Evolution law of pulsating seepage and thermal deformation by injecting high-temperature steam into coal for thermal coalbed methane recovery-深地科学

Evolution law of pulsating seepage and thermal deformation by injecting high-temperature steam into coal for thermal coalbed methane recovery

Abstract

Chinese coal reservoirs are characterized by low pressure and low permeability, which need to be enhanced so as to increase production. However, conventional methods for permeability enhancement can only increase the permeability in fractures, but not the ultra-low permeability in coal matrices. Attempts to enhance such impermeable structures lead to rapid attenuation of gas production, especially in the late stage of gas extraction. Thermal stimulation by injecting high-temperature steam is a promising method to increase gas production. The critical scientific challenges that still hinder its widespread application are related to the evolution law of permeability of high-temperature steam in coal and the thermal deformation of coal. In this study, an experimental approach is developed to explore the high-temperature steam seepage coupled with the thermal deformation in coal under triaxial stress. The tests were conducted using cylindrical coal specimens of ϕ50 mm × 100 mm. The permeability and thermal strain in coal were investigated when high-temperature steam was injected at 151.11, 183.20, 213.65, and 239.76°C. The experimental results reveal for the first time that as the amount of injected fluid increases, the steam permeability shows periodic pulsation changes. This paper introduces and explains the main traits of this discovery that may shed more light on the seepage phenomenon. When the injected steam temperature increases, the amplitude of pulsating permeability decreases, whereas the frequency increases; meanwhile, the period becomes shorter, the pulsation peak appears earlier, and the stabilization time becomes longer. The average peak permeability shows a “U-shaped” trend, decreasing first and then increasing as the steam temperature increases. Meanwhile, with the extension of steam injection time, the axial, radial, and volumetric strains of coal show a stage-wise expansion characteristic at different temperatures of steam injection, except for the radial strains at 151.11°C. A two-phase flow theory of gas–liquid is adopted to elucidate the mechanism of pulsating seepage of steam. Moreover, the influencing mechanism of inward and outward thermal expansion on the permeability of coal is interpreted. The results presented in this paper provide new insight into the feasibility of thermal gas recovery by steam injection.

Highlights

A novel phenomenon of pulsation of steam permeability in coal is discovered for the first time.
The mechanism of pulsating seepage of steam is interpreted using the theory of gas–liquid two-phase flow.
The effects of steam temperature on permeability present two expansion mechanisms for inward and outward expansions.

1 INTRODUCTION

Coal seam gas, also known as coalbed methane (CBM), is an unconventional natural gas with high calorific value. Compared with traditional coal, it is considered a cleaner source of fuel, as it produces fewer greenhouse emissions when burned to extract energy. In addition, extracting trapped CBM from coal seam can reduce its release into the atmosphere, which prevents uncontrolled emissions. Thus, the extraction of coal seam gas is of great significance for increasing clean energy supply, reducing greenhouse gas emission, preventing gas disasters in coal mines, and preserving natural ecosystems by reducing habitat disruption.

CBM in China is characterized by low permeability and low pressure (Liang et al., 2021). Various measures have been taken to increase the permeability of coal seam by means of advanced technologies including hydraulic fracturing, hydraulic cutting, and unloading of the protective layer (Fang et al., 2023; Liu et al., 2020; Lu et al., 2022). These measures can effectively improve the production of gas during the early stages of extraction. However, in the late stages, some problems may emerge, such as the rapid depletion of gas, which leads to vanishing flow rates and lower production. Therefore, a new technique is needed to improve the efficiency of gas extraction in the case of gas depletion.

The thermal stimulation of coal seams is a promising technology to increase gas production. To be specific, it accelerates the desorption of methane in coal seams and improves gas extraction. Thermal gas recovery techniques include injecting high-temperature steam, hot water, and hot gas into coal seams. Yang (2009) proposed a thermal gas recovery method by injecting steam into coal seam. Salmachi and Haghighi (2012) introduced a thermal method to increase gas production by injecting hot water into coal seam. Previously, most research activities on thermal gas recovery were devoted to numerical simulations. Yang and Zhang (2011) and Yang et al. (2013, 2021) established a seepage equation coupled heat–fluid–solid and carried out numerical simulations on the recovery of thermal CBM. Subsequently, they performed numerical simulations on the recovery of thermal gas from a multiwell combined well group (Yang et al., 2019). Tang et al. (2022) conducted numerical simulations on the recovery of thermal gas considering steam phase change. Their results show that hot steam has better recovery capacity than hot water. In recent years, researchers have attempted to conduct experiments of thermal gas recovery using hot fluids. Li et al. (2018) conducted an experiment to increase gas production using saturated steam, and their results show that the gas production is increased by 46.3% on injecting saturated steam. Li et al. (2019) investigated the variation of pores and fissures in the coal matrix after hot steam injection, and the results show that the sizes of pores and fissures increase after steam treatment. Li et al. (2023) investigated the effect of high-temperature steam on the pore structure and surface area of coal, and the results indicate that vapor is preferably adsorbed in the micropores of coal to undergo a phase change.

