Scale-up in froth flotation: A state-of-the-art review

Diego Mesa∗, Pablo R. Brito-Parada

Department of Earth Science and Engineering, Royal School of Mines,Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom

Abstract

Froth flotation has been one of the most important and widely used methods to concentrate minerals since itsintroduction over a hundred years ago. Over the last few decades, in order to process more mineral while reducingcapital costs, flotation equipment has become exponentially larger. The increase in tank volume, however, has broughtnew challenges in the operation and design of industrial flotation tanks. This review analyses the literature on flotationtank scale-up for the first time, contrasting several techniques and approaches used in both historical and state-of-the-art research. The study of flotation scale-up is crucial for the optimisation of industrial plant performance and themaximisation of laboratory-scale research impact. While important advances in our understanding of flotation have beenachieved, large flotation tank design and scale-up has, to a large extent, remained in-house know-how of manufacturingcompanies. This review of the literature relevant to flotation tank scale-up has resulted in a new classification, dividingthe scale-up literature into two main areas of study, namely “Kinetic scale-up” and “Machine design scale-up”. Thisreview indicates that current scale-up rules governing the design of flotation tanks focus mainly on pulp zone kineticparameters and neglect the effects on the froth zone, despite the importance of froth stability and mobility in determiningflotation performance. Froth stability and mobility are closely linked to the distance the froth needs to travel, whichincreases with tank diameter. Although including internal elements, such as launders and crowders, has been theindustrial solution for enhancing froth transport and recovery in larger tanks, the design and scale-up of these elementshave not been thoroughly studied. Gaps in our knowledge of flotation are discussed in the context of addressing thescale-up problem, considering froth transport and froth stability. Addressing these gaps will pave the way for the designand operation of large flotation tanks of enhanced performance.

Keywords: Froth flotation, scale-up, kinetics, flotation tank, design

1. Introduction

Froth flotation was patented in 1905 for the concentra-tion of ores (Sulman et al., 1905). It is now the most im-portant mineral processing method in the mining industry,because of its technical versatility and cost-effectiveness(Wills & Finch, 2016). Flotation is also used in otherindustries, such as oil sands concentration (Rao & Liu,2013), ionic flotation (Sebba, 1959; Polat & Erdogan, 2007),algae separation (Chen et al., 1998; Laamanen et al., 2016),paper deinking (Chaiarrekij et al., 2000; Vashisth et al.,10

2011), plastic recycling (Takoungsakdakun & Pongstabodee,2007; Wang et al., 2015; Negari et al., 2018) and wa-ter treatment (Rubio & Smith, 2002; Saththasivam et al.,2016).

Froth flotation works on the basis of surface chem-istry; fine mineral particles are separated according totheir hydrophobicity. This separation process dispersessmall bubbles of gas, generally air, inside a flotation tank,also referred to as flotation cell. The tank contains a

∗Corresponding authorEmail address: d.mesa16@imperial.ac.uk (Diego Mesa)

mineral suspension in an aqueous media, called the pulp.20

Chemical reagents, called collectors, are added to the pulpin order to selectively enhance the hydrophobicity of thevaluable minerals. These hydrophobic particles can attachto the gas bubbles and rise to form a froth layer, whichoverflows as the mineral-rich concentrate.

The throughput treated at industrial processing plantshas increased in the recent decades because of lower gradesand higher mining capacities (Prior et al., 2012). Insteadof the amount of cells and banks in the processing plantbeing increased, flotation equipment has become larger in30

order to process more mineral (Rao, 2004). Tank volumehas increased a thousandfold in the span of a century,as can be seen in Figure 1 (after that in Wills & Finch(2016)). This increase in tank size has allowed the utilisa-tion of economies of scale, by reducing the overall capitaland operating costs (Murphy, 2012). However, these lar-ger and more complex tanks have brought new challengesin performance, design and operation (Tabosa et al., 2016)in terms of pulp hydrodynamics and froth transport.

When confronted with the problem of processing a lar-40

ger throughput, other industries have taken a differentapproach, called process intensification. Process intensi-

Preprint submitted to Separation and Purification Technology 17th July 2018

1920 1940 1960 1980 2000 2020

Year

0.1

1

10

100

1000

Flo

tatio

n t

an

k v

olu

me

, m

3

Figure 1: Trend in flotation tank size over the last century, referringto the maximum tank volume commercially available. Data fromDreyer (1976); Lynch et al. (2007); Wills & Finch (2016); Lelinskiet al. (2017). Note that the y-axis is on logarithmic scale.

fication is defined in Chemical Engineering as the studyand design of ever smaller reactors. These small reactorsoperate by enhancing transport and processing rates, lead-ing to a better control of the kinetics, improving energyefficiency and reducing capital cost (Reay et al., 2008a).Process intensification has been applied in the design ofa broad range of equipment, including heat exchangers,reactors and separators (Ramshaw & Arkley, 1983; Reay50

et al., 2008c). In extractive metallurgy, a toroidal flu-idised bed used for ore roasting and drying, denominatedThe Torbed, was developed following the principles of pro-cess intensification (Groszek, 1990; Shu et al., 2000; Wanget al., 2017).

A recent review of the use of process intensificationin solids handling (Wang et al., 2017) included a sectionon particle separations and froth flotation. Some examplesmentioned are the Air-Sparged Hydrocyclone (ASH), whichachieved recoveries of 85-93% of pyrite with a mean resid-60

ence time of 1 second (Van Deventer et al., 1988), and theJameson Cell, which enhances the mixing intensity, max-imising the particle-bubble contact probability and achiev-ing high recoveries with a residence time of 5-10 s (Claytonet al., 1991; Glencore Technology, 2016). Other examplesinclude the HydroFloat cell, which is an aerated fluidised-bed that improves the recovery of coarse particles with lowresidence times, reducing the contact zone (Eriez, 2015;Miller et al., 2016), as well as several studies consideringmicrobubble generation for flotation (Rodrigues & Rubio,70

2007; Parmar & Majumder, 2013), including the cyclone-static microbubble column of Cao et al. (2009) and Zhanget al. (2013), which showed higher recoveries than a com-mon bench-cell.

However, despite being introduced more than two dec-ades ago, process intensification has been adopted slowlyat an industrial scale (Reay et al., 2008b). In minerals pro-cessing, and particularly in froth flotation, process intensi-fication has not taken off yet. While novel flotation tanks,

with designs that apply process intensification principles80

will no doubt play an important role in the future of min-eral separations, it is unlikely that new flotation tanks inprocessing plants will be considerably smaller in the nearfuture. Therefore, scale-up studies are, and will, remaincritical for the design of large flotation equipment. Scale-up studies are also relevant for the design of retrofits, thatcan be installed in existing flotation tanks to enhance theirperformance. These studies require a better understand-ing of the hydrodynamics phenomena at different scalesand their impact on performance, for both the pulp and90

froth zones in flotation tanks.The purpose of this review of scale-up in froth flotation

is twofold: (i) to highlight and classify the studies thathave been conducted on flotation scale-up, defining twosub-areas of study, namely “kinetic scale-up” and “designscale-up”, and (ii) to highlight the areas that require fur-ther research and better understanding for a more effectivescale-up of flotation tanks.

