M_Free_Peru_2012.pdf

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DEPARTMENT OF METALLURGICAL ENGINEERINGCOLLEGE OF MINES AND EARTH SCIENCES

Improved Modeling of MetalExtraction and Electrowinning

Michael L . Free

Department of Metallurgical Engineering

University of Utah


2/71


Ore leaching has important

application constraints thatneed to be considered to

predict performance


3/71


Importantfactors include

surface

dissolution,product layer

precipitation,

mineralalteration, and

interior

penetration.

host-rock particle

mineral alteration product layer

precipitation product layeracid dissolution of

mineral

Interior penetration


4/71


Valuable Mineral Particle Classification Fully Locked (dominant if the initial size of

valuable mineral particles [vmp] is much

smaller than host rock particles [hrp]) Partially Locked (dominant if the initial size

of valuable mineral particles is similar tohost rock particles)

Liberated (dominant if the initial size ofvaluable mineral particles is much largerthan host rock particles)


5/71


Based on size distributions of

valuable mineral particles and

host rock particles, the

probability for each classification

(fully locked, partially locked, orliberated) can be determined.


6/71


f(r)

rhrp50rvmp50

Partially or

fully locked

valuable

mineralparticle (vmp)

Partially

or fully

liberated

vmp

valuable mineral particle

size distribution

size

Comparison of valuable and host rock particle size distributions

host rock particle

size distribution

hrp size hrp size


7/71


If the selected valuable mineral particle is larger than the host rock particle,the valuable mineral particle is classified as a liberated particle because it

cannot reside within the corresponding host rock particle:

hrpvmp

Liberation probability can be described by:

)(...)2

()2

( hrpvmpvmp

hrpr vmpr

vmphrphrpLib rrforrr

rfrr

rfP


8/71


Classification of particles can be made by picking andcomparing particles from each distribution:

hrpvmp


9/71


The cumulative fraction of particles below a specified size

can be estimated using a cumulative size probability

function such as the Rosin-Rammler function:

)])([exp(1)(*

s

r

rrP

in which r*is the host rock particle reference size at with 62.3 % of the

material passes as undersize, Pis the probability or fraction of generally

liberated particles at the specified r, ris the particle size that is

evaluated, and sis a constant (generally between 1 and 2). Thus, the

fraction of particles between discrete intervals can be estimated by:

rr

rr

r

rr

rrf ss

])))

2(

([exp])

)2

(

(([exp)2

(**


10/71


The fraction of partially locked nonliberated particles is based on the partial

locking zone volume fraction.

)(;)(

13

3

hrpvmp

hrp

vmphrpkPartialLoc rrfor

r

rrP

zone of partial locking

rvmp

host rock particle (hrp)valuable mineral particle (vmp)

hrpr

vmp

r

Locking classification

is based on center

point position of the

vmp relative to rhrp.

When the center ofthe vmp is between

rhrpand (rhrprvmp)

the vmp is classified

as partially locked.

Otherwise, it is fully

locked.

zone of full locking

Canadian Metallurgical Quarterly, 47(3), 277-284, 2008.


11/71


The estimated probability of each classification is found using:

)...]...()(1))][)(exp(1)()(exp(1[ **3

*

**

*

**

*

**

. vmphrp

hr p

vmphron

hr p

hrpvmpn

vmp

hrpvmp

estLockedPartially rrfor

r

rr

r

rr

r

rrP hrpvmp

)))(exp(1)()(exp(*

**

*

**

.hrpvmp n

hrp

hrpvmpn

vmp

hrpvmp

estlibr

rr

r

rrP

).. .))]...()(exp(1)()(exp(1[ **

*

**

*

**

. vmphrp

n

hrp

hrpvmpn

vmp

hrpvmp

estLockedPartially rrforr

rr

r

rrP hrpvmp

).. .]...()())][)(exp(1)()(exp(1[ **3*

**

*

**

*

**

. vmphrp

hrp

vmphron

hrp

hrpvmpn

vmp

hrpvmp

estLockedFully rrforr

rr

r

rr

r

rrP hrpvmp

)......(0 **. vmphrpestLockedFully rrforP


12/71


This approach describes measured exposed mineral well

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 1 10 100

FractionofVal

uableMineral

rhrp/rvmp

Liberated

Part.Lock

Full.Lock

Exposed(calc.)

