Morrell SAG

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PergamonMinerals Engineering,Vol. 8, No. 11, pp. 1285-1297, 1995

Copyr ight 1995 Elsevier Sc ience LtdPrinted in Great Bri tain. All r ights reserved

0892-6875(95)00096--8 0892--6875/95 $9.50+0.00

T H E D E V E L O P M E N T O F A D Y N A M I C M O D E L F O R A U T O G E N O U S

A N D S E M I - A U T O G E N O U S G R I N D IN G

W. VA L E RY J n r a n d S . M O R R E L L

Ju l ius Kru t t schn i t t Mineral R esearch Cen t re , Univers i ty o f Queensland ,Is les Roa d , Indoo roop i l ly, Qld 4068 , Au st ra l iaReceived 16 June 1995; accepted 19 July 1995)

A B S T R A C T

To assist in the study and understanding of plant dynamics, circuit interactions, milloperational behaviour and automatic control schemes, a model of the dynamic behaviourof autogenous ag) and semi-autogenous mills sag) is currently under development at theJKMRC. The model is being developed to provide an accurate dynamic response in termsof power draw, grinding charge level, slurry level and product size distribution fo rchanges in feedrate, f eed size, feed hardness and water addition. The conceptual structureof the model is described together with dynamic data from 2 full scale high aspect ratioautogenous mills which will be used to validate the model. The data were obtained froma series O.f step tests and comprise trends in power draw, bearing pressure, solids and

water flowrates as well as an indication o f the fraction of coarse rocks in the feed. Thislatter quantity was obtained from a novel, yet simple device fo r counting rocks which willbe described. The mills measured response to these step changes is presented togetherwith an e~planation fo r their behaviour in terms of the physical changes which took placeinside the mill.

K e y w o r d sGr in d in g , au to g en o u s , semi -au to g en o u s , mi l l , d y n amic mo d e l , s imu la ti o n

I N T R O D U C T I O N

Fo r e f f ec t i v e AG /SA G mi l l o p era t io n an d co n t ro l , t h e measu remen t an d co n t ro l o f imp o r t an t mi l l v a r i ab l essuch as feed s ize , o re hardness and mi l l load are des i red , bu t no t a lways poss ib le . The lack of avai lab lein s t ru men ta t io n to measu re t h ese v a r iab l es is o n e f ac to r wh ich h as imp ed ed th e d ev e lo p m en t o f mo read v an ced an d e f f ec t i v e AG /SAG mi l l co n t ro l . On e so lu tio n to su ch a p ro b lem is a d y n am ic mo d e l t h a t canb e u sed to p red i c t i n fo rmat io n ab o u t t h e p ro cess t h a t can n o t b e eas i l y m easu red .

In t h i s p ap er a co n cep tu a l mo d e l i s d esc r ib ed wh ich i s b e in g d ev e lo p ed to p ro v id e accu ra t e d y n amicresp o n se i n t e rms o f p o we r d raw, ro ck an d s lu r ry l ev e ls a s we l l a s p ro d u c t s i ze d i st r ib u t io n . D y n am ic d a t awh ich h av e b een cc ,l lec ted t o as s is t w i th t h e d e v e lo p m en t an d v a l id a t io n o f t h e mo d e l a r e p resen t ed to g e th ewi th an i n t e rp re t a ti o n o f t h e o b se rv ed t r en d s an d th e way in wh ich th e p ro p o sed m o d e l wi l l r ep ro d u ce th em

P r e s e n t e d a tM i n e r a l s E n g i n e e r i n g 9 5 ,S t . I v e s , C o r n w a l l , E n g l a n d , J u n e 1 9 9 5

1 2 8 5


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1286 W. Valery Jnr and S. Morrell

D Y N A M IC M O D E L S T R U C T U R E

The mode l chosen to p rov ide the dynamic s t ruc tu re i s Whi ten ' s con ten ts based mode l [1 ] . The mode lcompr ises two equat ions which can be wr i t ten as :

dSi( t ) i -1-- f i - P i ~ a i j ' r j ' s i - ( r rS i- a i r r rSi ) (1)

d t jo i

P i ' - d i ' s i (2)

where:

si(t):ft.

Pi:ri:a j :

d i :

is the m ass o f mater ia l in s ize c lass i , a t t ime t , with in the m il l ,is the to ta l f low rate o f feed mater ia l in th is s ize c lass ,

is the to ta l f low rate o f d ischarge mater ia l in th is c lass ,is the ra te a t w hich p ar t ic les in s ize c lass i b reak ,is the breakage d is t r ibu t ion or appearance func t ion which descr ibes the f ract ion o f mater ia lbreaking in to s ize c lass i due to breakage of s ize c lass j , anddischarg e ra te o f c lass s ize i.

The so lu t ion to equat ions 1 and 2 provides pred ict ions o f the product s ize d is t r ibu t ion , load s ize d is t r ibu t ioand loa d mass and i s found v ia the u se o f a compu te r based a lgo r i thm wh ich i s ou t l ined in schem at ic fo rmin Figure 1 .

