modelo viscosidad napier

8/3/2019 Modelo viscosidad napier

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E L S E V I E R Int. J. Miner. Process. 47 (1996) 103-123

n I T E R I IR T I O f l l3 L J O l J m l f l L O FmlnERIILPRO(ESSlfl6

A m od e l for s lurry rheo logyF . N . S h i , T .J . N a p i e r - M u n n *

Julius Kru ttschn it t M inera l Resear ch Centre , U niversity o f Queensland, Brisbane, Au straliaRe ceived 4 Apri l 1995; accepted 20 N ovem ber 1995

Ab s t r a c t

A s e m i - e m p i r i c a l m o d e l h a s b e e n d e v e l o p e d t o p r e d i c t s l u r r y t h e o l o g y f r o m e a s i l y - m e a s u r e ds l u rr y p r o p e r t i e s. T h e m o d e l d e m o n s t r a t e s t h e c o m p l e x i n f l u e n c e o f th e s e p r o p e r t ie s o n r h e o l o g y ,a n d a l s o p e r m i t s t h e o l o g i c a l i n f o r m a t i o n t o b e p r e d i c t e d i n c a s e s w h e r e i t c a n n o t b e m e a s u r e d . I ti s i n t e n d e d f o r u s e w i t h s l u r r i e s c o m m o n l y e n c o u n t e r e d i n m i n e r a l p r o c e s s i n g .

T h e m o d e l f i r st p r e d ic t s m a c h i n e o u t p u t r e a d i n g s o f th e o n - l i n e D e b e x s l u rr y v i s c o m e t e r a tv a r i o u s b o l a b in r o t a t io n a l s p e e d s , f r o m s o l id s c o n c e n t r a t i o n , s o l id s s i z e d i s tr i b u t io n a n d t e m p e r a -t u r e . T h e m a c h i n e r e a d i n g s a n d t h e b o b b i n r p m a r e t h e n c o n v e r t e d t o s h e a r s t r e s s a n d s h e a r r a t eu s i n g t h e tu r b u l e n c e c o r r e c t i o n m e t h o d d e s c r i b e d i n a n a s s o c i a t e d p a p e r . ( T h e s i m u l a t i o n o f th eD e b e x i s a c o n v e n i e n c e ; t h e m e t h o d i s e s s e n t i a l ly i n d e p e n d e n t o f a n y p a r t i c u l a r in s t r u m e n t i f th ef u l l d a t a r e d u c t i o n p r o c e d u r e i s f o l l o w e d . )

T h e m o d e l h a s b e e n a p p l ie d t o 1 27 s e t s o f D e b e x v i s c o m e t e r m e a s u r e m e n t s o f a v a r ie t y o fs l u r r i e s t o t a l l i n g m o r e t h a n 1 2 0 0 d a t a p o i n t s , w i t h g o o d a g r e e m e n t b e t w e e n t h e p r e d i c t e d a n d t h em e a s u r e d d a t a . D i f f e r e n t s l u r r y t y p e s r e q u i r e d i f f e r e n t m o d e l p a r a m e t e r v a l u e s , b u t i t w a s f o u n dt h at t h e r h e o l o g y o f m a n y c o m m o n s lu r r ie s c o u l d b e d e s c r i b e d b y a s i n g le s e t o f p a ra m e t e r v a l u e so v e r a w i d e r a n g e o f c o n d i t i o n s . I n o t h e r c a s e s, a d j u s t m e n t s i n o n l y o n e o r t w o p a r a m e t e r s w e r er e q u i r e d .T h e s e p a r a t e e f f e c t s o f s o l i d s v o l u m e f r a c t i o n a n d p a r t i c l e s i z e o n s l u r r y r h e o l o g i c a l n a t u r e ,s i m u l a t e d u s i n g t h e m o d e l a n d t u r b u l e n c e - c o r r e c t e d b y t h e T C c u r v e p r o c e d u r e , a r e d e m o n s t r a t e dg r a p h i c a l l y . T h e i n f l u e n c e o f v a r i o u s f a c t o r s o n s l u rr y r h e o l o g y i s d i sc u s s e d , a n d i t i s s h o w n t h a t as i n g l e s l u n ' y c a n e x h i b i t m a n y d i f f e r e n t r h e o l o g i c a l n a t u r e s , d e p e n d i n g o n l y o n t h e c o n c e n t r a t i o na n d s i z e d is t r ib u t i o n o f th e s o l i d s . T h i s h a s i m p o r t a n t i m p l i c a t i o n s i n m i n e r a l p r o c e s s e s s u c h a sg r i n d i n g a n d d e n s e m e d i u m s e p a r a t i o n .

* Corresponding author.030 1-7 516 /96 /$ 15 .0 0 1996 Elsev ier Science B .V. Al l r igh ts reservedS S D I 0 3 0 1 - 7 5 1 6 ( 9 5 ) 0 0 1 0 1 - 8


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104 F .N . Sh i, T .J. N ap ie r -M unn / Int . J . Mine r . Proc e ss . 47 (1996 ) 10 3 - 12 3

I . I n t r o d u c t i o n

Se ve r a l s tud ie s ha ve a t t e s te d to the impor ta nc e o f s lu r r y r he o logy in the pe r f o r ma nc eo f mine r a l a nd c oa l p r oc e s s ing un i t ope r a t ions ( Kl impe l , 1982, 1983 ; Ka w a t r a a ndEis e le , 1988 ; M oy s , 1989 ; Fue r s te na u e t a l. , 1990 ; Na p ie r - M unn , 1990 ; Ho r s le y e t al .,1992 ) . Two i s s ue s a r i s e in s uc h inve s t iga t ions :

O b t a i n i n g r e l i ab l e m e a s u r e m e n t s o f s l u rr y r h e o l o g y , a n d Th e de pe n de n c e o f s lu r r y r he o logy on im por ta n t p r ope r t i e s o f s lu rr i e s, s uc h a s s o lid s

c onc e n t r a t ion a nd s iz e d i s t r ibu t ion .A ne w m e tho d o f ob ta in ing a f u l l f low c u r ve f o r s lu rr i e s u s ing a n indus t r i a l on - l ine

v i s c ome te r i s de s c r ibe d by the p r e s e n t a u tho r s in a n a s s oc ia te d pa pe r ( Sh i a nd Na p ie r -M unn , 1996 ). I n the p r e s e n t pa pe r , we d i s c us s a mo de l o f rhe o logy wh ic h a l lows thef low c u r ve to be p r e d ic te d f r om s lu r r y p r ope r t i e s , ba s e d on p r e d ic t ing the ou tpu t r e a d ingo f t h e v i s c o m e t e r .T h e r e a re a n u m b e r o f i n c en t i v e s fo r t h e d e v e l o p m e n t o f su c h a m o d e l . F o r e x a m p l e ,i t i s impor ta n t to unde r s ta nd how a l t e r a t ions in s lu r r y p r ope r t i e s l e a d to c ha nge s inr h e o l o g i c a l ty p e , s i n c e s u c h c h a n g e s a r e k n o w n t o a f f e c t as p e c ts o f t h e p e r f o r m a n c e o fun i t ope r a t ions s uc h a s g r ind ing a nd de ns e me d ium s e pa r a t ion . A ls o , the r e i s a g r e a tbody o f e x i s t ing da ta de s c r ib ing a va r ie ty o f un i t ope r a t ions in t e r ms o f s lu r r y p r ope r t i e s ,bu t wi thou t a s s oc ia te d r he o log ic a l in f o r ma t ion ; i t wou ld be he lp f u l to in f e r the r he o logyin s uc h c a s e s . F ina l ly , a qua n t i t a t ive c o r r e la t ion f o r r he o logy in t e r ms o f s lu r r yp r ope r t i e s wou ld a dd s ubs ta n t i a l ly to the u t i l i ty o f p r oc e s s mode l s a nd c on t r o l s y s te m sinc o r po r a t ing v i s c os i ty o r r he o logy ; i t wou ld a s s i s t in de c oup l ing the e f f e c t s o f v i s c os i tya n d s o l i d s c o n c e n t r a t i o n o n p e r f o r m a n c e ( s i n c e t h e s e p r o p e r t i e s c a n b e m o d i f i e di n d e p e n d e n t l y o f o n e a n o t h e r in s o m e c i r c u m s t a n c e s , t h u s a l l o w i n g b e t t e r c o n t ro l o f t h ep r o c e s s ) , a n d a l s o p e r m i t p r o c e s s p e r f o r m a n c e t o b e p r e d i c t e d f r o m s i m p l e s l u r r yp r ope r t i e s .

C o n s i d e r a b l e e f f o r t h a s b e e n e x p e n d e d i n t h e p a s t o n t h e d e v e l o p m e n t o f v i s c o si t ym o d e l s f o r s u s p e n s i o n s . R u t g e r s ( 1 9 6 2 ) a n d J i n e s c u ( 1 9 7 4 ) b o t h r e v i e w e d o v e r o n ehund r e d a r t i c l e s de s c r ib ing s uc h mo de l s . M os t o f the s e p r e d ic te d on ly the re la t ivev i s c o s i t y o f s u s p e n s i o n s a s a f u n c t i o n o f s o l i d s v o l u m e f r a c t i o n . T w o p r o b l e m s a r ea ppa r e n t wi th th i s a pp r oa c h . F i r s t ly , the s o l id s vo lume f r a c t ion i s no t the on ly f a c to rwh ic h a f f e c t s the r e la tive v i s c os i ty o f s u s pe ns ions , a l though i t i s the m a jo r f a c to r . The s ee qua t ions the r e f o r e f i t t e d we l l the da ta tha t the a u tho r s p r e s e n te d , bu t o f t e n ga ve poo rp r e d ic t ions in o the r c a s e s . Se c ond ly , i t is c l e a r tha t the a p pa r e n t v i s c os i ty i t s e l f i s no t theo n l y r h e o l o g i c a l p r o p e r t y a f f e ct i n g m i n e r a l p r o c e s s p e r f o r m a n c e . T h e r h e o l o g i c a l n a t u reo f the s lu r r y ( Ne w ton ia n , d i l a ta n t o r p s e udop la s t i c , a nd the p r e s e nc e a nd va lue o f a y ie lds t r e s s ) a l s o ha s a s ign i f i c a n t in f lue nc e on the p r oc e s s . The c u r r e n t ly a va i l a b le v i s c os i ty -s o l id s f r a c t ion e qua t ions c a n on ly p r e d ic t the v i s c os i ty va lue a t a f ixe d s he a r r a te ; the ya r e ge ne r a l ly no t s t r uc tu r e d to p r e d ic t the v i s c os i t i e s a t a r a nge o f s he a r r a te s a nd thusthe f u l l f low c u r ve s .

