# 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.

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Page 1

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

Page 2

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).

A. Busch et al. / International Journal of Coal Geology 60 (2004) 151–168

152

Page 3

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

A. Busch et al. / International Journal of Coal Geology 60 (2004) 151–168

153

Page 4

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.

A. Busch et al. / International Journal of Coal Geology 60 (2004) 151–168

154

Page 5

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

A. Busch et al. / International Journal of Coal Geology 60 (2004) 151–168

155

Page 6

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.

A. Busch et al. / International Journal of Coal Geology 60 (2004) 151–168

156

Page 7

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.

A. Busch et al. / International Journal of Coal Geology 60 (2004) 151–168

157

Page 8

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).

A. Busch et al. / International Journal of Coal Geology 60 (2004) 151–168

158

Page 9

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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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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