with a maximum resolution of 50 nm. Testing was conducted at the National Energy Shale Gas R&D Center, RIPED. Pore-throat structure analysis was performed using PerGeos software.

Table 1 HPMI experiment samples and their characteristics.
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Methods

Fractal theory, introduced by French mathematician Benoît Mandelbrot in 1967, is used to study the diversity and complexity of natural phenomena28. Currently, this method is applied in various fields such as material fracture prediction and pore structure analysis, effectively reflects rock characteristics29,30,31. In this study, fractal theory was employed to analyze the reservoir using HPMI porosimetry. The fractal dimension equation for pore structure is derived from the mercury saturation and capillary pressure obtained from HPMI as follows30,31,32:

$$\:\text{lg}{(1-S}_{Hg})=\left(D-3\right)\text{lg}{p}_{c}+C$$
(1)

where \(\:{\text{p}}_{\text{c}}\:\text{i}\text{s}\:\text{t}\text{h}\text{e}\:\text{c}\text{a}\text{p}\text{i}\text{l}\text{l}\text{a}\text{r}\text{y}\:\text{p}\text{r}\text{e}\text{s}\text{s}\text{u}\text{r}\text{e}\:\left(\text{M}\text{P}\text{a}\right)\); \(\:D\) is the fractal dimension; \(\:C\) is a constant; \(\:{S}_{Hg}\) is the mercury saturation (%).

The fractal dimension (D) can be calculated from the slope K of the \(\:\text{lg}{(1-S}_{Hg})\:vs.\:\text{lg}{p}_{c}\) plot as follows:

$$\text{D}=\text{K}+3$$
(2)

D typically ranges from 2 to 3; the closer it is to 3, the more complex the pore structure11,33.

Results

Pore types, sizes, and geometries

The pores in the reservoir are classified into primary and secondary types based on their genesis. Microscopic observations revealed that primary pores in the Chang 4 + 5 tight sandstones in the study area are mainly intergranular pores, while secondary pores are predominantly microfractures and dissolution pores. The primary pores typically form triangular or polygonal shapes with relatively uniform connectivity, distribution, and size (Fig. 2a,b).

Dissolution pores can be categorized into three types: intragranular dissolution pores, intergranular dissolution pores, and micropores within clay aggregates (pore diameter < 0.5 μm). Intergranular dissolution pores form by the interstitial matrix or dissolution of crystal edges, exhibiting various bay-like shapes (Fig. 2c,d,k). Intragranular dissolution pores, often appearing honeycombed, are formed by the dissolution of lithic fragments or feldspar (Fig. 2e). Feldspar intragranular dissolution pores typically follow the cleavage planes, with the main structure remaining intact (Fig. 2f). Micropores within clay aggregates are primarily intercrystalline pores of authigenic clay minerals such as illite and kaolinite, presenting as honeycomb or speckled patterns (Fig. 2g–i).

Scanning electron microscope (SEM) analysis indicates that kaolinite appears in accordion or vermicular forms, with sizes ranging from 0.2 to 10 μm (Fig. 2h). Due to the high content of brittle minerals such as quartz in the reservoir, microfractures are easily formed under stress conditions (Fig. 2j). These microfractures typically exhibit good connectivity and can extend over long distances.

Fig. 2
figure 2

Microscopic etching phenomena and pore types in Chang 4 + 5 tight sandstone. (a) Intergranular pores (red arrow) (PI), G115, 1973.5 m. (b) Triangular intergranular pores (PI), G115, 2005.7 m. (c) Feldspar intercrystalline dissolution pores (PD), G115, 1996.1 m. (d) Quartz clayification, G115, 1995.0 m. (e) Intra-crystalline dissolution pores formed by feldspar dissolution (PD), G115, 1993.5 m. (f) Feldspar intra-crystalline dissolution pores (PD), G115, 2005.7 m. (g) Illite and chlorite coexistence, micropores within clay aggregates (PM), G115, 2005.3 m. (h) Kaolinite, D40054, 2376.4 m. (i) Illite and its intragranular pores (PM), G115, 1974.9 m. (j) Microfractures (fracture space shown in blue) (CM), C205, 1955.4 m. (k) Intergranular dissolution pores (PD), intragranular dissolution pores (PD), matrix, sheet-shaped throats (TSS), curved-sheet-shaped throats (TCSS) and tubular-shaped throats (TTS), G115, 2004.8 m.

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Three-dimensional (3d) pore and throat connectivity

Computed Tomography (CT) technology utilizes the high penetration capability of X-rays, capturing energy attenuation data during penetration to visualize the internal structure of samples. This technology effectively reflects the distribution and morphology of the pore-throat structure within the samples34,35. High-resolution, non-destructive X-ray micro-computed tomography (micro-CT) was employed to create three-dimensional models of the pore-throat structures of the samples (Fig. 3).

