Trituración y Molienda

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AMV CONSULTORES SAC1

Partcula liberadaAMV CONSULTORES SAC2

2AMV CONSULTORES SAC3Anlisis MineralgicoObjetivo :

Identificacin de las especies mineralgicas y el conocimiento detallado de sus propiedades fsicas y qumicasAMV CONSULTORES SAC4Anlisis mineragrficoEntre otros objetivos :

Identificar para cada especie mineralgica sus intercrecimientos en cada tamao de mallaAMV CONSULTORES SAC5 LIBERACION DEL MINERALDentro del procesamiento de mineral en una Planta Concentradora , la conminucin tiene el objetivo de romper el mineral hasta un tamao pequeo suficiente para dejar libres los componentes de valor de la ganga que lo acompaa, para formar luego un concentrado con alto precio de venta.Para el diseo de la Planta Concentradora , es importante la eleccin del tamao final al cual se llevar la conminucin, para asegurar un nivel econmico de liberacin.AMV CONSULTORES SAC6La reduccin de tamao del mineral y la liberacin son interdependientes Por un lado, si la reduccin de tamao es insuficiente, no podrn recuperarse gran parte de los componentes valiosos ; mientras que, si la reduccin de tamao es excesiva , se tendrn exagerados costos de energa.Una partcula esta liberada cuando en un mtodo de concentracin se le recupera selectivamente dentro de un concentrado. AMV CONSULTORES SAC7Antes del rompimientoAsociaciones de minerales . Ejemplo de tres mineralesAMV CONSULTORES SAC8Especies liberadasCompsito binarioCompsito ternarioAMV CONSULTORES SAC9Mediciones de la liberacinEl mtodo clsico de medida es por identificacin manual , fraccionamiento y conteo bajo un microscopio binocular .Se requiere destreza para la identificacin mineral y un tiempo largo para el anlisis (anlisis mineralgico)El desarrollo de sistemas automatizados para la identificacin de las fases minerales ayud a mejorar el estudio de la liberacin en conminucin y su velocidad y exactitud constituyen la principal ventaja sobre el mtodo tradicionalAMV CONSULTORES SAC10La tcnica QEM*SEM desarrollada por la CSIRO Divisin of Minerals se emplea con mucha frecuencia.Quantitative Evaluation of Materials using Scanning Electron Microscopy El hardware comprende un microscopio electrnico de barrido controlado por computadora , adaptado con detectores de retorno de electrones dispersos y rayos xAMV CONSULTORES SAC11QEM*SEM usa las seales BSE (Back Scattered Electrn) para localizar rpidamente las partculas y proporcionar un numero atmico medio para la fase que est midindose. Simultneamente, un espectro de rayos x es colectado para que los elementos qumicos puedan ser identificados y estimados sus proporciones relativas.AMV CONSULTORES SAC12Diagramas de flujo de trituracin

Shut de alimentacinAMV CONSULTORES SAC13Tolva de gruesosTolva de finosCarga circulante

Flowsheet simplificado de unaPlanta de trituracin cribaTrituradora secundariaFaja transportadoraApronfeederTrituradora primariaGrizzlyAMV CONSULTORES SAC14

Alimentador de placas - Apron feederAMV CONSULTORES SAC15

Alimentador de oruga o placasAMV CONSULTORES SAC16Grizzly



NNI0-4 10-2 1 102 104 106Tamao de mineral, micrones108

106

104

102

1 -

10-2 -Energa consumida , kwh / tKick, n: 1Bond , n:1,5V. Rittinger, n:2Molienda TrituracindE = -k

Hukki (1975)


Durante la trituracin, la compresin es el mecanismo principal que origina la fractura en trozos de tamao parecido al inicial, sin embargo la abrasin y el desprendimiento de bordes y partes afiladas o salientes del mineral causa que se produzca mucha cantidad de finos (atriccin)


PITMANAMV CONSULTORES SAC22

Quijadas movil y fija AMV CONSULTORES SAC23




AMV CONSULTORES SAC27Trituradora de quijadasEmplea en triturar la mitad del tiempo de operacin Capacidad T = 0,6 L S0

T : ton/horaL : longitud de la abertura de ingreso, pulgadasS0 : set en posicin abierta, pulgEjm. Una trituradora de quijadas 10 x 16

T = 0,6 (16) (1) = 9,6 ton/hPara una fragmentacin efectiva, el ngulo formado por ambas mandbulas debe estar entre 20 y 22 AMV CONSULTORES SAC28

