on the validity of thermogravimetric determination of carbon gasication kinetics
TRANSCRIPT
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Chemical Engineering Science 57 (2002) 29072920
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On the validity of thermogravimetric determination ofcarbon gasication kinetics
Bo Feng, Suresh K. Bhatia
Department of Chemical Engineering, The University of Queensland, St Lucia, Qld. 4072, Australia
Received 4 January 2002; received in revised form 11 March 2002; accepted 23 April 2002
Abstract
Thermogravimetric analysis has been widely applied in kinetic studies of carbon gasication, with the associated temporal weight change
proles being used to extract kinetic information and to validate gasication models. However the weight change proles are not always
governed by the intrinsic gasication activity because of the eect of chemisorption and its dynamics. In the present work we theoretically
determine the criteria under which weight change proles can be used to determine intrinsic kinetics for CO2 and O2 gasication by
examining the region in which the chemisorption dynamics can be assumed pseudo-steady. It is found that the validity of the pseudo-steady
assumption depends on the experimental conditions as well as on the initial surface area of carbon. Based on known mechanisms and
rate constants an active surface area region is identied within which the steady state assumption is valid and the eect of chemisorption
dynamics is negligible. The size of the permissible region is sensitive to the reaction temperature and gas pressure. The results indicate that
in some cases the thermogravimetric data should be used with caution in kinetic studies. A large amount of literature on thermogravimetric
analyzer determined char gasication kinetics is examined and the importance of chemisorption dynamics for the data assessed.
? 2002 Elsevier Science Ltd. All rights reserved.
Keywords: Adsorption; Carbon; Energy; Gasication; Kinetics; Reaction engineering
1. Introduction
Thermogravimetry provides one of the most convenient
and widely used methods for analyzing the kinetics of
gassolid reactions, and distinguishing between competing
models. The method relies on the measurement of tempo-
ral variation of sample mass and of the rate of change of
mass, as reaction occurs, using a thermogravimetric ana-
lyzer (TGA). The resulting curve of variation of sample
weight with time, and of its derivative (the rate curve), is
then represented in terms of a rate-conversion curve thatis interpreted by means of a suitable model. In doing so
it is commonly assumed that the rate is proportional to
the geometric area of the gassolid interface, so that the
rate-conversion curve is then linearly related to the varia-
tion of the geometric surface area with conversion. Suitable
structural models are available for prediction of the evolu-
tion of surface area with conversion (Sahimi, Gavalas, &
Tsotsis, 1990; Bhatia & Gupta, 1994) and by this means
Corresponding author. Tel.: +61-7-3365-4263; fax: +61-7-3365-
4199.
E-mail address: [email protected] (S. K. Bhatia).
the TGA proles are interpreted and the reaction kinetics
analyzed. Carbon and char gasication perhaps provides the
most illustrative and interesting application of this method,
in which the often-observed maximum in reaction rate with
increase in conversion (Hashimoto, Miura, Yoshikawa, &
Imai, 1979; Ge, Kimura, Tone, & Otake, 1981; Su & Perl-
mutter, 1985) is explained by a variety of structural models
(Petersen, 1957; Bhatia & Perlmutter, 1980; Gavalas, 1980;
Miura & Hashimoto, 1984; Ballal & Zygourakis, 1987; Bha-
tia, 1998; Kantorovich & Bar-ziv, 1994). Perhaps the most
popular of these is the random pore model (Bhatia & Perl-mutter, 1980; Gavalas, 1980).
Although the above approach relating the measured rate
with surface area is long established and widely used, there
have been observations in the literature (Lizzio, Piotrowski,
& Radovic, 1988) suggesting that thermogravimetrically
determined rate-conversion curves must be corrected for
chemisorbed complexes on the carbon surface, and that the
rate maximum may be an artifact of the chemisorption dy-
namics. Thus the observed rate of weight change actually
represents the dierence between the rate of chemisorption
and desorption, and is not necessarily representative of the
intrinsic surface reaction rate (Lizzio et al., 1988).
0009-2509/02/$ - see front matter? 2002 Elsevier Science Ltd. All rights reserved.
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Lizzio et al. (1988) measured the gasication reactiv-
ity of a bituminous coal char in oxygen and carbon diox-
ide using TGA and product gas analysis (non-dispersive
infrared spectroscopy, i.r.). Dierences between reactivity
proles obtained by these two methods were observed and
attributed to signicant amounts of stable complex being
formed during the initial stages of reaction. The TGA reac-tivity proles become equivalent to i.r. reactivity proles,
when corrected to account for stable complex formation.
This suggests that the former may not provide accurate rep-
resentation of the variation in intrinsic reaction rate in this
case.
Guerin, Siemieniewska, Grillet, and Francois (1970) have
also observed the signicant eect of chemisorbed oxygen
on TGA reaction rates. The reactivities of a lignite char,
gasied at various partial pressures of oxygen at temper-
atures between 573 and 673 K, were determined by TGA
and i.r. analysis. Their comparison showed considerable dis-
agreement, particularly during the initial stages of gasica-
tion. They attributed this to the ability of the char to adsorb
large amounts of oxygen at the reaction temperature. During
the initial stages of gasication, even negative reactivities
were measured and interpreted to imply that the mass gain
due to chemisorption exceeded the mass loss due to char
gasication.
However gasication kinetics have also often been well
tted by the random pore model with parameters correspond-
ing to experimentally determined ones (Su & Perlmutter,
1985; Chi & Perlmutter, 1989; Ge et al., 1981; Lua & Guo,
2001). In these cases the TGA reactivity proles were tted
with chemisorption eects being neglected, and the struc-
tural parameters obtained by the model were close to thosemeasured by gas adsorption techniques. The location of the
maximum was also predictable by the model. This sug-
gests that chemisorption dynamics is not always important,
and in such cases TGA determination of reactivity can be
adequate.
The contradiction between the above investigations does
suggest that there exists a region of parameter values and
operating condition in which the eect of chemisorption
dynamics is not important but outside which the latter is im-
portant. The present paper attempts to locate this region for
carbon gasication in oxygen and carbon dioxide, by study-
ing the criteria of validity of the steady state assumption,i.e. the concentration of the oxygen complex remaining in
an apparent pseudo-steady state during reaction. At such a
pseudo-steady state, the rate of weight change due to accu-
mulation of surface complexes is negligible in comparison
to the total rate of weight change, so that the latter is es-
sentially determined by the intrinsic surface reaction rate.