The De be x on - l ine s lu r r y v i s c ome te r , de s c r ibe d in the a s s oc ia te d pa pe r , inc o r po r a te sa s imp le c y l ind r ic a l bobb in wi th c on ic a l e nds , r o ta te d a t a c on t r o l l e d s pe e d by a DCm i c r o m o t o r o r s t e p p e r m o t o r in a b a f f l e d c u p . T h e s l u rr y f lo w s i n h o m o g e n e o u ss us pe ns ion f r om the p r oc e s s , th r ough the c up a nd ba c k to the p r oc e s s . The r e ta r d ing


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106 F . N . Sh i, T . J. N a p i e r - M u n n / l n t . J . M i n e r . P r o c e s s . 4 7 ( 1 9 9 6 ) 1 0 3 - 1 2 3

D ata used in F ig . 1 i nc lude o ne Ne wto n ian f l u id (50 cS o i l ), one d i l a t an t s l u r ry ( af e r r o si l ic o n d e n s e m e d i u m s u s p e n s i o n o f R D 2 .8 ) , a n d t w o p s e u d o p l a s t i c s l u rr i es w i thy i e l d v a l u e s ( a g r o u n d p r o d u c t f r o m t h e E m u g o l d m i n e , 1 . 5 R D , a n d a g r o u n d p r o d u c tf rom the H e l lye r base me ta l mine , 2 .8 RD ) . The f i tt i ng exe rc i se i n F ig . 1 i nd i ca t e s t hef o l l o w i n g t w o c l e a r t re n d s :

T h e t h i r d - o r d e r p o l y n o m i a l e q u a t i o n f i t s t h e m e a s u r e d d a t a , b o t h N e w t o n i a n a n dn o n - N e w t o n i a n f l o w , v e r y w e l l . T h i s s u g g e s t s t h a t t h e a n g u l a r v e l o c i t y o f t h e b o b b i ni s t he dom inan t f ac to r con t ro l l i ng the shape o f the p lo t s , wh ich can b e we l l desc r ibedb y t h i s e q u a t i o n f o r m .Each se t o f da t a r equ i r e s i nd iv idu a l coe f f i c i en t s to desc r ibe t he r e l a t i on be tw een them e a s u r e d m V a n d t h e a n g u l a r v e l o c i t y , w h i c h i n t u r n s u g g e s t s t h a t s l u r r y p r o p e r t i e sd e t e r m i n e t h e c o e f f ic i e n t s o f t h e p o l y n o m i a l e q u at i o n .T w o f a c t o r s c o n t r o l li n g t h e D e b e x v i s c o m e t e r o u t p u t r e a d i n g s m u s t b e a c c o u n t e d f o r :

t he bobb in mechan ica l ac t i on and , sub jec t t o t he bobb in shea r ing e f f ec t , pa r t i c l eh y d r o d y n a m i c i n t e r a c t i o n s d u r i n g m e a s u r e m e n t . W e h a v e s e e n t h a t t h e b o b b i n a c t i o n i nr e l at io n t o t h e m V r e a d i n g s c a n b e d e s c r i b e d b y t h e t h i r d - o rd e r p o l y n o m i a l e q u a ti o n , b u tt h e p a r t i c l e d y n a m i c i n t e r a c t i o n s a r e m o r e c o m p l e x . T h e p r e s e n t w o r k w a s d i r e c t e d t oe x p l o r i n g t h e r e l a ti o n s h i p b e t w e e n t h e c o e f f i c i e n t s o f t h e p o l y n o m i a l e q u a t i o n a n d s l u rr yp r o p e r t i e s . T h e f o l l o w i n g i n i t i a l p h e n o m e n o l o g i c a l a s s u m p t i o n s w e r e m a d e i n d e v e l o p -ing th i s mode l :

Co ef f i c i en t a 0 in Eq . 1 i s on ly de t e rm ined by a va r i ab l e wh ich i s re l a t ed t o t he y i e lds t re s s o f t h e s l u r ry a n d t h e r e f o r e s t r o n g l y r e f le c t s t h e e f f e c t o f p a r ti c l e h y d r o d y n a m -ics. MVo i s t h e r e f o r e a b a s e v a l u e u p o n w h i c h t h e m V r e a d i n g s d e v e l o p .

Co e f f i c i en t a 1 i s a l so a func t ion o f the hy dro dy nam ic in t e r ac t ions o f t he pa r t i c le s .So l id s vo lume f r ac t ion , pa r t i c l e s i ze , s i ze d i s t r i bu t ion , pa r t i c l e shape , chemica lc o n d i t io n s a n d s l u r r y t e m p e r a t u r e m a y a f f e c t t h e i n t e n s it y o f th e s e i n t e r a c ti o n s .

C o e f f i c i e n t a z may a l so be a f f ec t ed by pa r t i c l e i n t e r ac t ions . W i th t he bobb in ac t ionge t t i ng s t ronge r in t he quadra t i c t e rm , how ever , t he e f f ec t o f t hese i n t e r ac t ions wi l lb e c o m e r e l a t i v e l y w e a k e r , t h o u g h t h e y s t i l l h a v e t o b e c o n s i d e r e d .

W i th bobb in ro t a t ion a s t rong func t ion in t he cub ic t e rm, pa r t i c l e i n t e r ac t ions may bei g n o r e d a n d c o e f f i c i e n t a 3 m a i n l y r e f l e c t s th e m e c h a n i c a l a c t io n o f t h e b o b b i n .As a sum m ary , F ig . 2 i l l u s t ra t e s t he gene ra l l og i c o f t he mod e l s t ruc tu re , wh ich

c o m b i n e s t h e b o b b i n m e c h a n i c a l a c t i o n a n d p a r t i c l e h y d r o d y n a m i c i n t e r a c t i o n s t op r e d i c t th e D e b e x v i s c o m e t e r r e a d i n g . S e m i - e m p i r i c a l e x p r e s s i o n s h a v e b e e n f o u n d t orep resen t t he func t iona l i t i e s i l l u s t r a t ed i n F ig . 2 .2.2. Modelling the coefficients in Eq. 12.2.1. Hydrodynamic term

T h e g e n e r a l h y d r o d y n a m i c b e h a v i o u r o f th e s l u r ry i s r e p r e s e n t e d b y a t e r m w h i c h i s af u n c t io n o f v o l u m e s o l i d s c o n c e n t r a t io n , p a r t ic l e s i z e a n d s l u r r y t e m p e r a t u r e .

A n e m p i r i c a l f o r m s i m i l a r t o M o o n e y ' s r e l a t i o n s h i p ( M o o n e y , 1 9 5 1 ) w a s a d o p t e d a sthe bas i s o f t h i s t e rm, i n wh ich so l id s vo lu m e f r ac t ion i s a ma jo r f ac to r :

rl~ = e x p 1 ----k'M4~ ( 2 )


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F.N. Shi, T.J. Napier-Mu nn / lnt. J. Miner. Process. 47 (1996) 10 3-1 23 10 7M V : a 0 + a l ~ + 8 2 ~ 2 + 8 3 ~ '-).

1 1 1 1

B o b b i n m e c h a n i c a l a c t i o nW e a k b S t ro n g

P a r t i c l e h y d r o d y n a m i c i n t e r a c t io n sS t ro n g ~ W e a k

w h er e ~ = so l ids vo lume f r ac tion ,P = par t ic le s ize,

T = s l u r r y t e m p e r a t u r e ,Q = b o b b i n a n g u l a r v e l o c i t y

Fig. 2. The structure of the mo del com bining bobbin m echanical action and particle hydrodynamic interac-tions.

w h e r er/r =4,=k M =

t h e r e l a ti v e v i s c o s i t y (r a t i o o f s lu r r y v i s c o s i t y t o c a r r y i n g l i q u i d v i s c o s i t y ) w h i c hi s i n a f u n c t i o n a l r e l a t i o n s h i p w i t h t h e D e b e x r e a d i n g ( m V ) ., , ; o l i d s v o l u m e f r a c t i o n .a fu n c t i o n o f th e m a x i m u m a t t ai n a b l e s o l i ds v o l u m e f r a c t io n , f m a x, w h i c hd e p e n d s o n t h e p a r t i c l e s i z e d i s t r i b u t i o n , p a r t i c l e s h a p e , a n d s l u r r y t e m p e r a t u r e .

T h e c o n s t a n t 2 .5 in M o o n e y ' s e q u a t i o n ( w h i c h a r is e s f r o m E i n s t e i n ' s e q u a t i o n f o rd i l u t e s u s p e n s i o n s o f s p h e r e s ) i s in c o r p o r a t e d i n f i t ta b l e p a r a m e t e r s i n t h e f i n a l m o d e l .k M is s tr u c t u r e d t o b e a f u n c t i o n o f t e m p e r a t u r e a n d p a r t i c l e s i z e . T h e t e m p e r a t u r e e f f e c ti s m o d e l l e d u s i n g J i n e s c u ' s r e l a t i o n ( J i n e s c u , 1 9 7 4 ):

r / = a e x p ( - b T ) ( 3 )w h e r e a a n d b a r e p a r a m e t e r s , a n d T i s t h e te m p e r a t u r e ( C ) . T h e p a r t ic l e s i z e i sm o d e l l e d a s a s i m p l e e x p o n e n t i a l f u n c t i o n o f a n a r b i tr a r y s i z e v a r ia b l e , i n i ti a l ly t a k e n t ob e t h e p e r c e n t p a s s i n g 3 8 / z m , " 3 8 . C o m b i n i n g t h e s e re l a t io n s a n d r a t i o n a l is i n gp a r a m e l e r s s u g g e s t s :

H D = e x p 1 - - ~ b Pc ~ e x p ( C 3 T ) ( 4 )w h e r e H D i s t h e h y d r o d y n a m i c t e r m , i n a r b i tr a r y u n i ts , a n d C 2 , C 3 a r e p a r a m e t e r s t o b ee s t i m a t e d f r o m d at a. ( H D c a n b e m a d e d i m e n s i o n l e s s b y n o r m a l i s i n g T t o s o m es t a n d a r d t e m p e r a t u r e , s u c h a s 2 0 .2 C , t h e te m p e r a t u r e a t w h i c h w a t e r h a s a v i s c o s i t y o f1 m P a . s , b u t t h is i s r e a l l y o n l y a n a r t e f a c t a n d h a s t h e r e f o r e b e e n i g n o r e d . )


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10 8 F . N . S h i, T . J. N a p i e r - M u n n ~ I n t . J . M i n e r . P r o c e s s . 4 7 ( 1 9 9 6 ) 1 0 3 - 1 2 3

2 . 2 . 2 . C o e f f i c i e n t a oT h e c o e f f i c i e n t a 0 in E q . 1 i s a s s u m e d t o b e re l a t e d t o t h e y i e l d s t r e s s o f th e s l u r r y .

