Heat–fluid–solid coupling model for gas-bearing coal seam and numerical modeling on gas drainage promotion by heat injection
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Improving the absorbed gas to active desorption and seepage and delaying gas drainage attenuation are considered as key methods for increasing drainage efficiency and gas output. According to the solid mechanics theory, the nonlinear Darcy seepage theory and thermodynamics, the heat–fluid–solid coupling model for gassy coal has been improved. The numerical model was founded from the improved multi-field coupling model by COMSOL Multiphysics and gas drainage by borehole down the coal seam enhanced by heat injection was modelled. The results show that the heat–fluid–solid model with adsorption effects for gassy coal was well simulated by the improved multi-field model. The mechanism of coal seam gas desorption seepage under the combined action of temperature, stress and adsorption can be well described. Gas desorption and seepage can be enhanced by heat injection into coal seams. The gas drainage rate was directly proportional to the temperature of injected heat in the scope of 30–150 °C and increasing in the whole modelled drainage process (0–1000 d). The increased level was maximum in the initial drainage time and decreasing gradually along with drainage time. The increasing ratio of drainage rate was maximum when the temperature raised from 30 to 60 °C. Although the drainage rate would increase along with increasing temperature, when exceeding 60 °C, the increasing ratio of drainage rate with rising temperature would decrease. Gas drainage promotion was more effective in coal seams with lower permeability than with higher permeability. The coal seam temperature in a 5 m distance surrounding the heat injection borehole would rise to around 60 °C in 3 months. That was much less than the time of gas drainage in the coal mines in sites with low permeability coal seams. Therefore, it is valuable and feasible to inject heat into coal seams to promote gas drainage, and this has strong feasibility for coal seams with low permeability which are widespread in China.
KeywordsGassy coal Heat–fluid–solid coupling model Heat injection Gas extraction Numerical modeling
Gas (coalbed methane) extraction from low permeability coal seams has been always a difficult problem for prevention gas disaster in underground coal mine and utilization of coal mine gas in the world (Yuan 2015; Li and Fang 2014; Esterhuyse 2017). The variation of gas flow in low permeability coal seam is mastered under the impact of multiple factors such as gas, stress and temperature. This has a great significance to study the theory and technology for efficient coal seam gas extraction.
Many previous researches have proven that coal is a porous material with a large internal surface area, and it physically adsorbs gas. The adsorption and desorption processes for gas are basically reversible, and the higher the temperature is, the lower the adsorption quantity of gas (Zhang et al. 2013). At present, technical means were used to improve the gas extraction efficiency of low permeability coal seams, such as pressure relief extraction, hydraulic punching, hydraulic fracturing, etc. (Uth 2014). The principles of reducing the influence of ground stress and increasing the local permeability of coal seams are involved in improving the extraction efficiency in a short time. However, the attenuation of extraction rate is faster, especially in soft coal seams. Due to artificial fractures closing quickly under stress, the permeability decreases rapidly. Therefore, new technical ways should be found to improve the gas desorption and seepage velocity and delay the gas extraction rate attenuation in low permeability coal seams.
Drawing on the heat injection technology in the petroleum industry, the idea was putting forward the increasing of coal seam temperature by injecting heat to accelerate and increase gas production. The study found that raising the coal seam temperature can accelerate the desorption and releasing of adsorbed gas and increase the seepage rate of gas in coal seam fissures, which may become an effective method to promote gas extraction efficiency (Shahtalebi et al. 2016; Zhao et al. 2018; Teng et al. 2018). Previous research showed that some experimental and theoretical studies on the influence of temperature on coal seam gas adsorption and seepage have achieved many valuable results. Anderson et al. (2011) studied the influence of temperature on its a and b values using Langmuir adsorption theory and analyzed the changes in the a and b values below 200 °C. The coal desorption and permeability change under the coupling condition of temperature and stress fields was carried out by Li et al. (2009a, b) to establish the seepage control equation and obtain the gas desorption and seepage change mechanism with the increase in temperature. The influence of temperature change on the initial speed of methane emission was studied, and the result indicated that the relation between emission and temperature showed a proportional to quadratic function (Tailakov et al. 2015). The studies of the characteristics of methane desorption in coal under