Experimental and Numerical Simulations of Pore Structures and Seepage Characteristics of Deep Sandstones

Abstract

Previously conducted studies have established that deep underground rock masses have complex pore structures and face complex geological conditions. Therefore, the seepage problem of such rock masses seriously affects engineering safety. To better explore the seepage law of deep rock masses and ensure engineering safety, indoor experimental methods such as casting thin sections, scanning electron microscopy, and mercury intrusion testing were utilized in this study. The microscopic pore shape, size, distribution, and other structural characteristics of sandstone in coal bearing strata were analyzed. The tortuosity calculation formula was obtained by the theoretical derivation method. And a numerical model was established for seepage numerical simulation research through microscopic digital image methods. The seepage law of surrounding rocks in the Tangkou Coal Mine roadway under different conditions is discussed. The research results indicate that the complexity of the pore structure in porous media leads to an uneven distribution of flow velocity and pressure within the medium. Meanwhile, with the change of physical properties, the fluid flow characteristics also undergo significant changes. The research results can effectively guide micropore water blocking, reduce the impact of groundwater on the environment, ensure the environment and safety of the project, and provide guidance for other geological projects.

1. Introduction

As the number of engineering construction projects increases, the safety requirements in underground spaces are also increasing [1,2]. Safety in underground spaces in coal mining is one example. Due to the long-term mining of coal resources, most open-pit coal mines and some shallower underground mines have gradually been exhausted [3,4]. The development of coal resources has gradually moved toward larger underground mines [5,6]. For mining deep coal resources, as the osmotic pressure increases, the increase in micropore seepages in coal-bearing strata sandstone leads to serious shaft wall deterioration, which is one of the main disasters endangering the safe production of mines [7,8]. At the same time, as the depth of mines continues to increase, the hydrogeological conditions of coal mines become increasingly complex [9,10], leading to pore channels suitable for fluid seepage in rock formations and altering the various original properties of the rock [11,12]. The probability of sweat seepage in coal-bearing strata has increased. All these factors have made mine water hazard prevention and control work more difficult [13,14]. Micropore water seepage has become an urgent problem that needs to be addressed in deep mining.

Previous studies on pore flow were usually divided into two aspects: rock seepage problems and analysis of pore structure.

In terms of rock seepage:

Some scholars have studied the seepage problem in mining engineering through experimental or numerical simulation methods. For example, Colas [15] explored the characteristics and solutions of water inrush in underground spaces after mining activities based on different numerical simulation solutions. They proposed measures to ensure safety and provided reference for relevant underground engineering. In Kovalski’s work [16], by providing a deeper understanding of the laws of destruction of the underlying rock mass and the likelihood of groundwater seepage, the study can serve as a guide for effective water blocking strategies, which mitigate the impact of groundwater penetration on the environment and improve the safety and environmental sustainability of deep-sea geological projects. Rybak [17] used numerical modeling based on the finite element method (FEM) in the FLAC 3D 5.01 software. The author analyzed the impact of underground mined-out voids on the occurrence of subvertical disturbance and their influence on the water-protective layer. Contour graphs of stresses were constructed, and strain changes were studied. Based on the data obtained, a method was proposed to minimize the development of subvertical fracturing, which will preserve the water-protective layer and prevent the mine from flooding. To explore the evolution of fine particle structure under different loading and deep current effects, Phan [18] established a calculation model for work from the perspective of doing work. The theory of this system provides reliable guidance for other underground projects.

However, these scholars lack the analysis of pore structure under different conditions and the microscopic study of rock pore structure.

In terms of pore structure research:

In the study of pore structure, we determine the physical properties of coal-bearing strata, the connectivity between pores, and the flow of fluids in microscopic pore throats [19]. The general appearance of the pores in the formation controls the seepage characteristics of the fluid in the coal-bearing sandstone pores.

The pore microstructure of sandstone in deep coal-bearing formations is complex, and the pores in the rock body are intertwined to form an intricate pore structure network, showing high randomness and heterogeneity [20,21,22]. The difficulty of characterizing the pore structure has increased. There are often more limitations in carrying out conventional microscopic pore structure characterization techniques. Generally, it is necessary to introduce new technologies and methods to analyze the microscopic pore structure [23,24,25].

On the one hand, the direct observation method is more common. Casting thin sections of cores can allow for the analysis of pore types, distribution, size, interconnectedness, and average pore radii of coal-bearing sandstone. Houseknechtp first studied the pore structure evolution using casting thin section image data in 1987 [26]. Liu et al. [27] used casting thin section image data to evaluate the physical parameters of sandstone. Nabawy et al. [28] used casting thin sections and high-pressure mercury injection to analyze the structural characteristics of microscopic pore throats in sandstone. In addition, the SEM method has been a more commonly used method by many scholars [29,30,31].

Indirect measurement methods have also been widely adopted. Some scholars [32,33] have used the gas adsorption method to explore the pore structure characteristics and have been able to describe the pore structure characteristics with a pore size of less than 2 nm.

With the advancement of technology, mercury porosimetry [34] has been widely used in pore structure testing. With regard to high-pressure mercury injection technology: Swanson et al. [35] discovered the inflection point parameters of the capillary pressure curve in 1981 and established a pore permeability prediction model for rock formations based on the data obtained from the above experiments. Yang et al. [36] conducted a joint experiment involving low-temperature nitrogen adsorption and high-pressure mercury intrusion to explain the influence of pore structure characteristics on the seepage process in rock formations. Sun [37] relied on the capillary pressure curve obtained by the mercury intrusion method to analyze the spatial distribution of sandstone pores and classify the pore types. Pittman et al. [38] analyzed the data obtained from high-pressure mercury intrusion tests and explained the relationship between the pore structure characteristics and physical properties of rock formations. Wang et al. [39] characterized the microscopic pore structure of sandstone in the study area based on the high-pressure mercury intrusion method and explained the strong heterogeneity of the pore structure in the rocks in the area. In addition, with regard to constant velocity mercury injection technology: Yuan and Swanson [40] were the first to manufacture a constant-speed mercury porosimeter that can operate automatically, thereby laying a good foundation for the subsequent application of this technology to the characterization of rock pore microstructures. Yu et al. [41], based on the analysis of the microscopic pore structure characteristics in the Ordos area, combined with mercury intrusion technology, found that the development of pores and throats greatly promoted the seepage of rock pores.

In addition to the above technologies, nuclear magnetic resonance technology can be used to test the percolation characteristics of pore structures. Guo et al. [42] studied the pore characteristic parameters of coal-bearing formations based on nuclear magnetic resonance technology, analyzed the main rock formations in the region, and characterized the connection between pores and throats. Li et al. [43] used nuclear magnetic resonance and mercury intrusion technology to study the relationship between the pore size distribution in coal-bearing formations and the pressure applied by the tests. Zhou et al. [44] proposed a new method based on tube model theory to evaluate the characteristics of pore structures based on capillary pressure curve data obtained from nuclear magnetic resonance tests. Some scholars [45,46,47] have used nuclear magnetic resonance testing technology to predict and analyze the physical properties of coal-bearing sandstone. Scholars He et al. [48,49] constructed the free water T2 distribution based on nuclear magnetic resonance technology and calculated the pseudocapillary pressure curve through a piecewise power function to characterize the pore structure characteristics of rocks.

In the study of pore structure seepage, Liu [50] found that the state of micropore throats in the micropore structures in rock formations plays a decisive role in the stress sensitivity of rock formations. Yu analyzed the microscopic pore structure of rock formations based on the combined experimental techniques of mercury intrusion and constant velocity mercury intrusion and discussed the relationship between stress sensitivity and seepage characteristics [41,51]. Based on Darcy’s law and the Fick diffusion law, Zhou [52] established the pore-fracture network fluid equation of coal-bearing formations to define the feasible range of Darcy’s law.

