Laboratory characterisation of fracture compressibility for coal and shale gas reservoir rocks: A review

International Journal of Coal Geology 204 (2019) 1–17

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International Journal of Coal Geology journal homepage: www.elsevier.com/locate/coal

Laboratory characterisation of fracture compressibility for coal and shale gas reservoir rocks: A review

T

⁎

Yuling Tana,b,c, Zhejun Panc, , Xia-Ting Fengd, Dongxiao Zhange, Luke D. Connellc, Shaojun Lia a

State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, China University of Chinese Academy of Sciences, Beijing 100049, China c CSIRO Energy, Private Bag 10, Clayton South, VIC 3169, Australia d Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang 110004, China e BIC-ESAT, ERE, and SKLTCS, College of Engineering, Peking University, Beijing 100871, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Coalbed methane Coal seam gas Gas shale Cleat Pore compressibility

Unconventional natural gas, including coalbed methane and shale gas, has become important natural gas resources. Coal and shale reservoirs are characterised by low porosity and low permeability and difficult for gas production. These reservoirs are also considered as fractured reservoirs, i.e. the natural fracture/cleat system in coals and bedding direction microfractures in shales. Permeabilities of these reservoirs are sensitive to stress change. During gas production, the pressure drawdown significantly increases effective stress, and thus decreases the absolute permeability. The relationship between permeability and stress is characterised by fracture compressibility, which is difficult and costly to be obtained from the field, but can be acquired easily from laboratory measurement. In this review article, the laboratory methods to obtain fracture compressibility were reviewed. Literature data on fracture compressibility for coals and shales were collated and the relationships between fracture compressibility and pressure, stress and rock properties were discussed. It is found that fracture compressibility is higher for coals than for shales, and the fracture compressibility for proppant supported fracture is even lower than that for the same shale or coal. Moreover, fracture compressibility is variable depending on gas type, gas pressure, and stress. Fracture compressibility has no correlation with absolute permeability in general, but has a weak positive correlation for the same sample.

1. Introduction

In Australia, CBM production reached about 27 bcm in 2016, which was about one fourth of the natural gas production, and has been served as a major gas source for liquefied natural gas (LNG) export (DNRM, 2017). Permeability is a key reservoir parameter for gas production from unconventional gas reservoirs (e.g., Cai et al., 2012; Laubach et al., 1998; Mckee et al., 1988; Palmer, 2009). The permeability of coal reservoirs is typically low in the millidarcy range (e.g., Moore, 2012; Roadifer et al., 2003) and the permeability of shale is even lower, typically in the nanodarcy to microdarcy range (e.g., Ghanizadeh et al., 2014; Tan et al., 2017). Shales and coals are typically considered as naturally fractured reservoir rocks with their fractures providing the main pathways for gas and fluid flow (Li et al., 2016). Coal reservoirs have two sets of vertical fractures, the face and butt cleats, which are nearly perpendicular to each other and their extending directions are closely related to in-situ stress (Laubach et al., 1998). Gas shale is also a typical fractured reservoir rock, while different from coal seams, the fracture network in gas shale is irregular and poorly connected (Slatt

Unconventional natural gas resources, including shale gas and coalbed methane (CBM), are becoming increasingly important worldwide. In 2016, 56% and 9% of the unconventional gas production in the world were shale gas and CBM, respectively (Cedigaz, 2017). For shale gas, about 16.76 trillion cubic feet (Tcf) or about 475 billion cubic metres (bcm) was produced in the United States in 2017, which was about 60% of total U.S. dry natural gas production in 2017 (EIA, 2018). China has booked 764.3 bcm proved shale gas reserve in July 2017, and produced 7.9 bcm of shale gas in 2016, which was almost a 76% year on year increase (Chen, 2018). CBM is another important unconventional gas. In 2016, U.S. CBM production was equal to about 4% of total U.S. natural gas consumption (EIA, 2017). CBM production in China reached about 4.43 bcm in 2015 (Li et al., 2018) and China ranks the third country rich in CBM resource, with 36.81 trillion cubic meters (tcm) stored in coal seams shallower than 2000 m (Li and Yang, 2011).

⁎

Corresponding author. E-mail address: [email protected] (Z. Pan).

https://doi.org/10.1016/j.coal.2019.01.010 Received 9 October 2018; Received in revised form 26 January 2019; Accepted 27 January 2019 Available online 30 January 2019 0166-5162/ © 2019 Elsevier B.V. All rights reserved.

International Journal of Coal Geology 204 (2019) 1–17

Y. Tan et al.

hydrostatic stress conditions using water as the permeating fluid (Zheng et al., 1992). Mineral dissolution and secondary mineralisation could also have effects on Cf following acidification with hydrochloric and hydrofluoric acid (HCl-HF) (Balucan et al., 2015). Moreover, coal and shale reservoirs are heterogeneous resulted from a combination of many geological factors (Fu et al., 2016; Tan et al., 2018b). Thus, the permeability and fracture compressibility are directional. Recently, some work are devoted to the anisotropy of fracture compressibility of coal and shale including experimental (e.g., Tan et al., 2017; Tan et al., 2018a) and modelling work (e.g., Chen et al., 2012). The accuracy of fracture compressibility as a key input becomes important to precisely predict the permeability change and gas production behaviour. Fracture compressibility is also one of the key factors in designing the drilling and completion of gas wells, besides its significance in simulating the fluids flow in reservoir and forecasting the gas production (He et al., 2016; Yuan et al., 2018; Zimmerman et al., 1986). It has been a topic gaining more research interests in the recent years. However, there has been no review on the fracture compressibility for the fractured unconventional reservoir rocks, as well as for proppant supported fractures. Therefore, it is timely to review the fracture compressibility work in the literature, focusing on the laboratory studies as fracture compressibility is difficult to gain from the field. In this review article, the definition of fracture compressibility and the experimental methods to obtain the fracture compressibility are first reviewed, then the fracture compressibility data for coals and shales published recently are collected and analysed, discussions on the relationships between fracture compressibility and other reservoir properties are also performed.

and O'Brien, 2011). Therefore, due to the low permeability of coal and shale reservoirs, hydraulic fracturing is required to make gas production commercially viable (e.g., Estrada and Bhamidimarri, 2016). Moreover, permeability of these unconventional reservoir rocks is strongly sensitive to the change of effective stress, which could lead up to several orders of magnitude change in permeability (e.g., Bustin et al., 2008; Dong et al., 2010; Mckee et al., 1988; Ohmyoung et al., 2001; Ross and Bustin, 2008; Seidle et al., 1992; Yang et al., 2019). Therefore, the knowledge of stress-dependent permeability is of great significance for gas production behaviour from unconventional gas reservoirs, as pore pressure drawdown leads to significant effective stress increase, which results in the reduction of porosity and permeability of the reservoir. Many models have been developed to describe the relationships between permeability and effective stress. Among those models, an exponential relationship between permeability and effective stress has been widely applied (e.g., Chen et al., 2015; Seidle et al., 1992; Shi and Durucan, 2010):

k = k 0 e−3Cf (σ − σ0)

(1)

where, k (m ) is the permeability at effective stress σ (MPa), k0 (m2) is the permeability at initial effective stress σ0 (MPa), and Cf (MPa−1) is fracture compressibility. Fracture compressibility, analogue to pore volume compressibility of conventional single porosity reservoirs, is a parameter to describe how sensitive the fracture porosity change with respect to stress (Seidle et al., 1992): 2

