Scale-Up in Froth Flotation: a State-Of-The-Art Review

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 its introduction over a hundred years ago. Over the last few decades, in order to process more mineral while reducing capital costs, flotation equipment has become exponentially larger. The increase in tank volume, however, has brought new challenges in the operation and design of industrial flotation tanks. This review analyses the literature on flotation tank 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 the maximisation of laboratory-scale research impact. While important advances in our understanding of flotation have been achieved, large flotation tank design and scale-up has, to a large extent, remained in-house know-how of manufacturing companies. This review of the literature relevant to flotation tank scale-up has resulted in a new classification, dividing the scale-up literature into two main areas of study, namely “Kinetic scale-up” and “Machine design scale-up”. This review indicates that current scale-up rules governing the design of flotation tanks focus mainly on pulp zone kinetic parameters and neglect the effects on the froth zone, despite the importance of froth stability and mobility in determining flotation performance. Froth stability and mobility are closely linked to the distance the froth needs to travel, which increases with tank diameter. Although including internal elements, such as launders and crowders, has been the industrial solution for enhancing froth transport and recovery in larger tanks, the design and scale-up of these elements have not been thoroughly studied. Gaps in our knowledge of flotation are discussed in the context of addressing the scale-up problem, considering froth transport and froth stability. Addressing these gaps will pave the way for the design and operation of large flotation tanks of enhanced performance. Keywords: Froth flotation, scale-up, kinetics, flotation tank, design

1. Introduction 20 mineral suspension in an aqueous media, called the pulp. Chemical reagents, called collectors, are added to the pulp Froth flotation was patented in 1905 for the concentra- in order to selectively enhance the hydrophobicity of the tion of ores (Sulman et al., 1905). It is now the most im- valuable minerals. These hydrophobic particles can attach portant mineral processing method in the mining industry, to the gas bubbles and rise to form a froth layer, which because of its technical versatility and cost-effectiveness overflows as the mineral-rich concentrate. (Wills & Finch, 2016). Flotation is also used in other The throughput treated at industrial processing plants industries, such as oil sands concentration (Rao & Liu, has increased in the recent decades because of lower grades 2013), ionic flotation (Sebba, 1959; Polat & Erdogan, 2007), and higher mining capacities (Prior et al., 2012). Instead algae separation (Chen et al., 1998; Laamanen et al., 2016), of the amount of cells and banks in the processing plant 10 paper deinking (Chaiarrekij et al., 2000; Vashisth et al., 30 being increased, flotation equipment has become larger in 2011), plastic recycling (Takoungsakdakun & Pongstabodee, order to process more mineral (Rao, 2004). Tank volume 2007; Wang et al., 2015; Negari et al., 2018) and wa- has increased a thousandfold in the span of a century, ter treatment (Rubio & Smith, 2002; Saththasivam et al., as can be seen in Figure 1 (after that in Wills & Finch 2016). (2016)). This increase in tank size has allowed the utilisa- Froth flotation works on the basis of surface chem- tion of economies of scale, by reducing the overall capital istry; fine mineral particles are separated according to and operating costs (Murphy, 2012). However, these lar- their hydrophobicity. This separation process disperses ger and more complex tanks have brought new challenges small bubbles of gas, generally air, inside a flotation tank, in performance, design and operation (Tabosa et al., 2016) also referred to as flotation cell. The tank contains a in terms of pulp hydrodynamics and froth transport.

40 When confronted with the problem of processing a lar- ∗Corresponding author ger throughput, other industries have taken a diﬀerent Email address: [email protected] (Diego Mesa) approach, called process intensiﬁcation. Process intensi-

Preprint submitted to Separation and Purification Technology 17th July 2018 1000 80 with designs that apply process intensification principles will no doubt play an important role in the future of mineral separations, it is unlikely that new flotation tanks in 3 100 processing plants will be considerably smaller in the near future. Therefore, scale-up studies are, and will, remain critical for the design of large flotation equipment. Scale- 10 up studies are also relevant for the design of retrofits, that can be installed in existing flotation tanks to enhance their performance. These studies require a better understand- 1 Flotation tank volume, m ing of the hydrodynamics phenomena at different scales

90 and their impact on performance, for both the pulp and froth zones in flotation tanks. 0.1 1920 1940 1960 1980 2000 2020 The purpose of this review of scale-up in froth flotation Year is twofold: (i) to highlight and classify the studies that have been conducted on flotation scale-up, defining two Figure 1: Trend in flotation tank size over the last century, referring to the maximum tank volume commercially available. Data from sub-areas of study, namely “kinetic scale-up” and “design Dreyer (1976); Lynch et al. (2007); Wills & Finch (2016); Lelinski scale-up”, and (ii) to highlight the areas that require fur- et al. (2017). Note that the y-axis is on logarithmic scale. ther research and better understanding for a more effective scale-up of flotation tanks. This is the first review to offer an in-depth analysis fication is defined in Chemical Engineering as the study 100 and critique of flotation scale-up studies, including exper- and design of ever smaller reactors. These small reactors imental studies and scale-up procedures suggested in the operate by enhancing transport and processing rates, lead- literature. The analysis of the literature shows that while ing to a better control of the kinetics, improving energy the scale-up process for the pulp zone in flotation tanks efficiency and reducing capital cost (Reay et al., 2008a). has been extensively studied, insufficient attention as so Process intensification has been applied in the design of far been paid to the scale-up process related to froth mo- a broad range of equipment, including heat exchangers, bility and stability. It is also highlighted that the liter- 50 reactors and separators (Ramshaw & Arkley, 1983; Reay ature available on the design of different inserts such as et al., 2008c). In extractive metallurgy, a toroidal flu- launders and froth crowders is scarce . The lack of fun- idised bed used for ore roasting and drying, denominated damental understanding of the effect of those inserts on The Torbed, was developed following the principles of pro- 110 flotation performance is discussed, which is essential for cess intensification (Groszek, 1990; Shu et al., 2000; Wang effective scale-up. et al., 2017). A recent review of the use of process intensification in solids handling (Wang et al., 2017) included a section 2. Flotation equipment on particle separations and froth flotation. Some examples The four main functions of a flotation tank are: (i) in- mentioned are the Air-Sparged Hydrocyclone (ASH), which troducing air bubbles into the pulp, (ii) providing an envir- 60 achieved recoveries of 85-93% of pyrite with a mean resid- onment that increases the probability of collision between ence time of 1 second (Van Deventer et al., 1988), and the those bubbles and the particles in the slurry, (iii) maintain- Jameson Cell, which enhances the mixing intensity, max- ing a stable pulp-froth interface and (iv) providing suffi- imising the particle-bubble contact probability and achiev- cient froth removal capacity (Degner, 1988; Gupta & Yan, ing high recoveries with a residence time of 5-10 s (Clayton 2006). Flotation equipment, regardless of its scale, can et al., 1991; Glencore Technology, 2016). Other examples 120 be classified into two main types: mechanical and pneu- include the HydroFloat cell, which is an aerated fluidised- matic cells, of which the former is the most widely used in bed that improves the recovery of coarse particles with low industry. residence times, reducing the contact zone (Eriez, 2015; Mechanical cells (Figure 2) are fitted with an impeller Miller et al., 2016), as well as several studies considering in order to generate a highly turbulent region, which keeps 70 microbubble generation for flotation (Rodrigues & Rubio, particles in suspension, generates and disperses bubbles, 2007; Parmar & Majumder, 2013), including the cyclone- and promotes bubble-particle collision (Deglon, 2005; Tabosa static microbubble column of Cao et al. (2009) and Zhang et al., 2016). Mechanical cells can be sub-classified by their et al. (2013), which showed higher recoveries than a com- air injection system into self-aerated and forced-air cells mon bench-cell. (Wills & Finch, 2016). Self-aerated cells use the negative However, despite being introduced more than two dec- 130 pressure of the vortex created through agitation to induce ades ago, process intensification has been adopted slowly air into the pulp. On the other hand, forced-air or super- at an industrial scale (Reay et al., 2008b). In minerals pro- charged cells are supplied with air from an external and cessing, and particularly in froth flotation, process intensi- controlled source. Both aerating technologies are widely fication has not taken off yet. While novel flotation tanks, used in processing plants, but forced-air cells allow for a 2 Air Concentrate Concentrate

