The Changing of Micromechanical Properties of Coal after Water Immersion: The Insight from Nanoindentation Test

Abstract

The application of the hydrodynamic method has enhanced the extraction of coal bed methane (CBM). In this method, fracturing fluid rapidly penetrates the coal reservoir, altering its intrinsic pore structure and microscopic mechanical properties. These changes impact the properties of the coal reservoir and CBM depletion. It is, therefore, crucial to explore how these micro-characteristics evolve following water invasion. In this context, using nanoindentation tests, the microscopic characteristics of three coal samples were measured under dry conditions and at water saturations corresponding to 44% and 75% relative humidity. The influence of water immersion on the pore structure was also assessed using mercury injection experiments. Moreover, cluster analysis was used to categorize the extensive measured data into three sub-components: fractures (large pores), inertinite, and vitrinite, to investigate the impact of water saturation on microscopic properties. The findings indicate that cluster analysis is well-suited to these data, showing excellent agreement with porosity and maceral tests. The relationship between the elastic modulus and hardness of dry and wet coal samples varies across the sub-components. There is a notable dependency in the case of vitrinite, whereas water content tends to reduce this dependency. It is also found that water content negatively affects elastic modulus and hardness and reduces the anisotropy ratio. The mechanical properties of inertinite are highly responsive to water immersion, whereas vitrinite exhibits lesser sensitivity. The softening mechanisms of coal when immersed in water, such as calcite phase dissolution, swelling stress fracturing, and weakening of macerals, are identified. This study offers new perspectives on the impact of moisture on the alteration of micromechanical properties in coal.

1. Introduction

Coal bed methane (CBM) exploitation offers multiple benefits, including enhancing the safety of coal mine operations, optimizing the energy structure, and reducing carbon emissions. However, it also presents considerable challenges [1,2,3]. Currently, low permeability remains a primary constraint on the efficacy of coal bed methane extraction. The adoption of hydraulic methods, such as hydraulic fracturing (Figure 1a), has advanced the gas extraction process. Nevertheless, the coal seam, characterized by its abundant micro-fractures and high capillary pressure, allows the fracturing fluid to swiftly infiltrate and diffuse into the coal matrix (Figure 1b), which includes minerals and macerals inertinite and vitrinite (Figure 1c).

This infiltration induces complex reactions within the coal rock [4,5], including clay mineral swelling and calcite dissolution (Figure 1d) [6]. As a result, the intrinsic pore structure and micro-mechanical properties of the coal reservoir change, impacting the reservoir properties and the characteristics of gas depletion [7,8].

Studies show that water invasion significantly affects the pore structure of coal. While much research has focused on the pore structure of dry coal, several studies have explored the effects of water on coal’s pore structure. For instance, Kang et al. [9] used nitrogen adsorption and SEM to explore the influence of treatment with fracturing fluid on coal samples, noting alterations in pore size distribution, specific surface area, and pore fractal dimension. Xiao et al. [10] showed that water intrusion increased pore volume and diameter, though the specific surface area remained largely unaffected. Si et al. [11] investigated micropores in coal using CO₂ adsorption experiments, discovering that water intrusion variably increased pore volume and specific area depending on the coal rank. Xue et al. [12] conducted low-temperature nitrogen adsorption/desorption experiments and nuclear magnetic resonance measurements to explore the impact of treatment on the coal pore structure. It was found that water-based fracturing fluid decreased the volume and area of pores. Song et al. [13] carried out low-temperature nitrogen adsorption experiments and observed that while water immersion had negligible impact on pore shape, it reduced specific surface area and adsorption capacity, and increased total pore volume and average pore diameter. In addition, the existence of water would also change the mineral structure. For example, (i) the swelling of clay minerals leads to uneven stress in the matrix, generating a large number of micro-cracks, and (ii) the calcite is prone to dissolution in high-concentration solution, creating some micro-pores [14,15]. These studies demonstrate that water intrusion significantly affects micropores and mineral structure. However, they did not address how changes in micropore structure impact the micro-mechanical properties of coal after water intrusion.

