Influence of Mixed Acids on Coal Fractal Characteristics and Permeability

Abstract

The acidification modification treatment of coal is a key technical means to improve the permeability of coal seams and enhance the efficiency of coalbed methane extraction. Yet, current acidic fracturing fluids are highly corrosive, corroding downhole pipelines and contaminating groundwater. By compounding environmentally friendly and non-polluting acidic fracturing fluids and combining fractal theory and the Frenkel–Halsey–Hill (FHH) model, this paper systematically investigates their effects on the pore structure, permeability, and mechanical properties of coal bodies. It was found that the complex acid treatment significantly reduced the surface fractal dimension D₁ and spatial fractal dimension D₂ of the coal samples and optimized pore connectivity, thus improving gas transport efficiency. Meanwhile, a static splitting test and digital image analysis showed that the fracture evolution pattern of the treated coal samples changed from a centralized strain extension of the original coal to a discrete distribution, peak stress and strain were significantly reduced, and permeability was significantly increased. These findings can offer dramatic support for the optimal optimization of acidic fracturing fluids.

1. Introduction

As China’s mines exploit shallow coal, resources are gradually being depleted and the extraction depth of coal is growing [1,2,3]. The low permeability of coalbed methane reservoirs and the poor development of fissure porosity make it difficult to mine most of the coal seams, as well as the associated coalbed methane in the reservoirs [4]. Therefore, how to improve the permeability of coalbeds is now an essential factor restricting the efficient exploitation of coalbed methane [5,6].

In recent years, scholars, both domestically and internationally, have optimized and modified hydraulic fracturing technology. For instance, replacing traditional fracturing fluids with acidic solutions enhances coal bed permeability, offering a valuable reference for fracturing fluid selection. Wang et al. [7] used infrared spectroscopy (FTIR) and X-ray diffraction (XRD) and found that acid-based fracturing fluids with a hydrochloric acid content of 3% were favorable for coalbed methane extraction. Zhang et al. [8] showed that the permeability of coal acidification was substantially increased under effective stress. Zhang et al. [9] examined the effects of hydrochloric acid (HCl) and cetyltrimethylammonium bromide (CTAB) on coal modification by low-temperature liquid nitrogen adsorption, and the results showed that the synergistic acidification of HCl and CTAB increased the connectivity of pores. Ni et al. [10] studied nitric-acid-modified solutions and revealed significant pore expansion by low-temperature nitrogen adsorption. Zhang et al. [11] investigated the pore structure and permeability of hydrochloric- and hydrofluoric-acid-treated coals with low-field nuclear magnetic resonance and established an equation between reservoir parameters and permeability. Luo et al. [12] examined the effects of different penetration enhancement methods on coal permeability and found that the effect of acidification was related to the initial permeability and mineral content of coal, while acidification induced the development of cracks and fissures. Wang et al. [13] investigated the permeability and pore architecture of coal treated with hydrogen sulfide (H₂S). It was noticed that the enclosed pores were transformed into half-enclosed pores and the carbonate was significantly reduced through dissolution, raising the connectivity between the pores and, thus, increasing the permeability. Balucan et al. [14] demineralized fissure compressibility and permeability in hydrochloric- and hydrofluoric-acid-treated coals by the means of permeability experiments in uniaxial compression, which revealed significant increases in the compression resistance and permeability of the coals. It can be demonstrated that acidic solvents have an effect on the architecture of coal.

At present, studies mainly focus on the modification of coal samples by single-component acids and organic solutions. Hydrochloric acid shows a remarkable acidification effect, but it possesses a high corrosiveness to downhole pipelines, and it is necessary to add a pickling corrosion inhibitor when it is used. Among them, imidazoline corrosion inhibitors are amphoteric surfactants, and, in addition to having a good environmental performance, can also effectively inhibit the corrosion of metals by hydrochloric acid, etc. They are widely used in petroleum and petrochemicals, chemical cleaning, atmospheric environment, and other fields [15,16]. Therefore, the compounding of hydrochloric acid and imidazoline corrosion inhibitors can regulate the reaction rate and maximize the acidification and penetration effects of the coal seam while ensuring the safety of equipment. Furthermore, previous studies have primarily focused on combining fractal theory with pore structure analysis, while few have conducted in-depth investigations into the correlation between such structural changes and gas permeability characteristics. Therefore, it is essential to develop a compound acid solution to explore the mechanism of permeability enhancement in coal.