This is the first review to offer an in-depth analysisand critique of flotation scale-up studies, including exper-100

imental studies and scale-up procedures suggested in theliterature. The analysis of the literature shows that whilethe scale-up process for the pulp zone in flotation tankshas been extensively studied, insufficient attention as sofar been paid to the scale-up process related to froth mo-bility and stability. It is also highlighted that the liter-ature available on the design of different inserts such aslaunders and froth crowders is scarce . The lack of fun-damental understanding of the effect of those inserts onflotation performance is discussed, which is essential for110

effective scale-up.

2. Flotation equipment

The four main functions of a flotation tank are: (i) in-troducing air bubbles into the pulp, (ii) providing an envir-onment that increases the probability of collision betweenthose bubbles and the particles in the slurry, (iii) maintain-ing a stable pulp-froth interface and (iv) providing suffi-cient froth removal capacity (Degner, 1988; Gupta & Yan,2006). Flotation equipment, regardless of its scale, canbe classified into two main types: mechanical and pneu-120

matic cells, of which the former is the most widely used inindustry.

Mechanical cells (Figure 2) are fitted with an impellerin order to generate a highly turbulent region, which keepsparticles in suspension, generates and disperses bubbles,and promotes bubble-particle collision (Deglon, 2005; Tabosaet al., 2016). Mechanical cells can be sub-classified by theirair injection system into self-aerated and forced-air cells(Wills & Finch, 2016). Self-aerated cells use the negativepressure of the vortex created through agitation to induce130

air into the pulp. On the other hand, forced-air or super-charged cells are supplied with air from an external andcontrolled source. Both aerating technologies are widelyused in processing plants, but forced-air cells allow for a

2

Air

Feed Tail

Concentrate

Figure 2: Schematic of a mechanical flotation cell. The impeller isshown agitating the pulp and generating bubbles from air injectedfrom the top. Valuable particles attach to bubbles and rise to thefroth zone, overflowing as concentrate, while gangue reports to thetailings at the bottom.

better control of the supplied air by decoupling this vari-able from impeller speed and pulp level. The control ofair flow rate and pulp level is crucial for optimising theflotation process (Laurila et al., 2002; Shean & Cilliers,2011).

Pneumatic cells do not use impellers. Instead, bubbles140

are generated by injecting the air into the cell at high pres-sure or speed. The pulp can be fed in separated from theair, like in a conventional flotation column (Figure 3), orinjected with the air at high pressure, enhancing the con-tact between bubbles and particles, like in the Jamesoncell. Flotation columns are tall cells where air is com-monly injected at the base using a sparging system andpulp is fed in near the top of the column (Dobby & Finch,1991; Filippov et al., 2000). Particles settle because ofgravity, while the swarm of bubbles rises because of their150

buoyancy. Bubble-particle collision probability dependson the distance between the feeding point and the base ofthe column. As such, the importance of both the heightof the column and the ratio between height and diameterhas been discussed at length (Yianatos et al., 1988; Finch& Dobby, 1991). The popularity of flotation columns hasfluctuated during the last 20 years, being mainly used inthe coal, phosphates and iron ore industries, and com-monly employed as cleaner stages in base metal plants(Harbort & Clarke, 2017).160

Both mechanical and pneumatic flotation machines canbe found at industrial scale, operating in different mineralprocessing plants around the world. The size of industrialflotation machines and limited control over operating vari-ables such as feed characteristics, combined with the costassociated to making changes on plant to accommodatetrials, are physical and financial barriers for on-site exper-imentation. Consequently, studies are usually performed

Concentrate

AirTail

Feed

Figure 3: Schematic of a flotation column, a type of pneumatic cell.The column is fed near the top, while the gas flow enters through asparger at the bottom.

on simplified laboratory-scale cells.Laboratory flotation machines are simplified and smal-170

ler flotation equipment. These laboratory machines areused in metallurgical tests, mainly focusing on reproducib-ility and achieving similar performance to industrial flota-tion operations (Gupta & Yan, 2006). Generally, there is atrade-off between these goals. Bench-scale laboratory cells,such as the one shown in Figure 4, are widely used. Labor-atory cells have proven to be useful for flotation testing,e.g. determining the choice of reagents and defining kin-etic parameters for modelling (Wills & Finch, 2016). How-ever, their small scale implies that most of these cells have180

important differences in impeller size, number of statorblades and in other geometric ratios when compared toindustrial cells.

More importantly, these laboratory machines are de-signed for batch testing, meaning that steady state cannotbe reached. In a batch test the pulp properties vary con-tinuously; water is added as froth overflows to maintainthe pulp level, changing the solid concentration, mineralgrade and reagents concentration over time (Runge, 2010;Wills & Finch, 2016).190

Some laboratory cells capable of running at steadystate have been developed. Examples include semi-continuoussystems, mainly based on batch cells, such as a modified3 litre Denver batch-flotation machine (Kaya & Laplante,1986) and a modified 3.5 litre Leeds batch cell (Vera et al.,2002). More recently, continuous laboratory systems havebeen introduced. Brito-Parada & Cilliers (2012) designeda 64 litre continuously operated cubic tank for studyingfoam transport phenomena, while Shean et al. (2017) useda 50 litre cylindrical tank, also operated with a two-phase200

3

Air

Concentrate

Figure 4: Laboratory bench-scale flotation equipment, widely used inindustry for batch laboratory tests. The volume of the cells typicallyranges between 1 and 5 litre. The pulp is poured into the cell andthe concentrate overflows the lip, while the pulp that remains aftera determined flotation time represents the tailings.

system. Li et al. (2015) used a 20 litre pilot scale flota-tion cubic tank, continuously operated, to study froth rhe-ology. Norori-McCormac et al. (2017) introduced a 4 litrecontinuously operated cylindrical tank based on the stand-ard stirred tank developed by Costes & Couderc (1988)(schematic shown in Figure 5). That 4 litre tank was usedto study particle size effects on froth stability. Morrison(2017) have used a 70 litre scaled-up version of the afore-mentioned tank, also operated with a three-phase flotationsystem.210

The previous examples highlight how new laboratoryflotation cells are not necessarily defined by their size, butby their simplicity in operation and modification of vari-ables. This characteristics allow a comprehensive studyof flotation phenomena. While laboratory flotation testsallow studying the effect of different variables in a singleflotation unit, pilot-scale testing is important for plant cir-cuit design (Wills & Finch, 2016). Pilot flotation equip-ment usually refers to small industrial flotation tanks, typ-ically varying between 60 and 150 litre tanks (Amini et al.,220

2016a; Deglon, 2005), such as the 100 litre Batequip mech-anical flotation cell (Shabalala et al., 2011). Pilot plantsare used for comparing equipment and circuit perform-ance, comparing costs associated to alternative processesand preparing large samples of concentrate for further test-ing. The process of translating experimental data fromlaboratory tests to industrial scale is known as scale-up,which is discussed in the context of froth flotation tanksin the next section.