Cf = −

1 ∂ϕf ϕf ∂σ

(2)

where ϕf (−) is the fracture porosity, σ (MPa) is stress. From the above equation, Cf can be estimated directly if the fracture porosity strain and its change with stress can be obtained. However, measuring the fracture volume change is difficult and time-consuming because of the extremely low fracture porosity for coal and shale samples, and the results of such measurements are often ambiguous (Liu and Harpalani, 2014; Seidle et al., 1992). Therefore, Cf is often estimated by using Eq. (1), i.e., through a series of permeability measurements with respect to stress in laboratory or fitting the field permeability data with reservoir pressure (Li et al., 2013). However, the issue of the constancy of fracture compressibility is controversial when using Eq. (1), especially over a wide range of stress change. Although laboratory data obtained using either water or gas over a small range of effectives stress change showed that fracture compressibility can be regarded as constant (e.g., Seidle et al., 1992; Zheng et al., 1992), other laboratory measurements showed that the cleat compressibility changes with stress (e.g., Chen et al., 2019; Dong et al., 2010; Zheng et al., 2012). Field evidence has also showed that the fracture compressibility is not constant with depletion in CBM wells (e.g., Palmer, 2009, 2010) and it is pressure-dependent (e.g., Mitra et al., 2012). Mckee et al. (1988) proposed an empirical equation to describe average pore compressibility change with respect to stress change:

Cp =

Cp0 α (σ − σ0 )

(1 − e−α (σ − σ0) )

2. Laboratory methods to obtain fracture compressibility Two types of laboratory methods are often used to obtain fracture compressibility, the direct method and the indirect method. Direct method measures compressibility through uniaxial or triaxial stress experiment. Indirect method estimates compressibility from correlations or other measurements, such as permeability or sonic velocity (He et al., 2016). Because direct measurement of rock compressibility requires high accuracy in strain measurement, indirect methods are more commonly used. As coal and shale can be considered as dual or even triple porosity reservoirs (Pan and Connell, 2015; Tan et al., 2018c), fracture is the main contributor for permeability and matrix pores typically contribute negligibly to reservoir permeability and they are regarded as a source of gas, which is often characterised by gas diffusion through the matrix pores to the fracture system (Pan et al., 2010b). Traditionally dualporosity reservoirs assume matrix blocks providing gas storage and fractures providing flow pathways (Shi and Durucan, 2003; Warren and Root, 1962). Therefore, the fracture compressibility is different from the pore compressibility for single porosity reservoirs, in which all pores more or less contribute to the permeability of the reservoir. Therefore, in this review article, it considers the fracture porosity only and the matrix pores are considered as part of the matrix. Thus, fracture porosity, ϕf (−), is defined as:

ϕf = Vp/ Vb

(3)

−1

where Cp (MPa ) is not constant but represents the average pore compressibility over the stress interval σ-σ0 (MPa), α (MPa−1) is decline rate of pore compressibility with effective stress increase, Cp0 (MPa−1) is initial pore compressibility at initial effective stress σ0 (MPa). Many factors affecting fracture compressibility, such as burial depth of reservoir, sample maturity and moisture, temperature, fluid types, stress state, pore pressure and the boundary conditions (e.g., Feng et al., 2016; Meng and Li, 2013; Zheng et al., 1992). For example, it was found that Cf decreases with the increase of the maximum vitrinite reflectance and with the decrease of moisture for coal (Meng and Li, 2013). Cf was found to vary with mean stress for fractured coal under

(4)

where Vp (m3) is fracture volume only and is not the total pore volume in coal or shale, Vb (m3) is the bulk volume of the rock. Note Vp is used instead of Vf to make the derivation of the compressbilities according to the poroelasticity notation convention.

2.1. Relationship between fracture compressibility and porous rock compressibilities Generally, in porous rocks, there are four different compressibilities (Zimmerman et al., 1986): 2

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Y. Tan et al.

Cbc = −

1 ⎛ ∂Vb ⎞ ⎜ ⎟ Vb ⎝ ∂pc ⎠ p

(5)

p

Cbp =

1 ⎛ ∂Vb ⎞ Vb ⎜ ∂pp ⎟ ⎝ ⎠ pc

Cpc = −

(6)

1 ⎛ ∂Vp ⎞ ⎜ ⎟ Vp ⎝ ∂pc ⎠ p

(7)

p

Cpp =

1 ⎛ ∂Vp ⎞ Vp ⎜ ∂pp ⎟ ⎝ ⎠ pc

(8)

3

3

where Vp (m ) and Vb (m ) represent the pore volume (fracture volume in this work) and the bulk volume in porous rocks, respectively; pp (MPa) and pc (MPa) represent pore pressure and confining pressure, respectively; Cbc (MPa−1) and Cbp (MPa−1) relate change in the bulk volume to change in the confining pressure and the pore pressure, respectively; and Cpc (MPa−1) and Cpp (MPa−1) relate change in the pore volume to change in the confining pressure and the pore pressure, respectively. Same to the rock compressibilities, two fracture compressibilities can be defined (e.g., Pan et al., 2010a):

Cfc = −

1 ⎛ ∂ϕf ⎞ ⎜ ⎟ ϕf ⎝ ∂pc ⎠ p

Fig. 1. The matchstick geometry (after Seidle et al., 1992).

deformation, nϕ, is 1 (Jaeger et al., 2006). 2.2. Fracture compressibility from permeability and stress relationship

(9)

p

1 ⎛ ∂ϕf ⎞ Cfp = ⎜ ϕf ∂pp ⎟ ⎝ ⎠ pc

Fractured reservoir permeability has been studied extensively and simplified geometrical matrix blocks, such as slides, matchsticks and cubes are often used to establish the relationship between permeability and porosity (van Golf-Racht, 1982). Since the coal cleat (fracture) system can be well idealised as a matchstick geometry as shown in Fig. 1, Seidle et al. (1992) applied this matchstick geometry to study the permeability-stress relationship. The permeability of the matchstick geometry is (Seidle et al., 1992):

(10) −1

−1

where Cfc (MPa ) and Cfp (MPa ) are the fracture compressibility with respect to change in the confining pressure and the pore pressure, respectively. Further derivation of these two porosity compressibilities can yield (Pan et al., 2010a):

( ) ⎞⎟ V

p ⎛ 1 ∂ Vb Cfc = −⎜ V ∂pc ⎜ p ⎝ Vb

( )

⎟ ⎠ pp

k=

1 ∂Vp ⎞ 1 ⎛ ∂Vb ⎞ = − ⎜⎛ + = Cpc − Cbc ⎟ ⎜ ⎟ Vp ⎝ ∂pc ⎠ p Vb ⎝ ∂pc ⎠ p p p

( ) ⎞⎟

where k (m ) is cleat permeability, a (m) is cleat spacing and ϕf (−) is cleat porosity. Seidle et al. (1992) conducted permeability experiments using water as fluid and derived the permeability-stress relationship under various pore pressures and constant confining pressure. Pan et al. (2010a) followed Seidle et al. (1992)’s work and re-derived the permeability-stress relationship for gas and compared the permeability-stress relationships under constant pore pressure varying confining pressures condition and under constant confining pressure varying pore pressures condition. In this review article, these derivations are revisited for using gas for both gas pressure change and confining pressure change. Following Seidle et al. (1992) and Pan et al. (2010a), taking the derivative of Eq. (17) with respect to confining pressure, pc, it yields:

V

( )

⎟ ⎠ pc

=

1 ⎛ ∂Vp ⎞ 1 ⎛ ∂Vb ⎞ − = Cpp − Cbp Vp ⎜ ∂pp ⎟ Vb ⎜ ∂pp ⎟ ⎝ ⎠ pc ⎝ ⎠ pc

(12)

From Zimmerman et al. (1986)’s work, the below relationships hold:

Cpp = Cpc − Cm and Cbp = Cbc − Cm where Cm (MPa

Cm =

−1

(13)

) is the compressibility of the matrix:

1 ∂Vm Vm ∂pp

2aϕf3 ∂a 3a2ϕf2 ∂ϕf ∂k = + ∂pc 48 ∂pc 48 ∂pc

(14)

where Vm (m3) is the matrix volume, it equals to Vb-Vp. For coal or shale, matrix swelling effect caused by gas adsorption (or matrix shrinkage caused by gas desorption) is also included in Cm. Therefore, from the above equations, it yields:

Cfc = Cfp

∂εϕf

∂pc

∂a ∂ε 1 aCbc =a =a = ∂pc ∂pc 3Kb 3

(15)

∂pc

dpc +

∂εϕf ∂pp

dpp = −

∂ϕf ϕf ∂pc

dpc −

∂ϕf ϕf ∂pp

(18)

