KINETIC MODEL OF OXIDATION REACTIONS BETWEEN
MOLTEN IRON OF HIGH CARBON CONCENTRATION AND
IRON OXIDE CONTAINING SLAG
Masamichi Sano
Department of Materials Processing Engineering
Graduate School of Engineering, Nagoya University
Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
Abstract: Oxidations of carbon and phosphorus in molten iron of high carbon
concentration ([%C]0=4.4) by iron oxide in molten CaO-Li2O-SiO2-FetO slag
((%FetO)0=3～20) were studied both theoretically and experimentally. It is found that
the carbon oxidation rate increases with increasing iron oxide concentration and is in
proportion to its activity (aFeO>0.05). Phosphorus in the slag largely reduces the
carbon oxidation rate due to its surface active nature. The phosphorus oxidation rate
increases with increasing iron oxide concentration. The ratio of the maximum
phosphorus concentration in the slag to the minimum phosphorus concentration in the
metal during the experimental run increases steeply with increasing molar ratio of
ferric iron to the total iron ion, Fe3+/(Fe2++Fe3+).
A reaction model of the simultaneous oxidations is developed to explain the
experimental results. The calculated results are in good agreement with the
experimantal ones. The oxygen potential at the slag-metal interface is estimated to be
10-16～10-15 atm, which is affected strongly by the carbon oxidation reaction.
1. INTRODUCTION
In the hot metal treatment, several oxidation reactions proceed simultaneously, such
as oxidation of silicon, carbon, phosphorus, etc. The carbon oxidation produces CO
bubbles at the slag-metal interface, which makes the reaction mechanism very
complex.
This paper is concerned with the oxidation of carbon and phosphorus in molten iron
of high carbon concentration by FetO in molten CaO-Li2O-SiO2 slag. The
experimental results are compared with those calculated from a mathematical reaction
model. The oxygen potential at the slag-metal interface is estimated by using the
model.
2. MATHEMATICAL MODEL OF SLAG-METAL REACTION
Generally, several slag-metal reactions proceed simultaneously, and they influence
each other, which makes the analysis of the reaction mechanism difficult. A
multi-component competitive reaction model was proposed by Robertson et al.(1)
The slag-metal reactions can be divided into two groups. One is oxidation reaction
of X in molten iron (except carbon).
X+BO=(XOB)
(1)
Typical examples are desiliconization and dephosphorization of molten iron. The
other is the reduction (substitution) reaction of Y:
Y+(MO)= (MY) + O
(2)
A typical example is desulfurization of molten iron.
79
When the slag-metal reaction is controlled by mass transfer, the equilibrium
relations among interfacial concentrations are given by Eqs. (3) and (4),
 XO B N XO B ,i
KX 
f X [% X]i a OB ,i
(3)
 S  XO B
 (% XO B ) i 



100CM XO B f X f OB  [% X]i [%O]iB 
 MY N MY ,i a O ,i
KY 
 MO N MO ,i f Y [% Y]i
(4)
M MO  MY f O  (% MY ) i [%O]i 