I N P U T- m i l l d es ig n- b r e a k a g e r a t e s- g e n e r a l a p p e a r a n c e f u n c t i o n- feed r a t e an d s i ze d i s t ri b u t io n- w a te r ad d i t i o n

I Calculate_ I - droph e ig h t~ - ~ . - - - - I ~ I -p o w e rE s t i m a t e t o n n e s o f i o a d i n r ni llj x \ , , / I -E cs

\x' / I "app earan ce unction\

\\

/ C a l c u l a t eB re a k lo ad . . . . . . b re ak ag e ra te s

C a l c u l a t eCa lculat. ~ - ~D i s c h a rg e l o a d~ d r n a xl o a d r e m a i n i n g d i : d m a x . c i

p i = d i . s i

~ C a i c u l s m m i l l p r o d u c tI

Fig .1 Ou t l ine o f Mode l A lgo r i thm


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Autogenous and semi-autogenous grinding 1287

Th e p ro g rams b e in g d ev e lo p ed fo r t h e d y n am ic s imu la ti o n mo d e l a r e co m p at ib l e with t h e ex is t in g s t ead ysta te s imulat ion models avai lab le a t the JKMRC. Subrout ines are used to s imulate the physical p rocessesin v o lv ed an d a t ime- seq u en c in g su b ro u t in e i s p ro p o sed wh ich co n t ro l s th e o p era t i o n o f ev en t s wi th in t hprogram, includ ing the in tegrat ion s tep .

Th e mo d e l co n ta in s 3 p a ramete r s wh ich m u s t b e d e t e rmin ed b e fo re th e eq u a t io n s 1 an d 2 can b e so lv edTh ese a re:

t h e b reak ag e r a tes ( r ) wh ich can b e r eg ard ed as t h e b reak ag e f r eq u en cy an d w h ich v a ry wi thfactors such as mi l l speed and charge s ize d is t r ibu t ion [2 ]

the appearance funct ion (a i j ) which descr ibes the s ize d is t r ibu t ion of the p roducts f rom breakageev en t s an d wh ich i s a fu n c t io n o f t h e o re t y p e an d th e sp ec i fi c b reak ag e en erg y.

the d isch arge ra te (d i ) wh ich re la tes the load to the f lowrate o f p roducts ou t o f the mi l l . I t is alum ped pvJ:ameter wh ich con tains bo th the effec t o f c lass i ficat ion o f so l ids by the g rate an d f lu id

f low effects which are re la ted to the ho ld-up of s lu r ry in the mi l l .

Breakage Ra te Function

Th e b reak ag e r a t e i s r e l a ted t o p a r t i c l e s i ze an d ty p i ca l ly tak es t h e fo rm sh o wn in F ig u re 2 . Th e b reak ag erate funct ion shape i s largely governed by the mi l l load par t ic le s ize d is t r ibu t ion and mi l l speed . In th ismo d e l t h e b reak ag e r a t es a r e r e l a t ed t o t h e l o ad s i ze d i s tr i b ut io n v i a emp i r i ca l eq u a t io n s d e t e rm in ed f ro ma l a rg e n u mb er o f p i l o t an d fu l l s ca l e mi l ls w h ere t h e l o ad s i ze d i s tr i bu t io n s were m easu red . F in e t u n in gof the equat ions wi l l be necessary fo r a par t icu lar mi l l us ing resu l t s f rom s teady-s ta te tes twork .

B r e a k ag e R a ta ~

a b r a s i o n / c h i p p i n g , ~

fP a r t i c l e S i z e

Fig .2 Ex amp le o f an AG/S AG m i ll b reak ag e r a t e fu n c t io n

Appearance F u n c t i o n

Th e ap p earan ce o r b reak ag e d i s t r i b u tio n fu n c t io n d esc r ib es t h e s i ze d i s t ri b u t io n f ro m a b reak ag e ev en t . I ti s d ep en d en t u p o n b o th t h e o re t y p e an d th e sp ec i f ic en erg y asso c i a ted wi th t h e b reak ag e ev en t . Th e mo d e

re l i e s o n th e u se o f l ab o ra to ry t u mb l in g an d imp ac t b reak ag e t e s t s o f t h e r e l ev an t o re t o p ro v id e are l a t i o n sh ip b e tween th e sp ec i f i c en erg y an d th e ap p earan ce fu n c t io n . Th e r esu l t s a r e co n v en ien t lyrep resen t ed in a r e l a t io n sh ip b e tween th e sp ec if ic en erg y an d th e b reak ag e p ro d u c t p a ramete r t l o a s fo l lo ws

tlo = A (1 - e( b Ecs)] (3)

H I E 8 : I I - C


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1288 w . ValeryJnr and S. Morrell

wh ere

A, b : are the o re speci f ic constan ts , andEcs : i s t h e sp ec if i c co m min u t io n en erg y (k Wh / t ) .

