Introduction

Coal, remaining as a crucial source of energy for China nowadays, is even projected to maintain the leading position in the foreseeable future due to the abundant coal resources and lack of oil/gas in China. However, along with the development of the coal production worldwide especially in China, the coal-field fires occur frequently. As a persistent threat to major coal producing countries, the coal-field fires distribute commonly in exposed coal-bed zones with a long burning history [1, 2], which not only cause the loss of valuable coal resources and the release of large amounts of heat, toxic, harmful or greenhouse gases (such as NOx, SO2 and CO2/CH4) [3,4,5,6], but also produce mine subsidence features like sinkholes and fracture [7,8,9].

In recent years, scholars have done large amount of works to prevent and control coal-field fires [5, 10,11,12,13,14,15,16,17]. Plenty of numerical computation methods and experimental methods have been carried out to investigate the process of coal combustion in coal-field fires zones [18,19,20,21]. Bustin et al. [22, 23] investigated the burning coal seam in South-Eastern British Columbia (Canada) and found that the upper 3 m of coal seam was being consumed and the fire zone was advancing at an angle of 45–70 °C to the strike of the coal seam. Elick [24] proposed the sinkholes and fractures occurred in alignment with thermal anomaly associated with gas and heat release by TIR, whose result indicated that mined-out coal beds acted as conduits for heat circulation or that multiple beds of anthracite coal were on fire in the subsurface in Centralia. Song and Kuenzer [25] explored multidisciplinary investigations associated with coal fires in China and concluded the distribution of coal-field fires of China. Zeng et al. [26] put forward a mathematical solution to define the equivalent permeability for element coal-fire zone and presented a new method for calculating oxygen consumption rate. Wang et al. [27] set up a model coupling seepage with thermal dynamics for coal-field fire and concluded that the combustion center centralizes near the roof and spreads to the outcrop direction quickly. Huang et al. [28] and Wessling [29] put forward the numerical simulation to explain the energy transport processes, which results indicated that the fractures or higher permeability was necessary to enhance natural convection and energy flux. Moreover, Someerton et al. [30] applied two-inch-diameter-cylindrical tests to determine permeability behavior of coal fracture systems, which indicated that the permeability was strongly stress dependent decreasing by more than two orders of magnitude in the stress range of 17.237–137.9 bar.

Furthermore, combustion of coal-field fires coupling the heat release and transfer with stress of overburden has been studied by several researchers. Abed and Sołowski [31] provided a finite element discretization of the equations and number of simulation to describe a thermo-hydro-mechanical framework. Zhao et al. [32] built up the FEM model for solid formation and gas seepage in rock fracture media to explain the gas seepage law and flow mechanism in fractured coal seam. Xia et al. [33, 34] and Wang et al. [35] put forward a coupled model of coal mechanical deformation, gas flow and transfer in fractures, simulated the heat release of coal to predict the time and locations of spontaneous combustion in underground gob and explained the fractured dome distribution. Wessling et al. [36] applied the operator-splitting approach to solve the problem of model coupled with hydraulic, thermal and chemical process, whose result showed that dynamic propagation strongly depended on permeability variations. Wolf and Burining [37] developed a two-dimensional model combining geomechanical effects and reactive flow effects to obtain temperature distribution and permeability distribution and found that the oxygen consumption by combustion of underground fire was approximately proportional to the square root of the average permeability.