T h e y i e l d s t r e s s i s d u e t o th e d e v e l o p m e n t o f s t r u c t u r e b e t w e e n t h e p a r t ic l e s , a n d m u s tt h e r e fo r e a l s o b e a f u n c ti o n o f h y d r o d y n a m i c p r o p e r t i e s , a s w e l l a s th e c h e m i c a le n v i r o n m e n t . T h e l a t t e r i s n o t m o d e l l e d e x p l i c i t ly b e c a u s e o f i ts c o m p l e x i t y , b u t it i se x p e c t e d t h a t s u c h e f f e c t s w i l l b e r e f l e c t e d i n t h e v a l u e s o f th e m o d e l p a r a m e t e r s t a k e nb y p a r t i c u l a r s l u r r y s y s t e m s , a 0 w i l l th e r e f o r e b e m o d e l l e d s i m p l y a s :

a 0 = C , ( H D - 1 ) ( 5 )

2 . 2 .3 . C o e f f i c i e n t a tT h e l i n e a r t e r m o f a n g u l a r v e l o c i ty i n E q . 1 i s b e l i e v e d t o b e a c o m b i n e d e f f e c t f ro m

t h e b o b b i n s h e a r i n g a c t i o n a n d t h e p a r t i c le h y d r o d y n a m i c s . C o e f f i c i e n t a I i s t h e r e f o r em o d e l l e d a l s o u s i n g t h e h y d r o d y n a m i c t e r m :

a 1 = C 4 H D ( 6 )

2 . 2 .4 . C o e f f i c i e n t a zI t i s a s s u m e d t h a t c o e f f i c i e n t a 2 is a fu n c t i o n o f s o l i d s v o l u m e f r a c t i o n a n d p a r t i c l e

s i z e , y e t in c o m p a r i s o n w i t h t h e q u a d r a t i c t e r m o f a n g u l a r v e l o c i t y , t h e e f f e c t s o f p a r t i c l ei n t e ra c t io n i s w e a k e r . T h e r e f o r e a 2 is m o d e l l e d a s

a 2 = C 5 ~ b P 3 8 ( 7 )

2 . 2 . 5 . C o e f f i c i e n t a sW i t h b o b b i n r o t a t i o n i n a v e r y s t r o n g a c t i o n i n t h e c u b i c t e r m , p a r t i c l e i n t e r a c t i o n s

m a y b e i g n o r e d a n d c o e f f i c i e n t a 3 m a i n l y r e f l e c ts t h e b o b b i n m e c h a n i c a l a c ti o n .a 3 = C 6 ( 8 )

C l , C a , C 5 , C 6 a r e s y s t e m p a r a m e t e r s t o b e d e t e r m i n e d f r o m d a t a .2 .3 . T h e f i n a l m o d e l

E q . 1 f o r t h e p re d i c t io n o f t h e D e b e x m V o u t p u t f o r a g iv e n s l u r ry a n d b o b b i n s p e e dc a n n o w b e w r i t t e n :

m V = C I ( H D - 1 ) + C n H D O + C s ~ bP 3 s /2 2 + C6~ '~ 3 ( 9 )T h i s m o d e l w a s f i t te d s u c c e s s f u l l y t o a n u m b e r o f d a t a s e t s , b u t i n t e s t i n g it w i t h a w i d er a n g e o f s lu r r y t y p e s i t b e c a m e a p p a r e n t t h a t t h e d e s c r i p t i o n o f p a r t i c l e s i z e b y a s in g l ev a r i a b le ( p e r c e n t p a s s i n g 3 8 # m ) w a s t o o r e s tr ic t iv e , a n d t h e r e w a s v a l u e i n r e p r e s e n t -i n g s iz e d i s tr i b u t i o n s b y t w o v a r i a b l e s , t h u s a c c o u n t i n g f o r b o t h t h e s c a l e a n d l o c a t i o n o ft h e d i s t r ib u t i o n . A n u m b e r o f o p t i o n s w a s t r ie d , i n c l u d i n g f o r e x a m p l e t h e tw op a r a m e t e r s o f t h e R o s i n - R a m m l e r f u n c t io n , b u t t h e b e s t r e s u lt s w e r e o b t a in e d u s i n gs i m p l y P 2 0 a n d P 8 0 ( t h e 2 0 % a n d 8 0 % p a s s i n g s iz e s r e s p e c t i v e ly , e x p r e s s e d i n r a m ) .


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T r i a l a n d e r r o r w a s u s e d t o f i nd th e b e s t f o r m i n w h i c h t o in c o r p o r a t e P 2 0 a n d P 8 0 ,w i t h t h e f o l l o w i n g r e s u l t :

m V = C I ( H D - 1 ) + C 4H D g 2 + C 5 ~ 8 0 ~'~2 -Jr C 6~ ( ~ 3 ( 1 0 )w h e r e ( 1 )I 3 = e x p _ . P 2 0 . C ~ e x p . C 3 T . ( 1 1 )a n d4 ,TOP 2 0P 8 0C 1 C 6

= v o l u m e so l i d s c o n c e n t r a t io n ( p r o p o r t i o n )= t e m p e r a t u r e ( C )= b o b b i n a n g u l a r v e lo c i ty ( r a d . s - a )= 2 0 % p a s s i n g s i ze o f s o l id s ( m m )= 8 0 % p a s s i n g s i ze o f s o l id s ( m m )= m o d e l p a r a m e t e r s to b e d e t e r m i n e d e x p e r i m e n t a l l y f o r p a r t ic u l a r s lu r r ie s o r:du r ry t yp es .

E q s . 1 0 a n d 11 r e p r e s e n t t h e fi n a l m o d e l f o r p r e d i c t in g t h e D e b e x i n s t r u m e n t r e a d in g .T h e f l o w c u r v e f o r t h e s l u r r y , a n d t h e l o c a l a p p a r e n t v i s c o s i t y , c a n t h e n b e o b t a i n e d b ya p p l y i n g t h e c a l i b r a t io n a l g o r i th m d i s c u s s e d i n t h e a s s o c i a t e d p a p e r (a s d i s c u s s e d f u r t h e rb e l o w ) .2.4. Fitting the parameters

I n o r d e r t o u s e t h e m o d e l , t h e s i x p a r a m e t e r s C 1 - C 6 m u s t b e e s t i m a t e d f r o m d a t a .D a t a o b t a i n e d f r o m m e a s u r e m e n t s o f g r i n d i n g s lu r r ie s in A b e r f o y l e R e s o u r c e s ' H e l l y e rb a s e m e t a l c o n c e n t r a t o r ( R i c h m o n d a n d L a i , 1 9 8 8 ) w e r e u s e d i n it ia l ly t o t e s t t h e m o d e l .S i x s ur w~ ys ( t w o o f t h e m r e p l ic a t e s ) w e r e m a d e a r o u n d t h e 4 .5 7 6 . 1 0 m p r i m a r y b a l lm i l l , a n d f o u r a r o u n d t h e l e a d r e g r i n d t o w e r m i l l . T h e s u r v e y s w e r e c o n d u c t e d u n d e rd i f f e r en t g r ind ing c ond i t i ons ove r a pe r iod o f s eve ra l days , i n Ju ly 1992 . Th e s lu r r i e sm e a s u r e d b y t h e v i s c o m e t e r t h e r e f o r e d i f f e re d s u b s t a n t i a l ly i n th e i r p r o p e r t ie s ( s e ecap t ion to F ig . 3 ) .

T h e D e b e x v i s c o m e t e r w a s u s e d t o m e a s u r e t he v i s c o s i ty o f e a ch s l u rr y. S a m p l e sf r o m t h e b a l l m i l l f e e d , b a l l m i l l d i s c h a r g e , t o w e r m i l l f e e d a n d t o w e r m i l l d i s c h a r g ew e r e t a k e n d u r i n g t h e s u r v e y s a n d f e d t o t h e s e l f - c o n t a i n e d c i rc u l a ti n g s y s t e m o f t h ev i s c o m e t e r f o r v i s c o s i ty m e a s u r e m e n t . T h e s l u r ry d e n s i t ie s o f e a c h s a m p l e w e r em e a s u r e d w i t h a M a r c y G a u g e , a n d t h e s l u r r y t e m p e r a t u r e w a s m e a s u r e d u s i n g a d i g i t a lt h e r m o m e t e r . T h e s l u rr y d e n s it i e s w e r e c o n v e r t e d t o th e s o l i d s v o l u m e f r a c ti o n b y t a k i n gthe so l id s RD as 4 .5 fo r t he ba l l mi l l c i r cu i t and 5 .3 fo r t he t ower mi l l c i r cu i t ( based ona v e r a g e s o f m e a s u r e d v a l u e s ). T h e s o l i d s w e r e s i z e d b y w e t s c r e e n i n g a n d c y c l o s i z i n g .

T h e p a r a m e t e r s C I - C 6 i n equa t ions 10 and 11 were e s t ima ted us ing a non- l i nea rf it ti n g p r o g r a m d e v e l o p e d a t t he J K M R C ( W h i t e n, 1 97 2 ), N L F M B . T h i s p r o g r a mi m p l e m e n t s a L e v e n b e r g - M a r q u a r d t l e a s t - s q u a r e s m e t h o d u s i n g n u m e r i c a l d e r i v a t i v e s


8/21

1 1 0 F.N . Sh i, T .J . N ap ie r -M unn / In t. J . Mine r . P roc e ss . 47 (1996 ) 10 3 - 12 3

T a b l e 1P a r a m e t e r s o f t h e m o d e l w i t h t h e i r s t a n d a r d d e v i a t i o n s ( H e l l y e r d a ta ) . D a t a S D . 1 .5 5P a r a m e t e r V a l u e s S .D . S D . ( % o f v a l u e )C t 1 . 1 1 6 0 . 0 7 7 6 . 9C 2 - 0 . 1 2 9 8 0 . 2 2 1 0 - 2 1 .7C 3 - 0 . 4 1 3 6 1 0 2 0 . 3 3 1 0 3 8 .0C 4 0 . 4 9 8 3 X 1 0 t 0 . 2 0 1 0 2 4 .0C 5 0 . 1 8 6 3 ) < 1 0 - 3 0 . 5 7 1 0 - 5 3 .1C 6 0 . 6 4 9 6 1 0 - 5 0 . 5 6 1 0 - 6 8 . 6

w i t h s o m e c o n t r o l o f d e r i v a t i v e a c c u r a c y . I t r e t u r n s t w o c r i t e r ia o f t h e f i tt i n g q u a l it y : t h ep a r a m e t e r S . D . ( s t a n d a r d d e v i a t i o n ) w h i c h i s a m e a s u r e o f p r e c i s io n o f th e f i tt e dp a r a m e t e r v a l u e s , a n d t h e d a t a S . D . w h i c h i s a s t a ti s ti c a l m e a s u r e o f a m o d e l ' s t o t a l" g o o d n e s s o f f i t " .