Exposed(meas)


13/71


Kinetics are determined using weighted models:Liberated Mineral (Pure Mineral Leaching):

Partially Locked Mineral (Pure Mineral Leaching):

Fully Locked Mineral (Shrinking Core Model):

])1(3

21[

23)( 3/2

2

FLFLeffxw

hrpfFLhrp

DCM

rSrt

))1(1()( 3/1libx

vmpRClibvmp

C

rkrt

])1(1[]

)

3

4(

4[)(

3/2

y

libvmpliblibvmp rkrt


14/71


The combined model, based on valuable mineral association withhost rock particles fits measured data reasonably well.

0

0.050.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 500000 1000000

F

ractionR

eacted

Time (sec)

Model pH 1.5

Measured pH 1.5

Model pH 2.5

Measured pH 2.5


15/71


The combined model, based on valuable mineral association withhost rock particles fits measured data reasonably well.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 500000 1000000

Fr

actionR

eacte

d

Time (sec)

Model 820 microns

Measured 820 microns

Model 1420 microns

Measured 1420 microns


16/71


Small scale leaching tests nearly always utilizesmall particles to decrease reaction time.Small particles contain a larger fraction of

material that is liberated or partially locked.Knowing the fraction of material in eachcategory allows for a more correct

determination of the relevant constants that

can then be used to predict leaching usinglarger particles provided that the appropriatemineral distribution information is available.


17/71


What is the effect of comminution on theliberated, partially-locked, and fully-locked

valuable mineral particles?


18/71


Consider a cube of valuable mineral in two locations inside

of a host rock particle


19/71


This estimation method or tool assumes uniform bindingand strength of the valuable and host rock phases.


20/71


3

3

8 )2(D

dP

3

32

4

])2()2([3

D

ddDP

The corresponding sizes and progeny scenario probabilities are:

4 progeny probability with an average of 1/4 of original volume

and (1/4)

1/3

or 0.63 of original size d:

8 progeny probability with an average of 1/8 th of

original volume and 1/2 of original size d:


21/71


3

2

2

])2

1(2[12

D

dDd

P

2480 1 PPPP

2 progeny probability with an average of 1/2 of original volume and

(1/24)1/3or 0.794 of original size d:

0 progeny probability with an average of original size d:

The resulting probability based size represents a reasonable

estimate of the progeny size resulting from fracturing the host rock

particle to one half of its original size.


22/71


The effectiveness of comminution on liberation decreases

rapidly below an initial size ratio of 10 to 1

1

1.1

1.2

1.3

1.4

1.5

1.61.7

1.8

1.9

2

0 20 40 60 80

hrp/v

mpsizereductio

nfactor

(assu

mes50%rhrpred

uction)

initial rhrp/rvmp


23/71


MODELING OF

ELECTROWINNING


24/71


electrons

Anode (+) Cathode (-)

H2O

2H++ 0.5 O2

2e-

2e-

V

M2+

M

Electrowinning is the process of reducing metal by applying a negative potential to an electrode (cathode) on which the

metal deposits by means of a power supply and a counter electrode and the associated reaction(s).

Other

reactions

also occur.

Gas bubbles


25/71


The mass of the deposit is related to

Faradays Law, which can be expressed as:

where Mis the mass of metal deposited, imetalis the

current density associated with the measured metal

deposition (assuming 100 % current efficiency), nis the

number of electrons transferred per mole of metal

reduction, Fis the Faraday constant (96,485 Coulombs

per mole of electrons transferred), andAwis the atomic

weight of the metal that is deposited.

nF

tAAiM cathodewmetal


26/71


Energy Consumption is expressed as:

where Eappliedis the overall voltage applied to the

electrochemical cell.

tEAitIEEnergy appliedcathodecathodeapplied


27/71


Substitution of the equation for mass of thedeposit into the expression for energy

consumption per unit of metal leads to:

metalw

appliedcathode

iA

EnFi


28/71


The current efficiency, , is the ratio of theamount of current theoretically needed to deposit

a unit mass of metal divided by the actual current

consumed at the cathode per unit mass of metal,which can be expressed mathematically as:

cathode

metal

i

i


29/71


Consequently, both voltage and current density

information must be determined to determine theenergy consumption per unit of metal produced.