In addition, researchers conducted many experimental and theoretical studies on gas production enhancement by hot gas injection. Teng et al. (2016, 2019) investigated CBM recovery by injecting hot nitrogen into coal. Mu et al. (2019) and Cheng et al. (2019) conducted numerical simulations to investigate the mechanical mechanisms and recovery effects of flue gas injection for enhancing CBM production. Liu et al. (2021) demonstrated that elevated temperatures significantly enhance coal permeability. Qu et al. (2012) and Fang et al. (2019) revealed that hot CO2 has a stronger effect on extraction.

Temperature and pressure are two critical parameters affecting the permeability of coal during thermal gas recovery. Li and Xian (2009), Li et al. (2009) and Yang and Zhang (2008) carried out experiments on the permeability of coal under varying temperatures and stress. Their findings reveal a distinctive “U-shaped” pattern in permeability with increasing temperature. Subsequently, Wang et al. (2017), Zhou et al. (2022) and Niu et al. (2014) confirmed a fluctuating permeability pattern associated with increasing temperature. J. Wang et al. (2019) and S. Wang et al. (2015, 2021) conducted experiments on the injection of hot water and hot nitrogen into coal and found that the permeability increases with increasing temperatures. These studies collectively demonstrated that high temperatures can greatly enhance coal permeability, which provides favorable conditions for thermal gas recovery.

The technology of heat injection for increasing gas recovery has been successfully applied in coal mines by Hu, Feng, Zhou and Wang ( 2023) and Hu et al. ( 2022, 2023). This implies that thermal gas recovery by high-temperature steam has broad application prospects. However, a number of important scientific issues still remain unresolved in terms of thermal gas extraction:

1.
Although researchers have conducted several studies on gas recovery by thermal steam, most of them focused on numerical simulations. The permeability of real steam in coal is an indispensable parameter for numerical simulation. However, most studies failed to obtain the critical parameter of steam permeability. The changing law of the permeability at high steam temperature in coal is still unknown, making the results of numerical calculations less credible.
2.
Similarly, the thermal deformation law of coal when high-temperature steam is injected into coal is still unknown, which leads to a lack of factual basis for interpreting the mechanism of steam permeability evolution and may generate misleading numerical calculations.

To address the above issues, this paper provides experimental results on the seepage and thermal deformation of coal subjected to injection with high-temperature steam. The variation of permeability and thermal strain with time during the injection of high-temperature steam into coal at different temperatures was determined. The conducted tests revealed a new phenomenon of pulsating seepage of steam. This paper elucidates the underpinning mechanism of this pulsating seepage using the slug flow theory. The influence of steam temperature on permeability is explained by considering the internal and external expansion.

2 SEEPAGE EXPERIMENT WITH HIGH-TEMPERATURE STEAM

2.1 Coal sample preparation

Raw coal was collected from the anthracite of Jincheng coal mine in the Shanxi Province in China. A cylindrical coal sample was created with a diameter of 50 mm and a height of 100 mm, and dried to remove the moisture before testing. The basic parameters of the coal sample are listed in Table 1. Aad, Vad, ρ, φ, and f represent the ash, volatile, apparent density, porosity, and firmness coefficient of the coal sample, respectively. The coefficient of firmness “f” represents the hardness of coal.

Table 1. Basic parameters of the coal sample.

Basic parameter	Value
Aad (%)	10.17
Vad (%)	8.90
ρ (g/cm3)	1.48
φ (%)	5.25
f	1.10

2.2 Experimental apparatus

The experiments on steam seepage and thermal deformation in coal were carried out using a self-developed apparatus designed for thermal gas recovery with high-temperature steam. As shown in Figure 1, our apparatus is mainly composed of five parts: the steam injection unit, the stress loading unit, the seepage measurement unit, the gas–liquid measurement unit, and the data monitoring unit.

Details are in the caption following the image — Figure 1
Open in figure viewer PowerPoint

Diagram of the experimental device for steam seepage.

The steam injection unit comprises a high-temperature steam generator with valve V1. This generator can continuously produce high-temperature steam ranging from room temperature to 300°C and from 0.1 to 30.0 MPa. The stress loading unit consists of an axial pressure pump and a radial pressure pump with valves V2 and V3, providing axial and radial pressures to simulate ground stresses.

The seepage measurement unit utilizes a triaxial gripper, allowing to determine thermal strain and measure seepage flow rate simultaneously. The gas–liquid measurement unit consists of an electromagnetic flowmeter, a wet flowmeter, a gas–liquid separator, and a valve V4. The data monitoring unit is made up of a computer connected to the strain gauge and flowmeter of the gas–liquid measurement unit, which can automatically collect the data of strain and permeability in real time during an experiment.

