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FLOTATION KINETICS A flotation model is similar to chemical kinetics dN/dt =-k 1 N 1 a - k 2 N 2 b 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 =-k 1 N 1 a

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ModelRelation Classic first order = [1 – exp (–k 1 t)] Modified first order = {1 – 1/(k 2 t)[1 – exp (–k 2 t)]} For reactor with ideal mixing = [1 – 1/(1 + t/k 3 )]* Modified for gas–solid adsorption = k 4 t/(1 + k 4 t)* Kinetics of second order = ( ) 2 k 5 t/(1 + k 5 t) Modified second order = {1 – [ln (1 + k 6 t)]/(k 6 t)} Two rate constants = [1– { exp (–k 7 t) + (1 – ) exp(–k 8 t)} Distributed rate constants = [1 – exp(–kt) f (k, 0) dk] * Equivalent models because k 3 = 1/k 4. – flotation recovery after time t, – maximum recovery, – fraction of particles having lower flotation rate constant, k7, k – flotation rate constant. Flotation kinetics models

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

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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),

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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),

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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

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Theoretical shape of the separation data in the Fuerstenau plot *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), * 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

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An example of separation results approximation using the Fuerstenau plot Polish copper ore – lab tests with xanthate a=~1000 a=100 a=~110

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Homework Calculate the rate constant and order of a set of yield flotation data

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Microlaboratory cells Laboratory cells Laboratory machines Industrial machines MechanicalPneumo-mechanicalPneumatic Pressurized (DAF) Other (sparged hydrocyclone, ASH)

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

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Laboratory Mechanobr flotation machine

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Laboratory Denver flotation machine

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EIMCO Product Leaflets, 2000 Industrial flotation

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Flotation machines are used individually and as a group (bank)

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Svedala Product Handbook, 1996 Flotation machines are rectangular and circular

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Constructions and impellers of flotation machines are different

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(FLSmidth Minerals) and ) Comparison of pneumo-mechanical (FLSmidth Minerals) and mechnical flotation machines (WEMCO) ) XCELL Flotation Machines. FLSmidth Mineralss brochure 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

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DenverMechanobr Fagergreen (WEMCO-EIMCO)

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DENVER

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Wemco-Fagergreen (V=0.085 ÷ 85m 3 ) Kelly E.G., Spottiswood D.J., Introduction to mineral processing. J.Wiley& Sons, N.Jork 1985

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

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Denver Denver Agitair Agitair Metso RCS (Metso Minerals) Metso RCS (Metso Minerals) Outotec (Outokumpu) Outotec (Outokumpu) X-Cell (FLSmidth Minerals) X-Cell (FLSmidth Minerals) Humbolt-Wedag Humbolt-Wedag IMN Gliwice IMN Gliwice

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Kelly E.G., Spottiswood D.J., Introduction to mineral processing. J.Wiley& Sons, N.Jork 1985 Industrial flotation machine (mechano-pneumatic, Agitair) Pressurized air froth product rotor rotors shaft

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Maszyna flotacyjna mechaniczno-pneumatyczna AS (Svedala/Metso Minerals), V=0,21 ÷ 16 m 3 Svedala Product Handbook, 1996

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Wills B.A., Mineral processing technology. Pergamon Press 1983 Fragment of mechano-pneumatic flotation machine (continueous, multi-impeller tankless Denver D-R

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Pneumo-mechanic multi-tank (15m 3 each) (Aker FM – Humbold Wedag) Humbold-Wedag Product Leaflets, 1998 feed tailing

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Maszyna jednowirnikowa Maszyna przepływowa wielowirnikowa Pneumo-mechanical flotation machines IMN

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New machines: large volume and output, saving energy Flotation technologies. Outotec Leaflets 2007 Historyczny rozwój pojemności maszyn flotacyjnych

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Outokumpu Oy Leaflets 2000 (Outokumpu OK-100, V= 100m 3 TankCell m 3 Flotation technologies, Outotec Oyj. Leaflets 2007

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© 2012 Outotec Oyj. Outotec TankCell 500 (500m 3 )

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RCS (Reactor Cell System) from 5 to 200 m 3 (Metso Minerals/Svedala) 1 -radial flow of slurry to tank wall 2 -primary slurry stream to benith impeller 3 -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 m 3 (Metso Minerals) Basics in mineral processing. Metso Minerals 2003

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RCS (Reactor Cell System) from 260 m 3 (Metso Minerals)

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pneumo-machanic XCELL (FLSmidth Minerals) XCELL Flotation Machines. FLSmidth Mineralss brochure 2008.

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FLOTATION COLUMNS Metso Metso Outotec (Outokumpu) Outotec (Outokumpu)

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Jameson Cell Jameson Cell Imhoflot Imhoflot Pneuflot (Humbolt-Wedag) Pneuflot (Humbolt-Wedag)

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Injection Jameson Cell

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Pneumatic PNEUFLOT Pneumatic flotation with PNEUFLOT® cells HUMBOLDT WEDAG leaflet 2009

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pneumatic PNEUFLOT

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Injection Imhoflot 2 Distributor of air and suspennion Pneumatic cell Imhoflot. Maelgwyn Mineral Service leaflet 4/06 Chile 2006 feed air flotation froth middlings to recirculation concentrate product tailing

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Pneumatic cell Imhoflot. Maelgwyn Mineral Service leaflet 4/06 Chile 2006 Multi-injection Imhoflot 3 (centrifugal flotation) concentrate tailing feed pump tailing pump feedreagents compressed air feed air plus suspension

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

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Dissolved air flotation (DAF)

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Pressurized flotation (separation of coal from sulfides) Rodrigues & Rubio, International Journal Of Mineral Processing. V. 82, P. 1-13, FGR - Flocs Generator Reactor

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Flotation, ZWR Polkowice

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