M MY  MO f Y  (% MO) i [% Y]i 
where KX and KY are the equilibrium constants of Eqs.(1) and (2), γis the Raoultian
activity coefficient, N is the molar fraction, a is the activity, f is the Henrian activity
coefficient, ρS is the slag density, M is the molecular mass, C is the total molar
concentration, the subscript i denotes the slag-metal interface, and the other subscripts
denote the reacting components.
The mass transfer fluxes are expressed as
J X   X ([% X ]  [% X ]i )   XO B ((% XO B ) i  (% XO B ))
(5)
(6)
J Y  Y ([% Y]  [%Y]i )  MY ((% MY)i  (%MY))
whereαj = ρkj / 100Mj, ρis the density of metal or slag, k is the mass transfer
coefficient, and the subscript j denotes the j component. As for iron oxide, only the
slag-phase mass transfer is considered.
J FeO   FeO ([% FeO]i  [% FeO])
(7)
The metal-phase mass transfer of oxygen is given by
JO=aO([%O]-[%O]i)
(8)
Carbon in the metal reacts with iron oxide at the slag-metal interface to produce CO
bubbles. The overall reaction is expressed as
C+(FeO)= Fe + CO
(9)
The elementary reactions of Reaction (9) are
(FeO)+CO=Fe + CO2
(10)
CO2+C = 2CO
(11)
The reaction kinetics of Reaction (9) has been investigated by many
researchers(2)-(4). Pan et al.(4) expressed the overall reaction rate as follows.
JC = kOV aFeO
(12)
2
where kOV is the overall reaction rate constant (mol/cm ･s),
kOV = 2.7×10-5 / (1 + 4.88×1011 aPO2.5)
(13)
Equation (13) clearly shows that the oxidation of carbon by iron oxide in the slag is
strongly influenced by the surface active component of PO2.5. SiO2 is also a
well-known surface active component. The activity of SiO2 in the present slag system
(38.4%CaO – 20.5% Li2O – 41.1% SiO2 in mass%) and the adsorption equilibrium
constant of SiO2 is estimated as aSiO2=4.2×10-3 and KSiO2=7, so that the effect of SiO2
on kOV is ignored in Eq. (13).
Moreover, the following relation exists among the fluxes of reacting components.
∑BJX–∑JY+JFeO – JO + JC = 0
(14)
With knowing the equilibrium constant of each reaction and giving the metal- and
slag-phase mass transfer coefficients as parameters, we can obtain the interfacial
80
concentration of each component by using Eq. (3)～(7), (12) and (14). Then the
change in concentration with time can be calculated from Eqs. (15) and (16).
d[%i]
 VM
 k i A([%i]  [%i]i )
(15)
dt
d (% j)
 VS
 k j A((% j)  (% j) i )
(16)
dt
where VM and VS are the metal and slag volumes, and A is the interfacial reaction
area.
The most appropriate mass transfer coefficients can be determined by comparing
the calculated and experimental results.
3. SIMULTANEOUS
CONTAINING SLAG
CONCENTRATION
OXIDATION REACTIONS BETWEEN FetO
AND MOLTEN IRON OF HIGH CARBON
Applicability of the above reaction model is investigated to the simultaneous
oxidation reactions of C and P in molten iron by FetO in molten CaO-Li2O-SiO2 slag.
3.1 Experimental
The experimental apparatus is shown in Fig.1. A SiC resistance furnace was used to
melt the metal and slag. The crucible used was made of alumina and its size was 48Φ
×40Φ×250mm. Both molten metal and slag was mechanically stirred by an
alumina rod stirrer. Its tip was placed 8mm above the crucible bottom. Experiments on
the carbon oxidation were made under argon atmosphere, and those on the
simultaneous carbon and phosphorus oxidations under argon or oxidizing atmosphere.
3.2 Oxidation of carbon in molten iron by FetO in molten slag
Figure 2 shows changes in dimensionless carbon concentration, [%C] / [%C] 0
( [%C]0: initial carbon concentration) and in FeO concentration with time. Here, for
simplicity, we neglect FeO1.5 contained in the slag, considering the rather low
concentration of FetO in the slag (<20mass%). It is seen that the carbon oxidation rate
(=－Δ[%C] / Δt) increases with increase in the initial FeO concentration in the slag,
