Experimental study on the relationship between the matric potential and methane breakthrough pressure of partially water-saturated shale fractures

Journal of Hydrology 578 (2019) 124044

Contents lists available at ScienceDirect

Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol

Research papers

Experimental study on the relationship between the matric potential and methane breakthrough pressure of partially water-saturated shale fractures

T

⁎

Pengju Cheng, Qingchun Yu

Beijing Key Laboratory of Water Resources and Environmental Engineering, School of Water Resource and Environment, China University of Geosciences (Beijing), 29 Xueyuan Road, Haidian Distric, Beijing 100083, China

A R T I C LE I N FO

A B S T R A C T

This manuscript was handled by Huaming Guo, Editor-in-Chief, with the assistance of Mingjie Chen, Associate Editor

The breakthrough pressures of shale fractures are of great significance for the understanding of shale gas seepage or accumulation, CO2 geological sequestration and radioactive waste storage in shale, and pollution problems caused by gas leakage. In this study, three shale cores taken from the eastern Qaidam Basin in China were used to investigate the breakthrough pressures of partially saturated shale fractures. The fractured shale core had a single longitudinal fracture across the core along the axis. A quantitative description of the relationship between the breakthrough pressure and the water content in the fracture is difficult because of the difficulty in the measurement of the water volume in the fracture. We propose a method to describe this relationship. In this method, the water content in the fracture is described by the matric potential. Cores with different matric potentials were prepared by moistening the cores in different humidity environments. Methane breakthrough experiments were conducted on three core samples under six different matric potentials. The six matric potential levels were −51.38 MPa, −39.08 MPa, −23.45 MPa, −8.55 MPa, −2.33 MPa, and 0 MPa. Based on the experimental results, we apply a conceptual model to qualitatively describe the relationship among the matric potential, water distribution in the fracture, and breakthrough pressure. At a low matric potential, water forms very thin water films on fracture surfaces, and the effect of water on the breakthrough pressure is not notable. As the matric potential increases, the thickness of water film in the fracture increases, and the increase in the breakthrough pressure become notably. We establish a mathematical model to quantitatively describe the relationship between the breakthrough pressure and matric potential. The experimental data show that the increase in breakthrough pressure with the matric potential is a process that proceeds from slow to fast, and there is a critical value of matric potential in this process. When the critical value is reached, the connected gas passages are gradually sealed by water films, and the breakthrough pressure begins to increase significantly.

Keywords: Shale fracture Breakthrough pressure Matric potential Partially saturated

1. Introduction Shales are commonly characterized by low porosities, low permeabilities, and complicated pore structure networks, which make shales both reservoir rocks and caprocks (Chandler et al., 2016). Due to the low porosity and low permeability values, shales are not only considered to be storage and migration sites for oil and gas resources (Ougier-Simonin et al., 2016) but also rocks of interest for CO2 geological sequestration as well as geological disposal of radioactive waste because of the excellent sealing efficiencies (Bolton et al., 2000; Tsang et al., 2012). The problem of gas escaping after overcoming the breakthrough pressure in a shale is becoming the intersection of many resource and environmental issues, such as the accumulation and exploitation of shale gas, the long-term safety of underground storage

⁎

projects in shales (CO2 geological sequestration, radioactive waste storage, and underground gas storage reservoir), and the pollution problems caused by gas leakage. In a shale gas reservoir, the excess pressure of shale gas (mainly CH4) generated from organic matter must not be higher than the breakthrough pressure of the shale, so that the gas can migrate and accumulate to form a gas reservoir in the trap structure (Romero-Sarmiento et al., 2013; Chapiro and Bruining, 2015). In the exploitation of low porosity and low permeability shale reservoirs, gas can migrate to the production wellbore only when the differential pressure between gas and water is higher than the breakthrough pressure of the formation fracture network (Zhang et al., 2015). In the long-term safety considerations of underground storage projects, the shale caprock must have a sufficiently high breakthrough pressure to prevent gas (CH4, CO2 or the additional gas produced by

Corresponding author. E-mail addresses: [email protected] (P. Cheng), [email protected] (Q. Yu).

https://doi.org/10.1016/j.jhydrol.2019.124044 Received 30 May 2019; Received in revised form 30 July 2019; Accepted 14 August 2019 Available online 16 August 2019 0022-1694/ © 2019 Elsevier B.V. All rights reserved.

Journal of Hydrology 578 (2019) 124044

P. Cheng and Q. Yu

breakthrough pressures. Therefore, the analysis of the breakthrough pressure of shales without considering the controlling effect of fractures will results in significant deviation, even mistakes in engineering applications. However, almost all existing breakthrough pressure studies fundamentally focused on the rock matrix, where there was little description and discussion on the fractures of the samples. To our knowledge, no quantitative studies on the breakthrough pressure of a fracture are available yet. Moreover, previous breakthrough pressure studies have been almost carried out on dry or fully water-saturated cores. However, due to the coexistence of water and gas in pores and fractures, shales deep within the earth are always partially water saturated (Birdsell et al., 2015). The theory of the breakthrough pressure in partially saturated shale fractures remains poorly understood, so it is necessary to conduct gas breakthrough experiments on partially saturated fractures to understand the relationship between the breakthrough pressure and the water content in the fracture. The gas breakthrough pressure of low-permeability rock is closely related to the water content in the rock (Zhang and Yu, 2016, 2017). The water content in a partially saturated porous medium is usually quantified by the water saturation, which can be obtained by weighing. However, for fractured cores, the water saturations of fractures cannot be measured due to the interconnected fracture and pore networks. It is very difficult to describe the relationship between breakthrough pressure and the water content in the fracture. Because the water saturation in an unsaturated porous medium can be represented by the matric potential. For a given matric potential, the water in the matrix pore spaces is in equilibrium with the water on the fracture surfaces. The water content in the fracture can be represented by the matric potential. When the matric potential is lower than a high extreme (close to zero), the fracture is partially saturated. Changes in the matric potential can alter the water content in the shale matrix and fracture, thereby resulting in a change in the breakthrough pressure. Therefore, to quantitatively describe the variation in the breakthrough pressure of a fracture with the water content, the relationship between the matric potential and breakthrough pressure of a partially saturated fracture need to be studied. In this study, methane breakthrough experiments were conducted on fractures in shale cores under various matric potentials. Three shale cores were obtained from the Carboniferous formation in the eastern Qaidam Basin in China. The shale core contained a single fracture located centrally and longitudinally through the whole core along the axis. A detailed description of the properties of shale core, preparation of fractures and experimental devices was provided in Section 2. The method for preparing water-saturated cores with different matric potentials and the procedure for measuring the methane breakthrough pressure of fractures under different matric potentials were provided in Section 3. Based on the experimental results, the relationship among the matric potential, the water content in the fracture, and the breakthrough pressure was qualitatively analyzed. The mathematical relationship between the matric potential and breakthrough pressure of fractures was established. The water film thicknesses on the fracture surfaces at various matric potentials were analyzed, and the gas flow mechanism in the fracture was preliminary discussed.

