Kinetic Model for the Uniform Conversion of Self Reducing Iron Oxide and Carbon Briquettes

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1. Introduction

Extensive research regarding the self-reducing mixture of

iron oxide and carbonaceous materials has been report-

ed.1–5) Iron oxide fines are generated at every stage of iron

oxide processing, leading to either a loss of the iron re-

source or the burden of higher utilisation costs. Being able

to utilise, economically, such iron oxide fines has the poten-

tial to provide significant benefits to the iron industry. The

self reducing mixture represents a possible solution to fine

iron oxide utilisation. In order to realise and optimise this

potential of the self reducing mixture, it is necessary to un-

derstand the fundamental reaction mechanisms. In this

paper, a shortcoming in an existing fundamental kinetic

model is addressed in order to better understand the self re-

duction reactions.

Common methods used to analyse the carbothermic re-

duction of iron oxide have either centred around the firstorder irreversible unimolecular model (i.e.: ln1 X kt ),

variants of the half-life method (e.g .: dX/dt t t o) or using a

rate equation to describe the gasification of carbon (the

Boudouard reaction) by CO2. Interestingly, all three meth-

ods require constant gas concentrations (whether describing

iron oxide reduction or carbon gasification). Self reducing

iron oxide–carbon reactions do not display constant gas

concentrations during reactions.6,7)

Additionally, while there is little doubt that the

Boudouard reaction displays a strong influence on the car-

bothermic reduction of iron oxide, the degree of control it

displays is unclear. This may well be due to the use of inap-

propriate kinetic models to describe the carbothermic re-

duction process.

Haque and Ray8) reviewed the topic of solid–solid reac-

tion for the carbothermic reduction of iron oxide, showing

that for practical situations, self reducing mixtures undergo

indirect reduction (solid iron oxide–gaseous intermediary–

solid carbon). These reactions are outlined in Reaction 1 to

Reaction 4.

Reduction

Reaction 1: 3Fe2O3CO→Fe3O4CO2

Reaction 2: Fe3O4CO→3FeOCO2

Reaction 3: FeOCO→FeCO2

Oxidation

Reaction 4: C(s)CO2(g)→2CO(g)

For the iron oxide–gas reaction (Reaction 1–Reaction 3),

Turkdogan9) examined the carbon monoxide reduction of iron oxide, and determined an activation energy of

47 kJ/mol. Of reactions which make up the iron oxide re-

duction process, the wüstite to iron step (Reaction 3) has

been shown to be the slowest step.1)

The oxidation of carbon by CO2 is an extremely impor-

tant reaction in general, and consequently has been widely

studied. However, activation energies for the CO2 oxidation

of graphite vary from 130kJ/mol (Tiwari et al .10)) to

370 kJ/mol (Turkdogan and Vinters11)). While there is a

wide variance in reported activation energies for the CO2

oxidation of graphite, it can be seen that the activation ener-

gy for CO2

oxidation of graphite is still considerably higher

than that for iron oxide reduction. Therefore the CO2 oxida-

tion of graphite is a more temperature sensitive reaction

than iron oxide reduction.

There is also a consensus among researchers that the

ISIJ International, Vol. 43 (2003), No. 8, pp. 1136–1142

© 2003 ISIJ 1136

Kinetic Model for the Uniform Conversion of Self Reducing Iron

Oxide and Carbon Briquettes

Jeremy MOON and Veena SAHAJWALLA

School of Materials Science and Engineering, University of New South Wales, Sydney 2052 NSW, Australia.

(Received on September 2, 2002; accepted in final form on February 5, 2003 )

A kinetic model has been developed to describe the uniform conversion of a self reducing mixture of iron

oxide and carbon. The model takes into account the reaction kinetics of both the iron oxide reduction and

carbon oxidation. The model is validated with experimental data. Rate constants are compared with those in

the literature.

The combination of existing reaction analysis techniques coupled with the model developed has shown

that for the experimental conditions used here, the Boudouard reaction controls the self reduction kinetics.

