the kinetics of interfacial transfer of sulfur during hot metal
TRANSCRIPT
1-139
The Kinetics of Interfacial Transfer of Sulfur During Hot metal Treatment with Magnesium
A.L. Rudenko
Iron and Steel Institute NASU, Dnipropetrovsk, Acad. Starodubova sq. 1, Ukraine
Keywords: mass transfer, mechanism boundary layer, specific surface, diffusion.
ABSTRACT
During magnesium desulfurization of molten iron, high-sulfur and heterogeneous slag with high
content of metal droplets is formed in ladle. Generally these slags are sour with various oxidizing
ability. The high content of sulfur in the slag increases the "danger" of the reversion of sulfur from
the slag to the melt.
In this paper the kinetics of sulfur transfer through the metal-slag interface surface was examined.
The results of hot metal treatment with magnesium in the factories in China served as a basis for
experimental data.
Using diffusion boundary layer theory the interfacial transfer of sulfur was modeled. The coefficient
values of sulfur mass transfer in the slag were determined by using a simplified expression of the
second Fick's law. While using these kinetic characteristics during calculations, it was proved that
after refining of hot metal with magnesium under present conditions, a fast return of the sulfur from
the slag into the metal droplets takes place. At the same time the estimated sulfur content in the iron
in the ladle remains practically invariable.
Introduction
Recently, the use of the magnesium as a desulfurizer for hot metal pre-treatment is arising intense
interest. As a result of this process a metal with an ultra-low level of sulfur and a small amount of
slag in the ladle is produced. As a consequence such slags contain high concentrations of sulfur and
metal droplets. Thus, the risk of sulphur reversion from the slag to the melt is increasing.
Long-term practice shows that under industrial conditions during ladle transportation into steel plant
the increase of sulfur in the iron does not occur [1]. However, a rapid and significant transfer of
sulfur from the slag into the metal droplets under industrial conditions [2] as well as during
laboratory studies [3] shows the possibility of the resulfurization process development. Among the
authors there is no mutual opinion about the mechanism of magnesium resulfurization of molten
iron.
The authors [4] explain the resulfurization absence under industrial conditions by low reactivity of
the slags, the paper [5] proved that the resulfurization is blocked due to residual magnesium presence
in hot iron. A number of studies [6, 7] are devoted to the explanation of resulfurization process
mechanism. However, these works are based on the influence of the various parameters on the
possible sulfur reversion into the metal during the decomposition or oxidation of magnesium
sulphide.
Whereas in real-life environment in the ladle slag after the desulfurization of iron with magnesium,
magnesium sulfide is absent [2, 8]. In addition, the number of works of the kinetics of this process is
sufficiently small, and the data on mass transfer coefficients of sulfur in the slag are cited only for the
most examined blast-furnace and steel slags.
The purpose of this paper is to study the kinetics of sulfur transfer through the metal - slag interfacial
surface during magnesium desulfurization of molten iron.
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Experimental
The results of hot metal treatment with magnesium in the factories in China served as a basis for
experimental data. After 5 minutes after magnesium desulfurization of molten iron the samples of
the metal and slag with the droplets were taken. During this time a large amount of sulfur passes into
the droplets. The content of the elements in metal and slag phases were determined by chemical
analyses. For all experiments (i = 1 ÷ 11) the following data were known: the mass of hot iron in the
ladle ( ), the concentration of slag with droplets ( ), the droplets concentration in the slag
with droplets ( ) etc. Extracted droplets were scattered in 6 fractions (j = 1 ÷ 6). The content of
each fraction in the slag and chemical composition of droplets were determined.
Details of the industrial research and results are given in the previous article [2].
Theoretical Considerations
A model of this process, according to which the concentration of diffusing element in the entire fluid
volume remains constant, is created. The boundary layers in each fluid occur on the border between
phases, where concentrations drop takes place. In accordance with the approximate theory of mass
transfer it is assumed that the concentration of the diffusing substance in the boundary layer varies
linearly, and the concentration gradient is constant throughout the thickness of this layer (Fig.1).
a)
b)
a – sulfur transition from slag into ladle metal or droplets,
b - sulfur transition from metal to slag
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Figure 1. Sulfur concentration distribution on the border between phases
where sl ,met - the metal and slag boundary layer, respectively
)(%],[% SS - actual sulfur concentration in the metal and slag, respectively;
metslSS /met/sl )(%,][% - sulfur concentration at the metal-slag interfacial area in the metal and
slag, respectively;
][%][%][% met/sl SSS - concentrations drop in the metal boundary layer;
sl/met)(%)(%)(% SSS - concentrations drop in the slag boundary layer;
][%
)(%
S
SLS - the actual sulfur distribution coefficient between slag and metal;
slmets
S
SL
/0
sl/met0
0
][%
)(% - sulfur distribution coefficient (close to equilibrium one) at the metal-slag
interfacial area.