radioactive waste) leakage from the shale into the shallow environment (Kim and Santamarina, 2013). The shale associated with a higher breakthrough pressure is accompanied by a higher sealing capacity. However, shale formation damage caused by induced fractures or reactivated pre-existing fractures due to tectonic activity, hydraulic fracturing or large-scale fluid injection (Fang et al., 2017) induces the gas to escape from the fracture network after overcoming the breakthrough pressure, thereby resulting in shallow groundwater or surface water contaminants (Osborn et al., 2011; Molofsky et al., 2013; Vidic et al., 2013) and atmospheric pollutions as well as the greenhouse effect (Montgomery et al., 2006; Howarth et al., 2011; Allen et al., 2015), which has been a global topic of discussion. The aforementioned issues highlight that an accurate measurement of the breakthrough pressure in shales is particularly important for the study of these resource- and environment-related issues. Shales serve as potential flow barriers against gas escaping outward through a capillary sealing mechanism controlled by the capillary pressures of small pores (Horsrud et al., 1998; Nojabaei et al., 2016). The breakthrough pressure is the critical capillary pressure in a series of interconnected pores of arbitrarily large sizes that the differential pressure between non-wetting phase (gas) and wetting phase (water) must overcome to break through the porous medium and form continuous gas pathways through the wetting phase (Hildenbrand et al., 2002; Li et al., 2005; Zhang and Yu, 2016). The breakthrough pressure (Pbt) has been comprehensively regarded as a characteristic core-scale parameter in the formation and exploration of oil and gas reservoirs as well as geological storage assessment (i.e., CH4, CO2) (Gao et al., 2014; Zhang and Yu, 2019), which can be described by the Young-Laplace equation as follows:

Pbt = Pn − Pw =

2σcosθ re

(1)

where Pn and Pw are the nonwetting (gas or oil) and wetting phase pressure (water), respectively; σ is the surface tension at the interface between the nonwetting and wetting phase; θ is the contact angle; and re is the effective radius of the pore throat or effective aperture of the fracture. The inverse dependence on re accounts for why the very fine pores of rocks can provide a large resistance to gas migration. However, since the aperture size of a fracture is several orders of magnitude larger than a matrix pore, the capillary resistance to the gas in a fracture is much lower than that in the shale matrix, with the result that fractures form preferential and primary flow paths (Karpyn et al., 2009; Zeng et al., 2013). Hence, fractures control gas migration, accumulation of reservoirs and the long-term sealing capacities of caprocks (Jarvie et al., 2007). Therefore, the breakthrough pressure of shale fractures can be considered as a critical parameter to better evaluate the hydrocarbon accumulation and exploitation and underground storage engineering in shales. Recently, many researchers have conducted gas breakthrough experiments on low-permeability sedimentary rocks to study the breakthrough pressure. Graham et al. (2002) performed breakthrough experiments on water-saturated clay specimens, and found that gas breakthrough occurred in discrete channels with the lowest capillary resistance. Amann-Hildenbrand et al. (2013) conducted breakthrough pressure experiments on completely saturated shales and found that the helium gas breakthrough pressure of shale matrix was higher than 20 MPa. Li et al. (2015) conducted breakthrough pressure experiments on dry and completely saturated shales and found that a completely saturated shale was hard to be broken through and the gas breakthrough process can be divided three stages. Rezaeyan et al. (2015) performed breakthrough experiments on saturated shale and anhydrite to analyze the effects of different parameters (overburden pressure, ambient temperature, gas mixture) on the breakthrough pressure. However, based on the breakthrough pressure measurements on watersaturated shales, Zhang and Yu (2016) found that microfractures in shales facilitated an easier gas breakthrough, resulting in lower

2. Experimental samples and apparatus 2.1. Shale samples Three shale cores for the methane breakthrough experiments were taken from the Carboniferous formation from the eastern Qaidam Basin in China. Carboniferous shale in the eastern basin is extensively developed and the sequence is complete (Gao et al., 2017). These three shale samples were extracted from ZK5-2 well from depths of 239.96 m, 380 m and 356.05 m (Fig. 1) and are referred to as samples S1, S2 and S3 in this study, respectively. The stratigraphic depth, lithology and sampling stratum for the ZK5-2 well are shown in Fig. 1. The samples 2

Journal of Hydrology 578 (2019) 124044

P. Cheng and Q. Yu

than 40 μm and 1 mm, respectively. A Leco carbon sulfur analyzer was used to measure the total organic carbon (TOC) content, and an MPV-SP micro photometer was applied to analyze the vitrinite reflectance (Ro). A fracture was artificially induced due to the difficulty in obtaining a core with a single fracture located centrally and longitudinally through the whole core during the coring process. To prepare a single fracture along the axis of the cylindrical sample, the cylindrical core was positioned into a uniaxial compression device. Two thin steel sheets were placed into small notches along both sides of the core length. To prevent core edge damage, the core was encased in a shrinkable tube during the fracturing experiment to avoid direct contact between the core and the steel sheets. Following the encasement, a uniaxial compression device was used to exert a load parallel to the bedding plane of the core on the thin steel notches to induce a single fracture. The advantage of this method of inducement is that the resulting fracture was suitably located centrally and ran longitudinally throughout the core along the axis of the core. Afterwards, both cylindrical halves of the fractured cores were joined together along the lateral boundaries using a silicon adhesive to avoid the slight offset of the fracture and make the fracture aperture remain constant during the experiment. The created cores (S1, S2 and S3) and the directions of splitting are displayed in Fig. 2. The pulse-echo method which offers a convenient way to analyze elastic modulus and Poisson's ratio without damaging the rock, was applied to measure the elastic modulus and Poisson's ratio of the fractured shale sample according to the method of American Society for Testing and Materials (1999). All of the measurement results (mineral content, TOC content, Ro, elastic modulus and Poisson's ratio) are shown in Table 2.

2.2. Experimental apparatus Fig. 3 shows a schematic of the experimental apparatus for the experiments to measure the breakthrough pressure and permeability. The experimental device contains a core clamping unit, a vacuum pumping system, a liquid injection system, a gas injection system, a confining pressure system, a detection unit and a data acquisition unit. The core clamping unit is mainly composed of a core holder and a fluororubber sleeve with a high elasticity, which is acid- and pressure-resistant. The core is wrapped in a fluororubber sleeve, put into the core holder and placed horizontally in a thermostat. An isotropic confining pressure is used to simulate the in-situ stresses and is continuously applied around the core using a syringe pump. The vacuum pumping system is designed to eliminate air from the pipelines. Gas can be injected into the core holder at a constant pressure by the gas injection system. The liquid injection system can pump liquid into the core holder at a constant flow rate. Two pressure sensors with a high precision (0–20 MPa, ± 0.1 kPa) are installed at both ends of the core holder to display the inlet and outlet pressures. When gas breaches the rock core, the detection system monitors bubbles at the outlet, and the gas flow rate can be measured by a gas flow meter under the experimental conditions. An electronic scale is used to weigh the water that is cumulatively collected in the liquid tank. Both the inlet and outlet pressures (relative to the atmospheric pressure) and the flow rates are recorded through a data acquisition system. As shown in Fig. 3, the gas and liquid containers, the gas and liquid injection systems, the core holder, the valves, and the pipelines connecting these systems are thermostatically controlled. Due to the low porosity and low permeability, it is very difficult to

Fig. 1. Stratigraphic histogram for the ZK5-2 well with sampling stratum marked by arrows.

were made into cylindrical cores. The dimensional specifications (depth, diameter and length) and properties (permeability) of these core samples are listed in Table 1. The absolute gas permeability (kabs) of the shale samples was measured with the steady-state flow method using methane as the penetrating fluid. The shale samples possess a low permeability in the range of 10−18–10−19 m2, which implies that the shale matrix has a high capillary resistance pressure. The nonclay mineral and clay mineral contents in the shale samples were measured by X-ray diffraction (XRD) using shale powders with particle sizes smaller

Table 1 The dimensional specifications (lithology, depth, diameter and length) and properties (matrix permeability) of the core samples. Sample

Lithology

Well

Depth (m)

Diameter (cm)

Length (cm)

Matrix absolute permeability (CH4) (m2)

S1 S2 S3

Black shale Gray shale Gray shale

ZK5-2 ZK5-2 ZK5-2

239.96 380.00 356.05

5.00 5.00 5.00

3.75 3.10 3.18

7.29 × 10−18 1.74 × 10−18 3.21 × 10−18

3

Journal of Hydrology 578 (2019) 124044

P. Cheng and Q. Yu

Fig. 2. Pictures of the fractured shale cores used in the experimental study.