3. Scale-up in flotation230

Early flotation tanks were machines of less than 1 m3

(Arbiter, 1999). Nowadays, most newly installed tanksare larger than 300 m3 (Murphy et al., 2014). FLSmidth’s660 m3 SuperCellTM at KGHM Robinson concentrator inUnited States is currently the largest operating tank (Lel-inski et al., 2017), followed by Outotec’s 500 m3 TankCell®

at Boliden Kevitsa concentrator in Finland (Mattsson et al.,2016). This increase in flotation tank volume offers tech-nical and economical advantages. Larger tanks imply thatfewer of them are needed, which results in less floor space,240

simpler operational control and lower power consumption(Arbiter, 1999; Murphy, 2012). However, new challengesappear when tanks are scaled-up to large industrial sizes,since fluid dynamic properties alter the performance offlotation equipment (Tabosa et al., 2016). On the onehand, pulp dynamics are affected by the size, shape, speedand position of the agitating mechanism (sparger, rotor-stator systems, etc.) (Deglon, 2005; Amini et al., 2016a).On the other hand, froth stability will change due to thegreater distance between the bulk of the froth and the250

discharge lip (Zheng et al., 2004; Coleman, 2009; Brito-Parada & Cilliers, 2012).

The concept of “scale-up” in flotation literature is usedin two ways, which has led to the development of twodifferent areas of study. The first and most researchedof these two areas focuses on the different procedures forscaling-up the kinetic parameters of flotation models ob-tained through laboratory tests, to predict plant behaviour(Gorain et al., 1998b; Amelunxen & Runge, 2003; Dobby& Savassi, 2005; Bulled, 2007; Yianatos et al., 2010). For260

the purposes of this review we refer to this area of studyas “kinetic scale-up”. The second area of study considershow flotation equipment design affects performance at dif-ferent scales. We refer to this second area as “machinedesign scale-up”. The latter has been mainly studied byconsidering the effects of hydrodynamic phenomena in thepulp zone, considering geometrical and dynamic similar-ities (i.e., keeping the same equipment shape and main-taining the same non-dimensional numbers relevant to theflow, respectively) (Nelson & Lelinski, 2000; Gorain et al.,270

2007; Truter, 2010), as well as by focusing on air injectiontechnologies and impeller design and speed (Gorain et al.,1995a,b, 1996, 1997; Grano, 2006; Newell & Grano, 2006,2007; Amini et al., 2016a, 2017).

Most research into machine design scale-up has focusedon the pulp zone, with no scientific studies published spe-cifically on the topic of froth zone scale-up. Only somerules of thumb have been published by Coleman (2009) asan industrial guide for tank and launder design selection,such as recommending the use of internal double launders280

for high-grade ores, external launders for ultrafine recov-ery and radial launders for applications with high massrecovery. Clearly, there is a knowledge gap between thein-house know-how of manufacturers and scientific literat-ure on the scale-up of flotation tanks. Although this gap

4

is to be expected to a certain degree due to commercialreasons, there is still an evident lack of published researchin the topic of flotation tank scale-up. Filling that gapis an opportunity, since more comparable works are verymuch needed to advance the field.290

Nowadays in several process industries, ComputationalFluid Dynamics (CFD) is routinely used for the scale-upof equipment. Stirred tanks are a common example, suchas those used as reactors and bioreactors (Nauha et al.,2015). However, despite the fact that the pulp zone inmechanical flotation cells is to some extent analogous tostirred tank systems, there are no publications on the useof CFD for flotation tank scale-up.

CFD has been used to model flotation tanks and toassess flotation performance (Koh et al., 2000; Koh &300

Schwarz, 2006, 2008; Evans et al., 2008; Brito-Parada et al.,2012b; Cole et al., 2012; Brito-Parada et al., 2013; Shiet al., 2015; Karimi et al., 2014a,b) but never combin-ing the froth and pulp zones. Although scientific public-ations on the use of CFD for equipment design are lim-ited (Neethling & Cilliers, 2003; Koh et al., 2003; Koh &Schwarz, 2007; Brito-Parada & Cilliers, 2012), companiesthat manufacture flotation equipment have continuouslyreported the use of CFD models for the design and scale-up of their larger flotation cells, e.g. Outotec’s Tanckcell310

e500 (Murphy, 2012) and FLSmidth’s SuperCell 660 (Lel-inski et al., 2017). However, the few published studies forthese very large tanks focus only on hydrodynamics eval-uation of the pulp zone, in most cases comparing CFDmodel predictions against tests run only with water.

3.1. Kinetic scale-up

Mathematical methods are used to translate kineticdata, obtained from laboratory-scale flotation experiments,to industrial plant performance. The main aim of kineticscale-up is to predict concentrate grade and recovery at320

industrial-scale, by analysing laboratory-scale data. Flot-ation equipment is considered an input, and only a fewvariables related to the equipment size and operation areconsidered, such as residence time.

Several kinetic flotation models have been published.In this section, only the applicability of those models into the scale-up process of flotation is discussed. A thor-ough review of kinetic models can be found in Gharai &Venugopal (2015). These models are defined on the basisof a simplification, by considering flotation as a kinetic rateprocess, analogue to chemical reactions. This considera-tion leads to the following ordinary differential equation:

dC

dt= −knCnCmb , (1)

where C and Cb are the concentrations of particles andbubbles, respectively, the exponents n and m are the reac-tion orders, t is time and k is the flotation rate constant.

The various flotation kinetic models presented in Table 1can be obtained by solving Equation (1). These differ-ent models are obtained by considering different simpli-330

fications, such as assuming a constant concentration ofbubbles, defining the order n, or assuming a certain resid-ence time distribution of the particles in the tank. Thesemodels aim to characterise the flotation phenomena withtwo or more kinetic parameters, such as k and Rmax (thetheoretical maximum recovery achievable), which are ob-tained by fitting the models to experimental data. Con-sequently, these parameters are not only dependent on thecharacteristics of the mineral, such as composition, particlesize distribution and liberation, but also on the operating340

conditions and the flotation equipment used.The introduction of the compartmental model for con-

tinuous flotation tanks (Dobby & Finch, 1991) allowed thefocus of the kinetic models to be placed on the collectionzone, practically ignoring the froth zone. This model di-vides the flotation process into two independent but inter-connected zones: the collection zone and the froth zone,both with their own recovery, as shown in Equation (2):

R = R∞RcRf

RcRf + (1−Rc), (2)

where R is the overall recovery of the cell, Rc is the recov-ery from the collection zone and Rf is the recovery fromthe froth zone. Dobby & Finch (1991) proposed that thefroth recovery can be defined as:

Rf =k

kc, (3)

where k is the overall flotation rate constant and kc isthe collection zone rate constant. This implies that thedifferent kinetic models shown in Table 1 can be used todefine both the collection recovery component as well asthe overall recovery of Equation (2).

