Analysis of the residence time distribution in large flotation machines

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Analysis of the residence time distribution in large
flotation machines q
D. Lelinski *, J. Allen, L. Redden, A. Weber
EIMCO Process Equipment Company, 669 West 200 South, Salt Lake City, UT 84110, USA
Received 2 October 2001; accepted 16 April 2002
Abstract
Residence time in a single flotation machine is one of the most important parameters necessary to properly design a flotation
circuit. The mean residence time for any particular cell design is usually determined from residence time distribution (RTD) ex-
perimental results. The comparison of the measured mean residence time with the expected residence time, as well as analysis of the
shape of the RTD curve, give the most useful and valid information about the mixing properties in the cell.
Experimental RTD results for three large flotation cells (Dorr-Oliver, Outokumpu and WEMCO�) discussed in this publication
were released by the Chuquicamata Division of CODELCO as a part of the competitive rougher flotation test report (CODELCO
(National Copper Corporation of Chile), Chuquicamata Division, 2000, Project IM2, No. 19/99; Final Report of the Evaluation of
Large Volume Flotation Cells). Evaluation of the results by CODELCO as well as by authors is provided. ‘‘Approximation of the
theoretical curve of a perfect mixer,’’ used by CODELCO as a base for cell categorization is analyzed and critiqued after comparing
to the criteria used by many authorities in the field.
Conclusions are drawn based on the multi-parameter flow model, showing existence of stagnant volume of 45% in Outokumpu,
35% in Dorr-Oliver, and 7% in WEMCO� flotation cell volumes.
� 2002 Elsevier Science Ltd. All rights reserved.
Keywords: Flotation machines; Froth flotation; Flotation kinetics; Mass balancing
1. Introduction
Flotation is a dynamic process and the efficiency is
directly related to the time material spends in the ma-
chine. To fully analyze this process, the distribution of
the time it takes for the material to proceed from the
inlet(s) to the outlet(s) has to be known. This distribu-
tion is the best indication of the flow patterns in the
vessel. The most common way of RTD determination is
to inject an impulse tracer (solid or water-soluble – de-
pending which RTD is to be obtained) and detect the
amount of this tracer emerging in the outlet(s) as a
function of time. The resulting patterns can be consid-
ered in terms of two ideal types: plug flow and perfect
mixing (Levenspiel, 1989, 1962; Kelly and Spottiswood,
1982). Distribution of residence times for both types of
the flow is presented in Fig. 1. The most important
characteristic of plug flow is equal residence time of all
elements in the cell. No mixing can occur in the flow
direction, but lateral mixing is allowed. Plug flow is
equivalent to a batch processing system (Kelly and
Spottiswood, 1982).
In perfect mixing, tracer input is immediately dis-
persed throughout the whole volume of the device. It
can be seen that some of the tracer leaves instanta-
neously, while some never leaves, so that there is a dis-
tribution of residence time from zero to infinity.
The most important outcome from RTD experiments
is the measured mean residence time. This is the main
reason why the experimental evaluation of the residence
time distribution is performed. The relationship between
experimentally measured and expected mean residence
times is the easiest-to-obtain indication of the hydro-
dynamics of a flotation cell. If they are equal, the cell is
most probably well mixed. If the experimental mean
is smaller than expected, it indicates that there are
dead volumes, short-circuiting, or other anomaly. The
cause of the difference usually can be determined by
Minerals Engineering 15 (2002) 499–505
This article is also available online at:
www.elsevier.com/locate/mineng
qThis paper was presented at the 10th Annual Minerals Engineering
Conference in Cape Town, South Africa, November 13–15, 2000.
*Corresponding author. Tel.: +1-801-526-2555; fax: +1-801-526-
2911.
E-mail address: dariusz.lelinski@eimcoprocess.com (D. Lelinski).
0892-6875/02/$ - see front matter � 2002 Elsevier Science Ltd. All rights reserved.
