Numerical simulation of magma intrusion on the thermal evolution of low rank coal

: To study the effect of magma intrusion on the thermal evolution of low-rank coal with high water content, the mathematical relationship between water content variation and thermal conductivity of low-rank coal was analyzed by COMSOL Multiphysics numerical simulation and field validation. Taking Daxing Mine in Tiefa coalfield as the research background, the effects of magma finite time intrusion mechanism and water volatilization in coal on thermal evolution and organic maturity of coal seam are investigated in this paper. The results show that as the sill thickness increases, the thermal evolution temperature of the coal seam increases, the required thermal evolution time increases and the final retention temperature increases after the coal seam is cooled down. Approaching the magma, the maximum temperature that the coal seam can reach increases, the maximum temperature lasts longer, and the final temperature retained by the coal seam becomes higher. The increase of water content of coal makes the thermal conductivity increase, and the rate of heat transfer from coal seam is accelerated, and more heat is transferred to distant places in the same time. At the same time, the heat lost by the magma in the same time increases, the time required for the cooling of the magma decreases, and the maximum temperature reached by the underlying coal seam is significantly lower. The presence of moisture weakens the thermal evolution of the magma to the coal seam and reduces the expected maturity of the coal. The results of average random vitrinite reflectance (R o ) and moisture examination of coal samples collected at the Daxing Mine site verified the numerical simulation results of magma thermal evolution. (R o ) back-calculated paleotherm results and showed that heat flow models based on simple conduction cooling in closed geological systems do not accurately calculate the temperatures reached during contact metamorphism. A heat conduction model was established to describe the heat dissipation of magmatic intrusions, and further combined with the EasyR o % model show that the effective thermal conductivity of unsaturated porous media is significantly affected by water content. Based on three theoretical models (parallel conduction model, series model and Woodside-Messmer model), the relationship between effective thermal conductivity and water content is calculated and verified by experiments. The results show that the experimental results are in good agreement with the theoretical values of WM model (Pan 2000). According to WM model, the relationship between moisture content and thermal conductivity is expressed as Eq. (11) (Pan 2000):


Introduction
Magmatic intrusion into coal-bearing strata occurs in many regions worldwide, such as the Colorado (Dutcher et al. 1968;Finkelman et al. 1998) in the United States, the Huaibei Mining District (Wang et al. 2014) in China, the Kyushu region (Sasaki 1959) in Japan, the west coast of Australia (Charles et al. 1998 simulation results, which fit well and showed that magma intrusion can significantly accelerate the rate of hydrocarbon generation in the surrounding rocks. There are also models that consider the role and importance of the latent heat of magma crystallization (Jaeger 1957;Carslaw and Jaeger 1959), the intrinsic heat of the intrusive body (Galushkin et al. 1997), the mechanism of magma intrusion (Yang et al. 1996), and the mode of heat flow (Jaeger 1959) on the thermal evolution of coal rocks.
Low rank coal is characterized by high natural water content, and the volatilization of pore water during the cooling of the magma intrusion when the coal seam contains water will significantly change the thermal evolution of the intruded coal seam (Jaeger 1959;Wang et al. 2007). The study of numerical simulation of magma thermal evolution showed that the volatilization of pore water would significantly reduce the predicted organic maturity of the surrounding rock ). In the study of numerically simulated magmatic thermal effects, saturated water treatment of coal was considered to compare the changes of thermal conductivity and diffusion coefficient of coal before and after treatment, and the results showed that the thermal conductivity and diffusion coefficient of rocks increase with decreasing temperature, and these properties become more obvious after saturated water treatment of rocks at low temperatures (Delaney 1988). However, in the literature on numerical simulation of magmatic thermal evolution of coal, there are few papers that consider the relationship between moisture and thermal conductivity of coal, and there are few studies on the issue that changes in moisture of coal seams affect the effect of magmatic thermal evolution of coal.
The low rank coal of Daxing Mine in Tiefa, China, is severely intruded by magma, and ten coal and gas outbursts have occurred in Daxing Mine since the construction of the mine, all of which occurred in coal seams near the igneous erosion zone, and 9 of them have occurred in the No.7 coal seam, which is severely intruded by magma. In this paper, we will simulate the 5 effects of different sill thickness, distance between magma and coal seam, and different moisture on the thermal evolution of coal seam with the help of COMSOL numerical simulation software, analyze the mathematical relationship between moisture and thermal conductivity of coal seam, and study the effect of moisture on the magma thermal evolution of coal. And the moisture and R o were measured by sampling in the coal seam in the magma intrusion area of Daxing Mine to carry out the validation study.