30/71


Voltage and current information can bedetermined by appropriate application

of thermodynamics, mass transport, and

electrochemical kinetics.


31/71


The general form for chemical equationscan be expressed as:

where vjis the stoichiometric coefficient of the

species,Xis the chemical formula of species j,

zjis the charge of species j, nis the number ofelectrons in half-cell reactions, which must be

written cathodically or as reduction reactions.

j

jz

jjXvne


32/71


Specific equations considered in thisexample include:

23 FeeFe

424

3 FeSOSOFe

24

2

4 SOFeeFeSO

424 HSOSOH

22 HeH

OHeHO 22 244

CueCu

2

2

ZneZn 22


33/71


The free energy of a reaction is expressed

as:

in which R is the gas constant, T is the absolute

temperature, and ajvjis the activity of species j.

The standard free energy of a reaction, Gro, is

expressed as:

j

jv

jorr aRTGG ln

o

jfjj

or GvG


34/71


At equilibrium, the free energy of the reaction equalszero and the equilibrium constant may be used to

represent the equilibrium activity relationship between

the species:

where:

KRTGor ln

j

jvjeq aK


35/71


The activity of an ion in aqueous media can be expressed

as:

The equilibrium electrochemical potential for

each half-cell reaction in the system isdetermined based on free energy using the

Nernst Equation:

jjj ma

jjv

jo

eq anF

RTEE ln

RT

GE

oro


36/71


The rate of each half-cell reaction can be expressed by:

in which iis the current density, a

is the anodic charge transfer

coefficient, Fis the Faraday constant, is the surface overpotential

or the difference between the surface potential (Esurf) and the

equilibrium reaction potential (Eeq), Ris the gas constant, Tis the

absolute temperature, kis constant that is directly related to the

equilibrium exchange current density, Cbis the bulk concentration,

Csis the surface concentration, and is a factor that depends uponreaction mechanisms and related factors and it is usually between

0.25 and 1 and cis the cathodic charge transfer coefficient. :

)]exp()()exp()(['RT

F

C

CC

RT

F

C

CCki cc

bc

scbc

aa

ba

saba


37/71


The transfer of electrons and charge must balance, thusthe system of Butler-Volmer equations that applies to a

given reaction scenario is subject to the constraint that:

When all currents are associated with the same

homogenous surface:

0 I

0

i


38/71


The current density of ion transport consists

of the sum of the ion flux densities of all ions

in the system:

where Njis the flux density of species j, cjis

the concentration of species j and uj, the ion

mobility of species j, is:

jj jjj jjj jjjj jj cDzFczFVcuzEFNzFi

22

RT

Du

jj

jj

r

RTD

6


39/71


The effect of gas generation on solution

conductivity, which is inversely related toresistivity, is often approximated using the

Maxwell equation:

Where k is the conductivity adjustment factor and f is the

void fraction associated with gas generation. In this

investigation the proportionality constant relating current

density associated with oxygen production and voidfraction was determined using experimental data (0.0002

m2/A within the range of 50 to 2000 A/m2for the oxygen

evolution reaction).

21

1

f

f


40/71


Fluid flow can be determined using the Navier-

Stokes equation:

in which is the density of the fluid, Vis the

velocity,pis the pressure, gis the gravitational

acceleration, his height, and is viscosity.

