dy of Moisture Transfer during the Strand Sintering Process
11
Study of oisture Transfer during the Strand Sintering Process F. PATISSON, J.P. BELLOT, and D. ABLITZER Moisture transfer during the strand sintering operation was studied both experimentally and using a mathematical model. The drying of iron ore pellets was found to occur in two distinct periods: one at a constant drying rate and the other at a decreasing drying rate, whereas the drying of zinc ore pellets always occurs at a decreasing drying rate. Characteristic drying curves were determined for both materials. The moisture transfer mechanisms during the sintering pro- cess were demonstrated in detail, including the recondensation of water in the cold layers of the bed and the formation of an inert, overmoistened zone. The mathematical model presented simulates all of these phenom ena and is used to calculate the variables related to moisture trans- fer. The model is adaptable to other processes where a hot gas passes through a moist packed bed. I. INTRODUCTION A. The Strand Sintering Process N ironmaking as well as in zinc metallurgy, the use of a blast furnace requires presintering of the mixture of ores to give them good mechanical (strength and per- meability) and chemical (reducibility) properties. The sintering operation is usually carried out on a moving grate (Figure 1). Pellets composed of ores, return sinter, fluxes, coke (in the case of iron), and water are loaded on a moving grate. After ignition under a hood, air blowing through the bed maintains a strongly exothermal reaction (coke combustion in the case of iron, sulfide roasting in the case of zinc). The bed attains a temperature of approx- imately 1300 ~ which causes partial melting of the charge and sintering of the pellets. The iron ore sintering and zinc ore sinter-roasting processes are fundamentally similar, differing only in the details of gas flow direction, ignition process, fuel, pel- let characteristics, and the chemical reactions involved. B. Importance of Drying The feed mixture to a sintering operation contains both constitutive water (water chemically bound to the solids) and free water. Constitutive water comes m ainly from ores and exists in low concentrations; its rem oval occurs by dehydration reactions. Free water comes from ores, fluxes, and mainly from water added to aid the pelletiz- ing process. It represents 6 to 12 wt pct of the feed mix- ture for iron ore, and 4 to 6 wt pet for zinc ore. Free water removal is an important step in the sintering op- eration because of the high thermal energy consumption required for drying (up to 25 pet of the requirements for iron ore sintering) and the reduced permeability of the F. PATISSON, Research Scientist from Centre National de la Recherche Scientifique CNRS), J.P. BELLOT,Assis tant Professor , and D. ABLITZER, Professor, are with the Laboratoire de Science et G6ni e des Mat 6daux M6talliqu es LSG2M), Ecole des Mines, 54042 Nancy Cedex, France. Manuscript submitted June 13, 198 8. overmoistened i.e., with excess water, after conden- sation) zone, which obstructs gas flow. As shown in Figure 2, when the hot gases leave the reaction zone and enter the moist zone, they dry the sol- ids and become loaded with water vapor. But, as will be shown, when these now very moist gases come in contact with the colder charge in the deep layers of the bed, water condenses on the solids. Therefore, the term moisture transfer will be used to include both drying and condensation. C. Previous Descriptions In the past, moisture transfer has been described in a rather simplified manner in various mathematical models of the sintering process. For drying, the simplest ap- proach considers that it takes place entirely at a fixed temperature of 100 Other authors introduce a two- stage drying model: first, drying occurs at a constant rate and, after, at a rate that decreases linearly with the mois- ture content, t4-9] Yoshinaga and Kubo [1~ mention a three- stage drying process but give a single equation where the drying rate decreases continuously with decreasing moisture content. Except for Cumming t al ., [11] who used semiempirical results obtained for hematite pellet s, [12] the specific transport properties of the materials have not been taken into account. Condensation has either been ig- nored [3-7,1~ or assumed to occur after the gas has becom e bulk-saturated (when the dew-point temperature is equal to the gas temperature), with the gas remaining saturated during condensation. [L2] Toda and Kato ES] and Kasai et al.[9] consider a condensation rate that depends on the difference between the gas humidity and the saturation humidity and an arbitrary constant. In the work of Cumming et al.,tH] it is assumed that condensation oc- curs when the gas is saturated at a temperature midway between that of the solids and the gases. Few papers are specifically concerned with the study of moisture transfer during the sintering operation. Korotic and Puzanov E~3]first explained the mechanism of the for- mation of an overmoistened zone. Wajima et al. ~4] stud- ied the influence of the amount of condensed water on the permeability of the bed, both experimentally and using METALLURGICAL TRANSACTIONS B VOLUME 21B, FEBRUARY 199 0-- 37
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Transcript of dy of Moisture Transfer during the Strand Sintering Process
7/23/2019 dy of Moisture Transfer during the Strand Sintering Process
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Study of o is ture Tran sfer
dur ing the St rand S inter ing Proc ess
F . P A T I S S O N , J .P . B E L L O T , an d D . A B L I T Z E R
M o i s t u r e t r a n s f e r d u r i n g t h e s t r a n d s i n t e r i n g o p e r a t i o n w a s s t u d i e d b o t h e x p e r i m e n t a l l y a n d
u s i n g a m a t h e m a t i c a l m o d e l . T h e d r y i n g o f i ro n o r e p e l l e ts w a s f o u n d t o o c c u r i n tw o d i s ti n c t
p e r i o d s : o n e a t a c o n s t a n t d r y i n g r a t e a n d t h e o t h e r a t a d e c r e a s i n g d r y i n g r a t e , w h e r e a s t h e
d r y i n g o f z i n c o r e p e l l e t s a l w a y s o c c u r s a t a d e c r e a s i n g d r y i n g r a t e . C h a r a c t e r i s t i c d r y i n g c u r v e s
w e r e d e t e r m i n e d f o r b o t h m a t e r i a l s. T h e m o i s t u r e t ra n s f e r m e c h a n i s m s d u r i n g t h e s i n te r i n g p ro -
c e s s w e r e d e m o n s t r a t e d i n d e t a il , i n c l u d i n g t h e r e c o n d e n s a t i o n o f w a t e r i n th e c o l d l a y e r s o f
t h e b e d a n d t h e f o r m a t i o n o f a n in e r t, o v e r m o i s t e n e d z o n e . T h e m a t h e m a t i c a l m o d e l p r e s e n t e d
s i m u l a t e s a l l o f t h e s e p h e n o m e n a a n d i s u s e d t o c a l c u l a t e t h e v a r i a b l e s r e l at e d t o m o i s t u r e t r a n s-
f e r . T h e m o d e l i s a d a p t a b l e t o o t h e r p r o c e s s e s w h e r e a h o t g a s p a s s e s t h r o u g h a m o i s t p a c k e d
b e d .
I . I N T R O D U C T I O N
A . T h e S t r a n d S i n t er i n g P r o c e ss
N
i r o n m a k i n g a s w e l l a s i n z i n c m e t a l l u r g y , t h e u s e o f
a b l a s t fu r n a c e r e q u i r e s p r e s i n t e r i n g o f t h e m i x t u r e o f
o r e s t o g i v e t h e m g o o d m e c h a n i c a l ( s t r e n g t h a n d p e r -
m e a b i l i t y ) a n d c h e m i c a l ( r e d u c i b i l i t y ) p r o p e r t i e s . T h e
s i n t e r i n g o p e r a t i o n i s u s u a l l y c a r r i e d o u t o n a m o v i n g
g r a t e ( F i g u r e 1 ) .
P e l le t s c o m p o s e d o f o r e s , r e t u rn s i n t e r, f l u x e s , c o k e
( in t h e c a s e o f ir o n ) , a n d w a t e r a r e l o a d e d o n a m o v i n g
g r a te . A f t e r ig n i t io n u n d e r a h o o d , a i r b l o w i n g t h r o u g h
t h e b e d m a i n t a i n s a s t r o n g l y e x o t h e r m a l r e a c t i o n ( c o k e
c o m b u s t i o n i n t h e c a s e o f i r o n , s u l f i d e r o a s t i n g i n th e
c a s e o f z in c ) . T h e b e d a t ta i n s a te m p e r a t u r e o f a p p r o x -
i m a t e l y 1 3 0 0 ~ w h i c h c a u s e s p a r ti a l m e l t i n g o f t h e
c h a r g e a n d s i n t e r i n g o f t h e p e l l e t s .
T h e i r o n o r e s i n t e r i n g a n d z i n c o r e s i n t e r - r o a s t i n g
p r o c e s s e s a r e f u n d a m e n t a l l y s i m i l a r , d i f f e r i n g o n l y i n t h e
d e t a i l s o f g a s f l o w d i r e c t i o n , i g n i t i o n p r o c e s s , f u e l , p e l -
l e t c h a r a c t e r i s t i c s , a n d t h e c h e m i c a l r e a c t i o n s i n v o l v e d .
B . I m p o r t a n c e o f D r y i n g
T h e f e e d m i x t u r e t o a s i n t e r i n g o p e r a t i o n c o n t a i n s b o t h
c o n s t it u t iv e w a t e r ( w a t e r c h e m i c a l l y b o u n d t o t h e s o l i ds )
a n d f r e e w a t e r . C o n s t i tu t i v e w a t e r c o m e s m a i n l y f r o m
o r e s a n d e x i s t s i n l o w c o n c e n t r a t i o n s ; i t s r e m o v a l o c c u r s
b y d e h y d r a t i o n r e a c t i o n s . F r e e w a t e r c o m e s f r o m o r e s ,
f l u x e s , a n d m a i n l y f r o m w a t e r a d d e d t o a id t h e p e l le t i z -
i n g p r o c e s s . I t r e p r e s e n t s 6 t o 1 2 w t p c t o f t h e f e e d m i x -
t u r e f o r i r o n o r e , a n d 4 t o 6 w t p e t f o r z i n c o r e . F r e e
w a t e r r e m o v a l i s a n i m p o r t a n t s t e p i n t h e s i n t e r i n g o p -
e r a t io n b e c a u s e o f th e h i g h t h e r m a l e n e r g y c o n s u m p t i o n
r e q u i r e d f o r d r y i n g ( u p t o 2 5 p e t o f th e r e q u i r e m e n t s f o r
i r o n o r e s in t e r i n g ) a n d t h e r e d u c e d p e r m e a b i l i t y o f t h e
F. PATISSON, Research Scientist from Centre National de la
Recherche Scientifique CNRS), J.P. BELLOT ,Assis tant Professor,
and D. ABLITZER, Professor, are with the Laboratoire de Science
et G6nie des Mat6daux M6talliques LSG2M), Ecole des Mines, 54042
Nancy Cedex, France.
Manuscript submitted June 13, 1988.
o v e r m o i s t e n e d
i . e . ,
w i t h e x c e s s w a t e r , a f t e r c o n d e n -
s a t i o n ) z o n e , w h i c h o b s t r u c t s g a s f l o w .
