Desulfurization Of Liquid Steel Containing Aluminum Or Silicon With Lime.pdf

Desulfurization of Liquid Steel Containing Aluminum or Silicon with Lime R. J . FRUEHAN The r e a c t i o n m e c h a n i s m s for the d e s u l f u r i z a t i o n of i r o n c o n t a i n i n g f r o m 0.04 to 1.5 pct a l u m i n u m or 1.1 to 3.7 pct s i l i c o n by CaO at 1600~ have b e e n e x a m i n e d . The d e s u l f u r i z a tion of Fe-A1 by Ca(9 is c o n s i d e r a b l y f a s t e r than that of F e - S i . T h e b a s i c d i f f e r e n c e b e t w e e n the two p r o c e s s e s is that Fe-A1 a l l o y s can be d e s u l f u r i z e d by the f o r m a t i o n of A1203, w h e r e a s for F e - S i m e l t s it is n e c e s s a r y to f o r m Ca2SiO4. T h e r a t e of d e s u l f u r i z a tion of F e - S i a l l o y s by Ca(3 is c o n t r o l l e d by the f o r m a t i o n of the g a s e o u s i n t e r m e d i a t e s , SiS and S, and is the s a m e as that for d e s u l f u r i z a t i o n in v a c u u m . T h e r a t e of d e s u l f u r i z a tion of F e - A 1 m e l t s is fast, and is a p p a r e n t l y c o n t r o l l e d by the diffusion of s u l f u r to the liquid m e t a l - C a O i n t e r f a c e . E x p e r i m e n t s w e r e a l s o conducted to d e m o n s t r a t e that s u l f u r could be t r a n s f e r r e d to CaO by the g a s e o u s i n t e r m e d i a t e s SiS and S.

THE

o v e r a l l d e s u l f u r i z a t i o n r e a c t i o n s of F e - C , F e - S i , and Fe-A1 a l l o y s with CaO can be r e p r e s e n t e d by S + CaO + C = CaS + CO

[1]

S + 2CaO + ~Si = CaS + ~CaeSiO4

[2]

3S + 4CaO + 2A1 = 3CaS + CaA1204.

[3]

As d i s c u s s e d in p r e v i o u s p u b l i c a t i o n s , ~-3 the r e a c t i o n s as w r i t t e n r e p r e s e n t the o v e r a l l r e a c t i o n ; to u n d e r s t a n d the d e s u l f u r i z a t i o n m e c h a n i s m the i n d i v i d u a l s t e p w i s e r e a c t i o n s should be c o n s i d e r e d . F o r e x a m p l e , Eq. [2] has a m i n i m u m of t h r e e p h a s e s p r e s e n t , a s s u m i n g that the CaO is i m p r e g n a t e d with liquid s l a g . F o r this case t h e r e is only a line of contact b e t w e e n the t h r e e p h a s e s which is not f a v o r able for r a p i d d e s u l f u r i z a t i o n . It has b e e n p r o p o s e d that an i m p o r t a n t step in the d e s u l f u r i z a t i o n of F e - S i m e l t s is the f o r m a t i o n of the v a p o r s p e c i e s SiS and that the CaO m e r e l y acts as a getter for the s u l f u r b e a r i n g g a s e s . It is one of the p u r p o s e s of the p r e s e n t work to p r o v e this h y p o t h e s i s . The d e s u l f u r i z a t i o n of F e - A 1 m e l t s m u s t p r o c e e d by m e a n s of a n o t h e r type of m e c h a n i s m s i n c e t h e r e is no s i g n i f i c a n t a l u m i n u m s u l f u r v a p o r s p e c i e s . The m e c h a n i s m of d e s u l f u r i z a tion of Fe-A1 alloys with CaO will a l s o be e x a m i n e d . It has b e e n r e c e n t l y p r o p o s e d by T u r k d o g a n 4 that liquid s t e e l c a n be d e s u l f u r i z e d e f f i c i e n t l y by i n j e c t i n g CaO with A1 or Si. By doing so a l a r g e CaO7 l i q u i d - m e t a l s u r f a c e a r e a is p r o v i d e d and a l o c a l l y high A1 or Si content at the i n t e r f a c e will e x i s t , both of which a r e f a v o r a b l e for r a p i d d e s u l f u r i z a t i o n . The p r e s e n t work was u n d e r t a k e n to d e t e r m i n e whether the d e s u l f u r i z a t i o n r e a c t i o n s a r e fast enough to make this p r o p o s e d p r o c e s s f e a s i b l e .

