Coupled flow and geomechanical processes during gas production from coal seams

International Journal of Coal Geology 79 (2009) 18–28

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International Journal of Coal Geology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i j c o a l g e o

Coupled flow and geomechanical processes during gas production from coal seams L.D. Connell CSIRO Petroleum, Ian Wark Laboratory, Clayton, Victoria, Australia

a r t i c l e

i n f o

Article history: Received 7 April 2008 Received in revised form 27 March 2009 Accepted 28 March 2009 Available online 5 April 2009 Keywords: Coal seam methane Coupled flow and geomechanics Reservoir simulation Coal permeability

a b s t r a c t Permeability in coal seams is sensitive to stress and pore pressure changes. An additional influence on this behaviour is the nature of the coal matrix to shrink with gas desorption and swell with adsorption. Concise relationships for permeability have been developed which incorporate these mechanisms, some of which are derived from a geomechanical basis such as the Shi–Durucan model and the Palmer–Mansoori model. While these expressions are attractive approaches for defining coal permeability during gas migration, the geomechanical behaviour has been simplified by assuming uni-axial strain and constant vertical stress. In this paper a coupled numerical model is developed and used to investigate the applicability of these geomechanical assumptions for gas drainage from coal seams. The modelling approach involved coupling the existing coal seam gas reservoir simulator, SIMED II, with the geomechanical simulator, FLAC3D. While SIMED II was used to simulate gas migration in a hypothetical coal seam and a series of production scenarios, FLAC3D simulated the geomechanical response of the coal and the adjacent non-coal geological formations to fluid pressure and gas content changes imported from SIMED II. The simulations, which considered a range of property values relevant to the San Juan basin, found that while the assumption of uni-axial strain introduced negligible discrepancy, the assumption of constant vertical stress leads to significant differences between the Shi–Durucan permeability estimate and that calculated from the SIMED–FLAC3D simulation, especially at early times during production. These differences were a result of the pressure and sorption strain changes induced by production leading to arching of stresses in the vicinity of the production well. The mechanism was shown to produce significant differences in the calculated gas rate particularly at early times during production. Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved.

1. Introduction Coal is often conceptualised as a continuum dual-porosity formation with a macro-porosity associated with the coal cleat system, and a micro-porosity, in the coal matrix. The macro-porosity dominates the Darcy flow behaviour, while the micro-porosity having comparatively small Darcy permeability is where the majority of gas is stored through adsorption. Permeability (associated with the macroporosity) is a key parameter for coal seam methane production but its behaviour is complicated by a number of processes. An important mechanical effect is the sensitivity of permeability to effective stress; increased effective stress acts to reduce the macro-porosity, and thus the permeability. Permeability, like most quantities in geological environments is affected by the intrinsic heterogeneity that is present. Typically permeability is described over an appropriate averaging volume, and it is this equivalent permeability that is referred to in this paper. While coal is highly heterogeneous and thus difficult to generalise, a popular starting point for characterizing coal permeability in a dualporosity framework has been the bundled-matchstick conceptual model (Seidle et al., 1992). In this model, it is assumed that the

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processes of cleat formation have led to two major cleat systems, the face and butt cleats, which are vertical and aligned at right angles to each other. The porosity of this cleat system has been related to the permeability using the following,  k = ko

/ /o

3

ð1Þ

where k is the permeability, ko is the initial permeability, ϕ is the cleat porosity and ϕo the initial cleat porosity. Alternatively the permeability has been related to effective stress, σe, according to the relationship, k = ko e

− 3C/σ ðσ e − σ eo Þ

ð2Þ

where Cϕσ is a compressibility parameter (referred to as cleat volume compressibility), σeo is the initial effective stress with σe = σ − αP where σ is the total stress, positive in compression, α is Biot's coefficient and P the pore pressure (associated with the macroporosity in the dual-porosity framework) (Seidle et al., 1992). Eq. (2) is well supported by a wide variety of experimental measurements. Another important effect on coal permeability is the coal matrix strain associated with changes in adsorbed gas content. As gas content

0166-5162/$ – see front matter. Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.coal.2009.03.008

L.D. Connell / International Journal of Coal Geology 79 (2009) 18–28

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Fig. 1. Schematic outlining the geological representation used in the SIMED and FLAC3D simulations.