Under this circumstance, TGA rate data will be adequate for
kinetic studies, and correction to account for chemisorption
dynamics is unnecessary. To perform the analysis we use
published mechanisms and rate constant values for gasica-
tion by carbon dioxide (Huttinger & Nill, 1990) and oxygen
(Hurt & Calo, 2001). Subsequently, a large amount of
literature on TGA-determined char gasication kinetics is
examined and the importance of chemisorption dynamics
for the data assessed.
2. Theoretical approach
The analysis method adopted involves normalization of
the rate equations and examination of the terms in the scaled
equations. The equations for the weight change of carbon as
well as the concentration of oxygen complex are rst written
based on the reaction mechanisms available in the literature
and form the starting point of the analysis. Each variable in
the equations is scaled to unit order of magnitude as is com-
mon to applications of the perturbation technique (Lin &
Segel, 1974; Nayfeh, 1981), in which the zeroth order and
successively improved solutions are obtained in terms of a
small parameter. The scaled equation for the weight change
of carbon is then analyzed for the necessary criteria bycomparing magnitudes of the various terms in the equation.
This approach has been successfully used by Bhatia (1987)
in analysis of pseudo-steady behavior of solid-catalyzed
reactions.
Two gasication models are studied here using this
approach: a well-known CO2 gasication model (Ergun,
1956) and a recently proposed oxidation model (Hurt
& Calo, 2001), which are discussed in the following
sections.
3. Gasication in carbon dioxide
3.1. Model formulation
The CO2 gasication model is formulated based on the
following assumptions:
1. The initial surface is fully accessible. In other words,
there is no blocked porosity that opens during the re-
action, although there is experimental evidence (Buiel,
George, & Dahn, 1999) that some micropores can be
blocked and become inaccessible to the gasifying gases
until after some conversion level. Thus all the initial sur-
face sites are available for gasication reactions. How-
ever, not all of these can actually react, as some maybe very stable basal plane sites. On the other hand, edge
sites and defective basal plane sites may participate in
reaction.
2. The area of a chemisorption site is approximately 8:3 A2
(Gregg & Sing, 1982). Therefore the initial active surface
area per unit mass of carbon, Sg0, can be related to the
initial amount of active sites, [Ct]0(expressed in mol=g),
as follows:
Sg0= [Ct]0 8:3 1020 6:023 1023
= 5:0
104
[Ct]0m
2=g:
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3. The mechanism for CO2 gasication is as follows
(Ergun, 1956):
Cf+ CO2k1k1
C(O) + CO
C(O)k2
CO + Cf; (1)
where Cf is the empty site ready for reaction and C(O)
is the oxygen complex formed by chemisorption of CO2on carbon surface. This two-step mechanism can ex-
plain most of the experimental observations while re-
maining simple in form. More elaborate mechanisms are
available in literature (Key, 1948; Koenig, Squires, &
Laurendeau, 1985; Adschiri, Zhu, & Furusawa, 1987;
Gadsby, Long, Sleightholm, & Sykes, 1948; McCarthy,
1986; Radovic, Jiang, & Lizzio, 1991; Kapteijn, Meijer,
& Moulijn, 1992), but without detailed kinetic data pro-
vided. The above Ergun mechanism has been studied by
many researchers and the kinetic constants are available
(Huttinger & Nill, 1990). Therefore it is used for this
analysis.
4. Diusional limitations are absent, and do not inuence
the kinetics.
Based on the above assumptions and mechanism given
in Eq. (1), the following equations can be written for the
weight change and the concentration of the intermediate
oxygen complex, C(O):
1
w0
dw
dt = (k1[Cf]PCO2 k1[C(O)]PCO)MO
k2[C(O)]MCO; (2)
d[C(O)]
dt =k1[Cf]PCO2 k1[C(O)]PCO k2[C(O)]: (3)
Here Cf is the amount of vacant or free sites per unit initial
mass (mol=g), at any time, w0 is the initial sample mass,
MO is the atomic weight of oxygen (=16) and MCO is the
molecular weight of carbon monoxide (=28).
3.2. Model scaling
When thermogravimetric proles, i.e. sample mass
changes, alone suce to determine the intrinsic rate, the rate
of weight change will be proportional to the total numberof surface sites, i.e.
1w0
dw
dt [Ct]; (4)
where Ctis the total number of sites per unit initial mass, at
any time. The criterion for suciency of the TGA proles
for determining the intrinsic kinetics may be determined by
examining the conditions under which the combination of
Eqs. (2) and (3) reduces to a form similar to Eq. (4). To
this end we utilize the site balance
[Ct] = [Cf] + [C(O)] (5)
along with Eq. (3) to obtain
[C(O)] = 1
ke
k1[Ct]PCO2
d[C(O)]
dt
; (6)
where
ke= k1PCO2 +k1PCO+k2: (7)
Eqs. (2) and (6) now combine to provide
dxdt
=k1k2MCke
[Ct]PCO2
+(keMO+k2MC)
ke
d[C(O)]
dt ; (8)
where
x= 1 ww0
(9)
is the carbon conversion andMC(=MCOMO) is the atomicweight of carbon. Reduction of Eq. (8) to a form simi-
lar to Eq. (4) now rests on the negligibility of the second
term on the right-hand side of Eq. (8) in comparison to the
rst. To obtain the associated criteria it is necessary to ap-
propriately scale the various terms and assess their relative
signicance.
From the rst term on the right-hand side in Eq. (8), it is
readily seen that the process time scale is given by
tc= ke
[Ct]0k1k2MCPCO2(10)
which is the appropriate characteristic value for scaling time.
A suitable scaling value for the amount of surface complex
per initial mass [C(O)] is given by its initial pseudo-steady
state value, obtained upon setting d[C(O)]=dt= 0 at t= 0.
Use of this condition in conjunction with Eqs. (2) and (5)
provides
[C(O)]SS0 =k1PCO2 [Ct]0
ke: (11)
The scaled form of Eq. (8) now follows
dx
d =C
t[Ct]0PCO2 k1(MOke+ k2MC)
k2e
dCC(O)
d ; (12)
where
Ct = [Ct]
[Ct]0(13)
and
CC(O)= [C(O)]
[C(O)]SS0(14)
are the scaled values of [Ct] and [C(O)] respectively and
=t=tc is the scaled time.