RESULTS AND DISCUSSION

EXPERIMENTAL T o d e m o n s t r a t e the e f f e c t i v e n e s s of s u l f u r t r a n s f e r f r o m l i q u i d - i r o n a l l o y s to CaO via the gas phase, a s e r i e s of e x p e r i m e n t s was made with F e - 3 . 0 pct CR. J. FRUEHAN is with U.S. Steel Research Laboratory, Monroeville, PA 15146 Manuscript submitted October 5, 1977. METALLURGICALTRANSACTIONS B

Si-S alloys at 1400~ About 8 g of the a l l o y was cont a i n e d in a ZrO2 c r u c i b l e (1.7 c m ID) and 1 g of g r a n u l a r CaO p a r t i c l e s w e r e s u s p e n d e d above the m e l t in a p l a t i n u m b a s k e t at a p r e d e t e r m i n e d d i s t a n c e (x) of 0.3, 0.8, or 2.5 c m above the m e l t . The s a m p l e s w e r e heated in a v e r t i c a l tube f u r n a c e (4.0 c m ID) with a top flow of A r at 1.5 1//min. T h e l i m e p a r t i c l e s , p r e v i o u s l y c a l c i n e d at 1500~ w e r e within the s i z e r a n g e f r o m 0.5 to 1 m m and had an i n t e r n a l p o r e a r e a of 0.3 m2//g. T h e i n i t i a l s u l f u r c o n t e n t of the m e l t was 0.1 pct and the Si c o n t e n t v a r i e d up to 3.8 pct. S e p a r a t e d u p l i cate e x p e r i m e n t s w e r e a l s o conducted in which t h e r e was no CaO p r e s e n t , with the d i s t a n c e by which the c r u c i b l e wall extended above the m e l t b e i n g the s a m e as the d i s t a n c e above the m e l t at which the CaO was suspended. In a s e c o n d s e r i e s of e x p e r i m e n t s 5000 g of an F e - C S, Fe-A1-S, or F e - S i - S alloy c o n t a i n e d i n a 9.6 c m ID z i r c o n i a c r u c i b l e was heated in a n induction f u r n a c e in a p r o t e c t i v e a t m o s p h e r e of flowing A r . A f t e r the t e m p e r a t u r e r e a c h e d 1600~ a s a m p l e of the m e l t was taken by s u c t i o n into a s i l i c a tube, a f t e r which powd e r e d l i m e (<0.1 mm) was added. U s u a l l y 125 g of CaO was used; however, in s e v e r a l c a s e s d u p l i c a t e e x p e r i m e n t s w e r e conducted in which 80 or 160 g of CaO w e r e u s e d . In a l l c a s e s the l i m e was s u f f i c i e n t to cover the e n t i r e s u r f a c e of the m e l t , and t h e r e was no d i f f e r e n c e in the r e s u l t s when the a m o u n t of CaO used was v a r i e d within this r a n g e . S a m p l e s w e r e t a k e n at r e g u l a r i n t e r v a l s and a n a l y z e d for s u l f u r and a l u m i n u m , s i l i c o n , or c a r b o n . E x p e r i m e n t s w e r e a l s o made with F e - A 1 - S a l l o y s u n d e r v a c u u m (10 Pa) with no CaO addition; the p r o c e d u r e used has b e e n d e s c r i b e d previously.~

The r e s u l t s o b t a i n e d with the CaO s u s p e n d e d 0.8 c m above the s u r f a c e of the 8 g m e l t a r e shown in F i g . 1. A s i m i l a r r e l a t i o n s h i p was o b t a i n e d with the Ca(3 for each of the other d i s t a n c e s above the m e l t . T h e r a t e of d e s u l f u r i z a t i o n i n c r e a s e d with i n c r e a s i n g Si c o n t e n t of the m e l t . It is also i m p o r t a n t to note that with 3.8 pct Si in the m e t a l the r a t e of d e s u l f u r i z a t i o n was

ISSN 0360-2141/78/0612-0287500.75/0 9 1978AMERICANSOCIETYFOR METALSAND THE METALLURGICALSOCIETYOF AIME

VOLUME 9B, JUNE 1978-287

In F i g . 2 the slopes of the line for In (pet S / p c t S o ) v s Lime a r e pioLted vs l / x ; the expected b e h a v i o r is observed. It is p o s s i b l e to e s t i m a t e the r a t e of d e s u l f u r i z a t i o n f r o m the t h e r m o d y n a m i c s of F e - C - S i - S alloys, the f r e e e n e r g y of f o r m a t i o n of SiS, and a n e s t i m a t e d value of rn. At 1400~ the e q u i l i b r i u m c o n s t a n t K for Eq. [9] is 0.496

s + s i : sis(g) Psis a s i f s pct S

-0.8

K=

F o r an alloy c o n t a i n i n g 3.8 pct Si and 3 pct C the a c t i v i t y coefficient of s u l f u r (fs) is 5 and the a c t i v i t y of s i l i c o n (asi) is 0.001.1 T h e r e f o r e the e q u i l i b r i u m p a r t i a l p r e s s u r e os SiS is given by

% 3.8O% Si

-,,2

[

I

l

200

400

600

[9]

TIME, rain

Fig. 1--Desulfurization of Fe-3.0 pct C-X alloys at 1400~ by vapor transport to porous lime granules suspended 0.8 em above the melt.

