ENERGY EXPLORATION & EXPLOITATION · Volume 32 · Number 4 · 2014 pp. 601–619
601
Effects of pressure and temperature on gas diffusion and
flow for primary and enhanced coalbed methane
recovery
Yidong Cai1, 2, Zhejun Pan2*, Dameng Liu1, Guiqiang Zheng1, Shuheng Tang1,
Luke D Connell2, Yanbin Yao1 and Yingfang Zhou3
1
Coal Reservoir Laboratory of National Engineering Research Center of CBM Development
and Utilization, China University of Geosciences, Beijing 100083, China
2
CSIRO Earth Science and Resource Engineering, Private Bag 10, Clayton South, Victoria
3169, Australia
3
International Research Institute of Stavanger, Stavanger, P.O. Box 8046, 4068 Norway
*Author for corresponding. E-mail: [email protected]
(Received 23 November 2013; accepted 18 March 2014)
Abstract
Due to the rapid increase of coalbed methane (CBM) exploration and
development activities in China, gas adsorption and flow behavior for Chinese
coals are of great interest for the industry and research community. How
pressure and temperature affect the gas adsorption and flow on different rank
coals are not only important for CBM recovery but also important for CO2 or N2
enhanced CBM recovery, since gases are often injected at a temperature
different to the reservoir temperature. In this work, gas adsorption and
permeability of three different rank Chinese coals are measured using CH4, N2
and CO2 at three temperatures, 20˚C, 35˚C and 50˚C. Gas diffusivity and
permeability with respect to gas species, pore pressure, effective stress and
temperature are studied. The three coals are SQB-1 from Southern Qinshui
Basin, JB-1 from Junggar Basin and OB-1 from Ordos Basin. Gas adsorption
results show that both pressure and temperature have significant impact on
adsorption behavior for SQB-1 and JB-1 using CH4. For higher rank coal SQB1, adsorption isotherm tends to reach adsorption capacity quicker with respect
to pressure. However, the maximum adsorption capacity is higher for the lower
rank coal JB-1. Moreover, temperature has a stronger effect on reducing
adsorption capacity for lower rank coal. Gas diffusivity results for OB-1 and JB1 show that CO2 diffusivity is generally higher than that of CH4 and then N2.
This could be related with their different kinetic diameters and their interaction
with the coal. Both pressure and temperature have impact on gas diffusivity. In
general, gas diffusivities increase with pressure and temperature. Permeability
results show that it varies greatly with respect to coal rank with highest rank coal
having the lowest permeability. Permeability is also strongly sensitive to
effective stress and pore pressure. Temperature has a noticeable impact on
permeability change. Permeability changes differently with temperature
602
Effects of pressure and temperature on gas diffusion and flow
for primary and enhanced coalbed methane recovery
increase for the different rank coal samples studied. This may be attributed to
the combined effect of coal strain change due to gas adsorption and thermal
expansion. These results have significant implications for the design of
enhanced CBM recovery and CO2 storage for different rank coals as injecting
gas at different temperature and pressure would affect the CO2 injectivity and
the CBM production rate.
Keywords: Pressure, Temperature, Gas diffusion, Flow, Coals
1. INTRODUCTION
In recent years, coalbed methane (CBM) has become an important source of energy in
the USA, Australia and Canada. China and India also have started CBM exploration
and production approaching commercial production stage. However, the production
mechanism of CBM is significantly different to that of conventional gas, as they have
different mechanisms for gas generation, preservation and flow (Wang, 2007). CBM
reservoirs are often characterized as dual porosity. Methane is predominantly stored in
the pores of the coal matrix with diameter less than 100nm at the adsorbed state.
During production, gas is desorbed from the pore surface and diffuses through the
matrix to the natural fracture system-the cleat system. Then it flows with water
through the cleat system to the production well. Thus the adsorption capacity, the gas
diffusivity in the matrix, and the permeability of the CBM reservoir are key
parameters for gas flow and production.
