Fractal Dimension and Nuclear Magnetic Resonance Characteristics of Surfactants for Coal Gas Desorption

Abstract

In this paper, the fractal dimension of coal surfaces was calculated using the fractal theory, and the influence of different surfactants on the fractal dimension of coal surface was studied. Six kinds of sustainable and traditional surfactants used in coal gas desorption processes were compared and analyzed. We used mineral gas fertilizer coal from Huainan Liuzhuang, China, as the research object and studied sodium dodecyl benzene sulfonate (SDBS), cohol diethanolamide (CDEA), nonylphenol polyoxyethylene ether (NP-10), tea saponin, sucrose ester and rhamnolipid surfactants used to modify coal. The methane adsorption capacity of coal before and after surfactant modification was measured by low field nuclear magnetic resonance methane adsorption, and Langmuir volume and Langmuir pressure were obtained according to the Langmuir fitting equation. The results showed that from the perspective of fractal dimensions, the best surfactant in the context of sustainability (in order) is rhamnolipid, CDEA, tea saponin, sucrose ester. According to the two important parameters V_L and P_L in the Langmuir equation, the coal sample modified by sucrose ester had the strongest gas adsorption capacity. According to the numerical analysis of the surface fractal dimension D_S of the coal modified by surfactants, the soluble organic matter in the raw coal samples dissolved, and the micropore morphology evolved to become mesoporous or macroporous, which is more favorable for desorption. The coal samples modified by rhamnolipid and SDBS had the strongest gas desorption ability.

1. Introduction

Since Mandelbort first proposed the concept of fractals in 1975 ([1]), fractal theory has become a powerful tool to analyze the geometric and structural characteristics of surface and pore structures ([2,3,4]). A fractal dimension is a term used in the mathematics field of geometry to provide a logical statistical index of a pattern’s level of complexity ([5]). In order to identify relationships between surface structure and scaling behavior and performance, such as frictional behavior, fractal dimensions are being used more and more in recent years ([6]). Although the mechanisms of gas adsorption, desorption, diffusion and other physical and chemical processes in coal seams are different, they have one thing in common, that is, the surface irregularity of coal samples has an important impact on these mechanisms ([7,8]). As the quantitative characterization and basic parameter of fractals, the fractal dimension which is an important parameter in fractal theory, can describe the complexity and irregularity of surfaces ([9,10,11]). There are many calculation methods, among which the gas adsorption method is a more common method. The Frenkel–Halsey–Hill (FHH) theory was used to analyze the adsorption isotherm to obtain the fractal dimension ([12,13]).

China is rich in coal resources, which are distributed in all provinces except Shanghai, but the distribution is extremely uneven. Up to 2018, the accumulative amount of coal resources in China has reached 2.01 × 10¹² t, including 0.23 × 10¹² t in the eastern belt, accounting for 11.4% of the country’s reserves; 1.52 × 10¹² t in the central belt, accounting for 75.6%; and 0.26 × 10¹² t in the western belt, accounting for 12.9% (see [14]). Coal is a kind of porous solid material with complex pore structures and surface fractal characteristics ([15,16,17]). Coal seams contain a lot of adsorbed gas, which is one of the main factors leading to mine outbursts and gas explosions. Studies have shown that the gas adsorption process of coal is mainly physical adsorption, and its adsorption capacity mainly depends on physical structures such as pore volume and pore surface ([4,18,19,20,21]). At present, many scholars have studied the modification mechanism (mainly wetting mechanism) of surfactants on coal ([22,23]), but there are relatively few studies on the influence of surfactant on the adsorption and desorption characteristics of gas in coal and its surface structure from the perspective of sustainable investment and environmental protection.

Coalbed methane mainly exists in the pores of coal in an adsorbed state. Existing studies mainly used high-pressure isothermal adsorption testing methods or coal volumetric methods to measure the adsorption and desorption performance of coal towards gas including electromagnetic methods ([24,25]), the Stehfest numerical inversion algorithm ([26]), X-ray diffraction analysis ([27]), surface functional group analysis ([28,29]), etc. However, these methods cannot continuously and dynamically detect the methane adsorption capacity at each pressure point. Nuclear magnetic resonance, as a new nondestructive testing technology, is based on the interaction of an external magnetic field, hydrogen nuclear spin of the test sample and radio frequency pulses (see [30,31,32] and their related reference). By establishing the scaling relationship between methane mass and 1 H nuclear magnetic resonance signals, it can realize the quantitative measurement of methane adsorption under the same temperature and different pressures, which is a new method for real-time, in situ and dynamic measurement of methane adsorption of coal ([33,34]).