Summarizing the above research, it can be found that previous studies have the following shortcomings:

(1)

Microscopic research on rock pore structure is relatively scarce, and engineering projects such as grouting and water blocking mostly rely on engineering experience, lacking theoretical support.

(2)

There have been microscopic studies on pore structure, but their research methods are singular, making it difficult to integrate multiple research methods and improve the credibility of research results.

(3)

Although scholars have conducted microscopic studies through mercury intrusion experiments, nuclear magnetic resonance, scanning electron microscopy, and other methods, previous studies have lacked research on the pore structure of surrounding rock in underground engineering at a depth of 1000 m, which is increasingly important as mining is developing deeper underground.

In response to the above problems, this article conducted the following research:

The object of this study is the pore of the rock at a depth of 1000 m (corresponding to the third problem above). This paper mainly uses a combination of laboratory tests (casting thin sections, scanning electron microscopy, mercury intrusion testing, SEM, XRD, and other methods were used for comprehensive analysis), theoretical analyses, and numerical simulations (corresponding to the second problem). Selecting the micropores of deep well coal-bearing sandstone as the research object and based on laboratory tests, we first characterize the microstructure of the test block and then perform simulations based on the obtained experimental characterization data. The tortuosity calculation formula is obtained by theoretical derivation method. The software COMSOL 5.0 Multiphysics performs numerical simulations of microporous seepage in sandstone. The theoretical system formed by the research results can provide effective guidance and reference for related projects (corresponding to the first problem).

2. Materials and Methods

2.1. Material

The researchers obtained rocks from a depth of 1000 m underground and performed steps such as coring, cutting, and grinding to obtain the required rock samples for the experiment, as shown in Figure 1a.

Due to the depth of Tangkou Coal Mine exceeding one kilometer, the depth of its goaf is approximately 1000 m. During the construction process, the researchers obtained rock samples from both sides of the excavated roadway (approximately 1000 m deep). Several irregular rocks were obtained. To avoid accidental errors and other reasons in the experiment, each experiment was tested at least three times.

2.2. Method

The main research contents and methods are as follows:

• Combined with casting thin section and X-ray data, the petrological type, clastic composition and characteristics, interstitial characteristics, and physical properties of the coal-bearing sandstone in a deep well at a depth of 1000 m in the Tangkou Coal Mine were summarized and analyzed to understand the arrangement between sandstone particles in coal-bearing strata in this area, the composition of cuttings, the volume content of interstitials, and other information.
• Scanning electron microscopy (SEM), mercury intrusion experiments and other methods of combining characterization techniques were carried out to qualitatively and quantitatively determine the type, distribution, geometric shape, size, and relationship between pores and throats in the study area. The interconnections were characterized. At the same time, the correlation between the pore structure parameters obtained in the experiment and the physical properties was established, and the influence of the pore structure on the seepage characteristics was analyzed.
• Combined with the foregoing research methods, a numerical simulation software was used to establish the actual microstructure model of the rock mass surrounding the roadway. The COMSOL Multiphysics numerical simulation software was used to study the seepage laws of fluids under different conditions in micropores.

3. Analysis of Basic Characteristics of Sandstone in Coal-Bearing Strata

3.1. Experimental Study on Petrological Characteristics of Coal-Bearing Strata

The test of petrological characteristics of coal-bearing strata provides a basis for the subsequent characterization of coal-bearing strata sandstone pore structure and analysis of fluid seepage laws in pores [53,54,55].

3.1.1. Analysis of Petrological Types of Coal-Bearing Strata

Casting thin section technology (Figure 1b) and XRD equipment at the Shandong University of Science and Technology Laboratory (Figure 1b) were utilized to quantitatively and qualitatively analyze the pore microphysical structure characteristics and rock phases of rock samples (Figure 1a).

The rock samples in this study were obtained from irregular rock blocks at depths of 1000 m during the mine construction process. The rock blocks were then transported to the surface, where standard-sized samples were taken in the laboratory by cutting machines and rock coring machines.

According to the analysis of the identification results of the sandstone rock experimental data, the rock composition is divided according to the three terminal components of quartz, cuttings, and feldspar, and a triangle diagram of the rock composition distribution of the deep sandstone in the Tangkou Coal Mine was drawn. The figure shows that the type of sandstone in the study area is mainly detrital feldspar sandstone, with a small amount of feldspar quartz sandstone and feldspar detrital sandstone (Figure 2), and the percentages are 65.4%, 19.2%, and 15.4%, respectively (Figure 3).

3.1.2. Analysis of the Composition and Characteristics of the Debris

The clastic rocks contain terrigenous clastics and interstitials (miscellaneous bases and cements). Through the observation and statistical analysis of casting thin sections and XRD experimental data in the study area, the volume fraction of the sandstone clastic components in the area accounts for 78.2~90.4% with an average of 84.4%. The clastics are mainly quartz and flint, followed by feldspar and rock debris; the volume fraction of quartz and flint is 50.8~70.7%, with an average of 59.8%, and the volume fraction of feldspar is 8.2~19.5%, with an average of 13.6%. For the rock debris, the volume fraction of chips is 5.1~21.3%, with an average of 11.1%, and contains a small amount of mica, with an average volume fraction of 1.9% (

Table 1. Statistical table of the volume fraction of sandstone detrital components in deep wells of the Tangkou Coal Mine.

Types	Terrigenous Debris Volume Fraction/%
	Quartz and Flint	Feldspar	Rock Debris			Mica
			Igneous Rock	Metamorphic Rock	Sedimentary Rock
Maximum	70.7	19.5	5.8	9.4	6.1	5.9
Minimum	50.8	8.2	0.4	3.2	1.5	1.1
Average	59.8	13.6	1.4	5.9	3.8	1.9

).

(a)

Granularity Characteristics

A BT-9300LD laser particle size analyzer was utilized to analyze and test the grain size of the coal-bearing formation sandstone clastic rock.

According to the commonly used sedimentary rock debris particle size classification standard, it was found that the deep well sandstone of the Tangkou Coal Mine is mainly fine sand and medium sand, using the image particle size analysis of the core well core in the study area, and the contents are 40.3% and 37.6%, respectively. Followed by coarse sand and very fine sand, and a small amount of clay and mud. The particle size is mainly between 0.18 and 0.5 mm.

(b)

Roundness

The degree to which the edges and corners of the outer surface of rock fragments are rounded during the transportation process, rolling, impacting, and hydrodynamic scouring is referred to as the roundness of the particles. According to the industry roundness classification standard (SY/T5368-2000) [56], the roundness of debris particles can be divided into 5 levels: edges, subedges, subround, round, and extremely round.

Through statistical analysis of thin sections of sandstone castings in coal-bearing strata (

Table 2. Statistical table of roundness of sandstone detrital particles in the deep well of the Tangkou Coal Mine.

Parameter Types	Percentage Content/%
	Subedges/%	Subcircle-Subedge/%	Subround/%
Tangkou deep well	85.4	11.5	3.1

and Figure 4), the rounding grades of clastic particles in coal-bearing strata sandstone in the Tangkou Coal Mine are mainly secondary edges (Figure 4a), followed by partial secondary edges. The percentages of circle-subedge (Figure 4b) and subcircle are 85.4%, 11.5%, and 3.1%, respectively, and the degree of rounding is relatively poor.

