mineral processing design and operation

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 vi 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 constan t a amplitud e m ap particl e acceleratio n m/s 2 A a constan t A apertur e micron s A are a m 2 Ac cross-sectiona l are a m 2 Ai abrasio n inde x Ay assa y of particle s in the i th . size and j th . densit y fraction s A E effectiv e are a m 2 A EFF area l efficienc y facto r Ao ope n are a % A 0 E effectiv e ope n are a % A M assa y of minera l % , g/t, ppm Ay underflo w are a m 2 b a constan t b Rosin-Rammle r distributio n paramete r By breakag e distributio n functio n c a constan t C a constan t C circulatio n rati o or load C concentration , (mas s solid/volum e of slurry ) kg/m 3 C A concentratio n of air kg/m 3 Cc averag e concentratio n of solid s in the compressio n zon e kg/m 3 C D dra g coefficien t Ci concentratio n of specie s i kg/m 3 Co initia l concentratio n (mas s of solid/volum e of slurry ) kg/m 3 CMA X maximu m concentratio n (mas s of solid/volum e of slurry ) kg/m 3 C t concentratio n at time t (mas s of solid/volum e of slurry ) kg/m 3 C S (c) concentratio n of solid (C = concentrate , F = feed , T = tail f = froth , P = pulp ) Cu, C F concentration s of the underflo w and feed respectively , kg/m 3 (mas s of solid/volum e of slurry ) CCRI T critica l concentratio n kg/m 3 C F correctio n facto r CI confidenc e interva l CR confidenc e rang e C S (u) solid s concentratio n in the underflo w (O = overflow, F = feed ) % concentratio n by mas s of solid s in the feed % xvi CvS(F) cc cv Coo d d d 32 dN dso, dsoc d B d F d L dMAX dMIN d\iiD dcutter dc d w D D D* D c D, Do Du e Ei E c E Ec E B Eo Eo E P Eu E T / /(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 floats at SG froth stability factor feed mass ratio (liquid/solid) settling factor % - - kg/m 3 - 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, - - - xvii Fgo F B FB Fc Fc F D Fg FG Fos FR F s Fs g G G,G bp G' AG h huh,* H H H t H B H B He He HOF HR H s Hu I I JB Jc JG JR Jp k k A ,k A k F , k s ki kc, k C5 o ks, k S5 o 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/C T 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 i th 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/s 2 %, 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/m 2 m 1 - - kW xviii L L A LAE LEFF Lc LcYL, LcONE L F LMW , LMAX LT I_I LVF m m muo o m k mu(O) m(r) m T mu(o> m i(U) M Mi M oi My M B M B M c Me M F M F M FT M F MMIN MR MR Mr M s M s length aperture size effective aperture effective grinding length length of cyclone length of cylindrical and cone sections Nordberg loading factor minimum and maximum crusher set crusher throw length of vortex finder length from end of vortex finder to apex of a cyclone moisture (wet mass/dry mass) mineralogical factor mass fraction of undersize in the feed mass fraction of makeup balls of size k mass fraction of undersize in the oversize cumulative mass fraction of balls less than size r mass rate of ball replacement per unit mass of balls mass fraction of undersize in the undersize mass of size i in the underflow (F = feed) mass mass mass/mass fraction of i* increment cumulative mass fraction retained on i* screen at zero time mass percent of the i* size fraction and j * density fraction mass of block mass of balls mill capacity mass of crushing weight mass of feed mass of fluid mass of floats Nordberg mill factor minimum mass of sample required mass of rock mass fraction of rock to total charge (rock + water) cumulative mass fraction of balls of size r in the charge mass of striking pendulum mass of solid m m m m m m - m m m m - kg/m 3 - - - kg/h.t - kg g kg,t kg,t % kg kg t/h kg t kg kg,t - kg,t kg - kg ke,t . sec), SO D n^ 5 of solid feed, concentrate and tailing respectively kg, t mass of solid in froth MS K mass of sinks kg , t M S {p) mas s of solid in the pulp kg , t AM(t) mas s of top size particl e kg , t Mj mas s of new feed g Mw mas