Introduction to Mineral Processing Design and Operation PDF

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Introduction to Mineral Processing Design and Operation PREFACE In nature minerals of interest exist physically and chemically combined with the host rock. Removal of the unwanted gangue to increase the concentration of mineral in an economically viable manner is the basis of mineral processing oper...

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Introduction to Mineral Processing Design and Operation PREFACE In nature minerals of interest exist physically and chemically combined with the host rock. Removal of the unwanted gangue to increase the concentration of mineral in an economically viable manner is the basis of mineral processing operations. This book treats the strategy of beneficiation as a combination of unit operations. Each unit process and its operation is therefore treated separately. Integration of these units leading to the development of viable flow sheets that meets the final objective, is then indicated. The greatest challenge to a mineral processor is to produce high grade concentrates consistently at maximum recovery from the ore body. To quantify recovery a reasonable idea of the initial concentration of mineral in a lode is required. Proper sampling representing the ore body is therefore essential. The book therefore commences with the techniques of sampling of ore followed by the design and operation of unit processes of comminution that help to release the mineral from the associated rocks. Separation and concentration processes using techniques involving screening, classification, solid-liquid separations, gravity separation and flotation then follow. In the book some early methods of operation have been included and the modern methods highlighted. The design and operation of each unit process is a study by itself. Over the years, improvements in the understanding of the complexities of these processes have resulted in increased efficiency, sustained higher productivity and grades. Mathematical modeling has helped in this direction and hence its use is emphasized. However, the models at best serve as guides to most processes operations that invariably involve complex interdependent variables which are not always easily assessed or manipulated. To solve the dilemma, plants are increasingly being equipped with instruments and gadgets that respond to changes much faster than humans can detect. Dynamic mathematical models are the basis of operations of these gadgets which are usually well developed, sophisticated, electronic equipment. In this book therefore, the basics of instrumental process control is introduced the details of which belong to the province of instrument engineers. This book is written after several years on plant operation and teaching. The book is biased towards practical aspects of mineral processing. It is expected to be of use to plant metallurgist, mineral processors, chemical engineers and electronics engineers who are engaged in the beneficiation of minerals. It is pitched at a level that serves as an introduction to the subject to graduate students taking a course in mineral processing and extractive metallurgy. For a better understanding of the subject solved examples are cited and typical problems are set. Most problems may be solved by hand-held calculators. However most plants are now equipped with reasonable numbers of computers hence solution to problems are relatively simple with the help of spreadsheets. The authors are grateful for the help received from numerous friends active in the field of mineral processing who have discussed the book from time to time. Particular thanks are due

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to Dr Lutz Elber and Dr H. Eren who painfully went through the chapter on process control. Authors are also grateful for permission received from various publishers who own material that we have used and acknowledged in the text. And lastly and more importantly to our respective families who have helped in various ways and being patient and co-operative.

A.Gupta and D.S.Yan Perth, Australia, January 2006

Symbols and Units A general convention used in this text is to use a subscript to describe the state of the quantity, e.g. S for solid, L for liquid, A for air, SL or P for slurry or pulp, M for mass and V for volume. A subscript in brackets generally refers to the stream, e.g. (O) for overflow, (U) for underflow, (F) for feed, (C) for concentrate and (T) for tailing. There are a number of additions to this convention which are listed below. a a ap A A A Ac Ai Ay AE AEFF Ao A0E AM Ay b b By c C C C CA Cc CD Ci Co CMAX Ct CS(c) Cu, C F CCRIT CF CI CR CS(u)

a constant amplitude particle acceleration a constant aperture area cross-sectional area abrasion index assay of particles in the i th . size and j t h . density fractions effective area areal efficiency factor open area effective open area assay of mineral underflow area a constant Rosin-Rammler distribution parameter breakage distribution function a constant a constant circulation ratio or load concentration, (mass solid/volume of slurry) concentration of air average concentration of solids in the compression zone drag coefficient concentration of species i initial concentration (mass of solid/volume of slurry) maximum concentration (mass of solid/volume of slurry) concentration at time t (mass of solid/volume of slurry) concentration of solid (C = concentrate, F = feed, T = tail f = froth, P = pulp) concentrations of the underflow and feed respectively, (mass of solid/volume of slurry) critical concentration correction factor confidence interval confidence range solids concentration in the underflow (O = overflow,F = feed) concentration by mass of solids in the feed

m m/s 2 microns m2 m2

m2 % % %, g/t, ppm m2

kg/m 3 kg/m 3 kg/m 3 kg/m 3 kg/m 3 kg/m 3 kg/m 3 kg/m 3 kg/m 3

% %

xvi

CvS(F)

cc cv Coo

d d d32 dN

dso, dsoc

dB dF dL dMAX dMIN d\iiD dcutter

dc dw D D D* Dc D, Do Du e Ei

Ec E Ec EB Eo Eo EP Eu ET / /(JB)