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3.3. Criteria for validity of the apparent pseudo-steady
state assumption inCO2 gasication
It is evident that all the terms in the above equation are
scaled to order unity. An apparent steady state concentration
of the surface complex exists if the second term on the
right-hand side is much less than the rst term, in which casethermogravimetric proles suce to determine reactivity.
This requires that
[Ct]0[CO2]k1(MOke+k2MC)
k2e6 0:1 (15)
or
k2e 10[Ct]0[CO2]k1MOke 10[Ct]0[CO2]k1k2MC 0:(16)
In interpreting the above criterion it should be noted that
the negligibility of the second term on the right-hand side
in Eq. (12) does not imply that d[C(O)]=dt= 0 at all times.
Indeed Eq. (3) may be rewritten as
dCC(O)
d =ketc(C
t CC(O)) (17)
so that true steady state on the surface is never achieved ex-
cept whenCt = C
C(O)= 0. The criterion in Eq. (15) merely
implies that the rate of weight change due to accumula-
tion of surface complex is negligible in comparison to that
measured. Proceeding with the analysis of the associated in-
equality in Eq. (16) provides the solution
ke b
b2 4c2
; (18)
where b=10[Ct]0PCO2 k1MOand c=10[Ct]0PCO2 k1k2MC.Equation (18) may be rewritten as
q2 80[Ct]0q1+ 0:5
25 600[Ct]
20q
21+ 480[Ct]0q1; (19)
whereq1= k1PCO2 =k2 andq2= 1 +q1+k1PCO=k2.
Under gasication conditions, the environment is ex-
pected to have a low CO concentration so that k1PCO=k21,and inequality (19) reduces to
q21{1 160[Ct]0} +q1{2 280[Ct]0} + 1 0: (20)Upon dening a1 = 1 160[Ct]0, b1 = 2 280[Ct]0, thesolution of inequality (20) is obtained as
a1 0; (21)
a16 0; q16b1
b21 4a1
2a1=q3: (22)
3.4. Valid region inCO2 gasication
From inequalities (21) and (22) it is clear that there are
two regions in which the steady state assumption is valid,
depending on whethera1 is larger or less than zero. Since
a1 is only a function of [Ct]0, there will be a critical value
of [Ct]0 separating the two regions. This critical value is
[Ct]cr= 1=160 according to the denition ofa1, which cor-
responds to the critical active surface area ofScr=312 m2=g
following assumption 2. This critical active surface area
is readily seen to be related to the specic monolayer ad-
sorption capacity. If the weight of the adsorbed oxygen at
complete coverage is less than 10% of the carbon weight,we have [Ct]0 166 0:1, which after rearrangement isthe rst criteria found for CO2 gasication. Therefore the
two valid regions are as follows for carbon gasication in
CO2:
Region 1: For carbons with initial active surface area of
less than Scr= 312 m2=g, the pseudo-steady state assump-
tion is always valid, independent of the experimental condi-
tions. For such carbons, negligible ( 10%) weight change
occurs even on complete monolayer coverage, and weight
change dynamics then suces in studying gasication
kinetics.
Region 2: For carbons with initial active surface area
larger than Scr = 312 m2=g, an apparent steady state
exists when q16 q3. From its denition it is evident
that q1 is a function of rate constants k1, k2 and gas
pressure, while q3 is only a function of active surface
area. The rate constants of Huttinger and Nill (1990):
k1=k2= 20:9 exp(25 000=RT) bar1, obtained for a carbonwith an initial total surface area of 1 m2=g, were used to
identify the valid region. Fig. 1 shows the variation of q3with [Ct]0, as well as ofq1 at various conditions for carbons
with a site density higher than [Ct]cr, and negligible CO in
the gas (i.e. PCO 0). The value ofq3 decreases quicklywith increase of [Ct]0 whileq1 is independent of [Ct]0. The
horizontal lines in Figs. 1(a)(d) represent the q1 valuesat four gasication conditions: at 973 K in 10 bar CO2, at
1500 K in 1 bar CO2, at 973 K in 1 bar CO2 and at 973 K
in 0.5 bar CO2. Clearly the valid region, in which q16 q3,
is the hatched area in each gure, which is the active sur-
face area region between the critical active surface area,
Scr(312 m2=g), and a certain active surface area, Svalid, at
whichq1 and q3 intersect. The value of the latter,Svalid, de-
pends on the experimental conditions, being 320; 354; 463
and 643 m2=g, respectively, in Figs. 1(a), (b), (c) and (d).
It is also evident that the valid active surface area region
enlarges with decrease of temperature and CO2 pressure.
Fig. 2 shows the variation of Svalid with temperature atvarious CO2 pressures. The region between 312 m2=g and
the Svalid curve is the area in which the steady state as-
sumption is valid at that CO2 pressure. It is clear for any
carbon with an active surface area larger than 312 m 2=g,
the CO2 pressure and reaction temperature should be low
enough to avoid signicance of the chemisorption eect
in kinetic studies in a TGA. In the cases of high-pressure
gasication, the valid active surface region is very narrow
from 312 m2=g to only slightly higher, suggesting that the
steady state assumption will generally be invalid for car-
bons with initial active surface area higher than 312 m2=g
when gasied at high pressures of CO2.