I t h as b een sh o wn [1 ] t h a t th e t l 0 , wh ich i s d e f in ed as t h e f r ac ti o n o f b ro k en p ro d u c t wh ich i s smal l e r t h anon e ten th o f the o r ig inal par t ic le s ize , can be eas i ly re la ted to the en t i re p rodu ct s ize d is t r ibu t ion . Equat ion3 can th e re fo re b e u sed to g en era t e t h e en t i r e p ro d u c t s i ze d i s t ri b u tio n fo r a g iv en sp ec if ic en erg y. A mo red e t a i l ed d esc rip t i o n o f t h e d a t a t r ea tmen t p ro cess ca n b e fo u n d e l sewh ere [1 ] .

Whi ls t the laboratory tes t s p rov ide a re la t ionsh ip between speci f ic energy and s ize reduct ion , the speci f icene rgy o f b reakage ev en ts wi th in the m i l l mu st s t i ll be es t imated . T his wi l l vary w i th such factors as mi l ld i amete r, sp eed , ch a rg e d en s i ty an d ch arg e l ev e l . Wi th in t h e m o d e l a s imp l i fi ed d esc r ip t i o n o f t h e ch arg esh ap e an d mo t io n i s u sed to ca l cu l a t e t h e mean h e ig h t t o wh ich th e ch arg e i s r a i sed , d ro p p ed an dsubseq uent ly b roken [2 ,3] . Th is i s then re la ted to the sp eci f ic ene rgy of b reakag e fo r each par t ic le s ize .

Discharge and Classification Functions

Th e d i sch arg e r a t e (d ) i s co n s id e red to b e t h e p ro d u c t o f two mech an i sms :

f lu id t ranspor t th rough the g rate , andso l ids c lass i f icat ion by the g rate .

W i th in t h e mo d e l , d i i s r e l at ed t o t h e co n ten t s an d p ro d u c t u s in g eq u a t io n 2 . Th i s eq u a t io n can b e ex p an d eto incorporate a d imension less c lass i f icat ion parameter (c ) and a f lu id f low-rela ted parameter (dmax) :

Pi = si (dmax c i) (4)

Th e c lass i f icat ion param eter (c ) i s re la ted to the g rate aper tu re o f the m i l l as sho wn in F igure 3 [4] .

C l a s s i f i c a t i o nF u n c t i o n Va l u e

1 . 0

0 .0xm Xg

L o g S i z e

Fig .3 Grate c lass i f ication funct ion

Th e v a lu e o f Xg i s t h e e f f ec t i v e g ra t e ap er ture , wh i ls t Xm i s th e max imu m p ar t i c le s i ze wh ich b eh av es l i k ewater , i e . i s no t sub ject to c lass i f icat ion . The funct ion a l lows for no c lass i f icat ion of par t ic les above theg ra t e s i ze (Xg ) b u t v a ry in g d eg rees o f c l ass i f ica t io n fo r p a r t i c le s b e lo w th e g ra t e s i ze b u t ab o v e X m.


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1290 W Valery Jnr and S Morrell

D:A ::

kt, km

gra te d es ign paramete ris the mil l d iam eter (m) ,is the to ta l open area o f grate aper tures (m2),is the f ract ion of cr i t ical speed , an dare constants.

Apar t f rom be ing u sed to es t imate dmax, equat ions 6 and 7 are used to determ ine wh ether f low is occurr ingonly v ia the gr ind ing media or whether a s lur ry pool has a lso formed. In the case of the la t ter the s lur rypoo l l eve l may a l so be de te rmined and i t s e f f ec t on power d raw es t imated u s ing the JKMRC's powermodel [3] .

P o w e r D r a w

Solu t ion of the gr ind ing mod el equat ions 1 and 2 g ives pred ict ions o f the produc t s ize d is t r ibu tion , chargs ize d i s t ribu t ion and charge mass . G iven the charge mass , mi l l d imens ions and m i l l speed , the po wer d rawcan also be es t imated . For th is purpose the JKMRC's power model is used [6] . This model u t i l ises the

same s imp l if ied charge shape and mo t ion tha t p rov ide the d rop he igh t da ta fo r the appearance func t ioncalculations (Figure 5) .

( a ) ( b )

G r a t e D i s c h a r g e O v e r f l o w D i s c h a r g e

90o

0 S

xso oo

J

Fig .5 Simplif ied gr ind ing media and s lur ry shape

The power m ode l equa t ion has the fo l lowing fo rm:

g i n

P ow er~ f{ VrLrg[pc(sin Os-s i n O T ) p p ( s i n O T- s i n O T O ) ] *0.5V r 3Lpxtri

where

L :r:ri:rm:Vr:

length o f cy l indr ical sect ion of the mil l l iners (m)rad ial posi t ion (m)radial posi t ion of the charge inner sur face (m)radius of the m il l ins ide l iners (m)tangen t ia l veloci ty of a par t ic le a t rad ial d is tance r (m.sec-1)