Pressure and temperature are two of the important factors for gas adsorption
capability, gas diffusivity and permeability (Yao and Liu, 2012; Clarkson and Bustin,
1999; Belmabkhout et al., 2004; Gensterblum et al., 2009; Busch et al., 2004;
Gensterblum et al., 2010). They are important factors for enhanced coalbed methane
recovery (ECBM) process that often associates injecting gas at different temperature
and pressure to the coal seam. Many studies have been performed to investigate the
effect of temperature and pressure on gas adsorption capacity of coals. It is wellknown that adsorption amount increases with respect to pressure, often described by
the Langmuir model, and the increase of temperature causes the reduction of gas
adsorption capacity on coal (Levy et al., 1997; Bustin and Clarkson, 1998; Sakurovs
et al., 2008; Crosdale et al., 2008). However, only few studies have been conducted to
investigate the effect of temperature and pressure on gas permeability under in-situ
stress conditions (Zheng et al., 2012) and these data are not sufficient to represent
conditions encountered in coal reservoirs for different rank coals. Nevertheless, it is
important to address the temperature and pressure effect since they have direct
influence on gas diffusivity and permeability in coal, thus on gas flow behaviors in the
CBM/ECBM processes. Permeability is dependent on the properties of fractures, such
as fracture spacing, apertures and orientation (Levine, 1996). Previous research found
that fracture (cleat) porosity of coals was related to coal composition, coal type and
coal rank (Close, 1993; Levine, 1993; Mukhopadhyay and Khatcher, 1993; Karacan
and Mitchell, 2003), e.g. permeability for high rank coal is lower (Cai et al., 2013).
However, only few researchers have discussed the permeability change behavior with
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603
respect to coal rank, temperature or stress conditions (Johnson and Flores, 1998;
Mathews et al., 2011; Qu et al., 2012). Nevertheless, this information is key to the
CBM production and CO2 injection in coal reservoirs.
In this work, three different rank coal samples were collected to study the effect of
temperature and pressure on gas adsorption capacity, gas diffusivity and permeability.
Three gases are used including N2, CH4, and CO2 to investigate the impact of different
gases on the gas adsorption and flow behaviors.
2. SAMPLES AND METHODS
2.1. Samples selection and coal analyses
Three coal samples with different ranks were selected with the aim of covering a good
range of petrophysical properties: an anthracite from an underground coal mine at
depth of 400-500m at Changzhi City in Southern Qinshui Basin (sample SQB), a low
volatile bituminous coal from an underground mine in Dongsheng coal field at depth
of 700-900 m in Ordos Basin (sample OB) and a high volatile bituminous coal from
an underground mine of Tiechanggou coal field at depth of 200-300 m in Junggar
Basin (sample JB). Southern Qinshui Basin and Ordos Basin are the two focal areas
for CBM exploration and production in China (Su et al., 2005a; Su et al., 2005b) and
the Junggar Basin is also an area with increasing CBM exploration and development
activities. The estimated CBM resources of southern Qinshui Basin is 3.28×1012 m3
(Cai et al., 2011), Ordos basin is 10.72×1012 m3 (Feng et al., 2002) and Junggar Basin
is 3.83×1012 m3 (Liu et al., 2007). Moreover, ECBM trials have been carried out in
Qinshui Basin (Wong et al., 2007) and Ordos Basin (Connell et al., 2012; Pan et al.,
2012) to study the CO2 storage behavior in coal with an aim to enhance CBM
recovery. Therefore, studying coal samples from these three selected basins will be of
great interest for better understanding the CBM/ECBM processes for Chinese coals.
Before the adsorption and permeability experiments, the fundamental coal analyses
including vitrinite reflectance (Ro, m) and proximate analysis for these three samples
were conducted and the results are shown in Table 1.
Table 1. Summary of proximate analysis.
Sample No.