Until now, several remarkable achievements have been attained worldwide, but specialized researches on the mechanism of the development of coal-fire fields are still required. The prevention for coal-field fires faces several new problems to be solved urgently, including the generation of new coal-fire fields, the characteristics and mechanism of the rapid spread of coal fires and the characteristics and indicators of resurgence governance for coal-fire fields. At present, the researches on the relationship between stress and combustion of coal-field fires mainly focus on the developing law of fractures and the characteristics of gas flow caused by changing structural stress in fractured coal rocks [27, 38, 39]. However, there are few studies on the self-ignition of the coal-field fires, as well as the diffusion mechanism of coal-fields fire under compression. Considering the topics, it is of great significance to focus on the influence of axial compression on the coal spontaneous combustion and heat transfer characteristics for coal-field fire. Therefore, in order to evaluate the oxidation behaviors and heat transfer characteristics of coal over stress, an axial compression equipped with temperature-programmed (ACTP) device will be utilized to test the characteristic parameters of coal spontaneous combustion under axial compressions, as well as the characteristics of combustion process under oxygen-poor conditions. Moreover, the concentrations of O2 are measured with increasing temperature over different axial compressions. In view of the influence of axial compressions on coal spontaneous combustion and heat transfer, the oxidation kinetics of coal and the thermal conductivity also should be discussed.

Experimental systems and methods

TP system of characteristic parameters for coal spontaneous combustion under axial compression

The ACTP system (see Fig. 1) consists of a TP oven, a heating device, insulating layer, gas path, piston, a cylindrical container of 100 mm in diameter and 150 mm in height, and three temperature sensors with an accuracy of 0.1 °C. The ACTP system could automatically heat the TP oven at a rate of 1 °C min−1. The inlet air could be heated to the same temperature with the oven. The gaseous products (such as CO, CO2, CH4, C2H2, C2H4, C2H6) from the coal samples are separately analyzed by a gas chromatograph with an accuracy of 10−4 ppm. The temperatures at three measuring points (see Fig. 2) in the oven are collected and obtained every 20 s.

Fig. 1
figure 1

The device and experimental system diagram for testing the characteristic parameters during coal spontaneous combustion

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Fig. 2
figure 2

The position of measuring points in the furnace

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Preparation of coal samples

A long-flame coal sample was collected from Geng-cun Colliery in Henan Province of China. The proximate and ultimate analyses of this coal samples are shown in Table 1.

Table 1 Proximate and ultimate analyses for the experimental coal/%
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Testing procedure in TP system

The coal sample of 5 kg was crushed and ground, and then, the particles with diameters of 2–6 mm were sieved out. After that, the sieved coal particles were dried in a vacuum (− 0.08 MPa in gauge pressure) at 30 °C for 72 h for avoiding the influence of water. 0.8 kg coal sample was put into the cylindrical container, which is sealed up for each test. Dry air was injected into the pipelines, and the gas tightness of the whole device was checked. The heating rate of the oven was set as 1.0 °C min−1, and the air flow rate was 1200 mL min−1. The coal spontaneous combustion was carried out under axial compressions of 0, 2, 4, 6 and 8 MPa, respectively. The experiments under each axial compression were conducted when the temperature of the measuring point 1 reached 30 °C, and the released gases were collected and analyzed by gas chromatograph upon 40 °C at the measuring point 1. After that, the significant gaseous products were analyzed every 10 °C from 40 to 450 °C.

The experimental procedures for the ACTP tests in detail are as follows:

  1. 1.

    Set the piston of the booster pump at the bottom level of the kettle. Put the prepared coal sample (about 0.8 kg each test) into the heating oven and seal the top of the reaction kettle. Connect the three thermocouple probes.

  2. 2.

    Set the axial compression at 2 MPa for the first test and hold the compression through the whole process within the pressurizing pump. Press the heating button of the experimental (set the heating rate at 1 °C min−1) device after turning on the power of the system. Inject the dry air and check the air tightness of the testing system. Then set the inlet air flow rate at 1200 mL min−1.

  3. 3.

    Turn on the software for measuring the data for the tests on the computer, and then set the initial temperature (40 °C), the termination temperature (about 450 °C) and the sampling interval (20 s) of the testing procedure. And then start the ACTP system and heat the coal sample in oven.

  4. 4.