(8 )


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Autogen ous and semi-autogenous grinding 1291

0s: angular d i~ ;p lacement o f sho ulder pos i t ion a t the mi l l shel l ( rads)0T: angu lar d i~ ;p lacement o f toe posi t ion a t the m i l l shel l ( rads)0 T O : an g u la r d i , ;p l acemen t o f su r face o f s lu r ry p o o l a t t h e t o e (r ad s)Pc: dens i ty o f to ta l cha rge (exclud ing exce ss s lu r ry) ( t .m -3)p p : d en s i ty o f t h e ex cess s lu r ry ( t .m 3 )

In cases wh ere s lu r ry fl o w i s o n ly t h ro u g h th e g r in d in g med ia t h e ch arg e p a t t e rn sh o w n in F ig u re 5 ( a ) wi lap p ly, i n wh ich case t h e re wi ll b e n o s lu rry p o o l an d 0 TO wi l l eq u al 0 T. Th e seco n d t e rm in eq u a t io n 8 wi lt h e re fo re eq u a l ze ro , Wh ere , u s in g eq u a t io n s 6 an d 7 , a s l u r ry p o o l i s i n d i cat ed t o h av e fo rm ed , 0 TO canb e ca l cu l at ed . F ro m eq u a t io n 8 i t can b e seen th a t i n t h i s case t h e seco n d t e rm wi l l b e n eg a t iv e g iv in g r i seto a l o wer p o w er d raw. In t h i s way th e mo d e l sh o u ld b e ab l e to mim ic t h e p o w er an d lo ad t r en d s as so c ia t edwi th ch an g es i n f l o wra t e t o t h e mi l l , i n c lu d in g th e e f f ec t o f t h e fo rmat io n o f a s lu r ry p o o l .

In p rac t i ce t h e e f f ec t o f a s lu r ry p o o l i s t o r ed u ce t h e p o wer d raw. Th i s can m an i fes t it s e l f i n c lo sed c i r cu i tmi l ls a s an o b se rv ed asso c i a t i o n b e tween th e amo u n t o f r ecy c l e an d th e p o w er d raw, wh ich d ro p s as t h erecy c l e i n c reases [711. Th e m ag n i tu d e o f t h e e f f ec t v a r ies an d in ex t r em e cases can cau se co n s id e rab l e p o wer

red u c t io n [8]. T h e e f f ec t i s il l u s tr a t ed u s in g d a t a r eco rd ed f ro m Mo u n t I sa Min e ' s co p p er co n cen t r a to r agmi l l . In th is exper iaaen t the mi l l was conf igured such that i t s d ischarge was pumped to a cyclone, theu n d er f lo w f ro m w h ich co u ld b e e i t h e r d iv e r t ed b ack to t h e mi l l o r co m b in ed wi th t h e cy c lo n e o v er f lo w an dsen t to the bal l mi l l (F igure 6 ) . In th is wa y the recy cle load co u ld be accurate ly con t ro l led .

To theSeconda ryGdndlngCircuit

by-pass

N e w F e e d

SAG Mi ll Sca t s. Wa t e r

Wa t e r A d d i t i o n

I .

( ~ S a m p lin g p o i n t s s u m p p u m p

Fig .6 Sch em at i c o f th e MIM p r imary g rin d in g c ir cu i t

In i t ia l ly the mi l l wa.,; run in op en c i rcu i t wi th a l l the cyclo ne underf low being d iver ted wi th the ove rf lowto the bal l mi l l . At t iLme equals to 200 min utes 70 % of the cyc lon e underf low was re tu rned to the ag m i l lf eed . F ro m F ig u re 7 i t can b e seen th a t t h e b ea r in g p ressu re in c reases in r esp o n se t o t h e accu mu la t io n o fs lu r ry i n t h e s lu r ry p o o l , wh i l s t a t t h e same t ime th e p o w er d ro p s an d r emain s a t t h e l o wer l ev e l . Th i s e f f ec


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1 2 9 2 W. Va l e r y J n r a n d S . M o r r e l l

o f in c reas in g lo ad y e t d ec reas in g p o w e r sh o u ld n o t b e co n fu sed w i th th a t a s so c ia t ed w i th a m i ll w h ich h asa n e x c e s s iv e g r in d i n g m e d i a c h a rg e ie g r e a te r th a n 4 5 - 5 0 % o f m i l l v o l u m e . A l t h o u g h t h e s y m p t o m s m a ybe s imi lar the causes are d i fferen t .

va

ria

bIes

s t e p c h a n g e7 - 6

~E~._~_ D--~3--D--[~--O-- J --[3--D--D--[ ~ " : D' --D~ D ~ , ~ D -

5 ............................................................................................................... .= ...........................................

I

i

= i . . .. .

