Modeling Anisotropic Permeability of Coal and Its Effects
on Coalbed Methane Reservoir Simulation
Geoff Wang
1
, Xiaorong Wei
2
, Hui An
1
, Fu-Yang Wang
1
and Victor Rudolph
1
1
School of Chemical Engineering, The University of Queensland, St Lucia, Brisbane, Qld 4072, Australia
2
Sinopec Oil & Gas Australia Pty Ltd, Level 1, 139 Coronation Drive, Milton, Brisbane, Qld 4064, Australia
Keywords: Coal, Coalbed Methane (CBM), Anisotropic Permeability, Reservoir Simulation.
Abstract: In this study, an alternative permeability model was developed and compared with data from laboratory
investigations. The model was further applied for reservoir simulation with several cases in order to
evaluate the effects of the anisotropic permeability variation on the CO
2
-sequestration and CO
2
-
sequestration enhanced coalbed methane (CO2-ECBM) recovery. The permeability model developed in this
study is based on a discontinuum medium approach, in which coal is treated as a discontinuum medium
containing anisotropic matrixes and cleats. The permeability variations and anisotropic permeability ratios
under isotropic net stresses were tested with relatively large coal samples. The simulations show good
agreements with the experimental data, revealing that the developed model is superior for describing stress-
and sorption-induced permeability variations in coals compared with models using constant values for
stress-dependent parameters. The results from reservoir simulation incorporating the developed permeability
model show the anisotropic permeability exhibit significant effect on CO2-ECBM recovery.
1 INTRODUCTION
Coal is typically an anisotropic porous media
consisting of butt and face cleats, featured by
anisotropy of the permeability to fluids flowing
through the cleats. The anisotropic permeability
often varies due to stress change and gas
adsorption/desorption occurring during coalbed
methane recovery. The deformations of coal and
permeability evolution have a significant influence
on reservoir performance. Therefore understanding
of coal deformation and permeability evolution
underlies the use, management and optimization of
deep coal as an economic resource for CO
2
sequestration, CBM recovery and underground
gasification. So far this phenomenon has not been
well understood (Wang et al., 2008; Wei et al.,
2007), and it is considered as one of the critical
problems for improved CO2-ECBM processes.
In the last several decades many attempts have
been made in both the theoretical and experimental
studies on the permeability of coal, including the
permeability evolution in underground coal
reservoirs associated with gas storage and gas
production. The currently published permeability
models can be generally classified into two types:
analytical permeability models (Gray, 1987;
Harpalani and McPherson, 1985; Puri and Seidle,
1991; Shi and Durucan, 2004; Somerton, 1975) and
coupled permeability models, which include
continuum medium coupled (CMC) model and
discontinuum medium coupled (DMC) model. Gu
and Chalaturnyk (Gu and Chalaturnyk, 2006)
compared these models and suggested that the DMC
model provides better estimates of permeability and
production than analytical models because it
includes the influences of many factors, such as
discontinuity and anisotropy. While considerable
efforts have been made in modelling permeability
changes during CO2-ECBM processes, significant
limitations exist in these permeability models due to
the complexity of the behaviour of coal under
dynamically changing stresses. So far there is no
model considering the anisotropic permeability
evolution associated with CO2-ECBM processes.
This work seeks to investigate anisotropic
physical and mechanical properties of in-situ coal
and to develop a more practicable and reliable model
for reservoir simulations. It will provide a better
understanding of structure and anisotropic
permeability evolution of coals for prediction and
simulation of processes associated with CO
2
477
Wang G., Wei X., An H., Wang F. and Rudolph V..
Modeling Anisotropic Permeability of Coal and Its Effects on Coalbed Methane Reservoir Simulation.
DOI: 10.5220/0005006504770483
In Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH-2014),
pages 477-483
ISBN: 978-989-758-038-3
Copyright
c
2014 SCITEPRESS (Science and Technology Publications, Lda.)
sequestration and CO2-ECBM recovery.
2 PERMEABILITY MODEL
Figure 1 shows the conceptual model of anisotropic
permeabilities for a coal core. The anisotropic
permeabilities of the coal specimens usually include
horizontal permeability and vertical permeability,
and the horizontal permeability can be divided into
two directional permeabilities of face cleats and butt
cleats. The vertical permeability consists of
contributions from both face and butt cleats.
Figure 1: Anisotropic permeability model of a coal
specimen.