Feed

Feed Tail

Figure 2: Schematic of a mechanical flotation cell. The impeller is shown agitating the pulp and generating bubbles from air injected from the top. Valuable particles attach to bubbles and rise to the Tail froth zone, overflowing as concentrate, while gangue reports to the Air tailings at the bottom. 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 a better control of the supplied air by decoupling this vari- sparger at the bottom. able from impeller speed and pulp level. The control of air flow rate and pulp level is crucial for optimising the flotation process (Laurila et al., 2002; Shean & Cilliers, on simplified laboratory-scale cells. 2011). 170 Laboratory flotation machines are simplified and smaller flotation equipment. These laboratory machines are 140 Pneumatic cells do not use impellers. Instead, bubbles are generated by injecting the air into the cell at high pres- used in metallurgical tests, mainly focusing on reproducib- sure or speed. The pulp can be fed in separated from the ility and achieving similar performance to industrial flota- air, like in a conventional flotation column (Figure 3), or tion operations (Gupta & Yan, 2006). Generally, there is a injected with the air at high pressure, enhancing the con- trade-off between these goals. Bench-scale laboratory cells, tact between bubbles and particles, like in the Jameson such as the one shown in Figure 4, are widely used. Labor- cell. Flotation columns are tall cells where air is com- atory cells have proven to be useful for flotation testing, monly injected at the base using a sparging system and e.g. determining the choice of reagents and defining kin- pulp is fed in near the top of the column (Dobby & Finch, etic parameters for modelling (Wills & Finch, 2016). How- 1991; Filippov et al., 2000). Particles settle because of180 ever, their small scale implies that most of these cells have important differences in impeller size, number of stator 150 gravity, while the swarm of bubbles rises because of their buoyancy. Bubble-particle collision probability depends blades and in other geometric ratios when compared to on the distance between the feeding point and the base of industrial cells. the column. As such, the importance of both the height More importantly, these laboratory machines are de- of the column and the ratio between height and diameter signed for batch testing, meaning that steady state cannot has been discussed at length (Yianatos et al., 1988; Finch be reached. In a batch test the pulp properties vary con- & Dobby, 1991). The popularity of flotation columns has tinuously; water is added as froth overflows to maintain fluctuated during the last 20 years, being mainly used in the pulp level, changing the solid concentration, mineral the coal, phosphates and iron ore industries, and com- grade and reagents concentration over time (Runge, 2010; monly employed as cleaner stages in base metal plants190 Wills & Finch, 2016). Some laboratory cells capable of running at steady 160 (Harbort & Clarke, 2017). Both mechanical and pneumatic flotation machines can state have been developed. Examples include semi-continuous be found at industrial scale, operating in different mineral systems, mainly based on batch cells, such as a modified processing plants around the world. The size of industrial 3 litre Denver batch-flotation machine (Kaya & Laplante, flotation machines and limited control over operating vari- 1986) and a modified 3.5 litre Leeds batch cell (Vera et al., ables such as feed characteristics, combined with the cost 2002). More recently, continuous laboratory systems have associated to making changes on plant to accommodate been introduced. Brito-Parada & Cilliers (2012) designed trials, are physical and financial barriers for on-site exper- a 64 litre continuously operated cubic tank for studying imentation. Consequently, studies are usually performed foam transport phenomena, while Shean et al. (2017) used 200 a 50 litre cylindrical tank, also operated with a two-phase

3 230 3. Scale-up in ﬂotation

Early flotation tanks were machines of less than 1 m3 (Arbiter, 1999). Nowadays, most newly installed tanks are larger than 300 m3 (Murphy et al., 2014). FLSmidth’s 660 m3 SuperCellTM at KGHM Robinson concentrator in United States is currently the largest operating tank (Lel- 3 Air inski et al., 2017), followed by Outotec’s 500 m TankCell® at Boliden Kevitsa concentrator in Finland (Mattsson et al., 2016). This increase in flotation tank volume offers technical and economical advantages. Larger tanks imply that

