Pore Structure Characterization, Classification, and Fractal Dimension Analysis of the Yanchang Formation Reservoir in the Ordos Basin—A Cue to Evaluate High-Quality Tight Sandstone Reservoirs

Abstract

The pore-throat structure is a key factor in the exploration and development of tight sandstone reservoirs. In the present study, 14 tight sandstone samples from the Chang 8 member of the Ordos Basin were analyzed using high-pressure mercury intrusion, cast thin section analysis, scanning electron microscopy and cathodoluminescence imaging techniques. Fractal dimensions, obtained from the slopes of log(S_W) versus log(P_c) double-logarithmic plots, were applied to quantitatively characterize pore-throat structures and classify reservoirs through multifractal analysis, and discuss the diagenetic controlling factors affecting the pore-throat structure of different reservoir types. The results showed that the Chang 14 tight sandstones are characterized as two segments fractal features, which indicated that these samples have complex pore-throat structure and consist of two types of spaces: mesopore-throat spaces and micropore-throat spaces. The mesopore-throat system shows a higher fractal dimension (D1: 2.74–2.99), indicating greater heterogeneity and irregularity, while the micropore-throat system exhibits a lower dimension (D2: 2.28–2.61). D1 exhibits a negative correlation with the porosity and permeability of mesopores, while D2 shows a weak positive correlation with the properties of micropores. The total fractal dimension (D) is weakly correlated with overall reservoir properties, confirming that reservoir storage and flow capacity are primarily governed by the mesopore system rather than the micropore system. By analyzing the contribution of pore throats to sample physical properties, the results indicate that the 14 samples can be classified into two types based on 35% porosity contribution and 60% permeability contribution thresholds. Type 1, reservoirs dominated by microporous throat space (D values ranging from 2.603 to 2.644); Type 2, reservoirs dominated by mesoporous throat space (D values ranging from 2.544 to 2.598). Type 1 is characterized by primary intergranular pores, residual intergranular pores and intergranular dissolution pores, which enhance connectivity and reduce network complexity, thereby improving fluid permeability. In contrast, Type 2 consists mainly of intragranular dissolution pores, intergranular gap pores and micro-dissolution pores in clay minerals, which significantly inhibit fluid mobility. Diagenesis, including compaction, dissolution and cementation, exerts a significant control on the fractal characteristics and pore-throat structure evolution. The fractal characteristics exhibited in the pore-throat structure could provide a desirable analytical method, distinguishing from classification based on scale or size, for the evaluation and classification of tight sandstone reservoirs.

1. Introduction

With the advancement of oil and gas exploration and development technologies, the proportion of unconventional hydrocarbon resources has been steadily increasing [1,2,3]. Unconventional reservoirs, represented by tight sandstone oil reservoirs, are playing an increasingly important role in the global energy supply [4]. Their efficient development relies on a precise understanding of the microscopic pore structure [5]. Compared to conventional reservoirs, the pore-throat system in tight sandstones exhibits significant heterogeneity, with a complex nonlinear relationship between permeability and microstructure [6]. Traditional evaluation methods rely on average parameters such as porosity, permeability, and throat radius, making it difficult to quantitatively describe structural complexity or reveal the dominant mechanisms governing fluid flow [2]. Therefore, accurately investigating and analyzing pore-throat structures is significant for the classification, evaluation, and development of tight sandstone reservoirs.

In previous works on the pore-throat microstructure of tight sandstone reservoirs, the methods used for characterization of the pore-throat distribution and irregularities are primarily divided into two categories: (1) direct imaging techniques, such as casting thin sections, scanning electron microscopy (SEM), transmission electron microscopy (TEM), micro-computed tomography (micro-CT), and small-angle neutron scattering (SANS); and (2) indirect fluid intrusion methods, including mercury injection porosimetry and gas sorption analysis. While substantial research has utilized these approaches to investigate pore-throat systems, each has notable limitations [7,8]. Direct imaging observations generally shown the limitations because of the high experimental costs and observation area [6]. Among indirect methods, high-pressure mercury intrusion (HPMI) remains the most widely adopted technique. Although HPMI data can reflect pore-throat distribution and overall structural features, conventional analysis frequently overlooks the quantitative irregularity of complex microstructures and fails to evaluate the distinct contributions of different pore types to reservoir storage and flow capacity [9].

The proposition of fractal theory provides a powerful solution for the quantification and evaluation of the pore-throat structure of fractal objects with complexity and irregularity in nature, which has been widely used to explain the microstructure of reservoirs in the exploration and development of the oil and gas field [10,11]. The application of fractal theory in reservoir engineering can be used to describe the complexity and heterogeneity of reservoirs and build a bridge between the microscopic structures and the macroscopic physical properties [9]. Calculating fractal dimensions based on experimental data such as high-pressure mercury intrusion has become a conventional method for evaluating reservoir heterogeneity. Progress has been made in areas such as pore-throat radius distribution and the permeability contribution of different pore types, confirming that reservoir spaces exhibit self-similarity and that fractal dimension is an effective parameter for characterizing their structural regularity and heterogeneity [12,13]. The fractal assessments based on fluid typing experiments have developed into a universal approach, which is based on the correlation between the volume of objects and the radius [14]. However, there are still some limitations in these studies: the fractal characteristics of different pore-throat combination types, the contribution of different reservoirs and the corresponding porosity and permeability contribution to spaces, and the controlling factors on reservoir types dominated by different pore-throat types have not been analyzed in detail [11,15,16]. Therefore, the discussion of the above issues in this paper from fractal perspectives appears to be of fully practical importance.

In this study, HPMI experiments are conducted for tight sandstone samples collected from the Chang 8 member of the Upper Triassic Yanchang Formation in the eastern Yanchang exploration area, Ordos Basin. The micro-nano pore-throat structures were analyzed, and the fractal dimensions were calculated and compared for the corresponding samples, based on the HPMI data and the corresponding characterization methods (casting thin sections, SEM images, and CL images).

However, most existing fractal studies on tight sandstones only calculate a single total fractal dimension, and cannot distinguish the respective contributions of mesopore-throat and micropore-throat systems to reservoir quality [11,14]. Meanwhile, few studies have established a quantitative link between two-segment fractal features, porosity contribution, permeability contribution, and reservoir classification. Traditional evaluation methods rely heavily on physical parameters or pore-size scales, making it difficult to reveal the dominant geological mechanism controlling fluid flow [2,6,7]. Furthermore, current fractal models rarely integrate diagenetic genesis with segmented fractal characteristics to explain the heterogeneity difference between meso- and micro-pore systems, nor do they clarify the threshold criteria for fractal dimension in reservoir quality grading [6,9]. Therefore, using fractal theory to quantitatively identify dominant pore systems and construct a new classification scheme for tight sandstone reservoirs remains a key research gap.

This paper has three purposes: (1) to analyze the pore-throat structure and fractal characteristics of tight sandstones, (2) to classify tight sandstone reservoirs from a fractal perspective, (3) to determine and explore the primary controlling factors on the fractal dimension and the geological significance of reservoir classification.

