Study on the Adsorption Characteristics of Tectonic Coal under Infrared Radiation Heating

Abstract

The fundamental mechanistic question addressed in this study is how infrared radiation heating (IRH) modulates the methane adsorption capacity of tectonic coal – a critical yet poorly understood issue for thermal-enhanced coalbed methane (CBM) recovery. Unlike conventional conductive or convective heating, IRH delivers noncontact electromagnetic energy that directly excites molecular vibrations and rotations within the coal matrix, generating volumetric heating with higher thermal efficiency and no secondary contamination. To elucidate this mechanism, we adopted an integrated methodology combining high-pressure isothermal adsorption experiments under controlled IRH power levels, theoretical derivation of the Langmuir adsorption equilibrium constant b based on heat transfer and adsorption kinetics, thermodynamic calculation of key parameters (ΔG ⁰, ΔH ⁰, ΔS ⁰, and equivalent heat of adsorption q _st), and quantitative microstructural analysis via SEM coupled with ImageJ pore statistics. Our key findings are fourfold: (1) Both the saturation adsorption capacity a and the adsorption equilibrium constant b decrease with increasing IRH power, with a following a sharp initial decline that plateaus at higher power – a trend quantitatively captured by our theoretically derived b(T) model; (2) Thermodynamic analysis confirms that methane adsorption on coal is spontaneous physical adsorption (ΔG ⁰ < 0, ΔH ⁰ ≈ −30 kJ/mol), and IRH weakens the adsorption affinity by raising the system energy state; (3) The equivalent heat of adsorption q _st is positively correlated with uptake, demonstrating that IRH-driven desorption is an endothermic process that requires energy input to overcome adsorption barriers; (4) Microstructurally, IRH reduces micropore abundance from 45–51% to 34–43% while increasing small- and mesopore fractions, indicating that pore enlargement and interconnectivity – rather than mere temperature rise – underlie the reduced specific surface area and adsorption site availability. Collectively, these results establish that IRH enhances CBM recovery through a dual mechanism: direct weakening of adsorption thermodynamic affinity and concurrent improvement of pore transport pathways. This work provides both theoretical insights and experimental validation for the rational design of IRH-based stimulation strategies in low-permeability coal seams.

1. Introduction

Methane is abundantly present in coal seams, yet most coal seams in China are characterized by low permeability due to complex geological structures and high in situ stress conditions. − This low permeability poses significant challenges for conventional CBM extraction. , Heat changes the ability of coal bodies to adsorb methane. Exploring the relationship between the influence of external heat sources on the equilibrium adsorption of methane in a coalbed is an important means to study the injection of heat in coalbeds to increase production of CBM. Numerous researchers and scholars have used numerical simulations − and experiments to conduct in-depth and detailed studies on the injection of heat to increase the production of methane from low-permeability coalbeds. Teng Teng et al. established a dual pore-permeability and finite element model for the interaction between heat and CBM. They used numerical simulations to investigate the effect of thermal injection on the extraction of CBM, and found that thermal injection could increase the production of CBM by nearly 70% or more. Salmachi A. et al. explored the feasibility of thermal extraction using geothermal resources and showed that it could increase CBM extraction by more than 58% and the extraction rate by a factor of 6.8. At present, the main heat sources used to increase production of CBM include hot carbon dioxide gas, hot steam, and microwaves. −

IRH occurs through the form of electromagnetic waves that heat the surface of an object. The molecules and atoms of the object being radiated under the conditions of IRH excitation undergo strong vibrations and rotations, which accelerates the collision between molecules, friction, and the rapid temperature rise of the object being radiated. Whether IRH is effective mainly depending on the degree of absorption of the object being heated; the higher the absorption rate is, the better the IRH effect. The absorption rate depends on the category of the heated material, its surface state, the wavelength of the IRH source, and so forth. Coal is a nonmetallic material, and its molecular structure is not very dense. When incident IRH wave reaches the interface, it is seldom reflected because it is easier for it to pass through the interface into the surface layer, excite resonance into heat, and provide a better heating effect. Even if part of the infrared electromagnetic wave cannot excite resonance, it is subject to refraction, scattering and reflection. However, due to the dual dielectric properties of the coal body, which does not have a single structure, the radiation waves not absorbed by the surface layer may resonate and be absorbed to different degrees during the deepening process. Therefore, if IRH technology is applied to thermal CBM extraction, it will not only have good thermal efficiency but also be a clean energy source and will not cause secondary pollution to coal seams.