The mechanical characteristics of coal change after water immersion. This issue has become a hot research topic in recent years. Wang et al. [16] carried out triaxial compression experiments on anthracite coal under natural and forced water saturation conditions, finding that the water content of coal negatively correlates with its elastic modulus exponentially. Ai et al. [17] conducted comprehensive uniaxial compression tests to analyze coal’s mechanical properties and deformation and failure under various water-soaking durations. Yao et al. [18] conducted similar tests with controlled moisture levels and observed that plastic deformation appeared on the full stress–strain curves at higher moisture contents. The results demonstrated that as moisture content increased, peak strain increased, while compressive strength decreased linearly. These studies predominantly employ uniaxial and triaxial mechanical tests to analyze the influence of fracturing fluid on the macroscopic properties of coal reservoirs [19,20,21]. It was found that gas depletion is partially influenced by the mechanical interaction among different coal sub-components [22,23]. Despite this, few studies have explored these aspects at the microscale due to the complex composition and high heterogeneity of coal [24,25]. Accordingly, examining the mechanical properties of coal at the microscale is crucial for understanding the mechanisms of weakening that occur after water immersion.

Nanoindentation is a testing technique that applies a load via a nano-indenter to assess the elastic modulus and hardness of materials [26]. This technology offers distinct advantages to explore the micromechanical characteristics of coal compared to macroscopic mechanical tests: (i) The high resolution in load and displacement enables the precise measurement of mechanical properties at the level of microscopic structural units. This enables exploration of microstructure heterogeneity and the relationship between the mechanical properties of each phase and their deformation responses [27,28]; (ii) it requires only small samples, such as drilling cuttings, sidewall cores, or fragments, making it less demanding in terms of sample size and integrity [29]; (iii) it provides the benefits of rapid testing speed, non-destructiveness, and high measurement accuracy [30]. A significant issue exists in how to link the numerous measured data points with their corresponding mineral phases.

As indicated earlier, moisture significantly influences the depletion of coalbed methane. Yet, the impact of moisture on the micromechanical properties of each phase remains largely unexplored (Figure 1d). Aiming at resolving this shortcoming, samples from the Wangpo coal mine were chosen for examination and prepared as cubes to measure in both horizontal and vertical bedding directions. A series of micromechanical property tests were conducted under dry conditions, and at moisture levels corresponding to 44% and 75% relative humidity. The influence of water–rock interaction on Young’s modulus was analyzed. Cluster analysis was used to categorize the measured data into three groups fractures, vitrinite, and inertinite. This study also extensively examined the mechanisms through which moisture affects the mechanical properties of coal and its sub-components. Finally, this study explored the relationship between changes in micromechanical properties and alterations in microscopic pore structure, offering theoretical insights into the formation of micro-fractures during hydraulic fracturing and the optimization of favorable development areas.

2. Experiments

2.1. Materials

Core samples were obtained from the Wangpo coal mine in Tiandi, China, at an approximate depth of 600 m, and were promptly transported to the laboratory for preparation. Six cubic samples, each measuring approximately 10 mm on each side, were extracted for the nano-indentation tests. Due to the roughness of the coal substrate surfaces, it was necessary to polish the samples to achieve the smoothest possible finish. To this end, the sample was polished three times. First, 600 mesh abrasive paper was employed, followed by 3000 mesh, and finally 7000 mesh.

2.2. Sample Saturation

The six samples were divided into three groups for the nanoindentation tests. The mechanical parameters of samples 1, 3, and 5 were tested along the vertical bedding direction, and those of samples 2, 4, and 6 along the horizontal direction. The relative humidity can be obtained by maintaining a constant partial pressure of water vapor of saturated salt solutions. Samples 3 and 4 were subjected to a sealed moisture equilibration process for several days to absorb moisture (Figure 2a). The saturated MgCl₂ salt solution was positioned at the bottom of the moisture equilibration chamber to uphold a relative humidity of approximately 44% at room temperature [31]. These samples were weighed periodically until moisture equilibrium at this humidity level was reached. Employing a similar approach, samples 5 and 6 were exposed to a saturated NaCl solution (Figure 2a) to attain a relative humidity of 75% [31]. Their masses were monitored at regular intervals until they reached moisture equilibrium.

2.3. Experiment Equipment

In this study, the KLA iMicro nano-indentation instrument, manufactured in the United States, is utilized (Figure 2b). This device features a highly sensitive three-piece capacitive sensor. The electromagnetic loading method is employed, achieving a loading accuracy of 6 nN, a displacement accuracy of 0.04 nm, and a thermal drift below 0.05 nm/s. The apparatus consists of a sample frame, probe, control system, and data acquisition system. The sample frame holds the test specimen. A diamond indenter with a top curvature radius of 20 nm is used for measuring the sample’s indentation. The control system manages the load and testing speed, while the data acquisition system records the outcomes, such as depth, load, and duration.