Conservation of mass in fluid flow leads to theequation of continuity:

VhgpVVt

V 2])([

0)(

V

t


41/71


The effect of the auxiliary cathode reactions and shortcircuits on current efficiency can be mathematically

written as:

The corresponding effect on current efficiency is,

therefore:

othermetalcircuitshortauxilliarymetalcathode iiiiii

othermetal

metal

ii

i


42/71


Comparison of measured and predicted data

Table 1: Comparison of model predictions and experimentaldata* for current efficiency and energy consumption for zincelectrowinning (55 gpl Zn, 35oC, 500 A/m2)

H2SO4

Concentration

(gpl)

Predicted

Current

Efficiency

Measured

Current

Efficiency

Predicted

Energy Use

(kWhr/ton)

Measured

Energy Use

(kWhr/ton)

65 98.1 97.4 2730 2912

110 96.1 95.7 2730 2870

155 93.5 93.6 2671 2773

*G. W. Barton and A. C. Scott, Validated Mathematical Model for a Zinc

Electrowinning Cell, J. of Applied Electroch., 22(2), 1992, 104-115.


43/71


Comparison of measured and predicted data

Table 1: Comparison of model predictions and experimentaldata* for current efficiency and energy consumption for zincelectrowinning (55 gpl Zn, 35oC, 500 A/m2) (US$ 0.03/kwhr)

H2SO4Concentration

(gpl)

PredictedCurrent

Efficiency

MeasuredCurrent

Efficiency

Predicted Cost($US/ton)

Actual Cost($US/ton)

65 98.1 97.4 81.90 87.36

110 96.1 95.7 81.90 86.10

155 93.5 93.6 80.13 83.19

*G. W. Barton and A. C. Scott, Validated Mathematical Model for a Zinc

Electrowinning Cell, J. of Applied Electroch., 22(2), 1992, 104-115.


44/71


Energy Use per Ton of Cu versus Current Density

1000

11001200

1300

1400

1500

1600

1700

1800

1900

2000

0 200 400 600 800

Current Density (A/m2)

Energ

yPerMetricTon

(kWhr/ton

Measured

Predicted

42 gpl Cu2+, 160 gpl

H2SO4, 0.06 gpl

Fe3+, and 0.06 gpl

Fe2+at 60oC using a

lead anode in a cell

with electrodes

spaced 1 cm apart.


45/71


Energy Cost per Ton of Cu versus Current Density

42 gpl Cu2+, 160 gpl

H2SO4, 0.06 gplFe3+, and 0.06 gpl

Fe2+at 60oC using a

lead anode in a cell

with electrodes

spaced 1 cm apart.

45

47

49

51

53

55

0 200 400 600 800

Current Density (A/m2)

Electrici

tyCostPerMetricTo

n($US/ton)

Measured

Predicted

(Assumes $0.03 per kilowatt hour)


46/71


Another factor that affects electrowinning performance is the

physical qualities of the cathode such as roughness and

nonuniform deposition. If the cathode has areas of high

growth, short-circuiting may occur, which lowers currentefficiency and requires additional maintenance and personnel

costs. Areas of high growth are often associated with areas

with high rates of deposition. Some of these effects can be

determined by appropriate modeling as well as by control ofsurface roughness.


47/71


Electrodeposit roughness has a substantialimpact on the properties of the deposited film

or the crystals that are harvested from

cathodes

Rough deposits can lead to short circuiting in

electrolysis or entrapment of electrolyte or

gasses.


48/71


Electrodeposit roughness is generallycontrolled by:

Initial Surface Topography

Coating Thickness

Nucleation

Growth


49/71


substrate

Height from low

to high point

Original nucleus

Low nucleus density results

initially in rough surfaces

High nucleus density results

initially in smoother surfaces

Roughness on smooth surfaces is a

function of nucleation and growth.

growth

Initial surface roughness is reduced by higher nucleus density


50/71


Nucleation and growth are the resultof the electrochemical and physical

properties that can be described

using thermodynamics,

electrochemical kinetics, ion

transport, fluid flow, and nucleation

equations.


51/71


Effect of mass transportFor mass transport controlling the current flow inthen the expression for the diffusion controlled

deposition rate, iLis

iL=nFDCb/

where iLis the diffusion controlled deposition rate (Amp/area),

F is Faraday constant,

n is the number of electrons transferred,D is the diffusivity of the reacting species,

is the thickness of the diffusion boundary layer

Cbis the bulk concentration.