increases the coal matrix swells in response; with decreases in gas content leading to coal matrix shrinkage. This change in coal matrix volume with gas content, or sorption strain, leads to changes in the cleat porosity and thus permeability. However the relationship is complicated by the geomechanical readjustments that take place in the coal seam and surrounding formations (Gray, 1987). One approach to characterize the permeability in coalbeds during gas production has been to describe the porosity behaviour and then use Eq. (1) to obtain the permeability. The Palmer and Mansoori (1998) model relates porosity response to pore pressure and sorption strain based on the assumptions of uniaxial strain and constant vertical (overburden) total stress. Another approach has been to link the pressure and strain to the effective stress and then permeability by Eq. (2). This is based on modifying the stress–strain relationships for isotropic linear elasticity by including the effect of sorption strain. Shi and Durucan (2004) a derived a relationship using the following incremental stress–strain relationships, for each normal effective stress component, 

 1 m 1 s ¯exx + ¯e + ¯e 1+m ð1 + mÞð1 − 2mÞ 3ð1 − 2mÞ   1 m 1 s e σ ¯ yy = E ¯eyy + ¯e + ¯e 1+m ð1 + mÞð1 − 2mÞ 3ð1 − 2mÞ   1 m 1 s e σ ¯ zz = E ¯ezz + ¯e + ¯e 1+m ð1 + mÞð1 − 2mÞ 3ð1 − 2mÞ e

σ ¯ xx = E

ð3Þ

where z is positive upwards, the overbar stands for ‘increment’, E is Young modulus, ν is Poisson ratio, the volumetric strain is defined as ε = εxx + εyy + εzz and εs is the volumetric adsorption strain (adsorption strains are assumed to be isotropic). Also, the sign convention is compression positive, except for adsorption strain which is positive in extension. _ _ Under uniaxial strain conditions (i.e. ε xx = ε yy = 0) and assuming _ the vertical _ stress is constant during production (σ zz = 0 and thus _e σ zz = −αP ), Shi and Durucan used Eq. (3) to derive the following relationship, e

e

σ ¯ xx = σ¯ yy = −

m E s α P¯ + ¯e 1− m 3ð1 − mÞ

ð4Þ

Eq. (4) with Eq. (2) provides an approach to calculating the variation in horizontal permeability with changes in pressure and gas content. A difference in these equations compared with those presented by Shi and Durucan is that the Biot coefficient, α, has been included. Eq. (4) is similar to that presented by Gray (1987) however Shi and Durucan use a different description of sorption strain. While Eq. (4) captures the effects of pressure and sorption strain on the horizontal effective stress, for the vertical permeability the vertical effective stress is unaffected by sorption strain being defined _ _ by the following σ ezz = − αP . Using a Langmuir equation to describe the sorption strain relationship to pressure, Shi and Durucan (2005) applied Eq. (4),

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L.D. Connell / International Journal of Coal Geology 79 (2009) 18–28

Fig. 2. The model grids used in the SIMED and FLAC3D simulations.

with constant Young's modulus and Poisson ratio, to the simulation of gas and water production from several San Juan basin coalbed methane wells and found that an improved history match with field observations could be obtained if the compressibility parameter Cϕσ was varied in time. It was proposed that this was a result of a departure from linear elasticity as the pore pressure was drawn down in the reservoir. Two important geomechanical assumptions employed in the derivation of Eq. (4), and also the Palmer and Mansoori relationship, are uniaxial strain and constant vertical stress. These assumptions allow the geomechanical aspects of the problem to be considerably simplified and a simple pore pressure based formulation for the permeability to be derived. During production from a coal reservoir, gas desorption will lead to coal shrinkage and reservoir compaction. In simulation the uniaxial strain and constant vertical stress assumptions mean that the overburden response to this reservoir compaction do not need to be considered and only the coal seam itself is represented. In conventional reservoirs these two assumptions are most accurate when there is a uniform drawdown of reservoir pressure leading to a one dimensional vertical response in reservoir subsidence (Jaeger et al., 2007). In Geertsma's (1973) model for stress change during conventional reservoir compaction, the change in total vertical stress (at the centre of the reservoir) is very small for laterally extensive reservoirs undergoing uniform drawdown. However where production creates gradients in pressure and subsidence towards the production well, shear stresses will be created in the overburden acting to reduce the vertical stress (Settari, 2002). Boade et al. (1989) found that production induced subsidence in the Ekofisk reservoir led to significant changes in the vertical stress as a result of stress arching in the overburden. Hetterna et al. (2000) found that uniaxial strain analyses could not explain the stress changes induced by production induced reservoir subsidence. During production of gas from a coal seam reservoir, gradients in pressure and gas content will be created towards the production well. The associated coal shrinkage will lead to subsidence of the coal seam, while relatively small, will thus not be laterally uniform. The response of the overburden to this vertical strain will determine the accuracy of the constant vertical stress assumption. In addition as stated above there is field evidence that uniaxial strain may not be universally accurate during reservoir subsidence. In this paper these assumptions will be investigated using a coalbed methane reservoir simulator (SIMED II) coupled to a geomechanical