As) /P,/F

fi

F microns F F F Fi

concentration by volume of solids in the feed concentration criterion coefficient of variation concentration at infinite time a constant particle size, diameter Sauter mean diameter nominal diameter cut or separation size, corrected cut size ball diameter 63.2% passing size in the feed liberation size largest dimension smallest dimension mid-range dimension cutter opening cylpeb diameter wire diameter discharge mass ratio (liquid/solid) displacement, distance, diameter dimensionless parameter cyclone diameter inlet diameter overflow diameter underflow diameter a constant partition coefficient of size i = recovery of size i in the U/F corrected partition coefficient energy corrected partition coefficient energy of rebound specific grinding energy efficiency based on oversize Ecart probability, probable error of separation efficiency based on undersize total energy a constant ball wear rate ball load-power function suspensoid factor function relating to the order of kinetics for pulp and froth mass fraction of size i in the circuit feed feed size

% kg/m3 m m m microns cm, m m m m m m m mm m m m m m m kWh Wh kWh/t kW kg/h cm,

floats at SG froth stability factor feed mass ratio (liquid/solid) settling factor

-

xvii

Fgo

FB FB

Fc Fc FD Fg FG

Fos FR

Fs Fs g G G,G b p

G' AG h huh,*

H H Ht HB HB

He He HOF HR

Hs Hu I I JB

Jc JG JR

Jp

k k A ,k A kF, k s ki

kc, kC5o ks, kS5o

K KDO

KE

80% passing size of feed Rowland ball size factor buoyancy force Bond mill factor centrifugal force drag force gravitational force correction factor for extra fineness of grind correction factor for oversized feed correction factor for low reduction ratio mass flow rate Bond slurry or slump factor gravitational constant (9.81) grade (assay) net grams of undersize per revolution grinding parameter of circulating load free energy parameter = X/CT diatances within the conical section of a mill hindrance factor height height at time t height of rebound pendulum height of bed height of ball charge height of the start of the critical zone in sedimentation height of the clarification zone (overflow) height of rest hindered settling factor mudline height at the underflow concentration height after infinite time impact crushing strength imperfection fraction of mill volume occupied by bulk ball charge fraction of mill volume in cylindrical section occupied by balls and coarse ore superficial gas velocity fraction of mill volume occupied by bulk rock charge fraction of mill volume filled by the pulp/slurry constant rate constant for air removal via froth and tailings respectively rate constant for fast and slow component respectively comminution coefficient of fraction coarser that ith screen screening rate constant, crowded condition, normal and half size screening rate constant, separated condition, normal and half size constant material constant kinetic energy

microns

N N N N -

kg/s,t/h -

m/s2 %, g/t, ppm g/rev J m -

m, cm m m

m m m m m m m kg.m/mm

m/s min"1

-

t/h/m2

m1 kW

xviii

length aperture size effective aperture LAE effective grinding length LEFF length of cyclone Lc length of cylindrical and cone sections LcYL, LcONE Nordberg loading factor LF minimum and maximum crusher set L M W , LMAX crusher throw LT length of vortex finder length from end of vortex finder to apex of a cyclone LVF moisture (wet mass/dry mass) m mineralogical factor m mass fraction of undersize in the feed muoo mass fraction of makeup balls of size k mk mass fraction of undersize in the oversize mu(O) m(r) cumulative mass fraction of balls less than size r mass rate of ball replacement per unit mass of balls mT mass fraction of undersize in the undersize mu(o> m mass of size i in the underflow (F = feed) i(U) mass mass M mass/mass fraction of i* increment Mi Moi cumulative mass fraction retained on i* screen at zero time My mass percent of the i* size fraction and j * density fraction mass of block MB mass of balls MB mill capacity Mc mass of crushing weight Me MF mass of feed mass of fluid MF mass of floats MFT Nordberg mill factor MF minimum mass of sample required MMIN MR mass of rock MR mass fraction of rock to total charge (rock + water) Mr cumulative mass fraction of balls of size r in the charge mass of striking pendulum Ms mass of solid Ms . sec), SOD n ^ 5 of solid feed, concentrate and tailing respectively mass of solid in froth MSK mass of sinks