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[Ct]0(moles surface sites/mg solid)
0.000 0.005 0.010 0.015 0.020
q1,q3
0
3
6
9
120 250 500 750 1000
[Ct]0(moles surface sites/mg solid)
0.000 0.005 0.010 0.015 0.020
q1,q3
0
3
6
9
120 250 500 750 1000
[Ct]0(moles surface sites/mg solid)
0.000 0.005 0.010 0.015 0.020
q1,q3
0
3
6
9
120 250 500 750 1000
[Ct]0(moles surface sites/mg solid)
0.000 0.005 0.010 0.015 0.020
q1,q3
0
3
6
9
120 250 500 750 1000
Svalid Svalid
(a) (b)
(c) (d)
Svalid
Svalid
active surface area (m2/g)
T= 973 K
PCO2 = 10 bar
q1
q3
active surface area (m2/g)
T= 973 K
PCO2
= 1 bar
q1
q3
active surface area (m2/g)
T= 973 K
PCO2
= 0.5 bar
q1
q3
active surface area (m2/g)
T=1500 K
PCO2= 1 bar
q1
q3
Fig. 1. Variation of q1 (the horizontal line) and q3 (the solid curve) with the initial density of active sites, [C t]0, for CO2 gasication of carbon at
various conditions. The region in which the steady state assumption is valid ( q16 q3) is the (hatched) area between the left solid vertical line ([Ct]cr)
and the dashed vertical line. The valid region corresponds to initial active surface area between (a) 312 and 320, (b) 312 and 354, (c) 312 and 463 and(d) 312 and 643 m2=g.
temperature (K)
1000 1100 1200 1300 1400 1500
activesurfacearea(m2/g)
300
400
500
600
700
PCO2
= 0.5 bar
PCO2=1.0 bar
PCO2= 5.0 bar
PCO2= 10.0 bar
PCO2= 20.0 bar
Fig. 2. Variation of maximum permissible initial active surface area,
Svalid, with reaction temperature at various CO2 pressures, in the case of
q1= q3 for carbons with active surface area of larger than 312 m2=g. The
region below each curve is the area in which the steady state assumption
is valid at that CO2 pressure.
Most of the carbons and chars used in kinetic studies and
in actual gasication have an active surface area less than
the critical value of 312 m2=g. Therefore, in most cases of
CO2 gasication the steady state assumption will be valid.
The carbon used by Huttinger and Nill (1990) has a total
surface area of 1 m2=g. Consequently, the kinetic data ob-
tained by them are unlikely to be inuenced by chemisorp-
tion dynamics. Thus, they could extract the rate constants
ofk1 and k2 from the gasication kinetics with the surface
under pseudo-steady state conditions.
To compare with the above results, we also studied an
oxidation model as below.
4. Gasication in oxygen
4.1. Model formulation
The oxidation model is formulated based on the following
assumptions:
1. The initial surface is fully accessible and all the surface
sites are available for reaction, though only the active
ones can actually participate in the reaction.
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2. The active surface area is related to the site density
following the relation given earlier: Sg0 = 5:0 104 [Ct]0 m
2=g.
3. The mechanism for carbon oxidation is as follows (Hurt
& Calo, 2001):
2Cf+ O2k1
2C(O);
C(O) + O2k2CO2+ C(O);
C(O)k3CO + Cf: (23)
In this mechanism, step 1 is similar to that in the Ergun
mechanism, except that here the reaction involves two
empty sites. Step 3 is exactly the same reaction as in
the CO2 gasication mechanism, and step 2 is a surface
reaction producing CO2. Any of the steps, particularly
step 2, may be a lumped description of several elementary
steps and probably involves two sites. For simplicity the
reactions are assumed rst order in site density. This
mechanism is capable of describing the major trends in
reaction order, activation energy and CO=CO2 ratio over
a wide range of temperature, and is supported recently
by Haynes (2001). The kinetic data were also given by
Hurt and Calo (2001) by tting the experimental data.
Therefore this mechanism for carbon oxidation is used
for analysis rather than the other mechanisms available
in literature (e.g. Essenhigh, 1981; Walker, Rusinko, &
Austin, 1959; Laurendeau, 1978; Zhuang, Kyotani, &
Tomita, 1995; Back, 1997; Walker, Taylor, & Ranish,
1991; Moulijn & Kapteijn, 1995; Chen, Yang, Kapteijn,
& Moulijn, 1993).
4. The kinetics is not inuenced by diusional limitations.Based on the above assumptions and mechanism given
in Eq. (23), the following equations can be written for the
temporal variation of sample weight and the concentration
of the oxygen complex, C(O):
1
w0
dw
dt =k1[Cf]PO2MO k2[C(O)]PO2MC
k3[C(O)]MCO; (24)
d[C(O)]
dt =k1[Cf]PO2 k3[C(O)]; (25)
where, w0 and w are the initial weight and weight at anytime, while k1, k2 andk3 are the reaction rate constants for
the three steps in Eq. (23).
4.2. Model scaling
The procedure for the normalization and analysis of the
above equation is similar to that in the analysis of the CO2gasication model. First we use the site balance, Eq. (5),
along with Eq. (25) to obtain
[C(O)] = 1
k1PO2 +k3
k1[Ct]PO2
d[C(O)]
dt
(26)
Eqs. (24) and (26) combine to provide
dxdt
=k1PO2 [Ct]MCk1PO2 + k3
{k2PO2 +k3}
+ ke
k1PO2 + k3
d[C(O)]
dt ; (27)
where
ke= k1PO2MO+k2PO2MC+ k3MCO: (28)
It is readily seen from the rst term on the right-hand side
in Eq. (27) that the process time scale is given by
tc= k1PO2 +k3
k1PO2 [Ct]0MC{k2PO2 + k3} (29)
which provides the appropriate characteristic value for scal-
ing time. Again a suitable scaling value for the amount
of surface complex per unit mass [C(O)] is given by its
initial pseudo-steady state value, obtained upon setting
d[C(O)]=dt=0 att= 0. Use of this condition in conjunction
with Eqs. (24) and (5) provides
[C(O)]SS0 =k1PO2 [Ct]0k1PO2 +k3
: (30)
The scaled form of Eq. (27) now follows
dxd
=Ct + kek1PO2 [Ct]0{k1PO2 +k3}2
dCC(O)
d ; (31)
whereCt andC
C(O) have the denitions as in Eqs. (13) and
(14), and =t=tc is the scaled time.