(%FeO)0, and that the FeO reduction rate decreases with decreasing FeO
concentration.
The carbon oxidation rate is plotted against the activity of FeO, a FeO (standard state:
liquid FeO of stoichiometric composition) in Fig.3. It is indicated that the rate
increases linearly with increase in aFeO for aFeO > 0.05. From the figure, we can obtain
Eq.(12).
The relation between the carbon oxidation rate and the stirring speed is shown in
Fig.4. It increases only slightly with increase in stirring speed.
It is interesting to note that phosphorus in the slag has a large effect on the FeO
reduction rate. Figure 5 clearly shows that higher (%P)0 gives a lower rate of FeO
reduction, from which Eq.(13) is obtained. In the experiments shown in Fig.5, (%P)
was kept almost constant during the run by changing [%P]0 according to (%P)0.
Considering the experimental results shown in Figs.2～5, the carbon oxidation rate
is assumed to be controlled by the chemical reaction at the gas bubble–slag interface,
mass transfer of CO2 in the bubble and chemical reaction at the gas bubble–metal
81
interface. The semi-analytical expression for kov is given by Eq. (13).
The calculated results are compared with the experimental results and shown in
Fig.5. As seen in the figure, the present model calculation can explain the
experimental results reasonably well.
3.3 Phosphorus oxidation between molten iron of high carbon concentration and
FetO containing slag
Figure 6 shows a typical example of the change with time in the concentrations of P
and C in the metal, and FetO and P in the slag. Initially, the decreases in [%P], [%C]
and (%FetO) and the increase in (%P) proceed simultaneously. The time changes in
the concentrations, however, become small with decrease in (%FetO). At t≒6min, the
phosphorus reaction changes from oxidation of P. i.e. dephosphorization to reduction
of PO2.5, i.e. rephosphorization. Hence the phosphorus concentration ratio, (%P) /
[%P], becomes maximum at t≒6min.
Figure 7 illustrates the change in [%P] and (%FetO) with time under conditions of
various PO2 in the atmosphere and constant (%FetO)0=15. From the figure, it appears
that with increasing PO2 , the rate of phosphorus oxidation at the initial period
increases and the minimum value of [%P] becomes lower. It is also seen that (%FetO)
increases at the later period in the case of higher PO2 (=0.15atm).
Figure 8 shows the relation between the maximum phosphorus concentration ratio,
((%P) / [%P] )max, and PO2 . The maximum ratio increases largely with the increase in
PO2 . As well known, under an oxidizing atmosphere, FeO in the slag is oxidized by
oxygen in the gas phase, and the concentration of FeO1.5 increase accordingly. In
order to clarify the effect of FeO1.5 on ((%P) / [%P] )max, the molar ratio of ferric iron
to total iron in the slag, Fe3+/(Fe2++Fe3+) is determined, and the relation between them
is shown in Fig.9. It is clearly seen that ((%P) / [%P] )max increases steeply with
increasing Fe3+/(Fe2++Fe3+), and the ferric iron can improve the dephosphorization.
These experimental results indicate that FeO and FeO1.5 should be treated
separately to evaluate the interfacial oxygen potential which influence the phosphorus
oxidation. Under oxidizing atmosphere, the following reactions occur simultaneously.
At the slag-gas interface :
FeO + 1/4O2 = FeO1.5
(17)
At the slag-metal interface :
FeO = Fe + O
(18)
FeO1.5 = Fe + 1.5O
(19)
P + 2.5O = PO2.5
(20)
C + FeO = CO + Fe
(21)
Here, it is assumed that the local equilibrium is established for phosphorus oxidation
(Eq.(20)) at the slag-metal interface because of the high temperature.
The equilibrium of Reaction (20) is given by
a PO
K P  2.5 2.5
(22)
aO aP
18422
logK P 
 14.53 (5)
(23)
T
We define the equilibrium phosphorus concentration ratio, LP, at the slag-metal
interface as
82
2.5
(%P) i K P f P a O,i
LP 

