Multicomponent mixed -tra nsport- control theory for kinetics of coupled slag/metal and slag/metal/gas reactions: application to desulphurization of molten iron.
I "
Multicomponent mixed - tra nsportcontrol theory for kinetics of coupled slag/metal and slag/metal/gas reactions: application to desulphurization of molten iron D. G. C. Robertson, B. Deo, and S. Ohguchi
I
tit
I"
1\ c , 1\,••
L I~
At 1\' I\'T'-4
o
Ox
P1 R S Su r r· I'
A completely
x
IJ
(I
[J
1984 The Metals Society Manuscript received 24 February , 1183.At the time the work was carried out. the authors were In lhe Department of Metallurgy and Materials SCience. Imperial College of SCience and Technology. London Or Ohquchr IS now • the Research and Development Laboratory Ill. Nippon Steel Corporation. Kltakyushl,C,ty. Japan
b t' Fe g I M m
o U\
Ox TOF SYMBOLS activin interfa'cial area. Ill: totar'molar concentrauon. krnol m d~ving force for sulphur transfer in metal phase (ue equation (58)) dIffusion coefficient first order C - 0 interaction coefficient in iron area for gas/metal/slag reaction divided by area of slag/metal reaction
constant
equilibrium
constant =
for the reaction
CaS + [0]
equilibrium constant for the reaction COl = CO+ [0] equilibrium constant for oxide reaction (\IT equation (10)) equilibrium constant for sulphide reaction (wc equation (I I}) sulphur distribution coeflicient using mole fractions sulphur distribution coefficient using molar concentrations sulphur distribution coefficient using mass fractions or weight percentages mole fraction of metallic component flux density. kmol m - 2 S 1 total metal flux density. k mol m - 2 S - 1 mole fraction of oxygen in metal mole fraction of oxide total pressure, atm gas constant. 0·082 atm m) kmol 1K 1 mole fraction of sulphur in metal mole fraction of sulphide time, s dimensionless time, rAkmSIVm 'total concentration', defined by equation (15) volume, m) molecular weight, kg krnol " I mole fraction in gas phase fraction of total slag/metal area not occupied b) CO Bubbles area occupied by bubbles on crucible wall divided by nominal slag/metal area activity coefficient stoichiometric constant mass fraction mass fraction
of component of component
in slag in metal
Subscripts Ca
©
cquihbnuru
[S] + CaO
TM general kinetic model. which can be .pplied to metals and slags containing any . number of components reacting to form any specified compounds of known stability, is outlined for the case where these compounds are oxides and sulphides. It is assumed that the reaction rates are controlled by mixed transport in the metal, slag, and gas phases. The key equations in the model evaluate the relevant interfacial oxygen and sulphur potentials which .re consistent with the equilibria and the fluxdensity equations. The model is applied to the kinetics of the desulphurization of molten iron .nd supplies many important insights into this industrially important class of reactions. IS/548
a rrro~ ITna Ic c',irrcrt uin f.1l'1or for (IX Idc' rl';Il'IIIl~ III IIIrl11 C() (, •.,. eq";IIIIII1 (XXII cII,rrrlrlll1 1;ll'lllI dchncd t>~ cquauon (1'.11 ,IIIIC,111I11 (.,,·llIr lklrlll'd h~ cqu.uron (X41 I'hl'IIIlllll'''IIIIl~II,tI rail' p.u amr tcr [or CO n(\IIIII"" m.rvv-t r.mvlc: coclhctcru. Ill' I k,C, kn,Cn• (.\1',' cquuuon-, (16) and (1711
S Su (:\1
bun, carbon calcium iron gas phase interface metallic component metallic phase ')\~~l'n
er ..ill oxide sulphur sulphide ~I,,!, pha-.c at mtcrfacc l)\
indicated
(w,
initial value (t = 0) denotes normalized (X/Xo)
mole
\-tg.2/
Superscripts
o •
Ironmakmg
and Sreelmakmg
fraction
of component
1984. Vol 11. No 1
41
42
Roberlson
,"
PI 81
" n
KinetIcs of slag/metal and slag/metal/gas
"
'.1
reacuons In desulphunzatron
I' 1
--.J
"
•
i
. ,
.i
SLAll
'\ \
,
".
j
~
\' ,)
k. (0 . - :,' ..•. ,
,,
MET AL'
.._,'
[.
.
~ .\.CRUCIBLE
'\
",
/; \.
.i
f\
+S=S! by the 'anodic' reaction 2
Fe = Fe leading
+2e
to an overall
Fe+S
= Fe
2
11 ha' occurred, The general scheme (If reaction" uh CO bubble formation is illuvtratcd In I I!! ~, 111 which the numberused in this paper to define the different reaction interface, arc shown circled. For carbonsaturated iron in a graphite crucihle. the rcuctionare identical at intcjfacc» 5 and ), and at interfaces 4 and 2, With an oxide crucible, interface, 4 and 5 will not occur The po"ihilil~ of reaction, invohing thin film' of metal pu-hcd up lilt" the slal-' hI rising bubbles i, not included in lig. ~, Such rcacuon"ill be roughly equivalent to those occurring at interfaces :' and 3. The growth of CO bubble> between the slag and metal phases decreases the true metal-slag contact area available for the coupled reactions given in equations (I) and (2)_ but CO.formation and oxide-reduction reactions can still occur across the gas bubbles when 'ferrying' of CO and CO2 across the bubbles occurs as follows: sas/metal
interface
uC+aC02 gas/slag
=
interface
aCO+ MO.