4.3. Criteria for validity of the apparent pseudo-steady
state assumption in oxidation
Eq. (31) indicates that for gasication in oxygen the
steady state assumption is valid when
kek1[O2][Ct]0{k1[O2] +k3}21 (32)
and as for the earlier case the inequality ()1 may be re-placed by ()6 0:1 for all practical purposes. Upon den-ingq1=k1[O2]=k3 and q2=k2[O2]=k3, inequality (32) then
becomes
q21{1 160[Ct]0}+q1{2 280[Ct]0120[Ct]0q2}+ 1 0 (33)
which can be rewritten as
a1q21+b1q1+ 1 0; (34)
where
a1= 1 160[Ct]0; (35)
b1= 2
280[Ct]0
120[Ct]0q2: (36)
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The solution of inequality (34) is obtained as follows:
a1 0; b1 0; (37)
a16 0; q16 b1+
b21 4a12a1
=q3; (38)
a1 0; b16 0; q1 b1
b21 4a1
2a1=q4;
or q16 q3: (39)
Upon substituting a1 and b1 in Eqs. (35) and (36) into
the above inequalities, the criteria become
[Ct]06 1=160; q26 0:333; (40)
[Ct]0 1=160; q16 q3; (41)
[Ct]06 1=160; q2 0:333; q1 q4 or q16 q3:
(42)
4.4. Valid region in oxidation
The rate constants of the reaction steps in Eq. (23)
have been given by Hurt and Calo (2001) as follows:
k1 = 3:3 104 exp(35000=RT)bar1, k2 = 5:7104 exp(130000=RT)bar1 and k3=exp(180000=RT).The rate constants were used here in the above equations to
determine the experimental conditions in which the steady
state assumption is valid.
Eqs. (40) (42) suggest that for oxidation, there are three
regions in which the steady state assumption is valid. How-
ever calculation results using the rate constants show thatwhen [Ct]06 1=160 andq2 0:333,q1 q4 is always true
whileq16 q3 is always false. Therefore the criterion in Eq.
(42) is never satised. As a result, as for the CCO2 reac-
tion, there are only two regions in which the steady state
assumption is valid, separately for carbons with initial site
density larger and less than [Ct]cr= 1=160:
Region 1: For carbons with active surface area less
than 312 m2=g, the steady state assumption is valid when
q26 0:333. Fig. 3 shows the variation ofq2 with temper-
ature at various O2 pressures. Clearly the size of the valid
region depends on both temperature and O2 pressure. At
low O2 pressure (0:05 bar) the steady state assumptionis always valid if the reaction temperature is higher than
Tvalid= 650 K. However at higher O2 pressure (1.0 bar) the
steady state assumption is valid only if the temperature is
higher than 950 K. The value of Tvalid rises with increase
of O2 pressure. Fig. 4 shows the region (hatched area) in
which the steady state assumption is valid for carbons with
active surface area less than 312 m2=g. It is clear that the
invalid region is larger than the valid one. The typical tem-
perature range in TGA studies varies from 600 to 1000 K.
In this temperature range only when the O2 pressure is
very low can we keep the steady state assumption valid.
High-pressure TGA experiments may always be expected
temperature (K)
500 1000 1500 2000 2500
q2=k2[O2]/k3
0.0
0.1
0.2
0.3
0.4
0.5
0.6
q2= 0.333
PO2
= 0.05 bar
PO2
= 0.2 bar
PO2
= 1.0 bar
PO2
= 5.0 bar
PO2
= 10.0 bar
Fig. 3. Variation of q2 with temperature and oxygen partial pressure incarbon oxidation. The region below q2= 0:333 is the area within which
the steady state assumption is valid for carbons with initial active surface
area less than 312 m2=g.
temperature (K)
500 1000 1500 2000
O2pressure
(bar)
0
4
8
12
16
20
temperature (K)
500 600 700 800 900 1000
O2pressure(bar)
0.0
0.2
0.4
0.6
0.8
1.0
Fig. 4. The region (hatched area) in which the steady state assumption isvalid for oxidation of carbons with active surface area less than 312 m2=g.
Inset shows the region for oxidation at O 2 pressure from 0 to 1 bar.
to suer from the eect of chemisorption, and product gas
analysis has to be performed in addition to monitoring the
weight change, for obtaining gasication kinetics.
Region 2: For carbons with initial active surface
area larger than 312 m2=g, inequality (41) species the
pseudo-steady state region. q3 varies strongly with [Ct]0,
and weakly with temperature and PO2 , especially at higher
temperatures ( 850 K), while q1 depends on temperature
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2914 B. Feng, S. K. Bhatia / Chemical Engineering Science 57 (2002) 29072920
[Ct]0(moles surface sites/gm solid)
0.00 0.01 0.02 0.03 0.04
q1and
q3
0.0
0.5
1.0
1.5
2.0
2.5
3.0
active surface area (m2/g)
0 500 1000 1500 2000
q3
T= 673 K
PO2= 1.0 bar
[Ct]0(moles surface sites/gm solid)
0.00 0.01 0.02 0.03 0.04
q1andq3
0.0
0.5
1.0
1.5
2.0
2.5
3.0
active surface area (m2/g)
0 500 1000 1500 2000
q1
T=1573 K
PO2
= 0.06 bar
q3
[Ct]0(moles surface sites/gm solid)
0.00 0.01 0.02 0.03 0.04
q1andq3
0.0
0.5
1.0
1.5
2.0
2.5
3.0
active surface area (m2/g)
0 500 1000 1500 2000
q1
T=1873 KP
O2= 0.06 bar
q3
(a) (b)
(c) (d)
[Ct]0(moles surface sites/gm solid)
0.00 0.01 0.02 0.03 0.04
q1and
q3
0.0
0.5
1.0
1.5
2.0
2.5
3.0
active surface area (m2/g)
0 500 1000 1500 2000
q1
q3
T=1573 K
PO2= 0.12 bar
Fig. 5. Variation ofq1 (the horizontal lines) and q 3 (the solid curves) with the initial density of active sites, [C t]0, for oxidation of carbons with initial
active surface area larger than 312 m2=g at various conditions. The region in which the steady state assumption is valid ( q16 q3) is the area between
the left solid vertical line ([Ct]cr) and the dashed vertical line. The valid region corresponds to initial active surface area between (a) 312 and 312, (b)
312 and 359, (c) 312 and 421 and (d) 312 and 1089 m2=g.
temperature (K)
800 1200 1600 2000
active
surfacearea(m2/g)
0
500
1000
1500
2000
2500
1
2
3
4
56
78
O2pressure
1 - 0.06 bar
2 - 0.12 bar
3 - 0.15 bar
4 - 0.21 bar
5 - 0.50 bar
6 - 1.0 bar
7 - 2.0 bar
8 - 5.0 bar
Fig. 6. Initial active surface area as a function of temperature and O2pressure, in the case of q1 = q3, for carbons with active surface area
larger than 312 m2=g. The region below each curve is the area in which
the steady state assumption is valid at that O2 pressure.