1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0-5

2 4 (

t i m e ( r a i n )

F e e d r a t e - - D Pow e r

, L o a dweight Wa t e r a d d i t i o n

F ig .7 Me asu red m i l l feed r at e , p o w er d raw an d lo ad w e ig h t ( r e la t iv e v a lu es )

d u r in g a s t ep t e s t o n th e s lu r ry l ev e l i n s id e th e m i l l

va

ria

bIes

F u r th e r co n f i rm a t io n o f th e e f f ec t o f t h e s lu rry p o o l can b e seen in F ig u re 8 w h e re th e f eed w assu b seq u en t ly s to p p ed to th e m i l l ( t im e = 1 7 5 m in ) . C o n t ra ry to n o rm al o p en c i r cu i t co n d i t io n s w h ere

s t e p c h a n g e p o w e r i n c r e a s e

6 - i i i / - 6 . 5

i I '

5 ................................................................ i .............................................. = .......... L ..........................

3 ~ . . . . . . . . . . . . . . . . . . . . . . ~ t3 ct ..........' i El,

~ , , ~ -- ~ : ~ :I : : : 1 1 ' , : ' , ' , ' , ' , ' , : : = = :: ~ , I , , , ~ : I I : ~ 9 ~ , I2 - ; ~ 5 . 5 . ,:: .. . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . i . . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .

i "

1 ............................................................................................................... | ............ . .. .. .. ..i

I i0 , , 5 .0

1 4 0 1 6 0 1 8 0

t i m e ( r a i n )

F e e d r a te - - - o - Pow e r

Fig .8

o Load weight L W ater addi t ion

Measu red m i l l f eed r a t e , p o w er d raw an d lo ad w e ig h t ( r e l a t iv e v a lu es )d u r in g a s t ep t e s t s to p p in g th e n ew feed to th e m i l l


9/13


t h e p o w er w o u ld n o l rm a lly d ro p in r e sp o n se to a r ed u c t io n in f eed ra t e (F ig u re 9 ) , i n th i s case th e p o w e rin i t ia l ly c l im b s as th e s lu r ry in th e p o o l f lo w s o u t o f t h e m i l l . T h i s e f f ec t t ak es a r e l a t iv e ly sh o r t t im e too ccu r ( th e v a r i ab les a re p lo t t ed fo r each m in u te in s t ead o f an av e rag e o f 5 m in u tes in th e o th e r f ig u res ) d u eto th e f a s t s lu r ry d ra in ag e . T h e r ed u c t io n in th e lo ad m ass d u e to g r in d in g o u t t h en ex e r t s an in f lu en ce an dth e p o w er th en d ro p =; in a p red ic t ed m an n er.

s t e p c h a n g e, - 6

va

ria

bI

e

s

6 -

4 -

2 -

O -

. . . . .. . . . . . . . . . . .. . . . . .. . . . . .. . . . .. . . . . . . .. . . . . .. . . . .. . . . . .. . . . . . . .. . . . . .. . . . . .. . . . . .. . ~ . . . . ~ . . . . . . .. i . . . . . .. . . . . .. . . . . .. . . . . .. .

2 0 4 0 6 0 8 0 1 0 0 1 2 0

t i m e ( r a i n )

- - - - 4 F e e d r a te D P o w e r

- - - -~ o L o a d w e i g ht = Wa t e r a d d i ti o n

F ig .9 ]Measured m i l l feed ra t e , p o w er d raw an d lo ad w e ig h t ( r e l a t iv e v a lu es )d u r in g a s t ep t e s t o n th e n ew feed r a t e

E f f e ct o f W a t e r A d d i t i o n

R ap id ly in c reas in g w a te r ad d i t io n to a m i l l i s o f t en u sed b y o p era to r s to q u ick ly r ed u ce th e p o w er d raww h e n i t th r e a te n s t o e x c e e d o v e r l o a d le v e ls . O n c e a g a i n u s i n g d a t a f r o m t h e M I M c o p p e r c o n c e n t ra t o r a gm i l l t h e e f f ec t i s i l lu s t r a t ed w e l l (F ig u re 1 0) . I t can b e s een a t t im e = 8 0 m in u tes th e w a te r ad d i t io n to th e

