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Modelling Permeability for Coal Reservoirs: A Review of Analytical Models and Testing Data

Zhejun Pan*, Luke D. Connell*

CSIRO Earth Science and Resource Engineering Private Bag 10, Clayton South, Victoria 3169, Australia

*Zhejun.Pan@csiro.au Tel.: +61 3 9545 8394 Fax.: +61 3 9545 8380

*Luke.Connell@csiro.au Tel.: +61 3 9545 8352 Fax.: +61 3 9545 8380

Abstract As with other reservoir types permeability is a key controlling factor for gas migration in coalbed methane reservoirs. The absolute permeability of coal reservoirs changes significantly during gas production, often initially decreasing but then increasing as the reservoir pressure and gas content is drawn down. It has also been observed to decrease markedly during CO2 injection to enhance coalbed methane recovery. In order to predict gas migration models for coal permeability must represent the mechanisms leading to these observed behaviours. The permeability of coal reservoirs behaves in a similar fashion to other fractured reservoirs with respect to effective stress, decreasing exponentially as the effective stress increases. However a unique effect of coal is that it shrinks with gas desorption and swells with adsorption. Within the reservoir this swelling/shrinkage strain leads to a geomechanical response changing the effective stress and thus the permeability. Modeling coal permeability incorporating the impacts from both effective stress and coal swelling/shrinkage dates back about 25 years. Since then a number of permeability models have been developed. In recent years this topic has seen a great deal of activity with a growing body of research on coal permeability behaviour and model development. This article presents a review of coal permeability and the approaches to modeling its behaviour. As an important part of this, the field and laboratory data used to test the models are reviewed in detail. This article also aims to identify some potential areas for future work.

Keywords: coalbed methane, enhanced coalbed methane recovery, CO2 sequestration, coal swelling, stress

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1. Introduction

The coal seam is both the source and the reservoir for coalbed methane (Clarkson and McGovern, 2005; Gash et al., 1992). Coalbed methane (CBM) or coal seam gas (CSG) is mainly stored within the coal matrix by adsorption. Primary recovery of this gas involves drawing down the reservoir pressure leading to gas desorption and free gas; this free gas then diffuses through the coal matrix to the coal’s natural fracture system, known as cleats (Pan et al., 2010b; Lu and Connell, 2007). It is commonly assumed that Darcy flow is a result of flow in the cleat system and that the contribution of flow in the coal matrix to Darcy flow can be neglected (Puri et al., 1991). Thus the permeability of a coalbed is a function of its cleat system and is a key property for understanding coalbed methane production (Palmer, 2009; Reid et al., 1992; Sparks et al., 1995). For many coalbed reservoirs water and gas are both present and so there is two-phase flow within the cleat system with the effective gas permeability a function of the relative gas permeability and the absolute permeability (Clarkson et al., 2008; Kissell and Edwards, 1975). Although relative permeability and capillary pressure are important properties for gas flow in coal seams (e.g. Dabbous et al., 1976; Gash, 1991; Ham and Kantzas, 2008; Mazumder et al., 2003; Meaney and Paterson, 1996; Ohen et al., 1991; Paterson et al., 1992; Plug et al., 2008; Puri et al., 1991; Reznik et al., 1974), the focus of this current paper is the absolute permeability which, for simplicity, will be referred to as the permeability. A complication with coal permeability is that it can vary significantly during gas production in response to decreases in pore pressure and gas desorption-induced coal matrix shrinkage (Gray, 1987). Therefore a challenge for accurate reservoir simulation is the representation of this behaviour. This permeability variation is also important for enhanced coalbed methane where gases, such as N2 and CO2, are injected to improve recovery of reservoir gases (Puri and Yee, 1990). Since coal can adsorb more CO2 than methane at the same pressure, CO2 injection can not only enhance CBM production, but could prove to be a viable option to reduce greenhouse gas emissions (Reznik et al. 1984). As with other naturally fractured formations coal permeability is determined by a range of fracture characteristics which may include size, spacing, connectedness, aperture and degree of mineral infill, and patterns of orientation (Laubach et al., 1998). Permeability may also have a relationship with coal type and rank due to the development of cleats during the coalification process. For example, Clarkson and Bustin (1997) found that the order of decreasing permeability with lithotype is: bright, banded, fibrous, banded dull and dull for the coal samples they studied. In general, coal is a weak rock with cleat aperture, and thus permeability, being sensitive to effective stress; as the effective stress increases the permeability decreases exponentially, a relationship supported by extensive laboratory (e.g. Somerton et al., 1975; Seidle et al., 1992) and field studies (e.g. Sparks et al., 1995; Enever and Hennig, 1997). However this decrease in permeability with effective stress is counteracted during primary production by a unique characteristic of coal; that is coal matrix shrinkage due to gas desorption (Gray, 1987). There is potential, during primary production, for the reservoir permeability to initially decline and then rebound as matrix shrinkage effects dominate over cleat compression. In contrast, the increase in gas content due to CO2 adsorption during enhanced coalbed methane leads to coal swelling and permeability decrease (e.g. van Bergen et al., 2006). Permeability

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models for conventional gas reservoirs do not include this coal swelling/shrinkage impact on permeability thus are not applicable to coal reservoirs since this can play a significant role in the permeability behaviour. Hence, in order to describe fluid flow behaviour correctly, coal permeability models account for the effects of stress as well as the coal swelling or shrinkage. There have been many models developed to describe coal permeability that include the impact of effective stress and coal swelling/shrinkage. While a number of empirically based models have been presented the focus of this paper will be those models classed as analytical, developed from a theoretical consideration of the processes affecting the permeability. An important challenge is the representation of the stress behaviour since this requires a description of the geomechanical processes. For models to be tractable concise functional forms are preferred and therefore simplifications are introduced into the model development. A significant simplification, which leads to a very concise and tractable relationship, was first introduced by Gray (1987) for coal permeability; uniaxial strain (where coal is constrained laterally) and constant vertical stress (determined by the weight of the overburden). The permeability models presented by Palmer and Mansoori (1998) and Shi and Durucan (2004) use this approach and have seen widespread practical application. Recently a number of models have been developed to describe coal permeability behaviour for more complicated conditions or using different interpretations (e.g. Connell et al., 2010; Gu and Chalaturnyk, 2010; Izadi et al., 2011; Ma et al., 2011; Liu and Rutqvist, 2010; Liu et al., 2010; Wang et al., 2009; Wu et al., 2010; Pan and Connell, 2011). In other work coupled flow and geomechanical simulation has been applied to CBM and ECBM to investigate the role of geomechanical processes on permeability behaviour (Connell, 2009; Connell and Detounay, 2009; Gu and Chalaturnyk, 2006, 2010; Wei and Zhang, 2010; Zhao et al., 2004; Zhu et al., 2007). A key step in establishing a level of confidence with the developed coal permeability models is application to relevant problems and comparison with observed behaviour. A focus with many permeability models has been to describe behaviour under reservoir conditions. However, a difficulty is that field data is difficult to obtain and may be subject to significant uncertainty. While laboratory measurements on coal core samples can be more readily obtained, the permeability model used needs to be appropriate for the test conditions. For example a model derived for the reservoir conditions of uniaxial strain and constant vertical stress would not be appropriate for a laboratory test under hydrostatic conditions. Hence, the data to be used to validate a permeability model depends on the conditions under which the model is developed. Palmer (2009 IJCG) presents a detailed review of four of the most widely used permeability models and Ma et al. (2011) presents a more general review in order to introduce their own modelling approach. Liu et al. (2011a) also presents a review with the focus on multi processes for gas flow in coal seams. However this very active area of research now has such an extensive and complicated range of published work that a dedicated review article is warranted. Hence, this paper presents a thorough review of analytical coal permeability models. The first section considers the theoretical basis for permeability modelling, including the assumptions and boundary conditions used. In the following section, the information used in model testing and

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validation is reviewed. In the final section, the potential directions for coal permeability model research are considered.

2. Coal permeability model development The common conceptual model applied to coal is that it is a dual-porosity reservoir, where gas is mostly stored in the coal matrix and Darcy fluid flow occurs in the natural fracture system (cleat or pores are also widely used in coal reservoir engineering to describe the natural fracture system). The flow capacity of fractured media depends almost entirely on the number and width of fractures and their continuity in the direction of flow (Somerton et al., 1975). Permeability, a measure of the flow capacity, is directly related to a range of pore characteristics including pore size (porosity), continuity, connectivity, wall roughness (Brown, 1987), and tortuosity (Tsang, 1984). Absolute permeability, which is measured using liquid, is an intrinsic property of the rock. However, since coal permeability is sensitive to stress, when absolute permeability is stated so should the stress conditions. Gas effective permeability in coal is more complex. It is related to the absolute permeability, water/gas saturation in the cleat, gas sorption induced swelling/shrinkage, and Klingkenberg Effect (Klingkenberg, 1941).

2.1 Linking porosity or stress to Permeability A conceptual schematic of a plan view through coal’s natural fracture or cleat system is depicted in Figure 1. Coal cleats are of two types: face cleats and butt cleats, which are often normal to the bedding plane and may be perpendicular to each other (e.g. Close 1993; Nelson, 2000; Pattison et al., 1996).

Fa

ce C

leat

Butt Cleat

Matrix Blocks Containing Micropores

Figure 1. Illustration of a plan view of coal structure.

The bundled matchstick conceptual model has been widely used as a basis to describe the coal cleat system and to derive a number of permeability models. Figure 2 presents a generalised form of this conceptual model as well as that used by Reiss (1980) where there are two cleat systems present. With this conceptual model flow through the cleat systems can be described by the cubic law for fracture flow, which is a direct extension from flow between parallel plates (Bai and Elsworth, 2000). For a

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set of parallel cleats, aligned with the principal Cartesian axes, with uniform aperture, bi, and spacing, ai, the cubic law can be written as,

3

12i

ji j

b pq

a xµ∂= −∂

(1)

where µ is the viscosity, p is the pressure, xj is the Cartesian coordinates where j = 1, 2, 3. Eq. (1) is for one cleat system contributing flow to the j’th direction, in this case, it is normal to the direction of flow. To account for surface roughness, tortuosity etc the cleat aperture, bi, is termed the effective hydraulic aperture and is usually distinct from (and less than) the apparent or mechanical cleat aperture (Bai and Elsworth, 2000; Gu and Chalaturnyk, 2010). From Eq. (1), the permeability is,

3

12i

ii

bk

a= (2)

or 3

0 0

i i

i i

k b

k b

=

(3)

where the subscript 0 refers to a reference state and assuming that the aperture is small compared to the spacing.

a) Anisotropic (3 cleat sets) b) Isotropic (with 2 cleat sets) Figure 2. Idealised coal cleat system geometries (after van Golf-Racht, 1982) For the anisotropic case presented in Figure 2(a) the porosity can be written as,

31 2

1 2 3

bb b

a a aφ = + + (4)

Under isotropic conditions,3b

aφ = , which can be substituted into Eq. (2) to give,

2 31

96k a φ= (5)

b1

b2

b3

a1

a2

a3

l1

l3

l2

6

or for 2 sets of cleats (as in the bundled matchstick model commonly used for coal)

where 2b

aφ = and the permeability can be written as,

2 31

48k a φ= (6)

from Reiss (1980). Of course the coal cleat structure is much more complicated than the simple conceptual models presented in Figure 2 with considerable variation in cleat characteristics. In reality an appropriate averaging would be required at a representative elementary volume scale.

2.1.1 Porosity-permeability relationship

From either Eq. (5) or Eq. (6), the permeability change with respect to a reference state can be easily obtained:

2 3

0 0 0

k a

k a

φφ

=

(7)

where the subscript 0 refers to the reference state. If the matrix size change due to swelling/shrinkage and mechanical forces such as compression is considered as negligible compared to porosity change:

0a a≈ (8)

Thus Eq. (7) can be simplified to: 3

0 0

k

k

φφ

=

(9)

Eq. (9) is widely applied to describe the permeability change with respective to porosity change (e.g. Palmer and Mansoori, 1996, 1998; Cui and Bustin, 2005). An important question with porosity based models is how well these account for the well known anisotropy of cleat systems. By definition with these models anisotropy can exist in the absolute permeability but, since the porosity is a property without directional attributes, directional aspects to the variation in permeability away from the reference state can not be represented.

2.1.2 Stress-permeability relationship

The cleat porosity in Eq. (9) must be estimated from flow measurements as it represents the effective porosity involved in fluid flow, in a similar fashion to the effective aperture discussed above. Another approach is to use relationships between stress and permeability where porosity has been eliminated from the expression. One approach to deriving the common expression that is used for this was presented by Cui and Bustin (2005) and was derived from differentiating the porosity bp VV=φ to

give the following,

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b p

dd d

φ ε εφ

= − (10)

where Vp is the cleat volume, Vb is the bulk volume, ppp VdVd −=ε is the

(differential) pore strain, and bbb VdVd −=ε the (differential) bulk rock strain.

Eq. (10) can be integrated to give the following relationship,

p b

p0 b0

p b0

exp d dε ε

ε ε

φ ε εφ

= − − ∫ ∫ (11)

where the bar is used to denote the variable of integration.

From Zimmerman et al. (1986) and Jaeger et al. (2007),

( )b b md C d dp C dpσε σ= − + and ( )p p md C d dp C dpσε σ= − + (12)

where bcC = ( )b bpV Vσ− ∂ ∂ , pC σ = ( )p pp

V Vσ− ∂ ∂ , σ is the mean stress and Cm

is the compressibility of the matrix. Substituting Eq. (12) into Eq. (11) and then into Eq. (9) leads to,

( ) ( )( )

( )

0 0

,p

0 p b

,p

k k exp 3 C C d dpσ

σ σσ

σ = − − −

∫ (13)

Since Cbσ << Cpσ and assuming constant compressibility leads to Cui and Bustin’s (2005) equation,

( ) 0 0 0exp 3 ( )pk k C p pσ σ σ= − − − − (14)

Seidle et al., (1992) derived a model for analysis of laboratory permeability measurements under hydrostatic stress which is a similar form of relationship to Eq. (14). In Shi and Durucan (2004) the Seidle et al. (1992) model is used but applied with the assumption that permeability is a function of the horizontal effective stress. This is consistent with the bundled matchstick model assumption of vertical face and butt cleats where stresses acting across these alter the cleat apertures, or that the vertical stress is determined by the lithostatic load and does not vary. However Eq. (14) would only be equivalent to that used in Shi and Durucan (2004) when the Biot coefficient in the effective stress was equal to 1. Replacing the mean stress by the horizontal stress and introducing the cleat volume compressibility, cf, Eq. (14) becomes,

( ) 0 0 0exp 3 ( )f h hk k c p pσ σ= − − − − (15)

Where ( )f pp p pc C V p Vσ

= = − ∂ ∂ . Cpσ equals to Cpp when Biot coefficient equals 1.

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Liu and Rutqvist (2010) developed a stress-permeability relationship based on the assumption that the cleat will retain some hydraulic aperture even at infinitely high stress conditions:

e fcr fb b b

σ−= + (16)

Where br is the residual cleat aperture, bf is the stress-sensitive portion of the fracture aperture. Using Eq. (16) with Eq. (3) the permeability change can be described as:

0

3

0

f

f

c

c

k e

k e

σ

σηη

−

−

+= + (17)

Where /r fb bη = . Eq. (17) reduces to Eq. (15) when residual fracture aperture is zero

or negligible. By fitting Eq. (15) to laboratory measurements of permeability at various pressures or confining pressures the cleat compressibility can be estimated. Seidle et al. (1992) used Eq. (15) with measurements of permeability to water at different pore pressures while keeping confining pressure constant. Other researchers used similar approaches (Harpalani and McPherson, 1986) However, since the effective stress coefficient or Biot coefficient is often less than unity (Chen et al., 2011; Zhao et al., 2003), assuming unity will overestimate the effective stress change and then underestimate the cleat compressibility. Pan et al., (2010) measured gas permeability with respect to confining pressure at a constant pore pressure. By keeping pore pressure constant the permeability measurements were not complicated by gas sorption induced swelling effects and eliminated the potential impact from the Biot coefficient so that the change in effective stress is only due to changing confining pressure. In Palmer and Mansoori’s (1996, 1998) model, neglecting the solid compressibility and swelling effects, the cleat compressibility had the following definition:

( )( )( )

1 1 21

1fcM E

ν νφ ν φ

+ −= =

− (18)

where M is the constrained axial modulus, ν is Poisson’s ratio, E is Young’s modulus. Thus the cleat compressibility is a function of the cleat porosity, increasing as the porosity decreases, assuming the other geomechanical properties are constant. Cleat compressibility becomes more complex when grain compressibility and matrix shrinkage are included. Furthermore, the cleat compressibility obtained from laboratory stress-permeability measurements varies with respect to gas type and stress (e.g. Durucan and Edwards, 1986; Pan et al., 2010a; Robertson and Christenson, 2007). However constant cleat compressibility can be a useful approximation and is often assumed (e.g. Seidle et al., 1992; Shi and Durucan, 2004). Stress dependent cleat compressibility has been used to describe the permeability observed in the field (Shi and Durucan, 2009, 2011). However, the underlying mechanisms for its relationship with gas type and stress are not well understood.