240 fewer of them are needed, which results in less floor space, simpler operational control and lower power consumption Concentrate (Arbiter, 1999; Murphy, 2012). However, new challenges appear when tanks are scaled-up to large industrial sizes, since fluid dynamic properties alter the performance of flotation equipment (Tabosa et al., 2016). On the one hand, pulp dynamics are affected by the size, shape, speed Figure 4: Laboratory bench-scale flotation equipment, widely used in and position of the agitating mechanism (sparger, rotor- industry for batch laboratory tests. The volume of the cells typically ranges between 1 and 5 litre. The pulp is poured into the cell and stator systems, etc.) (Deglon, 2005; Amini et al., 2016a). the concentrate overflows the lip, while the pulp that remains after On the other hand, froth stability will change due to the a determined flotation time represents the tailings. 250 greater distance between the bulk of the froth and the discharge lip (Zheng et al., 2004; Coleman, 2009; Brito- Parada & Cilliers, 2012). system. Li et al. (2015) used a 20 litre pilot scale flota- The concept of “scale-up” in flotation literature is used tion cubic tank, continuously operated, to study froth rhe- in two ways, which has led to the development of two ology. Norori-McCormac et al. (2017) introduced a 4 litre different areas of study. The first and most researched continuously operated cylindrical tank based on the stand- of these two areas focuses on the different procedures for ard stirred tank developed by Costes & Couderc (1988) scaling-up the kinetic parameters of flotation models ob- (schematic shown in Figure 5). That 4 litre tank was used tained through laboratory tests, to predict plant behaviour to study particle size effects on froth stability. Morrison (Gorain et al., 1998b; Amelunxen & Runge, 2003; Dobby (2017) have used a 70 litre scaled-up version of the afore- 260 & Savassi, 2005; Bulled, 2007; Yianatos et al., 2010). For mentioned tank, also operated with a three-phase flotation the purposes of this review we refer to this area of study 210 system. as “kinetic scale-up”. The second area of study considers The previous examples highlight how new laboratory how flotation equipment design affects performance at dif- flotation cells are not necessarily defined by their size, but ferent scales. We refer to this second area as “machine by their simplicity in operation and modification of vari- design scale-up”. The latter has been mainly studied by ables. This characteristics allow a comprehensive study considering the effects of hydrodynamic phenomena in the of flotation phenomena. While laboratory flotation tests pulp zone, considering geometrical and dynamic similar- allow studying the effect of different variables in a single ities (i.e., keeping the same equipment shape and main- flotation unit, pilot-scale testing is important for plant cir- taining the same non-dimensional numbers relevant to the cuit design (Wills & Finch, 2016). Pilot flotation equip- 270 flow, respectively) (Nelson & Lelinski, 2000; Gorain et al., ment usually refers to small industrial flotation tanks, typ- 2007; Truter, 2010), as well as by focusing on air injection 220 ically varying between 60 and 150 litre tanks (Amini et al., technologies and impeller design and speed (Gorain et al., 2016a; Deglon, 2005), such as the 100 litre Batequip mech- 1995a,b, 1996, 1997; Grano, 2006; Newell & Grano, 2006, anical flotation cell (Shabalala et al., 2011). Pilot plants 2007; Amini et al., 2016a, 2017). are used for comparing equipment and circuit perform- Most research into machine design scale-up has focused ance, comparing costs associated to alternative processes on the pulp zone, with no scientific studies published spe- and preparing large samples of concentrate for further test- cifically on the topic of froth zone scale-up. Only some ing. The process of translating experimental data from rules of thumb have been published by Coleman (2009) as laboratory tests to industrial scale is known as scale-up, an industrial guide for tank and launder design selection, which is discussed in the context of froth flotation tanks 280 such as recommending the use of internal double launders in the next section. for high-grade ores, external launders for ultrafine recovery and radial launders for applications with high mass recovery. Clearly, there is a knowledge gap between the in-house know-how of manufacturers and scientific literature on the scale-up of flotation tanks. Although this gap

4 is to be expected to a certain degree due to commercial fications, such as assuming a constant concentration of reasons, there is still an evident lack of published research bubbles, defining the order n, or assuming a certain resid- in the topic of flotation tank scale-up. Filling that gap ence time distribution of the particles in the tank. These is an opportunity, since more comparable works are very models aim to characterise the flotation phenomena with 290 much needed to advance the field. two or more kinetic parameters, such as k and Rmax (the Nowadays in several process industries, Computational theoretical maximum recovery achievable), which are ob- Fluid Dynamics (CFD) is routinely used for the scale-up tained by fitting the models to experimental data. Con- of equipment. Stirred tanks are a common example, such sequently, these parameters are not only dependent on the as those used as reactors and bioreactors (Nauha et al., characteristics of the mineral, such as composition, particle

2015). However, despite the fact that the pulp zone in340 size distribution and liberation, but also on the operating mechanical flotation cells is to some extent analogous to conditions and the flotation equipment used. stirred tank systems, there are no publications on the use The introduction of the compartmental model for con- of CFD for flotation tank scale-up. tinuous flotation tanks (Dobby & Finch, 1991) allowed the CFD has been used to model flotation tanks and to focus of the kinetic models to be placed on the collection

300 assess flotation performance (Koh et al., 2000; Koh & zone, practically ignoring the froth zone. This model di- Schwarz, 2006, 2008; Evans et al., 2008; Brito-Parada et al., vides the flotation process into two independent but inter- 2012b; Cole et al., 2012; Brito-Parada et al., 2013; Shi connected zones: the collection zone and the froth zone, et al., 2015; Karimi et al., 2014a,b) but never combin- both with their own recovery, as shown in Equation (2): ing the froth and pulp zones. Although scientific publications on the use of CFD for equipment design are lim- RcRf R = R∞ , (2) ited (Neethling & Cilliers, 2003; Koh et al., 2003; Koh & RcRf + (1 − Rc) Schwarz, 2007; Brito-Parada & Cilliers, 2012), companies where R is the overall recovery of the cell, R is the recov- that manufacture flotation equipment have continuously c ery from the collection zone and R is the recovery from reported the use of CFD models for the design and scale- f the froth zone. Dobby & Finch (1991) proposed that the 310 up of their larger flotation cells, e.g. Outotec’s Tanckcell froth recovery can be defined as: e500 (Murphy, 2012) and FLSmidth’s SuperCell 660 (Lel- inski et al., 2017). However, the few published studies for k these very large tanks focus only on hydrodynamics eval- Rf = , (3) kc uation of the pulp zone, in most cases comparing CFD model predictions against tests run only with water. where k is the overall flotation rate constant and kc is the collection zone rate constant. This implies that the 3.1. Kinetic scale-up different kinetic models shown in Table 1 can be used to Mathematical methods are used to translate kinetic define both the collection recovery component as well as data, obtained from laboratory-scale flotation experiments, the overall recovery of Equation (2). to industrial plant performance. The main aim of kinetic Flotation kinetics at industrial scale are not the same

320 scale-up is to predict concentrate grade and recovery at as at laboratory or pilot scale, meaning that klab, the k industrial-scale, by analysing laboratory-scale data. Flot- value obtained from laboratory data, and kplant, obtained ation equipment is considered an input, and only a few350 from plant data, are not equal. For example, k from Equa- variables related to the equipment size and operation are tions (4) and (5) are not necessarily the same as k from considered, such as residence time. Equations (6) and (7). This difference occurs because the Several kinetic flotation models have been published. residence time and the hydrodynamic conditions of the In this section, only the applicability of those models in flow are different. Therefore, obtaining the kinetic para- to the scale-up process of flotation is discussed. A thor- meters at industrial scale from the ones at laboratory scale ough review of kinetic models can be found in Gharai & is a complex process for each new combination of ore and Venugopal (2015). These models are defined on the basis equipment. This process is how the whole scaling-up prob- of a simplification, by considering flotation as a kinetic rate lem is defined from a kinetic point of view. Kinetic scale-up process, analogue to chemical reactions. This considera- has not been completely solved, and commonly results in tion leads to the following ordinary differential equation:360 laboratory data overpredicting industrial rate values. There are different empirical approaches available for dC n m scaling kinetic parameters. A common scale-up methodo- = −knC C , (1) dt b logy to estimate plant flotation rate is to divide the labor- where C and Cb are the concentrations of particles and atory flotation rate by a scaling factor, commonly between bubbles, respectively, the exponents n and m are the reac- 1.5 and 3 (Weiss, 1985; Degner, 1986; Wood, 2002). This tion orders, t is time and k is the flotation rate constant. scaling factor is calculated as a ratio of industrial and The various flotation kinetic models presented in Table 1 laboratory residence times. The methodology entails com- can be obtained by solving Equation (1). These differ- paring the residence time in a continuous flotation circuit