The thermodynamic possibilities of sulfur transfer depend on the difference between the actual and
equilibrium sulfur distribution coefficients. During the sulfur transition from slag into molten iron or
droplets (Fig.1(a)) the value of SL is falling. The actual sulfur concentration decreases in the slag
and increases in the metal.
The value of the actual sulfur distribution coefficient tends to the value of sulfur distribution
coefficient at the slag-metal interfacial area 0
SL . Due to the high temperatures of the metallurgical
processes the chemical reactions on slag-metal boundary are much faster than element diffusion in
the molten phases [9-13]. Therefore metslS /)(% и met/sl][%S values tend to equilibrium ones [12].
Then sulfur distribution coefficient at the metal-slag interfacial area is also close to equilibrium 0
SL .
While conducting one of the experiments, the lowest sulfur distribution coefficient for the smallest
droplets fraction was equal to 0.081. Taking into account the fact that the droplets of the smallest
fraction have the largest surface area, sulfur distribution coefficient for this droplets fraction might
have the closest to equilibrium value. As a comparison, the value of all experiments-averaged SL at
the end of experiments is much larger and equal to 0.675. Therefore, it can be assumed that 0
SL
~0,081.
This diagram illustrates that during the process of sulfur diffusion its concentration drop in boundary
layer of both slag and metal will decrease. The values of the actual sulfur content in the slag and the
metal will approach the equilibrium value. Thus, sulfur actual distribution coefficient will be tending
to equilibrium value as well.
In accordance with Fig.1(a) the examined heterogeneous process of sulfur transition from slag into
metal droplets consists of the following steps:
- the diffusion of sulfur - (S) from the slag volume to the metal-slag interfacial area,
- the chemical act of sulfur transfer from the slag into the metal: (S) → [S],
- the diffusion of sulfur [S] from the reaction zone in the metal volume
The concentration difference of diffusing substance at the entrance and exit of the step is considered
to be a driving force of each step ∆ iC . While the rate of any step depends on the Si - diffusion or
reaction surface, . In the metallurgical plants at high temperatures the diffusion of sulfur from the
slag into the slag-metal interface is the rate-controlling step of heterogeneous processes [9,10,13].
The rate of change of substance (i) concentration can be described by a simplified expression of
Fick's second law:
V
SC
Vd
dQ
d
dC ii )C(D1
iisur,
, (1)
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where Qi – mass of substance i, kgmol;
iC , isurС , - concentration of substance i in the phase volume and on the boundary with
another phase, respectively, kgmol/m3;
- diffusion time in the x direction, sec;
D - coefficient of molecular diffusion,
;
- the boundary layer thickness is chosen so that the calculation, based on the assumption of
transport purely molecular mechanism, provides the true intensity of substance transfer.
Therefore is the relative value, which is determined experimentally. By increasing the
thickness of contacting layer the thickness of the boundary layer increases as well, m;
S - surface, perpendicular to the direction of diffusion flow, ;
V – substance volume, ;
VS - “geometric” ratio,
;
i
D - the coefficient of substance i mass transfer,
.
While determining the transition rate of sulfur from the slag into metallic phase through the slag
boundary layer - Vs,sl , it is better to use slag specific surface area - sltm2
sl. s.sur. ,S instead of
"geometric" ratio.
Therefore it is possible to obtain the dependence of S s.sur. impact on the rate of the process. In order
to get it, both the denominator and numerator of equation (1) are multiplied by the density of the slag
melt 3, mtsl :
sl
sldrsl
sssslS
SCCV
sur
sl
.
