Methane and carbon dioxide adsorption–diffusion experiments on coal: upscaling and modeling

Abstract

Numerical modelling of the processes of CO2 storage in coal and enhanced coalbed methane (ECBM) production requires information on the kinetics of adsorption and desorption processes. In order to address this issue, the sorption kinetics of CO2 and CH4 were studied on a high volatile bituminous Pennsylvanian (Upper Carboniferous) coal (VRr=0.68%) from the Upper Silesian Basin of Poland in the dry and moisture-equilibrated states. The experiments were conducted on six different grain size fractions, ranging from <0.063 to ∼3 mm at temperatures of 45 and 32 °C, using a volumetric experimental setup. CO2 sorption was consistently faster than CH4 sorption under all experimental conditions. For moist coals, sorption rates of both gases were reduced by a factor of more than 2 with respect to dry coals and the sorption rate was found to be positively correlated with temperature. Generally, adsorption rates decreased with increasing grain size for all experimental conditions.Based on the experimental results, simple bidisperse modelling approaches are proposed for the sorption kinetics of CO2 and CH4 that may be readily implemented into reservoir simulators. These approaches consider the combination of two first-order reactions and provide, in contrast to the unipore model, a perfect fit of the experimental pressure decay curves. The results of this modeling approach show that the experimental data can be interpreted in terms of a fast and a slow sorption process. Half-life sorption times as well as the percentage of sorption capacity attributed to each of the two individual steps have been calculated.Further, it was shown that an upscaling of the experimental and modelling results for CO2 and CH4 can be achieved by performing experiments on different grain size fractions under the same experimental conditions.In addition to the sorption kinetics, sorption isotherms of the samples with different grain size fractions have been related to the variations in ash and maceral composition of the different grain size fractions.

Full text

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Methane and carbon dioxide adsorption–diffusion experiments
on coal: upscaling and modeling
Andreas Busch*, Yves Gensterblum, Bernhard M. Krooss, Ralf Littke
Institute of Geology and Geochemistry of Petroleum and Coal, Aachen University (RWTH-Aachen), Aachen, Germany
Received 5 January 2004; accepted 20 May 2004
Available online 14 August 2004
Abstract
Numerical modelling of the processes of CO2storage in coal and enhanced coalbed methane (ECBM) production requires
information on the kinetics of adsorption and desorption processes. In order to address this issue, the sorption kinetics of CO2
and CH4were studied on a high volatile bituminous Pennsylvanian (Upper Carboniferous) coal (VRr=0.68%) from the Upper
Silesian Basin of Poland in the dry and moisture-equilibrated states. The experiments were conducted on six different grain size
fractions, ranging from <0.063 to f3 mm at temperatures of 45 and 32 jC, using a volumetric experimental setup. CO2
sorption was consistently faster than CH4sorption under all experimental conditions. For moist coals, sorption rates of both
gases were reduced by a factor of more than 2 with respect to dry coals and the sorption rate was found to be positively
correlated with temperature. Generally, adsorption rates decreased with increasing grain size for all experimental conditions.
Based on the experimental results, simple bidisperse modelling approaches are proposed for the sorption kinetics of CO2and
CH4that may be readily implemented into reservoir simulators. These approaches consider the combination of two first-order
reactions and provide, in contrast to the unipore model, a perfect fit of the experimental pressure decay curves. The results of this
modeling approach show that the experimental data can be interpreted in terms of a fast and a slow sorption process. Half-life
sorption times as well as the percentage of sorption capacity attributed to each of the two individual steps have been calculated.
Further, it was shown that an upscaling of the experimental and modelling results for CO2and CH4can be achieved by
performing experiments on different grain size fractions under the same experimental conditions.
In addition to the sorption kinetics, sorption isotherms of the samples with different grain size fractions have been related to
the variations in ash and maceral composition of the different grain size fractions.
D 2004 Elsevier B.V. All rights reserved.
Keywords: Adsorption kinetics; Sorption isotherms; Carbon dioxide; Methane; Diffusion; CO2storage; Coalbed methane; Reservoir modeling
1. Introduction
Coalbed methane (CBM) production combined
with CO2injection is presently an issue of intense
investigation worldwide. This combination is expec-
ted to enhance CBM production (ECBM) while
providing an opportunity for subsurface storage of
large amounts of CO2. Apart from the increase in
CBM recovery efficiency, CO2 injection into coal
seams could contribute to the reduction of green-
house gas emissions as required by the 1997 Kyoto
agreement.
0166-5162/$ - see front matter D 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.coal.2004.05.002
* Corresponding author. Tel.: +49-241-80-98293; fax: +49-241-
80-92152.