2.3 Experimental method

The high-temperature steam injected into the coal sample is the saturated vapor at the corresponding temperatures, and the experimental parameters are shown in Table 2.

Table 2. Experimental parameters.

Axial stress (MPa)	Radial stress (MPa)	Steam temperature–pressure (°C/MPa)
6.0	4.0	151.11/0.4
		183.20/1.0
		213.65/2.0
		239.76/3.3

The experimental steps are as follows:

1.
The cylindrical coal sample prepared for testing is wrapped in a layer of heat-shrinkable sleeve, which is uniformly heated using a heat blower. After the heat-shrinkable sleeve conforms entirely to the coal sample, axial and radial strain gauges are affixed to the outside of the heat-shrinkable sleeve. Subsequently, the coal sample is placed into the triaxial gripper and evacuated to eliminate impurity gases.
2.
The axial and radial pressure pumps and valves V2 and V3 are turned on, which increases the pressure slowly to reach the stress level desired for the experiment. The axial stress required for the experiment is 6.0 MPa and the radial stress (confining pressure) is 4.0 MPa.
3.
The steam generator is started and preheated; when the steam in the steam generator reaches the saturated vapor temperature and pressure, valve V1 is opened to inject high-temperature steam into the coal sample in the triaxial gripper. After some time, the stream that flows out of the downstream end of coal is separated through a gas–liquid separator before entering a wet flowmeter and an electromagnetic flowmeter.
4.
The computer automatically collects the flowmeter data, immediately calculates the permeability in real time, and records the axial and radial thermal strains synchronously with a measurement duration of 120 min.
5.
The experiments of steam seepage and thermal deformation are first performed at 151.11°C/0.4 MPa. After that, the temperatures and pressures of saturated vapor are reset, and the above steps (3) and (4) are repeated to complete the experiments of steam seepage and thermal deformation at 183.20°C/1.0 MPa, 213.65°C/2.0 MPa, and 239.76°C/3.3 MPa sequentially.

2.4 Data processing

The experiments were conducted to test the permeability using the steady-state method. In this experimental setup, owing to a phase change of steam passing through the coal sample, only the mass flow rate of water at the outlet end was monitored. Thus, the measured permeability reflects the permeability of water. The following formula can be used to calculate the liquid-measured permeability:

� = \frac{� � �}{� � (�_{1} - �_{2})},

(1)

where

�

denotes the vapor permeability expressed in mD,

�

is the mass flow rate of water in g/s,

�

represents the viscosity of water in Pa·s,

�

denotes the length of the cylindrical coal sample in cm,

�

is the cross-sectional area of a cylindrical coal sample in cm 2,

�_{1}

is the pressure at the inlet end in MPa, and

�_{2}

is the pressure at the outlet end, which is the atmospheric pressure, 0.1 MPa, ρ is density of water.

The computer collects the pressures of upstream and downstream and flow rates. In addition, it calculates the liquid-measured permeability of the steam automatically using the above equation.

3 ANALYSIS OF EXPERIMENTAL RESULTS

3.1 Evolution law of pulsating seepage of steam in coal

Through the conducted experiments of high-temperature steam seepage, the variation pattern of liquid-measured permeability over time was observed while injecting high-temperature steam into coal. As shown in Figure 2, the liquid-measured permeability of steam at different temperatures and pressures shows a pulsating pattern with respect to time. To the best of the authors' knowledge, this phenomenon is reported for the first time, which marks a significant new discovery.

Figure 2a shows the variation of liquid-measured permeability with respect to time upon injecting steam into coal at 151.11°C. The figure shows that the permeability has intermittent pulsations as high-temperature stream percolates through coal. The permeability reaches the first peak at 38 min, the second peak at 69 min, and the third peak at 109 min.

Figure 2b shows the variation of steam permeability versus time when steam is injected at 183.20°C. The first peak in permeability occurs at 18 min. During 120 min, permeability shows 15 periodic pulsations, and the permeability peaks decrease and then increase slightly with time. The average amplitude of permeability pulsation is 14.11 mD, and the average period is 9.63 min.

It should be noted that there is still a tiny pulsation of permeability between peak permeability intervals. Small fluctuations occur as shown in Figure 2a,b, and similar phenomena appear as shown in Figure 2c,d.

Figure 2c shows the pulsation of steam permeability at 213.65°C. The first peak in permeability occurs at 10.5 min. After that, the peak permeability shows 11 periodic pulsations during 120 min, and the values of peak permeability decrease and then increase slightly with time. The average amplitude of permeability pulsation is 6.46 mD and the average period is 10.31 min.

The pulsating variation of steam permeability at 239.76°C is shown in Figure 2d. As can be seen, the first peak in permeability appears at 4.3 min. Subsequently, the peak permeability decreases and then increases slightly with time. After 27 min of injection, the pulsation frequency of permeability is significantly accelerated, and the pulsation period is shortened. The average amplitude of permeability pulsation is 9.87 mD, and the average period is 5.0 min. The duration of peak permeability is extended to 2 min.