2.2 Coal matrix swelling/shrinkage effects Coal swells during gas adsorption and shrinks during gas desorption. This sorption-induced coal matrix volume change is a unique phenomenon for coal reservoirs. Laboratory measurements have shown coal can swell up to a few percent volumetrically (e.g. Chikatamarla et al., 2004; Day et al., 2008; Durucan et al., 2009; Harpalani and Chen, 1995; 1997; Harpalani and Schraufnagel, 1990; Karacan 2003,

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2007; Levine, 1996; Moffat and Weale, 1955; Reucroft et al., 1983, 1986; Robertson and Christiansen, 2005; St. George and Barakat, 2001; Wang et al., 2010; Zarebska and Ceglarska-Stefanska; 2008). Within the reservoir this can have a significant impact on the cleat porosity and thus the permeability, since the initial reservoir cleat porosity is often less than 1% (Palmer and Reeves, 2007).

2.2.1 Role of swelling in the permeability vs stress relation

In Section 2.1.2 the exponential model for permeability was derived from the definition of porosity, Eq. (10). Cui and Bustin (2005) showed how this derivation should also include the effect of coal swelling. Using the terminology of Connell et al. (2010) the total derivatives in Eq. (10) can be partitioned into a mechanical component (with the subscript M below) and a swelling component (subscript S), written as,

M Sb b bd d dε ε ε= + and M S

p p pd d dε ε ε= + (19)

In Cui and Bustin (2005) it was assumed that bulk and pore swelling strains were equal (i.e. S S

b pd dε ε= ) and thus cancelled out upon substitution of Eq. (19) into (10).

Connell et al. (2010) did not invoke this assumption but did assume that the two strains were linearly related by a constant, γ. This assumption led to the following equation,

( )( ) 0 0 0exp 3 ( ) (1 )p sk k C p pσ σ σ γ ε= − − − − + − (20)

where εs is the bulk swelling strain.

2.2.2 Geomechanical response to swelling/shrinkage in permeability modelling

A common starting point to account for the geomechanical response to sorption-induced swelling/shrinkage strain is assuming that it is analogous to thermal expansion of rock (Palmer and Mansoori, 1996, 1998). Using this approach the standard geomechanical descriptions can be modified to include the effects of swelling/shrinkage strain. The resultant geomechanical relationships can then be used with the permeability models presented in the previous section to develop permeability models that integrate strain and pressure effects (eg. Cui and Bustin, 2005; Shi and Durucan, 2004). Shi and Durucan (2004) derived their permeability model from the constitutive relation for isotropic linear poroelasticity; with the assumption that sorption induced swelling is equivalent to thermal expansion. Using the Cui and Bustin (2005) form, this can be written as:

1 1 2ij ij b ij ij s ij

Ep K

νσ ε ε δ α δ ε δν ν = + + + + −

(21)

where the bar above the variables denotes that it is an increment, δij is the Kronecker delta, α is the Biot coefficient, K is the bulk modulus, E is the Young’s modulus, ν is the Poisson ratio, and εs is the bulk sorption strain ( s s s

s xx yy zzε ε ε ε= + + ).

Using the approach of Cui and Bustin (2005) but stating the resultant equation before simplifying assumptions, Connell (2009) rewrote Eq. (21) into the following form,

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sxx yy zz xx xx

E E 1 2p

1 1 1 1

ν νσ σ σ ε ε αν ν ν ν

−= = + + +− − − −

(22)

assuming isotropic swelling strain. This equation illustrates the contribution of the various effects on stress. The permeability models presented above are based on isotropic assumptions. Recently there has been work where anisotropy has been considered. The more general stress-strain relationship for anisotropic conditions is presented below (e.g. Jaeger et al. 2007; Pan and Connell, 2011);

,

e ezij ji s

ij ij ji ij ij T ijj x j ii j

TE E

σ σε δ ν ε δ α δ

= ≠

= − + +

∑ , ,i x y z= (23)

Where eijσ is the effective stress, sijε is the sorption-induced swelling strain, αΤ is the

thermal expansion coefficient, T is temperature. Eq. (23) can be simplified to the stress-strain relation used by Shi and Durucan (2004) for isotropic coal reservoirs. In Eq. (23), directional swelling strain is considered as if it will have the same impact as thermal expansion in each direction. Other methods have been developed to account for swelling strain in modeling permeability. For instance, in the model presented by Liu et al. (2010) gas sorption-induced coal directional permeabilities are linked to the directional strains through an elastic modulus reduction ratio, Rm. This is the ratio of the bulk coal elastic modulus to coal matrix modulus (0<Rm<1) and represents the partitioning of total strain for an equivalent porous coal medium between the fracture system and the matrix. Liu et al. (2011b) also suggested that permeability is initially controlled by the internal fracture boundary condition and then the external boundary condition depending on the stages of matrix swelling.

2.2.3 Modelling the swelling/shrinkage strain

The apparent or measured swelling strain with gas adsorption comprises two effects; the result of swelling due to gas adsorption and the compression effect due to confining and pore pressure. In order to estimate the swelling strain for models derived using Eq. (21) these compression effects need to be subtracted from the measured strain. Much of the published work presenting swelling strain measurements does not allow for the effects of pore or confining pressure and simply presents the strain as measured. Gray (1987) used a linear relationship between the swelling/shrinkage strain and pressure in his permeability model. For his strain measurements Levine (1996) found that a linear relationship would overestimate the impact from swelling/shrinkage, especially at high pressures and used a Langmuir-like equation to describe the measured swelling behaviour;

1l SL

SL

p p

p p

εε =+

(24)

Where εl is the maximum swelling strain when fitting with the Langmuir like equation, pSL is the Langmuir pressure for the swelling isotherm (in some models to be presented below this is replaced by B = 1/pSL). The Langmuir-like equation to describe swelling strain has been widely used (eg., Palmer and Mansoori, 1998; Shi

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and Durucan; 2004). In order to describe swelling induced by mixed-gas adsorption, an extended Langmuir-like equation has been applied (e.g. Mavor and Gunter, 2006; Mitra and Harpalani, 2005). Another approach is to relate the measured strain to the gas content. Sawyer et al. (1990) used a linear relationship between the swelling strain and total adsorbed amount. Harpalani and Chen (1995) found that the magnitude of volumetric strain was almost proportional to the sorbed gas volume. Seidle and Huitt (1995) also used a linear relationship with gas content to describe the behaviour of matrix shrinkage. This can be stated as,

aVε α= (25)

Where ε is the swelling strain, α is the swelling/adsorption ratio, Va is the total adsorption amount. Many researchers (e.g. Shi and Durucan 2005; Cui and Bustin, 2005; Connell and Detournay, 2009; Connell, 2009) apply this linear relationship between the swelling strain and total adsorbed amount in their permeability models. All these approaches have simple functional forms and are straight forward to apply in permeability models. However, they are empirical and can only be applied for a certain pressure range. Measurements by Moffat and Weale (1955) showed that the swelling strain increased with gas pressure and then decreased after reaching a maximum, while the adsorption approached a plateau at high pressures. Moreover, Pekot and Reeves (2002) found that measured swelling strain is different for different gas species even if the adsorbed amount is the same when examining the measurements by Levine (1996) and named this phenomenon differential swelling. Thus, the statement that constrained swelling is proportional to adsorption amount is problematic. These empirical models may lead to large errors when describing mixed-gas adsorption induced coal swelling (Mitra and Harpalani, 2007). Hence, theoretical coal swelling models with simple mathematical forms are of great importance in permeability modelling. However, there have been few theoretical models developed to describe adsorption induced coal swelling. Pan and Connell (2007) present a theoretical model based on adsorption thermodynamics and elasticity theory, using a structure model developed by Scherer (1986). This model describes gas adsorption-induced swelling by assuming that the surface energy change caused by adsorption is equal to the elastic energy change of the coal solid. The Pan and Connell swelling model is able to describe coal swelling in different gases based on one set of coal property parameters and adsorption isotherms for different gases. This model has been readily extended to describe coal swelling in mixed-gas adsorption by using the same set of coal property parameters and mixed-gas adsorption isotherms. It has been shown that the Pan and Connell model can accurately describe experimental measurements of coal swelling in mixed gas (Clarkson et al., 2010). Furthermore, this model has a simple analytical form and is easy to be applied in permeability modelling. The model has also been applied with the Palmer and Mansoori (1998) permeability model to accurately describe CBM production data from a San Juan Basin CBM well, in which a high concentration of CO2 is produced with methane (Clarkson et al., 2010). Nevertheless, the Pan and Connell model is only applicable at coal reservoir conditions and where gas is adsorbed on the coal surface. At elevated temperatures, the coal properties may change (Larsen, 2004). Thus, if the gas and coal interactions exceed physical adsorption, the mechanism of swelling becomes more

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complex. When using the Langmuir adsorption model to describe the surface potential, the Pan and Connell coal swelling model is expressed as:

( ) ( ) ( )ln 1 , 1 2ss s

s s

PRTL BP f x

E E

ρε ν ν= + − − (26)

Where, ε is the swelling strain, sρ is the density for the coal solid, sE is the Young’s

modulus for the coal solid, x is a coal structure parameter, sυ is the Poisson’s ratio for

the coal solid. f is a function describing coal’s structure:

( ) ( ) ( )[ ] ( )[ ]( )( )cx

cxcxxf

s

sssss 3253

21453112,

−−−−−+−−=

νννννν (27)

Where c is a constant which equals to 1.2. x is related to the porosity of micropores by:

( )21 3 1x cxφ π= − − (28)

where φ is porosity of micropores Vandamme et al. (2010) developed a framework that describes the macroscopic strain caused by fluid adsorption to the pore surface of a porous medium. The developed framework provides a way of calculating macroscopic strains from results obtained at the molecular scale directly using a thermodynamic approach where the authors extend poromechanics to surface energy and surface stress. Their focus was on how the surface stress is modified by adsorption and how the adsorption behaviour is estimated through molecular simulations. The developed swelling model can be expressed as:

( )max 1

1F

FF

p

F FRTs F

pd

K f e

µ

ε µµε α µ−=−∞

∆ = − + Γ+∫ (29)

Where p is pressure, Ks is the solid bulk modulus, αs is a constant material parameter,

the maxFΓ and fF are two parameters which determine the shape of the adsorption

isotherm for each pore fluid, µF is the chemical potential of the pore fluid. Yang et al. (2010) used the quenched solid density functional theory (QSDFT) to study methane adsorption on coal under reservoir conditions. The main focus is on coal deformation in response to adsorption that may result in either expansion (i.e. swelling) or contraction, depending upon the pressure, temperature, and pore size. Two qualitatively different types of deformation behaviour were found depending upon the pore width. Type I shows a monotonic expansion over the whole pressure range. This behaviour is characteristic of the smallest pores < 0.5 nm that cannot accommodate more than one layer of methane. Type II displays contraction at low pressures followed by expansion. Type II behaviour was found for several groups of pores, which can accommodate dense packing with an integer number (2 to 6) of adsorbed layers. Yang et al. (2010) established the relationships between the methane capacity and the solvation pressure that it exerts on the coal matrix and the depth of coal bed for pores of different sizes. They found that the coal deformation depends upon the bed depth, and at different depths, it either swells or contracts depending upon the pore size distribution. Their model can be expressed as:

sfk

φε = (30)

where φ is the porosity and k is the elastic modulus, which is related to the bulk modulus K, by K=k/φ, fs is the solvation pressure as defined below:

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, ,

1s

T A

f pA H µ

∞∂Ω = − ∂

(31)

where A is the surface area, Ω is the grand free energy and is described below, H is the pore width, T is the temperature, µ is the chemical potential, and p∞ is the bulk

fluid pressure.

( ) ( ) ( ) ( )int i i i i ii

r F r dr r rρ ρ ρ ψ µΩ = + − ∑∫ (32)

where Fint is the intrinsic Helmholtz free energy, ρi and µi are the local number density and chemical potential of component i, respectively, and ψi is the local external potential. For some coals the swelling/shrinkage displays strong anisotropy, with more swelling in the direction perpendicular to the bedding than that parallel to the bedding (Day et al., 2008; Levine, 1996; Majewska and Zietek, 2007). Based on the coal swelling model developed by Pan and Connell (2007), Pan and Connell (2011) developed an anisotropic coal swelling model with the hypothesis that swelling anisotropy is caused by anisotropy in the coal’s mechanical properties and matrix structure. The developed anisotropic swelling model is able to accurately describe the experimental data, with one set of parameters to describe the coal’s properties, matrix structure and different gas adsorption isotherms. This developed model is also applied to describe anisotropic swelling measurements from the literature where the model was found to provide excellent agreement with measurements. The anisotropic coal swelling model is also applied to an anisotropic permeability model to describe permeability behaviour for primary and enhanced coalbed methane recovery. It was found that the permeability calculated allowing for anisotropic swelling is significantly different to that assuming isotropic swelling. This demonstrates that for coals with strong anisotropic swelling, permeability models need to allow for this behaviour (Pan and Connell, 2011).

2.3 Reservoir conditions for permeability model development As discussed in the pervious sections, permeability models can be developed from a cleat porosity point of view or a stress change point of view, both with strain as an intermediate variable. A key challenge is describing the geomechanical behaviour under reservoir conditions in such a way that the analytical permeability model is concise. The most widely applied assumptions used to simplify the geomechanical description are that reservoir conditions are uniaxial strain ( 0xx yyε ε= = ) and constant

overburden stress ( 0zzσ = ) (Gray, 1987). With these two assumptions Eq. (23) can be

simplified, for isotropic and isothermal conditions, to the following:

1 1e e sxx yy xx

Ep

νσ σ εν ν

= = − +− −

(33)

where the Biot coefficient, α, is equal to 1. Cui and Bustin (2005) and Connell (2009) present a stress based form of Eq. (33) which includes the Biot coefficient,

1 2

1 1s

xx yy xx

Ep

νσ σ α εν ν

−= = +− −

(34)

14

Permeability models were also developed using other set of assumptions, such as constant volume assumption. Permeability models were often developed from a porosity point of view, applying various assumptions. A brief summary of the models is provided in the next section.

2.4 Permeability models A number of permeability models have been developed accounting for both the geomechnical effect and sorption-induced coal swelling. In this section, a brief review of the permeability models is presented with the focus on isotropic permeability models. A brief review on the anisotropic permeability models is carried out in the next section. Empirical permeability models, such as Harpalani and Zhao (1989) model, are not discussed though. Gray Gray (1987) proposed the first coal permeability model which accounts for both geomechanical effects and sorption-induced swelling/shrinkage behaviour, using a stress approach:

( ) ( )0 01 1e e Sh h S

S

Ep p p

p

ευσ συ υ

∆− = − − + ∆− − ∆

(35)

Where Sp∆ is change in equivalent sorption pressure, S

Sp

ε∆∆

is strain caused by a unit

change in equivalent sorption pressure. Thus in the model swelling/shrinkage strain is proportional to the equivalent sorption pressure. An equation of similar form to Eq. (15) was used to relate stress change to permeability. Sawyer et al. Sawyer et al., (1987, 1990) proposed a model, based on the porosity change, as shown below. This model is often referred as ARI model (Palmer, 2009).

