SCIENCE CHINA Technological Sciences • Article •

doi: 10.1007/s11431-016-0478-5

CO2 permeability of fractured coal subject to confining pressures and elevated temperature: Experiments and modeling JU Yang1,2*, WANG JianGuo1, WANG HuiJie3, ZHENG JiangTao4, RANJITH Pathegama G5 & GAO Feng1 1

State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining & Technology, Xuzhou 221116, China; 2 State Key Laboratory of Coal Resources & Safe Mining, China University of Mining & Technology, Beijing 100083, China; 3 College of Engineering, Peking University, Beijing 100871, China; 4 Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing 100084, China; 5 Department of Civil Engineering, Monash University, Melbourne VIC 3800, Australia Received June 19, 2016; accepted October 9, 2016; published online November 16, 2016

The CO2 permeability of fractured coal is of great significance to both coalbed gas extraction and CO2 storage in coal seams, but the effects of high confining pressure, high injection pressure and elevated temperature on the CO2 permeability of fractured coal with different fracture extents have not been investigated thoroughly. In this paper, the CO2 permeability of fractured coals sampled from a Pingdingshan coal mine in China and artificially fractured to a certain extent is investigated through undrained triaxial tests. The CO2 permeability is measured under the confining pressure with a range of 10–25 MPa, injection pressure with a range of 6–12 MPa and elevated temperature with a range of 25–70°C. A mechanistic model is then proposed to characterize the CO2 permeability of the fractured coals. The effects of thermal expansion, temperature-induced reduction of adsorption capacity, and thermal micro-cracking on the CO2 permeability are explored. The test results show that the CO2 permeability of naturally fractured coal saliently increases with increasing injection pressure. The increase of confining pressure reduces the permeability of both naturally fractured coal and secondarily fractured coal. It is also observed that initial fracturing by external loads can enhance the permeability, but further fracturing reduces the permeability. The CO2 permeability decreases with the elevation of temperature if the temperature is lower than 44°C, but the permeability increases with temperature once the temperature is beyond 44°C. The mechanistic model well describes these compaction mechanisms induced by confining pressure, injection pressure and the complex effects induced by elevated temperature. CO2 permeability, fractured coal, confining pressure, elevated temperature, thermal effects, mechanistic models Citation:

Ju Y, Wang J G, Wang H J, et al. CO2 permeability of fractured coal subject to confining pressures and elevated temperature: Experiments and modeling. Sci China Tech Sci, doi: 10.1007/s11431-016-0478-5

1 Introduction The emission reduction of carbon dioxide (CO2) has become a common concern in global greenhouse gas control. CO2 from the combustion of fossil fuels is regarded as one *Corresponding author (email: [email protected]) © Science China Press and Springer-Verlag Berlin Heidelberg 2016

of the primary greenhouse gas sources. As one of the mostly effective control techniques, geological sequestration of CO2 is the first choice for the mitigation of greenhouse gas effects [1–5]. Previous works reveal that a coal seam is an effective and economical option for geological sequestration of CO2 because coal seams have much a stronger adsorption capacity for CO2 than that for CH4 [6–11]. The injection tech.scichina.com link.springer.com