Table 1. Summary of most relevant research.

Study	Fractal Dimension	Coal Physical Structures	Surfactant on Coal	NMR
Ren et al. (2022) [3]	√	√
Yuan et al. (2022) [4]	√	√
Zhao et al. (2021) [33]	√	√		√
An et al. (2018) [22]			√
This study	√	√	√	√

shows the differences between the existing literature and this study.

In recent years, the development of sustainable energy, including solar and wind, ushered in a good opportunity ([35,36,37,38,39]); however, as the main traditional energy, coal still occupies the main share of the energy market ([40,41]). How to use coal more efficiently, more cleanly, in a more environmentally friendly manner and sustainably is still an important topic. In [42], the impact of surfactants on coals was evaluated, and their findings demonstrated that surfactants significantly improved coal wetting performance. By using a commercial bubble analyzer, [43] examined the fluctuation in bubble size under various aqueous conditions, including saline and surfactant solutions, with varying gas injection rates. More studies related to surfactants can be found in [44,45,46], etc. In this paper, six kinds of surfactants (namely sodium dodecyl benzene sulfonate (SDBS), cohol diethanolamide (CDEA), nonylphenol polyoxyethylene ether (NP-10), tea saponin, sucrose ester and rhamnolipid) used in coal gas desorption processes are compared and analyzed from the angle of sustainable investment and environmental protection.

In this paper, surfactants with good wettability, dispersibility, stability, safety and are environmentally friendly were selected to treat coal samples. Supercritical CH₄ was used to carry out low-field nuclear magnetic resonance isothermal adsorption tests and the FHH method was used to calculate the fractal dimension of the coal. Combined with the results of the gas adsorption experiment, the influence of different surfactants on the fractal dimension of coal surfaces was analyzed.

2. Experimental Methods

2.1. Preparation of Coal Sample

The coal sample was collected from the Huainan Liuzhuang Mine, China, and the vitrinite reflectance and industrial analysis were carried out (see [4]). The basic parameters of the coal sample are shown in

Table 2. Basic parameters of coal sample.

Sample Mine	Depth/m	Coal Type	Metamorphic Stag	Ro,max/%	Mad/%	Aad/%	Vdaf/%	Fcd/%
Huainan Liuzhuang	607	Gas fertilizer coal	III	0.87	1.83	14.44	33.38	50.35

.

After crushing the original coal sample, the coal powder with a particle size of 60~80 mesh was screened out, which was placed in distilled water and different modified solutions, soaked for 48 h, and stirred every 12 h to make the solution fully contact and react with the coal sample. After the coal sample was fully reacted with the modified solution, distilled water was used for multiple washes to avoid the influence of reagent precipitation on the test results. After cleaning and filtering, the coal sample was dried in a drying box at 60 ℃, aliquoted by weight, bagged and sealed, and numbered for use. For the convenience of reading,

Table 3. Abbreviations and symbols.

Notations	Meaning	Notations	Meaning	Notations	Meaning
SDBS	sodium dodecyl benzene sulfonate	Ro,max	maximum reflectance of vitrinite	Fcd	air-dried basis fixed carbon
CDEA	cohol diethanolamide	Mad	air-dried basis moisture	LD50	lethal dose, 50%
NP-10	nonylphenol polyoxyethylene ether	Aad	air-dried basis ash
CH4	methane	Vdaf	air dried basis volatile

lists the abbreviations and symbols used in this paper.

2.2. Preparation of Surfactants

According to the wettability, dispersibility, stability and other performance requirements of surfactants, and in line with the selection principle of safety, high efficiency, economy and convenience, we selected six commonly used surfactants as the main agents of this experiment. According to previous studies, when the concentration of surfactant solution reaches a certain value, the surfactant solution will wet the coal particles. Therefore, the surfactant concentration was set at 0.5 wt% in this paper. The selected six surfactants’ types and basic properties are shown in

Table 4. Types and basic properties of surfactants.

