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1/18

Moly-Cop Tools, Version 3.0

About the BallBal_DirectSpreadsheet ...

Scope :

The BallBal_Directspreadsheet was designed to o!p"te the Size-by-Size Mass Balancearo"nd the HydrocycloneClassifierso# an$ gi%en Conventional Ball Millir"it& operating "nder the Directon#ig"ration 'see Flowsheet(& on the)asis o# at"al plant !eas"re!ents.

Theoretical Fraewor! :

*hene%er at"al grinding data are olleted in a plant en%iron!ent& the$ will in%aria)l$ )e a##eted )$ nat"ral experi!ental

and !eas"re!ent errors& in s"h a wa$ that the )asi !ass )alane e+"ation aro"nd the h$dro$lones& #or partiles o#si,e di:

fiCF CF " fi

## $ fi%% &&& & #or i - 1&n

will ne%er )e satis#ied. n the a)o%e expression CF& #and %represent the !ass #lowrate o# solids in the $lones #eed&"nder#low and o%er#low strea!s& respeti%el$. i!ilarl$& fi

CF& fi#and fi

%represent the #ration o# those total respeti%e

strea!s orresponding to partiles o# si,e di.

The Ballbal_Directro"tine allows #or the al"lation o# a whole new set o# orresponding ad"sted or #itted %al"es fiCF

, fiU

and fi

O& s"h that the o)eti%e #"ntions :

i " ' wCF(fi

CF- fiCF)*$ w#(fi

#- fiU)*$ w%(fi

%- fiO)*+ or e%er$ partile si,e di

are !ini!i,ed and the ad"sted %al"es so generated stritl$ satis#$ the !ass )alane restritions :

fiCFCF = fi

UU+ fiOO & #or i - 1&n

where wCF& w#and w%are "serde#ined weighting #ators inl"ded to represent the relati%e +"alit$ and relia)ilit$ o# thesa!ples #ro! eah o# the 3 strea!s and the !ass #lowrates CF& Uand Oare al"lated as :

CF " F (, $ C) U " F (C) O " F


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3/18

Moly-Cop Tools, Version 3.0

About the Ballbal_DirectSpreadsheet ...

where ' error( orresponds to the o!)ined sa!pling and !eas"ring error perentage. *eighting #ators !"st ne%er )eset e+"al to ,ero.

The leasts+"are !ini!i,ation pro)le! stated a)o%e !a$ )e lineari,ed and sol%ed thro"gh the a/ran/e M.ltipliersMethod'see 3bo.t 444 in Cyclobal_Sin/le(.

"rther re#ine!ent o# the ad"sted %al"es so o!p"ted is ahie%ed )$ i!posing the ondition that these %al"es !"ston#or! to the 5litt6s Classification 7fficiency"r%e : 'see 3bo.t 444 in Cyclosi_Sin/le(

7i" Bpf $ (, - Bpf) (, - e8p ' - 94;< (di1d=9c)+)

with the aid o# the xel ")ro"tineSolverto !ini!i,e a leasts+"are error o)eti%e #"ntion with respet to para!etersp#& d50

and !.

inall$& the si,e distri)"tions #or the re!aining strea!s o# the ir"it '#resh #eed& !ill #eed and !ill disharge( are al"latedon the )asis o# the ad"sted %al"es so o)tained.

Data >np.t and 5ro/ra 78ec.tion :

ost o# the data re+"ired )$ the !odel !"st )e de#ined in eah orresponding "nproteted white bac!/ro.nd cellinside the red do")lelined )order o# the here attahed Data_Fileworsheet. ?ray bac!/ro.nd cellsontain the res"ltso# the orresponding #or!"la there de#ined and are proteted to a%oid an$ aidental editing.