The results indicate that the pore diameters in the samples range from 1.57 to 55.2 μm, with most pores falling between 5 and 20 μm. The throat radii range from 0.61 to 46.1 μm, with the throats exerting significant control over permeability ranging from 5 to 46.1 μm. The three-dimensional pore-throat images reveal that the samples predominantly develop spherical and flattened interconnected pores (Fig. 3a), while isolated micropores are sparsely distributed in dotted or banded patterns (Fig. 3c). The overall pore-throat network connectivity is relatively good, which explains the intrinsic mechanism that allows oil and gas to permeate through the tight sandstone reservoirs, despite the presence of small pore-throat dimensions (Fig. 3b).

Fig. 3
figure 3

3D pore-throat connectivity of Chang 4 + 5 tight sandstone using µ-CT. (a) Grid plot of the pore-throat structure (white arrows indicate throats). (b) Pore-throat ball-and-stick model. (c) 3D spatial distribution of pore-throat (red arrows indicate isolated pores).

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Pore-throat structure characteristics

HPMI analysis of 33 samples, parameters such as capillary pressure, mercury saturation, and average throat radii were obtained. Based on these parameters, the tight sandstone samples from the Chang 4 + 5 member in the study area were classified into four types (Fig. 4; Table 2).

Type I: The type has the widest distribution range of pore radii (0.006–20 μm). The capillary pressure curve exhibits a prolonged “gentle slope” segment, with relatively low threshold pressure (average 0.15 MPa). The average pore radius, porosity, permeability, and maximum mercury injection saturation (average 76.5%) are all at their highest levels (Table 2). The pore radius distribution curve exhibits the highest peak value (average 2.1), predominantly multi-peaked with lower mercury injection volumes at the peaks (Fig. 5a). The pores are predominantly intergranular and dissolution pores (Fig.s 2a, c), with throats mainly in lamellar or curved laminar shapes (Fig. 2k). This tight sandstone reservoir type has the best physical properties and the least heterogeneity, with a total of 7 samples.

Type II: The pore radius distribution ranges from 0.006 to 5 μm, narrower than type I, predominantly between 0.025 and 6 μm. The distribution curve’s peak value increases (average 1.73), predominantly exhibiting single or double peaks, with the mercury intrusion volume at the main peak significantly higher than that of type I (Fig. 5b). The capillary pressure curve shows a shorter smooth segment, with a markedly higher threshold pressure (average 1.51 MPa). The average pore radius, porosity (average 7.37%), permeability (average 1.74 × 10− 3 μm2), and maximum mercury saturation decrease (Table 2). Pores are primarily dominated by feldspar dissolution pores (Fig. 2e, f), while throat structures are predominantly curved laminar shape with accompanying laminar shape (Fig. 2k). This type of reservoir exhibits good petrophysical properties and comprises a total of 11 samples.

Type III: The pore radius distribution ranges between 0.006 and 1 μm, with predominantly single or double peaks. The main peak shifts to the left, and the capillary pressure curve shows an increased smooth segment, with a slightly elevated threshold pressure (Fig. 5c). Compared to type II, the average pore radius, porosity, permeability, and maximum mercury saturation are lower. The throat sorting coefficient is higher than that of types II and IV, with the highest coefficient of variation (Table 2). The pores are primarily intergranular pores and feldspar dissolution pores (Fig. 2f, b), while the throats are mainly tubular and curved laminar shapes (Fig. 2k). This type has poorer reservoir properties but better pore throat sorting, comprising a total of 9 samples.

Type IV: The capillary pressure curve of this reservoir type exhibits a long smooth segment with the highest threshold pressure (average 2.94 MPa) (Fig. 4d). The pore radius distribution ranges from 0.006 to 0.8 μm, with the smallest peak value (average 1.41) and is primarily unimodal (Fig. 5d). This type has the smallest average pore radius (average 0.92 μm), porosity, permeability, and maximum mercury saturation (Table 2). Pores are primarily dissolution pores, intergranular pores (Fig. 2b, c), and tubular throats (Fig. 2k). This type exhibits the poorest reservoir properties, with a total of 6 samples.

Fig. 4
figure 4

HPMI capillary pressure curves. (a) Type I; (b) Type II; (c) Type III; (d) Type IV.

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Fig. 5
figure 5

HPMI pore radius distribution curves. (a) Type (I) (b) Type (II) (c) Type (III) (d) Type IV.