m i l l w a s i n c r e a s e d f r o m 2 2 3 m 3 / h r t o 31 6 m 3 / h r. A l t h o u g h t h e p o w e r d r a w c a n b e s e e n t o h a v e b e e n s l o w l yd ec l in in g th e ad d i t io n o f t h e ex t r a w a te r cau ses a v e ry sh a rp d ro p in th e p o w er d raw. U n l ik e th e p rev io u scase w h ere an in c rease in s lu r ry to th e m i l l cau sed a l a s t in g d ro p in p o w er, w h en th e w a te r w as in c reasedth e p o w er d ro p w as t em p o ra ry an d b eg an to c l im b b ack u p a f t e r 1 0 m in u tes . In th i s case th e in i t i a l e f f ec to f t h e w a te r su rg e i s t o flu sh accu m u la ted f in e r so lid s o u t o f t h e m i l l an d h en ce th e ch a rg e d en s i ty an dp o w e r d raw d ec reased . I t i s p o ss ib l e th a t i f t h e w a te r i n c rease i s l a rg e en o u g h a s lu r ry p o o l m ay a l so fo rman d fu r th e r a s s i s t w i th th e d ro p in p o w er. H o w ev er a s th e f in e r so l id s a re f lu sh ed o u t t h e g r in d in g m ed iav o id ag e w i l l i nc rease,, a l lo w in g th e s lu r ry l ev e l t o d ro p . F in e so l id s w i l l t h en b e g in to accu m u la te , cau s in gth e p o w er d raw to r i se ag a in . In t e res t in g ly, t h e ch a rg e m ass , a s i n d ica t ed b y th e b ea r in g p ressu re ( lo adw eig h t i n th e F ig u re 1 0 ) , d id n o t d ro p w h en th e w a te r w as in c reased . T h i s m ay b e d u e to so m eco m p en s a t io n as so c ia t ed w i th b u i ld -u p o f w a te r an d a s im u l t an eo u s lo ss in f in es . In o th e r m i ll s s tu d ied i t

h as b een fo u n d th a t ch a rg e m ass in i t i a l ly d ec reases a s th e w a te r i s i n c reased .

Wi th in th e m o d e l t h e in c rease in w a te r f lo w ra te w i l l b e r e f l ec t ed in an in i t i a l i n c rease in d m ax an d h en cea co r resp o n d in g in c rease f lo w o f so l id s o u t o f t h e m i l l. T h e p o w er w i l l a l so b e p red ic t ed to d ro p d u e to th ed ec rease in ch a rg e d en s i ty. F o l lo w in g th e lo ss o f f in e so l id s th e s lu r ry l ev e l w i l l d ro p cau s in g d m ax tod ec rease an d th e f in e so l id s , ch a rg e d en s i ty an d p o w er d raw to in c rease ag a in .


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1294

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W. V alery Jnr and S. Mo rrell

s t e p c h a n g e; - 6

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I . . . . . . . . . . . . . . . . . . . . ._ . . . . . . ..... .. ~...... ...........

= | | a '4

6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0

t i m e ( r a i n )

F ig .1 0

A F e e d r a t e [ ] P o w e r

o L o a d w e i g h t L Wa t e r a d d i t io n

Measu red m i l l f eed r a t e , p o w er d raw an d lo ad w e ig h t ( r e l a t iv e v a lu es )d u r in g a s t ep t e s t o n w a te r ad d i t io n

F e e d S i z e E f f e c t s

F e e d s i ze d i st r ib u t io n c h a n g e s a r e o n e o f t h e m o s t c o m m o n c a u s es o f e rr a ti c b e h a v i o u r i n a g a n d s a g m i l ls .T h i s r e su l t s f ro m th e g r in d in g m ed ia b e in g o b ta in ed f ro m th e f eed . F ro m th i s , i t n a tu ra l ly fo l lo w s th a t t h eb eh av io u r o f t h e m i l l w i l l a l so b e d ep en d en t o n th e f eed s i ze d i s t r ib u t io n . In th e m o d e l , a s t h e f eed s i zed i s t r ib u tio n v a r i e s th e lo ad s i ze d i s t r ib u t io n w i l l a lso v a ry. T h e b rea k ag e r a t e d i s t r ib u tio n w i l l th en ch an g ean d in tu rn cau se a ch an g e in th e lo ad s i ze d i s t r ib u t io n . T h i s p ro cess w i l l i t e r a t e u n t i l s t ead y s t a t e i sp red ic t ed to h av e b een r each ed .

M easu rem e n t o f t h e d y n am ic r e sp o n se to ch an g es in th e f eed s ize d i s t r ib u t io n a re d i f f icu l t t o o b ta in , m ak in gt h e t a s k o f v a l i d a t i o n o f t h e m o d e l s r e s p o n s e e q u a l l y d i ff ic u lt . T h i s i s d u e t o t h e p r o b l e m s o f m e a s u r i n g f e e ds i ze d i s t r ib u t io n s o n - l in e . In an a t t em p t to o b ta in o n - l in e s i ze d a ta a s im p le ro ck c o u n te r w as d ev e lo p e d an din s t a l l ed a t 2 s i t e s . A n in f ra red sen so r w as in s t a l l ed o n th e f eed b e l t w i th th e b eam b e in g t r an sm i t t ed an d