( ) ( ) ( )00 0 0 0

0

1 1p m

pc p p c C C

Cφ φ φ ∆

= + − − − − ∆ (36)

Where cp is pore volume compressibility, cm is matrix compressibility. φ0 is the initial pore volume, p0 is the initial reservoir pressure, C is the reservoir gas content, C0 is the initial reservoir gas content. Pekot and Reeves (2003) extended this model to account for differential swelling behaviour, where the coal swelling is different for each gas type at the same pressure:

( ) ( ) ( ) ( )00 0 0 0

0

1 1p m k t

pc p p c C C c C C

Cφ φ φ ∆

= + − − − − + − ∆ (37)

Where ck is the differential swelling coefficient, Ct is the total reservoir gas content. Eq. (9) was used to relate the porosity change with permeability. Seidle and Huitt Seidle and Huitt (1995) proposed a model based on porosity change but only considered impact from coal swelling/shrinkage:

00 0

0 0

21

1 1l

Bp Bp

Bp Bpφ φ φ ε

φ

= + + − + + (38)

15

Eq. (9) was used to relate the porosity change with permeability. Harpalani and Chen Harpalani and Chen (1995) developed a permeability model, based on assuming swelling occurred within a constant volume, using matchstick geometry:

3*

0*

21

1

m

new

old m

l p

k

k l p

φ ∆+ =

− ∆ (39)

Where knew is permeability at pressure p, kold is original reservoir permeability, *ml is

the change in the dimension of the coal matrix block in horizontal direction with pressure, φ0 is the initial pore volume. Ma et al. (2011) related *

ml P∆ to

swelling/shrinkage strain and pore pressure change as:

( )* 00

0

11 1

1 1m l l

Bp Bpl p p p

Bp Bp E

νε ε −∆ = − + + − + − + +

(40)

Eq. (40) is then applied to Eq. (39) to calculate permeability change with respect to pore pressure change and swelling/shrinkage strain. Levine Levine (1996) developed a model with a view that the new cleat aperture width is equal to the previous cleat aperture with plus the closure due to cleat compressibility and opening due to matrix shrinkage:

( )( )

( )500 02

50

1 2new old lb b pp p p p

a a E p p

εν−= + − + −+

(41)

Where bnew is the new cleat width, a is the cleat spacing, bold is the initial cleat width, p50 is the Langmuir parameter for the swelling/shrinkage strain. Permeability is given by:

( )9 31.013 10

12newb

ka

×= (42)

If considering matchstick geometry, b/a is cleat porosity. Thus, this model is also a porosity based model. Eq. (42) can be converted to Eq. (9). Palmer and Mansoori Palmer and Mansoori (1996, 1998) assumed uniaxial strain and constant vertical stress conditions and developed a permeability model as presented below. These assumptions allow a simple, concise relationship to be derived for cleat porosity changes due to both pore pressure and coal swelling/shrinkage.

( ) 00 0

0

1 11 1m l

BpK Bpc p p c

M Bp Bpφ φ

= − − + − − + +

(43)

where φ is the porosity, 0φ is the porosity at reference pressur, cl and B are fitting parameters for the Langmuir-like model to describe volumetric strain with gas adsorption, K is the bulk modulus, M is the constrained axial modulus (Palmer and Mansoori, 1996, 1998). The following definitions were provided:

11m r

Kc f c

M M = − + −

(44)

16

(1 )

(1 )(1 2 )

EM

νν ν

−=+ −

(45)

3(1 2 )

EK

ν=

− (46)

where f is a fraction from 0 to 1, rc is grain compressibility, E is the Young’s modulus and ν is the Poisson’s ratio. Eq. (9) is then used to relate permeability to porosity. Palmer et al. (2007) modified the original P&M model to account for the exponential increase of absolute permeability, with a newly defined cm function:

1m r

g Kc f c

M M = − + −

(47)

where g is a geometric term related to the orientation of the natural cleat system. Gilman and Beckie Gilman and Beckie (2000) proposed a simplified mathematical model by assuming that an individual fracture reacts as an elastic body upon a change in the normal stress component. Other assumptions include a relatively regular cleat system, methane storage by adsorption, an extremely slow mechanism of methane release from the coal matrix into the cleats and a significant change of permeability due to desorption. Using the uniaxial strain assumption and Terzaghi formula, the 1-D effective stress change (x direction) with respect to pore pressure change and swelling strain was expressed as:

1 1

ex s

Ep S

νσ αν ν

∆ = − ∆ + ∆− −

(48)

The permeability is related to the stress change using the equation below:

0

3exp

ex

F

k

k E

σ ∆= −

(49)

where FE is analogous to Young’s modulus but for the fracture, E is the Young’s

modulus of the bulk coal, S∆ is the change of the adsorbate mass and sα is the

volumetric welling/shrinkage coefficient (thus it is assumed there is a linear relationship between amount adsorbed and swelling strain). Eq. (49) is essentially the same form as the Shi and Durucan (2004) equation (Eq. (50)) and Gray (1987) equation (Eq. (35)). Shi and Durucan Shi and Durucan (2004, 2005) developed a permeability model from the constituitive equations for isotropic linear poroelasticity (presented above as Eq. (21)). They also assumed uniaxial strain and constant vertical stress conditions and the model is presented below:

( ) ( )0 01 3 1e e sh h

Ep p

ενσ σν ν

− = − − +− −

(50)

In the Shi-Drucan model Eq. (15) with Eq.(50) is used to relate the permeability with effective stress. Cleat compressibility, cf, in Eq. (50) is referred to as the cleat volume compressibility with respect to changes in the effective horizontal stress normal to the cleats (Shi and Durucan, 2004). Cui and Bustin

17

Cui and Bustin (2005, 2007) also used linear poroelasticity (modified to include coal swelling) to derive a stress-dependent permeability model. Two models were developed from Eq. (22) assuming uniaxial strain and constant lithostatic sress; one model expressed the permeability behaviour with respect to stress and the other related to porosity change. The stress change can be written as:

( )( ) ( ) ( )0 0 0

2 1 2

3 1 s sp p Kυ

σ σ ε ευ

− − = − − + − −

(51)

Eq. (51) relates the change in the mean stress, the average over the three principal axes noting that σxx = σyy and σzz = 0. This expression for the mean stress was substituted into the exponential permeability relationship presented above which Cui and Bustin also re-derived from a consideration of the total derivative for the porosity and Jaeger et al.’s (2000) relationships for compressibility. Eq. (51) is in contrast to the assumption used in some other models that it is the horizontal stress (acting normal to cleats) that determines the response of permeability. The porosity based model was developed from the relationship for the total derivative of porosity assuming that the magnitude of the porosity was small with the mean stress defined by Eq. (51). This can be written as:

( ) ( )( ) ( ) ( )0 0 0

1 2 1 2 1 2

1 3 1 s sp pE

υ υ υφ φ ε ευ υ

− + − = + − − − − − (52)

Eq. (9) was used with Eq. (52) to provide the relationship to permeability. Robertson and Christiansen Robertson and Christiansen (2006) developed a permeability model under variable stress conditions commonly used during measurement of permeability data in the laboratory. The model was derived for cubic geometry under biaxial or hydrostatic confining pressures with consideration of swelling/shrinkage impact on permeability. The model can be written as:

( ) ( ) ( ) ( )max

0 00 0 0

1 233 ln

0

L Lf

L L

P P Pc P P P P

E P P P Pke

k

ν εφ

− + − + − − + + = (53)

Cleat compressibility is viable and is defined as:

( )( )00

0

1f

cc e α σ σ

α σ σ− − = − −

(54)

Liu and Rutqvist Liu and Rutqvist (2010) developed a coal permeability model based on uniaxial strain and constant confining stress conditions. They also introduced an internal swelling stress concept to account for the impact of matrix swelling/shrinkage on fracture aperture changes resulting from partial separation of matrix blocks by fractures that do not completely cut through the whole matrix. The stress change can be described by:

( )1 1

s fEP

ε ενσν ν

∆ − ∆∆ = − ∆ +

− − (55)

Where

( )0

11

2fc

f e σε φ − ∆∆ = − (56)

18

Eq. (15) is used to relate stress change to permeability change. Liu et al. Liu et al. (2010b) considered that the interactions of the fractured coal mass where cleats do not create a full separation between adjacent matrix blocks but where solid rock bridges are present. They accommodated the role of swelling strains both over contact bridges that hold cleat faces apart but also over the non-contacting span between these bridges. The effects of swelling act competitively over these two components: increasing porosity and permeability due to swelling of the bridging contacts but reducing porosity and permeability due to the swelling of the intervening free-faces. The fracture permeability was expressed as:

( )3

0 0

(1 )1f m

v sf f

k R

kε ε

φ −= + ∆ − ∆

(57)

where vε∆ is the volumetric strain, and 0fφ is initial fracture porosity, Rm is the

modulus reduction ratio, which is the ratio of rock mass modulus to rock matrix modulus (Liu and Elsworth, 1997). This study also considered the resultant change in coal permeability, which combined the result of the reduction in fracture opening due to coal matrix swelling and effective stress change and the decrease in effective stress due change in fluid pressure and confining stress for matrix system, as defined below

( ) ( )3

000

0

3

000

0

0

111

∆−∆−+

++

+

+= sv

f

m

fm

fm

m

m

fm

m R

kk

k

K

pR

kk

k

k

k εεφφ

(58)

Where subscriptsmand f refer to matrix and fracture system respectively. Connell et al. Connell et al. (2010) presented analytical permeability models for tri-axial strain and stress conditions, derived from the general linear poroelastic constitutive law, that include the effects of tri-axial strain and stress for coal undergoing gas adsorption induced swelling. Their approach distinguishes between the sorption strain of the coal matrix, the pores (or cleats) and the bulk coal. The models were developed from the permeability model presented above, Eq. (20)to describe the laboratory permeability measurements under various triaxial conditions. 1. Non-hydrostatic Confining Constraints

( ) ( )0

1exp 3 2 1

3Mpc r z p sk k C p p p γ ε

= − + − − −

(59)

Where MpcC is the cleat compressibility, pr is the radial confining pressure, pz is the

axial confining pressure, pp is the pore pressure, γ is the portion of matrix swelling strain on bulk swelling strain, sε is the sorption-induced bulk volumetric strain, hat

“~” means the incremental from the original state. 2. Unjacketed Confining Constraints ( pzr ppp ~~~ ** == )

( )0 exp 3 1 sk k γ ε= − ɶ (60)

3. Rigid Confining Constraint

19

a) Full rigid confining constraint, where no bulk strain changes at any direction.

( )( ) ( ) 0 exp 3 1 1Mpc p s Sk k C p Kα ε γ ε = − − + + − − (61)

Where α is Biot Coefficient. b) Rigid lateral confining constraint, where no strain changes in radial directions.

( )( ) ( )*

0

2 3 2 3exp 3 1

3 3 3 1Mpc p s z s

Kk k C p p

α νε γ εν

+ − = − − + + − − −

(62)

c) Rigid end confining constraint, where no strain changes in axial direction.

( ) ( )*0

2 1exp 3 1 1

3 9 9Mpc r p s s

E Ek k C p p

K

ν α ε γ ε + = − − + − − −

(63)

2.5 Considering anisotropy in permeability modelling The permeability models derived above assume isotropic permeability behaviour. However, permeability is typically anisotropic because of differences between face and butt cleat properties and in-situ anisotropic stress conditions. From Figure 1, it can be seen that the aperture and matrix size in the face and butt cleat directions can potentially be different, and more importantly, the connectivity of face and butt cleat system are potentially different, leading to permeability anisotropy. For example Koenig and Stubbs (1986) have reported a horizontal permeability ratio of 17:1. Wold and Jeffrey (1999) conducted a four well injection interference test to measure the overall seam permeability anisotropy and found that different seams and even different regions within a composite seam can have significantly different permeability anisotropy ratios. Permeability anisotropy plays an important role in determining the optimal arrangements for wells, in particular the orientation of horizontal wells, and the CBM production rate (Chaianansutcharit et al., 2001; Wold and Jeffrey, 1999). Furthermore, hydraulic fractures tend to propagate in the maximum stress direction, which is generally parallel the predominant structural trend and maximum permeability direction. Permeability anisotropy, if ignored, can result in under-design of fracture treatments, and inefficient well layouts. For horizontal CBM wells, and for mine gas drainage boreholes, orientation can generally be chosen to take advantage of anisotropy by drilling perpendicular to the major horizontal permeability component (Sung and Ertekin, 1987; Wold and Jeffrey, 1999). Gu and Chalaturnyk A few models have been developed to describe anisotropic permeability. Gu and Chalaturnyk (2005; 2010) developed a porosity based permeability model and applied this in coupled flow and geomechanical simulation. In order to describe the anisotropy the matrix spacing and cleat apertures for the face and butt cleats were different. A discontinuous coal mass (containing cleats and matrix) was considered to be an equivalent elastic continuum and the anisotropy of coalbeds in permeability, matrix shrinkage/swelling due to gas desorption/adsorption, thermal expansion due to temperature change and mechanical parameters, were included. The permeability can be expressed as:

20

( )

3

,,

,,0, , ,

1

1

jn

jf j

m ji

m jt tiL j f j L j

j

a

bkbka

ε

ε ε ε

+ ∆

=+ ∆ − ∆ + ∆

, , ;i j x y i j= ≠ (64)

, , , ,tL i LS i LD i LT iε ε ε ε∆ = ∆ + ∆ + ∆ (65)

( )m nf

b

aε

∆∆ = (66)

Where a is the width of the coal matrix, b the mechanical aperture of cleat, tLε∆ is the

total change of linear strain, LSε∆ is change of linear strain due to effectives stress,

LDε∆ is the change of linear strain due to sorption of gases, LTε∆ is the change of

linear strain due to temperature change.. Wang et al. Wang et al. (2009) developed a model which incorporates anisotropy in structural and mechanical properties to describe the directional permeability of coal. In this model, the mechanical and swelling deformations of coal under the confinement and stress conditions that occur in coal reservoirs were taken into account. The mechanical deformation is the stress-dominated deformation which was described using the general stress–strain relation and nonmechanical deformation is sorption-induced matrix swelling/shrinkage which was treated using a thermal expansion/contraction analogy. A strain factor, dependent on coal properties and sorption characteristics such as coal type and rank, and gas type, was introduced to improve the agreement between the strains obtained theoretically with those measured in the laboratory where unconstrained (or hydrostatic) conditions are widely used. The permeability model is described below:

( )000

, 1

cnzj ji i

i ji sn nj x j i ni j

q qE E µ µ

σ σσ σε ν λ α= ≠ =

−−∆ = − + −

∑ ∑ , ,i x y z= (67)

( )3

0,

1z

j j i ii x i j

k k ζ ε= ≠

= − ∆ ∑ (68)

Where λ is a strain factor, αsn is matrix swelling/shrinkage coefficient of the n-component gas, qµ is the amount of gas adsorption, ζ is the shape factor. Liu et al. Liu et al. (2010) developed an anisotropic permeability model under the full spectrum of mechanical conditions spanning prescribed in-situ stresses through to constrained displacement. In the model, gas sorption-induced coal directional permeability was linked into directional strains through an elastic modulus reduction ratio, Rm. This ratio defines the ratio of coal mass elastic modulus to coal matrix modulus (0<Rm<1) and represents the partitioning of total strain for an equivalent porous coal medium between the fracture system and the matrix. Where bulk coal permeability is dominated by the cleat system, the portioned fracture strains may be used to define the evolution of the fracture permeability, and hence the response of the bulk aggregate. The derived directional permeability expression is defined as:

21

∑≠

∆−+=

jiej

f

m

i

i R

k

k3

00

)1(31

2

1 εφ

(69)

where 0fφ is the initial fracture porosity at reference conditions, zyxji ,,, = .