model (FLAC3D). This simulator calculates gas and water migration allowing for coupled stress–strain behaviour including the effects of sorption strain during pressure drawdown in response to primary production of coalbed methane. Gu and Chalaturnyk (2005a,b, 2006) used the reservoir simulator GEM coupled to FLAC3D to investigate coupled flow and geomechanical processes during coalbed methane production. This work established, in the example considered, that existing permeability models, including Eq. (4), did not compare well with an approach that included geomechanical effects calculated with FLAC3D. Further work is required to identify how this behaviour varies with respect to coal properties and the reasons for the differences. In contrast to the work of Gu and Chalaturnyk where permeability was related to the linear strain, the current work uses the well established permeability vs stress relationship (Eq. (2)).

Table 1 Model properties that were fixed across the simulations of primary production. Properties

Value

Initial reservoir pressure Initial methane content Water and gas relative permeabilities Absolute permeability Cleat compressibility Well operational conditions A. Fast drawdown B. Intermediate drawdown

4000 kPa 16.5 m3/t Linear interpolation between zero and saturation

C. Slow drawdown Depth to seam Depth to top of FLAC3D model Desorption time Langmuir isotherm properties Pressure Volume Geomechanical Overburden bulk modulus, shear modulus, bulk density Base layer bulk modulus, shear modulus, bulk density

10 mD 2.9 × 10− 7 Pa− 1 200 kPa bottomhole pressure Initial water rate of 4 m3/day until bottomhole pressure = 200 kPa, then fixed bottomhole pressure 2 m3/day until 200 kPa 400 m 200 m 1 day 395 kPa 32.8 m3/t 6.90 GPa; 4.96 GPa; 2500 kg/m3 7.29 GPa; 5.93 GPa; 2500 kg/m3

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If the compressibility is constant Eq. (6) leads to the following,

Table 2 Coal bed geomechanical properties and sorption strains.

− Cbσ;i ðσ ejj − σ ejjo Þ

ð7Þ

Properties

Case 1

Case 2

Case 3

bi = bio e

Geomechanical Young's modulus Poisson ratio Bulk density Maximum volumetric sorption strain with CH4

0.855 GPa 0.39 1500 kg/m3 a. 0.5% b. 1%

1.965 GPa 0.39 1500 kg/m3 a. 0.5% b. 1%

3.068 GPa 0.39 1500 kg/m3 a. 0.5% b. 1%

With Eqs. (5) and (7) the relationship between coal permeability for each axis and the effective stress can be expressed by

1.1. Modelling approach 1.1.1. Permeability description Since sorption strain is usually anisotropic (Levine, 1996), this needs to be allowed for in descriptions of the permeability. In what follows, it is assumed that the cleat system is characterized by three orthogonal planes, and that the reference axes are chosen to align in the principal directions of permeability. With this, a form of Eq. (2) allowing for permeability anisotropy can be derived from the cubic flux law for flow in fractures, whereby  ki = kio

bi bio

3

ð5Þ

where bi is a macroscopically averaged cleat aperture for flow along the i-axis. Assuming that the bulk compressibility of the coal is localized in the cleat, the cleat aperture will be governed by the ‘effective stress’ normal to the cleat plane (difference between normal stress and pore pressure in the cleat). If we now adopt the concept of an equivalent porous media for the macro-pores in which effective stress is defined as a continuum variable, then, consistent with the definition of compressibility, we can write: Cbσ ;i

1 dbi = − bi dσ ejj

− 3Cbσ;i ðσ jj − σ jjo Þ e

ki = kio e

where Cbσ,i is the cleat volume compressibility in the i-direction (i stands for x, y, or z). σejj is the effective stress in the j-direction, normal to the cleat plane contributing to i-axis permeability and can be defined as σejj = σjj − αP, where σjj is total normal stress, α is the Biot coefficient and P is the pore pressure in the macro pores.