KEY WORDS: mathematical modelling; kinetics; uniform conversion model; self-reduction; iron oxide; car-

bon; reduction; oxidation.



Boudouard reaction (Reaction 4) displays a highly control-

ling influence on the overall carbothermic reduction of iron

oxide.1–5) The degree of control the Boudouard reaction dis-

plays, as reported by different researchers, however, is seen

to vary. There is agreement in literature that the overall self

reduction reaction rate is seen to increase with increasing

carbon content; increasing carbon surface area; and in the

presence of Boudouard reaction catalysing agents (includ-

ing metallic iron). These effects are consistent with the

Boudouard reaction displaying a significant influence on

the overall self reduction reaction.

The overall self reduction reaction rate, however, is seen

to level off at higher carbon contents12,13); higher tempera-

tures14,15); and is seen to be improved by decreasing the iron

ore particle size (with the inference of increased surface

area).14) These effects suggest that there is a limitation to

the control the Boudouard reaction displays, which is not

yet fully understood. Such incomplete understanding (re-

garding the degree of control the Boudouard reaction dis-

plays on the overall self reduction rate) introduces difficultyin being able to kinetically describe the reaction system.

Adding to the complexity of unclear controlling reac-

tions is the issue of non-isothermal reactions occurring

within a self-reducing pellet or briquette. In the self reduc-

ing briquette, the reactants are intimately mixed and the re-

action proceeds when a sufficient temperature is achieved

by all or part of the mixture. The very nature of the having

combined, thermally activated reactants raises difficulties

when studying the reaction kinetics.

Work has been conducted, examining the possibility of

briquettes reacting non-homogenously when the tempera-

ture is raised. Several researchers have shown the non-isothermal nature of the self-reducing mixture.16–19) Work

by Seaton et al .18) showed the temperature profile through

the mixture changed with increasing reaction temperature.

They indicated that the mode of reaction changed to a

shrinking core style with increasing temperature.

Accordingly, the complexity of the physical and chemi-

cal system makes the selection of an appropriate reduction

model difficult. The self reduction process is made up of

complimentary oxidation and reduction reactions. However,

investigations have only focussed on the kinetics of either

the oxidation or reduction reactions. The aim of this study

is to provide a method to describe the carbothermic reduc-

tion of iron oxide, taking into account both the iron oxide

reduction reactions and the Boudouard reaction. The effect

of the temperature profile on such an approach is also ex-

amined.

2. Theoretical Background

2.1. Determination of Controlling Reaction

Analysing the reaction off-gas provides an effective and

dynamic method to assist in the determination of the reac-

tion controlling the self reduction process. The oxygen po-

tential of the reaction off gas can be calculated in terms of

P CO/ P CO2and can then be compared against equilibrium

P CO/ P CO2 of the individual component reactions.1) Figure 1shows an example of reaction equilibrium P CO2

/ P CO values

from a standard phase diagram, for the temperature of

1 000°C.

The component reaction which is controlling could then

be determined by a process of elimination. However, as dis-

cussed earlier, it is assumed that if the iron oxide reduction

is rate limiting, then the slowest step is the reduction of

wüstite.

To determine which of the reactions are controlling, it is

first necessary to identify the reaction at equilibrium. A

given reaction is at equilibrium when the off gas P CO/ P CO2

concentration falls on the equilibrium P CO/ P CO2 value for that reaction. Accordingly, the complimentary (reduction of

wüstite/oxidation of carbon) reaction is taken to be the con-

trolling reaction. For example, if the off-gas P CO/ P CO2con-

centrations indicate that the wüstite–iron reaction is at equi-

librium, then it can be inferred that the complimentary

Boudouard reaction is the controlling reaction.

ISIJ International, Vol. 43 (2003), No. 8

1137 © 2003 ISIJ

Fig. 1. Illustration of the method used to determine equilibrium ( P CO2/ P CO) for a given temperature from the iron–oxygen

phase diagram.