[%P]i
CγPO2.5
(24)
where the symbol C´ is the conversion factor which relates (%P) to the molar fraction
of PO2.5.
Since the rate of the mass transfer from the atmosphere to the gas-slag interface and
the details of the mechanism of FeO oxidation at the interface are unknown, the
following empirical equation is adopted to express the rate of FeO oxidation at the
interface.
2
1/ 2

(25)
J sg
FeO1.5  k (% FeO) sg PO2
where the subscript sg denotes the slag-gas interface and k´ is the apparent reaction
rate constant. The molar fluxes of FeO and FeO1.5, J´FeO and J´FeO1.5 at the slag-gas
interface are given by
J FeO  FeO % FeO   % FeO sg 
(26)

JFeO1.5  FeO1.5 %FeO1.5   %FeO1.5 sg

(27)
where j  k j s 100M j and k´j is the mass transfer coefficient of j component for the
slag-gas interface, which is assumed to be k´j = kj.
There are the following relations among fluxes of reacting components.


(28)
J sg
FeO1.5  J FeO  J FeO1.5
and
2.5J PO2.5  J C  J FeO  J FeO1.5  0
(29)
where J P O2.5 and J FeO1.5 are
J PO2.5   PO2.5 % PO 2.5 i  % PO 2.5 
J FeO1.5   FeO1.5 % FeO1.5 i  % FeO1.5 
(30)
(31)
and JFeO is given by Eq.(7). In Eq.(29), JO is neglected.
The interfacial equilibria of the reactions of Eqs.(18), (19) and (20) can be
represented by the following relations.
a O,i
(32)
KFeO 
(% FeO) i
a 1O.5,i
K FeO1.5 
(33)
(% FeO1.5 ) i
(% PO 2.5 ) i
(34)
KPO2.5 
[% P]i a O2.5,i
The values of mass transfer coefficients, apparent chemical reaction rate constant,
equilibrium constants and physical properties are listed in Table 2. The details are
explained in the author’s paper.(6)
Figure 10 shows a typical example of the model calculation, which is compared
with the experimental result. The calculated result is in good agreement with the
experimental one. It is to be noted that the carbon oxidation reaction rate obtained in
3.2(Eq.(13)) is used in the calculation. Obviously the present mathematical model can
explain reasonably well the complex simultaneous reactions between FetO containing
slag and molten iron of high carbon concentrations.
3.4 Estimation of oxygen potential at slag-metal interface
83
The interfacial oxygen potential strongly affects the simultaneous oxidation
reaction between FetO containing slag and molten iron of high carbon concentration.
Its quantitative aspects have, however, not yet been established. Since equilibrium
data of the slag-metal reactions are not available, we estimate the interfacial oxygen
potential from the kinetic data shown in the previous section 3.3.
An example of the kinetics data is shown in Fig.11, where the phosphorus reaction
changes from dephosphorizations to rephosphorization at t≒15 min. At this time
point, [%P] takes the minimum value, [%P]min, while (%P) takes the maximum value,
(%P)max, and the phosphorus reaction rate, d [%P] / dt, equals to zero. Hence, we
can assume that at t≒15min.
[%P] = [%P]min = [%P]i and
(%P)=(%P)max=(%P)i
(35)
On the assumption that the equilibrium of the phosphorus reaction prevails at the
slag-metal interface, we have the following ratio of the phosphorus distribution
between slag and metal.
(% P) i (% P) max  (% P) 
LP 


(36)

[% P]i [% P]min  [% P]  max
The phosphorus capacity is represented by
5 / 4
(% PO 34 ) PO2
C PO3 
(37)
1/ 2
4
PP2
With using Eq.(38)-(40),
1
P2  P
(38)
2
(39)
G  157700  5.4T (J)(7)
(40)
a P  f P [%P]
the following equation is derived,
5 / 4
(% P) e PO2
5
(41)
C PO3  2.759  10
4
f P [% P]e
where the subscript represents the equilibrium between slag and metal. Substituting
((%P) / [%P])max in Eq.(36) for ((%P) / [%P])e in Eq.(41), and rewriting PO2 and fP in
Eq.(41) as PO* 2 and fp,i which are the corresponding values at the interface, we obtain
 1  (% P)  
P  2.252  10 C PO3
 
 
4
f
[%
P
]