2. Geological Setting

As the second-largest sedimentary basin in China, the Ordos Basin is structurally located at the transition zone between Yishan Slope and Tianhuan Depression (Figure 1), with an approximate area of 250,000 km², where five units are tectonically subdivided: the northern Yi-meng uplift, the eastern Jinxi fault-fold belt, the southern Weibei uplift, the western Tian-Huan syncline and West thrust and the Yi-Shan slope in the middle [17]. The central Ordos Basin contains sedimentary sequences ranging from the Upper Proterozoic to the Middle Jurassic [18]. During the Mesozoic, deposition transitioned from Permian marine environments to Triassic continental settings. The Upper Triassic Yanchang Formation, representing a typical lacustrine deposit in an inland basin, can be subdivided into ten intervals (Chang 10 to Chang 1 from bottom to top) [19]. The target reservoir of this study is the Chang 8 member, located in the southwestern part of the Yishan Slope (Figure 1), characterized by a westward-plunging monocline structure with a dip angle of less than 1° [20]. Sedimentologically, the Chang 8 section was deposited in subaqueous distributary channels at the forearm of a shallow-water braided delta, forming the primary oil-bearing sandstone body. This gentle and stable tectonic setting resulted in weak tectonic reworking, meaning that pore-throat structure evolution was primarily controlled by sedimentary facies and diagenesis [13,17].

The Triassic Chang 8 reservoir is characterized by poor porosity and poor permeability under strong diagenetic reformations, including strong compaction, oversize of quartz, cementation of carbonate (mainly ferroan dolomite), authigenic kaolinite, and clay minerals [21,22]. The reservoir is about 100–130 m thick and consists of a rhythmic alternation of sandstone and mudstone, which is the most significant production reservoir in the eastern Yanchang exploration area. Diagenesis played a decisive role in reshaping pore-throat structure: intense compaction and cementation greatly reduced primary pores and generated abundant micropores, while dissolution of feldspar and volcanic debris improved pore connectivity and promoted the development of mesopore-throat systems [2,4]. The strong diagenesis resulted in the heterogeneity and complexity of the Chang 8 tight sandstone reservoirs.

3. Experiments and Methodology

3.1. Sampling

A total of 14 tight sandstone samples of the Chang 8 member are collected from different wells, whose depths range from 534.48 m to 794.65 m (

Table 1. Basic information and description obtained from routine rock properties measurements.

Sample	Well	Depth (m)	Formation	Porosity (%)	Permeability (mD)	Description
#1	Y1	608.81	Chang 8	1.32	0.046	Silt-fine grained sandstone, moderate sorted, subrounded grains.
#2	Y2	534.48	Chang 8	1.57	0.040	Silt-grained sandstone, moderate sorted, subangular grains, dark grey.
#3	Y3	535.51	Chang 8	7.72	0.474	Silt-grained sandstone, well sorted, subrounded grains, grey.
#4	Y4	671.45	Chang 8	5.76	0.104	Silt-fine grained sandstone, moderate sorted, subrounded grains, dark grey.
#5	Y5	650.28	Chang 8	4.75	0.101	Silt-fine grained sandstone, moderate sorted, subangular grains, dark grey.
#6	Y6	772.34	Chang 8	7.64	0.315	Silt-fine grained sandstone, moderate sorted, subrounded grains, light grey.
#7	Y7	794.65	Chang 8	6.49	0.073	Silt-fine grained sandstone, poorly sorted, subangular grains, dark grey.
#8	Y8	749.33	Chang 8	3.38	0.014	Silt-fine grained sandstone, poorly sorted, subangular grains, dark grey.
#9	Y9	625.74	Chang 8	2.63	0.057	Silt-fine grained sandstone, moderate sorted, subangular grains, grey
#10	Y10	568.92	Chang 8	3.91	0.012	Silt-grained sandstone, moderately poorly sorted, subrounded grains, dark grey
#11	Y11	698.57	Chang 8	6.49	0.073	Silt-fine grained sandstone, well sorted, subrounded grains, dark grey
#12	Y12	726.81	Chang 8	6.15	0.105	Silt grained sandstone, poorly sorted, subangular grains, grey
#13	Y13	594.36	Chang 8	10.01	0.449	Silt-fine grained sandstone, well sorted, subangular grains, light grey
#14	Y14	761.29	Chang 8	7.62	0.361	Silt-grained sandstone, moderate sorted, subrounded grains, light grey

). The basic physical properties, including porosity, permeability, and lithological characteristics are also presented in Table 1. The lithology of the Chang 8 samples is mainly characterized as silt-fine-grained sandstones with relatively low texture maturity. The 14 core samples from multiple wells distributed across the eastern Yanchang exploration area, covering the main sedimentary microfacies of the Chang 8 member, including subaqueous distributary channels, interdistributary bays and crevasse splays. Samples were selected to cover the full range of porosity (1.32–10.01%) and permeability (0.012–0.474 mD) observed in the target interval, ensuring representativeness of reservoir quality variations.

To conduct the HPMI experiments, the 14 samples are processed into cylindrical plugs with a diameter of approximately 2.5 cm and a length of approximately 2.5 to 3.5 cm. Porosity and permeability were determined through the helium-based porosity and the nitrogen-based permeability of the 14 cylindrical samples. The rest samples from the same rocks are also prepared for casting thin sections, scanning electron microscope (SEM) images, and cathodoluminescence images (CL) to conduct supplementary observations of pore-throat microscopic structures. The casting thin sections were used to obtain the sandstone composition, grain size distribution, and diagenetic characteristics. SEM images were used for the observations of mineral types and geometry, and CL images were employed to identify the diagenetic periods by the devolvement of calcite with or without iron.

3.2. High Pressure Mercury Intrusion (HPMI) Experiments

(1)

Sample pretreatment: Cylindrical samples were cleaned with petroleum ether and ethanol to remove residual oil and salt, then dried in a vacuum oven at 60 °C for 48 h to a constant weight. And the cooled samples were placed in core holders.

(2)

Instrument calibration: The porosimeter was calibrated with standard pore-size samples before testing to ensure accuracy of pressure and volume readings.

(3)

Vacuum evacuation: The sample chamber and mercury chamber were evacuated to a vacuum degree <50 μm Hg to eliminate air interference.

(4)

Mercury injection: The AutoPore IV 9505 automatic mercury porosimeter was used to conduct HPMI experiments on 14 dense sandstone samples. Low-pressure (<0.01 MPa) filling was first completed, then high pressure was applied stepwise up to 400 MPa, with data recorded at each pressure point. The mercury intrusion capillary pressure curve was obtained by measuring mercury injection volume at different mercury pressure increments.

(5)

Data resolution: The mercury volume injected into the pore throat space at a specific pressure reflects the volume of the corresponding pore throat space, which can be calculated based on Laplace’s capillary pressure equation [23]. Pore-throat radius, cumulative intrusion volume and saturation were resolved using the Washburn equation. Ultimately, capillary pressure curves for eight dense sandstone samples were plotted based on the correlation between injection pressure and mercury saturation.

(6)

Post-test treatment: Mercury was recovered, and samples were removed and cleaned to avoid contamination.