2.2. Controlling Kinetic Model

The complexity of the reactions involved in the carbo-

thermic reduction of iron oxide has led to difficulty in the

selection of an appropriate model. There are several meth-

ods generally used to describe the kinetics of the carbother-

mic reduction of iron oxide, such as:

• The first order unimolecular irreversible uniform conver-sion of a self reducing briquette (i.e. ln(1 X ) vs. time,

and its variants), that is1,2);

ln(l X )k · t ..............................(1)

• The comparison of dX /dt at a given time (e.g . t 0). A

variant on this is the examination of the time required to

attain a given degree of reduction (e.g . t / t X )4,5); and

• Given the high degree of control that the Boudouard reac-

tion displays on the overall carbothermic reaction, there

have been attempts to describe iron oxide reduction rates

in terms of carbon gasification rates (Langmuir–

Hinshelwood style equation, see Eq. (5).10)

Interestingly, one of the more common methods, usingln(1 X ), assumes a reaction mechanism of a single mole-

cule reactant, A(s), converting to the reaction products, as is

shown in Eq. (2). For the reduction of iron oxide, the reac-

tion involves more than one molecule (e.g . A(s) and B(g))

and is more like that shown in Eq. (3).

A(s)→ products ..............................(2)

A(s)B(g)→ products..........................(3)

The rate of removal of oxygen for an Eq. (3) style reaction

is of the type:

.......(4)

where the solid removable oxygen concentration in the mix-

ture is represented by C [O]; k O is the rate constant for oxy-

gen removal; A is the reaction area of the controlling reac-

tion; and the gaseous CO driving force is represented by

(C COC COeq.) For the gaseous reduction of iron oxide, the

(C COC COeq.) term is constant and therefore independent of

C [O] which allows the use of the first order irreversible uni-

molecular model (or ln(1 X )).

In the self reducing briquette of iron oxide and carbon,

however, the term (C COC COeq.) is dependent upon theBoudouard reaction. The CO content of the reaction gas is

renewable and cannot be rewritten in terms of C [O]. The rate

of oxygen removal must, nevertheless, be dependent upon

the gas reducibility (C COC COeq.), so therefore the term is re-

tained in the development of a rate equation.

In the case of carbothermic reduction, the P CO/ P CO2com-

position of the reaction gas during the course of reduction

has been shown to vary with degree of reduction.

Accordingly, the rate of the Boudouard reaction cannot be

taken as being constant throughout the reaction process.

It is commonly accepted that the Boudouard reaction fol-

lows a Langmuir–Hinshelwood style equation.

20–23)

TheLangmuir–Hinshelwood style equation (Eq. (5)) describes a

two stage process. The first stage is the reversible adsorp-

tion of an oxygen atom from the gas (i.e. CO2) onto a free

reaction site (Cf ), and hence the formation of a gaseous

CO(g) molecule (Reaction 5). The terms i1 and j 1 are the rate

constants for the forward and reverse reactions respectively.

The second stage is the desorption of the C(O) from the

carbon solid to form a gaseous CO molecule (Reaction 6),

the rate constant of which is the term j 3.

.................(5)

Reaction 5:

Reaction 6:

The reaction order of Boudouard reaction is seen to vary

between 0 and 1. Zeroth order kinetics occur when the con-ditions of k 2 P CO1 and k 3 P CO2

1 are met. First order ki-

netics occur when the conditions of k 2 P CO1 and

k 3 P CO21 are met.20,24,25) Von Fredersdorff and Elliot25)

state that for all other conditions, the kinetics are first order

with respect to CO2 with hindrance from CO and CO2.

During the carbothermic reduction of iron oxide, the P CO

levels are expected to be high, such that the term k 2 P CO is

not insignificant. Therefore, an approximation of first order

kinetics for the carbothermic reduction of iron oxide ap-

pears justified for the model development.

As mentioned earlier, literature has shown that the

Boudouard reaction is considered a controlling reaction in

the overall iron oxide–carbon system.1–5) Therefore, any de-

viation of the reaction gas P CO/ P CO2from the iron oxide

equilibria (and hence the formation of a CO driving force)

is a result of CO production from the Boudouard reaction.