The re!aining in#or!ation re+"ired to r"n the progra! is entered in the Control_5anelworsheet& where the "ser isre+"ested to pro%ide initial g"esses o# the p#& d50

and ! para!eters 'see 3bo.t 444in Cyclosi_Sin/le(. The p

para!eter is rarel$ "sed and was inorporated to tae into ao"nt the possi)le shortir"it o# oarse partiles to theo%er#low 'as o"ld )e the ase in highl$ press"ri,ed $lones(. inall$& the "ser !"st spei#$ the relati%e weighting #ators#or the %ario"s #eed& "nder#low and o%er#low strea!s pl"s the relati%e weighting #ators #or the si,e distri)"tion and perentsolids !eas"re!ents.

To r"n the progra!& selet the o)eti%e #"ntion Cell 7*


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Moly-Cop Tools/ 294202387.xlsx 11/09/2015 / 13:36:2

Saple @ 1

ei/htin/ Factors :

Streas :

resh eed 0

ill =isharge 1

$lone eed 1

$lone >?#low 1

$lone ;?#low 1

Size Distrib.tions 1

E Solids 1

>nitial ?.esses :

p# p d50 !

0.275 0.131 124.3 1.591 4

%b4 F.nction : G;4,

Classifier Constants :a1 11.08

a2 2.392

a3 30.17

a4 0.107 1.328

Moly-Cop Tools TM (Version 3.0)

Ballbal_Direct :M3SS B33@C7 C%S#A7 3A%#@D 3 B3 M> ?A>@D>@? C>AC#>T

@ote: "rrent al"lations are not %alid& i# ;@AB has not )een r"n a#ter the last data !odi#iation.

10 100 1000 10000

1

10

100

ill =isharge

$lone >?#low

$lone ;?#low

ol"!n

ol"!n

ol"!n C

5article Size icrons

E 5assin/


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Circ.it Type D>A7CT

Aear!s ase ase xa!ple

Mill Diensions and %peratin/ Conditions 113 alls

##. =ia!. ##. @ength peed harge alls nterstitial @i#t 0 ;%er#illing

#t #t ritial illing& illing& l"rr$ illing& ngle& 'D( 22 l"rr$

6.0 12.0 76.0 38.00 38.00 100.00 33.8 135 @et 5ower

rp! 23.8 10.0 @osses

,=9 ?ross !

Cyclone Diensions (inches) and %peratin/ 5ress.re (psi)


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10 10 1700 2003 0.00 0.00 100.0 0.00 0.00 100.00 0.00 0.00

11 14 1180 1416 0.00 0.00 100.0 0.00 0.00 100.00 0.00 0.00

12 20 850 1001 0.00 0.00 100.0 0.00 0.00 100.00 0.00 0.00

13 28 600 714 0.00 0.00 100.0 0.00 0.00 100.00 0.00 0.00

14 35 425 505 0.00 0.00 100.0 0.00 0.00 100.00 0.00 0.0015 48 300 357 66.24 66.24 33.8 0.00 0.00 100.00 0.00 0.00