Following Seidle et al. (1992)’s work, under constant pore pressure varying confining pressures condition, ∂a can be rewritten as:

Therefore, for the rest of the paper, Cf is used to represent Cfc or Cfp. Moreover, considering the deformation of the porosity strain:

dεϕf =

(17) 2

(11) p ⎛ 1 ∂ Vb Cfp = ⎜ V ∂pp ⎜ p ⎝ Vb

1 2 3 a ϕf 48

(19)

where ε (−) represents strain, Kb (MPa) represents bulk modulus, pc (MPa) is confining pressure. Therefore, Eq. (18) can be rewritten as:

∂k 2 = k ⎡ Cbc − 3Cfc⎤ ∂pc ⎣3 ⎦

dpp = Cfc dpc − Cfp dpp (16)

(20)

Again, under constant confining pressure varying pore pressures condition, taking a derivative of Eq. (17) with respect to pore pressure,

Since Cfc = Cfp, the effective stress coefficient for porosity 3

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Y. Tan et al.

permeability calculation and reservoir simulation (Mckee et al., 1988; Pekot and Reeves, 2003; Pomeroy and Robinson, 1967). However, experimental results have shown that the fracture compressibility varies with respect to stress. It may change significantly with stress for coal (e.g., Mitra et al., 2012; Palmer, 2009; Palmer and Mansoori, 1998; Rushing, 2008; Shi and Durucan, 2010; Zheng et al., 2012; Zhou et al., 2011) and for shales (e.g., Chen et al., 2019; Dong et al., 2010), especially when the stress change range is large. Mckee et al. (1988) were probably the first ones to develop a non-constant compressibility model and they assumed that fracture compressibility declines exponentially with stress:

pp, it yields:

2aϕf3

∂k ∂a = + ∂pp 48 ∂pp

3a2ϕf2

∂ϕf

48

∂pp

(21)

Similar to Eq. (20) but considering gas pressure induced swell of the matrix, Eq. (21) can be written as:

∂k 2 2 s s⎤ = k ⎡ Cbp + Cbp − 3Cfp − 3Cfp ∂pp 3 ⎣3 ⎦

(22)

−1

s

where Cbp (MPa ) is the bulk compressibility contributed from gas adsorption induced matrix swelling, and Cfps (MPa−1) is the fracture compressibility contributed from gas adsorption induced matrix swelling. Considering:

dk =

∂k ∂k dp + dp ∂pc c ∂pp p

Cf = Cf 0 e−α (σ − σ0)

and obtained the average fracture compressibility over the stress interval from σ0 (MPa) to σ (MPa):

Cf =

(23)

Combining Eqs. (20), (22) and (23), it yields:

dk 2 2 2 s s ⎤ = ⎡ Cbc − 3Cfc ⎤ dpc + ⎡ Cbp + Cbp − 3Cfp − 3Cfp dpp k 3 ⎣3 ⎦ ⎣3 ⎦

(24)

(25)

(29)

Vp = VC + VIC

(26)

(30)

where VC (m3) is compressible volume and VIC (m3) is incompressible volume. Therefore, Cp (MPa−1) is given by:

where, k0 (m2) is the permeability at reference confining pressure pc0 (MPa). The above relationship has also be used to obtain fracture compressibility from field test of permeability with respect to stress. Mckee et al. (1988) obtained the fracture compressibility of 0.133 MPa−1 for a San Juan Basin coal seam. However, due to the high cost, few field fracture compressibility measurements have been reported. Note that the above derivations are used for fractured unconventional reservoirs, such as shales and coals, the permeability in the fracture system is much higher than that in the matrix, and direct measurement of fracture porosity change is difficult for dual porosity reservoir rocks. For single porosity reservoirs, such as sandstones, pore compressibility can also be obtained via the porosity and stress relationship (e.g., Dong et al., 2010):

ϕ = e−β (pe − p0 ) ϕ0

(1 − e−α (σ − σ0) )

where α (MPa ) defines the rate of decline of fracture compressibility as effective stress increases, Cf0 (MPa−1) is the fracture compressibility at initial effective stress σ0 (MPa), and σ (MPa) is the current stress (Mckee et al., 1988). Shi and Durucan (2010) used this stress-dependent fracture compressibility and matched the permeability data from the San Juan Basin coal reservoirs. However, Eq. (28) is an empirical model. Li et al. (2013) derived a relationship between fracture compressibility and stress based on an assumption made by Liu and Rutqvist (2010). Liu and Rutqvist (2010) considered that the fracture has two portions, the residual fracture aperture which is not compressible and a stress-sensitive portion of the fracture aperture. Li et al. (2013) assumed that the fracture porosity, Vp, has two portions, the compressible pore volume VC and incompressible pore volume VIC (Li et al., 2013):

Integrate Eq. (25), it yields:

k = k 0 e−3Cf (pc − pc0 )

Cf 0 α (σ − σ0 )

−1

From above equation, it is clear that for changing pore pressure using adsorbing gas, the permeability and pore pressure relationship is complex due to the adsorption induced swelling, therefore, it is difficult to obtain Cf. Hence, changing confining pressure is a preferred method to obtain fracture compressibility when using adsorbing gases. Eq. (24) can be simplified for constant pore pressure and considering Cbc is much smaller than Cfc:

dk = −3Cfc dpc k

(28)

Cp = −

1 dVp 1 dVC VC ⎛ −1 dVC ⎞ =− = Vp dσ VC + VIC dσ VC + VIC ⎝ VC dσ ⎠ ⎜

⎟

(31)

By further assuming constant compressibility for the compressible pore volume, Ck (MPa−1):

−

1 dVC = Ck VC dσ

(32)

Thus, VC is given by (Li et al., 2013):

VC = VC 0 e−Ck (σ − σ0)

(33)

where σ0 (MPa) is initial stress, VC0 (m3) is the volume of the compressible pore under initial stress condition. Thus Eq. (31) can be rewritten to (Li et al., 2013):

(27)

−1

where β (MPa ) is the pore compressibility. If this method is applied for fractured reservoirs, the porosity change measured has to be for the fracture, not for the total porosity. Other methods can also obtain pore compressibility, for instance, Gutierrez et al. (2015) used Constant Rate of Strain (CRS) consolidation method to measure the continuous change of the pore volume compressibility for shale samples. However, the relationship between permeability and confining pressure is the most widely used method in the laboratory to obtain fracture compressibility.

Cp =

Ck e−Ck (σ − σ0 ) − C k e (σ − σ0) + VIC / VC 0

(34) 3

To simply Eq. (33) when the stress change is small, VC (m ) can be approximated by (Li et al., 2013):

VC =

VC 0 1 + Ck (σ − σ0 )

(35)

Substituting Eq. (35) into Eq. (34), it yields (Li et al., 2013):

Ck VC 0 VC 0 + VIC + Ck VIC (σ − σ0 )

2.3. Fracture compressibility and stress relationship

Cp =

The above derivation assumed that fracture compressibility is constant and fracture compressibility was often treated as constant in

Defining VC0/VIC = a and (VIC + VC0-VICCkσ0)/(VICCk) = b, Cp (MPa−1) can be rewritten as (Li et al., 2013): 4

(36)

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Y. Tan et al.