No.	Main Component	Ion Type	Status	Performance and Safety
1	Nonylphenol polyoxyethylene ether (NP-10)	Non-ion	Colorless, transparent liquid	Easy to dissolve in water with good wetting, emulsifying, dispersing and leveling properties, and low toxicity (with LD50 ≤ 2000 mg).
2	Sodium dodecyl benzene sulfonate (SDBS)	Anion	White, solid flakes	Difficult to volatilize, soluble in water to form a translucent solution. In alkali solutions, dilute acids, or hard water, it is chemically stable and slightly toxic (with LD50 ≤ 1260 mg).
3	Tea saponin	Non-ion	Fine yellowish powder	Insoluble in cold water, slightly soluble in warm water, easily soluble in aqueous ethanol. With good emulsification, has dispersion, foaming, wetting and other functions. Natural extraction, safe and non-toxic (with LD50 ≥ 7940 mg).
4	Cocolate diethanolamide (CDEA)	Non-ion	Thick, yellowish to amber liquid	Easy to dissolve in water, with good foaming, foam stability, penetration, decontamination, hard water resistance and other functions. Synthesized from coconut oil as raw materials, safe and non-toxic (with LD50 ≥ 12,200 mg).
5	Sucrose ester	Non-ion	White powder	Slightly soluble in water, soluble in ethanol, harmless to human body, good emulsification of oil and water, does not stimulate the skin and mucosa, non-toxic (with LD50 ≥ 30,000 mg). No pollution, and completely biodegradable.
6	Rhamnolipid	Anion	Pale yellow paste	It is soluble in methanol, chloroform and ether, and shows good solubility in alkaline aqueous solutions. Both good chemical and biological characteristics. It has good wetting, emulsifying, dispersing and foaming properties. It can be used under extreme conditions of temperature, pH and salinity and is non-toxic (with LD50 ≥ 31,500 mg) and biodegradable.

Note: LD₅₀ is the abbreviation for “lethal dose, 50%”. LD₅₀ is an acute toxicity indicator. A lower LD₅₀ is indicative of increased toxicity, and the higher LD₅₀ value the safer the surfactant is.

.

Figure 1 shows the six surfactants’ LD₅₀ values. In the context of sustainable considerations, SDBS and NP-10 are not sustainable surfactants because of their toxicity, and the safest surfactant is rhamnolipid, then sucrose ester, CDEA, and finally tea saponin.

2.3. Low Field NMR Methane Adsorption Experiment

Gases are mainly adsorbed into pores in coal. Combined with the nuclear magnetic resonance theory, it is known that the transverse relaxation time T₂ of coal seam gas is proportional to the radius r of the coal pores. In the T₂ spectrum curve of coal seam gas adsorption, each T₂ time corresponds to a gas signal amplitude on the longitudinal axis, and the NMR spectrum amplitude is proportional to the measured gas amount in the sample. Therefore, each T₂ value can be used to correspond to the superposition of gas signal amplitudes, namely, the T₂ spectral curve amplitude integral (i.e., peak area) represents the actual adsorption and desorption amount of gas in the coal, and this characteristic parameter is used to quantitatively study the law of gas adsorption in coal.

A low-field NMR analyzer (see Figure 2) was used to conduct methane adsorption experiments on the coal samples. Five pressure points were selected within the range of 0–6 MPa. Under the condition of a constant temperature of 30 °C, isothermal adsorption tests were conducted on the coal samples according to the measurement parameters in

Table 5. NMR adsorption measurement parameters.

Pressure/Mpa	0~2	2~3	3~4	4~5	5~6
Waiting time /ms	3000	3000	3000	3000	3000
Number of echoes	32	32	32	32	32
Echo time /ms	0.2	0.2	0.2	0.2	0.2
Stacking number	32	32	32	32	32

to analyze the dynamic change process and nuclear magnetic resonance characteristics of methane adsorption into coal.

We used mineral gas fertilizer coal from Huainan Liuzhuang in China as the research object and studied six surfactants used to modify coal. The methane adsorption capacity of the coal before and after surfactant modification was measured by low-field nuclear magnetic resonance methane adsorption experiments, and the Langmuir volume and Langmuir pressure were obtained according to the Langmuir fitting equation.