)()()(,V
)( , (2)
where )(s - sulfur mass transfer coefficient in the boundary layer of droplets,
;
dr sl,S - the slag-droplets interfacial area, ;
– slag volume,
Therefore:
slsurssssS SCCVsur ..)()(sl)(sl, )( , (3)
where slsls К ,1)( - proportionality coefficient of sulfur diffusion rate in the slag boundary
layer, sec
slt 2 m
Then the equation (3) can be presented as follows:
slsurssssls SCCKVsur ,.)()(,1sl, )( (4)
By analogy with the slag, it is possible to obtain the equation for sulfur diffusion through the
boundary layer in the droplets:
sl s.sur.,,2sl, )(sur
SCCКV sssls (5)
Let us consider the stationary process of sulfur diffusion in the slag and metal. During this process
the rates of both steps will be the same, as they are limited by the slowest step [1,3,4]:
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drsss VV
d
SdV ,sl,
%
Therefore:
drsursdrsls SSSКSSSК
d
SdV .,.dr/sl
0
,2sls.sur.,sl/dr0
,1 )%%()))(%)((%%
, (6)
It is difficult to determine sl s.sur.,S value by calculation. Therefore the values
sl s.sur.,S to dr s.sur.,S can be
replaced with each other. Based on the total surface area between phases, the following equation is
obtained:
drslslsurs QSQS dr s.sur.,.,. Therefore: sl
dr
slsursQ
QSS drs.sur.,.,. ,
Or in the general view: sl
dr
Q
Qn , then nSS slsurs drs.sur.,.,. (7)
where drQ , slQ - the mass of droplets and slag, respectively, which are involved in the sulfur
diffusion transfer between them
Then the coefficient of proportionality is transformed into:
nK slssl )(
'
1 (8)
The equation (6) may be transformed using formulas (7) and (8):
dr s.sur.dr/sl
0
,2dr s.sur.sl/dr0'
1 )%%())(%)(%%
SSSКSSSКd
SdV drsls
, (9)
In order to get rid of one unknown in the expression (9), the expression for the sulfur distribution
coefficient between the slag and metal, which (as stated above) is close to its equilibrium value -
0
0
0
%
)(%
S
SLs , will be used Then equation (9) will look as follows:
Vs = '
1slК ((%S)-(%S) sl/dr) s.sur.dr.S = drК ,2 ×(0
sl/dr0)(%
sL
S-[%S]) s.sur.dr.S , (10)
Using equation (10), it is possible to determine:
0
'
,1
,2
'
,1
'
,20
0
,
])[%)((%
)(%
s
sl
dr
sl
dr
s
drsl
LK
K
SK
KSL
S
(11)
By substituting to the expression (10), the following is obtained:
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Vs= s.sur.dr
0
'
,1
,2
0
,2 ])[%)((%'
S
LK
K
SLSK
s
sl
dr
sdr
(12)
Naturally for heavy slag 0
'
,1
,2
s
sl
drL
K
K , 0
sL value can be neglected. On this assumption droplets’
resulfurization rate is described by the following equation:
Vs= drs.sur,
0'
,1 ])[%)((% SSLSK ssl (13)
As follows from the formula (13) the rate-controlling step is the diffusion in the slag. That complies
with the conditions of our studies. Based on the calculations of the process rate, it is possible to
deduce an equation for determining the sulfur content in metal droplets, depending on the duration of
their interaction with sulfur-bearing slag.
As appears from the equations (7, 13), during the process of sulfur transition from the slag into
droplets, the process rate slows down. This happens because sulfur content in the slag is decreasing,
while it is increasing in metal droplets. As a result, the drop of sulfur concentrations in the slag
boundary layer is decreasing )(%S .
On the basis of sulfur balance in the system, the value of one variable is obtained:
nSSSS )][%]([%)(%)(% inin , (14)
where (% S) and [% S] – sulfur concentration in the slag and metal at the moment .
Substitution of equation (14) into (13) leads to the formula:
])[%])[%]([%)((% 0
inins.sur.dr
'
,1 SLnSSSSKV SslS
Transforming the latter equation, the following is obtained:
][%)()][%)((%][% 0
s.sur.drр
'
,1inins.sur.dr
'
,1 SnLSKnSSSKd
SdV SslslS
(15)
In the case of constant values of '
,1 slK , s.sur.drS , in)(%S , in][%S , n the equation (15) may be
simplified by using constants:
)][%)((% inins.sur.dr
'
,11 nSSSKC sl and )( 0
s.sur.dr
'
,12 nLSKC ssl (16)
These formulas may be simplified:
][%][%
21 SCCd
Sd
(17)
Further transformations enable to obtain the following equation:
dSCC
Sd
][%
][%
21
, (18)
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which is by changing variables and then integrating them converted into an equality:
02
][%
][%2121
in21])[%ln( СSCC
SCC
SСС
.
By exponentiating the logarithmic expression, the value of sulfur concentration in the metal in a time
τ is found:
2)][%(][% in
2
1
2
1 CeS
С
C
C
CS
, (19)
Results and Discussion
The obtained experimental data varied greatly. The amount of ladle slag with metal droplets ranged
from 0.17% to 3.8% with respect to the mass of hot metal. The content of metal droplets in the slag
ranged from 4.66% to 73.9% with sulfur concentration in them of 0.16% to 5.8%. The hot metal
composition with terms of sulfur content also varied greatly within the range of 0.020% – 0.003%.