A s s h o w n i n F i g u r e 2 , w h e n t h e h o t g a s e s l e a v e t h e
r e a c t io n z o n e a n d e n t e r t h e m o i s t z o n e , t h e y d r y t h e s o l-
i d s a n d b e c o m e l o a d e d w i t h w a t e r v a p o r . B u t , a s w i ll
b e s h o w n , w h e n t h e s e n o w v e r y m o i s t ga s e s c o m e i n
c o n t a c t w i t h t h e c o l d e r c h a r g e i n th e d e e p l a y e r s o f th e
b e d , w a t e r c o n d e n s e s o n t h e s o li d s . T h e r e f o r e , t h e t e r m
m o i s t u r e t r a n s fe r w i l l b e u s e d to in c l u d e b o t h d ry i n g
a n d c o n d e n s a t i o n .
C . P r e v i o u s D e s c r i p t i o n s
I n t h e p a s t , m o i s t u r e t r a n s f e r h a s b e e n d e s c r i b e d i n a
r a t h e r s im p l i f i e d m a n n e r i n v a r i o u s m a t h e m a t i c a l m o d e l s
o f t h e s i n t e ri n g p r o c e s s . F o r d r y i n g , t h e s i m p l e s t a p -
p r o a c h c o n s i d e r s t h a t i t t a k e s p l a c e e n t i r e l y a t a f i x e d
t e m p e r a t u r e o f 1 0 0 O t h e r a u t h o rs i n t ro d u c e a t w o -
s t a g e d r y i n g m o d e l : f i r s t , d r y i n g o c c u r s a t a c o n s t a n t r a t e
a n d , a f t e r , a t a r a t e t h a t d e c r e a s e s l i n e a r l y w i t h t h e m o i s -
t u r e c o n t e n t , t4 -9 ] Yo s h i n a g a a n d K u b o [1~ m e n t i o n a t h r e e -
s t a g e d r y i n g p r o c e s s b u t g i v e a s i n g l e e q u a t i o n w h e r e
t h e d r y i n g r a t e d e c r e a s e s c o n t i n u o u s l y w i t h d e c r e a s i n g
m o i s t u re c o n te n t. E x c e p t f o r C u m m i n g t al ., [11] who u s e d
s e m i e m p i r i c a l r e s u l t s o b t a i n e d f o r h e m a t i t e pe ll et s, [12] t h e
s p e c i fi c t r a n s p o rt p r o p e r t i e s o f t h e m a t e r i a l s h a v e n o t b e e n
t a k e n i n to a c c o u n t . C o n d e n s a t i o n h a s e i th e r b e e n i g -
n o r e d [3-7,1~ o r a s s u m e d t o o c c u r a f t e r t h e g a s h a s b e c o m e
b u l k - s a t u r a t e d ( w h e n t h e d e w - p o i n t t e m p e r a t u r e i s e q u a l
t o th e g a s t e m p e r a t u r e ) , w i t h t h e g a s r e m a i n i n g s a t u ra t e d
d u r i n g c o n d e n s a t i o n . [L 2] T o d a a n d K a t o ES] a n d K a s a i
et al.[9]
c o n s i d e r a c o n d e n s a t i o n r a t e t h a t d e p e n d s o n t h e
d i f f e r e n c e b e t w e e n t h e g a s h u m i d i t y a n d t h e s a t u r a ti o n
h u m i d i t y a n d a n a r b i t ra r y c o n s t a n t. I n th e w o r k o f
C u m m i n g e t a l . , tH] i t i s a s s u m e d t h a t c o n d e n s a t i o n o c -
c u r s w h e n t h e g a s i s s a t u r a t e d a t a t e m p e r a t u r e m i d w a y
b e t w e e n t h a t o f t h e s o l i d s a n d t h e g a s e s .
F e w p a p e r s a r e s p e c i f i c a l l y c o n c e r n e d w i t h t h e s t u d y
o f m o i s t u r e t r a n s f e r d u r i n g t h e s i n t e r i n g o p e r a t i o n . Ko r o t i c
a n d P u z a n o v E~3] f i r st e x p l a i n e d t h e m e c h a n i s m o f t h e f o r -
m a t i o n o f an o v e r m o i s t e n e d z o n e . W a j i m a
et al. ~4]
s t u d -
i e d th e i n f lu e n c e o f t h e a m o u n t o f c o n d e n s e d w a t e r o n
t h e p e r m e a b i l i t y o f t h e b e d , b o t h e x p e r i m e n t a l ly a n d u s i n g
METALLURGICAL TRANSACTIONS B VOLUME 21B, FEBRUARY 1990--37
7/23/2019 dy of Moisture Transfer during the Strand Sintering Process
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r e s
Ftuxes
I g n i t i o n
ater
1 1 1 1 1
s i n te r
Roughing 1
t A I A t l l / l ? / oo no
S c r e e n i n g
G~ : 02 N2 C02 CO H20 etc' l
Undersized Slnter o
slnter blostfurnece
F i g . 1 - S i n t e n n g m a c h i n e ( ir o n o r e) .
a m o d e l . R a n k i n a n d R o l l e r [15] s t u d i e d e x p e r i m e n t a l l y
t h e i n fl u e n c e o f c o n d e n s a t i o n o n b e d p e r m e a b i l i t y .
D . O u t l i n e
I n o r d e r t o o p t i m i z e t h e i r o n o r e s i n t e r i n g a n d z i n c o r e
s i n t er - r o a st i n g p r o c e s s e s , a m a t h e m a t i c a l m o d e l o f t h e
o p e r a t i o n h a s b e e n d e v e l o p e d . T h e m o d e l , d e s c r i b e d i n
p r e v i o u s a r t i c l e s , [ 16 1 7,1 8]
p e r m i t s c a l c u l a t i o n o f t h e t i m e -
d e p e n d e n t t e m p e r a t u r e s a n d c o m p o s i t i o n s o f th e s o l id s
a n d g a s e s t h r o u g h o u t t h e b e d . I n t h e p r e s e n t p a p e r , t h e
s t u d y o f m o i s t u r e t r a n s f e r d u r i n g t h e s t r a n d s i n t e r i n g
p r o c e s s i s f u l l y d i s c u s s e d , g i v i n g p a r t i c u l a r a t t e n t i o n t o
d e s c r i b i n g , f r o m a m a c r o s c o p i c v i e w p o i n t , t h e m o i s t u r e
t r a n s f e r p h e n o m e n a d u r i n g t h e d r y i n g o f a p a c k e d b e d
b y h o t g a s e s , a n d f r o m a m i c r o s c o p i c v i e w p o i n t , t h e
m o i s t u r e t r a n s p o r t p r o p e r t i e s o f t h e d r y i n g m a t e r i a ls .
T h e m e c h a n i s m s f o r m o i s t u r e t r a n s f e r i n a p a c k e d b e d ,
i n c l u d in g r e c o n d e n s a t i o n o f w a t e r i n t h e d e e p l a y e r s , a r e
d e s c r i b e d a n d e x p l a i n e d . T h e m o d e l p r o p o s e d i s a l s o a p -
p l i c a b l e t o o t h e r p r o c e s s e s i n w h i c h s i m i l a r d r y i n g o c -
c u r s . T h e m o d e l i s v a l i d a t e d b y c o m p a r i n g i t s r e s u l t s
w i t h m e a s u r e m e n t s t a k e n d u r i n g p r e d r y i n g e x p e r i m e n t s
o n a p i l o t p o t .
T h e m o i s t u r e t r a n s p o r t p r o p e r t i e s o f t h e d r y i n g m a -
t e r i a l s h a v e b e e n s t u d i e d e x p e r i m e n t a l l y t o c h a r a c t e r i z e
t h e b e h a v i o r o f i ro n a n d z i n c o r e p e l l e ts .
os
T e m p e r o t u r e o f s o l i d s ~ o r ~
] i F
t . )
t -
4 J
t,~
~
F i g . 2 - - F o u r z o n e s o f t h e b e d ( i ro n o r e) .
: l n t e r e d z o n e
R e o c t i n z o n e
D r i e d z o n e
M o i s t z o n e
I I . E X P E R I M E N T A L S T U D Y
O F D R Y I N G O F O R E P E L L E T S
A . D e s c r i p ti o n a n d R e s u lt s
T h e e x p e r i m e n t a l w o r k w a s c a r r i e d o u t b y t h e r m o -
g r a v i m e t r y . T h e m o i s t e n e d p e l l e t s w e r e p l a c e d i n a w i re -
m e s h b a s k e t a n d t h e n d r i e d i n a f u r n a c e b y a f o r c e d f l o w
o f h o t g a s. T h e w e i g h t l o s s w a s c o n t i n u o u s l y r e c o r d e d .
T h e o p e r a t i n g c o n d i t io n s a r e g i v e n i n T a b l e I . W h e n a
s a m p l e s t o p p e d l o s i n g w e i g h t , i t w a s w e i g h e d , p l a c e d i n
a n o v e n a t 1 50 ~ f o r s e v e r a l h o u r s , a n d t h e n w e i g h e d
a g a i n to d e t e r m i n e i t s d r y m a s s . C u r v e s s h o w i n g d r y i n g
r a t e v s m o i s t u r e c o n t e n t a r e c a l c u la t e d f r o m t h e w e i g h t
l o s s
v s
t i m e i n f o r m a t i o n . E x a m p l e s o f t h es e c u r v e s a r e
g i v e n i n F i g u r e 3 .
B . I n t e r p r e t a t i o n
T h e s e e x p e r i m e n t s c l e a r l y s h o w t h a t t h e d r y i n g p r o -
c e s s i s d i v i d e d i n t o t w o c h a r a c t e r i s t i c p e r i o d s , o n e a t a
c o n s t a n t d r y i n g r a t e a n d o n e a t a c o n t i n u o u s l y d e c r e a s i n g
r a te . T h i s b e h a v i o r , t y p i c a l o f p o r o u s m a t e ri a l s, c a n b e
e x p l a i n e d a s f o l l o w s .
1 . F i r s t p e r i o d - - c o n s t a n t d r y i n g ra t e
D u r i n g t h i s p e r i o d , h e a t f r o m t h e g a s e s i s f u l l y u t il i z e d
t o e v a p o r a t e w a t e r o n t h e s u r f a c e o f t h e s o li d s. T h e s y s -
t e m i s in a s t a t e o f d y n a m i c e q u i l i b r i u m . T h e s u r f a c e
t e m p e r a t u r e r e m a i n s c o n s t a n t
i . e . ,
a t th e w e t - b u l b t e m -
p e r a t u r e ,
Tw),
a n d t h e s u r f a c e i s s a t u r a t e d w i t h w a t e r .