m m m m m m m m m m kg/m3

MS{p) AM(t) Mj Mw n n

kg, t kg, t g kg, t min"1

L LA

I_I

mass of solid in the pulp mass of top size particle mass of new feed mass of water number of revolutions/min number of increments, measurements

kg/h.t kg g

kg,t kg,t % kg kg t/h kg t kg kg,t kg,t kg kg ke,t kg, t kg, t

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n n(r) ns N N N NL N' Oi

P Pi

P Pso p p p p p p PA, PC, PE, PF PcON PCYL PD PG

P« PL PM PM PNET PNL

Pos PR

Ps Ps PE AP q Q QB QH

Qo Qu QMSOT QMSCQ QM(F)

Qv(C), (T), (F) QvL(O)

order of rate equation cumulative number fraction of balls of size less than r number of sub-lots number of mill revolutions number of strokes/min number number of presentations per unit length number of particles/gram mass fraction of size i in the overflow binomial probability of being selected in a sample mass fraction of size i in the new feed product size 80% passing size of product proportion of particles pressure Powers roundness factor Jig power JKSimFloat ore fioatability parameter probability probability of adherence, collision, emergence, froth recovery power of the conical part of a mill power for the cylindrical part of a mill particle distribution factor proportion of gangue particles proportion of particles in the i . size and j * . density fractions liberation factor proportion of mineral particles mill power net mill power draw no load power period of oscillation relative mill power particle shape factor power at the mill shaft potential energy pressure drop alternate binomial probability = 1 — p capacity makeup ball addition rate basic feed rate (capacity) tonnage of oversize material capacity of the underflow flowrate of solids by mass in the overflow (U = U/F, F = feed) mass flow of solid in concentrate capacity, of feed slurry by mass flowrate by volume in concentrate, tailing and feed respectively capacity (flowrate) of liquid by volume in the overflow (U=underflow, F=feed)

min'1 nf1 g"1 microns microns Pa W kW kW kW kW kW s kW kW kPa t/h kg/day t/h/m t/h t/h t/h t/h t/h m3/h nrVh

xx

QVOP(U) QVOL(U)

Qvos(u) Qvs(O) Qv(f) Qv(O) Qw r0 r r ri, r2 R R R Ri,R2,R3 R R' R' Re ReA, Rec Re P RF Ri Ro RP RRO RT Rv Roo S S S SB SB S; SF S S SG, SGs T TN t to tR tu tio tA

flowrate by volume of entrained overflow pulp in the U/F flowrate by volume of entrained overflow liquid in the U/F m 3 /h flowrate by volume of entrained overflow solids in the U/F m 3 /h flowrate by volume of solids in the overflow (U = U/F, F = feed) flowrate by volume in the froth flowrate by volume of overflow (pulp) (U = underflow) ball wear rate fraction of test screen oversize ball radius ratio of rate constants = ICA /(kA+kA) radius within the conical section of a mill radius recovery reduction ratio Dietrich coefficients the mean radial position of the active part of the charge fractional recovery, with respect to the feed to the first cell mass of test screen oversize after grinding radius of cone at a distance Lj from cylindrical section Reynolds number in the apex and cone section respectively particle Reynolds number froth recovery factor radial distance to the inner surface of the active charge mass of test screen oversize before grinding radial distance of particle from the centre of a mill optimum reduction ratio radius at the mill trunnion recovery of feed volume to the underflow recovery at infinite time speed sinks at SG surface area surface area of ball bubble surface area flux breakage rate function Nordberg speed factor spacing, distance dimensionless parameter specific gravity, specific gravity of solid period of pulsation mass percent passing 1/N of the original size time detention or residence time effective residence time time for all solids to settle past a layer of concentration C size that is one tenth the size of original particle mean time taken for active part or charge to travel from the toe to the shoulder

m 3 /h m 3 /h m 3 /h m 3 /h mm/h m m m

m m

m g m m m/s m2 m2 s"1 min"1 m

h, min, s h s

h mm s

xxi

U Up

V V* Vc Vc VCONE

L(F)

Vo VR

VB° VB 1

vs° Vs1

var(d) var(c) var(pa) var(t) var(x) w w W W WE

W;