(c)

Particle Contact Method

Through thin-film analysis and observation of sandstone core castings in coal-bearing strata in the Tangkou Coal Mine, the contact mode of sandstone debris particles in deep wells in the mining area is mainly line contact. At the same time, point-line contact can be seen in some areas, and the debris particles are mainly supported by particles. The results of microscopic analysis and observation of sandstone core casting thin sections in the coal bearing strata of Tangkou Coal Mine are shown in Figure 5.

(d)

Sortability

The sorting property is generally used to evaluate the uniformity of the clastic particle size, which is mainly controlled by the sedimentary environment and natural geographical factors.

At the same time, according to the fourth edition of Sedimentary Petrology prepared by Zhu Xiaomin, the particle size of the sandstone clastic particles in the deep well of the Tangkou Coal Mine was analyzed, and the results show that the overall sortability of the sandstone clastic particles in the study area was in the middle. The sorting medium samples accounted for 47.86% of all samples. The statistical table of sorting characteristics of sandstone debris particles in deep wells of Tangkou Coal Mine is shown in

Table 3. Statistical table of the separation properties of sandstone detrital particles in the deep well of the Tangkou Coal Mine.

Parameter Types	Percentage Content/%
	Poor	Medium-Poor	Medium	Good-Medium	Good
Tangkou deep well	12.33	18.43	47.86	15.77	5.61

.

3.1.3. Analysis of Interstitial Characteristics

Through analyzing and researching experimental data, such as thin sections of coal-bearing stratum sandstone castings in the mining area and scanning electron microscopy, the main interstitial features and cementation types of the deep sandstone in the Tangkou Coal Mine were obtained.

(a)

Interstitial Distribution

Sandstone clastic interstitials in the deep well of the Tangkou Coal Mine are mainly composed of carbonate minerals, clay minerals, chlorite, and silica. The analysis of the thin section data of sandstone castings in the study area shows that the volume content of interstitial materials in this area is 12.7%. Among them, chlorite is mainly used, whose volume fraction is approximately 3.2%; the volume fraction of kaolinite is approximately 2.1%, illite is 1.4%, siliceous is 1.6%, calcite is 2.4%, dolomite is 1.5%, and some rock samples contain pyrite with a volume fraction of 0.5% (Figure 6). From the above analysis, it can be seen that the contents of carbonate and chlorite In the sandstone clastic interstitials in the coal-bearing strata of the Tangkou Coal Mine are relatively high. The seepage process has a certain impact (Figure 7).

(b)

Type of Cement

In clastic rocks, we usually define the distribution of cements and interstitials or the relationship between them and rock clastic particles as the type of clastic rock cementation. Cementation types of debris structures can generally be divided into four types: base cementation, pore cementation, contact cementation, and mosaic cementation. Through the analysis of the casting thin section data, it can be obtained that the sandstone cementation type of the deep coal-bearing strata in the Tangkou Coal Mine is mainly pore cementation (Figure 8).

Compared with shallow rocks, deep rocks have a more complex mineral composition, lithic composition, darker color, and finer grain size. The particle size is moderately uniform, and the roundness has a certain edge. In addition, the interstitials of deep rocks are basically all kinds of rocks or minerals.

3.2. Study on the Physical Properties of Coal-Bearing Strata

In the process of evaluating coal-bearing strata, analyzing the relationship between porosity and permeability provides a static basis for the quality evaluation of coal-bearing strata. These data provide support for the subsequent analysis of coal-bearing formation heterogeneity and the characterization of pore microstructure [27,57]. To further analyze the physical characteristics of coal-bearing strata in the study area, this paper subdivides its parameters according to the physical property classification scheme of clastic coal-bearing strata (

Table 4. Physical property classification scheme of clastic coal-bearing strata.

Classification of Porosity Types in Clastic Coal-Bearing Strata		Classification of Permeability Types of Clastic Coal-Bearing Strata
Porosity Types	Porosity (Φ/%)	Permeability Types	Permeability (k/10−3 μm2)		Subcategory
Ultra high hole	Φ ≥ 30	Extra high osmosis	k ≥ 2000
High hole	25 ≤ Φ < 30	High osmosis	500 ≤ k < 2000
Medium hole	15 ≤ Φ < 25	Medium osmosis	50 ≤ k < 500
Low hole	10 ≤ Φ < 15	Low osmosis	10 ≤ k < 50		I
Extra low hole	5 ≤ Φ < 10	Extra low osmosis	1 ≤ k < 10	5 ≤ k < 10	IIa
				1 ≤ k < 5	IIb
Ultra low hole	5 < Φ	Ultra low osmosis	k < 1	0.5 ≤ k < 1	IIIa
				0.1 ≤ k < 0.5	IIIb
				k < 0.1	IIIc

).

3.2.1. Characteristics of the Physical Parameters of Coal-Bearing Strata

The measurement method for 3H-2000PAGP (Best Instrument Technology Co., Ltd., Beijing, China) rock high-pressure permeability tester is as follows: Apply a gradually increasing gas pressure to one side of the sample. When the gas pressure reaches a pressure greater than the surface tension of the wetting liquid in a certain aperture, the wetting liquid in that aperture will be pushed out by the gas. Due to the smaller pore size, the higher the pressure generated by surface tension, the higher the gas pressure required to extract the infiltrating liquid from it. It is also known that the infiltrating liquid in the pore size will be first pushed out, allowing gas to pass through. Then, as the pressure increases, the pore size will increase from large to small, and the infiltrating liquid in the pores will be pushed out in sequence, allowing gas to pass through until all the pores are opened, achieving the same permeability as the dry film. The pressure corresponding to the first opened hole is the bubble point pressure. The aperture corresponding to this pressure is the aperture. During this process, real-time recording of pressure and flow rate is performed to obtain a pressure flow curve. Pressure reflects information on pore size, while flow reflects information on the number of pores in a certain pore size. Then, the pressure flow curve of the dry film can be tested, and the pore size, average pore size, small pore size, pore size distribution, permeability, etc. of the test sample can be calculated according to the corresponding formula.

The 3H-2000PAGP (Best Instrument Technology Co., Ltd., Beijing, China) rock high-pressure permeability tester and the automatic mercury porosimeter were adopted to test the physical properties of the deep well sandstone in the Tangkou Coal Mine, it can be seen that the sandstone porosity of the deep coal-bearing strata in the study area is distributed between 4.5% and 29.8%. They are mainly distributed in 18.4~21.6%, with an average value of 20.3%. As shown in Figure 9, the distribution of porosity is similar to the normal distribution. The porosity is dominated by medium holes, with a peak frequency of 54.8%, followed by high holes and low holes, with a distribution frequency of 16.8% and 19.7%, respectively. At the same time, it also contains a very small amount of extra low holes and ultra low holes.

The sandstone permeability of coal-bearing strata in the Tangkou Coal Mine area of Jining has a wide range of distribution (1.2~1245 × 10⁻³ μm²), mainly distributed in 1123~441 × 10⁻³ μm², and the average is 267 × 10⁻³ μm². The overall permeability of the core samples showed a good normal distribution. The overall permeability level of the study area is mainly medium osmosis, and it also contains samples with hyper osmosis and low osmosis. The statistical analysis of physical properties shows that the interlayer heterogeneity in the area was stronger.

3.2.2. Correlation Analysis of Physical Properties

Through research on the physical conditions of the coal-bearing strata sandstone in the deep mine of the Tangkou Coal Mine, the results show that there is a certain positive correlation between the porosity and permeability of the coal-bearing strata sandstone (Figure 10). The fitted exponential equation is y = 0.0215e^0.2284x, and the correlation coefficient R² = 0.6982. The permeability is controlled by the porosity; the greater the porosity, the larger the pore space in the rock, and the fluid is obstructed by the solid framework during the seepage process. At the same time, the physical properties of coal-bearing sandstone are also affected by factors such as sandstone particle size and sorting properties.

