Residence time distribution in large industrial flotation cells

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Residence time distribution in large industrial flotation cells
Francisco Díaz1 and Juan Yianatos2 
1Nuclear Applications Department
Chilean Commission of Nuclear Energy
P.O. Box 188-D, Santiago, Chile
fdiaz@cchen.cl
2Department of Chemical Engineering
Santa María University
P.O. Box 110-V, Valparaíso, Chile
juan.yianatos@usm.cl
ABSTRACT
In order to study the hydrodynamic behavior of large flotation cells, the radioactive tracer technique was used 
to measure the residence time distribution (RTD) of the liquid and solid in an industrial rougher flotation 
bank consisting of 7 cells of 130 m3. Thus, a pneumatic system of high reliability was used in order to 
introduce a small amount of radioactive tracer (around 100 mL of liquid or pulp) at the feed pulp entrance. 
Then, the time response of the radioactive tracer was measured on-line, at different points along the bank, 
using non-invasive sensors located directly in the discharge pipe of each cell. Activity (cps) was measured by 
scintillating crystal sensors of NaI(Tl) of 1”x1.5”, Saphymo Srat, thus allowing the simultaneous data 
acquisition of up to 12 control points, with a minimum period of 50 milliseconds. 82Br in solution was used 
as liquid tracer, while mineral gangue was used as solid non-floatable tracer. The solid tracer was also tested 
at three size classes (coarse: +150, intermediate: -150+45 and, fine –45 microns) in order to evaluate solids 
segregation. An advantage of using the radioactive tracer technique is the direct testing of the actual solid 
particles (similar physical and chemical properties, size distribution, shape, etc.). tracer injection is almost 
instantaneous, because only a small amount of radioactive tracer is required. Another advantage is its 
capability for on-line measurements at various points inside the system without disturbances related to 
process sampling. Also, the individual performance of each cell along the bank was evaluated by a series of 
tests performed around each cell. The RTD was measured on-line in the tailings stream of each cell. The 
procedure was repeated for the 7 cells of the flotation bank.
From a hydrodynamic point of view, the new experimental data has confirmed that single mechanical 
flotation cells, of large size, can deviate significantly from perfect mixing, while in terms of process 
modelling the mixing conditions in a flotation bank of mechanical cells (3, 5 or 7 cells in series) can be well 
described as a series of N continuous perfectly mixed reactors, where N corresponds to the actual number of 
cells in the bank. 
Keywords: residence time distribution, radioactive tracer, froth flotation, flotation machines, modelling.
1. INTRODUCTION
Industrial flotation cells need to accomplish several functions such as: air bubble 
dispersion, solid suspension as well as to provide the best conditions for bubble-particle 
collision and aggregate formation. For this reason, cells are typically provided with 
mechanical agitation systems which generate well mixed conditions for the pulp and air 
bubbles. In an industrial mechanical cell, however, the mixing condition prevents that 
particles have the same opportunity to be collected because a significant fraction of them 
actually spent a very short time in the cell (in a well-mixed condition almost 40% of 
particles stay in the cell for less than a half of the mean residence time). Because of the 
large short circuit in single continuous cells, the industrial flotation operation considers the 
arrangement of cells in banks. Thus, banks of 5-10 cells in series are commonly used in 
plant practice. 
mailto:fdiaz@cchen.cl
2. EXPERIMENTAL
 The largest flotation cells presently used in industrial flotation operation are 130, 160 
and 250 m3. Figure 1 shows the main characteristics of a self-aerated cell, where the feed 
pulp circulates upwards through a draft tube by the rotor. Also, the air is self-aspirated 
from the upper part of the cell by the rotor.
Figure 1. Large flotation cell
Experimental tests were developed in an industrial rougher flotation circuit consisting 
of 4 parallel banks, each one provided with 7 cells of 130 m3. Figure 2 shows the flotation 
banks arrangement.
Figure 2. Flotation banks arrangement.
2.1. Tracer technique
 An advantage of using the radioactive tracer technique is the direct testing of the 
actual solid particles (similar physical and chemical properties, size distribution, shape, 
etc.), tracer injection is almost instantaneous, because only a small amount of radioactive 
tracer is required. Another advantage is its capability for on-line measurements at various 
points inside the system without disturbances related to process sampling and because of 
the existence of dilution effects, possible radiological problems to the environment or to 
workers do not exist. 
 