3. Results and Discussions

3.1. NMR Characteristics of Coal Gas Adsorption

3.1.1. Marking Equation Establishment

The label equation was established by conducting NMR measurements of pure methane under different pressures and the conditions of temperature set in the experiment, obtaining the total semaphore of methane in the reference chamber under pressure, calculating the methane mass according to the known volume of the reference chamber, and establishing the relationship between the T₂ spectral curve amplitude integral (i.e., peak area) and the methane mass. The conversion of the methane signal amplitude and mass was realized.

According to the selected measurement parameters, the methane quantity under the set pressure was injected into the reference chamber. When the pressure was stable, NMR measurements were performed on pure methane under different pressures to obtain the nuclear magnetic T₂ spectrum of methane.

As can be seen from Figure 3, the T₂ spectral peak area of pure methane increased with the increase in pressure, and the peak point of the spectral peak gradually moved towards the direction of increasing relaxation time. This phenomenon can be explained as follows: the relaxation characteristics of methane are mainly spin-spin. With the increase in pressure, the mean free path of methane molecules decreases, resulting in the increase of the relaxation time of methane in the free state.

According to the obtained nuclear magnetic T₂ spectrum of methane and the temperature, pressure and known reference chamber volume recorded during the experiment, the mass of methane under each corresponding pressure was calculated using the gas equation of state (

Table 6. NMR test results of pure methane.

Pressure	Peak Area	Methane Mass/mol
0.64	1859.494	0.010483977
1.15	3151.737	0.018838396
1.98	5333.893	0.032434804
3.08	8254.245	0.05045414
4.43	11,880.851	0.072568779

), and the marked conversion equation of methane was established (Figure 4). As can be seen from Figure 4, the peak area of methane had a good linear relationship with methane mass (R² = 0.9999).

3.1.2. Analysis of NMR Spectroscopy Test Results of Coal Gas Adsorption

At the set pressure point, the methane in coal was measured by NMR. According to the obtained methane nuclear magnetic T₂ spectra, the coal samples treated with raw coal and distilled water were compared to analyze the methane adsorption characteristics and migration rules of coal samples treated with different surfactant solutions at the pressure point. Therefore, the methane adsorption process of samples under pressure points in the low-pressure range of 0–2 MPa and the high-pressure range of 5–6 MPa were selected as examples for analysis. The T₂ spectra results are shown in Figure 5 and Figure 6.

As can be seen from Figure 5 and Figure 6, the T₂ spectral curve in the process of coal sample gas adsorption had a three-peak structure, marked as Q₁, Q₂ and Q₃ from left to right, and the relaxation time was around 0.1~1 ms, 10 ms and 100~1000 ms. Combined with the test results of the free-state gas NMR spectra in Figure 4, it can be determined that Q₁, Q₂ and Q₃ represent the adsorption, free and free gas spectra peaks, respectively.

In the low-pressure range of 0–2 MPa, combined with the nuclear magnetic T₂ spectra in Figure 5, it can be seen that the peak signal amplitude of Q₁ of coal samples treated with tea saponin was the largest, while that of coal samples treated with SDBS was the smallest. In the high-pressure range of 5–6 MPa, combined with the nuclear magnetic T₂ spectra in Figure 6, it can be seen that the peak signal amplitude of Q₁ showed a small increase, but the peak signal amplitude of raw coal Q₁ increased the most.

It can be seen from the experimental results that under the action of a surfactant solvent, the growth amplitude of the Q₁ peak decreased with the increase in pressure compared with raw coal. However, the Q₂ peak always increased slower than raw coal, and the range of change was larger. This indicated that the modified solution could not only slow down the transition from the free state to the adsorptive state, but also promote the transition from the free state to the free state, which was conducive to increasing the desorption capacity.

3.2. Analysis of Low-Field NMR Adsorption Experiment Results

In this paper, the nuclear magnetic method was used to calculate methane adsorption capacity, and the relationship between methane semaphore and mass was established through the marked line conversion equation. According to the established line equation, the peak area of methane in the adsorption equilibrium was calibrated to obtain the adsorbed methane amount of the sample.