Figure 2e shows the variation patterns of steam permeability at different temperatures. At high temperatures of saturated steam, the pulsation amplitudes of the steam permeability decrease, the period shortens, and the frequency increases.

As shown in Figure 3, the maximum and minimum values of steam permeability at different temperatures in Figure 2 are averaged to reveal the effect of injected steam temperature on the permeability. As shown in Figure 4, the peak values of permeability at different temperatures in Figure 2b–d are selected to obtain the changing law of peak permeability with time.

As illustrated in Figure 3, with the increase of injected steam temperature, the average maximum values of steam permeability show a turning point at 213.65°C, showing a trend of initial decrease, followed by a slight increase. Similarly, with the increase of injected steam temperature, the average minimum values of steam permeability show a sharp decrease, followed by a sharp increase and reverse at 183.20°C. In general, the average extreme values of steam permeability show a “U-shaped” pattern with increasing injected steam temperature. Figure 4 shows that the peak values of steam permeability at different temperatures decrease and then increase slightly with the injection time.

Due to the large differences between the peak values of permeability at 151.11°C and those at 183.20, 213.65, and 239.76°C, it is not obvious to compare them in a single figure. Thus, the peak values of permeability at 151.11°C are not included in Figure 4.

From the above, it is evident that the steam seepage in coal shows the following characteristics:

1.
The permeability of high-temperature steam in coal shows a periodic pulsation pattern with an increase in injection time.
2.
With the increase in injected steam temperatures and pressure, the amplitude of peak permeability decreases, the period shortens, the frequency increases, and the first peak permeability appears earlier.
3.
As the injected steam temperature increases, the average maximum and minimum values of steam permeability show a “U-shaped” pattern of change.
4.
The peak permeability of steam shows a pattern of initial decrease, followed by an increase with injection time.

3.2 Evolution law of thermal deformation of coal during steam injection

The injection of saturated steam at different temperatures and pressure into coal affects not only the permeability but also the deformation of coal. Following the principles of coal-rock mechanics, this paper defines positive strain as coal compression and negative strain as coal expansion. The axial, radial, and volume strains of coal for steam injection at different temperatures are shown in Figure 5.

As shown in Figure 5a, the axial, radial, and volumetric strains increase gradually when the steam is injected into coal at 151.11°C. Positive radial strains indicate that the coal sample is gradually compressed in the radial direction; negative axial strains indicate that the coal sample expands gradually; and negative volumetric strains indicate that the coal sample is overall in an expanded state.

Figure 5b illustrates that axial, radial, and volumetric strains of coal expand in a stepwise pattern with time when steam is injected into coal at 183.20°C. The radial and axial strains expand rapidly to −0.49 × 10−4 and −0.39 × 10−4, respectively, during 0–6 min at the initial injection stage, stabilize during 6–33 min, and continue to expand slowly and stabilize during 33–120 min. The volumetric strains expand rapidly to −1.31 × 10−4 in 0–7 min, stabilize during 7–33 min, expand rapidly again to −2.55 × 10−4 within the period of 33–56 min, and expand slowly and gradually stabilize during 56–120 min.

Figure 5c shows the axial, radial, and volumetric strains of coal after the injection of steam at 213.65°C. The radial, axial, and volumetric strains expand rapidly in 0–14 min during the initial injection period, stabilize in 14–28 min, expand rapidly again in 28–38 min, and then expand slowly and gradually stabilize during 38–120 min.

Figure 5d shows the axial, radial, and volumetric strains at 239.76°C. At the initial stage of injection, the radial, axial, and volumetric strains expand rapidly in 0–7 min, stabilize in 7–23 min, expand rapidly again in 23–33 min, expand slowly in a pulsating pattern in 33–120 min, and gradually stabilize.

To compare the effect of steam temperature on thermal deformation of coal, the radial, axial, and volumetric strains are plotted against steam temperature as shown in Figure 6.

Figure 6a shows that the axial strains expand with time. Among them, the axial strains at 151.11 and 183.20°C expand slowly with the increase of steam injection time, and the axial strains at 213.65 and 239.76°C expand in stages with time. Except for the case at 151.11°C, the higher the injected steam temperature, the larger the axial expansion strain.

Figure 6b indicates that the radial strains increase with the increase of steam injection time. The radial strain at 151.11°C is compressive and those at temperatures of 183.20, 213.6, and 239.76°C are expansion strains. The higher the temperature of the injected steam, the higher the radial expansion strain.

Figure 6c indicates that the volumetric strains increase at all temperatures with steam injection time, and they are all expansion strains. The higher the temperature of steam injected, the greater the volumetric expansion strain.