Then, the saturated core was placed in a constant humidity chamber, where the fixed RH was controlled through saturated salt solutions of various compositions (Greenspan, 1977) and the constant temperature (25 °C, ± 0.05 °C) was maintained by a thermostat. The temperature and RH (0–100%, ± 0.01%) were monitored by a probe during the experiment. The salt solutions and corresponding RH in this experiment were provided in Table 3. Theoretically, the water content in the fractured core ultimately reaches a stable value when the water potential and the total pore liquid chemical potential in the fractured core reach equilibrium. The total potential in the fractured core is the sum matric potential and osmotic potential. In pure water and fractured shale system, the osmotic potential contribution little to the total potential, and the osmotic potential can be ignored. The assumption is justified in nearly all of vapor pressure equilibration system (Tokunaga et al., 2003). The core was then weighed every 24 h. When the core weight did not change for 7 consecutive days (recorded as m2), the equilibrium condition was reached, and the water in matrix pores and in the fracture was in equilibrium. At this point, the matric potential is approximately equal to the water potential, and can be calculated from the Kelvin’s law as follows (Delage et al., 1998):

saturate a massive shale through immersion. Therefore, an experimental apparatus is designed to obtain a completely saturated shale core as shown in Fig. 4. This device consists of a stainless steel container, a liquid injection unit, a gas compression unit, a gas injection unit, and a vacuum pumping unit. The basic principle of the device is to use gas pressure to force water to penetrate into the pores and fractures of tight shale. The amount of He adsorbed in shale can be considered negligible (Wang et al., 2016). In addition, He gas is hard to dissolve in water and does not interact with water and minerals in shale. He gas is used as the non-wetting fluid to pressurize the system. 3. Experimental procedures 3.1. Moistening the samples to various matric potentials The partially saturated fractured shale samples with various matric potentials were obtained by using the relative humidity (RH) to control the balance between the water potential (φw) and matric potential (φm) (Tokunaga et al., 2003; Silva et al., 2008; Ferrari et al., 2014). We first obtained a fully saturated fractured sample and then placed the saturated sample into a constant humidity chamber to balance the water potential and matric potential. First, the apparatus shown in Fig. 4 was used to obtain a fully saturated fractured core. The shale core was dried at 105 °C for 8 h, and the dry weight (m0) was measured. The dry core was then placed into the stainless steel container, and the air in the core and pipelines was removed by the vacuum pumping unit. Subsequently, distilled water was injected into the core container, and the core was fully immersed in water to ensure uniform saturation. Then, He gas with a pressure of 10 MPa was introduced into the container to pressurize the system for at least 2 days until the weight of the core did not change, and the completely saturated weight was recorded as m1. At this point, the matrix and fracture were completely saturated, and the matric potential in the completely saturated core is regarded as zero.

φm = φw =

RTρw ln (RH ) Mw

(2)

where R is the gas constant, T is the Kelvin temperature, ρw and Mw are the density and the molecular mass of water. The water saturation of the fractured shale core (Sw) was calculated as follows:

Sw =

m2 − m 0 × 100% m1 − m 0

(3)

After reaching equilibrium at the highest RH, cores were then moistened at various saturated salt-controlled environments for preparing the matric potential from −2.33 MPa down to −51.38 MPa.

Table 2 Mineral composition (nonclay minerals and clay minerals), Organic Matter (TOC content, kerogen type, and Ro) and geophysical parameters (elastic modulus and Poisson's ratio) of the shale samples. Sample

Mineral composition Nonclay minerals and clay minerals Quartz %

S1 S3

26 49

Calcite % 41 18

Dolomite % 11 1

Pyrite % 10 7

Clay minerals Clay % 12 25

I% 10 8

K% 40 13

Organic Matter C% 4 4

Note: I is illite; K is kaolinite; C is chlorite; I/S is illite-smectite mixed layer; E is elastic modulus. 4

I/S % 46 75

TOC % 1.61 0.10

Kerogen type II2 II2

Geophysical parameters Ro % 1.38 1.42

ν

E MPa 4

2.525 × 10 2.068 × 104

0.245 0.043

Journal of Hydrology 578 (2019) 124044

P. Cheng and Q. Yu

Fig. 3. Schematic diagram of the apparatus used to measure the gas breakthrough pressure and permeability.

Fig. 4. Schematic diagram of the apparatus used to conduct the water saturation experiments.

at a given matric potential, the fractured core was moistened according to Section 3.1. The wetted core was then placed in the core holder. The confining pressure was set to 16 MPa during the experimental run to prevent the core from being hydraulically fractured. The core holder was placed under the confining pressure for 48 h and both ends of the core holder were in communication with a humidity environment of the same water potential as where the core samples were moistened. Whether 48 h is long enough for the samples to reach equilibrium remains to be further studied. Subsequently, the entire detection system was vacuumed to remove the residual gas in the pipeline. After that, CH4 was injected into the inlet of the core holder at a desired lower pressure value initially, and the outlet was detected by the gas detector throughout the whole experiment process. The inlet pressure of the CH4 was then increased in a stepwise manner, and adequate time intervals were offered for each step of the continuous injection process. In this study, to avoid overshooting and overestimating of breakthrough pressures, when the injection pressure was less than 0.5 MPa, the pressure increment in each step is 0.002–0.005 MPa, and 0.01–0.02 MPa when the injection pressure was higher than 0.5 MPa. The time-lag of each step increment should be 30 min when the injection pressure is lower than 2 MPa, 45 min when the pressure is between 2 and 5 MPa according to the Determination Method of Gas Breakthrough Pressure in Rock (The People's Republic of China Standards of the Petroleum and Natural Gas Industry, SY/T 5748-2013). Theoretically, when the gas phase reaches the fracture, due to the heterogeneous aperture structure and the rough surface, at the capillary entry pressure the gas begins to enter the largest aperture. An increase in gas

Table 3 The salt solutions and the relative humidity levels measured using the humidity probe at a temperature of 298.15 K as well as the corresponding water potentials in this study (RH is the relative humidity, φw is the corresponding water potential). Salt solution

KI

NaCl

KCl

KNO3

K2SO4

RH (%) φw (MPa)

68.86 −51.38

75.84 −38.08

84.34 −23.45

93.98 −8.55

98.32 −2.33

3.2. Breakthrough pressure experiments Three methods were used to conduct the gas breakthrough experiments: mercury injection method, residual capillary pressure approach and step-by-step method. The step-by-step method, which is most representative and reliable method to conduct breakthrough experiments (Li et al., 2005; Boulin et al., 2013; Zhao and Yu, 2017, 2019), was applied in this study. Prior to breakthrough experiment, a solid nonporous 50 mm diameter stainless steel cylinder was subjected to the methane experimental program to ensure there was no leakage of gas between the core and the fluororubber sleeve. We found that there was no measurable gas leakage across the steel sample when the confining pressure was maintained 4 MPa above the injection pressure. After checking the airtightness of the apparatus, the breakthrough pressure and gas permeability of the dried cores were first measured. Then, methane breakthrough experiments were conducted on the partially saturated fractured shale cores. To obtain a partially saturated fracture 5