andPO2 and is independent of [Ct]0. Fig. 5 shows the vari-
ation of q1 (horizontal lines) and q3 (solid curves) with
the initial site density. As in Fig. 1 the active surface area
range in which the steady state assumption is valid can be
identied in Fig. 5 as the region between the left solid ver-
tical line ([Ct]cr) and the dashed vertical line. At low re-
action temperatures, q1 is very large and consequently this
region is very small (Fig. 5(a)). The region becomes larger
when temperature is higher and oxygen pressure lower. Asshown in Fig. 5(b), at 1573 K in 0:12 bar O2, the valid ac-
tive surface area region is between 312 and 359 m 2=g. At
1573 K and 0.06 bar O2, the region expands to from 312
to 421 m2=g (Fig. 5(c)). When temperature is even higher
at 1873 K in 0:06 bar O2, the region is rather large between
312 and 1089 m2=g (Fig. 5(d)). Evidently high temperature
and low oxygen pressure should be used for kinetic stud-
ies of carbons with initial active surface area larger than
312 m2=g. This is similar to that for the carbons in region
1. Fig. 6 shows the region in which the steady state as-
sumption is valid in carbon oxidation for carbons in region
2. The region is that between 312 m2=g and each curve for
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B. Feng, S. K. Bhatia / Chemical Engineering Science 57 (2002) 29072920 2915
Table 1
Summary of the analytical results
Reaction Valid regions Key f eatures of valid region
CO2
gasication
(i) Sg 312 m2=g or Always valid for carbon with
active surface area less than
312 m
2
=g(ii) 312 m2=g Sg
Svalid(T; PCO2 ),
Svalid(T; PCO2 ) depicted
in Fig. 2
Low temperature and low
CO2 partial pressure for car-
bons with active surface area
larger than 312 m2=g
O2gasication
(i) Sg 312 m2=g, T
Tvalid(PO2 ), Tvalid(PO2 )
depicted in Fig. 4 or
Low O2 pressure and high
temperature for carbons with
active surface area less than
312 m2=g
(ii) 312 m2=g Sg
Svalid(T; PO2 ),
Svalid(T; PO2 ) depicted in
Fig. 6
Low O2 pressure and high
temperature for carbons with
active surface area larger than
312 m2=g
that O2 pressure. Clearly the region shrinks with increase of
O2 pressure. Also in the typical temperature range of TGA
studies, the region is very small, suggesting that the steady
state assumption is unlikely to be valid in the oxidation of
carbons with active surface area larger than 312 m2=g.
For most carbons the active surface area is expected to
be smaller than 312 m2=g, and the rst criterion will apply.
As discussed above, this provides a limited region in O2pressuretemperature space in which chemisorption dynam-
ics are unimportant. Therefore unlike in CO2 gasication,
the valid region for the steady state assumption in oxidation
is very limited, and it appears that the steady state assump-tion is generally invalid in the typical conditions of TGA
studies unless very low oxygen pressure ( 0:1 bar) is used.
5. Discussion
The above results show that the steady state assump-
tion, and TGA determination of kinetics, can be inade-
quate in some cases, and this depends on the chemical re-
action involved (gasication by CO2 or oxygen), the reac-
tion rate constants, the experimental conditions (temperature
and pressure) and the physical properties of the carbon used(initial active surface area). The results are summarized in
Table 1.
It is interesting to note that the initial active surface
area is very important in determination of the validity of
the steady state assumption. Also a critical active surface
area of 312 m2=g was found for both CO2 gasication
and oxidation. For kinetic studies of CO2 gasication, low
temperature and low pressure should be used for carbons
with initial active surface area larger than 312 m2=g. This
critical active surface area has been shown previously to
be related to the specic monolayer adsorption capac-
ity. Of course there is a limit to which the temperature
can be raised before diusional eects are signicant.
However for kinetic studies of carbon oxidation, low oxy-
gen pressure and high temperature should be used for all
carbons. Also the validity of the steady state assumption is
determined by the value ofq1 which is the multiplication
of the gas pressure and the ratio of rate of the chemisorp-
tion reaction to that of the desorption reaction, for a carbonwith a given initial site density, as suggested in Eqs. (22)
and (41). The steady state assumption is valid when the
value ofq1 is small enough. In CO2 gasication this value
decreases with decrease of temperature and pressure, while
in oxidation it decreases with increase of temperature and
decrease of pressure. Therefore, low temperature and low
pressure in CO2 gasication, and high temperature and low
pressure in oxidation, are favorable for the validity of the
steady state assumption.
Most of the carbons used in kinetic studies have initial
total surface area less than 312 m2=g. Since the active sur-
face area is only part of the total surface area, the initial ac-
tive surface area of the carbons is also less than 312 m2=g.
Therefore, chemisorption dynamics is not important in CO2gasication and the TGA weight change proles are accurate
for kinetic studies. However it can be important in carbon
oxidation in the typical TGA experimental conditions as dis-
cussed above. Indeed the eect of chemisorption dynamics
in carbon oxidation has been apparently overlooked in many
of the TGA studies in literature, as shown in Fig. 7, which
is a compilation of the experimental conditions for carbon
oxidation used by various investigators, showing that many
conditions are outside of the valid region. The fact that the
TGA weight change prole can be inuenced by chemisorp-
tion dynamics may explain several discrepancies reported inthe literature, assuming that the reported TGA proles are
free from diusional limitations. Such limitations can arise
due to transport resistance in the sample holder, in the parti-
cle bed and in the particles themselves. However, it is usual
to conduct control studies with various ow rates, sample
and particle sizes to ensure the absence of diusional limi-
tations.