T h e p a r a m e t e r v a l u e s a r e li s te d i n T a b l e 1 , a n d t h e o b s e r v e d a n d p r e d i c t e d m Vr e a d i n g s a r e p l o t t e d i n F i g . 3 ( th e r a n g e s o f f a c t o r v a l u e s a r e a l s o l is t e d in F i g . 3 ) . T h eq u a l i t y o f th e f i t i s se e n t o b e g o o d .

3 . M o d e l t e s t i n g

T o t e s t t h e u t il i ty o f th e m o d e l , i t w a s a p p l i e d t o v i s c o s i t y d a t a o b t a i n e d o n a v a r i e t yo f s l u r ri e s b y s e v e r a l i n v e s t i g a t o r s u s i n g t h e D e b e x v i s c o m e t e r .

6 0 , , , , J , E . , ,o5 0

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o0 1 0 2 0 3 0 4 0 5 0 6 0

M e a s u r e d m YF i g . 3 . A C o m p a r i s o n o f t h e D e b e v is c o m e t e r r e ad in g s p r e d i c t e d f r o m t h e m o d e l w i t h t ho s e me a s u re d f r o mt h e H e l l y e r s u r v e y s ( u s i n g t h e H e l l y e r p a r a m e t e r s , T a b l e l ) . T o t a l 3 1 s e t s o f b a l l m i l l a n d t o w e r m i l l s a m p l e sg i v i n g 3 7 2 m e a s u r e m e n t p o i n t s . S o l i d s S G 4 . 5 f o r b a l l m i l l s l u rr y , 5 .3 f o r t o w e r m i l l s l u rr y . S o l i d s v o l u m ef r a c t i o n s f r o m 0 . 2 0 to 0 .5 4 . P 8 0 f r o m 0 . 0 31 t o 0 . 2 7 9 m m , P 2 0 f r o m 0 . 0 0 3 t o 0 . 0 6 0 m m . S l u r r y t e m p e r a t u r ef r o m 1 6 C t o 4 0 C . B o b b i n r p m f r o m 2 0 t o 1 0 0 0 .


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F.N . Sh i, T .J . Nap i er -M unn l i n t . J . Miner . Process . 47 (1996) 103 -123 111

3 .1 . C o p p e r o r e f r o m a g r in d i n g c i r c u i tD a t a w e r e o b t a i n e d b y C a s t r o ( 1 9 9 0 ) w h o m a d e 2 2 s e t s o f m e a s u r e m e n t s o n

h y d r o c y c l o n e f e e d in t h e M o u n t I s a C o p p e r C o n c e n t r a to r g ri n d in g c i r c u it u s in g t h eDebex i tns t rument in March 1989. Slur ry and sol ids dens i ty , t empera ture and par t ic les iz e w e r e a l s o m e a s u r e d . S i z i n g w a s c o n d u c t e d u s i n g s c r e en s ( + 3 8 / x m ) a n d t h e L e e d sa n d N o r t h r u p M i c r o t r a c P a r ti c le S i z e A n a l y z e r ( - 3 8 / zm ) . T h e s i z in g d a ta f r o m t h eM i c r o t r a c A n a l y z e r w e r e p r o c e s s e d b y a M i c r o t r a c - s i e v e i n t e r - c o n v e r s i o n p r o c e d u r e .Th e so li ds vo l u me f rac t i ons , P2 0s and P8 0s w ere ca lcu l a t ed f rom t hese da t a.

The rheo l ogy mode l w as t hen app l i ed t o t hese da t a w i t h t he s i x pa r ame t e r va l uesde t e rmi ned f rom t he H e l l ye r su rveys kep t cons t an t ( no f i t t i ng w as i nvo l ved i n t heapp l i ca t i on ) . The ca l cu l a t ed mV s a r e p l o t t ed aga i ns t t he measured ones f rom t he 22 se t so f t e s ts w i t h 215 d a t a po i n t s in F i g . 4 . The p r ed i c t i on e r ro r s a re gene ra l l y l e ss t han 15%r e la t iv e . T a k i n g i n t o c o n s id e r a ti o n t h e D e b e x v i s c o m e t e r m e a s u r e m e n t e r r o r o f 1 3 .5 %re l a t i ve i n t he i ndus t r i a l env i ronment ( t w i ce t he S . D . o f r ep l i ca t e measuremen t s a tH e l l ye r ) (Sh i , 1994) , t he p r ed i c t i ons a r e s een t o be s a t is f ac t o ry . I t is w or t h emph as i s i ngt h a t t h e s a m e s e t o f p a r a m e t e rs d e t e r m i n e d f r o m H e l l y e r l e a d - z i n c - c o p p e r s l u r ri e s a reappropr i a t e f o r MIM copper s l u r r i e s , sugges t i ng t ha t such s l u r r i e s exh i b i t s i mi l a rr h e o l o g i c a l b e h a v i o u r .3 .2 . G o l d o r e f r o m a g r i n d in g c i r c u i t

S u r v e y s w e r e c o n d u c t e d i n t h e p r i m a r y a n d s e c o n d a r y g r i n d i n g c i r c u i t s o f t h e E m ugol d p l an t o f W es t e rn M i n i ng C o rpora t i on i n Wes t e rn A us t r a l ia . B u l k s am pl es o f s l u r ryw e r e r e t u r n e d t o t h e J K M R C w h e r e m e a s u r e m e n t s w e r e m a d e w i t h t h e D e b e x v i s c o m e -

3 5

0 Q D 2 5

o. Io

5

0 i i

0 5 10 15 20 25 30 35M e u u r e d m V

F i g . 4 . C o m p a r i s o n o f p r e d i c t e d viscometer o u t p u t w i t h a c t u a l measurements f o r M I M c o p p e r s l u rr ie s (u s i n gparameters determined from Hellyer surveys without re-fitting). Total 22 tests giving 215 measurement points.Solids SG 3.0. Solids volume fractions from 0.24 to 0.51. P80 from 0.258 to 1.34 ram, P20 from 0.004 to0.043 mm. Slurry temperature from 42C to 52C. Bobbin rpm f rom 100 to 1000.


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112 F.N. Shi, T.J. Na pier-M unn / ln t. J . Miner. Proc ess . 47 (1996 ) 10 3-1 233530

2520

1510

50

aD ~ ] .. , r , . , , , , .

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3530

2520

15

10

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b , . , , . . . .

/+/'~ *i i I L i i i i i L i i i

0 5 10 15 20 25 30 35Measured m V

Fig. 5. Comparison of predicted viscometer output with the actual me asurements for Emu gold slurries (a)using Hellyer parameters, (b) re-fit parameter C I only. Total 5 tests giving 50 measurement points. Solids SG2.7. Solids volume fractions from 0.11 to 0.29. P80 = 0.059, P20 = 0.0003 mm. Slurry temperature 20C.Bobbin rpm from 100 to 1000.

t er . F i g . 5 a s h o w s t h e p r e d i c te d m V r e a d i n g s u s i n g t h e H e l l y e r p a r a m e t e r s , c o m p a r e dwi th t hose ac tua l ly ob t a ined wi th t he i n s t rumen t .

I t i s o b v i o u s t h a t t h e m o d e l u s i n g t h e H e l l y e r p a r a m e t e r s c o n s i s t e n t l y u n d e r - p r e d i c t sthe r ead ing . The r eason was be l i eved to be t he e f f ec t o f t he h igh con ten t o f f i nes i n t heE m u s l u r r i e s . T h e P 2 0 e x t r a p o l a t e d f r o m t h e E m u s i z e d i s t r i b u t i o n d a t a i n d i c a t e s av a lu e o f 0 .3 m i c r o n c o m p a r e d w i th t he m i n i m u m P 2 0 o f 3 m i c r o n i n th e H e l l y e r t o w e rmi l l s l u r ry . The h igh con ten t o f ve ry f i ne pa r t i c l e s wou ld be expec t ed to i nc reases ign i f i can t ly t he y i e ld s t r e s s o f t he s lu rry . Pa ram e te r C l , wh ich i s a s sum ed to be r e l a t edto t he y i e ld s t r e s s (Eq . 10 ) , was t he re fo re r e - f i t t ed t o t he Emu da t a , keep ing the o the rpa rame te r s cons t an t . F ig . 5b shows the r e su l t s : t he ag reemen t i s exce l l en t . The r ev i sedva lue o f C~ ( toge the r w i th a l l t he pa ra m e te r va lues o f t he s lu r r i e s desc r ibed in th i spape r ) i s g iven in Tab le 2 . I t i s s een to be abou t t h r ee t imes t ha t o f t he He l lye r va lue ,i m p l y i n g a c o r r e s p o n d i n g d i f f e r e n c e i n p r e v a i l i n g y i e l d s t r e s s .3 .3 . D e n s e m e d i u m

T h e r h e o l o g y o f a w i d e r a n g e o f a t o m i s e d a n d m i l l e d f e rr o s i li c o n d e n s e m e d i u ms l u r r i e s w a s d e t e r m i n e d a t t h e J K M R C i n 1 9 9 0 u s i n g t h e D e b e x v i s c o m e t e r . T h ea t o m i s e d m a t e r i a l i s s p h e r o i d a l i n s h a p e a n d g e n e r a l l y e x h i b i t s l o w e r v i s c o s i t i e s f o r ag iven s lu r ry dens i ty and pa r t i c l e s i ze t han the i r r egu la r shaped mi l l ed ma te r i a l (Co l l i n se t a l ., 1974). S i z ing o f t he m a te r i a l was condu c ted us ing w e t s c r eens abo ve 38 mm andt h e M i c r o t r a c i n s t r u m e n t b e l o w 3 8 / x m ( w i t h a c o r r e c t i o n t o c o n f o r m t o t h e s c r e e ns iz ings) .3 . 3. 1 . M i l l e d f e r r o s i l i c o n

T h e v i s c o s it y o f S a m a n c o r m i l le d g r a d e s 2 7 0 D , 1 0 0D , 6 5 D a n d 4 8 D w a s m e a s u r e du s i n g t h e D e b e x v i s c o m e t e r ; 2 7 0 D i s t h e f i n e s t g r a d e , a n d 4 8 D t h e c o a r s e s t ( C o l l i n s e ta l., 1974). The m eas u rem en t s w ere m ade a t a r ange o f s lu r ry dens i t i e s fo r each g rade .