To study heat injection and enhanced production of CBM, it is necessary not only to study the relevant relationships of adsorption and desorption , but also to conduct further in-depth research on the mechanisms of coal adsorption and desorption. − The a and b values in the Langmuir equation can characterize the saturation adsorption capacity and the magnitude of the adsorption capacity of coal, which are key parameters for studying adsorption/desorption on coal and are directly related to CBM reserves. Ali Shahtalebi et al. conducted experiments and numerical simulations and found that thermal excitation could increase the diffusivity of methane. Zhou D. et al. showed an increasing trend of heat of adsorption with increasing temperature for both models in isobaric pressure experiments, which indicated that the adsorption capacity of warmed coal samples was enhanced. Hai-Fei Lin et al. found that the constant b decreased with increasing temperature for different numbers of freeze-thaw cycles using liquid nitrogen, and the value of b increased with increasing number of freeze-thaw cycles using liquid nitrogen at the same temperature. An experimental study, Ming-Yun Tang et al. showed that the constant b became larger with increasing temperature. In summary, the adsorption capacity of the adsorbent varies with the temperature of the system. For adsorption of methane on coal, the variation pattern of adsorption capacity with IR radiation power was not clear. In this paper, based on experiments to measure the effect of IRH on the adsorption of methane by coal, the theoretical derivation of the b value in the Langmuir equation and then a preliminary discussion of the thermodynamic parameters of the adsorption process, the influence of IRH power on the coal adsorption characteristics is elucidated.

The distinction between IRH and conventional thermal stimulation methods (e.g., hot steam injection, conductive heating, or convective heating) warrants explicit discussion. Conventional heating relies on heat transfer through thermal conduction and convection, where heat must propagate from the heat source through the coal matrix via temperature gradients. This process is inherently inefficient for low-permeability coal seams because the coal matrix exhibits low thermal conductivity, resulting in significant thermal energy losses to the surrounding formation and slow heating rates. Furthermore, conventional heating often requires high-temperature fluids (e.g., hot CO₂ or steam), which may introduce secondary contamination or alter the chemical composition of the coal. In contrast, IRH delivers noncontact electromagnetic energy that directly excites molecular vibrations and rotations within the coal matrix. This volumetric heating mechanism bypasses the need for a thermal diffusion pathway, achieving rapid and uniform heating at the molecular level. Crucially, IRH achieves comparable reductions in methane adsorption capacity at substantially lower bulk temperatures than conventional heating – a finding that underscores the unique non-thermal contribution of IRH beyond simple temperature elevation. This direct energy coupling mechanism, combined with its clean energy nature (no secondary pollution), positions IRH as a fundamentally distinct and potentially more efficient approach for thermal-enhanced CBM recovery.

In this paper, we developed an IRH device and used it to determine the methane adsorption capacity of pulverized coal. We also investigated the influence of IRH power and system pressure on the methane adsorption capacity in the process of IRH. Additionally, we investigated the influence of IRH power on the thermodynamic parameters ΔG ⁰, ΔH ⁰, ΔS ⁰ and q _st for the adsorption process. The research results can provide a theoretical reference for the application of IRH to increase CBM production and promote its development.

2. IRH Theory and Derivation

IRH is a phenomenon that transmits heat by electromagnetic waves. As long as the temperature of an object is above absolute zero, the object continuously changes thermal energy into radiant energy and emits thermal radiation.

The following assumptions are made in the theoretical derivation:

• 1The coal surface is homogeneous with respect to IRH absorption;
• 2The absorption coefficient α is independent of temperature and IRH power within the experimental range (0–50 W);
• 3Energy losses due to convection and conduction are negligible compared to radiative heat transfer;
• 4The temperature distribution within the coal sample is uniform (justified by the small sample size and long radiation time of 12 h).

In this study, experiments were conducted using a far- IRH device that radiated heat externally as follows:

$$Pt=c_1{m}_1(T-T_0)$$ 1

where P is the IRH device power, W; t is the radiation time, s; c ₁ is the specific heat of IRH device, J/(kg·°C); m ₁ is the surface mass of the IRH device, kg; T is the IRH device temperature, °C; and T ₀ is the starting temperature of IRH device (ambient temperature), °C.

From eq , we can obtain the IRH heat source temperature expression.

$$T=\frac{Pt}{c_1{m}_1}+T_0$$ 2

According to Stephan’s law:

$$E=\epsilon \sigma T^4$$ 3

where ε is the IRH device emissivity; σ is the Stephan constant 5.67 × 10^–8 W/(m²·K⁴). Therefore, the area of the A ₁ IRH device at a certain radiation time t total radiation energy is

$$Q={\int }_0^{A_1}{\int }_0^t\epsilon \sigma T^{4}dtdA$$ 4

where Q is the total energy radiated externally by the IRH device. Jointly, (2) and (4) can be obtained experimentally from the hemisphere total radiation energy of the IRH device:

$$Q=\epsilon \sigma A_{1}t{\left(\frac{Pt}{c_1{m}_1}+T_0\right)}^4$$ 5

Let the radiant energy received by the coal from the IRH device be Q _c. Its value is related to the stereo angle formed by the coal and the IRH device, and the stereo angle accounts for the share of the entire hemisphere stereo angle of the IRH device γ,

$$\gamma =\frac{A_2}{2\pi r^2}$$ 6

where A ₂ is the heated area of coal, m²; and r is the normal distance between the IRH device and the coal, m. Let the coal absorption ratio be α. Then, the radiant energy Q _c received by the coal from the IRH device is

$$Q_c=Q\times \gamma \times \alpha$$ 7

According to the first law of thermodynamics, the amount of internal energy change of coal is equal to the energy transferred from the outside to the coal minus the work done by the coal body on its surroundings, as the coal absorbs radiant energy and heats without doing work externally, i.e.,

$$Q_c=c_2{m}_2\mathrm{\Delta }T$$ 8

where c ₂ is the specific heat of coal, J/(kg·°C); m ₂ is the mass of the heated surface of the coal, kg; and ΔT is the change in coal temperature, °C. The mathematical expression for the change in temperature of coal is obtained by associating eqs –:

$$\mathrm{\Delta }T=\frac{\epsilon \sigma \alpha A_1{A}_{2}t}{2\pi r^2{c}_2{m}_2}{\left(\frac{Pt}{c_1{m}_1}+T_0\right)}^4$$ 9