s of water kg , t n numbe r of revolutions/mi n min" 1 n numbe r of increments , measurement s xix n n(r) ns N N N N L 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 - - - - min' 1 - nf 1 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 m 3 /h nrVh (U=underflow, F=feed) xx QVOP(U ) flowrat e b y volum e o f entraine d overflo w pul p in th e U/ F QVOL(U ) flowrat e b y volum e o f entraine d overflo w liqui d in th e U/ F m 3 /h Qvos(u ) flowrat e b y volum e o f entraine d overflo w solid s i n th e U/ F m 3 /h Qvs(O ) flowrat e b y volum e o f solid s i n th e overflo w ( U = U/F , F = feed ) Qv(f ) flowrat e b y volum e i n th e frot h Qv(O ) flowrat e b y volum e o f overflo w (pulp ) ( U = underflow ) Q w bal l wea r rat e r 0 fractio n o f tes t scree n oversiz e r bal l radiu s r rati o o f rat e constant s = IC A /(kA+kA ) ri , r 2 radiu s withi n th e conica l sectio n o f a mil l R radiu s R recover y R reductio n rati o Ri,R2,R 3 Dietric h coefficient s R th e mea n radia l positio n o f th e activ e par t o f th e charg e R ' fractiona l recovery , wit h respec t t o th e fee d t o th e first cel l R ' mas s o f tes t scree n oversiz e afte r grindin g R e radiu s o f con e a t a distanc e L j fro m cylindrica l sectio n ReA , Re c Reynold s numbe r i n th e ape x an d con e sectio n respectivel y Re P particl e Reynold s numbe r R F frot h recover y facto r Ri radia l distanc e t o th e inne r surfac e o f th e activ e charg e Ro mas s o f tes t scree n oversiz e befor e grindin g R P radia l distanc e o f particl e fro m th e centr e o f a mil l RR O optimu m reductio n rati o R T radiu s a t th e mil l trunnio n R v recover y o f fee d volum e t o th e underflo w Ro o recover y a t infinit e tim e S spee d S sink s a t S G S surfac e are a S B surfac e are a o f bal l S B bubbl e surfac e are a flu x S; breakag e rat e functio n S F Nordber g spee d facto r S spacing , distanc e S dimensionles s paramete r SG , SG s specifi c gravity , specifi c gravit y o f soli d T perio d o f pulsatio n T N mas s percen t passin g 1/ N o f th e origina l siz e t tim e to detentio n o r residenc e tim e t R effectiv e residenc e tim e tu tim e fo r al l solid s t o settl e pas t a laye r o f concentratio n C tio siz e tha t i s on e tent h th e siz e o f origina l particl e t A mea n tim e take n fo r activ e par t o r charg e t o trave l fro m th e to e t o th e shoulde r 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 m 2 m 2 s" 1 min" 1 m h, min , s h s h m m s xxi U Up V V* V c Vc VCONE L(F ) Vo VR VB ° VB 1 vs° Vs 1 var(d) var(c) var(pa) var(t) var(x) w w W W WE W; W s x x x Xj X mean time for free fall from the shoulder to the toe s 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 d 50 in the feed (V d 5o/V S ( F )) - volume m 3 dimensionless parameter volume of the mill charge m 3 volume of the compression zone m 3 volume of conical section of mill m 3 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) m 3 volume of mill m 3 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) m terminal velocity m/ s unknown true value velocity of block pendulum before impact m/s velocity of block pendulum after impact m/s velocity of striking pendulum before impact m/s velocity of striking pendulum after impact m/s distribution variance composition variance preparation and analysis variance total variance variance thickness of slurry m fraction of feed water in the underflow width m dimensionless parameter effective width m Bond Work Index kWh/ t Bond Work Index, laboratory test kWh/ t operating work index kWh/ t corrected operating work index kWh/ t water split = QML(O)/QML<F ) deviation from the true assay geometric mean of size interval micron s Rosin-Rammler size parameter micron s Sample mean i* measurement deviation from standard unit xxii a a a, a 0 ttr» «s «TS Y T YSA > YSL > TL A £ e A K 9 -e- <)) 4>c ¥>¥» Vw VCRIT (1 P Pb PC PB PF Po PL PR ps PSL Pw PM> pG U 0 A CL CTM 0p Op A CT S 0 T 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/m 2 /s kg/m 2 /s kg/m 2 /s - kg/m 3 , t/m 3 kg/m 3 ,- t/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 kg/m 3 , t/m 3 - - - - - - - - s radians, degree viscosity velocity critical speed mNm, Pa.s m/s rpm [...]