The high-pressure mercury injection method, widely regarded as the standard technique for pore characterization, relies on correlating the pressure of injected mercury with the pore structure to derive information about pore size and distribution. In this study, the MicroActive AutoPoreV9600, manufactured in the United States and capable of a maximum injection pressure of 61,000 psi, is used to detect pore characteristics. Pore size is estimated based on the injection pressure using the Washburn equation.

The organic components present in organic rocks are categorized into maceral groups (liptinite, inertinite, and huminite/vitrinite), which further consist of individual macerals within these groups. The maceral group is identified as the fundamental components of coal, observable under an optical microscope, and classified into maceral groups and individual macerals in those groups. In this research, the Axio Scope.A1, manufactured in Germany, is employed to detect maceral groups.

2.4. Experimental Method

Coal samples were subjected to indentation using the iMicro Nano-indentation under constant temperature conditions. Each sample received at least 100 indentations on its surface using a Berkovich pyramidal indenter. About 100 nano-indentation tests were conducted with a spacing of 30 µm between each point to minimize mechanical interference from adjacent indentations. The duration of contact between the indenter and the sample was 5 s, while the indenter load was set at 5 mN. Figure 3a displays the optical image of the relatively smooth sample surface captured in real-time by the instrument’s optical imaging system. Figure 3b captures optical images of cracks or defects on the sample surface, also collected in real-time.

Six samples are divided into two groups: one for mercury injection tests and another for maceral analysis. The prepared samples are immediately used for mercury injection tests after a drying process. The other group is processed into coal flakes, followed by vitrinite reflectance tests conducted under oil immersion at room temperature. A total of 500 points are measured for each sample.

2.5. Determination of Micromechanical Parameters

In this investigation, the micro-mechanical characteristics of coal samples are evaluated using nano-indentation tests. These tests entail the application of an indenter with defined mechanical and geometrical properties to the surface of the sample while recording a force–displacement response curve throughout the loading and unloading phases [32]. Figure 2c illustrates a typical indentation profile and load-displacement curve [33].

Indentation hardness, which measures the material’s load-bearing capacity per unit area, is defined as follows [34]:

$$H=P/A$$

(1)

where H (in Pa) represents the material’s hardness, P (in N) denotes the load exerted by the indenter. A (in nm²) represents the interface area between the indenter and the sample surface and can be written as follows [35]:

$$A=24.56\times h_c^2$$

(2)

where h_c indicates the contact depth (in nm) and is calculated as follows:

$$h_c=\frac{2\times (v_e-1)}{2\times v_e-1}\times h_m$$

(3)

where v_e is the elastic to energy ratio. The contact stiffness S (in N/m), which is defined as the slope of the upper part of the quantized unloaded portion (h_m), can be obtained as follows:

$$S=0.75\times (2\times v_e-1)\times \frac{p_m}{h_m}$$

(4)

The reduced modulus E_r (in Pa) is then obtained from the contact stiffness as follows:

$$E_r=\frac{\sqrt{\pi }\times S}{2\times \sqrt{A_c}}$$

(5)

The Young’s modulus of a material E (in Pa) can be derived from the equation as follows:

$$\frac{1}{E_r}=\frac{1-v^2}{E}+\frac{1-{v_i}^2}{E_i}$$

(6)

in which the subscript i refers to the Berkovich indenter. Both the hardness and elastic modulus can be calculated through the above equations with the maximum indentation depth.

2.6. Classification of Measured Data

In this study, the Gaussian equation is employed to describe the distribution of mechanical properties of a certain component. Therefore, several Gaussian functions are employed to fit the frequency versus Young’s modulus profile [36]. The multivariate cluster modeling is utilized to distinguish the measured mechanical data (Young’s modulus and hardness) into mineral phases. Specifically, sklearn.mixture is used to deconvoluting the hardness and Young’s module data [37].

Assuming a mixture of normal components, the corresponding probability density function p(x_i) within a mixture of k components, can be expressed as follows [38,39]:

$$p(x_i)={\displaystyle \sum _{j=1}^k{f}_j}c(x_j;{\mu }_j,{\sum }_j)$$

(7)

where 0 ≤ f_j ≤ 1 is the fraction for component and μ_j and ∑_j are the means and covariance matrices for component j, respectively.