Lizzio et al. (1988) and Guerin et al. (1970) found the
importance of oxygen chemisorption while Su and Perlmut-
ter (1985) did not. Fig. 8 shows the experimental conditions
of Lizzio et al. (1988) and Su and Perlmutter (1985). The
region below the solid curve is the valid region. It is eas-ily seen that Lizzio et al.s experimental conditions are far
from the valid region while Su and Perlmutters conditions
are partly in the valid region. Lizzio et al. (1988) attributed
the dierences in the reactivity proles of the Illinois coal
char reacted in oxygen and carbon dioxide to the extent to
which the stable oxygen complex forms during char gasi-
cation. Much less oxygen complex was formed during CO2gasication than during oxidation, and therefore the eect of
chemisorption was considered less important in CO2 gasi-
cation. However this may be also explained by the fact
that in CO2gasication, the steady state assumption is valid
while in oxidation it is not. The carbon used in Guerin
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Fig. 7. Experimental conditions used in some TGA investigations in literature, and the critical curve below which the chemisorption dynamics is
unimportant.
temperature (K)
500 600 700 800 900
O2
pressure(bar)
0.0
0.3
0.6
0.9
1.2
Lizzio et al. (1988)
Su & Perlmutter (1985)
Fig. 8. Experimental conditions used in Lizzio et al. (1988) and Su
and Perlmutter (1985), and the critical curve below which chemisorption
dynamics is unimportant.
et al.s experiments has a total surface area of 520 m2=g.
However the active surface area is not known and thus
whether the active surface area is higher or lower than
312 m2=g is unknown. Therefore the experimental condi-
tions are shown in Fig. 9 considering both possibilities. In
the latter case (Fig. 9(a)), the experimental conditions are
in the invalid region in which chemisorption dynamics is
important, particularly for condition 1. In the former case
(Fig. 9(b)), the experimental conditions are also in the in-
valid region. Here it is assumed that the active surface areais equal to the total surface area. Also it is clear in Fig. 9(b),
even if the active surface area is not equal to the total sur-
face area, as long as the active surface area is larger than
312m2=g, the experimental conditions will be very likely in
the invalid region because the valid region is extremely nar-
row. The eect of chemisorption dynamics would then be
important in their case, consistent with their ndings.
Tseng and Edgar (1984) found the characteristic curve,
df=dversus conversion f(=t=t0:5, where t0:5 is the time
to reach 50% conversion), of a lignite is dierent in dier-
ent oxidation temperature ranges (below 400
C and above
400
C). In both of the temperature ranges the reaction is not
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temperature (K)
500 1000 1500 2000
activesurfacearea(m2/g)
200
400
600
800
temperature (K)
500 600 700 800 900
O2pressure(bar)
0.0
0.3
0.6
0.9
1.2
1
2 3 4
1 2 3 4
(a)
(b)
Fig. 9. Experimental conditions used in Guerin et al. (1970), and the
critical curves below which the chemisorption dynamics is unimportant,
assuming (a) the active surface area is less than 312 m2=g and (b)
the active surface area is larger than 312 m2=g but equal to the total
surface area. Numbers 14 correspond to four experimental conditions:
1: 300
C, 0:6 bar O2; 2: 350
C, 0:1 bar O2; 3: 375
C, 0:1 bar O2; 4:
400
C, 0:1 bar O2.
inuenced by particle scale diusional resistances, so that
the characteristic curves should have been the same. They
attributed the dierence in the combustion behavior in these
two temperature ranges to micropore diusional eects. At
lower temperature, the reaction rate is slow enough that the
reactant gas has enough time to diuse into the ultramicro-
pores, while at higher temperature the ultramicropores can-
not be reached by the reactant gas. However this might be
also explained by the dierence in the eect of chemisorp-
tion dynamics in the two temperature ranges. Fig. 10 shows
the experimental conditions they have used, as well as the
temperature (K)
500 600 700 800 900
O2pressure(bar)
0.0
0.3
0.6
0.9
1.2
1
2
3
4
Fig. 10. Experimental conditions used in Tseng and Edgar (1984, 1985),
and the critical curve below which the chemisorption dynamics is unim-
portant. Areas 1 and 2 correspond to conditions for lignite oxidation and
3 and 4 for oxidation of a bituminous coal and an anthracite.
region in which chemisorption dynamics is not important
(below the solid curve). Areas 1 and 2 correspond to the
conditions in the two temperature ranges for lignite oxida-
tion. In area 1 the eect of chemisorption dynamics is more
important than that in area 2. Thus it will certainly inuence
the characteristic curve in area 1 more than that in area 2.
Areas 3 and 4 in Fig. 10 correspond to the experimental con-ditions that Tseng and Edgar (1985) used for the study of
the combustion behavior of a bituminous and an anthracite
coal char. Again the eect of chemisorption in area 3 is more
important than that in area 4. This may partly explain their
observation that the characteristic curve at 600
C is dierent
from that below 600
C, in addition to the diusional eects
at 600
C observed by them.
Miura and Silveston (1989) and Miura, Makino, and Sil-
veston (1990) measured the gasication reactivity of many
Canadian coals and used the random pore model (Bhatia &
Perlmutter, 1980) to analyze the data. They found that al-
though the random pore model tted the experimental datavery well, the tted structural parameter did not agree with
the value estimated from gas adsorption for some coal chars.
They attributed the discrepancy to the inaccuracy of the
techniques for pore structure characterization, and=or the un-
realistic assumptions in the random pore model. Here the
possibility that the eect of chemisorption dynamics is im-
portant for those coals is explored. As discussed above and
shown in Figs. 4 and 6, the region in which chemisorption
dynamics is unimportant is dierent for carbons with ini-
tial active surface area below and above 312 m2=g. Thus
we divide the coal chars in Miura et al. (1990) into two
groups: total surface area below and above 312 m2=g. Again
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because the active surface area is unknown, the active sur-
face area of the coal chars with total surface area larger than
312 m2=g is assumed to be less than 312 m2=g, or larger than
312 m2=g but equal to the total surface area. Figs. 11 and
12 show their experimental conditions as well as the valid
region (below the solid curve) for carbons in groups 1 and
2, respectively. The experimental conditions for carbons ingroup 1 are partly in the region in which chemisorption dy-
namics is unimportant, while those for carbons in group 2
are completely outside the region. In other words, the eect
of chemisorption dynamics is more important for carbons in
group 2 with surface area higher than 312 m2=g. Upon ex-
amining their experimental data we can see that more chars
in group 1 have tted structural parameter close to the mea-
sured one. This implies that the eect of chemisorption dy-
namics can be another reason for the discrepancy between
the tted and measured structural parameter. The coals in
group 2 are generally low-rank coals, which are known to
be very disordered and reactive. It is possible that there are
many defects on the basal planes of the crystallites in these
coals so that the active surface area is close to the total sur-
face area for these coals. However, this needs to be veried
experimentally although there are some related discussions
in literature (Walker et al., 1991).