330 ent models are obtained by considering diﬀerent simpli- or tank with the residence time needed in a batch experi- 5 Table 1: A selection of ﬂotation kinetic models

st −k t Classical 1 -order model (Garc´ıa-Zu˜niga,1935) for batch R(t) = Rmax 1 − e (4) tests h i st 1 −kmax t 1 -order model with rectangular distribution of ﬂotation R(t) = Rmax 1 − 1 − e (5) kmax t rates (Klimpel, 1980), for batch tests

st kτ Continuous 1 -order model (Arbiter & Harris, 1962) R = Rmax 1+kτ (6)

h ln(1+kmaxτ) i Continuous Klimpel model (Klimpel, 1980) R = Rmax 1 − (7) kmaxτ

∞ st R −k t General 1 -order model for batch tests (Imaizumi & Inoue, R(t) = Rmax 1 − e f(k) dk (8) 1963; Polat & Chander, 2000) 0

∞ ∞ st R R −k t General 1 -order model (Yianatos & Henr´ıquez,2006) R(t) = Rmax 1 − e f(k)E(t) dkdt (9) 0 0

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 of internal 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.

370 ment, in order to achieve the same recovery (Weiss, 1985; where kapp is the apparent flotation rate constant, which Gochin & Smith, 1987). is the measured value of k in plant, modified by the effects Further developments on the use of the scaling factor of the froth zone (ζ), mixing (η) and solid segregation (ψ). k approach can be illustrated by a series of works published The froth effect was defined as ζ = app/kc, following the by Yianatos et al. (2003, 2006, 2010). Yianatos et al. model of Dobby & Finch (1991) shown in Equation (3). (2003) used the scaling factor concept in a case study at El The collection zone rate constant was calculated by Yi- Salvador concentrator, employing separability curves (the anatos et al. (2010) as a function of the bubble loading ratio of mineral recovery to yield) to select the compar- (λb) and the grade of the minerals collected by true flota- ison recovery. This comparison recovery was defined at380 tion, both estimated using the USM-Bubble Load Sensor the optimum separability point, that is when the concen- (Yianatos et al., 2008b). However, all those studies still trate incremental grade equals the feed grade. The scale- neglects the effect of entrainment, do not consider the de- up factor was defined as kPlantτ = kLabt, obtaining as an tachment of particles in the sampling process, and do not k average result over a period of 10 months a Lab/kPlant ra- include other effects of the froth zone such as liquid drain- tio of 2.26 ± 0.35. For another case study, Yianatos et al. age and transport phenomena. (2006) introduced a dimensionless scaling parameter ϕ, as Another approach for kinetic scale-up has been pro- shown in Equation (10): posed by Gorain et al. (1998b). Following the work of Dobby & Finch (1991), Gorain et al. (1998b) have pro- τ k Plant = ϕ Lab , (10) posed that k can be expressed as: tLab kPlant k = PSb Rf , (12) to separate the effects that mixing and kinetic changes have on the time scale-up factor. The last study resul- which is the same as considering kc = PSb. In those equations S is the bubble surface area flux (s−1), defined as ted in a ϕ value of 1.26, a time scale-up factor τ/t of 3.2 b J k Sb = 6 g/d32, where Jg is the gas superficial velocity (cm/s) and a kinetic rate constant ratio Lab/kPlant of 2.5. How- ever, these two studies did not consider various effects of and d32 the bubble Sauter mean diameter (mm). P is the tank size, such as those affecting the froth zone, differ-390 floatability index, a dimensionless parameter that only de- ences in cell mixing and solids segregation. Yianatos et al. pends on the ore characteristics (later considered as the (2010) incorporated those issues by considering the scale- flotation probability by Koh & Schwarz (2006)). k The objective of this modelling approach is to decouple up factor ξ = ac/kLab. In that definition, kac is the actual or real value of k at the plant, that can be estimated using the ore characteristics, represented by P , from the operat- Equation (11) ing variables and the flotation equipment design, represented by Sb, so the scale-up process would only depend on kapp = kac ζ η ψ , (11) the latter. Further research into the bubble surface area 6 flux was carried out by Gorain et al. (1999), who proposed These parameters are defined as: an empirical expression for Sb that related it to impeller design and operating conditions, on the basis of several k = PSb æ EVF , (15) experiments performed on different mechanical flotation d ε0.25 n where æ = 32 (16) cells. This relationship is shown in Equation (13): ν0.75 b c d e Sb = a Ns Jg As P80 , (13) is the hydrodynamic factor. ε represents the turbulent kinetic energy dissipation rate (TKEDR, in m2/s3) (Schubert, where Ns is the peripheral velocity of the impeller, As is 430 1999; Amini et al., 2016a), ν is the fluid kinematic viscos- the aspect ratio between the diameter and the height of ity (cm2/s) and n is a fitting parameter estimated through the impeller, and P80 relates to the feed particle size. The a number of flotation tests over a range of operational con- constants a, b, c, d and e are empirical values obtained from ditions. EVF, the Effective Volume in Flotation, is calcu- experimental data analysis (123, 0.44, 0.75, -0.10 and - lated as the fraction between the volume of the cell where 0.42, respectively). However, this empirical approach only the TKEDR is higher than 0.1 m2/s3 and the total volume considers the hydrodynamic effects produced due to the of the cell. 400 impeller type and its operating conditions, omitting other Nevertheless, all these kinetic scale-up methodologies considerations involving tank size and shape. are based on deterministic kinetic models. Deterministic The model of Gorain et al. (1998b) has been later com- kinetic models have received several critiques, in particular bined with the compartmental model (Equation (2)) and 440 in relation to their prediction capacity (Heiskanen, 2013) expanded by Savassi et al. (1998) to incorporate entrain- and their applicability within the industry (Yianatos, 2007; ment mechanisms. It was also modified by Welsby et al. Amelunxen, 2013). Most of those critiques argue that de- (2010b) to account for particle size and liberation, result- terministic models tend to oversimplify the interactions ing in Equation (14): between variables, such as considering k as time independent, neglecting all the chemical and transport phenomena, (ki,jτ)(1 − Rw) + ENTiRw R = , (14) or treating forces as scalars, not considering spatial inter- i,j (1 + k τ)(1 − R ) + ENT R i,j w i w actions (Heiskanen, 2013). These considerations are es- where the subscripts i and j represent size and liberation pecially important when using such models for scaling-up purposes. classes, respectively, Rw is the water recovery to the concentrate and ENT is the degree of entrainment (Trahar, Probabilistic models have been proposed by several au- 1981). thors (e.g. Schuhmann, 1942; Sutherland, 1948; Schulze, 1984; Pyke et al., 2003; Yoon et al., 2016); further de- The combination of Sb and the compartmental model is widely used by several plant design and simulation soft- tails can be found in Gharai & Venugopal (2015) review ware programs such as JKSimFloat (Harris et al., 2002; on kinetic models. Probabilistic models consider that k is Welsby et al., 2010b) (based on Equation (14)), FLEET the result of combining the probabilities of particle-bubble