    As the temperature of coal in oven reaches 40 °C, the gas generated from the oxidizing coal is imported to the gas chromatograph for about 30 s to distinguish the gas component/concentration. Subsequently, repeat the gas testing every about 10–20 °C from 40 to 450 °C. While the ACTP system is working and coal sample is warming up, keep the axial compression at 2 MPa steadily and record the changing volumes of the coal sample in the oven.

  5. 5.

    While the temperature at the center measurement point of the coal reaches the termination temperature, shut down the heating program and the dry air supply, finally exit the ACTP system.

  6. 6.

    Repeat the testing procedures and test the coal samples within the ACTP at 0, 4, 6 and 8 MPa in turn (0 MPa means without loading the axial compression). Each test under the same axial compression was repeated 3 times.

Oxidation kinetics method

As reported in the literature [40], Ea is expressed by Eq. (1).

$$\ln \frac{{C_{{{\text{O}}_{2} - }}^{0} C_{{{\text{O}}_{2} }} }}{{C_{{{\text{O}}_{2} }} }} = - \frac{{E_{\text{a}} }}{RT} + \ln \left( {\frac{{VA_{0} }}{Q}} \right)$$
(1)

Here, the value of \(C_{{{\text{O}}_{2} }}^{0}\) is 21.5%; \(C_{{{\text{O}}_{2} }}\) is shown in Fig. 7a. It is clear that \(\ln \frac{{C_{{{\text{O}}_{2} }}^{0} - C_{{{\text{O}}_{2} }} }}{{C_{{{\text{O}}_{2} }} }}\) has a linear relationship with \(\frac{1}{T}\) so that Ea could be obtained from the slope.

Experimental results and discussion

Characteristics of stages for coal oxidation process

Figure 3 shows the temperature history of the coal samples acquired by the ACTP system under various compressions at point 1.

Fig. 3
figure 3

Temperature of coal under axial compressions

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Figure 4 shows the heating rates of coal at the center of the container under different axial compressions. As the axial compression is loaded at 2 MPa, there is no significant influence on the porosity of coal in low temperature due to the low stress so that the heating rate of coal is almost the same as the one at 0 MPa. As the temperature of coal increases, a large number of cracks in the coal particles were generated due to continuous pressurization, which could expand the gas seepage channels to promote the oxidation reaction and would not compress the space of the coal particles like other compressions so that the heating rate is larger than the other cases. Thus, the maximum heating rate for the tests appeared at the case of 2 MPa (as shown in Fig. 4). Referring to the method mentioned in the literature [41], the heat generating rates over temperature of coal are illustrated in Fig. 5. In view of the data in Fig. 5a, the valley value of the heat generation rate at the compression of 2 MPa appears at 91.7 °C (noted as Tc), and the peak one at 249.6 °C (named as Tg), which divides the process of coal oxidation into three stages. Stage I is an endothermic period (30–91.7 °C), when the heat absorbance from outside dominates the coal oxidation; Stage II is an accelerated oxidation period (91.7–249.6 °C), when the additional energy is released from coal oxidation which increases with coal temperatures; Stage III is a steady oxidation period (more than 249.6 °C), where the heat release falls off, and then, it is prone to be steady for the same axial compression because the oxygen supplement is consumed inside the container. Other peak-to-valley values of the heat generation rates at various compressions are shown in Table 2 by the same methods.

Fig. 4
figure 4

The heating rate of coal under axial compressions. a The peak values for heat generation rate (2 MPa), b the heat generation rate

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Fig. 5
figure 5

Heat generation rates of coal samples in container over temperature at different compressions

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Table 2 The critical temperatures of coal at different axial compressions
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Coal oxidation kinetics on axial compressions

In order to prevent and control the progress of coal-field fires in the early stage, oxidation dynamics on Stage I and II should be followed closely. The porosity of coal samples in the container is estimated by Eq. (2):

$$n = \left( {\varphi_{\text{p}} - \varphi_{\text{b}} } \right)/\varphi_{\text{p}}$$
(2)

Figure 6 demonstrates the fitting curves of the average porosity of coal, showing an inverse proportion to the increasing axial compressions in Stages I and II.