PSiS = 2.5 • 10 "a (wt pct S), a i m

[10] P s i s = 2.5 x 102 (wt pct S) Pa.

about the s a m e with or without the CaO at a d i s t a n c e of 0.8 cm above the m e l t . T h e s e r e s u l t s s u g g e s t that the r a t e is c o n t r o l l e d p r i m a r i l y by diffusion of SiS v a p o r through the s t a g n a n t gas l a y e r over the m e l t . The r e a c t i o n of SiS with CaO on the pore w a i l s of the l i m e p a r t i c l e s may be r e p r e s e n t e d , for e x a m p l e , by SiS(g) + 2CaO = CaS + ~Ca2SiO4 + ~ S i ( / ) .

[4]

T h e e q u i l i b r i u m p a r t i a l p r e s s u r e of SiS for this r e a c t i o n at 1400~ is 2 • 10 "~ Pa, z'5 which is s e v e r a l o r d e r s of m a g n i t u d e lower than that at the s u r f a c e of the a l loys i n v e s t i g a t e d . T h e r e f o r e , the p a r t i a l p r e s s u r e of SiS at the CaO s u r f a c e can be a s s u m e d to be z e r o and the r a t e e q u a t i o n for d e s u l f u r i z a t i o n c a n be r e p r e s e n t e d by d pct S dt

3200 A RTW

-

m PSiS

[5]

where A R W T Psis

= = = = =

s u r f a c e a r e a of the m e l t (2.27 cm2), gas c o n s t a n t , weight of the m e l t (8 g), a b s o l u t e t e m p e r a t u r e (K), the e q u i l i b r i u m vapor p r e s s u r e of SiS which is p r o p o r t i o n a l to the s u l f u r content.

It is p o s s i b l e to e s t i m a t e m by u s i n g Eq. [8]. The value of D is e s t i m a t e d to be 3 c m 2 / s f r o m the data and equations given by H i r s c h f e l d e r , e t a l . 6 At a dis" Lance of x = 0.8 c m the c a l c u l a t e d v a l u e of k ' m is 7 • 10 -5 s "I c o m p a r e d with the o b s e r v e d value of 4 • 10 -~ s -z. The a g r e e m e n t is good c o n s i d e r i n g the u n c e r t a i n t i e s in the t h e r m o d y n a m i c s and the e s t i m a t i o n of m . I n p r e v i o u s work done in v a c u u m 1 it was found that the r a t e of d e s u l f u r i z a t i o n of F e - S i - S alloys was p r i m a r i l y c o n t r o l l e d by a slow c h e m i c a l r e a c t i o n for the f o r m a t i o n of SiS, the r a t e of which was 1/10 the r a t e for f r e e v a p o r i z a t i o n of SiS. At 1400~ the r a t e cons t a n t for the f o r m a t i o n of SiS is 0.02 s -z. A p p r o x i m a t ing m by D / x gives x = 25 /zm as the c r i t i c a l d i s t a n c e b e t w e e n the lime p a r t i c l e s and the s u r f a c e of the m e l t for a p p r o a c h to the m a x i m u m r a t e of d e s u l f u r i z a t i o n ; that is, the r a t e i n c r e a s e s as the d i s t a n c e between the CaO p a r t i c l e and the m e l t d e c r e a s e s u n t i l that d i s t a n c e is 25 tzm. T h e r e f o r e , in w e l l - s t i r r e d l i q u i d - F e alloys c o n t a i n i n g s i l i c o n , the r a t e of d e s u l f u r i z a t i o n by l i m e in d i r e c t contact with the m e l t will be c l o s e to that a c h i e v e d in v a c u u m . T h i s c o n c l u s i o n w i l l be f u r t h e r s u b s t a n t i a t e d by the r e s u l t s to follow. ,=

The i n t e g r a t e d f o r m of this equation is ln Pct S = - k ' m t [6] pct So w h e r e k ' is a c o n s t a n t dependent on the p r e s s u r e of

SiS, As shown in Appendix A the mass-transfer coefficient, m, is expected to v a r y with the d i s t a n c e f r o m the m e l t to the CaO and is given by 1

1

m

m o

[7]

D

w h e r e m o is the m a s s - t r a n s f e r coefficient at the top of the c r u c i b l e o r at the CaO p a r t i c l e s and D is the i n t e r d i f f u s i v i t y . In the p r e s e n t work m o is r e l a t i v e l y l a r g e and Eq. 7 r e d u c e s to D .~

288

:

- .