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1 1 4 F.N . Sh i, T .J. N ap i e r -M unn / l n t . J . Mine r . P roc e ss . 47 (1996 ) 10 3 - 12 3

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F i g . 6 . C o m p a r i s o n o f p r e d i c t ed v i s c o m e t e r o u t p u t w i t h th e a c t u a l m e a s u r e m e n t s f o r m i l l e d f e r r o s i l ic o ns l u rr i e s, ( a ) u s i n g p a r a m e t e r s d e t e r m i n e d f r o m t h e H e l l y e r s u r v e y s f o r f o u r F e S i g r a d e s , 2 4 s e t s d a t a o f s l u r r yd e n s i t i e s l e s s t h a n 3 0 0 0 k g / m 3 w i t h 1 9 2 m e a s u r e d p o i n t s ; ( b ) u s in g p a r a m e t e r s d e t e r m i n e d f r o m t h e H e l l y e rs u r v e y s f o r f o u r F e S i g r a d e s , 1 3 s e t s d a t a o f s l u r r y d e n s i t i e s g r e a t e r t ha n 3 0 0 0 k g / m 3 w i t h 1 0 4 m e a s u r e dp o i n t s ; ( c ) r e - f i t a l l p a r a m e t e r s t o t h e f o u r g r a d e s m i l l e d F e S i , 3 7 t e s ts w i t h 2 9 6 d a t a p o i n t s. S o l i d s S G 6 . 7 .S o l i d s v o l u m e f r ac t i o n s f r o m 0 .0 9 to 0 .4 3 . P 8 0 f r o m 0 . 0 3 7 t o 0 . 1 1 4 m m , P 2 0 f r o m 0 . 0 1 8 to 0 .0 3 2 m m .S l u r r y t e m p e r a t u r e f r o m 3 2 C t o 5 0 C . B o b b i n r p m f r o m 1 0 0 t o 8 0 0.

T h e m o d e l w a s f i r s t a p p l i e d t o t h e d a t a w i t h t h e s a m e s e t o f p a r a m e t e r s d e t e r m i n e df r o m t h e H e l l y e r d a t a ( T a b l e 1 ) . I t w a s f o u n d t h a t a t s l u r r y d e n s i t i e s l e s s t h a na p p r o x i m a t e l y 3 0 0 0 k g / m 3 ( 3 5 % s o l i d s b y v o l u m e ) th e pr e d ic t ed m V s f r o m a l l g r a d e st e s t e d w e r e i n g o o d a g r e e m e n t w i t h t h e m e a s u r e d o n e s ( r e f e r t o F i g . 6 a ) . A t s l u r r yd e n s i t ie s a b o v e 3 0 0 0 k g / m 3 , h o w e v e r , t h e p r e d ic t ed m V s w e r e c o n s i s t e n t l y l o w e r t h ant h e m e a s u r e d ( F i g . 6 b ) . T h i s s u g g e s t s t h a t a t h i g h d e n s i t y , d y n a m i c i n t e r a c t i o n s a m o n gt h e F e S i p a r t ic l e s a n d b e t w e e n t h e r o t a ti n g b o b b i n a n d t h e s l u rr y w e r e s t r o n g e r t h a nt h o s e o f t h e g r i n d i n g s l u r r i e s e n c o u n t e r e d i n t h e H e l l y e r c i r c u i t . T h e r e f o r e a l l s i xp a r a m e t e r s o f t h e m o d e l w e r e r e - f it te d t o t h e m i l l e d F e S i d a ta ( o n e s e t o f p a r a m e t e r s fo ra l l g ra d e s ) , i n c o r p o r a t i n g al l d e n s i t i e s i n c l u d i n g t h e + 3 0 0 0 k g / m 3 d a t a . T h e f i t t in gr e s u l t s a r e p r e s e n t e d g r a p h i c a l l y i n F i g . 6 c . T h e n e w p a r a m e t e r v a l u e s a r e s h o w n i n


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F.N . Sh i , T . J . Nap i er -Munn / l n t . J . Miner . Process . 47 (1996) 103-123 115

Tab l e 2 . I t i s c l ea r t ha t t he r e - f i t i s good , and i t i s l i ke l y t ha t t he mode l w i t h t hesep a r a m e t e r v a l u e s c a n b e u s e d t o p r e d i c t t h e r h e o l o g y o f a l l s u c h m i l l e d f e r r o s i l i c o nm e d i a ( u n l e s s c o n t a m i n a t e d b y m a t e r ia l o t h e r th a n F e S i ).3 . 3 .2 . A t o m i s e d f e r r o s i l i c o n

Th e v !is cositi es o f Sam anc or a t omi sed f e r ros i l i con g r ades C y c l on e 40 and C y c l on e 60w ere a l so measured . Th e mo de l w i t h the H e l l ye r pa r am e t e r s w as f i r st app l i ed t o t he da t a(w i t hou t r e - f i t t i ng o f any o f t he pa r ame t e r s ) . F i g . 7a show s t he r e su l t s . The re i s anobv i ous b i a s , t he p r ed i c t ed mV s be i ng cons i s t en t l y g r ea t e r t han t he measured ones a th i ghe r r ead i ngs .

Th e sph e ro i da l shape o f a t omi sed f e r ros i l icon sugges t s t ha t , s ince pa r ame t e r s C 4 andC 5 in t he m ode l (Eq . 10 ) a r e r e l a t ed t o t he pa r t i c le hyd rody nam i c i n t e r ac t i ons and t hecoa r se r [>a rtic le s i ze e f f ec t (P 80 ) , t hese t w o pa ram e t e r s shou l d be r e - f i t ted . Th i s w asd o n e , t h e o t h e r f o u r p a r a m e t e r s r e m a i n i n g u n c h a n g e d . T h e n e w v a l u e s a r e g i v e n i nTab l e 2 , and F ig . 7b show s t he f it t ing r e su l t s, w i t h good ag reem en t appa ren t be t w ee n t hepredic ted[ and measured values .3 . 4 . L i m e s t o n e s l u r r y

C a s t r o ( 1 9 9 0 ) a l s o m a d e v i s c o s i t y m e a s u r e m e n t s w i t h t h e D e b e x i n s t r u m e n t o nl i m e s t o n e s l u rr ie s w h i c h h e w a s u s i n g i n e x p e r i m e n t s w i t h h y d r o c y c l o n e s . D a t a f r o m 2 0of h i s te :g ts we re u t i l i sed in the presen t wo rk. Pa r t ic le s ize d i s t r ibut ion w as d eterm inedb y w e t s!ie vin g ( + 3 8 F m ) a n d th e M i c r o t r a c i n s tr u m e n t ( - 3 8 / x m ) , w i t h th e M i c r o t r a cda t a aga i n be i ng co r r ec t ed fo r con fo rm i t y w i t h t he s i ev i ng me asurem en t s . F i g . 8 show st he obse rved mV read i ngs fo r t hese l i mes t one s l u r r i e s vs t hose p r ed i c t ed by t he mode l .

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F i g . 7 . C o m p a r i s o n o f p r e d ic t e d v i s c o m e t e r o u tp u t w i t h t h e a c t u a l m e a s u r e m e n t s f o r a t o m i s e d f e r r o s il i co ns l u r r i e s, ( ~L ) u s i n g p a r a m e t e r s d e t e r m i n e d f r o m H e l l y e r s u r v e y s ; ( b ) r e - f i t p a r a m e t e r s C 4 a n d C 5 t o t h ea t o m i s e d F 'e S i C 4 0 a n d C 6 0 d a ta . T o t a l 1 2 te s t s g i v i n g 9 6 m e a s u r e m e n t p o i nt s . S o l id s S G 6 . 7 . S o l i d s v o l u m ef r a c ti o n s fi~ om 0 . 2 6 to 0 . 4 8 . P 8 0 f r o m 0 . 0 3 9 t o 0 .0 5 5 m m , P 2 0 f r o m 0 . 0 1 3 t o 0 .0 1 7 m m . S l u r ry t e m p e r a t u r ef r o m 3 7 C t o 5 0 C . B o b b i n r p m f r o m 1 0 0 to 8 0 0 .


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1 16 F.N . Sh i , T . J . Nap i er -Munn l i n t . J . Miner . Process . 47 (1996) 103-1234 0

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10 20 30 40M e a s u r e d m V

Fi g . 8 . Com parison of predicted viscometer output wi th the actual measurements for limestone slurries, ( a )calculated by parameters determined from Hellyer surveys w ithout re-fitting; (b) fit parameters for 16 testswith 160 data points; (c) fit parameters for 4 tests with fine size, hig h solids concentrations w ith 40 datapoints. Solids S G 2 . 7 . Solids volume fractions from 0.12 to 0.49 for ( b ) , 0 . 3 2 t o 0 .4 2 f o r (c ) . P 8 0 f r o m 0 . 3 9 to0 . 6 2 m m f o r ( b ) , 0 . 33 t o 0 . 4 5 m m f o r (c ). P 2 0 f r o m 0 . 0 0 0 6 t o 0 . 1 3 6 m m f o r ( b ), 0 .0 0 0 4 t o 0 .0 0 0 5 m m f o r ( c ).S l u r r y temperature from 21C to 3 0 C . B o b b i n rpm from 100 to 1000.

I t w a s f o u n d t h at w h e n t h e H e l l y e r p a r a m e t e r s w e r e a p p l i e d t o t h e l i m e s t o n e s l u r r i e s ,t h e p r e d ic t e d m V s w e r e c o n s i s t e n t l y l o w e r t h a n t he m e a s u r e d ( F i g . 8 a ) , i n d i c a t i n gd i f f e r e n t r h e o l o g i c a l b e h a v i o u r b e t w e e n t h e t w o s l u r r ie s . T h e m a j o r c h a r a c te r i s t ic o f t h el i m e s t o n e s lu r r y w a s t h e h i g h c o n t en t o f f i n e s ( a p p r o x i m a t e l y h a l f o f t h e da ta e x h i b i t e d aP 2 0 l e ss t ha n 1 m i c r o n , c o m p a r ed w i t h t h e m i n i m u m P 2 0 o f 3 m i c r o n in th e H e l l y e rs u r v e y s ) . A l l p a r a m e t e r s w e r e t h e n r e - f it t e d t o t h e 2 0 s e t s o f t e s t s, b u t th e r e s u l t s w e r es c a tt e r ed . I t w a s f o u n d t h a t t h e p o i n t s f r o m t h e f o u r t e s t s t h at w e r e t h e m o s t s c a t te r e dw e r e a s s o c i a t e d w i t h v e r y f i n e s iz e s ( P 2 0 a r o u n d 0 . 5 m i c r o n ) a nd v e r y h i g h s o l i d sc o n c e n t r a t i o n s (a b o u t 4 0 % s o l i d s b y v o l u m e ) . T h e s e f o u r d a ta s et s ( w i t h 4 0 d a t a p o i n ts )w e r e t h e r e f o r e p r o c e s s e d s e p a r a t e ly , w i t h o n e s e t o f p a r a m e t e r s fi t te d t o 1 6 te s t s, a n d as e p a r a te s e t o f p a r a m e t e r s f it t ed t o t h e f o u r r e m a i n i n g t es t s. T h e r e s u l t s a r e s h o w n i n


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F.N. Shi , T.J. Napier-Munn / Int . J. Miner. Process . 4 7 (1996) 10 3-123 117F i g . 8 b a n d c r e s p e c t i v e l y , b o t h d e m o n s t r a t i n g g o o d a g r e e m e n t b e t w e e n t h e p r e d i c t e da n d m e a s u r e d m V s . A l l t h e f i t t e d p a r a m e t e r v a l u e s a r e g i v e n i n T a b l e 2 .