As can be seen from Figure 7, the gas nuclear magnetic adsorption curves of all coal samples basically conformed to Type I isothermal adsorption curves, and the correlation coefficients of the fitting curves based on the Langmuir equation were all greater than 0.80, and half of them were above 0.90, indicating a good fitting degree. Two important parameters in the Langmuir equation, V_L and P_L, represent the ultimate adsorption capacity of coal sample and the adsorption rate at low pressure, respectively. The larger the value of V_L, the smaller the value of P_L, indicating a stronger adsorption capacity of the coal sample towards gas; otherwise, it indicates that the coal sample is more conducive to gas desorption. As can be seen from

Table 7. Fitting results of gas nuclear magnetic adsorption experiment.

Sample	VL (mL/g)	PL(MPa)	R2
Raw coal	39.00	9.27	0.90711
Water	30.00	8.73	0.95351
SDBS	17.89	6.82	0.94757
CDEA	19.99	7.37	0.88649
Rhamnolipid	19.35	7.77	0.85078
Tea saponin	16.87	6.87	0.93374
NP-10	23.05	5.66	0.83819
Sucrose ester	23.92	4.89	0.84716

, the V_L of the coal samples decreased from 39.00 m L/g to 16.87 m L/g, and P_L also decreased from 9.71 MPa to 4.89 MPa, indicating that the adsorption capacity of the coal samples treated with the six different surfactants was different. The V_L value of the coal treated with sucrose ester was the highest, while that of the coal treated with NP-10 was the lowest.

Different coal samples had different growth rates of their gas adsorption capacity. As can be seen from Figure 7, compared with raw coal, the growth rate of the gas adsorption capacity of treated coal samples was relatively slow, among which the Langmuir isotherm curves of the SDBS-treated coal samples and rhamnolipid-treated coal samples were the closest. However, among the modified coal samples, the growth of gas adsorption capacity of some coal samples was obviously slow, while that of other coal samples increased rapidly in the low-pressure stage and tended to be gentle in the high-pressure section. For example, although the V_L value of the coal treated with tea saponin and sucrose ester was lower than that of the coal treated with distilled water, the adsorption capacity in the low-pressure section was higher than that of the coal treated with distilled water. This shows that using the modified solution with tea saponin and sucrose ester that are added in actual coal mine production or gas extraction processes, makes the adsorption of gas by the modified coal sample more difficult. This conclusion was also verified by the NMR T₂ spectra in Figure 5.

It can be concluded from the analysis in Table 7 that among the six surfactants, sucrose ester had the largest V_L value and the smallest P_L value, and its modified coal sample had the strongest gas adsorption capacity. For rhamnolipid with the largest P_L value and NP-10 with the lowest V_L value, it can be inferred from the combination of Figure 7 that the coal samples treated with NP-10, SDBS and rhamnolipid had relatively strong gas desorption capacity.

Following from Table 7, after the use of the six surfactants, in terms of coal desorption capacity, they are ranked as shown in Figure 8 below. This indicate that the optimal surfactant is (in order): tea saponin, SDBS, rhamnolipid, CDEA, NP-10, and sucrose ester. In the context of sustainable consideration, the optimal surfactant investment is (in order): tea saponin, rhamnolipid, CDEA, and sucrose ester. SDBS and NP-10 are excluded from the ranking due to their toxicity.

3.3. Fractal Characteristics of Micro-Surface Pore Structure of Raw Coal and Modified coal

3.3.1. Calculation Method of Surface Fractal Dimension of Pulverized Coal

Fractal dimension is a comprehensive reflection of the degree of irregularity and complexity of pore structures ([31,32,47,48]). The fractal dimension determines the porosity, and the larger the fractal dimension, the smaller the porosity. Coal with a low fractal dimension has simple pore morphology and is mainly composed of open pores with good connectivity between pores ([3,16]). The gas adsorption method is a common method to calculate the fractal dimension. Combined with the experimental data of gas nuclear magnetic adsorption, the FHH model is used to calculate the fractal dimension of coal. The calculation formula is as follows:

$$\ln V=\left(D_S-3\right)\ln \left[\ln \raisebox{1ex}{$P_0$}\!\left/ \!\raisebox{-1ex}{$P$}\right.\right]+C,$$

(1)

where V is the gas adsorption amount under the equilibrium pressure P; P is the equilibrium pressure of gas adsorption; P₀ is the saturated vapor pressure of the gas given by the following Formula (2); D_S is the surface roughness parameter in fractal theory (fractal dimension), namely the fractal dimension, whose magnitude is calculated by the slope of the line lnV and ln [ln (P₀/P)]; and C is the fitting constant.