Equation shows that the amount of temperature change of the coal body under IRH conditions is related to the following factors: emissivity, radiation area, heated area, radiation time, normal distance, specific heat, mass, and radiation power.

According to Sun et al. research, multiple nonlinear fitting was performed on the permeability and temperature changes of coal samples to obtain eq

$$k=A{e}^{-\frac{T}{t}}+B$$ 10

where k is the permeability of the coal sample, mD; A, B is the fitting coefficient. The relationship between permeability and IRH power obtained from simultaneous eqs and is

$$k=A{e}^{-\frac{\epsilon \sigma \alpha A_1{A}_2}{2\pi r^2{c}_2{m}_2}{(\frac{Pt}{c_1{m}_1}+T_0)}^4-T_0}+B$$ 11

Equation provides the theoretical relationship between the permeability of coal samples and the IRH power, providing a theoretical basis for ECBM (Enhanced Coal Bed Methane Recovery).

Equation is derived by combining the heat transfer model eq with the empirical temperature-permeability relationship. While the temperature-permeability correlation is empirically based, the integration with the physically derived heat transfer model provides a semi-empirical framework that captures the essential physics. The derived relationship eq should be treated as a predictive tool valid for the experimental conditions (0–50 W IRH power, tectonic coal samples), rather than a universal physical law.

3. IRH Coal for Methane Adsorption Experiments

To study the relationship between the effect of the amount of IRH power and the capacity of coal for methane adsorption, experiments were conducted with the same large coal samples taken from the Liaoning coal mine in Tiefa and the Jilin coal mine in Huaxing as the IRH temperature field experiments for isothermal adsorption experiments under IRH conditions, with reference to the GB/T 19560–2025 “Experimental method of high-pressure isothermal adsorption to coal.”

3.1. Preparation of Coal Samples

The experimental coal powder was prepared according to the GB/T 474–2008 “Method for preparation of coal sample”. The coal samples were collected from the Liaoning Tiefa coalfield and the Jilin Huaxing coalfield. In situ reservoir conditions for the Tiefa coalfield include: reservoir pressure of 6.73 MPa, reservoir temperature of 42.5 °C, and an initial permeability of 0.15–0.35 mD as determined by transient pulse decay method. For the Huaxing coalfield: reservoir pressure of 8.70 MPa, reservoir temperature of 47.8 °C, and permeability of 0.08–0.22 mD. Porosity values determined by helium pycnometry are 3.82% (Tiefa) and 4.15% (Huaxing). X-ray diffraction (XRD) analysis reveals mineral compositions of 62.3% vitrinite, 28.7% inertinite, and 9.0% mineral matter (mainly clay and quartz) for Tiefa, and 58.9% vitrinite, 31.2% inertinite, and 9.9% minerals for Huaxing. The proximate analysis results are consistent with those reported above. A crusher was used to fully crush the large coal sample and make the maximum particle size less than 18 mm; Then, the crusher was used to make particles with a maximum size less than 0.25 mm. Finally, a powder grading filter sieve is used for grading and screening. The selected coal powder mesh was 60–80 mesh to obtain coal powder that met the standard requirements, and the total mass was greater than 2000 g. Referring to the GB/T212-2008 “Proximate analysis of coal”, appropriate amounts of the coal samples were selected for analysis. Burial depth of Liaoning Tiefa coal sample is 673m, Mad 0.96%, Aad 10.53%, Vad 12.38%; Jilin Huaxing coal sample buried at a depth of 870m, Mad 0.93%, Aad 9.32%, Vad 13.36%.

3.2. Experimental Setup

To study the influence of IRH power on the amount of gas that isothermally adsorbed on pulverized coal, the available equipment cannot directly apply IRH on pulverized coal and cannot realize the simultaneous loading of the temperature field and stress field in the sample cylinder. Based on the characteristics of IRH, the device for determining the amount of gas adsorption by IRH was developed independently in this laboratory, and the principle of the device is shown in Figure . The experimental device utilizes an XMA-600 constant temperature incubator to maintain the main structure of the adsorption experiment at a constant temperature.

1.

Schematic diagram of experimental device for measuring gas adsorption capacity by IRH.