Fajas Transportadoras


ElectroimanAMV CONSULTORES SAC31

Polines de carga AMV CONSULTORES SAC32

Criba vibratoriaAMV CONSULTORES SAC33



MOLINOSEquipos de reduccin de tamao del mineral ( ltima etapa de conminucin )Casco de forma cilndrica que al girar permite que las fuerzas desarrolladas internamente para los elementos moledores acten por impacto, abrasin o atriccin sobre los minerales produciendo los sucesivos rompimientos AMV CONSULTORES SAC37

Impacto: Ocurre cuando la energa aplicada est sobre-excedida de aquella necesaria para fracturar la partcula. El resultado es un gran nmero de partculas con un amplio rango de tamaos


Agua Apex Vortex AlimentacinMolienda - ClasificacinOverflowUnderflow

AguaAMV CONSULTORES SAC39

39FACTORES DE INTERACCIN EN LA MOLIENDAElementos moledores:

Esferas de acero de diferentes dimetrosAMV CONSULTORES SAC40

Medios de moliendaAMV CONSULTORES SAC41

Vista interior de un molino - liners - bolasAMV CONSULTORES SAC42

Tamao de los medios de moliendaAMV CONSULTORES SAC43

Esferas grandes impactan y fracturan mejor a los minerales grandesAMV CONSULTORES SAC44


Tamao del mineralVelocidad de fractura

AMV CONSULTORES SAC46Factor de llenado jjAMV CONSULTORES SAC47Dimetro del molino DAMV CONSULTORES SAC48Velocidad del molino % Cs

AMV CONSULTORES SAC49Tamao del mineral de alimentacinF80P80AMV CONSULTORES SAC50Agua Apex Vortex AlimentacinOverflowUnderflow

AguaCarga circulanteAMV CONSULTORES SAC5151Distribucin de bolas de acero por tamaosF. Bond :

Tamao mayor B = (F80/k)0,5 ( WI / % Cs )1/3

Peso acumulado por tamao = 100 (d/B)3,84

Clculo del peso de acero a cargar al molino: Para un molino 8 x 8 que girar a 20 rpm con j = 0,4El mineral tiene densidad media 2,8 g / cm3 y WI 12 kwh / TM AMV CONSULTORES SAC52

Indice de trabajo WIvelocidad crtica CsAMV CONSULTORES SAC53


Grfico110430

Valores Y

Hoja1Valores XValores YTamao2.7103.244330Para cambiar el tamao del rango de datos del grfico, arrastre la esquina inferior derecha del rango.

Grfico110430

Valores Y

Hoja1Valores XValores YTamao2.7103.244330Para cambiar el tamao del rango de datos del grfico, arrastre la esquina inferior derecha del rango.

About ...About the Media Charge_Strings Spreadsheet ...

&L&"Arial,Bold"&8Moly-Cop Tools&"Arial,Regular" / &F&R&8&D / &TScope :

The Media Charge_Strings spreadsheet was designed to perform all calculations related to the volume, area and size composition of the "string" of balls generated inside any given grinding mill, at equilibrium conditions, as a result of the continuous recharge of a single make-up ball size or a combination of two different sizes.

Theoretical Framework :

The most widely accepted mathematical description of the gradual consumption process experienced by a grinding ball inside a tumbling mill is known as the Linear Wear Theory, by which the mass rate of consumption of a grinding ball is described as directly proportional to the surface area exposed by such ball to the various wear mechanisms (abrasion and/or corrosion) active in the mill charge environment :

Wt = d(mb)/d(t) = - km Ab

where :

Wt = mass wear rate, kg/hr mb = ball weight, kg; after t hours of being charged into the mill. Ab = exposed ball area, m2 km = mass wear rate constant, kg/hr/m2.

Equivalently, taking into account the geometry of the grinding body (sphere or cylinder), one obtains :

d(d)/d(t) = - 2 km / rb = - kd

where :

d = size (diameter) of the grinding ball, mm; after t hours of being charged into the mill. rb = grinding ball density, ton/m3 kd = wear rate constant, mm/hr.

If kd is to remain unaffected by the extent of wear; that is, kd is not a function of the current ball size d - a condition satisfied by most grinding media varieties and normally referred to as Linear Wear Kinetics - the above expression may be simply integrated to obtain :

d = dR - kd t

where dR represents the initial size of the balls.

Ideally, the periodic recharging of balls to the mill must be performed in an almost continuous fashion, in order to maintain a constant charge level inside the mill. When the required amount of balls of a single size dR are continuously charged to the mill at an appropriate constant rate (as dictated by the overall media consumption rate), the Linear Wear Theory described above predicts that - at equilibrium, inside the mill - there will be the exact same number of new and partially worn balls of every possible size.In mathematical terms, this implies that the number density function of the probabilistic distribution of ball size d is solely determine by the make-up size dR in the expression :

f0(d) = 1 / dR ; for 0 < d < dR

in such a way that the product f0(d)d(d) = d(d)/dR represents the fraction (by number) of balls in the charge whose size is in the infinitesimal range [d, d + d(d)]. Upon proper integration, this equation yields :

F3(d) = ( d/dR )4 ; for 0 < d < dR

where F3(d) represents the fraction (by weight) of balls of size less than d, in the mill charge.