3.3. Fractal Dimension Calculation Method

The microstructure of pore-throat in tight reservoirs is considered to have fractal features [11,24]. The different fractal dimension calculation methods are all derived from a power-law function, which is used to characterize the fractal features of porous media [14].

$$\mathrm{N}\left(>\mathrm{r}\right)\propto {\mathrm{r}}^{-\mathrm{D}}$$

(1)

where r is the dimension of a unit in the porous medium, and $\mathrm{N}(>\mathrm{r})$ is the number of units with a dimension larger than $\mathrm{r}$. In tight sandstones with complex microstructure, there is a correlation between $\mathrm{N}(>\mathrm{r})$ of pore-throat and $\mathrm{r}$ from the following function [14].

$$\mathrm{N}\left(>\mathrm{r}\right)={\int }_{\mathrm{r}}^{{\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}\mathrm{P}\left(\mathrm{r}\right)\mathrm{d}\mathrm{r}=\mathrm{a}{\mathrm{r}}^{-\mathrm{D}}$$

(2)

where $\mathrm{r}$ is the radius of pore-throat in μm, ${\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum radius of pore-throat in μm, $\mathrm{P}\left(\mathrm{r}\right)$ is the distribution density function of pore-throat radius in %, $\mathrm{a}$ is a proportionality constant, and $\mathrm{D}$ is the fractal dimension. Taking the derivative of Equation (2),

$$\mathrm{P}\left(\mathrm{r}\right)={\displaystyle \frac{\mathrm{d}\mathrm{N}\left(>\mathrm{r}\right)}{\mathrm{d}\mathrm{r}}}=-\mathrm{a}{\mathrm{D}\mathrm{r}}^{-\mathrm{D}-1}$$

(3)

The cognition of micropore-throat with complex topology in tight sandstones is an evolving process. Many models of pore characterization have been put forward: cylindrical pore, spherical pore, and slit pore [13]. In this work, the model of a spherical pore is introduced to calculate the fractal dimensions of the pore system. The volume of a single pore can be expressed as

$$\mathrm{V}={\displaystyle \frac{4}{3}}\mathsf{\pi }{\mathrm{r}}^3$$

(4)

where $\mathrm{r}$ is the radius of the pore in μm. Substituting Formula (3) into the Formula (2), the cumulative volume of the pore system with a radius larger than r can be expressed as

$${\mathrm{V}}_{\left(>\mathrm{r}\right)}={\displaystyle \underset{\mathrm{r}}{\overset{{\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}{\int }}}\mathrm{P}\left(\mathrm{r}\right){\displaystyle \frac{4}{3}}\mathsf{\pi }{\mathrm{r}}^3\mathrm{d}\mathrm{r}={\displaystyle \underset{\mathrm{r}}{\overset{{\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}{\int }}}(-\mathrm{a}{\mathrm{D})\mathrm{r}}^{-\mathrm{D}-1}\ast {\displaystyle \frac{4}{3}}\mathsf{\pi }{\mathrm{r}}^3\mathrm{d}\mathrm{r}$$

(5)

Equation (5) can be expressed after integration:

$${\mathrm{V}}_{\left(>\mathrm{r}\right)}=-{\displaystyle \frac{4\mathsf{\pi }\mathrm{a}\mathrm{D}}{3\left(3-\mathrm{D}\right)}}{\mathrm{r}}^{3-{\mathrm{D}}_{\mathrm{f}}}\left|\begin{array}{c}{\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\\ \mathrm{r}\end{array}\right.=-{\displaystyle \frac{4\mathsf{\pi }\mathrm{a}\mathrm{D}}{3\left(3-\mathrm{D}\right)}}\left({{\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}^{3-\mathrm{D}}-{\mathrm{r}}^{3-\mathrm{D}}\right)$$

(6)

where ${{\mathrm{V}}_{(>\mathrm{r})}}^{\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{e}}$ is the cumulative volume of the pore system with a radius larger than $\mathrm{r}$, $\mathrm{r}$ is the radius of pores in μm, and ${\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum radius of pores in μm. Similarly, the cumulative volume of the pore system with a radius less than r can be expressed as

$${\mathrm{V}}_{\left(<\mathrm{r}\right)}={\displaystyle \underset{{\mathrm{r}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}{\overset{\mathrm{r}}{\int }}}\mathrm{P}\left(\mathrm{r}\right){\displaystyle \frac{4}{3}}\mathsf{\pi }{\mathrm{r}}^3\mathrm{d}\mathrm{r}={\displaystyle \underset{{\mathrm{r}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}{\overset{\mathrm{r}}{\int }}}(-\mathrm{a}{\mathrm{D})\mathrm{r}}^{-{\mathrm{D}}_{\mathrm{f}}-1}\ast {\displaystyle \frac{4}{3}}\mathsf{\pi }{\mathrm{r}}^3\mathrm{d}\mathrm{r}$$

(7)

$${\mathrm{V}}_{\left(<\mathrm{r}\right)}=-{\displaystyle \frac{4\mathsf{\pi }\mathrm{a}\mathrm{D}}{3\left(3-\mathrm{D}\right)}}{\mathrm{r}}^{3-\mathrm{D}}\left|\begin{array}{c}\mathrm{r}\\ {\mathrm{r}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\end{array}\right.=-{\displaystyle \frac{4\mathsf{\pi }\mathrm{a}\mathrm{D}}{3\left(3-\mathrm{D}\right)}}\left({\mathrm{r}}^{3-\mathrm{D}}-{{\mathrm{r}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}^{3-\mathrm{D}}\right)$$

(8)

where ${{\mathrm{V}}_{(<\mathrm{r})}}^{\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{e}}$ is the cumulative volume of the pore system with a radius less than $\mathrm{r}$, $\mathrm{r}$ is the radius of pores in μm, and ${\mathrm{r}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ is the minimum radius of pores in μm. The total pore volume of the pore system can be obtained by Equations (6) and (8):

$${\mathrm{V}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}=-{\displaystyle \frac{4\mathsf{\pi }\mathrm{a}\mathrm{D}}{3\left(3-\mathrm{D}\right)}}{\mathrm{r}}^{3-\mathrm{D}}\left|\begin{array}{c}{\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\\ {\mathrm{r}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\end{array}\right.=-{\displaystyle \frac{4\mathsf{\pi }\mathrm{a}\mathrm{D}}{3\left(3-\mathrm{D}\right)}}\left({{\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}^{3-\mathrm{D}}-{{\mathrm{r}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}^{3-\mathrm{D}}\right)$$

(9)

where ${{\mathrm{V}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}}^{\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{e}}$ is the total pore volume of the pore system in ${\mathsf{\mu }\mathrm{m}}^3$. For pores in tight sandstones, the total pore volume can be obtained by experimental data of rate-controlled mercury injection. The cumulative volume fraction of the pore system with a radius larger than r can be obtained from the ratio between ${\mathrm{V}}_{(>\mathrm{r})}$ and ${\mathrm{V}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$.

$${\mathrm{S}}_{\mathrm{H}\mathrm{g}\left(>\mathrm{r}\right)}={\displaystyle \frac{{{\mathrm{V}}_{\left(>\mathrm{r}\right)}}^{\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{e}}}{{{\mathrm{V}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}}^{\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{e}}}}={\displaystyle \frac{{{\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}^{3-\mathrm{D}}-{\mathrm{r}}^{3-\mathrm{D}}}{{{\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}^{3-\mathrm{D}}-{{\mathrm{r}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}^{3-\mathrm{D}}}}={\displaystyle \frac{1-{\left(\frac{\mathrm{r}}{{\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}\right)}^{3-\mathrm{D}}}{1-{\left(\frac{{\mathrm{r}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}{{\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}\right)}^{3-\mathrm{D}}}}$$