Wu et al. Wu et al. (2010) extended their previous work to define the evolution of gas sorption-induced permeability anisotropy under the full spectrum of mechanical conditions spanning prescribed in situ stresses through to constrained displacement. In this study, the permeability for each arrangement was separate, which is in contrast to Gu and Chalaturnyk’s work (2010). The resultant expression was,

∑≠

∆−∆+∆+

−=ji

eisTf

fi

i

KT

K

Kk

k

3

00

1

3

1

3

13

11

2

1 σεαφ

zyxji ,,, = (70)

where 0fφ is the initial fracture porosity at reference conditions,. T∆ , sε∆ , eiσ∆ refer

to the change in temperature, sorption-induced strain and mechanical effective stress. Pan and Connell Pan and Connell (2011) present a model for anisotropic permeability incorporating a theoretical anisotropic coal swelling model to evaluate the impact of anisotropy in swelling on anisotropy in permeailbity. This approach is in in contrast to previous studies that have been focused on applying isotropic coal swelling in an anisotropic permeability model. Their starting point was the constitutive equation for anisotropic poroelasticity with orthorhombic symmetry (Jaeger and Cook, 1969) and with anisotropic coal matrix swelling and thermal expansion, the strain and stress relationship for the coal reservoir can be written as:

,

zj si

i ji i ij x j ii j

TE E

σσε ν ε α= ≠

∆∆∆ = − + ∆ + ∆

∑ , ,i x y z= (71)

A similar equation as Eq. (71) has also been derived by Gu and Chalaturnyk (2010) to describe the strain and stress relationship for coal reservoirs considering anisotropy. Eq. (71) can be simplified to the stress-strain equation used by Shi and Durucan (2004) for isotropic coal reservoirs. Permeability is related to stress change as:

( ),03

.0f i ic

i ik k eσ σ− −= i=x,y (72)

3. Model testing As can be seen from the previous section there is a wide, and still growing, range of coal permeability models. There are two important drivers in this research; one is the development of models that provide a practical means for explaining the behaviour of permeability for the analysis of reservoir behaviour or laboratory testing. Another important motivation for research on coal permeability behaviour is improving our fundamental understanding of the mechanisms that control permeability and thus these models may have a more theoretical focus. While testing forms an important part of establishing the relevance of new models this could comprise hypothetical analyses as well as the use of observations. For models which are intended to be a

22

practical tool for routine use, testing against observations would be expected to play an important role. Various data sets can be used to validate the developed permeability models. The most direct approach would be to compare the model predictions with permeability measurements from well tests. Another means of testing permeability models is through reservoir simulation and history matching production data or CO2 injection data in enhanced coalbed methane. However, since a reservoir model includes many processes, such as relative permeability, gas storage behaviour etc, uncertainties in these may complicate testing the permeability model. In some areas CBM production data is considered commercially sensitive and so use of this in publications is restricted. ECBM data, however, is often more accessible since several of these projects have been publicly funded with the results published. Laboratory measurements are easier to obtain and often considered alternatives to field measurements for model validation. However, it is difficult to replicate reservoir conditions, particularly the stress state, in the laboratory. When using laboratory measurements to test permeability models, differences in the boundary conditions and other assumptions have to be considered and addressed.

3.1 Measurements of reservoir permeability Field permeability measurements, especially those measured during depletion, are not well documented in the literature. The most common data that is publicly available is from the San Juan basin and this has formed the basis for much of the permeability model testing. In this section the various data sets are reviewed.

3.1.1 Black Warrior Basin permeability data

Early efforts to produce coalbed methane in the Black Warrior Basin were led by the US Bureau of Mines and were directed toward mitigating natural gas hazards in underground coal mines. Coalbed methane has been produced commercially from the basin since 1980, and the basin remains one of the world’s most prolific, with 4,180 wells that have produced 3.4 Bcm (billion cubic metres i.e. 109 m3) of gas from 19 fields as of 2004 (Pashin, 2007). The first coalbed methane wells in the Black Warrior Basin of Alabama were drilled in 1971, and a larger-scale experimental drilling project began in 1976. As of December, 1996, over 4500 coalbed methane wells had been drilled in Alabama, most of these not directly associated with coal mining (Bodden and Ehrlich, 1998). The relationship between permeability and minimum effective in-situ stress was investigated by correlating permeability data with stress data for the Cedar Cove and the Oak Grove areas. The Cedar Cove permeability values were obtained from late time falloff data of water injection/falloff tests. The Oak Grove permeability data was derived from slug testing, an analogue to the drill stem test (DST). The permeability and minimum effective stress correlation for areas in the Cedar Cove and Oak Grove fields are shown in Figure 3 and Figure 4, respectively. Although the scatter in the original data was substantial (vertical bars denote ± one standard deviation for each class interval), the average values suggest distinct trends of decreasing permeability with increasing stress (Sparks et al., 1995).

23

Figure 3. Correlation of permeability and minimum effective stress for coal seams in the Cedar Cove area (Sparks et al., 1995).

Figure 4. Correlation of permeability and minimum effective stress for coal seams in the Oak Grove area (Sparks et al., 1995). For these data the relationship between permeability and effective stress under reservoir conditions followed the exponential form of Eq. (15). However, the impact from coal shrinkage due to gas drainage does not impact on this data as the areas were not under production.

3.1.2 Australian coal basins

Figure 5 presents Enever and Hennig’s (1997) summary of permeability measurements from a program of well testing across Australia’s major coal basins. While this data does have significant scatter due to the broad range of sites that encompass distinct influences there is a clearly discernable exponential relationship with respect to effective stress that further supports the use of Eq. (15). Enever and Hennig (1997) also present comparisons between Oak Grove and Cedar Cover data of

24

the Black Warrior basin. This data does not have the influence of matrix shrinkage due to gas desorption.

Figure 5. Summary of well test permeability with respect to minimum effective stress for a range of Australian coal basins (from Enever and Hennig, 1997).

3.1.3 San Juan basin permeability data – Valencia Canyon wells

The San Juan Basin, which is located in Colorado and New Mexico, is the leading CBM production basin in the world. A well known data set of permeability was obtained from well tests in three wells in the San Juan basin Fruitland formation located in the Valencia Canyon (VC) area. These three wells, VC 29-4, VC 32-1, and VC 32-4, are located in La Plata County, Colorado. Open hole drill stem tests (DST) were conducted in each of the three wells during drilling. Shut-in tests were performed later during production to estimate the gas and water effective permeability and then the absolute permeability. The measurements found that the absolute permeability of coal natural fracture system increased significantly with gas production. This phenomenon caused gas-production rates to be many times greater than that expected from the early production history. There are two sources of evidence for increased absolute permeability with gas production for the three Valencia Canyon (VC) area wells. The first is absolute permeability estimates obtained from well-test data measured during the producing life of the wells. The second is from bottomhole pressures that increased during periods of constant gas-production rates. This observation was the opposite of that expected from conventional applications of Darcy’s law with constant absolute permeability that

k =11.73e-0.001σeh

25

predict decreasing bottomhole pressure when gas rate is constant and the reservoir pressure is drawdown. (Mavor and Vaughn, 1998) Table 1 summarises these test results for the three VC wells, the ratios between the absolute permeability and pressure estimates relative to the initial DST values are also summarised. Palmer and Mansoori model was applied by Mavor and Vaughn (1998) to describe the permeability behaviour and the results are presented in Figure 6. Although the Palmer and Mansoori model was calibrated to the VC 32-1 permeability ratio, it can also explain the permeability ratios for Wells VC 32-4 and VC 29-4 without further adjustments (Mavor and Vaughn, 1998). Table 1. Summary of absolute permeability measured through well testing for the Valencia Canyon wells (Mavor and Vaughn, 1998).

Permeability and pressure measurements alone may not reliably validate a permeability models as a range of properties need to be determined through fitting. such as the coal swelling/shrinkage behaviour with respect to pressure. Since there were no swelling measurements available for Fruitland coal for their analysis, Mavor and Vaughn (1998) assumed that the coal swelling behaviour was similar to that measured by Levine (1996) on Illinois coal. Shi and Durucan (2004) also used this data set to validate the model they developed.

Figure 6. Valencia Canyon well-test-derived permeability ratios

26

3.1.4 San Juan basin Fairway permeability measurements

McGovern (2004) reported a general empirical permeability-multiplier curve for a group of six wells, showing an exponential increase in the absolute permeability (relative to its value at a reservoir pressure of 800 psi) as the reservoir pressure was drawn down from 800 psi. Essentially the same set of data, but normalised to the permeability at 600 psi, has been presented by Clarkson and McGovern (2003) (and also presented in Shi and Durucan, 2010).

Figure 7. San Juan basin Fairway coalbed methane wells pressure-dependent permeability-multiplier curve (Shi and Durucan, 2010). This data set has been widely used to test various permeability models such as Shi and Durucan (2005, 2010), Palmer (2009), Ma et al., (2011).

3.1.5 San Juan basin, northeast of Fairway permeability data

Gierhart et al. (2007) summarised the permeability measurements from infill wells in the northeast of the production fairway, San Juan basin, as presented in Figure 8 and Figure 9. Figure 8 presents the permeability measured from 28 wells from pressure-buildup (PBU) tests with two measurements points per well: one at 3 months after the well comes online and one at 3 years, and both have been corrected to absolute permeability. The tests were all from new wells (circa 2000–2001) in coals that had already experienced some pressure depletion. Although there is considerable scatter in the data, a strong trend of permeability increasing with depletion is clear (Palmer, 2009). Figure 9 presents the permeability results from 10 wells using PBU tests with three data points per well. Shi and Durucan (2010) digitised the pressure/permeability data for the 10 wells and the data are listed in Table 2.

27

Figure 8. Absolute permeability versus reservoir depletion: 28 infill wells NE of fairway, each with two pressure-buildup measurements (Palmer, 2009).

Figure 9. Absolute permeability versus reservoir depletion: 10 infill wells NE of fairway, each with three pressure-buildup measurements (Palmer, 2009).

28

Table 2. Field permeability measurements NE of the Fairway (Shi and Durucan, 2010).

Reservoir pressure (psi) / permeability (mD) Well no. 1st point 2nd point 3rd point

A-1 923 / 3.9 693 / 4.9 568 / 5.6 A-2 791 / 3.1 601 / 10.2 439 / 30.5 A-3 730 / 1.6 628 / 2.5 488 / 3.2 A-4 703 / 7.2 452 / 16.5 352 / 20.6 A-5 669 / 1.7 510 / 2.7 441 / 2.9 A-6 655 / 4.0 439 / 18.5 300 / 28.3 A-7 499 / 9.3 431 / 11.4 276 / 11.6 A-8 4490 / 9.3 417 / 9.6 320 / 16.2 A-9 464 / 10.6 360 / 14.5 298 / 23.5 A-10 432 / 11.5 306 / 24.3 284 / 28.8 B-1 1165 / 8.2 422 / 36.2 - B-2 177 / 26.9 100 / 43.8 -

3.1.6 San Juan basin Fairway permeability data

Clarkson et al., (2007, 2008a) and Clarkson et al. (2008b; 2010) reported production data for a Fruitland coal Fairway CBM well. History matching of the flowing material balance found a 10 fold increase of the gas effective permeability from 932 psi to approximately 100 psi (see Figure 10).

1

10

100

50 150 250 350 450 550 650 750 850 950Estimated Re se rvoir Pres sure (psia)

kg/

kg@

932

psi

Field P&C/P&M Model

Figure 10. Gas permeability estimated from field data (see Clarkson et al., 2007). Base permeability is referenced to the permeability estimated from field data at the initial pressure of the well (932 psia). (Clarkson et al., 2008a)

29

This analysis was performed on production data from a period of more than 10 years, where matrix shrinkage could be expected to display a significant impact on permeability change. This data set was also used by Shi and Durucan (2010).

3.2 History matching of CBM production data Permeability can also be estimated through reservoir simulation and history matching of production data. In this section the literature presenting these studies is considered.

3.2.1 Cedar Hill Field, Northern San Juan basin

Cedar Hill is located in the north-eastern part of San Juan County, New Mexico. CBM production is from coal seams occurring within the basal portion of the Upper Cretaceous Fruitland formation (Young et al., 1991). Production commenced from the first well, Cahn 1, in the Cedar Hill field in May 1977. Six other production wells started producing gas between May 1977 and December 1985. Gas production rates were reported for three production wells, Cahn 1, Schneider B-1s, and State BW-1 by Young et al. (1991). Data has not been presented for the other four wells, which were put on production at later times. However, the bottomhole pressure data was not available from the production wells. There were three pressure monitoring wells, Cahn 2, Schneider B-1, and Leeper B-1. The layout of the wells is presented in Figure 11.

Figure 11. Well layout in Cedar Hill field (Young et al., 1991) Using this data set, a history matching exercise was used to fit the permeability and, since this is a multi-well data set, the permeability anisotropy was also determined from the history matching. Permeability anisotropy is difficult to reliably fit using single well production history matching and this usually requires observations from several wells. Young et al. (1991) found that the directional permeability ratio was about 2-4 times that found for the Cedar Hill Field from their history match results. The behaviour of permeability with depletion was not described in their simulation.

30

The water and gas production rates for wells, Cahn 1, Schneider B-1s, and State BW-1 and the reservoir pressure for monitoring wells, Cahn 2, Schneider B-1, Leeper B-1 are reported by Young et al. (1991). These can be used in history matching the reservoir permeability behaviour during depletion.

3.2.2 Boomer Fairway well B #1, San Juan basin

Palmer and Mansoori (1996) present CBM production data for a Boomer Fairway well. The gas and water production rate, and bottomhole pressure calculated from casing pressure are presented in Figure 12 to Figure 14, respectively. The very strong gas production increase with time is a characteristic of “boomer” Fairway wells. This behaviour is anomalous in that dewatering does not appear to explain the strong gas production response (Palmer and Mansoori, 1996). Furthermore, when casing pressure is reduced, as shown in Figure 14, there was a significant increase in gas production, more so than that expected from permeability behaviour where matrix shrinkage effects are neglected (Palmer and Mansoori, 1996). Automated history matching was used by Palmer and Mansoori (1996) with the Palmer and Mansoori permeability model (Eq.(43)) to determine the properties that provided the best agreement between model results and observations of production, presented in Figure 13 and Figure 14. The optimal permeability behaviour is presented in Figure 15 labelled as Case 1, where significant permeability rebound during reservoir pressure drawdown was modelled. Thus it is necessary to include a mechanism (such as matrix shrinkage) by which absolute reservoir permeability increases as the reservoir is depleted. (Palmer and Mansoori, 1996). Shi and Durucan (2004) also used the predicted permeability curve shown as Case 1 in Figure 15 to test the permeability model they developed.

Figure 12. Gas production rate for Fairway well B #1 (Palmer and Mansoori, 1996)

31

Figure 13. Water production rate for Fairway well B #1 (Palmer and Mansoori, 1996)

Figure 14. Bottomhole pressure for Fairway B #1 (Palmer and Mansoori, 1996)

Figure 15. Permeability curves to fit the production data (Palmer and Mansoori, 1996)

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3.2.3 Valencia Canyon area well VC 32-1, San Juan basin

In the previous section, permeability measurements for the three Valencia Canyon (VC) wells were reviewed. Mavor and Vaughn (1998) present the gas and water production rate, and the bottomhole pressure for well VC 32-1 as shown in Figure 16 and Figure 17. During the relatively constant gas-production-rate period between 70 and 165 days, illustrated in Figure 16, the measured bottomhole pressure in Figure 17 was increasing with time (Mavor and Vaughn, 1998). After considering various possibilities for this behaviour, Mavor and Vaughn (1998) found that increasing absolute permeability was most likely explanation.

Figure 16. Gas and water production rates for well VC 32-1 (Mavor and Vaughn, 1998).

Figure 17. Bottomhole pressure behaviour for well VC 32-1 (Mavor and Vaughn, 1998).

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3.2.4 Horseshoe Canyon, Western Canadian basin

Gerami et al. (2008) present the pressure and gas rate for a well producing from the Horseshoe Canyon coals of the Western Canadian Sedimentary basin. As this well did not produce water, any water present in the reservoir was thus immobile and therefore relative permeability did not play a role in the production behaviour simplifying the history matching exercise (Gerami et al., 2008). Reservoir properties such as the temperature, pressure, thickness, porosity, and Langmuir volume and pressure were provided by Gerami et al. (2008) as part of their analyses. The properties are listed in Table 3. However, other parameters, such as swelling/shrinkage, were not reported.