uniaxial stress and temperature concluded that temperature rise was a key reason for the large amount of desorption of adsorbed gas (Wang et al. 2013). Zhu et al. (2013) carried out research on the mechanical properties of coal samples for gas adsorption under the influence of temperature changes. It is believed that the adsorption capacity of coal samples was directly affected by the temperature changes, resulting in an increase in free gas content, thus reducing the strength of coal containing gas as a whole. Yin et al. (2013) and Zhang et al. (2018b) carried out permeability experiments to change the stress and temperature conditions of coal samples and discovered that permeability decreasing in the scope of 0–80 °C, while increasing sharply when the temperature exceed 80 °C. The COMSOL software was used to numerically simulate the solid–gas–heat coupling effect of gas-bearing coal & rock masses and obtained the gas seepage mechanism near the heading face but did not consider the temperature effect (Li et al. 2017). Ju et al. (2016) and Alam et al. (2015) tested the change mechanism of permeability under the change in temperature (below 80 °C) and confining pressure and believed that the increase in temperature will expand the coal matrix, resulting in pore closures and a decrease impermeability. Zhang et al. (2018a) introduced the theory of coal & gas two-state adsorption heat, constructed the control equation for the coal seam temperature field, improved the heat–fluid–solid coupling mathematical model of coal seam gas flow, and theoretically explained the interaction mechanism of adsorption and desorption, stress, temperature and seepage fields in the process of coal seam gas flow. Shan and Lai (2018) conducted seepage tests under different temperatures and pore pressures. It was believed that the increase in pore pressure can reduce permeability to a certain extent whereas the increase in temperature increases permeability. Wang et al. (2015) carried out experiments on the variation of coal sample permeability under different temperatures and axial pressures. It was concluded that the increase in axial strain will obviously reduce the permeability, and the reduce rate will gradually decrease with the increase in strain. The influence of temperature on permeability was related to the stress state inside the coal sample.
The above research results further prove that temperature has an important influence on gas adsorption and seepage flow. However, the coupling theory considering the heat–fluid–solid coupling and gas adsorption–desorption effects still needs improvement. In addition, there were few studies on the extraction of gas by injecting heat into coal seams close to the in-site conditions. Therefore, this paper aimed at the in-site conditions of coal heat injection and gas extraction, the heat–fluid–solid coupling model of gas-bearing coal was improved, and the variation state and extraction efficiency of coal seam gas were studied based on the actual conditions of low permeability coal seams after injecting heat by using numerical simulation.
2 Mathematical model of heat–fluid–solid coupling for gas-bearing coal
Coal seams contain complex fissures and pores of different scales resulting in rich adsorption potential. A large number of gas molecules are adsorbed in the cracks and pores of coal. Coal seam temperature and stress interact with gas desorption and seepage coupling. The heat–fluid–solid coupling model of coal-containing gas needs to fully consider the changes in coal permeability and gas flow under the influence of multiple factors.
2.1 Fundamental assumptions
A coal seam is a uniform porous material with pores and fissures;
Gas drainage has little influence on the overall deformation of a coal seam;
The temperature change in the seepage process does not affect the gas dynamic viscosity;
The free gas in the coal seam satisfies the ideal gas state;
The coal matrix at any point in the coal seam is consistent with the gas temperature;
The pore pressure is consistent with the gas pressure in the fissures;
The influence of moisture on coal bed adsorption and seepage can be ignored.
2.2 Coal deformation control equation
Solid equilibrium equation
Constitutive equation of a coal body considering deformation of adsorbed gas
2.3 Gas seepage control equation
2.3.1 Coupling relationship among three fields
2.3.2 Seepage control equation
The above formula was the coal seam seepage equation of adsorbed gas containing the source and sink term I. The permeability k and porosity ϕ here varied with the strain, gas seepage and temperature fields, so the seepage field equation not only reflected gas seepage but also the coupling change in the coal seam stress and temperature fields. The solution could be obtained only when the stress field equation, seepage field equation and temperature field equation of coal body were obtained.
2.4 Temperature field control equation
3 Numerical modelling of heat injection enhanced drainage in a gas-bearing coal seam
According to the above-mentioned heat–fluid–solid coupling model, a numerical model was established by using COMSOL Multiphysics to simulate the process of enhancing gas extraction by injecting heat into coal seam boreholes.
