Download Flotation Kinetics

Flotation Kinetics &
Flotation Circuit Design
DMR Sekhar
Contents
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Introduction
Bubble Particle Attachment
Order of Rate of Flotation
Flotation Kinetic Data: Sargepalli Copper Lead Ore
Flotation kinetic Data : Jhamarkotra Phosphate Ore
Flotation Circuits
Conceptual Flotation Circuit & Material Balance
Rougher/Scavenger: Flotation Times & Scale Up
Summary
References
Introduction
• Flotation kinetics is the study of mineral recovery as a function of
time.
• The results of kinetic studies are useful in optimising primary grind of
ores, comparing the performance of flotation reagents and designing
of flotation circuits.
Bubble Particle Attachment
• (1) Initially air bubbles are fully loaded with
floatable particles as the total of area of
bubble surfaces is less than the area required
for floatable particles. This condition is
described as inhibited/explosive/loaded
flotation.
(2) After some time air bubbles are sparsely
loaded as the total of area of bubble surfaces is
more than what is required by the floatable
particles at a particular time. This condition is
described as free flotation.
(3)Transitional flotation is where all the
conditions of (1) and (2) may exist.
v
v
v
v
v
v
Order of Rate of Flotation
• Where N is the number of bubbles per unit volume at any time t, n is
the number of particles per unit volume of pulp floated in time t and
n0 is the number of particles when t = 0, according to Tomlinson and
Fleming,
Condition 1) All the bubbles raising through the pulp are fully loaded
such that dn/dt is dependent on the rate of aeration only and if this is
constant,
dn/dt = kN = k0 which represents zero order law. Thus under
inhibited/loaded conditions flotation process obeys zero order.
(continued)
Order of Rate of Flotation
(continued from previous slide)
(2) The relationship between N and (n0 - n) where floatable particles are
sparsely attached to the air bubbles and at no time there is deficiency of air
bubbles for a single species of particle at constant bubble rate,
dn/dt = k1 (n0 – n) which on integration takes the form,
log 1/(1-r) = k1t where r the recovery = n/n0 , which is a form of 1st order
rate law.
• Under practical conditions the flotation process initially is loaded/explosive
flotation followed by free flotation and depending on the persistence of
loaded or free flotation the net effect may appear as zero, first or any other
order by chance.
Cumulative Pb recovery
Kinetic Data of Pb flotation, Sargepalli copper/lead Ore
100.00
80.00
60.00
40.00
20.00
0.00
0.000
1.000
2.000
3.000
4.000
(1/t), t = Cumulative time
Normal Xanthate Floatation Of Lead : Sargepalli Copper Lead Ore
r = R - R/(kt), where r is recovery of mineral at time t, R is ultimate overall recovery at infinite time and k is the rate
constant. This is a version of Klimpel’s model as modified by Prof. TC Rao that shows flotation as “apparently first
order rate process”.
7.8
14.9
4.5
2.47
90
35.6
Cumulative recovery of Pb
80
70
41.7
% Pb in concentrates, incremental
% Pb in feed 6.7
60
50
40 66
30
20
Loaded
floatation
10
Free floatation
0
0
1
3
5
6
4
7
t (cumulative time)
Sargepalli copper-lead ore: xanthate floatation of lead (galena)
2
8
9
Kinetic Data of Dolomite Floatation: Jhamarkotra phosphate ore
90
R² = 0.9916
Cumulative recovery of MgO
80
70
60
50
40
30
20
10
0
0
1
2
3
4
5
Cumulative time (t)
6
7
8
9
Cumulative recovery of MgO
90
80
9.2
MgO in the feed= 12.5%
Incremental grade of MgO for each float
70
12.10
60
50
14.5
40
30
15.30
R² = 0.9893
20
Free
floatation
10
16.1
Loaded floatation
0
0
0.1
0.2
0.3
0.4
1/t
(t = cumulative time)
0.5
0.6
0.7
Flotation Circuits
• Any process run in stages is efficient and this applies to the
flotation circuits as well. Thus flotation circuits have rougher,
scavenger and cleaner stages.
• Scavenger stage is necessary to recover slow floating fine sized
minerals and interlocked mineral particles.
• Rougher concentrate will invariably have gangue minerals
“mechanically entrapped” between bubbles and water in the froth will
also carry gangue minerals into the froth. And hence the need to clean
the rougher concentrate.
• The recirculating streams, scavenger concentrate and cleaner tail,
should have higher grade of the mineral being recovered than the
receiving stream say feed to rougher. That is the streams being mixed
should have “quality resemblance”.