Flotation kinetics at industrial scale are not the sameas at laboratory or pilot scale, meaning that klab, the kvalue obtained from laboratory data, and kplant, obtainedfrom plant data, are not equal. For example, k from Equa-350

tions (4) and (5) are not necessarily the same as k fromEquations (6) and (7). This difference occurs because theresidence time and the hydrodynamic conditions of theflow are different. Therefore, obtaining the kinetic para-meters at industrial scale from the ones at laboratory scaleis a complex process for each new combination of ore andequipment. This process is how the whole scaling-up prob-lem is defined from a kinetic point of view. Kinetic scale-uphas not been completely solved, and commonly results inlaboratory data overpredicting industrial rate values.360

There are different empirical approaches available forscaling kinetic parameters. A common scale-up methodo-logy to estimate plant flotation rate is to divide the labor-atory flotation rate by a scaling factor, commonly between1.5 and 3 (Weiss, 1985; Degner, 1986; Wood, 2002). Thisscaling factor is calculated as a ratio of industrial andlaboratory residence times. The methodology entails com-paring the residence time in a continuous flotation circuitor tank with the residence time needed in a batch experi-

5

Table 1: A selection of flotation kinetic models

Classical 1st-order model (Garcıa-Zuniga, 1935) for batchtests

R(t) = Rmax

(1− e−k t

)(4)

1st-order model with rectangular distribution of flotationrates (Klimpel, 1980), for batch tests

R(t) = Rmax

[1− 1

kmax t

(1− e−kmax t

)](5)

Continuous 1st-order model (Arbiter & Harris, 1962) R = Rmaxkτ

1+kτ (6)

Continuous Klimpel model (Klimpel, 1980) R = Rmax

[1− ln(1+kmaxτ)

kmaxτ

](7)

General 1st-order model for batch tests (Imaizumi & Inoue,1963; Polat & Chander, 2000)

R(t) = Rmax

∞∫0

(1− e−k t

)f(k) dk (8)

General 1st-order model (Yianatos & Henrıquez, 2006) R(t) = Rmax

∞∫0

∞∫0

(1− e−k t

)f(k)E(t) dkdt (9)

Rmax (or R∞) is the theoretical maximum recovery achievable, considering the equipment efficiency and mineral liberation.τ is the residence time in the tank, i.e. the average amount of time that a particle spends in the system. Is calculated as the ratio ofinternal volume of the tank to the volumetric flow rate through it (τ = V/Q).(1 − e−k t

)is the recovery of the floatable species according to a first order model and f(k) is the flotation rate distribution.

E(t) is the residence time distribution.

ment, in order to achieve the same recovery (Weiss, 1985;370

Gochin & Smith, 1987).Further developments on the use of the scaling factor

approach can be illustrated by a series of works publishedby Yianatos et al. (2003, 2006, 2010). Yianatos et al.(2003) used the scaling factor concept in a case study at ElSalvador concentrator, employing separability curves (theratio of mineral recovery to yield) to select the compar-ison recovery. This comparison recovery was defined atthe optimum separability point, that is when the concen-trate incremental grade equals the feed grade. The scale-up factor was defined as kPlantτ = kLabt, obtaining as anaverage result over a period of 10 months a kLab/kPlant ra-tio of 2.26± 0.35. For another case study, Yianatos et al.(2006) introduced a dimensionless scaling parameter ϕ, asshown in Equation (10):

τPlant

tLab= ϕ

kLabkPlant

, (10)

to separate the effects that mixing and kinetic changeshave on the time scale-up factor. The last study resul-ted in a ϕ value of 1.26, a time scale-up factor τ/t of 3.2and a kinetic rate constant ratio kLab/kPlant of 2.5. How-ever, these two studies did not consider various effects oftank size, such as those affecting the froth zone, differ-ences in cell mixing and solids segregation. Yianatos et al.(2010) incorporated those issues by considering the scale-up factor ξ = kac/kLab. In that definition, kac is the actualor real value of k at the plant, that can be estimated usingEquation (11)

kapp = kac ζ η ψ , (11)

where kapp is the apparent flotation rate constant, whichis the measured value of k in plant, modified by the effectsof the froth zone (ζ), mixing (η) and solid segregation (ψ).The froth effect was defined as ζ = kapp/kc, following themodel of Dobby & Finch (1991) shown in Equation (3).The collection zone rate constant was calculated by Yi-anatos et al. (2010) as a function of the bubble loading(λb) and the grade of the minerals collected by true flota-tion, both estimated using the USM-Bubble Load Sensor380

(Yianatos et al., 2008b). However, all those studies stillneglects the effect of entrainment, do not consider the de-tachment of particles in the sampling process, and do notinclude other effects of the froth zone such as liquid drain-age and transport phenomena.

Another approach for kinetic scale-up has been pro-posed by Gorain et al. (1998b). Following the work ofDobby & Finch (1991), Gorain et al. (1998b) have pro-posed that k can be expressed as:

k = P SbRf , (12)

which is the same as considering kc = PSb. In those equa-tions Sb is the bubble surface area flux (s−1), defined asSb = 6Jg/d32, where Jg is the gas superficial velocity (cm/s)and d32 the bubble Sauter mean diameter (mm). P is thefloatability index, a dimensionless parameter that only de-390

pends on the ore characteristics (later considered as theflotation probability by Koh & Schwarz (2006)).

The objective of this modelling approach is to decouplethe ore characteristics, represented by P , from the operat-ing variables and the flotation equipment design, repres-ented by Sb, so the scale-up process would only depend onthe latter. Further research into the bubble surface area

6

flux was carried out by Gorain et al. (1999), who proposedan empirical expression for Sb that related it to impellerdesign and operating conditions, on the basis of severalexperiments performed on different mechanical flotationcells. This relationship is shown in Equation (13):

Sb = aNsb Jg

cAsd P80

e , (13)

where Ns is the peripheral velocity of the impeller, As isthe aspect ratio between the diameter and the height ofthe impeller, and P80 relates to the feed particle size. Theconstants a, b, c, d and e are empirical values obtained fromexperimental data analysis (123, 0.44, 0.75, -0.10 and -0.42, respectively). However, this empirical approach onlyconsiders the hydrodynamic effects produced due to theimpeller type and its operating conditions, omitting other400

considerations involving tank size and shape.The model of Gorain et al. (1998b) has been later com-

bined with the compartmental model (Equation (2)) andexpanded by Savassi et al. (1998) to incorporate entrain-ment mechanisms. It was also modified by Welsby et al.(2010b) to account for particle size and liberation, result-ing in Equation (14):

Ri,j =(ki,jτ)(1−Rw) + ENTiRw

(1 + ki,jτ)(1−Rw) + ENTiRw, (14)

where the subscripts i and j represent size and liberationclasses, respectively, Rw is the water recovery to the con-centrate and ENT is the degree of entrainment (Trahar,1981).

The combination of Sb and the compartmental modelis widely used by several plant design and simulation soft-ware programs such as JKSimFloat (Harris et al., 2002;Welsby et al., 2010b) (based on Equation (14)), FLEET(Dobby & Savassi, 2005) and AminFloat (Amelunxen et al.,410

2014); a comparison of these programs can be found inSoni (2013). Equation (14) has also been used for kin-etic scale-up by Welsby et al. (2010b), who defined a cellscale-up number C as the kcont/kbatch, obtained at the samerecovery. By using Equation (12) for the definition ofthe continuous kinetic constant rate, this scale-up proced-ure accounts for the differences in Sb and Rf . In thatwork, Welsby et al. (2010b) compared a 40 litre continuoussquare pilot cell (Welsby et al., 2010a) and a 4 litre batchcell with the same shape, obtaining a value C = 0.53.420

It is worth noting that in the scale-up number C, thekinetic ratio is the inverse of that used in most studies.C−1 = 1.89 offers a similar value to the methodologiesdiscussed earlier. However, while this work uses a differ-ent kinetic model (Equation (14)), the scale up method-ology still depends on directly comparing a batch and acontinuous kinetic model at a specific recovery.