E-mail address: busch@lek.rwth-aachen.de (A. Busch).
www.elsevier.com/locate/ijcoalgeo
International Journal of Coal Geology 60 (2004) 151–168

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In Europe, the feasibility of CO2storage in coal
seams is presently being investigated in the EC
RECOPOL project, which involves laboratory tests,
numerical modelling and a pilot injection of CO2into
Pennsylvanian (Upper Carboniferous) coal seams in
the Upper Silesian Basin of Poland. RECOPOL is the
first project of this kind outside North America. The
laboratory tests performed at RWTH-Aachen provide
fundamental data on the gas storage capacity of CO2
and CH4of dry and moist coal (Krooss et al., 2002;
Busch et al., 2003a) and information on the adsorp-
tion behaviour of mixtures of the two gases (prefer-
ential sorption, Busch et al., 2003b) as well as on the
pore structure of coals of different rank (Prinz et al.,
2004).
AnotheraspectofmajorimportanceforCO2storage
and CO2-enhanced CBM recovery is the rate of CO2
adsorption and CH4desorption. To address this issue,
adsorptionkineticexperimentswithbothCO2and CH4
were performed on six different grain size fractions
(<0.063 to f3 mm) of a coal sample from the Upper
Silesian Coal Basin in Poland. The purpose of this
study was (I) to define a simple empirical model
describing the adsorption rates of the two gases, (II)
to attempt an extrapolation of the data from the labo-
ratory to the reservoir scale, (III) to relate sorption
isotherms to different coal properties of different par-
ticle sizes, and (IV) to contribute to a better under-
standing of the combined CO2storage and CBM
production technologies.
1.1. Processes and mechanisms of gas transport and
sorption in coal
The development and implementation of reservoir
simulators for CBM production, ECBM processes,
and CO2storage requires detailed and reliable infor-
mation on fluid transport processes in coal. An im-
proved understanding of these processes from the
macroscopic to the microscopic scale is important
for the accurate prediction of gas and water produc-
tion rates as well as CO2injection rates. The mech-
anisms of storage and transport of gas and water in
coal differ significantly from conventional gas reser-
voirs. Commonly, gas transport in coal is considered
to occur at two scales: (I) laminar flow through the
cleat system, and (II) diffusion through the coal
matrix. Flow through the cleat system is pressure-
driven and may be described using Darcy’s law,
whereas flow through the matrix is assumed to be
concentration-driven and is modeled using Fick’s law
of diffusion. Gas storage by physical adsorption
occurs mainly in the coal matrix (Harpalani and Chen,
1997).
Literature on gas–coal interactions focuses mainly
on the adsorption capacity of coal at pressure–tem-
perature conditions in the CO2-subcritical state, while
adsorption rates have received little attention. Some
exceptions are the works of Marecka and Mianowiski
(1998), Ciembroniewicz and Marecka (1993), Clark-
son and Bustin (1999a,b), Laxminarayana and Bustin
(2003), Seewald and Klein (1986) and Smith and
Williams (1984) as well as some very early works
that arose from the German hard coal mining (Dam-
ko ¨hler, 1935; Ju ¨ntgen and Langhoff, 1964; Schilling,
1965).
Sorption kinetic data may be obtained by monitor-
ing the rate of pressure equilibration during individual
pressure steps of volumetric sorption experiments.
These measurements can be readily combined with
the determination of adsorption isotherms for the
assessment of the gas sorption capacity (e.g. Clarkson
and Bustin, 1999b). Investigations of the degassing of
CH4from produced coal have typically considered
processes occurring at atmospheric pressure or during
rapid transfer of coal samples from in situ pressure to
the surface (Smith and Williams, 1984; Schilling,
1965).
Only a few studies (e.g. Marecka and Miano-
wiski, 1998; Ciembroniewicz and Marecka, 1993;
Siemons et al., 2003) report experimentally deter-
mined CO2sorption rates in coal, even though CO2
may be a significant component of coalbed gas
(Greaves et al., 1993). Such studies are also impor-
tant when considering coal seams as storage media
for CO2.
1.2. Theoretical and modeling aspects of sorption
kinetics and diffusion
The interpretation of adsorption rate experiments
requires a combined diffusion–adsorption model on
the coal particle scale. One of the best-known mod-
eling approaches is the bidisperse diffusion model by
Ruckenstein et al. (1971). Other diffusion–adsorption
models are summarised in the paper of Bhatia (1987).
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Clarkson and Bustin (1999a,b) provided an excellent
overview of this topic by combining theoretical and
experimental approaches. Their study discussed uni-
pore as well as bidisperse transport models for dull
and bright coals of different pore size distributions.
Furthermore, their research provides a modification of
the bidisperse transport model of Ruckenstein et al.