(10)

where the ${\mathrm{S}}_{\mathrm{H}\mathrm{g}(>\mathrm{r})}$ is the non-wetting phase saturation in pores. The radius of pores in tight sandstones is widely distributed from 0.03 μm to 2 μm [24], which indicated that the ${\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is far greater than the ${\mathrm{r}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$. Equation (10) can be simplified as

$${\mathrm{S}}_{\mathrm{H}\mathrm{g}\left(>\mathrm{r}\right)}=1-{\left({\displaystyle \frac{\mathrm{r}}{{\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}}\right)}^{3-\mathrm{D}}$$

(11)

The correlation between ${{\mathrm{S}}_{\left(>\mathrm{r}\right)}}^{\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{e}}$ and D can be obtained from natural logarithm processing of Equation (11):

$$\log \left(1-{\mathrm{S}}_{\mathrm{H}\mathrm{g}\left(>\mathrm{r}\right)}\right)=\left(3-\mathrm{D}\right)\log \left({\displaystyle \frac{\mathrm{r}}{{\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}}\right)$$

(12)

According to the Laplace capillary pressure equation [23],

$${\mathrm{P}}_{\mathrm{c}}={\displaystyle \frac{2\mathsf{\sigma }\cos \mathsf{\theta }}{\mathrm{r}}}$$

(13)

where ${\mathrm{P}}_{\mathrm{c}}$ is capillary pressure corresponding to $\mathrm{r}$, $\mathsf{\sigma }$ is surface tension, and $\mathsf{\theta }$ is the contact angle of liquid. Substituting Equation (13) into Equation (12),

$$\log \left(1-{\mathrm{S}}_{\mathrm{H}\mathrm{g}\left(>\mathrm{r}\right)}\right)=\left(3-\mathrm{D}\right)\log \left({\displaystyle \frac{{\mathrm{P}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}{{\mathrm{P}}_{\mathrm{c}}}}\right)$$

(14)

$$\log \left(1-{\mathrm{S}}_{\mathrm{H}\mathrm{g}\left(>\mathrm{r}\right)}\right)=\left(3-\mathrm{D}\right)\log {\mathrm{P}}_{\mathrm{m}\mathrm{i}\mathrm{n}}-\left(3-\mathrm{D}\right)\log {\mathrm{P}}_{\mathrm{c}}$$

(15)

$$\log \left({\mathrm{S}}_{\mathrm{W}\left(>\mathrm{r}\right)}\right)=\left(\mathrm{D}-3\right)\log {\mathrm{P}}_{\mathrm{c}}-\left(\mathrm{D}-3\right)\log {\mathrm{P}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$$

(16)

where ${\mathrm{S}}_{\mathrm{W}(>\mathrm{r})}$ is the wetting phase saturation, ${\mathrm{P}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ is the minimum entrance capillary pressure, which is corresponding to the ${\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$. The fractal dimension of pores in tight sandstones can be finally calculated from the slope of the linear function between $\log \left(1-{\mathrm{S}}_{\mathrm{H}\mathrm{g}(>\mathrm{r})}\right)$ and $\log {\mathrm{P}}_{\mathrm{c}}$.

4. Results

4.1. Physical Properties

The detailed petrophysical test results (porosity and permeability) for the 14 tight sandstone samples are presented in Table 1. The data indicate that the Chang 8 formation in the Ordos Basin is a typical tight sandstone reservoir, and the lithology is dominated by Silt-fine grained sandstone. However, the porosity and permeability of 14 tight sandstone samples exhibit considerable variations, with porosity ranging from 1.32% to 10.01% (average: 5.39%) and permeability ranging from 0.012 mD to 0.474 mD (average: 0.159 mD).

4.2. Characteristics of Pore-Throat Structures

The pore-throat radius distribution diagram, based on high-pressure mercury injection (HPMI) data, clearly reveals the complex structural characteristics of the reservoir space in the Chang 8 tight sandstones (Figure 2). The pore-throat radius of all samples are primarily concentrated within the nano- to micrometer range of 0.004 to 0.63 μm, with distribution patterns categorized into irregular unimodal and bimodal types. Unimodal samples (e.g., #1, #2, #8, #9, #10) exhibit relatively concentrated pore-throat distributions, which can be further subdivided into right-skewed (main peak < 0.01 μm) and left-skewed (main peak between 0.01 and 0.1 μm) subcategories, suggesting their pore structures may be controlled by a single dominant diagenetic process. The bimodal samples (e.g., #3, #4, #5, #6, #12, #13, #14) show curves with two distinct peaks across the 0.001–0.63 μm range, with the primary peak typically located between 0.01 and 0.1 μm. This bimodal characteristic often indicates the superposition of multiple diagenetic events, such as the coexistence of larger pores formed by early dissolution and micropores resulting from late-stage authigenic mineral filling or intense compaction. Samples with a bimodal pore-throat distribution typically exhibit superior permeability, which indicates the superposition of multiple diagenetic processes (such as the coexistence of larger pores formed by early dissolution and micropores created by late autogenous mineral filling or intense compaction), suggesting that such multi-peak structures can form more favorable pore-throat configurations and connectivity, thereby enhancing fluid flow. In terms of volume proportions by pore-throat type, the reservoir space is dominated by mesopores (100–1000 nm, accounting for 57%) and micropores (<100 nm, 43%), while macropores (>1000 nm) are scarcely developed, severely limiting the flow capacity of the reservoir.

Table 2. Evaluation parameters of tight sandstones with complex structure from HPMI data. ${\mathrm{S}}_{\mathrm{H}\mathrm{g}\mathrm{m}\mathrm{a}\mathrm{x}}$—the maximal mercury saturation corresponding to maximal injection capillary pressure in %; the ${\mathrm{P}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$—threshold pressure corresponding to the mercury first enters the pore-throat in Mpa; ${\mathrm{P}}_{50}$—pressure corresponding to 50% cumulative mercury intrusion saturation in Mpa; ${\mathrm{r}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$—pore-throat radius corresponding to the ${\mathrm{P}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ in μm; ${\mathrm{r}}_{\mathrm{a}\mathrm{v}\mathrm{e}}$—average pore-throat radius in μm; ${\mathrm{r}}_{50}$—pore-throat radius corresponding to 50% cumulative mercury intrusion saturation in μm; ${\mathrm{r}}_{40}$—pore-throat corresponding to 40% cumulative mercury intrusion saturation in μm; ${\mathrm{r}}_{30}$—pore-throat corresponding to 30% cumulative mercury intrusion saturation in μm; ${\mathrm{r}}_{20}$—pore-throat corresponding to 20% cumulative mercury intrusion saturation in μm; ${\mathrm{r}}_{\mathrm{K}}$—pore-throat radius corresponding to the maximum permeability contribution in μm.