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of CO2 into a coal seam for methane recovery enhancement through CO2-CH4 displacement is a double-benefit option: the first benefit is the extraction rate enhancement of coalbed methane and the dramatic reduction of the potential risks of devastating gas outburst disasters in coal mines. The second benefit is a more sustainable supply of clean energy for higher coalbed methane recovery. Therefore, the CO2 permeability in a coal seam is a key issue not only to greenhouse gas control but also to clean energy production. A coal seam is usually fractured, even at deep burial locations. To achieve CO2 storage and the displacement of methane in coal seams, it is imperative to understand the CO2 permeability of fractured coals under different geological and mining conditions. Previous studies have found that the CO2 permeability of fractured coals are affected by multiple factors, such as geo-stress, pore pressure, the chemical and/or physical properties of coal matrix, and the fracture network of the coal. Current research is roughly carried out in three categories: 1) macroscopic laboratory studies on the CO2 permeability of coals through phenomenological methods [12–18]; 2) meso- or micro-scale laboratory tests to explore the contributions of discontinuities including micro fractures or micro pores to gas permeability [19–23]; and 3) numerical simulations to investigate the interactions among CO2 adsorption/desorption and its flow in coals and to understand their impacts on CO2 permeability [14,24–27]. The CO2 permeability of coals is usually measured through triaxial tests. The experimental procedure is to allow CO2 flow through a specimen until it reaches a steady flow. The CO2 permeability is calculated according to both pressure difference and flow rate. It is crucially essential to well understand the influences of fracture extent on the CO2 permeability of fractured coal. Fracture extent, such as additional or secondary fractures, may heavily impact the CO2 permeability of a fractured coal. Basically, CO2 injection offsets the initial balance of geological stress in coal strata and may result in further extension or growth of the pre-existing fractures and trigger secondary fractures. Previous studies indicate that this dynamic evolution of fractures significantly impacts the CO2 permeability of fractured coals [19,20,22]. However, accurately characterizing the dynamic evolution of natural fractures as well as secondary fractures and their influences on CO2 flow still remains a challenge. CO2 geosequestration in fractured coal seams is typically manipulated under high geological pressure and high temperature. To date, the majority of laboratory studies on the CO2 permeability of coals were conducted under relatively low confining pressure and at room temperature [28,29]. Such experimental conditions may not be suitable for the CO2 sequestration in deep coal seams because some coal seams are generally at one to two kilometers beneath the ground surface, where the impacts of high pressure and high

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temperature (e.g., higher than 70°C) on CO2 permeability may be strong. Temperature could affect the swelling of coal particles, induce fracture extension, and alter gas sorption capacity, thereby modifying the CO2 permeability of coals [25,29–32]. Temperature also affects fluid properties, such as viscosity and density. Some researchers have investigated the effect of temperature on coal permeability [30,32], but few studies are available for the combined effects of high pressure and high temperature on the CO2 permeability of fractured coals due to the challenges in experimental techniques. It is noted that the Monash University (Australia) developed a high-pressure triaxial system to test the coupling effects of confining pressure and temperature during CO2 geosequestration. This apparatus can be used to measure the CO2 permeability of fractured coals with different fracture extents subject to the coupling effects of high injection pressure, high confining pressure and elevated temperature [33,34]. This study investigates the comprehensive impacts of geostress, injection pressure and elevated temperature on the CO2 permeability of fractured coals with different fracture extents. The confining pressure or geostress ranges from 10 to 25 MPa and the injection pressure varies from 6 to 12 MPa. Further, the temperature varies from 25 to 70°C, which can express the temperature change from the ground surface to 800 m in depth. Special attention is paid to the coupling effect on the CO2 permeability of triggered secondary fractures. The permeability of the naturally fractured coal and the secondarily fractured coal is comparatively studied. Finally, a mechanistic model is proposed to describe the effects of thermal expansion and temperature-induced reduction of the adsorption capacity on the CO2 permeability.

2 2.1

Experiments and methodology Materials and specimen preparation

The naturally fractured coal was sampled from the coal seam at a depth of 690 m in Mine #8 of the Pingdingshan Coalfields, Northeast China. Preliminary tests indicate that the coal in this area is comprised of an abundance of vitrinite (50%–80%), inertinite (15%–40%), a minor amount of liptinite, and other mineral matters. The initial microscopic fractures are well developed with an approximate average density of 2 to 52 cm−2. Most of their apertures are less than 5 μm, and their lengths are less than 300 μm [35]. The average uniaxial compressive strength of the coal spans from 17.15 to 23.85 MPa [36]. The specimens for CO2 permeability tests were cylinders with 25 mm in diameter and 50 mm in length. The cylinders were first covered with 2 mm-thick silicone glue for twelve hours and subsequently sealed by heat-shrinkable rubber tubes before they were installed into the high-pressure chamber.