Figure 18. Production history for Horseshoe Canyon Coal (Gerami et al., 2008) Table 3. Reservoir properties for Horseshoe Canyon Coal (after Gerami et al., 2008)

Temperature (K) 289 Initial reservoir pressure (kPa) 1413 Coal density (kg/m3) 1468 Langmuir pressure (kPa) 4652 Langmuir Volume (std m3/m3) 13.49 Thickness (m) 8.99 Well radius (m) 0.0914 Porosity (-) 0.005 Initial water saturation (-) 0.1

3.3 Field ECBM data Unlike production data, where permeability change due to coal matrix shrinkage may show an impact at a late stage of production, coal swelling induced permeability loss can be observed at early stages of CO2 injection. This is due to CO2 being injected at pressures significantly above the initial reservoir pressure and the higher adsorption capacity of CO2 compared with methane that leads to significant permeability and

34

injectivity loss. Gas injectivity can be defined as the gas injection rate divided by the down hole pressure differential required to inject the gas (Mavor and Gunter, 2004). Loss of permeability and injectivity has been observed in many CO2-ECBM field trials and these field data clearly demonstrate the response of permeability to matrix swelling/shrinkage and thus are important for permeability model testing.

3.3.1 Allison Unit CO2-ECBM, San Juan basin

The Allison unit in the San Juan basin is the world’s first and by far the largest experimental (pure) CO2-ECBM pilot, with about 336,000 metric tonnes of CO2

injected over a 6-year period. The field originally began production in 1989, with CO2 injection beginning in 1995. CO2 injection operations were suspended in mid-2001 to evaluate the impact on methane recovery. (Reeves, 2003) While the Unit consists of many wells, the pilot area for CO2 injection consisted of 16 coalbed methane (CBM) producer wells, 4 CO2 injectors, and one pressure observation well (POW #2). The pilot area well pattern is illustrated in Figure 19. At the centre of the pilot area is a five-spot of CBM producers on nominal 320 acre spacing (wells 130, 114, 132 and 120 at the corners, and well 113 in the centre), with the four CO2 injectors roughly positioned on the sides of the five-spot between the corner producer wells (creating a nominal 160 acre spacing between injectors and producers). POW #2 is located on the eastern border of the central pattern, and the remaining CBM producers surround this central pattern (Reeves and Oudinot, 2005a).

Figure 19. Producer (red) /Injector (green) well pattern, Allison Unit (Reeves and Oudinot, 2005a) The producing history for the study area is shown in Figure 20. Upon commencement of the injection operations, the five producer wells in the central five-spot pattern

35

were shut in. The purpose was to facilitate CH4/CO2 exchange in the reservoir. After about six months, CO2 injection was suspended for about another six months, during which time the five shut-in producers were re-opened. These activities can be clearly identified in Figure 20. Shortly after CO2 injection began, a program of production enhancement activities unrelated to the CO2-ECBM pilot was implemented. Those activities included well recavitations, well reconfigurations (conversion from tubing/packer completions to annular flow with a pump installed for well dewatering), line pressure reductions due to centralized compression, and also the installation of on-site compression. These activities largely coincided with the dramatic increase in production observed beginning in mid-1998 (Reeves and Oudinot, 2005a).

Figure 20. Producing history, Allison Unit study area (Reeves and Oudinot, 2005a) In addition, a plot of injection rate and pressure history for injector well # 143 is shown in Figure 21. Injection was performed at a constant surface pressure, and rate was allowed to vary. Note the reduction in injection rate during early time, presumably due to coal swelling and permeability reduction. The rebound in injectivity during later times is believed to be due to overall reservoir pressure reduction and resulting matrix shrinkage that occurred near the injector wells (Reeves and Oudinot, 2005a).

36

Figure 21. Injector Well # 143 injection and pressure history (Reeves and Oudinot, 2005a) The Allison ECBM data were well documented and reservoir simulation has been performed (Reeves et al., 2003). Permeability loss due to CO2 adsorption induced swelling was modelled to describe the injection data. Other researchers have also performed reservoir simulation to characterise the permeability loss due to swelling using different permeability models (Shi and Duracan, 2004b)

3.3.2 Tiffany Unit N2-ECBM, San Juan basin

The Tiffany Unit ECBM pilot is located in La Plata County, northern Colorado, in close proximity to the border with New Mexico. While the Unit consists of many wells, the pilot area for N2 injection consisted of 34 CBM producer wells and 12 N2 injectors. The study area well pattern is illustrated in Figure 22 (Reeves and Oudinot, 2005b).

Figure 22. Tiffany unit well pattern (Reeves and Oudinot, 2005b)

37

The producing history for the study area is shown in Figure 23. The field originally began production in 1983, with N2 injection beginning in January, 1998. Production just prior to N2 injection was about 5 MMcfd, or about 150 Mcfd per well. Injection was suspended in January 2002, after four years of intermittent N2 injection, to evaluate the results. N2 injection only occurred during the winter months due to the supply constraints. A plot of injection rate and pressure for one of the injectors is provided in Figure 24. Furthermore, the methane production response to N2 injection was rapid and dramatic. During the initial injection period, total methane rate jumped from about 5 MMcfd to about 27 MMcfd, over a factor of 5. Production responses to subsequent shut-down and injection periods were also pronounced (Reeves and Oudinot, 2005b). Unlike in CO2-ECBM in Allison unit, permeability in Tiffany unit improved because N2 is less adsorbing than CH4 leading to a net matrix shrinkage effect (Oudinot et al., 2007).

Figure 23. Tiffany Unit production history (Reeves and Oudinot, 2005b)

Figure 24. N2 injection rate and pressure profile for a Tiffany Unit injection well (Oudinot et al., 2007)

38

3.3.3 Fenn and Big Valley CO2/N2-ECBM, Alberta, Canada

The Alberta Research Council have performed extensive field tests that include efforts on two wells located near the towns of Fenn and Big Valley in Alberta that penetrated Medicine River (Mannville) coal seams. In the first well (FBV 4A), 91,500 m3 of CO2 vapour was injected in 12 separate injection cycles. Although CO2 reduced the absolute permeability, injectivity actually increased in this field trial. The CO2 was allowed to soak into the coal and then the well was returned to production. Post-injection testing was to determine the CO2 sweep efficiency as well as the ECBM and CO2 storage potential. Fourteen months later, 83,500 m3 of flue gas was injected using underbalanced drilling equipment that was followed by a post injection-production test. A second well (FBV 5) was drilled 487 m north of the first well. N2 injectivity test were performed before injecting 75,483 m3 of a 53%-47% mixture of N2 and CO2. The gas mixture was allowed to soak into the coal and the well was returned to production (Mavor and Gunter, 2004). The injectivity with respect to total injected volume is shown in Figure 25.

Figure 25. Injectivity comparison (Mavor and Gunter, 2004) It was generally thought that CO2 injection would be hindered by coal swelling caused by CO2 sorption. It is found in this field trial the opposite to the case as CO2 injectivity was greater than for weakly adsorbing N2 through the use of alternating injection shut-in sequences and perhaps as the result of coal weakening (Mavor and Gunter, 2004). Coal reservoir properties are provided by Mavor and Gunter (2004) to allow history match to validate the permeability models.

3.3.4 Yubari CO2/N2-ECBM, Japan

A CO2-ECBM project was carried out near the town of Yubari on the island of Hokkaido in northern Japan. The target coal seam was a 5–6 m thick Yubari coal seam located at the depth of 900 m. The micropilot test with a single well and multi-

39

well CO2 injection tests, involving an injection and production wells, were carried out between May 2004 and October 2007. A variety of single well tests were conducted in the injection well (IW-1), including initial water injection fall-off test and a series of CO2 injection and fall-off tests (Fujioka et al., 2010; Yamaguchi et al., 2006). Following the micro-pilot at IW-1, two multi-well tests were carried out in 2004 and 2005 to investigate the impact of CO2 injection at Well IW-1 on gas production from well PW-1, located 60 m up-dip. The first multi-well test in 2004 involved two production periods of about 35 days at well PW-1, one prior to and the other shortly after the start of CO2 injection. During the 15-day injection period, the injection rates varied between 1.76 and 2.87 t/day (896–1460 std m3/day) as shown in Figure 26(a). In the second test in 2005, a much longer injection period (40 days) was sustained, with the injection rates increasing steadily from 1.69 to 3.50 t/day (861–1781 std m3/day) as shown in Figure 27(a). The measured injection bottomhole pressures are shown in Figure 26(b) and Figure 27(b) for the two injection tests. It was noted that whereas the CO2 injection bottomhole pressure rose steadily from 14.1 to 15.5 MPa in 2004, it remained almost constant at about 15.5 MPa during the 2005 test. (Shi et al., 2008)

Figure 26. 2004 multi-well test results: (a) field CO2 injection and gas production

rates; (b) field injection well bottomhole pressure (Shi et al., 2008)

Figure 27. 2005 multi-well test results: (a) field CO2 injection and gas production

rates; (b) field injection well bottomhole pressure (Shi et al., 2008)

One of the original objectives of the planned field investigations was to observe CO2 breakthrough at well PW-1. However, CO2 breakthrough was not observed. Thus, a controlled N2 flooding field trial at Yubari was performed in the Spring of 2006. The N2 flooding test consisted of three injection stages: preflooding CO2 injection to establish a baseline injectivity, N2 flooding, and post-flooding CO2 injection.

40

Concurrent with gas injection at well IW-1, gas and water were produced from well PW-1. Figure 28 presents the injection schedule and the daily amount of CO2 or N2 injected, and the gas production rates over the whole test period. It can be seen that gas production rate increased significantly in response to N2 injection as well as CO2 injection. Prior to the N2 flooding, 23.0 t of liquid CO2 were injected in three separate episodes over a 30-day period, at an average rate of 2.30 t/day. This was followed with a total of 31.94 t or 25,500 std m3 (1 t = 800 std m3) of N2 injection into well IW-1, at an increasing rate, from less than 1 t/day to nearly 7 t/day (with the last day having only 10 h of injection), over a 9-day period. Figure 29 shows early N2 breakthrough from the production well PW-1. (Shi et al., 2008)

Figure 28. Field daily amount of injected CO2/N2 gas and gas production rates (Shi et al., 2008)

Figure 29. N2 breakthrough time and molar fraction (Shi et al., 2008) It was speculated that low injectivity of CO2 was caused by the reduction in permeability induced by coal swelling. The N2 flooding test showed that daily CO2 injection rate was boosted, but only temporarily. Moreover, the permeability did not return to the initial value after CO2 and N2 were repeatedly injected. It was also indicated that the coal matrix swelling might create a high stress zone near to the injection well. Shi et al. (2008) simulated the CO2 injection behaviour and demonstrated that permeability decreased due to swelling in the field. Coal swelling in

41

N2 and CO2 for a coal sample obtained near the Yubari field trial is report by Kiyama et al., (2011). This may be used in combination with the field data to model the permeability behaviour.

3.3.5 RECOPOL CO2-ECBM project

This ECBM field experiment was in the upper Silesian coal basin in Poland. An existing coalbed methane well (MS-4) was cleaned up, repaired, and put back into production in May 2004 to establish a baseline production. A new injection well was drilled 150 m away from the production well. Initial injection of CO2 occurred in August 2004 in three seams of Carboniferous age in the depth interval between 900 and 1250m. Several actions were taken to establish continuous injection, which was eventually reached in April 2005 after stimulation of the reservoir by a frac job. In May 2005, approximately 12– 15 t/day were injected in continuous operations. A total of 692 t of CO2 were injected in the reservoir. Compared to baseline production, the production of methane increased significantly because of the injection activities as shown in Figure 30, which also shows the water production rates. The gas composition of the produced gas is shown in Figure 31. From November 2004 onward, a slow rise in the CO2 content in the production gas above the baseline was observed (maximum 10%), which could be attributed to the injected CO2. During the fall-off period in the second half of February, the CO2 content in the gas decreased to approximately 3%, still higher than the baseline content.CO2 breakthrough quickly after the frac job in April 2005. Overall recovery of methane is, however, low, which is probably related to low diffusion rates into and out of the coal. (van Bergen et al., 2006)

Figure 30. Gas production from MS-4 well between May 2004 and April 2005 (van Bergen et al., 2006)

42

Figure 31. Composition of the production gas of the MS-4 well (van Bergen et al., 2006) First injection tests with water occurred at the beginning of July 2004. Liquid CO2 from an industrial source was injected for the first time at the beginning of August 2004. From the start, it was not possible to maintain continuous injection. Required injection pressures with the applied injection rates (about 0.01 m3/min) appeared higher than initially anticipated. The injection of CO2 was therefore realised by intermittent pumping up to 9 MPa at the well head, followed by a fall-off period. In the second half of December, adaptation of the injection equipment allowed higher injection pressures up to 14 MPa (2031 psi) at the well head. Still, no continuous injection could be established. The injection was estimated at approximately 1–1.3 t/day in the buildup and fall-off cycles. Between mid-February and March 2005, injection stopped in order to have a long fall-off period to be able to determine the permeability. Despite the difficulties in the interpretation, the data clearly showed that the permeability of the coal seams decreased in time. The reduced injectivity is presumably the result of swelling of the coal after contact with the CO2. Figure 32 shows the well head pressure history before and after the frac job in April 2005 (van Bergen et al., 2006). The data, especially those before the frac job, are readily used to calibrate the permeability models.

43

Figure 32. Pressure at the injection well head, showing the intermittent injection

before the frac job and the continuous injection after the frac job (van Bergen et al., 2006)

3.3.6 CO2-ECBM/storage at San Juan Basin’s Pump Canyon

As part of the Southwest Regional Partnership for Carbon Sequestration, the Pump Canyon CO2-ECBM/sequestration demonstration in New Mexico has for objectives to prove the effectiveness of CO2 sequestration in deep, unmineable coal seams via a small-scale geologic sequestration demonstration. (Oudinot et al., 2009). A new injection well was drilled in the high-permeability fairway of prolific CBM production in the northern New Mexico portion of the San Juan Basin.

44

Figure 33. Injection well rate and well head pressure for CO2-ECBM/storage in Pump Canyon of San Juan Basin (Koperna et al., 2009, SPE 124002) The injection started on July 30th, 2008 and ended on August 12th, 2009. Figure 33 shows the injection rate and wellhead pressure injection pressure over the course of the injection period. A total of 18,407 tons of CO2 was injected. Injection rate decrease is obvious in this test. CO2 inject rate decreased from more than 3000 Mcf/d at the early stages to around 500 Mcf/d after almost 8 months of CO2 injection. Average initial permeability is about 550md. The drop of injectivity is speculated due to matrix swelling and permeability reduction as CO2 is being adsorbed onto the coal. (Oudinot et al., 2009).

3.3.7 Qinshui Basin CO2- ECBM, China

CO2 injection in a single well of a 9 well field in the southern part of the Qinshui basin, Shanxi Province, China was performed to evaluate ECBM processes in an anthracitic coal. Before the CO2 injection, the well was on production for 134 days starting on October 28, 2003. Injection of CO2 started on April 6, 2004. Liquid CO2 was injected at a pressure lower than the fracturing pressure of approximately 8 MPa. 192 metric tonnes of CO2 were successfully injected into the coal seam through 13 injection cycles, each cycle based on injecting one truck load of CO2. Each injection cycle was a daily cycle of injection and soak. A slug of 13–16 metric tonnes of CO2 was injected each day. The evaluation of the shut-in/fall-off data during the soak period between injection cycles was performed. CO2 injection was completed on April 18. The well was shut-in for an extended soak period of about 40 days to allow the CO2 to come to equilibrium with the coal. The injection history is shown in Figure 34. The well was placed on production from June 22, 2004 for 30 days. Due to a number of operational problems, the well was shut-in for a period of time during the production. The production rate is shown in Figure 35. A final shut-in test was carried out to obtain estimates of reservoir properties and near-well conditions. The well was shut-in on August 2, 2004. The self-contained pressure gauges were retrieved on August 18, 2004. The bottomhole pressure behaviour is shown in Figure 36.

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Figure 34. Injection of liquid CO2 (Wong et al., 2007)

Figure 35. Post-injection production testing (Wong et al., 2007)

Figure 36. Bottom-hole pressures measurement (Wong et al., 2007) Clear bottom-hole pressure build-up can be observed from Figure 36. This may due to the permeability loss caused by CO2 adsorption-induced coal swelling. The produced gas composition is shown in Figure 37, which is important for validate reservoir behaviour and permeability model.