Journal of Hydrology 578 (2019) 124044

P. Cheng and Q. Yu

the adsorption and capillary forces, which affects the migration of the gas phase in the pore spaces. The gas breakthrough pressure, which is the capillary pressure between the water phase and gas phase, is mainly affected by the water content. A quantitative description of the relationship between the breakthrough pressure and water content is needed.

pressure causes the gas to advance through the interconnected void spaces to the smaller aperture, where the additional pressure is balanced by a higher capillary pressure. The gas pressure continues to increase until the gas pressure is sufficiently high to overcome the capillary pressure of the narrowest aperture in the channel, the gas breaks through the core, and the gas migrates along the continuous pathway through the fracture. Therefore, when continuous gas bubbles were observed at the outlet, a continuous pathway for CH4 to pass through was formed, and the gas broke through. The pressure difference between the inlet pressure of the last step and the outlet pressure was recorded as the gas breakthrough pressure (Pbt). At this point, the gas source was closed, and the inlet pressure variation was recorded until no gas was emitted at the outlet. Subsequently, the inlet pressure was increased to value of breakthrough pressure to measure the effective permeability. The permeability measurements lasted 0.5 h to obtain the effective CH4 permeability, thereby obtaining the effective aperture. The gas permeability of the fracture (kg) can be calculated as follows (Persoff and Pruess, 1995; Bertels et al., 2001):

kg =

2P0 QμLZ A (P12 − P22 ) Za

4.1. Describing the water content in a fracture by the matric potential The quantitative description of the water content in a partially saturated porous medium usually depends on the water saturation. Due to the difficulty in measurement of water volume in the fracture in the fractured shale, it is difficult to separately extract the water saturation of the fracture in a fractured shale core. We use the matric potential to describe the water content in a partially saturated fracture. The water phase in unsaturated porous media is reserved by both adsorption and capillarity (Buckingham, 1907), and the matric potential (φm) encompasses the adsorptive and capillary effects on the water phase (Sposito, 1981; Tokunaga and Wan, 1997; Or and Tuller, 2000). In constant humidity environment, the water potential in a fracture is equal to the matric potential when the water in the fracture and matrix pores is in equilibrium. At this point, the water content in the fracture can be described by the matric potential. Determining the water content and water distribution in a fracture at various matric potentials is key to the subsequent analysis of the gas breakthrough mechanism. The water saturations of fractured samples under various matric potentials are provided in Fig. 5. As shown in Fig. 5, increasing the matric potential causes more pores to be filled with water, thereby resulting in a gradual increase in the water saturation of core. At the beginning of the saturation process, water preferentially enters the small pores and dead-end pores through the large and interconnected pores and fractures. As the matric potential increases, water then begins to accumulate in the large and interconnected pores and fractures. Until the matric potential increases to zero, the fractured samples are completely water saturated. The water retained in the fractured sample is composed of the water in the matrix pores and in the fracture, and the water in the matrix pore spaces is in equilibrium with the water on the fracture surface. The increasing matric potential results in an increase in the water saturation in the fracture. The water content in the fracture is determined by the amount of water in the matrix through the matric potential. In the process of saturation, water gradually enters the fracture under the actions of adsorption and capillary forces. The total amount of water in the fracture is composed of the water film adsorbed on the solid surface and the capillary water held in the depressions on the fracture surface, and both are termed films in a macroscopic sense (Tokunaga and Wan, 1997). At a low matric potential, the water content in the fracture is low. At this point, the capillary-filled water is discontinuous, and the adsorptive film contribution to the water

(4)

where P1, P2 and P0 are the inlet pressure, outlet pressure and standard atmospheric pressure, respectively; Q is the volumetric flow rate of gas under standard atmospheric pressure; μ is the gas dynamic viscosity under the experimental temperature and pressure conditions; Z is the compressibility factor at the experimental temperature and pressure conditions; Za is the compressibility factor at the experimental temperature and atmospheric pressure; A is the cross section and L is the length of the core. The fracture intrinsic permeability (kf) is a function of the hydraulic aperture (Brush and Thomson, 2003; Konzuk and Kueper, 2004):

kf =

e2h 12

(5)

where eh is the hydraulic aperture, which is defined as the aperture of a smooth fracture with the same dimensions generating the same volumetric flow as the rough fracture. Moreover, the cross section can be calculated by Eq. (6), where w is the width of the fracture along the cross section: (6)

A=e h w

Combined with Eqs. (5) and (6), Eq. (4) can be derived as follows: 2

kf =

1 ⎛ 12μQZ 2P0 L ⎞ 3 ⎜ ⎟ 12 ⎝ wZa P12 − P22 ⎠

(7)

Because only a small portion of the interconnected pores is involved in the gas migration process (Hildenbrand et al., 2004), the effective aperture at the time of gas breakthrough can be obtained from Eqs. (5) and (7). It is noted that to apply Eq. (7) to calculate the fracture gas permeability, it must be assumed that the contribution of the matrix to gas flow is negligible. Thus, prior to the experiment, to determine whether the flow through the shale matrix is negligible, gas percolation experiments were conducted on the samples before and after fracturing. We found that the flow rates of the shale samples after fracturing were more than three orders of magnitude greater than those of the cores before fracturing for the same inlet pressure. This indicated that matrix flow had little influence on the measurement of fracture permeability; all pressure and flow measurements were directly related to the fracture. All breakthrough tests were performed at a temperature of 25 °C. 4. Results and discussion Gas breakthrough from water-saturated rocks is a complex process involving the interaction between solid phase, liquid phase and gas phase. The water phase forms a water film on the solid particles under

Fig. 5. The water saturation of fractured shale cores as a function of the matric potential for samples. 6

Journal of Hydrology 578 (2019) 124044

P. Cheng and Q. Yu

At relatively lower matric potentials, the amount of water in the fracture is small, and the water film on the fracture surface slowly increases with matric potential. The film at this point is still very thin, which only has a slight effect on the gas pathway connectivity (Fig. 8a). At this stage, the CH4 breakthrough pressure is low and increases slowly with the matric potential (Fig. 7). The effect of the water film on the breakthrough pressure is not notable. As shown in Fig. 8b, as the matric potential continues to increase, the water film increases to a certain thickness where the two films form a water bridge, and certain small apertures are blocked by water (Tuller et al., 1999). This situation results in a remarkable reduction in the effective aperture and gas pathway connectivity. As a result, it is more difficult for gas to break through the fracture to form a continuous channel. At this point, according to the Laplace equation, the breakthrough pressure increases notably with increasing matric potential (Fig. 7), and the water film begins to act to prevent gas from escaping from the fracture. A further increase in the matric potential results in an increasing number of apertures sealed by water. The breakthrough pressure continues to increase rapidly. Until the matric potential increases close to 0, the fracture and matrix are fully saturated, as shown in Fig. 8c. The fracture is completely blocked by water, and the breakthrough pressure reaches a maximum. To quantitatively describe the relationship between the breakthrough pressure of partially saturated fracture and the matric potential in the above experimental results, the exponential model was fitted to the results for samples. The high correlation coefficient (R2) in Fig. 7 demonstrates that the exponential model can accurately represent the relationship between the breakthrough pressure of a fracture and the matric potential of each sample, which can be uniformly described as follows:

retained on the fracture surface is dominant (Or and Tuller, 2000). The water films adsorbed on the walls of the fracture are thin and cannot be freely removed. As the matric potential increases, the adsorptive film and capillary water film gradually become thicker. The relatively thick films on the rough surfaces are generally conceptualized as networks of surface capillary channels attached to thin adsorbed films (Tokunaga and Wan, 1997; Tuller and Or, 2002). As the amount of water in the fracture increases, the small apertures are gradually sealed up by the water film, and the capillary contribution to the water film thickness gradually becomes dominant. Subsequently, the increasing matric potential causes the interconnected large apertures in the fracture to be gradually sealed by water film. When the matric potential increases towards approximately zero, the fracture is completely saturated by a water film. 4.2. The relationship between the breakthrough pressure of a fracture and the matric potential Samples 1 and 3 successfully survived all of the breakthrough pressure tests, while sample 2 was crushed during the breakthrough experiments. The breakthrough pressure measurement results for two samples under various matric potentials were shown in Table 4 and the breakthrough pressure measurement processes were provided in Fig. 6. After gas breakthrough, when gas continuously flows through the core, the effective CH4 permeability was also measured. The results of the effective CH4 permeability (keff) and the effective aperture (eeff) were also provided in Table 4. As shown in Table 4, with the matric potential increasing, the capillary breakthrough pressure of the fracture increases significantly and the breakthrough time becomes increasingly longer (Fig. 6), and the effective gas permeability and corresponding effective aperture gradually decrease. Through analysis of the experimental results, we found that the relationship between the breakthrough pressure and effective aperture under various matric potentials can be described by the Young-Laplace equation (Eq. (1)). The breakthrough pressure at a matric potential higher than −51.38 MPa was larger than that of the dry core. This result can be attributed to the presence of water in the fracture. Fig. 7 shows that increasing the matric potential results in an increase in the breakthrough pressure of the fracture, and the breakthrough pressure increases slowly in the early stage and remarkably increases in the later stage. This phenomenon may be caused by the reduction in the effective aperture resulting from the increase in the water film thickness in the fracture with increasing matric potential. It is noted that water and air coexist within a partially saturated fracture, and the amount of water as well as the distribution of water in the unsaturated fracture depend on the matric potential. Therefore, based on the experimental results and water distribution characteristics of the fracture, we establish the conceptual model of breakthrough pressure formation in unsaturated shale fractures shown in Fig. 8. The model qualitatively describes the relationship among the matric potential, the water distribution characteristics of the fracture, and the breakthrough pressure. As depicted in Fig. 8, with increasing matric potential, the water distribution in the rough fracture can be divided into three stages.

Pbt = a × e bφm + P0

(8)

where a, b and P0 are fitting parameters, which vary with the aperture size and roughness of the fracture. The sum of a and P0 is equal to the breakthrough pressure of fracture when the matric potential is 0; the value of P0 is the breakthrough pressure of the fracture without water. It can be seen from the exponential equation that the function of the growth rate dPbt /dφm is monotonically increasing, and the growth rate reaches a maximum when the matric potential is equal to zero. From Fig. 7, we found that the increase in breakthrough pressure with the matric potential proceeds from slow to fast process, during which there is a turning point that begins to notably increase. Hence, we define a critical value of the matric potential (φc), of which its corresponding growth rate is equal to one-tenth of the maximum growth rate, and this growth rate is regarded as a criterion for determining the rapid growth. When the matric potential is lower than φc, the growth rate of the breakthrough pressure is low. When the matric potential is higher than φc, the growth rate of the breakthrough pressure begins to rapidly increase. This critical value indicates that when the matric potential is equal to φc, the small apertures in the gas pathways are blocked by water films, and the water films begin to act to prevent gas from escaping from the fracture. The critical value of two samples is −4.3 MPa,

Table 4 Experimental results of the breakthrough pressure, effective permeability and effective aperture under different matric potentials for samples (φm is the matric potential; Pbt is the breakthrough pressure; keff is the effective permeability; eeff is the effective aperture). Sample

φm (MPa)

∞

−51.38

−39.08

−23.45

−8.55

−2.33

0

S1

Pbt (MPa) keff (m2) eeff (μm)

0.001 1.52 × 10−11 13.484

0.0058 5.80 × 10−12 8.340

0.0068 3.52 × 10−12 6.499

0.0088 8.09 × 10−13 3.115

0.0098 7.45 × 10−13 2.990

0.0248 3.95 × 10−13 2.177

0.1048 2.50 × 10−13 1.733

S3

Pbt (MPa) keff (m2) eeff (μm)

0.0036 2.03 × 10−12 4.932

0.0282 8.92 × 10−13 3.271

0.0461 2.06 × 10−13 1.573

0.0516 9.15 × 10−14 1.048

0.1115 2.49 × 10−14 0.546

0.4638 1.05 × 10−14 0.3556

2.035 7.16 × 10−16 0.0927

Note: ∞ represents the matric potential of the fracture without water. 7

Journal of Hydrology 578 (2019) 124044

P. Cheng and Q. Yu

Fig. 6. Breakthrough pressure testing process under different matric potentials for samples (only two curves are shown in the diagram for simplicity).

fracture. As shown in Fig. 9, the effective CH4 permeability of the fracture decreases significantly with increasing matric potential. This is because as the matric potential increases, the water film thickness in the fracture gradually increases, and the volume of the water-sealed apertures increases, thereby leading to a reduction in the connectivity of the gas channels. This in turn causes a decrease in the effective CH4 permeability. From Fig. 9 an exponential relationship between the effective CH4 permeability of the fracture and the matric potential can be found, which can be defined as follows:

keff = m × e nφm

(9)

where m and n are fitting parameters, which are constant for a given fracture. The inlet gas pressure curves with time for samples in Fig. 10 are used to analyze the gas breakthrough process. After gas begins to break through, the curve can be divided into three stages according to the rate of decrease of the gas pressure. During the first stage, the gas pressure drops rapidly as an approximately straight line. In the second stage, the gas pressure decreases slowly. During the third stage, the gas pressure drops to a stable value. These three stages are consistent with the breakthrough process of gas breaking through a saturated shale matrix in the study by Hildenbrand et al. (2002). In stage one, because of the heterogeneous aperture size and structure, the gas breakthrough process starts with the large apertures and channels with a suitable connectivity. The displacement rate is high, and the gas pressure thus drops rapidly. In the second stage, as the gas pressure declines, spontaneous imbibition of some water occurs. The water displaced in this stage is mainly residual water and re-adsorbed water, and it is not easy to form more channels in this stage. The gas pressure thus decreases slowly or remains constant. In the third stage, as gas breakthrough progresses, an increasing amount of water in the fracture is displaced. More channels for gas to pass through are formed. However, there are still some apertures that are blocked by the residual water. The displacement rate gradually decreases to 0. The gas pressure thus decreases until a stable value. Fig. 7. The breakthrough pressure of the fracture under different matric potentials for samples.