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2.2 High-pressure triaxial testing system and test procedures A high-pressure triaxial apparatus was used to investigate the comprehensive effects of confining pressure, injection pressure, and elevated temperature on the CO2 permeability of the fractured coals. Figure 1 shows the triaxial testing system [33,34]. The specimen was first vertically mounted on the pad. CO2 was then injected from the bottom of the specimen, and the pore pressure was measured at the top of the specimen. A thin paper filter was inserted between the specimen and the pad to prevent the specimen debris during fracturing from blocking gas permeation. The two ends of the specimen were connected to the loading plates of the chamber. The specimen was sealed using silicone glue for twelve hours at room temperature until the sealing was completely solidified. A triaxial undrained method was used, where the injection pressure at upstream was kept constant and the downstream valve was closed. The development of CO2 pressure at downstream was measured. The upstream injection pressure and the injection flow flux could be controlled, so this downstream pressure could be used to determine the downstream flow rate and calculate the permeability of the fractured specimen (Section 2.3 presents the permeability calculation method). An acoustic emission kit was attached to the triaxial chamber to monitor the fracture

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initiation inside the specimen [37]. Different combinations of confining pressure, injection pressure and temperature were used in the tests. Firstly, the influence of injection pressure was investigated by performing triaxial tests of the naturally fractured specimens at a constant temperature of 35°C. The injection pressure at the upstream varied from 6–12 MPa with an increment of 1.0 MPa. The confining pressure was set as 10, 15, and 20 MPa, respectively. These confining pressures represent the burial depth of coal seams from 400 to 800 m. Table 1 lists their confining pressures and injection pressures. Secondly, the effect of elevated temperature was investigated under various confining pressures and injection pressures. The CO2 permeability of both the naturally and secondarily fractured coals at temperatures of 25, 44, 58, and 70°C were measured. Such a range of temperatures represents the temperature at burial depths from several meters to one thousand meters [38,39]. Table 2 lists the confining pressure and injection pressure at each temperature. Specimens with three fracture extents are tested to explore the influence of facture extent on the CO2 permeability. The original fracture extent is referred to the elementary fractures in the naturally fractured coal. The natural specimen is hence known as the elementarily fractured coal. The CO2 permeability of the elementarily fractured coal was measured using the aforementioned testing procedure without any load. In addition to the original fracture extent, an axial compressive stress up to 50 MPa was applied, which is two to three times that of the uniaxial compressive strength of this coal, approximately reflecting the effects of the burial depth of coal seams, and a confining pressure of 10 MPa to the naturally fractured specimen to create the secondary fracture extent. The secondary fracturing process was ceased by removing the axial force at the moment when the acoustic emission (AE) reached a sufficient number. The newly fractured specimen is denoted as the secondarily fractured coal hereinafter. The CO2 permeability of the secondarily fractured coal was investigated using the same Table 1 Experimental parameters for permeability tests on naturally fractured coal specimens at a temperature of 35°C Confining pressure (MPa) 10 15 20

6

7 7

Injection pressure (MPa) 8 8 9 10 11 8 9 10 11

12 12

Table 2 Experimental parameters for temperature effect tests on both naturally and secondarily fractured specimens

Figure 1 (Color online) Photograph of the high-pressure triaxial testing system [34] (a) and its work schematic (b) for gas permeability tests.

Test temperature (°C) 25 44 58 70

Confining pressure (MPa)

Injection pressure (MPa)

15 20 25

7

8

9

10

11

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undrained testing procedure. The fracture extent was further generated at the third level, i.e., the post-secondary fracture extent, by reloading the axial compressive stress to 30 MPa on the secondarily fractured specimen until the same acoustic emission number as that of the second-level fracturing was counted. The fractured specimen at this level is thus referred to as the post-secondarily fractured coal. The same undrained testing procedures were applied to measure the CO2 permeability of the post-secondarily fractured specimen. The permeation test lasted for approximately 15 min for each injection pressure. 2.3

Principles for gas permeability calculation

For a transient flow, the gas flow rate through a specimen can be calculated as [40]

Q

dp V , dt

(1)

where Q represents the flow rate at downstream, dp/dt is the pressure rate at downstream,  is the adiabatic compressibility of the gas, and V is the downstream volume. The flow rate can be determined once the pressure fluctuation rate, the downstream volume, and the gas compressibility are obtained. Eq. (1) can be solved numerically to get the flow rate at downstream [40], and the permeability can be calculated based on the relationship between pore pressure and time. Experimental data [14] indicated that the following formula can be used to calculate the gas permeability:

k

2Qp0  L

A  pi2  p02 

,

(2)

where μ, p0, pi, A, L, and k refer to the gas viscosity, downstream pore pressure, upstream pore pressure, cross-sectional area, mean length, and permeability of the specimen, respectively. The adiabatic compressibility and viscosity values were determined using the REFPROP database (http:// www.nist.gov).

