08 flotation machines

7/21/2019 08 Flotation Machines

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FLOTATION KINETICS

A flotation model is similar to chemical kinetics

dN/dt =-k1 N1a- k2N2

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 andb signify the order of the process

Since flotation seems to depend only on particles concentration

dN/dt =-k1 N1a


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Model 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 gassolid adsorption

=k4t/(1 + k4t)*

Kinetics of second order= (

)2k5t/(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]

0

* 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


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Selected kinetic equations (recovery of a component in separation product, maxmaximum recovery of the

same component in separation product, krate constant of separation, tseparation time

Model Formula

Zeroth-order model tk (1)

First-order model tke 1max (2)First-order with rectangular distribution of

floatabilities

tke

tk 1

11

max (3)

Fully mixed reactor model

k

t

1

11max

(4)

Improved gas/solid adsorption model

tk

tk

1max

(5)

2

3 -order model

2

max

max

2

11

11

tk

(6)

Second-order modeltk

tk

max

2

max

1 (7)

Second-order model with rectangular offloatabilites

tktk

1ln1

1max

(8)

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

more


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0

20

40

60

80

100

0 10 20 30

recoveryofacomponentin

conc

entrate,,

%

separation time, min

remaining components

component 1

Flotation kinetics of the whole mass and components

components (recovery vs time)

0

10

20

30

40

0 10 20 30

yieldofconcentrate,,

%


sum of kinetics of

component 1 and

remaining components

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


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0

20

40

60

80

100

0 10 20 30

recoveryofcomponent1in

concentrate,

1,c,

%


component 1

0

20

40

60

80

100

0 20 40 60 80 100

recoveryofcomponent1in

con

centrate,1,c,

%

recovery of component 2 in concentrate,

2,c, %

ideal upgrading

idealupgrading

Fuerstenau curve

0

20

40

60

80

100

0 10 20 30

re

coveryofcomponent2in

concentrate,2,c,

%


component 2

a b

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, PhysicochemicalProblem of Mineral Processing, 49(2), 443-451


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c,1

c,2

0 12

3 2

0,c

k,c

21

100

2ln

1,c

k',c

2)

251(

111001

,ck

,c

)2100(100

21

,c

,ck'

,c

1

100

2ln1

,c

k,c

k

,c

,c

100

210011001

2

100

2100ln51

11100

1

,c

k

,c

1

100

2100

ln100

100

2100

ln2

100

1

,c

k

,c

k

,c

2

3

2)251(

111001

,ck'

,c

2

100

2100

ln51

11100

1

,c

k'

,c

2

2100

)2

10010(1

11100

1

,c

,ck

,c

2

)2

100(20

21

111001

,c

,ck'

,c

2)2100(100

21

,c

,ck

,c

1100

2100

ln100

100

2100

ln2

100

1

,c

k'

,c

k'

,c

2

)2

100(20

21

11100

1

,c

,ck

,c

100)1(2

2100

1

k,c

,ck

,c

ugrading curves (here Fuerstenaus) equations based on kinetics of flotation

c,1recovery of component 1 in concentrate c,2recovery of component 2 in concentrate

4

9

7

13


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0

20

40

60

80

100

0 20 40 60 80 100

recoveryofcomponen

t1inconcentrate,1,c,

%

recovery of component 2 in concentrate, 2,c, %

k=1.5

k=3

k=0.5

k=1

0

20

40

60

80

100

0 20 40 60 80 100

recoveryofcomponent1

inconcentrate,1,c,

%


k=5

k=2

k=0.4

k=1

Theoretical shape of the separation data in the Fuerstenau plot

0

20

40

60

80

100

0 20 40 60 80 100

recoveryofcompo

nent1inconcentrate,1,c,

%


k=0.005

k=0.5

k=0.02

k=1

4 97

0

20

40

60

80

100

0 20 40 60 80 100

recoveryofcomp

onent1inconcentrate,1,c,

%


k=3

k=0.5

k=0.2

k=1

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


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An example of separation results approximation using the Fuerstenau plot

plant 3, trial 1

a=102.28

0 20 40 60 80 100

r

0

20

40

60

80

100

= a(100-

r)/(a-

r)

Polish copper orelab tests with xanthate

0 20 40 60 80 100

component 2 in product 2,%

0

20

40

60

80

100

(component1

inproduct1)%

ideal upgrading

F= (89/89)

no upgrading

a=100


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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

Mechanical

Pneumo-mechanical

PneumaticPressurized (DAF)

Other (sparged hydrocyclone, ASH)


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gas

magnetic stirrer

porous glass

water level

froth

product

x

gas

deflector

stirrer

flotaton pr

water level

porous glass

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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air

drive

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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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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Denver

AgitairMetso RCS (Metso Minerals)

Outotec (Outokumpu)

X-Cell (FLSmidth Minerals)

Humbolt-WedagIMN Gliwice


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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 (15m3 each)

(Aker FMHumbold Wedag)

Humbold-Wedag Product Leaflets, 1998

tailing


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Maszyna

jednowirnikowa

Maszyna przepywowa

wielowirnikowa

Pneumo-mechanical flotation machines IMN

New machines: large volume and output saving energy


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New machines: large volume and output, saving energy

Flotation technologies. Outotec Leaflets 2007

Historyczny rozwj pojemnoci maszyn flotacyjnych

(Outokumpu OK 100 V= 100m3


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Outokumpu Oy Leaflets 2000

(Outokumpu OK-100, V= 100m3

TankCell300300m3

Flotation technologies, Outotec Oyj. Leaflets 2007

Outotec TankCell 500 (500m3)


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2012 Outotec Oyj. www.outotec.com

Outotec TankCell 500 (500m )


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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 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 2003


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


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pneumo-machanic

XCELL (FLSmidth Minerals)

XCELLFlotation Machines. FLSmidth Mineralss brochure 2008.


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FLOTATION COLUMNS

MetsoOutotec (Outokumpu)


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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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Multi-injection Imhoflot 3 (centrifugal flotation)


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Pneumatic cell Imhoflot. Maelgwyn Mineral Service leaflet 4/06 Chile 2006

u jec o o o 3 (ce ug o o )

concentrate

tailing

feed pump tailing pump

feed reagents

compressed

air

feed

air plus

suspension

Injection column


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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)

Di l d i fl t ti (DAF)


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Dissolved air flotation (DAF)


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Flotation ZWR Polkowice


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Flotation, ZWR Polkowice

08 flotation machines

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