X

V O L U M E 9B, J U N E 1 9 7 8

K

4

x +

8 I

[8]

I

I

I

1

2

3 1 ~.

cm t

Fig. 2--Rate constant for the desulfurization of Fe-3.8 pet Si-3 pct C melts at 1400~ as a function of the reciprocal of the diffusion distance to lime particles above the melt. METALLURGICAL

TRANSACTIONS B

T y p i c a l r e s u l t s obtained with 5000 g m e l t s at 1600~ with CaO in d i r e c t contact with F e - A 1 a l l o y s are g i v e n in F i g . 3 for an initial sulfur content of 0.1 pct and in Fig. 4 for 0.031 pct i n i t i a l s u l f u r . The A1 content changed during the c o u r s e of the e x p e r i m e n t , partly b e c a u s e of the r e a c t i o n i t s e l f but p r i m a r i l y b e c a u s e of oxygen pickup f r o m the a t m o s p h e r e . In the e x p e r i m e n t s in w h i c h no CaO was added at a t m o s p h e r i c p r e s s u r e or in v a c u u m , there was no a p p r e c i a b l e d e s u l f u r i z a Lion, indicating that there is no s i g n i f i c a n t v o l a t i l e a l u m i n u m - s u l f u r s p e c i e s as in the c a s e of s i l i c o n . The i n i t i a l rate of d e s u l f u r i z a t i o n of F e - A 1 m e l t s i s v e r y rapid. A s shown in F i g . 5, within l e s s than 20 rain the sulfur content was reduced below that for e q u i l i b r i u m with A1203. 3S + 3CaO + 2A1 = 3CaS + A12Oa.

0,OOlB

~

|

3S + 2AI + 3CaO = AI20 3 + 3CaS EQUILIBRIUM O 20 MINVTES

0.0OB

~

9 120 MINUTES

u~ 0.004

0.00"2

[11]

FIowever, in g e n e r a l e v e n at long t i m e s , 120 min, the s u l f u r content w a s s t i l l higher than that in e q u i l i b r i u m with CaA1204. 5 In s e v e r a l c a s e s the sulfur content of the m e t a l i n c r e a s e d at long t i m e s b e c a u s e the A1 content was d e c r e a s i n g . It appears that the r e a c tion s e q u e n c e

I

4CaO + 2AI + 3S = 3CaS + CaAI204

EQUILIBRIUM I

I

I

I

0.2

i

0.4

0.6

AI, wt %

S + CaO = O + CaS

[12]

2A1 + 3 0 = A1203

[13 ]

F i g . 5 - - S u l f u r c o n t e n t s a s a f u n c t i o n of a l u m i n u m 20 and 120 rain.

contents

at

0.1

is v e r y rapid and goes to c o m p l e t i o n e a s i l y . The f o r 0,06 0,1q

l

I

I

I O E] 9 9 9

0,05

I

0.04

Al(initi~) /Ill fir~l 0.06 0.03 0,60 0.04 0,14 0.0O 0.42 0.36 1,51 1.50

0.02

0,02

0.01 Si

'~ u~

O

0.01

0.006 0.004

0.005

0.602

~

9I

0.601

o.601

I

20

I

40

I

I

60

I

60

I

160

120

0.04~

l

l

I

I

40

~

Si

0

"I

80

~

I

1120

TIME, rain

140

F i g . 6 - - D e s u l f u r i z a t i o n of F e - S i a n d F e - C m e l t s by CaO a t

TIME, rain

F i g . 3 - - D e s u l f u r i z a t i o n of F e - A 1 m e l t s

3.70%

0.602

1600~

w i t h C a O a t 1600~

l

I

at atmospheric

pressure.

m a t i o n of the a l u m i n a t e is apparently m u c h s l o w e r s i n c e this r e q u i r e s a s o l i d - s o l i d r e a c t i o n

I

AI(5 minuZe~l All~al~ 002

D

0,09

0.04

O

0,32

0,20

A1203 + CaO = CaA1204

[14]

or the d i r e c t r e a c t i o n indicated by Eq. [3]. T h e i n i t i a l rate of d e s u l f u r i z a t i o n of F e - A 1 a l l o y s by CaO is v e r y fast and is p o s s i b l y c o n t r o l l e d by the diffusion of s u l f u r f r o m the bulk to the liquid m e t a l CaO s u r f a c e . The integrated f o r m of the rate equation for m a s s - t r a n s f e r c o n t r o l i s given by

001

0.606

In pct S t - pct S e = - k t pct S o - pct S e

o.ooi

I

20

I

40

I

I

60

80 TIME,

I

100

I

120

min

F i g . 4 - - D e s u l f u r i z a t i o n of F e - A I m e l t s w i t h C a O at 1600~ METALLURGICAL

TRANSACTIONS

B

140

[15]

w h e r e h is the m u s s - t r a n s f e r c o e f f i c i e n t for an ind u c t i v e l y s t i r r e d m e l t . A s s u m i n g that the A1 c o n c e n tration at the s u r f a c e is a p p r o x i m a t e l y equal to that in the bulk and the o x y g e n potential is d e t e r m i n e d by the A1 - AI~O~ e q u i l i b r i u m , it i s p o s s i b l e to c a l c u l a t e VOLUME

9B, JUNE 1978-289

0

'

I

I

r a t e c o n t r o l l i n g r e a c t i o n is the f o r m a t i o n of SiS

r

%.

St + S -- SiS(g).