In recent years, citric acid, as a common organic acid, has been widely used in water treatment [17,18] because of its good flocculation effect and biodegradability. Compounding citric acid with other acids will not only raise the flocculation rate, but also enhance the acidifying effect. In summary, a compound acid system was prepared in this paper by compounding hydrochloric acid and imidazoline corrosion inhibitors and adding a citric acid solution with a flocculation effect. Our aims were to analyze the modified coal samples for changes in mechanical properties, fractal characteristics, and permeability and study the fracture evolution law by digital image technology. The influence of mixed acid on coal permeability was explored, and the results of the study have certain theoretical implications for the development of acid fracturing technology.

2. Experiments

2.1. Materials

The main selection in this paper is a mixed acid solution composed of different proportions of hydrochloric acid, imidazoline-type surfactant (corrosion inhibitor), and citric acid solution, configured with a total concentration of 3% [19,20,21]. The specific acid formulation is shown in

Table 1. The mixed acid solution formulations.

Number Proportions	S0	S1	S2	S3	S4	S5
HCl	0	0	1	2	1	1
Imidazoline surfactants	0	0	1	1	1	2
Citric acid	0	0	1	1	2	1

, in which the raw coal is labeled as S0, with water treatment provided for the S1 coal samples.

The experimental coal samples were taken from the gas coal of Liuzhuang coal mine in China, with a volatility ranging from 32% to 40%, a bond index ranging from 70 to 85, an average burial depth of 720 ± 25 m, and a Platts hardness coefficient of 0.4–0.6. Standard cylindrical coal samples of 100 mm in height and 50 mm in diameter were fabricated for permeability testing and discs of 25 mm in height and 50 mm in diameter were fabricated for static Brazilian splitting tensile tests according to the dimensional requirements of ISRM standards [22]. The cut specimens were placed in a container with 500 mL of compounded acid solution, and after 24 h, the coal samples were filtered out and washed well with water to remove residual acid. They were dried in a desiccator at 35 °C, sealed in a Ziploc bag, and labeled for subsequent experiments. In order to ensure the reliability of the experimental data, a strict pre-treatment and repeated testing program was used in this study. All coal samples were vacuum dried for 24 h prior to testing to completely eliminate the potential impact of residual moisture on the test results. At least three independent measurement repetitions were made for each test condition so that an average value could be obtained to ensure the accuracy of the results.

2.2. Experimental Steps

2.2.1. Low-Temperature N₂ Adsorption on Coal Samples

The pore structure of coal samples was analyzed using a Micromeritics ASAP 2460 BET analyzer (Micromeritics Instrument Corporation, Norcross, GA, USA), which was designed to measure changes in the pore volume, pore structure, and other physical characteristics of coal samples [23]. An in-depth analysis was conducted to investigate how mixed acid solutions altered coal sample pore structure, examining their impact on porosity characteristics [24].

In this study, the FHH fractal model was used to analyze the low-temperature nitrogen adsorption experimental data of coal, which can effectively characterize the porous structure of coal by resolving the adsorption isotherms [25,26,27]. The FHH model is based on the theory of multilayer adsorption, which can accurately describe the nitrogen adsorption behavior in coal pores (including single-layer adsorption, multilayer adsorption, and the capillary cohesion effect) and is especially suitable for the characterization of the complex structure of the coal multiscale pore space. During the experiments, the coal samples were degassed under vacuum at 105 °C for 12 h to remove surface adsorbates, followed by nitrogen adsorption tests at 77 K. The relative pressures (P/P₀) were set in the range of 0.005–0.995. To ensure the reliability of the data, at least three parallel measurements were performed for each pressure point. Compared with other fractal analysis methods, the FHH model has the advantage of quantitatively characterizing pore surface roughness and spatial structural complexity at the same time, which provides a reliable analytical tool for the study of the pore structure of coal.

