Prediction of the Water ‐ Bearing Capacity of Coal Strata by Using the Macro and Micro Pore Structure Parameters of Aquifers

: Accurate prediction of the water ‐ bearing capacity of aquifers is crucial for protecting the surface ecological environment and ensuring safety during coal mining. In this study, a macro– micro combination was used to investigate the water ‐ bearing capacity of bedrock aquifers. At the micro ‐ level, the micro pore parameters of various sandstones were determined through cast sheet ‐ ing. At the macro ‐ level, the porosity and water absorption rate of various sandstones were deter ‐ mined experimentally. After that, a new index weighting method was proposed to comprehensively evaluate the water ‐ bearing capacity index of sandstone. According to this method, the water ‐ bear ‐ ing capacity of aquifers in the Guojiahe coalmine were evaluated. The research results revealed that the water ‐ bearing capacity of sandstone was mainly related to its pore connectivity, and the water ‐ bearing capacity of sandstone in the Luo’he and Zhi’luo formation was considerably greater than that in the Yan’an formation. The water bearing capacity of strata in the eastern part of the mining area is lower than that in the western part of the mining area. The research results can provide considerable money savings for coal mining and protect the ecological environment and ground ‐ water resources in the region. the model analysis found that the actual water capacity in there is no need to perform large ‐ scale pumping, geophysical before The results


Introduction
The increase in energy demand is mainly due to the increase in the population and industrialization [1][2][3]. The large-scale development of energy will lead to a violent conflict between man and nature [4][5][6][7]. Mining activities will inevitably cause surface subsidence, water waste and pollution, air pollution and a series of related problems, especially for the fragile ecological environment in some areas; moreover, mining easily causes injury and even death [8][9][10][11]. Water inrush is the main disaster of coal mining. Mastering the water content of strata is helpful to protect the groundwater from waste and pollution, and also to help the safe production of coal mining [8,[12][13][14].The water-bearing capacity of the strata is crucial for predicting sudden roof water rush accidents. Therefore, accurate and reliable evaluation of aquifer water distribution is critical. Many studies have focused on the water distribution evaluation of aquifers. Wei performed classification and partition clustering analysis on roof sandstone aquifers [15]. Wu used the graphic information system (GIS) information joint function to establish an aquifer water-rich evaluation model [5]. Chen used fuzzy clustering method combined with analytic hierarchy process (AHP) to divide the formation water abundance [16,17]. In fact, the water capacity of sandstone aquifer is closely related to its own pore structure. At present, there are many researches on the pore morphology and size of sandstone in the field of oil and gas [18,19]. The application of various technologies, including low field nuclear magnetic resonance (LF-NMR) [20], nuclear magnetic resonance (NMR) and mercury intrusion porosimetry (MIP) [21], X-ray diffraction (XRD) analysis, thin section, scanning electron microscopy (SEM) [22], small Angle neutron scattering (SANS) [23], X-ray computed tomography (XCT) [24,25], low temperature nitrogen adsorption (LTNA), rate-controlled mercury intrusion (RCMI) and high pressure mercury intrusion (HPMI) [26,27]. These experiments provide advanced methods for the study of the microscopic pore structure of sandstone. However, few scholars pay attention to the effect of pore structure on the waterbearing capacity of sandstone in the field of water control in coal mining.
Therefore, based on previous studies, this study considered the Guojiahe coal mine as an example. Sandstone-type water-bearing capacity has been comprehensively analyzed from the micro and macro perspectives. On the micro level, the plane porosity (PP), average pore diameter (APD), average specific surface (ASS), pore sorting coefficient (PSC), and throat homogenization coefficient (THC) of sandstone with various lithologies are determined through cast sheeting. On the macro level, the porosity and natural water absorption of various sandstone types are obtained by measuring pressure porosity and rock natural water absorption (NWA).
Through exploratory data analysis (EDA) of the indexes, it was found that there is a strong correlation between the indicators. Therefore, this paper proposes a new index weighting method that may well identify factors affecting the water-bearing capacity of sandstone formations. Grey relational analysis (GRA) method may be effective for evaluating the correlation between indicators and ranking different indicators according to their importance, but it cannot accurately provide quantitative weight assignment [28][29][30]. The new method considers the basis of the grey correlation coefficient, quantitatively estimates the change trend between sequences, considers the analysis of the nonlinear relation between multiple variables which is used to determine the grey correlation coefficient, and then establishes an objective evaluation based on the grey correlation coefficient matrix and computing feature vector according to different characteristics of the matrix vector value of sensitivity calculation [31][32][33][34]. On this basis, the model of sandstone water capacity is established. Then, the water-bearing capacity of groundwater was evaluated, and it was found that the water-bearing capacity of bedrock aquifer in the second mining area is weak, so large-scale geophysical exploration and water exploration and release work may not be conducted. The purpose of this study is to evaluate the water-bearing capacity of the bedrock strata in the study area through experiments on the water-bearing capacity of the strata, so as to ensure the safety of coal mining while protecting the groundwater resources from being wasted.