 max 
P
,
i

Since [%C]i ≒ [%C], fP,i is given by
log f P,i  e PP [% P]min  eCP [%C]
*
O2
4
4/5
4 / 5
(42)
(43)
where e represents the interaction parameter ( e  0.0643 and e  0.19 ).
When the carbon concentration of the metal is high, FetO concentration is lowered
considerably at the slag-metal interface. Then, we can adopt the C PO3 value of the
j
i
P
P
C
P
4
*
O2
LiO2-CaO-SiO2 primary slag to calculate P
from Eq.(42). To estimate the
C PO3 value of the FetO free slag, we measured the phosphorus distribution ratio
4
between the slag and the carbon saturated molten iron under the condition of P CO=1
atm. From the experimental result, we obtain
84
C PO3  4.89  10 24
(44)
4
In Fig.12, the calculated results of PO* 2 with using Eq.(42) are plotted against the
molar fraction of the total iron oxide in the slag, i.e. N Fe tO  N FeO  N FeO1.5 . The
figure shows that the interfacial oxy+gen potential PO* 2 has the value of the order of
10-16 ～ 10-15 atm, which suggests that the interfacial oxygen potential of the slag /
molten iron of high carbon concentration is affected strongly by Reaction (9).
4. CONCLUSION
A kinetic study was made on carbon and phosphorus oxidation reactions between
molten iron of high carbon concentration ([%C]0=4.4) and CaO-Li2O-SiO2-FetO slag
((%FetO)0=3～20) under mechanical stirring. A reaction model for simultaneous
carbon and phosphorus oxidations was developed. The following results were
obtained.
(1)The carbon oxidation rate increases linearly with increasing iron oxide activity
(aFeO>0.05).
(2)Phosphorus in the slag strongly affects the carbon oxidation rate. Slight increase in
phosphorus concentration in the slag reduces the rate.
(3)The higher the initial iron oxide concentration is, the larger is the phosphorus
oxidation rate.
(4)The ratio of the maximum phosphorus concentration in the slag to the minimum
phosphorus concentration in the metal during the experimental run steeply increases
with increasing molar ratio of ferric iron to total iron ion, Fe3+/(Fe2++Fe3+).
(5)On the basis of these experimental results, a reaction model of the simultaneous
oxidations of components in the metal by iron oxide in the slag is developed, which
can explain the results reasonably well.
References
(1)Ohguchi S., Robertson D.G.C., Grieveson P. Deo.B. and Jeffes J.H.E.:
‘Simultaneous dephosphorization and desulfurization of molten pig iron’. Ironmaking
Steelmaking 1984 11(4) 202-213.
(2)Tarby S.K. and Philbrook W.O.: ‘The rate and mechanism of the reduction of FeO
and MnO from silicate and aluminate slags by carbon-saturated iron’.
Trans.Metall.Soc.AIME 1967 239(7) 1005-1017.
(3)Sommerville I.D., Grieveson P. and Taylor J.: ‘Kinetics of reduction of iron oxide
in slag by carbon in iron’. Ironmaking Steelmaking 1980 7(1) 25-32.
(4)Pan W., Sano M., Hirasawa M. and Mori K.: ‘Kinetics of carbon oxidation reaction
between molten iron of high carbon concentration and iron oxide containing slag’.
ISIJ Int. 1991 31(4) 358-365.
(5)Mori T., Ichise E. and Moro-oka A.: Tekko binran (Handbook of iron and steel).
Tokyo, Maruzen, 1981, Vol.1.
(6)Pan W., Sano M., Hirasawa M. and Mori K.: ‘Kinetics of phosphorus transfer
between iron oxide containing slag and molten iron of high carbon concentration
under Ar-O2 atmosphere’. ISIJ Int. 1993 33(4) 479-487.