PII: S0892-6875 (02 )00070-5
mail to: dariusz.lelinski@eimcoprocess.com
comparing the shapes of the RTD curves for ideal case
and the case in question. The description of the method
and many examples can be found in the Levenspiel’s
textbook ‘‘The Chemical Reactor Omnibook’’ (Leven-
spiel, 1989). Also, the analysis of the RTD for flotation
is discussed in detail by Nesset (1988).
2. Large flotation cell evaluation
On April 3, 2000, the Chuquicamata Division of
CODELCO released its report entitled ‘‘Final Report of
the Evaluation of Large Volume Flotation Cells’’
(CODELCO, 2000). This report summarizes the com-
petitive flotation test conducted at Chuquicamata over
the period of 20 October 1998 to 14 May 1999. This
competitive test was part of a project, ‘‘Improvement of
Cu and Mo Recovery in the Concentrator plant at
Chuquicamata,’’ which had the goal of obtaining an
increase in recovery of 5.5% total Cu and 9.0% Mo.
Tests at the Chuquicamata Concentrator Plants were
performed in three phases: start up, optimization of the
cell operation, and the period of official evaluation, in-
cluding the residence time distribution test.
Suppliers invited to participate were Dorr-Oliver,
EIMCO/Baker Process (manufacturer of the WEMCO�
SmartCell), and Outokumpu. The flotation cells offered
by these companies were designed and constructed exclu-
sively for testing at Chuquicamata. The nominal volumes
of the cells were: Dorr-Oliver – 148 m3; WEMCO� –
160 m3, and Outokumpu – 160 m3. The cells were used
in rougher duty and the operational parameters for flo-
tation feed are presented in Table 1.
All experimental results and procedures used in this
article are taken from CODELCO final tabulation of the
data, which was made available to all three vendors
(CODELCO, 2000).
3. Methodology
Throughout the competitive test campaign, operating
and metallurgical performance data were collected and
analyzed by CODELCO. In the course of the testing,
CODELCO also commissioned the Chilean Commis-
sion of Nuclear Energy (CCHEN), Section of Tracers to
perform measurements of residence time distribution in
each of the three flotation machines. CCHEN’s findings
appear as Appendix 4, ‘‘Analysis of Residence Time
Distribution,’’ following Chapter IV of the CODELCO
report (Diaz et al., 2000).
The general objective of the RTD experiment was to
characterize the fluid dynamic behavior of the large
flotation cells manufactured by the Dorr-Oliver, EI-
MCO/Baker Process, and Outokumpu. It was accom-
plished by determining the residence time distribution in
each of the cells, in separate experiments, using the pulse
tracer method. Selection of radioactive tracers was
based on the following properties:
• The physico-chemical behavior should be suitable for
the material being traced. In this case it was necessary
to trace solid material that is not floatable. Final con-
centrator tailings of distinct particle sizes were used to
study the effects of this parameter.
• The lifetime of the radioactive isotope should be com-
patible with the duration of the experiment, in this
case several minutes.
• The type and energy of radiation from the isotope
must permit its detection in an adequate form relative
to the characteristics of the background where the
work is being conducted.
Selection of an appropriate tracer isotope was subject
to several constraints. To facilitate automated data ac-
quisition in real time, CCHEN preferred to employ
tracers emitting gamma radiation. The tracer should be
non-floating ore material from the Chuquicamata con-
centrator, and this material must contain an element
that could be neutron-activated in CCHEN’s reactor.
After analysis of the neutron activation spectrum and
radioactive decay curves of the Chuquicamata material,
sodium was identified as the only suitable element for
activation.
Table1
Operational parameters for flotation feed (CODELCO, 2000)
Operational
parameters
Values Units
Dry feed tonnage 5800–15 800 metric tons/day
Particle size 28–30 % > 65 mesh
% Solids 38–42 wt%
Primary collector
SF-113
25 g/metric ton
Secondary collector
AP-7518
8 g/metric ton
Chuqui frother mix 15 g/metric ton
pH 10.5–10.8
Fig. 1. Distribution of residence times for plug flow and perfect
mixing.