Sample	${\mathbf{S}}_{\mathbf{H}\mathbf{g}\mathbf{m}\mathbf{a}\mathbf{x}}$ (%)	${\mathbf{P}}_{\mathbf{m}\mathbf{i}\mathbf{n}}$ (Mpa)	${\mathbf{P}}_{50}$ (Mpa)	${\mathbf{r}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$ (μm)	${\mathbf{r}}_{\mathbf{a}\mathbf{v}\mathbf{e}}$ (μm)	${\mathbf{r}}_{50}$ (μm)	${\mathbf{r}}_{40}$ (μm)	${\mathbf{r}}_{30}$ (μm)	${\mathbf{r}}_{20}$ (μm)	${\mathbf{r}}_{\mathbf{K}}$ (μm)
#1	53.765	2.964	165.285	0.085	0.012	0.005	0.005	0.007	0.013	0.063
#2	62.471	0.735	141.021	0.028	0.007	0.005	0.006	0.009	0.016	0.016
#3	86.118	0.268	17.479	0.514	0.057	0.043	0.070	0.010	0.162	0.250
#4	89.882	0.459	10.399	0.298	0.062	0.072	0.102	0.115	0.162	0.163
#5	74.941	0.141	56.049	0.246	0.038	0.013	0.024	0.058	0.102	0.160
#6	89.882	0.347	8.663	0.894	0.123	0.087	0.203	0.304	0.416	0.625
#7	59.681	3.101	22.060	0.202	0.054	0.034	0.047	0.062	0.094	0.115
#8	47.261	7.1	/	0.091	0.032	/	0.028	0.039	0.051	0.063
#9	78.699	2.964	75.757	0.116	0.016	0.009	0.011	0.022	0.036	0.063
#10	46.854	3.101	/	0.117	0.037	/	0.033	0.042	0.057	0.063
#11	59.681	3. 101	22.059	0.202	0.054	0.034	0.047	0.062	0.094	0.115
#12	82.353	0.735	18.036	0.245	0.049	0.042	0.071	0.102	0.127	0.158
#13	82.554	0.627	4.595	1.067	0.281	0.163	0.293	0.536	0.721	0.630
#14	90.235	0.346	8.006	0.671	0.101	0.094	0.162	0.253	0.343	0.412

presents the evaluation parameters for complexly structured tight sandstone based on HPMI data. The maximum mercury saturation (S_Hgmax) ranges from 47.26% to 90.24%, with only sample #8 below 50% (Table 2). The threshold pressure (P_min) varies between 0.14 MPa and 7.1 MPa, while the median pressure (P₅₀) ranges from 4.60 MPa to 165.29 MPa (Table 2). The pore-throat radius corresponding to P_min (r_max) spans a wide interval of 0.028–1.067 μm, with a mean of 0.212 μm (

Table 3. The correlation analysis from multiple fractal dimension curves. K represents the slope of the double logarithmic curve between $\log \left({\mathrm{S}}_{\mathrm{W}}\right)$ and $\log {\mathrm{P}}_{\mathrm{c}}$, and R-squared values between $\log \left({\mathrm{S}}_{\mathrm{W}}\right)$ and $\log {\mathrm{P}}_{\mathrm{c}}$ for mesopore-throat spaces and micropore-throat spaces in 14 samples.

No.	Type	Porosity (%)	Permeability (mD)	Break Radius (μm)	Porosity Contribution of Mesopore-Throat (%)	Permeability Contribution of Mesopore-Throat (%)	Mesopore-Throat		Micropore-Throat		Total Pore-Throat
							D1	R21	D2	R22	D
#1	2	1.32	0.046	0.01	31.2	42.1	2.936	0.972	2.444	0.965	2.544
#2	2	1.57	0.04	0.017	30.3	46.6	2.947	0.85	2.448	0.919	2.549
#3	1	7.72	0.474	0.102	54.6	90.7	2.798	0.865	2.429	0.989	2.633
#4	1	5.76	0.104	0.253	52.7	83.2	2.87	0.808	2.432	0.994	2.614
#5	1	4.75	0.101	0.022	54.6	97.9	2.82	0.96	2.432	0.998	2.644
#6	1	7.64	0.315	0.022	75.1	97.0	2.742	0.981	2.297	0.998	2.631
#7	1	6.49	0.073	0.074	41.4	75.1	2.844	0.823	2.457	0.999	2.617
#8	2	3.38	0.014	0.106	16.8	9.5	2.992	0.844	2.519	0.994	2.598
#9	2	2.63	0.057	0.015	34.9	42.6	2.876	0.84	2.463	0.981	2.578
#10	2	3.91	0.012	0.147	15.2	22.6	2.986	0.99	2.613	0.987	2.569
#11	1	6.49	0.073	0.074	41.4	66.5	2.843	0.822	2.457	0.996	2.611
#12	1	6.15	0.105	0.251	39.7	69.1	2.872	0.913	2.592	0.988	2.603
#13	1	10.01	0.449	0.106	77.4	94.4	2.665	0.988	2.379	0.985	2.628
#14	1	7.62	0.361	0.025	71.9	93.9	2.742	0.951	2.284	0.997	2.614

). The average pore-throat radius (r_ave) is 0.007–0.281 μm (mean 0.068 μm). Radii at cumulative mercury intrusion saturations of 50%, 40%, 30%, and 20% (r₅₀, r₄₀, r₃₀, r₂₀) show mean values between 0.048 μm and 0.177 μm, and the radius contributing most to permeability (r_K) averages 0.215 μm (Table 3). These parameters reflect strong complexity and heterogeneity in the pore-throat radius distribution of the Chang 8 tight sandstones. The maximum injection pressure reached 182.04 MPa in this experiment, with a pore-throat radius measurement accuracy of 0.004 μm.

4.3. Fractal Dimension Characteristics of Tight Sandstone from HPMI

By analyzing the fractal characteristics of high-pressure mercury injection curves, dense sandstones are characterized and classified. In a double-logarithmic coordinate system, the fractal dimension (D) is derived based on the log(S_W)–log(P_c) relationship. The curves of 14 samples exhibit two well-defined linear segments (Figure 3), indicating that Chang 8 dense sandstone conforms to fractal geometric properties. The left first fractal segment (blue points on the left) corresponds to larger pore-throat systems (mesopores), with slopes ranging from −0.335 to −0.009 (average −0.128) and correlation coefficients ranging from 0.808 to 0.991 (average 0.907) (Figure 3). The second fractal segment (red points on the right) exhibits lower slopes, corresponding to micropore-throat systems (micropores), with slopes ranging from −0.837 to −0.408 (average −0.570) and correlation coefficients ranging from 0.914 to 0.999 (average 0.980) (Figure 3). Fractal dimensions for the mesopores and micropores of the eight samples are calculated and listed in Table 3. The results show that the fractal dimension D1 for mesopores ranges from 2.742 to 2.992 (average 2.852), with an average correlation coefficient of 0.901. The fractal dimension D2 for micropores ranges from 2.284 to 2.613 (average 2.446), and its average correlation coefficient (0.985) is slightly higher than that of the mesopores. The higher D1 values indicate stronger heterogeneity and irregularity of mesopore-throats, which are closely associated with uneven dissolution, particle sorting differences, and complex pore connectivity. Lower D2 values suggest relatively regular and homogeneous micropore structures, which are mainly controlled by simple diagenetic processes such as clay mineral transformation and intragranular dissolution.

