Gerson Sandoval Zambrano
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Transcript of Gerson Sandoval Zambrano
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Assessing uncertainties of flotation
kinetics derived from measured operatingvariables
G. Sandoval-Zambrano and G. Montes-Atenas
The University of Queensland, Australia
Santiago, December 2011
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Outline of work
Background
Objective
Methodology
Results Key findings
Implications
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Background AMIRA P9 Model
( )
( ) ( ) wiwijwiwij
ij RENTRk
RENTRk
R ++
+
=
11
1
(1)
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Background: Propagation of error
Propagation of error analysis
Specific SensitivitySensitivity
Depends on:
the nature of the variable
the technique used to measure reproducibility/repeatability
Depends on the
operating conditions
of the cell
Depends on the
operating conditions
of the flotation cell
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Objectives of work
To obtain the best operating conditions for
which the error in the predictions offlotation kinetics can be minimised;
To explore possible explanations for higher
errors of recovery and residence time
components of the PPBM model.
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I) Data:
Welsby et al (2010)
II) Methodology: Propagation of error analysis to
equation 2:
Methodology
6
(3)
(2)
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Methodology and data analysis
Sensitivity coefficient (SC) expressions for
equation 2
( )
22
1
=
w
w
i
ij
R
R
ENT
k
( )
2
2
2
1
=
i
w
ij
R
ENT
R
k
(4) (5)
( ) ( )( ) ( )
2
2
2
11
11
=
wij
wijijwiij
RR
RRRRENTk
( )
2
2
2
1
1
=
ijij
ij
RR
k
(6) (7)
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Measured and calculated variables used in PPBM methodology
Methodology: operating conditions
Variable Estimated value Number of data sets
RijSee in Sandoval-Zambrano & Montes-
Atenas (2011)7 x 11
8
w .
4.68 1
ENT 0.14 1
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Results: SC of residence time
2.E+00
4.E+00
6.E+00
8.E+00
1.E+01
(k/)^2
[+106m]
2.E+01
4.E+01
6.E+01
8.E+01
(k/)^2
[-38+28m]
5.E-01
1.E+00
2.E+00
2.E+00
(k/)^2
[-10m]
2.E-06
4.E-06
2.E-02
4.E-02
6.E-02
8.E-02
1.E-01
(k/)^2
[+106m]
1.0E-02
2.0E-02
5.0E-01
1.0E+00
1.5E+00
2.0E+00
(k/)^2
[-38+28m]
1.E-03
2.E-03
3.E-03
4.E-03
2.E-02
4.E-02
6.E-02
8.E-02
(k/)^2
[-10m]
100% apparently liberated galenaLow and intermediate galena liberation
1.E-080 1 2 3 4 5 6 7
Residence time (min)
(+106m,100%)
0.E+00
0 1 2 3 4 5 6 7
Residence time (min)
(-38+28 m,100%)
0.E+00
0 1 2 3 4 5 6 7
Residence time (min)
(-10 m,100%)
0.E+000.E+00
0 1 2 3 4 5 6 7
Residence time (min)
(+106m,50-60%) (+106m,0-10%)
0.0E+000.0E+00
0 1 2 3 4 5 6 7
Residence time (min)
(-38+28 m,50-60%) (-38+28 m,0-10%)
-9.E-190.E+00
0 1 2 3 4 5 6 7
Residence time (min)
(-10m,50-60%) (-10m,0-10%)
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Results: SC of recovery
Entrainment
2,0
3,0
4,0
ENT)^2
0,04
0,06
0,08
/Rw)^2
Entrainment vs. water recove
0,0
1,0
0,0 0,2 0,4 0,6
(
k
Water Recovery (-)
=0.5 =2 =4.7 =6
0,00
0,02
0,0 0,2 0,4 0,6
(k
Water recovery (-)
ENT=0.05 ENT=0.1 ENT=0.14 ENT=0.3
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Key findings
Intermediate particle size and high liberation
classes reported the highest sensitivity
coefficient values for recovery of galena;
It was found a threshold in the residencetime around 1.2 minutes.
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Implications
Insights into the current PPBM model weaknesses,
not previously addressed;
O ortunit to develo novel strate ies to correct
the use of the model.
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Acknowledgements
Professor T. Napier-Munn, Dr. E. Wightman and
Prof. D. Bradshaw for the technical discussions
Financial support provided by the Julius
The authors would like to acknowledge the
sponsors of the AMIRA P9O project for funding this
research work.
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