More recently, Amini et al. (2016c) modified Equa-tion (12) to enhance the scale-up capabilities of the model,by introducing two dimensionless parameters: æ and EVF.

These parameters are defined as:

k = P Sb æ EVF , (15)

where æ =

(d32 ε

0.25

ν0.75

)n(16)

is the hydrodynamic factor. ε represents the turbulent kin-etic energy dissipation rate (TKEDR, in m2/s3) (Schubert,1999; Amini et al., 2016a), ν is the fluid kinematic viscos-430

ity (cm2/s) and n is a fitting parameter estimated througha number of flotation tests over a range of operational con-ditions. EVF, the Effective Volume in Flotation, is calcu-lated as the fraction between the volume of the cell wherethe TKEDR is higher than 0.1 m2/s3 and the total volumeof the cell.

Nevertheless, all these kinetic scale-up methodologiesare based on deterministic kinetic models. Deterministickinetic models have received several critiques, in particularin relation to their prediction capacity (Heiskanen, 2013)440

and their applicability within the industry (Yianatos, 2007;Amelunxen, 2013). Most of those critiques argue that de-terministic models tend to oversimplify the interactionsbetween variables, such as considering k as time independ-ent, neglecting all the chemical and transport phenomena,or treating forces as scalars, not considering spatial inter-actions (Heiskanen, 2013). These considerations are es-pecially important when using such models for scaling-uppurposes.

Probabilistic models have been proposed by several au-thors (e.g. Schuhmann, 1942; Sutherland, 1948; Schulze,1984; Pyke et al., 2003; Yoon et al., 2016); further de-tails can be found in Gharai & Venugopal (2015) reviewon kinetic models. Probabilistic models consider that k isthe result of combining the probabilities of particle-bubblecollision (Pc), attachment (Pa) and detachment (Pd), asshown in Equation (17):

k = ZP = ZPcPa(1− Pd) , (17)

where Z is the rate of collision. In particular, the modelproposed by Pyke et al. (2003) for the rate of collision,shown in Equation (18), has been used for the developmentof a CFD kinetic model (Karimi et al., 2014a). That CFDmodel has been validated for a chalcopyrite and galenasystem by varying hydrophobicity, agitation rate and gasflow rate (Karimi et al., 2014b). In the model by Pykeet al. (2003), k is defined as:

k =

[7.5

π

Qgd32Vr

] [0.33 ε4/9d

7/932

ν1/3 ui

(ρs − ρlρl

)2/3]

[P ], (18)

where Qg is the gas flow rate, Vr is the reference volume, ε450

is the turbulent dissipation rate (cm2/s3), ρs is the solidsdensity (g/cm3), ρl is the liquid density (g/cm3) and ui isthe turbulent fluid velocity (cm/s).

All the terms in Equations (17) and (18) have beenextensively studied and modelled (e.g. Abrahamson, 1975;

7

Dukhin, 1983; Dobby & Finch, 1987; Ralston et al., 1999;Dai et al., 2000; Albijanic et al., 2010) but despite theefforts to provide valuable information about the mech-anisms governing flotation, the complexities of multiphaseflotation systems are not fully captured by those models.460

Heiskanen (2013) attributed this lack of detailed represent-ation to the fact that general conclusions are often drawnfor continuum phenomena from theoretical work at a muchsmaller scale.

Since froth phenomena is not a kinetic process, kineticmodels are necessarily focused on pulp zone phenomenaonly. Therefore, scale-up processes based on current kin-etic models are not able to account for the changes thatoccur in the froth zone in larger tanks, which is furtherdiscussed in Section 3.2.1. Not including the froth zone470

transport and stability implies that kinetic models are notsufficient for understanding the effects of tank scale onflotation, so they cannot be used for effective tank design.The design of large flotation tanks is the focus of the nextsection.

3.2. Machine design scale-up

The work developed in this area aims to define theimpact of equipment design, shape and size on flotationperformance. A key goal would be to generate clear pro-cedures for flotation machine scale-up, enabling the trans-480

ition from laboratory-scale to plant-scale with minimumcompromise in performance. Since flotation phenomenainvolves several micro-, meso- and macro-scale mechan-isms that are independent, flotation machine scale-up is adifficult process. For that reason, it has traditionally beensimplified, using similitude considerations and dimension-less analysis (Gorain et al., 2007). The main simplificationhas been to scale-up only the pulp zone as it is done forstirred tanks, in which the different phases are mixed in aturbulent region.490

In Chemical Engineering, the design and scale-up ofcontinuous stirred-tank reactors (CSTR) is a problem thathas been extensively studied (Evangelista et al., 1969; Ni-enow, 1997; Nauha et al., 2015). When designing a CSTR,the recommended engineering approach involves definingthe process mixing requirements and then finding the ap-propriate impeller type to meet that requirement, depend-ing on the fluid system (Paul et al., 2004). Once theimpeller type is defined, parameters such as the numberof impellers and impeller size, speed and energy require-500

ments are assessed, while other parts such as baffles tendto be used to achieve the desired flow patterns (Paul et al.,2004).

The stirred tank scale-up process involves the designof a large system that will achieve the same mixing qual-ity as the laboratory-scale one. Some scale-up methodsconsider geometric similarity, keeping constant specific di-mensional ratios such as those of the impeller diameter tothe tank diameter (D/T ), the impellers blade width to theimpeller diameter (W/D) and the impeller clearance from510

the bottom to the tank diameter (C/T ) (see Figure 5).

Figure 5: Standard stirred tank (From Paul et al. (2004)) with asingle Rushton impeller, H=T.

Figure 6: Power number for different impellers Reynolds number(From Bates et al. (1963)). Np becomes constant at high Re values.

In the mineral processing literature, the use of non-geometrical ratios and dimensionless numbers for the designof froth flotation tanks has also been proposed (Gorainet al., 2007; Truter, 2010; Boeree, 2014). These dimen-sionless numbers are detailed in Table 2. For example,the Reynolds number, Re, and Power number, Np (Equa-tions (22) and (23)), are used to calculate the power con-sumed by different impellers, as shown in Figure 6.

For flotation systems, Arbiter (1999) proposed keep-ing the Power number and the power per volume (P/V )constant by varying the rotor diameter (D) and rotationalspeed (N), according to the following empirical relation-ships:

D3 = 2.4022 + 0.0142V (19)

ND = 6.66 + 0.0743V (20)

When a rotor-stator system is used, the scale-up pro-cess suggested in the mixing literature usually considerskeeping the rotor tip speed constant (Vtip = πND). Thisconsideration is equivalent to keeping the nominal shearrate (γ) constant (Paul et al., 2004), as shown in Equa-tion (21),

γ =πND

δ, (21)

where δ is the shear gap width, a value that does not520

depend of the rotor-stator scale. Although tip speed and

8

Table 2: Dimensionless numbers suggested for flotation tank scale-up

Reynolds number, Re (Reynolds, 1883). A measurement of turbulencein the system.