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Table 2 HPMI parameter statistics for Chang 4 + 5 member reservoir in the Dingbian area.
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Table 3 Fractal characteristic parameter statistics of four types of typical samples in tight sandstone reservoirs.
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Pore fractal dimensions

Eight representative samples, 2 from each of the 4 reservoir types, were selected to construct \(\:\text{lg}{(1-\text{S}}_{\text{H}\text{g}})\:\text{v}\text{s}.\:\text{lg}{\text{p}}_{\text{c}}\) plots (Fig. 6). Distinct inflection points are observed in the scatter plot in Fig. 6\(\:{\text{p}}_{\text{c}}\) = 0.0735 MPa (r = 10 μm), \(\:{\text{p}}_{\text{c}}\) = 0.735 MPa (r = 1 μm), and \(\:{\text{p}}_{\text{c}}\) = 7.35 MPa (r = 0.1 μm), dividing the data into four segments: low-pressure, medium-pressure, high-pressure, and overpressure. These segments correspond to macropores (> 10 μm), mesopores (1–10 μm), micropores (0.1–1 μm), and nanopores (< 0.1 μm). According to Fig. 6, the pore-size fractal characteristics for each sample were obtained (Table 3), including the fractal dimensions (D) and correlation coefficients (R2) for macropores, mesopores, micropores, nanopores, and the overall sample. All curves in the Fig. 6 exhibit good fitting, with R2 values all greater than 0.8, indicating that fractal theory can effectively reflect the pore structure of reservoirs.

The overall trend across the reservoirs from type I to type IV shows a gradual decrease in macropores, leading to reduced reservoir heterogeneity and a decrease in fractal dimension (D) (Fig. 6; Table 3). Type III and type IV reservoirs contain only nanopores and micropores, with type III having smaller fractal dimensions for each pore type compared to type IV. For all pore types across the 4 reservoir types, fractal dimensions increase from type I to type IV, indicating an increase in the number of pores, pore connectivity complexity, and greater reservoir heterogeneity (Fig. 6; Table 3). Notably, in type II reservoirs, sample 31 exhibits an unusually low fractal dimension for micropores (D2), suggesting a lower content of micropores and simpler internal connectivity in this particular sample.

Fig. 6
figure 6

Pore fractal characteristic curves of four types of reservoir samples.

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Discussion

Reservoir quality index (RQI)

The permeability and porosity tests of 33 samples from the study area show that the porosity ranges from 2.4 to 13.05% (average of 8.17%). Permeability ranges from 0.08 to 3.18 × 10− 3 μm2 (average of 1.18 × 10− 3 μm2) (Table 2). Figure 7a shows a strong positive correlation between permeability and porosity (R2 = 0.8287).

The Reservoir Quality Index (RQI) is an important metric for evaluating the physical properties of oil and gas reservoirs. It was proposed by Amaefule et al.36. The calculation equation is:

$$\:RQI=0.0314\times\:\sqrt{\frac{k}{{\phi\:}_{e}}}=\frac{{\phi\:}_{e}}{1-{\phi\:}_{e}}\frac{1}{\sqrt{{F}_{s}\tau\:{S}_{gv}}}$$
(3)

Where \(\:{\:\phi\:}_{e}\) is porosity, (%) k is permeability, (×10− 3 μm2 );\(\:{\:S}_{gv}\) is the surface area per unit volume; \(\:{F}_{s}\) is the shape factor of the pores; \(\:\tau\:\) is the tortuosity of the capillaries.

From a macroscopic perspective, RQI is determined by both porosity and permeability. It is inversely proportional to porosity and directly proportional to permeability. From a microscopic perspective, RQI is influenced by the pore shape factor (\(\:{F}_{s}\)), capillary tortuosity (\(\:\tau\:\)), and surface area (\(\:{\:S}_{gv}\)). When the pore shape is more complex (larger \(\:{F}_{s}\)), the throats are more tortuous (larger \(\:\tau\:\)), and the capillaries are finer (larger \(\:{\:S}_{gv}\)), the RQI decreases, indicating a more complex pore structure. Consequently, RQI shows a strong negative correlation with threshold pressure (R2 value is -0.5932) (Fig. 7b). The throat sorting coefficient, which reflects the heterogeneity of throat distribution, has a certain positive correlation with the RQI (R2 value is 0.4058) (Fig. 7c).

Fig. 7
figure 7

Cross-plots of reservoir pore-throat structure parameters. (a) Porosity vs. Permeability. (b) RQI vs. threshold pressure. (c) Throat sorting coefficient vs. RQI.

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Relationship between pore-throat structure parameters and fractal dimension

The fractal dimension of nanopores (D1) exhibits a strong negative correlation with both porosity and permeability (Fig. 8a, b). In contrast, the total fractal dimension (D) shows a weaker negative correlation with porosity, and no significant correlation with permeability (Fig. 8a, b). This indicates that nanopores significantly influence the physical properties of tight sandstone reservoirs, while the total fractal dimension (D) is affected by macropores, leading to a lack of clear correlation with reservoir properties.