re f l ec ted ac ro ss th e b e l t. T h e sen so r w a s p l aced a t t h e f eed ch u te ( th e f l a t te s t p a r t o f t h e b e l0 to av o idc o u n t i n g r o c k p i l es . T h e a i m o f th i s i n s tr u m e n t w a s t o m e a s u r e t h e n u m b e r o f r o c k s p e r m i n u t e l a rg e r t h a na ce r t a in s i ze a s d e f in ed b y th e h e ig h t o f t h e b eam ( i . e . l a rg e r th an 2 0 0 m m a t Mo u n t I sa an d l a rg e r th an1 0 0 m m a t H e l ly e r ) . E ach t im e th e in f ra r ed b ea m w as in t e r ru p ted b y co a r se ro ck s , a d ig i t a l s ig n a l w as sen tt o th e c o n t r o l s y st e m . T h e o u t p u t o f t h is r o c k c o u n t e r w a s m o n i t o r e d a n d r e c o r d e d a s t h e n u m b e r o f r o c k sp er m in u te l a rg e r th an a ce r ta in s i ze . I t w as fo u n d , h o w ev er, t h a t a l th o u g h s o m e s ig n i f i can t t r en d s w eres o m e t i m e s a p p a r e n t , f o r m u c h o f t h e t i m e l i tt le a s s o c i a t io n b e t w e e n t h e f r e q u e n c y o f c o a r s e r o c k s a n d m i l lb eh a v io u r w as seen . T h i s i s d u e to th e f ac t t h a t t h e f eed s i zedistribution i s j u s t , i f n o t m o re , im p o r t an t t h ant h e a m o u n t o f c o a r s e ro c k s .

T h i s l a t t e r f ac t i s c l ea r ly sh o w n f ro m t es tw o rk co n d u c ted a t t h e H e l ly e r Min e . T h e c i r cu i t i s sh o w n in

F ig u re 11 . T h e m i l l i s a h ig h asp ec t r a t io ag m i l l i n c lo sed c i r cu it w i th a p eb b le c ru sh e r an d D S M sc reen s.

T h e p eb b le c ru sh e r c i r cu i t i s co n f ig u red su ch th a t t h e c ru sh e r can b e eas i ly b y -p assed , i n w h ich case th ep eb b le s t r eam i s r e tu rn ed to th e m i l l . T h e m in e u ses th i s f ac i l i t y in a n o v e l m an n er to t i g h t ly co n t ro l t h em i l l p o w e r i n a v e r y n a r r o w b a n d . T h i s i s d o n e b y a n a u t o m a t i c c o n t r o l s c h e m e w h i c h b r i n g s t h e c r u sh e ro n l i n e w h e n t h e p o w e r d r a w r e a c h e s a n u p p e r l i m i t a n d t a k es t h e c r u s h e r o f f l i n e w h e n t h e p o w e r d r o p s


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below a low er l imit . The act ion of th is contro l s t ra tegy is c lear ly i l lus tra ted in Figure 12 . W hen the crusheis b rough t on l ine the powe r imm ed ia te ly beg ins to d rop . A l though the re i s no load ind ica t ion fo r th i s mi li t is m os t l ike ly tha t the load level w ou ld a l so be f a ll ing . W hen the c ru sher goes o f f l ine the powe r ( andload level) begin to r ise again . This produces the osci l la t ing power t rend seen in Figure 12 . I t is po in tedou t tha t the am p l i tude o f the o sc i l la t ions i s app rox imate ly 20 kW wi th a mea n powe r d raw o f 1440 kW.

Crusher

New Feed~ m ~ - ( ~ - ~ :

by-pass ( c r u s h e r o f f )

( ~ s a m p l i ng p o i n t s

( ~ ) f l o ~ r a t e m e a s u r e m e n t s

SAG Mill

To t he Se c onda r yGrinding Circui t

va

ria

bIe5

Fig .11 Schemat ic o f He l lye r p r imary g r ind ing c i rcu i t

o f f o n o f f o n o f fii

i

| ' ; ,: | , ,

I 1

I I I I II l I l lI I I II ~ _ , - IL ~ ~ i ~ ; i i ~ [

m .o_ . _ . ~ o - ~ D ' ~ ~, ~ B ' ~ D .~ i, ~ _ ~ n - ~ : ~ - ~ - o- n ~ x ~ -o . ~ _ |[ ) - [ i ~ - [ ~ " E T. : . ' ~ = I ' l i lT ' ,

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t i m e ( m i n )

- . , ~ F e e d r a t e - - o P o w e r , Wa t e r a d d i ti o n

Fig .12 Effec t o f the recycle crushe r (changing feed and load s ize d is t r ibu t ion)on the Hel lye r sag mi l l pe r fo rmance


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1296 W Valery Jnr and S Morrell

In terms of the feed s ize d is t r ibu t ion to the m i l l , the effe ct o f the recyc le crusher i s to substan t ia l ly mod ifyi t. Th e ac t io n o f t h e r ecy c l e c ru sh er can th e re fo re b e v i ew ed as cau s in g a s t ep ch an g e in t h e f eed s i zed i s tr ib u tio n . Th e r easo n fo r t h e o b se rv ed e f f ec t o f t h e c ru sh er h as t o d o wi th t h e i n f lu en ce o f th e so -ca l ledcr i tica l s ize f ract ion in the mi ll . Th is i s typ ical ly in the 2 5- 50 m m size range. In ma ny m i l ls i t wi ll be foundthat th is f ract ion const i tu tes a very large p ro por t ion o f the mi l l load . I t i s therefore respon sib le fo r d rawinga s ig n if ican t amo u n t o f p o we r as we l l a s o ccu p y in g a l a rg e amo u n t o f mi l l v o lu me . B y ex t r ac t in g a l a rg epropor t ion of th is mater ia l and reducing i t to a s ize which can ex i t the c i rcu i t and /or i s bet ter ab le to beg ro u n d b y th e m i ll , red u c t io n s i n mi l l l o ad an d p o wer can b e ach i ev ed . Th e e f f ec t i s mu ch mo re n o t i ceab lwh en th e c ru sh er is k ep t o n l i n e as can b e seen in F ig u re 1 3. Mi l l p o w er i n t h is case f a l l s b y 3 5 % y e t t h ethroughput increases by 15%.