Coal mine / field
SQB-1
Changzhi
Proximate analysis
Coal lithotype
Ro, m (%)
9.5
Semi-bright
1.89
Cad (%)
Had (%)
Mad (%)
Aad (%)
74.8
14
1.7
OB-1
Dongsheng
82
4.8
0.4
7.7
Semi-dull
1.2
JB-1
Tiechanggou
42.8
40.1
4.9
12.3
Semi-dull
0.62
Cad-- Fixed carbon as received basis; Ro, m-- maximum vitrinite reflectance
2.1. Sample preparation
Cylindrical cores (50 mm in diameter and ~ 100 mm in length) drilled parallel to the
bedding planes for each coal sample were prepared. Plaster was applied to smooth the
sample cylindrical surface to prevent the thin lead foil from possible damage by the
rough surface of the core. The lead foil was used to prevent the gas diffusion from the
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Effects of pressure and temperature on gas diffusion and flow
for primary and enhanced coalbed methane recovery
sample to confining fluid (Pan et al., 2010). The core sample was then placed into a
heated vacuum oven at 50˚C for several days to remove moisture. Weight was
measured every two hours at the first two days, and then every six hours till the weight
remained unchanged. The sample was wrapped with a thin lead foil and a rubber
sleeve, and then installed in the cell. After that, the sample was vacuumed for a few
days to remove the residual gas before it was ready for the adsorption and permeability
experiments.
2.1.1. Adsorption isotherm and rate
Adsorption rate and isotherm measurements were performed using the experimental
apparatus sketched in Figure 1. The experimental procedures have been fully
described in the previous research (Zheng et al., 2012; Pan et al., 2010a; Pan et al.,
2010b). Brief description is included below. The temperature for the experiments was
controlled at 20˚C or 50˚C. Since the room temperature was about 25˚C, a chiller was
used to cool the water tank so that the heating element in the water tank can control
the water temperature at 20˚C. The water was then circulated to control the system
temperature at 20˚C. For experiments at 50˚C, the chiller system was not used.
Figure 1. Schematic diagram of the experimental apparatus.
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The Gibbs excess adsorption can be calculated directly from the experimental
measurements when the adsorption reaches equilibrium. A known quantity of gas
(Ninj) was injected from the injection pump (pump A) into the sample. Some of the
injected gas was adsorbed to the coal, and the remainder (Nua) was free gas, which
stayed in the void volume of the manifold and cell. A mass balance equation was used
to calculate the amount adsorbed (Zheng et al., 2012; Pan et al., 2010a):
Gibbs
N ads
= N inj − N ua = (
PV
P∆V
) Pump − ( void )
ZRT
ZRT
(1)
Where void volume, Vvoid, was pre-determined using a series of helium injections,
since helium is considered to be non-adsorptive to coal. Eq. (2) was then used to
calculate the absolute adsorption from the measured excess adsorption:
Abs
Gibbs
N ads
= N ads
(
ρ ads
)
ρ ads − ρ gas
(2)
Where ρads is the adsorbed phase density, ρgds is the free gas phase density.
To study the adsorption rate, the fraction of amount of gas adsorbed with respect to
time was calculated. It is the ratio of the amount of gas adsorbed at time t and the
amount of gas adsorbed when reaching equilibrium. The adsorption steps were
repeated sequentially to higher pressures to examine the impact of pressure on gas
diffusion. These steps also yielded a complete adsorption isotherm. After completing
the adsorption experiment on one temperature, the system temperature was changed to
study its impact on gas adsorption and diffusion.
To describe the adsorption rate, previous research found that bidisperse model can
well represent the gases adsorption/desorption rate behavior for coals with multimodal
pore distribution (Clarkson and Bustin, 1999; Crosdale et al., 1998). The simplified
bidisperse model has a fast macropore diffusion stage and a much slower micropore
diffusion stage. The uptakes of gas are given by (Pan et al., 2010a; Ruckenstein et al.,
1971):
Ma
D n2 π 2t
6 ∞ 1
= 1 − 2 ∑ 2 exp(− a 2 )
M a∞
π n=1 n
Ra
(3)
Mi
D n2 π 2t
6 ∞ 1
= 1 − 2 ∑ 2 exp(− i 2 )
M i∞
π n=1 n
Ri
(4)
Where Ma is the total amount of gas adsorbed/desorbed in the macropores at time
t, Ra is the macrosphere radius and Da is the macropore effective diffusivity. Mi is the
total amount of gas adsorbed/desorbed in the micropores at time t, Ri is the
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Effects of pressure and temperature on gas diffusion and flow
for primary and enhanced coalbed methane recovery
microsphere radius and Di is the micropore effective diffusivity. Thus, the overall
uptake (Pan et al., 2010a) can be rewritten as:
Mt
Ma + Mi
M
M
=
= β a + (1 − β ) i
M ∞ M a∞ + M i∞
M a∞
M i∞
Where β =
(5)
M a∞
is the ratio of macropore adsorption/desorption to the total
M a∞ + M i∞
adsorption/desorption.