T h e n e e d t o m o d i f y t h e m o d e l p a r a m e t e r s , a n d i n p a r t i c u l a r t o m a k e s p e c i a l p r o v i s i o nf o r t h e v e r y f i n e s l u rr i es a t h i g h c o n c e n t r a ti o n s , d e m o n s t r a t e s t h e d i f f e r e n t n a tu r e o ft h e s e l i m e s t o n e s l u rr i es t o t h e o t h e r s m e a s u r e d . I n s p e c t i o n o f T a b l e 2 s h o w s t h a t t h el i m e s t o n e p a r a m e t e r v a l u e s a r e v e r y d i f f e r e n t t o t h e o t h e r s l i s t e d i n T a b l e 2 ( a n d t om a n y o t h e r s t e s t e d b u t n o t r e p o r t e d h e r e ) . I t i s n o t k n o w n w h y t h i s s h o u l d b e s o , b u t i tm a y b e a t t r i b u t a b le t o d i f f e r e n c e s i n th e p h y s i c o c h e m i c a l p r o p e r t i e s o f t h e l im e s t o n e .3 . 5. D i s c u s s i o n o f t e s ts

A s u m m a r y o f th e p a r a m e t e r v a l u e s o b t a i n e d in t h e t e s ts i s g i v e n in T a b l e 2 . I t isc l e a r t h a t th e 6 - p a r a m e t e r m o d e l c a n b e f i tt e d w e l l t o a n y g i v e n d a t a s e t , a n d u s e ds u c c e s s f u l l y t o p r e d i c t th e m V i n s t r u m e n t o u t p u t f o r a g i v e n s e t o f c o n d i t io n s f o r t h ats l ur ry . T h e q u e s t i o n w h i c h a r i s e s is h o w t o c h o o s e a p p r o p r i a t e v a l u e s f o r t h e p a r a m e t e r sfo r o the r unmeasu red s lu r r i e s . I t i s r emarkab le , and s ign i f i can t , t ha t one se t o f va lues ( i nt h is c a s e o b t a i n e d f r o m l e a d - z i n c b a l l m i l l a n d t o w e r m i l l s lu r r ie s a t H e l l y e r ) s a ti s f a c to -r i l y d e s c r i b e s c o p p e r s l u r r i e s f r o m a s e c o n d s i t e ( M I M ) a n d , w i t h a c h a n g e t o o n l y o n epa rame te r t o accoun t fo r a l a rge r y i e ld s t r e s s , t o go ld s lu r r i e s f rom a t h i rd s i t e (Emu) .O n l y t w o o f th e s i x p a r a m e t e r s r e q u i r e d r e - fi t ti n g f o r th e a t o m i s e d f e r r o si l ic o n m e d i a(due pre ,sumab ly to t he d i f f e r ence i n shape ) . A l l t he pa rame te r s r equ i r ed r e - f i t t i ng fo r t hem i l l e d t e r r o s i l ic o n , b u t t h e v a l u e s t a k e n w e r e n o t g r e a t l y d i f f e r e n t to t h e H e l l y e r v a l u e s .T h e l i m e s t o n e p a r a m e t e r s w e r e h o w e v e r s i g n i f i c a n t l y d i f f e r e n t t o a l l t h e o t h e r s .

The mode l on ly accoun t s fo r va r i a t i ons i n s i ze d i s t r i bu t ion , so l id s concen t r a t i on andt e m p e r a t u r e . T h e r a n g e s o f t h es e v a r i a b l e s te s t ed ( o u t s i d e w h i c h e x t r a p o l at i o n is u n w i s e )w e r e :P a r ti c le s i ze P 8 0 : 4 0 - 1 3 0 0 / . t mP a rt ic le s iz e P 2 0 : 0 . 3 - 1 4 0 / x mS o li ds c o n c e n tr a ti o n , v / v : 0 . 0 9 - 0 . 5 4

T e m p e r a t u r e : 1 6 - 5 2 CI t i s a s e m i - e m p i r i c a l m o d e l , a n d d o e s n o t a c c o u n t e x p l i c i t l y f o r o t h e r v a r i a b l e s s u c h

as pa r t i c l e shape , ex t r em e va lues o f pa r t ic l e s i ze (pa r t i cu l a r ly f i nes ) , e l ec t ro chem ica lc o n d i ti o n s , o r c o m p l e x i n t e r a c t io n s o f th e s e v a r i a b l e s . I t i s th e p a r a m e t e r v a l u e s w h i c htake up these va r i a t i ons . I n pa r t i cu l a r i t i s be l i eved tha t e l ec t rochemis t ry , wh ich can bed o m i n a n t i n d e t e r m i n i n g s l u r r y r h e o l o g y u n d e r s o m e c o n d i t i o n s , i s r e s p o n s i b l e f o r s o m eo f t h e m a j o r c h a n g e s o b s e r v e d i n f i t t e d p a r a m e t e r v a l u e s .

I n p r a c t i c e , a s d e m o n s t r a t e d i n t h e s e r e s u l t s a n d o t h e r s w h i c h c o n t i n u e t o b ea c c u m u l a t e d b y t h e a u t h o r s a n d t h e i r c o l l e a g u e s , i t i s l i k e l y t h a t e a c h s l u r r y t y p ec o m m o n l y e n c o u n t e r e d i n m i n e r a l p r o c e s s i n g c a n b e d e s c r i b e d b y a s i n g l e p a r a m e t e r s e to v e r q u it e a w i d e r a n g e o f c o n d i ti o n s . O n c e t h e s e p a r a m e t e r s h a v e b e e n e s t i m a t e d , t h e yc a n b e u s e d w i t h s o m e c o n f i d e n c e i n o t h e r s i t u a t i o n s .


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118 F.N . Sh i , T . J . Nap i er -Munn / ln t . J . Miner . Process . 47 (1996) 103-1234 . P r e d i c t i n g s l u r r y r h e o l o g y u s in g t h e m o d e l - - v a l i d a t i o n

T h e m o d e l d i s c u s s e d t h u s f a r p r e d i c t s t h e m V o u t p u t o f t h e D e b e x i n s t r u m e n t f o r ag i ven s l u r ry t ype and se t o f cond i t i ons . Th i s i s o f l i t t l e va l ue , w i t hou t be i ng ab l e t oe s t i m a t e t h e c o r r e s p o n d i n g f l o w c u r v e f r o m t h e p r e d i c t e d m V r e a d i n g a t a r a n g e o fbobb i n speeds . Th i s i s done us i ng t he p rocedure desc r i bed i n t he a s soc i a t ed pape r ,i n c o r p o r a ti n g th e T C - c u r v e t u r b u l e n c e c o r re c t i o n m e t h o d ( S h i a n d N a p i e r - M u n n , 1 9 9 6) .The to ta l procedure i s i l lus t ra ted in Fig . 9 . Stage 1 i s the model f i t t ing , s tage 2 thepred i c t i on o f i n s t rumen t ou t pu t f r om t he p r e sen t mode l us i ng t he f i t t ed pa r ame t e r s ( o rany appropr i a t e pa r ame t e r s ) , and s t age 3 t he p roduc t i on o f t he shea r r a t e - shea r s t r e s sf l ow curve ( s ) .

I n o rde r t o demo ns t r a t e t he e f f i cacy o f the m ode l i n a l l ow i ng t he fu l l f l ow c urve t o beaccura t e l y e s t i ma t ed f rom t he p r ed i c t ed i ns t rumen t r ead i ng , F i g . 10 show s t he obse rvedand p r ed i c t ed f l ow curves fo r t w o qu i t e d i f f e r en t s l u r ry t ypes , a t spec i f i c dens i t i e s . Theobse rv ed po i n t s a r e t hose ca l cu l a t ed d i r ec t ly by ap p l y i ng t he TC -cor r ec t i on t o t he ac t ua lv i scom et e r mea surem en t , w h i l st t he p r ed i c t ed l i nes ar e t hose ob t a i ned by ap p l y i ng t heT C - c o r r e c t io n to t h e m e a s u r e m e n t p r e d i c te d b y t h e m o d e l f o r th a t s l u rr y . T h e a g r e e m e n ti n each case i s c l ea r l y good .

S i mi l a r ly , F ig . 11 show s t he f l ow curv es o f f ou r dens i t ie s o f 65D mi l l ed f e r ros i l i cond e n s e m e d i a, p r e d i c t e d b y t h e m o d e l f r o m p a r a m e t e r s o b t a in e d e x p e r i m e n t a l ly a t th eJK MR C i n 1990 (Tab l e 2 ) . The po i n t s a r e measuremen t s f r om d i f f e r en t f e r ros i l i consampl es , ob t a i ned ex pe r i m en t a l l y in 1995 . A ga i n , t he ag reem en t i s s a t is f ac t o ry , sugges t -i ng t ha t t he mode l i s good a t desc r i b i ng gene r i c s l u r ry t ypes .

5 . T h e n a t u r e o f s l u r r y r h e o l o g ySi mul a t i on o f s l u r ry rheo l ogy a s a f unc t i on o f va r i ous s l u r ry p rope r t i e s w as ca r r i ed

ou t us i ng t he mode l t o i l l u s t r a t e t he na t u r e o f t he e f f ec t s o f so l i ds concen t r a t i on and

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E xper iment a l Inpu t ne w des i r eddat a ( r pm, mY , cond i t ions ( bobb in r pm,temp erature, temp erature, sol idsso l ids vo lume vo lume f r ac tion , and P 8 0f r ac tion , and par t ic le and P 2 0 )s i z e d e te r m i n e d a sP 8 0 a n d P 2 0 )

V iscomet er geomet r yand ca l ib r a t ion da t a ,s l u r r y cond i t ions(densi ty , temperature)

Fig. 9. Procedurefor predictinga flow curve.