410 (Dobby & Savassi, 2005) and AminFloat (Amelunxen et al., collision (Pc), attachment (Pa) and detachment (Pd), as 2014); a comparison of these programs can be found in shown in Equation (17): Soni (2013). Equation (14) has also been used for kinetic scale-up by Welsby et al. (2010b), who defined a cell k = ZP = ZPcPa(1 − Pd) , (17) scale-up number C as the kcont/k , obtained at the same batch where Z is the rate of collision. In particular, the model recovery. By using Equation (12) for the definition of proposed by Pyke et al. (2003) for the rate of collision, the continuous kinetic constant rate, this scale-up proced- shown in Equation (18), has been used for the development ure accounts for the differences in S and R . In that b f of a CFD kinetic model (Karimi et al., 2014a). That CFD work, Welsby et al. (2010b) compared a 40 litre continuous model has been validated for a chalcopyrite and galena square pilot cell (Welsby et al., 2010a) and a 4 litre batch system by varying hydrophobicity, agitation rate and gas 420 cell with the same shape, obtaining a value C = 0.53. flow rate (Karimi et al., 2014b). In the model by Pyke It is worth noting that in the scale-up number C, the et al. (2003), k is defined as: kinetic ratio is the inverse of that used in most studies. −1 C = 1.89 offers a similar value to the methodologies " 7/9 2/3# 7.5 Q 0.33 ε4/9d ρ − ρ discussed earlier. However, while this work uses a differ- k = g 32 s l [P ], (18) π d V 1/3 ρ ent kinetic model (Equation (14)), the scale up method- 32 r ν ui l ology still depends on directly comparing a batch and a 450 where Q is the gas flow rate, V is the reference volume, ε continuous kinetic model at a specific recovery. g r is the turbulent dissipation rate (cm2/s3), ρ is the solids More recently, Amini et al. (2016c) modified Equa- s density (g/cm3), ρ is the liquid density (g/cm3) and u is tion (12) to enhance the scale-up capabilities of the model, l i the turbulent fluid velocity (cm/s). by introducing two dimensionless parameters: æ and EVF. All the terms in Equations (17) and (18) have been extensively 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 the eﬀorts to provide valuable information about the mechanisms governing ﬂotation, the complexities of multiphase

460 ﬂotation systems are not fully captured by those models. Heiskanen (2013) attributed this lack of detailed represent- ation to the fact that general conclusions are often drawn for continuum phenomena from theoretical work at a much smaller scale. Since froth phenomena is not a kinetic process, kinetic models are necessarily focused on pulp zone phenomena only. Therefore, scale-up processes based on current kin- Figure 5: Standard stirred tank (From Paul et al. (2004)) with a etic models are not able to account for the changes that single Rushton impeller, H=T. occur in the froth zone in larger tanks, which is further

470 discussed in Section 3.2.1. Not including the froth zone transport and stability implies that kinetic models are not sufficient for understanding the effects of tank scale on flotation, so they cannot be used for effective tank design. The design of large flotation tanks is the focus of the next section.

3.2. Machine design scale-up The work developed in this area aims to deﬁne the impact of equipment design, shape and size on ﬂotation performance. A key goal would be to generate clear pro-

480 cedures for flotation machine scale-up, enabling the trans- ition from laboratory-scale to plant-scale with minimum compromise in performance. Since flotation phenomena Figure 6: Power number for different impellers Reynolds number involves several micro-, meso- and macro-scale mechan- (From Bates et al. (1963)). Np becomes constant at high Re values. isms that are independent, flotation machine scale-up is a difficult process. For that reason, it has traditionally been In the mineral processing literature, the use of non- simplified, using similitude considerations and dimension- geometrical ratios and dimensionless numbers for the design less analysis (Gorain et al., 2007). The main simplification of froth flotation tanks has also been proposed (Gorain has been to scale-up only the pulp zone as it is done for et al., 2007; Truter, 2010; Boeree, 2014). These dimen- stirred tanks, in which the different phases are mixed in a sionless numbers are detailed in Table 2. For example, 490 turbulent region. the Reynolds number, Re, and Power number, Np (Equa- In Chemical Engineering, the design and scale-up of tions (22) and (23)), are used to calculate the power con- continuous stirred-tank reactors (CSTR) is a problem that sumed by different impellers, as shown in Figure 6. has been extensively studied (Evangelista et al., 1969; Ni- For flotation systems, Arbiter (1999) proposed keep- enow, 1997; Nauha et al., 2015). When designing a CSTR, ing the Power number and the power per volume (P/V ) the recommended engineering approach involves defining constant by varying the rotor diameter (D) and rotational the process mixing requirements and then finding the ap- speed (N), according to the following empirical relation- propriate impeller type to meet that requirement, depend- ships: ing on the fluid system (Paul et al., 2004). Once the impeller type is defined, parameters such as the number D3 = 2.4022 + 0.0142 V (19) 500 of impellers and impeller size, speed and energy require- ND = 6.66 + 0.0743 V (20) ments are assessed, while other parts such as baffles tend to be used to achieve the desired flow patterns (Paul et al., When a rotor-stator system is used, the scale-up pro- 2004). cess suggested in the mixing literature usually considers The stirred tank scale-up process involves the design keeping the rotor tip speed constant (Vtip = πND). This of a large system that will achieve the same mixing qual- consideration is equivalent to keeping the nominal shear ity as the laboratory-scale one. Some scale-up methods rate (γ ˙ ) constant (Paul et al., 2004), as shown in Equa- consider geometric similarity, keeping constant specific di- tion (21), πND mensional ratios such as those of the impeller diameter to γ˙ = , (21) the tank diameter (D/T ), the impellers blade width to the δ

510 impeller diameter (W/D) and the impeller clearance from520 where δ is the shear gap width, a value that does not the bottom to the tank diameter (C/T ) (see Figure 5). depend of the rotor-stator scale. Although tip speed and 8 Table 2: Dimensionless numbers suggested for ﬂotation tank scale-up

ρ N D2 ND2 Reynolds number, Re (Reynolds, 1883). A measurement of turbulence Re = µ = ν (22) in the system.

P Power number, Np (Bates et al., 1963). Relates the torque and inertial Np = ρN 3D5 (23) forces that must be overcome to rotate the impeller at a given rate.