The volume fraction estimate, denoted as f_j = ∑_i^Nτ_ij, in which τ_ij is the posterior probability that x_i belongs to the ith k component. Thus, the function c(x_i; μ_j, ∑_j) aligns with the multivariate Gaussian normal density:

$$c(x_j;{\mu }_j,{\sum }_j)=\frac{1}{\sqrt{2\pi }}{({\sum }_j)}^{-\frac{1}{2}}\exp (-\frac{1}{2}{(x_j-{\mu }_j)}^T{({\sum }_j)}^{-1}(x_j-{\mu }_j))$$

(8)

The three unknown parameters, μ_j, ∑_j, and f_j, for each component are determined through the maximum likelihood approach, employing the expectation-maximization method.

In this work, we assume that the (i) amount of the component is four: vitrinite, inertinite, fracture, and anomaly, and the distribution of mechanical properties of a certain component follows a Gaussian equation; (ii) the distribution of each component is convex-shaped, and there is an intersection between varied components; (iii) the size of each component (the number of included measured date) can be estimated through product of the probability of the integral value in a given interval with the number of sample points in that interval. The contour coefficient, determined by the distance between the cluster and the nearest neighbor cluster, is employed to judge the applicability of clustering analysis. The value of the contour coefficient ranges from −1 to 1. The closer it is to 1, the better, and the value of 0.5 is to achieve 75% fitness.

3. Results

This section presents the mechanical parameter values and cluster analysis results for six samples in vertical and horizontal bedding directions. It should be noted that the test results might be biased due to irregularities, potentially including outliers with significant individual deviations.

3.1. Porosity and Maceral

The distribution of pore diameters before and after water immersion is depicted in Figure 4. Samples contain both micro-pores (R < 1000 nm) and macro-pores (R > 10,000 nm).

The proportion of large pores (R > 10,000 nm) significantly increases with water immersion, whereas no substantial change is noted for smaller pores (diameter less than 10,000 nm). The application of a NaCl solution with 75% humidity results in a greater change in pore diameter compared to a MgCl solution at 44% humidity. Moreover, porosity increases to 0.16 with 75% humidity and to 0.12 with 44% humidity, relative to 0.08 in the dry sample. Thus, the pore structure is significantly altered by water immersion, with larger pores and increased porosity more readily observed under higher humidity conditions.

Maceral analysis conducted on three samples is summarized in

Table 1. Maceral composition of samples.

	Maceral Composition (Volume %)			Minerals (Volume %)
	Vitrinite	Inertinite	Liptinite	Clay	Monox	Others
Dry sample	90.0	6.2	--	2.6	0.6	0.6
Sample with 44% humidity	87.2	6.6	--	3.2	1.0	2.0
Sample with 75% humidity	83.0	8.2	--	4.6	2.2	2.0

.

The results indicate that macerals dominate, constituting more than 80% of each sample, followed by inertinite (more than 5%) and a mixture of clay and other minerals (approximately 5%). Notably, no liptinite is detected. Additionally, the proportion of macerals decreases with water immersion, while the proportions of inertinite and other minerals increase.

3.2. Experimental Results

This section focuses on the test results for six samples. These include vertical and horizontal tests of dry samples, as well as samples at 44% and 75% humidity.

3.2.1. Dry Sample

Figure 5 displays the results of nano-indentation tests conducted on dry samples. The hardness is observed to correlate with Young’s modulus, a relationship consistent with previous experimental findings [40].

In the horizontal direction, 100 indentation points are tested, with Young’s modulus ranging from 4.33 to 14.87 GPa, and hardness from 0.18 to 1.49 GPa. In the vertical direction, 130 indentation points are tested, with Young’s modulus from 3.68 to 10.38 GPa, and hardness from 0.22 to 1.26 GPa. Young’s modulus in the vertical direction is generally lower than in the horizontal direction.

3.2.2. Sample with 44% Humidity

Results of nano-indentation tests for a sample with 44% humidity in both vertical and horizontal bedding directions are shown in Figure 6, indicating that hardness correlates with Young’s modulus.