(1971) by taking into account the effect of non-linear
sorption isotherms. Recently, Shi and Durucan (2003)
presented a bidisperse pore diffusion model for the
displacement and desorption of CH4in coal by CO2.
In order to test the validity of the existing theoretical
concepts and modify them if required, there is an
increasing demand for reliable experimental data on
the adsorption–desorption kinetics of CH4and CO2
on natural coals.
2. Sample
All experiments reported here were performed on a
single coal sample. The coal was obtained as a block
from a depth of about 900 m from the Silesia mine
(315 LW 155) in the Upper Silesian Basin of Poland.
It was ground and sieved into six different grain size
fractions. This high volatile bituminous Pennsylva-
nian (Upper Carboniferous) coal had a mean random
vitrinite reflectance of 0.68%. The maceral composi-
tion was found to vary strongly with grain size
fraction. Vitrinite contents showed a variation from
60.3 for the smallest up to 72.0% for the largest
fraction. Inertinite contents ranged from 38.7% to
22% and the liptinite contents from 1% to 6% (Table
1). Moisture contents were quite similar for the
individual grain size fractions, whereas ash contents
varied from 10.4 for the smallest to 4.5% for the
largest grain size fraction.
3. Methods
3.1. Sample preparation
The crushed Silesia coal sample was divided and
aliquots were sieved into six different grain size
fractions: <0.063, 0.063 ?0.177, 0.177 ?0.354,
0.354?0.707, 0.707?2.0 and f3 mm. For adsorp-
tion measurements on dry coal, the powdered samples
were dried in the adsorption cell under vacuum for at
least 1.5 h at a temperature of 105 jC. The sieving
process may result in partial enrichment or depletion
of coal macerals in certain grain size fractions. Cloke
et al. (2002) performed a very detailed study of
maceral and ash fractionation during sieving. This
issue will be addressed later in this paper.
Moisture equilibration was carried out according to
the standard ASTM D 1412-93 procedure. After
moisturising, the sample material was transferred
immediately to the adsorption cell. An aliquot was
used for determination of the moisture content. For
further details, see Krooss et al. (2002).
3.2. Experimental
experiments
setupfor sorptionkinetic
Fig. 1A shows the experimental setup for single-
component gas adsorption and sorption kinetic experi-
ments. The device consists of a stainless steel sample
cell, a set of actuator-driven valves, and a high-
precision pressure transducer (maximum pressure 25
MPa, with a precision of 0.05% of the full-scale
value). The volume between valves V2and V3, in-
cluding the dead volume of the pressure transducer,
was used as a reference volume (see below) and was
determined by helium expansion in a calibration run.
The powdered coal samples were placed into the
Table 1
Analytical data of grain size fractions of the coal sample from the Silesia mine, Poland used for CO2and CH4sorption kinetic experiments
Grain size (mm) VRr(%)Liptinite (%)Vitrinite (%) Inertinite (%)Ash (%)Moisture (%)
<0.063
0.063–0.177
0.177–0.354
0.354–0.707
0.707–2
f3
0.68
0.68
0.68
0.68
0.68
0.68
1
2.9
4.7
4.9
5.4
6
60.3
64.5
66.4
68.2
72
72
38.7
32.6
28.8
26.9
22.6
22
10.42
8.62
5.41
4.66
4.33
4.49
2.76
2.57
3.66
3.63
3.16
3.68
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calibrated sample cell. An in-line filter with 2 Am pore
size was used to prevent coal or mineral particles from
entering the valves. The sample cell was kept in a
temperature-controlled oven, the temperature of
which was held constant to F0.1 jC of the set point.
Fig. 1B shows the volumetric parameters used for the
evaluation of the measurements.
To monitor the rate of the sorption process, pres-
sure data-points were initially taken every second and
then at 1-min intervals until equilibration of the gas
phase with the coal was complete. The resulting
pressure decay curves recorded for different grain size
fractions of the coal were then analysed to determine
the gas sorption rate.
A total of 20 sorption kinetic experiments were
performed with CH4and CO2, respectively, on dry
and moist samples of the Silesia 315 LW 155 coal.
Measurements on dry coal were conducted at 45 jC
on six different grain size fractions (listed in Tables 1
and 2). Experiments with CO2and CH4on moist
samples were performed at 45 jC on three grain size
fractions. For comparison, one CO2 and one CH4
sorption experiment was conducted on dry coal at 32
jC. Sorption equilibration was monitored at 3–10
different pressure levels.
4. Results
4.1. Dependence of sorption rate on particle size
The normalised sorption equilibration curves for
the first pressure step on different grain size fractions
of the dry Silesia coal are shown in Fig. 2A and B for
CH4and CO2. The relative pressures were calculated.