The capacity of most ladles was 50-56 tons of hot metal and only one of ladles had 140 tons.
Therefore the obtained main characteristics that describe the processes occurring between the slag
and the metal phases were averaged. Due to the fact that there were 6 droplets fractions in 11
experiments, during their treatment 11×6=66 values of droplets and sulfur mass in tones were
obtained. It is possible to obtain the total content by summing these values up:
droplets
of sulfur in the droplets
of slag
of sulfur in the slag
The main parameters of droplets were determined and presented in Table 1.
Using data on the total weight of the droplets and the amount of dissolved sulfur in them (see above),
the average value of sulfur content in the droplets is obtained:
This value corresponds to the sulfur concentration in the droplets in 5 minutes after the end of hot
metal desulphurization with magnesium.
According to the experience, sulfur concentration in hot metal during 5-minute exposure under the
slag after magnesium desulfurization practically does not change. On this assumption the sulfur
content in the droplets and iron immediately after injection will be the same and equal to 0.00902%
(see above). Then the average experimental rate of sulfur transition into droplets for 5 minutes is: Vs
= Δ [% S] / τ = (0.8986-0.00902) / 300 = 296.533 × 10-5 % / sec. It is assumed that this rate is
achieved within the first 2.5 minutes, and this time interval is an initial point for further calculations.
Accordingly, the sulfur content in the droplets at this time will be: [%S]dr,ip=(0.00902 +0.8986) / 2
= 0.45381%. Consequently, part of the sulfur was transferred from slag into droplets: . If this amount of sulfur is converted to mass, it will be added to
the droplets and pass from the slag: 0.44479 / 100% × 3,1098 = 0.013832 tons of sulfur .
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Table 1. The main droplets parameters for different fractions (j=1-6) of all experiments
№ Droplets parameters j=1
d=,14mm
j=2
d=0,5mm
j=3
d=1,5mm
j=4
d=2,5mm
j=5
d=4 mm
j=6
d=5 mm
Note
1 Droplets mass
0,137 0,4563 0,6251 0,3393 0,4697 1,0824
2 Mass of one droplet: Qdr,i=Vdr ,
0,01034 0,69781 12,717 58,875 241,152 471 -
3 Droplets quantity Кdr,j=
t 13,2485 0,65390 0,049155 0,005763 0,001948 0,002298
4 Droplets quantitative part:
0,94892 0,04684 0,003521 0,000413 ,0001395 ,0001646 1
5 Part of each fraction during average
droplet diameter determination:
0,13285 0,0267 0,005282 0,00132 0,000558 0,000823
6 Droplets specific surface ( in mm)
167 208 333 555 1462 5952 -
7 Droplets mass fraction
0,0441 0,1467 0,20101 0,10911 0,15104 0,34806 -
8 Part of every fraction in determination
Ss.sur.dr
262,4832 214,4754 111,5606 36,3326 31,4161 58,1264 Average value:
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1-148
By using the value ( it is possible to obtain the total sulfur mass in the initial point state:
. Consequently, the sulfur concentration in the slag at this time
will be:
Applying the equation (13) the
following is obtained:
sec1005723.0)45381,0081,076156,0(4,714
10533,296
][%)((%
255
0
..
'
,1
mtSLSS
VK
insindrsurs
dr
sl
In this work it can be assumed that LS0
~0,081. This value equals to the lowest sulfur distribution
coefficient for the smallest droplets fraction in one of the experiments. Taking into account the fact
that the droplets of the smallest fraction have the largest surface area, sulfur distribution coefficient
for this droplets fraction might have the closest to equilibrium value. As a comparison, the value of
all experiments-averaged is much larger and equal to 0.675.
By using formula (8) sl
dr
sQ
QK sl)(sl
, where dr
sl
dr nQ
Q
Therefore, indrsl
sl
slsn
K
,
),(
, where 43825,0013832,00506,7
013832,01098,3
Q insl,,
indr,,
,
Qn indr
While determining indrn ,
, the transition of sulfur from slag into droplets was taken into account.
Then:
sec1036274,0
4325,06,3
105723,0 55
)(m
s
From the equation (16) and the data (Table 1), it is possible to define constants ( , ):
=0,5723×10-5
×714.4×(0,76156+0,43825×0,45381)=392,67×10-5
=0,5723×10-5
×714.4×(0,081+0,43825)=212,29×10-5
In order to calculate sulfur concentration in the droplets, the equation (19) and the values of
constants will be used. As a reference point for determining the value of τ for this equation
the initial point is used. This point corresponds to 150 sec of the system duration after the end of
magnesium desulfurization. For example, the value of τ = 2,5 min = 150sec corresponds to 300sec
(5min) of metal-slag system duration in the ladle.