T h e d r y i n g r a t e d u r i n g t h is p e r i o d c a n b e c a l c u la t e d f r o m
e x t e r n a l h e a t o r m a s s t r a n s f e r b a l a n c e s .
2 . S e c o n d p e r i o d - - d e c r e a s i n g d r y in g ra t e
W h e n t h e m o i s t u r e c o n t e n t o f t h e s o li d s d e c re a s e s , t h e
i n t e r n a l t r a n s p o r t o f wa t e r t o t h e s u r f a c e i s n o t f a s t e n o u g h
t o m a i n t a i n s a t u r a t i o n o n t h e e n t i r e s u r f a c e . T h e m o i s -
t u r e c o n t e n t a t t h i s p o i n t i s c a l l e d t h e c r i t ic a l m o i s t u r e
c o n t e n t , Wcr. T h e d r y i n g r a t e b e g i n s t o d e c r e a s e , a s t h e
i n t e r n a l r e s i s ta n c e t o m o i s t u r e t r a n s f e r b e c o m e s s i g n i f i -
c a n t . V a r i o u s s h a p e s o f t h e e n d s o f t h e d r y i n g c u r v e s a r e
o b s e r v e d , d e p e n d i n g o n t h e m a t e r i a l b e i n g d r i e d .
T h e c r i t i c a l m o i s t u r e c o n t e n t w a s f o u n d t o b e d i f f e r e n t
f o r i ro n o r e ( - ~ 5 p c t) t h a n f o r z i n c o r e ( > 1 0 p c t ) . F o r
i r o n o r e p e l l e t s , s e v e r a l a u t h o r s t4'6,81 h a v e u s e d a v a l u e
o f 2 p c t , w i t h o u t s t a t in g t h e o r i g i n o f t h is v a l u e . I f th e
T a b l e I O p e r a t i n g C o n d i t i o n s
f o r T h e r m o g r a v i m e t r y E x p e r i m e n t s
Composi t ion of the Pe l l e t s
I r o n Or e Z i n c Or e
Mixture of Severa l
R i c h Or e s Us e d a t
S O L L A C , D u n k i r k
Mixture of Blende
(St -Sa lvy) and
Galena (Tara)
Ga s mixture dry a i r dry a i r
Ga s t empera ture 22 ~ to 100 ~ 30 ~ to 90 ~
Super f i c ia l
ve loc i ty 3 .5 to 5 .4 cm . s -~ 7 cm . s -~
Ini t ia l mass about 1 g about 1 g
Ha r m o n i c
d i a m e t e r 2 . 8 m m 5 . 0 m m
Ini t ia l m ois ture
content up to 12 pc t up to 12 pc t
3 8 - - V O L U M E 2 1 B , F E B R U A R Y 1 99 0 M E T A L L U R G I C A L T R A N S A C T I ON S B
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0 8
~ 0.6
0 4
e
':~ 0.2
[ ] T g =
59 C
x Tg =
9 9 %
c r i t i c a l m o i s t u r e
c o n t e n t l o c u s
X X i X X X X X
I
l
I
] const nt r a t e
/ d r y i
ng
x
x
x
x
x
x
x f l l i n g
r te
x
d r y i n g
x
x O 0 0
D
O 0 o
X X
O ~ 0 0 o o o o 0 0 o
2 q 6 8 10
Solid moisture content ( )
(a)
X
X
12
0 8
E
~0.6
0.4
e
0 2
T g = 7 0 ~
+ + +
+ Tg g0*C] + + + +
§
[
+ + c o n s t a n t
r a t ~
/ d ~ i
n g
~ g r o s c o p i c + [
nonhygroscopic
/
b e h a v i o r
b e h a v i o r
+ I
~ m s s ~ s ~ m ~
r ~ s
2 .? '
t r a n s i t i o n
m i s t u r e
c o n t e n t l o c u s
+
s
0 2 4 6 8 1 0 1 2
Solid moisture content (%)
(b)
F i g . 3 - - E x p e r i m e n t a l d r y i n g r a t e v m o i s t u r e c o n t e n t : a ) ir o n o r e
p e l l e t s a n d b ) z in c o r e p e l l e t s .
critical moisture contents are compared to the usual ini-
tial moisture contents for the sintering process (5 to 12 pct
for iron ore and 4 to 5 pct for zinc ore), it is concluded
that the drying of iron ore pellets during the sintering
operation occurs in two periods (at constant and at de-
creasing rate), whereas for zinc ore sinter-roasting, the
decreasing rate drying commences directly.
In addition, the shape of the drying curves is different.
In the case of iron ore (Figure 3(a)), during the second
period, the curve is concave downward. This is char-
acteristic of hygroscopic behavior. The final (equilib-
rium) moisture content, We q , is close to zero. In the case
of zinc ore (Figure 3(b)), a period is observed during
which the curve is concave upward, characterizing non-
hygroscopic behavior. Later, below a transition moisture
content, W t , hygroscopic behavior appears. Such fea-
tures can also be found during the drying of other ma-
terials, such as wo od, for example , t~9] In the case o f zinc
ore, the equilibrium moisture content is about 1 pet.
C . C h a r a c t e r i s t i c D r y i n g C u r v e
The drying curves obtained were normalized in the form
of a reduced drying rate, Rr , v s a reduced moisture con-
tent, W, as follows:
(1) In the case of iron ore,
R r = R / R M (drying rate/drying rate
during the first period)
W r = W / W c r (equilibrium moisture
content is zero)
(2) In the case of zinc ore,
R ~ = R / R t r (drying rate/drying rate
when W = W,r)
W r = W - W e q ) ] / W t r - W eq
These two different normalizations were based on phys-
ical considerations. In the case of zinc ore, the transition
point is the experimental characteristic point, whereas
for iron ore, the critical point is obviously the reference
to be considered.
In each case, a single curve was obtained, which is
characteristic of the drying of iron ore pellets (Figure 4(a))
and of zinc ore pellets (Figure 4(b)). The drying rate at
any instant is calculated from the known ma ximum drying
rate, Ru (see Section II I- B) , and the equation of the
characteristic drying curve, P ( W r ) , obtained by poly-
nomial regression. In the case of iron ore, the drying rate
is given by
R = R M P ( W r ) [la]
P ( W r ) = 1 - (1 - Wr) (1 - 1.796Wr + 1 .0593W~)
[lbl
Since, in the case of zinc ore, R,~ is not known analyt-
ically, we use
R = f . R u P ( W ~ ) [2a]
P(Wr) = -0. 0560 3 + 3 .2 15 5Wr - 3.9223W 2
+ 2.2488W~ - 0.4 914W 4 [2b]
The value off = R J R u was experimentally determined
to be about 0.7.
I I I. M A T H E M A T I C A L M O D E L I N G
O F M O I S T U R E T R A N S F E R D U R I N G
T H E SI N T E R I N G O PE R A T I O N
A . G e n e r a l E q u a t i o n s
As noted earlier, the present model o f moisture trans-
fer during the sintering operation is part of a compre-
hensive model that simulates the entire sintering
proce ss. [16JTA8l The equat ions used to descr ibe heat and
mass transfer in the moist zone are as follows (see
Nomenclature for symbols):
Thermal balance of the gases:
0 0
upgCpg Ox Tg -ep gC pg Ot Tg + agh(T s - Tg) [3]
M E T A L L U R G IC A L T R A N S A C T IO N S B V O L U M E 2 1 B , F E B R U A R Y 1 9 9 0 - -3 9
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1 . 2
x
o
9
_
e 2 ~ I ~ 0
O I 0 r 9
0 8 = ~ j ~
I ~ ~
I~l m 111
k.. ~
c n n K I } 1 ~ 0 , c o n s t a n t r a t e
. ~ ~ ~ ~ I d r y i n g
x ~ 0 . / I ~ J e
f l l i n g
r a t e i
I t
i
0 0 5
I
1 5 2 2 5 3
Re duc e d
m o i s t u r e c o n t e n t ( g /W c r )
(a)
1 4
k .
~ 1 . 2
~ o ~
~ 0 . 6
~ 0 J 4
0.2
O i l
o
i
i n o n y g r o s c o p i c
I b e h a v i o r [ ]
i [ ]
i
i [ ]
0
~
Q_S W -~
o x ~ t ~ R
a ~ h y g r o s c o p i c
o X t 3 ? ~
beh vior
0 . 2 O d t 0 , 6 0 . 8 1 1 . 2 1 , g
Re duc e d
m o i s t u r e c o n t e n t ( [ W - W e o I /[ g t r - W e q ] )
b )
F i g . 4 - - C h a r a c t e r i s t i c d r y i n g c u r v e : a ) ir o n o r e p e l le t s a n d b ) z i n c
o r e p e l l e t s t h e v a r i o u s m a r k e r s r e p r e s e n t r u n s c a r r i e d o u t u n d e r d i f -
f e r 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 ) .
T h e r m a l b a l a n c e o f t h e s o l i d s :
0
p a C m - ~ t T s = a g h T g - T s ) -
M H 2 O
r a 2 o L ~ T ~ )
[ 4 ]
W a t e r v a p o r b a l a n c e :
0 0
OX
U C H 2 0
: e Ot
C H 2 0 r H ~ o [5]
M o i s t u r e b a l a n c e o f t h e s o l i d s :
0
Ot O n t o - - M H 2 0 rH20 [6]
T h e a b o v e c o u p l e d e q u a t i o n s , p l u s th e e q u a t i o n s w h i c h
r e p r e s e n t t h e t o t a l m a s s b a l a n c e s o f t h e g a s e s a n d s o l i d s
a n d t h e l o c a l m o m e n t u m b a l a n c e ( u s i n g E r g u n ' s r e l a -
4 0 - - V O L U M E 2 1 B , F E B R U A R Y 1 9 9 0
t i on s h i p P ~ w e r e s o l v e d b y u s i n g a n i t e r a ti v e i m p l i c i t
f i n i t e d i f f e r e n c e m e t h o d .