Basic theory of heat flow
Heat conduction, heat convection and heat radiation are the three forms of heat flow (Yang et al. 2006). The way of heat flow by heat conduction only depends on the thermal motion of micro particles. The heat conduction of porous media includes three processes: the heat conduction process of solid particles; the heat conduction process between fluids in pores and between solid particles and fluids; and the heat conduction process when there is contact thermal resistance between solid particles (Yang et al. 2006). As a kind of porous medium, coal is more complex than single solid in the heat flow process. The process of heat flow is more complex and accompanied by material migration.
Magmatic intrusion is an unsteady process, which causes the strata to reach a high temperature in a short time. After magma intrusion, it mainly transfers heat to surrounding coal by means of heat conduction. Although heat convection and heat radiation also exist, it is much weaker than heat conduction. The study of heat conduction is mainly about the spatial distribution of temperature over time, expressed by T, which is expressed as Eq. (1) Where x, y, z are three-dimensional coordinates and t is time. The intrusion process of magma is an unsteady heat conduction process, t≠0. Fourier law reveals the relationship between the heat flux density and the temperature gradient in a heat conducting object, and the mathematical expression is Eq. (2): Where q is the heat, J; λ is the thermal conductivity, W·(m·K) -1 ; F is the heat area, m 2 ; a negative sign indicates that the heat is transferred towards the direction of low temperature.
The thermal evolution of magma on the surrounding rock or coal can improve the organic maturity of the surrounding rock (Rahman et al. 2014;Wang et al. 2010a). The R o of coal is usually used to represent its organic maturity. The paleotemperature T peak (Barker et al. 1994) of thermal evolution of magma can be inverted by coal rock R o , which is expressed as Eq. (3):

Magmatic rock heat flow model considering the influence of coal water
Magma intrusion is a long-term and complicated process, and the heat flow of porous media is also very complicated. The change of coal seam temperature is affected by many factors. In order to facilitate research, the process needs to be simplified and assumed. It is assumed that the skeleton of coal is stable and not deformed during magma intrusion; there is no internal heat source in coal and no heat is generated; magma intrusion mechanism is instantaneous intrusion mechanism; the heat flow mode is heat conduction, and the influence of convection and heat radiation on magmatic intrusion process is ignored. The coal seam has uniform moisture, and the water content is the same everywhere in the coal seam.
Where ρ 1 is the density of magma, kg/m 3 ; L c is the latent heat of magma transformation, kJ/kg; Tc 1 -Tc 2 is the temperature range of magma transformation, that is, magma transformation occurs in this temperature range. According to the law of conservation of energy, the heat input per unit time is equal to the sum of the heat output per unit time, the change of the internal energy of the derived magma, and the internal energy consumed by the phase transformation of the magma, which is expressed as Eq. (6) (Wang et al. 2014): In engineering problems, it is often considered that the thermal conductivity of an object is the same everywhere under the same condition. The formula can be simplified as Eq. (7): Where λ 1 is the thermal conductivity of magma, W·(m·K) -1 ; c 1 is the specific heat capacity of magma, J·(kg·K) -1 . The coal seam is baked by magma, and the temperature rises continuously. After reaching a certain temperature, the water in the coal seam will change phase. At this time, the coal seam continues to absorb heat, but the temperature is no longer rising, and the absorbed heat is used for water phase transformation ( Where ρ w is the density of water, kg/m; L v is the latent heat of phase change of water, kJ/kg; w is the water content, dimensionless; T v1 -T v2 is the temperature range of phase change, that is, the phase change of water occurs in this temperature range. Based on the law of conservation of energy, the heat introduced into the coal micro element in unit time is equal to the sum of the heat derived from the coal micro element in unit time, the change of the internal energy of the coal micro element and the internal energy absorbed by the water contained in the coal micro element in phase change, which is expressed as Eq. (9): Assuming that the thermal conductivity of the coal seam is the same, the simplified differential equation of heat conduction is shown in Eq. (10): Where λ2 is the thermal conductivity of coal, W·(m·K) -1 ; ρ2 is the density of coal, kg/m 3 ; c2 is the specific heat capacity of coal, J·(kg·K) -1 .