The 3-dimensional stress and strain relationship for
an isotropic specimen can be described as
1
12
1
1
1
(1)
where E is Young’s modulus,
is Poison’s ratio,
and
are effective stress and strain, respectively.
The subscripts B, F, and V means butt cleat, face
cleat and vertical direction, respectively.
,
and
represent the effective stresses of butt cleat,
face cleat and the cleat in vertical direction,
respectively
Due to sorption induced dimensional changes
(Gilman and Beckie, 2000), Equation (1) can be
extended to
1
12
1
1
1
1
12
1
1
1
312
∆
1
1
1
(2)
where
is the volumetric swelling coefficient, S is
the adsorbed mass,
S is the variation of the
adsorbed mass,
SB
,
SF
and
SV
are the sorption
induced strains in three directions.
For the problem of CO2-ECBM recovery from a
coal reservoir, we may well assume that overburden
stress is constant and uniform. The following
assumptions are made
0
∆
(3)
where P
f
is the pressure in fractures.
Applying Equation (3) to Equation (2), the
Equation (2) can be simplified to
1
∆
312
∆
(4)
For isotropic coal specimens, since the cleats are
nearly vertical, we have
(5)
where a is the mean fracture aperture and E
f
is the
Young’s modulus for the fracture. The vertical
permeability can be represented as (Wang, et al.,
2008)
(6)
where c is a constant depending on cleat geometry
and surface roughness, h is the cleat spacing, and
f
is the fracture tortuosity. Through calculus and
algebraic operations on Equation (6), we obtain
3
3
(7)
Substituting Equation (5) to Equation (7) gives
3
(8)
The vertical permeability variations during CO
2
SIMULTECH2014-4thInternationalConferenceonSimulationandModelingMethodologies,Technologiesand
Applications
478
sequestration and enhanced coalbed methane
recovery processes can be estimated as
3
1
1
9
where subscript 0 represents initial condition, and
the adsorbed mass S can be estimated based on
Langmuir isotherm under following assumptions: 1)
The adsorbed phase should be in instantaneous
equilibrium with the cleat pressure; and 2) The
Langmuir isotherm is valid for the determination of
the adsorption equilibrium.
For anisotropic coal specimens, the contributions
from face cleats and butt cleats can be treated
independently. The vertical permeability consists of
contributions from both butt and face cleats,
represented by
3
3
(10)
where K
FV
and K
BV
are vertical permeability
contributions from face and butt cleats, respectively;
E
Ff
and E
Bf
are Young’s moduli for face cleats and
butt cleats, respectively. Thus
exp3
1
exp3
1
(11)
Preliminary experimental results obtained from our
lab suggested that the variations of anisotropic
permeabilities of coals with average net stress,
defined by the difference between confined stress
acting on a coal sample and fluid pressure in pores,
are similar in three directions. Therefore, to simplify
the model, we assumed that the permeability
variations with average net stress are approximately
the same in different directions. Three parameters
PAR
FB
, PAR
FV
and PAR
BV
are defined in the model
to describe the anisotropic permeability ratios of
face cleat to butt cleat, face cleat to vertical direction
and butt cleat to vertical direction, respectively.
Thus, the horizontal permeabilities, i.e. face cleat
and butt cleat permeabilities, can be estimated using
the following equations.
(12)
3 MODEL PARAMETERS
The model as indicated in Eq. (9) deals with some
stress-dependent parameters such as directional
permeability, compressibility and Young’s modulus
for cleats. Those parameters can only be determined
experimentally, as shown in Figures. 2-3.
Figure 2: Helium permeabilities through face cleat, butt
cleat and vertical directions of a 80 mm cubic coal sample.
Figure 3: Compressibility factor of coal varying with
average net stress.
Mechanical properties of bulk coals such as bulk
moduli and total bulk moduli Young’s modulus are
also stress-dependent and can be estimated as
follows.