500 D. Lelinski et al. / Minerals Engineering 15 (2002) 499–505
Based on these conditions, it was determined that
quantities of 2 mCi of Na-24 were sufficient to obtain an
adequate appraisal in each of the experiments using
solid material. For experiments with liquid, 5 mCi of Br-
82 was the indicated amount, based on the other ex-
periments in similar equipment.
Table 2 shows the characteristics of the tracer solids
in each case.
CCHE used scintillation detectors, 1� 1:5 in., Tl-
doped NaI with associated electronics. The probe was
connected to the data acquisition system, which, besides
providing power to the probe, also acquires the data,
records them on the hard disc, and permits an adequate
visualization of the data during the experiment.
4. Experimental results
Chilean Commission of Nuclear Energy (CCHEN)
corrected the collected raw data for radioactive decay,
which was not negligible in this case because of the re-
lationship between the duration of the experiment (some
hours), and the half-life of the irradiated tailing (be-
tween 15 and 30 h). Data were also corrected for natural
background (cosmic) radiation. Figs. 2 and 3 are ex-
amples of corrected data.
The mathematical expression that summarized the
calculation of radiation intensity was
ACOR ¼ ðAmed � BGÞ exp 0:693
�
� t
t1=2
�
;
where ACOR is the activity corrected for background and
radioactive decay, Amed is the measured activity, BG is
the background (cosmic) radiation, t is the measurement
time and t1=2 is the half-life of the irradiated tailings.
The experimental mean residence time was calculated
from the RTD curve
texp ¼
R
tCðtÞdtR
CðtÞdt ffi
P
i tiCiP
i Ci
for equal time intervals Dti;
where texp is the experimental mean residence time, t is
the measured time and CðtÞ is the tracer concentration at
time t.
Data calculated from tracer experiments are shown in
Table 3 and Fig. 4.
Table 2
Characteristics of tracer solids (Diaz et al., 2000)
Cell Tracer mass (g) Tracer size designation Tracer particle size
Dorr-Oliver 75 Global No separation
Dorr-Oliver 75 Intermediate +325, �100 mesh
Dorr-Oliver 60 Fine �325 mesh
Dorr-Oliver 75 Coarse +100 mesh
WEMCO� 75 Global No separation
WEMCO� 75 Intermediate +325, �100 mesh
WEMCO� 60 Fine �325 mesh
WEMCO� 75 Coarse +100 mesh
Outokumpu 75 Global No separation
Outokumpu 75 Intermediate +325, �100 mesh
Outokumpu 75 Fine �325 mesh
Outokumpu 75 Coarse +100 mesh
Fig. 2. Residence time distributions for liquid (DO – Dorr-Oliver, WE WEMCO�, TK – Outokumpu) (Diaz et al., 2000).
D. Lelinski et al. / Minerals Engineering 15 (2002) 499–505 501
5. Analysis by CODELCO
CODELCO’s analysis was based on the data pro-
vided by CCHEN and consisted of fitting models of
mixing to the experimental data and calculating the
mean residence time. The model curves obtained were
compared with the ideal cases to approximate how
closely each one approached conditions of ideal mixing.
The expected residence time was calculated for each cell
and served as a reference standard.
The experimental data were corrected for natural or
‘‘background’’ radiation, and all the measurement times
were standardized, with measurements taken between
the time of injection and the time at which the measured
radiation reached the background level. The tails of the
curves were ‘‘trimmed’’ to avoid errors generated were
the measuring standards were low, at extended times
(Heresi et al., 2000). Table 3 compares mean residence
times obtained by CCHEN and CODELCO. The dif-
ference between both calculations is the method of data
correction. CCHN corrected the data for radioactive
decay and natural background radiation and CODE-
LCO, in addition to CCHN corrections, standardized all
measurement times and cut tails of the curves. The ad-
ditional data modification by CODELCO had a minor
influence on the final results.
The calculation of expected residence time is very
simple, as given by the equation below
texp ¼ Veff=Q;
where Veff is the effective cell volume and Q is the vol-
umetric flow rate.