3.1 Numerical model and parameters
Property parameters in the numerical model
Young’s modulus of coal E (GPa)
Young’s modulus of coal skeleton Es (GPa)
Poisson’s ratio of coal ν
Coal density ρ (kg/m)
Langmuir volume constant VL (m3/kg)
Adsorption constant b (1/MPa)
30.12–0.20T + 0.000325T2
Gas density in standardized status ρg (kg/m)
Coefficient of viscosity μ (Pa s)
1.84 × 10−5
Initial porosity of coal seam φm0
Initial permeability of coal seam kf0 (m2)
1.0 × 10−19
Specific heat of coal cs (J/[K Kg])
Specific heat of gas cg (J/[K Kg])
Thermal expansion coefficient αs (1/K)
0.1 × 10−6
coefficient of heat conduction kt (W/[m K])
Extraction pressure Pa (MPa)
Langmuir strain constant εL
Moisture in coal M (%)
Ash content of coal A (%)
The heat injection temperature was various, and five numerical calculation schemes were designed, namely, no heat injection (keeping the original temperature at 30 °C) and heat injection temperature Tz at 60 °C, 90 °C, 120 °C and 150 °C. Other conditions of the model remained unchanged.
3.2 Initial conditions
Gas and stress initial conditions: when t = 0, the original coal seam gas pressure p0(x, y, z) = 3 MPa. The stress field initial displacement ui = 0(i = 1, 2, 3).
Boundary conditions: assuming that the roof and floor are impermeable strata, the boundary conditions of the seepage field were: p = p0. Coal seam boundary gas flow qs = 0. The drainage borehole boundary pressure p = Pa.
Stress boundary condition: the top boundary of the coal seam (z = 10 m) bears the gravity of the overlying strata of 10 MPa.
Displacement boundary conditions: lower boundary (z = 0) and surrounding boundaries (x = 0, x = 50, y = 0, y = 50) are displacement constraints.
Initial conditions of the temperature field: initial coal seam temperature was T0 = 30 °C, and the heat injection hole temperature was Tz which according to the modelling case.
The unit of calculation time t was d, and the calculation time range was 0–1000 d for the above five schemes.
3.3 Numerical modelling results
3.3.1 Temperature and gas distribution in the coal seam after heat injection
Figures 4 and 5 showed the distribution of temperature values at different times in the coal seam when the heat injection temperature was 90 °C, showing the heat transfer process after injection in the coal seam borehole.
Heat was transferred outward after injection from the heat injection hole. When the heat was injected for 10 d, the rising temperature range was small, affecting only about 2.5 m around the heat injection hole. When the heat was injected for 100 d, the rising temperature range expands to 15 m, and the temperature of drainage hole that 5 m away from the heat injection hole increased to about 39.6 °C. When the heat was injected for 500 d, the temperature increased extended to the whole model range and the temperature of the drainage hole increased to 56.7 °C. At 1000 d of heat injection, the drainage hole temperature increased to 64.6 °C.
When the drainage time reached 100 d, the influence range of the drainage borehole was little, limited to about 5 m, and the overall reduction of coal seam gas content was very low. Different heat injection temperatures had a certain influence on the reduction of coal seam gas content. The higher the injection temperature, the greater was the reduction of gas content. However, the influence of temperature was also limited to a small range near the heat injection hole and the drainage hole, and there was almost no difference in the influence of temperature on the gas content of the coal seam beyond the 5 m on the right side of the drainage hole.
At 500 d of extraction, the coal seam gas content decreased within the whole model range, and the largest decrease was near the extraction borehole, which was close to 50% of the original content. The higher the heat injection temperature, the lower was the residual gas content. According to the comparison on different temperature for gas extraction, the residual gas content decreased more significantly when temperature rise from 30 to 60 °C.
3.3.2 Effect of injection on the gas extraction rate and accumulative yield
Comparison of the output rate and output production of gas with different injection temperatures
Extraction time (d)
Extraction rate (m3/d)
Cumulative output (m3)
3.3.3 Effect of heat injection temperature on gas extraction of coal seams with different permeability rates
Coal seam permeability is one of the main factors affecting the gas extraction efficiency and yield. The increase in the coal seam temperature will promote gas desorption, but the expansion deformation of the coal matrix caused by the temperature increasing will adversely affect permeability. Therefore, the initial coal seam permeability needs to be changed in the numerical model process.
When the coal seam temperature was 30 °C (that was, no heat being injected), the rate of extraction and the cumulative output were proportional to permeability. Because of 1.0 × 10−19 m2 was a typical low permeability level for the coal seam, increasing the permeability would greatly increase the drainage efficiency. When the heat injection temperature was 90 °C, for all coal seams in this research with different permeability, the drainage rate increased. The corresponding drainage output were also significantly improved, but the enhancement of coal seam temperature on low permeability was more obvious considering the different permeability between the extraction rate and cumulative output for the relative difference between the reductions.