Relationship between moisture and thermal conductivity of low rank coal
Phase change materials are involved in the mathematical model of heat flow considering the influence of water, and the physical and chemical properties will change before and after phase change, which has a great influence on the simulation results. In the process of simulating temperature change, the thermal conductivity of material is very important, and the relationship between moisture of coal and thermal conductivity needs to be studied.
Where λ e is the effective thermal conductivity, W·(m·K) -1 ; α is the correction coefficient, dimensionless, different values for different materials, this paper takes 0.8; λ 0 is the thermal conductivity of skeleton, W·(m·K) -1 ; λ w is the thermal conductivity of water, W·(m·K) -1 ; λ g is the thermal conductivity of air, W·(m·K) -1 .

Numerical simulation
In order to study the temperature change law of low rank coal with high water content after magma intrusion, COMSOL Multiphysics numerical simulation software was used to study the temperature distribution law of heat conduction between sill and Water-bearing coal seams, and the influence of different water content of coal seam on the temperature change of coal seam after magmatic intrusion.
Before the numerical simulation, the relevant parameters are assigned, and the parameter content and assignment basis are shown in Table 1  Since the influence of moisture is considered in the simulation, the physical property parameters before and after the phase change of the material need to be set. The setting content and basis are shown in Table 2 (Wang et al. 2017).
In this simulation, four kinds of water content are selected as 50%, 30%, 8%, and 3% respectively. According to Eq. (11), the thermal conductivity of coal can be calculated. The results are shown in Table 3.

Analysis of the influence of sill thickness on the thermal evolution of coal seams
Based on the multi-physics coupling software COMSOL with finite element solution, a numerical simulation of the heat conduction temperature distribution between magma and surrounding rock was established. Before the simulation, the relative positions of the simulated sill, coal, and surrounding rock need to be simplified and the boundary should be set, and then the three are modeled in COMSOL. Since the thermal conductivity of the three main bodies is different and the initial temperature is different, the whole model needs to be divided into three in the modeling. The model set up the minefield is 2000m long and 1000m wide; the sill is 1000m long and its thickness can be adjusted. According to No. 7 coal seam of Daxing Mine, the coal seam is located 10m below the sill, and the set coal seam is 1800m long, 3.5m thick, and 10m away from the magma floor. A model is established as shown in Fig. 2.
Set surface temperature T 1 to 20℃, surrounding rock temperature T 2 to 30℃, initial magma temperature T 3 to 1000℃, other parameter settings are shown in Table 1, magma thickness is set to 50m, 80m, 10m, simulation time is set to 1000a. The simulation results are shown in Fig. 3. Fig. 3 indicates that the temperature of the coal seam rises sharply after magma intrusion, reaching the highest temperature in the first 100 years, and then the temperature begins to decrease slowly. The greater the thickness of the magma, the higher the maximum temperature reached by the coal seam. When the thickness of magma is 50m, the maximum coal seam temperature is 380℃; when the thickness of magma is 80m, the maximum coal seam temperature reaches 420℃; when the thickness of magma is 100m, the maximum coal seam temperature is close to 450℃. As the thickness of magma increases, the maximum coal seam temperature lasts longer. When the thickness of magma is 50m, 80m and 100m, the time for the coal seam to reach the maximum temperature is 30a, 50a and 70a respectively. This is roughly consistent with the temperature variation trend in the simulation results of Wang et al. (2014). However, the distance between the sill and the coal field roof is far greater than the simulated distance set in this study, so the temperature variation is lower than the temperature variation results in this study.