The study of coal as a porous solid material requires the classification of the pore structure. Pore size is an essential parameter affecting the flow of gas within coal and is the most easily observed feature, so pore size is frequently used as a benchmark for classification [21]. Many scholars categorize the pore structures of porous solid materials such as coal into different types based on pore size, such as macropores, mesopores, transition pores, micropores, extreme micropores, and ultramicropores [28]. Combined with the research content and methodology of this paper, the pore size classification in this paper is set as follows: micropores (<10 nm), transition pores (10~100 nm), and mesopores (100~1000 nm) [29,30,31].

2.2.2. Static Brazilian Split Tensile Test on Coal Samples

The loading process of the static Brazilian split tensile test is shown schematically in Figure 1.

2.2.3. Permeability Test on Coal Samples

The permeability of coal samples was measured using the steady-state method, and the experimental setup and schematic diagram of coal sample permeation are shown in Figure 2 and Figure 3. The experiments were carried out at a constant temperature (298 ± 0.5 K) and high-purity methane (99.99%) was used as the permeation medium. The perimeter pressure was set at 4 MPa, the inlet pressure at 0.5–3 MPa, and the outlet pressure was kept at atmospheric pressure (0.101 MPa), taking into account that the perimeter pressure should always be at least 1 MPa greater than the inlet pressure to ensure that the permeation environment is airtight. The following are the exact steps of the operation.

(1)

Wrap the coal sample with heat-shrink tubing and install the sample in the triaxial pressure chamber after checking the air tightness.

(2)

Control the perimeter pressure system so that the perimeter pressure reaches a predetermined value.

(3)

When the perimeter pressure is kept constant, adjust the gas control system to apply air pressure to the coal sample for permeability measurement. The formula for the permeability of the coal sample according to Darcy’s law is [32] as follows in Equation (1):

$$K={\displaystyle \frac{2q\mu L{p}_0}{A(P_2^2-P_1^2)}}$$

(1)

where $q$ is the gas flow rate, m³/s; $\mu$ is the gas viscosity, Pa·s; $A$ is the cross-sectional area of the coal sample, m²; $L$ is the thickness of the coal sample, m; $p_0$ is the atmospheric pressure in the laboratory, Pa; and $P_1$ and $P_2$ are the gas pressures at the outlet and inlet, respectively, Pa.

2.2.4. DIC Test on Coal Samples

The DIC method (digital image technique) can analyze the strain field evolution of coal samples during splitting and stretching to quantify crack emergence and expansion characteristics from the viewpoint of microscopic mechanics [33]. Since the strain cloud map requires a high-integrity coal sample surface, the DIC data on the coal sample surface is invalidated when a macroscopic crack appears on the surface of the specimen, so only part of the strain cloud map before damage to the surface of the coal sample is collected to be analyzed.

As shown in Figure 4, an RMT rock mechanics testing machine was used for the test. The test device loading plate can automatically adjust the force balance to make the specimen end face uniform pressure, reducing the impact of boundary conditions. Axial displacement control loading with a loading rate of 0.002 mm/s was used for splitting tensile tests. Meanwhile, a camera was used to capture images of the displacement field of the specimen surface during loading. The analysis system adopted DIC-2D processing software (version 2017) to import the captured images into the analysis system for strain calculation, obtain the strain cloud map, and then analyze the crack evolution process of the coal samples [34].

2.2.5. SEM Test

The Flex SEM 1000 scanning electron microscope (Hitachi High-Tech Corporation, Tokyo, Japan) was employed to examine the surface pore characteristics of the coal samples following treatment with complex acid solutions. The instrument was operated under high-vacuum conditions (resolution: 4.0 nm) with an adjustable acceleration voltage ranging from 0.3 to 20.0 kV. The magnification could be continuously adjusted between 6× and 300,000× to achieve optimal imaging. To prepare the samples for analysis, they underwent a drying and dehydration process before being coated with a thin gold layer to improve their electrical conductivity, thereby ensuring high-quality imaging while protecting the microscope components.