In order to analyze the influence of heat injection temperature and permeability on the extraction rate in different stages, based on the coal seam temperature of 30 °C (no heat injection), the relative drainage rate Δq was defined as the ratio of the drainage rate at different heat injection temperatures to the drainage rate at 30 °C at the same drainage time, and this could reflect the change in drainage rate caused by heat injection temperature.
A variety of complex multi-field coupling problems were involved in the gas desorption seepage induced by heat injection in coal seams. The deformation of solids under stress, temperature, adsorption, desorption and the effect on permeability were considered and applied to the mathematical model. Although there was a certain difference with real coal seam conditions, the extraction rate and amount calculated numerically did not fully correspond to the real physical values. However, the simulated temperature, coal seam pressure and extraction rate may give some valuable results of in-site engineering.
The results showed that a temperature increase significantly affects the drainage rate but the effect was different in different temperature scope. From 30 to 60 °C, the ratio of drainage efficiency increasing was largest. The energy consumption for increasing drainage rate was smallest. It was no wonder that the result was consistent with previous research (Zhang 2011; Zhao 2012). When the coal temperature increased to 60 °C, the desorption rate increased most obviously. Although the continued increase in coal seam temperature could continuous to increase the drainage efficiency, with the excessive energy consumption and the impact of the mining environment, the difficulties of in-site implementation will be multiplied. Therefore, the coal seam was raised from the original temperature (20–30 °C) to 60 °C by injecting hot steam and other methods, which owned significant advantages, such as saving energy and easy operation while achieving a significant increase in the coal seam gas drainage rate.
The most common technique to extract gas for low permeability coal seams is bedding drilling, the simplest and most effective method to improve the drainage rate is reduce the spacing of drilling holes. Some coal mines’ drilling hole spacing, even for 1–2 m (Zhang 2011; Zhao 2012; Lu et al. 2015), increases the amount of drilling engineering and costs a lot of manpower and resources. However, the achievement was not as expected. Although coal seams are low thermal conductivity substances (thermal conductivity generally in the range of 0.2–0.5 W m−1 K−1), with steam injection heating, in about 3 months, the surrounding 5 m range of the coal seams can be heated to around 60 °C (Fig. 5). It doesn’t take long to heat the coal seam compared with the gas extraction time in coal mines. In addition, according to the simulation results, it is better to improve the drainage rate of low permeability coal seams by injecting hot heating steam. The low permeability coal seam drainage rate attenuation is fast, which is related to the difficulty of gas desorption from coal seam. The coal seams heating are required for a certain period of time, just coincident with the initial easy extraction time. The coal seam heating will slow down the drainage rate attenuation, increase the drainage rate and then enhance the double effect of the drainage output.
The multi-physical field coupling model of heat transferring and adsorption in gas-bearing coal seams has been improved and solved by COMSOL Multiphysics. The desorption and seepage process of coal seam gas under the combined action of temperature, stress and adsorption affect can be well simulated to some extent.
In the range of 30–150 °C, gases desorption and seepage flow will be promoted at higher temperatures. The gas drainage rate is proportional to temperature. During the extraction time of 0–1000 d, the increase in gas drainage rate was largest at the initial stage and reduces gradually with time.
Different scope of temperature rise has different effects on increasing the gas extraction rate. From 30 to 60 °C, the ratio of increase is the largest. It will still increase with the temperature rise, but the increase ratio will reduce and there will be a remarkable increase in energy consumption, which will also worsen the in-site environment of underground coal mines.
Comparing the gas extraction by injecting heat into coal seams with different permeability, the results show that the increase in temperature has the more obvious effect on the extraction efficiency of low permeability coal seams.
Although the thermal conductivity of coal is low, injecting atmospheric pressure or pressurized steam into the coal seam will still raise the coal seam temperature within 5 m range of the hot injection borehole to about 60 °C in 3 months, which is much less than the gas extraction times in the coal mine. Therefore, coal seam heat injection was considered an efficient auxiliary means of gas extraction, with strong feasibility for low permeability coal seams in China.
The authors acknowledge the financial support from the Natural Science Foundation of China (U1704131), Program for Science & Technology Innovation Talents in Universities of Henan Province (18HASTIT018) and the Program for Changjiang Scholars and Innovative Research Team in University (IRT_16R22).
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