#### 1. Introduction

Coal is a kind of porous solid medium with developed pore structure. The abundant pore structure in the coal body is not only a place for gas storage, but also a channel for gas production. The adsorption state of gas in coal makes the mechanical properties of gas-containing coal different from non-adsorption media. Gas-containing coal is a multi-phase porous medium with temporal and spatial variability, which is composed of pore fluid, matrix pores and micro-fractures. The distribution and connectivity of coal pore directly affect the migration and diffusion of gas. In the process of coal seam mining or gas drainage, the coal seamstress field, fissure field, and gas seepage field change. Fracture expansion and penetration of coal and rock mass caused by mining unloading will change the interaction between coal and gas.

A typical soft coal body has a smaller consolidation coefficient and a larger initial dispersion rate. This manuscript takes typical soft coal seams and contrasting hard coals as the research objects. Using scanning electron microscope, low-temperature nitrogen adsorption test and isothermal adsorption test, combined with fractal geometry theory, the pore structure characteristics of soft coal and hard coal and their influence on gas adsorption characteristics are studied. In order to quantitatively characterize the pore distribution characteristics of soft coal and hard coal, the mechanical properties of soft coal and the gas flow law in soft coal are studied. The research results of this manuscript will provide a theoretical basis for in-depth analysis of the adsorption/desorption mechanism of coalbed methane in soft coal seams and the formulation of practical coalbed methane control measures.

#### 2. Experimental

##### 2.1. Experimental Apparatus

The self-developed high/low-temperature pressure swing adsorption-desorption experimental system is shown in Figure 1. The experimental equipment mainly consists of an adsorption system, a gas desorption system, a refrigeration system, an electrical control system, and a computer data acquisition and processing system. The gas adsorption experiment adopts the pressure range is 0–8 MPa. The working temperature is 0–40°C.

The low-temperature nitrogen adsorption test uses the ASAP-2020 specific surface and pore size analyzer produced by Mircromeritics. The pore volume is less than 0.0001 cm3/g, the pore size analysis range is 0.35 to 500 nm, and the specific surface area analysis range is 0.0005 to 5000 m2/g. The pore size classification method defined by the International Union of Pure and Applied Chemistry (referred to as IUPAC) is used. Using the ΣIGMA scanning electron microscope produced by Zeiss, the acceleration voltage range of the instrument is 0.1–30 kV, and the magnification range is 12–500 kX. It can analyze the microstructure of powder, block, and film samples.

##### 2.2. Sample Preparations

The soft coal sample used in the test was taken from the Lvtang Coal Mine (LT) in Bijie District, Guizhou, China, and the hard coal used was taken from the Quanlun Coal Mine (QL) in Qinglong County, Xingyi City. The geographical location of the LT and QL is shown in Figure 2.

Each coal sample is not less than 1 kg. According to the China Coal Industry Standard  to prepare the coal sample for proximate analysis and gas adsorption experiment, the humidification process for coal samples is shown in Figure 3.

The data of proximate analysis of coal samples, coal hardiness coefficient, and initial gas diffusion velocity of coal are shown in Table 1. Select a small coal sample with a flat cross section with a particle size of 1 to 2 cm3 for low-temperature nitrogen adsorption test. It should be handled with care during operation. Table 1 data display that the firmness coefficient of soft coal is significantly lower than that of hard coal, and the initial rate of dispersal is greater than that of hard coal.

##### 2.3. Experimental Methods

Coal sample gas desorption process simulation was conducted by employing the experimental device shown in Figure 3. The gas desorption environment of the sample was always maintained at a temperature of 30 ± 1°C and a gas outlet pressure of 0.1 MPa during the measurement process, and gas desorption of the coal sample could be considered to be an isothermal and isostatic desorption process. The experiment is conducted following the steps:(1)The experimental coal sample is loaded into the coal sample tank.(2)The coal sample tank and the reference tank are fully degassed using a vacuum pump.(3)When the vacuum in the experimental system reaches 25 kPa, gas is introduced into the reference tank. When the gas pressure is stable, the coal sample tank and the reference tank are connected to conduct gas adsorption.(4)As gas adsorption balance in the coal sample is reached, the gas inlet valve is first closed, and the gas outlet valve is opened second to conduct the gas desorption experiment.(5)After the experiment is completed, the measured gas desorption amount is converted into volume in the standard state.

#### 3. Experimental Results

##### 3.1. Pore Microstructure Analyses

The coal sample from the Lvtang coal mine showed a microscopic breccia structure when observed under a microscope, as shown in Figure 4(a). Its characteristic is that the coal body is broken into particles of different sizes, some of which have more obvious edges and corners. The particles on the coal surface are mostly irregular polyhedrons with sharp edges and corners. It shows that the coal sample has poor plasticity and high brittleness. At the same time, it can be seen that a large number of irregular pores are developed on the surface of the coal sample, and the size of the pores is different. The existence and density of the pores indicate that the coal has a certain gas storage capacity. In addition, the existence of a large number of holes reduces the mechanical strength of coal, which is one of the reasons why soft coal is easily broken.