3 Experimental results and discussion 3.1

Figure 2 (Color online) Pressure difference between upstream and downstream vs injection time of the naturally fractured coal (a), the secondarily fractured coal (b), and the post-secondarily fractured coal (c) subject to various initial injection pressures at a constant confining pressure of 15 MPa and an elevated temperature of 35°C, IP stands for the CO2 injection pressure imposed to the specimens.

Effect of injection pressures on CO2 permeability

The effect of injection pressure on CO2 permeability is investigated. The measured downstream pore pressures are plotted against the CO2 injection time in Figure 2. The fractured specimens with three fracture extents were tested at a constant temperature of 35°C and a stationary confining pressure of 15 MPa. The injection pressure varied from 7 to 11 MPa with an increment of 1.0 MPa. Figure 2(a)–(c) present the pressure difference between the upstream and the downstream locations versus injection time of the elementarily fractured coal, the secondarily fractured coal, and the

post-secondarily fractured coal. The pressure drop between the two ends varies with the fracture extent. Generally, higher initial injection pressure has a larger pressure drop, and the fracture extent slightly impacts this pressure drop. For the naturally fractured coal, the pressure drop is a constant as the injection time elapses. This phenomenon was observed when the initial injection pressure is not larger than 11 MPa. Once the initial injection pressure is over 11 MPa, the pressure drop descended with time. This implies that the natural fracture system does not

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provide sufficient passageways for CO2 flow. The injected CO2 might absorb to the surfaces of the mineral particles of the fractured specimen. This situation was changed for the sequentially fractured coals. Both the secondarily fractured and the post-secondarily fractured specimens show that their downstream pressure drops sequentially decrease with the increase of gas injection time. These results indicate that CO2 can quickly flow through the fracture system and reach the downstream end of the specimen. Further uniaxial loads enhance the fracture extent of coals and provides more passageways for CO2 free flow through the system with less adsorption compared to the natural system. The postsecondary fracture, i.e., the unloading event from the previous compression level of the secondary fracture extent and the reloading to the previous fracture extent corresponding to the same acoustic emission number, exhibits less influence on the pressure drop compared with the secondary fracture case. This finding implies that the reloading procedure does not create more fractures. Instead, reloading causes some of the previous fractures to be closed such that CO2 flow is impeded and the pressure drop is increased compared to the case of secondary fracture. The influence of injection pressures on the CO2 permeability is investigated for fractured coals with different fracture extents. Figure 3 plots the curves of CO2 permeability vs. injection pressure of the specimens with three fracture extents. The confining pressure is 10, 15, and 20 MPa, respectively. Generally, larger injection pressure enhances higher CO2 permeability of the fractured coals. This enhancement depends on the amplitudes of the confining pressure. It is found that for the larger the confining pressure the less the injection pressure contributes to the CO2 permeability enhancement. The enhancement is particularly significant in the case when the confining pressure is as low as 10 MPa. The results clearly demonstrate that the post-secondary fractures created from unloading to reloading do not ameliorate the CO2 transport properties of coals compared to the secondary fracture status. This result is in agreement with the measurement of downstream injection pressures as demonstrated in Figure 2. Considering the effects of stationary confining pressure and constant ambient temperature, if the pressure reduction in the connected tubes can be neglected, it is concluded that the injection pressure drop between the two ends of a fractured specimen offsets the applied confining pressures, compacts granules, drives the gas to flow through fractures, and modifies the gas sorption capacity and matrix swelling [41–43]. 3.2

Effects of confining pressure on CO2 permeability

The compaction effect of confining pressure on the CO2 permeability of the fractured coal is investigated. The change of permeability with confining pressure is presented in Figure 4. For all coals with different fracture extents, the injection pressure is 8 MPa and the temperature is 35°C.

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Figure 3 Relationships of CO2 permeability vs injection pressure of the fractured coal specimens with varied fracture extents subject to the confining pressure increasing from 10 MPa (a), 15 MPa (b), to 20 MPa (c).