V

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b

I

e

s

0

1 O 0

: c r u s h e r o f f = : c r u s h e r o n :

i i '

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i i i i i i i ii i i i [ : , [ . . . .

. . . . . . . . i . . . . . . . . . . . . I . . . . . . . . . . . . i . . . .1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 4 5 0 5 0 0 5 5 0

t i m e ( m i n )

F e e d r a t e - - 0 P o w e r ~ W a t e r a d d i t io n

Fig .1 3 Effec t o f t h e r ecy c l e c ru sh er (o f f l i n e an d th en b ro u g h t o n l in e )o n th e He l ly e r sag mi l l p e r fo rman ce

C O N C L U S I O N S

A co n cep tu a l d y n a mic ag / sag m i ll mo d e l h as b een d ev e lo p ed fo r th e p red i c t io n o f t h e p o wer d raw, l o ad

level and product s ize d is t r ibu t ion . The s t ructure o f the model i s such that i t should p rov ide real i s t icresponses to ch anges in fee drate , water add i t ion , recy cle load , feed s ize d is t r ibu t ion and o re hardness .

Dy n am ic d a t a h av e b een co l l ec t ed f ro m a n u m b er o f mi l l s t o a s si s t w i th t h e d ev e lo p m en t an d v a l id a t io n o fth e mo d e l . Fu r th e r d a t a wi l l b e co l l ec t ed o n th e sp eed r esp o n se o f mi l l s t o en h an ce th i s d a t a b ase . Th ep ro j ec t ed o u t co me f ro m th e p ro j ec t wi l l b e a v e r sa t i l e d y n amic mo d e l p ro v en u s in g a wid e r an g e o findustr ial data.

A C K N O W L E D G M E N T S

Th e au th o r s th an k th e f i n an c ia l su p p o r t f ro m CN Pq (Braz il ) t h ro u g h th e Yo u n g S c i en t is t AwardSch o la r sh ip as we l l a s t h e JKM RC Po s t Grad u a te S tu d en t Aw ard . Th e co n t r ib u t io n s o f Mo u n t Isa Min esan d H e l ly e r (Ab er fo y le Reso u rces L td . ) t h ro u g h th e A u s t ra l i an M in era l In d u st ri e s Resea rch A sso c i a ti o n(AMIRA Pro j ec t P9 ) a re a l so g ra t e fu lly ack n o wled g ed . Th e au th o r s wo u ld a l so li k e t o t h an k Do n M cKee ,To n i K o jo v ic an d Ad r i an Dan ce fo r t h e i r k in d co o p era t i o n in t h i s s t ud y.


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3.

4.

5.

6.7.

8.

R E F E R E N C E S

Whiten, W .J., A matrix theory of com min ution machines,Chem. Eng . Sci .No. 29:585-599, (1974).Morrell, S.,et al . ,Pow er Draw o f Grinding M ills - - Its mea surem ents and Prediction,Proc. Fif thMi l l Oper~ to rs Conference ,Roxby Downs, Austral ia, AuslMM, 109-114 (1994).

Morrell , S,et al . , The Prediction of Power Draw in Wet Tumbling Mills ,Ph.D. Thesis,TheUn ivers ity of Queensland, Australia, (1993).Leun g, K., An En ergy Based Ore Specific M odel for Autogeno us and Semi-Autogenous GrindingMills,PhD Thesis , TheUn iversity o f Queensland, Australia, (1987).Morrell, S. & Stephenson, I ., Slurry Discharge C apacity of Auto genou s and Se mi-A utogenou s Milland th e Effect of Grate D esign,In t . Jou rna l o f Minera ls Pro cess ing ,Elsevier, In Press, (1995).Morrell, S., The Prediction of Grinding Mill Pow er,Trans IM M ,101, C25-32, (1991).Morrell, S.~ Simulations of Bauxite G rinding in a Serni-Autogenous Mill and DS M Scre en CircuitM.Eng.Sc Thesis , TheUn ivers ity o f Queensland, Australia, (1989).Warder, J. & Davies, M., Autogenous milling at Leinster Nickel Operations,Pro c . F i fth M i l l Op s .Conf. ,Roxlby Downs, A uslM M 115-121 (1994).

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