As expected, sorption equilibrium is reached fastest
for the smallest grain size fraction. For CH4, equili-
bration times are between about 6 h for the largest and
about 1 h for the smallest grain size fraction. Experi-
ments with CO2show similar trends but significantly
shorter equilibration times of about 2 h for the largest
and about 0.5 h for the smallest grain size fraction.
Fig. 1. Schematic diagram of the experimental set up for single component gas adsorption on coals (A). Volume between V2and V3including
dead volume of pressure transducer used as reference volume. Definitions for the volumetric method for gas sorption measurements (B):
Vref=reference cell volume; Vvoid=void volume of sample cell; Vsample=sample volume; Vsample cell=sample cell volume.
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Direct comparison of the normalised sorption
equilibration curves for CO2 and CH4 in Fig. 3
reveals the relative rates of equilibration for the two
gases. From this diagram, it is evident that sorption
equilibration is significantly faster for CO2than for
CH4.
4.2. Temperature dependence of sorption rate
A comparison of sorption equilibration curves
(first pressure step) recorded at 32 and 45 jC
revealed that for both gases pressure equilibration
is reached fastest for the experiment performed at
45 jC (Fig. 4). For this grain size fraction
(0.707–2 mm), equilibration times for CH4 and
CO2at 45 jC are about 10 and 1 h, respectively,
whereas equilibration times for the 32 jC meas-
urements are about 18 and 2 h for CH4and CO2,
respectively. Therefore a decrease in sorption rates
by a factor of about 2 can be observed upon
temperature reduction by 13 jC.
4.3. Gas sorption rates on dry and moist coal
A comparison of sorption equilibration curves
for dry and moist coal (grain size fraction 0.707–2
mm) is shown in Fig. 5. For both gases, the
sorption equilibration curves measured with the
dry samples show a much steeper decline than
those obtained with the moist samples, indicating
Table 2
Parameters for CH4and CO2sorption rates on dry and moist Silesia coal samples of different grain sizes (Eq. (5))
CH4
‘‘Average’’ grain size
radius (mm)
Fraction sorption
sites I (Q0V)
t1/2[s]=ln(2)/kV
Fraction sorption
sites II (Q0W)
t1/2[s] =ln(2)/kW
45 jC (dry)
P(ini)=3.3825 Mpa
P(ini)=1.84 MPa
P(ini)=2.44 Mpa
P(ini)=2.2075 MPa
P(ini)=2.532 MPa
P(ini)=1.3175 MPa
1.58e?02
2.85e?02
4.43e?02
8.83e?02
3.23e?01
1.25e?00
61%
93%
79%
70%
68%
64%
51.6
89.3
115
159
145
178
39%
7%
21%
30%
32%
36%
478
2030
2270
3780
2470
3820
45 jC (moist)
P(ini)=6.38 MPa
P(ini)=3.12
P(ini)=3.300 MPa
4.43e?02
8.83e?02
3.23e?01
81%
53%
43%
294
439
1150
19%
47%
57%
9650
7610
24800
32 jC (dry)
P(ini)=1.9575 MPa3.23e?01 69% 23331%9290
CO2
‘‘Average’’ grain size
radius (mm)
Fraction sorption
sites I (Q0V)
t1/2[s]=ln(2)/kV
Fraction sorption
sites II (Q0W)
t1/2[s]=ln(2)/kW
45 jC (dry)
P(ini)=0.58 Mpa
P(ini)=0.4775 MPa
P(ini)=0.6775 MPa
P(ini)=0.8525 MPa
P(ini)=0.96 MPa
P(ini)=0.575 MPa
1.58e?02
2.85e?02
4.43e?02
8.83e?02
3.23e?01
1.25e?00
79%
95%
96%
88%
86%
78%
46 21%
5%
4%
12%
14%
22%
11800
1250
1620
1360
585
3070
7.1.7
74.2
86.6
86.0
120
45 jC (wet)
P(ini)=1.5925 MPa
P(ini)=1.7375 MPa
P(ini)=1.435 MPa
4.43e?02
8.83e?02
3.23e?01
86%
58%
47%
114
78.8
156
14%
42%
53%
7670
1160
2850
32 jC (dry)
P(ini)=0.625 MPa3.23e?01 83%64.1 17%691
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much shorter equilibration times. Equilibration
times for CH4 on this grain size fraction were
about 8 and 45 h for the dry and the moist
sample, respectively. For the moist sample, equi-
librium may not even have been reached during
this time period.
For the CO2sorption kinetics experiments (Fig.
5), pressure decline curves on dry and moist Silesia
coal indicate that equilibration times were suffi-
ciently long. Here, equilibrium was reached after
f2 h for the dry and f8 h for the moist coal
experiment.