4.3. Water film thickness affecting gas breakthrough under various matric potentials

−5.2 MPa, respectively. We find that the critical value is consistent with the corresponding matric potential when the curve in Fig. 7 begins to increase notably. After preliminary analysis, the critical value is related to the aperture size and roughness of the fracture. After gas breakthrough, the effective aperture at the time of gas breakthrough can be obtained from effective CH4 permeability. By comparing the experimental results, we found that effective permeability was one to three orders of magnitude lower than the gas permeability of the dry fracture. This finding shows that the presence of water in the fracture greatly affects the ability of gas to pass through the

The water film in a fracture causes a reduction in the effective aperture, thereby resulting in an increase in the breakthrough pressure. We attempt to mathematically analyze the water film thickness that influences the gas breakthrough from a rough fracture under various matric potentials. We assume that a simple geometrical model of the fracture surface is composed of a number of individual rough elements, as shown in Fig. 11. where α is the angle, which is the roughness parameter of a single roughness element, and ranges from a value of π/ 2 for a smooth plane surface to the limiting value 0 for an extremely rough surface. 8

Journal of Hydrology 578 (2019) 124044

P. Cheng and Q. Yu

Fig. 8. Conceptual model diagram of breakthrough pressure formation in an unsaturated fracture adapted from Tokunaga and Wan (2001): (a) at lower matric potential, water film on the fracture surface is very thin. (b) as the matric potential increases, the water film become thicker and small apertures ware blocked. (c) the fracture is fully saturated.

Fig. 9. The relationship between the effective permeability of the fracture and the matric potential for samples.

We first analyze the water film adsorbed on the flat surface using the Derjaguin-Landau-Verwey-Overbeek theory. The disjoining pressure, which is the sum of the van der Waals forces, the electrostatic forces and structural forces, determines the stability and thickness of the water film adsorbed on the solid surface (Derjaguin et al., 1987). Thus, equating the disjoining pressure to the negative matric potential, the adsorbed film thickness (h) can be calculated as follows (Li et al., 2016):

−Aslg h3

+

h εr ε0 1 (ξ − ξ2 )2 2 + fe− λ = −φm 8π 1 h

thickness (heff) in the fracture can be calculated as follows:

1 h heff = ⎛ − 1⎞ r + sinα ⎝ sinα ⎠

From Fig. 12, we found that as the matric potential increases, the water film thickness increases slowly in the early stages and increases remarkably in the later stage. This phenomenon is consistent with the growth trend of the breakthrough pressure with the matric potential. When gas invades a partially saturated fracture, the gas-liquid meniscus is in contact with the water films on the fracture surfaces. The effective aperture at the time of gas breakthrough is approximately equal to the initial aperture without water minus the thickness of the water film. However, we found that even under very rough conditions (α = 10°), the difference between the initial aperture without water and the effective aperture in Table 4 is much larger than the total film thickness (2heff). This inconsistency may be caused by the assumption that the total flow of gas in the fracture is entirely due to the Darcy flow. This assumption overestimates the permeability of the fracture and therefore the fracture aperture. Darabi et al. (2012) also found that the apparent gas permeabilities in nanometer- to micrometer-size pores of shale are as much as 10 times greater than the gas permeability values obtained by Darcy flow predictions. In fact, the flow mechanism of gas in the nanometer-size to micrometer-size pores of shale is very complicated, which consists of Darcy flow, slip flow, and Knudsen diffusion flux (Javadpour, 2009; Gao et al., 2017). The total gas mass flux is the linear superposition of Darcy flow, slip flow, and Knudsen diffusion flux, which can be expressed as follows:

(10)

where Aslg is the Hamaker constant for the interactions between the solid substrate, water film and air; ε0 is the vacuum permittivity; εr is the relative permittivity of water; ξ1 is the potential between the solid and water phase; ξ2 is the potential between the water phase and air phase; f is the structural strength coefficient; and λ is the characteristic length of the water molecule. In this study, using Aslg = 1 × 10−20 J; εr = 8.85 × 10−12F/m; ε0 = 81.5; ξ1-ξ2 = 50 mv; f = 1 × 10−7 N/m2; λ = 1.5 nm (Li et al., 2016). Subsequently, we analyze the capillary water retained in the groove (Fig. 11). According to the augmented Young-Laplace equation, the radius of the water-air meniscus curvature (r) for the unsaturated situation, which is dependent on the matric potential, can be calculated as follows:

r=−

σ φm

(12)

(11)

where α is the surface tension at the interface between the water phase and air phase (σ = 72.7 mN m−1); Therefore, the effective film 9

Journal of Hydrology 578 (2019) 124044

P. Cheng and Q. Yu

Fig. 10. Inlet gas pressure variation process with time for samples (only one curve is shown in the diagram for simplicity).

Jtot = JDarcy + Jslip + Jkn

pressure; bk is the gas slippage factor; ϕ is the porosity and τ is the tortuosity; and kB is the Knudsen diffusion coefficient. Under partially water-saturated conditions, these parameters change with the water content in the pores of shale, and the gas flow becomes more complicated (Gao and Yu, 2018). This finding may indicate that after gas breakthrough the partially saturated fracture, the gas flow in fractures needs to consider the slip flow and diffusion.

(13)

The apparent gas permeability of shale can be expressed as follows:

kapp = k +

2∅kB Tμ kbk + P 3τπδ 2P 2

zRT πM

(14)

where k is the intrinsic permeability of the shale medium; P is the pore

Fig. 11. Schematic sketch of partially saturated fractured shale and definition sketch for a single roughness element representing an unsaturated rough fracture. 10

Journal of Hydrology 578 (2019) 124044

P. Cheng and Q. Yu

Fig. 12. Model calculations of the effective film thicknesses of a single element at various matric potentials under different rough conditions.

5. Conclusions

partially saturated conditions remain to be further studied.

Quantitative descriptions of the relationship between the breakthrough pressure and water content are extremely important for the study of many resource- and environment-related topics. The water content in a rock is usually quantified by the water saturation. The quantitative description of the relationship is difficult for fractures. The reason is that there is no way to describe the water saturation in a fracture because of the difficulty in the measurement of the water volume in the fracture. We propose a method to describe the relationship between the breakthrough pressure and the water content in a fracture. In this method, the relationship between the matric potential and water content of a core is determined experimentally. Under constant humidity conditions, the water potential in a fracture is equal to the matric potential when the water in the fracture and matrix pores reaches equilibrium. The water content in the fracture can be described by the matric potential. By studying the relationship between the breakthrough pressure of the fracture and the matric potential, the relationship between the breakthrough pressure and water content in the fracture is quantitatively described. Based on the experimental results, we apply a conceptual model to qualitatively describe the relationship among the matric potential, the water distribution in the fracture, and the breakthrough pressure of the fracture. At a low matric potential, water forms very thin water films on the walls of the fracture, and the effect of water on the breakthrough pressure is not distinct. As the matric potential increases, the increasing thickness of the water film results in a decrease in the effective aperture, thereby causing an increase in the breakthrough pressure. The breakthrough pressure of the fracture increases monotonically as an exponential relationship. The increase in breakthrough pressure with the matric potential is a process from slow to fast. We define a critical value of the matric potential, and the growth rate of the critical value serves as a criterion for determining the rapid growth. When the matric potential is higher than the critical value, the breakthrough pressure of the fracture begins to increase rapidly. The critical value is related to the fracture aperture size and roughness of the fracture. The thicknesses of water films under various matric potentials were calculated. Our experimental data show that the difference between the initial aperture without water and the effective aperture at the time of breakthrough calculated by Darcy's law is much larger than the calculated water film thickness. This finding may indicate that gas seepage in partially saturated fractures is complex and slip flow and diffusion need to be considered. The gas seepage mechanisms in shale fractures under

