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), 443-451
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), 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 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), 443-451
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. www.outotec.com
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