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FLOTATION KINETICSA flotation model is similar to chemical kinetics

dN/dt =-k1 N1a- k2 N2b

N - species (1 and 2) concentration t- time k - rate constant(s)a, b process order-negative sign indicates that the concentration is diminishing due to the loss of particles being floated. -exponents a and b signify the order of the process

Since flotation seems to depend only on particles concentration

dN/dt =-k1 N1a

ModelRelationClassic first order = [1 exp (k1t)]Modified first order = {1 1/(k2t)[1 exp (k2t)]}For reactor with ideal mixing = [1 1/(1 + t/k3)]*Modified for gassolid adsorption = k4t/(1 + k4t)* Kinetics of second order = ()2 k5t/(1 + k5t)Modified second order = {1 [ln (1 + k6t)]/(k6t)}Two rate constants = [1 { exp (k7t) + (1 ) exp(k8t)}Distributed rate constants = [1 exp(kt) f (k, 0) dk]

* Equivalent models because k3 = 1/k4. flotation recovery after time t, maximum recovery, fraction of particles having lower flotation rate constant, k7, k flotation rate constant.Flotation kinetics models

A. Bakalarz, J. Drzymala, 2013, Interrelation of the Fuerstenau upgrading curve parameters with kinetics of separation, Physicochemical Problem of Mineral Processing, 49(2), 443-451more

Flotation kinetics of the whole mass and components components (recovery vs time)

Flotation results plotted as a relationship between recovery of each component in concentrate and separation time (a), yield of components forming concentrate vs. separation time (b)product (yield vs time)A. Bakalarz, J. Drzymala, 2013, Interrelation of the Fuerstenau upgrading curve parameters with kinetics of separation, Physicochemical Problem of Mineral Processing, 49(2), 443-451

relation between flotation kinetics and upgrading curves The kinetics of separation of feed components (a) provide separation results in the form of the Fuerstenau upgrading curve (b).A. Bakalarz, J. Drzymala, 2013, Interrelation of the Fuerstenau upgrading curve parameters with kinetics of separation, Physicochemical Problem of Mineral Processing, 49(2), 443-451

ugrading curves (here Fuerstenaus) equations based on kinetics of flotation c,1 recovery of component 1 in concentrate c,2 recovery of component 2 in concentrate 4 9 7 13

Theoretical shape of the separation data in the Fuerstenau plot

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13*for a suitable equation see previous slide (more plots in A. Bakalarz, J. Drzymala, 2013, Interrelation of the Fuerstenau upgrading curve parameters with kinetics of separation, Physicochemical Problem of Mineral Processing, 49(2), 443-451*Remeber: for characterizing separation results we need either two parameter or a law governing separation and then you can use one parameter which can be called selectivity as in these plots selectivity k An example of separation results approximation using the Fuerstenau plot

Polish copper ore lab tests with xanthate

a=~1000a=100a=~110HomeworkCalculate the rate constant and order of a set of yield flotation data FLOTATION DEVICESMicrolaboratory cellsLaboratory cells Laboratory machines Industrial machinesMechanical Pneumo-mechanical PneumaticPressurized (DAF)Other (sparged hydrocyclone, ASH)10

Other laboratory flotation devicescylindrical cell equipped with magnetic stirrer (Fuerstenau, 1964)laboratory flotation device of Partridge and Smith, 1971Laboratory cells

Laboratory Mechanobr flotation machine

Laboratory Denver flotation machine

EIMCO Product Leaflets, 2000Industrial flotation Flotation machines are used individually and as a group (bank)

Svedala Product Handbook, 1996Flotation machines are rectangular and circular Constructions and impellers of flotation machines are different

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Comparison of pneumo-mechanical (FLSmidth Minerals) and mechnical flotation machines (WEMCO) )XCELL Flotation Machines. FLSmidth Mineralss brochure 2008. pneumo-mechanical mechanical Mechanical (self air aspiration)Pneumo-mechanical (air is forced and mechanically dispersed Pneumatic (air is forced)Injection ( air and slurry go together) Pressurized (dissolved air flotation DAF)Other (air sparged hydrocyclone, ASH)

injection pressurized 20FLOTATION MACHINESMECHANICALDenverMechanobrFagergreen (WEMCO-EIMCO)21DENVER