AI (0,32- 0,04) SO (0,10-0,031) 1 --

The r e m a i n i n g r e a c t i o n s for d e s u l f u r i z a t i o n a r e fast and it is u n c l e a r what the exact r e a c t i o n s might be. F o r e x a m p l e the r e a c t i o n might p r o c e e d by Eq. [4] or a s follows:

,:Z: =

2P

%.

,%

3--

8 %.

X 4

4

8 TIME, rain

Fig. 7--Desulfurization of Fe-A1 melts by CaO at 1600~ in an inductively stirred melt. the e q u i l i b r i u m s u l f u r content (pet Se). U s i n g the a v e r a g e A1 c o n t e n t s the r e s u l t s a r e plotted in F i g . 7 in a c c o r d a n c e with Eq. [15]. It should be noted that in g e n e r a l t h e r e is a dual diffusion p r o c e s s , with A1 a l s o diffusing to the s u r f a c e , but for this r o u g h a p p r o x i m a tion this was n e g l e c t e d . The r e s u l t s fit the e q u a t i o n o v e r a f a i r l y wide r a n g e of A1 contents; and the slope of the l i n e , which is the m a s s - t r a n s f e r coefficient, a g r e e s within a f a c t o r of two with that c a l c u l a t e d f r o m the e q u a t i o n s developed by M a c h l i n 7 for m a s s t r a n s f e r in an i n d u c t i v e l y s t i r r e d m e l t . T h i s a g r e e m e n t is r e a s o n a b l e c o n s i d e r i n g the a p p r o x i m a t i o n s made in the calculations. Although the r e s u l t s a r e i n s u f f i c i e n t to prove conc l u s i v e l y that the i n i t i a l r a t e of d e s u l f u r i z a t i o n of F e - A 1 a l l o y s by CaO in the p r e s e n t work is c o n t r o l l e d by the diffusion of s u l f u r to the s u r f a c e , this a s s u m p tion a p p e a r s r e a s o n a b l e and the r e s u l t s a r e c o n s i s t e n t with this i n t e r p r e t a t i o n . In any case the r a t e is v e r y f a s t and t h e r e is no e v i d e n c e of a slow c h e m i c a l r e a c tion. As shown in F i g . 6, the r a t e of d e s u l f u r i z a t i o n of F e - S i a l l o y s is c o n s i d e r a b l y s l o w e r than that of Fe-A1 a l l o y s . F o r F e - S i a l l o y s the d e s u l f u r i z a t i o n r e a c t i o n in which SiO2 is f o r m e d is not t h e r m o d y n a m i c a l l y f a v o r a b l e u n d e r the c o n d i t i o n s of the p r e s e n t work 2S + 2CaO + Si = SiOz + 2CaS.

[19]

SiO(g) + 2CaO + O = Ca2SiO4.

[20]

In pct S _

100A (klaSi +

pcs%

w

k2)fst

[21]

where /el = /e2 = A = W= asi =

the the the the the

r a t e c o n s t a n t for the f o r m a t i o n of SiS, r a t e p a r a m e t e r for f r e e v a p o r i z a t i o n of S, s u r f a c e a r e a of the melt, weight of the melt, a c t i v i t y of s i l i c o n .

F r o m the t h e r m o d y n a m i c p r o p e r t i e s for the alloys given p r e v i o u s l y 2 the r a t e c o n s t a n t s d e r i v e d f r o m the s l o p e s of the r a t e c u r v e s in F i g . 5 a r e plotted in Fig. 8 in a c c o r d a n c e with Eq. [21] along with the r e s u l t s of p r e v i o u s work o b t a i n e d in v a c u u m . 2 8-~ The p r e s e n t r e s u l t s obtained at a t m o s p h e r i c p r e s s u r e with CaO a r e in e x c e l l e n t a g r e e m e n t with those obtained under v a c u u m with no CaO. T h e r e f o r e the r a t e of d e s u l f u r i z a tion of F e - S i - S alloys by CaO is p r i m a r i l y c o n t r o l l e d by the r a t e of f o r m a t i o n of SiS and S, and the rate is the s a m e as that achieved in v a c u u m . SUMMARY AND CONCLUSIONS T h e m e c h a n i s m s of d e s u l f u r i z a t i o n of s t e e l containing A1 o r Si by CaO have b e e n e x a m i n e d . F o r F e - S i a l l o y s the i m p o r t a n t step in the p r o c e s s is the f o r m a tion of SiS(g). The r a t e of d e s u l f u r i z a t i o n is c o n t r o l l e d

[17]

J

The following m e c h a n i s m i n v o l v i n g the v a p o r s p e c i e s SiS is p r o p o s e d for the r e a c t i o n m e c h a n i s m . The slow

t

J

J

9

J f

p

f

f

f

J

J

V /

x VA

V v

/ o

-- V

// OHNO a ISHIDA

o/f /

VACUO

SEFIGAL SEHGAL & MITCHELL

/ Mt

jl CoO

~d

J

FRUEHAN & TURKDOGAN O PRESENT WORK (ATMOSPHERIC PRESSURE)