The surface of the coal sample in Quanlun Coal Mine is relatively flat, and a large, dominantly developed fissure can be seen to develop stably in the longitudinal direction. The fissure penetrates the entire coal surface in the visible range, as shown in Figure 4(b). The surface of the coal sample is distributed with some inorganic components such as point-like and pile-like clay materials. On the one hand, the presence of inorganic components increases the strength of the coal and acts as the skeleton of the coal; on the other hand, it destroys the uniformity of the coal and softens when exposed to water, which directly reduces the anti-destructive ability of the coal body itself.

##### 3.2. Specific Surface Areas and Pore Volume Characteristics

Two sets of soft coal experiment coal samples from LT and two sets of hard coal experiment coal samples from QL were selected, and a total of 4 sets of nitrogen adsorption tests were carried out. The pore volume characterization method adopts the BJH method, and the specific surface area characterization method adopts the BET method and the Langmuir method. The pore structure characteristics of the soft and hard coal surface are analyzed from different angles. The results of the low-temperature nitrogen adsorption test are shown in Table 2.

##### 3.3. Relationship between Adsorption/Desorption Curve and Pore Structure Characteristics

The shape of the different relative pressure sections of the adsorption isotherm reflects the physical characteristics of the coal surface and the relationship between the coal and gas. The relative pressure can evaluate the performance of the coal reservoir, especially the permeability of the coal. The low-temperature nitrogen adsorption/desorption curve of a typical soft and hard coal sample is shown in Figure 5.

##### 3.4. Fractal Geometric Characteristics of Coal Surface

The fractal dimension can be used to characterize the fractal characteristics of the pore surface of coal, and its numerical value can be obtained from low-temperature nitrogen adsorption test data. Calculating and analyzing from different angles, taking the adsorption capacity at the inspection point, the relationship between fractal dimension and adsorption capacity is as follows :where P is nitrogen partial pressure, MPa; Q is the adsorption capacity when the equilibrium pressure is P, cm3/g; P0 is saturated vapor pressure of gas adsorption, MPa; Df is fractal dimension, which characterizes the fractal characteristics of coal pore surface, dimensionless; and C is constant, dimensionless.

Taking the specific surface area of coal as an investigation point, the relationship between fractal dimension and specific surface area is as follows :where A is specific surface area of coal surface, m2/g; other parameter symbols have the same meaning as above.

In the low-temperature nitrogen adsorption experiment, a straight line can be obtained by plotting LnQ and LnA against Ln(LnP0/P), and the fractal dimension can be obtained from the slope of the straight line. According to formula (1) and (2), the size of the fractal dimension of the coal sample surface can be calculated, and the calculation results are shown in Table 3.

The data in Table 3 shows that the calculation results of formula (1) and (2) are slightly different, and the calculation result of formula (1) is slightly larger than that of formula (2). This difference may be due to the micropores or mesopores in the coal. The difference in the pore size of the micropores or mesopores results in the difference in the adsorption potential of the micropores for nitrogen, so that nitrogen molecules cannot completely and effectively fill all mesopores. The scoring dimension results of the two calculation formulas reflect the characteristics of coal pore structure to a certain extent. It can be seen from Table 3 that the calculation results of the surface fractal dimension of soft coal are between 2.12 and 2.35, the calculation results of the surface fractal dimension of hard coal are between 1.43 and 1.62, and the average surface fractal dimension of soft coal is 1.47 times that of hard coal. The larger the fractal dimension, the rougher the surface and the larger the specific surface area of coal pores. This also reflects that soft coal has more developed pores than hard coal.

##### 3.5. Characteristics of Coal Gas Adsorption

Constant temperature adsorption experimental data of soft and hard coal are shown in Table 4, and the constant temperature adsorption test curve is shown in Figure 6.

Comprehensive analysis of Table 4 and Figure 6 can be drawn that, under the same experimental conditions, the soft coal adsorption constants a and b are both larger than the hard coal adsorption constants. Soft coal has a larger saturated adsorption capacity than hard coal, and at the same time soft coal reaches the saturated adsorption capacity faster. It shows that the gas adsorbs and stays on the pore surface of the soft coal for a long time, the gas coverage is high, and the soft coal has a stronger ability to adsorb gas.