Wemco-Fagergreen (V=0.085 85m3)Kelly E.G., Spottiswood D.J., Introduction to mineral processing. J.Wiley& Sons, N.Jork 1985

23 Wemco-Fagergreen (WEMCO-EIMCO) mechanical flotation machines EIMCO Product Leaflets, 2000

24FLOTATION MACHINES PNEUMO-MECHANICAL Denver Agitair Metso RCS (Metso Minerals) Outotec (Outokumpu) X-Cell (FLSmidth Minerals) Humbolt-Wedag IMN Gliwice

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Kelly E.G., Spottiswood D.J., Introduction to mineral processing. J.Wiley& Sons, N.Jork 1985Industrial flotation machine (mechano-pneumatic, Agitair)Pressurized airfroth productrotorrotors shaft 26

Maszyna flotacyjna mechaniczno-pneumatyczna AS (Svedala/Metso Minerals), V=0,21 16 m3Svedala Product Handbook, 199627Wills B.A., Mineral processing technology. Pergamon Press 1983Fragment of mechano-pneumatic flotation machine (continueous, multi-impeller tankless Denver D-R

28Pneumo-mechanic multi-tank (15m3 each) (Aker FM Humbold Wedag)

Humbold-Wedag Product Leaflets, 1998feedtailing29

Maszyna jednowirnikowaMaszyna przepywowa wielowirnikowa

Pneumo-mechanical flotation machines IMN30New machines: large volume and output, saving energy Flotation technologies. Outotec Leaflets 2007

Historyczny rozwj pojemnoci maszyn flotacyjnych

Outokumpu Oy Leaflets 2000(Outokumpu OK-100, V= 100m3

TankCell 300 300m3Flotation technologies, Outotec Oyj. Leaflets 2007 32

2012 Outotec Oyj. www.outotec.comOutotec TankCell 500 (500m3)RCS (Reactor Cell System) from 5 to 200 m3 (Metso Minerals/Svedala)1-radial flow of slurry to tank wall2-primary slurry stream to benith impeller3-secondary recirculation towards upper part of tank Basics in mineral processing. Metso Minerals 2003

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RCS (Reactor Cell System) from 5 to 200 m3 (Metso Minerals)Basics in mineral processing. Metso Minerals 200335

RCS (Reactor Cell System) from 260 m3 (Metso Minerals)36pneumo-machanic XCELL (FLSmidth Minerals)

XCELL Flotation Machines. FLSmidth Mineralss brochure 2008. 37PNEUMATIC FLOTATION MACHINESFLOTATION COLUMNS Metso Outotec (Outokumpu)

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INJECTION FLOTATION MACHINES Jameson Cell Imhoflot Pneuflot (Humbolt-Wedag)

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Injection Jameson Cell41

Pneumatic PNEUFLOTPneumatic flotation with PNEUFLOT cells HUMBOLDT WEDAG leaflet 2009

43Pneumatic flotation with PNEUFLOT cells HUMBOLDT WEDAG leaflet 2009

pneumatic PNEUFLOT44Injection Imhoflot 2

Distributor of air and suspennion Pneumatic cell Imhoflot. Maelgwyn Mineral Service leaflet 4/06 Chile 2006feedairflotation froth middlings to recirculation concentrateproduct tailing 45

Pneumatic cell Imhoflot. Maelgwyn Mineral Service leaflet 4/06 Chile 2006Multi-injection Imhoflot 3 (centrifugal flotation)concentrate tailing feed pumptailing pumpfeed reagentscompressed airfeed air plus suspension47Siemens SIMINE Hybrid Flot

Metals and Mining, Siemens VAI, No. 1, 2011Injection column

PRESSURIZED FLOTATION MACHINES

Dissolved air flotation (DAF)49Dissolved air flotation (DAF)

50Pressurized flotation (separation of coal from sulfides)

Rodrigues & Rubio, International Journal Of Mineral Processing. V. 82, P. 1-13, 2007.FGR - Flocs Generator Reactor

Flotation, ZWR Polkowice

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