Background of the Study Area
The Guojiahe coal mine is located in Shanxi Province, China. Many folds and faults occur in the mining area and the groundwater resources are rich. In August 2020, during the mining of the 1309 working face in the first mining area, a serious water inrush accident occurred, with the maximum water inrush reaching 1200 m 3 /h. The maximum water depth of approximately 1 m and the cumulative water inflow was approximately 12.6 × 10 4 m 3 . The collapse of the hydraulic support for coal seam protection in mining reduced the transportation efficiency of the belt conveyor and caused an economic loss of nearly 10 million US dollars [35,36]. The second mining area to be mined in the future is located west of the Guojiahe coal mine. The thickness of the aquifer in part of the second mining area is similar to that of the 1309 working face. Therefore, to ensure coal mining safety, large-scale geophysical exploration was planned to be carried out in the second mining area, covering nearly 11 km 2 . Then, 80 boreholes were designed in the second mining area to extract water from the aquifer. The plan would cost a lot of time and money and cause irreparable damage to groundwater ( Figure 1). The main mining coal seam is the Jurassic 3 # coal seam, and the main roof aquifers are the Cretaceous Luo'he Formation and Jurassic Zhi'luo and Yan'an formations. The average thickness of the Luo'he Formation is 191 m, and its main lithology is brown-red sandstone with weak cementation. The average thickness of the Zhi'luo Formation is 42.5 m, and its main lithology is greyish green sandstone with medium sorting, secondary calcareous cementation and high hardness. The average thickness of the Yan'an Formation is 27.6 m and its main lithology is greyish black sandstone, which is poorly sorted and contains fine quartz gravel. In general, sandstone aquifers have large pores and locally developed fractures in water-rich heterogeneous layers ( Figure 2).
In this experiment, sandstone samples were obtained from the Luo'he, Zhi'luo and Yan'an formations to conduct porosity and water absorption measurement experiments to predict the water-bearing capacity of aquifers with various lithologies.