Figure 5 presents that the CO2 permeability descends with the increase of confining pressure at all fracture extents. The CO2 permeability of the naturally fractured, secondarily fractured, and post-secondarily fractured coals at the confining pressure of 20 MPa is dramatically reduced by 99.8%, 87.7%, and 87.6%, respectively, from their original values. The permeability of the post-secondarily fractured coal varies between the values. This implies that the increase of burial depth of coal seams (by the increase of confining pressure) significantly impairs the transport capability of CO2 in fractured coals. This damage of CO2 permeability is primarily attributed to the compaction effects of effective stress. It has been documented that the high effective stress shrinks the fractures that provide the connected channels for

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Figure 4 The CO2 permeability curves of various fracture extents against confining pressure at an injection pressure of 8 MPa.

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CO2 migration [44–46]. The shrinkage breaks the conductivity of the fracture system, increases the tortuosity of gas transport and thus slows down the seepage of CO2 [47–49]; this leads to the reduction of CO2 permeability. Nevertheless, it is noteworthy that the confining pressure insignificantly affects the change of CO2 permeability once the effective stress exceeds a threshold value, and this value is between 15 and 20 MPa according to the test results. Below the threshold value, CO2 permeability sharply decreases with the increase of confining pressure. Similar phenomena were observed in some previous experimental investigations. For example, it was found that the permeability decrease of the tight rock comprising a number of microcracks slowed as the confining pressure fell within the range of 20–30 MPa [28,50–52]. The closure effect of microcracks due to the increases of confining pressure was considered as the major factor responsible for the slowdown of permeability decrease. The magnitudes of CO2 permeability reduction in the coals with different fracture extents indicate that naturally fractured coal is more sensitive to confining pressure or effective stress than secondarily fractured and post-secondarily fractured coals. This can be attributed to the well-developed fracture system created by external loads, such as the secondarily fractured network, that maintains better residual connectivity and conductivity of the fractures as the confining pressure increases compared with the poorly-developed system, such as the naturally fractured network. The increase of confining pressure damages some part of the well-developed fractures, lowering the overall permeability; however, a relevant portion of fractures still remain open and connected, leading to a relative larger residual permeability compared to the naturally fractured coal. For the postsecondarily fractured coals, the reloading procedure does not cause any more fractures to the secondary system after unloading. Instead, part of fractures initiated by axial compression is closed due to the unloading effect. Therefore, the CO2 permeability of the post-secondarily fractured coal at each confining pressure is lower than that of the secondarily fractured coal but higher than that of the initially fractured coal. 3.3 Effects of elevated temperature on CO2 permeability

Figure 5 The CO2 permeability varying with elevated temperature under various injection pressures and confining pressures of 15 MPa (a), 20 MPa (b), and 25 MPa (c).

The effects of elevated temperature on the CO2 permeability of fractured coals were examined. In these tests, CO2 was injected into the secondarily fractured coal with pressures of 7, 8, 9, 10, and 11 MPa, respectively. This secondarily fractured coal was generated by applying an axial compression of 30 MPa and a confining pressure of 10 MPa. Three confining pressures of 15, 20, and 25 MPa are applied to the specimen. The ambient temperature was set as 25, 44, 58, and 70°C. The coals were heated for one hour at each elevated temperature and then CO2 was injected into the specimen with the above CO2 pressures. Figure 5 plots the change of CO2 permeability with temperature at the confin-