#### 4. Discussion

##### 4.1. The Influence of Pore Type on Gas Adsorption
###### 4.1.1. The Superposition of Adsorption Potential Energy in the Micropores

The abundant pore structure in the coal body is not only a place for gas storage, but also a channel for gas migration and diffusion. In particular, the presence of micropores greatly increases the surface area of the coal body. Since the size of the micropores is similar to the size of the gas molecules, the gas molecules are surrounded by the micropores. The adsorption force field in the micropores produces a superposition effect, so that the adsorption potential energy is greatly enhanced compared with the adsorption potential energy on the flat pore wall surface. Under low relative pressure, it has stronger adsorption attraction for gas molecules. Studies have shown that the adsorption potential is greatly enhanced in circular pores less than six molecular diameters and in slit pores less than two molecular diameters. The relationship between micropore adsorption volume and adsorption potential energy can be expressed as where φ is adsorption volume, cm3; φ0 is maximum adsorption volume, cm3; K is constant related to the micropore structure, dimensionless; and ε is adsorption potential energy, J.

In formula (3), ε2 reflects the superposition of the adsorption potential field on the micropore wall.

###### 4.1.2. Diffusion in Mesopores

The analysis of mesopores is closely related to the nitrogen adsorption/desorption curve, and the specific form of the adsorption hysteresis ring corresponds to different mesopore structures. The large range of the hysteresis ring indicates that the corresponding pores are smooth and the pores have high air permeability, which is conducive to the migration and diffusion of gas. The diffusion of gas in mesopores satisfy Fick diffusion, and the diffusion rate can be expressed aswhere is gas diffusion rate, kg/s; D0 is gas diffusion coefficient, m2/s; Ag is the gas diffusion area in the channel, m2; and is gas concentration gradient, kg/(m3·m).

In formula (4), “−” means that the direction of gas diffusion in the channel is opposite to the direction of the gas concentration gradient.

The relationship between the number of gas molecules and the adsorption residence time τ can be expressed aswhere n is the number of gas molecules that collide on the surface of the coal body in a unit time, unit; NA is Avogadro’s constant, which is 6.02 × 1023 mol−1; P is gas pressure, MPa; M is the relative molecular mass of adsorption, dimensionless; R is the ideal gas constant, which is 8.314 J/(mol·K); T is the thermodynamic temperature, K; and τ is adsorption residence time, S.

##### 4.3. The Influence of Fractal Characteristics on Gas Adsorption

The difference in the fractal characteristics of the coal surface reflects the change of the coal pore structure. The pore size of the soft coal gradually decreases with the increase of the fractal dimension of the coal surface. The change curve of the calculation result using formula (1) is shown in Figure 7.

The larger the fractal dimension, the higher the surface roughness of the coal and the increase of pores per unit volume. The radius of the pore channel decreases, which increases the pore volume and specific surface area. The gas adsorption sites provided by the pore surface of the coal increase, and the gas adsorption capacity is enhanced.

According to the theory of fractal geometry, there is the following relationship between the pore radius and the cumulative number in coal :where N is the total number of pores per unit volume of coal, unit; r is the radius of the pores in the coal, nm; Af is does not significantly include the proportional coefficient of Df; rm is maximum radius of the pore, nm; r0 is minimum radius of pore, nm; and λ is the ratio of the minimum and maximum pore radius.

From formula (7), the distribution density function of the pore radius in the coal body can be obtained:

From formula (8), the average radius of pores in the coal body can be obtained as

Analyzing formula (9), it can be obtained that the average radius of coal pores depends entirely on the fractal dimension Df of the coal, the upper and lower limits rm and r0 of the pore distribution in the coal, and the total number of pores in the porous medium per unit volume N.

In addition, upper and lower limits rm and r0 of the pore distribution in the coal body and the total number N of pores per unit volume of porous media are constant. Then, the average radius of the pore gradually decreases with the increase of the fractal dimension Df.
{"ft_lang_label":"__label__en","ft_lang_prob":0.9066714,"math_prob":0.9619137,"size":34629,"snap":"2023-40-2023-50","text_gpt3_token_len":7756,"char_repetition_ratio":0.20089531,"word_repetition_ratio":0.099910475,"special_character_ratio":0.21395363,"punctuation_ratio":0.1336142,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95378584,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-29T13:27:05Z\",\"WARC-Record-ID\":\"<urn:uuid:ff068e91-8bad-40bb-ac25-be82bb7fdb22>\",\"Content-Length\":\"345620\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b4c178d1-4729-4c9a-866f-e4bc4724d8a7>\",\"WARC-Concurrent-To\":\"<urn:uuid:6b8c6670-d4ad-4c51-8fd9-6d356267dc99>\",\"WARC-IP-Address\":\"104.18.40.243\",\"WARC-Target-URI\":\"https://www.hindawi.com/journals/ace/2021/1425227/\",\"WARC-Payload-Digest\":\"sha1:DC36AFQQISYKWITPYMY3A5NQZM2BAEYT\",\"WARC-Block-Digest\":\"sha1:QKAU2BKLE263O5E5UNG3IPPAUCQZ5GMV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510516.56_warc_CC-MAIN-20230929122500-20230929152500-00460.warc.gz\"}"}