The rate of CO production (using simplified first order ki-

netics) by the Boudouard reaction can be written in terms

of CO2 consumption, as shown in Eq. (6).

.........(6)

where AC is the area of the carbonaceous material and

(C CO2C eq.

CO2) is the Boudouard Reaction driving force (sim-

plified to make an irreversible first order equation). In the

case where the Boudouard reaction displays a strong con-

trolling influence, any formation of an iron oxide reduction

driving force, (C COC eq.CO), is dependent upon the produc-

tion of CO from the Boudouard reaction. The CO produc-

tion in turn is dependent upon the CO2 driving force.

Accordingly, the term (C COC eq.CO) can be replaced by

2k C · (C CO2C eq.

CO2), so that Eq. (4) accommodates both the

Boudouard reaction and iron oxide reduction:

..........(7)

The A, k O and k C terms are constants and can be grouped,

dC

C k k A C C dt

[O]

[O]

O C CO CO

eq.

2 2

2 ⋅ ⋅ ⋅ ⋅( )

1 1 1

2

2

2

A

dC

dt A

dC

dt A

dC

dt

k C C C

C

C

CO

C

CO

C CO CO

eq.

2

⋅⋅ ( )

C(O) CO(g) j 3 →

C CO C(O) COf 2(g) (g) → j ←

j 1

1

RateCO

CO CO

CO

CO CO

2

2

2

i P

j

j P

j

j P

i P

k P k P

1

1

3

1

3

1

2 3

1

1

2

( )

Rate[O]

[O]

O [O] CO COeq.

dC

dt k A C C C ⋅ ⋅ ⋅( )


© 2003 ISIJ 1138



along with the area constant, into a single overall kinetic

constant k . It is also possible to rewrite the oxygen concen-

tration in terms of fraction converted ( X ):

C [O]C °[O] · (1 X )............................(8)

and

dC [O]C °[O] ·dX ..............................(9)

Where C°[O] is the initial solid removable oxygen concentra-

tion in the mixture. In doing so, Eq. (7) can be rewritten as:

..........(10)

Which on solving becomes:

......................(11)

The model developed here is for a uniform conversion of a self reducing briquette, taking into account both the oxi-

dation and reduction reactions.

3. Experimental Procedure

Two briquette recipes were used in these experiments.

The first recipe comprised of iron oxide and coke and the

second recipe comprised of iron oxide, coke and kaolin.

Briquettes manufactured from the first recipe displayed suf-

ficient strength for kinetic studies, however such briquettes

disintegrated when thermocouples were inserted into the

briquette. Therefore, the second recipe included kaolin ad-ditions for binding strength and were used for temperature

profiling. A molar C/O ratio of 1 was used in these recipes,

being an optimum choice, as a further increase in this ratio

did not have any significant effect on reduction kinetics.

Analysis of the briquette recipes is given in Table 2.

Cylindrical briquettes were produced by pressing the pre-

pared material in a 22 mm diameter punch and die appara-

tus at 38.7MPa (1.5 ton).

Briquettes prepared for temperature profile analysis were

produced in the above manner prior to drilling an axial

hole, to the centre of the briquette, to house a thermocouple

(K Type).

The briquettes were reduced in a purpose built Thermo-

Gravimetric Analyser (TGA). A schematic of the TGA is

shown in Fig. 2. The furnace was resistance heated using

Super-Kanthal elements, producing a 125 mm hot zone. A

feature of the design is the raisable furnace which encom-

passes the sample allowing high heating rates. A bellows

system around the sample facilitated gas purging of the

TGA whilst the furnace is in the lowered position. High pu-

rity nitrogen was supplied as the inert gas through the bot-

tom of the furnace at a rate of 3 l /min using a mass flow

controller. Sample ports at the top of the reaction tube al-

lowed constant sampling and logging of exit gas composi-tion by an infrared (IR) CO/ CO2 analyser. Weight loss dur-

ing a reaction was monitored and logged by computer via a

digital balance.