46

Figure 37. Gas composition of produced gas (Wong et al., 2007)

3.4 Laboratory Permeability data Laboratory measurements offer a cost effective way of investigating permeability behaviour. However, laboratory measurements are conducted on small samples, which sometimes may not represent the field coal properties. In addition, laboratory conditions are often different to field conditions, thus using this data to validate the models of reservoir permeability should be done with care. Nevertheless, laboratory conditions are often well-controlled and readily-known and they tend to provide a more complete data set. Hence they can play an important role in improving our understanding of permeability behaviour and are useful for permeability model development. Early laboratory measurements were focused on permeability-stress behaviour using air or water. More recently measurements are using gases often with permeability and swelling/shrinkage both measured. This allows modelling of the impact of stress as well as of gas adsorption-induced swelling on permeability.

3.4.1 Dabbous et al. data

Air and water permeability of a large number of samples from the Pittsburgh and Pocahontas coals were measured at various overburden and mean flow pressures by Dabbous et al. (1974). The Pittsburgh and Pocahontas coals represent two types: a friable Pocahontas coal and a less friable, fairly solid Pittsburgh coal (Dabbous et al., 1974). To investigate the impact of overburden stress on permeability, samples were subjected to pressure cycles of loading and unloading and the permeability was measured at each point of the stress cycle. Results for two Pittsburgh coals using air are shown in Figure 38 and strong permeability hysteresis was observed. Most other coals studied by Dabbous et al., (1974) showed similar behaviour. The fast rate of decrease in permeability with increasing overburden pressure is quite evident in Figure 38. At the maximum pressure attained, the slope of the loading curve is not zero, indicating that the permeability would be further reduced by an appreciable amount at still higher overburden pressures (Dabbous et al., 1974). Strong hysteresis may mean that cleat compressibility is different at loading and unloading cycles. It may also be time dependent as shown in Figure 38 that after 36 hours, the permeability increased slightly after the release of stress.

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Figure 38. Permeability hysteresis, effect of overburden pressure for Pittsburgh coals (Dabbous et al., 1974)

3.4.2 Somerton et al. data

Permeability measurements with respect to hydrostatic stress were reported by Somerton et al. (1975) for samples from Pittsburgh seam, Virginia Pocahontas, and Lower Freeport seam (referred as Greenwich coal). Permeability using N2 and CH4 were measured at various stress conditions. Permeability-stress relationship for a selected coal samples using N2 are shown in Figure 39. The permeability measurements show a strong dependency on stress and are also stress history dependent. The greater decrease for lower permeability samples is compatible with similar observations for rocks (Somerton, et al., 1974) and this may attributed to porosity and pore compressibility.

Figure 39. Permeability of Pittsburgh coal – hydrostatic stress (Somerton et al., 1975)

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Table 4 listed the permeability-stress relationship for the coal sample using methane. Permeability of coal to methane is generally lower than the permeability to nitrogen. Sample comparison of permeability to methane and nitrogen are shown in Table 5. Reduction in permeability of 20-40 percent is generally much higher than would be expected due to molecular diameter or sorption of the gas on coal fracture surfaces (Somerton et al., 1975).

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Table 4. Permeability stress relationship using methane (after Somerton et al., 1975)

* Ruptured hassler sleeve; test specimen altered.

Loading conditions

Maximum principal

stress (psi)

Mean stress (psi)

sample 1

sample 2

sample 3

sample 4

sample 5

sample 6

sample 7

sample 8

sample 9

sample 10

sample 11

sample 12

sample 13

260 260 7.34 11.2 0.501 49.9 0.156 1.71 0.35 26.2 0.52 1.89 35.1 2.88 78.5 521 521 3.92 4.4 0.165 33.2 0.058 0.90 0.121 13.9 0.32 1.16 21.2 1.66 73.7 781 781 1.76 2.3 0.117 19.3 0.022 0.43 0.050 6.86 0.14 0.53 9.0 0.79 43.3 1042 1042 1.30 1.4 0.113 12.0 0.012 0.16 0.022 3.91 0.07 0.29 6.8 0.59 1562 1562 0.58 0.011 6.1 0.03 0.005 1.46 0.03 0.12 2.7 0.26

test 1 hydro-static loading

2083 2083 0.28 3.0 0.01 0.001 0.73 * 260 170 8.51 92.2 0.312 51.2 0.215 1.84 0.264 10.60 45.9 2.59 9.0 1.76 52.1 521 340 5.82 61.5 0.180 33.0 0.114 0.85 0.235 6.84 33.6 1.55 5.1 1.02 21.1 781 510 4.22 41.7 0.091 23.9 0.060 0.58 0.140 5.46 28.1 1.08 3.9 0.67 15.7 1042 680 3.04 32.0 0.055 17.7 0.038 0.43 0.090 4.03 25.9 0.63 3.4 0.46 1562 1020 1.60 17.7 0.026 10.2 0.012 0.18 0.034 2.46 15.4 0.40 1.3 0.24

test 2 Maximum principal stress axial 2083 1360 0.98 11.1 7.7 0.005 0.07 0.016 1.58 11.0 0.29

260 215 3.14 36.1 0.211 36.5 0.344 0.47 0.155 7.44 139.9 1.31 25.1 1.27 58.5 521 430 1.74 24.7 0.105 33.6 0.144 0.38 0.078 3.81 57.3 0.79 16.8 1.23 53.1 781 645 1.05 15.2 0.033 13.9 0.058 0.13 0.037 2.50 35.7 0.47 14.8 0.96 39.7 1042 860 0.65 9.8 0.018 10.1 0.030 0.07 0.019 1.75 26.8 0.27 11.9 0.73 31.3 1562 1290 0.31 5.7 5.2 0.008 0.02 0.005 0.82 0.12 7.1 0.54 19.4

test 3 Maximum principal stress radial 2083 1720 3.9 0.003 0.44 4.5 0.35 11.6

260 260 2.57 25.5 0.183 27.6 0.099 0.33 0.155 7.47 18.2 1.08 23.0 0.90 43.7 521 521 1.24 14.7 0.054 16.5 0.036 0.20 0.082 3.80 13.2 0.65 18.6 0.77 28.9 781 781 0.76 9.3 0.022 10.7 0.013 0.09 0.029 1.90 9.3 0.39 11.3 0.47 17.3 1042 1042 0.49 10.6 0.013 7.4 0.006 0.04 0.016 0.33 7.5 0.24 8.9 0.31 12.1 1562 1562 0.27 7.1 0.004 4.0 0.002 0.01 0.004 0.01 4.6 0.14 4.0 0.12 7.3

test 4 Hydro-static loading

2083 2083 2.8 0.004 0.90 43.7

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Table 5. Effect of type of gas flowing on permeability (after Somerton et al., 1975) Hydrostatic stress (psi)

Permeability to nitrogen (md)

Permeability to methane (md)

Permeability to nitrogen (md)

Pittsburgh No. 12 260 0.143 0.139 0.235 521 0.059 0.034 0.093 1042 0.011 0.009 0.023

Greenwich No. 2 260 24.4 14.5 24.8 521 15.3 9.5 14.5 1042 9.3 5.2 9.4

3.4.3 Rose and Foh data

Liquid permeability measurements were performed on samples from the San Juan, Piceance, and Appalachian basins as function of net stress (Rose and Foh, 1984). The descriptions of the samples are listed in Table 6. Permeability at different confining pressures (Pc) and fluid pressure (Pf) were performed for different samples, for instance, the fluid pressure was almost constant for the permeability measurements on the San Juan basin coal sample, and whilst for a Piceance coal, the confining pressure was almost constant (Rose and Foh, 1984). The experimental results are listed in Table 7 and plotted in Figure 40. The permeability decreased almost exponentially with respect to stress for some samples studied. However, for samples No. 2 and 4, permeability decreased more rapidly at lower stress regime than higher stress regime. This may suggest that cleat compressibility may also change with stress for some coals. Biot coefficient was assumed unity when plotting the Figure 40. Table 6. Description of coal samples (after Rose and Foh, 1984)

No. Basin Seam Depth (feet)

Rank Plug Axis

1 San Juan Menefee

(top) pit mined subbituminous

bedding plane

2 Piceance Cameo 2767 bituminous Face Cleat

Bedding

3 Piceance Cameo 2766 bituminous Bedding

plane

4 Appalachina Pittsburgh 300 bituminous butt cleat

Table 7. Permeability stress relationship (after Rose and Foh, 1984)

Pc Pf Pc-Pf k No. psia MPa psia MPa psia MPa md

564 3.89 306 2.11 258 1.78 3.23E-02 634 4.37 306 2.11 328 2.26 2.74E-02

1

637 4.39 307 2.12 330 2.28 2.58E-02

51

632 4.36 291 2.01 341 2.35 2.32E-02 806 5.56 305 2.10 501 3.45 1.44E-02 953 6.57 306 2.11 647 4.46 6.90E-03 974 6.72 310 2.14 664 4.58 7.90E-03

1160 8.00 312 2.15 848 5.85 2.90E-03 671 4.63 323 2.23 348 2.40 1.48E-02

2751 18.97 1535 10.58 1216 8.38 8.30E-06 2485 17.13 1500 10.34 985 6.79 9.60E-06 2252 15.53 1443 9.95 809 5.58 1.33E-05 1885 13.00 1346 9.28 539 3.72 3.89E-05

2

1864 12.85 1121 7.73 743 5.12 1.77E-05 2627 18.11 1619 11.16 1008 6.95 2.34E-04 2596 17.90 1345 9.27 1251 8.63 1.45E-04 2643 18.22 1340 9.24 1303 8.98 1.50E-04 2613 18.02 1068 7.36 1545 10.65 8.70E-05 2601 17.93 757 5.22 1844 12.71 3.90E-05 2627 18.11 476 3.28 2151 14.83 1.90E-05 2601 17.93 151 1.04 2450 16.89 9.00E-06 2610 18.00 154 1.06 2456 16.93 9.00E-06 2607 17.97 150 1.03 2457 16.94 9.00E-06 2748 18.95 1426 9.83 1322 9.11 4.80E-05

3

2753 18.98 1522 10.49 1231 8.49 5.00E-05 315 2.17 156 1.08 159 1.10 1.80E+00 310 2.14 106 0.73 204 1.41 1.50E+00 400 2.76 154 1.06 246 1.70 9.00E-01 397 2.74 108 0.74 289 1.99 7.00E-01 504 3.47 208 1.43 296 2.04 5.00E-01 481 3.32 158 1.09 323 2.23 5.00E-01 482 3.32 158 1.09 324 2.23 5.00E-01 480 3.31 106 0.73 374 2.58 4.00E-01 642 4.43 163 1.12 479 3.30 3.00E-01

4

638 4.40 99 0.68 539 3.72 2.00E-01

y = 0.098e-0.583x

R2 = 0.988

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Pc - Pf (MPa)

Per

mea

bili

ty (m

d)

San Juan Basin

Hysteresis test

y = 0.0001e-0.3246x

R2 = 0.8744

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

Pc - Pf (MPa)

Per

mea

bili

ty (m

d)

Piceance basin

Hysteresis tests

52

y = 0.0028e-0.3375x

R2 = 0.9965

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

3.0E-04

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0

Pc - Pf (MPa)

Per

mea

bili

ty (m

d)

Piceance

Hysteresis tests

y = 3.618e-0.814x

R2 = 0.921

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0Pc - Pf (MPa)

Per

mea

bili

ty (m

d)

Appalachian Basin

Figure 40. Permeability-stress relationship (after Rose and Foh, 1984)

3.4.4 Durucan and Edwards data

Coal samples from Turkey and UK were studied. Coal lumps free from visible fractures were cast in concrete and cored parallel to the bedding planes, using a 38 mm diamond bit. These were then machined to 76 mm long cylindrical specimens to fit the triaxial cell designed for this purpose. Proximate analysis and uniaxial compressive strength measurements were also carried out and the results are shown in Table 8. (Durucan and Edwards, 1986) Axial stress (σ1) was applied by a conventional testing machine through two spherical seated platens, placed one at each end. These platens also served as the gas inlet and outlet for permeability measurements via two stainless steel mesh discs placed between the specimen and the platens. Radial stress (σ3) was applied using a hand-operated hydraulic pump. Nitrogen was used as the flowing media supplied from a bottle through a 0-2.8 MPa pressure gauge to monitor the upstream gas pressure. The flow of nitrogen at the downstream end of the specimen was measured using two flow meters having 2-25 cm3/min and 40-500 cm3/min flow capacity, respectively. Table 8. Structural and mechanical properties of the coals tested (Durucan and Edwards, 1986)

53

The permeability of coal in general was found to be highly stress-dependent, decreasing as the level of stress was increased. The rate of reduction in permeability, when subjected to the same levels of stress, was not the same for coals of different seams. When a coal specimen was loaded and unloaded, two main patterns of structural changes were observed, respectively dependent upon the mechanical strength and upon the degree of propagation of existing hairline fractures under stress. Coals with a high degree of elasticity and no apparent fractures usually remained structurally unaffected after a series of loading/unloading cycles. On the other hand, highly fissured and/or low-mechanical strength friable coals usually microfractured under the stress conditions created in the laboratory. Therefore, the change in permeability of a coal specimen was either caused by the compression of the pores and flow channels only (Figure 41(a)), or by the combined result of both compression and microfracturing of the coal material (Figure 41(b)). (Durucan and Edwards, 1986). As illustrated in all the stress-permeability curves in Figure 41, the permeability of coal decreases first sharply then gently as the applied stress is increased. It is believed that the steep gradient at the beginning mainly results from the immediate closure of existing microfractures under very low stresses, and therefore only the second section of these curves was taken to represent the real behaviour of coal material under stress. Figure 42 show the first loading stress- permeability curves for all Acilik and Banbury specimens tested. Although the stress-permeability curves for each specimen follow a different path, it is evident that the gradients are similar and characteristic of the coal concerned. (Durucan and Edwards, 1986).

(a) Deep Hard coal

(b) Barnsley coal

54

Figure 41. The effect of stress on permeability (Durucan and Edwards, 1986)

(a) Acilik coal

(b) Banbury coal

Figure 42. First loading stress-permeability curves (Durucan and Edwards, 1986)

3.4.5 Seidle et al. data

Permeability-stress experiments were undertaken using coal samples from the Warrior and San Juan basins. Water was used to measurement the permeability and the results for the San Juan basin and Warrior basin samples are summarised in Table 9 and Table 10, respectively. Table 9. San Juan Basin coal samples (after Seidle et al., 1992) Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 σh

(Psi) k

(md) σh

(Psi) k

(md) σh

(Psi) k

(md) σh

(Psi) k

(md) σh

(Psi) k

(md) σh

(Psi) k

(md) 300 1.5 300 0.28 0 11.6 0 3.87 0 5.93 0 5.14 600 1.1 600 0.12 434 1.06 250 0.27 190 2.21 373 0.61 900 0.73 895 0.042 557 0.680 613 0.033 445 0.450 547 0.320 1200 0.50 1200 0.025 651 0.380 876 0.041 699 0.120 738 0.190 1500 0.24 1500 0.015 871 0.220 850 0.150 1800 0.18 1800 0.007 2100 0.12 2100 0.005 Table 10. Warrior coal samples (after Seidle et al., 1992)

σh (Psi) k (md) 250 0.64

55

530 0.35 750 0.25 1000 0.19 1750 0.12

0.001

0.01

0.1

1

0 500 1000 1500 2000

σh2-σh1

kf/

kfi

sample 1

sample 2

sample 3

sample 4

sample 5

sample 6

Figure 43. San Juan basin permeability-stress data (after Seidle et al., 1992 and Palmer, 2009) The permeability-stress is also plotted in Figure 43 and Figure 44 for San Juan basin and Warrior basin samples, respectively. As shown in the figures, the permeability-stress is non-exponential, although permeability should decrease exponentially with stress as derived by Seidle et al. (1992). The non-exponential permeability decrease with net hydrostatic stress behaviour could be because of the cleat compressibility which is not constant over the whole stress as suggested by Palmer (2009) and/or because of Biot coefficient which was set to unity in calculating the net stress.