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ing pressure of 15, 20, and 25 MPa. This figure shows that the permeability decreases with temperature when the temperature is from 25–44°C. It is also found that higher injection pressure decreases the permeability. When the temperature is over 44°C, the permeability increases with temperature, rising until the temperature reaches 70°C. The value of 44°C appears to be a critical temperature that discriminates the different thermal effects on the CO2 permeability of fractured coals. It is noteworthy that the temperature effect on CO2 permeability appears more obvious as the confining pressure is greater than 15 MPa. The larger the confining pressure the more apparent the temperature effect on the permeability. Additionally, the increase of confining pressure also considerably lowers the permeability of fractured coal at high temperature. In fact, the strong temperature influence on CO2 permeability is attributed to the elevated temperature that results in both thermal stress and matrix swelling. This temperature process can modify the effective stress, the fluid flow property, and the CO2 adsorption capacity within the fractured coals [25,29]. As the temperature is not higher than 44°C, the heating process causes the thermal expansion and swelling of the coal matrix particles. Considering the constraint effects of confining pressure, the thermal expansion of particles squeezes the space that is occupied by the existing fractures, narrowing the fracture apertures, and therefore resulting in the reduction of CO2 permeability. Stronger confining constraints have more reduction of gas permeability, implying that in the low temperature range (25–44°C) the coupling effect of heating and confining pressure plays the dominant role in reducing the CO2 permeability of fractured coals. As coal is continuously heated to the temperature over 44°C, the effect of thermal expansion becomes even stronger. Meanwhile, considering the fact that CO2 turns into a supercritical state as the temperature exceeds 31.1°C and the pressure is more than the critical value of 7.38 MPa [2,53], the elevated temperature increases the viscosity of liquid CO2 compared to that of gaseous CO2. The increased viscosity impacts the CO2 permeability; however, the transition from the gaseous state to the liquid state of CO2 lowers the gas adsorption capacity, improving the fluidity and permeability. Moreover, the elevated temperature improves the kinetic energy of CO2 molecules, which benefits the permeable property of CO2 within fractures. Finally, the combined effects of the CO2 adsorption capacity reduction and the CO2 permeable property improvement surpass the effect of thermal expansion. As a result, the CO2 permeability rises with the increase of temperature.

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effective stress, pore pressure and elevated temperature on CO2 permeability. Essentially, the CO2 permeability of fractured coals could be affected by multiple factors, including the fracture characteristics, connectivity, physical or mechanical properties of coal matrices, and their evolution induced by multiphysical processes. 4.1

Characterization of fractures and permeability

Often, coal fractures are not straight and have two separate parallel faces. The connections between faces impose constraints on either mechanical deformation or swelling of the porous media. Figure 6 conceptually presents the connection between two fracture faces. It postulates that the fracture has two parallel faces, and the connection may constrain the local deformation at the initial stage of swelling but has no constraint on the macro-free deformation in the later stage [54–56]. Neglecting turbulent flow effects and assuming only steady flow within the fracture system, the initial permeability of a set of parallel fractures can be expressed by the cubic law as

k0 

b03 , 12s0

where b0 is the initial fracture aperture, and s0 refers to the initial fracture spacing. Any aperture change, b, as well as fracture spacing, s, will modify the permeability as: 3

k  b   s0  = 1  ,  k0  b0   s 

(4)

where k represents the instant permeability of the fracture system. Considering the relationship between the fracture system change (Figure 6) and the macro volumetric deformation of coal, the following expression is assumed [5]:  v 

b , b0

(5)

where v refers to the increment of the volumetric strain of

4 A mechanistic model for effective stress, pore pressure and thermal micro-cracking A mechanistic model is proposed to consider the effects of

(3)

Figure 6

A conceptual model for fracture distribution.

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coal that experienced multiphysical processes. The equation for determining the instant permeability k of the fracture system can be then rewritten as s k  (1   v )3  0  s

  k0 . 

(6)

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 L  p, T  is the Langmuir strain constant which represents the maximum swelling capacity at the temperature T and the pressure p. When the state changes from the initial state  p0 , T0  to the current state

 p, T  ,

the swelling strain increment is

then calculated by 4.2

Swelling effect induced by multiphysical processes

In this experiment, the volumetric strain increment has the following components:  v   vM   vp   T   s ,

(7)

where  vM denotes the volumetric strain increment induced by the mechanical deformation;  vp is the volumetric strain increment caused by pore pressure; T and

 s refer to the volumetric strain increments induced by thermal expansion and gas adsorption. The stress-strain relationship between the volumetric strain and confining pressure can be described by an exponential form as  vM =a exp  b c  ,

(8)

where the indices a and b are material constants, and  c is the effective confining pressure. The volumetric strain increment induced by the pore pressure can be written as  vp =

 3K

p,

(9)

where  is the Biot coefficient and K is the bulk modulus. In this study,  was set to be 0.67. The variable p refers to the pore pressure increment. The volumetric strain brought by thermal expansion can be similarly calculated by  T =

T 3

T ,

(10)

where T is the thermal expansion coefficient, T  2.4  105 /K , and T denotes the temperature increment. The gas adsorption-induced swelling strain increment can be expressed by  s   s   s 0 .