3. Results

3.1. Mechanical Performance Analysis

Changes in the mechanical properties of the coal body directly control the whole process of coalbed methane desorption–diffusion–seepage. Therefore, by the means of Brazilian splitting experiments, this study quantitatively analyzes the change rules of mechanical parameters such as the splitting strength, modulus of elasticity, brittleness index, and fracture toughness of coal samples modified by compound acid. The experimental results are shown in Figure 5. The stress–strain curves of each group of coal samples show similar trend changes, and the axial stress suddenly drops to zero after the stress reaches the peak value, which indicates that all groups of coal samples show typical sudden damage characteristics.

The Brazilian splitting tensile strength ${\sigma }_r$ is given by Equation (2) [35] and the modulus of elasticity E is expressed by Equation (3) [36].

$${\sigma }_r={\displaystyle \frac{2P}{\pi DL}}$$

(2)

where $P$ is the maximum splitting damage load on the coal sample, N; $D$ is the diameter of the coal sample, m; and $L$ is the thickness of the coal sample, m.

$$E={\displaystyle \frac{2Pt}{\pi DL}}{\displaystyle \frac{0.8376D}{\Delta u}}$$

(3)

where $P_t$ is the destructive load of the coal sample, N; $D$ is the diameter of the coal sample, m; $L$ is the thickness of the coal sample, m; and $\Delta u$ is the final tensile deformation of the coal sample.

The calculations yielded the mechanical parameters of the coal samples, such as their split tensile strength and modulus of elasticity. As shown in Figure 6a, after the coal samples were treated with different ratios of acid solutions, the split tensile strengths and moduli of elasticity of all coal sample groups decreased, indicating that the dissolution and leaching treatment with mixed acid solutions had a significant deteriorating effect on the mechanical properties of the coal samples. Weakening of the mechanical properties would reduce the adsorption binding force of the coal matrix to methane and accelerate desorption. Among them, the split tensile strength and modulus of elasticity of S4 were lower than those of S5, which could be attributed to the excessive concentration of imidazoline in S5 that led to the aggregation of corrosion inhibitor molecules and the formation of an inhomogeneous protective film that partially enhanced the rigidity of the material. In contrast, the moderate concentration of corrosion inhibitor in S4 resulted in a superior corrosion inhibition effect, leading to a material that was more susceptible to plastic deformation and, thus, exhibited lower mechanical properties.

To further evaluate the mechanical properties of the coal samples, the brittleness index (Equation (4)) and fracture toughness (Equation (5)) of the coal samples can be calculated from the force–displacement curves obtained from the Brazilian splitting test. The calculation method is as follows [37]:

$$BI={\displaystyle \frac{{\sigma }_r}{{\epsilon }_r}}$$

(4)

where ${\sigma }_r$ is the Brazilian splitting tensile strength and ${\epsilon }_r$ is the axial strain at the peak force point.

$$K_{IC}={\displaystyle \frac{P_t\times Y}{\sqrt{\pi R\cdot L}}}$$

(5)

where $P_t$ is the maximum splitting damage load on the coal sample, $R$ is the radius of the coal sample, mm; $L$ is the thickness of the coal sample, mm; and $Y$ is the geometric correction factor, 1.1368.

As shown in Figure 6b, coal samples treated with different ratios of acid solutions exhibited obvious brittleness enhancement characteristics, and their brittleness indices were significantly higher than those of the original coal and water-treated coal samples. Meanwhile, the original coal had the highest fracture toughness, while the fracture toughness of the acid-treated coal samples showed a decreasing trend, in which the fracture toughness value of the S4 group decreased to 0.0376 MPa-m^1/2. This change in mechanical properties weakened the coal body structure and increased the brittleness of the material. The reduction in fracture toughness made the coal body more prone to generate new fissures under mining stress and promoted the expansion of existing fissures, which effectively improved methane desorption efficiency.