0.1

1

0 500 1000 1500 2000

πh2-πh1

kf/

kfi

Warrior basin sample

56

Figure 44. San Juan basin permeability-stress data (after Seidle et al., 1992 with different trend lines)

3.4.6 Harpalani and Chen data

Harpalani and Chen (1997) measured permeability using an 8.9 cm diameter coal sample prepared from a well-preserved block of coal from the San Juan Basin. The effective stress was maintained at 5.4 MPa during the entire experiment and the temperature was kept constant at 44°C. Helium was used first as the gas to obtain the Klinkenberg coefficient, with a decreasing pressure range from 5.2 to 0.34 MPa. The pressure gradient across the sample was kept between 0.21 and 0.26 MPa. The permeability vs pore pressure for Helium is shown in Figure 45. Figure 46 shows the measured variation in the overall permeability of the coal sample to gas mixture with 93% CH4, 5% CO2 and 2% N2. It includes the effects of gas slippage and matrix shrinkage. The effect of slippage, which is estimated from the Helium Klinkenberg coefficient, is shown as the lowermost curve in Figure 46. The effect of shrinkage, which is obtained by subtracting the effect of slippage, is shown as the middle curve in Figure 46. It can be seen that, for a pressure decrease from 6.2 to 0.62 MPa, the total permeability of coal increased by almost 17 times, 12 times of which is due to matrix shrinkage and approximately 5 times due to gas slippage. Also, when the gas pressure is above 1.7 MPa, the effect of matrix shrinkage dominates. As gas pressure falls below 1.7 MPa, both gas slippage and matrix shrinkage effects play important roles in influencing the permeability (Harpalani and Chen, 1997).

Figure 45. Permeability as a function of the reciprocal of mean gas pressure

(measured for helium and estimated for methane) (Harpalani and Chen, 1997)

57

Figure 46. Measured variation in permeability with decreasing gas pressure (Harpalani and Chen, 1997)

3.4.7 Robertson (2005) data

The coal samples studied were subbituminous coal from Anderson seam of the Powder River basin and High-volatile bituminous coal from Gilson seam of Uinta-Piceance basin (Robertson, 2005). Cores were drilled parallel to the bedding plane. The cores are of 2-inch in diameter. All permeability measurements were made at 80° F with gas as the flowing fluid. Repeatable permeability response was achieved by varying the overburden pressure until permeability hysteresis was minimized or eliminated. During the first overburden pressure cycling for a core, there would typically be quite a bit of hysteresis with the permeability data. However, additional overburden pressure cycles reduced the hysteresis until a repeatable permeability curve was obtained as a function of net stress (overburden pressure). Figure 47 shows the results of these core preparation permeability tests and shows the permeability hysteresis diminishing with repeated tests for the Anderson 01 core (a) and the Gilson 02 core (b) (Robertson, 2005). Cleat compressibility data can be obtained from the above measurement shown in Figure 47.

58

Figure 47. Results of core preparation permeability tests showing permeability hysteresis diminishing with repeated tests (Robertson, 2005) Another series of experiments was conducted where pore pressure was varied while holding constant the confining pressure at 1000 psia. High net stress was selected as the starting point for initial stress condition to be consistent with the varied overburden pressure tests, which required the initial pore pressure to be low. Because pore pressure was varied, sorption of gases and the resulting strain was expected to affect the permeability of each of the cores to a different degree depending on the sorbing gas. Permeability was monitored in real time and pressure was changed only after equilibration of the permeability values. The results are shown in Figure 48.

59

Figure 48. Model results compared to permeability data. Confining pressure was 1000

psia and temperature was 80° F

Samples from the same coal blocks in the permeability measurements were used to measure the linear strain in coal induced by the sorption of gases using to an optical method. Measurements of unconfined strain were performed for two coal samples subjected to CO2, CH4, and N2 at pressures up to 1000 psia (6.8 MPa). When comparing the strain curves for a given coal sample caused by the sorption of different gases, CO2 adsorption caused the highest strain, followed by CH4, and N2 adsorption as shown in Figure 49. The Langmuir like equation parameters for the swelling curves for the two coals at different gases are listed in Table 11.

60

Figure 49. Strain curves for two different coals subjected to three different pure gases at various pressures. Solid circles are strain data for the Anderson coal and open circles are strain data for the Gilson coal. Lines are model fit using the Langmuir like equation. (Robertson, 2005).

Table 11. Langmuir strain constants for sorption-induced strain for Anderson and Gilson coals at 80°F (26.7°C) (Robertson, 2005)

Gas Coal Smax PL, psia Anderson 0.03447 529.19

CO2 Gilson 0.01596 581.32 Anderson 0.00777 618.98

CH4 Gilson 0.00958 1070.82 Anderson 0.00429 1891.44

N2 Gilson 0.00112 348.41 Swelling strain subjected to mixed gas adsorption (51% N2 + 49% CO2) was also reported by Robertson (2005) and is shown in Figure 50. However, adsorption isotherms were not reported for either the pure gases or the mixed gas. Thus the relationship between adsorbed amount and swelling strain could not be examined.

61

Figure 50. Strain of Anderson and Gilson coal caused by the adsorption of a gas mixtureof 51% N2 and 49% CO2 (Robertson, 2005) Model fit using three permeability models, Shi & Durcan model, Palmer & Mansoori model, and Seidle & Huitt model, were used to fit the permeability results, which are also plotted in Figure 48 (Robertson, 2005). However the model fits were not good, due to the experimental conditions different to the models assumed uniaxial conditions. In the experimental conditions, the coal was allowed to expand to the confining fluid. Thus the cleat was not closed as much as the models would expect. Hence the data shows more rebound but models would predict decline as pore pressure increases.

3.4.8 Mazumder et al. data

Two coal samples are measured in this work. The samples used were from the South Wales coal field (Selar Cornish) in the U.K. and the Warndt Luisenthal coal field in Germany. The sample properties are listed in Table 12. Permeability with respect to pore pressure change was measured for the two coal samples. The effective stress was maintained at around 6 MPa for the Warndt Luisenthal coal and around 4 MPa for the Selar Cornish coal. The results are shown in Figure 51. Permeability increased significantly with pore pressure while the effective stress was constant. This is on the contrast to Harpalani and Chen (1997) results, which shows permeability decrease with pore pressure increase at constant effective stress condition. Table 12. Sample Properties (Mazumder et al., 2006) Sample Rank (%

Rmax) Length (mm)

Diameter (mm)

Specific surface area (m2/g)

Micropore volume (cm3/g)

Selar Cornish

2.41 268 72 208 0.071

Warndt Luisenthal

0.71 154 74.78 104 0.03545

62

(a) Warndt Luisenthal coal

(b) Selar Cornish Coal

Figure 51. permeability vs pore pressure (Mazumder et al., 2006) Swelling was also measured on the coal samples after the sample was measured with helium compliance, which was used to estimate the mechanical compliance coefficient of the coal (Mazumder et al., 2006). This was used to single out the effect of adsorption induced coal swelling from compression. The Helium compliance results are shown in Figure 52. Experiments were performed to determine the swelling of coal with CO2 as a function of the mean pore pressure and constant effective stress, which was kept at 4 MPa. The results for swelling on the two coals are shown in Figure 53. However, the measured strain was not able to be fit by the Langmuir like equation (labelled as theoretical strain in Figure 53).

(a) Warndt Luisenthal coal

(b) Selar Cornish Coal

Figure 52. Volumetric strain response to the helium injection (Mazumder et al., 2006)

(a) Warndt Luisenthal coal

(b) Selar Cornish Coal

Figure 53. Experimental and theoretical strain (Mazumder et al., 2006)

63

3.4.9 Pini et al. data

Pini et al. (2009) presented gas permeability results on coal cores under hydrostatic conditions, using a transient step method. Helium, N2, and CO2 have been injected at pressure ranging from 10 to 80 bars and at confining pressures varying between 60 and 140 bars. The experiments with helium were used to study the mechanical compliance of the coal core, whereas those with the adsorbing N2 and CO2 to study the effects of adsorption and swelling on the flow dynamics. Coal from the Monte Sinni coal mine in the Sulcis Coal Province (Sardinia, Italy) was used. The transient step method was used to carry out the flow experiments. This technique has been widely used to measure the permeability of rocks, in particular of low permeability rocks, due to the advantage of measuring pressures instead of flow rates in a high-pressure experiment (Pini et al., 2009). Results showed increase in permeability with decreasing effective pressure on the sample and, when an adsorbing gas was injected, a reduction in permeability caused by swelling, with CO2 having a stronger effect compared to N2. The permeability and swelling strain results are shown in Table 13 Table 15 for Helium, CO2 and N2, respectively. Adsorption results were also measured and reported for the samples by Pini et al. (2009).

Table 13.Porosity (swelling strain?) and Permeability Data at 45 C Obtained at the

End of Each Transient Step When Helium Is Injected (Pini et al., 2009)

64

Table 14. Porosity (swelling strain?) and Permeability Data at 45 C Obtained at the End of Each Transient Step When CO2 Is Injected (Pini et al., 2009)

Table 15. Porosity (swelling strain?) and Permeability Data at 45 C Obtained at the End of Each Transient Step When N2 Is Injected (Pini et al., 2009)

3.4.10 Pan et al. data

In this work a triaxial cell was used to measure gas permeability, adsorption, swelling and geomechanical properties of coal cores at a series of pore pressures and for CH4, CO2 and helium with pore pressures up to 13 MPa and confining pressures up to 20 MPa. Properties for the permeability models such as cleat compressibility, Young’s modulus, Poisson’s ratio and adsorption-induced swelling are calculated from the experimental measurements. Measurements on an Australian coal showed that permeability decreases significantly with confining pressure and pore pressure. The permeability decline with pore pressure is a direct result of adsorption-induced coal swelling. Coal geomechanical properties show some variation with gas pressure and gas species (Pan et al., 2010). The measurements show permeability declines with increasing pore pressure at constant effective stress in response to coal swelling with gas adsorption with the magnitude of the decline depending on the gas type. Figure 54 shows the cleat compressibility results is also gas type dependent, which suggests that modelling of gas permeability in coal should also consider the impact from different gases.

65

Figure 54. Cleat compressibility by helium, methane and CO2

3.4.11 Huy et al. (2010) data

CO2 Gas permeability measurements were performed on coal samples from Vietnam, Australia and China using the relative permeability testing apparatus from Core Laboratory, USA to investigate the effect of effective stress on gas permeability. The stress load on the coal core sample was increased from 1 to 6 MPa. The average gas pressure (pore pressure) changed from 0.1 to 0.7 MPa depending on the effective stress. The results are shown in Figure 55 to Figure 57 for Vietnamese, Australian and Chinese coals, respectively. All results show that permeability decrease exponentially with respect to effective stress with larger reduction in low permeability coal samples. This may be attributed to the small size of pores. When the effective stress increases, the flow channels within micro-fractures become narrower, and some may close completely. Consequently, the permeability decreases dramatically at high effective stress levels, and gas permeability may even become almost zero when the effective stress is more than 5 MPa (MK-1 sample).

66

Figure 55. Gas permeability versus effective stress of Vietnamese coal (Huy et al., 2010)

Figure 56. Gas permeability versus effective stress of Australian coal (Huy et al., 2010)

Figure 57. Gas permeability versus effective stress of Chinese coal (Huy et al., 2010)

3.4.12 Kiyama et al. data

In order to verify the permeability and injectivity loss in the Yubari field ECBM trial in Japan, laboratory measurements of gas permeability and coal swelling strain were carried out. Coal cores were taken from a large coal block which was mined from the Bibai seam at an open-cut mine also located in the Ishikari basin. A series of measurements of CO2 and N2 injection were performed to displace previous adsorbed N2 or CO2 (Kiyama et al., 2011).

67

Figure 58 presents the relationship between pore pressure and permeability during the tests. In the figure, G stands for gas and SC stands for supercritical. As the volume of the pore fluid injected into the core was much larger than the pore volume in the three injection tests, the pore fluid previously stored in the core was considered to be completely displaced by the injected fluid. Before the first CO2 injection test was performed, the permeability was estimated at 5.6×10−4–8.5×10−4 Darcy with an effective stress of 1 MPa and a pore pressure of 10 MPa under N2 flooding conditions. When supercritical CO2 was injected into the core saturated with N2, the permeability decreased to 2.2×10−4–2.4×10−4 Darcy. After the N2 was re-injected to the CO2 saturated sample, the permeability was estimated at 2.4×10−4–2.6×10−4 Darcy and only slight permeability recovery was observed compared to the permeability measured during the CO2 injection test. A second CO2 injection was performed to the N2 saturated sample, the permeability was 1.8×10−4–2.3×10−4 Darcy when flow reached stead state. Slight permeability decrease was observed, but was comparable to the permeability measured during the first CO2 injection test.

Figure 58. Relation between pore pressure and permeability. Abbreviation; G: gas, SC: supercritical. When Supercritical CO2 was first injected into the coal core sample saturated with N2, the strain gauge closest to the inlet plane first detected a swelling displacement of about 5000–8000 µ, followed by the other gauges in order of distance, within 30 min after injection. Then when N2 was injected into the core saturated with CO2, a shrinking displacement of about 5000–7500 µ was detected sequentially by strain gauges closest to the inlet plane. When supercritical CO2 was again injected into the core saturated with N2, the strain gauges detected the same swelling displacements as those prior to the second N2 inject test. These strain results can be used with the permeability results to validate permeability models.

3.5 Laboratory ECBM data

3.5.1 Tsotsis et al. data

Experiments were performed to study CBM core behaviour during CO2 sequestration for a highly volatile bituminous core sample from Jamestown coal seam in Illinios (Tsotsis et al., 2004). After degassing by vacuuming, the core was allowed to equilibrate in the CH4 atmosphere until it reached equilibrium. The core was then loaded with additional CH4, and the procedure was repeated for many cycles until the

68

core completely saturates with methane at the desired pressure and temperature. Once the sample was completely saturated with CH4, the CO2 sequestration experiment began. The pressure downstream of the core and either the CO2 injection rate or the pressure upstream of the core can be controlled. As the CO2 flows into the core, the exit gas stream’s flow rate and composition are continuously measured. Figure 59 shows the data from a simulated CO2 sequestration experiment. In this experiment, carried out at room temperature (22-23 °C), the downstream and upstream pressures were kept constant at 25.14 and 28.59 bar, respectively. the composition of the exit stream is shown as a function of the dimensionless exit volume of gas, which is defined as the volume of gas exiting the autoclave divided by the amount of methane gas that was uptaken by the sample prior to the initiation of the simulated CO2 sequestration experiment; the latter is calculated on the basis of the total amount of methane loaded into the system minus the methane volume corresponding to the “dead space” in the system.

Figure 59. Methane (empty diamond) and carbon dioxide (solid dot) volume fractions

vs dimensionless exit volume of gas (Tsotsis et al., 2004)

69

Figure 60. (a) Methane and carbon dioxide volume fractions and methane recovery vs dimensionless exit volume of gas. (b) Dimensionless sequestered amount of carbon

dioxide vs dimensionless exit volume of gas (Tsotsis et al., 2004) Figure 60 (a) shows another simulated CO2 sequestration experiment, in which the downstream core pressure was kept constant in the range of 28.59-28.93 bar and the CO2 injection rate was set equal to 86.8 ml at standard conditions. In addition to the gas composition in Figure 60 (a), dimensionless methane recovery ratio was also plotted. Figure 60 (b) shows the dimensionless sequestered amount of CO2 (defined as the ratio of CO2 injected minus the amount exiting the autoclave divided by the total amount of methane originally injected in the autoclave). At the point the experiment was terminated, its value was 0.91, which upon subtraction of the dead volumes for both methane and carbon dioxide gives a value of 1.95 molecules of CO2 that were sequestered in the core for every molecule of methane that was produced. This is in very good agreement with the sorption experiments. The laboratory ECBM experiments can be used to characterise the permeability change vai history matching the injection and production data. Permeability behaviour due to swelling/shrinkage can be more readily examined since these experiments were often performed at constant pore and confining pressures.

3.5.2 Jessen et al. data

The samples from a coalbed in the Powder River Basin, Wyoming were characterized by methane, carbon dioxide, and nitrogen sorption isotherms, as well as porosity and permeability measurements. The samples were ground coal material with a mean size of the coal particles of 0.25mm. Coal particles were formed into a coalpack by pressing the ground coal into cylindrical shapes (Jessen et al., 2008). A series of ECBM experiments were conducted using N2 or CO2 to displace CH4. However, since these cores were not natural coal cores thus cleat structure was not preserved, these data were of limited value to characterise permeability behaviour.