B . K i n e t i c E q u a t i o n s f o r M o i s t u r e T r a n s f e r
T h e i m p o r t a n t t e r m i n t h e a b o v e b a l a n c e e q u a t i o n s i s
the r a te o f m ois tu r e t r ans f e r , r H~o ( m ol - S - 1 m f f3) . To
c a l c u l a t e r n ~ o , w e f i r s t c a l c u l a t e t h e m a s s t r a n s f e r r a te i n
t h e b o u n d a r y g a s l a y e r , r R , w h i c h i s a f u n c t i o n o f t h e
d i f f e r e n c e i n v a p o r p r e s s u r e a t t h e s u r f a c e o f t h e p a r t i c l e
( a s s u m e d t o b e s a t u r a t e d ) a n d o f t h e b u l k g a s , g i v e n b y
agk
rR = - ~ pv , , Ts ) - Pn :o ) [7]
w h e r e ag i s t h e s p e c i f i c a r e a o f t h e b e d ,
ag
= 6(1 -
e ) / d e
[8]
T h e t e r m p ~ , i s t h e s a t u r a te d v a p o r p r e s s u r e , e x p r e s s e d
f r o m d a t a r e p o r t e d b y K e e y , p q a s
( 5 2 1 1 ~
p v , , T s ) = e x p 2 5 . 5 4 1 - T~ / [9 ]
T h e t e r m P H : o i s t h e v a p o r p r e s s u r e i n t h e b u l k g a s , a n d
k is the ma ss t ran sfer coef f ic ient , as def in ed by Kr ische r . I22~
hTg
k = [ 1 0 ]
3 . 1 5 5 P ~ ( 1 - 0 .2 4X m )( 1 + ~ ) ( 1 - - X m )
T h e t e r m X m i s t h e l o g a r i t h m i c m e a n o f t h e m o l a r f r a c -
t i o n o f v a p o r i n t h e b u l k g a s a n d a t t h e s a t u r a t e d s u r f a c e .
T h e v a l u e o f r R i s u s e d t o d e t e r m i n e t h e r e g i m e o f
m o i s t u r e t r a n s f e r (d r y i n g o r c o n d e n s i n g ) a n d , h e n c e , t h e
a p p r o p r i a t e f o r m o f t h e e q u a t i o n s .
I f rR < 0 , t h e r e is c o n d e n s a t i o n , a n d rHz0
=
rR.
I f rR -- 0 , t h e r e i s d r y i n g , a n d r n 2 o d e p e n d s o n t h e
c a s e c o n s i d e r e d . F o r ir o n o r e , i f W -> W e t , e q u i l i b r a t e d
( f i r s t -pe r iod) d r y ing takes p lace , and r n2o = r R. I f W <
Wcr, d e c r e a s i n g r a t e d r y i n g o c c u r s , a n d r n 2 o i s c a l c u l a t e d
f r o m t h e c h a r a c t e r is t i c d r y i n g c u r v e u s i n g E q . [ 1 ]. F o r
z i n c o r e , d r y i n g a l w a y s o c c u r s a t d e c r e a s i n g r a t e , a n d
rnzo i s ca lcu la ted f r om the ch a r ac te ri s t ic d r y ing cur ve us ing
Eq. [2] .
T h e v a l u e o f rM i n E q s . [ 1] a n d [ 2] c a n b e d e t e r m i n e d
f r o m t h e m a s s t r a n s f e r r e l a t i o n s h i p ( rM = rR Tw)) o r f r o m
t h e t h e r m a l b a l a n c e o f t h e s o l i d s , s i n c e d u r i n g t h e f i r s t
p e r i o d , d r y i n g t a k e s p l a c e a t a r a t e s u c h t h a t t h e t e m -
p e r a t u r e o f t h e s o l i d s r e m a i n s c o n s t a n t a n d e q u a l t o T ~ .
T h i s t h e r m a l b a l a n c e i s w r i t t e n
agh Tg - Tw ) = MH 2or MLv Tw ) [111
( h e a t b r o u g h t b y g a s e s ) ( h e a t f o r e v a p o r a t i o n )
I n th i s e q u a t i o n , t h e h e a t i n g o f v a p o r i s n e g l e c t e d , t h e
w e t - b u l b t e m p e r a t u r e , T w , i s a f u n c t i o n o f m o i s t u r e c o n -
t e n t , p r e s s u r e , a n d t h e t e m p e r a t u r e o f t h e g a s e s , a n d t h e
l a t e n t h e a t o f v a p o r i z a t i o n o f w a t e r , Lv, i s a f u n c t i o n o f
t e m p e r a t u r e ( o b t a i n e d b y l i n e a r r e g r e s s i o n f r o m d a t a r e -
po r ted by K ee y [211)
Lv Tw) = 3 . 1563 x 106 - 2396 . 6Tw
M E T A L L U R G IC A L T R A N S A C T IO N S B
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T h u s , t h e t w o r e l a t i o n s h i p s c o n t r o l l i n g t h e f i r s t p e r i o d
o f d r y i n g a r e
agh
rM (Tg Tw)
I 1 2 ]
MrhoLv(Tw)
a u k
ag h (Tg - Tw) = (Pv+a,(Tw)
Pn2o) [ 13]
MH2oLv(T w ) - ~ g
I n p r a c t ic e , E q . [ 1 3 ] i s u s e d t o o b t a i n
Tw
a n d E q . [ 1 2 ]
t o c a l c u l a t e r M .
C . P a r a m e t e r s o f t h e M o d e l
T h e p a r a m e t e r s e ,
ag, h,
a n d
de are
a s s u m e d t o b e
c o n s t a n t i n t h e m o i s t z o n e . P a r t i c u l a r l y , t h e c h a n g e i n
p o r o s i t y w i t h m o i s t u r e c o n t e n t h a s n o t b e e n i n t r o d u c e d .
I n s p it e o f th e w o r k b y W a j i m a
e t
a l [ 1 4 1 a n d R a n k i n a n d
R o l l e r , tim t h e m e a n s t o p r e d i c t q u a n t i t a t i v e l y t h e i n f l u -
e n c e o f m o i s t u r e c o n t e n t o n p o r o s i t y a n d p e r m e a b i l i t y
a r e n o t p r e s e n t l y a v a i l a b l e . T h e p a r a m e t e r s
p~, pg, Cps,
a n d
Cpg are
t r e a te d a s f u n c t i o n s o f t e m p e r a t u r e a n d
c o m p o s i t i o n .
I V . V A L I D A T I O N O F T H E M O D E L
A G A I N S T P I L O T P O T E X P E R I M E N T S
A . S p e c if i c P r e d r y i n g E x p e r i m e n t s o n P i l o t P o t
I n o r d e r t o v a l i d a t e t h e m o d e l a n d t o + o b t a i n e x p e r i -
m e n t a l o b s e r v a t i o n s c o n c e r n i n g m o i s t u r e t r a n s f e r d u r i n g
t h e s in t e r i n g o p e r a t i o n , i r o n o r e p r e d r y i n g e x p e r i m e n t s
( c a s es A a n d B i n T a b l e I I ) h a v e b e e n u n d e r t a k e n u s i n g
t h e I n s t i t u t d e R e c h e r c h e s d e l a S i d 6 m r g i e ' s ( I R S I D ) p i l o t
p o t .
1 . Pr inc ip l e
H o t a i r l e a v i n g a C o w p e r s t o v e p a s s e s t h r o u g h t h e
c h a r g e a n d d r i e s i t . T h e r m o c o u p l e s a r e u s e d t o m e a s u r e
t h e t e m p e r a t u r e s o f t h e s o l i d s a n d o f t h e in l e t a n d o u t l e t
g a s . G a s f l o w r a t e a n d p r e s s u r e d r o p a r e c o n t r o l l e d . I n
o r d e r t o d e t e r m i n e t h e m o i s t u r e c o n t e n t o f t h e o u t l e t g a s ,
t h e p o t h a s b e e n f i t t e d w i t h a h y g r o m e t r i c m e a s u r e m e n t
a p p a r a t u s t h a t i n c l u d e s a g a s c o l l e c t o r i n t h e e x h a u s t p i p e
a n d a Li C 1 h y g r o m e t e r to m e a s u r e t h e d e w p o i n t . H o w -
e v e r , t h i s m e a s u r e m e n t i s a f f e c t e d b y c o n d e n s a t i o n o f
Ta bl e I I Br i e f De s c r i p t i o n
o f t h e E x p e r i m e n t s S i m u l a t e d
A i ron ore
B i ron ore
C z inc ore
D i ron ore
E i ron ore
predrying exper iment in p i lo t pot :
hot a i r through mois t r aw bed
s imi la r to A but in te r rupted when
d r y i n g wa s 1 / 3 c o m p l e t e d
predrying of f i c t i t ious mois t r aw
charge wi th a i r a t 350 ~ (ca l -
cula t ion run only)
comple te s in te r ing exper iment in
pi lo t pot , in usua l condi t ions
s imi la r to D, but the raw charge i s
ini t ial ly at 60 ~ (calculat ion run
only)
M E T A L L U R G I C A L T R A N S A C T I O N S B
w a t e r a t th e b o t t o m o f th e p o t . H e n c e , a v a l v e h a s b e e n
i n s ta l le d t o d e c a n t t h e c o n d e n s e d w a t e r . T h e v o l u m e o f
t h e d e c a n t e d w a t e r i s m e a s u r e d .
2 . R e s u l t s
F r o m t h e s e e x p e r i m e n t s , w e h a v e d e t e r m i n e d t h e v a r i -
a t i o n i n t i m e o f t h e t e m p e r a t u r e o f t h e s o l i d s a t v a r i o u s
p o s i t i o n s a n d t h e t e m p e r a t u r e a n d m o i s t u r e c o n t e n t o f
t h e o u t l e t g a s .
B . C o m p a r i s o n o f C o m p u t e d a n d M e a s u r e d R e s u lt s
U s i n g t h e m o d e l b a s e d o n t h e e q u a t i o n s a l r e a d y d e -
s c r i b e d , p r e d r y i n g e x p e r i m e n t s o n t h e p i l o t p o t h a v e b e e n
s u c c e s s f u l l y s i m u l a te d . T h e r e s u lt s o f t h e s e s i m u l a t i o n s
a r e p r e s e n t e d b e l o w . T h e d i s c u s s i o n a n d i n t e r p r e t a t i o n
o f t h e s h a p e o f t h e c u r v e s a r e g i v e n l a t e r in S e c t i o n V .
F i g u r e 5 s h o w s t h e c o m p a r i s o n b e t w e e n t h e c o m p u t e d
Ts(t)
c u r v es a n d t h o s e m e a s u r e d b y s e v e n t h e rm o c o u p l e s
p l a c e d i n t h e c h a r g e f o r e x p e r i m e n t A ( T a b l e I I ). V e r y
g o o d a g r e e m e n t b e t w e e n p r e d ic t io n s a n d m e a s u r e m e n t s
i s n o t e d . A t a g i v e n d e p t h , t h e e v o l u t i o n o f th e t e m p e r -
a t u r e c u r v e s h o w s s e v e r a l s t a g e s :
( 1 ) a s h o r t p l a t e a u a t t h e i n i ti a l t e m p e r a t u r e ( 2 5 ~
( 2 ) a s m a l l a n d r a p i d r i s e ;
( 3 ) a p l a t e a u w i t h te m p e r a t u r e s b e t w e e n 5 5 ~ ( a t t h e
b e g i n n i n g ) a n d 4 5 ~ ( a t t h e e n d ) ; f o r a u s u a l c o m p l e t e
s i n t e r i n g e x p e r i m e n t , t h e s e t e m p e r a t u r e s wo u l d b e s l i g h t l y
g r e a t e r ; a n d
( 4 ) a n i n c r e a s e i n t e m p e r a t u r e u p t o t h e t e m p e r a t u r e o f
t h e d r y i n g g a s .