Experiment on the Pore Structure Characteristics
The water storage space of sandstone aquifer contains various pores of different origins. The primary pores are gradually compacted and filled during deposition, burial, and diagenesis [37][38][39]. Simultaneously, the particles are destroyed by dissolution, resulting in secondary pores and a change in the primary pore structure. The number, size, and connectivity between primary and secondary pores are critical factors affecting strata aquifers.
The microscopic observations of casting sheets can be used to effectively study the size, distribution, type, connectivity, characteristics, and geometric morphology of rock pores; average pore throat ratio; average pore radius; throat; coordination number; fracture length and width; and fracture rate [40,41]. These parameters determine the pore structure characteristics of the rock. Therefore, after the collection of the rock samples from the coal mine, cast thin sections were made with a rock pore casting instrument, and microscopic analyses were performed using an Axio Scope A1 Pol optical microscope. The microscopic pore characteristics of rocks were studied using the fractal theory [42].
The macro pore characteristics of sandstone can be investigated using porosity and NWA. Sandstone aquifer is a rock mass formed during geological evolution and is formed through the diagenesis of clastic materials. The water-bearing capacity of sandstone aquifer is closely related to porosity and NWA [43]. The Poropdp-200 porosity measuring instrument was used to measure the porosity of the samples ( Figure 3) [44,45]. The equipment constitutes a data control and analysis module, pulse attenuation control module, pressure pump, porosity measurement module, and high-precision pressure sensors with a pressure range of 0-200 psi, and the accuracy of ±0.1% of the full range was used in the study. Helium was used as the test medium. According to Boyle's law, the sample's pore volume was calculated using the helium pressure difference before and after the test to calculate its porosity. The NWA of rock is a critical physical and mechanical property and refers to the ratio between the maximum weight of water absorbed by a rock sample under atmospheric pressure and the specimen's drying weight (Equation (1)). The NWA size mainly depends on the number, size and opening degree of pores and fissures in the rock, which can effectively reflect the water-holding capacity of rock and the connectivity between rock pores. Before measurement, the rock samples to be tested were placed in a vacuum oven and dried at 110 °C for 24 h. Next, the samples were weighed to the accuracy of 0.1 g after cooling to room temperature. The weighed test pieces were then placed in the water tank. Subsequently, water was injected to 1/4 of the test pieces' height and filled to 1/2 and 3/4 places every 2 h. After 8 h, all the core samples were immersed. Next, the sample quality was measured every 8 h until no change was observed in the sample quality. Finally, Equation (1) was used to calculate the NWA of the sample.

Weighting Method of Eigenvector Based on the GRA
The structure and properties of sandstone determine its water-bearing capacity. The evaluation of the water-bearing capacity of sandstone essentially refers to the coupling of all the influencing indexes. Therefore, the determination of the index weight is the key to solving the multi-attribute decision-making problem. As an objective analysis method, GRA can be used to compare various influencing factors pairwise, observe the grey relational grade (GRG) between the reference and comparison sequences, evaluate the correlation between various indexes from the data level, and sort the correlation. However, combining all indexes and obtaining quantitative evaluation is difficult in GRG [31,46]. Therefore, based on GRA, an improved index weighting algorithm was proposed in which the index importance can be ranked by estimating the similarity between the data, and the evaluation matrix was established based on this. Then, the eigenvector of the matrix was calculated, and the evaluation model was finally established. The detailed steps of the algorithm are as follows.
First, the evaluation object and evaluation criteria are determined. The reference sequence is recorded as After standardizing the comparison sequence, according to Equation (2), the following evaluation matrix (2) is established: Second, using Equation (3), the grave correlation coefficient (GCC) was calculated as follows: Then, using Equation (4), we calculated the GRG of each evaluation index.
The relational degree sequence of the evaluation object is established through GRG, and the relational degree is sorted. The larger the GRG is, the better the correlation is.
Next, the evaluation matrix containing all the indexes was established. The relation degree of the level set, ij a , is closely related to the judgement index and is determined using ( , ) G n i .
Next, using Equation (7), the eigenvector corresponding to each matrix is calculated as follows: where i W is the influence intensity of a comparison sequence on the reference sequence as well as the weight value of the factors in the comparison sequence. To ensure the validity of Equation (7), the matrix completed through calculation is tested for consistency (Equation (8)).
The consistency test refers to determining the allowable range for judgement matrix A. The unique nonzero characteristic root of the n × n consistency matrix is n. The largest characteristic root of the n × n positive matrix,  , is greater than or equal to n, if and only if  = n, then matrix A is consistent.
When CR < 0.1, the judgement matrix passes the consistency test. Thus, the weight distribution is reasonable.