2.1.2. Permeability
The transient Brace method (Zheng et al., 2012; Pan et al., 2010b) was used to
measure the permeability. This method involves observing the decay of the differential
pressure across the sample from upstream and downstream cylinders. The pressure
decay curve can be described by (Pan et al., 2010b; Pan and Connell, 2012):
( Pup − Pdown )
( Pup ,0 − Pdown,0 )
= e −α t
(6)
Where Pup – Pdown is the pressure difference between the up and down stream
cylinders, in the experimental facility used for this work, measured by a differential
pressure transducer; Pup,0 – Pdown,0 is the pressure difference between the up and
downstream cylinders at initial stage, t is time and a is described below:
α=
k
1
1
V( +
)
2 s
Vup Vdown
µβ L
(7)
Where k is permeability; β is the gas compressibility; L is the sample length; VR is
the sample volume; Vup and Vdown are the volume of the up and downstream cylinders.
For permeability measurements, the adsorption equilibrium was reached first. Then
the upstream and downstream cylinders were charged to the pressures about 40 kPa
above and 40kPa below the pore pressure, respectively. Then the valves connecting
the cylinders and the core sample were opened to allow gas to flow through the
sample. The effective stress was set to be 1 MPa, 2 MPa, 3 MPa, 4 MPa and 5 MPa
by changing the confining pressure, which was provided by an ISCO syringe pump
(pump B in Fig. 1). Then the relationship between permeability and stress at each pore
pressure can be studied. Four gases, He, N2, CH4 and CO2, were used in sequence to
measure the permeability at different pore pressures and effective stresses and at
different temperatures.
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3. RESULTS AND DISCUSSION
3.1. Adsorption capability
3.1.1. Effect of gas pressure on adsorption on different rank of coals
Gas adsorption depends on the chemical potential energy of the free gas as well as the
composition of the coal surface. Thus it is dependent on the adsorption temperature
and pressure, the gas and coal types. The adsorption isotherms measured using CH4
for SQB-1 and JB-1 are shown in Figure 2. In order to describe the amount of gas
adsorbed with respect to pressure, Langmuir model was used (Langmuir, 1918):
V=
VL p
p + pL
(8)
Where, V is the volume of gas adsorbed (cm3/g), p is the gas pressure (MPa), VL is
Langmuir volume, which represents the maximum storage capacity of the coal, and PL
is Langmuir pressure, which represents the pressure at half of the maximum
adsorption capacity.
The results showed that the adsorbed amount of CH4 for higher rank SQB-1 sample
was generally higher than that of the lower rank JB-1 sample with pressure up to 4
MPa. This shows that the coal sample from the southern Qinshui basin was more
preferential to CH4 adsorption at low pressures compared with lower rank coal JB-1.
However, the increment of the adsorption amount for SQB-1 is less than JB-1 at high
pressure region. Although the experiments only reached about 4 MPa and all the
measured adsorption was lower for the lower rank JB-1 below 4 MPa, it can be
expected that the adsorption amount for JB-1 would exceed that for SQB-1, as
indicated by the Langmuir model prediction shown in Figure 2. The difference of
adsorption amount at different pressure for different rank coals is likely caused by the
differences in coal composition, mineral matters and pore structures for the coals with
different rank (Radovic et al., 1997; Mahajan, 1991). Moreover, the results in this
work showed that lower rank coal could have higher maximum adsorption capacity.
This can be explained by the correlation between coal carbon content and its gas
Figure 2. Adsorption isotherms for SQB-1 and JB-1using CH4 at 20˚C and 50˚C.
