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    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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    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 [email protected] 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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    Moly-Cop Tools/ 294202387.xlsx 11/09/2015 / 13:36:23

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

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

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

    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 [email protected] 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

    1