3.2. Pore Structure Analysis

3.2.1. Pore Type

Coal is a typical porous medium, and its internal gas is mainly stored in the complex pore network in the adsorption state. The study of the pore structure characteristics of coal (including pore type and pore size characteristics) is of key guiding significance for the efficient exploitation of coalbed methane (CBM) and the prevention and control of gas disasters. Pore type directly affects the connectivity of the gas transport channel, while pore size characteristics determine the desorption behavior of the gas. Under the condition of a certain temperature, the adsorption volume of the solid changes with a change in pressure. As shown in Figure 7, the liquid nitrogen adsorption processes of different coal samples present a clear two-stage feature. In the lower relative pressure range (P/P₀ = 0–0.52), the gently increasing trend of the adsorption isotherm reflects the monomolecular layer adsorption process on the surface of the coal matrix, when nitrogen molecules form a monolayer cover on the pore surface, mainly through van der Waals forces. As the relative pressure increases to the range of P/P₀ = 0.52–0.99, the isotherms show a rapid increase in characteristics. This suggests that, on the basis of the formed monomolecular layer, the system undergoes both multimolecular layer adsorption and capillary coalescence effects in mesoscopic pores, and the synergistic effect of the two mechanisms together leads to a significant increase in adsorption [38].

The sorption and desorption curves of the coal samples all appeared to have significant hysteresis, i.e., the adsorption and desorption curves did not coincide. The main cause was the occurrence of capillary coalescence in the transition pores and mesopores of the test samples. When the relative pressure was minor, the capillary coalescence phenomenon struggled to occur, so the hysteresis phenomenon disappeared. At the same time, the hysteresis ring types of the samples represented different pore structures, with S0 dominated by cylindrical pores open at one end and closed at the other end, with pointed split pores. The hysteresis ring type did not change significantly before and after the modification of the coal samples, indicating that the pore type was not significantly altered. However, the change in the hysteresis loop size suggested that the pore structure might have been altered in other aspects. In order to further explore the reasons for the hysteresis ring changes, the pore size characteristics and pore size distribution of the coal samples were subsequently systematically analyzed.

3.2.2. Pore Size

The pore space of coal not only constitutes the main site for methane adsorption, but also the key pathway for methane desorption and its diffusive transport. Modification of the coal body by applying a mixed acid solution can significantly adjust its pore structure and, thus, change the methane permeability. Therefore, the pore structure characteristics of coal before and after modification and its evolution law are the focus of analyzing the mechanism of mixed acid solution’s effect on coal permeability.

It is clear from

Table 2. Variation in pore parameters of coal samples.

Samples	Volume (10−3 cm3/g)			TPV (10−3 cm3/g)	Average Pore Size (nm)
	Micropore	Transition Pore	Mesopore
S0	0.91	6.53	0.88	8.32	14.3
S1	0.88	6.77	1.12	8.77	14.6
S2	0.85	6.89	1.24	8.98	15.1
S3	0.82	7.02	1.28	9.12	15.3
S4	0.79	7.11	1.32	9.22	16.2
S5	0.84	7.07	1.19	9.10	14.9

that the coal samples treated with the mixed acid solution displayed distinct changes in terms of average pore diameter and pore volume compared to the S0 coal. The measured average pore diameters ranged from 14.3 to 16.2 nm, and the pore capacities ranged from 8.32 × 10⁻³ to 9.22 × 10⁻³ cm³/g.

In terms of the change in the average pore size, the modifying effect increased the pore size, among which the S4 coal showed the largest increase in average pore size, which rose by 13.3% compared with the original coal. Considering the change in pore volume, the pore volume of the coal samples appeared to increase to some extent, among which the pore volume of the S4 coal showed the most dramatic growth, with an increment of 10.8%. This pore volume increase resulted from mineral and matrix dissolution [39,40,41] in the coal samples due to the mixed acid treatment, improving pore development and connectivity. Thereby, this promoted the development of transition pores and mesopores, and the number of microscopic pores decreased. According to the distribution of pore volume, there was basically no change in the distribution of pore volume before and after modification. The pore volume was most developed between the transition pores, and secondly in the mesopores. Compared with the pore volume of the original coal, the alteration in pore volume with modification of the coal samples was mainly concentrated between the transition pores, and the pore volume of other pore sizes did not change much. However, in terms of the pore volume size, the effect of acid solution modification with different ratios was not consistent. The share of transition pores increased the most in S4 coals, with an increase of 8.88%. This was because the S4 complex system formed a synergistic dissolution effect by hydrochloric acid dissolving carbonate minerals and citric acid chelating clay metal ions, while the optimized concentration of imidazoline both stabilized the nascent pore structure and avoided excessive clogging, which ultimately led to the merging of micropores to form a transition pore network and achieve an increase in transition pores. In general, the modifying effect of the mixed acid solution resulted in an increase in the quantity of transition pores and mesopores, a pore shape favoring structurally simple pores, and a decrease in the number of micropores.

