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**FLOTATION KINETICS A 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

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**Flotation kinetics models**

Relation Classic 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 gas–solid 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.

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more 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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**product (yield vs time)**

Flotation kinetics of the whole mass and components product (yield vs time) 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) 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 Fuerstenau’s) equations based on kinetics of flotation**

4 7 9 13 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**

4 * 7 9 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 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),

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**Polish copper ore – lab tests with xanthate**

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

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

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**FLOTATION DEVICES Microlaboratory cells Laboratory cells**

Laboratory machines Industrial machines Mechanical Pneumo-mechanical Pneumatic Pressurized (DAF) Other (sparged hydrocyclone, ASH)

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**Laboratory cells Other laboratory flotation devices**

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

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**Laboratory Mechanobr flotation machine**

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**Laboratory Denver flotation machine**

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Industrial flotation EIMCO Product Leaflets, 2000

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

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**Flotation machines are rectangular and circular**

Svedala Product Handbook, 1996

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**Constructions and impellers of flotation machines are different**

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**pressurized mechanical injection pneumo-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) pressurized mechanical injection pneumo-mechanical XCELL™ Flotation Machines. FLSmidth Mineralss brochure 2008. Comparison of pneumo-mechanical (FLSmidth Minerals) and mechnical flotation machines (WEMCO) )

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**FLOTATION MACHINES MECHANICAL**

Denver Mechanobr Fagergreen (WEMCO-EIMCO)

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DENVER

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**Wemco-Fagergreen (V=0.085 ÷ 85m3)**

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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**FLOTATION MACHINES PNEUMO-MECHANICAL**

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

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**Industrial flotation machine (mechano-pneumatic, Agitair)**

Pressurized air froth product rotor’s shaft rotor Kelly E.G., Spottiswood D.J., Introduction to mineral processing. J.Wiley& Sons, N.Jork 1985

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**Maszyna flotacyjna mechaniczno-pneumatyczna AS (Svedala/Metso Minerals), V=0,21 ÷ 16 m3**

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 Wills B.A., Mineral processing technology. Pergamon Press 1983

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

feed tailing Humbold-Wedag Product Leaflets, 1998

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**Maszyna przepływowa wielowirnikowa Maszyna jednowirnikowa**

Pneumo-mechanical flotation machines IMN Maszyna przepływowa wielowirnikowa Maszyna jednowirnikowa

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**New machines: large volume and output, saving energy**

Historyczny rozwój pojemności maszyn flotacyjnych Flotation technologies. Outotec Leaflets 2007

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**(Outokumpu OK-100, V= 100m3 TankCell 300 300m3**

Outokumpu Oy Leaflets 2000 Flotation technologies, Outotec Oyj. Leaflets 2007

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Outotec TankCell 500 (500m3) © 2012 Outotec Oyj.

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**RCS™ (Reactor Cell System) from 5 to 200 m3 (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 m3 (Metso Minerals)**

Basics in mineral processing. Metso Minerals 2003

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**RCS™ (Reactor Cell System) from 260 m3 (Metso Minerals)**

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**XCELL (FLSmidth Minerals)**

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

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**PNEUMATIC FLOTATION MACHINES**

FLOTATION COLUMNS Metso Outotec (Outokumpu)

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**INJECTION FLOTATION MACHINES**

Jameson Cell Imhoflot 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 Pneumatic flotation with PNEUFLOT® cells HUMBOLDT WEDAG leaflet 2009

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**Injection Imhoflot 2 Distributor of air and suspennion feed air**

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

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**Multi-injection Imhoflot 3 (centrifugal flotation)**

feed compressed air air plus suspension feed reagents concentrate tailing feed pump tailing pump Pneumatic cell Imhoflot. Maelgwyn Mineral Service leaflet 4/06 Chile 2006

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**Injection column Siemens SIMINE Hybrid Flot**

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

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**PRESSURIZED FLOTATION MACHINES Dissolved air flotation (DAF)**

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**Dissolved air flotation (DAF)**

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**Pressurized flotation (separation of coal from sulfides)**

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

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**Flotation, ZWR Polkowice**

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