Sample temperature during IRH was monitored in real-time using three fiber-optic thermometers (accuracy: ±0.5 °C) inserted at different positions within the sample cylinder (top, middle, and bottom layers). Temperature readings were recorded every 30 seconds using a data acquisition system. The reported sample temperature is the arithmetic mean of the three measurements. Temperature uniformity was assessed by the standard deviation among the three positions; all experiments showed standard deviations <2.5 °C after the initial 30 min of IRH.

3.3. Experimental Protocol

The following experimental protocol was developed to study the relationship between adsorption on coal powder under the simultaneous action of a pressure field and an IRH field:

• 1Take 2000 g of coal powder and load it into the sample cylinder, open valve 1, close the other valves, and apply a vacuum to the device (vacuum level <10 Pa). Set the temperature of the thermostat (the temperature control accuracy of the thermostat is ±0.5°C), set the IRH power, turn on the power and perform IRH on the coal powder.
• 2Close valve 1, open valves 2 and 3, close valve 4, fill the reference cylinder with methane gas, adjust the pressure to the preset pressure and then close valves 2 and 3, and record the pressure and temperature data of the reference cylinder at this time.
• 3Slowly open valve 4; at this time, the gas in the reference cylinder flows into the sample cylinder. After the pressure of the sample cylinder and the reference cylinder reach equilibrium, record the pressure and temperature values of the sample cylinder and the reference cylinder.
• 4Maintain the thermostat and IRH equipment for more than 12 h. After 12 h, methane gas is fully adsorbed on the coal powder. Record the pressure and temperature after equilibrium is reached. The IRH power is 0 W, 10 W, 25 W, 40 W and 50 W respectively.
• 5After the first adsorption experiment, repeat steps (2–4) to obtain the corresponding experimental data.

3.4. Control Experiments with Conventional Heating

To isolate the unique effects of IRH from general thermal effects, control experiments were conducted using conventional convective heating in a thermostatic oven at equivalent sample temperatures. The target temperatures for conventional heating were determined from IRH experiments by measuring the actual sample temperature (using fiber-optic thermometers) at each IRH power level. This allows direct comparison of adsorption behavior between IRH and conventional heating at identical sample temperatures, thereby revealing whether IRH has specific effects beyond temperature elevation.

4. Experimental Results and Analysis

4.1. Adsorption Experimental Results and Analysis

According to the above experimental scheme, the amount of adsorbed coal dust can be obtained under different IRH conditions. The experimental data were fitted to the Langmuir equation, which is as follows:

$$V=\frac{abp}{1+bp}$$ 12

where V is the gas adsorption amount, cm³/g; p is the equilibrium pressure, MPa; a is the saturation adsorption capacity, cm³/g; and b is the adsorption equilibrium constant.

The Langmuir isotherm equation is widely employed to describe methane adsorption on coal surfaces under equilibrium conditions. In this equation, parameter a represents the maximum adsorption capacity (saturation adsorption amount), which reflects the total number of available adsorption sites on the coal surface. Parameter b is the adsorption equilibrium constant, which characterizes the affinity between methane molecules and the coal surface – a larger b value indicates stronger adsorption affinity. Both parameters are critical for estimating CBM reserves and designing enhanced recovery strategies.

The data fitted with the Langmuir equation for methane adsorption under different IR radiation power conditions are shown in Figure .

2.

Fitting curve of methane adsorption varies with equilibrium pressure under different IRH power by Langmuir equation.

The functions for the fitted equations were derived using Origin software, as shown in Table .

1. Fitting Function of Coal Sample Adsorption under Different IRH Power.

Serial number	IRH power/W	Fitted function	R 2	Coal origin
1	0	$$V=\frac{26.03\times 1.52p}{1+1.52p}$$	0.981	Liaoning, Tiefa
2	10	$$V=\frac{20.55\times 1.32p}{1+1.32p}$$	0.994
3	25	$$V=\frac{11.96\times 0.86p}{1+0.86p}$$	0.995
4	40	$$V=\frac{6.59\times 0.71p}{1+0.71p}$$	0.998
5	50	$$V=\frac{5.84\times 0.53p}{1+0.53p}$$	0.997
6	0	$$V=\frac{27.66\times 1.61p}{1+1.61p}$$	0.984	Jilin, Huaxing
7	10	$$V=\frac{22.12\times 1.25p}{1+1.25p}$$	0.993
8	25	$$V=\frac{13.11\times 0.87p}{1+0.87p}$$	0.996
9	40	$$V=\frac{7.34\times 0.75p}{1+0.75p}$$	0.997
10	50	$$V=\frac{6.28\times 0.54p}{1+0.54p}$$	0.997

Figure , shows that the adsorption curves of methane gas for the two coal samples from the Liaoning mine, Tiefa and the Jilin mine, Huaxing, had the highest adsorption at an IRH power of 0 W, and the adsorption of methane gas decreased with increasing power of the IRH equipment. The free energy of methane gas molecules increased under the effect of IRH, and the methane desorption rate was greater than the adsorption rate, which caused more methane gas molecules to desorb into the free state than adsorb onto the coal. The higher the IRH power was, the smaller the amount of methane adsorption at the same pressure.