0

( J

I

I

2

4

I

Fig. 8--Desulfurization

I s

~x

2 9 0 - V O L U M E 9B, J U N E 1978

of d e s u l f u r i z a t i o n f o r m a t i o n of SiS, o b s e r v e d in p r e v i o u s l y 1,2 is

[16]

T h e e q u i l i b r i u m s u l f u r c o n t e n t for Eq. [16] at 1 pct Si is over 0.1 pct. 5 D e s u l f u r i z a t i o n by the f o r m a t i o n of CaSiO3 is a l s o not f a v o r a b l e , with e q u i l i b r i u m s u l f u r content b e i n g 0.07 pct at 1 pct Si. It is t h e r e f o r e n e c e s s a r y for Ca2SiO4 to f o r m a s i n d i c a t e d by Eq. [2], for which the e q u i l i b r i u m s u l f u r c o n t e n t is about 0.001 pct at 1 pct Si. It is difficult to conceive that the d e s u l f u r i z a t i o n m e c h a n i s m is by the d i r e c t r e a c t i o n given by Eq. [2] b e c a u s e it r e q u i r e s Si and S a t o m s in the m e t a l to collide s i m u l t a n e o u s l y with a CaO p a r t i c l e . It a l s o does not s e e m likely that the m e c h a n i s m c o n s i s t s of a f o r m a t i o n of SiO2 f i r s t , followed by the s o l i d - s o l i d r e a c tion SiO2 + 2CaO = Ca2SiO4.

SiS(g) + CaO : CaS + SiO(g)

As d i s c u s s e d e a r l i e r , if the r a t e of F e - S i a l l o y s is c o n t r o l l e d by the the r a t e should be the s a m e as that v a c u u m . The r a t e e q u a t i o n d e r i v e d

I

I

o

[18]

J

I 8

I lo

lo 4

r a t e c o n s t a n t a s a f u n c t i o n of s i l i c o n

activity at 1600~ METALLURGICAL TRANSACTIONS B

by the r a t e of f o r m a t i o n of SiS and is the s a m e as that a c h i e v e d in v a c u u m when no CaO is p r e s e n t . T h e r a t e of d e s u l f u r i z a t i o n of F e - A 1 with CaO is c o n s i d e r a b l y f a s t e r , and the i n i t i a l r a t e in the p r e s e n t w o r k is p r o b a b l y c o n t r o l l e d by the m a s s t r a n s f e r of s u l f u r to the r e a c t i o n i n t e r f a c e . T h e b a s i c d i f f e r e n c e b e t w e e n the d e s u l f u r i z a t i o n of F e - A 1 and F e - S i a l l o y s with CaO is that f o r F e - A 1 a l l o y s s i g n i f i c a n t d e s u l f u r i z a t i o n can o c c u r when the r e a c t i o n p r o d u c t is the s i m p l e oxide A1203, for which the d i r e c t r e a c t i o n s a r e f a s t . F o r F e - S i a l l o y s it is n e c e s s a r y to f o r m Ca2SiO4 to a c h i e v e a p p r e c i a b l e d e s u l f u r i z a t i o n . T h e f o r m a t i o n of t h i s m o r e c o m p l e x oxide is slow and r e q u i r e d the u se of the g a s e o u s i n t e r m e d i a t e s SiS and S f o r a f a s t r e a c tion. Th e t r a n s f e r of s u l f u r to CaO by SiS and S was d e m o n s t r a t e d in a s e p a r a t e s e t os e x p e r i m e n t s . T h e t e c h n i q u e p r o p o s e d by T u r k d o g a n f o r d e s u l f u r i z i n g s t e e l by the i n j e c t i o n of A1 and CaO with an i n e r t gas (Ar fo r e x a m p l e , t h r o u g h a Q - B O P t u y e r e ) a p p e a r s f e a s i b l e in that the k i n e t i c s of the r e a c t i o n a r e f a s t .

6

I

I

T

I

I

I

5

X = 0.8 cm

.~

O

X = 1,9cm

J

I

I

I

t

i

2

4

6

8

10

12

u, cm/s

Fig. A-2--Mass-transfer coefficient for Pb in flowing Ar at ll00~

,sf

,

,

,

,

APPENDIX A u = 1.6 eml~

Gas-Phase Mass-Transfer Coefficient for Crucible Geometry Many experimental investigations of the rate of chemical reactions involving liquid metals use an experimental arrangement similar to the one employed in part of the present study; that is, liquid metal in a crucible supported in a vertical tube furnace with the reacting or neutral gas flowing in the reaction tube. Since in many cases gas-phase mass transfer may be affecting the rate of the reaction, the gas-phase mass transfer for this experimental geometry was investigated. In a previous measurement of the rate of oxidation of carbon by CO2 with a similar experimenta!

crn/s 1.0

E

0 u

,

I

,

1.0

8

:: I

.6 cm/s

I /

2.0 X. cm

Fig. A-3--Mass-transfer coefficientfor vaporizationof Pb in He and Ar at II00~ as a functionof the distance X. geometry, it was found that the mass transfer coefficient (m) was given approximately byz3 D m

= -

[A-1]

x d

-- ~

X = 0.8 cm

where

D = interdiffusivity, x = the d i s t a n c e f r o m the top of the c r u c i b l e to the reaction surface. In this s i m p l e a n a l y s i s no a c c o u n t was t a k e n of the gas v e l o c i t y or the m a s s - t r a n s f e r c o e f f i c i e n t when x =0.