4 GENERAL PRINCIPLES OF PULSATILE TWO-PHASE FLOW

4.1 Two-phase flow patterns of gas–liquid

High-temperature steam undergoes a phase change in contact with the coal and flows in a gas–liquid mixture inside the coal. However, the flow pattern of the gas–liquid two-phase mixture in the coal remains invisible. Accordingly, the flow patterns of gas–liquid two-phase flow in coal are analyzed by drawing parallels with gas–liquid two-phase flow in a pipeline. Influenced by the respective pressure, density, temperature, and flow rate of fluids, the two-phase flow of gas–liquid shows different flow patterns, which are referred to as the flow patterns of the fluid. The typical flow patterns of gas–liquid two-phase flow in a vertical tube include bubble flow, slug or plug flow, churn flow, and annular flow, as shown in Figure 7.

1.
Bubble flow:
As shown in Figure 7a, when a low-velocity gas flows through a vertical tube filled with a low-velocity liquid, the gas is dispersed in the liquid in the form of bubbles due to the low gas flow rate and its small proportion in a two-phase flow. In such instances, the two-phase flow pattern is known as bubble flow.
2.
Slug or plug flow:
In Figure 7b, the liquid velocity is assumed to be constant while increasing the gas flow rate. Then, the bubble content increases, causing tiny bubbles to merge into larger bullet-shaped bubbles. This flow pattern is appropriately called a bullet-shaped flow. Due to the segmental blockage between gas and liquid, the gas–liquid two-phase flow becomes intermittent, marked by unstable behavior. This flow pattern is generally named as slug or plug flow.
3.
Churn flow:
As shown in Figure 7c, if the gas velocity further increases, the bubbles in the plug flow continue to grow. Large bubbles begin to collapse and form lumpy bubbles of various sizes and shapes, leading to a more random unsteady flow. This flow pattern is known as churn flow.
4.
Annular flow:
In Figure 7d, as the gas flow rate increases further, the ruptured bubbles merge into a continuous gas flow. The liquid is pushed away from the center of the pipe by the gas to form a thin liquid film on the pipe wall. Since the gas velocity is much higher than the liquid velocity, part of the liquid will be carried into the gas phase to form small droplets. This flow pattern is called annular flow.

4.2 Pulsating flow mechanism of slug flow

Depending on the flow patterns, the pulsations display different morphologies. The bubble flow in Figure 7a and the annular flow in Figure 7d only produce small pulsations due to a large proportion of liquid or gas phase, resulting in pulsations with low amplitude but high frequency. The slug or plug flow in Figure 7b and the churn flow in Figure 7c can generate large pulsations with high amplitude but low frequency, which are the main flow patterns with unsteady flow. Recognizing the similarity between slug flow and churn flow, this paper suggests a unified framework, categorizing both flow patterns as slug or plug flow.

As shown in Figure 8, the pulsation process of slug flow comprises four stages: (1) slug flow generation; (2) slug flow formation; (3) bubble penetration; and (4) gas emission. Schmidt et al. ( 1980) identified this process as the cause of the flow cycle, which would result in either no gas–liquid flow or very high flow cycle pulsations. In Figure 8, it is assumed that a pipe consists of three parts: a bottom bend (A), a vertical pipe (B), and a top straight pipe (C). When there is a two-phase flow of gas and liquid in the pipe, the pressure in the tube changes according to four stages, as shown in Figures 8 and 9:

1.
Slug flow generation stage:
Figure 8a illustrates the pressure inside the tube, which is low at the beginning of the flow. The gas–liquid two-phase flow coexists in the form of separation of gas (vapor) and liquid. Part A of the elbow is partially clogged by the liquid phase, resulting in the generation of the slug flow. In the stage of slug flow generation, the gas pressure is low and the liquid phase flows preferentially. Under the support of the gas phase, the liquid level and the pressure in the tube increase gradually. This stage of increasing pressure takes a long time, as shown in Figure 9(1).
2.
Slug flow formation stage:
Figure 8b shows the continuous inflow of liquid; the liquid phase gradually occupies the gas phase in section C of the top straight tube, forming a liquid plug. After that, the liquid in sections B and C is supported by the gas phase in section A, which creates a higher pressure and is maintained for some time, as shown in Figure 9(2).
3.
Bubble penetration stage:
Figure 8c illustrates the pressure of the liquid in the tube as it reaches a level high enough for the gas in section A of the tube to flow in; the gas gradually penetrates the liquid in section B. Thus, the liquid in sections B and C is gradually drained out, and the pressure in the tube slowly decreases, as shown in Figure 9(3).
4.
Gas emission stage:
Figure 8d shows how the liquid in section C is gradually drained out as the gas occupies section C. Therefore, there is no longer a liquid blockage, and the gas flows out of section C rapidly, resulting in a sharp pressure drop in the tube. This stage is a short period, as illustrated in Figure 9(4).