Influence of the distance from magma on the thermal evolution of coal
Model 2 sets up a minefield of 2000m long and 1000m wide; the magmatic rock mass is 1000m long and 50m thick; the coal seam is 1800m long and 2m thick. The distances from the floor of the sill are 10m, 20m, 30m, 40m, and 50m, respectively. Model 2 is shown in Fig. 4.
Set the surface temperature T 1 to 20℃, the surrounding rock temperature T 2 to 30℃, the initial magma temperature T 3 to 1000℃, the other parameters are shown in Table 1, and the simulation time is set to 1000a. The simulation results are shown in Fig. 5. Fig. 5 (a) shows the coal seam temperature rose sharply after magma intrusion, reaching the highest temperature in the first 100a, and then decreasing slowly. Closer the coal seam is to the magma, higher the maximum temperature of the coal seam is, and the required time is 20a, 40a, 60a, 90a, 120a respectively. After the magma cools, the closer the magma is, the higher the final temperature of the coal seam, but the difference is smaller. Fig. 5(b) shows that the closer the distance to the magmatic rock, the R o of coal and the peak temperature of magma thermal evolution have an increasing trend. It shows that the thermal evolution of magma significantly improves the organic maturity of coal. From 50m to 10m away from the magma, the R o of coal increases by 11.32% from 1.25%, and the peak temperature of magma increases from 180.18 ℃ to 462.50 ℃.

Effect of water content on coal seam heat conduction during magma cooling
In order to study the influence of different water cuts during the cooling process of magma intrusions on the thermal evolution of coal seams, the model is further simplified, assuming that the thermal conductivity of surrounding rock and coal sea. Model 3 set up the mine field 1000m long and 500m wide; the magmatic rock mass is 400m long, 50m wide and 225m above the ground. Model 3 is shown in Fig. 6.
Set the surface temperature T 1 to 20℃, the surrounding rock temperature T 2 to 30℃, the initial magma temperature T 3 to 1000℃, the other parameters are shown in Table 1, and the simulation time is set to 1000a. The simulation result is shown in Fig.7.
The heat lost by the magma in the same time is used for its own phase change and heat flow in coal, which increases with the decrease of the central temperature of the magma. 12 Therefore, with the increase of coal seam moisture content, the heat loss of magma increases in the same time. Fig. 7(a) indicates that after 100a, the coal seam moisture content increases from 0% to 50%, and the maximum temperature reached by the coal seam decreases from 540℃ to 280℃.Under high temperature conditions, coal will go through two stages of drying degassing and coal matrix pyrolysis (Su et al. 2020), and part of the heat of magma intrusion was absorbed in the degassing process of water in coal, so the higher the moisture of coal seam, the lower the temperature after magma intrusion.
Comparing magma intrusion at 100a, 500a and 1000a, the water content is the same, and the temperature of the coal seam at the same depth is lowered. Comparing Figs. 7(a), 7(b), and 7(c), it can be seen that as the simulation time increases, the coal temperature has a decreasing trend. The greater the water content of coal, the smaller the increase in temperature near the magmatic coal. This is because the increase of the water content of coal leads to the greater the thermal conductivity of its own, the more heat transferred to the distance. In addition, more heat is consumed for the phase transition of water, the lower the coal temperature is.
The time required for magma cooling decreases with the increase of water content. Fig. 7(c) indicates that at 1000a, when the water content is 0%, 3%, and 8%, the temperature of the magma center is higher and the temperature changes at different depths. When the water content is 30% and 50%, the temperature change is small, and the magma cools quickly. It is studied that after 8000 years of magma intrusion in coal mines, magma and surrounding rocks reach a geothermal balance, but the deep geothermal of coal mines is abnormal, and its stratigraphic characteristics, geological structure and groundwater flow activities are the main factors leading to its abnormality (Feng et al. 2020). After the magma was cooled, the greater the water content, the lower the temperature retained by the coal seam. After 1000a of magma intrusion, the water content increased from 0% to 50%, and the coal seam retention temperature decreased from 95°C to about 87°C.