Fig. 6
figure 6

The change of the average porosity of coal with the axial compression

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  1. (1)

    Apparent activation energy Ea and porosity in ACTP

A lower apparent activation energy indicates an easier oxidation of coal. Figure 7 displays Ea of coal with axial compressions from 0 to 8 MPa in Stage I and Stage II.

Fig. 7
figure 7

Ea under different axial compressions in Stage I and Stage II. a The volume fraction of oxygen over temperature, b the values of Ea at various compression

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As the results in Fig. 6 and Fig. 7(b) shown in Stage I, when the axial compression is not applied (0 MPa), the value of Ea can reach to 65.907 kJ mol−1. Compared to the value of Ea at 0 MPa, the apparent activation energy Ea of coal under the compression of 2, 4, 6 and 8 MPa changes by 0.55%, − 95.4%, 90.1% and − 71.8%, respectively. Besides, the porosity of coal, another important factor for coal oxidation, also should be attended. As the axial compression is loaded as 2, 4, 6 and 8 MPa, the porosity of coal all decreases obviously compared with the value of porosity at 0 MPa, while Ea varies, respectively, by 0.36, − 62.88, − 59.38 and − 47.33 kJ mol−1. Larger compression leads to smaller porosity, and the porosity values become less with temperature increase (especially at the compression more than 4 MPa, as shown in Fig. 6). At the axial compression of 4 MPa, the value of Ea reaches the minimum (as shown in Fig. 7b), and then rises up to the value at 8 MPa. According to the result of Fig. 7, the least value of Ea occurs which indicates the easiest coal oxidation under axial compression of 4 MPa.

Above all, in Stage I, a lower critical temperature results in a less Ea with an easier oxidation of coal. Moreover, this result coincides well with the experimental values as illustrated in Table 2. When the axial compression reaches 2 MPa, the average porosity of the coal decreases, which reduces the contact area between coal and oxygen, thus leading to an increased Ea of coal. However, the slight change of Ea indicates a weak effect of porosity change on Ea of coal. Moreover, the average porosity increases to 0.2038 under 4 MPa, implying the fractures of coal with newly penetrating cracks being generated. It may be caused by the generation of a large amount of free radicals, as well as the increased gas seepage velocity through the pore space, which promotes the reaction between coal and oxygen and leads to the minimum Ea. Unexpectedly, the Ea does not continue to decrease under higher axial compressions, i.e., 8 MPa witnessing a slight increase in Ea. It may be possibly caused by the decrease in average porosity of the coal reducing the surface of coal–oxygen reaction.

In Stage II, the values of Ea are 37.650, 38.10, 24.410, 39.340 and 21.690 kJ mol−1 under the compressions of 0, 2, 4, 6 and 8 MPa, showing a less Ea range ability than those in Stage I. With the increase in axial compression, Ea shows two increase–decrease fluctuating cycles. Whether Ea increases or decreases, the rate of change increases with increasing axial compressions. While the axial compression is loaded at 2, 4, 6 and 8 MPa, the porosity of coal decreases, respectively, by 2.83%, 10.16%, 23.28% and 55.83% at Stage II, and the values of Ea increase, respectively, by 0.450, − 13.244, 1.683 and − 15.963 kJ mol−1. Furthermore, the value of Ea increases due to the porosity of the coal decrease under the axial compression from 0 to 2 MPa and 6 MPa, which reduces the reaction sites between coal and oxygen. Besides, as the axial compression is loaded at 4 MPa and 8 MPa each, Ea decreases sharply. This may be caused by the developed fractures of coal and generated free radicals with increasing axial compression [20], enabling more collision between the active groups and oxygen.