Obtaining the value of Q is straightforward, but ob-
taining a value of Veff requires making some assump-
tions. In a flotation cell the effective volume is
Veffective ¼ Voverall � Vair � Vfroth:
One of the parameters, Vair, the content of air in the
pulp, is difficult to estimate. Gorain and co-workers
(Gorain et al., 1995) conducted experiments for mea-
Table 3
Experimental mean residence times (Diaz et al., 2000, Heresi et al., 2000)
Tracer Mean residence time (min)
Outokumpu Dorr-Oliver WEMCO�
CCHEN CODELCO CCHEN CODELCO CCHEN CODELCO
Liquid 3.3 3.2 5.3 5.3 6.4 6.2
All solids 3.2 3.1 3.7 3.2 5.5 5.1
Fine solids 2.7 2.6 3.8 3.4 5.8 5.5
Intermediate solids 2.9 3.0 3.3 2.9 5.4 5.0
Coarse solids 2.9 3.1 4.1 3.9 5.3 5.2
Fig. 3. Residence time distributions for all solids (DO – Dorr-Oliver, WE – WEMCO�, TK – Outokumpu) (Diaz et al., 2000).
Fig. 4. Experimental mean retention time. Data from Heresi et al.,
2000.
502 D. Lelinski et al. / Minerals Engineering 15 (2002) 499–505
suring gas holdup in a pneumatic, industrial-scale flo-
tation cell, operating over a range of air flows (1–
3:4 m3=min) and impeller speeds (105–245 rpm). It was
found that the volume of air (air holdup) increased with
the velocity of the impeller and increased airflow. The
largest value measured was 33%. Glemboskii (Glem-
botskii et al., 1972) indicate that well-aerated pulp
contains between 20% and 30% of air by volume. They
also developed an equation for the calculation of the air
volume in a flotation cell, with the pulp density as the
principal variable.
When the volume of air in each of the three machines
was calculated using the equation of Glembotskii
(Glembotskii et al., 1972) the values varied between 24%
and 32% of the total volume. Considering that these
values were higher than those obtained by other au-
thors, the estimates of expected times were made with
the assumption that the air holdup was 25% in all cases.
It is also necessary to subtract the volume of froth
from the volume of the cell. Froth volume was not
calculated, but was estimated at 2% of cell volume. The
expected time calculations are shown in Table 4.
Final CODELCO conclusions were based on the
‘‘approximation of the theoretical curve of a perfect
mixer’’. The validity of this assumption is discussed in
the next chapter. In general, the distributions of resi-
dence times in all three cells were concluded to be close
to that for ideal mixing. The only one that presented a
small deviation was the WEMCO� cell. No significant
anomalies, such as dead volume, short-circuiting, or
pulp recirculation, were noted by CODELCO in any of
the cells.
In all cells the RTD curves for distinct size fractions
of solids are practically coincidental, and the differences
between the respective mean residence times are mini-
mal. This indicates that the three cells have more than
adequate capacity for suspension of solids. Other pa-
rameters can be used to characterize fluid-dynamic
performance, including power number, air flow number,
bubble flow, and mixing time, but these depend on
specific operations data and details of cell geometry that
were unknown at that time.
6. Analysis by EIMCO/Baker Process
The RTD experiment was professionally designed
and flawlessly executed by the Section of Tracers of the
Chilean Commission of Nuclear Energy.
There are three main points that have to be made in
regard to the CODELCO analysis of the results.
First, the most important single piece of information
to be gained from tracer experiments of this type is the
meanresidence time. True (measured rather than cal-
culated) mean residence time provides the greatest op-
portunity for inference about flow through the cell,
especially when the measured residence times for a few
cells of the same volume and flow rate can be compared.
Table 3 shows that for all components the longest resi-
dence times were observed in the WEMCO machine.
Since the probability of flotation increases with the
amount of time a floatable particle remains in the cell,
residence time should carry significant weight in evalu-
ation of flotation machines.