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F . N . S hi , T. J. N a p i e r - M u n n l i n t . J . M i n e r . P r o c e s s . 4 7 ( 1 9 9 6 ) 1 0 3 - 1 2 3 11 910 i i i

- - Mo de l p r e d i c t e dO EM U/1.5 D (measured. . . . . M o d e lprecllctod8 x He llyer/2.2 D (measured)ml, i

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0 50 100 150 200S h e a r r a t e ( e " l)

F i g . 1 0 . F l o w c u r v e s o f E m u g o l d s lu r r y a n d H e l l y e r t o w e r m i l l d is c h a r g e s lu r r y - - a c o m p a r i s o n o f t h ep r e d i c t io n o f t h e m o d e l a g a i n s t t h e a c t u a l m e a s u r e m e n t .

p a r t i c l e , ; i z e o n r h e o l o g y . T h e H e l l y e r s l u r r i e s a n d a s s o c i a t e d p a r a m e t e r s w e r e u s e d a st h e b a s e c a se . T h e f l o w c u rv e s w e r e c o m p u t e d f o r P 2 0 a n d P 8 0 v a l u e s c o r r e s p o n d i n gt o 2 0 % , 5 0 % a n d 9 5 % p a s s i n g 3 8 / z m , a n d f o r so l id s c o n c e n t r a ti o n s o f 0 . 1 5 , 0 . 3 0 a n d0 . 4 5 v / v , u s i n g t h e p r o c e d u r e s d i s c u s s e d a b o v e (F i g . 9) . In th e s i m u l a t i o n , s lu r r yt e m p e r a t u r e w a s k e p t c o n s t a n t a t 2 0 C a t w h i c h t h e v i s c o s i t y o f w a t e r i s a p p r o x i m a t e l y 1m P a - s .

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F i g . 1 1 . F l o w c u r v e s o f F e S i 6 5 D p r e d i c t e d b y t h e m o d e l u s i n g p a r a m e t e r s d e t e r m i n e d f r o m d a t a o b t a i n e d in1 99 0 ( a s s h o w n i n T a b l e 2 ) , c o m p a r e d w i t h e x p e r i m e n t a l p o i n t s o b t a i n e d i n 1 9 9 5.


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1 2 0 F.N . Sh i, T .J . Nap i er -Munn / l nt . J . Miner . Process . 4 7 (1996) 103 -12 3

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Fig. 12. The simulated flow curves of Hellyergrinding slurries.

9 5

T h e r e s u l t a n t f l o w c u r v e s a r e p r e s e n t e d f o r e a s y c o m p a r i s o n i n o n e g r a p h i n F i g . 1 2w i t h t h e x - a x i s s h o w i n g c h a n g e s i n t h e p a r t ic l e s i z e a n d t h e y - a x i s r e p r e s e n t i n g t h eso l id s vo lu m e f rac t ion . In spec t ion o f F ig . 12 shows c l ea r ly t ha t t he s imu la t ed s lu r r ie se x h i b i t t w o q u i t e d i f f e r e n t t y p e s o f f l o w c u r v e , d i l a t a n t a n d p s e u d o p l a s t i c , d u e o n l y t oc h a n g e s i n s o l i d s v o l u m e f r a c t i o n a n d p a r t i c l e s i z e .

A t l o w s o l i d s c o n c e n t r a t i o n ( 1 5 % s o l i d s b y v o l u m e ) , t h e s l u r r y b e h a v e s a s a d i l a t a n tm a t e r i a l . I n c r e a s i n g t h e f i n e s c o n t e n t f r o m 2 0 % t o 9 5 % p a s s i n g 3 8 / z m l e a d s t o a ninc rease i n t he d i l a t an t t r end , and a l so t he deve lopmen t o f a y i e ld s t r e s s . A t i n t e rmed ia t es o l id s c o n c e n t r a t io n ( 3 0 % s o l id s b y v o l u m e ) a n d r e l a t i v e l y c o a r s e s iz e ( 2 0 % - 3 8 / x m ) ,t h e f l o w c u r v e e x h i b i ts t h e c h a r a c t e ri s t ic s o f a c l a s s i c B i n g h a m p l a st ic . A t a n i n t e r m e d i -a t e dens i ty w i th a h igh con ten t o f f ines , ho we ver , t he d i l a t an t t r end i s s ti l l appa ren t .

A s s l u r r y d e n s i t y i n c r e a s e s t o 4 5 % s o l i d s b y v o l u m e a n d t h e f i n e s c o n t e n t e x c e e d s2 0 % - 3 8 / x m a ll ~ lu rr ie s b e h a v e a s p s e u d o p l a s t i c s w i t h a y i e l d st re s s . T h e h i g h e r th ef ines con ten t o f t he s lu r ry t he mo re app a ren t i s the pseu dop las t i c t r end .A n i m p r e s s i v e m a n i f e s t a t i o n o f th e y i e l d s t r e ss i s o b s e r v e d i n F i g . 1 2. A n i n c r e a s e i ne i the r s lu r ry dens i ty o r f i nes con ten t gene ra l ly r e su l t s i n an i nc rease i n y i e ld s t r e s s , w i th


19/21

F . N . S hi , T . Z N a p i e r -M u n n l i n t . J . M i n e r . P r o c e ss . 4 7 ( 1 9 9 6 ) 1 0 3 - 1 2 3 121t h e d e n s k y e f f e c t o n t h e y i e l d s t r es s b e i n g s t r o n g e r t h a n t h a t o f p a r t ic l e s i ze . H o w e v e rt h e i n t e r a c ti v e e f f e c t o f s l u r r y d e n s i t y w i t h p a r t ic l e s i z e c a n n o t b e i g n o r e d ; t h e e f f e c t o ff ines con~Een t on y i e ld s t r e s s i s ve ry sma l l a t t he l ow so l id s conce n t r a t i on .

T h i s , ; i m u l a t e d r h e o l o g i c a l b e h a v i o u r t a l l i e s w e l l w i t h m a n y o b s e r v a t i o n s f r o mindus t r ia l g r ind ing s lu r r ie s . A sepa ra t e i ndus t r i a l s t udy o f rheo lo g ica l e f f ec t s i n g r ind ing(Sh i , 1994) gen e ra t ed the fo l l ow ing s imi l a r t r ends : W h e n a s l u rr y c o n t a i n s r e l a ti v e l y lo w s o l id s c o n c e n t r a ti o n a n d a h i g h c o n t e n t o f f i n e s

( a t y p i c a l r a n g e b e i n g l e ss t h a n 4 2 % s o l id s b y v o l u m e , a n d m o r e t h a n 2 5 - 3 5 % - 3 8/xm, eg . t e r t i a ry mi l l o r r eg r ind mi l l d i s cha rge s lu r r i e s ) , i t s r heo log ica l cha rac t e r i sl i ke ly t o be d i l a t an t .

W h e n t h e s l u rr y d e n s i t y i n c re a s e s a n d f i n e s c o n t e n t r e d u c e s , fo r e x a m p l e 4 4 % - 5 8 %s o l id s b y v o l u m e a n d l e s s t h a n 2 0 % - 3 8 / x m , t h e ty p i c a l s tr e a m b e i n g p r i m a r y o rseconda ry g r ind ing mi l l d i s cha rge , t he s lu r ry i s l i ke ly t o exh ib i t a p seudop las t i ccha rac t e r . I nc reas ing e i t he r f i nes con ten t o r s lu r ry dens i ty l eads t o i nc reased y i e ld s t r e s s fo rb o t h d i l a t a n t a n d p s e u d o p l a s t i c f l o w s .

T h e s e t r e n d s a l s o a g r e e w i t h o t h e r i n v e s t i g a t o r s . F o r e x a m p l e , K l i m p e l ( 1 9 8 2 ) s t a t e d : M any coa l s and mine ra l s l u r r i e s exh ib i t d i l a t an t cha rac t e r a t r e l a t i ve ly l ow s lu r ry

d e n s i ti e s - - l e s s t h a n 4 0 - 4 5 % s o l id s v o l u m e f o r t y p i c a l s i z e d i s tr i b u ti o n s . I nc rezLs ing s lu r ry dens i ty cau ses a t rend tow ard pseu dop las t i c behav iou r .

Y e t t h e re a r e s o m e f e a t u r e s o f s lu r r y r h e o l o g y r e f l e c te d i n t h e s i m u l a t io n s w h i c h h a v en o t b e e n r e p o r t e d i n th e l i te r a tu r e . F o r e x a m p l e K l i m p e l ( 1 9 8 2 ) s u g g e s t e d t h e a d d it i o n o ff ines t o mi l l f eed , t o r each a p seudop las t i c r eg ion , fo r be t t e r g r ind ing e f f i c i ency . Thepresen t work sugges t s t ha t t h i s i s co r r ec t on ly when s lu r ry dens i ty i s h ighe r t hana p p r o x i m a t e l y 3 0 % s o l i d s b y v o l u m e ( F i g . 1 2 ) , i n w h i c h c a s e i n c r e a s i n g f i n e s c o n t e n tdoe s l ead to t he pseud op las t i c t r end . I f t he s lu r ry dens i ty i s l ow er t han 30% so l id s byv o l u m e , h o w e v e r , i n c r e a s i n g t h e f i n e s c o n t e n t w o u l d r e s u l t i n a t r e n d m o r e t o w a r dd i l a t an t behav iou r , wh ich i s no t des i r ab l e .

6 . C o n c l u s i o n s

A m o d e l h a s b e e n d e v e l o p e d c a p a b l e o f p re d i c t in g s l u rr y r h e o l o g y a n d v i s c o s i t y f r o mc o m m o n l y a v a i l a b l e a n d e a s i l y m e a s u r e d s l u rr y p r o p e r t ie s (E q s . 1 0 a n d 1 1). T h e m o d e lt akes a new appro ach , f i r s t p r ed i c t i ng the i n s t rum en t ou tpu t r ead ing s o f a pa r t i cu l a rr o t at i o n a l v i s c o m e t e r a t v a r i o u s b o b b i n s p e e d s f r o m t h e s l u rr y p r o p e r t ie s . T h e p r e d i c t e dr e a d i n g s a n d c o r r e s p o n d i n g b o b b i n r p m a r e t h e n c o n v e r t e d t o s h e a r s t r e s s a n d s h e a r r a t ea f t e r c o r r e c t io n f o r t u r b u l e n c e i n t h e p r e d i c t e d m e a s u r e m e n t d a t a . T h u s r h e o l o g i c a l f l o wcurves ( , ; hea r s t r e s s a t a r ange o f shea r r a t e s ) a r e e s t ab l i shed , and the appa ren t v i scos i tya t a des i r ed shea r r a t e can then be de t e rmined . I t shou ld be no ted tha t a s l ong a s t hep a r a m e t e r s u s e d i n a n y p a r t i c u l a r a p p l i c a t i o n a r e a p p r o p r i a t e , t h e f a c t t h a t t h e m e t h o dh a s b e e n c o n s t r u c t e d w i t h r e f e r e n c e t o o n e p a r t i c u l a r i n s t r u m e n t t y p e b e c o m e s i r r e l e -v a n t . T h u s t h e f u ll d a t a r e d u c t io n p r o c e d u r e c a n b e c o n s i d e r e d a s a n a l g o r i th m i n it s o w nr i g h t , i n d e p e n d e n t o f t h e p a r t i c u l a r i n s t r u m e n t o n w h i c h i t h a p p e n s t o b e b a s e d .