Derivation of X

The mass loss of the briquette is a combined mass loss of

ln( )

( )

1 X

C C k t

CO CO

eq.

2 2

⋅

dX

X k C C dt

X t

( )( )

10 0

⋅ ⋅∫ ∫ CO CO

eq.

2 2


1139 © 2003 ISIJ

Table 1. List of rate constants (k ).

Table 2. Analysis of briquette recipes.

Fig. 2. Schematic representation of key elements of Thermo-Gravimetric Analyser (TGA) and Infra-red Analyser (IR).



in-solid removable oxygen, carbon and any other remov-

ables such as LOI and adsorbed oxygen. A series of as-

sumptions are required to enable the calculation of the de-

gree of reduction, X . These assumptions are:

• The LOI component is removed from the briquette first

and does not partake in any reaction;

• Adsorbed oxygen is removed from the briquette and re-

acts with carbon. The adsorbed oxygen accounts for the

oxygen which is present in the briquette’s porosities and

that which is adsorbed on the surface of the carbon. The

adsorbed oxygen portion is calculated for the carbona-

ceous materials. It is determined by producing plain car-

bon briquettes and exposing them to reaction tempera-

tures in inert atmospheres. The mass loss and oxygen out-

put is analysed to obtain a weight fraction of adsorbed

oxygen of a given carbon type (Table 2); and

• Once the weight loss attributable to LOI and to Adsorbed

Oxygen have been accounted for, the rest of the oxygen

removed is attributed to X .

The number of moles of oxygen and carbon are calculated from a mass balance, facilitating the calculation of the de-

gree of reduction ( X ). A sample plot of X against time is

given in Fig. 3, where the time lag evident at the beginning

of the plot is accounted portions of LOI and Adsorbed

Oxygen portions.

4. Results and Discussion

A significant difference between a shrinking core style

and a uniform conversion style model is in the temperature

profile through the sample during the course of reaction. An

uniform conversion model, by its definition, is applicable

when there is an uniform temperature profile throughout the

reactants. In the case of a shrinking core model, alternative-

ly, there is a temperature differential between the centre and

the surface of the reacting sample.

To examine the temperature profile in this study, a pre-

liminary experiment was conducted on briquette manufac-

tured from recipe 2, with thermocouples placed inside and

outside the briquette. The result of this experiment is plot-

ted along with the degree of briquette reduction ( X ) in Fig.

4. The temperature profile shows that the centre of the bri-

quette has reached close to reaction temperature before any

significant degree of reduction has been attained (15%).

This indicates that the briquette reacts essentially homoge-neously.

The degree of reduction from experiments conducted on

briquettes made from recipe 1 and recipe 2 are compared in

Fig. 5. There is no significant difference in the shape of the

reduction curve between the two recipes indicating that, in

the case of both the briquettes, the same physical model

(uniform conversion) is applicable, and that the temperature

profile displayed in Fig. 4 is valid for recipe 1 briquettes.

Taking the reaction off-gas as an indication of the reac-

tions which are in equilibrium, and accordingly inferring

those which are controlling, the P CO/ P CO2ratios of the reac-

tion off gas are provided in Fig. 6. The plot shows that thewüstite – iron reaction has reached equilibrium after some

800 s and therefore the Boudouard reaction can be inferred

as being the controlling reaction in the case of both the bri-

quettes (recipe 1 and 2).

It can be seen from the results shown in Figs. 4 and 6 that

briquettes react homogeneously and that the controlling re-

action is the Boudouard reaction. Such a situation suits the

application of the uniform conversion model, as shown in

Eq. (11). The uniform conversion model is applied to the

reaction data, and the results, along with the reaction off

gas P CO/ P CO2, are shown Fig. 7. The strong linearity of themodel for both recipes is evident.

It can be seen from Fig. 7 that the linearity of the pro-

posed model does not begin to occur until the stabilisation

of the wüstite – iron reaction. Once stabilisation of the


© 2003 ISIJ 1140

Fig. 3. A typical plot of degree of reduction ( X ) against time, il-

lustrating the time lag at the beginning of the reduction.