The steady state region identied in the present study is
admittedly dependent on the mechanism used, and the pub-
lished kinetics of the reactions in the mechanism. However,
the approach can be used for any mechanism provided the
rate constants of the reactions in the mechanism are avail-
able. Further, in the analysis we have used, the admittedly
subjective criterion that
1 can be replaced by 6 0:1.
Even smaller values of the upper limit (e.g. 0.05 or 0.01)may be considered, and will yield more conservative crite-
ria. The choice of this value depends on the accuracy de-
sired in evaluating rate constants and reaction kinetics. How-
ever, given the accuracy with which process variables such
as gas concentration, ow rate and temperature are known,
it is unlikely that it is justiable to adopt a more conser-
vative approach. Nevertheless, regardless of the degree of
conservatism adopted, the essential and important result of
the analysis is that there is a critical active surface area that
governs the adequacy of TGA proles in determining the
reaction kinetics.
It appears that the TGA is sucient for studies of CO2gasication as long as the active surface area of the carbon
studied is less than 312 m2=g, because the steady state as-
sumption is then always valid. However for studies of gasi-
cation by oxygen, there is strong possibility that the TGA
reactivity prole is inuence by oxygen chemisorption. In
particular, at high O2 partial pressure, the TGA reactivity
prole alone is almost always inadequate for kinetic studies
because the steady state assumption is unlikely to be valid
at low temperatures. The product gases must be analyzed to
obtain the true reactivity in this case. Oxygen partial pres-
sure of less than 0.1 bar is recommended for use to remain
in the valid region of the steady state assumption, so that the
temperature (K)
500 600 700 800 900
O2pressure(bar)
0.0
0.3
0.6
0.9
1.2
Fig. 11. Experimental conditions used in Miura et al. (1990) for carbons
with initial active surface area less than 312 m2=g, and the critical curve
below which the chemisorption dynamics is unimportant.
temperature (K)
500 1000 1500 2000
activesurfacearea(m2/g)
200
400
600
800
PO2
= 0.21 bar
Fig. 12. Experimental condition area (hatched) used in Miura et al. (1990)for carbons with initial active surface area larger than 312 m2=g, based
on the assumption that the active surface area is equal to the total surface
area, and the critical curve below which the chemisorption dynamics is
unimportant.
TGA reactivity proles can be used directly without correc-
tion for chemisorption. In practical combustors in which the
temperature is very high ( 1373 K) and oxygen pressure is
low (0.05 0.21 bar), the steady state assumption is expected
to be valid. This implies that if the TGA reactivity pro-
les are not corrected, the kinetic parameters obtained from
the data are not representative of those at high temperature.
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Actually, even after the TGA reactivity proles are cor-
rected, the kinetic data obtained at low temperature cannot
be used at high temperature because in dierent temperature
range dierent reaction steps are in control (Hurt & Calo,
2001).
6. Conclusions
The validity of the steady state assumption, or the negli-
gibility of chemisorption dynamics in thermogravimetry, in
carbon gasication in CO2 and O2 was studied. A critical
initial active surface area of 312 m2=g, which corresponds
to the monolayer adsorption amount being 10% of the ini-
tial carbon weight, was found to be crucial to the validity of
the steady state assumption.
There are two regions in which the steady state assump-
tion is apparently valid, and the chemisorption dynamics
does not signicantly inuence thermogravimetric data, for
gasication in CO2 and in oxygen. Regions correspond tocarbons with active surface area below and above the criti-
cal value. These two regions are summarized in Table 1.
In the typical conditions of TGA studies, the steady state
assumption seems always valid in CO2 gasication, while
it is generally invalid in oxidation. The results suggest that
low oxygen pressure ( 0:1 bar) should be used in kinetic
studies of oxidation using a TGA.
Although the above results depend on the validity of the
mechanisms used and the accuracy of the rate constant of
the reactions in the mechanisms, the approach utilized in the
present work can be used for any mechanism provided the
rate constants in the mechanism are available.
Notation
a1 parameter, 1 160[Ct]0b parameter in Eq. (18)
b1 parameter, 2 280[Ct]0 or 2 280[Ct]0120[Ct]0q2
c parameter in Eq. (18)
C(O) density of C(O); mol=g
[Cf] density of Cf; mol=g
[Ct] site density, mol surface sites=g solid
[Ct]0 initial site density, mol surface sites=g solidCcr critical site density, 1=160 mol=g
Cf empty site ready for reaction
C(O) oxygen complex
CC(O) dimensionless term, [C(O)]=[C(O)]0Ct dimensionless term, [Ct]=[Ct]0k1 rate constant of the rst reaction in Eqs. (1) and
(23), bar1
k1 rate constant of the backward reaction of the rst
reaction in Eq. (1), bar1
k2 rate constant of the second reaction in Eq. (1),
and in Eq. (23), bar1
k3 rate constant of the third reaction in Eq. (23)
ke rate constant (=k1PCO2 + k1PCO + k2 or
k1PO2MO+k2PO2MC+k3MCO) g=mol
MC atomic weight of carbon, 12 g=mol
MCO molecular weight of CO, 28 g=mol
MO atomic weight of oxygen, 16 g=mol
PCO pressure of CO, bar
PCO2 pressure of CO2, barq1 dimensionless term,k1PCO2 =k2for CO2gasica-
tion, ork1PO2 =k3 for oxidation
q2 dimensionless term, 1+q1 +k1PCO=k2for CO2gasication ork2PO2 =k3 for oxidation
q3 parameter, (b1
b21 41)=2a1q4 parameter, (b1+
b21 4a1)=2a1
Sg0 initial active surface area, m2=g
t time, s
tc characteristic time in Eqs. (10) and (29), s
w weight of carbon,g
w0 initial weight of carbon, g
x conversion level, 1 w=w0Greek letters
scaled time,t=tc
Acknowledgements
The nancial support of the Australian Research Council
under the Large Grant Scheme is gratefully acknowledged.
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