Acknowledgments This work was supported by the National Natural Sciences Foundation of China (Grant Nos. 41877196, U1612441 and 41272387) and the Fundamental Research Funds for the Central Universities of China (Grant No. 53200759754). The authors are very grateful for the help of the Rock Fracture WorkGroup. References Allen, D.T., Pacsi, A.P., Sullivan, D.W., Zavalaaraiza, D., Harrison, M., Keen, K., et al., 2015. Methane emissions from process equipment at natural gas production sites in the united states: pneumatic controllers. Environ. Sci. Technol. 49 (6), 633–640. https://doi.org/10.1021/es5040156. American Society for Testing and Materials, 1999. Standard test method for laboratory determination of pulse velocities and ultrasonic elastic constants of rock. Designation D 2845–95, 6. Amann-Hildenbrand, Alexandra, Bertier, Pieter, Busch, Andreas, Krooss, Bernhard M., 2013. Experimental investigation of the sealing capacity of generic clay-rich caprocks. Int. J. Greenhouse Gas Control 19, 620–641. https://doi.org/10.1016/j.ijggc. 2013.01.040. Bertels, S.P., Dicarlo, D.A., Blunt, M.J., 2001. Measurement of aperture distribution, capillary pressure, relative permeability, and in situ saturation in a rock fracture using computed tomography scanning. Water Resour. Res. 37 (3), 649–662. https://doi. org/10.1029/2000WR900316. Birdsell, D.T., Rajaram, H., Lackey, G., 2015. Imbibition of hydraulic fracturing fluids into partially saturated shale. Water Resour. Res. 51 (8), 6787–6796. https://doi.org/10. 1002/2015WR017621. Bolton, A.J., Maltman, A.J., Fisher, Q., 2000. Anisotropic permeability and bimodal poresize distributions of fine-grained marine sediments. Mar. Pet. Geol. 17 (6), 657–672. https://doi.org/10.1016/S0264-8172(00)00019-2. Boulin, P.F., Bretonnier, P., Vassil, V., Samouillet, A., Fleury, M., Lombard, J.M., 2013. Sealing efficiency of caprocks: experimental investigation of entry pressure measurement methods. Mar. Pet. Geol. 48 (48), 20–30. https://doi.org/10.1016/j. marpetgeo.2013.07.010. Brush, D.J., Thomson, N.R., 2003. Fluid flow in synthetic rough-walled fractures: NavierStokes, Stokes, and local cubic law simulations. Water Resour. Res. 39 (4), 1085–1100. https://doi.org/10.1029/2002wr001346. Buckingham, E., 1907. Studies on the Movement of Soil Moisture. Gov. Print. Off., Washington, D.C. China National Petroleum Company SY/T 5748-2013, 2006. Determination Method of Gas Breakthrough Pressure in Rock. Petroleum Industry Press, Beijing. Chandler, M.R., Meredith, P.G., Brantut, N., Crawford, B.R., 2016. Fracture toughness anisotropy in shale. J. Geophys. Res.-Solid Earth 121 (3), 1706–1729. Chapiro, Grigori, Bruining, Johannes, 2015. Combustion enhance recovery of shale gas. J. Petrol. Sci. Eng. 127, 179–189. https://doi.org/10.1016/j.petrol.2015.01.036. Darabi, H., Ettehad, A., Javadpour, F., Sepehrnoori, K., 2012. Gas flow in ultra-tight shale strata. J. Fluid. Mech. 710, 641–658. https://doi.org/10.1017/jfm.2012.424. Delage, P., Howat, M.D., Cui, Y.J., 1998. The relationship between suction and swelling properties in a heavily compacted unsaturated clay. Eng. Geol. 50 (1–2), 31–48. https://doi.org/10.1016/S0013-7952(97)00083-5. Derjaguin, B.V., Churaev, N.V., Muller, V.M., 1987. Wetting films. Surface Forces

11

Journal of Hydrology 578 (2019) 124044

P. Cheng and Q. Yu

conductivity of rough surfaces. Water Resour. Res. 36 (5), 1165–1177. https://doi. org/10.1029/2000WR900020. Osborn, S.G., Vengosh, A., Warner, N.R., Jackson, R.B., 2011. Methane contamination of drinking water accompanying gas-well drilling and hydraulic fracturing. Proc. Natl. Acad. Sci. U.S.A. 108 (20), 8172–8176. https://doi.org/10.1073/pnas.1100682108. Ougier-Simonin, A., Renard, F., Boehm, C., Vidal-Gilbert, S., 2016. Micro-fracturing and micro-porosity in shales. Earth-Sci. Rev. 162, 198–226. https://doi.org/10.1016/j. earscirev.2016.09.006. Persoff, Pruess, 1995. Two-phase flow visualization and relative permeability measurement in natural rough-walled rock fractures. Water Resour. Res. 31 (5), 1175–1186. https://doi.org/10.1029/95WR00171. Rezaeyan, A., Tabatabaei-Nejad, S.A., Khodapanah, E., Kamari, M., 2015. Parametric analysis of caprock integrity in relation with CO2 geosequestration: capillary breakthrough pressure of caprock and gas effective permeability. Greenh. Gases 5 (6), 714–731. https://doi.org/10.1002/ghg.1516. Romero-Sarmiento, M.F., Ducros, M., Carpentier, B., Lorant, F., Cacas, M.C., PegazFiornet, S., et al., 2013. Quantitative evaluation of toc, organic porosity and gas retention distribution in a gas shale play using petroleum system modeling: application to the Mississippian Barnett shale. Mar. Petro. Geol. 45 (4), 315–330. https://doi.org/ 10.1016/j.marpetgeo.2013.04.003. Silva, M.R.D., Schroeder, C., Verbrugge, J.C., 2008. Unsaturated rock mechanics applied to a low-porosity shale. Eng. Geol. 97 (1–2), 42–52. https://doi.org/10.1016/j. enggeo.2007.12.003. Sposito, G., 1981. The Thermodynamics of Soil Solutions. Clarendon, Oxford, U. K., pp. 223. Tokunaga, T.K., Wan, J., 1997. Water film flow along fracture surfaces of porous rock. Water Resour. Res. 33, 1287–1295. https://doi.org/10.1029/97WR00473. Tokunaga, T.K., Wan, J., 2001. Approximate boundaries between different flow regimes in fractured rocks. Water Resour. Res. 37, 2103–2111. https://doi.org/10.1029/ 2001WR000245. Tokunaga, T.K., Olson, K.R., Wan, J., 2003. Moisture characteristics of Hanford gravels: bulk, grain-surface, and intragranular components. Vadose Zone J. 2 (3), 322–329. https://doi.org/10.2113/2.3.322. Tsang, C.F., Barnichon, J.D., Birkholzer, J., 2012. Coupled thermo-hydro-mechanical process in the near field of a high-level radioactive waste repository in clay formations. Int. J. Rock Mech. Min. 49 (1), 31–44. https://doi.org/10.1016/j.ijrmms.2011. 09.015. Tuller, M., Or, D., Dudley, L.M., 1999. Adsorption and capillary condensation in porous media: liquid retention and interfacial configurations in angular pores. Water Resour. Res. 35 (7), 1949–1964. https://doi.org/10.1029/1999wr900098. Tuller, M., Or, D., 2002. Unsaturated hydraulic conductivity of structured porous media: a review of liquid configuration-based models. Vadose Zone J. 1, 14–37. https://doi. org/10.2113/1.1.14. Vidic, R.D., Brantley, S.L., Vandenbossche, J.M., Yoxtheimer, D., Abad, J.D., 2013. Impact of shale gas development on regional water quality. Science 340 (6134), 1235009. https://doi.org/10.1126/science.1235009. Wang, J., Liu, H., Yu, W., Cao, F., Sepehrnoori, K., 2016. Necessity of porosity correction before simulation and re-understanding of the effects of gas adsorption on production in shale gas reservoirs. J. Pet. Sci. Eng. 139, 162–170. https://doi.org/10.1016/j. petrol.2015.12.022. Zeng, W., Zhang, J., Ding, W., Song, Z., Zhang, Y., Liu, Z., et al., 2013. Fracture development in Paleozoic shale of Chongqing area (South China). part one: fracture characteristics and comparative analysis of main controlling factors. J. Asian Earth Sci. 75 (8), 251–266. https://doi.org/10.1016/j.jseaes.2013.07.014. Zhang, X.L., Xiao, L.Z., Guo, L., Xie, Q.M., 2015. Investigation of shale gas microflow with the lattice Boltzmann method. Petrol. Sci. 12 (1), 96–103. https://doi.org/10.1007/ s12182-014-0004-7. Zhang, C., Yu, Q., 2016. The effect of water saturation on methane breakthrough pressure: an experimental study on the Carboniferous shales from the eastern Qaidam Basin. China. J. Hydrol. 543, 832–848. https://doi.org/10.1016/j.jhydrol.2016.11. 003. Zhang, C., Yu, Q., 2019. Breakthrough pressure and permeability in partially water-saturated shales using methane-carbon dioxide gas mixtures: an experimental study of Carboniferous shales from the eastern Qaidam Basin, China. AAPG Bull. 103 (2), 273–301. https://doi.org/10.1306/07111818018. Zhao, Y., Yu, Q., 2017. CO2 breakthrough pressure and permeability for unsaturated low permeability sandstone of the Ordos Basin. J. Hydrol. 550, 331–342. https://doi.org/ 10.1016/j.jhydrol.2017.04.050.