N 2 D Froude number, F r (Kramers et al., 1953). The ratio of inertial and F r = ρl js (24) (ρs−ρl) g gravitational forces. 0.2 Zwietering constant, S (Zwietering, 1958). A function of impeller type 0.1 0.45 D 0.13 S = ReimpF r d X (25) and geometry. p

Qg Air flow number, Na (Arbiter et al., 1976) or Air capacity number, Ca Na = Ca = ND3 (26) (Nelson & Lelinski, 2000) 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 the gravitational acceleration. Reimp is the Reynolds generated by each particular impeller, dp is the particle size mean (m) and X is the mass ratio of suspended solids to liquid. 3 Qg is the gas inflow rate (m /s).

shear rate control have been reported in various flotation- pliers, as shown in Figure 7. related publications (Lelinski et al., 2005; Govender et al., 3.4 2014; Amini et al., 2016b), these criteria only consider the Qg ∝ Ql ∝ T (28) agitation phenomena of the liquid phase, neglecting the presence of solids and air bubbles in flotation systems. For solid suspensions, the Zwietering criterion (Zwieter- ing, 1958), defined as the condition at which the maximum surface area of the particles is exposed to the fluid, is used for tank design and scale-up. This criterion is also known as the “just suspended” condition. It is physically determined by Njs, the minimum agitation speed at which all particles reach complete suspension, as shown in Equa- tion (27):

0.45 0.1 g (ρs − ρl) 0.13 0.2 −0.85 Njs = S ν X dp D , (27) ρl

where s is the Zwietering constant shown in Equation (25), dp is the particle size mean and X is the mass ratio of suspended solids to liquid. This criterion has been used Figure 7: Wemcor 1+1™ flotation machine hydrodynamic performance map (From Degner (1988)). 530 for the scale-up of stirred tanks in mixing applications (Buurman et al., 1986; Kraume & Zehner, 2002; Jirout & Rieger, 2009). It has also been implemented in the char- Wemcor 1+1™ scale-up procedure consists on keep- acterisation of flotation equipment (Schubert, 1999, 2008; ing the Air Flow Number (Na) constant (Arbiter et al., van der Westhuizen & Deglon, 2008). However, the just- 1976; Weber et al., 1999; Souza Pinto et al., 2017). This suspension condition does not involve the gas phase. parameter, also called Air Capacity Number (Ca) (Nelson When considering gas injection and bubble formation & Lelinski, 2000; Gorain et al., 2007), is defined in Equa- in the flotation scale-up process, it is a common practice tion (26). Wemco’s procedure also considers keeping Jg to keep constant the relationships between gas flow rate,550 relatively constant and under 2.5 cm/s. liquid flow rate and tank diameter, as shown in Equa- Although CFD has been used for flotation equipment design, the literature about its use for the scale-up of flot- 540 tion (28) (Paul et al., 2004; Gorain et al., 2007). An example of this practice are the hydrodynamic performance ation cells is scarce. An example of the use of CFD in maps that used to be provided by flotation equipment sup- flotation equipment design and flotation modelling is the

9 work of Koh et al. (2003), who developed a 3-D CFD flot- plexity of the problem was not taken into account. Their ation model. The main variables were the Cartesian ve- work is the only published comparison between two similar locity components, pressure and turbulence according to flotation tanks of different scales using CFD. This study Navier-Stokes equations. The turbulence viscosity in the presented the opportunity to clarify many doubts around liquid phase was calculated using the standard k − ε tur- different scale-up procedures. It was performed using two

560 bulence model (Launder & Spalding, 1974). Two diﬀerent tanks that had already been scaled-up, built and installed, ﬂotation agitation mechanisms were modelled, one from so the results could have been crucial. However, not many Metso and another from Outokumpu. However, the val- details are included in the results and discussion, probably

idation of the models were run in water-only experiments.620 because of commercial reasons. The results did not compare the agitation mechanisms, The studies discussed in this section deal with different but only the flexibility of the models to adjust to differ- techniques for machine design scale-up but few comparis- ent geometries. Another example of CFD applications for ons can be made, since each technique has been applied, the study of equipment design is the work of Shi et al. in isolation, to different tanks and at different operating (2015). In that study, the fluid dynamics performance conditions. Further research comparing scale-up methods, of impellers with different blade angles were studied using both theoretically and experimentally, is needed. Also,

570 water-only experiments and CFD. The CFD code used was most of the published literature is either on generic mixing CFX 14.0, implemented with a standard k − ε turbulence reactors or from a few proceedings and studies published model. The results shown that a backward impeller and by ﬂotation tank manufacturer companies. This gap in

a radial impeller would be a better choice for large recir-630 the scientific literature needs to be addressed, both to al- culation volumes. Also, the backward impeller incurred low flotation scale-up methodologies to be peer reviewed in a considerably lower power consumption than the other and identify important gaps in knowledge that can lead designs. to further research. This will certainly lead to the further CFD has been used for machine scale-up in similar in- enhancing of flotation efficiency and performance. dustries. For instance, the scale-up of fluidized-bed hydro- A major critique to most of the machine scale-up pro- dynamics has been studied using CFD (Knowlton et al., cedure is that all the techniques based on dimensionless

580 2005). It was shown that the correct diameter of the tank numbers discussed before can only be used to obtain sim- depended on the particle size of the system and turbulence ilar particle suspension and agitation, but it has not been of the ﬂow. CFD has been also used for understanding the proved that those considerations correspond with obtain-

scale-up of binder agglomeration processes (Mort, 2005).640 ing similar metallurgical performance (Gorain et al., 2007). Although the agglomeration process is considerably differ- The link between achieving similar hydrodynamic para- ent to flotation, some of the conclusions obtained in that meters in the pulp zone and obtaining similar metallurgical study could be considered. Mort (2005) found that the results is not straightforward, because a flotation machine operating conditions tend to affect more than one process cannot be defined simply as a stirred tank. While the within the whole agglomeration system. It was found that pulp zone can be modelled as a stirred tank, which implies after reaching a certain scale, it would be advisable to not considering the collection of particles, the froth zone