A l l o f t h e s e s t a g e s a r e r e p r o d u c e d b y t h e c a l c u l a t io n s ,
a n d , p a r t i c u l a r y , t h e l e n g t h o f t h e p l a t e a u i s w e l l r e p -
r e s e n t e d f o r a l l d e p t h s . A f e w e x p e r i m e n t a l p o i n t s a t h i g h
t e m p e r a t u r e s d e v i a t e f r o m t h e s i m u l a t i o n r e s u l ts , b u t s i n c e
t h e s e p o i n ts i n d i c a t e t e m p e r a t u r e s g r e a t e r th a n t h o s e o f
t h e d r y i n g g a s , i t i s c o n c l u d e d t h a t t h e d i s c r e p a n c i e s a r e
c a u s e d b y i r r e g u l a r i t i e s i n t h e m e a s u r e m e n t s .
F i g u r e 6 s h o w s t h e c o m p a r i s o n b e t w e e n t h e d e w - p o i n t
t e m p e r a t u r e o f th e o u t l e t g a s e s m e a s u r e d b y t h e h y g r o m -
e t e r a n d c o m p u t e d b y t h e m o d e l f o r t h e s a m e e x p e r i -
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F i g . 5 C o m p a r i s o n o f e x p e r i m e n t a l a n d c o m p u t e d s o l i d t e m p e r a -
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t i m e d u r i n g p r e d r y i n g e x p e r i m e n t A ( ir o n o r e ) .
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d e t e r m i n i n g t h e h u m i d i t y o f t h e g a s . T o a c c o u n t f o r th e
r e s p o n s e t i m e o f t h e h y g r o m e t e r ( e x p e r i m e n t a l l y m e a -
s u r e d a s 2 2 0 s e c o n d s ) , t h e e x p e r i m e n t a l c u r v e h as b e e n
s h i f t e d 2 2 0 s e c o n d s t o t h e le f t ( d o t t e d l i n e ). A v e r y g o o d
a g r e e m e n t b e t w e e n e x p e r i m e n t a l a n d c a l c u l a t e d t e m p e r -
a t u r e s i s t h e n s e e n , p a r t i c u l a r l y a t t h e m a x i m u m t e m -
p e r a t u r e (5 5 ~ a n d a l o n g t h e p l a t e a u (4 5 ~
T h e p o s i t i v e r e s u l t s o f t h is v a l i d a t i o n s t e p a l l o w t h e
c o n f i d e n t u s e o f th e m o d e l f o r a n a l y t i c a l a n d p r e d i c t i v e
p u r p o s e s .
V D I S C U S S I O N
A . M o i s t u r e T r a n s fe r P h e n o m e n a d u r i n g t he
S i n t e r i n g P r o c e s s
B a s e d o n t h e r e s u l t s o f t h e p il o t p o t a n d t h e r m o -
g r a v i m e t r y e x p e r i m e n t s a n d th e c a l c u l a t io n s u s i n g t h e
v a l i d at e d m o d e l , a r e p r e s e n ta t i o n o f th e p h e n o m e n a c o n -
c e r n i n g m o i s t u r e t r a n s f e r i n a s i n t e r i n g b e d i s p r o p o s e d .
T h e r e p r e s e n t a t i o n i s g i v e n i n F i g u r e 7 f o r t h e c a s e o f
i r o n o r e . T e m p e r a t u r e a n d m o i s t u r e c o n t e n t p r o f il e s a r e
t w o c o m p l e m e n t a r y f a c to r s u s e d i n t h e e x p la n a t i o n . T h e
p u r p o s e o f t h e d r y i n g r a t e i s i ll u s t r a ti v e . A t a g i v e n t i m e ,
t h e m o i s t z o n e c a n b e d i v i d e d i n t o v a r i o u s s u b z o n e s ,
c h a r a c t e r iz e d b y t h e m e c h a n i s m s o f h e a t a n d m o i s t u r e
t r a ns fe r i nvo lve d . The se a re de sc r ibe d be low , i n t he o rde r
e n c o u n t e r e d b y t h e f l o w i n g g a s .
1 . D r y i n g s u b z o n e s
H o t g a s e s l e a v i n g t h e d r i e d z o n e a c t t o d r y t h e f i r s t
l a y e r s o f th e c h a r g e e n c o u n t e r e d . I n t h i s r e g i o n , t h e
m o i s t u r e c o n t e n t o f t h e s o l i d s d e c r e a s e s w i t h t im e . B u t
a s d e t e r m i n e d b y t h e t h e r m o g r a v i m e t r y e x p e r im e n t s , t w o
d r y i n g p e r io d s o c c u r , c o r r e s p o n d i n g t o t w o s u b z o n e s a c -
c o r d i n g t o t h e m o i s t u r e c o n t e n t o f t h e s o l i d s . T h e f i r s t
o f t h e s e s u b z o n e s i s c h a r a c t e r i z e d b y a d e c r e a s i n g d r y i n g
r a t e , w h i l e t h e s e c o n d h a s a c o n s t a n t o r e q u i l i b r a t e d
d r y i n g r a t e .
I n t h e d e c r e a s i n g d r y i n g r a t e s u b z o n e , t h e m o i s t u r e
c o n t e n t o f t h e s o l i d s i s l o w e r t h a n t h e c r i t i c a l m o i s t u r e
c o n t e n t , a n d t h e t e m p e r a t u r e o f t h e s o l id s i n c r e a s e s w i t h
t i m e . D r y i n g r a t e is a f u n c t i o n o f T , , T g , a n d W , a n d
c a l c u l a t i o n s h o w s t h a t i t fi r s t i n c r e a s e s ( e f f e c t o f t h e i n -
c r e a s i n g t e m p e r a t u r e o f t h e d r y i n g g a s ) , t h e n d e c r e a s e s
(e f fe c t o f t he de c re a s ing m o i s tu re c on te n t ) w i th t ime . Th i s
subz one e x t e n ds f r om po in t ( a ) (r r~2o = 0 , T , -~ 200 ~
to po in t (b ) (W = W c r ) i n F igu re 7 .
T h e e q u i l i b r a t e d d r y i n g s u b z o n e c o r r e s p o n d s t o t h e
d y n a m i c e q u i l i b r iu m o f t h e f i r s t d r y i n g p e r i o d o f t h e p e l -
l e t s obse rve d du r ing the rmogra v ime t ry e xpe r ime n t s . H e re ,
h o w e v e r , t h e d r y i n g r a te i s n o t c o n s t a n t , b e c a u s e t h e e x -
t e r n a l d r y i n g c o n d i t i o n s ( g a s c h a r a c t e r i s ti c s ) a r e n o t . B u t
t h e t e m p e r a t u r e o f th e s o l i d s , w h i c h i s e q u a l t o t h e w e t -
b u l b t e m p e r a t u r e ( a b o u t 5 0 ~ r e m a i n s n e a r l y c o n s t a n t .
T h i s s u b z o n e e n d s a t p o i n t ( c ) , w h e r e t h e d r y i n g r a t e
b e c o m e s z e r o , a n d , t h e r e f o re ,
Ts ~- Tw ~-- Tg.
A t th i s po in t ,
Tw i s t h e a d i a b a t i c s a t u r a t i o n t e m p e r a t u r e .
F o r z i n c o r e , a u n i q u e d r y i n g s u b z o n e e x i s t s , a s a l l o f
t h e d r y i n g o c c u r s i n t h e d e c r e a s i n g r a t e r e g i m e .
2 . O v e r m o i s t e n e d s u b z o n e
T h e z o n e b e t w e e n p o i n t s ( c ) a n d ( d ) i s t h e o v e r -
m o i s t e n e d s u b z o n e . I n t h i s s u b z o n e , a r e m a r k a b l e
t h e r m o d y n a m i c e q u i l i b r i u m t a k e s p l a c e , d e f i n e d b y T s =
T g = T w = T d T d
b e i n g t h e d e w - p o i n t t e m p e r a t u r e) . T h i s
e qu i l i b r ium i s c a l l e d qua s i - a d i a ba t i c sa tu ra t ion . A t ( c ) ,
g a s e s w h i c h h a v e b e e n l o a d e d w i t h w a t e r a n d d e c r e a s in g
i n t e m p e r a t u r e f r o m ( a ) t o ( c ) a r e s a t u r a te d ( T g =
T a ,
sin ce Pn2o = pv,,,(Tw) = pvs= Tg)) a t t he a d i a ba t i c sa tu ra -
t i on t e mpe ra tu re (T~ = T w = T g ) . T h e r e i s n e i t h e r m o i s -
t u r e t r a n s f e r n o r h e a t t ra n s f e r . T h i s c o n d i t i o n c o n t i n u e s
a s l o n g a s t h e s o l i d s a r e a t t e m p e r a t u r e Tw.
A s i n t h e p a p e r b y K o r o t i c a n d P u z a n o v , ~ a n d i n
c o n t r a s t t o o t h e r w o r k s w h e r e t h i s s u b z o n e i s n o t d i s t i n -
g u i s h e d f r o m t h e c o n d e n s a t i o n z o n e , t h e f o r m a t i o n o f
t h e o v e r m o i s t e n e d s u b z o n e i s t h o u g h t t o b e t h e r e s u l t o f
t h e p a s s i n g o f a r e l a t i v e l y n a r r o w c o n d e n s a t i o n f r o n t
t h r o u g h t h e b e d , w h i c h l e a v e s b e h i n d a z o n e o f s l i g h t l y
h e a t e d s o l i d s ( 5 0 ~ t o 6 0 ~ e n r i c h e d in m o i s t u r e ( re l -
a t i ve i nc re a se o f 10 to 15 pc t w i th r e spe c t t o t he i n i t i a l
m o i s t u r e c o n t e n t ) .