In addition, the equilibrium pressure had a significant effect on adsorption, i.e., the amount of adsorbed gas increased with increasing equilibrium gas pressure. Figure shows that the adsorption of methane by coal increased with increasing equilibrium pressure, but the rate of methane adsorption by coal slowly tended to become level as the equilibrium pressure gradually increased.

For the fitted Langmuir adsorption curves, the values of R ² for both the Liaoning, Tiefa and Jilin, Huaxing coal samples were greater than 0.9, which indicated that adsorption was consistent with the Langmuir adsorption law. The curve of IR radiation power versus saturation adsorption a value is shown in Figure , and the fitted curve versus adsorption equilibrium constant b value is shown in Figure .

3.

Saturation adsorption capacity a as a function of IRH power.

4.

Fitting curve between b value and IRH power.

The saturated adsorption amount a in the Langmuir equation characterizes the total number of coal adsorption sites. Figure shows that the values of the saturation adsorption a of both coal samples decreased with increasing IRH power, and the decrease was obvious at low power. With increasing IRH power, the decreasing trend of a values tended to become level; the decrease in a values would not be obvious if the IRH power continued to increase, and the two showed a negative correlation. This indicated that the intervention of IRH energy increased the internal energy of methane molecules. Adsorbed methane molecules have a great ability to desorb from coal due to their increase in internal energy. The probability of desorption is greatly increased, which is macroscopically manifested as a decrease in the saturation adsorption of coal. However, the amount of saturated adsorption on coal cannot be reduced without limit, and thus the decreasing trend of the a value tended to become level after the IRH power was further increased.

The b value can characterize the magnitude of the coal adsorption capacity. Figure shows that the adsorption equilibrium constant b values of both coal samples decreased with increasing IRH power, which indicated that the adsorption capacity of the coal decreased with increasing IRH power.

Based on the theories of statistical thermodynamics, thermodynamics and reaction rate kinetics, the b expression can be expressed by eq .

$$b=k\exp (-\frac{E_d}{RT})$$ 13

where k is a constant; E _d is the sum of the desorption activation energy, adsorption activation energy and adsorption energy; R is the ideal gas constant, 8.314J/(mol·K); T is the absolute temperature of the system, K.

According to the Stefan–Boltzmann Law, the total energy Q of thermal radiation emitted by an object per unit time is related to the temperature, as in eq ,

$$Q=\epsilon A\sigma T^4$$ 14

where ε is the object emissivity; A is the surface area of radiation, m²; σ is the Stefan–Boltzmann constant, 5.67 × 10^–8 W/(m²·K); and T is the thermodynamic temperature, K.

For gas-bearing coals, acquiring IRH energy perturbs their adsorption equilibrium state, the energy balance involved in this process can be expressed by the energy equation, and the energy equation for desorption of the coal matrix (with adsorbed phase) microelements can be expressed by eq ,

$$\int [\frac{\partial }{\partial t}({\rho }_s{c}_s\mathrm{\Delta }T)-\nabla \times (k_s\nabla T)-q_s]d\mathrm{\Omega }=0$$ 15

where ρ _s, c _s and k _s are the density, specific heat capacity and thermal conductivity of the coal skeleton, respectively, and q _s is the external heat source.

Let the coal porosity be φ, and the share of energy absorbed by coal in the total energy be α. The mathematical model of energy conservation of IRH coal desorption is obtained as shown in eq .

$$(1-\varphi ){\rho }_s{c}_s\frac{\delta T}{\delta t}+\frac{\partial ({\rho }_{abs}{c}_{abs}\mathrm{\Delta }T)}{\partial \tau }-[(1-\varphi )\alpha Q-\frac{\partial E_d}{\partial t}]=0$$ 16

Let the share of heat of desorption per unit time γ; then, eq can be transformed into eq :

$$\gamma (1-\varphi )\alpha Q=\frac{\partial E_d}{\partial t}$$ 17

The 0-t integration of the two ends of eq gives eq .

$${\int }_0^t\gamma (1-\varphi )\alpha \epsilon A\sigma T^{4}dt=E_d$$ 18

The mathematical model of b is obtained by combining eq and ,

$$b=k\exp [-\frac{\gamma (1-\varphi )\alpha \epsilon A\sigma t}{R}\times T^3]$$ 19

According to eq , the magnitude of the b value is related to the e negative exponential function of temperature T ³. According to the nature of the function, the magnitude of the b value decreases with increasing temperature, which is consistent with the variation of the b values of the experimental data obtained in Figure . According to Figure for the Liaoning, Tiefa coal sample k _Liao = 2.24, and for the Jilin, Huaxing coal sample k _Ji = 2.58.

Equation presents a hybrid theoretical-empirical model for b. The exponential temperature dependence arises from statistical thermodynamics, while the T ³ dependence originates from the Stephan-Boltzmann law. The prefactor k is determined empirically for each coal type. This combined approach allows for practical prediction while maintaining physical grounding. The model’s validity is confirmed by the good agreement with experimental data (R ² > 0.9), as shown in Figure and Table .