590 separate the diﬀerent processes in staged units operations. presents a number of complexities of its own that must be This is similar to what has been proposed with several considered in order to predict performance. Froth scale-up ﬂotation cells that separate the collision/collection stage is the focus of the discussion in next section. from the separation stage, such as the Contact cell (Ame-

lunxen, 1993) or the Jameson cell. An interesting view650 3.2.1. Froth zone scale-up of how this reactor-separator approach could be used at While the scale-up for the mixing process in the flot- industrial scale is detailed in the review of Finch (1995). ation pulp zone has been extensively studied, the same Despite not mentioning it, the view proposed in that re- cannot be said for processes in the froth zone. Indeed, view followed concepts of process intensification. Paul et al. (2004) stated: In flotation there is only one study published on the “No well-defined criteria are published for design- 600 use of CFD for comparing the effect of machine scale-up. Lichter et al. (2007) used CFD and DEM (discrete ele- ing gas/suspension mixing in flotation systems. ment modelling) to compare the pulp behaviour between However, all the mixing/contacting strategies a 50 m3 and a 160 m3 industrial Metso tanks (RCS50 and attempt to create small gas bubbles and en- RCS160, respectively). They found that the ratio between sure efficient bubble/suspension contact in a the feed inlet flow and the mechanism pumping rate, i.e.,660 well-mixed zone.” the flow just off the blades of an impeller (Nienow, 1997), Nevertheless, some efforts have been made to include was smaller in the RCS50. The larger tank achieves a froth transport phenomena and tank size into flotation similar or higher ratio before overloading the mechanism, models. The first step was to conceptually divide the tank implying that larger tanks can process more feed than in into two different systems, with a collection zone recov- 610 a linear estimation. However, the work of Lichter et al. ery (R ) and a froth zone recovery (R ) (Dobby & Finch, (2007) did not consider air injection, so the whole com- c f 10 1991). Gorain et al. (1998a) included the froth transport- model, expressed in Equation (31), does not depend on ation distance, L, into a froth recovery model as shown the size of the tank, because of some simplifications, such below: as assuming that Hf , hf and εg,f do not vary with r. b τf R R Rf = a exp − (29) 0 tf (r)dV (Hf + hf ) εg,f L τf = R = (31) R Jg 0 dV Rf = a exp (−b τfs) , Fundamentally based models that consider froth phys- where a and b are adjustment parameters and τf is the ics have also been developed and implemented in CFD froth residence time. But the authors observed that froth modelling frameworks. These models have been used to residence time increases in larger tanks, so they defined predict the performance of flotation froths (Neethling & τ the specific froth residence time as τfs = f/L, discarding Cilliers, 2003; Brito-Parada et al., 2012a; Brito-Parada & any other distance effect. Cilliers, 2013; Neethling & Brito-Parada, 2018). The tra- It has been noted by several authors and practition- jectory of flowing foams and froths is solved in 2D or 3D. ers that when increasing the distance that froth has to These trajectories are achieved using Laplace’s equation travel, the residence time increases. This increase in resid- for a scalar potential field. As a key boundary condi- ence time generates large scale stagnant zones of low froth tion, those models use the concept of air recovery (α), 670 transport and therefore low froth recovery, as shown in defined as the fraction of the air injected into the cell that Figure 8 (Zheng et al., 2004). Therefore, the optimal op- overflows through the lip as unburst bubbles (Moys, 1978, eration of increasingly large tanks relies on effective froth 1984; Ventura-Medina & Cilliers, 2002). This value is cal- transport and recovery (Gorain et al., 2007). culated as shown in Equation (32),

Qout ζ vf hw w vf hw w α = = ≈ (32) Qin JgA JgA

where ζ is the gas hold-up of the overflowing froth (usually assumed as 100%, equivalent to εg,f in Equation (30)), vw (m/s) is the overflowing velocity, hw (m) is the height of the overflowing froth over the lip (equivalent to hf in Equation (30)) and w (m) the lip length or perimeter. Air recovery takes into account lip length, which var-

680 ies with tank design, as well as operating variables like air inflow and froth height. It can be measured and predicted (Neethling & Cilliers, 2008). The importance of air recov- Figure 8: Schematic of froth transport model by Zheng et al. (2004). ery is that it is correlated with metallurgical performance Froth that is further away from the discharge lip tends to burst (Hadler & Cilliers, 2009; Hadler et al., 2010; Smith et al., without reporting to the concentrate, generating a stagnant zone far from the discharge launder. 2010). Therefore, this parameter should be considered in future froth scale-up models. Zheng et al. (2004) proposed a model to describe froth Further work on this topic is undoubtedly needed. New residence time related to the radius of the cell R (assuming mathematical models for froth zone phenomena need to a cylindrical tank). This model represents the residence be developed to provide a better understanding of froth time of an attached particle entering the froth at a distance690 transport in large flotation tanks. These new models need r from the centre of the tank as shown in Equation (30): to take into account changes in froth stability and bubble bursting rates. Such models could in turn be implemen- Hf εg,f 2 hf εg,f R ted in CFD simulators to inform the scale-up of flotation tf (r) = + ln , (30) tanks. Jg Jg r

where Hf is the froth depth (distance between the laun- 3.2.2. Internal elements scale-up der lip level and the pulp-froth interface), εg,f is the gas As discussed before, froth ﬂotation tanks have become hold-up of the froth zone and hf is the froth height (dis- increasingly large and scale-up heuristics based on pulp tance between the launder lip level and the top of the froth zone phenomena can be inadequate to predict the perform- layer). The ﬁrst term in Equation (30) does not depend ance of large equipment. In particular, the characteristics

on tank size but only on froth depth, representing the time700 and behaviour of the froth zone do not scale like those that takes to a particle to get to the top of the froth. The in the pulp. The increase in flotation tanks volume and second term increases when the particle enters the froth particularly the increase in the distance that the froth has closer to the centre of the tank, but is zero at the peri- to travel, has resulted in reduced flotation tank perform- meter. However, the mean froth residence time for this ance due to the limitations of froth stability and mobility, 11 Internal radial Perimetral Doughnut Perimetral as shown in Figure 8. These froth related problems have launder launder launder launder created the necessity of improvements in froth handling, which has been achieved by the introduction of crowders and more complex launder designs. Different tank designs have been proposed (e.g. Imhof

710 et al., 2005; Jameson, 2010; Dickinson & Galvin, 2014; Eriez, 2015; Glencore Technology, 2016) on the basis of process intensification, that could help avoiding the problems associated to large tanks. Replacing existing capacity, however, incurs large capital costs. Retrofit modifications, on the other hand, allow new designs to be implemented in existing operating equipment at lower costs, (a) (b) adding flexibility to the operation. Internal elements such Figure 9: Internal launders. (a) Radial launder, discharging into the as launders and crowders, are engineering solutions to the peripheral launder (b) Doughnut launder, with an internal system problem of froth scale-up. Although the use of these in- of discharge. In both figures the grey zone represents the top of the froth and the grey arrows represent the direction of froth flow. 720 ternal elements has increased in the last years, there is little published research on their design and scale-up process, at least on the public domain. It is interesting to is the case for launders, crowders also reduce the average point out that the design of these internal elements fol- distance travelled by the froth. low the logic of process intensification, since they enhance transport phenomena at low capital costs. A launder is a channel in which the froth is collected after overflowing (Brito-Parada & Cilliers, 2012). Stand- ard flotation cells that only include a launder along the periphery of the tank can face the problem of having a