T h e e x i s t e n c e o f t h is i n e rt o v e r m o i s t e n e d s u b z o n e h a s
b e e n p r e v i o u s l y d e m o n s t r a t e d t131 a n d i s c o n f i r m e d f o r t h e
p r e s e n t p i l o t p o t e x p e r i m e n t s b y F i g u r e s 6 a n d 8 . I t i s
s e e n t h a t a f t e r a r i s e i n g a s t e m p e r a t u r e a n d a m a x i m u m
in the de w -po in t t e mpe ra tu re ( c o r re spond ing to t he e x i t i ng
o f t h e c o n d e n s a t i o n f r o n t ) , t h e g a s t e m p e r a t u r e r e m a i n s
c o n s t a n t a n d e q u a l t o t h e d e w - p o i n t t e m p e r a t u r e ( s a t u -
r a t i o n ). D u r i n g l o n g e r e x p e r i m e n t s ( F i g u r e 6 ; c a s e A ,
T a b l e I I ) , t h e s e t e m p e r a t u r e s r e m a i n c o n s t a n t u n t i l t h e
d r y i n g f r o n t a r r iv e s , w h i c h d e t e r m i n e s t h e l en g t h o f t i m e
t h a t t h e o v e r m o i s t e n e d s u b z o n e i s p r e s e n t a t t h e b o t t o m
o f t h e b e d .
T h e h a r m f u l i n f l u e n c e o f th i s o v e r m o i s t e n e d z o n e c o m e s
f r o m i t s p o o r p e r m e a b i l i t y . I n d e e d , e x c e s s w a t e r c a n r e -
d u c e p o r o s i t y b y i ts o w n v o l u m e a n d b e c a u s e i t w e a k e n s
t h e c o n c e r n e d l a y e r s , p r o m o t i n g t h e i r c o l la p s e . W a j i m a
et a1.[14] h a v e n o t e d t h a t c o n d e n s e d w a t e r a b o v e a c r i t i c a l
l e v e l r e s u lt s i n t h e r e l e a s e o f t h e a d h e r i n g f i n e p a r t i c l e s ,
w i t h s u b s e q u e n t b r e a k i n g u p o f t h e p a r t ic l e s a n d a d r a s t ic
r i s e i n t h e r e s i s t a n c e t o g a s f l o w .
3 . C o n d e n s a t i o n s u b z o n e
B e y o n d p o i n t ( d ) , t h e s a t u r a t e d g a s e s a r e in c o n t a c t
w i t h c o l d e r s o l i d s . T h e t r a n s p o r t e d w a t e r c o n d e n s e s o n
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F i g . 7 - - M e c h a n i s m s o f m o i s t u re t ra n s f e r i n t h e s i n t e ri n g b e d i r o n o r e ) .
t h e s e s o l id s a n d w a r m s t h e m b y t h e r e l e a s e o f th e l a t e n t
h e a t o f c o n d e n s a t i o n . T h i s s u b z o n e e n d s a t p o i n t ( e ) ,
w h e r e t h e v a p o r p r e ss u r e o f t h e g a s e s a g a i n b e c o m e s e q u a l
t o t h e s a t u r a ti o n v a p o r p r e s s u r e a t t h e te m p e r a t u r e o f t h e
c o l d s o l i d s . T h e t h i c k n e s s o f th i s s u b z o n e i s o f t h e o r d e r
o f a f e w c e n t i m e t e r s , r o u g h l y b e t w e e n 4 t'31 a n d 8 ( t h is
s t u d y ) .
I n c o n t r a s t t o t h e d r y i n g f r o n t , t h e c o n d e n s a t i o n f r o n t
r a p i d l y p a s s e s t h r o u g h t h e b e d ; i n l e s s t h a n a p p r o x i -
m a t e l y 4 m i n u t e s ( h e n c e , b e f o r e t h e e n d o f th e i g n i t i o n
p e r i o d i n t h e c a s e o f th e i r o n o r e p r o c e s s ) , t h e c o n d e n -
s a t i o n s u b z o n e a n d t h e r a w s u b z o n e ( d i s c u s s e d i n t h e
n e x t s e c t i o n ) c o m p l e t e l y d i s a p p e a r .
E x p e r i m e n t a l r e s u lt s c l e a r l y s h o w t h e f o l l o w i n g e v o -
l u t i o n o f t h e c o n d e n s a t i o n f r o n t . I n t h e t e m p e r a t u r e o f
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ime s )
F i g. 8 - - E x p e r i m e n t a l t e m p e r at u r e a n d d e w - p o in t t e m p e r a tu r e o f t h e
o u t l e t g a s d u r i n g p r e d r y i n g e x p e r i m e n t B i r o n o r e ) .
t he s o l id s
vs
t i m e c u r v e s ( F i g u r e 5 ) , t h e s m a l l r i s e i n
t e m p e r a t u r e f r o m 2 5 ~ t o 5 0 ~ i n d i ca t e s t h e c o n d e n -
s a t io n p e r i o d . T h i s r i s e t a k e s p l a c e v e r y e a r l y i n t h e p r o -
c e s s, e v e n i n t h e d e e p e s t l a y e rs o f t h e b e d , a n d c a n o n l y
b e a t t r i b u t e d t o th e h e a t o f c o n d e n s a t i o n . I n d e e d , h e a t
t r a n s f e r c a l c u l a t i o n s s h o w t h a t i t i s n o t p o s s i b l e t o r e a c h
a t e m p e r a t u r e o f 5 0 ~ i n t h e d e e p l a y e r s , i n l es s t h a n
4 m i n u t e s , b y s i m p l e h e a t c o n v e c t i o n . I n F i g u r e 8 , t h e
p a s s ag e o f t h e c o n d e n s a t i o n f r o n t t h r o u g h t h e e n d o f t h e
b e d ( b e t w e e n 2 a n d 4 m i n u t e s) c o i n c i d e s w i t h t h e m a x -
i m u m o f t h e d e w - p o i n t t e m p e r a t u r e ( a f t e r c o r r e c t io n f o r
t h e h y g r o m e t e r ' s r e s p o n s e t i m e ) a n d t h e r i se i n g a s t e m -
p e r a t u r e . I n a d d i t i o n , t a p p i n g o f t h e l i q u i d w a t e r c o n -
d e n s e d a t th e b o t t o m o f t h e p o t s h o w s a s t ro n g m a x i m u m
i n t h e c o n d e n s a t i o n r a t e a t t h i s t i m e .
C o n d e n s a t i o n i s an i n c o n v e n i e n t p h e n o m e n o n d u r i n g
t h e s i n t e r in g p r o c e s s f o r t w o r e a s o n s . F i r s t , i t l e a d s t o
t h e f o r m a t i o n o f a b a r e l y p e r m e a b l e o v e r m o i s t e n e d z o n e ,
a n d , s e c o n d , i t d e l a y s t h e d r y i n g s t e p , s i n c e t h e c o n -
d e n s e d w a t e r r e p r e s e n ts e x c e s s w a t e r w h i c h m u s t b e r e -
m o v e d . T o r e d u c e o r s u p p r e ss c o n d e n s a t i o n , s e v e ra l
a l t e r n a t e p r a c t i c e s m a y b e c o n s i d e r e d , s u c h a s p r e h e a t -
i n g o f t h e c h a r g e .
4. Ra w subzone
T h e r a w s u b z o n e c o n s i st s o f t h a t p o r t io n o f t h e c h a r g e
w h e r e m o i s t u r e tr a n s f e r h a s n o t y e t c o m m e n c e d . I t e x -
t e n d s f r o m p o i n t ( e ) t o t h e b o t t o m o f t h e b e d .
B. Representa t ion U sing Mo l l ie r s Diagram
T h e m o i s t u r e t r a n s f e r m e c h a n i s m s c a n b e i l lu s t ra t e d
i n a n o t h e r w a y , u s i n g a M o l l i e r d i ag r a m w h i c h d e s c r ib e s
t h e t h e r m o d y n a m i c c h a r a ct e r is t ic s o f t h e g a s ( t e m p e r a -
tu re
Tg,
w e t - b u l b t e m p e r a t u r e
Tw,
a b s o l u t e h u m i d i t y X ,
a n d r e l a t i v e h u m i d i t y ~ b ) . F i g u r e 9 s h o w s t h e M o l l i e r
d i a g r am s f o r p r e d r y in g a m o i s t c h a r g e ( e x p e r i m e n t A f o r
i r o n o r e , F i g u r e 9 ( a ) , a n d e x p e r i m e n t C f o r z i n c o r e ,
M ETA LLU RG ICA L TRA N S A CTIO N S B V O LU M E 21B, F EBRU A RY 1990- -4 3
7/23/2019 dy of Moisture Transfer during the Strand Sintering Process
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o ,
2~.o
220
200 9
180 \
160
lt~O
120
80 \ ~
6o ~
~ O \ /
9
20
120
100
ta
9
80
o
~ ~0
0
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4o
- 60
Absolute humidity glkg dry air)
20 t~O 60 80
_ a ? - -
' C
- ~ 7 o
, J c l l & - c t _ _ 1 o .
~'0
32cm
32cm
100 120
\
\
[0~
-- 20~
<"
~ 1 ~ "1_ 60
...-,
16cm
6 18cm
. . . . . wet-bulb temperature ( )
. . . . . relative humidity ( )
5 nm
between each point
0
0
[] 2cm
o ~ ~ ~ 5 c | ~"6"0~
0 0 %
0
0 , , / , ' 0 0 0 0
7.5cm 0 o' - 10cm 0 B' 16cm OR B
-
12cm
32cm
O 0 0 O 0
O 0 0 0 0 0 0 0 O 0
A b s o l u t e humidity g / k g dry air
2~0 0 20 ~0 60 BO
220
200 ~o
~.J 180
16o
1~0
120 lO~
,00 , . ? - . - - _ .20
8 0 ~ ~ 0 ~
6o
t00%
40 r cm y -6.5cm
2 0 ] ~ _ . t - b u l b t s (~
~ t ~ ~ e l a t i v e humidity
( )
5m between each point
1~)0
8O
9
m. 60
5
~ 0
- 20
a,O-6cm
0
Cl
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~os
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ae
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o
o
0
0
0
0 0
3 2 c m l 2 ~ 1
O o D o O D O 0
10 20 30 t~O 50 60 70 80 gO 100 110 120 130 10 20 30 40 50 60 ?0
A b s o l u t e h u m i d i t y ( g / k g d r y a i r ) Absolute humidi ty ( g / k g d r y a i r
( a ) ( b )
80 90
'-6,5cm
F i g .
9 - - M o l l i e r d i a g r a m s o f t h e g a s a n d c o r r e s p o n d i n g d r y i n g r a t e d u r i n g a p r e d r y i n g e x p e r i m e n t : a ) i r o n o r e c a s e A ) a n d b ) z i n c o r e c a s e
C ) .