Existing studies often use N₂ adsorption isotherms to calculate the fractal dimension of solid materials ([21]). In this paper, the supercritical methane adsorption isotherm is used to calculate the fractal dimensions of the coal samples. Under the supercritical condition, methane cannot be liquefied and there is no saturated vapor pressure. Therefore, the saturated vapor P₀ used in this paper is only an assumption value that satisfies the requirements of the equation and has no actual physical significance. The calculation formula of $P_0$ is as follows:

$$P_0=P_C{\left(\raisebox{1ex}{$T$}\!\left/ \!\raisebox{-1ex}{$T_C$}\right.\right)}^2$$

(2)

where P_C and T_C are the critical pressure and critical temperature of methane, respectively.

3.3.2. Fractal Dimensions of the Microscopic Surface of Raw Coal and Modified Coal and Its Variation Characteristics

The fractal dimensions of the micro-surface pore structures of the coal samples before and after modification by six different surfactants was calculated according to Formula (1), and the results are shown in Figure 9 and

Table 8. Calculation results of fractal dimensions of raw coal and modified coal microscopic surfaces.

Sample	Fit the Slope of the Curve		Fractal Dimension DS	R2
Raw coal	−0.69108		2.30892	0.87506
Water	−1.04384		1.95616	0.85543
	Adjusted	−0.58279	2.41721	0.89159
SDBS	−1.00613		1.99387	0.99639
	Adjusted	−0.97268	2.02732	0.99611
CDEA	−0.90286		2.09714	0.96876
Rhamnolipid	−0.92486		2.07514	0.92669
Tea saponin	−0.73473		2.26527	0.96444
NP-10	−0.86518		2.13482	0.85415
Sucrose ester	−0.70419		2.29581	0.94979

.

It can be seen from Figure 9 and Table 8 that the fractal dimension calculation of the surface pore structures of raw coal, coal samples treated with distilled water and modified coal samples treated with six different surfactants had a good fit, indicating that the surface pore structure of the coal samples basically conformed to the characteristics of fractal theory. According to the classical fractal concept, the value range of the fractal dimension is generally 2.0–3.0, but the surface fractal dimension of some coal samples in this paper was lower than 2. This is because in the low P/P₀ stage, when the overlying layer approaches and drops below the single layer, the isotherm is controlled by attractive and repulsive gas/solid interactions. The fractal curve often deviates from linearity, resulting in the inability to effectively detect coal surface geometry under low pressure. Therefore, it is necessary to modify the surface fractal dimension D_S of some coal samples and remove the data of the lowest pressure point for the fitting calculation. When [30] used the FHH model to fit the adsorption data, they believed that when P/P₀ was less than 0.5, gas adsorption mainly depended on van der Waals forces in the low-pressure segment, and the calculated surface fractal dimension was obtained. In this paper, the P/P₀ values were concentrated in the range of 0.1 to 0.5, and the surface fractal dimension D_S values obtained from the eight samples of raw coal and modified coal are concentrated in the range of 2.02732 to 2.41721.

By comparing the surface fractal dimensions of the raw coal and the modified coal of the eight coal samples in Table 8, it can be found that the surface fractal dimensions of the modified coal samples treated with surfactant were all smaller than that of the raw coal, while the fractal dimensions of the coal treated with distilled water were larger than that of the raw coal. The results show that the micropores blocked by soluble organic matter in the raw coal sample were “dredged” by water, and the number of micropores on the surface of pulverized coal increased, but not to the extent that the micropore morphology changed. After the treatment with surfactant solution, the soluble organic matter in the raw coal sample was dissolved, and the micropore morphology changed into medium or large pores, indicating that the soaking of these surfactants plays a role in expanding the pore volume of the medium-ranked coal samples.