Re = ρN D2

µ = N D2

ν (22)

Power number, Np (Bates et al., 1963). Relates the torque and inertialforces that must be overcome to rotate the impeller at a given rate.

Np = PρN3D5 (23)

Froude number, Fr (Kramers et al., 1953). The ratio of inertial andgravitational forces.

Fr = ρl(ρs−ρl)

N2jsD

g (24)

Zwietering constant, S (Zwietering, 1958). A function of impeller typeand geometry.

S = Re0.1impFr0.45

(Ddp

)0.2X0.13 (25)

Air flow number, Na (Arbiter et al., 1976) or Air capacity number, Ca(Nelson & Lelinski, 2000)

Na = Ca =Qg

ND3 (26)

ρ is the pulp density (kg/m3), µ is the dynamic viscosity of the fluid (Pa s or kg/m s) and ν is the kinematic viscosity (m2/s).P is the power consumed by the impeller (W).ρl and ρs are the average densities of the liquid and the solid phases, respectively, Njs is defined in Equation (27) and g is thegravitational acceleration.Reimp is the Reynolds generated by each particular impeller, dp is the particle size mean (m) and X is the mass ratio of suspendedsolids to liquid.Qg is the gas inflow rate (m3/s).

shear rate control have been reported in various flotation-related publications (Lelinski et al., 2005; Govender et al.,2014; Amini et al., 2016b), these criteria only consider theagitation phenomena of the liquid phase, neglecting thepresence of solids and air bubbles in flotation systems.

For solid suspensions, the Zwietering criterion (Zwieter-ing, 1958), defined as the condition at which the maximumsurface area of the particles is exposed to the fluid, is usedfor tank design and scale-up. This criterion is also knownas the “just suspended” condition. It is physically de-termined by Njs, the minimum agitation speed at whichall particles reach complete suspension, as shown in Equa-tion (27):

Njs = S ν0.1[g (ρs − ρl)

ρl

]0.45X0.13 d0.2p D−0.85 , (27)

where s is the Zwietering constant shown in Equation (25),dp is the particle size mean and X is the mass ratio ofsuspended solids to liquid. This criterion has been usedfor the scale-up of stirred tanks in mixing applications530

(Buurman et al., 1986; Kraume & Zehner, 2002; Jirout &Rieger, 2009). It has also been implemented in the char-acterisation of flotation equipment (Schubert, 1999, 2008;van der Westhuizen & Deglon, 2008). However, the just-suspension condition does not involve the gas phase.

When considering gas injection and bubble formationin the flotation scale-up process, it is a common practiceto keep constant the relationships between gas flow rate,liquid flow rate and tank diameter, as shown in Equa-tion (28) (Paul et al., 2004; Gorain et al., 2007). An ex-540

ample of this practice are the hydrodynamic performancemaps that used to be provided by flotation equipment sup-

pliers, as shown in Figure 7.

Qg ∝ Ql ∝ T 3.4 (28)

Figure 7: Wemcor 1+1™ flotation machine hydrodynamic perform-ance map (From Degner (1988)).

Wemcor 1+1™ scale-up procedure consists on keep-ing the Air Flow Number (Na) constant (Arbiter et al.,1976; Weber et al., 1999; Souza Pinto et al., 2017). Thisparameter, also called Air Capacity Number (Ca) (Nelson& Lelinski, 2000; Gorain et al., 2007), is defined in Equa-tion (26). Wemco’s procedure also considers keeping Jgrelatively constant and under 2.5 cm/s.550

Although CFD has been used for flotation equipmentdesign, the literature about its use for the scale-up of flot-ation cells is scarce. An example of the use of CFD inflotation equipment design and flotation modelling is the

9

work of Koh et al. (2003), who developed a 3-D CFD flot-ation model. The main variables were the Cartesian ve-locity components, pressure and turbulence according toNavier-Stokes equations. The turbulence viscosity in theliquid phase was calculated using the standard k − ε tur-bulence model (Launder & Spalding, 1974). Two different560

flotation agitation mechanisms were modelled, one fromMetso and another from Outokumpu. However, the val-idation of the models were run in water-only experiments.The results did not compare the agitation mechanisms,but only the flexibility of the models to adjust to differ-ent geometries. Another example of CFD applications forthe study of equipment design is the work of Shi et al.(2015). In that study, the fluid dynamics performanceof impellers with different blade angles were studied usingwater-only experiments and CFD. The CFD code used was570

CFX 14.0, implemented with a standard k − ε turbulencemodel. The results shown that a backward impeller anda radial impeller would be a better choice for large recir-culation volumes. Also, the backward impeller incurredin a considerably lower power consumption than the otherdesigns.

CFD has been used for machine scale-up in similar in-dustries. For instance, the scale-up of fluidized-bed hydro-dynamics has been studied using CFD (Knowlton et al.,2005). It was shown that the correct diameter of the tank580

depended on the particle size of the system and turbulenceof the flow. CFD has been also used for understanding thescale-up of binder agglomeration processes (Mort, 2005).Although the agglomeration process is considerably differ-ent to flotation, some of the conclusions obtained in thatstudy could be considered. Mort (2005) found that theoperating conditions tend to affect more than one processwithin the whole agglomeration system. It was found thatafter reaching a certain scale, it would be advisable toseparate the different processes in staged units operations.590

This is similar to what has been proposed with severalflotation cells that separate the collision/collection stagefrom the separation stage, such as the Contact cell (Ame-lunxen, 1993) or the Jameson cell. An interesting viewof how this reactor-separator approach could be used atindustrial scale is detailed in the review of Finch (1995).Despite not mentioning it, the view proposed in that re-view followed concepts of process intensification.

In flotation there is only one study published on theuse of CFD for comparing the effect of machine scale-up.600

Lichter et al. (2007) used CFD and DEM (discrete ele-ment modelling) to compare the pulp behaviour betweena 50 m3 and a 160 m3 industrial Metso tanks (RCS50 andRCS160, respectively). They found that the ratio betweenthe feed inlet flow and the mechanism pumping rate, i.e.,the flow just off the blades of an impeller (Nienow, 1997),was smaller in the RCS50. The larger tank achieves asimilar or higher ratio before overloading the mechanism,implying that larger tanks can process more feed than ina linear estimation. However, the work of Lichter et al.610

(2007) did not consider air injection, so the whole com-

plexity of the problem was not taken into account. Theirwork is the only published comparison between two similarflotation tanks of different scales using CFD. This studypresented the opportunity to clarify many doubts arounddifferent scale-up procedures. It was performed using twotanks that had already been scaled-up, built and installed,so the results could have been crucial. However, not manydetails are included in the results and discussion, probablybecause of commercial reasons.620

The studies discussed in this section deal with differenttechniques for machine design scale-up but few comparis-ons can be made, since each technique has been applied,in isolation, to different tanks and at different operatingconditions. Further research comparing scale-up methods,both theoretically and experimentally, is needed. Also,most of the published literature is either on generic mixingreactors or from a few proceedings and studies publishedby flotation tank manufacturer companies. This gap inthe scientific literature needs to be addressed, both to al-630

low flotation scale-up methodologies to be peer reviewedand identify important gaps in knowledge that can leadto further research. This will certainly lead to the furtherenhancing of flotation efficiency and performance.