During Stage II, Ea undergoes fluctuations with the axial compressions. There are inflection points at 2 MPa and 6 MPa with Ea of 38.104 and 39.337 kJ mol−1,respectively (see Fig. 7). It is observed that from Figs. 6 and 7, the average porosity of coal decreases while the axial compression reaches 2 MPa, reducing the contacts between coal and oxygen leading to an increased Ea. As the axial compression becomes 4 MPa, which is although unfavorable for the average porosity, new cracks and free radicals could be generated with an accelerated gas seepage velocity, resulting in a decreased Ea. Furthermore, the average porosity of the coal decreases under the axial compression of 6 MPa, and new penetrating cracks are also completely destroyed to increase Ea. Finally, as the axial compression reaches 8 MPa, the average porosity of the coal sample continues to decrease and the newly penetrated cracks appear in the coal body, which leads to accelerated oxygen flow rates resulting in reduced Ea.

  1. (2)

    The average oxygen consumption rate of coal


Oxygen concentration has a great influence on the oxygen consumption rate of coal which could be expressed as Eq. (3) [42].

$$r_{{{\text{O}}_{2} }} \left( T \right) = Q\left( {C_{{{\text{O}}_{2} }}^{0} - C_{{{\text{O}}_{2} }} } \right)/SL$$
(3)

Figure 8 presents the oxygen consumption rate of coal at various temperatures under each compression.

Fig. 8
figure 8

The oxygen consumption rate of coal under the axial compression

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In Stage I, as shown in Fig. 6, the coal porosity at various temperature decreases obviously with the increasing compressions leading to the decreased average oxygen consumption rates of coal (see Fig. 7). As the compressions on coal samples were loaded within the compressions more than 4 MPa, the coal porosity drops significantly. Meanwhile, a large number of penetrating cracks are generated making the specific surface area of coal samples to increase. It enables the oxygen concentration inside the coal to increase rapidly, thereby increasing the oxygen consumption rate of the coal. Furthermore, the oxygen seepage velocity is greatly accelerated, while the oxygen cannot fully react with coal owing to a large number of penetrating cracks, so that the oxygen consumption rate of coal under 6 MPa reaches the maximum (as shown in Fig. 8). Finally, it is observed that the average porosity of coal is the smallest and the oxygen concentration in coal is the lowest under 8 MPa, leading to the smallest average oxygen consumption rate in Stage I and Stage II.

The oxygen consumption rates of coal samples indicate the reaction rate of coal with oxygen. It is reported that the oxygen concentration has a great influence on the oxygen consumption rate of coal. A higher oxygen concentration leads to a faster oxygen consumption rate of coal generally [43,44,45].

In Stage I, compared with the case of 0 MPa, when the axial compression reaches 2 MPa, the average porosity of coal decreases and the oxygen concentration in the coal sample drops, so that the average oxygen consumption rate of coal decreases. While the coal sample is loaded within the axial compression of 4 MPa, the coal particles in the container could generate a large number of penetrating cracks which cause the rapid increase in oxygen concentration in the coal sample, and thus increase the oxygen consumption rate of the coal. When the compression reaches 6 MPa, most cracks become non-penetrating cracks so that a large amount of oxygen accumulates in coal particles, greatly increasing the oxygen concentration. Furthermore, the average porosity of coal is the smallest and the oxygen concentration in coal is the lowest at the 8 MPa of axial compression, leading to the smallest average oxygen consumption rate.

Besides, in Stage II, the average porosity of coal at 2 MPa decreases compared to the case of 0 MPa, making the oxygen concentration reduce and the oxygen consumption rate of coal decrease. However, a large number of free radicals are generated in coal by the strong axial compression of 4 MPa, which accelerates the average oxygen consumption rate of coal. Also, under the axial compression of 6 MPa, a large amount of free radicals are continuously generated and a large number of non-penetrating fissures are generated at the same time, which leads to the more oxygen in coal compared to the case of 4 MPa. Thus, the average oxygen consumption rate of coal is more than that under 4 MPa. When the axial compression becomes 8 MPa, the porosity of the coal turns to be very small resulting in the decrease in oxygen concentration, as well as the very low average consumption rate.