F i g u r e 9 ( b ) ) . T h e g a s s t a t e is p r e s e n t e d a t t w o t i m e s : a t
4 0 o r 6 0 s e c o n d s ( w h e n t h e c o n d e n s a t i o n f r o n t i s p r e s en t
i n th e b e d ) a n d a t 3 0 0 s e c o n d s ( w h e n t h e c o n d e n s a t i o n
f r o n t h a s p a s s e d ) . I n t h i s f i g u r e , b o t h t h e e v o l u t i o n o f
t h e g a s c h a r a c t e r i s t i cs t h r o u g h t h e b e d a t a g i v e n t i m e
a n d th e ir e v o l u t i o n w i t h t i m e c a n b e fo l l o w e d . B e l o w
t h e M o l l i e r d i a g r a m s , t h e c o r r e s p o n d i n g d r y i n g r a te s ar e
p l o t t e d t o c o m p l e t e t h e p i c t u r e .
1 . I r o n o r e c a s e F i g u r e 9 a ) )
A t 6 0 s e c o n d s , s t a rt i n g f r o m t h e b e d e n t r a n c e ( n o t p ic -
t u r e d i n t h e d i a g r a m ) t o p o i n t a ( x = 3 . 5 c m ) , s e c o n d -
p e r i o d d r y i n g t a k e s p l a c e . F r o m p o i n t a t o p o i n t 7 ( w h e r e
t h e m o i s t u r e c o n t e n t i s g r e a t e s t, x = 1 6 c m ) , f i r s t -p e r i o d
d r y i n g o c c u r s , l e a d i n g t o m o i s t u r e e n r ic h m e n t o f t h e g a s
u p t o t h e s a t u r a t i o n p o i n t . A r o u n d 3 , ( f r o m / 3 , x = 1 2 c m
t o 6 , x = 1 8 c m ) , t h e g a s i s n e a r l y s a t u r a t ed , a n d t h e
d r y i n g r a t e i s p r a c t i c a l l y z e r o ; t h i s i s t h e o v e r m o i s t e n e d
s u b z o n e . T h e n , f r o m 6 t o t h e e n d o f t h e b ed , t h e g a s
r e m a i n s s a t u r a te d ( p o i n t s o n t h e c u r v e ~b = 1 ) , w h i l e t h e
d r y i n g r a t e i s n e g a t i v e ; t h i s i s t h e c o n d e n s a t i o n s u b z o n e .
I n th i s c a s e , t h e r a w s u b z o n e h a s a l r e a d y d i s a p p e a r e d
f r o m t h e b e d .
A t 3 0 0 s e c o n d s , t h e s i t u a t i o n i s r a t h er d i f fe r e n t. D r y i n g
h a s a d v a n c e d d o w n w a r d , a n d t h e f i rs t p o i n t i n th e d ia -
g r a m i s n o w a t 7 . 5 c m . T h e g a s i s c o o l e d i n th e d r i ed
z o n e ; t h u s , d r y i n g i s l e s s i n t e n s e , a n d t h e g a s h u m i d i t y
i s lo w e r , w h i c h i s s h o w n i n t h e d i a g r a m b y t h e p o in t s
f u r th e r t o th e le f t. T h e s e c o n d - p e r i o d d r y i n g s u b z o n e ( t o
p o i n t a , x = 1 0 c m ) i s f o l l o w e d b y t h e f i r s t - p e r i o d d r y i n g
s u b z o n e ( fr o m a t o / 3 , x = 1 6 c m ) . P o i n t s c o r r e sp o n d -
i n g t o f i r st - p e r io d d r y i n g e x a c t l y f o l l o w a n is o - w e t - b u l b
t e m p e r a t u r e l i n e , t h e e q u i l i b r a t e d d r y i n g b e i n g s t ab i -
l i z e d . T h i s w a s n o t s o a t 6 0 s e c o n d s b e c a u s e o f a t ra n -
s i ti o n a l e f fe c t l i n k e d t o c o n d e n s a t i o n . T h e c o n d e n s a t i o n
s u b z o n e h a s c o m p l e t e l y d i s a p p e a r e d , a n d th e in e r t o v e r -
m o i s t e n e d s u b z o n e e x t e n d s o v e r h a l f o f th e b ed ( f r o m
/3 t o t h e e n d o f t h e b e d ) .
2 . Z i n c o r e c a s e F i g u r e 9 b ) )
T h e s h a p e o f t h e c u r v e s i n F i g u r e 9 ( b ) i s s i m i l a r t o
t h a t o f F i g u r e 9 ( a ) ; t h u s , o n l y t h e m a i n d i f f e r e n c e s w i l l
b e m e n t i o n e d . T h e s e a r e m o s t l y a t t r ib u t e d t o th e s o l i d
c h a r g e c h a r a c t e r is t i c s.
T h e b e d t e x t u r e ( l a r g e r p a r t i c l e s i z e , s m a l l e r s p e c i f i c
a r e a ,
e t c .
a n d t h e d i f f e r e n c e s i n t h e o p e r a t i n g c o n d i t i o n s
4 4 - - V O L U M E 2 1 B , F E B R U A R Y 1 9 90 M E T A L L U R G I C A L T R A N S A C T I O N S B
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b e t w e e n p r e d r y i n g e x p e r i m e n t s A a n d C i n d u c e l o w e r
d r y i n g r a te s , l e a d i n g t o lo w e r g a s h u m i d i t i e s. M o r e i m -
p o r t a n t l y , t h e c r i t i c a l m o i s t u r e c o n t e n t o f z i n c o r e p e l l e ts
i s s u c h t h a t n o e q u i l i b r a t e d d r y i n g p e r i o d c a n o c c u r .
T h e r e f o r e , t h e p o i n t s d o n o t l i e o n a n i s o - w e t - b u l b t e m -
p e r a t u r e l i n e , a n d t h e g a s l e a v i n g t h e d r y i n g s u b z o n e i s
n e v e r c o m p l e t e l y s a tu r a t ed . T h u s , a t 4 0 s e c o n d s , t h e g a s
r e l a t i v e h u m i d i t y i s a b o u t 7 0 t o 8 0 p c t d u r i n g c o n d e n -
s a t io n . A t th i s t im e , t h e p r e s e n c e o f t h e r a w s u b z o n e
( f r o m p o i n t e , x = 2 6 c m t o th e e n d o f t h e b e d ) c a n a l s o
b e n o te d . A t 3 0 0 s e c o n d s , t h e o v e r m o i s t e n e d s u b z o n e
a g a i n e x te n d s o v e r h a l f o f th e b e d ( f r o m / 3 ' , x = 1 5 c m
t o t h e e n d ) , b u t th e g a s r e l a t i v e h u m i d i t y r e m a i n s s l i g h t l y
l o w e r th a n 1 .
C Influence of Various Factors on the Drying
of the Sintering Bed
1 Influence of drying kinetics
F i g u r e 1 0 s h o w s t h e e f f e c t o f C o n s i d e r i n g th e d e c r e a s -
i n g r a te p e r i o d ( c a s e A , i r o n o r e ) c o m p a r e d t o d r y i n g a t
c o n s t a n t r a t e f o r a ll m o i s t u r e c o n t e n t s . I n t h e l a t te r c a s e ,
a s e x p e c t e d , t h e p l a t e a u a t t h e w e t - b u l b t e m p e r a t u r e i s
a l it tl e l o n g e r , b u t t h e t o t a l d u r a t i o n o f d r y i n g i s s l i g h t l y
l e s s . I n t h e c a s e o f z in c o r e , t h e d i f f e r e n c e w o u l d b e
g r e a te r , a s i t h a s b e e n s h o w n t h a t n o c o n s t a n t r a te d r y i n g
t a k e s p l a c e i n u s u a l i n d u s t r i a l c o n d i t i o n s .
2 Influence of condensation
F i g u r e 1 1 s h o w s t h e i n f l u e n c e o f c o n s i d e r in g c o n d e n -
s a t i o n ( c a s e C , z i n c o r e ) . I t i s s e e n t h a t i f c o n d e n s a t i o n
i s n e g l e c t e d , t h e i n i t i a l r i s e i n t e m p e r a t u r e i s p o o r l y d e -
s c r i b e d , a n d t h e t o t a l d u r a t i o n o f d r y i n g i s o v e r l y r e -
d u c e d . T h i s c o m p a r i s o n s h o w s a s w e l l t h e h a r m f u l
i n f lu e n c e o f c o n d e n s a t i o n o n t h e r a t e o f w a t e r r e m o v a l
a n d , c o n s e q u e n t l y , o n t h e p r o d u c t i v i t y o f th e s i n t e r in g
o p e r a t i o n . S i m i l a r r e s u l t s a r e o b t a i n e d f o r t h e c a s e o f
i r o n o r e .
3 Influence of preheating the charge
I n d u s tr i a l e x p e r i m e n t s h a v e s h o w n t h a t in o r d e r t o r e -
d u c e c o n d e n s a t i o n , i t m i g h t b e i n t e r e s t i n g t o p r e h e a t t h e
c h a r g e , f o r e x a m p l e , b y u s i n g h o t r e t u r n s in t er . T h e m o d e l
h a s a s c e r t a i n e d th e s e r e s u l ts . I n F i g u r e 1 2 , t h e c o m p u t e d
5
two p e r i o d s first e r i o d o n l y
C 400
~= 300
cm
2 o
0
3 6 6 9 d o 1 2 6 I ; o o 1 8 o o
T i m e
s)
F i g. 1 0 - - C o m p a r i s o n o f t h e c o m p u t e d s o li d te m p e r a tu r e
v
t i m e d u r -
i n g a p r e d r y i n g e x p e r i m e n t w h e n d r y i n g o c c u r s i n f i r s t p e r i o d o n l y
and in tw o per iods cas e A , i r on o r e ) .
5
w i t h c o n d e n s a t i o n w i t h o u t c o n d e n s a t i o n
G q00
o
~ 300
/
2
o
u~ I
0
2 ; 4 ; 6 ; 8 b l o o o
T i m e s )
F i g . 1 1 - - C o m p a r i s o n o f t h e c o m p u t e d s o l i d t e m p e r a t u r e
v
t i m e d u r -
i n g a p re d r y i n g e x p e r i m e n t w i t h c o n d e n s a t i o n c a s e C , z i n c o r e ) a n d
w i t h o u t c o n s i d e r i n g c o n d e n s a t i o n .
m a p s o f t h e m o i s t u r e c o n t e n t o f t h e s o l i ds d u r i n g a n o r -
m a l o p e r a t i o n ( c a s e D ) a n d d u r i n g a n o p e r a t i o n w i t h a
p r e h e a t e d c h a r g e ( 6 0 ~ c a s e E ) a r e p r e s e n t e d . T h e a b -
s c i s s a r e p r e s e n t s t i m e ( e q u i v a l e n t t o d i s t a n c e a l o n g t h e
g r a t e ) , a n d t h e o r d i n a t e t h e h e i g h t i n t h e b e d . T h e d o t t e d
l in e i n d i c a te s t h e b o u n d a r i e s o f th e o v e r m o i s t e n e d z o n e .