CELL 1 CELL 2 CELL 3 CELL 4 CELL 5 CELL 6 CELL 7 
 FEED 
ban k 4 
ban k 3 
ban k 2 
ban k 1 
 
 
ROTOR 
 
TAIL 
 
 
 
PULP/FROTH 
INTERFACE 
 
 
 
 
 
FEED 
FEED PULP 
CIRCULATION 
 
 
 
 
 AIR FROTH 
CROWDER 
 
CONCENTRATE 
In this work a small amount of radioactive tracer (around 100 mL of liquid or pulp) 
was introduced at the feed pulp entrance by means of a pneumatic system of high 
reliability. The time response of the radioactive tracer was measured on-line, at different 
points along the bank, using non-invasive sensors located directly in the discharge pipe of 
each cell. Activity (cps) was measured by scintillating crystal sensors of NaI(Tl) of 
1”x1.5”, Saphymo Srat, thus allowing the simultaneous data acquisition of up to 12 control 
points, with a minimum period of 50 milliseconds. 82Br in solution was used as liquid 
tracer (50 mCi), while mineral gangue was used as solid non-floatable tracer (25 mCi in 
24Na). The solid tracer was also tested at three size classes (coarse: +150, intermediate: 
-150+45 and, fine –45 microns) in order to evaluate solids segregation. 
The RTD was measured on-line in the tailings stream of each cell. Figure 3 shows the 
flotation bank arrangement, 1x2x2x2, the impulse tracer injection point at the feed entrance 
and the sensors location in the bank. 
Figure 3. Tracer impulse test and sensors location in a flotation bank
The same procedure was repeated to characterize the individual performance of each 
cell along the rougher flotation bank. 
2.2. RTD Modelling
The residence time distribution “RTD”, where measure the tracer recovery is not 
important, of mechanical cells arranged in banks has been typically represented by a model 
of N perfect mixers in series (Mavros, 1992; Yianatos et al., 2001, 2005), 
( ) ( )[ ]
)()/(
/exp)
1
NN
NLtLtE(t N
N
Γ⋅
⋅−−−=
−
τ
τ
for t > L (1) 
where τ is the mean residence time, L is the lag time and the Gamma function Γ(N) 
replaced the factorial term (N-1)! in order to account for the non integer solutions of N. 
 
 On the other hand, from experimental evidence it was found that the RTD of a single 
large flotation cell can be better described by a LTST (large and small tank in series) 
model, consisting of one large perfect mixer, with residence time τL, and one small perfect 
mixer, with residence time τS, in series plus a dead time L. Figure 4 shows the model 
description.
 
 
1 1 2 4 5 7 3 6 
E(t) 
t 
τ 
FEED 
RTD 
CELL1 
RTD 
CELLS 1 to 3 
RTD 
CELLS 1 to 5 
RTD 
CELLS 1 to 7 
TAIL 
CONCENTRATE 
 
Lag 
S τ L τ L 
PM 
Large PM 
 Small 
Figure 4. Large and small tank-in-series model
 The analytical solution for the LTST model is given by (Tello, 2006), 
[ ] [ ]
( )Ls
Ls LtLttE
ττ
ττ
−
−−−−−
=
/)(exp/)(exp
)( (2)
and the overall mean residence time τ isgiven by,
LLs ++= τττ (3)
3. RESULTS
3.1. Flotation Bank RTD
 Figure 5 shows the liquid residence time distribution after 1, 3, 5 and 7 cells in the 
bank, which clearly shows the significant decrease in the pulp short-circuit by increasing 
the number of cells in series in the flotation bank arrangement. Also, the continuous lines 
show the good agreement between the data points and the RTD model, which was 
described by Eq.(1). 
0,0000
0,0005
0,0010
0,0015
0,0020
0,0025
0,0030
0,0035
0 500 1000 1500 2000 2500 3000 3500 4000
Time, s
R
TD
, E
(t)
 
Figure 5. RTD in a flotation bank after 1, 3, 5 and 7 cells in series. 
Figure 6 shows the residence time distribution of fine non-floatable minerals (-45 microns) 
reported to the concentrate of cells 1, 2, 3 and 4, by solids entrainment in the froth.
 