ð8Þ

The stress–strain constitutive relations allowing for anisotropic sorption strain used here are derived from the equations for linear poro-elasticity (Bai and Elsworth, 2000). While anisotropy is allowed for in the sorption strain it is assumed that the geomechanical properties, such as Young's modulus and the Poisson ratio are still isotropic. The incremental equations for the normal stress/strain components are written here as,    1 σ ¯ yy −ð1 − 2mÞα P¯ ¯ xx − m σ¯ zz + σ E  1 s σ¯ − mðσ ¯ xx + σ¯ zz Þ −ð1 − 2mÞα P¯ ¯eyy + ¯eyy = E yy    1 e¯zz + ¯ezzs = σ ¯ xx + σ ¯ yy −ð1 − 2mÞα P¯ ¯ zz − m σ E s ¯exx + e¯xx =

ð9Þ

These equations assume that the principal directions for sorption strain are aligned with the coordinate axes, and that the poro-elastic properties are not influenced by sorption. Eq. (9) reduces to Eq. (3) for isotropic sorption strain. In this work it is assumed that sorption strain is a linear function of total gas content (Harpalani and Chen, 1995; Seidle and Huitt, 1995; Pan and Connell, 2007). Thus the following relationship can be written, s

eii = βi G ð6Þ

e

ð10Þ

where (Einstein summation convention on repeated indices does not apply) βi is a constant property (i.e. maximum sorption strain/ Langmuir volume for direction i) and G is the total gas content. 1.1.2. Modelling methodology The simulation procedure used in this work involved coupling the dual-porosity coalbed methane simulator, SIMED II (Stevenson, and

Fig. 3. Flamed simulated volumetric strain in a vertical X–Z plane through the production well in the vicinity of the coal seam for Case 2b properties and Well B operational conditions at the 246 day time level.

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Fig. 4. Vertical stress behaviour in the well grid block during primary production calculated using Flamed with Case 2b properties and for the well operational practices described in Table 1. The dotted line indicates the stress due to the weight of the overlying geology.

Pinczewski, 1995; Spencer et al., 1987) to the geomechanical simulator FLAC3D (Itasca Consulting Group, 2005); the resultant coupled simulator was called Flamed. In this arrangement SIMED II was used to represent gas and water migration with adsorption in the dual porosity coal structure through time. Capillary pressure was neglected, so there was only one fluid pressure associated with the macro-porosity. The SIMED II fluid pressure associated with the macro-porosity and the gas content were passed to FLAC3D at a series of consecutive time intervals. At each time FLAC3D then performed a quasi-static poro-elastic calculation using the constitutive relationships defined by Eq. (10). The mechanical effect induced by the change in fluid pressure between time intervals was accounted for in the geomechanical calculations. However, the change of fluid pressure caused by mechanical deformation was neglected. Also, permeability was assumed to be isotropic for the numerical simulations. The effective stress field obtained for a particular time interval was used to calculate a new permeability via Eq. (2), which was then used by SIMED II for the next time interval. The time interval between geomechanical solutions varied throughout the simulation, initially small and

Fig. 5. Simulated sorption strain increment and vertical stress with time in the grid block with the production well; Case 2b properties and Well B operational conditions were used.

Fig. 6. Flamed simulated vertical stress variation with time at a series of distances away from the production well for Case 2b properties and Well B operational conditions. The dotted line indicates the vertical stress due to overburden geology.