I

I

I

I

I

I

2

4

6

8

10

12

u, cm/s

Fig. A - l - - M a s s - t r a n s f e r coefficient for Pb in flowing He at 1100~ METALLURGICAL TRANSACTIONS B

In the p r e s e n t w o r k the r a t e of v a p o r i z a t i o n of Pb in flowing A r or He was m e a s u r e d . T h e liquid Pb w a s c o n t a i n e d in an a l u m i n a c r u c i b l e with a 2.5 c m ID and was heated in a v e r t i c a l tube f u r n a c e with a 5.5 c m ID. Th e A r or He e n t e r e d f r o m the top of the f u r n a c e and the gas v e l o c i t y at t e m p e r a t u r e v a r i e d f r o m 0.8 to 12.8 c m / s . T h e d i s t a n c e x was v a r i e d f r o m 0.1 to VOLUME 9B, JUNE 1978-291

1.9 c m . T h e r a t e of v a p o r i z a t i o n w a s m e a s u r e d w i t h a s e m i m i c r o r e c o r d i n g b a l a n c e and a l l m e a s u r e m e n t s w e r e m a d e at l l 0 0 ~ The mass-transfer c o e f f i c i e n t is g i v e n b y Jpb(RT)

m-

PPb

[A-2]

where Jpb R T PPb

= = = =

t h e f l u x of P b in m o l e s / c m 2 s, the gas constant, absolute temperature, t h e v a p o r p r e s s u r e of P b . 14

The measured mass-transfer coefficients for flowing He and A r a r e g i v e n in F i g s . A - 1 and A - 2 a s a f u n c t i o n of g a s v e l o c i t y . O n t h e b a s i s of p r e v i o u s w o r k it is r e a s o n a b l e to a s s u m e t h a t the m a s s - t r a n s f e r coefficient will be g i v e n a p p r o x i m a t e l y by 1 _ 1 + x m m o D

[A-3]

w h e r e m o i s the m a s s - t r a n s f e r c o e f f i c i e n t f o r the l i m i t i n g c a s e w h e n x = 0. T h e e x p e r i m e n t a l r e s u l t s a r e p l o t t e d in a c c o r d a n c e w i t h E q . [A-3] in F i g . A - 3 f o r g a s v e l o c i t i e s of 1.6 and 12.8 c m / s . T h e e x p e r i m e n t a l r e s u l t s fit E q . [ A - 3 ] r e a s o n a b l y w e l l , and t h e s l o p e s of t h e l i n e s a r e n e a r l y i n d e p e n d e n t of g a s v e l o c i t y . T h e g a s v e l o c i t y h a s a l a r g e i n f l u e n c e on t h e i n tercept or the mass-transfer coefficient when x = O(mo).

T h e s l o p e s of the l i n e s s h o u l d be p r o p o r t i o n a l to 1//9. T h e s l o p e of the l i n e s f o r He g i v e a v a l u e of 7.1 c m 2 / s f o r t h e i n t e r d i f f u s i v i t y of P b and He, w h i c h is in e x c e l l e n t a g r e e m e n t w i t h the v a l u e of 7.2 c m 2 / s c a l c u l a t e d f r o m the d a t a and e q u a t i o n s g i v e n by H i r s c h f e l d e r , e t a l . 6 In the c a s e of A r t h e s l o p e s g i v e v a l u e s of 2.0 and 2.2 f o r the i n t e r d i f f u s i v i t y of P b and A t , w h i c h is s o m e w h a t l a r g e r t h a n the c a l c u l a t e d v a l u e of 1.5 cm2//s. H o w e v e r , the g e n e r a l b e h a v i o r is in good a g r e e m e n t with Eq. [A-3]. T h e v a l u e of m o b e c o m e s i m p o r t a n t f o r low g a s v e l o c i t i e s and l i g h t e r g a s e s . F o r e x a m p l e the u s e of the s i m p l e E q . [ A - l ] , w h i c h n e g l e c t s m o , c o u l d l e a d to s i g n i f i c a n t e r r o r s in t h e c a s e of H e . It is a p p a r e n t the g a s v e l o c i t y a f f e c t s the v a l u e of m o . F o r a j e t s t r e a m i m p i n g i n g on a f l a t s u r f a c e , S c h o l t z and T r a s s ~ o b tained a correlation experimentally for the masstransfer coefficient. The average mass-transfer coe f f i c i e n t f o r t h e e n t i r e p l a t e (m) is g i v e n b y