Generally, the influence of axial compression on the oxygen consumption rate of coal could be reflected by the change of the porosity of the coal sample, which finally makes effect on the oxygen concentration of coal.

The heat transfer characteristics of coal in TP under axial compression

  1. (1)

    The change of the thermal conductivity with temperature

Heat transfer characteristics of coal are one of the important origins for the spread of coal-field fires. During the low-temperature oxidation (below Tc), the temperature of the point 1 mainly depends on the heat conduction from the point 3. According to the literature [46], the formula for the thermal conductivity λ is expressed as follows:

$$\rho_{\text{e}} C_{\text{e}} \frac{\Delta T}{\Delta t} = \lambda \frac{{T_{3} - {\text{T}}_{1} }}{\Delta x}$$
(4)

As the temperature of coal exceeds the critical temperature Tc, the increase in coal temperature is mainly due to the exothermic effect of an intense oxidation reaction. Accordingly, the formula for calculating the thermal conductivity can be described as Eq. (5), ignoring the heat loss by the wind [47]:

$$\rho_{\text{e}} C_{\text{e}} \frac{\Delta T}{\Delta t} = \lambda \frac{{T_{3} - T_{1} }}{\Delta x} + \left( {1 - n} \right)q$$
(5)

where q is the heat release intensity [48], J m−3 s−1; n is the porosity. Based on Eqs. (4) and (5), the thermal conductivity λ over temperature was calculated and is shown in Fig. 9.

Fig. 9
figure 9

The values of λ with temperatures under different axial compressions

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In the stage of low-temperature oxidation before Tc, the thermal conductivity of coal decreases linearly with the increasing temperatures, which is mainly influenced by the moisture in the coal particles. Moreover, the thermal conductivity of water (0.62 W m−2 K−1) is much higher than air (0.024 W m−2 K−1) and coal solid (0.012 W m−2 K−1). Therefore, as the moisture is evaporated, the thermal resistance of coal increases so that the thermal conductivity decreases as the temperature continues to increase. The thermal conductivity of coal nearly keeps constant under various axial compressions, which implies that the thermal conductivity of coal is mainly affected by temperatures rather than the axial compression during the low temperature.

If the temperature coal exceeds Tc, as the axial compression increases up to 2, 4, 6 and 8 MPa in turn, the thermal conductivity of coal change with temperatures differs from that under the axial compression of 0 MPa (see Fig. 9). When there is no compression (0 MPa), the thermal conductivity of coal increases firstly with increasing temperature, and then reaches to the peak value followed decreasing slowly. Furthermore, the maximum value of the thermal conductivity of coal for each test under a single compression all appears around 250 °C. Besides, as Fig. 9 shows, the largest thermal conductivity exists at the axial compression of 8 MPa among all the curves. When the temperature exceeds 100 °C, the moisture in the coal has completely been evaporated. If the temperature rises, the solid and gas molecules in coal become active, so that the thermal conductivity of coal increases. Along with the temperature more than 250 °C, a lot of cracks would be generated due to the rapid combustion, leading to a sudden increase in the specific surface area for coal oxidation.

  1. (2)

    The change of the thermal conductivity with axial compressions


It has been shown that the thermal conductivity of coal during the high temperature is not only affected by the temperature, but also the axial compressions. Figures 10 and 11 present the variation of the average thermal conductivity of coal with the axial compressions in Stage I and II separately, which also figures the fitted curves.