608
Effects of pressure and temperature on gas diffusion and flow
for primary and enhanced coalbed methane recovery
adsorption capacity (Hirsch, 1954; Moffat and Weale, 1955; Faiz, 2007). Gas
adsorption capacity follows a U-shaped variation with carbon content, where the
medium volatile bituminous coal with around 83.5% fixed carbon content is at the
bottom of that U-shape (Gensterblum et al., 2010; Gurdal and Yalcin, 2001). As
shown in Table 1, fixed carbon content is 74.8% for SQB-1 and 42.8% for JB-1. Thus
our results agree well with the findings in the literature.
3.1.2. Effect of temperature on adsorption
As can be seen from Figure 2, temperature has significant influence on CH4 adsorption
isotherms for both coals. The adsorbed amount of CH4 at 50˚C decreases about 25%
and 35% compare to CH4 adsorbed at 20˚C at about 4 MPa for SQB-1 and JB-1,
respectively. This suggests that temperature have a stronger impact on the reduction
of adsorption capacity for lower rank coal. These results are in accordance with the
results by other studies that temperature has different impact on adsorption capacity
for different coals (Radovic et al., 1997; Mahajan, 1991). This different temperature
impact on adsorption may also be attributed to the differences in coal composition,
mineral matters and pore structures.
Langmuir volume, VL, and Langmuir pressure, PL, for different temperatures are
summarised in Table 2. It can be seen that Langmuir volume for high rank coal SQB1 at 50˚C is less than that at 20˚C as expected but the Langmuir pressure is almost the
same as shown in Table 2. For low rank coal JB-1, the Langmuir volume increased
from 26.26 m3/t to 29.02 m3/t for JB-1 from 20˚C to 50˚C. While the Langmuir
pressure is 1.69, 5.48 MPa for JB-1 at 20˚C and 50˚C, respectively. High Langmuir
pressure means low adsorption at low pressure range. These results suggest that the
reduction of adsorption at lower pressure region with respect to temperature change is
stronger for lower rank coal.
Table 2. Langmuir constants for CH4 at different temperatures.
SQB-1
(˚C)
3
JB-1
3
VL (m /t)
PL (MPa)
VL (m /t)
PL (MPa)
20
24.81
1.14
26.26
1.69
50
18.26
1.14
29.02
5.48
3.2. Rates of adsorption
3.2.1. Effect of gas species on adsorption kinetics
The results for sample OB-1 using the bidisperse diffusion model are summarised in
Table 3. CO2 diffusivities are greater than those for CH4 for the same pore pressure step
as shown in Table 3. The diffusivity of CO2 in coal is greater than that of CH4 is wellknown (Clarkson and Bustin, 1999; Gensterblum et al., 2010). Previous research
revealed that CH4 molecules could be impeded in some pores which are only accessible
to CO2 molecules because of their different kinetic diameters (0.33 nm and 0.38 nm for
CO2 and CH4 respectively) (Nandi and Walker, 1975; Cui et al., 2004; Shieh and
ENERGY EXPLORATION & EXPLOITATION · Volume 32 · Number 4 · 2014
609
Chung, 1999). The kinetic diameter, which is close to the gas molecular sieving
dimension, is one of the sensitive parameters which control gas flow in porous media
(Shieh and Chung, 1999). The kinetic diameter for N2 molecules is 0.36nm, which is
in between those for CO2 and CH4. As can be seen from the Table 3, the effective
macro diffusivity for CH4 is greater than that for N2 for the same pore pressure step;
however, the effective micro diffusivity for CH4 is only marginally greater than that
for N2. The previous research showed that the apparent diffusivity of the three gases
in the coal macropores (>50nm) decrease in the order of CO2, CH4, and N2, while the
diffusivity of the three gases in the coal micropores (<2nm) decrease in the order of
CO2, N2 and CH4 (Shieh and Chung, 1999).
Table 3. Summary of gases diffusivities for sample OB-1 at 35˚C.