Compared with the shallow rock, the porosity of the deep rock usually reaches mesopores, and the permeability has reached the medium permeability, but this does not fully indicate that the permeability of the deep rock is better than that of the shallow rock. This needs to be comprehensively determined by various conditions, such as rock particle shape and pore distribution.

4. Experimental Study on the Micropore Structure of Sandstone

In this chapter, the analysis methods are combined with multiple experiments, such as casting thin sections under mirrors, scanning electron microscopy, mercury intrusion experiments, etc. The microscopic pore structure of coal-bearing sandstone is characterized from two perspectives, qualitative and quantitative, to provide certain data support for subsequent research on sandstone seepage characteristics.

4.1. Pore and Throat

The study of the characteristics of pores and throats is an important part of the characterization of the microscopic pore structure of coal-bearing formation sandstones. As fluid storage and seepage space, its microstructure characteristics greatly affect the characteristics and seepage capacity of coal-bearing formation sandstones.

4.1.1. Pore Types

Secondary pores are mainly the pores produced by the dissolution and fracture of particles after the diagenesis of coal-bearing strata [58,59], including intragranular dissolved pores, superlarge pores, and intercrystalline pores [60,61].

According to the statistical analysis of the casting thin section and laboratory scanning electron microscopy data in the study area, the pore type of the deep coal-bearing strata sandstone of the Tangkou Coal Mine is mainly intergranular pores, followed by feldspar dissolved pores, which also contain some lithic dissolved pores, and intercrystalline pores and microcracks can be seen locally. The proportion of each type of pore is shown in

Table 5. Statistics of the deep well sandstone pore types in the Tangkou Coal Mine.

Research Area	Parameter Type	Absolute Content/%
		Intergranular Pores	Feldspar Pores	Karst Pores	Intercrystalline Pores
Tangkou Coal Mine	Maximum	6.7	2.4	1.1	0.6
	Minimum	1.4	0.7	0.1	0.05
	Average	2.1	1.0	0.3	0.15

.

(a)

Intergranular Pores

Due to the influence of sediment particle size, roundness, and sorting properties, the intergranular pores in this area often show irregular shapes, such as polygons. At the same time, the pore radius of the intergranular pores is mainly distributed between 20 and 300 μm, which has the characteristics of a large pore throat radius, good connectivity, and strong permeability (Figure 11).

(b)

Intragranular Dissolution Pores

According to the observation and analysis of the coal-bearing sandstone strata in the study area under a microscope, the intragranular dissolved pores of the deep coal-bearing sandstone strata in the Tangkou area are mainly feldspar granular dissolved pores, while some lithic dissolved pores can be seen (Figure 12).

Feldspar pores:

The dissolved pores of the feldspar particles in the study area are connected to the primary intergranular pores to form larger pores. According to the image statistics of the thin-film data of the sandstone castings in the study area, the feldspar dissolved pores in the study area have a wide range of pore diameter distributions, and the pore size is significantly increased. It is the main place for fluid storage and migration in the area (Figure 12a).

Regarding dissolved pores in cuttings:

The composition of the cuttings in the study area is mainly metamorphic rock, the pore diameter of the cuttings is relatively small, and the contribution rate to the seepage characteristics of the rock mass is low (Figure 12b).

(c)

Intercrystalline Pores

Through joint experimental analysis, such as casting thin sections and scanning electron microscopy, it can be seen that the pores are generally smaller, with poor connectivity between pores. Such pores are basically not developed in coal-bearing strata in this area. The microscopic characteristics of intercrystalline pores are as follows (Figure 13).

(d)

Fissure

The rock fractures or dissolution fractures mostly formed due to the impact of tectonic stress caused the rock particles to break and are called microfractures, which can connect the pores in the rock body and play a certain role in the fluid seepage characteristics. There is almost no development in the study area (Figure 14).

4.1.2. Throat Types

According to research on the characteristics of clastic rock throats and the throat classification method proposed by Shan [62], they can be divided into the following types:

(a)

Flaky and Curved Throats

Such roaring channels are mostly seen in clastic particles whose interparticle connection is mainly line contact. After the influence of rock diagenesis, the particles develop into narrow flaky and curved throats, which become channels connecting pores. Because this type of pore throat has a small radius, it has a weaker contribution to the fluid seepage capacity of the entire coal-bearing formation, but it has better seepage capacity than other shapes of throats (Figure 15a,b).

(b)

Constricted Throat

This type of throat is significantly affected by rock compaction and cementation and is common in sandstone rock masses where the contact between particles is point contact. The throat radius is small, showing the characteristics of large pores and thin throats, which are mainly developed in intergranular pores and dissolved pores (Figure 15c).

(c)

Bundle Throat

The distribution of this type of throat often presents irregular tube bundles, where the particles are filled with clay minerals and the connecting throat spaces between the pores are narrow. Therefore, a fine pore network is often formed inside the rock mass, which contributes little to the seepage capacity of the rock formation (Figure 15d).

According to the analysis of test data, such as casting thin sections and scanning electron microscopy, the connection between coal-bearing strata sandstone particles in the Tangkou area is mainly line contact, and the main types of throats are sheet and curved sheet throats (Figure 15).

4.2. Characterization of Pore Throat Structure based on the Mercury Intrusion Test

The mercury injection method can quantitatively characterize the microscopic pore structure of sandstone by observing the characteristics of the capillary pressure curve.

In this paper, the mercury intrusion test analysis uses a fully automatic mercury intrusion instrument. The maximum working pressure of the experiment can reach 413 MPa, the measuring aperture range is 0.003~1000 μm, and the mercury volume measurement accuracy is 0.1 mL. Before the experiment, the sandstone samples were dried (drying temperature: 105 °C), the experimental temperature was 24 °C, and the humidity was 55%. The experimental methods and data processing are strictly implemented in accordance with the industry standard Measurement of Rock Capillary Pressure Curve SY/T5324-2005 [63].

4.2.1. Capillary Pressure Curve Characteristics

The capillary pressure and mercury injection volume curves are usually divided into three sections: the initial mercury injection stage, the main mercury injection stage, and the mercury injection end stage. Although some scholars have used resolution graph clustering to classify capillary pressure [64], in this study, in addition to considering the characteristics of capillary pressure, experimental parameters such as pore throat radius distribution were also considered. The pressure curve is divided into four types.

(a)

Type I Low Mercury Inlet Pressure-Mesoporous Type

The number of such rock samples is 17, accounting for 56.7% of the total number of samples. Through the analysis of the capillary pressure curve (

Table 6. Mercury intrusion experiment parameters table (Type I).

Curve Type	Range	Porosity/%	Permeability/10−3 μm2	Aperture/μm
I	Maximum	24.3	521	300
	Minimum	15.6	90	30
	Average	20.3	248	100

and Figure 16a), this type of core sample has a faster cumulative mercury volume increase in the low pressure section, and it is relatively easy to inject mercury into the rock space. The main mercury injection pressure is between 2 and 10 psi. In the meantime, there are more large pores in the rock samples. The porosity of the rock is mainly between 18.4% and 21.6%; the permeability is mainly distributed in 123~441 × 10⁻³ μm², the sandstone of the coal-bearing formation has good physical properties, and the pore permeability is strong. The pore size is mainly distributed in 50~120 μm (Figure 16b). The pore radius is relatively large. The pore types are mainly intergranular pores and dissolved pores–intergranular pores. The pore size distribution is mainly unimodal. The types are mostly flaky and curved, and the pore structure has better overall connectivity.

