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

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(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


(-38+28 m,100%)

0.E+00

0 1 2 3 4 5 6 7


(-10 m,100%)

0.E+000.E+00

0 1 2 3 4 5 6 7


(+106m,50-60%) (+106m,0-10%)

0.0E+000.0E+00

0 1 2 3 4 5 6 7


(-38+28 m,50-60%) (-38+28 m,0-10%)

-9.E-190.E+00

0 1 2 3 4 5 6 7


(-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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Gerson Sandoval Zambrano

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