In the horizontal bedding direction, 100 indentation points were evaluated, revealing Young’s modulus range from 3.90 to 12.63 GPa and hardness between 0.19 and 1.06 GPa. Similarly, 100 indentation points were assessed in the vertical bedding direction, with Young’s modulus varying from 3.38 to 11.75 GPa and hardness from 0.20 to 1.33 GPa.

3.2.3. Sample with 75% Humidity

Figure 7 illustrates the outcomes of the samples exposed to 75% humidity. Similar to the previous case, the hardness and Young’s modulus relationship is evident.

In the horizontal bedding direction, 90 indentation points were examined, with Young’s modulus ranging from 3.87 to 9.04 GPa and hardness from 0.22 to 0.83 GPa. In the vertical bedding direction, Young’s modulus spanned from 3.55 to 8.29 GPa and hardness from 0.19 to 0.86 GPa, across the same number of indentation points.

3.3. Results of Cluster Analysis

This study grouped nanoindentation data from six samples using a hierarchical clustering method, forming a tree-like nested cluster structure to divide the data into different levels and clusters. The clusters were categorized into three groups: fracture (big pores), vitrinite, and inertinite. Fracture and pore were grouped together due to their larger proportion, while the minerals group was not assigned due to its smaller relative size.

3.3.1. Dry Sample

Analysis and discussion of the dry sample’s measured data are presented in Figure 8. The fracture group, representing only a small number of points (three in the vertical and four in the horizontal direction), contrasts with the vitrinite group, which comprises the largest proportion. The inertinite group falls in between in terms of quantity. Notably, the fracture group exhibits the lowest Young’s modulus (approximately 4 GPa), while the highest values, exceeding 8 GPa in both directions, are found in the inertinite group. The variability in Young’s modulus and hardness, particularly in the horizontal direction within the inertinite group, suggests variability due to the inclusion of some mineral data. Figure 8 shows the extracted correlation between Young’s modulus and hardness, demonstrating a positive correlation between these two properties. However, the fracture and inertinite groups display a negative correlation along the vertical direction. Meanwhile, all groups demonstrate a positive trend along the horizontal direction. Vitrinite achieves good fitting results in both directions, while the fracture and inertinite groups show poor performance.

3.3.2. Sample with 44% Humidity

The results for the sample with 44% humidity are presented in Figure 9. The fracture group is noted for having the smallest Young’s modulus and the lowest proportion. In contrast, the inertinite group is distinguished by the highest Young’s modulus. It is important to mention that outlier data present in the vertical direction should be excluded from further analysis, as these may be related to mineral data. The measured data for the inertinite group show less variability compared to the dry sample. When comparing with the dry sample, Young’s modulus for the inertinite group shows a significant decline, while a slight decrease is observed in the fracture group. No notable changes are detected in the vitrinite group. Additionally, the correlation between Young’s modulus and hardness alters following water immersion. Initially, a low R-squared value of 0.12 was recorded for the inertinite group, prompting the exclusion of outlier data to improve the fit. Changes in the extracted correlation are also noted: the negative correlation for the fracture and inertinite groups in the horizontal direction shifts to positive. Conversely, the positive relationship remains in the vitrinite group, which also shows a larger slope, indicating a strong dependence of Young’s modulus on hardness.

3.3.3. Sample with 75% Humidity

The measured data for the sample with 75% humidity are detailed in Figure 10. A notable difference in this case is the increased data points for the fracture group. The Young’s modulus for the fracture group is confined to a narrow range of around 4 GPa. The range for Young’s modulus in the vitrinite group narrows as well, spanning 4–7 GPa in the vertical direction and 4–8 GPa in the horizontal direction. Similarly, Young’s modulus for the inertinite group reduces to 7–9 GPa in the vertical direction and 8–10 GPa in the horizontal direction. A comparative analysis reveals that Young’s modulus values are generally lower than those observed in the dry sample. For the inertinite group in the horizontal direction, two outlier data points are removed for the inertinite group in the horizontal direction to achieve a higher R-squared value. In this 75% humidity scenario, all three groups exhibit a positive correlation with hardness. The vitrinite group further shows the largest slope. Across the three cases studied, the slope for vitrinite exhibits a negative correlation with water saturation, reflecting the dependence of Young’s modulus on hardness weakens with higher moisture content.