(11)

The Langmuir isotherm is used to describe the swelling strain as [39]

s 

 L ( p, T ) p p  PL ( p, T )

,

(12)

where PL  p, T  is the Langmuir pressure constant, and

 s   s   s 0 

 L  p, T  p

p  PL  p, T 



 L 0  p0 , T0  p0

p0  PL 0  p0 , T0 

.

(13)

Most studies regard both PL and L as constants, regardless of pore pressure and temperature, i.e., PL  PL 0 and  L   L 0 . However, it does not describe the thermal effect of coal on the adsorption capacity. If the adsorption capacity of coal changes with pore pressure and temperature, eq. (13) is still applicable. 4.3

Thermal effects on gas adsorption capacity

In general, temperature affects the thermal expansion strain and also modifies the Langmuir constants and the local dilation. Experimental data imply that both pore pressure and temperature influence the gas adsorption capacity and matrix swelling. Zhu et al. [57] used the following modification to consider the influences of pore pressure and temperature: 

 c2 Ta  Tr  T  ,  1  c1 p 

 L  p, T     0 exp  

(14)

where c1 is the pore pressure coefficient, and c2 is the temperature coefficient; Ta = 273.14 K and represents the temperature at the standard condition; Tr is the reference temperature for the adsorption test. 4.4

Thermal micro-cracking

The temperature causes the thermal expansion of the coal matrix and modifies the microstructures of the matrix due to gas desorption and change of internal stress [25]. The temperature-induced micro-cracking in matrix causes the microcrack density to vary with temperature after the temperature is over a certain critical value, which is thermal microcracking. Based on this understanding, the following expression is proposed to consider the change of microcrack spacing:

1, s0   T   s exp  r    1  ,     Tc 

T  Tc , T  Tc ,

(15)

where Tc is the critical temperature of the coal, and r is

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the material constant. Substituting eqs. (8)–(15) into eq. (7), the gas permeability of the fractured media can be obtained. 4.5

Model performance and verification

4.5.1 Effect of confining pressures on CO2 permeability The proposed mechanistic model (i.e., eqs. (7)–(15)) is applied to the coals of three fracture extents to investigate the effect of confining pressure on the CO2 permeability for the examination of model performance and accuracy. In the computation, the injection pressure is assumed to be 8 MPa. Figure 7 illustrates the comparison between the model calculations and the experimental data, and good agreement is observed. This comparison also shows that the permeability follows different rates of decay with further compaction. The permeability of the naturally fractured coal decays fastest with the increase of confining pressure. The permeability becomes higher with further fracturing when the secondary fracture extent is achieved. The permeability of the post-secondarily fractured coal varies between these two conditions. Thus, fracturing modifies the microstructure of the fractured media and causes the CO2 permeability to evolve at different rates. 4.5.2 Effect of injection pressure on CO2 permeability Generally, injection pressure has the following three effects: reducing the effective confining pressure (making coal rebound), compacting coal particles, and modifying gas adsorption capacity and swelling. Figure 8 compares the model predictions with the test data on the evolution of CO2 permeability with injection pressure. The confining pressure is 20 MPa. Good agreement is observed between the predictions and the experimental measurements. For the naturally fractured coal sample, the predicted permeability is slightly lower than the experimental data. A large deviation is observed for the post-secondarily fractured sample, but the model predicts the permeability trend with injection pressure.

  Figure 7 Comparison of the modelling predictions and the experimental data of the gas permeability of coals with various fracture extents and confining pressures subjected to a constant injection pressure of 8 MPa.

  Figure 8 Comparison between the model predictions and the experimental data of the gas permeability of coals with various fracture extents and injection pressure subjected to a constant confining pressure of 20 MPa.