(b)

Type II Low Mercury Inlet Pressure-Small Hole Type

The number of such rock samples is six, accounting for 20% of the total number of samples. The capillary pressure curve of this type of core sample can be analyzed (

Table 7. Mercury intrusion experiment parameters table (Type II).

Curve Type	Range	Porosity/%	Permeability/10−3 μm2	Aperture/μm
II	Maximum	18.9	156	26
	Minimum	6.5	43	0.1
	Average	12.6	83	7

and Figure 17a), and the mercury volume increase interval of this type of sample is mainly concentrated in the pressure range of 10~100 psi. The pore types are dominated by intergranular pores–intragranular dissolution pores and dissolved pores. The throat types are mostly constricted throats and contain some flaky and curved throats. The porosity of the rock is mainly concentrated in 10.3~15.7%, the permeability is mainly distributed in 62~106 × 10⁻³ μm², and the fluid seepage ability is good. The pore size is mainly distributed in the 1~15 μm range (Figure 17b), and the pore size distribution curve of some samples shows a bimodal state.

(c)

Type III Medium Mercury Inlet Pressure-Fine Pore Type

The number of such rock samples is four, accounting for 13.3% of the total number of samples. Based on the feedback capillary pressure curve analysis of mercury intrusion experiment data (

Table 8. Mercury intrusion experiment parameters table (Type III).

Curve Type	Range	Porosity/%	Permeability/10−3 μm2	Aperture/μm
III	Maximum	10.5	105	10
	Minimum	2.8	5	0.05
	Average	6.2	44	1.6

and Figure 18a), this type of core sample requires a higher pressure to inject mercury into the rock space. When the pressure is between 100 and 1000 psi, the mercury volume increases significantly. The types of rock pores are mostly intercrystalline pores and dissolution pores. The throat types are mainly constricted throats and tube bundle throats, with poor overall connectivity. The porosity of the rock is mainly concentrated in 5.4~7.7%, and the permeability is mainly distributed in 10~56 × 10⁻³ μm². The rock physical properties are poor, and the permeability is weak. The pore size is mainly distributed in the 0.1~6 μm range (Figure 18b), and the pore size distribution curve of some samples shows a unimodal state.

(d)

Type IV High Mercury Inlet Pressure-Microporous Type

The number of such rock samples is three, accounting for 10% of the total number of samples. According to the analysis of mercury intrusion experiment data (

Table 9. Mercury intrusion experiment parameters table (Type IV).

Curve Type	Range	Porosity/%	Permeability/10−3 μm2	Aperture/μm
IV	Maximum	6.9	54	100
	Minimum	2.1	2.6	0.01
	Average	3.5	5.8	0.1

and Figure 19a), the mercury intrusion pressure curve of this type of sandstone core sample is mainly concentrated in 1000~10,000 psi, which is the highest compared to the other three types of mercury intrusion pressure. The pore type is dominated by intercrystalline pores, and the throat type is mainly tube-bundle-type throats. In summary, the overall connectivity of the pore structure of this type of rock sample is poor. Rock porosity is distributed below 5%, permeability is generally lower than 10 × 10⁻³ μm², and coal-bearing strata have poor physical properties and weak fluid seepage ability. The pore size is mainly distributed in the 0.01~0.7 μm range (Figure 19b).

4.2.2. Characteristics of Pore Structure Parameters

According to the pore structure parameters obtained from mercury intrusion experiment data, combined with the pore structure information of the rock, such as scanning electron microscopy, XRD, casting thin section, etc., the microstructure of deep well sandstone pores can be characterized more accurately and intuitively. There are certain differences in the physical properties of sandstone samples, with complex pore structures and strong heterogeneity in the rock samples. Therefore, it is necessary to combine the analysis of permeability and porosity to achieve better and better results. The pore structure characteristics of coal-bearing formations were accurately characterized. Representative pore structure parameters of coal-bearing strata sandstone samples in the study area were selected for analysis and research.

(a)

The Impact of Pore Size on Physical Properties

The parameters that can reflect the pore size mainly include the median pore size and the mean radius. According to the capillary pressure curve obtained in the experiment, the median pore size and the mean radius are analyzed and studied:

①

Median aperture

When the mercury inlet saturation reaches 50%, the corresponding mercury inlet pressure is called the median pressure, and the median radius is the corresponding pore radius under this pressure. The pore radius of the sandstone determines the size of the fluid storage space of the coal-bearing formation and has an important influence on the seepage capacity. Generally, the median radius is directly proportional to the porosity and permeability of the coal-bearing formation. Based on the analysis of mercury intrusion experiment data, the correlation between the pore radius and the physical properties of coal-bearing formations is established. The results show that the pore radius has a good positive correlation with permeability (R² = 0.85323) and porosity (R² = 0.68867) (Figure 20). The median pressure and pore size statistics of mercury intrusion samples in the research area are shown in

Table 10. Statistical table of median pressure and pore size parameters of mercury injection samples in the study area (pressure/psi, aperture/μm).

	I		II		III		IV
	Pressure	Aperture	Pressure	Aperture	Pressure	Aperture	Pressure	Aperture
Maximum	7.4	68	170	9	605	0.65	2451	0.11
Minimum	3.1	28.8	23	1.2	310	0.33	2121	0.08
Average	5.4	44.6	75	5.5	503	0.44	2314	0.09

.

②

Mean pore size

The average radius is usually used to represent the average value of the pore size distribution of core samples. The statistical table for the mean radius of mercury intrusion samples in the study area is shown in

Table 11. Statistical table of mean pore size parameters of mercury injection samples in the study area.

	Mean Pore Size/μm
	I	II	III	IV
Maximum	31.5	4.15	0.47	0.0655
Minimum	15.9	0.75	0.25	0.058
Average	21.8	2.67	0.36	0.0605

.

Analyzing the data obtained from the mercury intrusion experiment and establishing the correlation between the average pore diameter and the physical properties of the study area, it was found that the average pore diameter and permeability (R² = 0.79201) and porosity (R² = 0.67692) of the deep well sandstone in the study area appeared to have a good positive correlation (Figure 21), and the physical properties of coal-bearing formations are highly affected by the pore size.

Through the above analysis, it can be seen that the median pore diameter and the mean radius have a better correlation with permeability, and the porosity is slightly worse. The correlation coefficients between the two and the permeability are 0.85323 and 0.79201, respectively, so the pore size often controls the permeability of sandstone. Larger pores in coal-bearing strata are the main factor restricting the strength of fluid seepage. At the same time, it is not difficult to see that the median pore size has a greater influence on the physical properties of coal-bearing strata than the average radius.

(b)

The Influence of Characteristic Parameters of Pore Sorting on Physical Properties

①

Sorting coefficient

Statistics about the sorting coefficient of core samples in the study area include the following. The distribution area is between 0.88 and 2.68, mainly concentrated between 1.4 and 2.6, and the overall pore size of the sample has good sorting properties (

Table 12. Statistical table of mercury injection sample sorting coefficients.

	Sorting Coefficient
	I	II	III	IV
Maximum	2.68	1.46	1.68	1.33
Minimum	2.21	0.81	0.75	0.67
Average	2.41	1.24	0.98	0.88

).

The analysis of the mercury intrusion data of core samples in the study area shows that there is a correlation between the pore structure sorting coefficient of deep well sandstone in the Tangkou Coal Mine and the porosity (R² = 0.75641) and permeability (R² = 0.63306) of coal-bearing formations (Figure 22).

②

Skewness

We usually introduce the concept of skewness (S_kp) to characterize the rock pore size distribution asymmetry. The value of S_kp mainly varies between ±1. When S_kp = 0, the pore distribution curve is symmetrical. S_kp > 0 denotes roughness, and S_kp < 0 denotes fineness.