16 65 212 252 3.52 3.52 30.2 0.00 0.00 100.00 0.00 0.00

17 100 150 178 3.10 3.10 27.1 0.00 0.00 100.00 0.00 0.00

18 150 106 126 5.69 5.69 21.4 0.00 0.00 100.00 0.00 0.00

19 200 75 89 3.77 3.77 17.7 0.00 0.00 100.00 0.00 0.00

20 325 44 57 6.86 6.86 10.8 68.63 86.54 13.5 155.17 86.54

21 325 0 22 10.81 10.81 0.00 10.68 13.46 0.00 24.14 13.46

Totals ,99499 ,99499 K;4


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Saple @ 1

Char/e Mill Char/e ei/ht tons 3pparent

ol.e all l"rr$ Density

!3 harge nterstitial xess ton/!3

3.66 17.12 3.41 0.00 5.6

Feedrate ton1hr (dry) 100.0

%re Density ton1< 3.20

Aolls Density ton1< 7.80

TA>B#T>%@S Cyclone #6flow Cyclone %6flow

Passing ton/hr Betained Passing ton/hr Betained Passing

100.00 100.00 100.00

100.00 0.00 0.00 100.00 0.00 0.00 100.00100.00 0.00 0.00 100.00 0.00 0.00 100.00

100.00 0.00 0.00 100.00 0.00 0.00 100.00

100.00 0.00 0.00 100.00 0.00 0.00 100.00

100.00 0.00 0.00 100.00 0.00 0.00 100.00

100.00 0.00 0.00 100.00 0.00 0.00 100.00

100.00 0.00 0.00 100.00 0.00 0.00 100.00

100.00 0.00 0.00 100.00 0.00 0.00 100.00

Circ.it


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100.00 0.37 0.47 99.53 0.17 0.17 99.8

100.00 0.97 1.23 98.30 0.40 0.40 99.4

100.00 2.41 3.04 95.27 0.94 0.94 98.5

100.00 6.71 8.46 86.81 1.85 1.85 96.6

100.00 12.01 15.14 71.67 3.99 3.99 92.6100.00 14.42 18.18 53.49 5.73 5.73 86.9

100.00 14.04 17.71 35.78 11.03 11.03 75.9

100.00 7.65 9.65 26.13 9.24 9.24 66.6

100.00 8.25 10.41 15.72 11.23 11.23 55.4

100.00 3.41 4.30 11.42 10.89 10.89 44.5

13.46 3.93 4.95 6.47 15.42 15.42 29.1

0.00 5.13 6.47 0.00 29.10 29.10 0.00

K;4


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Moly-Cop Tools/ 294202387.xlsx / lowsheet 11/09/2015 / 13:36:23

Saple @ ,

Aear!s ase ase xa!ple

41.49 olids

79.86 i,e 18

psi 11.00 ,94L 5L9

G o# $lones 1

Aortex 7.00 ir. @oad 115.10

pex 3.50 0.275 p# 245

0.207 pw

olids 75.73

*ater&

133.9

ton1hr ,9949 *ater& 5.1

80 396

?ross ! ,=949*h/ton 1.50 alls 38.00

*io 3.23 ritial 76.00

olids 83.00

olids 54.73

Moly-Cop Tools TM (Version 3.0)

!3/hr

!3/hr

!3/hr


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Saple: ,

B3B3Hrinding ir"it ass alane sti!ator

Be!ars: ase ase xa!ple

C>AC#>T M3SS B33@C7Configuration D!"#CT

Fresh Mill Mill S.p Cyclone Cyclone Cyclone

Feed Feed Dischar/e ater Feed #6flow %6flow

;re& ton/hr 100.0 215.1 215.1 0.0 215.1 115.1 100.0 *ater& !3/hr 2.0 38.9 44.1 133.9 177.9 36.9 141.0

l"rr$& ton/hr 102.0 254.0 259.2 133.9 393.0 152.0 241.0

l"rr$& !3/hr 33.3 106.1 111.3 133.9 245.1 72.9 172.3

l"rr$ =ens.& ton/!3 3.065 2.393 2.329 1.000 1.603 2.086 1.399

olids ')$ %ol"!e( 93.9 63.3 60.4 0.0 27.4 49.4 18.1

olids ')$ weight( 98.0 84.7 83.0 0.0 54.7 75.7 41.5

i esh ;pening

1 1F 25400 100.00 100.00 100.00 0.00 100.00 100.00 100.00

2 3/4F 19050 100.00 100.00 100.00 0.00 100.00 100.00 100.00

3 5/8F 15875 100.00 100.00 100.00 0.00 100.00 100.00 100.00

4 1/2F 12700 100.00 100.00 100.00 0.00 100.00 100.00 100.00

5 3/8F 9500 100.00 100.00 100.00 0.00 100.00 100.00 100.00

6 1/4F 6700 100.00 100.00 100.00 0.00 100.00 100.00 100.00

7 4 4750 100.00 100.00 100.00 0.00 100.00 100.00 100.008 6 3350 100.00 100.00 100.00 0.00 100.00 100.00 100.00

9 8 2360 100.00 100.00 100.00 0.00 100.00 100.00 100.00

10 10 1700 100.00 99.83 99.80 0.00 99.80 99.67 99.94

11 14 1180 100.00 99.38 99.29 0.00 99.29 98.85 99.80

12 20 850 100 00 98 31 98 05 0 00 98 05 96 84 99 45

ol$op ToolsT& Aersion 3.0

5article Size Distrib.tions(Cummulative % assin!"


