On the Validity of Thermogravimetric Determination of Carbon Gasication Kinetics

8/13/2019 On the Validity of Thermogravimetric Determination of Carbon Gasication Kinetics

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Chemical Engineering Science 57 (2002) 29072920

www.elsevier.com/locate/ces

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.

PII: S 0 0 0 9 - 2 5 0 9 ( 0 2 ) 0 0 1 8 9 - 6


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2908 B. Feng, S. K. Bhatia / Chemical Engineering Science 57 (2002) 29072920

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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B. Feng, S. K. Bhatia / Chemical Engineering Science 57 (2002) 29072920 2909

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


0.000 0.005 0.010 0.015 0.020

q1,q3

0

3

6

9

120 250 500 750 1000


0.000 0.005 0.010 0.015 0.020

q1,q3

0

3

6

9

120 250 500 750 1000


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


T= 973 K

PCO2

= 1 bar

q1

q3


T= 973 K

PCO2

= 0.5 bar

q1

q3


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


8/14


[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


0 500 1000 1500 2000

q3

T= 673 K

PO2= 1.0 bar


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


0 500 1000 1500 2000

q1

T=1573 K

PO2

= 0.06 bar

q3


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


0 500 1000 1500 2000

q1

T=1873 KP

O2= 0.06 bar

q3

(a) (b)

(c) (d)


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


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


9/14


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


10/14


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


11/14


temperature (K)

500 1000 1500 2000


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


12/14


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


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.


13/14


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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Documents

On the Validity of Thermogravimetric Determination of Carbon Gasication Kinetics