D1 shows a strong negative correlation with the average throat radius (Fig. 8c). The throat sorting coefficient shows a strong negative correlation with both D1 and the overall fractal dimension (D), with correlation coefficients of 0.6212 and 0.7778, respectively (Fig. 8d). This suggests that as D1 decreases, the average throat radius increases, making the reservoir denser and its storage properties poorer. As the throat sorting coefficient increases, both D1 and the total fractal dimension (D) decrease, indicating that throat sorting becomes poorer and the heterogeneity of the throat structure intensifies.

Threshold pressure reflects the concentration and size of pore-throat distribution in the reservoir. As shown in Fig. 8e, D1 and the overall fractal dimension (D) exhibit a strong positive correlation with threshold pressure. Additionally, both D1 and D show a strong negative correlation with the maximum mercury saturation (Fig. 8f). This indicates that higher threshold pressures correspond to a greater minimum pressure required for mercury to flow continuously through the reservoir, signifying a more concentrated pore-throat distribution and smaller pore-throat diameters, leading to higher fractal dimensions. Reservoirs with higher threshold pressures have smaller effective porosity and lower maximum mercury saturation, indicating increased reservoir density and reduced permeability.

In conclusion, the analysis indicates that nanopores play a crucial role in influencing the pore structure of the Chang 4 + 5 tight sandstone reservoir. As nanopores develop more extensively, the denser the reservoir becomes. Consequently, D1 increases, while the reservoir permeability, porosity, throat sorting coefficient, maximum mercury saturation, and average pore radius decrease, and the threshold pressure increases. Generally, reservoirs with poorer storage performance exhibit more concentrated pore size distribution, weaker heterogeneity, and a higher prevalence of nanopores and nano-throats.

Fig. 8
figure 8

Cross-plots of fractal dimension and pore structure parameters. (a) Porosity vs. Fractal dimension (D/D1). (b) Permeability vs. Fractal dimension(D/D1). (c) Average throat radius vs. Nanopore fractal dimension. (D1) (d) Throat sorting coefficient vs. Fractal dimension(D/D1). (e) Threshold pressure vs. Fractal dimension(D/D1). (f) Maximum mercury saturation vs. Fractal dimension(D/D1).

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Fig. 9
figure 9

Relationship between reservoir characteristics and oil saturation. (a) Oil saturation vs. Threshold pressure. (b) Nanopore fractal dimension (D1) vs. Oil saturation. (c) RQI vs. Oil saturation.

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Relationship between reservoir characteristics and oil saturation

The microscopic pore structure of reservoirs is closely related to their oil saturation. The connectivity of reservoir pore throats is a key internal factor determining fluid flow and controls the oil saturation. Significant differences in pore-throat sizes are observed among samples with different oil saturations37,38. As shown in Fig. 9a, there is a negative correlation between HPMI threshold pressure and reservoir oil saturation. Higher threshold pressures correspond to poorer oil saturation. Additionally, D1 shows a strong correlation with oil saturation (correlation coefficient 0.8412); the better the oil saturation, the smaller D1 (Fig. 9b). The Reservoir Quality Index (RQI) also has a certain correlation with oil saturation (correlation coefficient 0.4813). Samples with better oil saturation typically exhibit higher RQI values (Fig. 9c). This indicates that better reservoir physical properties, characterized by a greater number of macropores and higher RQI, correspond to higher oil saturation.

Conclusion

  1. 1.

    The tight sandstone reservoirs in the study area primarily consist of three types of pores: microfractures, primary intergranular pores, and secondary dissolution pores. Dissolution is the main mechanism for the formation of secondary pores, which increases the reservoir porosity and enhances oil and gas storage capacity. Various clay minerals observed under the microscope can easily block pore-throat, reducing the reservoir’s permeability.

  2. 2.

    Using HPMI parameters, the reservoirs are classified into four types. From type I to type IV, the smooth segments of the capillary pressure curve increase, the threshold pressure gradually rises, the pore-throat radius distribution range narrows, and the reservoir properties deteriorate, while heterogeneity intensifies. Overall, from type I to type IV, as the pore types decrease, the overall heterogeneity of the reservoir pores weakens, and the fractal dimension decreases. For each pore type, the fractal dimension increases from type I to type IV, indicating an increase in the number of pores, more complex connectivity, and increased heterogeneity within the reservoir.

  3. 3.

    The Reservoir Quality Index (RQI) is directly proportional to permeability and inversely proportional to porosity. When the pore shapes are more complex, the throats more tortuous, and the capillaries finer, the RQI decreases, indicating poorer reservoir properties. There is a strong positive correlation between reservoir porosity and permeability. Better reservoir properties are associated with a higher number of Macropors, resulting in a higher RQI and, consequently, better oil-bearing potential of the reservoir.