It is also noted that the compaction of the coal sample is the primary factor that determines the evolution rate of permeability with injection pressure. Different fracture extents have different swelling capacities, implying that fracturing extents can modify the adsorption-induced swelling during the experimental period. 4.5.3 Effect of temperature on CO2 permeability The effect of temperature on CO2 permeability is investigated by applying the model to predict the permeability of the secondarily fractured coals. In the computations, the injection pressure ranges from 7 to 11 MPa with a stationary confining pressure of 20 MPa. Figure 9 compares the model estimations with the experimental data; Figure 9(a) presents a comparison when the change of fracture spacing is considered, and Figure 9(b) illustrates the results if the fracture spacing does not change. The comparison demonstrates that the estimations are better when the change of fracture spacing is considered. However, both tests do not well predict the CO2 permeability at either low or high temperatures. Particularly, the initial reduction of the permeability is not well predicted at all injection pressures. The better predictions are attributed to the two competitive factors that prevail in affecting the CO2 permeability of fractured coals. The thermal expansion of the coal matrix reduces the permeability because it makes the flow passage narrower. However, gas desorption causes the matrix to shrink and widen the flow channels. Further, desorption and the temperature induced internal stress may significantly modify the existing flow channels and generate more microcracks, thus reducing the fracture spacing. This is obviously observed by the comparison of Figure 9(a) and (b) when the temperature is over the critical value. The calculation also indicates that more microcracks are generated at a higher injection pressure. Higher injection pressure leads to lower effective confining pressure and a higher initial permeability.

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Figure 9 Estimation of the temperature effects on the gas permeability of a secondarily fractured sample at a confining pressure of 20 MPa under various injection pressures. (a) Change of fracture spacing; (b) no change of fracture spacing.

5 Conclusions Triaxial undrained tests were successfully conducted to measure the CO2 permeability of fractured coals. The effects of injection pressure, confining pressure, and elevated temperature on the CO2 permeability of the coal samples with three fracture extents were investigated. A mechanistic model was then proposed to explore the mechanism of permeability evolution. Based on these experimental measurements and the model analysis, the following understandings and conclusions can be drawn. Firstly, the CO2 permeability of naturally fractured coal increases with the increase of injection pressure, and it significantly decreases with the increase of confining pressure. The increase of injection pressure reduces the effective confining stress on the coal sample and causes the pore space to expand for gas movement, resulting in the enhancement of permeability. Conversely, the increase of effective stress imposes confinement to the specimen, which narrows the fracture pore space available for CO2 movement, resulting in the reduction of permeability. Secondly, fracture extent has significant impacts on the evolution of permeability. The experimental data show that

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the CO2 permeability significantly increases after the secondarily fractures but decreases after the post-secondary fractures. Further fracturing may cause the initially formed fractures to be closed. Additionally, the generation of new fractures incites a different response to the flow passage and thus reduces the permeability increment trend with the increase of injection pressure. Thirdly, the effect of elevated temperature on the CO2 permeability is complex. This study investigated the temperature effect on the CO2 permeability of only the post-secondarily fractured coal samples, and the temperature varies from 25–70°C. It is found that the CO2 permeability reduces with the increase of temperature at low values (25–44°C), but the permeability increases with the increase of temperature beyond 44°C. The higher the confining pressure and injection pressures, the more signifycant the temperature effect on CO2 permeability. The 44°C is a critical temperature for this fractured coal. It is the complex result of different thermal effects on the gas permeability. Finally, the proposed mechanistic model provides a good estimation of the gas permeability of fractured coals when the injection pressure, confining pressure and temperature are changed. Through this mechanistic model, it is found that compaction is the main factor to affect the permeability; however, the effect of temperature is complicated. Varied temperature can cause coal matrix expansion, alter the fracture system, and change the internal effective stress and gas adsorption capacity, thus causing different results before and beyond the critical temperature. Beyond the critical temperature, thermal micro-cracking may occur and enhance the permeability of the fractured coal. This work was supported by the National Natural Science Foundation of China (Grant Nos. 51374213 & 51674251), the State Key Research Development Program of China (Grant No. 2016YFC0600705), the National Natural Science Fund for Distinguished Young Scholars (Grant No. 51125017), Fund for Creative Research and Development Group Program of Jiangsu Province (Grant No. 2014-27), Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 51421003), and the State Key Research Development Program of China (Grant No. 2016YFC0600705). 1 2 3 4 5

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