52/71


Often, the combination of diffusion and electrochemical kinetics

are sufficient to predict electrochemical reaction rates


53/71


The closer the deposition current is to themass transport limited current density understeady-state conditions, the closer the

surface concentration of depositing speciesapproaches zero. As the surface

concentration approaches zero, the lower theNernst Potential becomes and the greater therequired applied potential becomes to beginnucleation. Consequently, as i/ilapproaches

one, it becomes difficult to initiate newnuclei, thereby increasing the tendency for

growth from limited nuclei.


54/71


ion flux lines ion flux lines

asperity asperity

Under mass transport controlled electrodeposition, surface asperities receive

more of the available flux of depositing ions than areas between asperities.Consequently, asperities grow faster than other areas. As the asperities grow

rapidly and nuclei initiate and grow on the asperities, dendritic, granular

deposits become the dominant morphology.


55/71


Nucleation and Growth are OftenPartially Controlled Using Additives:

A balance between activators, inhibitors, and

modifiers or smoothing agents is often used tocontrol electrodeposit morphology.

Smoothing agents often consist ofmacromolecules.


56/71


Base solution: 0.1 M CuCl, 4 M NaCl, and 0.01 M HCl

Experiment condition:i = -15 mA/cm2, 1,000 RPM, and deposition time = 15 hours

a) no additive b) 0.013 g/L gelatin

The colors indicate the height of the copper deposit.

Using organic additives to obtain smooth copper electrodeposits

from halide media.


57/71


0

10

20

3040

50

60

70

8090

100

0 0.5 1

RSMRoughness(m)

i/iL

no additivegelatin 0.1% by volume

Q = 6000Coulombs/cm2

Comparison of RMS roughness and i/ilvalues for electrodeposits (6000

Coulombs per centimeter squared) obtained from a bath containing 0.1

mol/L CuCl, 4.0 mol/L NaCl and 0.01 mol/L HCl under direct current

conditions 25 mA/cm2).
http://www.utah.edu/


58/71


Department of Metallurgical Engineeri ng, University of Utah

Nucleation is Controlled by: Species Concentrations

Applied Potential Substrate Properties

N l ti
http://www.utah.edu/http://www.utah.edu/


59/71


Nucleation

The steady-state nuclei formation rate can be described

mathematically by the equation:

2exp

formation

s

dNN

dt T

where Nformationis the number density of new nuclei, tistime, Nis the baseline rate of nuclei formation, is aconstant (and Nare functions of valence, geometry,surface energy, and frequency of attachment and

detachment), Tis temperature, sis the surfaceoverpotential. (R. T. C. Choo, J. M. Toguri, A. M El-Sherik, U.Erb,J.Appl.Electrochem., , 384, (1995). E. B. Budevski, in Comprehensive Treatiseof Electrochemistry, Vol. 7, B. E. Conway, J. OM. Bockris, E. Yeager, S. U. M.

Khan, and R. E. White, Editors, Plenum, New York, p. 441, 1983.)


60/71


Copper nucleation on chloride media on copper

Solution:Base solution with 0.1 % by volume Gelatin

Experiment condition: Stationary copper electrode, 1 sec deposition

microns

m

icrons

0 155

3

0.1

0.2

0.3

0.4

0.5

microns

m

icrons

0 155

103

0.1

0.2

0.3

0.4

0.5

0.6

0.7

a) 100 mV below OCP b) 200 mV below OCP

103

OCP = open circuit potential

Effect of gelatin concentration on RMS Roughness


61/71

0

5

10

15

20

25

30

35

0 0.2 0.4 0.6 0.8 1 1.2

% by volume gelatin

RMS

Roughness(m

)

Effect of gelatin concentration on RMS Roughness

The surface morphology remains almost the same when the gelatin

Concentrations are in the range of 0.01 to 1% by vol.