12/18

Saple: ,



C3SS>F>7AS 57AF%AM3@C7


13/18


14/18

Saple: ,



B3 M> 57AF%AM3@C7

##. =ia!eter& #t 6.0 150

##. @ength& #t 12.0 135

peed& ritial 76.0 Thro"ghp"t& ton/hr 215.1

pp. =ensit$& ton/!3 5.61 olids ')$ weight( 84.7

harge @e%el& 38.0 p. nerg$& I*E/ton 0.70alls illing& 38.0 Bed"tion Batio 1.38

@i#t ngle& 'D( 33.8 r)iter?s low


15/18

Page 15


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Page 16

17 150 178.32555 0.6955009 11.21 7.7962592 3.41 6.25 8.13 4.09

18 106 126.0952 0.5768161 12.93 7.4602389 5.47 7.21 7.78 6.57

19 75 89.162773 0.4744378 9.49 4.5030688 4.99 5.29 4.69 5.98

20 44 57.445626 0.3844301 65.02 24.996724 40.03 36.26 26.05 48.01

21 0 22 0.3009842 30.84 9.2824212 21.56 17.20 9.67 25.86

Total 179.31 95.95 83.36 100.00 100.00 100.00


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Page 17

Passing '!odel( Passing 'exp( '*eighted rror(J2

$lone $lone $lone $lone $lone $lone $lone $lone $lone

eed >?#low ;?#low eed >?#low ;?#low eed >?#low ;?#low

1 1 1

100.00 100.00 100.00 100.00 100.00 100.00

100.00 100.00 100.00 100.00 100.00 100.00 0.000 0.000 0.000

100.00 100.00 100.00 100.00 100.00 100.00 0.000 0.000 0.000

100.00 100.00 100.00 100.00 100.00 100.00 0.000 0.000 0.000

100.00 100.00 100.00 100.00 100.00 100.00 0.000 0.000 0.000

100.00 100.00 100.00 100.00 100.00 100.00 0.000 0.000 0.000100.00 100.00 100.00 100.00 100.00 100.00 0.000 0.000 0.000

100.00 100.00 100.00 100.00 100.00 100.00 0.000 0.000 0.000

100.00 100.00 100.00 100.00 100.00 100.00 0.000 0.000 0.000

99.80 99.67 99.94 99.80 99.53 99.83 0.000 0.021 0.013

99.29 98.85 99.80 99.29 98.30 99.43 0.000 0.309 0.138

98.05 96.84 99.45 98.05 95.27 98.49 0.000 2.715 0.952

94.88 91.69 98.56 94.88 86.81 96.64 0.000 31.623 3.947

88.96 82.08 96.87 88.96 71.67 92.65 0.000 211.323 20.826

81.50 70.18 94.54 81.50 53.49 86.92 0.000 973.581 76.897

72.22 56.32 90.52 72.22 35.78 75.88 0.000 3296.500 371.964


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Page 18

65.97 48.20 86.42 65.97 26.13 66.65 0.000 7131.849 880.519

58.76 40.42 79.86 58.76 15.72 55.42 0.000 24683.759 1945.454

53.46 35.73 73.87 53.46 11.42 44.53 0.000 45300.057 4344.273

17.20 9.67 25.86 17.20 6.47 29.10 0.000 2455.153 124.274

;%erall

4425.626 408.908 2417.267