# FLOTATION KINETICS A flotation model is similar to chemical kinetics

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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

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.

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

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),

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),

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

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),

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

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

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

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

Laboratory Mechanobr flotation machine

Laboratory Denver flotation machine

Industrial flotation EIMCO Product Leaflets, 2000

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

Flotation machines are rectangular and circular
Svedala Product Handbook, 1996

Constructions and impellers of flotation machines are different

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) )

FLOTATION MACHINES MECHANICAL
Denver Mechanobr Fagergreen (WEMCO-EIMCO)

DENVER

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

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

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

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

Maszyna flotacyjna mechaniczno-pneumatyczna AS (Svedala/Metso Minerals), V=0,21 ÷ 16 m3
Svedala Product Handbook, 1996

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

Pneumo-mechanic multi-tank (15m3 each) (Aker FM – Humbold Wedag)
feed tailing Humbold-Wedag Product Leaflets, 1998

Maszyna przepływowa wielowirnikowa Maszyna jednowirnikowa
Pneumo-mechanical flotation machines IMN Maszyna przepływowa wielowirnikowa Maszyna jednowirnikowa

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

(Outokumpu OK-100, V= 100m3 TankCell 300 300m3
Outokumpu Oy Leaflets 2000 Flotation technologies, Outotec Oyj. Leaflets 2007

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

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

RCS™ (Reactor Cell System) from 5 to 200 m3 (Metso Minerals)
Basics in mineral processing. Metso Minerals 2003

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

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

PNEUMATIC FLOTATION MACHINES
FLOTATION COLUMNS Metso Outotec (Outokumpu)

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

Injection Jameson Cell

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

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

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

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

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

PRESSURIZED FLOTATION MACHINES Dissolved air flotation (DAF)

Dissolved air flotation (DAF)

Pressurized flotation (separation of coal from sulfides)
FGR - Flocs Generator Reactor Rodrigues & Rubio, International Journal Of Mineral Processing. V. 82, P. 1-13, 2007.

Flotation, ZWR Polkowice

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