Table 4
Expected mean residence times (Heresi et al., 2000)
Test number Cell Q (m3/min) Veffective (m3) Texpected (min)
1 Dorr-Oliver 20.2 104 5.2
2 Dorr-Oliver 20.8 104 5.0
3 Dorr-Oliver 20.1 104 5.2
4 Dorr-Oliver 19.5 104 5.3
5 Dorr-Oliver 20.4 104 5.1
Average 5.2
1 WEMCO� 20.9 117 5.6
2 WEMCO� 20.6 117 5.7
3 WEMCO� 21.2 117 5.5
4 WEMCO� 21.2 117 5.5
5 WEMCO� 20.2 117 5.8
Average 5.6
1 Outokumpu 21.0 117 5.6
2 Outokumpu 20.9 117 5.6
3 Outokumpu 21.4 117 5.5
4 Outokumpu 21.0 117 5.6
5 Outokumpu 22.3 117 5.2
Average 5.5
D. Lelinski et al. / Minerals Engineering 15 (2002) 499–505 503
Second is the lack of comparison between experi-
mental and expected mean residence times. Of course,
both were calculated from experimental data (see Tables
3 and 4) but not compared. The comparison is made in
Table 5.
Comparison between the measured and theoretical
residence times is another opportunity for inference
about the flow characteristics of the flotation vessels.
CODELCO chose to ignore the theoretical residence
times and focused on the measured values. Table 5
presents the comparison, with a column showing the per-
centage that each measurement deviates from the theo-
retical value. The ideal situation would be for the
deviation to be zero in all cases. The WEMCO� flota-
tion machine shows the smallest absolute deviations
from the expected or theoretical value. Literature in this
field (Levenspiel, 1962, 1989; Kelly and Spottiswood,
1982; Mehrotra and Saxena, 1983; Weber and DiGiano,
1996) offers three physical conditions that can be in-
ferred when the measured mean residence time is lower
than the expected (or theoretical) value: (1) the vessel
has dead spaces, where the medium is stagnant, and (2)
there is bypass flow, where a portion of the input
flow passes directly to the outlet and does not disperse
through the total volume, or (3) there is recycle flow,
where a portion of the contained volume continuously
remixes with the incoming feed.
These explanations are intuitive. If a medium transits
a vessel faster than the V =Q ratio would suggest, then a
portion of the medium must ‘‘short-circuit’’ to the exit,
or the actual volume through which the medium dis-
perses must be reduced by a certain amount of dead
space. Based on the shapes of the experimental RTD
curves, and comparing with the diagnostic examples
presented by Levenspiel (Levenspiel, 1989) it can be
inferred that the Outokumpu and Dorr-Oliver flota-
tion machines contained stagnant backwaters, or dead
spaces, at the time these measurements were made. The
amount of negative deviation of the measured residence
time from the expected value is an indication of the
fraction of the vessel’s volume that is stagnant. This
fraction is presented in Table 6. There may be sound
reasons for operating a flotation cell with a large stag-
nant volume, but the operator must recognize that this
reduces the effective residence time and consequently the
net probability of recovering the floatable particles in
the feed.
The higher measured value of liquid residence time in
theWEMCO� machine is in excellent agreement with the
findings of Jowett (Jowett, 1961). He obtained similar
results and suggested that calculations of the expected
residence time for liquid do not consider agitation and
air injection, and thus neglect the processes of macro-
and micro-turbulence produced mechanically. Jowett
further concluded that the effective residence time for
flotation is always more than the expected.
A final, third, point regarding CODELCO’s analysis
relates to their use of the perfect mixing model as a
standard for comparison of the measured RTD’s of the
three machines. Previous studies on the mixing charac-
teristics of flotation cells (Dinsdale and Berube, 1972;
Bull and Spottiswood, 1974; Harris and Cuadros-Paz,
1978; Harris et al., 1975, 1976, 1978; Gardner et al.,
1980) show that perfect mixing is neither a valid nor
desirable approximation for flotation cells. In all of
these studies the authors chose to interpret the tracer
response data using the multiple-parameter model ap-
proach developed and discussed by Levenspiel (1962,
1989) and Wen and Fan Wen and Fan (1975) among
many others.