The research results show that the variation range of deep shaft sandstone distortion in the Tangkou Coal Mine is −1.54~2.59 (

Table 13. Statistical table of mercury injection samples in the study area.

	Skewness
	I	II	III	IV
Maximum	2.59	2.47	−0.31	−1.201
Minimum	0.71	−0.16	−0.62	−1.54
Average	1.43	0.65	−0.45	−1.48

), which is mainly distributed in 1.21~2.43, that is, the main manifestation is roughness. The skewness distribution interval indirectly indicates that the pore structure of the study area is biased toward larger pores, which has a significant impact on the physical properties of coal-bearing strata (Figure 23).

(c)

The Influence of Pore Connectivity Parameters on Physical Properties

①

Mercury removal efficiency

Due to the large pore size of the rock samples of Type I and Type II, the mercury inlet pressure is relatively small, which results in a low pressure attenuation gradient. Therefore, when studying the mercury removal efficiency, we only refer to the capillary pressure curve of type III and type IV rock samples. The statistical table of mercury removal efficiency in the research area is shown in

Table 14. Statistical table of mercury removal efficiency in the study area.

	Mercury Removal Efficiency
	III	IV
Maximum	68.52	60.66
Minimum	56.15	51.75
Average	64.96	57.41

.

Through analysis and comparison, it is not difficult to see that, with the deterioration of the physical conditions of the rock sample, the mercury removal efficiency of the rock gradually decreases.

②

Tortuosity

Due to the complex distribution of pore structures in the internal structure of porous media, the fluid seepage process in coal-bearing sandstone formations in actual situations often does not flow along a straight line but in a tortuous way from high pressure to low pressure. The concept of tortuosity is introduced to characterize the tortuosity of the fluid seepage curve, which is defined as the ratio of the actual length of the fluid seepage channel to the straight length of the porous medium [27,50,57,65] (Figure 24), that is, the unit distance for the fluid to pass through the pore structure of the coal-bearing formation sandstone is the ratio of the actual length of the motion curve to the actual conditions inside the tunnel.

$$\tau =\frac{L_1}{L_0}$$

(1)

where τ is the tortuosity;

L₁ is the actual seepage length, m;

L₀ is the linear length of porous media, m.

According to the generalized Hagen–Poiseulle equation, the fluid flow rate per unit volume can be calculated by the following formula:

$$Q=NA\frac{\pi }{8}\frac{\Delta P}{21}\frac{{\overline{r}}^{-4}}{N}$$

(2)

In the formula: N refers to the number of fluid channels per unit area;

$\overline{r}$ is the average value of the hydraulic radius of the hole, mm;

$\Delta P$ is the pressure difference between the two ends of the pore, Pa;

A is the pore characterization area, m².

According to Darcy’s Law:

$$Q=\frac{KA\Delta P}{\mu L}$$

(3)

K is the pore permeability coefficient, m²;

$\mu$ is the hydrodynamic viscosity coefficient, Pa/m.

The expression of coal-bearing formation porosity is:

$$\Phi =\frac{NA\pi {\overline{r}}^{-2}{L}_1}{AL}$$

(4)

In the formula: Φ denotes the porosity.

Combined with Equations (1)–(4), the porosity, average radius, and permeability coefficient are taken as the main parameters, and the remaining parameters are simplified:

$${\tau }^2=\frac{\Phi {\overline{r}}^2}{8K}$$

(5)

Therefore, the tortuosity of sandstone in coal-bearing formations is not only related to the porosity of the rock formation but is also closely related to the permeability of the sandstone. Through calculation, the tortuosity of the sandstone in the study area is mainly between 1.6 and 2.2 (

Table 15. Statistical table of rock sample tortuosity in the study area.

	Tortuosity
	I	II	III	IV
Maximum	1.907	2.778	3.011	3.288
Minimum	1.566	2.214	2.172	2.907
Average	1.732	2.379	2.673	3.013

). The smaller the tortuosity, the less the fluid will be hindered when flowing through the porous medium of the coal-bearing stratum, indicating that the physical properties of sandstone samples from coal bearing strata are relatively good. In contrast, when the fluid seepage path is tortuous and the connectivity between pores is poor, this leads to poor physical properties of the rock formation.

By analyzing the correlation between the tortuosity and physical properties of the study area, it can be seen that the rock porosity and the tortuosity have a good correlation (R² = 0.77334). Compared with porosity, the correlation between permeability and tortuosity is poor (R² = 0.64387). The relationship between physical properties and tortuosity in the study area is shown in Figure 25.

5. Establishment of Pore Structure and Seepage Flow Model of Sandstone Digital Image

Based on the sandstone microscopic pore structure characterization data obtained in this chapter, the SEM experimental data were processed based on digital image processing technology. Combined with the actual situation of coal-bearing formation sandstone, a sandstone seepage mathematical model was constructed to lay the foundation for subsequent numerical simulation analysis.

5.1. Pore Structure Modeling Based on Digital Images

The nontransparency of the microstructure of porous media hinders the in-depth study of the fluid seepage process in the pore structure of porous media in deep environments. Through the introduction of digital image processing, the sandstone pore structure network model was constructed, and then a numerical simulation analysis was carried out to study the microscopic seepage of the sandstone pore structure in coal-bearing formations. This section introduces in detail the creation of SEM image data into a finite element network model that can be used for calculation [66,67], which lays the foundation for subsequent numerical simulation analysis [68,69].

The image processing method can be divided into the following parts:

• Grayscale processing of SEM images

The image processing software R2V 5.5 [70,71,72] was used to perform grayscale processing on the pore structure image of the sandstone obtained by SEM, and the result is shown in Figure 26.

2.

Use the threshold function to distinguish the skeleton and the pores and use the filter function to process the fragmented pores and solid particles in the image to correct the morphological characteristics of the sandstone pore structure.

By collecting the obtained grayscale image, the image information can be expressed as a two-dimensional discrete function, and its expression is as follows:

$$I=\mathrm{f}\left(\mathrm{x},\mathrm{y}\right),0\le \mathrm{f}\left(\mathrm{x},\mathrm{y}\right)\le 255$$

(6)

To extract the solid skeleton information of the sandstone pore structure in the image and better restore the real situation of the pore structure, a threshold function was introduced to process the image. Using design interval [low, high], if the gray value is within this interval, output 1; otherwise, output 0. The threshold function is expressed as:

$$T\left(\mathrm{f}\left(\mathrm{x},\mathrm{y}\right), \mathrm{low}, \mathrm{high}\right)=\{\begin{array}{l}1 \mathrm{if} \left(\begin{array}{l}\mathrm{low}\le \mathrm{f}\left(\mathrm{x},\mathrm{y}\right)\\ \le \mathrm{high}\end{array}\right)\\ 0 \mathrm{othervise}\end{array}$$

(7)

After threshold processing, there may be some fragmented pores and solid particles in the image pore structure information. The pore structure information is corrected using the average filter function with a threshold value. When the threshold value is less than the average difference between the gray value of a certain part of the image and the gray value of its neighboring area, the gray value of this place will be output as the average gray value of the similar area; otherwise, the original gray value will be the retained gray value. Its functional form can be expressed as:

$$\mathrm{f}\left(\mathrm{x}, \mathrm{y}\right)=\{\begin{array}{l}\frac{1}{M}{\displaystyle \sum _{\left(\mathrm{i}, \mathrm{j}\right)\in C}\mathrm{f}\left(\mathrm{i}, \mathrm{j}\right)} \mathrm{if} (\left|\mathrm{f}\left(\mathrm{x}, \mathrm{y}\right)\right|\\ -\frac{1}{M}{\displaystyle \sum _{\left(\mathrm{i}, \mathrm{j}\right)\in C}\mathrm{f}\left(\mathrm{i}, \mathrm{j}\right)>T)}\\ \mathrm{f}\left(\mathrm{x}, \mathrm{y}\right) \mathrm{othervise}\end{array}$$

(8)

In the formula: C is the image field;

M is the number of pixels.