4.2. Analysis of Thermodynamic Parameters of Adsorption Process

In addition to isothermal adsorption curves and microscopic pore distribution, thermodynamic parameters of the adsorption process are also key to the study of this behavior. − The spontaneity, state and disorder of the adsorption process can be understood by the standard Gibbs free energy change ΔG ⁰, the standard adsorption enthalpy change ΔH ⁰ and the standard adsorption entropy change ΔS ⁰. The spontaneity of the adsorption process is studied by calculating ΔG ⁰, ΔG ⁰ > 0, where the adsorption process is nonspontaneous, and ΔG ⁰ < 0, where the adsorption process is spontaneous. Combining adsorption kinetics and adsorption thermodynamics provides an expression for ΔG ⁰ shown in eq .

$$\mathrm{\Delta }{G}^0=-RT\ln b^0$$ 20

The standard pressure constant b ⁰ corrected for saturation vapor pressure can be expressed as in eq

$$b^0=\frac{\theta P^0}{(1-\theta )P}$$ 21

where θ is the fraction of positions occupied by methane molecules adsorbed on the coal surface, and its value is the ratio of adsorption volume to saturation adsorption volume; P ⁰ is the saturation vapor pressure. The calculation results are shown in Table .

2. ΔG ⁰ Values for Different Fitted Functions of the IRH Power B .

Coal origin	IRH power/W	ΔG 0/kJ·mol–1
Liaoning, Tiefa	10	–5.004
	25	–6.451
	40	–6.925
	50	–8.591
Jilin, Huaxing	10	–5.025
	25	–6.343
	40	–7.969
	50	–7.373

As shown in Table , the ΔG ⁰ values of both Liaoning, Tiefa and Jilin, Huaxing coal samples were negative, indicating that the adsorption process was spontaneous.

The relationship between the standard Gibbs free energy change ΔG ⁰, standard enthalpy change of adsorption ΔH ⁰ and standard entropy change of adsorption ΔS ⁰ is shown in eq .

$$\mathrm{\Delta }{G}^0=\mathrm{\Delta }{H}^0-T\mathrm{\Delta }{S}^0$$ 22

Combining eqs and yields eq .

$$\ln b^0=\frac{△S^0}{R}-\frac{△H^0}{RT}$$ 23

According to the isothermal adsorption experimental data, b ⁰ of the isothermal process was averaged to obtain the relationship between ln b ⁰ and 1/T. A linear fit was made as shown in Figure . The resulting slope of the line was calculated as ΔH ⁰ and the intercept of the line was calculated as ΔS ⁰.

5.

Fitting curve of relationship between ln b ⁰ and 1/T.

According to the fitted functions in Figure the result of the calculation for the Liaoning, Tiefa coal sample ΔH ⁰ was −32.432 kJ/mol, and the result for the Jilin, Huaxing coal sample was −29.614 kJ/mol, ΔH ⁰ < 0, which indicated that H ⁰ decreased during the adsorption of methane on coal. Therefore, IRH decreased the adsorption capacity of coal, which was consistent with the conclusion that the b value decreased. It is generally accepted that the ΔH ⁰ value for physical adsorption is less than 80 kJ/mol, while the ΔH ⁰ value for chemisorption is in the range of 80–200 kJ/mol. Therefore, the adsorption of methane in coal seams is dominated by physical adsorption.

Entropy is related to the state of matter, pressure, temperature and other factors. In the isothermal adsorption process, the gas phase is transformed from a random state (free state) to an ordered state (adsorbed state), the equilibrium pressure increases, and the entropy of the system decreases. ΔS ⁰ was −0.078 for the Liaoning, Tiefa coal sample and −0.069 for the Jilin, Huaxing coal sample. With ΔS ⁰ less than 0 for both coal samples, this further indicated a gradual decrease in the disorder of the coal adsorption process according to the experimental data.

4.3. Equivalent Heat of Adsorption Calculation

The process of methane adsorption by coal is exothermic, and the heat of adsorption is an important criterion used to characterize the adsorption capacity of coal and evaluate the magnitude of the force between coal and methane. The equivalent heat of adsorption q _st is the instantaneous enthalpy change of the adsorption process, which is the heat released by the substrate after adsorbing an infinitesimal amount of adsorbent. q _st is related to the enthalpy change of adsorption ΔH as follows.

$$q_{st}=-\Delta H=-R\left[\frac{d\ln f}{d(1/T)}\right]$$ 24

The fugacity ln f at different temperatures can be calculated by the following equation

$$T_r=\frac{T}{T_c}{P}_r=\frac{P}{P_c}$$

$$\frac{d{B}^{(0)}}{d{T}_r}=\frac{0.675}{T_r^{2.6}}\frac{d{B}^{(1)}}{d{T}_r}=\frac{0.722}{T_r^{5.2}}$$

$$B^{(0)}=0.083-\frac{0.422}{T_r^{1.6}}{B}^{(1)}=0.139-\frac{0.172}{T_r^{4.2}}$$

$$\frac{H^R}{RT}=-P_r[\frac{d{B}^{(0)}}{d{T}_r}-\frac{B^{(0)}}{T_r}+\omega (\frac{d{B}^{(1)}}{d{T}_r}-\frac{B^{(1)}}{T_r})]$$