After the pressure drops inside the tube, the liquid in the straight tube of section B flows back, and the liquid enters into section A again, leading to the generation of a liquid slug in sections A and B again and the start of a new pulsating cycle. This phenomenon is well known in fluid mechanics of pipelines/riser systems (Fabre et al., 1990; Jansen et al., 1996), but it has never been explored in the context of poromechanics.

5 MECHANISMS OF PULSATING SEEPAGE OF STEAM AND THERMAL EXPANSION OF COAL

5.1 Mechanism of pulsatile seepage of steam in coal

Based on the above general principle of pulsating flow of gas–liquid two-phase flow, the pulsating seepage mechanism of high-temperature steam in coal can be elucidated. The experiment of steam seepage at 183.20°C in Figure 2b can be taken as an example. The steam is condensed into water due to a phase change after being injected into the coal. The mixed hot fluids circulate in the micropores of coal, manifesting gas–liquid two-phase flow with various patterns. During this process, the steam flowing in the coal creates a phenomenon of pulsating seepage as a result of the change in the flow patterns of the thermal fluid.

1.
Increasing pressure stage (steam–water slug generation):
At the initial stage of high-temperature steam injection into the coal, due to the low temperature of the coal, part of the steam would be condensed into water. The mixed thermal fluids in the pores of coal coexist in a state of more water and less gas when the gas–liquid flows in the coal in a pattern of bubble flow. Consequently, during the initial period of steam injection into the coal (0–18 min), only a slight pulsatile seepage occurs in the permeability of coal, as shown in Figure 2b.
As the injection time increases (0–7 min), the temperature of the coal gradually increases, thus increasing the proportion of the gas (vapor) phase in the coal pores. The small vapor bubbles gradually evolve into larger bubbles, and the slug (or plug) flow is generated in some pores of the coal. This period is the liquid accumulation stage. As the injection time increases, the pressure of the liquid phase increases rapidly, leading to a rapid expansion of the coal and a rapid increase in the volumetric strains, as shown in Figure 5b.
2.
Pressure stabilization stage (steam–water slug formation):
As the injection time increases, the steam in the coal pores continues to condense into water. This is a severe slug flow stage, and the pressure of the liquid phase stabilizes at a certain level in the period.
3.
Liquid drainage and depressurization stage:
As the injection time increases, the steam enters and pushes the liquid inside the coal continuously to the outlet end. After 18 min, the liquid is rapidly drained after reaching a sufficiently high pressure, at which time the vapor–liquid-measured permeability shows the first peak. After the liquid is discharged, the liquid-phase pressure in the coal falls back rapidly, and the liquid-measured permeability decreases sharply, as shown in Figure 2b.
4.
Steam emission and depressurization stage:
As the pressure of the mixed thermal fluid reduces, the gas–liquid discharges almost simultaneously and this stage occurs over a short time of 4 min (18–22 min) only, as shown in Figure 2b. It should be pointed out that the steam emission is not directly observed due to the condensation of vapor in a long pipe.

After the vapor is discharged, the pressure of the gas phase in the coal decreases, causing the liquid to flow back, and thus forming a new liquid plug. The liquid mixes with the steam and forms a slug flow again, allowing the liquid pressure to accumulate again and a new pulsating seepage to restart. Thus, a periodic cycle of pulsating seepage is produced.

As shown in Figure 2, when the injected steam temperature increases, the steam phase change is less plausible. The proportion of liquid phase in the gas–liquid two-phase flow decreases, and the proportion of the gas phase increases. Meanwhile, the gas–liquid is discharged quickly, resulting in a decrease in the accumulative pressure, and a shortening of the accumulation and drainage time. This is characterized by an earlier time of the first pulsation, a decrease in the amplitude of the pulsating permeability, a shorter period, and an increased frequency.

The mechanism of pulsatile seepage of steam in coal can be summarized as follows. The hot steam enters the pores in the coal and condenses into water, which causes a liquid plug to form in the mixed fluid. As the steam is continuously injected, the pore pressure in the coal accumulates. When the pore pressure increases to a certain level, the liquid plug is driven out first, followed by the rapid outflow of the gas–liquid mixture; meanwhile, the peak of the liquid-measured permeability occurs. After the gas–liquid mixture flows out, the pore pressure decreases rapidly, the effective stress increases, and the permeability decreases sharply. When the pore pressure decreases to a certain level, the fluid falls back and the liquid plug forms again. As the low pore pressure is unable to drive the liquid plug, the pore pressure accumulates again, allowing the effective stress to decrease, the permeability peaks to appear, and a new fluctuation cycle to begin again.

5.2 Influence mechanism of temperature and effective stress on steam permeability

In addition to showing a pulsation pattern caused by the influence of the slug flow, the steam permeability in the coal is also affected by the temperature and pressure of the steam. The gas–liquid pressure and the axial, radial pressure make up the effective stress, and the temperature produces thermal stress on coal. Under the combined influence of thermal and effective stresses, the extreme values of steam permeability in coal show a non-monotonic trend. Figure 3 indicates that the average extreme permeability of steam shows a “U-shaped” pattern of change with the increase in steam temperature.