After the image information is processed in the abovementioned manner, the pore structure of sandstone can be corrected, and the microscopic pore structure characteristics of coal-bearing strata can be more accurately reflected. The processed image is shown in Figure 27. This method makes the image noise reduction processing results different, and the difference in the final pore structure characteristics is very small, that is, the obtained results have very small errors.

3.

Digital image vectorization by importing the image into AutoCAD for drawing

The image obtained in the above steps was imported into AutoCAD for drawing, and the processed vector diagram is shown in Figure 28.

4.

Import numerical simulation software to generate a finite element model

We imported the CAD image information into the simulation software COMSOL Multiphysics to complete the reading and drawing of the model image data, and loaded the curve into the calculation software to generate the corresponding pore body physical model, and mesh the model.

5.2. Fluid Flow Model of Sandstone Pores

To further study the fluid seepage process in the pores of the coal-bearing strata in the Tangkou Coal Mine, some existing conditions are simplified before the mathematical model is established. After referring to the Biot model [66] of homogeneous and isotropic porous media, the following basic assumptions are made for the porous media and fluids in the study area (the model assumptions in the following chapters are completely consistent with this section):

• Due to the random distribution of coal-bearing strata in this area, the basic physical properties of coal-bearing sandstone are regarded as homogeneous.
• The fluid in the pores of coal-bearing stratum sandstone is groundwater single-phase fluid, and the influence of gas flow on the seepage process is not considered. The flow of groundwater in the pores of coal-bearing stratum sandstone is regarded as an isothermal and steady-state seepage process, which does not consider energy loss during the flow of groundwater.
• During the flow of groundwater in the pores of coal-bearing formations, it is assumed that the groundwater is incompressible.
• The strain of porous media only considers the strain change of the skeleton and ignores the strain change of the solid particles.

6. Numerical Simulation of Micropore Seepage Flow Characteristics in Sandstone

6.1. Establishment of the Seepage Flow Model

In this section, a one-way flow model is established to verify and analyze the factors affecting the flow of groundwater in pores.

We imported the CAD vector diagram obtained according to the digital image processing technology in Chapter 3 into COMSOL Multiphysics and then constructed the entity of the image (Figure 29). Finally, the pore structure was separated from the solid skeleton, as shown in Figure 30. The subsequent model processing method in this chapter is consistent with this method, so no further explanation will be given later.

We established a two-dimensional model diagram of the pore microstructure of deep well sandstone in the study area (Figure 31). The white area in the figure is the porous medium, and the blue area is the groundwater seepage space inside the sandstone.

6.1.1. Model Boundary Conditions and Setting of Definite Solution Conditions

The initial conditions of the model and definite solution conditions are shown in

Table 16. Setting of initial conditions and fixed solution conditions for the model.

Condition Setting	Definite Solution Condition
Initial displacement	$u{|}_{t=0}=u_i$ $\frac{\partial y}{\partial x_i}{|}_{t=0}=v_i$
Displacement boundary	$u{|}_{\mathrm{boundary}}=u{|}_1$
Stress boundary condition	${\sigma }_{ij}·\overrightarrow{n_j}{|}_{\mathrm{boundary}}=T{|}_i$
Initial pressure	$P{|}_{t=0}=P_i$
Pressure boundary condition	$P{|}_{\mathrm{boundary}}=p_1$
Flow boundary conditions	$u{|}_{\mathrm{boundary}}=u{|}_1$

below.

The different research contents and appropriate initial conditions and boundary conditions were selected, and the corresponding numerical solution could be obtained by analysis with simulation software.

6.1.2. Calculation Model Parameter Settings

According to the characteristics of the coal-bearing formation fluid and rock material characteristics, the calculation model parameter settings are shown in

Table 17. Basic parameter settings for the model.

	Calculation Parameters	Value	Unit
Assignment parameters	Model height	H = 500	μm
	Model width	L = 280	μm
	Water inlet pressure	P1	MPa
	Outlet pressure	P2	MPa
	Fluid flow rate	$v$	m/s
	Fluid density	${\rho }_{\mathrm{fluid}}$ = 1	g/cm3
	Fluid modulus of elasticity	6	Gpa
	Dynamic viscosity	$\eta$ = 0.001	Pa·s
	Rock density	${\rho }_{\mathrm{rock}}$ = 2.27	g/cm3
	Rock elastic modulus	40	Gpa
	Poisson’s ratio	$\lambda$ = 0.21	/

. The numerical simulation model parameters were selected according to this table, so no further explanation will be given later.

6.2. Analysis of Fluid Seepage Characteristics under Different Inlet Pressures

6.2.1. Selection of Model Control Equations

The laminar flow interface was selected according to the simulation requirements. Laminar flow is used to calculate the velocity field and pressure field of single-phase laminar flow. When the Reynolds number of the fluid is below a critical value, it will maintain laminar flow. The model area is 500 μm × 280 μm; the fluid generally flows along the entire structure from left to right, and the fluid does not invade the solid particles.

In the physical boundary of the model, the corresponding outlet and inlet pressures are known. It is assumed that the fluid does not enter the crystal interface during the seepage process, and the velocity at the interface is 0, that is, the nonslip condition is complied, and the upper boundary and lower boundary flow are symmetrical. The specific boundary conditions are shown in

Table 18. Model boundaries.

Boundary Type	Boundary Setting	Value	Mathematical Model
Entrance	Pressure, viscous stress	$P=\{\begin{array}{l}5000 \mathrm{Pa}\\ 10000 \mathrm{Pa}\\ 20000 \mathrm{Pa}\end{array}$	$\overrightarrow{n}·\mu \left(\nabla u+{\left(\nabla u\right)}^T\right)=0$
Exit	Pressure, viscous stress	P = 0 Pa	$\overrightarrow{n}·\mu \left(\nabla u+{\left(\nabla u\right)}^T\right)=0$
Wall	Wall surface	—	$u=0$
Symmetrical boundary	Symmetry	—	$\overrightarrow{n}·u=0$,$\overrightarrow{t}·\mu \left(-P\mathrm{I}+\nabla u+{\left(\nabla u\right)}^T\right)\overrightarrow{n}=0$
Fixed wall boundary	Fixed	—	—

. The parameter settings in Table 16 and Table 18 are set in the COMSOL 5.0 software and can be found in the COMSOL software manual.

The convergence of numerical simulation is based on the fluid transport state in numerical simulation software. When the fluid transport reaches a stable flow state, it is considered that the numerical simulation calculation converges.

6.2.2. Results

Under the same conditions of other physical parameters, this section is the most appropriate to simulate and analyze the seepage characteristics of porous media under different inlet pressure conditions. The inlet pressure was set to 5 × 10³ Pa (Figure 32a), 1 × 10⁴ Pa (Figure 32b), and 2 × 10⁴ Pa (Figure 32c). Subsequently referred to as Group A, Group B, and Group C. The outlet pressure is 0 Pa.