3.5.3 Yu et al. data

The coals used in this experiment originated from the Jincheng and Luan mines, Qinshui basin, North China, which was selected for small-sized pilot, the Sino-Canada cooperative project on “CBM technology development/CO2 sequestration in China” and was the first CBM basin to be developed commercially in China (Su et al., 2005). CO2 injection at 4.5 MPa followed after CH4 was injected to the sample. The desorbed volumes and volume fraction of CO2 and CH4 in desorbed gases are shown in Figure 61 for Jincheng coal (A) and Luan coal (B). As the outlet pressure of the coal column decreases to 0 MPa from 4.16 MPa for Luan coal and 4.01 MPa for Jincheng coal, the desorbed-CH4 volume is 2619 cm3 for Luan coal and 3140 cm3 for Jincheng coal, respectively, and the desorbed CO2 volume is 262 cm3 for Luan coal and 260 cm3 for Jincheng coal, respectively. As compared with CH4 desorption, the CO2 desorption is very small, accounting for 7.60% and 9.08% of the desorbed gas mixture for Jincheng coal and Luan coal, respectively. The initial CH4 displacement with CO2 is not associated with CO2 release, which shows no CO2 breakthrough in the coal column at beginning of CH4 desorption. With increase of replaced-CH4 volume, the discharge capacity of CO2 increases slowly. With CO2 breakthrough, the volume

70

fraction of CO2 increases slowly during CH4 displacement, which expresses constant CO2 breakthrough as compared with CH4 desorption.

Figure 61. Desorbed volume of CH4, CO2 and their volume fraction during gases

desorption on Jincheng coal (A) and Loan coal (B) (Yu et al., 2008)

3.5.4 Mazumder and Wolf (2008)

Five different flooding experiments were conducted on coal cores drilled from the samples mentioned from the Beringen coal mines (Beringen 770) in Belgium, the Silezia coalfield in Poland (Silezia 315 II) and the Tupton coalfields in UK (Mazumder and Wolf, 2008). The details of the coal cores and their experimental conditions are in listed in Table 16. Table 16. Details of the coal cores used for the differential sorption experiments, the

experimental conditions, injection rates and methane saturation (Mazumder and Wolf, 2008).

The experiments range from sub-critical to super-critical CO2 conditions. Experiments I and II were conducted on the Beringen 770 sample from Belgium. Both experiments were conducted on dry coal samples. Experiments III and IV were conducted on the Silezia 315 II sample from Poland. Experiment III was carried out on moisture-equilibrated coal sample while experiment IV was carried out on a dry coal sample. The effect of moisture is evident from the low sweep efficiency. Experiment V was performed on a dry coal sample from UK (Tupton) at a very high mean pore pressure of 23 MPa. The test procedure to measure permeability change during the differential sorption experiments, involved the simultaneous injection of CO2 and production of the mixed gas under steady pressure conditions (Mazumder and Wolf, 2008). Because gas pressure varied across the sample, the average of the two end gas pressures was used in the calculation of the effective stress. As permeability is a

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function of the effective stress, it was kept constant during the experiment. The flow measurements for a particular permeability step were only used when all equilibrium conditions were satisfied. Figure 62 shows the estimated permeability variation for dry Silezia 315 II coal under constrained conditions using experimentally determined permeability data from experiment IV. More experimental data can be found in Mazumder and Wolf (2008) and Mazumder et al. (2008).

Figure 62. Estimated permeability variation for dry Silezia 315 II coal under constrained conditions using experimentally determined permeability data from experiment IV (Mazumder and Wolf, 2008)

3.5.5 Connell et al., data

The core floods or ECBM were performed on a coal sample from Bowen basin, Australia at two pore pressures, 2 MPa and 10 MPa, and involve either nitrogen or flue gas (90% nitrogen and 10% CO2) flooding of core samples initially saturated with methane. At the end of the nitrogen floods the core flood was reversed by flooding with methane to investigate the potential for hysteresis in the gas displacement process. Figure 63 shows one of the experimental results using pure N2 to displace Methane and reversed core flood at 2 MPa. More results using flue gas injection and at different pressures can be found in Connell et al. (2011). To describe the permeability behaviour during the experiment, The Connell, Lu and Pan hydrostatic permeability model (Connell et al., 2010) was applied in the reservoir simulator SIMED II. Excellent agreement was obtained between simulated and observed gas rates, breakthrough times and total mass balances for the nitrogen/methane floods. Prior to the core flooding an independent characterisation programme was performed on the core sample where the adsorption isotherm, swelling with gas adsorption, cleat compressibility and geomechanical properties were measured. This information was used in the history matching of the core floods to reduce the amount of unknown parameters required by the history matching (Connell et al., 2011).

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Figure 63. Simulated and measured gas rates (left) and upstream pressure, Pup, and downstream pressure, Pdown, (right) for the binary core floods at 2 MPa: the top figures are for N2 displacement of CH4; the lower figures for the subsequent core flood where CH4 displaced N2 (Connell et al., 2011)

4. Discussion As can be seen from the review above there has been significant work on modelling of coal permeability and good progress with field and laboratory measurements for model testing. However, due to the complex nature of permeability in coal reservoirs, there are still areas where there is uncertainty and a need for further research. The sections below consider some topics for further work.

4.1 Reservoir strain and stress conditions During production or enhanced coalbed methane recovery the pore pressure and gas content change. Pore pressure changes lead to compressibility responses from the solid and pore structure of the coal. At the same time gas content changes lead to strain from the coal matrix. Within the reservoir these strain changes are coupled to changes in the stress state; for a coal that is isotropic and responds in a linear elastic manner, this coupling can be described by Eq. (21). In order to derive concise reservoir models for coal permeability, for example Eq. (43) and Eq. (50), two assumptions are commonly invoked; uniaxial strain and constant overburden stress. Uniaxial strain is where strain within the horizontal plane is zero but vertical strain may occur (Palmer and Reeves, 2007). Constant overburden stress means that the stress due to the weight of the overburden geology overlying a reservoir does not change. An important question is how accurate is this assumption, particularly in the area local to a production or injection well, where the rest of the coal reservoir may act as an elastic boundary rather than strictly comply with uniaxial strain.

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Furthermore, how shear stress in the roof and floor of the coal seam due to coal deformation could impact on the assumption of constant overburden stress. To investigate these questions Connell (2009) used a coupled flow and geomechanical model and found that the vertical stress is not constant close to the wellbore, due to stress arching, and in an unfractured wellbore the permeability increases by 2–3 times. This result suggests that constant overburden stress may introduce some inaccuracy, especially near wellbore. Permeability prediction, in turn, will be significantly different using different overburden stress assumptions. Constant volume is another assumption that has been employed. With this the decrease in the size of the coal matrix due to compression would be equal to the increase in the dimension of cleat aperture (Ma et al., 2011). Thus, there is no volumetric change for the coal seam during pore pressure drawdown in the primary CBM recovery process. However, the coal reservoir volume may reduce from 0.05% to 0.28% from the initial state (Massarotto et al., 2009) and this reduction may be mainly the result of change in the cleat porosity. Hence, the accuracy of the constant volume assumption will require further investigation. Coal failure can increase permeability rebound. It has been proposed that drawdown can induce failure in the reservoir due to increases in stress resulting from matrix shrinkage. Failure can lead to increased permeability via the phenomenon of dilatancy (Palmer and Mansoori, 1996). This effect has been observed in the laboratory in experiments which attempt to replicate uniaxial strain conditions. However, coal failure occurs relatively readily in the laboratory when CO2 displaces methane under uniaxial strain conditions. A possible explanation is that differential expansion occurring on microscopic levels, due to the heterogeneous and anisotropic nature of coal, result in sample failure. There appears to be a strong similarity between the observed behaviour and thermal cycling in hard rocks, which is known to result in weakening of the rock. Regardless of the explanation, the impact of this on field applications could be significant. If coal fails readily with CO2 injection, then it is likely to affect the coal permeability and injectivity (Harpalani and Mitra, 2010). A challenge is representing this behavior in coal permeability modeling. Nevertheless, the coupled flow and geomechanical process, although complex, may be a useful tool to reveal more about reservoir stain and stress change during primary and enhanced CBM process. This method may even be extended to include coal failure to investigate its impact on coal permeability. Thus, the results from coupled flow and geomechanical process will help to further develop analytical permeability model, which is preferred in reservoir simulation due to its simplicity.

4.2 Effective stress and Biot Coefficient In most of the previous permeability modelling work, the Biot coefficient or effective stress coefficient is often set as unity for coal. Laboratory measurements have shown that Biot coefficient is less than unity (Zhao et al., 2003; Chen et al., 2011). From Biot theory of poroelasticity (Biot, 1941), Biot coefficient can be determined by (Nur and Byerlee, 1971; Robin, 1973):

1 sK Kα = − (73)

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where K is bulk modulus of the bulk rock, Ks is the bulk modulus of the solid grain material. It should be noted that Eq. (73) is defined for single porosity rocks. For dual porosity material such as coal, there are three bulk modulus: (1) bulk modulus of the bulk coal including cleats (K); (2) bulk modulus of the coal matrix (Km); (3) bulk modulus of the coal solid grain (Ks). How these three bulk modulus would impact the effective stress coefficient is not well understood. However, the impact of the effective stress coefficient on permeability modelling is obvious. Assuming effective stress coefficient to be unity will lead to overestimating the effective stress change during pressure drawdown. Thus it may lead to overestimation of permeability change. Connell et al. (2010) presents measurements of the solid and bulk modulus and the resultant Biot coefficient for a Bowen Basin and a Hunter Valley coal sample. The Biot coefficient ranged from 0.8 for the Hunter Valley sample and 0.87 for the Bowen Basin coal. The permeability calculated using these values of the Biot coefficient was compared to that calculated using the Shi and Durucan model where Biot is equal to one. It was found that the differences in permeability were up to 15%. Another aspect of impact of effective stress on permeability is what effective stress to use the permeability modelling. For instance, Shi and Durucan model (2004) applies the horizontal stress change. Cui and Bustin (2005) model applies averaged stress change including the horizontal and vertical stress changes. Mazumder et al. (2006) point out that changes in cleat permeability are primarily controlled by the prevailing effective horizontal stress that acts across the cleats. However, what is the impact of effective stress change parallel to the cleat on permeability requires further investigation. This may become even more important if considering face and butt cleat properties, anisotropy in coal’s geomechanical properties and so on.

4.3 Cleat compressibility Permeability is directly related to the cleat compressibility through the stress-permeability relationship, Eq. (15). Thus it is one of the most important parameters in permeability modelling. To a certain extent, cleat compressibility is directly related to cleat porosity and the elastic behaviour of the cleat (Harpalani, 1999). Currently, it is broadly accepted that the cleat compressibility is not constant. Laboratory measurements show that cleat compressibility changes with respect to effective stress (eg., Durucan and Edwards, 1976), gas type and gas pressure (eg. Pan et al., 2010a). McKee et al., (1988) proposed an exponential equation (Eq. (54)) to describe cleat compressibility change with respect to stress change. Robertson and Christiansen (2006) applied this equation in their permeability model. Shi and Durucan (2011) have applied McKee et al.’s exponential relationship between stress and cleat compressibility to model a set of field permeability data and achieved good results. However, the possibility of relating the cleat compressibility to the cleat porosity and cleat geomechanical properties has not been addressed. Furthermore, the relationship of cleat compressibility to gas type, gas content and gas pressure has not been considered due to the limited measurements available. Moreover, how cleat compressibility changes with two phase flow of gas and water is not understood. Although this is out of the scope of the current work on permeability modelling, it is of importance for modelling gas flow in coal.

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4.4 Coal geomechanical properties It is possible that the coal strength could increase during drawdown (i.e. Young’s modulus might increase) since cleats are unable to close on asperities, coal fines or mineralisation. This would diminish the effect of stress on permeability (Palmer and Mansoori, 1996). Laboratory measurements have demonstrated that coal becomes stiffer with increased confining stress (Gentzis et al., 2007; Massarotto et al., 2011; Pan et al., 2011). The Young’s modulus of a coal core sample in laboratory testing was found to increase more than 20% from 1 MPa effective stress to 3 MPa effective stress for an Australian coal from the Hunter Valley (Pan et al., 2011). In a second sample from the Bowen Basin the Young’s modulus increased significantly with effective stress from 2 MPa to 12 MPa (Massarotto et al., 2011). This will need to be considered in permeability modelling when effective stress changes become significant, due to the nonlinear elastic behaviour for coals especially for low rank coals. Coal’s geomechanical properties, such as Young’s modulus may also change with gas type and gas pressure and temperature (Pan et al., 2011; Viete and Ranjith, 2006). However, this behaviour is not well studied or understood.

4.5 Anisotropy in swelling/shrinkage and permeability To date the focus with modelling coal permeability has been on isotropic behaviour. However, coal is typically highly anisotropic for a range of properties, including permeability. Recently there has been some work on permeability modelling for anisotropic conditions. This is more important for lower rank coals whose coal properties are somewhat more anisotropic than high rank coals, for example, in the anisotropy of swelling (Day et al., 2008). A few anisotropic permeability models have been developed over the past few years. However, the impact of directional swelling (swelling anisotropy) on anisotropic permeability has not been well addressed. Representing the anisotropic response of permeability is particularly relevant for horizontal wells, or multi-lateral horizontal wells, a technology which has a growing importance for CBM production. The permeability perpendicular to the well branch plays a key role for production and its change with directional stress conditions and directional swelling behaviour an important aspect in predicting production. Furthermore, how directional coal properties, such as the Young’s modulus and cleat compressibility, change under reservoir conditions needs to be investigated. This also presents challenges for laboratory measurements, for instance, how to measurement cleat compressibility separately for face cleat and butt cleat. A three dimensional set up may be useful in measuring anisotropic behaviours (Massarotto et al., 2010). In most of the modelling work, vertical permeability is often ignored since bedding planes do not normally have a role in conducting fluids due to the overburden weight and thus are of little interest in the flow of gas in coal (Harpalani, 1999). Gash et al., (1993) reported that the ratio of the face cleat to the vertical permeability was 144.3, and the butt cleat to vertical permeability ratio was 78.2 for one coal. For this sample the face to butt cleat permeability ratio was 1.84 (Mavor and Gunter, 2006). Compared to the permeability in the horizontal plane, vertical permeability is almost negligible for this coal. However, vertical permeability is often assumed to be 1/10 of the horizontal permeability (eg., Shi and Durucan, 2008). Thus, vertical permeability

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may become important especially for thick coal seams and for horizontal well applications where vertical flow plays a significant role.

5. Conclusions Representing the behaviour of the absolute permeability of coal is central to a range of gas migration questions in coalbed methane. The developments in modelling coal permeability and the data used to test the models have been reviewed in this article. This active area of research has led to the development of a number of permeability models and this is still growing. Some models have proven popular with practitioners such as the Palmer-Mansoori and Shi-Durucan models. These concise models integrate the effects of matrix shrinkage and pore compressibility into one closed form equation. However coal permeability is complex being coupled to gas content and to the geomechanical behaviour. There are also other effects that are poorly understood such as anisotropy in swelling and geomechanical properties, which have only recently been considered but where more work is warranted. While it is possible to derive increasingly complex models that better represent the detail of permeability behaviour, this has to be balanced with the ability to meaningfully estimate the properties involved. The objective is to optimise model complexity (and parameter requirements) with the accuracy of representing gas migration. Thus an important step with any model is establishing how well it represents the reality of reservoir behaviour; that the assumptions and approximations implicit and explicit in model development still allow the process of interest to be satisfactorily represented. This is extremely challenging for gas migration in coal reservoirs as these are expensive to observe and thus observations tend to be limited and subject to uncertainty. It is clear that further work is required in order to improve our understanding of the reservoir behaviour of coal permeability.

Acknowledgement

Financial support from CSIRO Advanced Coal Technology Portfolio is acknowledged. The authors also thank Mr Zhongwei Chen, Mr Guiqiang Zheng and Ms Hongyan Qu for their help during the preparation of this review article.

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