 Mineral Fino en Concentrados Celdas 1 a 4
0,0000
0,0005
0,0010
0,0015
0,0020
0,0025
0,0030
0,0035
0,0040
0,0045
0 500 1000 1500 2000 2500
Time, s
N
or
m
al
iz
ed
 A
ct
iv
ity
, 1
/s
Conc. Cell 1
Conc. Cell 2
Conc. Cell 3
Conc. Cell 4
Figure 6. RTD of fine mineral entrained into concentrate in cells 1, 2, 3 and 4. 
Table 1 shows the mean residence time of liquid reported to the tails, Fig. 5, and the mean 
residence time of entrained minerals into the concentrate, Fig. 6. The increase in the ratio 
between the residence time of entrained minerals and the liquid reported into tailings can 
be attributed to the larger drop-back and recirculation of non-floatable solids from the froth 
to the pulp zone, because of the decrease of froth stability due to the lower collection of 
minerals downwards in the flotation bank.
Table 1. Mean residence time of entrained minerals to concentrate and liquid to tails
Cell number 1 2 3 4 5 6 7
Concentrate time, s 227.4 473.8 711.1 994.8
Tailings time, s 283.5 782.3 1331 1858
Time ratio: conc./tail 0.80 0.91
3.2. Flotation Cell RTD
Figure 7 shows the RTD of the liquid in the first cell of the flotation bank. This result 
confirms that the pulp zone in a large flotation cell was not perfectly mixed. Also, a good 
agreement between the experimental data and the LSTS model, Eq. (2), can be observed.
0,0000
0,0004
0,0008
0,0012
0,0016
0,0020
0,0024
0,0028
0 200 400 600 800 1000 1200 1400 1600 1800
Time, s
R
es
id
en
ce
 ti
m
e 
di
st
rib
ut
io
n,
 E
(t)
DATA
LSTS
Figure 7. RTD of liquid in a large flotation cell 
Figures 8, 9 and 10, show the results for the RTD of fine (-45 microns), intermediate (+45-
150 microns) and coarse (+150 microns) particles of non-floatable minerals, in the pulp 
zone of the 130 m3 cell. Again, for all particle size classes it was observed a good 
agreement between the experimental data and the LTST model, Ec. (2), used to describe 
the RTD of solids in the large size cell.
0,0000
0,0005
0,0010
0,0015
0,0020
0,0025
0,0030
0,0035
0 200 400 600 800 1000 1200
Time, s
R
es
id
en
ce
 T
im
e 
D
is
tri
bu
tio
n Data
LTST model
Figure 8. RTD of fine mineral (-45 microns) in a large flotation cell 
-
0,0005
0,0010
0,0015
0,0020
0,0025
0 200 400 600 800 1000 1200 1400 1600 1800
Time, s
R
es
id
en
ce
 T
im
e 
D
is
tri
bu
tio
n
Data
LSTS
Figure 9. RTD of intermediate mineral (+45-150 microns) in a large flotation cell 
0,0000
0,0003
0,0006
0,0009
0,0012
0,0015
0,0018
0,0021
0,0024
0 200 400 600 800 1000 1200 1400 1600 1800
Time, s
R
es
id
en
ce
 ti
m
e 
di
st
rib
ut
io
n,
 E
(t) DATA
LSTS
Figure 10. RTD of coarse mineral (+150 microns) in a large flotation cell 
4. CONCLUSIONS
The residence time distribution of liquid in the pulp zone of a flotation bank, consisting of 
130m3 flotation cells, was determined for different number of cells in series (1,3,5 and 7). 
Results confirmed that the classical model of N tanks-in-series was adequate for estimation 
of the RTD of flotation banks consisting of different numbers of cells, where N represents 
the actual number of cells in series.
The mineral entrainment in large flotation cells was characterized by measuring the RTD 
of non-floatable mineral, fine particles (-45 microns) reported to the concentrate.
It was confirmed that the flow regime in large self-aerated flotation cells was not perfectly 
mixed, and can be well described by the LSTS model, which combines a large and a small 
tank in series plus dead time. Results showed a good agreement between experimental data 
and model prediction for the liquid as well as for mineral particles of different size classes.
ACKNOWLEDGEMENTS
The authors are grateful to El Teniente Division Codelco-Chile for providing access to 
their plant and for valuable assistance in the experimental work. Funding for process 
modelling research is provided by CONICYT, project Fondecyt 1070106, Chilean 
Commission of Nuclear Energy, and Santa María University, project 270522.
REFERENCES
Mavros, P., 1992. Mixing and hydrodynamics in flotation cells. Innovations in flotation 
technology. P. Mavros and K.A. Matis, eds., NATO ASI Series, Kluwer Academic 
Pub., London, 211-234.
Tello, K., 2006. Caracterización hidrodinámica y metalúrgica de un banco de flotación 
industrial. Met. Eng. Thesis, Santa Maria University, Chile.
Yianatos, J.B., Bergh, L.G., Díaz, F., Rodriguez, J., 2005. Mixing characteristics of 
industrial flotation equipment. Chemical Engineering Science, Vol. 60, pp.2273-2282.
Yianatos, J.B., Bergh, L.G., Condori, P., Aguilera, J., 2001. Hydrodynamic and 
metallurgical characterization of industrial flotation banks for control purposes. 
Minerals Engineering, Vol.14, N°9, pp. 1033-1046.
	Residence time distribution in large industrial flotation cells
	Francisco Díaz1 and Juan Yianatos2