3)
(interface
aKO (interface
= M
=
+aC02
FOR
For each reaction at the slag metal interface, it is possible to write the relevant equilibrium constants which relate the interfacial concentrations of the components (subscript i for interface), since the reactions are assumed to be 'fast', For each component
1\ ~
(4)
(5)
M+aCO
=
(6)
"MS)"M a~
Slag and metal b) the equations
(7)
surface
concentrations
can thus
be related
Ox; = 1\0. M, 07
Dd that the electrons can flow through uce metal at some other site
+ 2ae- =
MATHEMATICAL FORMULATION SLAG/METAL MODEL Equilibria
1\. = ""IO.taM"~)
Usually the initial oxygen potential in the slag is small and reaction in equation (5) will initially be slow, It is umed, therefore, that the initial effect of CO bubbles, ich will nucleate and grow immediately because of high I supersaturations. is to separate the phases over a rtion of the slag/metal nominal contact area, so easing the area available for the initially dominant ~pled reactions given in equations (I) and (2), Later. hen the oxygen potential in the slag is high, significant :Olide reduction to metal may occur as a result of the ctions given in equations (3) and (4), The situation is even more complex if the reactions are , out in a graphite crucible, This is because oxides in slag phase can react with carbon at the slag 'gas and /graphite-crucible interfaces (interfaces 4 and 5, respec'vely, in Fig, 2), King and Ramachandran ' suggest that overall slag gas graphite-crucible reaction may be
l ••
n)
2)
overall
aC+MO.
fUII1.llT I' 1'(l11'ldl'l'l'd (', (I,~ "t""SI. ~ (1,1 "I'''"S, c.u hou '"il'I,llnl "I I .u m ('Of. t hc tlnh unportn nt v ol.u i lr 'I'l" )," I' \1\ '1 hi' !!"Ill'I.ltl" a PI,'''trrl' of ah(lllt -1 > III 'atm at 1-1(,' ( rI~l'l ~I 'I hu-, t hr 1ll.t\lllllllll ptl"lhk dill III~ r"lll' f,or 1.,11.,u.ui-Jcr I' -1. III • aun (from rnctal io ~la!!1 l or an 1l\~~"11 l'"t"lltl.tlll1 t hc ,I;I!! tell urnc tha t ill the mct.il. thl' drrllll!! Iorcc for CO: transfer i~ 90 x III 'atm thueven SIS trauspor: is relatively unimportant under the-e conduionx. It is concluded. therefore. that. in an) full devcripuon of the desulphurization of pig iron, the reactions given in equation, (I) and (~J (occurring at the true slagmetal interface) would have to be combined with the rcacuongilen in equations and (41 (occur rmc an"" i hc ga, bubble- separating the phases), However. th~ ~Ia!! metal model i, of sufficient interest in it~ own right to rncru a full discussion. and leads to some very important insight" It is. therefore, presented first.
the graphite
to
M
Su, = I\suM;S~
,
(9)
where Ox and Su represent. respectively, oxide and sulphide mole fractions in the slag: M, 0, and S represent the relevant mole fractions in the metal. For any component 1\0.
=
(;'Mi'0'-,'0.)1\4
Ksu = (i'Mi'Vi'sull\
(ID) (11)
5
The i'o.- and i'su-values are those of Raoultian activity coefficients, while the i'M-' -,'s-, and -,'o-values are those for dilute components in the metal. The K4' and K 5-values used in this paper are given in Table I, For the purpose of presenting the theory, the exact values are not too important. Workers who wish to apply the theory to a particular set of experimental data "ill. however. need to take some trouble to estimate the i'-yalue, carefully for their particular slag and metal compositions, since the i'-values in both phase, are sometimes strongly composition dependent.