As illustrated in Figure 10, when the steam is injected at 151.11°C, the temperature and pressure of the steam are relatively low; the thermal stress experienced by the coal is minor; and the effective stress is higher. As the steam temperature increases, the coal matrix constrained by a high effective stress cannot expand outward only into the pore and fissures. The inward expansion narrows the pore throat in coal, resulting in a lower average extreme permeability with steam injection at 183.20°C. When the steam is injected at 213.65 and 239.76°C, the temperature and pressure of steam are higher, resulting in higher thermal stresses and lower effective stresses on the coal. Meanwhile, the thermal stresses partially offset the effective stresses, causing the coal matrix to expand outward predominantly. As a result, the pores are widened, increasing the average extreme permeability.

The average maximum permeability in Figure 3 reflects the average permeability when the internal liquid–phase pressure reaches the peak. At this point, the liquid–phase pressure inside the pores of coal is high, and the effective stress is low, creating enough space in coal to produce inward expansion. Only at a higher temperature does outward expansion occur, attributed to pore closure. As a result, the average maximum permeability shows a slight “U-shaped” change with the increase of steam temperature. The average minimum permeability reflects the average permeability after gas–liquid drainage, characterized by low liquid-phase pressure in coal. Constrained by the high effective stress, the coal matrix expands inward at a lower temperature, and then outward at a higher temperature. Therefore, the average minimum permeability shows a more obvious “U-shaped” trend.

In Figure 4, as the injection time increases, the steam permeability also presents a “U-shaped” change at the same steam temperature. At the beginning of steam injection, the gas–liquid temperature and pressure in coal are low. Accordingly, the coal matrix undergoes an inward expansion, leading to a decrease in permeability with time. In the middle and later stages of injection, the gas–liquid temperature and pressure in coal gradually increase with time, and the coal matrix undergoes outward expansion, resulting in an increase in permeability with time.

5.3 Mechanism of temperature and effective stress on strain in coal

When the steam is injected with high temperature and pressure, the induced effective stress and thermal stresses are, respectively,

�_{r}^{'} = �_{r} - � �,

(2)

�_{T} = \frac{�_{T} � �}{(1 - 2 �)},

(3)

where α denotes Biot's coefficient or the effective stress coefficient that can be taken as 1, α T is the thermal expansion coefficient, E is Young's modulus and ν is Poisson's ratio,

�_{r}^{'}

is the effective stress in the radial direction, for convenience,

�_{T}

is the thermal stress,

�_{r}

is radial stress, and

�

is steam pressure, t is temperature.

At the initial stage of steam injection, the effective stresses in the radial direction are 3.6, 3.0, 2.0, and 0.7 MPa when high-temperature steam is injected at 151.11, 183.20, 213.65, and 239.76°C, respectively. Based on the experiments, the parameters can be obtained as follows: αT = 0.00008, $�$ = 0.27, and $�$ = 2000 MPa.

Substituting the parameters into Equation ( 3), high-temperature steam at 151.11, 183.20, 213.65, and 239.76°C produces thermal stresses of 1.33, 1.68, 2.02, and 2.30 MPa, respectively, when the steam injection is completed. The coal volumetric strains show a nonstationary change under the influence of vapor pressure and thermal stress, which can be divided into four stages, as shown in the bulk strains of Figure 6c.

1.
First rapid expansion stage:
When the high-temperature steam is injected into the coal at the initial stage, the steam produces a phase change. The gas–liquid pressure accumulates and increases, whereas the effective stress decreases. The influence of steam pressure on the deformation of the coal is predominant, causing the coal to expand outward rapidly.
2.
Deformation stabilization stage:
When the liquid-phase pressure accumulates to a certain level, the effective stress tends to stabilize. When gas–liquid is partially discharged, the axial, radial, and volumetric strains of the coal show a slight drop and stabilize for some time.
3.
Second rapid expansion stage:
Midway through the steam injection process, after the gas–liquid is discharged, the subsequently injected steam condenses, and the gas–liquid pressure starts to build up again. The coal rapidly expands again under the gas–liquid pressure, resulting in a rapid increase in axial, radial, and volumetric strains in the coal. It should be noted that the thermal stress gradually increases in 30–60 min due to the increasing temperature in the coal. The rapid expansion at this point includes the combined effects of gas–liquid pressure and thermal stress.
4.
Slow expansion and stable deformation stage:
At the later stage of steam injection, the gas–liquid pressure tends to stabilize gradually, and the influence of thermal stress on the deformation of the coal becomes gradually dominant. Under the influence of high temperature, the thermal stress in the coal offsets part of the effective stress, and the coal deformation undergoes a slow expansion and then gradually stabilizes.