4. Discussion

4.1. The Applicability of Cluster Analysis

In this study, cluster analysis is utilized to categorize the data points into three groups: vitrinite, inertinite, fracture, and other minerals. The contour coefficients of all these cases are above 0.7 indicating a perfect fitness. The distribution of each group under varying experimental conditions is also presented in

Table 2. Component proportion calculated by cluster analysis.

		Dry		44% Humility		75% Humility
		H	V	H	V	H	V
Component proportion (%)	Vitrinite	88.4	91	91	93	85.7	83.9
	Inertinite	8.5	6	5	4	8.2	9.7
	Fracture	3.1	3	4	3	6.1	6.4

. Consistent with previous findings, the vitrinite group constitutes the largest proportion, exceeding 80%, while the fracture group has the smallest, less than 8%. These proportions change with water saturation levels: the proportion of the fracture group increases from 3% in the dry sample to 6% in the sample with 77% humidity. Moreover, the sample with 77% humidity is noted for having the smallest proportion of vitrinite but the largest fracture. This increase in fracture proportion can be attributed to the tendency of fractures to swell when exposed to water, resulting in a larger surface area. Nano-indentation tests, conducted on the surface of the samples, typically identify more fracture data at higher water saturations. However, the data for the sample with 44% humidity deviate from this trend, which may be due to factors such as experimental errors or inaccuracies in cluster analysis. The proportions derived from cluster analysis are validated against those obtained from maceral testing (Figure 11). High consistency is found in the cases of the dry sample and the sample with 77% humidity, whereas consistency is lower in the sample with 44% humidity. Overall, the results from cluster analysis align well with those from maceral testing, affirming the effectiveness of the clustering approach.

To further validate the applicability of cluster analysis and the accuracy of the measured data in this study, comparisons with prior research are presented in

Table 3. Comparisons of measured data with previous work.

		Dry
		H	V	Cai et al. [41]	Liu et al. [42]	Zhang et al. [24]
Young’s modulus (GPa)	Vitrinite	5–11	4–8	2–5	2–15	0.5–15
	Inertinite	11–15	8–10	3–9
Hardness (GPa)	Vitrinite	0.3–0.9	0.2–0.8	0.2–0.4	0.2–1.4	--
	Inertinite	0.4–1.4	0.7–1	0.4–1.4		--

. Cai et al. [41] employed nano-indentation to explore the properties of the vitrinite and inertinite groups, distinguishing the various components visually under a microscope. The ranges of Young’s modulus and hardness measured by Cai et al. [41] align closely with our values in the vertical direction. Additionally, the measured data from Liu et al. [24,42] and Zhang et al. [24] include our findings. These similarities underscore the effectiveness of cluster analysis for classifying measured data in this context.

4.2. Impact of Water Saturation on the Characteristics of Maceral Components

The mechanical properties of coal maceral components (vitrinite, inertinite, and chitin) vary, significantly affecting the macroscopic mechanical properties of coal seams. Traditional mechanical experiments, which are conducted at a macroscopic scale, often fail to distinguish and consider these maceral components. Micromechanical analysis using nano-indentation addresses this limitation by specifically exploring the characteristics of vitrinite and inertinite across various water saturations. The findings reveal that Young’s modulus and hardness of inertinite are consistently higher than those of vitrinite, both in dry conditions and under various levels of water saturation. The variation in micromechanical properties among different components is attributed to the molecular structure of plant lignocellulose, which forms under conditions of reduction and oxidation [26]. The vitrinite component, which contains more high-plastic organic matter, typically exhibits lower measured values [41].

Additionally, the presence of water significantly affects the characteristics of each component. The distributions of Young’s modulus and hardness for each component before and after water immersion are depicted in Figure 12, Figure 13 and Figure 14, illustrating both horizontal and vertical bedding directions. Water immersion notably decreases Young’s modulus. For the fracture component, the modulus decreases from 4.6–4.8 GPa in dry conditions to 3.4–3.6 GPa at 77% humidity in the horizontal direction, with a similar reduction observed in the vertical direction from 3.7–3.9 GPa to 3.2–3.4 GPa. Although both vitrinite and inertinite are organic matter, the modulus of inertinite decreases more than that of vitrinite. This disparity is largely due to the formation mechanisms of each group: vitrinite forms through the gelation of plant roots, stems, and leaves under water-reducing conditions, making it less sensitive to water. In contrast, inertinite originates from plant materials deposited in peat bogs and subjected to sericarbonization under relatively dry, oxidative conditions, rendering it more sensitive to the presence of water.