increasing with time in order to properly capture change in the permeability. The initial vertical stress was in equilibrium under gravity. The initial horizontal stresses assumed K0 =ν / (1−ν) (uniaxial deposition). While the SIMED II simulation represented flow within the coal seam only, the FLAC3D calculation included non-coal formations above and below the target coal seam to include the geomechanical response of these formations to strains associated with gas and water production from the coal. The assumption here was that the geological units in the immediate vicinity of the coal seam are of much lower permeability than the coal and that pore pressures variation is confined to the coal seam. This is consistent with many depositional settings for coal where it is found with shales and siltstones in close proximity. These neighbouring geological units tend to have very low permeabilities and are considered here to be confining units for water flow; this approach is consistent with common practice in simulation of coal bed methane. The conceptual arrangement of the geology is presented in Fig. 1. The overlying formations are represented to 200 m above the target coal seam with a constant load applied to represent the weight of formations above this point. The model grid exploits the symmetry of flow around a production well and thus represented only one quarter of the affected region. The model domain was 200 m × 200 m horizontally and would be equivalent to a regularly spaced well field with one well per 16 ha (see Fig. 1). This well spacing is closer than that commonly used in the San Juan basin and was chosen here in order to decrease the time required to drawdown the reservoir and

Fig. 7. Simulated horizontal displacement in the well grid block calculated using Flamed during primary production (expressed as a percent of the corresponding in time value of the vertical displacement) for the same simulations and location presented in Fig. 4.

L.D. Connell / International Journal of Coal Geology 79 (2009) 18–28

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permeability and cleat compressibility were assumed to be isotropic. The cleat compressibility is from Mavor and Vaughn (1998) derived from history matching of production from Valencia Canyon wells in the San Juan and the desorption time, while hypothetical, is of the same order as that reported by Mavor and Vaughn. It should be noted that for these hypothetical simulations it was assumed that the coal seam permeability was isotropic. Typically coal permeability is anisotropic reflecting the orientation of the coal cleat system and the local stress field. Since the focus of this paper is the effect of the coupled geomechanics on coal permeability it was decided that representing anisotropy in permeability would act to complicate the interpretation of the simulations. The simulations comprised a set of cases which considered the effect on permeability of the magnitude of sorption strain and Young modulus for the coal. In the Shi–Durucan model these two parameters appear only in the second term of the effective stress relation, Eq. (4). However in the proposed coupled model the relationship between effective stress, strength and sorption strain is more general. Another expression for the effective horizontal stress for the case considered can be derived from Eq. (9), by taking into account the _ _ problem symmetry: with σxx =σ yy and some manipulation, this leads to, e

σ ¯ xx =

Fig. 8. A vertical section along the X–Z plane through the model domain depicted in Fig. 2 showing the vertical stress (σzz) during primary production calculated using Flamed with Case 2b properties and B well operational conditions at the 246 day time level.

ð11Þ

Thus the change in horizontal effective stress is the sum of contributions from vertical stress, horizontal strain, horizontal sorption strain and pressure changes. For isotropic sorption strain, the difference between Eq. (11) and the Shi–Durucan equation, Eq. (4), is, e

drain gas. The overall objective was to reduce the computational time required for each simulation and thus improve the tractability of performing the multiple simulations needed to investigate the coupled processes. The SIMED and FLAC3D models used matching grids to represent the coal seam (thus allowing for a one to one correspondence between SIMED grid block and FLAC3D grid zone). The coal seam was represented with a single layer of blocks in the SIMED and FLAC3D models (implying that fluid flow in the vertical direction was neglected within the coal layer as the coal seam was thin compared with the horizontal scale of the seam) with a series of layers of increasing thickness in the non-coal formations above and below the coal seam as depicted in the 3D view of the FLAC3D grid presented in Fig. 2. In the horizontal plane there was increased grid refinement towards the production well within each layer, as shown in Fig. 2, and this horizontal spacing was uniform through the vertical sequence of layers which comprised the FLAC3D model grid.

m E E m s αP¯ σ ¯ + ¯e + ¯e − 1 − m zz 1 − m xx 1 − m xx 1− m

σ ¯ xxDiff =

m E σ e¯ ¯ + 1 − m zz 1 − m xx

ð12Þ

Eq. (12) represents the impact of the two key approximations associated with the derivation of the Shi–Durucan relation for

2. Simulation of primary production 2.1. Introduction A series of simulations of primary production from a hypothetical coal seam reservoir were conducted. The model properties are presented in Table 1. The simulations to be presented here are hypothetical and not intended to replicate a particular field site but in order for these to be physically relevant, property values were chosen from the literature from studies on the San Juan basin. The three geomechanical cases presented in Table 2 are based on the range for Young's modulus given by Palmer and Mansoori (1998) for large-scale San Juan basin and the value for Poisson's ratio is from this source as well. In this work, as a first approximation it was assumed that the Biot coefficient, α, was equal to 1. The methane adsorption characteristics are from Levine (1996), and the cases for sorption strain broadly based on information reported in this source. In this analysis sorption strain,

Fig. 9. A vertical section through the model domain showing the shear stress (σxz) during primary production at 246 days from the same simulation as presented in Fig. 8.