%83449,0)45381,01029,212
1067,392(
1029.212
1067,392][% 1501029,212
5
5
5
55
eS
The sulfur concentration for different time is calculated by analogy. The results are presented in
Table 2.
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Table2. Change in the droplet's sulfur concentration vs. the contact time with slag
Duration ,
min 0 2,5 5 7,5 10,5 12,5 17,5 22.5
[S]dr,% 0,00902 0,45381 0,83449 1,11134 1,34582 1,45914 1,64310 1,74041
System Slag – Metal
In order to calculate sulfur distribution between the slag and hot metal in the ladle, the same
equations are used. As a starting point Ds )( is used, which was obtained while examining the
kinetics of the process with droplets. Due to the fact that the slag is common for both processes, the
diffusion coefficient D will be the same. However, the thickness of slag boundary layer , which is
the relative value, will be different.
With the increase of the slag layer the sulfur diffusion rate is decreasing and, therefore, increases as
well. Therefore, the ratio between the slag layer over the droplet (h) and slag layer in the ladle over
hot metal (H) is calculated. Thus, at the beginning the volume of droplets and slag is calculated by
using the previously mentioned calculations and the data (table1). The sum of the droplets and slag
volume is determined. Then it is divided by the number of droplets with the slag, what results in
rdr,sl=0,3447mm.
According to the Table 1 rdr is equal to 0.0836 mm. Then slag layer surrounding the droplet (h) is
equal to 0.2611 mm. In order to determine the thickness of slag layer over the hot metal, the data on
the slag mass and droplets mass is used, also the inner diameter of the ladle at the top will be taken as
equal to 2.6 m. Then the ratio H / h ≈ 2000 and the path of sulfur diffusion through the slag to the
droplets will be more than three times shorter than to the surface of the metal ladle.
Consequently, the relative boundary-layer thickness in the slag over the hot metal in the ladle ( )
should be increased by more than three times. The change of the boundary layer thickness leads to
the corresponding change of mass transfer coefficient. Then the value of over the hot metal
should be equal to ≈ 0,36274 × 10-8
m / sec.
The sulfur distribution between the slag and hot metal in the ladle, depending on the time of their
contact with each other, is calculated. The average slag mass in one ladle is calculated by analogy to
the item 5 in Table 1 and amounts to 0.9122 t, the average mass of hot iron in the ladle is 639/11 =
58,1 tons , respectively, and the mass ratio of metal and slag is n = 58,1 / 0,9122 = 63,6922. Also, 2
.. .09134,01,58/3066,5 mS metsurs is determined (the number in the numerator is the average value
of hot metal surface area in the ladle). By using formulas (8) and (16) the rate constant in the
slag boundary layer over the hot metal and constant (С1, C2) are determined. The value of sulfur
concentration in hot metal is determined from the equation (19). For example, for 300 it is possible to obtain the following:
%00904,0)00902,010491,484
101502,10(
10491.484
101502,10][% 30010491,484
8
8
8
88
eS
Table 3 illustrates data on changes in the sulfur content in hot metal, depending on hot metal duration
time under the slag after magnesium desulfurization.
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Table3. Effect of hot metal duration under the slag on changes in [%S]
Duration, min 0 3 5 8 10 15 20
, % 0,00902 0,00903 00,00904 0,00906 0,009064 0,00909 0,00911
According to the data (Table 3), the change of sulfur concentration in the hot metal almost does not
occur and it is commensurate with the accuracy of chemical analysis of metal samples. Further
calculation shows that during 110,5 min, sulfur concentration in the hot metal will be constant and
equal to 0.009%.
Conclusion
The calculation procedure of the kinetic characteristics of sulfur interfacial transition process during
hot metal treatment with magnesium was developed. The diffusion boundary layer theory served as a
basis for this procedure. The results of hot metal industrial treatments, which led to the formation of
high-sulfur slag with a high content of droplets, were used as the experimental data. In order to make
experimental determination of kinetic constants, the data on time changes of sulfur concentration in
slag and droplets was used. The theoretical explanation of kinetic constants correction for the
conditions of hot metal duration under the ladle slag was made.
The kinetic characteristics calculated using the proposed model provide good description for
industrial results. Thus, it was proved that after refining of hot metal with magnesium under specific
conditions, a fast return of the sulfur from the slag into the metal droplets takes place. At the same
time the estimated sulfur content in the iron in the ladle remains practically invariable during 2
hours. The obtained results indicate that the rate-controlling step of hot metal resulfurization is
sulfur diffusion in the slag.
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