Cp =

a σ+b

3.2. Fracture compressibility for shales

(37)

Over the last few years, fracture compressibility for shales has been reported extensively in the literature. Shale fracture compressibilities have been obtained by laboratory work (e.g., Li et al., 2016; Pan et al., 2015b; Shi and Durucan, 2016; Tan et al., 2017; Tan et al., 2018a; Zhang et al., 2015), most of Cf are obtained using Eq. (1), excluding the data of Li et al. (2016), which are average fracture compressibility calculated using Eq. (29). Some other experimental work reported stress-dependent shale permeability without reporting compressibility (e.g., Bhandari et al., 2015; Cho et al., 2013; Ghanizadeh et al., 2014; Ghanizadeh et al., 2015; Heller et al., 2014), therefore, the fracture compressibilities for their work were calculated using Eq. (1) in this work. Detailed information about the experimental conditions, sample description, and method used from each paper are summarised in Table 2 and fracture compressibilities are plotted with respect to pore pressure in Fig. 4. In these measurements, most of them used gas as permeating fluid, however some papers, such as Chenevert and Sharma (1993) and Metwally and Sondergeld (2011) used water. As can be seen from the fracture compressibilities shown in Fig. 4, they vary significantly between 0.001 MPa−1 and 0.5 MPa−1. However, most of the facture compressibility results are between 0.01 and 0.1 MPa−1. This is lower than the typical fracture compressibilities for coal, which are between 0.04 and 0.2 MPa−1. There are a few outliers. The highest compressibilities are from Li et al. (2016) and Chen et al. (2015), in which the data from Dong et al. (2010) were used. In both papers, Eq. (29) was used and Cf0, instead of Cf, was obtained and plotted in Fig. 4. Usually Cf and Cf0 values are close, however, the Cf0 value is also dependent on the α value in the model Eq. (29). It is noticed that these large Cf0 values correspond to large α values, therefore, these large Cf0 values may be a modelling artefact. It is also worth noting that low compressibility was reported by Dong et al. (2010). Those were for the silty shales and this may be the reason for the lower compressibility as the rest of the shales in Fig. 4 are mostly organic rich shales or mudstones.

Since the experimental results are average pore compressibility, the average pore compressibility, Cp (MPa−1) using Eq. (37) can be calculated as (Li et al., 2013):

Cp =

1 σ − σ0

∫σ

σ

0

a dσ σ+b

(38)

Resolve Eq. (38) it gives (Li et al., 2013):

Cp =

a σ+b⎞ ln ⎛ σ − σ0 ⎝ σ0 + b ⎠ ⎜

⎟

(39)

It should be noted that the above derivation is for Cp, not Cf. Nevertheless, as demonstrated earlier, the difference between Cp and Cf is negligible. 3. Review of fracture compressibility values 3.1. Fracture compressibility for coals Coal permeability with respect to stress has been studied in laboratory from the 1970s, such as Dabbous et al. (1974) and Somerton et al. (1975). Pan and Connell (2012) has reviewed all these data published up to 2011. Therefore, the stress sensitive permeability data and fracture compressibility data mostly published after 2010 are collected and summarised in this review article. A summary of these data are provided in Table 1. The method to calculate the fracture compressibility was also included in the table. In these data, gases were typically used, including non-adsorbing gas Helium and adsorbing gases such as CH4 and CO2 (e.g., Connell et al., 2016; Gensterblum et al., 2014; Meng et al., 2015; Mitra et al., 2012; Pan et al., 2010a; Peng et al., 2017; Robertson and Christiansen, 2007; Tan et al., 2017; Zheng et al., 2012). Other measurements used water (e.g., Li et al., 2013; Seidle et al., 1992). Most of the measurements were performed at various confining stresses and pore pressures, but some were performed at fixed pore pressures (e.g., Meng and Li, 2013). Fracture compressibilities results in the literature are plotted in Fig. 2. Most of them were calculated from the permeability and stress relationship (Eq. (1)), excluding those from Peng et al. (2017) and Li et al. (2013), and the data of Robertson and Christiansen (2007) in Fig. 2 are average fracture compressibility calculated using (Eq. (29)). The fracture compressibility for coals are typically between 0.04 and 0.2 MPa−1 for the data collected. Two papers showed low fracture compressibility results. The first one is from Li et al. (2013), who used water as the medium to measure the pore volume change using NMR method, meaning that the fracture compressibility obtained is not using the gas permeability and stress relationship. The other one is Peng et al. (2017), in which CH4 was used for a core sample parallel to the bedding in the face cleat direction, from Chengzhuang coal mine in Qinshui Basin and the coal sample was a high rank coal with Ro,max of 2.87%, and they included a term of gas sorption-induced swelling/shrinkage in the compressibility equation. Furthermore, the results from one paper showing high compressibility (Chen et al., 2011) and it was using CO2 for a coal core from Sydney Basin, Australia. For other compressibility results using Helium and CH4, the compressibility results are mostly around 0.1 MPa−1. Connell et al. (2016) experimentally measured coal permeability on seven core samples from northern Bowen Basin, Australia and the fracture compressibility was calculated by using Eq. (1). As they reported a large number of compressibility data, their results are presented separately in Fig. 3. Four gases were used including Helium, N2, CH4, and CO2 and the fracture compressbilities are typically between 0.02 and 0.12 MPa−1. These results are within the range illustrated in Fig. 2, although they are in the lower range.

3.3. Proppant propped fractures As shales and coals typically have low to ultra-low permeabilities, hydraulic fracturing stimulation is required for economic production of the gas (Estrada and Bhamidimarri, 2016). In this process, proppant such as sand is injected to support the opening of the hydraulic fractures to obtain high fracture conductivity (e.g., Hou et al., 2017). Therefore, studying the fracture compressibility of proppant propped hydraulic fractures is highly desirable for analysing reliable well performance and optimizing fracturing design. Previous laboratory work on shale and coal permeability generally focused on the original reservoir samples, however, there have been few studies on proppant supported fracture permeability and compressibility and they are reviewed in this section. Alramahi and Sundberg (2012) measured conductivity of shale fractures supported with proppant, focusing on the impact of proppant embedment on permeability change. However, little has been done to study the fracture compressibility for proppant supported fracture. Recently, Tan et al. (2017) performed experiments to investigate shale permeability and its anisotropy with respect to gas pressure, effective stress and gas type for a naturally fractured shale sample and its fracture supported with two types of proppant, using both adsorbing gas (CH4) and non-adsorbing gas (Helium). They used their permeability data under constant gas pressure and increasing confining pressure to calculate fracture compressibility by using Eq. (1). Their results are plotted in Fig. 5. In their work, Cases 1 and 3 are for naturally fracture without proppant, Case 2 is for fracture supported with glass beads of 0.1 mm in average diameter, and Case 4 is for fracture supported with glass beads of 0.539 mm in average diameter. It can be seen from Fig. 5 5

Southern Sydney basin, Australia

Bowen Basin, Australia

Taroom coal measure, Surat Basin, Queensland, Australia

Jiulishan Coal Mine, Henan Province, China Ordos Basin; Qinshui basin and SanjiangMulinghe coal-bearing zone, China Yingjiahao, Luzhongde and Yushe coal mines in the Western Guizhou Basin, China Ordos Basin in northwest China

1

2

3

4

6

12

11

Chengzhuang coal mine in Qinshui Basin, China

Pittsburgh seam from Appalachian basin Menefee formation in the King mine, San Juan basin Cameo seam from a depth of 2766 ft., Piceance Basin Cameo coal sample from a depth of 2767 ft., Piceance Basin Northern San Juan Basin Southern Sydney basin, Australia

9

10

Southern Qinshui Basin, China

8

7

6

5

Sample info

No.

Core (D: 2.54; L: 5)

Core (D: 4.50; L:10.55)

–

Core (D: 2.51–2.52 cm; L: 4.75–5.11) – –

–

Transient method

He, CH4, CO2 CH4, CO2

CH4

He

–

Steady-state method Transient method

–

Nuclear magnetic resonance

Core (D: 2.54; L: 3)

–

32

water

–

Core (D: ~25; L: 23.67–42.89)

–

–

CO2

–

Core (D: 2.54; L: 5)

40

45

–

–

20, 30, 60

–

20

35

He, Ar, N2, CH4, CO2 CH4

Steady-state method

Core (D: 3.8; L: 1.87–2.49)

35

N2, CH4, CO2

Transient method

45 for No.1; 35 for No.2

He, CH4, CO2

Transient method

Temperature (°C)

Fluid

Measurement method

Core (D: 5; L:10–15)

Core No.1 (D: 4.50; L:10.55); core No.2 (D: 4.55; L:10.10)

Sample size (cm)

Table 1 Summary of Cf results for coal.