Ws x x x Xj

X

mean time for free fall from the shoulder to the toe mass fraction of size i in the underflow fraction of void space between balls at rest, filled by rock fraction of the interstitial voids between the balls and rock charge in a SAG mill occupied by slurry of smaller particles volume fraction of solids in the overflow, (U=underflow, F=feed) volume fraction of solids finer than the d50 in the feed (Vd5o/VS(F)) volume dimensionless parameter volume of the mill charge volume of the compression zone volume of conical section of mill volume of solids finer than the dso in the feed percent of mill volume occupied by balls volume dilution in the feed = VL(F/VS(F) volume of liquid in the feed, (U=underflow, F=feed) volume of mill volume dilution in the overflow = VL(O/VS(O> or QVL(O/QVS(O) percent of mill volume occupied by rock volume of solids in the feed, (U = underflow, O = overflow) terminal velocity unknown true value velocity of block pendulum before impact velocity of block pendulum after impact velocity of striking pendulum before impact velocity of striking pendulum after impact distribution variance composition variance preparation and analysis variance total variance variance thickness of slurry fraction of feed water in the underflow width dimensionless parameter effective width Bond Work Index Bond Work Index, laboratory test operating work index corrected operating work index water split = QML(O)/QML YSL> T L A £

e A K

9 -e-

c ¥>¥» Vw VCRIT (1

P Pb PC PB

PF

Po PL PR

ps PSL

Pw PM> pG U 0A CL CTM 0p Op A CTS 0T

e

fractional average mineral content Lynch efficiency parameter angle toe and shoulder angles of the charge the slurry toe angle function of charge position and mill speed volume fraction of active part of the charge to the total charge surface energy, surface tension, interfacial tension coefficient of restitution void fraction a ball wear parameter a ball wear parameter, wear distance per unit time porosity of a ball bed ratio of experimental critical speed to theoretical critical speed fraction with the slow rate constant fraction of critical speed settling or sedimentation flux withdrawal flux critical flux coefficient of friction specific gravity (dimensionless) or density density or SG of balls bulk density of the total charge, rock + balls + water bulk density density of fluid density of ore density of liquid density of rock density of solid density of slurry density of water density of the mineral and the gangue respectively standard deviation (where o 2 = var(x)) statistical error in assay standard deviation of a primary increment standard deviation on a mass basis standard deviation of the proportion of particles in a sample standard deviation of preparation and assay statistical error during sampling total error nominal residence time angle

radians radians radians N/m kg/m2/s kg/m2/s kg/m2/s kg/m3, t/m3 kg/m3,t/m3 kg/m3 kg/m3 kg/m3 kg/m3 kg/m3 kg/m3 kg/m3 kg/m3 kg/m3, t/m3 s radians,

viscosity velocity critical speed

mNm, Pa.s m/s rpm

degree

xxiii

VF VN

Vo v

O(i)

VR

VR

Vs VSo

Vst VT VT CO CO COp

?

%s

velocity across a screen normalised tangential velocity = VR/VT overflow rate ideal overflow rate tangential velocity at distance Rp rise velocity settling velocity initial settling velocity settling velocity at time t tangential velocity at the inside liner surface terminal velocity rotational speed, angular velocity mean rotational speed rotational speed of a particle at distance Rp a milling parameter = function of volumetric filling of mill percent solids

m/min rpm m/s m/s rpm m/s m/s m/s m/s rpm m/s s"1, rpm, Hz rpm s'1, rpm %

Chapter 1. Mineral Sampling 1. INTRODUCTION A processing plant costs many millions of dollars to build and operate. The success of this expenditure relies on the assays of a few small samples. Decisions affecting millions of dollars are made on the basis of a small fraction of the bulk of the ore body. It is therefore very important that this small fraction is as representative as possible of the bulk material. Special care needs to be taken in any sampling regime and a considerable effort in statistical analysis and sampling theory has gone into quantifying the procedures and precautions to be taken. The final sampling regime adopted however is a compromise between what theory tells us should be done and the cost and difficulty of achieving this in practice. 1.1. Statistical Terminology A measurement is considered to be accurate if the difference between the measured value and the true value falls within an acceptable margin. In most cases however the true value of the assay is unknown so the confidence we have in the accuracy of the measured value is also unknown. We have to rely on statistical theory to minimise the systematic errors to increase our confidence in the measured value. Checks can be put in place to differentia...