Gas species
CH4
Pressure (MPa)
From
To
0
1.75
1.75
2.84
2.84
0
CO2
2.15
3
N2
3.93
2.15
3
4.13
Di / Ri2 (S-1)
Da / Ra2 (S-1)
0.78
3.19 10-6
5.34 10-5
0.78
2.88 10-5
1.04 10-4
-6
0.78
8.5 10
0.83
4 10
-5
1 10
-4
0.83
0.83
5.5 10-5
5.27 10-4
4.07 10
-5
7.95 10-4
-6
1.08 10-5
1.78 10-5
0
1.73
0.56
3.12 10
1.73
3
0.56
7.31 10-6
3
4.31
0.56
7.35 10-4
9 10
-6
5 10-5
3.2.2 Effect of temperature on adsorption kinetics
Experiments on CH4 sorption kinetics, performed on the dry JB-1 coal at the same
equilibrium pressure for two different temperatures 20˚C and 50˚C were performed to
evaluate the effect of temperature on gas diffusivity. The experimental results showed
that the sorption rate increased with increasing temperature. The diffusivity results are
shown in Table 4. The diffusivity increased with temperature increase and this is in
good agreement with literature data (Busch et al., 2004; Krooss et al., 2002; Charrière
et al., 2010). Another interesting aspect was that β changed from 0.7 to 0.56 when the
temperature increased from 20˚C to 50˚C. β is the ratio of the marcopore adsorption to
the total adsorption as shown in Eq (5) and a decrease of β means that relatively more
gas is adsorbed in the microspores. Although the value of β is larger than its true value
using the bidisperse model (Clarkson and Bustin, 1999), a change of value of β indicates
that temperature has an effect on gas adsorption partitioning between the pores.
3.2.3. Effect of gas pressures on adsorption kinetics
Experiments of the sorption of pure CO2, CH4 and N2 were conducted for sample OB1 at 35˚C for three pressures and the pressure steps were also shown in Table 3. During
the experiment, the time to reach equilibration was approximately 24 h at 2.15 MPa
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Effects of pressure and temperature on gas diffusion and flow
for primary and enhanced coalbed methane recovery
and 10 h at 4.13 MPa for CO2, and 110 h at 1.75 MPa and 65 h at 3.93 MPa for CH4,
and 130 h at 1.73 MPa and 55 h at 4.31 MPa for N2. For all gases, this equilibrium
time has an obvious decrease trend with the increasing pressure. The sorption rate of
all these three gases depended strongly on pressure. Normally the sorption rate has an
increasing trend with the increasing pressure steps both in macropores and micropores.
At the temperature of 20˚C, the effective macropore diffusivity and micropore
diffusivity increased from 9.16×10-6 (s-1) to 7.35×10-5 (s-1) and 9.26×10-7 (s-1) to
1.68×10-6 (s-1) with pressure increasing from 1.03 MPa to 3.8 MPa, respectively. At
the temperature of 50˚C, the effective macropore diffusivity and micropore diffusivity
increased from 1.94×10-3 (s-1) to 2.1×10-3 (s-1) and 6.83×10-6 (s-1) to 1.5×10-5 (s-1) with
increasing pressures (from 1.03 MPa to 3.8 MPa) respectively. Results from the
experiments of pure CH4 on sample JB-1 at two temperatures for three pressure steps
also showed similar trend as can be seen from Table 4.
Table 4. CH4 diffusivity for sample JB-1 under different temperatures.
3.3. Permeability
3.3.1. Effects of effective stress on permeability
Permeability with respect to different pore pressures, effective stresses and
temperatures using CH4 were measured. All the permeability measurements were first
performed at 20˚C. When the pore pressure reached maximum pore pressure at around
4 MPa, the system temperature was increased to 50˚C and then permeability was
measured again. At each pore pressure, permeability was measured at five confining
pressure steps to study the relationship between permeability and effective stress. In
this work, effective stress was used to describe pressure difference between the
confining and pore pressures as a convenience. Permeability decreased exponentially
with the increased effective stress as shown in Figure 3. Furthermore, for the same
effective stress and different pore pressures, the permeability has a big difference. The
permeability decreased with respect to pore pressure may be attributed to coal swelling
to partially close cleat aperture during the experimental conditions (Connell et al.,
2010) and/or effect from effective stress coefficient (Chen et al., 2011).
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611
Figure 3. Permeability of JB-1 measured using CH4 under different pore pressures at
20˚C and 50˚C.