2.1–10.1 (He); 0.9–12.8 (CH4); 3.0–13.3 (CO2) 1–6

0.3–6.2

2.14

1.03

–

Inlet air pressure: 3

0.1

Outlet gas pressure: 0.6, inlet gas pressure: 1.6 INLET gas pressures: 0.3–4.1

Mean pore pressure: 0.1–0.6

No.1: 2.1–10.1 (He); 0.9–12.8 (CH4); 3.0–13.3 (CO2). No.2: 2.0–5.0 (He); 1.3–5.0 (CO2) 1–10

Gas pressure (MPa)

Effective Horizontal Stress: 0.25–3.3 5.1–13.1 (He); 2.9–18.8 (CH4); 5.0–19.3 (CO2) Constant effective stress: 5.0

0.882–0.977 (He); 0.253–0.837 (CH4); 0.0525–0.572 (CO2) 0.45–2.02 (CH4)

–

Eq. (42) (Eq. 12 in Peng et al., 2017's paper)

Eq. (1)

Eq. (1)

0.0485–0.0848 (He); 0.0366–0.0507 (CH4); 0.0606–0.1211 (CO2) 0.016–0.19

0.092

Cf0: 0.261

Confining pressure: 1.28–18.97

Eq. (29)

0.112

0.271

Confining pressure: 18

Eq. (1)

Eq. (1)

Peng et al. (2017)

Mitra et al. (2012) Pan et al. (2010a)

Mckee et al. (1988)

Meng et al. (2015)

Meng and Li (2013)

Li et al. (2013)

Li et al. (2014)

Guo et al. (2017)

Gensterblum et al. (2014)

Connell et al. (2016)

Chen et al. (2011)

Reference

(continued on next page)

0.0263–0.0784 (dry samples); 0.0381–0.0737 (wet samples) 0.087–0.18

low rank: 0.0051–0.064; medium rank: 0.0152–0.0172; high rank: 0.0051–0.0092

0.044–0.1

0.051–0.077

0.015–0.10 (He); 0.0081–0.114 (N2); 0.0069–0.135 (CH4); 0.0107–0.102 (CO2) 0.052–0.07

No.1: 0.0485–0.0848 (He); 0.0366–0.0507 (CH4); 0.0606–0.1211 (CO2). No.2: 0.098–0.118 (He); 0.142–0.687 (CO2)

Cf (MPa−1)

0.194

0.2–1.8

0.027–4.26

Eq. (1)

Eq. (38)

–

–

Eq. (1)

Eq. (1)

0.045–1.402

0.1926

Eq. (1)

Eq. (1)

–

0.85–5.5

Eq. (1)

Formula

No.1: 0.882–0.977 (He); 0.253–0.837 (CH4); 0.0525–0.572 (CO2). No.2: 0.752–0.937 (He); 0.008–0.574 (CO2)

Permeability (mD⁎)

Initial effective stress: 1.72

3.5–10.0

Effective stress: 2.5–20

0–10

2.4–5.5

Effective stress: 2–10

7.5–12.5

2–12

No.1: 5.1–13.1 (He); 2.9–18.8 (CH4); 5.0–19.3 (CO2). No.2: 4.0–8.0 (He); 3.3–9.0 (CO2)

Confining pressure (MPa)

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International Journal of Coal Geology 204 (2019) 1–17

7

San Juan Basin

Leichhardt seam, northern Bowen Basin, Queensland

Bituminous coal from Chongqing, China

Changzhi of Qinshui Basin and Tiechanggou coal field of Junggar Basin

15

16

17

18

⁎

Transient method

CH4

Transient method

Cube with each side of 2.3

Core (D: 5; L: 10)

–

–

–

He, N2, CH4, CO2

CH4

Water

–

Core (D: 5.08)

Transient method

N2

–

Core (D: 5.08)

core (D: 3.80; L: 6.76)

Fluid

Measurement method

Sample size (cm)

1 mD = 0.9869233 × 10−15 m2.

Powder River basin of Wyoming, and UintaPiceance basin of Utah, USA Oak Grove Field in the Black Warrior Basin of Alabama San Juan Basin

13

14

Sample info

No.

Table 1 (continued)

35, 40, 45

41

34.5

–

Ambient temperature

26.67

Temperature (°C)

1.1–7.3

0.4–9.6

0.22–4.71

–

0.69

Gas pressure (MPa)

2.1–12.3

1.38–14.6

up to 9

–

Net Hydrostatic Stress: 1.72–12.07 (Black Warrior Basin)

Overburden pressure: 2.07–6.89

Confining pressure (MPa)

0.227–7.77 (He); 0.129–5.2 (N2); 0.046–4.39 (CH4); 0.016–1.52 (CO2)

0.034–0.293

0.08–3.04

0.005–11.6 (San Juan basin, vertical direction) –

0.12–0.64 (Black Warrior Basin, vertical direction)

250–570 (No.1); 0.03–0.105 (N0.2)

Permeability (mD⁎)

Eq. (1) Eq. (41) (Eq. 3 in Tan et al., 2018b's paper) Eq. (1) Eq. (41) (Eq. 8 in Wu et al., 2018's paper) Eq. (1)

Eq. (29)

Eq. (1)

Eq. (29)

Formula

0.09–0.15 (He); 0.092–0.18 (N2); 0.085–0.17 (CH4); 0.095–0.17 (CO2)

0.1007–0.114 0.109

0.059–0.15 0.064–0.13

0.062–0.513 (San Juan Basin) Cf0: 0.12–0.59

0.084 (Black Warrior Basin)

Cf0: 0.0245–0.0273

Cf (MPa−1)

Zheng et al. (2012)

Wu et al. (2018)

Shi and Durucan (2010) Tan et al. (2018b)

Seidle et al. (1992)

Robertson and Christiansen (2007)

Reference

Y. Tan et al.

International Journal of Coal Geology 204 (2019) 1–17

International Journal of Coal Geology 204 (2019) 1–17

Y. Tan et al.

Fig. 2. Fracture compressibility data for coals.

compressibility may have a complex relationship with stress. Tan et al. (2018a) further experimentally study the impact of the layer number, type and distribution of proppant on shale fracture permeability and compressibility. In Tan et al. (2018a), glass beads and sands of different number of layers were added into an artificial fracture and different cases, including original sample, non-propped fracture, and four kinds of propped fractures were considered. The Cf values obtained by fitting Eq. (1) are presented in Fig. 6. Case 2 represents the sample after cutting fracture without adding proppant; Case 3 to Case 6

that there is a decreasing trend of Cf with pore pressure, especially for Cases 2 and 4 (the fracture is supported with proppants). Gas type has little effect on fracture compressibility, but there is a difference when comparing different directions using the same gas. Moreover, Case 2 has the lowest overall average compressibility while Case 4 has the highest overall average compressibility, because the large proppants were added in Case 4 thus the fracture is more easily compressed (Tan et al., 2017). It should be noted that in their work, the proppants added in the fracture were distributed sparsely, therefore, the fracture

Fig. 3. More fracture compressibility data for coal (Connell et al., 2016). 8

Barnett Shale in the Mississippian Barnett Formation Muskwa shale from Northeatern British Columbia; Woodford shale; Barnett shale, Fort Worth Basin; the Ohio shale from Big Sandy Field, Kentucky; and the Colorado Group in the Western Canadian Sedimentary Basin Cambrian Niutitang shale and Silurian Longmaxi Shale

1

Middle Bakken formation at 9026 ft. in the Williston Basin of North Dakota Chinshui Shale in Dakeng, Taichung City, western Taiwan

5

9

Devonian gas shale

Outcrops of the Silurian Longmaxi formation in Shizhu, Sichuan Basin, southwest China Barnett Shale from the Fort Worth Basin in North Central Texas Lower Silurian Longmaxi formation

8

10

11

13

12

9

Lower Toarcian Posidonia Shale samples from Haddessen well in northern Germany Duvernay Formation in westcentral Alberta, Canada Barnett, Eagle Ford, Marcellus, and Montney shales

7

6

Wellington and Pierre shales

4

3

2

Sample info

No.

Table 2 Summary of Cf results for shales.