T h e c o n s i d e r a b l e d e c r e a s e o f t he e x t e n t o f t h is z o n e a f t e r
p r e h e a t i n g s h o u l d b e n o t i c e d , a s w e l l a s t h e a p p r e c i a b l e
d e c r e a s e o f m a x i m u m a t t a i n e d m o i s t u r e c o n t e n ts .
V I . C O N C L U S I O N S
T h i s s t u d y h a s y i e l d e d a p r e c i se u n d e r s t a n d i n g o f t h e
m o i s t u r e t r a n s f e r m e c h a n i s m s i n t h e s i n t e r i n g p r o c e s s .
D r y i n g o f i ro n o r e p e l l e t s o c c u r s i n t w o p e r i o d s : o n e a t
c o n s t a n t r a t e a n d th e o t h e r a t d e c r e a s i n g r a t e . T h e c r i t i c a l
u
c
d : Y i n g ' r ~ 8 4 0 r , e 0 z 0 n e
. o v e r . o i s t e n e d . . . . i . i t
c o n - -
lL oora e~
~ M O ~ i t Z ~ ~ c~ rate rying
40
a ) I n i t i a l s o l i d
Time s) 2880
temperature:25*C.Case D Jron ore).
, ~ N V . O % . d r y i n g f ro n t Dried zone
~a con~e nsat ion~ ~< ~ . .
, - ~ .~ ~ , ~ : c - - T a t t l n g r a t e d r y i n g
~7 , over-- ~ ~ '~
m o i s t e n e d z o n e l ' z m l , , , , -
~ 17 6 e . l i m ~ . ~ c o n s t a n t r a t e
drying
40 9 Y Moist z o n e ~
0 Time s) 2880
( b ) I n i t i a l s o l i d t e m p e r a t u r e : 6 0 C . C a se E ( i r o n o r e ) .
F i g. 1 2 - - I n f l u e n c e o f p re h e a t i n g o f t h e c ha r g e o n t he c o m p u t e d m a p
o f s o l i d m o i s t u r e c o n t e n t fo r a c o m p l e t e s i n t e r i n g o p e r a t i o n i r o n o re ) .
M ETA LLU RG ICA L TRA N S A CTIO N S B V O LU M E 21B, F EBRU A RY 1990- -4 5
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m o i s t u r e c o n t e n t h a s b e e n d e t e r m i n e d , a n d t h e c h a r a c -
t e r i s ti c d r y i n g c u r v e h a s b e e n g i v e n . D r y i n g o f z i n c o r e
p e l l e t s a l w a y s t a k e s p l a c e w i t h a d e c r e a s i n g r a t e , b e -
c a use the c r i t i c a l mo i s tu re c on te n t i s h ighe r t ha n the u sua l
m o i s t u r e c o n t e n t s f o r t h e s i n te r i n g p r a c t ic e . T h e c h a r -
a c t e r i s t i c d r y i n g c u r v e h a s a l s o b e e n g i v e n . I n t h e s i n -
t e r i n g p r o c e s s , g a s e s l e a v i n g t h e d r y i n g z o n e a r e h i g h l y
l o a d e d w i t h w a t e r , a n d d u r i n g t h e e a r l y s t a g e s o f t h e
o p e r a t i o n , t h i s w a t e r c o n d e n s e s i n c o l d e r l a y e r s . P a s s a g e
o f t h e c o n d e n s a t i o n f r o n t l e a v e s b e h i n d a n o v e r -
m o i s t e n e d ( + 1 t o 2 p c t w a t e r ) , i n e r t ( w i t h o u t h e a t o r
m o i s t u r e t r a n s f e r ) , h e a t e d ( t y p i c a l l y 5 5 ~ a n d l o w
p e r m e a b i l i t y z o n e , w h i c h r e m a i n s u n t il t h e d r y i n g f r o n t
a r r i v e s .
A n a c c u r a te d e s c r i p t io n o f t h e s e p h e n o m e n a u s i n g a
m a t h e m a t i c a l m o d e l h a s a l l o w e d u s t o s u c c e s s f u ll y s i m -
u l a t e p r e d r y i n g e x p e r i m e n t s o n a p i l o t p o t a n d t o c a l -
c u l a t e a l l o f t h e v a r i a b l e s r e l a t i v e t o m o i s t u r e t r a n s f e r .
T h e n e c e s s i ty o f d e s c r i b i ng b o t h t h e t w o p e r i o d s o f d r y i n g
a n d t h e c o n d e n s a t i o n p e r i o d h a s b e e n s h o w n a n d t h e i n-
f l u e n c e o f c h a n g i n g o p e r a t i n g c o n d i t i o n s , s u c h a s p r e -
h e a t i n g t h e c h a r g e t o r e d u c e c o n d e n s a t i o n , h a s b e e n
s t u d i e d . I t i s b e l i e v e d t h a t t h i s a p p r o a c h c a n b e d i r e c t l y
a da p te d to o the r p roc e sse s w he re a ho t ga s pa sse s t h rough
a m o i s t p a c k e d b e d .
g
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s p e c i f i c a r e a o f t h e b e d
(m 2
m ~ 3)
m o l a r w a t e r v a p o r c o n c e n t r a t i o n i n g a s e s
( m o l - m - 3 )
s p e c i f i c h e a t o f t h e g a s e s ( J . k g - 1 9K - I )
s p e c i f i c h e a t o f t h e s o l i d s ( J . k g - t 9K -1)
e q u i v a l e n t d i a m e t e r o f p a r t ic l e s ( m )
r a t i o
R t r / R M - )
h e a t t r a n s f e r c o e f f i c i e n t ( W . m - 2 . K - I )
w a t e r m a s s t r a n s f e r c o e f f i c i e n t ( m - s - I )
h e a t o f v a p o r i z a t i o n o f w a t e r ( J . k g - ~ )
m o l e c u l a r w e i g h t o f w a t e r ( k g . m o l - t )
p a r t i a l v a p o r p r e s s u r e o f w a t e r ( P a )
s a t u r a t io n v a p o r p r e s s u r e o f w a t e r ( P a )
t o t a l p r e s s u r e o f g a s e s ( P a )
p o l y n o m i a l r e p r e s e n t at i o n o f t h e
c h a r a c t e r i s t i c d r y i n g 1 q u a t i o n ( - )
d r y i n g r a te ( m o l - s - 9m ~ )
d r y i n g r a t e d u r i n g t h e f i r s t p e r i o d o f d r y i n g ,
( m o l - s - l . m b ~ ) a n d ( k g . m - 3 - s - l ) ,
r e s p e c t i v e l y
d r y i n g r a t e c a l c u l a t e d f r o m t h e p a r t i a l
p r e s s u r e d i f f e r e n c e ( t o o l - s - i . m b 3 )
c o n s t a n t o f i d e a l g a s l a w ( J . m o 1 - 1 - K - t )
d r y i n g r a te ( k g .
m -3 S -t)
r e d u c e d d r y i n g r a t e ( - )
d r y i n g r a t e a t t r a n s i t i o n p o i n t W = Wtr
(kg . m -3~ s -1 )
t i m e ( s )
d e w - p o i n t t e m p e r a t u r e ( K )
t e m p e r a t u r e o f t h e g a s e s ( K )
t e m p e r a t u r e o f t h e s o l id s ( K )
w e t - b u l b t e m p e r a t u r e ( K )
s u p e r f i c i a l v e l o c i t y o f t h e g a s ( m - s - l )
m o i s t u r e c o n t e n t o f th e s o l id s ( k g / k g d r y )
c r i t i ca l m o i s t u r e c o n t e n t o f t h e s o l id s ( - )
~ q
W,r
x
x~
E
4
Pa
Pg
~ 1 2 O
e q u i l i b r i u m m o i s t u r e c o n t e n t o f t h e s o l id s
- )
r e d u c e d m o i s t u r e c o n t e n t o f t he s o l id s ( - )
m o i s t u r e c o n t e n t a t t r a ns i t io n p o i n t ( - )
h e i g h t i n t h e b e d ( m )
l o g a r it h m i c m e a n m o l a r f r a c t i o n o f v a p o r
- )
p o r o s i t y o f t h e b e d ( - - )
r e l a ti v e h u m i d i t y o f t h e g s P n 2 o / P v S a t ) - - )
a p p a r e n t d e n s i t y o f t h e b e d ( k g - m ~ 3 d )
c lensl ty o t the gas (1~"m " )
m o i s t u r e c o n t e n t o f th e s o l i d s p e r u n i t
v o l u m e o f t he b e d ( k g . m ~ 3)
CKNOWL E DGME N T S
T h i s s t u d y h a s b e e n p e r f o r m e d w i t h t h e s c i e n t i f i c a n d
f i n a n c i a l s u p p o r t o f I R S I D , w h i c h i s i n t e r e s t e d i n m o d -
e l i n g t h e i r o n o r e s i n t e r i n g p r o c e s s , a n d M I N E M E T
R E C H E R C H E , w h i c h i s i n t e r e s t e d i n m o d e l i n g t h e
z i n c o r e s i n t e r - r o a s t i n g p r o c e s s . A t I R S I D , w e t h a n k
D r s . E . M a r l i ~ r e , C . D u l c y , J . M . S t e i l e r, a n d P . R i b o u d
f o r t h e i r c o l l a b o r a t i o n a n d f o r a l l o w i n g u s t o h a v e p i l o t
p o t e x p e r i m e n t s a t o u r d i s p o s a l . S i n c e 1 9 8 4 , t h e i r o n o r e
s i n te r in g s t u d y h a s b e e n p a r t o f t he G r o u p e m e n t
S c i e n t if i q u e " F o n t e d e h a u t e p u r e t 6 , " j o i n t l y f i n a n c e d b y
I R S ID a nd C N R S . A t M I N E M E T R E C H E R C H E , w e
t h a n k D r s . G . S a n c h e z a n d S . J o r g e t f o r t h e i r c o l l a b o -
r a t i o n . I n a d d i t i o n , w e w i s h t o t h a n k D r . B . L a l l y , w h o
k i n d l y a s s i s t e d w i t h t h e E n g l i s h t r a n s l a ti o n o f t h i s p a p e r .
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46--VOLUME 21B, FEBRUARY 1990 METALLURGICAL TRANSACTIONS B
7/23/2019 dy of Moisture Transfer during the Strand Sintering Process
http://slidepdf.com/reader/full/dy-of-moisture-transfer-during-the-strand-sintering-process 11/11
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METALLURGICAL TRANSACTIONS B VOLUME 21B, FEBRUARY 1990--47