To further analyze the differences between the two types of tight sandstone samples from a fractal perspective, the break radius between mesopores and micropores was calculated based on the fractal characteristics. This radius corresponds to the inflection point on the log(S_W)–log(P_c) plot, and represents either the minimum radius of mesopores or the maximum radius of micropores (Figure 3). The break radius ranges from 0.01 to 0.253 μm, with an average of 0.04 μm (Figure 3, Table 3). This indicates that pore-throats with radii larger than 0.04 μm are predominantly mesopores, while those with radii smaller than 0.004 μm are mainly micropores. This break radius represents the critical threshold that distinguishes effective flow-controlling mesopore-throats from micropore-throats that contribute little to permeability. This threshold is consistent with microscopic observations of pore types and diagenetic origins, validating the rationality of fractal segmentation.

4.4. Classification of Tight Sandstones Based on Fractal Dimension

The strong diagenesis has resulted in strong complexity and heterogeneity of the Chang 8 tight sandstones; however, the tight sandstones with complex pore-throat structures have been proven to have fractal characteristics. Based on the discussion in the previous section, the spaces in the Chang 8 tight sandstones are primarily characterized as two categories on double logarithmic curves (

Table 4. Comparations of two categories of reservoirs from 14 tight sandstone samples.

Reservoir Type	1	2
Spaces	Mesopore-throat spaces dominated	Micropore-throat spaces dominated
Samples	#3, #4, #5, #6, #7, #11, #12, #13, and #14	#1,#2, #8, #9, and #10
Fractal dimensions (D)	2.603–2.644	2.544–2.598
Primary pore-throat types	Original intergranular pores, residual intergranular pores, and intergranular dissolution pores	Intragranular dissolution pores, intercrystallite pores, and scrobiculate dissolution pores in clay minerals
Porosity contribution of mesopore-throat spaces	39.7–77.4%	15.2–34.9%
Permeability contribution of mesopore-throat spaces	66.5–97.9%	9.5–46.6%
Pore-throat radius distribution

, Figure 4): mesopore-throat spaces and micropore-throat spaces. According to the discrepancies of two categories of spaces exhibited in the fractal dimension curves, we can then calculate the total fractal dimensions (D) to comprehensively characterize the complexity and heterogeneity of reservoirs. They could be obtained through the volume percentage of two categories of spaces to the total pore-throat spaces from Equation (18), where the average weight of different fractal dimensions can be expressed by the percentage of mercury saturation corresponding to different types of pore-throat spaces.

$$\mathrm{D}={\displaystyle \frac{{\mathrm{V}}_{\mathrm{H}\mathrm{g}\left(<\mathrm{r}\right)}}{{\mathrm{V}}_{\mathrm{H}\mathrm{g}\left(\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\right)}}}\ast {\mathrm{D}}_{\left(<\mathrm{r}\right)}+{\displaystyle \frac{{\mathrm{V}}_{\mathrm{H}\mathrm{g}\left(>\mathrm{r}\right)}}{{\mathrm{V}}_{\mathrm{H}\mathrm{g}\left(\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\right)}}}\ast {\mathrm{D}}_{\left(>\mathrm{r}\right)}$$

(17)

$$\mathrm{D}={\mathrm{S}}_{\mathrm{H}\mathrm{g}\left(<\mathrm{r}\right)}\ast {\mathrm{D}}_{\left(<\mathrm{r}\right)}+{\mathrm{S}}_{\mathrm{H}\mathrm{g}\left(>\mathrm{r}\right)}\ast {\mathrm{D}}_{\left(>\mathrm{r}\right)}$$

(18)

where the $\mathrm{D}$ is the fractal dimensions of the total pore-throat, ${\mathrm{S}}_{\mathrm{H}\mathrm{g}\left(\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\right)}$ is the maximum mercury saturation in %, ${\mathrm{D}}_{(<\mathrm{r})}$ or ${\mathrm{D}}_{(>\mathrm{r})}$ is the fractal dimension of the pore-throat with a radius less or larger than that corresponding to an inflection point on double logarithmic coordinates. The detailed calculation results of fractal dimensions were listed in Table 4.

The results showed that the D for the total spaces of samples is in a range of 2.544–2.644 with an average of 2.602 (Table 4, Figure 4). It is indicated that the pore-throat spaces of Chang 8 tight sandstones are complex and heterogeneous.

Two categories of spaces primarily developed in the Chang 8 tight sandstones in this study: mesopore-throat and micropore-throat spaces, with mesopore-throat spaces dominating. As the mesopore-throat paces are the most significant reservoir types in this study, the contribution of mesopore-throat spaces to the porosity and permeability of reservoirs are then calculated to effectively distinguish between the two categories of reservoirs. The porosity contribution of mesopore-throat spaces can be expressed as the percentage of cumulative mercury saturation with corresponding pore-throat space types, which is shown in Equation (17). The permeability contribution of mesopore-throat spaces can be obtained from cumulative permeability contribution curves of the HPMI data, which is part of the cumulative permeability contribution curves corresponding to the pore-throat radius larger than the break radius.

As shown in Table 3, the porosity contribution of mesopore-throat spaces ranges from 15.2% to 77.4% with an average of 45.5 and the permeability contribution of mesopore-throat spaces is in a range of 9.5% to 97.9% with an average of 66.5%. According to the cross plot of the porosity contribution and permeability contribution of mesopore-throat spaces to total pore-throat spaces in Figure 4, the 14 tight sandstones present a significant hierarchical feature, with nine samples located in the top right corner and five samples located in the bottom left corner. Therefore, the 14 samples can be divided as the following standard is shown in Figure 4: spaces of mesopore-throat dominance (porosity contribution > 35% and permeability contribution > 60%), and spaces of micropore-throat dominance (porosity contribution < 35% and permeability contribution < 60%).

Based on the detailed fractal analysis in Table 4, the D of the 9 samples in the red box of Figure 4 ranges from 2.603 to 2.644 with an average of 2.622, while the D of the five samples in the green box of Figure 4 is in a range of 2.544–2.598 with an average of 2.568. The D of samples with spaces of mesopore-throat dominated is generally greater than that of samples with spaces of micropore-throat dominated. It is indicated that the samples with spaces of mesopore-throat dominance have more complexity and heterogeneity in pore-throat structure than those of samples with spaces of micropore-throat dominance. Meanwhile, the D of 2.6 is a significant threshold value for two categories of reservoirs (Figure 4): high fractal dimension category (D > 2.6) corresponds to the reservoir types with spaces of mesopore-throat dominance (Figure 4, Table 4), while low fractal dimension category (D < 2.6) corresponds to the reservoir types with spaces of micropore-throat dominance (Figure 4, Table 4). Therefore, we established the classification methods of Chang 8 tight sandstone reservoirs from a fractal perspective.