(7)The 19th Committee on Steelmaking, The Japan Society for the Promotion of
Science: Steelmaking data source, New York, Gordon and Breach Press, 1988.
85
Table 1 Experimental conditions.
Carbon oxidation
Phosphorus oxidation
Metal mass (g)
300
300
Primary slag mass (g)
30
30
metal
slag
metal
slag
[%C]0
(%FeO)0
[%C]0
(%FeO)0
Initial concentration
= 4.4
=
4.4
= 5～20
= 3～15
[%P]0
[%P]0
(%P)0
(%P)0
= 0～0.1
= 0～0.1
= 0, 1.1
= 0～2
Rotating speed of stirrer (rpm)
50～400
30～300
Oxygen partial pressure (atm)
0
0～0.2
Temperature (K)
1573
1573
Table 2 Mass transfer coefficients, apparent reaction rate constants, equilibrium
constants and physical properties.
kP
0.05 cm/s
k PO2.5
0.003 cm/s
k FeO
k FeO1.5
k´
K´FeO
K FeO1.5
K PO2.5
ρm
ρS
0.003 cm/s
0.003 cm/s
(6.14～8.44)×10-7mol/(%2･atm1/2･s)
1.23×10-3
1.19×10-3
4.086×109
6.99 g/cm3
2.45 g/cm3
Stainless rod
Gas inlet tube
Slag holder
Mullite tube
Alumina crucible
Alumina stirrer
Molten slag
Molten metal
Pt-Pt13Rh
thermocouple
SiC heater
Gas outlet tube
86
Fig.1. Experimental apparatus.
Fe-C
200rpm
20
(%FeO)
0.98
10
0.96
Fe-C
200rpm
0.94
0
5
Time (min)
10
0
0
5
Time (min)
(%FeO)0 = 4.6 , (%P)0 = 0.9
20
17.5
15
4
12.5
10
2
Fe-C
200rpm
0
0.5
1.0
12
1.5
aFeO ×10
2.0
Fig.3. Relation between rate of carbon
oxidation and aFeO.
4.7
200rpm
Cal.
4.5
(%P) 0= 0.07 [%P] 0= 0.005
(%P) 0= 0 [%P] 0= 0
[%C]
0.5
(%FeO)0
(%P)0= 1.8 [%P] 0= 0.05
(%P) 0= 0.4 [%P] 0= 0.02
(%P) 0= 0.25 [%P] 0= 0.01
(%FeO)0 = 10 , (%P)0 = 1.8
(%FeO)
-△[%C] / △t ×102 (% / min)
16
1.0
6
0
10
Fig.2. Changes in [%C]/[%C]0 and (%FeO)
with time.
8
4.3
4.1
4
200rpm
Cal.
0.1
10
50
100
0
500
0
180
360
540
3.9
0
Time (s)
Stirring speed (rpm)
180
360
540
Time (s)
Fig.4. Effect of mechanical stirring on
Fig.5. Comparison of changes in (%FeO),
rate of carbon oxidation.
[%C] with time between experiment
and calculation for various (%P)0 in slag.
PO2 = 0 200rpm
15
[%C]0 = ~ 4.4 PO2 (atm)
0
(%P)0 = 0
0.1
200rpm
0.15
0.4
8
(%FetO)
(%P)
0
0.1
0.2
(%P)
10
0
[%P]
(%FetO)
(%FetO)
16
[%C]
0.06
5
4.4
4.2
0
0
5
10
[%P]
0.05
[%C]
[%P]
[%C] / [%C]0
[%C]0
4.47
4.47
4.45
-△[%C] / △t ×102 (% / min)
(%FeO)0
10
15
20
1.00
0.04
0.02
0
4.0
Time (min)
0
10
20
Time (min)
87
30
0
500
(%FetO) 0 = 15
[%P] 0 = ~ 0.04
(%P) 0 = 0
[%C] 0 = ~ 4.4
200rpm
100
( (%P) / [%P] ) max
( (%P) / [%P] ) max
500
50
10
100
50
10
0
0.1
(%FetO)0 = 15
[%P]0 = ~ 0.04
(%P)0 = 0
[%C]0 = ~ 4.4
200rpm
0.2
0
0.2
Fe3+
PO2 (atm)
/(
04
Fe3+ +
Fe2+
)
4.2
0.06
[%P]
(%FeO), ( %FeO1.5 )
PO2 = 0.1atm 200rpm
(%FetO)0 = 15
4.4
Cal.
[%P]
(%P)
0.6
0.04
0.4
0.02
0.2
0
0
12
24
(%P)
[%C]
Fig.6. Changes in (%FetO), (%P), [%P]
Fig.7. Changes in (%FetO) and [%P] with
and [%C] with time.
time for various PO2.
Fig.8. Relationship between ( (%P) /
Fig.9. Relationship between ((%P)/
[%P] ) max and PO2.
[%P] )max and Fe3+/(Fe3+ + Fe2+).
(%FeO)
(%FeO1.5)
Cal.
18
16
12
8
4
0
0
0
12
24
Time (min)
Time (min)
Fig.10. Comparison of changes in (%FeO), (%FeO1.5), (%P), [%P] and [%C] with
time between experiment and calculation.
(%FetO)0
~10
~15
~15
~20
R (rpm)
~200
~200
=200
~200
10-15
O *
2
=
P
O
2
,s
10-14
P
PO2 * (atm)
10-13
10-15
10-14
10-13
PO2 ,s (bulk slag) (atm)
88
10-12
[%P]
0.04
PO2 = 0.1atm
(%FetO)0 = 15
R = 200rpm
0.02
(%P)
0
0.4
0.2
0
0
10
20
30
Time (min)
Fig.11. Changes in [%P] and
Fig.12. Relationship between the oxygen potential
(%P) with time.
in the bulk slag and that at the slag-metal interface.
89