From Figure 32:

• Under similar conditions, as the inlet pressure continues to increase, the flow velocity at the outlet also increases accordingly, and there is a certain linear correlation between the two. At the same time, the overall flow velocity of the coal-bearing formation flow field also increases correspondingly with increasing inlet pressure.
• In the narrow pores, the fluid velocity is significantly faster, and the velocity of the pore flow is relatively small where the cross section of the pore flow becomes larger. Therefore, the higher pressure in the pores is mainly distributed in the areas with smaller pore diameters, indicating that, in some areas of the bellows with smaller pore diameters, larger pressure conditions are often required for the fluid to obtain a certain flow rate.
• This figure can clearly define the stagnant area where the fluid velocity is 0 in the model, indicating that there are a certain number of “dead holes” in the sandstone pore structure in the study area.
• On the two-dimensional plane model of the pore structure of coal-bearing strata, the fluid velocity distribution is extremely uneven. The larger flow velocity is mainly concentrated in the central area of the model, while the edge area has a smaller velocity. This shows that the stratum pores in the study area are more developed in the center of the rock formation, with better pore connectivity, and relatively less developed in the marginal area, with poor pore connectivity.

From Figure 33, we can intuitively observe that, near the rock wall, the groundwater velocity is smaller than that in the middle of the pore; a thin layer of fluid with a clearer velocity gradient is often formed near this area, which is the boundary layer effect of the fluid. Therefore, we can conclude that there is also a boundary layer effect in the process of fluid seepage within the pore structure of sandstone.

From Figure 34, the pressure distribution of the overall structure is transmitted from the inlet to the outlet, where it gradually decreases. The pressure gradient changes significantly at the narrow pores, and the fluid has a higher flow velocity. It is not difficult to see that, in the area near the outlet, although there is a smaller pressure gradient and larger pores, the area also has a higher flow velocity due to the confluence of multiple tributaries.

6.3. Analysis of Fluid Percolation Characteristics under Different Physical Properties

6.3.1. Image File Import

The quality of rock physical conditions plays an important role in the characteristics of rock pore seepage. After testing the physical conditions of coal-bearing sandstone, it can be seen that the physical conditions of sandstone in the study area are quite different. To better analyze the fluid seepage law, according to numerical simulation, the fluid seepage characteristics of porous media under different physical conditions are analyzed. The porosity is selected as 25%, the permeability is 400 × 10⁻³ μm² (Figure 35a), the porosity is 20%, the permeability is 100 × 10⁻³ μm² (Figure 35b), the porosity is 15%, and the permeability is 25 × 10⁻³ μm² (Figure 35c). Subsequently, they were referred to as Group A1, B1 and C1.A schematic diagram of a two-dimensional model of pore structure was established by using scanning electron microscope image data of three sets of rock samples, and the model parameters were set according to the physical conditions of the rock samples (

Table 19. Parameter additions to the porous media model.

	Variable	Symbol	Unit	Model One	Model Two	Model Three
Assignment parameters	Porosity	n	%	25	20	15
	Permeability	$K$	${\mathsf{\mu }\mathrm{m}}^2$	400 × 10−3	100 × 10−3	25 × 10−3

).

6.3.2. Selection of Model Control Equations

The selection of the control equation in this section is consistent with the previous section, so no explanation is given. For the physical boundary of the model, the inlet pressure is set to a fixed value: 1 × 10⁻³ Pa, and the outlet pressure is 0. Other boundary conditions and basic assumptions are the same as those in Table 17.

6.3.3. Results

Under the same conditions of other physical parameters, this section simulates and analyzes the seepage characteristics of porous media under different physical conditions. As shown in Figure 36 below, the characteristics of the seepage velocity of the rock formation under three groups of different physical conditions are studied.

According to Figure 36, the following can be analyzed:

• With the decrease in porosity and permeability, the solid framework particles of sandstone increase, and the number of seepage channels in the pore structure of the rock formation shows a decreasing trend. With the deterioration of physical conditions, the distribution of pore structure inside the rock mass and the tortuous degree of fluid seepage routes gradually become more complicated.
• The velocity of fluid in coal-bearing formations is closely related to the physical conditions of the formations. With the deterioration of physical conditions, the fluid flow rate continues to decrease under the same inlet pressure.
• By comparing Figure 36a–c, it is found that there is often a large number of disconnected pores in rock formations with poor physical properties. Changes in the physical conditions of coal-bearing formations have significant effects on the connectivity and seepage characteristics of the pore structure of the formation.

The analysis of Figure 37 shows the following:

• The physical condition of coal-bearing strata plays a vital role in the process of fluid seepage. When the physical conditions are good, the pressure overcome by the fluid seepage process in the porous medium is smaller, and the fluid flow is easier. With the deterioration of physical conditions, the pressure to overcome fluid seepage further increases, and the fluid flow process is highly blocked.
• When the same inlet pressure is given to formations with different physical conditions, the lower the porosity and permeability of the formation, the faster the pressure attenuation. Therefore, in the actual grouting process, to spread the grout to a certain position in the rock formation, it is often necessary to increase the grouting pressure.

The velocity streamline diagram under different physical conditions is presented in Figure 38. The blue curve in the figure represents the flow trajectory of groundwater in the pore structure of sandstone. According to Figure 38:

• The flow area of groundwater in the pores of sandstone is mainly concentrated in the middle area of the structure, and seepage is always along the narrow and long channels of large pores with better connectivity.
• There are some areas within the pores of sandstone where the groundwater flow velocity is 0, that is, there are some unconnected pore spaces in the internal pore structure of sandstone. Due to the existence of these blind-end pores, the groundwater seepage process is hindered to a certain extent. This also explains why the porosity measured by the image processing software is often greater than the actual porosity of the sandstone.

7. Conclusions

Based on the three problems raised in this study, this paper carried out an in-depth analysis of the petrological and physical characteristics of coal-bearing sandstone in the Tangkou Coal Mine (1000 m underground) and the microscopic pore structure of deep-well sandstones by carrying out various characterization techniques, such as casting thin sections, scanning electron microscopy, and mercury intrusion experiments. The tortuosity calculation formula was obtained by the theoretical derivation method. In addition, based on numerical simulation technology, a theoretical analysis of fluid seepage characteristics under different inlet pressures, different seepage flow rates, and different physical properties in the study area was carried out. The results solve the three problems raised in this study. The main conclusions of this study are as follows:

• Summary of microstructure: The matrix porosity is mainly 18.4~21.6%, the matrix permeability is mainly 123~441×10⁻³ μm², the porosity and permeability have a positive correlation, and there is moderate deviation in the overall correlation. The types of pores are mainly intergranular pores and dissolved pores. The main types of throats in the coal-bearing strata are sheet-shaped, curved, and sheet-shaped throats. Through mercury intrusion experiments, the coal-bearing strata in the study area were divided into four types according to the mercury inlet pressure and pore size. The seepage capacity of coal-bearing formations is mainly controlled by factors such as the pore type, pore throat distribution, sorting ability, and overall connectivity. Therefore, strengthening the exploration of sandstone pore structure plays a decisive role in studying fluid seepage characteristics in porous media.
• A theoretical model of tortuosity applicable to the conditions of this study has been established. It provides a strong theoretical basis for the development of numerical simulations. At the same time, it further verifies the microstructure parameters. According to the numerical simulations, the pressure distribution of fluid in the process of porous media percolation is clearly not uniform, and the pressure and flow velocity of the fluid constantly attenuate.
• This study solves the three problems raised and obtains the following research rules to guide the project construction: The smaller the median pore diameter of the rock samples in the study area and the worse the pore structure characteristic parameters, the worse the overall lithofacies quality, indicating that the physical conditions and connectivity of the coal-bearing sandstone are worse, and the resistance that the fluid needs to overcome to enter the pore structure also becomes greater. The research conclusions obtained in the mine have general applicability to common sandstone in deep rock masses and can be extended to other projects with similar depths and similar geological conditions. Each characteristic pore structure parameter has a certain prerequisite relationship with the physical properties of the study area.