It should be noted that for the permeability measured at 20˚C with pore pressure at
1 MPa, the core may not consolidated thus the permeability measured at low confining
pressures could be high. After the core undergone a series of confining pressure steps,
the core was consolidated and the permeability measured afterwards would be on the
same ground for comparison.
3.3.2. Temperature effect on permeability
The permeability of SQB-1 and JB-1 were measured using CH4 under different
temperatures (20˚C and 50˚C). Before conducting the permeability measurements, it
normally took several days to reach the sorption equilibrium at certain temperature
condition. Permeability was measured at two different pore pressures (1 MPa and 4
MPa) for CH4 to study the temperature effect. The effect of increased temperature on
permeability can be speculated on the effect of temperature on coal strain change,
which is a combined effect including coal strain decrease resulted from reduced
adsorption and thermal expansion due to elevated temperature.
To illustrate the effect of temperature on permeability, the CH4 permeability with
respect to effective stress for JB-1 is plotted in Figure 3. It shows that the impact of
temperature on permeability is significant with a temperature change of 30 degrees.
612
Effects of pressure and temperature on gas diffusion and flow
for primary and enhanced coalbed methane recovery
The permeability decreased dramatically from 14.6 mD to 4.37 mD when the effective
stress is 1 MPa, however, most of the decrease may be attributed to the coal
consolidation mentioned earlier. Nevertheless, it also showed a similar trend of
permeability decrease with temperature increase with pore pressure at 4 MPa.
Compared with the literature data (Zheng et al., 2012), the magnitude of the
permeability decrease with respect to temperature is larger for JB-1.
The relative change of permeability with respect to temperature for low rank coal
(JB-1) and high rank coal (SQB-1) are shown in Figure 4. For JB-1, the permeability
change at pore pressure of 1 MPa from 20˚C to 50˚C is about 70% with effective stress
up to 5 MPa, while the permeability change at pore pressure of 4 MPa from 20˚C to
50˚C is about 25%-55% with effective stress up to 5 MPa. For higher rank SQB-1
coal, the permeability change at pore pressure of 1 MPa from 20˚C to 50˚C is about 65 to -90% with effective stress up to 5 MPa, and the permeability change at pore
pressure of 4 MPa from 20˚C to 50˚C is about -45% to -15% with effective stress up
to 5 MPa. These results demonstrated that temperature has a significant effect on
permeability change and the impact of temperature on permeability change is more
significant at lower pore pressures. The results also show different permeability
change trend for different rank coals. For lower rank coal (JB-1), permeability
decreases with respect to temperature increase, while for higher rank coal (SQB-1),
permeability increases with respect to temperature increase. This may be attributed to
the different gas adsorption behavior and its induced coal swelling behavior, and
thermal expansion for different rank coals. The impact of matrix swelling effect on
coal permeability can be described by (Shi and Durucan, 2004):
σ −σ 0 = −
EεV
ν
P − P0 ) +
(
1− ν
3(1 − ν )
(9)
Where σ is the effective horizontal stress, σ0 is the effective horizontal stress at the
initial reservoir pressure, εV is the volumetric swelling/shrinkage strain (Shi and
Durucan, 2004). To relate the permeability with effective stress, the equation below is
used:
k = k0 e
−3c f (σ −σ 0 )
(10)
Where cf 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).
The volumetric swelling/shrinkage strain, εV, is a combined by sorption induced
swelling/shrinkage, εad, and thermal expansion, εT:
εV = ε ad + εT
(11)
Thus the overall permeability change due to temperature will depend on the net
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swelling/shrinkage effect. On one hand, with temperature increasing, the gas
adsorption amount will decrease at the same gas pressure, leading to coal matrix to
shrink in corresponding to the reduced adsorption amount with temperature increase.
Coal matrix shrinkage will lead to permeability increase. On the other hand, with
temperature increasing, coal matrix swells due to thermal expansion. Coal matrix
swelling will lead to permeability to decrease. For the two samples, it can be inferred
that there is net matrix swelling for the lower rank coal (JB-1) and net matrix
shrinkage for the higher rank coal (SQB-1) with respect to temperature, indicating
different temperature effect on the adsorption induced swelling and thermal expansion
for different rank coals. This is of great importance to design ECBM processes for
different rank coals, because gas permeability is a key parameter for ECBM via CO2
storage in coal.