Measurement of Pore Structure Parameters
In this case, 18 sandstone slices with various physical properties were selected for analysis. The pore size and connectivity of the samples were determined by measuring the PP, APD, ASS, PSC and THC of the samples. The PP refers to the percentage of pore and throat area in the total area of the slice. The equivalent area circle diameter represents the APD. The ASS relates to the ratio of pore surface area to volume or the ratio of equal circle surface area to volume. The THC is the average pore diameter divided by the maximum pore diameter. Figure 4 displays the microscopic structures of the samples. Figure 5 shows an SEM image of the samples.
The minerals of the sandstone in the Luo'he formation are dominated by quartz and feldspar, with a particle size of 500-1000 μm. These are subangular, with poor roundness, poor sorting and pore cementation (Figure 4a). Intergranular pores are developed, and pore throat is large (Figure 5a). Feldspar dissolution occurs, and a large amount of kaolinite is formed (Figure 5b).
The porosity of the sandstone in Zhi'luo and Yan'an formations is less than that in the Luo'he formation, indicating their poor packing pattern and intergranular space (Figure 4b,c). Mineral composition mainly constitutes quartz and feldspar. The particle size is mostly between 250 and 500 m, with pore type cementation and particle support, and some pores are filled with organic matter (Figure 5c,d). The quartz grains are granular aggregate, with calcite cementation (Figure 5e).

Macro Pore Characteristics of the Aquifer
In this experiment, 18 groups of core samples were selected to measure the porosity and NWA. The sampling depth of sandstone in the Luo'he formation was 460-570 m; that in the Zhi'luo formation was 750-810 m, and that in the Yan'an formation was 810-890 m. According to the differences in depth, the overburden pressure gradient was approximately 328.08 psi/m. Table 2 presents the porosity measurement data of the sandstone core samples from various formations. The average porosities of the Yan'an, Zhi'luo and Luo'he formations were 8.48%, 14.50% and 21.89%, respectively. The experimental results of NWA are presented in Table 3. The NWA rates of sandstone in the Luo'he, Zhi'luo and Yan'an formations were 7.42-7.63%, 5.2-5.4% and 4.54-4.68%, respectively, with average values of 7.53%, 5.31% and 4.6%, respectively.

Information Fusion of Micro Pore Parameters
Seven factors, namely NWA, porosity, PP, APD, ASS, PSC and THC, were used to establish the calculation model for sandstone water-carrying capacity.
Considering PP, APD, ASS, PSC, THC, porosity and NWA as reference sequences, the GCC of each index was calculated based on Equation (4). The GRG calculation of the evaluation index, the GCC of each index and the relationship between the comparison and reference sequences are illustrated in Figure 6. Considering PP as the comparison sequence, the sensitivity of each factor to PP is as follows:

Porosity>THC>PSC>NWA>ASS>APD
Assuming APD as the comparison sequence, the sensitivity of each factor to APD is as follows:

NWA>Porosity>THC>PP>PSC>ASS
Considering ASS as the comparison sequence, the sensitivity of each factor to ASS is as follows:

PP>Porosity>PSC>THC>NWA>APD
With the PSC comparison sequence, the sensitivity of each factor to PSC is as follows:

THC>PP>Prosity>NWA>APD>ASS
Assuming THC as the comparison sequence, the sensitivity of each factor to THC is as follows:

Prosity>PP>NWA>APD>PSC>PP
Assuming porosity as the comparison sequence, the sensitivity of each factor to porosity is as follows:

PP>THC>NWA>PSC>APD>ASS
With NWA as the comparison sequence, the sensitivity of each factor to NWA is as follows:

APD>THC>Porosity>PP>PSC>ASS
According to Equation (5), the GRG of each evaluation index is as follows: According to differences between the GRG values of each index, a nine-level scaling method was established (Table 4), and a judgement matrix A was established based on Table 4. The judgement matrix A is presented in Table 5. Table 4. Five-level scale method improved using the GRG.

Scale
Meaning Expression of the GRG 1 The two factors have the same importance 0 < G(n,i)-G(n,j) < 0.01 2 One factor was slightly important than the other 0.01 < G(n,i)-G(n,j) < 0. 3 3 One factor is important to other factors 0.03 < G(n,i)-G(n,j) < 0.06 4 One factor is more important than other factors 0.06 < G(n,i)-G(n,j) < 0.09

5
One factor is much more important than the other factors G(n,i)-G(n,j) > 0.09  Equation (9) is the evaluation model of the water-bearing capacity of sandstone. The water-bearing capacity of three sandstone types in the study area was calculated and evaluated using this expression (Table 6). According to Table 6, the average water-bearing capacity index of sandstone in the Luo'he, Zhi'luo and Yan'an formations is 0.917, 0.423 and 0.076, respectively. The comparison index revealed that the water-bearing capacity of sandstone in the Luo'he and Zhi'luo formations was higher than that in the Yan'an formation.