Pressuretransmission technique Transient method

Core (D: 2.54; L: < 5.08)

Cube with each side of 2.1

Cubes with each side of 10

34.5

25

N2

He

–

CH4

~25

N2

A new pressure transmission technique Steady state method

Core (D: 2.54; L: 5.08)

–

He

Steady state or pulse decay

0.5–4.5

Upstream: 5.5; downstream: 3.5–5.5 Inlet pressure: 4 MPa; outlet: atmospheric pressure 3.45

Mean gas pressure: 6.89 Up to 27.6

–

Core (D: 2.54 or 3.81; L: 2.54 or 3.8)

Mean gas pressure: 0.4–1.6

Upper pressure: 0.2–2 MPa; lower: atmospheric pressure

45

N2

He, Ar, CH4

Steady state technique

Core 1 (D: 2.72; L: 2.67); core 2 (D: 2.805; L: 0.847)

Room temperature

–

Transient method

N2

Steady state method

Core (D: 1.996–2.580; L: 0.268–3.396)

0.5 to 10

30

Upstream: 17.24; downstream: 0.69 Average pore pressure: 7.24 0.34

–

–

At ambient condition

Effective stress: 3.5–35.0

Gas pressure (MPa)

30

Temperature (°C)

Core (D: 3.8)

He

water

–

Steady state

Transient method

Core (D: 2.54; L: 2.03–3.81)

Core (D: 3.18; L: 0.64–1.28)

He

He

Transient method

Transient method

Ar

Transient method

Core 1 (D: 3.78; L: 1.63); core 2 (D: 3.78; L: 1.76) –

Core (D: 5.0; L: 10.0)

Fluid

Measurement method

Sample size (cm)

Confining pressure: 6.89–34.47 Up to 9

10–60

effective stress: 1.9–38.91

Effective stress: 3.45–40.365 Effective stress up to 27.6

Effective stress: 6–37

3–120

Effective stress: 12.53–59.87 Effective stress: 8.66–55.49 6.89–34.47

Effective stress from 1.5 to 49.5

Confining pressure: 10.3–41.4 Effective stress: 3.44–34.52

Confining pressure (MPa)

3.58 × 10−5– 5.43 × 10−4

Eq. (1) Eq. (40)

Eq. (1)

Eq. (1) and Eq. (29)

3.13 × 10−41.49 × 10−2

Parallel to bedding plane: 0.05–17.54

Eq. (1)

Eq. (1)

Eq. (1)

Dong et al. (2010): Eq. (1)Chen et al. (2015): Eq. (1) and Eq. (29) Eq. (1)

Eq. (1)

Eq. (1)

0.006–0.079 0.0088–0.073

0.015–0.063

0.0137–0.4496

Pan et al. (2015b)

Lu (2012)

Metwally and Sondergeld (2011) Li et al. (2016)

Ghanizadeh et al. (2015) Heller et al. (2014) in Shi and Durucan (2016)

Ghanizadeh et al. (2014)

Dong et al. (2010); Chen et al. (2015)

Cho et al. (2013)

Chenevert and Sharma (1993)

Chen et al. (2019)

Bustin et al. (2008)

Bhandari et al. (2015)

Reference

(continued on next page)

Barnett: 0.0329–0.0334 Eagle Ford: 0.0232–0.0823 Marcellus: 0.0325 Montney: 0.0293 0.044–0.073 (N2); 0.0033–0.041 (water)

0.016–0.033

0.0039–0.017

Dong et al. (2010): 0.0016–0.0145; Chen et al. (2015): 0.06–0.43

0.024

0.038

Intact samples: 0.0069–0.0828; Fractured samples: 0.0181–0.182 0.013

Eq. (1)

Barnett: 1.00 × 10−4–1.20 × 10−3 Eagle Ford: 1.50 × 10−5–9.00 × 10−3 Marcellus: 3.50 × 10−5 Montney: 1.10 × 10−2 3.0 × 10−7–1.03

2.2 × 10−5–1.7 × 10−3

Parallel to bedding plane: 0.014–0.097

1 × 10−5–1

1.00–2.31

1.38 × 10−7–5.30 × 10−5

8.27 × 10−7–6.32 × 10−6

Intact samples: 1 × 10−6–1 × 10−3; Fractured samples: 0.01–10.0

0.025–0.12

0.016

Cf (MPa−1)

Eq. (1)

Eq. (1)

Parallel to bedding plane: 9.5 × 10−5–2.1 × 10−5 4.12 × 10−7–0.61

Formula

Permeability (mD⁎)

Y. Tan et al.

International Journal of Coal Geology 204 (2019) 1–17

International Journal of Coal Geology 204 (2019) 1–17

1.9 × 10−2– 5.1 × 10−2

Eq. (1) Eq. (27)

0.0169–0.04 0.0194–0.05

Soeder (1988) in Chen et al. (2015) Zhang et al. (2015) 0.016–0.06 Eq. (1) Huron samples: < 1 × 10−4; Marcellus sample: ~2 × 10−2

7

–

–

N2

N2 Transient method

Ohio shale and Marcellus shale

Silurian Longmaxi Formation

1 mD = 0.9869233 × 10−15 m2.

18

⁎

4.1. Relationship between fracture compressibility and gas type, pore pressure and effective stress

17

core (D: 2.54; L:5)

Estimations of fracture compressibility can be easily performed in the laboratory through a series of permeability measurements with respect to effective stress, as demonstrated earlier. Permeability and fracture compressibility are rock properties, however, gas type, gas pressure, and effective stress may influence the results of the calculated fracture compressibility. In this section, the relationships between Cf and other rock or permeating fluid properties are discussed briefly.

Devonian and Ordovician age shale

core (D: 3.81; L: 3.81)

–

Parallel to bedding plane: 4.3 × 10−6–0.07 Confining pressure: 6.89–34.45

Constant upstream: 0.69; initial downstream:0 0.52–6.89 – N2 A pressure build up technique –

4. Discussion

16

15

represents fracture with one layer of glass proppants (uniform sphere with 0.539 mm in diameter), multiple layers of glass proppants, one layer sand proppants (the range of the length of long axis for sand grains is about from 0.43 mm to 1.07 mm) and multiple layers of sand proppants, respectively. The Cf ranges from 0.037 to 0.070 MPa−1 for Case 2 (fracture without proppant), higher than that in Cases 3–6 (with proppants) which are from 0.002 to 0.015 MPa−1, meaning that fracture permeability is less sensitive to stress after adding proppant. The comparison of Cf for adding proppant cases in Tan et al. (2017) and Tan et al. (2018a) is shown in Fig. 7. It can be clearly seen that for proppant cases, Cf for CH4 and Helium have no difference in Tan et al. (2017), while Cf in Tan et al. (2017) are higher than those in Tan et al. (2018a). This is perhaps because the proppants were not fully filled in the fracture in the work of Tan et al. (2017), however, the proppants were fully filled in the fracture in the work of Tan et al. (2018a). As the fracture is well supported by proppants, it becomes less sensitive to stress thus lower fracture compressibility. The above mentioned work are for shales, Wu et al. (2018) performed permeability measurements on a coal sample with an artificial fracture supported by glass beads and sands. They used non-adsorbing gas (Helium) and adsorbing gas (CH4) to investigate the relationship between permeability and stress. The Cf values for proppant cases are from 0.005 to 0.0757 MPa−1 and lower than no proppant case which are approximately 0.1 MPa−1 (Fig. 8). Comparing the results in Fig. 8 and Fig. 2, the proppant supported fracture compressbility is also lower than those shown in Fig. 2, suggesting that proppant filled fracture are less senstive to stress change. Fig. 8 shows that Cf has a slightly increasing trend with increasing pore pressure, and there is no obvious difference for fracture compressibility between different proppant types. Moreover, the fracture compressibility by using Helium are lower than that by using CH4 (Wu et al., 2018). All the data for proppant supported fracture compressibility are also summarised in Table 3.