4.4. Sorption isotherms
The equilibrium sorption isotherms for CH4and
CO2were calculated for the different grain size frac-
tions on a dry, ash-free basis. Experimental errors for
the excess sorption isotherms were below 3% as calcu-
latedbytheGausserrorpropagationlaw.Generally,we
expected to find the same sorption isotherms for all
grain size fractions unless maceral fractionation oc-
curred during sieving.
Fig. 6 shows the CO2and CH4isotherms measured
on dry coal at 45 jC for the six different grain size
Fig. 2. Comparison of normalised CH4(A) and CO2(B) sorption equilibration curves for different grain size fractions of Silesia 315 coal in the
dry state.
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fractions. Obvious variations exist in the isotherms.
These are stronger for CO2but no specific trend can
be observed in terms of shape or maximum sorption
capacities.
5. Interpretation of experimental data
5.1. Single-step model (unipore model)
Various approaches have been used by different
authors to describe the kinetics of gas sorption on
coal and to link this information to pore structure
models. The present work has produced a large
amount of experimental sorption kinetic data under
conditions considered to be relevant for CBM
production and CO2storage in coal. To make these
results applicable for prediction and modeling pur-
poses we have parameterised the experimental
equilibration curves to develop simple, empirical
or semi-empirical equations. These parameterised
equilibration curves may be used in the develop-
ment of more sophisticated sorption models in the
future.
Fig. 4. Comparison of CO2and CH4pressure equilibration curves for the 32 and 45 jC measurements. Grain size fraction: 0.707–2 mm.
Fig. 3. Comparison of CO2and CH4pressure equilibration curves on the f3 mm fraction of the Silesia 315 coal (dry) for two different
pressure levels.
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The first parameterisation involved application of a
simple model for diffusion in homogeneous spherical
particles (Crank, 1975).Althoughthis method does not
provide a perfect fit of the measured data it may be
sufficient, as a first-order approximation for certain
purposessuchasmakingafirstestimateofthetransport
rates in a specific coal reservoir. Among others, Clark-
sonandBustin(1999b) andSmithandWilliams (1984)
have used the unipore approach of Crank (1975) to fit
their experimental data. This model assumes a constant
gas concentration at the surface of the spheres through-
out the sorption process. In the experimental approach
used in this study, the gas concentration is not constant
but decreases with time due to adsorption on the coal
surface. The diffusion model applied instead assumes a
sphere or a number of spheres with radius a, placed in a
fixed volume where the free volume (i.e. not occupied
by the particles) is V. The concentration of sorptive gas
in the free volume is always uniform and is initially C0.
The initial concentration of sorbate within the spheres
is zero. The total amount Mtof gas sorbed after time tis
expressed as a fraction of the corresponding quantity
Fig. 6. CO2and CH4sorption isotherms of different grain size fractions. All measurements performed on dry coal at 45 jC. CO2in solid lines,
CH4in dashed lines. Three percent error bars are given in the diagram for each isotherm.
Fig. 5. Comparison of equilibration times for CH4and CO2on wet and dry coal of the same grain size fraction (0.707–2 mm).
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Mlafterinfinitetimebytherelationship(Crank,1975,
Eq. (6.30)):
Mt
Ml
¼ 1 ?
X
n¼1
l
6aða þ 1Þexpð?Dq2
9 þ 9a þ q2
nt=a2Þ
na2
ð1Þ
Here, qnare the non-zero roots of
tan qn¼
3qn
3 þ aq2
n
;
ð2Þ
whereaistheratioofthevoidvolumeVandthevolume
of the solid spheres, D is the diffusion coefficient, and t
is the equilibration time.
The parameter a is expressed in terms of the final
fractional uptake of gas by the sphere by the equation,
Ml
VC0
¼
1
1 þ a
ð3Þ
Since many CBM/ECBM reservoir simulators operate
witha single-step unipore diffusionmodel,it is usefulto
provide a unipore approximation of the experimental
data. Fig. 7 depicts an attempt to match a fractional
uptake curve with the simple unipore diffusion model
given in Eqs. (1)–(3) (particle size: f3 mm). The best
fit of the experimental data was obtained with an
effective diffusion coefficient of 7.88?10? 11m2/s. For
comparison, the model curves for diffusion coefficients
of 7.88?10? 10and 7.88?10? 12m2/s are also plotted in
this diagram. Though not perfect, the simple unipore
diffusionmodel yieldsa first-orderapproximationofthe
experimental results. Furthermore, it can be easily inte-
grated into existing CBM/ECBM reservoir simulators.
5.2. Two combined first-order rate functions (bidis-
perse model)
While the unipore diffusion model yields an ap-
proximation of the experimental sorption kinetic data,
animprovedparameterisationofgassorptionprocesses
on coal requires at least the assumption of a two-step
process (cf. Siemons et al., 2003; Cui et al., 2004; Shi
andDurucan,2003). Thisreflects thefact that transport
and successive sorption in macro- and micropores
occurs at different time scales.