Micro Pore Structure Parameters of Various Types of Sandstone
The microscopic pore parameters of various groups of sandstone differ considerably due to the differences in their sedimentary environment, tectonic stress and burial depth. Figure 7 displays the diagram of the pore structure of the sample. The graph provides an intuitive comparison of the differences and trends of the same pore structure parameters of various samples. Figure 7a reveals that the PP of various formation samples exhibits obvious step changes, which indicates that the sedimentary environments of the Luo'he, Zhi'luo and Yan'an formations differ considerably, and their pore content is different. In all the formations, the coefficient of variation of PP of different samples is 0.1599 at most, indicating that PP of different samples is stable in the same stratum.
As described in Figure 7b, the APD of Luo'he sandstone is considerably larger than that of the Zhi'luo and Yan'an sandstone, whereas the APD of Zhi'luo and Yan'an sandstone is similar. Thus, the pore connectivity of the Luo'he formation is considerably superior to that of the Zhi'luo and Yan'an formations. In all the formations, the coefficient of variation of APD of different samples is 0.074 at most; APD fluctuations in the same formation do not exceed 8 μm. Figure 7c illustrates that the ASS of the sandstone in the Luo'he formation differs less from that of the sandstone in the Zhi'luo formation, whereas the ASS of Yan'an sandstone is considerably smaller than Luo'he and Zhi'luo sandstone. The particles of the Luo'he and Zhi'luo formations are rough, with poor roundness and strong adsorption capacity. In all formations, the coefficient of variation of ASS of different samples is 0.093 at most; ASS fluctuations in the same formation do not exceed 0.13 μm −1 .
As displayed in Figure 7d, the PSC of the sandstone in the Luo'he formation is large. The PSC between Zhi'luo and Yan'an sandstone has a few differences. The sandstone of the Luo'he formation exhibits superior seepage capacity compared with that of the Zhi'luo and Yan'an formations. In the same formation, the coefficient of variation of PSC of different samples is no more than 0.0456, indicating that the PSC of the same layer is similar. Figure 7e displays the variation trend of the THC, which is similar to the variation trend of Figure 7a. The THC of various formation samples exhibits considerable step change. In the same formation, the coefficient of variation of THC of different samples is no more than 0.0682, indicating that the THC of the same layer is similar. The microscopic pore structure parameters of different samples in the same formation are similar, and the microscopic pore parameters of the samples in different formations show large differences. Therefore, sandstone in the same formation can be considered to belong to the same category when calculating the water-bearing capacity. Figure 7f displays the radar chart of characteristic parameters of the pore structure test. The variation trends of various structural parameters among all the samples are generally similar, which indicates that PP, APD, AAS, THC and PSC are closely related. A strong correlation exists between the parameters. Therefore, the advantages and disadvantages of the reservoir space can be evaluated through comprehensive information fusion according to the similarity of the five parameters.   Figure 9 displays the time-varying fitting curves of NWA of the three types of sandstone. The blue, green and red curves represent sandstones in the Luo'he, Zhi'luo and Yan'an formations, respectively. The points in Figure 9 represent the experimental data, and the curve represents the relevant results. The fitting effect is excellent, indicating that the experimental results are accurate. The NWA rate of the sample increased rapidly in the initial 48 h and remained stable during the next 48 h. After 64 h, the NWA rate did not change. Therefore, the experimental time was set for 72 h.

Macro Pore Structure Parameters of Various Types of Sandstone
The final experimental results revealed limited difference in the samples from Luo'he and Zhi'luo formations, both of which are high-quality aquifers. The NWA rate of the samples from Yan'an formation was inferior; therefore, it was not considered the main aquifer.