... heterogeneous (liberated) and see Table 1.3 for intermediate material) m = mineralogical factor The mineralogical factor, m, has been defined as: (1-7) where a is the fractional average mineral content and PM and po the specific gravity of the mineral and the gangue respectively The liberation factor, PL, is related to the top size, d A and to the liberation size, dL of the MX mineral in the sample space... fraction and j density fraction as MM and 3 Consider Ay and Py as the assay and the proportion of particles in the i size and j * density fractions For sampling a mixture of two components (mineral and gangue) the proportion of particles in the ij fraction would be; 12 12 ( Eh/-?) } And the assay of the mixture, Ay will be approximately equal to: A IPM(PB-PO)IOOJ = where PM = density of the mineral and. .. proportion of mineral particles proportion of gangue particles number of particles Then the standard deviation of the proportion of mineral particles in the sample, Gp; will be: 9 (1.9) aP = The standard deviation on a mass basis (CTM) can be written in terms of the percent mineral in the whole sample provided the densities (p) are known Thus if pM and PG are the densities of the mineral and gangue,... percent of mineral in the entire sample, consisting of mineral and gangue (the assay), will be: AM = 100 PM p M P (1-10) M P M + P G PG assuming the particles of mineral and gangue have the same shape and size dA The standard deviation of the entire sample is given by a T = —— a p or T _ I (10Q-AM)PM+AMPG I ,„„ / ' AM(100-AM) N Example 1.3 Regular samples were required of the feed to a copper processing. .. important role in defining the difference between random variations and systematic errors and in quantifying both 2 ASSAY Random error Systematic error True value, v SAMPLE Fig 1.1 Representation of a random and systematic error 1.1.1 Mean The most important parameter for a population is its average value In sampling and weighing the arithmetic mean and the weighted mean are most often used Other measures... (American Society for Testing and Materials) Cleaned Top Size in mm 1 Uncleaned Mass in kg Number Mass in kg Number 1 15 15 15 1 3 7 35 35 35 16 50 150 3 7 The overall standard deviation of sampling, sample preparation and assay is a function of the variability of the particulate material, the number and mass of the increments and the random errors associated with sample preparation and assay It can be expressed... particle in kg Experience and theory are embodied in a number of national and international standards on sampling of particulate materials where the sampling regimes are defined in terms of the total number of increments, and the average mass of a primary increment It is generally accepted that a primary increment should contain no less than one-thousand (1,000) particles In the standard on sampling of... infinite degrees of freedom and if the number of replicate results exceeds 8 then a factor of 1.0 is an acceptable approximation 1.2 Mineral particles differing in size - Gy's method Representing large bodies of minerals truly and accurately by a small sample that can be handled in a laboratory is a difficult task The difficulties arise chiefly in ascertaining a proper sample size and in determining the... as: ^ where (1.19) . Introduction to Mineral Processing Design and Operation PREFACE In nature minerals of interest exist physically and chemically combined with the host rock. Removal. material) m = mineralogical factor The mineralogical factor, m, has been defined as: (1-7) where a is the fractional average mineral content and PM and po the specific gravity of the mineral and the. 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