Over the past 20–30 years, numerous attempts have
been made to model experimental sorption data by
using bidisperse diffusion models. Among these, the
approach by Ruckenstein et al. (1971) is well known
andusedwidelyinitsoriginalorextendedversion.This
approach assumes a pore model consisting of spherical
particles (macrosphere) containing microspheres of
uniform size. Model equations and solutions are given
elsewhere (Ruckenstein et al., 1971). This model was
found to be inadequate to fit the data obtained in this
study. Clarkson and Bustin (1999b) and Shi and Dur-
ucan (2003) already pointed out the problems encoun-
teredby this model infittinghigh-pressure adsorption–
desorption data, because it assumed linear adsorption
Fig. 7. Fit of experimental sorption rate data using a single-step or unipore diffusion model approach.
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159

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isotherms for CO2and CH4. Generally, sorption iso-
therms for coals are known to be non-linear.
Bhatia (1987) compared different sorption kinetic
models and concluded that a reasonable fit with the
bidisperse model by Ruckenstein et al. (1971) can be
achieved but that inconsistencies exist due to Ruck-
enstein’s assumption of linear isotherms.
Considering the deficiencies of the complex bidis-
perse Ruckenstein model it was decided, mainly for
practical purposes, to describe the gas sorption pro-
cesses in terms of a combination of two first-order rate
functions with different rate constants.
Thenormalisedequilibrationcurveswereexpressed
in terms of the residual (unoccupied) sorption capacity,
Qresidual, as a function of time:
QresidualðtÞ ¼PðtÞ ? Pl
P0? Pl
Here P0and Pldenote the initial and final system
pressures of a given pressure step, and P(t) is the
system pressure at time t.
Qresidual(t) is then expressed by the combined first-
order rate function,
ð4Þ
QresidualðtÞ ¼ Q0V ? expð?kV ? tÞ þ Q0W ? expð?kW ? tÞ
ð5Þ
where Q0V, Q0W are the normalised sorption capacities
withQ0W=1?Q0V,andKV ,KWarethetwofirst-orderrate
constants.
Fig. 8 shows a comparison of two approaches to
match the experimental pressure decline curve. The
first approach based on a single first-order rate sorp-
tion model gives only a rough approximation. When
using two combined first-order rate functions, a per-
fect fit of the data can be achieved.
6. Results using the first-order kinetic model
6.1. Grain size dependence
Evaluations of the experimental data with the
bidisperse first-order kinetic approach revealed that,
for measurements on dry samples and depending on
the grain size, 77–95% of the CO2adsorption and
65–93% of the CH4adsorption is accounted for by
a rapid sorption step followed by a slow sorption
step accounting for 5–23% of the CO2and 7–35%
of the CH4 sorption (Fig. 9). In this diagram, the
smallest grain size fraction (<0.063 mm) has been
excluded, because this fraction is considered to
contain an extraordinarily high percentage of mac-
roporosity (Nandi and Walker, 1975), which makes
it unusable for comparison.
With an increase in the average grain size radius,
the fraction of the sorption capacity associated with
the slow sorption process increases for both gases
while the sorption capacity associated with the rapid
sorption process decreases.
Fig. 8. Comparison of the fits of an experimental pressure decline curve with a single first-order rate function and with two combined first-order
rate functions.
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Half-life times as characteristic parameters of the
combined adsorption–diffusion processes are plotted
in Fig. 10 (CH4) and Fig. 11 (CO2) as a function of
grain size. As expected, for the dry samples half-life
times for sorption increase with increasing grain size
for CH4(rapid and slow sorption process) and for the
rapid sorption process of CO2. Quite unexpectedly, for
the slow CO2sorption process the half-life times show
a tendency to decrease with increasing particle size
(Fig. 11). The reasons for this behaviour are so far not
understood and additional measurements are required
to confirm this observation. All trends (rapid and slow
sorption process; CO2and CH4) approach a constant
value for the larger grain size fractions.
6.2. Pressure dependence of sorption kinetics
To evaluate the dependence of the sorption rate on
the gas pressure and, correspondingly, surface cover-
age (Mt/Ml), the 0.707–2 and f3 mm fractions
were analysed in detail with respect to variations in
sorption half-life times as a function of surface cov-
erage. Results of these evaluations are given in Figs.
12–15.
Fig. 9. Normalised sorption capacity versus average radius of grain size fraction for CH4and CO2on dry Silesia coal at 45 jC (fast sorption
process: regression in solid lines; slow sorption process: regression in dashed lines).