Figure 4. Relative change of CH4 permeability with respect to temperature at pore
pressures of 1 MPa and 4 MPa.
Measurement should be taken on the adsorption induced swelling and thermal
expansion to better understand the relation between permeability change and
temperature. Due to the limitation of the experimental setup, it was not possible for this
work but definitely worth investigating in future work.
614
Effects of pressure and temperature on gas diffusion and flow
for primary and enhanced coalbed methane recovery
3.3.3. Permeability for different rank coals
Figure 5 tries to compare permeability with respect to different rank. Since the
experiment temperature was different for OB-1, which was 35˚C, comparisons were
made to permeability measured at both 20˚C and 50˚C for samples SQB-1 and JB-1.
As can be seen from Figure 5, in which the primary axis shows the permeability results
and the secondary axis shows the permeability change ratio, there is an obvious trend
that the permeability increases with the decreasing coal rank. Furthermore, the change
of permeability with respect to effective stress differs significantly for different coals.
For instance, for SQB-1, permeability decreases from 0.0592 mD to 0.0163 mD with
effective stress from 1 MPa to 5 MPa at pore pressure of 1 MPa, which is almost 73%
reduction in permeability. For JB-1, permeability decreases from 14.6 mD to 1.92 mD
with effective stress from 1 MPa to 5 MPa at pore pressure of 1 MPa, which is almost
87% reduction in permeability. These differences demonstrate that the cleat structures
for the three samples are different and their responses to stress are different.
Figure 5. Relationship between CH4 permeability and effective stress for different
rank coals.
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4. CONCLUSIONS
Gas adsorption and permeability of three different rank Chinese coals were measured
using N2, CH4, and CO2 at three temperatures, 20˚C, 35˚C and 50˚C. Gas diffusivity
and permeability with respect to gas species, pore pressure, effective stress and
temperature were studied. The conclusions can be summarized as follows:
(1) Gas adsorption results show that both pressure and temperature have
significant impact on adsorption behavior for SQB-1 and JB-1 using CH4. For
higher rank coal SQB-1, adsorption isotherm tends to reach adsorption
capacity quicker with respect to gas pressure. However, the adsorption
capacity is higher for the lower rank coal JB-1. Moreover, temperature has a
stronger effect on reducing adsorption capacity for the lower rank coal.
(2) Gas diffusivity for OB-1 and JB-1 reveals that CO2diffusivity is generally
larger than that of CH4 and then N2. This could be related to the different
kinetic diameters of the molecules and their interaction with the coal. Both
pressure and temperature have impact on gas diffusivity. In general, gas
diffusivities increase with pressure and temperature.
(3) Permeability varies greatly with respect to coal rank with highest rank coal
having the lowest permeability. Permeability is also strongly sensitive to
effective stress and pore pressure. Temperature has a noticeable impact on
permeability change. Permeability increases with temperature increase for
the higher rank coal but decreases for the lower rank coal sample studied.
This may be attributed to the combined effect of coal swelling change due to
gas adsorption and thermal expansion.
These results provide important information for the understanding of gas storage
and transport behaviors in different rank coals and would be useful for the reservoir
simulation of CBM/ECBM processes for better understanding of the temperature and
pressure impact on the field scale.
ACKNOWLEDGEMENTS
The financial support from the Australian and Chinese Government Joint
Coordination Group on Clean Coal Technology Research & Development Scheme is
greatly acknowledged.
This research was also funded by the National Major Research Program for Science
and Technology of China (Grant No. 2011ZX05034-001), the National Basic
Research Program of China (Grant No. 2009CB219604), the National Natural Science
Foundation of China (Grant No. 40972107), the PetroChina Innovation Foundation
(Grant No. 2010D-5006-0101), the PCSIRT (Grant No. IRT0864) and the Research
Program for Excellent Doctoral Dissertation Supervisor of Beijing (YB20101141501).
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