A major critique to most of the machine scale-up pro-cedure is that all the techniques based on dimensionlessnumbers discussed before can only be used to obtain sim-ilar particle suspension and agitation, but it has not beenproved that those considerations correspond with obtain-ing similar metallurgical performance (Gorain et al., 2007).640

The link between achieving similar hydrodynamic para-meters in the pulp zone and obtaining similar metallurgicalresults is not straightforward, because a flotation machinecannot be defined simply as a stirred tank. While thepulp zone can be modelled as a stirred tank, which impliesnot considering the collection of particles, the froth zonepresents a number of complexities of its own that must beconsidered in order to predict performance. Froth scale-upis the focus of the discussion in next section.

3.2.1. Froth zone scale-up650

While the scale-up for the mixing process in the flot-ation pulp zone has been extensively studied, the samecannot be said for processes in the froth zone. Indeed,Paul et al. (2004) stated:

“No well-defined criteria are published for design-ing gas/suspension mixing in flotation systems.However, all the mixing/contacting strategiesattempt to create small gas bubbles and en-sure efficient bubble/suspension contact in awell-mixed zone.”660

Nevertheless, some efforts have been made to includefroth transport phenomena and tank size into flotationmodels. The first step was to conceptually divide the tankinto two different systems, with a collection zone recov-ery (Rc) and a froth zone recovery (Rf ) (Dobby & Finch,

10

1991). Gorain et al. (1998a) included the froth transport-ation distance, L, into a froth recovery model as shownbelow:

Rf = a exp

(−b τf

L

)(29)

Rf = a exp (−b τfs) ,

where a and b are adjustment parameters and τf is thefroth residence time. But the authors observed that frothresidence time increases in larger tanks, so they definedthe specific froth residence time as τfs = τf/L, discardingany other distance effect.

It has been noted by several authors and practition-ers that when increasing the distance that froth has totravel, the residence time increases. This increase in resid-ence time generates large scale stagnant zones of low frothtransport and therefore low froth recovery, as shown in670

Figure 8 (Zheng et al., 2004). Therefore, the optimal op-eration of increasingly large tanks relies on effective frothtransport and recovery (Gorain et al., 2007).

Figure 8: Schematic of froth transport model by Zheng et al. (2004).Froth that is further away from the discharge lip tends to burstwithout reporting to the concentrate, generating a stagnant zone farfrom the discharge launder.

Zheng et al. (2004) proposed a model to describe frothresidence time related to the radius of the cell R (assuminga cylindrical tank). This model represents the residencetime of an attached particle entering the froth at a distancer from the centre of the tank as shown in Equation (30):

tf (r) =Hf εg,fJg

+2hf εg,fJg

ln

(R

r

), (30)

where Hf is the froth depth (distance between the laun-der lip level and the pulp-froth interface), εg,f is the gashold-up of the froth zone and hf is the froth height (dis-tance between the launder lip level and the top of the frothlayer). The first term in Equation (30) does not dependon tank size but only on froth depth, representing the timethat takes to a particle to get to the top of the froth. Thesecond term increases when the particle enters the frothcloser to the centre of the tank, but is zero at the peri-meter. However, the mean froth residence time for this

model, expressed in Equation (31), does not depend onthe size of the tank, because of some simplifications, suchas assuming that Hf , hf and εg,f do not vary with r.

τf =

∫ R0tf (r)dV∫ R0

dV=

(Hf + hf ) εg,fJg

(31)

Fundamentally based models that consider froth phys-ics have also been developed and implemented in CFDmodelling frameworks. These models have been used topredict the performance of flotation froths (Neethling &Cilliers, 2003; Brito-Parada et al., 2012a; Brito-Parada &Cilliers, 2013; Neethling & Brito-Parada, 2018). The tra-jectory of flowing foams and froths is solved in 2D or 3D.These trajectories are achieved using Laplace’s equationfor a scalar potential field. As a key boundary condi-tion, those models use the concept of air recovery (α),defined as the fraction of the air injected into the cell thatoverflows through the lip as unburst bubbles (Moys, 1978,1984; Ventura-Medina & Cilliers, 2002). This value is cal-culated as shown in Equation (32),

α =Qout

Qin=ζ vf hw w

JgA≈vf hw w

JgA(32)

where ζ is the gas hold-up of the overflowing froth (usuallyassumed as 100%, equivalent to εg,f in Equation (30)),vw (m/s) is the overflowing velocity, hw (m) is the heightof the overflowing froth over the lip (equivalent to hf inEquation (30)) and w (m) the lip length or perimeter.

Air recovery takes into account lip length, which var-ies with tank design, as well as operating variables like air680

inflow and froth height. It can be measured and predicted(Neethling & Cilliers, 2008). The importance of air recov-ery is that it is correlated with metallurgical performance(Hadler & Cilliers, 2009; Hadler et al., 2010; Smith et al.,2010). Therefore, this parameter should be considered infuture froth scale-up models.

Further work on this topic is undoubtedly needed. Newmathematical models for froth zone phenomena need tobe developed to provide a better understanding of frothtransport in large flotation tanks. These new models need690

to take into account changes in froth stability and bubblebursting rates. Such models could in turn be implemen-ted in CFD simulators to inform the scale-up of flotationtanks.

3.2.2. Internal elements scale-up

As discussed before, froth flotation tanks have becomeincreasingly large and scale-up heuristics based on pulpzone phenomena can be inadequate to predict the perform-ance of large equipment. In particular, the characteristicsand behaviour of the froth zone do not scale like those700

in the pulp. The increase in flotation tanks volume andparticularly the increase in the distance that the froth hasto travel, has resulted in reduced flotation tank perform-ance due to the limitations of froth stability and mobility,

11

as shown in Figure 8. These froth related problems havecreated the necessity of improvements in froth handling,which has been achieved by the introduction of crowdersand more complex launder designs.

Different tank designs have been proposed (e.g. Imhofet al., 2005; Jameson, 2010; Dickinson & Galvin, 2014;710

Eriez, 2015; Glencore Technology, 2016) on the basis ofprocess intensification, that could help avoiding the prob-lems associated to large tanks. Replacing existing capa-city, however, incurs large capital costs. Retrofit modi-fications, on the other hand, allow new designs to be im-plemented in existing operating equipment at lower costs,adding flexibility to the operation. Internal elements suchas launders and crowders, are engineering solutions to theproblem of froth scale-up. Although the use of these in-ternal elements has increased in the last years, there is720

little published research on their design and scale-up pro-cess, at least on the public domain. It is interesting topoint out that the design of these internal elements fol-low the logic of process intensification, since they enhancetransport phenomena at low capital costs.