The bulk modulus is defined as
1
312
(13)
where K
bt
is the total bulk moduli of coal, including
the contributions from cleats (or fractures) and
matrix; C
p
denotes coal compressibility; E
t
and
ModelingAnisotropicPermeabilityofCoalandItsEffectsonCoalbedMethaneReservoirSimulation
479
represent the Young’s modulus and Poison’s ratio of
coal, respectively. The contributions of cleats and
matrix to total bulk moduli of coal are largely
depended on the coal compressibility, which can be
approximately estimated using the correlation as
follows
1
1
⁄
⁄
(14)
where K
bf
and K
bm
are cleat (fracture) and matrix
bulk moduli, respectively; denotes stress; and
max
is the maximum stress above which the
compressibility variation in coal can be negligible,
that is, the cleat or fracture contribution to the coal
compressibility approaches zero. If the Poison’s
ratio in Eq. (13) is a constant, the Young’s modulus
can be estimated by
1
1
⁄
⁄
(15)
where E
f
and E
m
are defined as the moduli for cleats
and coal matrix, respectively.
Figure 5: Comparison of methane permeability variations
with net stress.
Given the Young’s modulus for the coal matrix as
2.8210
6
MPa, the estimated maximum stress
max
is
about 20MPa. Thus the estimated Young’s modulus
for cleats can be estimated using Eq. (15), as shown
in Figure 4. The results show that the Young’s
modulus for cleats increases remarkably in the lower
stress range and then slowly approaches ~2.1010
6
MPa at an average net stress of 60 MPa.
4 RESERVOIR SIMULATION
The methane permeability variations with average
net stress under constant pore pressure can be
comparatively calculated using three permeability
models, i.e. the model developed in this study, Shi-
Durucan model and Gilman-Beckie model. The
calculated results were then compared with the
experimental data, as shown in Figure 4. The
experimental data of methane permeability
variations were measured under constant pore
pressure (7.2 MPa) at different average net stresses.
Figure 4 shows that the predicted results using the
model developed in this study fit the experimental
data very well, while the other two models
apparently underestimated permeability at higher
average net stresses. This is because the values of
compressibility factor and Young’s modulus for
cleats are constant in these two models, ignoring
changes in net stresses. In other words, these two
models cannot predict the permeability variation
with average net stress well by not taking into
account the influence of compressibility and
Young’s modulus for cleats on permeability,
particularly at a higher average net stress.
In order to evaluate the effects of the anisotropic
permeability variation on the CO
2
-sequestration and
CO
2
-sequestration enhanced coalbed methane (CO
2
-
ECBM) recovery, a 3-dimensional and two-phase
numerical reservoir model was further developed for
reservoir simulations by incorporating the developed
permeability model to simulate the multi-component
gas and water diffusion and flow in coal seams.
Details on the reservoir simulation will be reported
separately and some results will be discussed later.
5 RESULTS AND DISUSSION
A base case was designed for the reservoir
simulations. A five-spot well pattern with one
vertical injector in the centre of four horizontal
producers was used to represent a pilot-scale project,
as shown in Figure 5. The orientation of horizontal
producers was assumed to be parallel to the direction
of butt cleats. Methane production took place one
year before CO
2
injection-ECBM recovery was
initiated. The production and injection wells are to
be shut-in at the time of CO
2
breakthrough, at which
the mole fraction of CO
2
in the gas production
stream is equal to 5%. The parameter values used in
simulations for the base case are listed in Table 1.
SIMULTECH2014-4thInternationalConferenceonSimulationandModelingMethodologies,Technologiesand
Applications
480
Table 1: Parameter values used in simulations.
Parameter Value
Reservoir drainage area (ft
2
) 25.00×10
6
Coal seam thickness (ft) 10.00
Initial coal seam porosity (%) 2.00
Initial pressure (psia) 800.00
Coal density (g/cc) 1.36
Face, butt and vertical
permeability (mD)
1.95, 0.23, 1.35
Poisson’s ratio 0.32
Young’s modulus for coal matrix
(MPa)
2.82×10
6
Micropore diffusion coefficient of
CH
4
, CO
2
(ft
2
/day)
8.37×10
-5
, 7.44×10
-4
Cleat spacing (in) 0.50
Sorption time constant (days) 7.60
Sorption volume (CH
4
, CO
2
)
(scf/ton)
600.00, 1500.00
Sorption pressure (CH
4
, CO
2
)
(psia)
700.00, 300.00
Critical saturation (gas, water) (%) 0.00, 10.00
Initial water saturation (%) 45.00
Initial mole fraction of coal gas
(CH
4
, CO
2
) (%)
100, 0
Reservoir temperature (ºF) 113.00
Wellbore radius (ft) 0.25
Skin factor 0.00
Figure 5: Well patterns for base case (thick lines
representing horizontal producers).