3.2.3. Pore Size Distribution

The commonly adopted method for analyzing pore size is the BJH method, but this method is not suitable for analyzing micropores or narrower mesopores, especially when the pores in the coal are less than 10 nm, as it underestimates pore size. The DFT method can accurately describe the interaction between adsorbed molecules and pore materials, predict the position and adsorption energy of adsorbed molecules in porous materials, and is applicable to the full scope of pore size analysis. Therefore, the DFT method was selected for the pore size distribution analysis in this paper.

The pore size distribution curve in Figure 8 reflects the relationship of pore volume variation with pore size, where the vertical coordinate dV/dD indicates the amount of pore volume variation (dV) per unit pore size interval (dD). This parameter can quantitatively characterize the degree of contribution of pores to the total pore volume in different pore size intervals. The size of the peak width reflects the number of holes in the corresponding interval, and a wider peak width indicates that the number of holes in the interval is larger and more widely distributed [42]. The narrower the peak width, the more concentrated the pore size distribution and the more uniform the number of holes. In the meantime, the higher the value of the vertical coordinate corresponding to a certain aperture size, the higher the number of holes of that aperture size. The peak then represents the maximum value of the proportion of holes, i.e., the number of holes is most intensive at that aperture size.

Under the action of mixed acid solution, the peak areas of coal samples in each pore size range varied and were characterized by multiple peaks. The peaks were mostly concentrated within 38.2–58.4 nm, indicating that the number of peaks in this aperture range was high. The micropores were diminished relative to the original coal, suggesting that the modification was more favorable for attenuating the gas adsorption capacity. With the increasing pore size, the peak area fluctuated more in the range of transition pores and mesopores, which was more favorable for the generation of free gas.

3.2.4. Pore Fractal Characterization

Fractal porosity is a key parameter for characterizing the multiscale structural complexity of coal body pore systems, and the self-similarity of the pore structure is quantitatively characterized by the fractal dimension (D). Based on the FHH (Frenkel–Halsey–Hill) model theoretical system established by Pfeifer, the fractal dimension can be used as an effective index to measure the degree of irregularity of pore geometry. The fractal dimension is calculated as shown in Equations (6) and (7). V represents the equilibrium gas adsorption capacity per unit mass of the sample, measured in cm³/g under a specific equilibrium pressure P. C denotes the y-axis intercept obtained from linear regression analysis of the adsorption isotherm, serving as a dimensionless constant that reflects the adsorption affinity. A is a scaling parameter intrinsically linked to the surface fractal dimension calculation. P₀ indicates the saturation vapor pressure of the adsorbate gas at the experimental temperature, while P corresponds to the actual equilibrium pressure during measurement, both expressed in MPa.

$$\ln V=C+A\left[\ln \left(\ln \left({\displaystyle \frac{P_0}{P}}\right)\right)\right]$$

(6)

$$A=-{\displaystyle \frac{3-D}{m}}$$

(7)

In this study, m = 1 was used to establish Equation (6) to better characterize the mesopore/mesopore connectivity where capillary forces dominate (whereas m = 3 was used for systems where van der Waals forces dominate).

$$D=A+3$$

(8)