It may also be demonstrated that for a monosize recharge practice with balls of size dR, the total area exposed by the ensemble of balls is inversely proportional to dR :

a = (A/Vap) = 8000 (1 - fv) / dR

where :

a = specific charge area, m2/m3 (apparent) Vap = apparent volume occupied by the balls in the charge (including all interstitial voids), m3 fv = volumetric fraction of interstitial voids in the ball charge (typically 40%).

When two different make-up sizes d1R and d2R are charged in a r1 : r2 proportion (by weight), the overall area exposed may be obtained from :

a = (A/Vap) = v1 a1 + (1 - v1) a2

where v1 - the volumetric fraction of String 1 in the mill - is given by :

v1 = r1 a2 / [(1 - r1) a1 + r1 a2]

and where the areas a1 and a2 are calculated from the "monorecharge" equation above for d1R and d2R, respectively.

Finally, the size distribution of the composite string resulting from the combination of the two independent "monorecharge" strings - corresponding to each make-up size - may be calculated as a weighted average of the two strings with v1 and (1-v1) as the respective weighting factors.

Data Input :

All data required by the model must be defined in each corresponding unprotected white background cell of the here attached Mixed_Strings worksheet. Gray background cells contain the results of the corresponding formulas there defined and are protected to avoid any accidental editing.

New Moly-Cop Tools users are invited to explore the brief inserted comments in the most relevant cells, rendering the attached worksheet self-explanatory.

Mixed_StringsMoly-Cop Tools TM (Version 2.0)BALL CHARGE COMPOSITION AT EQUILIBRIUMRemarks :Base Case ExampleMill Dimensions and Operating Conditions :Eff. Diameter, ft18.50Eff. Diameter, m5.64Eff. Length, ft22.00Eff. Length, m6.71Ball Dens., ton/m3 (app)4.65Mill Volume, m3167.79Ball Filling, % (app)38.00Charge Weight, tons296.22Scrap Size, in0.50Balanced Charge :OverallString 1String 2Charge AreaTop Size, in1.001.00Current MixSpecific Area, m2/m3176.38176.38176.38Recharge Policy, %100.000.00Target ValueMill Charge Content, %100.000.0065.60Excess Area110.78Balanced Charge,InitialBall Size, in% Passing% Passing% RetainedMid-PointsString 1String 2CombinedCharge1.0100.00100.0080.001.0100100100800.50.000.0020.000.7071067812202020200.50.000.000.000.500000.50.000.000.000.500000.50.000.000.000.500000.50.000.000.000.500000.50.000.000.000.500000.50.000.000.000.500000100Weight, tons296.220.00296.22Volume, m3 (app)63.760.0063.76Area, m211246011246# Balls per ton321093210932109Tamao de Recarga, pulgadasDim. de Bola, pulgadas6.05.55.04.54.03.53.02.52.01.51.06.016.05.525.717.45.019.327.319.04.514.119.929.221.04.09.914.020.531.223.43.515.19.413.720.933.526.53.012.08.613.221.136.030.62.59.07.612.220.838.636.12.06.16.310.719.841.043.91.53.56.011.022.942.456.31.013.743.8100.0

&L&"Arial,Bold"&8Moly-Cop Tools&"Arial,Regular" / &F&R&8&D / &TAs defined in the attached Optimal Ball Size worksheet.As defined in the attached Optimal Ball Size worksheet.As defined in the attached Optimal Ball Size worksheet.As defined in the attached Optimal Ball Size worksheet.As defined in the attached Optimal Ball Size worksheet.Commercially available sizes only !Commercially available sizes only !As recommended by the user, with the aid of the attached Optimal Ball Size worksheet.To determine the proper combination of the 2 strings to yield the Target Area level, set this value to zero using the function Tools / Goal Seek, by changing Cell D21.If less than 10%, it is recommended to simply add this proportion to the neighboring ball size fractions.If less than 10%, it is recommended to simply add this proportion to the neighboring ball size fractions.If less than 10%, it is recommended to simply add this proportion to the neighboring ball size fractions.If less than 10%, it is recommended to simply add this proportion to the neighboring ball size fractions.If less than 10%, it is recommended to simply add this proportion to the neighboring ball size fractions.If less than 10%, it is recommended to simply add this proportion to the neighboring ball size fractions.If less than 10%, it is recommended to simply add this proportion to the neighboring ball size fractions.If less than 10%, it is recommended to simply add this proportion to the neighboring ball size fractions.

Trituración y Molienda

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