Th e :du rry p rop e r t i e s i nco rpo ra t ed in the mo de l a r e t he so l id s vo lum e f r ac t ion ,


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122 F.N . Sh i, T . J . Nap i er -M unn / l n t . .1. Miner . Process . 4 7 (1996) 1 03- 123

p a r t ic l e s i ze d e t e r m i n e d a t t w o p o i n t s ( 8 0 % p a s s i n g s iz e , P 8 0 , a n d 2 0 % p a s s i n g s i z e,P 2 0 ) , a n d s l u r r y t e m p e r a t u r e .

T h e s i x m o d e l p a r a m e t e r s w e r e f i r s t e s t a b l i s h e d b y f i t t i n g t h e m o d e l t o 3 1 s e t s o fg r i n d i n g s u r v e y s f r o m t h e H e l l y e r b a s e m e t a l c o n c e n t r a t o r , c o n t a i n i n g 3 7 2 d a t a p o i n t s( F ig . 3 ) . The mode l w as t hen t e s t ed aga in s t add i t i ona l da t a s e t s f r om va r ious s l u r r i e s . I tw a s f o u n d t h a t t h e i n s t r u m e n t r e a d i n g s f r o m s o m e s l u r r i e s c a n b e w e l l p r e d i c t e d u s i n gt he s a m e s e t o f H e l l y e r p a ra m e t e r s . H o w e v e r , d u e t o t h e c o m p l e x i t y o f th e m i n e r a l o g y ,c h e m i s t r y a n d p a r t i c l e s h a p e o f s l u r r i e s ( w h i c h a r e n o t i n c o r p o r a t e d s p e c i f i c a l l y i n t h em o d e l ) , t h is s e t o f p a r a m e t e r s i s n o t u n i v e rs a l . U n d e r s u c h c i r c u m s t a n c e s p a r t o r a ll o ft h e p a r a m e t e r s m a y n e e d t o b e r e - f i t t e d t o m e a s u r e m e n t d a t a f r o m a p a r t i c u l a r s l u r r y . I na l l c a s e s t e s t e d t h e m o d e l p r e d i c t i o n s w e r e f o u n d t o b e i n a g o o d a g r e e m e n t w i t h t h em e a s u r e d d a t a a f t e r f it ti n g .

T h e m o d e l , t o g e t h e r w i t h t h e a s s o c i a t e d t u r b u l e n c e c o r r e c t i o n m e t h o d ( F i g . 9 ) , i sv a l u a b l e i n tw o w a y s . F i rs t ly , i t c a n b e u s e d t o in f e r r h e o l o g y w h e n n o m e a s u r e m e n t sw e r e m a d e , e i t h e r u s i n g a n e x i s t i n g p a r a m e t e r s e t , o r i n m a n y c a s e s b y f i t t i n g o n l y o n eo r t w o p a r a m e t e r s t o d a t a s e t s f r o m s i m i l a r s l u r r i e s . T h i s p r o v i d e s a u s e f u l m e t h o d t or e - a c c e s s p r e v i o u s e x p e r i m e n t a l d a t a s e t s i n w h i c h n o r h e o l o g i c a l i n f o r m a t i o n w a sc o l l e c t e d , o r t o p r e d i c t r h e o l o g y i n c a s e s w h e r e p h y s i c a l m e a s u r e m e n t i s v e r y d i f f i c u l t ,e .g . ins ide a gr ind ing mi l l .

Seco nd ly , i t c an be u s ed i n s imu la t i on t o exp lo r e t he na tu r e o f s l u r ry r heo lo gy i nr e l a t i o n t o v a r i o u s s l u r r y p r o p e r t i e s . T h e s e p a r a t e e f f e c t s o f s o l i d s v o l u m e f r a c t i o n a n dp a r t ic l e s i z e o n t h e r h e o l o g i c a l p r o p e r t i e s o f t h e H e l l y e r g r i n d i n g s l u r r ie s a r e d e m o n -s t r a t ed g r aph i ca l l y i n F ig . 12 .

I t h a s b e e n s h o w n t h a t a s in g l e t y p e o f s l u r ry c a n e x h i b i t a w i d e r a n g e o f r h e o l o g i c a lb e h a v i o u r , f r o m p s e u d o p l a s t i c t o d i l a ta n t a n d w i t h v a r y i n g y i e l d s tr e ss , d e p e n d i n g o n t h ep r e v a i l i n g p a r t i c l e s i z e a n d s o l i d s c o n c e n t r a t i o n . T h e s e t r e n d s c o n f o r m t o o b s e r v a t i o n sm ad e i n i ndus tr i a l g r i nd ing c i r cu i ts , and t he mo de l m ay t he r e f o r e o f f e r a f a c i l it y f o rp r e d i c t i n g r h e o l o g y i n g r i n d i n g c i r c u i t c o n t r o l s y s t e m s .

F u t u r e w o r k w i l l c o m p r i s e t h e a c c u m u l a t i o n o f t y p i c a l p a r a m e t e r v a l u e s f o r a w i d er a n g e o f s l u rr y t y p e s, a n d e x p e r i m e n t s t o d e t e r m i n e w h e t h e r th e g e n e r a l a p p r o a c h c a n b ee x t e n d e d t o o t h e r i n s t r u m e n t s .

7 . N o m e n c l a t u r e

a o - a 3 -----coe f f i c i en t s in Eq . 1C l - C 6 = m o d e l p a r a m e t e r s (E q s . 1 0, 1 1 )H D --- h y d r o d y n a m i c t e r m ( E q . 1 1 )k M --- f u n c ti o n o f m a x i m u m a t t a i n a b l e s o l id s v o l u m e f r a c ti o nm V = D e b e x v i s c o m e t e r r e ad i n g ( m V )PS = pa r t i c l e s i z e ( a r b i t r a r y de f in i t i on )P38 --- pe r cen t pa s s ing 38 / zm ( % )P 2 0 --- 2 0 % p a s s i n g s i z e ( m m )P 8 0 = 8 0 % p a s s in g s iz e ( m m )T --- s l u r r y t em pe r a tu r e ( C)


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124 ,

F.N . Sh i, T . J. Nap i er -M unn / l n t . J . Miner . Process . 47 (1996) 103 -12 3

= b o b b i n a n g u l a r v e l o c i ty ( r a d / s )= s o l i d s v o l u m e fr a c t i o n

12 3

A c k n o w l e d g e m e n t s/

T h e ~L Uthors w i s h t o t h a n k S a r a P o r t e r , w h o m a d e t h e 1 9 9 0 f e r r o s i l i c o n m e a s u r e m e n t sq u o t e d i n t h e p a p er , a n d O s c a r C a s t r o f r o m w h o s e M a s t e r s t h es i s o t h e r v i s c o m e t e rm e a s u r e m e n t s w e r e o b t a in e d . M i c h a e l D u n g l i s o n a n d L i n d a l B e a u m o n t c o l l e c te d t he1 9 9 5 f e r r o s i l i c o n d a t a r e c o r d e d i n F ig . 1 1. S a m a n c o r L i m i t e d k i n d l y s u p p l i e d t h ef e r r o s i l i c o n in b o th c a s e s. T h e a u t h o rs a l s o t h a n k W e s t e r n M i n i n g C o r p o r a t i o n , M o u n tI s a M i n e s a n d A b e r f o y l e R e s o u r c e s f o r p r o v i d i n g a c c e s s t o th e i r c o n c e n t r a t o rs f o r th ec o l l e c t io n o f t h e i nd u s tr i a l v i s c o m e t e r d a t a q u o t e d i n t h e pa p e r . M u c h o f th e w o r k w a ss u p p o r t e d b y a J K M R C p r o j e c t i n m i n e r a l p r o c e s s i n g ( P r o je c t P9 ) , f u n d e d t h r o u g h t h eA u s t r a l i a n M i n e r a l I n d u s t r ie s R e s e a r c h A s s o c i a t i o n , o f w h i c h t h e fo u r c o m p a n i e s n a m e da b o v e w e r e s p o n s o r s .

Re f e r e n~ c e sCastro, O. , 1990. An invest igat ion of pulp rheo logy effects and their appl ication to the dimensionless type

hydrocyclone models. M.Eng .Sc. thesis, University of Queensland (JKM RC).Collins, B., Napier-Munn, T.J. and Sciarone, M., 1974. The production, properties and selection of ferrosilicon

powd ers fo r hea vy medium separation. J. S.A. Inst. Min. M et., 75(5): 103-119.Fuerstenau, D .W., Ka pur, P.C. and Velamakanni, B.V., 1990. A multi-torque model for the effects o fdispersants and slurry viscosity on ball milling. Int. J. Miner. Process. 28: 81-98.Horsley, R.R. , Tran, Q -K , and Reizes, J .A., 1992 . The effe ct of rheology on the performance of hydrocy-

clones. In: Svarovsky and Thew (Editors), Proc. 4th Int. Conf. on Hydrocyclones, Southampton (BHRA).Kluwe, , pp. 215-227.

Jinescu, V.V., 1974. Th e rheology of suspensions. Int. Chem . Eng., 14: 397 -42 0.Kaw atra, S.K. and Eisele, T.C., 198 8. Rheological effe cts in grinding circuits. In t. J. Miner. Process., 22:

2 5 1 -2 5 9 .Klimpel, R.R., 1982. Slurry rheology influence on the performance of m ine ra l/c oa l grinding circuits. Part 1.

Min. Eng., 34(12): 1665-1668.Klimpel, R.R., 1983. Slurry rheology influence on the performance of min er al/ co al grinding circuits. Part 2.

Min. Eng. , 35(1): 21-26.Mo oney, M ., 19 51 . Th e viscosity of a concentrated suspe nsion of spherical particles. J. Colloid Sci., 6:162-170.Moys, M H ., 1989. Slurry rheology - - the key to a further advance in grinding mil l control . In: A.L. M ular

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modelo viscosidad napier

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