4.5. Special Structural Discrepancies of Reservoirs with Different Fractal Dimensions

For tight sandstones dominated by mesoscale pore-throat spaces, intergranular dissolution pores are extensively distributed in dissolved feldspar grains, volcanic rock fragments, and cement (Figure 5A,B,D,I). These pores are characterized by relatively large pore bodies and isolated distribution; meanwhile, the well-developed throats ensure good connectivity between them, making them the primary storage spaces (Figure 5A). Reservoirs of this type contain abundant intergranular pores and throats, which account for a significant proportion of total pore volume and exhibit considerable connectivity. In contrast, tight sandstones dominated by microscale pore-throat spaces mainly consist of intragranular dissolution pores, intercrystalline pores, and sieve-like dissolution pores in clay minerals. These pores develop between calcite or silica minerals, with intragranular dissolution pores locally forming along the edges and inside rock fragment grains (Figure 5C,F). Authigenic minerals, mostly of the pore-bridging type, are observed in such reservoirs (Figure 5H). Additionally, some microscale intercrystalline pores occur within authigenic minerals (e.g., chlorite, illite, mixed illite/smectite layers, and kaolinite), though their microstructure contributes minimally to reservoir physical properties (Figure 5G,I).

5. Discussion

5.1. Low Permeability, Tightness, and Strong Heterogeneity of the Chang 8 Reservoir

The present study analyzed the pore-throat structure characteristics of the Chang 8 dense sandstone reservoir through physical property measurements and high-pressure mercury infiltration (HPMI) experiments, confirming it as a typical low-permeability dense reservoir with extremely strong heterogeneity (Figure 2 and Figure 3; Table 1 and Table 2). This characteristic is not caused by a single factor but results from the combined effects of pore-throat scale, distribution patterns, and fluid occurrence state [9]. From the perspective of fundamental pore-throat characteristics, the Chang 8 reservoir features a fine pore-throat system. Experimental data show that the median pore-throat radius can be as low as 0.005 µm, corresponding to median mercury intrusion pressures ranging from tens to over a hundred megapascals (Table 2). This fine pore-throat radius generates significant capillary resistance, leading to extremely poor natural flow capacity of formation fluids, which is the fundamental physical cause of the reservoir’s low initial productivity [25]. Consequently, the development of the Chang 8 reservoir necessitates technologies such as hydraulic fracturing to artificially connect the dispersed throat network through induced fractures [26].

The complexity and spatial variation in pore-throat distribution further exacerbate reservoir heterogeneity. Experiments observed various pore-throat radius distribution patterns in the Chang 8 reservoir, including unimodal and bimodal modes, with key parameters (maximum pore-throat radius, median pressure, pore-throat sorting coefficient) exhibiting orders-of-magnitude differences (Figure 2). This directly reflects the spatial unevenness of sedimentary and diagenetic processes. Among these, samples with bimodal distribution demonstrate better flow potential: the larger peak is mostly concentrated in the 0.01–0.1 µm range, forming the “dominant flow pathways” within the reservoir, which provide the main routes for fluid flow. In contrast, samples with a unimodal distribution exhibit the poorest reservoir quality due to the lack of effective flow pathways. This distinction provides clear microscopic criteria for reservoir zoning and classification, underscoring the necessity of differentiation [27].

5.2. Causes of Multiple Fractals in the Pore Structure

The data of this study reveals that the Chang 8 tight sandstones commonly exhibit a two-segment fractal characteristic, which directly reflects the physical nature of the reservoir pore system—the pore space consists of two subsystems, the meso and micropore-throat systems, with distinct genetic origins and structural properties. The two-segment fractal behavior has a clear physical meaning, and relatively large pore-throats (mesopore-throats) and small pore-throats (micropore-throats), which are formed by different diagenetic processes and show different heterogeneity, connectivity, and contributions to physical properties. The fractal segmentation corresponds to the threshold radius that distinguishes dominant flow spaces from ineffective storage spaces, and thus has substantial geological significance for reservoir quality classification. The fractal dimension D1 corresponding to the mesoporous throat system ranges from 2.74 to 2.99, indicating a relatively high fractal dimension. This characteristic is closely related to the formation mechanism of mesopores, which primarily result from the preservation of primary intergranular pores during diagenesis and subsequent dissolution. Although their pore sizes are relatively large (0.01–0.1 µm), variations in particle sorting and uneven dissolution intensity lead to highly irregular pore morphology, high tortuosity of pore networks, and complex connectivity pathways [9].

The fractal dimension D2 corresponding to the micropore-throat subsystem ranges from 2.30 to 2.61, which is significantly lower than D1, indicating a relatively homogeneous structure. Genetically, micropore-throat are dominated by intragranular and intercrystallite pores, primarily controlled by single diagenetic processes such as intraparticle dissolution or intercrystallite pores formed by clay mineral transformation. Their formation process is relatively uniform, resulting in stable pore morphology patterns and lower structural complexity, which is reflected in the low D2 values [6].

The correlations shown in Figure 6A,B corroborate this perspective: D1 is significantly negatively correlated with mesopore porosity (R² = 0.5197) and mesopore permeability (R² = 0.8005), with a stronger correlation for permeability, indicating that higher heterogeneity in mesopore-throats directly impedes fluid flow. Higher D1 values indicate more complex mesopore-throat structures, poorer throat connectivity, and fewer effective flow paths. Even with sufficient pore volume, fluid flow remains inefficient. This finding challenges the simplistic notion that “higher structural complexity equates to poorer reservoir quality,” clearly indicating that complexity must be analyzed in conjunction with pore types [6]. In contrast, D2 shows a weak positive correlation with micropore porosity and permeability (R² < 0.2), suggesting that micropore structure has limited influence on macroscopic physical properties, and its distribution appears scattered as porosity changes, indicating that micropore-throat contribute limitedly to overall flow capacity, and their structural complexity (low D2) has a minimal effect on enhancing reservoir quality [27].

The key insight from the analysis of the two-segment fractal characteristic is that the relationship between the fractal dimensions of the two subsystems and macroscopic physical properties follows distinctly different patterns. Specifically, D1 shows a significant negative correlation with the porosity and permeability of the mesopore-throat system: higher D1 values indicate more complex mesopore-throat structures, poorer throat connectivity, a lower proportion of effective flow paths, and consequently, hindered fluid flow even when pore abundance is adequate. This pattern demonstrates that complexity must be analyzed in relation to pore scale and origin [28]. Reservoir quality evaluation must transcend the limitations of unidimensional criteria. Even reservoirs with high porosity often exhibit low permeability if their pore space consists primarily of micropores and micropore throats. Thus, high porosity does not equate to high-quality reservoirs. Similarly, high structural complexity does not necessarily imply poor reservoir quality; the key lies in determining which pore subsystem this complexity originates from [29]. High complexity in the mesopore-throat system (high D1) significantly deteriorates the reservoir, whereas low complexity in the micropore-throat system (low D2) has limited potential to improve reservoir quality [26]. Furthermore, when scaled to the total fractal dimension (D), its correlation with porosity and permeability parameters weakens significantly (Figure 6C,D). This weak correlation is statistically confirmed by low R² values, meaning that total D cannot serve as a direct indicator of reservoir physical properties. This indicates that although the mesopore-throat system exerts far stronger control over reservoir physical properties than the micropore-throat system, D, as a blended signal of D1 and D2, cannot clearly reflect the independent role of either subsystem. This further underscores the necessity of conducting fractal analysis and quantitative assessment of subsystem contributions. The macroscopic uniformity and complexity exhibited by reservoirs are jointly governed at the microscopic level by both micro- and mesopore systems, with the mesopore system exerting a more pronounced influence on the complexity of pore structures.