The fractal characteristics of the pore structure were analyzed using low-temperature nitrogen adsorption data. By performing linear regression of $\ln V$ versus $\left[\ln \left(\ln \left({\displaystyle \frac{P_0}{P}}\right)\right)\right]$, the slope parameter A was determined and subsequently applied in Equation (6) to calculate the fractal dimension D. The FHH analysis revealed the following two distinct regimes: the surface-dominated region (P/P₀ = 0–0.52) and the spatial structure region (P/P₀ = 0.52–1). The surface fractal dimension D₁ (D₁ = 3 + A₁) quantifies pore wall roughness, where higher values correspond to greater surface irregularity and an enhanced gas adsorption capacity. The spatial fractal dimension D₂ (D₂ = 3 + A₂) characterizes pore network complexity, with reduced values indicating decreased homogeneity and the formation of preferential flow pathways that improve permeability. The calculated fractal dimensions are presented in

Table 3. Fractal feature parameters.

Coal Sample	Fractal Dimension
	D1	R2	D2	R2
S0	2.5867	0.9986	2.6325	0.9964
S1	2.5786	0.9921	2.6197	0.9935
S2	2.5534	0.9976	2.6254	0.9981
S3	2.4936	0.9897	2.6078	0.9943
S4	2.4877	0.9883	2.6022	0.9925
S5	2.5239	0.9985	2.6132	0.9954

.

It can be seen from Figure 9 and Table 3 that D₁ ranges from 2.4877 to 2.5867 and D₂ ranges from 2.6325 to 2.6022. The values of the fitted curves R² (an index characterizing the goodness of fit of the model, where the closer its value is to 1, the higher the fit) were all greater than 0.98, which indicates that the pore structure of the coal samples exhibited significant fractal characteristics throughout the relative pressure interval. The fractal dimension D₁ of the acid-modified coal samples was reduced compared to the original coal due to the carbonate minerals in the coal being solubilized and the clay minerals expanding to make the pore surfaces smoother. The D₂ of the coal samples was decreased after the mixed acidification and modification treatment. This was because the acid dissolved minerals and organic matter from the coal, simplifying its pore structure and enhancing connectivity. It can be seen that the FHH model and fractal theory adopted in this paper can more accurately describe the permeability changes in acidified coal compared to traditional models (e.g., Cubic Law or Kozeny–Carman), because acidification treatment significantly changes the pore connectivity and fractal characteristics of coal.

3.3. Gas Permeability Analysis

The permeability of coal is an intrinsic physical quantity that characterizes the ability of a fluid to pass through a porous medium, and its value depends on pore structure and connectivity characteristics. In this study, the gas permeability of coal samples was determined by the steady-state method, which reflects the ability of the interconnected pore network and natural fissure system in the coal seam to conduct gas transportation.

The change in the internal pore structure and change in the mechanical properties of the coal after modification with different ratios of acid solutions also had effects on permeability. As shown in Figure 10, when the perimeter pressure was 4 MPa, the inlet pressure increased from 0.5 MPa to 3 MPa, and the permeability of all groups of coal samples, in general, decreased. At an inlet pressure of 0.5 MPa–1 MPa, the permeability of coal dropped at a rapid speed. The rate of descent of coal permeability was considerably more sluggish when the inlet pressure was above 2.5 MPa. This was caused by the intensification of the swelling effect due to adsorption within the coal as the inlet pressure increased, and the seepage path was squeezed and deformed [43,44,45], resulting in a decrease in permeability [46].

As shown in Figure 11, the permeability of coal samples treated with the mixed acid solution was remarkably larger than that of the original coal at the same inlet pressure. With the inlet pressure was 1 MPa, the permeability of coal samples rose by 17–428%. At an inlet pressure of 2.5 MPa, the permeability of the coal samples rose by 6.61–366%. Obviously, the incremental permeability of coal samples improved the ability of gas flow between coal seams, thereby improving the gas extraction efficiency.

3.4. DIC Analysis

As shown in Figure 12, it is easy to quickly understand the differences in strain distribution by setting the strain in the form of percentage. The strain cloud maps of each group of coal samples show two different processes of change, with M0 (i.e., the original coal) strain change being more centralized and the centralized area expanding along the axial direction, while the internal strains of each mixed-acid-solution-treated coal sample showed discrete distributions upon stressing. This was because the coal samples treated with mixed acid solution became more porous, which made the strain dispersed. This is consistent with the results of the change in pore structure in Section 3.2.