327–367. https://doi.org/10.1007/978-1-4757-6639-4_10. Fang, Y., Elsworth, D., Wang, C., Ishibashi, T., Fitts, J.P., 2017. Frictional stability-permeability relationships for fractures in shales. J. Geophys. Res.-Solid Earth 122 (3), 1760–1776. https://doi.org/10.1002/2016JB013435. Ferrari, A., Favero, V., Marschall, P., Laloui, L., 2014. Experimental analysis of the retention behavior of shales. Int. J. Rock Mech. Min. 72 (1987), 61–70. https://doi.org/ 10.1016/j.ijrmms.2014.08.011. Gao, S., Wei, N., Li, X., Wang, Y., Wang, Q., 2014. Cap rock CO2 breakthrough pressure measurement apparatus and application in Shenhua CCS project. Eng. Proced. 63, 4766–4772. https://doi.org/10.1016/j.egypro.2014.11.507. Gao, J., Yu, Q., Lu, X., 2017. Apparent permeability and gas flow behavior in carboniferous shale from the Qaidam basin, China: an experimental study. Transp. Porous Media 116 (2), 585–611. https://doi.org/10.1007/s11242-016-0791-y. Gao, J., Yu, Q., 2018. Effect of water saturation on pressure-dependent permeability of carboniferous shale of the Qaidam basin, China. Transp. Porous Media 123 (1), 147–172. https://doi.org/10.1007/s11242-018-1029-y. Graham, J., Halayko, K.G., Hume, H., Kirkham, T., Gray, M., Oscarson, D., 2002. A capillarity-advective model for gas break-through in clays. Eng. Geol. 64, 273–286. https://doi.org/10.1016/S0013-7952(01)00106-5. Greenspan, L., 1977. Humidity fixed-points of binary saturated aqueous solutions. J. Res. Natl. Bureau Standards—A: Phys. Chem. 81 (1), 89–96. Hildenbrand, A., Schlomer, S., Krooss, B.M., 2002. Gas breakthrough experiments on finegrained sedimentary rocks. Geofluids 2 (1), 3–23. https://doi.org/10.1046/j.14688123.2002.00031.x. Hildenbrand, A., Schlomer, S., Krooss, B.M., Littke, R., 2004. Gas breakthrough experiments on pelitic rocks: comparative study with N2, CO2 and CH4. Geofluids 4 (1), 61–80. https://doi.org/10.1111/j.1468-8123.2004.00073.x. Horsrud, P., SØnstebØ, E.F., BØe, R., 1998. Mechanical and petrophysical properties of north sea shales. Int. J. Rock Mech. Min. 35 (8), 1009–1020. https://doi.org/10. 1016/S0148-9062(98)00162-4. Howarth, R.W., Ingraffea, A., Engelder, T., 2011. Should fracking stop? Nature 477 (7364), 271–275. https://doi.org/10.1007/s10584-011-0061-5. Jarvie, D.M., Hill, R.J., Ruble, T.E., 2007. Unconventional shale-gas systems: the Mississippian Barnett shale of north-central Texas as one model for thermogenic shale-gas assessment. AAPG Bull. 91 (4), 475–499. https://doi.org/10.1306/ 12190606068. Javadpour, F., 2009. Nanopores and apparent permeability of gas flow in mudrocks (shales and siltstone). J. Can. Pet. Technol. 48 (8), 16–21. Karpyn, Z.T., Alajmi, A., Radaelli, F., Halleck, P.M., Grader, A.S., 2009. X-ray CT and hydraulic evidence for a relationship between fracture conductivity and adjacent matrix porosity. Eng. Geol. 103 (3–4), 139–145. https://doi.org/10.1016/j.enggeo. 2008.06.017. Kim, S., Santamarina, J.C., 2013. CO2 breakthrough and leak-sealing – experiments on shale and cement. Int. J. Greenh. Gas Control 19 (11), 471–477. https://doi.org/10. 1016/j.ijggc.2013.10.011. Konzuk, J.S., Kueper, B.H., 2004. Evaluation of cubic law based models describing singlephase flow through a rough-walled fracture. Water Resour. Res. 40 (2), W02402. https://doi.org/10.1029/2003WR002356. JingLi, Xiangfang Li, Wang, Xiangzeng, Li, Yingying, Keliu, Wu, et al., 2016. Water distribution characteristic and effect on methane adsorption capacity in shale clay. Int. J. Coal Geol. 159, 135–154. https://doi.org/10.1016/j.coal.2016.03.012. Li, S., Dong, M., Li, Z., Huang, S., Qing, H., Nickel, E., 2005. Gas breakthrough pressure for hydrocarbon reservoir seal rocks: implications for the security of long-term CO2 storage in the Weyburn field. Geofluids 5 (4), 326–334. https://doi.org/10.1111/j. 1468-8123.2005.00125.x. Li, Y., Li, X., Wang, Y., Yu, Q., 2015. Effects of composition and pore structure on the reservoir gas capacity of Carboniferous shale from Qaidam Basin. China. Mar. Pet. Geol. 62, 44–57. https://doi.org/10.1016/j.marpetgeo.2015.01.011. Molofsky, L.J., Connor, J.A., Wylie, A.S., Wagner, T., Farhat, S.K., 2013. Evaluation of methane sources in groundwater in northeastern pennsylvania. Ground Water 51 (3), 333–349. https://doi.org/10.1111/gwat.12056. Montgomery, L.J., Jarvie, D.M., Bowker, K.A., et al., 2006. Mississippan Barnett shale, Fort Worth basin, north-central Texas: gas-shale play with multi-trillion cubic foot potential. AAPG Bull. 90 (6), 963–966. Nojabaei, B., Siripatrachai, N., Johns, R.T., Ertekin, T., 2016. Effect of large gas-oil capillary pressure on production: a compositionally-extended black oil formulation. J. Pet. Sci. Eng. 147, 317–329. https://doi.org/10.1016/j.petrol.2016.05.048. Or, D., Tuller, M., 2000. Flow in unsaturated fractured porous media: hydraulic

12