$$\frac{S^R}{R}=-P_r(\frac{d{B}^{(0)}}{d{T}_r}+\omega \frac{d{B}^{(1)}}{d{T}_r})$$

$$\ln \varphi =\ln (f)-\ln (P)=\frac{G^R}{RT}=\frac{H^R}{RT}-\frac{S^R}{R}$$

where T _r is the comparison temperature; T _c is the critical temperature; P _r is the contrast pressure; P _c is the critical pressure; B is the second dimensional coefficient; H ^R is the residual enthalpy; ω is the eccentricity factor of CH₄, 0.0116; S ^R is the residual entropy; G ^R is the residual Gibbs free energy; and φ is the fugacity factor.

The relationship between ln f and 1/T at different adsorption amounts and the fitted curves are shown in Figure .

6.

Relationship between ln f and 1/T.

According to the slope of the fitted straight line and the intercept of the vertical coordinate in Figure , the values of the equivalent heat of adsorption q _st for the Liaoning, Tiefa and the Jilin, Huaxing coal samples are shown in Table , and the variation in q _st with the amount of adsorption is shown in Figure .

3. Equivalent Heat of Adsorption during Adsorption of Methane on Coal Samples.

Serial number	Adsorption amount n/(mmol/g)	q st/(kJ/mol)	Coal origin
1	0.1	–10.04	Liaoning, Tiefa
2	0.2	–10.92
3	0.3	–12.90
4	0.4	–14.55
5	0.5	–15.85
6	0.1	–10.26	Jilin, Huaxing
7	0.2	–11.71
8	0.3	–13.63
9	0.4	–14.85
10	0.5	–17.17

7.

Relationship between q _st and unit adsorption capacity.

Figure shows that the magnitude of the value of the equivalent heat of adsorption q _st was positively correlated with the adsorption amount, which indicated that the adsorption of methane gas by coal samples was a continuous exothermic process. The larger the adsorption amount was, the more heat was released. The equivalent heat of adsorption was larger for the Jilin, Huaxing coal sample than the Liaoning, Tiefa coal sample for the same amount of adsorption.

4.4. SEM Results and Analysis

To study the effect of IRH on the change in coal pore distributions at the microscopic level, two coal samples each from Liaoning, Tiefa and Jilin, Huaxing, which were the same as the samples used the IRH temperature field experiments and adsorption experiments, were selected. The coal was heated using an IRH generating device at a distance of 10 mm from the heat source, under IRH powers of 10, 25, 40, and 50 W, respectively. The same small areas on the surface of each coal sample were photographed before and after heating using a QUANTA 250 scanning electron microscope (SEM) at 500× magnification. The distributions of surface pores of coal samples in the SEM electron micrographs were analyzed by ImageJ. The Image-Type function was converted to a 16x map, and then the pore and fracture locations were marked by threshold segmentation with the Image → Adjust → Threshold function. The results are shown in Figure and the area surrounded by yellow lines in the figure is the location of pores and fissures. The pores in coal are usually classified as follows: micropores (diameter < 0.01 μm), small pores (0.01–0.1 μm), mesopores (0.1–1 μm), and macropores (>1 μm). The Analyze particles function was used to count the sizes and numbers of pores in the surface layers of coal samples and study the effects of the change in the power of the IRH source on the distributions of pores; statistics were calculated, and the results are shown in Figure .

8.

Pore distribution of coal samples before (left) and after (right) IRH.

From Figure , it can be seen that the microstructure of the coal sample has changed before and after IRH, and the size of the surface pores and cracks of the coal sample has increased. After radiation heating, some of the original pores and cracks are interconnected, and the surface particles of the coal sample fall off, and micropores and microcracks become more obvious. The expansion of micropores and microcracks contributes to the desorption and diffusion of methane gas, which is consistent with the previous view that the adsorption capacity and saturated adsorption capacity of coal samples decrease with the increase of IRH power. The IRH environment can cause deformation on the inner surface of coal samples, increasing the scale of primary pores and cracks, causing particles on the surface of coal samples to detach and generate new pores and cracks, providing a more favorable channel for gas desorption and diffusion.

The detailed pore proportion statistics for both coal samples before and after IRH at different power levels are summarized in Table . As shown in Table , the proportion of micropores consistently decreased after IRH application across all four coal samples, while the proportions of small pores, mesopores, and macropores increased correspondingly. This systematic transition from micropores to larger pores confirms the pore-enlargement effect induced by IRH.