5.1 Impact of Anisotropic Permeability
In order to investigate the effects of anisotropic
permeabilities on the gas production, six cases were
designed based on the experimental measurements.
Table 2 lists the cases with different PARs for model
simulations.
The values of directional permeabilities used in
the six cases were set to be 1.7 times higher or lower
than those in base case. The results from the
simulations are shown in Figure 6. This forms two
groups of data for a better comparative study, i.e. the
first three cases comparing with the base case, and
Cases 4-6 forming the other group, which will be
discussed in details as follows.
Table 2: Cases designed for simulations.
Cases
K
vertical
(mD)
K
butt
(mD)
K
face
(mD)
PAR
FB
PAR
FV
PAR
BV
Base
case
1.35 0.23 1.95 8.48 1.44 0.17
Case 1
1.35 0.39 1.95 5.00 1.44 0.29
Case 2
2.28 0.23 1.95 8.48 0.86 0.10
Case 3
1.35 0.23 1.15 5.00 0.85 0.17
Case 4
0.80 1.44 4.32 3.00 5.40 1.80
Case 5
0.80 2.45 4.32 1.76 5.40 3.06
Case 6
0.80 1.44 2.54 1.76 3.18 1.80
Figure 6: The effects of anisotropic permeability ratios on
gas productions.
The comparison of base case and first three cases
suggested that face cleat permeability has major
effect on CH
4
and CO
2
production. The vertical
permeability has major effect on CO
2
injection, but
little influence on methane production. For coal
reservoir with lower PAR
BV
, the influence of
directional permeabilities on CO
2
breakthrough time
deceases in the order of face cleat permeability,
vertical permeability and butt cleat permeability. For
the cases with higher PAR
BV
, i.e. Cases 4-6, the face
cleat permeability has major effect on CH
4
ModelingAnisotropicPermeabilityofCoalandItsEffectsonCoalbedMethaneReservoirSimulation
481
production and CO
2
injection, while butt cleat has
major effect on CO
2
production. Increasing butt
cleat permeability may expedite CO
2
breakthrough
in produced gas.
5.2 Influence of Permeability Variation
Figure 7 shows the cumulative productions of CH
4
and CO
2
and associated mole fraction of CO
2
in gas
production predicted in the designated base case
using three permeability models, i.e. model
developed in this study, Shi & Durucan model and
Gilman & Beckie model.
In fact, the latter two models are essentially one
model in which the isotropic permeability is used. In
this comparison study, an initial isotropic
permeability used in Shi & Durucan model and
Gilman & Beckie model was 1.35 mD.
Permeability variation of coal reservoirs is not
only affected by the changing stress during the gas
production but also, maybe more importantly,
controlled by permeability anisotropy of coal. It can
be seen from Fig. 8 that the anisotropic permeability
clearly has some effect on CH
4
and CO
2
productions
using the model developed in this study, compared
with Shi & Durucan model and Gilman & Beckie
model. The new model predicts that cumulative CH
4
Figure 7: The calculated results of three permeability
models for the base case.
production will be lower, but cumulative CO
2
production will be higher than results predicted by
the other two models. Additionally, CO
2
breakthrough time will be shorter. These comparison
results suggest that the permeability anisotropy has
major effects on gas flow dynamics in coal
reservoirs, although stress- and sorption-induced
permeability variations also affect gas productivity
to some extent.
6 CONCLUSIONS
An alternative permeability model was developed to
describe anisotropic permeability variations of coal
due to stress change and gas sorption. The model has
unique features by taking into account separate
Young’s moduli for coal matrix and cleats, stress-
dependent Young’s modulus for cleats, and
anisotropic permeability ratios etc. These make the
model more practicable and reliable to be
incorporated into reservoir simulations for the gas
and water flow in coal reservoirs. The simulations
provide further information to investigate the effects
of anisotropic permeability variations on CO
2
-
ECBM recovery. The results suggested that
anisotropic permeability has significant effects on
gas production and CO
2
breakthrough time,
implying it is a critical parameter in determining
well pattern and orientation of horizontal wells.
ACKNOWLEDGEMENTS
This work was supported by the Australian Research
Council (ARC). Thanks to Dr. Paul Massarotto and
Professor Sue Golding of the University of
Queensland for their helpful discussion. It is
thankful to Dr. Dean Biddle for provision of
experimental data used in this study.
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