Effective stress: 12.07, 20.68 and 41.37 7–32

Tinni et al. (2012) 0.012–0.085

Tan et al. (2017) 0.029–0.18 0.058–1.01

(1) (40) and (29) (1) Eq. Eq. Eq. Eq. 2.17–9.05 0.48–0.50 34.5 CH4, He Transient method Cube with each side of 2.1

3.54 × 10−5–2.28 × 10−3

Tan et al. (2018a) 0.015–0.102 0.014–0.10 Eq. (1) Eq. (40) No fracture: 6.98 × 10−5– 4.02 × 10–4; with fractured: 0.39–8.02

Outcrop of Cambrian Niutitang Formation at Sangzhi, Hunan Province, China Longmaxi Shale, China 14

0.56–2.46

Up to 9 34.5 CH4 Transient method Cube with each side of 2.0

Sample info No.

Table 2 (continued)

Gas pressure (MPa) Temperature (°C) Fluid Measurement method Sample size (cm)

Confining pressure (MPa)

Permeability (mD⁎)

Formula

Cf (MPa−1)

Reference

Y. Tan et al.

The impact from different gases on fracture compressibility is of interest, because during enhanced coalbed methane recovery (ECBM), gases such as CO2 are injected. Therefore, different types of gases were used in the measurement. For example, Pan et al. (2010a) studied fracture compressibility for an Australia coal from Sydney Basin using three different gases, Helium, CH4 and CO2. Their results showed that fracture compressibility vary significantly with gas types and pore pressure. The impact of gas type is mainly from the properties of the gas and the interaction between gas and the rock. However, it is difficult to generalise the trend among different gases, such as non-adsorbing gas, weakly adsorbing gas and adsorbing gas. It has been well-known that gas adsorption induces coal matrix swelling (e.g. Pan and Connell, 2007), and gas adsorption also induces shale matrix swelling (e.g., Chen et al., 2016, 2018). The swelling of the coal or shale matrix will reduce the fracture porosity of the rock, thus change its permeability and its relationship with stress. Although typically, there is an increase trend using different gases on permeability results from highly adsorbing gases to non-adsorbing gas (e.g., Gensterblum et al., 2014; Pan et al., 2010a; Zheng et al., 2012), the fracture compressibility results have no such trend (Connell et al., 2016 (Fig. 3); Gensterblum et al., 2014; Pan 10

International Journal of Coal Geology 204 (2019) 1–17

Y. Tan et al.

Fig. 4. Fracture compressibility data for shales.

Fig. 5. Fracture compressibility data for shale from Tan et al. (2017) (H1: Horizontal direction 1; H2: Horizontal direction 2). 11

International Journal of Coal Geology 204 (2019) 1–17

Y. Tan et al.

Fig. 6. Fracture compressibility data for shale from Tan et al. (2018a) (H1: Horizontal direction 1; H2: Horizontal direction 2).

et al., 2010a) or even show a reversed trend (Zheng et al., 2012) with gas adsorbing capability. For shales, the trend is also not evident. Fig. 9 shows compressibility results using different gases, Helium, Ar and CH4, for two shales, from the work of Ghanizadeh et al. (2014). It can be seen that the compressibility results using different gases for the two samples have different trend: for sample 1, compressibility results are in the sequence of Helium > CH4 > Ar, however, for sample 2, they are in the sequence of Ar > CH4 > Helium. Gas pressure also have an impact on permeability results and thus may impact the fracture compressibility. For instance, experimental results have shown that Cf initially decreases with increasing pore pressure then increases slightly at higher pore pressures (Zheng et al., 2012). Gensterblum et al. (2014) found that pore volume compressibility decreases with gas pressure in general however the pore volume compressibility increases with pressure initially then deceases for one of the coal samples using Helium, Ar, and N2. Pan et al. (2010a) found that fracture compressibility increases with pressure for CO2 but decreases for CH4 for the coal sample studied. Therefore, there is no general trend on compressibility change with gas pressure from the experimental work in the literature. The relationship between pore pressure and fracture compressibility could be affected by factors such as gas adsorption induced swelling and the slippage effect, however, it requires further investigation to better understand the impact of gas pressure on fracture compressibility. For non-adsorbing gas, Klinkenberg constant and fracture compressibility can be obtained by fitting the permeability data with respect to both confining pressure and gas pressure (e.g., Pan et al., 2015b):

Fig. 7. Comparison of proppant supported fracture compressibility for shales in Tan et al. (Tan et al., 2017; Tan et al., 2018a).

b⎞ ⎛ k = ka ⎜1 + ⎟ e−3Cf (σ − σ0) pp ⎝ ⎠

(40)

where, b (MPa) is Klinkenberg constant. Therefore, instead of obtaining Cf for each gas pressure, one Cf value can be obtained for a set of permeability data with respect to both confining and gas pressures. However, as described in section 2 that fracture compressibility generally decreases with increasing net stress, Cf in Eq. (40) needs to be stress-dependent to better describe the data especially when Cf changes significantly with stress.

Fig. 8. Fracture compressibility data for coal from Wu et al. (2018). 12

International Journal of Coal Geology 204 (2019) 1–17

Wu et al. (2018) 0.0133–0.0757 (CH4); 0.005–0.011 (He) 0.017–0.028 (CH4)

(41)

Eq. (41) (Eq. 8 in Wu et al., 2018's paper)

Tan et al. (2018a) 0.002–0.015 0.003–0.013

0.5–9.4

1.52–14.4

15–250 (CH4); 243–490 (He) 41 He, CH4

As suggested above, Cf is related to rock properties, especially the mechanical properties of the fractures. Coals with different rank have different textures and thereby the fractures response to effective stress vary (Meng and Li, 2013). The experimental result comparisons among the low, medium and high rank coal samples show that the fracture compressibility decreases with the increase of the maximum reflectance of vitrinite (Meng and Li, 2013). Their results also suggested an increase in fracture compressibility with increasing volatile content up to a critical value of 36%, and then a decrease towards the lower-rank coals. Furthermore, Meng et al. (2015) studied the stress-dependent porosity and permeability of an anthracite coal at varying temperature and moisture content. Their results showed that with the increase of moisture content and temperature, the permeability damage rate and fracture compressibility increased. For shales and coals, permeability is anisotropic among the different directions (e.g., Ijeje et al., 2019; Ma et al., 2016; Pan et al., 2015a) and fracture compressibility is also anisotropic, as demonstrated in Tan et al., (Tan et al., 2017; Tan et al., 2018a), even that the flow is in the same fracture, such as the same proppant supported fracture. These suggest that the gas flow pathways in the same fracture at different directions are different and the impacts of stress on the flow pathways

Cf = ln

b⎞ ⎛ k ∗ = ka ⎜1 + ⎟ e−3Cf 0 (Δσ − βpp ) pp ⎝ ⎠

3

εmax Pε (p − p0 ) ⎤ ⎫ E k ⎧ ⎡ / −3 f ⎢ 3(1 − 2ν ) (p + Pε )(p + Pε ) ⎥ ⎬ k0 ⎨ 0 ⎦⎭ ⎩ ⎣

Transient method Core (D: 3.80; L: 6.76)

Transient method

Outcrop of Cambrian Niutitang Formation at Sangzhi, China Bituminous coal from Chongqing, China 2

Cube with each side of 2.0

0.61–2.57

up to 9

19.4–208.1 34.5 CH4

Eq. (1)

Tan et al. (2017) 0.016–0.091 0.041–0.99

Eq. (1) Eq. (40) and Eq. (29) Eq. (1) Eq. (40) 2.16–9.06 0.48–3.86 Transient method Longmaxi Shale, China 1

Cube with each side of 2.1

Confining pressure (MPa) Gas pressure (MPa) Measurement method Rock type, info

Sample size (cm)

3.66 × 10−2–1.40 34.5 CH4, He

4.3. Relationship between fracture compressibility and rock properties

Permeability (mD) Temperature (°C)

4.2. Relationship between fracture compressibility and permeability As permeability and fracture compressibility are both properties of the fracture, it would be interesting to study the possible relationship between Cf and permeability from the laboratory measurements. Fig. 10 shows the results of compressibility with respect to absolute permeability for coals. It can be seen from the figure there is no trend between compressibility and absolute permeability, however, weak correlation can be observed from the same set of measurement in many papers shown in the figure. Fig. 11 shows the results of fracture compressibility with respect to absolute permeability for shales. These data show a much wider absolute permeability range from a few nanodarcy to > 10 millidarcy than that for coals. Same to the coal compressibility results, there is no obvious trend between compressibility and absolute permeability for shales, however, weak correlation can be observed from the same set of measurement in many papers shown in the figure. Fig. 12 shows the results of compressibility with respect to absolute permeability for proppant supported shale and coal fractures. Again, no trend can be generalised, however, weak correlation can be observed from the same set of measurement in most papers shown in the figure. Therefore, it is partially proved that the compressibility is not only related to absolute permeability, which is related to fracture porosity, but also related to the mechanical properties of the fracture, as shown in the fracture compressibility definition, Eq. (2).