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_ effective stress, that is, uni-axial strain conditions apply (i.e. ε xx = 0) _ and overburden stress is invariant (i.e. σ zz = 0). These assumptions are also used in the derivation of the Palmer–Mansoori equation. 2.2. Simulation results 2.2.1. Stress behaviour during primary production This section considers the geomechanical behaviour during primary production for a hypothetical, but physically realistic problem. One set of simulation results is presented with the objective of illustrating the behaviour and considering in detail the applicability of the key assumptions of constant vertical stress and uniaxial strain adopted in the well known Shi–Durucan and the Palmer–Mansoori models. The magnitude of the impact of these assumptions on permeability and gas production will be considered in the subsequent sections. The coal bed property values used for the simulations are listed in Table 2, under Case 2b. Fig. 3 presents the volumetric strain calculated using Flamed after 246 days of primary production with the B well operational conditions listed in Table 1. These results show the net volumetric compaction in the coal associated with production, including matrix shrinkage associated with gas desorption and compressive strains caused by the decrease in fluid pressure. Fig. 4 presents the Flamed calculated vertical stress in the well grid block (which is 2 m × 2 m in area) for the three well

operational conditions described in Table 1. For the slow and intermediate drawdown cases the well is initially produced at a constant water rate and then changes to a constant bottomhole pressure when the well is drawn down to 200 kPa. For the fast drawdown case the bottomhole pressure is 200 kPa from the start of the simulation. As discussed above in order to derive the Shi–Durucan and Palmer–Mansoori coal permeability models it is assumed that the vertical stress is constant. The results presented in Fig. 4 for the vertical stress behaviour show that the deviation from the initial state of 10 MPa is significant. This response is driven by the sorption and compression strains associated with pressure and gas content decline in the vicinity of the production wells. With time the spatial gradients within the coal seam in gas content and thus sorption strain diminish as the reservoir is drained and, because the constitutive behaviour is assumed to be elastic, the vertical stress gradually returns to that determined by the weight of the overburden geology. The results presented in Fig. 4 show that the departure from the overburden stress is sensitive to the manner in which the reservoir is drawn down. In particular the initial behaviour is determined by the rapid drawdown of pressure and thus gas content in the well grid block because of its small size (and thus storage). For the simulation results using well operational conditions C, the slow drawdown case, the vertical stress has a more gradual decline and the magnitude of the divergence from the overburden stress is less.

Fig. 10. The spatial distribution of the change in gas content, effective stress and pressure from their initial states at 246 days and the difference between the Flamed and Shi–Durucan calculated permeabilities (expressed as the % of the Shi–Durucan result) for Case 2b properties and well operational conditions B.

L.D. Connell / International Journal of Coal Geology 79 (2009) 18–28

Fig. 11. Permeability with respect to pressure calculated using Flamed compared with the Shi–Durucan result at four distances away from the production well using Case 2b properties and well conditions B.

An important factor contributing to this early time behaviour in the results presented in Fig. 4 is the short desorption time of 1 day. The desorption time is a property introduced through the Warren and Root description of the mass exchange between the coal matrix and cleat system. It combines the effective gas diffusion coefficient with geometric properties of the coal matrix. The transfer rate is driven by the gas concentration gradient between cleat and matrix and is inversely proportional to the desorption time. In Fig. 5 the simulated sorption strain increment is presented with the vertical stress with respect to time for two desorption times; one set of results is for the desorption time of 1 day presented in Table 1 and used for Fig. 4. The other results are with a desorption time of 20 days. The results presented in Fig. 4 show how the local maxima or ‘bumps’ in vertical stress align with maxima in the sorption strain. However there is a slight misalignment in the times at which these occur for this location, the grid block that the production well is completed in. This is due to the vertical stress reflecting the overburden response to the larger scale sorption strain behaviour, rather than that at the production well. The sorption strain increment is changing with the gas content as