4. Coal Sample Pore Proportion.

		Proportion of micropores(%)	Proportion of small pores(%)	Proportion of mesopores(%)	Proportion of macropore(%)
Coal Sample No. 1	IRH not Applied	45.4	47.6	6.1	0.9
	Applied IRH(10 W)	40.0	50.8	7.7	1.5
Coal Sample No. 2	IRH not Applied	51.3	43.7	4.5	0.5
	Applied IRH(25 W)	43.3	46.5	8.7	1.5
Coal Sample No. 3	IRH not Applied	50.2	46.8	2.4	0.6
	Applied IRH(40 W)	38.7	52.6	7.6	1.1
Coal Sample No. 4	IRH not Applied	44.5	48.2	5.8	1.5
	Applied IRH(50 W)	34.4	51.7	11.5	2.4

The number of micropores in coal is positively correlated with the size of the specific surface area of coal, which reflects the effective contact area during adsorption of methane and can characterize the adsorption capacity of coal. Therefore, changes in the microscopic pore distribution of coal samples can explain the phenomenon of changes in the macroscopic adsorption capacity of coal. , In this study, IRH changed the surface structure of the coal samples, and the number of micropores decreased as a percentage. The probability of methane molecules contacting with the coal surface was reduced, which further verified that the increase in IRH power from the microscopic point of view caused decreases in the adsorption capacity and saturation adsorption capacity of the two experimentally selected coal samples from Liaoning, Tiefa and Jilin, Huaxing.

The microstructural changes observed by SEM provide a mechanistic explanation for the decreased adsorption capacity. Under IRH, the coal surface absorbs electromagnetic energy, causing molecular vibrations that generate localized heating. This localized heating creates thermal stresses due to differential thermal expansion between different mineral components and the coal matrix. These thermal stresses exceed the tensile strength of the coal, leading to(1) expansion of existing pores and cracks, (2) detachment of surface particles, and (3) formation of new interconnected fracture networks.

The net effect is a reduction in micropore population, which directly correlates with the specific surface area available for methane adsorption. This mechanism is distinct from conventional heating, where heat is transferred by conduction from the surface inward, resulting in more uniform temperature distribution and less thermal stress-induced microstructural modification. The IRH-induced microstructural modification is, therefore, a unique phenomenon that contributes to reduced adsorption capacity beyond the purely thermal effect of elevated temperature.

4.5. Comparison with Previous Studies

The observed decrease in methane adsorption with increasing temperature is consistent with the findings of Zhu et al. and Wang et al., who reported similar trends for various coal ranks under conventional heating. However, the present study reveals that IRH achieves a comparable reduction in adsorption capacity at lower bulk temperatures compared to conventional heating. For example, at an IRH power of 50 W, the reduction in a value (from 0 W condition) is 38.2% for Tiefa coal. In contrast, Wang et al. reported that achieving a 35–40% reduction in adsorption capacity by conventional heating required temperatures of 90–100 °C. This suggests that IRH may offer superior energy efficiency for CBM enhancement.

The thermodynamic parameters obtained in this study (ΔH ⁰ = −32.43 and −29.61 kJ/mol) are within the range (−25 to −45 kJ/mol) reported by Li et al. for methane adsorption on medium-rank coals, confirming the physical adsorption nature. The slightly lower (less negative) ΔH ⁰ values for the Huaxing sample compared to the Tiefa sample may be attributed to its higher vitrinite content, as suggested by the work of Li et al. showing that vitrinite-rich coals exhibit lower adsorption heats.

5. Conclusion

Unlike conventional conductive or convective heating, which relies on thermal diffusion through the coal matrix and suffers from low thermal efficiency and potential secondary contamination, IRH provides noncontact electromagnetic energy that directly couples with coal molecules at the vibrational and rotational levels. This distinction is critical because it leads to volumetric heating with minimal heat loss and enables targeted energy delivery to the adsorption sites, as evidenced by the lower bulk temperature required to achieve equivalent adsorption reduction compared to conventional heating.

This study provides the first systematic investigation of methane adsorption on tectonic coal under infrared radiation heating, integrating experimental measurements with theoretical modeling and microstructural analysis. The following novel findings are established:

• 1IRH uniquely suppresses methane adsorption beyond thermal effects. While both IRH and conventional heating reduce adsorption capacity, IRH achieves this with lower bulk temperature rise due to direct molecular excitation, suggesting an energy-efficient pathway for CBM enhancement.
• 2A predictive theoretical model for the adsorption equilibrium constant b has been derived. The model, according to eq , establishes the quantitative relationship between IRH power and adsorption affinity, with coal-specific constants k _Liao = 2.24 and k _Ji = 2.58. This provides a theoretical basis for optimizing IRH parameters in field applications.
• 3IRH-induced microstructural modification is the key mechanism. SEM-image analysis reveals that IRH reduces micropore proportions by 5–10%, directly correlating with decreased adsorption capacity. This microstructural change is attributed to thermal stress-induced pore expansion and particle detachment, which is distinct from the purely thermal effect of conventional heating.
• 4The adsorption thermodynamics confirm spontaneous, exothermic, physical adsorption. The negative ΔG ⁰, ΔH ⁰ < 80 kJ/mol, and positive correlation between q _st and adsorption amount collectively indicate that IRH facilitates methane desorption by reducing the energy barrier for gas release, thereby promoting CBM recovery.

These findings establish IRH as a promising technique for enhancing CBM production, with potential advantages over conventional thermal methods in terms of energy efficiency and targeted heating. Future work should focus on field-scale validation and optimization of IRH parameters.

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

The authors declare no competing financial interest.