Solution:Base solutionExperiment condition:i = -25 mA/cm2, 3 hours plating, and 1000 RPM



62/71

Gelatin chemistryTypical structure:

-Ala-Gly-Pro-Arg-Gly-Glu-4Hyp-Gly-Pro-

Descriptions:

preparing by the thermal denaturation of collagen,

containing between 300 - 4000 amino acids.

containing approximately 33% glycine, 22% proline and 11% hydroxyproline

11% glutamic acid, 11% arginine, and 11% alanine.



63/71


Effect of amino acids

0

5

10

15

20

25

3035

40

0 0.02 0.04 0.06 0.08 0.1 0.12

Concentration (Molarity)

RMSRoughness(m)

Glycine

Proline

Solution:Base solutionExperiment condition:i = -25 mA/cm2, 3 hours plating, and 1,000 RPM

Glycine and proline do not significantly smoothen the surface

morphology as separate entities.



64/71


Assumptions:

1) spherical shape additive molecules.2) depositing ions access to the surface via pore area between the additive molecules

not through the additive molecules.

Hence, the diffusion through the pore area between the adjacent molecules is used to evaluate the effect of

the polymeric additives in electrodeposit nucleation.

Effective

adsorbate

layer

Effective

adsorbate

layer

Deposition surface

Effective

pore

M+ M+ M+

Side view

3 additive molecules

Top view

additive

additive additive

Depositing ions

Depositing ions

Depositing ions

Effect of additive sizes on nucleation rate density


65/71


View of Unit Cell of Macromolecules or Spheres

Top view of Ions diffusing through a pore between additive

molecules or nanoparticles on an electrode that have movedapart by diffusion during the time needed by the depositing

ions to diffuse to the surface

Additive orparticle DepositingionsDepositing

ions

Additive or

particle

Additive or

particle

Unit cell length

(2r +(2Dt)0.5)

Relevant equations


66/71


Relevant equations

electroactD

rt 2

2

Simultaneous solution of these equations can be performed to determine

the effects of adsorbate molecules on surface nucleation.

Finding Cs

Knowing Cs helps to find s

Obtaining relative nucleation rate density

a nat.rxnp c nat.rxnpspore o

b

F(E-E ) - F(E-E )Ci = i [exp( )-exp( )]

C RT RTPoreEst

Appl Pore

tot

Ai =i

A2

ads ads

poreEst ads

r 3r+(r+ 2D t )( 3(r+ 2D t ))-rA = ;..for( 2D t


67/71


Molecular weights can confine the plating so that

the nucleation rate density increases at a reasonable size.

Theoretical values vs. Experimental values

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300

Effective Adsorbate Radius (nm)

RelativeNuc

leationRateDensity

Theoretical Values

Experimental Values SiO2

Experimental Values PEG &PEO

Deposit Morphology Modeling (effect of fluid flow and current)


68/71


68

Arrows

represent

local fluid

velocityvectors.

Colors

represent

depositing

species

conc.

White

above the

thin darklower line

represents

the deposit.

Modeled using Comsol Multiphysics Software with significant modifications

Deposit Morphology Modeling (effect of fluid flow and current)


69/71

69Modeled using Comsol Multiphysics Software with significant modifications

Arrows

represent

local

currentvectors.

Colors

represent

depositing

species

conc.

White

above the

thin darklower line

represents

the deposit.

Axis

values

are in

cm

2 5


70/71

Comparison of RMS roughness and i/ilvalues for predicted and

measured results. Predictions were based on a solution obtained using

the previous equations associated with copper electrodeposits obtained

from a bath containing 0.1 mol/L CuCl, 4.0 mol/L NaCl and 0.01 mol/L HCl

under direct current conditions.

0

0.5

1

1.5

2

2.5

0.00 0.20 0.40 0.60 0.80

i/iL

RM

SROUGHNES

S(m) EXPERIMENTAL DATA

MODEL PREDICTION


71/71


Improved methods of modeling

provide tools to more appropriately

include natural phenomena inpredictions that can be used to

optimize performance of metal

extraction and electrowinningoperations

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