4.3. Influence of Water on Coal Mechanical Properties

As noted, the presence of water significantly reduces the value of Young’s modulus across all groups. For a detailed visualization, all measurements under varied water saturation conditions in both horizontal and vertical directions are depicted in Figure 15. It is observed that Young’s modulus exhibits a negative correlation with water content, and water presence lowers the slope in Young’s modulus versus hardness profile. This is particularly more pronounced at 75% humidity, indicating a reduced dependency between the two parameters. Notably, Young’s modulus of the fracture and inertinite groups shows minimal correlation with hardness, with the change primarily driven by variations in the vitrinite group.

Box plots before and after water immersion are illustrated in Figure 16 to provide clearer insight. These plots reveal some outlier data, possibly associated with minerals. All key statistical indicators, including the upper quartile, lower quartile, median, and mean value, decrease with water content, with a more pronounced decrease in the horizontal direction. Moreover, water presence also narrows the distribution of Young’s modulus.

The anisotropy ratios of mechanical parameters for three humidity conditions are presented in

Table 4. Anisotropy ratios of mechanical parameters for three humidity conditions.

	Dry	44% Humidity	75% Humidity
Anisotropy ratio of Young’s modulus	1.27	1.20	1.11
Anisotropy ratio of hardness	1.17	1.06	0.98

. For the dry sample, Young’s modulus and hardness in the horizontal bedding direction exceed those in the vertical bedding direction. This observation aligns with the findings reported in the literature [19,43]. Further, it is demonstrated that mechanical anisotropy is prevalent in coal and rock. This behavior can be attributed to the unique characteristics of coal, which differs from well-cemented sedimentary rocks due to its non-continuous, non-uniform, anisotropic, and nonlinear elastic nature. Under loads perpendicular to the bedding plane, coal demonstrates heightened deformation capability. As indicated in Table 4, the anisotropy ratios of both Young’s modulus and hardness gradually decrease with rising moisture levels.

4.4. Soften Mechanism of Coal after Immersion in Water

The mechanical characteristics of coal change after water immersion. For example, Ren et al. [44] tested the mechanical properties of typical Chinese bituminous coals with varied water saturation and found that the moisture mainly softened and lubricated the coal, thus reducing the compressive strength and elastic modulus. Yao et al. [45] also determined that the elastic modulus showed a negative exponential relationship with the moisture content. These observations can be explained by the findings in this work.

The indentation modulus significantly decreased following water immersion, as shown in Figure 13 and Figure 14. In the horizontal direction, the average indentation modulus declined from 7.5 to 5.1 GPa, and the moduli distribution became considerably narrower, with a range of from 2 GPa between the upper and lower quartiles for the dry sample compared to 1.5 GPa for the sample at 75% humidity. In the vertical direction, the average indentation modulus decreased from 6 to 4.4 GPa, with a slight narrowing of the modulus distribution. This substantial reduction in indentation moduli aligns with data reported in the literature.

Several factors contribute to this decrease: (i) an increase in porosity, where, as depicted in Figure 4, the proportion of large pores significantly expands after water immersion. Additionally, in the nano-indentation test, increased detection of fracture group data is observed; (ii) the dissolution of minerals, where outliers, initially characterized by high Young’s modulus, are prevalent in the dry sample but less so following water immersion. This trend is more pronounced in the horizontal direction. These high-value data points likely represent stiff minerals, and their decreased presence may result from mineral dissolution. For example, water adsorption into the coal matrix likely compromises the calcite mineral phase, leading to its weakening. Furthermore, matrix swelling generates stress that fractures the unswelling minerals. Thus, the coal sample experiences substantial weakening due to water adsorption, primarily through the dissolution of the calcite phase and the fracturing induced by swelling stress.

4.5. Application to the Field

The findings in this work can also give some insight into the theoretical and practical support for the study of CBM migration and extraction. This aim can be achieved with the assistance of the coupling model of reservoir deformation and gas flow. For example, Ye et al. [46,47] proposed a power-law seepage model to accurately characterize the impact of microevolution on extraction under multi-field coupling effects. Additionally, in our previous work, we have also determined that the micro-structure and micro-mechanical properties of the matrix significantly impact the gas flow in a porous medium [22,48,49].