A launder is a channel in which the froth is collectedafter overflowing (Brito-Parada & Cilliers, 2012). Stand-ard flotation cells that only include a launder along theperiphery of the tank can face the problem of having astagnant froth zone at the centre (as shown in Figure 8).730

This stagnant froth zones occur because of the long dis-tance that the froth has to travel to the lip of the cell.This transport can be avoided by increasing the numberof launders. For instance, by using internal launders tocollect froth in the middle of the tank and not only at itsperiphery (Yianatos et al., 2006; Brito-Parada & Cilliers,2012). Adding launders to a cell increases its lip length(w) and decreases the average distance travelled by thefroth, which helps decreasing the froth residence time andincreasing the froth recovery (Zheng et al., 2004). Two740

common launders configurations are radial and doughnutlaunders (see Figure 9), although more complex launderdesigns are being introduced these days for large tanks.Radial launders are commonly used when the process re-quires increased lip length, such as applications with highmass recovery. In a central doughnut launder, froth flowsinto both sides of the launder. Doughnut launders canbe used in addition or instead of the peripheral launder(Coleman, 2009).

A crowder is an insert that occupies froth volume, as750

shown in Figure 10. The main function of a crowder isto improve froth removal dynamics by directing the frothtowards the overflowing lip of the tank. This improvementin froth mobility is done by decreasing the cross sectionalarea at the top of the froth (Cole et al., 2012). The reduc-tion in cross sectional area increases the local superficialgas velocity (Jg), improving aeration, froth velocity andmass pull. The most common type of crowder is a trun-cated, inverted cone inserted at the centre of the tank.This shape directs the froth upwards and towards the laun-760

der, increasing froth velocity (Yianatos et al., 2008a). As

Perimetral launder

Internal radial launder

(a)

Perimetral launder

Doughnut launder

(b)

Figure 9: Internal launders. (a) Radial launder, discharging into theperipheral launder (b) Doughnut launder, with an internal systemof discharge. In both figures the grey zone represents the top of thefroth and the grey arrows represent the direction of froth flow.

is the case for launders, crowders also reduce the averagedistance travelled by the froth.

Figure 10: Cross-section and plan view of a crowder (From Yianatoset al. (2008a)). The cross-section (left) shows a truncated conicalcrowder changing the froth flow, redirecting it towards the peripherallaunder. The plan view (right) shows the position of the crowder atthe centre of the tank, and how radial launder could be attached toit.

Crowders and launders can be used together, in config-urations such as the one showed at Figure 10, with a cent-ral crowder and radial or doughnut launders. Althoughboth inserts are widely used in large industrial flotationtanks for improving froth transport and overall perform-ance (Zheng et al., 2004; Yianatos et al., 2008a), thereis, to date, little published experimental work on these770

two types of froth zone internal elements. Therefore, theirdesign and scale-up processes have not been studied thor-oughly.

An exception can be found in the work of Neethling& Cilliers (2003), who performed 2D simulations of dif-ferent froth handling designs in cylindrical flotation cells.Three designs were assessed: a crowder, a crowder anddoughnut launder, and two-crowders. The simulations,which agreed with industrial data, showed that a radi-ally outward movement of the froth was necessary to pro-780

mote drainage and thus reduce gangue entrainment. Whilerecoveries obtained with the doughnut launder and two-crowders designs were similar, Neethling & Cilliers (2003)

12

concluded that the latter should be preferred when a singleoverflow does not result in sufficiently high recoveries, sincethis design provides more pulp-froth interface for drainageto occur. More recent studies of crowder design, albeit fora two-phase foam (Cole et al., 2012), showed good agree-ment between simulations and experiment data obtainedfor a quasi-2D cell. In all the 2D-crowders used by Cole790

et al. (2012), the air recovery increased in comparison tothe base case design. However, neither 3D simulations norrigorous 3D experimentation have been published on thestudy of launders and crowders. This is another area ofstudy that requires further research, given the role of in-ternal elements in enhancing froth transport in large flot-ation tanks and their importance for the scale-up of thefroth zone.

4. Conclusions

Flotation equipment has become substantially larger800

over the last few decades. The increase in tank volumehas brought new challenges in the performance, designand operation of large industrial flotation tanks. Most ofthese challenges are related to problems around pulp hy-drodynamics and froth transport, such as stagnant zones,low froth mobility and froth recovery. In order to tacklethese issues, a better understanding of flotation scale-upis needed.

This review has analysed for the first time the literat-ure on flotation tank scale up. As a result, this review has810

classified the flotation scale-up studies into two categories,“kinetic” and “machine design” scale-up, given the differ-ent approaches, assumptions and techniques involved. Themain difference between these two sub-areas is that kineticscale-up has not considered tank design or size, but onlytakes into account operational considerations such as themean residence time. Machine design scale-up studies theimpact of equipment design, shape and size on the per-formance, focusing mainly on the hydrodynamic effects ofthose variables. After reviewing the literature published,820

it is clear that further research is needed to advance flot-ation scale-up. The lines of study that are critical for abetter understanding of the flotation phenomena in largetanks have been highlighted. Exploring these avenues ofresearch will certainly impact the design and performanceof newer and larger tanks.

In kinetic scale-up, it is necessary to include machinehydrodynamics in the models. Further application of CFDtechniques to model the collection zone, taking into con-sideration three phases and 3D flotation systems, is key830

to improve the predicting capabilities of current models.While it is important to recognise that kinetic models havecertainly been useful in the study and improvement of flot-ation performance over the last century, because of theirintrinsic oversimplifications they are unfit for the furtherunderstanding and comprehensive modelling of the flota-tion process. A more fundamental approach that takesinto account the physical interactions between the phases

involved would help to overcome the limitations of currentscale-up methodologies.840

In machine design scale-up, more research comparingand confronting different scale-up methodologies is neededto show their effectiveness in achieving similar metallur-gical performance. Current studies tend to use simplestirred tanks or to use only water, which are not represent-ative systems and therefore do not allow for a full under-standing of the flotation phenomena involved. New studiesneed to be specifically designed for flotation tanks, usingthree phases systems and taking into consideration boththe pulp and froth zone. In order to fill the gap between850

scientific literature and in-house knowledge, further stud-ies of the froth zone are required. These studies will beuseful for generating better models of froth transport andfroth stability, which are key for large tanks where frothhas to travel long distances to the overflowing lip.

Moreover, both areas of study should converge to anoverall understanding of the scale-up process in flotation.This synergy could be achieved by developing comprehens-ive fundamental models that can also be implemented inCFD simulators. The use of such models would allow the860

estimation of flotation performance in equipment of differ-ent scales and aid the design process.

Alternatives to tackle some of the problems associatedwith large scale flotation tanks are discussed in this review.One possibility would be to simply use smaller and moreefficient equipment, which is known as process intensific-ation. However, the main problem is that implementingany new equipment in an ongoing operation would carryimportant capital costs, as well as the uncertainty and riskassociated to new technologies.870

An engineering solution, the implementation of internalelements, has become the most commonly used approachto tackle the problems associated with froth mobility inlarge tanks. Internal elements such as launders and crowdersare cost-effective inserts that improve froth recovery andfacilitate froth transport in large flotation tanks. Althoughinternal elements have emerged as the most promising solu-tion for froth transport problems, their design and scale-uphas not been thoroughly studied. There is therefore an im-portant opportunity in the study of these inserts to reach880

improvement in overall metallurgical performance throughenhanced design and implementation.

Acknowledgements

D. Mesa would like to acknowledge the Chilean Na-tional Commission of Science and Technology (CONICYT)for funding this research with a scholarship from “BecasChile”.

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