Flux-density
h a reaction sequence is considered by the present thors to be unlikclv. since the first reaction involves ,pha\e, TIll' dh.',! "f t h,: ,LIt: !'". t'r.trhltl'-crucihk lions will be exactlv the same a, that of an increase in ,area available for the reactions in equations (3) and (4) point will be considered furthcr."beJ(l\\ n, I,he case of dcvulphurr/unon ()'I 'Ir,'n. rcducuon of sla!, nSlng CO bubble- '.!!', I, n"L'kl'tcJ. ,in" t hc bubbleonly to absorb a \ cr~ ,mall' amount of oxygen in the of CO2 to attain a CO CO, ratio which is in 'brium with the slag composition For an oxygen ti~1 in the slag ten times that in ihe metal. x('o: at num is only about 0)" q~estion of volatile sulphide and oxide species is one WIll not be discussed in detail in this paper. for the brevity, If a typical hot metal from the iron blast
(8)
equations
There are 11flux-density equations, for the transfer of the 11 metallic components, and tw o more for oxygen and 'lIlrl~u' h'r the metallic 1\11 components rate of transfer
Table 1
out of metal
= rate of transfer
Stoichiometric constants IT and dynamic equilibrium constants K model calculations at 1465 C
into slag ( 12)
ther rno used in
Component Fe
S,
Ca
1 5534 1,75
2 5·15.10" 353
1 7,32.10" 1·14 x 10"
U'
(1
K, (OXIde) K, (sulphrde)
Ironmaking
and Sleelmakmg,
1984, VD! 11 No
1
1$
44
Bobertson
er
K,netlcs ot slag/metal and slag/metal/gas
1/1
reactions in dosutphunzauon
i.c. ~,,,,,(',,,(M,,-M,I
1.".Ct
.Sb
0,6
0·4
o 11
8
4
Comparison of predictions
to
10
of Model C (full lines) with those of multicomponent
(S + 1e = S~ -) is then ascribed to oxygen transfer in the metal (O~ - = 0 + 1e -) than to iron transfer to the slag (Fe = Fe1- +1e-). In Fig. 11. the predictions of Model C are compared with those of the multicomponent model using almost the same \ alues of the equilibrium constants. The agreement for sulphur is very good. but Model C predicts slightly higher values for OXF ,-
- --
.
{,/
(F ea)
_\....._------
(FeO)
15
20
15
5
20
a (Sl~] ~ O. b (S,g] = 042 wt·% 17
Effect of silicon addition to metal on predictions
of modified slag/metal
rate is very slow. The reduction of silica is also calculated to be slow for the same rea on. One possible way out of the difficulty would be to take a negative value for e~ (carbon decreases the activity coefficient of oxygen I. as has been reported b) a number of investigators (see Ref. 7). If e~ were - O' 25 instead of + 0'1, the oxygen 'solubility' in carbon-saturated iron at I atm CO would be increased sixty-fold. This would. however. be a serious error. Nobody has challenged the data of EIKaddah and Robertson." w ho have provided internal checks on the accuracy of their data and arguments as to why the reported negative values are incorrect. The approach taken. therefore. is one which considers that e~ is indeed + 0·1. and which looks elsewhere for an explanation ofihe lack of agreement between the model calculations and the experimental data. The reason is in fact associated with the slag metal gas reactions discussed above. The reactions in equations (J)
model
and (4) lead to the reduction of oxides by oxygen transf across the gas bubbles separating the phases. In Appendix 2 it is shown that these reactions can be taken into account in a semiquantitative manner in a modified slag metal model b) increasing the flux density of oxygen into the metal phase by a constant factor Fo· This factor is predicted to be about 100. but must be treated as a parameter in the model. because of its approximate nature and because of a lack of knowledge of the fraction of the nominal slag metal and slag crucible areas occupied by gas bubbles. The effect of modifying the slag, metal model to allow for the slag metal gas reactions by using F 0 is shown in Fig. 15. Quite good agreement between calculation and experimental data is obtained for an Fo value of 100. The full results of the modified slag 'metal model calculations with F 0 = 60 are shown in Fig. 16. The slag FeO and FeS contents initially rise rapidly. then decline as
0·1:,,--------------, ( b)
(a)
Fo
= 60
Fo = 60
= ..•... Q)
- 1
....•
--J
'
o a(FeO)~~O
18
15
b(FeO)g=02wt
and Sreelmakmg
7984
20
5
%
Effect of FeO addition to slag on predictions
Ironmakmg
200
vot
77
No
7
of modified slag/metal
model
.1 III
Roberl50n
Kinetics of ,Iag/metal
o
( a)
'\
\ . \
and 'Iag/metal/wos
10
IS
7~
reaction.
In desulphuriretion
1 WI "'u 7~ ~i'
3)
40
4~
~Q
-,
\
,," "-
c;
~
-.0
•.....•
\tarc a, follows: w
Ii} it i\ gcncrallv agreed that the rate, of most sim ,1;1l: tuct.rl rc.icuonv. 11'. [M) + (0) = (MO). a f;t ,j I I 1111tlu- paper has \hp\\ n that 10\\ overall rates can obi.uncd a\ a rc-ult of mixed transport control the la tcr stage, of the reactions considered. main because of the low driving forces for CO C ferrying and [OJ transport at low oxygen potentia hence it is unnecessary to postulate a slow chemi step to explain the observed low overall r,ates. . lili} for the data of King and Ramachandrarr' shown Fig. 20. the measured CO evolution rate in t initial stages (say. r ~ 10 min) was 3700 mrn ' s - I the reaction temperature (1502 C). The metal-ph mass-transfer coefficient is unknown. but can estimated using the formula 12 k~
BD·Qdc-.fl
=
where B is a constant (= 10 mm - I). Q' the diffusion coefficient (mm! S-I). Q the gas flowrate crossing the slag metal interface (mrn ' s - I). and de