Different hydraulic methods, such as hydraulic fracturing and hydraulic slotting, will lead to divergences in the water saturation of surrounding coal because of the disparity in operation time and parameters. The value of water saturation can be estimated with Darcy flow together with the two-phase flow equation. As indicated in this work, the micromechanical properties of coal can be significantly reduced, affecting the microflow characteristics of coal. Therefore, the gas extraction method can be optimized with different hydraulic methods, and gas extraction efficiency can be guaranteed.

In addition, the water saturation varies with the gas extraction process, and this change would lead to the variation of micromechanical properties of the coal matrix and, therefore, the micro-flow ability. The dependence of micromechanical properties on water saturation can be estimated with the results in this work while the variation in flow ability can be determined with previous work. Therefore, effective extraction management modes can be formulated in different extraction periods to delay the decay time of gas extraction concentration.

4.6. Limitations and Future Work

In this study, a nanoindentation test was conducted to explore the impact of water content on macroscopic properties. In the measurement, the varied water saturation states and bedding directions were conducted on different samples with a total of six samples employed. Even though the samples were collected from the same coal block, the anisotropy of the sample definitely affected the experimental results. Besides that, the test area is artificially selected, which inevitably leads to errors. Cluster analysis was utilized to establish relationships between numerous measured points and varied components. The current clustering analysis algorithm presents several limitations: (i) it assumes a normal distribution of Young’s modulus for each component, which may not hold true for certain minerals; (ii) it cannot address situations where there is overlapping of Young’s modulus values between different components; and (iii) the current classification may be inadequate as outlier data are detected. The influence of water saturation was examined using varied samples, and the heterogeneity of the samples was found to impact the results significantly. In the future, the development of a novel clustering analysis algorithm or another mathematical method is warranted. Such an approach should accommodate cases of non-Gaussian distributions, such as Weibull distributions, and should distinguish the contributions of each term in overlapping scenarios.

Only micro-scale analysis was conducted in this study; therefore, additional experiments should be performed to determine the impact of water saturation on the macroscopic properties. For instance, uniaxial or triaxial compression tests could be used to measure compressive strength. Furthermore, a method should be proposed to link the mechanical properties at micro and macro scales. The following steps may facilitate achieving this objective: (1) the TESCAN Integrated Mineral Analyzer (TIMA) could be used to acquire diverse mineral microstructures before and after water immersion within coal; (2) a combination of nano-indentation and clustering analysis could determine the variation of mechanical properties with different levels of water saturation; (3) a scale model upgrading approach should be developed to translate the elastic attributes of minerals from the nanoscale to the macroscopic scale. Besides this, a gas–water two-phase multi-physics coupling model is necessary to investigate the impact of the evolution of pore structure caused by water immersion on gas depletion characteristics. In this model, the water saturation can be estimated from the Darcy two-phase flow or storage model [6,50] and a theoretical model should be proposed to describe the impact of water immersion on matrix properties.

5. Conclusions

In the present study, six samples were selected to compare nanoscale mechanical properties under different humidity conditions. This study also examined the physical and micromechanical properties of coal using mineral composition tests, mercury injection tests, and nanoindentation tests. The key findings are as follows:

(1)

The measured data can be categorized into three groups: fracture, vitrinite, and inertinite, and the specified Young’s modulus for each group falls within the range reported in prior studies. Nanoindentation test results reveal a positive correlation between the elastic modulus and hardness, although this relationship does not hold for all components. Fracture and inertinite groups show little correlation, while a strong dependence exists for vitrinite, although water content reduces this dependence.

(2)

Water content adversely affects the elastic modulus and hardness. Additionally, the anisotropy ratios of these measures decrease progressively with increasing moisture. The emergence of larger pores, changes in the mechanical properties of sub-components, and mineral dissolution are likely contributors to these observations.

(3)

The response of mechanical properties to water immersion varies among sub-components. An increase in data associated with the fracture group is likely due to the appearance of larger pores. The mechanical characteristics of inertinite are particularly sensitive to water immersion, whereas those of vitrinite exhibit less sensitivity.

(4)

The sample heterogeneity and the randomness of the test area would lead to some errors in the experiment result. Additionally, the cluster analysis, based on the Gaussian distribution, may not be the best choice for data classification. As a future work, a method will be established to link the mechanical properties at micro and macro scales, and a gas–water two-phase multi-physics coupling model should be proposed to investigate the impact of water immersion on gas depletion characteristics.