25

the drawdown in reservoir gas content migrates out from the production well. Fig. 6 presents the vertical stress behaviour for Case 2b properties and B well operational conditions for a series of increasing distances away from the production well. The region where vertical stress is affected increases with time as the pressure and gas content is drawn down. As the gradients in the reservoir diminish this zone of influence decreases and the vertical stress returns to that determined by the weight of the overburden. Another assumption with the derivation of Shi–Durucan and Palmer–Mansoori is that the uniaxial strain assumption is applicable; that is horizontal strain is zero. Fig. 7 presents the horizontal displacement for the simulations described above. For the cases considered there are only relatively small departures from the zero horizontal strain assumption, relative to the vertical displacement. Fig. 8 presents the vertical stress in a vertical section that intersects the production well through the FLAC3D model grid. The results presented in this figure are from the time where the deviation from the assumptions of constant vertical stress is greatest. These results show that the vertical stress is decreased around the well as a result of the coal shrinkage associated with gas drainage. Fig. 9 presents the shear stress across the same vertical section and at the same time as the results in Fig. 8. The gradients in volumetric strain induced within the coal seam by gas drainage around the production well generate shear stresses in the overlying and underlying geology and lead to the reduced vertical stress observed in the simulation results presented above. As demonstrated by the results presented in Fig. 8 the vertical stress is reduced below the coal seam as well since this reduction effect is simply transmitted to the underlying formations until the shear stresses are dissipated. 2.2.2. Permeability behaviour The previous section presented an example which illustrated the geomechanical behaviour associated with primary production of coal seam methane. While the strain behaviour was found to be close to uniaxial strain conditions there were significant departures from the assumption of constant vertical stress in the vicinity of the well, at early time in the production. In this section the impact of this on the

Fig. 12. Contributions to the change in effective horizontal stress calculated using the terms in Eq. (11) for the permeability results presented in Fig. 11.

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Fig. 13. The difference between Flamed and SIMED (using Shi–Durucan model) permeabilities for the property cases presented in Table 2 and for well operational condition B in the well grid block (1.4 m from the production well).

calculation of permeability will be considered through a series of simulations. Fig. 10 presents the spatial distribution within the coal seam of the change in pressure, gas content and effective stress from the initial state after 246 days of primary production for Case 2b properties and well operational conditions B. Also presented in Fig. 10 is the difference between the Flamed calculated permeability and that calculated using the Shi–Durucan model. The difference is significant in the vicinity of the well but diminishes with distance such that the two sets of results are equivalent at 100 m. Fig. 11 presents the Flamed and Shi–Durucan calculated permeabilities with respect to pressure for the same simulation at a series of distances away from the production well. In the vicinity of the production well the differences increase as the reservoir is drawn down and reach a maximum but as the spatial gradients in pressure and sorption strain decrease the Flamed calculated permeability trends towards the Shi–Durucan result. For the 50 m location the Flamed and Shi–Durucan results are very close, consistent with the behaviour of the vertical stress presented in Fig. 6 for this location. Fig. 12 presents the contribution in time of the four terms, identified in the right hand side of Eq. (11), to the effective stress used to calculate permeability in Flamed. These terms include 1) a vertical stress term, 2) a horizontal strain term, 3) a sorption term, and 4) a pressure term. The same four locations as used with Figs. 6 and 11 are considered: 1.4 m, 8 m, 16 m, and 50 m radial distance from the production well. This figure illustrates that the differences between the Shi–Durucan and Flamed permeability results are almost entirely due to the contribution from changes in the vertical stress. For the well grid block (1.4 m from well) the vertical stress term is initially large but decreases with time and the Flamed permeability approaches that calculated using Shi–Durucan. The role of this vertical stress contribution is significant since the sorption strain and pressure terms act in opposite directions during primary production and thus in the Shi–Durucan approach the effective stress is significantly smaller than the Flamed calculation at early times. At 50 m from the well, where the Flamed permeability is equivalent to the Shi–Durucan result (see Fig. 11), the vertical stress contribution is negligible, as it does not vary from its initial state, compared with that from the sorption strain and pressure. For both locations the contribution from the horizontal strain term, is not significant, consistent with the uniaxial strain assumption. Fig. 13 presents the differences between Flamed and SIMED II (using Shi–Durucan) calculated permeabilities for the property cases presented in Table 2 and well condition B. The difference is most