730 stagnant froth zone at the centre (as shown in Figure 8). This stagnant froth zones occur because of the long distance that the froth has to travel to the lip of the cell. This transport can be avoided by increasing the number of launders. For instance, by using internal launders to collect froth in the middle of the tank and not only at its periphery (Yianatos et al., 2006; Brito-Parada & Cilliers, Figure 10: Cross-section and plan view of a crowder (From Yianatos et al. (2008a)). The cross-section (left) shows a truncated conical 2012). Adding launders to a cell increases its lip length crowder changing the froth flow, redirecting it towards the peripheral (w) and decreases the average distance travelled by the launder. The plan view (right) shows the position of the crowder at froth, which helps decreasing the froth residence time and the centre of the tank, and how radial launder could be attached to it. 740 increasing the froth recovery (Zheng et al., 2004). Two common launders configurations are radial and doughnut launders (see Figure 9), although more complex launder Crowders and launders can be used together, in config- designs are being introduced these days for large tanks. urations such as the one showed at Figure 10, with a cent- Radial launders are commonly used when the process re- ral crowder and radial or doughnut launders. Although quires increased lip length, such as applications with high both inserts are widely used in large industrial flotation mass recovery. In a central doughnut launder, froth flows tanks for improving froth transport and overall perform- into both sides of the launder. Doughnut launders can ance (Zheng et al., 2004; Yianatos et al., 2008a), there be used in addition or instead of the peripheral launder770 is, to date, little published experimental work on these (Coleman, 2009). two types of froth zone internal elements. Therefore, their design and scale-up processes have not been studied thor- 750 A crowder is an insert that occupies froth volume, as shown in Figure 10. The main function of a crowder is oughly. to improve froth removal dynamics by directing the froth An exception can be found in the work of Neethling towards the overflowing lip of the tank. This improvement & Cilliers (2003), who performed 2D simulations of dif- in froth mobility is done by decreasing the cross sectional ferent froth handling designs in cylindrical flotation cells. area at the top of the froth (Cole et al., 2012). The reduc- Three designs were assessed: a crowder, a crowder and tion in cross sectional area increases the local superficial doughnut launder, and two-crowders. The simulations, which agreed with industrial data, showed that a radi- gas velocity (Jg), improving aeration, froth velocity and mass pull. The most common type of crowder is a trun-780 ally outward movement of the froth was necessary to pro- cated, inverted cone inserted at the centre of the tank. mote drainage and thus reduce gangue entrainment. While recoveries obtained with the doughnut launder and two- 760 This shape directs the froth upwards and towards the launder, increasing froth velocity (Yianatos et al., 2008a). As crowders designs were similar, Neethling & Cilliers (2003) 12 concluded that the latter should be preferred when a single involved would help to overcome the limitations of current

overflow does not result in sufficiently high recoveries, since840 scale-up methodologies. this design provides more pulp-froth interface for drainage In machine design scale-up, more research comparing to occur. More recent studies of crowder design, albeit for and confronting different scale-up methodologies is needed a two-phase foam (Cole et al., 2012), showed good agree- to show their effectiveness in achieving similar metallur- ment between simulations and experiment data obtained gical performance. Current studies tend to use simple

790 for a quasi-2D cell. In all the 2D-crowders used by Cole stirred tanks or to use only water, which are not represent- et al. (2012), the air recovery increased in comparison to ative systems and therefore do not allow for a full under- the base case design. However, neither 3D simulations nor standing of the flotation phenomena involved. New studies rigorous 3D experimentation have been published on the need to be specifically designed for flotation tanks, using study of launders and crowders. This is another area of three phases systems and taking into consideration both

study that requires further research, given the role of in-850 the pulp and froth zone. In order to fill the gap between ternal elements in enhancing froth transport in large flot- scientific literature and in-house knowledge, further stud- ation tanks and their importance for the scale-up of the ies of the froth zone are required. These studies will be froth zone. useful for generating better models of froth transport and froth stability, which are key for large tanks where froth 4. Conclusions has to travel long distances to the overflowing lip. Moreover, both areas of study should converge to an

800 Flotation equipment has become substantially larger overall understanding of the scale-up process in ﬂotation. over the last few decades. The increase in tank volume This synergy could be achieved by developing comprehens- has brought new challenges in the performance, design ive fundamental models that can also be implemented in

and operation of large industrial flotation tanks. Most of860 CFD simulators. The use of such models would allow the these challenges are related to problems around pulp hy- estimation of flotation performance in equipment of differ- drodynamics and froth transport, such as stagnant zones, ent scales and aid the design process. low froth mobility and froth recovery. In order to tackle Alternatives to tackle some of the problems associated these issues, a better understanding of flotation scale-up with large scale flotation tanks are discussed in this review. is needed. One possibility would be to simply use smaller and more This review has analysed for the first time the literat- efficient equipment, which is known as process intensific-

810 ure on flotation tank scale up. As a result, this review has ation. However, the main problem is that implementing classified the flotation scale-up studies into two categories, any new equipment in an ongoing operation would carry “kinetic” and “machine design” scale-up, given the differ- important capital costs, as well as the uncertainty and risk

ent approaches, assumptions and techniques involved. The870 associated to new technologies. main difference between these two sub-areas is that kinetic An engineering solution, the implementation of internal scale-up has not considered tank design or size, but only elements, has become the most commonly used approach takes into account operational considerations such as the to tackle the problems associated with froth mobility in mean residence time. Machine design scale-up studies the large tanks. Internal elements such as launders and crowders impact of equipment design, shape and size on the per- are cost-effective inserts that improve froth recovery and formance, focusing mainly on the hydrodynamic effects of facilitate froth transport in large flotation tanks. Although

820 those variables. After reviewing the literature published, internal elements have emerged as the most promising solu- it is clear that further research is needed to advance ﬂot- tion for froth transport problems, their design and scale-up ation scale-up. The lines of study that are critical for a has not been thoroughly studied. There is therefore an im-

better understanding of the flotation phenomena in large880 portant opportunity in the study of these inserts to reach tanks have been highlighted. Exploring these avenues of improvement in overall metallurgical performance through research will certainly impact the design and performance enhanced design and implementation. of newer and larger tanks. In kinetic scale-up, it is necessary to include machine Acknowledgements hydrodynamics in the models. Further application of CFD techniques to model the collection zone, taking into con- D. Mesa would like to acknowledge the Chilean Na- 830 sideration three phases and 3D flotation systems, is key tional Commission of Science and Technology (CONICYT) to improve the predicting capabilities of current models. for funding this research with a scholarship from “Becas While it is important to recognise that kinetic models have Chile”. certainly been useful in the study and improvement of flotation performance over the last century, because of their intrinsic oversimplifications they are unfit for the further References understanding and comprehensive modelling of the flota- Abrahamson, J. (1975). Collision rates of small particles in a vigor- tion process. A more fundamental approach that takes890 ously turbulent fluid. Chemical Engineering Science, 30 , 1371– into account the physical interactions between the phases 1379. doi:10.1016/0009-2509(75)85067-6. 13 Albijanic, B., Ozdemir, O., Nguyen, A., & Bradshaw, D. (2010). A puter Aided Process Engineering (pp. 1143–1147). 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