Fig. 10
figure 10

The thermal conductivity under axial compressions during the low temperature (Stage I)

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Fig. 11
figure 11

The thermal conductivity under axial compression during the high temperature (Stage II)

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Whether in Stage I or Stage II, the average thermal conductivity of coal change with axial compression follows a cubic function (Figs. 10, 11). The relationship between the thermal conductivity of coal and the axial compression could be written in Eqs. (6) and (7).

$$y = - 6.91e - 6x^{3} + 1.61e - 4x^{2} - 0.00115x + 0.01234$$
(6)
$$y = 0.00452x^{3} - 0.053x^{2} + 0.155x + 0.04$$
(7)

During the stage of low temperature, the movement of solid molecules of coal is inactive and the heat transfer mainly depends on the conduction. As the value of axial compression is 5.57 MPa, the average thermal conductivity of coal appears to be a minimum value of 0.0097 W m−2 K−1 according to Eq. (6). Furthermore, the average thermal conductivity of coal decreases with increasing axial compressions as the axial compression is less than 5.57 MPa. It is mainly due to that the average porosity of the coal decreases with the increasing axial compressions. Meanwhile, as the axial compression exceeds 5.57 MPa, higher axial compression results in lower thermal resistance of the coal with the higher the thermal conductivity. When the axial compression reaches 9.97 MPa, the average thermal conductivity of coal approaches a maximum value of 0.01 W m−2 K−1. In case the axial compression exceeds 9.97 MPa, penetrating cracks begin to generate in coal with sufficient surface area of coal gradually being increased, as well as the decreased average thermal conductivity of coal.

During the high temperature stage, the solid molecules of coal become more active. As the axial compression is loaded at 1.95 MPa according to fitting curves based on Eq. (7), the average thermal conductivity of coal presents a maximum value of 0.174 W m−2 K−1. If the axial compression is below 1.95 MPa, the average porosity of the coal decreases with increasing axial compressions while the thermal conductivity of the coal increases. When the loaded compression is higher than 1.95 MPa, the coal is squeezed which limits the vibration of the solid molecules and restricts the thermal diffusion, and thus reduces the thermal conductivity.

Summary and conclusions

  1. 1.

    In order to investigate the influence of axial compression on spontaneous combustion and heat transfer characteristics of coal, three stages were divided according to the two critical temperatures (Tc and Tg). Stage I (less than Tc), the process of coal with mild oxidation; Stage II (Tc ~ Tg), the rapid oxidation process of coal; Stage III (more than Tg), the steady combustion process in the tests.

  2. 2.

    The effects of axial compressions on the apparent activation energy, the oxygen consumption rate of coal and the thermal conductivity were all studied. The results show that the apparent activation energy (Ea) in Stage I has the similar trend compared with the one in Stage II as the axial compression increases. The values of Ea in Stage I and II all present two increase–decrease fluctuations (shown in Fig. 7), where they both reach the valley value under the axial compression of 4 MPa. The oxygen consumption rates of coal at 8 MPa are much lower than the one at 0, 2, 4 and 6 MPa in Stage I and II. However, the oxygen consumption rate at 0 MPa is the lowest and the ones at 8 MPa reach the maximum due to its thermal conductivity in Stage III.

  3. 3.

    The average porosity of coal decreases linearly with increasing axial compressions. The average oxygen consumption rate of coal is mainly dependent on the oxygen concentration generally. A higher oxygen concentration usually results in a greater average oxygen consumption rate of coal. In Stage I and Stage II, when the axial compression reaches 2 MPa, the oxygen consumption rate of coal decreases compared to 0 MPa. When the compression reaches 4 MPa or 6 MPa, the oxygen consumption rate increases greatly. The case of 8 MPa results in the very low oxygen consumption rate.

  4. 4.

    The thermal conductivity of coal decreases linearly with rising temperatures during the stage of low temperature. During the high temperature stage, the thermal conductivity of coal at 0 MPa increases firstly with increasing temperatures, and then decreases. However, in the case of 2, 4, 6 and 8 MPa, the thermal conductivity of coal increases at the beginning with increasing temperatures and then descends. Moreover, the thermal conductivity of coal changing with the axial compression was fitted as a cubic function. As the axial compressions increase, the thermal conductivity of coal underwent a decrease–increase–decrease route below Tc. While the coal temperature exceeds the critical point Tc, the thermal conductivity of coal underwent an increase–decrease–increase route with axial compressions.