significant at early times where the gradients in gas content, and thus sorption strain, are also large. Consistent with the results for Case 2b presented in Fig. 12 the differences between the two sets of permeability results decrease with time as the Flamed values trend to the Shi–Durucan result, reflecting the vertical stress returning to that determined by the weight of overburden (see Fig. 4). There is a clear correlation with the coal elastic properties, the difference being inversely related to Young modulus. For the lowest modulus case considered, Case 1, the relative difference increases with sorption strain, whereas for the highest Young modulus coal, Case 3, the difference is slightly lower for the higher sorption strain case, Case 3b. For most results there is a peak in the difference, reflecting the peak in the vertical stress deviation from its initial state that can be observed in Fig. 12 for the Case 2b simulation results. 2.2.3. Simulated gas rate Fig. 14 presents the gas rates calculated using Flamed and SIMED (with the Shi–Durucan model) for Case 2b properties and well operational conditions B. The significantly larger permeabilities calculated with the coupled geomechanical approach in Flamed lead to much higher peak gas rates than with the Shi–Durucan permeability. The gas is drained more quickly leading to lower gas rates after approximately 700 days than the simulation results calculated with SIMED using the Shi–Durucan permeability model.

Fig. 14. Gas rate calculated using Flamed for the same simulation (Case2b properties with well conditions B) as presented in Fig. 10 compared with the gas rate calculated using SIMED with the Shi–Durucan model.

L.D. Connell / International Journal of Coal Geology 79 (2009) 18–28

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Fig. 15. The difference between Flamed and SIMED (using Shi–Durucan model) calculated gas rates for the property cases presented in Table 2 and for well operational condition B.

Fig. 15 summarises the differences between the Flamed and SIMED II (using the Shi–Durucan permeability model) gas rates for the various property cases presented in Table 2. The results presented in this figure show that the behaviour of the difference is a complex function of the magnitude of the swelling and the geomechanical properties. For a maximum sorption strain of 0.5% the three geomechanical cases have a similar maximum difference in magnitude and timing but the results diverge at longer times. For these longer times the magnitude of the difference is closely related to the coal Young modulus; increasing with E. With the results presented in Fig. 15 for a maximum sorption strain of 1% for modulus cases 1 and 2 there is greater sensitivity to the coal modulus; the difference in gas rate decreases as the Young modulus increases for the early time data, where the gas rate is at its highest. This behaviour is complicated by the results presented for the high strength case, Case 3, where the difference at early times is small. For these results the permeability increases significantly as the pressure and gas content decreases leading to very large simulated gas rates and rapid drainage of the seam. By approximately 1000 days the gas rate is small and the permeability calculated by Flamed identical to that using the Shi–Durucan approach. 3. Conclusions In the simulations presented in this work it was found that the uniaxial strain assumption was representative in that strain in the horizontal plane was small relative to vertical strain and made a negligible contribution to the permeability. However the assumption of constant vertical stress introduced significant error in the vicinity of the production well as the coal was drained of gas leading to shrinkage and the creation of shear stresses in the overlying geology which acted to reduce the vertical stress. As the coal seam is drained of gas, gradients in pressure and sorption strain in the region around the production well decreased and the vertical stress over time returned to that resulting from the weight of overburden. This variation in vertical stress is not represented in the Shi– Durucan and Palmer–Mansoori coal permeability models. It was found that this additional component in the effective stress leads to a significant departure from Shi–Durucan model permeability, a function of a range of reservoir and well operational conditions. In the examples considered the maximum difference was between 100 and 350% of the Shi–Durucan permeability. As the seam was drained of gas, horizontal gradients in pressure and strain decreased and the permeability calculated using the coupled model converged to the Shi–Durucan result. The impact of these differences in permeability on the gas production rate were considered and also found to be significant. These results compare well with the study of Cui and Bustin (2005) who found that fast drawdown of reservoir pressure

leads to higher gas rates during early production. However Cui and Bustin found that higher Young's modulus decreased the permeability reduction and increased permeability rebound in later production which appears in contrast to the Case 3 results presented in Fig. 15. This paper has shown that coal permeability and gas migration is complicated by the geomechanical behaviour of the coal seam and surrounding geology. Existing reservoir simulation approaches use coal permeability models based on simplifications to the geomechanical response to pressure and sorption strain changes during gas drainage. However this approach was found to lead to significant error in the simulation of coal permeability changes and the associated gas drainage behaviour when the geomechanical behaviour is more accurately described.

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