Temperature variation with time for coals with different water content
Wang Dayong et al. created a magma intrusion model, compared the numerical simulation with the measured results, and studied the effect of pore water volatilization and supercritical state on the degree of coal metamorphism. The results show that when a limited 13 time intrusion mechanism is used, the effect of pore water on the degree of metamorphism is predicted. The deviation is slightly lower, which indicates that the limited time intrusion mechanism of magma and the volatilization of pore water may represent natural conditions ). In order to study the influence of water content on coal seam temperature and degree of metamorphism, combined with the actual situation of the Daxing Mine field, Model 4 sets the mine field 2000m long and 1000m wide; the magmatic rock mass is 1000m long and 50m wide. The coal seam is 1800m long, 4m wide, and 50m away from the magma floor. Model 4 is shown in Fig. 8.
Set the surface temperature T 1 to -10℃, the surrounding rock temperature T 2 to 30℃, the initial magma temperature T 3 to 500℃, the other parameters are shown in Table 1, and the simulation time is set to 5000a. The simulation result is shown in Fig. 9. Fig. 9(a) shows that as the moisture content increases, the maximum temperature reached by the coal seam decreases significantly, and the time to reach the maximum temperature becomes shorter.
When the moisture content increases from 0% to 50%, the maximum coal seam temperature drops from about 120°C to 35°C (Fig.9a). The coal R o is reduced from 0.78% to 0.40% (Fig.9b).
The comparative analysis of Figs. 5 and 9 shows that the presence of moisture reduces the maximum temperature that the coal seam can reach, weakens the thermal evolution of magma on the coal seam, and thereby weakens the degree of coal seam metamorphism. In the previous study, 15 coal samples were taken from No.7 coal seam in the range of 0 to 250m from the sill, and the industrial analysis and vitrinite reflectance measurement were carried out in the laboratory. Based on the determination results of moisture and R o (Jiang et al. 2016), the relationship between moisture content, R o and the distance between coal sample and sill is plotted, as shown in Fig. 11. Fig. 11 indicates that the intrusion of sill reduces the moisture content of coal and improves the metamorphic degree of coal. Near the sill, the water content of coal decreases from 7.5% to 1.6%, and R o increases from 0.53% to 1.58% (Fig.11a). The peak temperature of magmatic thermal evolution increases from 82.52°C to 210.67°C when the distance changes from 264 m to 0.1 m (Fig.11b). The above research results to some extent verify the numerical simulation results of magma thermal evolution coal. The thermal evolution of magma increases the degree of metamorphism of low-rank coals. Magma baking or heat conduction reduces the vaporization and evaporation of water in coal. In addition, due to high water content (7.5%) of low rank coal in Daxing Mine, the thermal effect of magma intrusion on coal reduced to a certain extent, thereby reducing the degree of coal metamorphism.

Conclusions
In this paper, the relationship between moisture content and thermal conductivity of coal is investigated by using numerical simulation and field verification method. The relationship between sill thickness, distance from igneous sill, organic maturity of coal and time of magma thermal evolution are analyzed by numerical simulation. Further, the temperature of the cooled coal is analyzed in relation to the moisture content, and the main conclusions are as follows: 1) The establishment of magma thermal evolution coal and heat flow model shows that the main factors affecting the change of coal seam temperature are: initial magma temperature, thickness of magma, thermal conductivity of coal and the distance between coal and magma. There is an inherent relationship between the thermal conductivity of coal and the moisture content. As the moisture content increases, the thermal conductivity increases. 15 The calculation results show that when the water content is 3%, 8%, 30%, 50%, the thermal conductivity of coal is 0.291, 0.358, 0.887, 2.024 W·(m·K) -1 , respectively.
2) The simulation results using COMSOL numerical software show that the greater the thickness of magma, the higher the maximum temperature reached by the coal seam, the longer the duration, and the higher the final temperature retained. The closer the distance to the magma, the higher the temperature reached by the coal seam and the longer it will take.
After the magma cools, the closer to the magma, the higher the final retention temperature of the coal seam, but the difference is small. Close to the magma, the R o of coal and the peak temperature of magma tend to increase. The results show that the thermal evolution of magma significantly improves the organic maturity of coal. The distance to the magma decreases from 50m to 10m, the R o of coal increases from 1.25% to 11.32%, and the peak magma temperature increases from 180.18 ℃ to 462.50 ℃.
3) With the increase of water content, the thermal conductivity of coal increases, and the heat flow rate increases. The heat transferred from the magma to the distance increases, so does the heat loss from magma. With the increase of water content, the cooling time of magma decreases, the maximum temperature of coal seam decreases significantly, and the time to reach the maximum temperature is also shorter. As the water content increases from 0% to 50%, the maximum temperature of coal seam decreases from 120 ℃ to 35 ℃. The R o of coal decreases from 0.78% to 0.40%. It shows that the existence of water significantly reduces the maximum temperature of coal seam, weakens the thermal evolution of magma on coal, and causes the metamorphic degree of coal to be lower than expected.      Table 2 Physical parameters of phase change materials Table 3 Thermal conductivity of coal under different moisture content