Table 5
Comparison of measured and expected values of residence time (min)
Material Flotation cell
Dorr-Oliver Outokumpu WEMCO�
Meas. Theor. % Diff. Meas. Theor. % Diff. Meas. Theor. % Diff.
Liquid 5.3 5.2 +1.9 3.2 5.6 )42.9 6.2 5.6 +10.7
All solids 3.2 5.0 )36.0 3.1 5.6 )44.6 5.1 5.7 )10.5
Fine solids 3.4 5.2 )34.6 2.6 5.5 )52.7 5.5 5.5 0
Interm. solids 2.9 5.3 )45.3 3.0 5.6 )46.4 5.0 5.5 )9.1
Coarse solids 3.9 5.1 )23.5 3.1 5.2 )40.4 5.2 5.8 )10.4
Table 6
Stagnant portions of the flotation machines
Material Dorr-Oliver (%) Outokumpu (%) WEMCO� (%)
Liquid 0 43 0
All solids 36 45 10
Fine solids 35 53 0
Interm. solids 45 46 9
Coarse solids 23 40 10
504 D. Lelinski et al. / Minerals Engineering 15 (2002) 499–505
In this model, a flotation cell consists of different
regions representing perfect mixing, dead volume, by-
pass, recycling and plug flow. The main reason cited for
the existence of stagnant portions of the flotation ma-
chines is insufficient turbulence. This portion of the
machine is usually located in the corners and upper part
of the vessel. The part of the cell where mixing is com-
plete and there is no variation in composition is con-
sidered the effective volume. Bypass or short-circuiting
represents that part of the feed, which goes directly to
the exit stream without being dispersed in the cell.
Similarly, that part of the feed which may be recircu-
lated through the impeller zone due to intense stirring
action in that zone represents recycling (Mehrotra and
Saxena, 1983).
Approximation to perfect mixing is not necessarily
the ‘‘perfect’’ operating mode for a flotation machine.
Harris (Harris, 1976) has noted that the different stages
of the flotation operation (e.g., suspension, bubble for-
mation, particle–bubble contact, and separation) all re-
quire different levels of turbulence, and that the different
regimes noted in the multiple-parameter model are ac-
tually the preferred situation.
In the case of perfect mixing, any input would be
immediately dispersed uniformly throughout the whole
cell. This prohibits part of the feed to be pumped
through the rotor space. In all types of flotation ma-
chines, volume inside the rotor is the place where the
majority of particle–bubble contact takes place. Without
a particle–bubble contact flotation can not take place;
this is the first, necessary step.
7. Conclusions
The work of CCHEN with subsequent analysis by
CODELCO has provided a valuable measurement of
the RTD of both liquid and particles in large flotation
machines. Coupled with knowledge of the expected
residence time, this provides new insight into the flow
characteristics of the individual machines that were
evaluated. Each of the flotation machines contained a
certain amount of stagnant volume, and this varied from
7% of the WEMCO machine’s effective volume to 45%
of the Outokumpu volume.
Although the concept of ‘‘perfect’’ mixing is seducing,
the best method to interpret the residence time distri-
bution data is to use a multiple-parameter model. Ap-
plication of the perfect mixing model to the flotation
machine is a simplistic approach that ignores the many
unit functions of a large modern flotation machine.
Taking into consideration the necessity ofthe flow
through rotor, the slurry pumping rate together with the
highest achievable mean residence time in a flotation cell
is the best possible indication of cell performance.
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D. Lelinski et al. / Minerals Engineering 15 (2002) 499–505 505
	Analysis of the residence time distribution in large flotation machines
	Introduction
	Large flotation cell evaluation
	Methodology
	Experimental results
	Analysis by CODELCO
	Analysis by EIMCO/Baker Process
	Conclusions
	References