Fig. 4. Recipe 2 briquette’s inner and outer temperatures as a

function of time, also plotted is degree of reduction.

Fig. 5. Plot of X as a function of time for briquettes made from

recipe 1 and recipe 2.



wüstite – iron reaction is achieved, the analysed gas compo-

sition is indicative of the controlling reaction being the

Boudouard reaction.

The common analysis method of a self reducing sample

is to plot ln(1 X ) vs. time, and such a plot is shown in Fig.

8. The non-linearity of Fig. 8 contrasts with the linearity of

Fig. 7. Using the model proposed in this paper, the non-lin-

earity can easily be explained by the changing P CO/ P CO2,and hence the gaseous driving force, in the reaction gas.

Using Eq. (11), it is possible to extract values for the rate

constant (k ) from Fig. 7. The rate constants (k ) for the two

recipes used are given in Table 1. The model proposed in

this paper differs from the commonly used first order irre-

versible unimolecular model (Eq. (1)) in that it includes a

term for the Boudouard reaction, (C CO2C eq.

CO2). To relate

the kinetic data (k ) extracted from the use of this model

(Eq. (11)) to the kinetic data of the first order irreversible

unimolecular form (k , Eq. (1)), equilibrium CO2 concen-

trations of the different iron oxide oxidation states and the

equilibrium Boudouard reaction CO2 concentrations can be

used for the C CO2and C eq.

CO2terms (Eq. (11)) respectively. At

1000°C, the equilibrium CO2 concentrations are listed in

Table 3.Through multiplying the k values obtained from Fig. 7 by

the (C CO2C eq.

CO2) values of the various iron oxide reaction

values (Table 3), it is possible to produce a series of series

of k values for Eq. (1). The result is a set of theoretical


1141 © 2003 ISIJ

Fig. 6. Measured and equilibrium ln( P CO/ P CO2) values for the self reducing briquette at 1000°C.

Fig. 7. Dependency of

ln(1

X )/(CCO2

C

eq.

CO2) and ln( P CO/ P CO2) on time.

Fig. 8. Dependency of ln(1 X ) on time.

Table 3. Equilibrium CO2 concentrations at 1 000°C (assum-

ing P CO P CO21).



slopes for the first order irreversible unimolecular model re-

lating to the different iron oxide reactions. The slopes are plotted against the experimentally obtained plots in Fig. 9

and it can be seen that they are tangent to the experimental

ln(1 X ) – time plot. This is to be expected as the P CO/ P CO2

ratio increases with the lowering iron oxide oxidation state,

and therefore, the Boudouard reaction rate decreases. Such

a consideration is not present in the first order irreversible

unimolecular model, despite its common usage to describe

the carbothermic reduction of iron oxide.

5. Summary

A rate equation was developed for the description of theuniform carbothermic reduction of iron oxide, which in-

cluded terms for both the iron oxide reduction and the car-

bon oxidation. The rate equation was tested at 1 000°C,

where it was shown that the rate equation fitted the experi-

mental data well.

The use of existing experimental techniques (namely re-

action off gas measurements, analysis of the gas in context

of thermodynamic equilibria and thermogravimetric analy-

sis), coupled with the model developed here, has allowed

for a greater appreciation of the role of the constituent reac-

tions within a self reducing briquette.

The reaction model used in this paper illustrated that

while the Boudouard reaction was controlling, its rate was

heavily influenced by the P CO/ P CO2levels within the bri-

quette during the course of conversion.

The influence of the P CO/ P CO2levels on the reaction ki-

netics of the self reduction reaction has been missing from

previous models.

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© 2003 ISIJ 1142

Fig. 9. Dependence of ln(1 X ) on time with reaction rates cal-

culated from Fig. 7 recalculated for different oxide equi-

librium partial pressures.

Documents

Kinetic Model for the Uniform Conversion of Self Reducing Iron Oxide and Carbon Briquettes