6 DISCUSSION

It is worth pointing out that the strains measured in the experiments are the overall strains of the coal, which respond slowly to the gas–liquid pressure and temperature in coal with a lag time. In this sense, they fail to precisely correspond to the pulsation time of the permeability.

Probably due to experimental errors, the radial strains at 151.11°C in Figures 5a and 6b are positive compressive instead of negative expansion strains. The axial strains at 151.11°C are larger than those at 183.20 and 213.65°C presented in Figure 6a. The above phenomena need to be validated by more experiments in the future.

7 CONCLUSIONS

In this study, seepage experiments of steam injection into coal at different temperatures were carried out. The variations of permeability and thermal deformation under the considered experimental factors were obtained. On this basis, this study elucidated the mechanism of pulsating seepage of steam and that of temperature on permeability and deformation of the coal. The main conclusions are as follows:

1.
A new phenomenon of pulsation of steam permeability is discovered. When the high-temperature steam is injected into coal, the permeability of the steam shows a periodic pulsation phenomenon. As the steam temperature increases, the amplitude of the pulsating permeability of the steam decreases, with the period shortening, and the frequency increasing. This is a novel seepage phenomenon that may require more attention in the future for the adequate prediction of CBM production and coal stability.
2.
The theory of gas–liquid two-phase flow in tubes is adopted to interpret the mechanism of pulsating seepage of steam. After the steam is injected into coal, a part of the steam condenses into water, resulting in the presence of steam in coal with various flow patterns, such as bubble flow, slug flow, churn flow, and annular flow. Among them, slug or plug flow is the main flow pattern. The slug flow of steam in coal undergoes four stages: slug flow generation, slug flow formation, bubble penetration, and gas emission. The gas–liquid pressure change of steam inside the coal has four stages: pressure increase, pressure stabilization, liquid drainage and depressurization, and steam emission and depressurization. These four stages are repeated in cycles, creating a periodic pulsation of steam permeability.
When the steam temperature is higher, the proportion of the gas phase increases and the accumulated pressure decreases, leading to a reduction in the pulsation amplitude. At the same time, the gas–liquid drainage time is shortened, resulting in a shorter pulsation period and a faster frequency.
3.
The effect of steam temperature on permeability presents two expansion mechanisms. First, the average extreme permeability shows a “U-shaped” pattern, initially decreasing and then increasing with the injected steam temperature. Second, with an increase in steam injection time, the peak permeability also shows a “U-shaped” pattern, initially decreasing and then increasing. The common mechanisms are as follows: when the temperature and pressure of the injected steam are low, the thermal stress is minor, and the inward expansion of the coal matrix leads to a decrease in permeability. On the contrary, when the temperature and pressure of injected steam are high, the outward expansion of the coal matrix leads to an increase in permeability.
4.
After high-temperature steam is injected into coal, the coal mainly expands outward, and the higher the injected steam temperature, the greater the axial, radial, and volumetric strain expansion of the coal. With the injection time, the three strains undergo four stages: rapid expansion, stabilization, rapid expansion again, and slow expansion. The external strain of the coal samples shows a hysteresis effect on the response to pore pressure and temperature, which does not correspond to the pulsation period of permeability.

ACKNOWLEDGMENTS

This study was supported by the Fundamental Research Funds for the Universities of Henan Province (no. NSFRF180305).

CONFLICT OF INTEREST STATEMENT

The authors declare no conflict of interest.

Biographies

Zhiqiang Li is currently an associate professor at the Henan Polytechnic University, China. He is also a visiting scholar at the University of Western Australia. He received his PhD degree in Safety Technology and Engineering from Chongqing University, China. His research fields include coalbed methane extraction, mechanics of multiphase and multiscale diffusion-seepage coupled multiphysics fields, and coal-rock mechanics. His research interests mainly focus on CBM recovery by thermal stimulation seams, multiscale diffusion and seepage of gas in coal with ultra-low permeability, and the theory of high-temperature multiphase flow. In recent years, he has been devoting himself to research on the theory and technology of thermal gas recovery by injecting hot fluids into coal. He has published more than 100 papers. His most famous representative achievements are as follows: He proposed the theory of the “inward and outward thermal expansion” effect of temperature on coal permeability coupled with stress. This work has been cited more than 420 times to date. For his outstanding achievement, he was awarded the Front Runner 5000 (F5000) twice. He discovered the phenomenon of multiscale diffusion and seepage of gas in coal seams and put forward the multiscale theory of gas diffusion–percolation. This work was cited more than 400 times. Due to his distinctive contribution, he received a new Front Runner 5000 (F5000).
Jinsheng Chen, PhD, is a teacher and master's tutor at the Henan Polytechnic University in China. His main research interests are in coal mine gas disaster prediction and prevention, occupational safety, and health. He has published more than 20 scientific research papers. As the project leader and the main person for the completion of the project, more than 30 projects entrusted by coal mining enterprises have been completed, and nine national invention patents and five utility model patents have been authorized.