292-VOLUME 9B, JUNE 1978

= 0.5 D v "~/4 d 1/4 S c 1/3 R e 3/4

[A-4]

w h e r e d is the n o z z l e d i a m e t e r , in the p r e s e n t c a s e the d i a m e t e r of t h e f u r n a c e , and r is the r a d i u s of the p l a t e . A l t h o u g h t h e gas s t r e a m in the p r e s e n t e a s e is not a j e t and t h e R e y n o l d s n u m b e r (10 to 50) is l o w e r t h a n t h a t r e c o m m e n d e d (>500) t h i s is the b e s t c o r r e l a t i o n a v a i l a b l e . T h e c a l c u l a t e d v a l u e s f o r A r and He f o r t h e p r e s e n t e x p e r i m e n t a l c o n d i t i o n s a r e a b o u t 11 c m / s and 12.8 c m / s , a s c o m p a r e d w i t h the o b s e r v e d v a l u e of m o of 5.5 and 11 e m / / s r e s p e c t i v e l y . W h e r e a s the a g r e e m e n t f o r He i s e x c e l l e n t , that f o r A r i s not v e r y good. H o w e v e r , the g e n e r a l a g r e e m e n t is f a i r c o n s i d e r i n g t h a t t h e e x p e r i m e n t a l c o n d i t i o n s do not s a t i s f y the l i m i t a t i o n s of E q . [ A - 4 ] . It is r e c o m m e n d e d t h a t if it is n e c e s s a r y to e s t i m a t e the g a s - p h a s e m a s s - t r a n s f e r c o e f f i c i e n t f o r the e x p e r i m e n t a l g e o m e t r y c o n s i d e r e d , E q . [A-4] s h o u l d be u s e d to c a l c u l a t e m o and E q . [A-3] to c a l c u l a t e m . F o r e x a m p l e , in t h e p r e s e n t w o r k the c a l c u l a t e d m a s s t r a n s f e r c o e f f i c i e n t f o r P b in He at a g a s - f l o w r a t e of 12.8 e m / s a n d x = 0.8 e m is 4.9 c m / s , c o m p a r e d w i t h 4.5 c m / s o b s e r v e d e x p e r i m e n t a l l y . F o r s i m i l a r c o n d i t i o n s f o r A r the c a l c u l a t e d v a l u e is 1.6 c m / s and the o b s e r v e d is 1.9 c m / s . T h e s e v a l u e s c o m p a r e reasonably well so that the effect gas-phase mass t r a n s f e r m a y h a v e on t h e o v e r a l l k i n e t i c s of t h e r e a c t i o n o r p r o c e s s b e i n g c o n s i d e r e d c a n be e s t i m a t e d . REFERENCES 1. R. J. Fruehan and E. T. Turkdogan: Met. Trans., 1971, vol. 2, pp. 895-902. 2. G. R. Belton, R. J. Fruehan, and E. T. Turkdogan: Met. Trans., 1972, vol. 3, pp. 596-98. 3. E. T. Turkdogan, R. J. Fruehan, and R. H. Tien: Physical Chemistry in Metallurgy, Darken Conference,U.S. Steel Research Laboratory, Monroeville,Pa., 1976. 4. E. T. Turkdogan: private communication, U.S. Steel Corporation, Monroeville,Pa. 5. E. T. Turkdogan: Physical Chemistry o f Oxygen Steelmaking Thermochemistry and Thermodynamics, vol. 2, pp. 1-190, Monograph Series on Basic OxygenSteelmakingAIME, 1975. 6. J. O. Hirschfelder,C. F. Curtiss and 1LM. Bird: Molecular Theory o f Gases and Liquids, Wiley,New York,1965. 7. E. S. Machlin: TMS-AIME, 1960, vol. 218, pp. 314-26. 8. T. P. Floridis: TMS-AIME, 1970, vol. 215, pp. 870-71. 9. R. Ohno and T. Ishid: J. 1ton Steellnst., 1968, vol. 207, pp. 904-08. 10. V. D. Sehgal:.L Iron Steellnst., 1969, vol. 207, pp. 95-100, 1507-11. 11. V. P. Sehgal and A. Mitchell:.t Iron Steel Inst., 1964, vol. 202, pp. 216-20. 12. E. T. Turkdogan: Method of Producing Low Sulfur Steel, U.S. Patent No. 3,985,550, October 12, 1976. 13. R. J. Fruehan and L. J. Martonik,MeL Trans., 1974, vol. 5, pp. 1027-32. 14. O. Kubaschewski, E. L. Evans, and C. B. Alcock,Metallurgical Thermodynamics, Pergamon Press, New York, 1967. 15. M. T. Scholtz and O. Trass, AIChEJournal, 1963, vol. 9, pp. 548-54.

METALLURGICAL TRANSACTIONS B