In

Table 4. Corresponding schedules of DIC strain maps for each group of coal samples.

Samples	T1 (s)	T2 (s)
S0	3.26	12.15
S1	3.26	9.87
S2	3.26	8.24
S3	3.26	7.66
S4	3.26	7.14
S5	3.26	7.32

, the time required for the coal samples treated with mixed acid solution to reach the T2 moment was dramatically reduced compared to S0 (i.e., the original coal) by 18.7%, 32.1%, 36.9%, 41.2%, and 39.6%, respectively. The shorter time required to observe the first visible cracks can be attributed to the different ratios of acid solution removing some of the inorganic minerals in the coal to make the pore structure simpler, which reduced the static toughness of the coal samples. This is in line with the change in fracture toughness in Section 3.1.

3.5. SEM Test Results and Analysis

In order to deeply analyze the modification mechanism of heterogeneous damage to the coal body by compound acid, the pore structures of coal samples before and after acid treatment were characterized and analyzed by a scanning electron microscope. Taking the specimens from the S0 and S4 groups as examples, their micro-morphological features are shown in Figure 13a,b. The surface of the raw coal particles showed an obvious granular morphology, and the surface of the treated pulverized coal particles was smoother. The reason for this was that the compound acid dissolved the mineral components in the coal samples and reduced the number of surface particles. Meanwhile, the dissolution process formed a more developed pore network in the coal matrix. This heterogeneous damage feature coincides with the discrete strain analysis in DIC.

3.6. Mechanism of Penetration Enhancement of Coal by Mixed Acid Solutions

From Figure 14, it is clear that coal is a porous medium with many pore channels [47]. The pore channels are filled with small soluble components and organic minerals, resulting in poor connectivity between the pores [48]. After entering the pores, the acid solutions with different ratios firstly immersed and dissolved substances with larger molecules, which enlarged the fracture space of the coal body [49]. After treatment with different ratios of acid solutions, the fractal dimension D₁ of coal decreased and the fractal dimension D₂ showed an improvement in pore connectivity. At the same time, weakening of the mechanical properties of coal would reduce the fracture initiation pressure of hydraulic fracturing, promote the formation of multi-branched fracture networks, reduce the tortuosity of the gas diffusion path, and increase permeability [50,51,52].

4. Conclusions

We explored an acid solution to promote the permeability of coal seams and gas extraction efficiency. The permeability-enhancing effects of different acid components in mixed solutions were studied from four distinct aspects, namely, the mechanical properties, fractal characteristics, changes in permeability, and fissure evolution law of the modified coal samples. The main findings of the study are as follows:

(1)

After treatment with different ratios of acid solutions, the fractal dimension D₁ and fractal dimension D₂ of the coal samples decreased, indicating that the pore connectivity was improved, the tortuosity of the gas diffusion paths was reduced, and the gas transportation efficiency was enhanced.

(2)

The Brazilian splitting experiments indicated that the main damage mode of coal samples was brittle damage. After modification by the mixed acid solution, all coal sample groups exhibited reductions in both splitting tensile strength and elastic modulus, demonstrating that the mixed acid treatment significantly degraded their mechanical properties.

(3)

The treatment with mixed acid solution caused the internal microscopic pore structure and macroscopic mechanical properties of the coal to alter, and the permeability of the coal samples treated with mixed acid solution was obviously greater than that of the raw coal.

(4)

Under the action of mixed acid solution, the evolution of cracks in the coal samples showed two different processes. The strain change in the original coal was more concentrated, and the concentrated area was extended along the axial direction, while the internal strain of the treated coal samples showed a discrete distribution when subjected to force.

The compounding of acid in coal seams may face the risks of uneven acid distribution within fractures, leading to localized over-etching, increased wellbore corrosion, and secondary precipitation plugging. To address these challenges, a gel-based acid system can be used to improve acid diversion, optimize corrosion inhibitor formulations to protect wellbore equipment, and work with drainage aids to promote the return of residual acid. These measures can significantly improve the uniformity and safety of acid treatment.