Evaluation Model of Formation Water-Bearing Capacity in the Guojiahe Coal Mine
The established water-bearing capacity model was used to measure the water-bearing capacity. The thickness statistics and calculation results of various types of sandstone in the study area are displayed in Table 7. Next, the contour map ( Figure 10) was drawn to comprehensively evaluate the water-bearing capacity of 3 # coal roof. -2  211  185  24  273  G17-5  170  32  30  171  G5-3  224  124  79  264  bk-1  308  32  4  296  G6-1  145  31  20  147  bk-2  292  24  34  281  G6-2  139  27  16  140  bk-3  308  41  10  300  G6-3  142  29  12  143  bk-4  348  165  77  395  G6-4  153  55  45  167  c1  365  53  11  358  G6-5  240  51  29  243  C9  190  31  22  189  G6-6  294  41  20  289  c10  237  47  17  238  G7-2  143  50  37  155  c11  281  46  18  279  G7-3  360  46  18  351  C14  200  24  20  195  G7-5  159  34  10  161  C15  180  42  6  183  G8-3  201  42  28  204  C17  228  33  14  224  G8-4  329  30  4  315  C21  171  36 22 174  Figure 10a presents the contour map of cumulative thickness of 3 # coal roof aquifer in the study area. In the 1309 working face water inrush, the aquifer thickness was 380 m, and its maximum thickness was large. In the study area in the east, a piece of aquifer thickness was a >400 m area (red rectangle). If the region is in high-risk areas, drilling should be performed in advance before pumping water, which is not only costly but also destroys the groundwater resources and affects the ecological balance of the region. Figure 10b displays the contour map of equivalent thickness of coal roof aquifer in the third research area and reveals the water inrush that occurred in the 1309 working face, with aquifer thickness of up to 330 m, which is similar to that presented in Figure  10a. By contrast, in the east, the red rectangle area within the aquifer thickness decreased to 250 m and was less dangerous primarily because the aquifer in the area of Yan'an group was large and thick. The water capacity was weak and the impact on mining was small. When mining in this area, geophysical exploration surveys can guarantee safety.

Conclusions
The following conclusions can be drawn from the study: (1) The results of the microscopic experiment showed that the APD and PSC of Luo'he formation sandstone were larger than those of Zhi'luo formation sandstone, but the APD and PSC of Zhi'luo and Yan'an formation sandstone do not differ considerably. The pore connectivity of Luo'he formation sandstone was much better than that of Zhi'luo and Yan'an formation sandstone. The Luo'he formation is the main aquifer in this region.
(2) The results of the macroscopic experiment revealed that the average porosity of Luo'he formation sandstone was 7.39% higher than that of Zhi'luo formation sandstone and 13.41% higher than that of Yan'an formation sandstone. The Luo'he and Zhi'luo formations exhibit weak compaction, develop pores and have strong water-bearing capacity. The porosity of the Yan'an formation is low, and its water-bearing capacity is weak. In addition, the NWA difference between sandstone in the Zhi'luo and Yan'an formations was 0.62%, and the difference between sandstone in the Luo'he and Zhi'luo formations was 2.31%. The water-carrying capacity of the sandstone in Luo'he and Zhi'luo formations was considerably higher than that of the sandstone in the Yan'an formation.
(3) An objective weighting model based on the similarity between indexes was proposed. This model was used to analyze pore structure parameters of various formations in the Guojiahe coal mine. The calculation model of water-bearing capacity of various formations was established. According to this model, the water-carrying capacity of 3 # coal roof in the study area was analyzed. The results of previous mining studies indicated that there is a large-scale area with strong water inrush risk in the east of the study area, which is prone to water inrush if normal mining continues in the future. However, according to the model analysis in this paper, it was found that the actual water capacity in this area is medium, and there is no need to perform large-scale pumping, drilling or geophysical exploration before mining. The research results can save money for coal mining, which is beneficial for protecting the ecological environment and groundwater resources.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.