5.3. Mechanism Underlying the Lower Total Fractal Dimension in High-Quality Reservoirs

Further analysis in the present study revealed that high-quality reservoirs dominated by the mesopore-throat system (Type I) exhibit a higher total fractal dimension (D, 2.603–2.644) compared to poorer reservoirs dominated by the micropore-throat system (Type II, D, 2.544–2.598). This phenomenon represents one of the important findings of this research. The mechanism lies in the fact that the total fractal dimension D is a weighted average of D1 and D2 based on their respective pore volume contributions. In Type I reservoirs, although the mesopore-throat system itself has a high D1 value, it holds an absolute dominance in pore volume (contribution >35%), and its exceptionally high permeability contribution (>60%) governs fluid flow (Table 4). This results in an overall reservoir characterized by a relatively efficient connected network. The structural heterogeneity in these reservoirs is primarily reflected in the pore size distribution rather than in topological complexity that impedes flow, leading to a higher overall D value. In contrast, in Type II reservoirs, an effective mesopore-throat work is underdeveloped (low permeability contribution). Although the micropore-throat system has a modest D2 value, its larger volume proportion (typically high porosity contribution) and ineffective storage capacity dominate the system’s properties, thereby elevating the weighted average D value. Consequently, the D value is not an absolute measure of the reservoir’s inherent complexity but rather a comprehensive indicator that reflects the type of dominant pore system and the effectiveness of its structure within the reservoir [28].

5.4. Controlling Effect of Diagenesis on Fractal Dimensions

The complex and irregular pore-throat structure of tight sandstones exhibits distinct fractal characteristics. In the studied of Yanchang Formation, deep burial and intense diagenetic alteration have led to significant loss of primary porosity and further increased pore-throat complexity [30]. The main diagenetic processes affecting the Chang 8 tight sandstones include compaction, dissolution, cementation, and the precipitation of authigenic clay minerals, all of which collectively reshape the pore-throat system by destroying, preserving, or generating porosity. Compaction reduces primary porosity through mechanisms such as long-grain contact, grain rearrangement, and quartz grain fracturing (Figure 5E,F). This process diminishes the volume of primary pores and throats, resulting in more complex pore-throat configurations and higher fractal dimensions. Additionally, intense compaction promotes the development of numerous micropores and throats, facilitating the precipitation of diagenetic minerals such as siliceous cements, calcite, and clay minerals (Figure 5A,D,G,H).

Dissolution plays a crucial role in forming secondary porosity, creating features such as intergranular dissolution pores (Figure 5A,B), dissolution pores within volcanic fragments (Figure 5C,F), and residual intercrystalline pores (Figure 5E). Although feldspar dissolution can enhance secondary porosity, it often triggers the precipitation of authigenic clay minerals, which may fill intergranular pores and reduce pore-throat radii. In the Chang 8 reservoir, dissolution pores are mainly observed in the micropore-throat system and contribute limitedly to reservoir properties. Authigenic clay infill further disrupts throat connectivity, amplifies pore-throat radius heterogeneity, and partially diminishes the fractal signature of the mesopore-throat system. Cementation in the Chang 8 sandstones primarily involves calcite and authigenic clay minerals. Calcite cement occurs in two forms: early-stage (eogenetic) cement, which partially fills pores (Figure 5A) and may help preserve porosity by inhibiting compaction, and late-stage ferroan calcite cement, which extensively fills intergranular pores (Figure 5D) and significantly reduces porosity and fractal dimension. Authigenic clay minerals, dominated by chlorite with minor kaolinite, influence pore-throat structure in two ways: grain-coating chlorite protects primary porosity by limiting quartz cementation and enhancing compaction resistance (Figure 5A,B,G), whereas pore-filling and bridging clays increase pore-throat heterogeneity and raise the fractal dimension, especially within the micropore-throat system (Figure 5H) [30,31]. In summary, diagenesis indirectly influences fractal dimensions by altering pore-throat structure. Constructive processes such as dissolution and clay coating tend to preserve or improve pore connectivity, reducing fractal dimensions in mesopore-throatsystems. In contrast, destructive processes including compaction, cementation, and clay filling increase structural complexity and elevate fractal dimensions, particularly within micropore-throat systems.

5.5. Implication and Perspective

The present study, through high-pressure mercury injection experiments and fractal analysis, revealed that the pore throat characteristics and the strong capillary resistance under high injection pressure in the Chang 8 reservoir are the fundamental causes of its low initial productivity. The significant variation in pore-throat distribution patterns provides a microscopic basis for reservoir zonation and classification. Among these, the dominant flow pathways within the mesopore-throat system of bimodally distributed reservoirs are key to enhancing percolation capacity. Two segment fractal characteristics further demonstrate the distinct influences of the fractal dimensions of the meso- and micropore-throat subsystems. The mesopore-throat system exerts a significant control over both porosity and permeability, while the contribution of the micropore-throat system to flow capacity is negligible. This revealed a more nuanced relationship between pore structure complexity and reservoir quality than previously recognized. Moreover, the total fractal dimension should be interpreted alongside the dominant pore throat system. High-quality reservoirs dominated by mesopore-throats exhibit a lower total fractal dimension than those dominated by micropore-throats, as their greater pore volume share and permeability contribution govern overall connectivity efficiency. Diagenesis exerts a dual control on fractal features, with both constructive and destructive processes collectively shaping the pore-throat structure [9]. These conclusions provide precise theoretical support for optimizing fracturing designs and establishing a differentiated reservoir evaluation system.

6. Conclusions

Based on a detailed fractal characteristic analysis of Chang 8 tight sandstone samples via HPMI experiments, the pore-throat structure and physical properties of the samples were clarified, and a fractal-based classification method for high-quality tight sandstones was established. Key findings and implications are summarized as follows:

Chang 8 tight sandstone exhibits typical two-segment fractal characteristics, comprising mesopore-throat (D1: 2.74–2.99) and micropore-throat (D2: 2.28–2.61) subsystems. The higher D1 is attributed to structural heterogeneity from uneven diagenetic dissolution and particle sorting, while the lower D2 results from homogeneous pore morphology controlled by single diagenetic processes.

The mesopore-throat system is the dominant storage and flow space, exerting a decisive control on reservoir porosity and permeability, whereas the micropore-throat system contributes weakly to fluid flow. The total fractal dimension (D) is a pore volume-weighted average of D1 and D2, with D = 2.6 as the critical threshold for distinguishing high- and low-quality reservoirs.

Based on mesopore-throat contributions, Chang 8 reservoirs are divided into two types: Type 1 with well-connected primary and intergranular dissolution pores; Type 2 with immobility-limiting intragranular dissolution and clay intercrystalline pores.

Diagenesis exerts differential control on fractal characteristics and reservoir quality: destructive processes (intense compaction, carbonate cementation, clay filling) increase pore-throat complexity and fractal dimension to deteriorate reservoirs; constructive processes (feldspar dissolution, chlorite coating) preserve porosity, reduce mesopore-throat fractal dimension and improve reservoir quality.

Overall, the proposed fractal-based classification method makes up for the limitations of traditional classification relying on single physical parameters, providing a new quantitative approach for evaluating tight sandstone reservoirs.