Conceptual Flotation Circuit & Material Balance
Final tail
T, t
Cleaner
Bank
Cleaner tail
Cleaner
Concentrate
C, c
F, f
Scavenger
Bank
Rougher
Bank
Rougher
concentrate
Feed
C+T=F
Fxf=Cxc+Txt
% Recovery = [(f-t) x c / (c-t) x f ] x 100
Weight % Recovery = C/F x 100 = [(f-t)/(c-t) ] x 100
F = weight of feed, C = Weight of concentrate,
F = mineral content in the feed, c = mineral content in the
concentrate, t = mineral content in the tails.
Special Cases
• The conceptual flow sheet is what is generally followed. There may be special cases that
warrant deviation.
• Take for example galena flotation from a feed analysing 6.7% Pb. As per the “quality
resemblance rule” scavenger concentrate analysing anything below 6.7% Pb is to be
discarded. What if the scavenger concentrate has 4.5% Pb due to liberated fine sized
galena particles? Should we lose them? This situation warrants a second scavenger bank
and the concentrate of the second scavenger may be recirculated to rougher tails that is
feed to first scavenger.
• Some Lead/Zinc ores have graphite which is highly floatable. The current practice is to
depress graphite while floating galena. However substantial quantity of graphite reports
to lead concentrate spoiling the grade and some of it comes back to rougher feed! That is
unwanted recirculation of graphite. The possible remedy is to remove graphite at the
first instance before galena flotation (“pre floatation” of graphite) so that the highly
floatable graphite is removed once and for all, giving a very short floatation time or
provide a “cleaner scavenger” to collect galena from cleaner tails to send it back to
cleaner and discard cleaner scavenger tails.
Rougher/ Scavenger Flotation Times & Scale Up
N = Vm t/ Vk k
N= number of cells
Vm = feed flow rate, m3 / minute
Vk = volume of one cell
K = cell constant (for effective volume which is 0.7 to 0.75), that takes care of air holdup and dead
zones in the cell which depends on a particular type of cell design.
t = floatation time which needs to be multiplied by a scale up factor from 1.6 to
2.6 , if t is taken from open cycle bench scale studies. Choosing a scale up factor depends on
the recirculating loads from scavenger concentrate and 1st cleaner tail and number of cleaning
stages. If t is taken from pilot plant studies or from similar industrial plant, scale up factor is 1.
Notes
(1) Rougher floatation time in the plant should cover till the loaded
floatation exhausts. Rougher flotation may be in stages the first stage
targeting good grade of concentrate and medium recovery and the
second stage to maximise recovery.
(2) Total volume of scavenger cells should be equal or may exceed the
total volume of rougher cells in special cases.
(3) Total cleaner cells retention time is 75% of the total retention time
of the rougher cells.
(4) On important factor that is often ignored is that the capacity of a
cell or a bank of cells is dependant not only on the volume of the cell
but also the air flow rate into the cell.
Summary
• Initially air bubbles in the flotation pulp are fully loaded (Loaded Flotation,
LF) and reach the froth bed in the cell followed by sparsely loaded (Free
Flotation, FF) air bubbles reaching the froth bed.
• Depending on the persistence of LF or FF as time lapses, Flotation may
appear following Zero, First or any other order by chance.
• For rougher flotation bank, sufficient residence time is to be provided to
collect all the fully loaded bubbles.
• For scavenger flotation bank, residence time be provided to accommodate
free flotation, till scavenger concentrate grade falls to “not less than the
grade of feed to rougher flotation” to ensure “quality resemblance”.
• It should be loaded flotation in the cleaner cells.
References
• Tomlinson,HS and Fleming, MG, “Flotation Rate Studies”, Mineral Processing Proceedings
of the sixth International Congress, Cannes, May 26th to 2nd June, 1963.
• Rao TC et al, “Effect of Mesh of Grind on Flotation of Rakha Ore”, IE(I) Journal,MM,Vol.64, July 1983.
• Glembotskii, V.A., Klassen, V.I., Plaksin,I.N., Flotation, Primary Sources, New York, 1972.
• Sekhar DMR and Rama Shankar, Flotation Kinetics: an overview, Process and Plant
Engineering, VOL. XIX. NO 5, Annual, 2001.
https://www.researchgate.net/publication/235943994_Flotation_Kinetics
• Sekhar, DMR, Scale up and design of flotation circuits, Plant and Process Engineering , Vol
XIX, NO 3, 2001. http://www.researchgate.net/publication/235944468
• Basics in Minerals Processing, metso.
Thanks
• Thanks to Prof. ChVR Murthy, Principal, AU College of Engineering for
making this Work Shop happen.
• Thanks to Prof. V. Sujata, Prof. SV Naidu and Prof. P. King and to the
Department of Chemical Engineering for whole hearted support.
• Thanks to Prof. TC Rao and Er. DV Subba Rao Garu who are central to
this work shop.