It can be seen from the fractal dimensions of the microscopic surface of raw coal and modified coal that, under the action of surfactant solvents, the surface roughness of the coal samples gradually decreased. Because the adsorption capacity of the coal samples is mainly affected by micropores and mesoporous pores, especially micropores, the smaller the D_S value, the smoother the surface of coal, and the stronger the gas desorption capacity of coal. It was also found in Figure 9 that the number of micropores in the nuclear magnetic adsorption experiment decreased significantly after treatment, and the comparison of several modified coal samples shows that the modification of SDBS and rhamnolipid had the highest pore volume expansion efficiency and the strongest gas desorption capacity.

Following from Table 8, after the use of the six surfactants, in terms of fractal dimension D_S, they are ranked as shown in Figure 10 below. This indicates that the optimal surfactant order is: SDBS, rhamnolipid, CDEA, NP-10, tea saponin, and sucrose ester. In the context of sustainable considerations, the optimal surfactant order is: rhamnolipid, CDEA, tea saponin, and sucrose ester. This order is slightly different with that in terms of the NMR results.

4. Conclusions

In this paper, six sustainable and traditional surfactants used in coal gas desorption processes were compared and analyzed from the perspective of sustainable investment and environmental protection. The results show that the surfactants for coal gas desorption play significant roles in the fractal dimension and nuclear magnetic resonance characteristics. The research findings can be summarized as follows:

(1) The fractal dimension calculation of the surface pore structure of raw coal, coal samples treated with distilled water and modified coal samples treated with six different surfactants had a good fit (with R² greater than 0.85), indicating that the surface pore structures of coal samples basically conform to the characteristics of fractal theory.

(2) A low-field NMR experiment was used to test the gas adsorption and desorption capacity of coal samples treated with the six surfactants. The Langmuir equation was used to fit the experimental data, and it was found that the adsorption gas quantity and gas pressure fit well, and the methane adsorption isotherm of the coal samples was type I. There are two adsorption mechanisms in type I isotherms: single molecule adsorption or volume filling. Methane is a supercritical gas at 298 K and cannot be liquefied or used for volume filling. The adsorption of supercritical methane can be explained by the single molecule adsorption mechanism.

(3) According to the low-field NMR adsorption T₂ spectrum curves, it was found that under the action of surfactant solvents, not only slowed down the transition of the methane in the coal samples from the free state to the adsorbed state, but also promoted the transition from the free state to the free state, which is conducive to increasing the desorption capacity of coal.

(4) According to the nuclear magnetic isothermal adsorption curve of gas, it was found that the adsorption capacity of different coal samples was different. Compared with raw coal, the growth rate of gas adsorption capacity of the modified coal samples was relatively slow. Compared with the coal sample modified by distilled water, the coal samples modified by tea saponin and sucrose ester had lower gas desorption capacities, while the desorption capacity of the other surfactants was improved. Among the six surfactants, according to the values of the two important parameters (V_L and P_L) in the Langmuir equation, it can be inferred that the coal sample modified by sucrose ester had the strongest gas adsorption capacity, while the coal samples modified by NP-10, SDBS and rhamnolipid had relatively stronger gas desorption capacities.

(5) The pore structure of the microscopic surface of pulverized coal can be characterized by the fractal geometry theory. The surface fractal dimension of raw coal, coal treated with distilled water and modified coal treated with the six different surfactants were obtained by fitting calculations. It was found that after adding a surfactant solvent, the soluble organic matter in raw coal was dissolved, and the shape of the micropores changed to medium or large pores, and the overall number of micropores decreased. Because the adsorption capacity of coal samples is mainly affected by micropores and mesoporous pores, especially micropores, the smaller the D_S value, the smoother the surface of the coal, and the stronger the gas desorption capacity of coal. Compared with the modified coal samples of the six different surfactants, the coal samples modified by SDBS and rhamnolipid had the strongest gas desorption abilities.

(6) In the context of sustainable considerations, the optimal surfactant order is: rhamnolipid, CDEA, tea saponin, and sucrose ester, from the perspective of fractal dimension D_S. Meanwhile, from the perspective of NMR, the optimal surfactant order is: tea saponin, rhamnolipid, CDEA, and sucrose ester.

(7) By comparing isothermal adsorption curves and surface fractal dimensions of the six surfactant solutions, it was concluded that coal samples modified by natural non-ionic surfactants, such as saccharolipids and saponins have reduced gas desorption, while coal samples modified by anionic surfactants, such as SDBS and rhamnolipid, have increased gas desorption.