No.

Table 3 Summary of Cf results for proppant supported fracture.

Fig. 9. Fracture compressibility data in Ghanizadeh et al. (2014).

Fluid

Formula

Cf (MPa−1)

Reference

(40)

Y. Tan et al.

13

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Fig. 10. Absolute permeability and fracture compressibility/initial fracture compressibility relationship for coals.

Fig. 11. Absolute permeability and fracture compressibility/initial fracture compressibility data for shales.

effective stress change is an area of high research interest. Most of the published work studied fracture compressibility with effective stress up to 30 MPa (Chen et al., 2019). Fig. 13 shows the compressibility with effective stress up to about 60 MPa for the different shale samples and the compressibility tends to plateau at high stress (Chen et al., 2019). However, more experimental data are required for validating the fracture compressibility models such as the ones discussed in Section 2.3 or developing new models. Both organic rich shale and coal adsorb significant amount of CH4 and this induces matrix swelling, which has a significant impact on

of the different directions are also different. Although it is evident that fracture compressibility is closely related to rock properties, more studies in these areas are required to better understand the impacts of rock properties on fracture compressibility. 4.4. Potential research topics As shale gas reservoirs are typically deep and the reservoir rocks would experience large effective stress change during the life of gas production, fracture compressibility change with respective to large 14

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0.04 and 0.2 MPa−1 for coal and between 0.01and 0.1 MPa−1 for shales. Compressibility is higher for coals than for shales in general. (2) Proppant supported fracture compressibility is typically smaller than that for natural fractures or original samples. This is because the support of the proppant, which often has higher elastic modulus than coals or shales. (3) Fracture compressibility is variable and dependent on gas type, gas pressure, and stress used in the measurement. Fracture compressibility decreases with stress and models are available to describe this relationship, however, fracture compressibility and gas pressure or gas type relationships cannot be generalised, as different results show different trends. (4) Fracture compressibility has no correlation with absolute permeability in general from the data analysed above. Fracture compressibility was found to decrease with the increase of coal rank. However, little has been done to understand the fracture compressibility relationship with other rock properties, therefore, more experimental work are required to enable the establishment of the relationships between fracture compressibility and high stress and important rock properties.

Fig. 12. Absolute permeability and proppant supported fracture compressibility relationship.

Acknowledgement The authors acknowledge the Funding support from Joint Research Fund for Overseas Chinese Scholars and Scholars in Hong Kong and Macao (41728005) and National Natural Science Foundation of China (Grant Nos. 51839003 and U1765206). Support from CSIRO Energy is acknowledged. A scholarship from the China Scholarship Council for the first author is also acknowledged. References Alramahi, B., Sundberg, M.I., 2012. Proppant embedment and conductivity of hydraulic fractures in shales. In: Presented at 46th U.S. Rock Mechanics/Geomechanics Symposium, Chicago, Illinois, 24–27 June. ARMA-2012-291. Balucan, R.D., Turner, L.G., Steel, K.M., 2015. The influence of cleat demineralisation on the compressibility of coal. In: Presented at SPE Asia Pacific Unconventional Resources Conference and Exhibition, Brisbane, Australis, 9–11 November. SPE 176960. Bhandari, A.R., Flemings, P.B., Polito, P.J., Cronin, M.B., Bryant, S.L., 2015. Anisotropy and stress dependence of permeability in the Barnett shale. Transp. Porous Media 108, 393–411. Bustin, R.M., Bustin, A.M.M., Cui, X., Ross, D.J.K., Pathi, V.S.M., 2008. Impact of shale properties on pore structure and storage characteristics. In: Presented at the SPE Shale Gas Production Conference, Fort Worth, Texas, USA, 16–18 November. SPE 119892. Cai, J., You, L., Hu, X., Wang, J., Peng, R., 2012. Prediction of effective permeability in porous media based on spontaneous imbibition effect. Int. J. Mod. Phys. C. 23 (07), 1250054. Cedigaz, 2017. Natural Gas in the World – 2017 Edition. http://www.cedigaz.org/ documents/2017/NGW%202017/NGW2017EditionSUMMARY.pdf. Chen, J., 2018. Shale gas exploration and development progress in China and the way forward. Earth Environ. Sci. 113, 012178. Chen, Z., Pan, Z., Liu, J., Connell, L.D., Elsworth, D., 2011. Effect of the effective stress coefficient and sorption-induced strain on the evolution of coal permeability: experimental observations. Int. J. Greenh. Gas Control 5 (5), 1284–1293. Chen, Z., Pan, Z., Liu, J., Connell, L.D., 2012. Characteristic of anisotropic coal permeability and its impact on optimal design of multi-lateral well for coalbed methane production. J. Pet. Sci. Eng. 88–89, 13–28. Chen, D., Pan, Z., Ye, Z., 2015. Dependence of gas shale fracture permeability on effective stress and reservoir pressure: model match and insights. Fuel 139, 383–392. Chen, T., Feng, X., Pan, Z., 2016. Experimental study of swelling of organic rich shale in methane. Int. J. Coal Geol. 150, 64–73. Chen, T., Feng, X., Pan, Z., 2018. Experimental study on kinetic swelling of organic-rich shale in CO2, CH4 and N2. J. Nat. Gas Sci. Eng. 55, 406–417. Chen, T., Feng, X., Cui, G., Tan, Y., Pan, Z., 2019. Experimental study of permeability change of organic-rich gas shales under high effective stress. J. Nat. Gas Sci. Eng. https://doi.org/10.1016/j.jngse.2019.01.014. (Accepted). Chenevert, M.E., Sharma, A.K., 1993. Permeability and effective pore pressure of shales. SPE Drill. Complet. 8 (01), 28–34. Cho, Y., Apaydin, O.G., Ozkan, E., 2013. Pressure-dependent natural-fracture permeability in shale and its effect on shale-gas well production. SPE Reserv. Eval. Eng. 16 (2), 216–228. Connell, L.D., Mazumder, S., Sander, R., Camilleri, M., Pan, Z., Heryanto, D., 2016. Laboratory characterisation of coal matrix shrinkage, cleat compressibility and the geomechanical properties determining reservoir permeability. Fuel 165, 499–512.

Fig. 13. Fracture compressibility decrease with effective stress (from Chen et al., 2019).

fracture opening and thus fracture compressibility. As mentioned earlier, the impact of gas adsorption and its induced swelling on fracture compressibility was not well studied, modelling work in particular is required as there have been plenty of laboratory measurements in the literature. Permeability shows strong anisotropy for coal and shale reservoirs and so is fracture compressibility. This has significant impact on the gas production behaviour especially when a horizontal well is used. As gas flows through the same fracture network in the reservoir, compressibility between different directions would have a relationship, which would be an interesting area of research. 5. Conclusions In this review article, the definition of fracture compressibility, fracture compressibility effective stress relationship, the experimental methods on obtaining the compressibility as well as the recent literature results on fracture compressibility for coals and shales are reviewed. A brief discussion on the relations between fracture compressibility and rock and permeating fluid properties are performed. The below conclusions can be drawn: (1) Fracture compressibility is the parameter to describe permeability stress relationship and laboratory measurement is widely used to obtain this parameter. Fracture compressibility is typically between 15

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