Fig. 10. Half-life sorption times versus grain size for CH4on dry Silesia coal at 45 jC.
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Figs. 12 and 13 show the half-life sorption times
for the rapid and slow sorption processes of CH4. The
two processes generally show distinctly different
behaviour with increasing values of Mt/Ml. While
for the rapid sorption process a slight decrease at low
Mt/Ml values is observed, followed by a slight
increase in half-life sorption times with increasing
Mt/Mlvalues, the slow sorption process shows no
variations initially but a strong and sudden increase in
half-life sorption times at high Mt/Mlvalues.
A similar behaviour is observed for CO2. The rapid
sorption process shows only slight variations in half-life
sorption times with increasing Mt/Mlvalues. At a
higher surface coverage, similarly to CH4, a strong
increase in half-life sorption times can be observed
aboveMt/Mlvaluesofabout0.6–0.7(Figs.14and15).
7. Discussion
7.1. Effect of grain size
The decreasing relative sorption capacity as well as
the increasing sorption rates observed for the rapid
Fig. 12. CH4half-life sorption time of the rapid sorption process as a function of Mt/Mlfor the grain size fractions 0.707–2 and f3 mm. Dry
coal at 45 jC.
Fig. 11. Half-life sorption times versus grain size for CO2on dry Silesia coal at 45 jC.
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process with increasing grain sizes may be attributed to
more complex pore structures on different scales in the
larger particles. It can be assumed that these pore
structures are partly destroyed during grinding of the
coal. Nandi and Walker (1975) observed similar effects
of increasing diffusion rates with decreasing grain size.
They concluded that grinding produces additional
macropores, resulting in a positive influence on the
sorption rate. Siemons et al. (2003) performed a
similar set of experiments and found that above a
certain particle diameter (f0.5–1.0 mm) the sorption
rates remain more or less constant. This effect is
confirmed by investigations by Airey (1968) and
Bertand et al. (1970). They concluded from their
studies that if a particle exceeds a certain size (f6
mm), increasing the size affects the diffusion coeffi-
cient only slightly (Airey, 1968). This is because, in
larger particles, transport along cracks or cleats
becomes the controlling factor while the inter-cleat
diffusion distances remain essentially constant. Kara-
can and Mitchell (2003) stated that gas sorption rates
in vitrinite and liptinite are low due to their micropo-
Fig. 14. CO2half-life sorption time of the rapid sorption process as a function of Mt/Mlfor the grain size fractions 0.707–2 and f3 mm. Dry
coal at 45 jC.
Fig. 13. CH4half-life sorption time of the slow sorption process as a function of Mt/Mlfor the grain size fractions 0.707–2 and f3 mm. Dry
coal at 45 jC.
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rous nature. The current sample set showed the largest
vitrinite and liptinite contents as well as the lowest
sorption rates in the larger particles, therefore confirm-
ing the observations of Karacan and Mitchell (2003).
With respect to the sorption isotherms, no specific
trend was observed for the two gases or between the
two gases. The variability in the isotherms may be due
to variations in maceral composition and ash content of
the different particle size fractions. Cloke et al. (2002)
analysed maceral and proximate properties of different
coals worldwide with respect to different grain sizes
(<38 to f212 Am). They found the highest ash
contents and the lowest fusinite (inertinite) contents
in the smallest grain size fractions. On the other hand,
liptinite content increased with particle size due to its
reduced grindability. Fixed carbon and volatile matter
concentrations did not show a trend with increasing
grain size and vitrinite content. Bustin and Clarkson
(1998) have shown that for isorank coal samples there
is a ‘‘poor to good’’ positive correlation (depending on
the coal seam) between vitrinite content and CH4
adsorption capacity. This observation is supported by
Lamberson and Bustin (1993) and Crosdale et al.
(1998), who found that vitrinite has a greater adsorp-
tion capacity than inertinite. The maceral variations
given in Table 1 confirm the results of Cloke et al.
(2002). It can be assumed that the varying vitrinite
contents throughout the different grain sizes could be a
controlling factor of the varying sorption capacities.
To eliminate the effect of varying ash contents in
the individual grain fractions, sorption capacities and
isotherms were calculated on a dry, ash-free basis.
Mineralization in the fractures might have an influ-
ence on the transport properties (laminar flow or
diffusion) in the coal by blocking certain pathways
(Gamson et al., 1993). This should affect larger
particles because it is assumed that in these particles
macro- and microfractures are preserved better than in
smaller particles. In conclusion, a combination of
factors can be assumed to influence the isotherms
measured for the different grain size fractions. Vitri-
nite is more abundant in larger particles, resulting in a
larger sorption capacity. On the other hand, possible
mineralization in large particles might cause an oppo-
site effect. It is further considered that larger particles
contain a smaller percentage of macroporosity (Nandi
and Walker, 1975). It is well known that macro-
porosity has lower sorption capacities than micropo-
rosity, which would be a hint for lower sorption
capacities in smaller particles. Therefore it is assumed
that the excess sorption isotherms in Fig. 6 are a
combination of these effects which would explain
their non-linearity with grain size.
7.2. Effect of moisture
Suuberg et al. (1993) theorised that water is a good
swelling agent, therefore reducing gas diffusivity and
Fig. 15. CO2half-life sorption time of the slow sorption process as a function of Mt/Mlfor the grain size fractions 0.707–2 and f3 mm. Dry
coal at 45 jC.
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permeability in coal. According to Jahne et al. (1987),
diffusivityofCH4andCO2inwaterareverysimilar (in
the order of 10? 5cm2/s) and, hence, diffusion through
water does not play a major role in the transport
processesincoal.ThimonsandKissell(1973)assumed
an accumulation of water by multilayer adsorption and
capillary condensation in the coal structure. The result-
ing effect would be a reduction of the pore radii and
thus a reduction of gas diffusion rates.
7.3. Effect of temperature
It is generally observed that the sorption capacity
for individual gases (CO2and CH4) increases with a
decrease in temperature (e.g. Schilling, 1965; Krooss
et al., 2002). The sorption rate is also affected by
temperature (Fig. 4). This is evident from the pressure
equilibration curves for CH4and CO2: Equilibration
times for measurements at 32 jC are significantly
longer than those at 45 jC due to a decrease in
diffusion rates.
7.4. Effect of pressure
Few data are available regarding the effects of gas
pressure on transport processes in coal, specifically
with respect to CO2. One exception is the work by Cui
et al. (2004) who were able to show a clear negative
correlation of micro- and macropore diffusivity with
pressure over a broad pressure range (0 to f6 MPa)
for CO2, CH4and N2.
In the present work, a clear reduction of sorption
rate with pressure or surface coverage was observed
only for the slow sorption processes of CO2and CH4,
and only at elevated pressures. For CH4, even a slight
decrease in the half-life sorption time (increase in
sorption rate) with pressure was observed. This ob-
servation is supported by Nandi and Walker (1975),
who performed CH4desorption experiments at 25 jC
on coal samples of different maturity. They found that
a high volatile A bituminous coal sample did not show
any change of desorption rate with pressure up to 2.1
MPa. In the present study, a clear pressure dependence
of adsorption rate was observed, however, for higher
rank coals. The sudden increase in sorption half-life
time was attributed to a concentration effect or swell-
ing of the coal matrix. This would imply that the
effect of swelling on the sorption rate is only impor-
tant at high pressure or high surface coverage. This
observation contrasts the results of Cui et al. (2004)
that documented a continuous and gradual decrease of
diffusion rates with pressure.
7.5. Methane versus carbon dioxide
Throughout this study, it was observed that CO2
sorption rates are consistently higher by a factor of 2–
3 (for moist samples by a factor of 5–6) than those for
CH4, when comparing single-gas sorption experi-
ments. The fact that the diffusivity of CO2in dry coal
is higher than that of CH4has already been pointed
out by Clarkson and Bustin (1999b) based on exper-
imental data and numerical calculations. Cui et al.
(2004) arrived at the same conclusion from theoretical
considerations. Larsen (2004) concluded from his
study that CO2 has a more favourable interaction
enthalpy than hydrocarbons, which enables it to
diffuse more rapidly into coals.
It is well known from polymer science that CO2has
a higher diffusion coefficient in polymer membranes
than CH4(Shieh and Chunh, 1999; Xu et al., 2003).
This observation is attributed to its lower kinetic
diameter (CO2: 3.3; CH4: 3.8) and higher solubility
in polymer membranes. Sorption experiments with
CO2/CH4mixtures, have shown that, particularly at
low pressure (<6 MPa), CH4may become preferen-
tially adsorbed with respect to CO2both on dry and
moist coal (Busch et al., 2003a,b; Krooss et al., 2002).
Furthermore, preferential desorption of CO2as com-
pared to CH4has been observed during gas mixture
experiments on different coal samples. This indicates
that the adsorption–desorption behaviour of gas mix-
tures cannot be readily derived from single-gas sorp-
tion measurements or results from polymer science,
especially in the case of supercritical CO2. The effects
causing preferential or selective sorption from gas
mixtures on natural coal are still poorly understood.
7.6. Upscaling from laboratory to reservoir scale
In combination with the sorption kinetic experi-
mental data, the simple modeling approach used in
this study provides a first step for the implementation
of sorption kinetics into CBM/ECBM reservoir sim-
ulators and to extrapolate from laboratory to reservoir
scale.
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