ra

de C

HydrometallurgySimulation

nt Eg cmaConucti

in a stripping stage of a copper plant. The model includes a non-trivial settler hydrodynamics represented

mandcoppelvent

For example, uncontrolled organic and aqueous ow-rates maycause inefcient phase separation, leading to entrainment and pro-cess instability. These, in turn, reduce cathodes quality, increasethe consumption of valuable chemicals, contaminate the electro-lyte solutions, cause premature corrosion of expensive anodesand increase organic phase losses. Additionally, copper concentra-tion and pH are usually sampled and regulated manually by oper-ators. Since the samples are analyzed in the laboratory, taking 4 h

effectively to develop and test estimation and control strategiesbefore they are implemented on-line, reducing the risks ofcatastrophic operational events, and the time and costs ofdevelopment.

Despite that several SX process models have been presented inthe literature, many of them are steady state or either too simple torepresent realistic industrial data or too complex to calibrate.Moreover, there are still many phenomena in SX processes thatare not well understood. For example, Van Bochove et al. (2000)developed a thermodynamic model that predicts exactly the iso-therms of equilibrium. However, this model is very complex and

* Corresponding author. Tel.: +56 3544258; fax: +56 3545803.

Minerals Engineering 22 (2009) 13501358

Contents lists availab

n

elsE-mail address: perez@ing.puc.cl (J.R. Prez-Correa).winning circuit (LXSXEW) (see Fig. 1) is one of the most effectiveprocesses for this purpose. In this work, we focus on the liquidli-quid extraction SX process, since many of the difcult to handleoperational problems within this circuit are related to SX malfunc-tion. Critical problems normally found in SX plants, which have aconsiderable impact in extraction efciency and selectivity, are:crud formation, organic and aqueous phase entrainments, and var-iable and unpredictable phase separation times in the settlers(Bergh and Yianatos, 2001).

this process.Consequently, on-line measurement of copper concentrations

in the main process streams together with an effective automaticcontrol strategy, should stabilize the process, improve cathodesquality and homogeneity, and reduce operational costs. Unfortu-nately, it is not possible to measure on-line copper concentrationswith affordable and reliable instrumentation. In addition, it isexpensive and risky to develop and test control strategies directlyin the process plant. Alternatively, dynamic simulation can be used1. Introduction

Due to increasing copper world detive to apply different processes tograde ores. The copper Leaching, So0892-6875/$ - see front matter 2009 Elsevier Ltd. Adoi:10.1016/j.mineng.2009.09.003by a set of nonlinear differential equations for both mixer and settler units. The mixer is modelled as acontinuous stirred tank reactor and the settler as a hydrodynamic circuit combining series and parallelconnections of continuous stirred tank and plug ow reactors. The model was calibrated with industrialplant data, resulting in realistic simulations of outlet copper concentrations. Using the proposed model,we obtained better tting than that achieved with simpler settler models that include only a time delay.The model tting parameters provide sufcient exibility to accurately reproduce the dynamics of differ-ent units in industrial plants.

2009 Elsevier Ltd. All rights reserved.

, there is a strong incen-r extraction from lowExtraction and Electro-

in average, it is not surprising that process regulation is poor. As aresult, strong disturbances are unavoidable and many of themmaypass unnoticed and uncontrolled for at least 4 h. Hence, it can beargued that many of the SX operational problems are related tothe lack of effective monitoring and control systems specic forKeywords:Extractive metallurgy

and assess more effective control strategies. In this work we present a general dynamic model for SXmixersettlers, and applied it to two different units, one located in an extraction stage and the otherDynamic modelling of copper solvent ext

C.M. Moreno a, J.R. Prez-Correa a,*, A. Otero b

aDepartment of Chemical and Bioprocesses Engineering, Ponticia Universidad CatlicabMining Centre, Ponticia Universidad Catlica de Chile, Casilla 306, Santiago 22, Chile

a r t i c l e i n f o

Article history:Received 30 January 2009Accepted 4 September 2009Available online 7 October 2009

a b s t r a c t

The copper Leaching, Solvetive processes for extractintion SX sub-process, sincerelated to SX malfunction.recovery and copper prod

Minerals E

journal homepage: www.ll rights reserved.ction mixersettler units

hile, Casilla 306, Santiago 22, Chile

xtraction and Electrowinning circuit (LXSXEW) is one of the most effec-opper from low grade ores. This work focuses on the liquidliquid extrac-ny difcult to handle operational problems within LXSXEW circuits aretrolling these problems better can reduce operational costs and increaseon. Realistic dynamic simulation is a standard tool nowadays to design

le at ScienceDirect

gineering

evier .com/ locate/mineng

Nomenclature

A extraction equilibrium isotherm parameter (g L1)a1A aqueous active zone fraction of rst CholetteCloutier

unita1O organic active zone fraction of rst CholetteCloutier

unita2A aqueous active zone fraction of second CholetteClou-

tier unit

C.M. Moreno et al. /Minerals Engina2O organic active zone fraction of second CholetteCloutierunit

B extraction equilibrium isotherm parameter (g L1)b1A aqueous dead zone fraction of rst CholetteCloutierrequires a great deal of specic experimental information, not nor-mally found in an industrial environment. Using simple isothermscalibrated with plant data, Aminian et al. (1998) obtained good

unitb1O organic dead zone fraction of rst CholetteCloutier unitb2A aqueous dead zone fraction of second CholetteCloutier

unitb2O organic dead zone fraction of second CholetteCloutier

unitf plug ow fraction of slow owing branchC stripping equilibrium isotherm parameterD stripping equilibrium isotherm parameter (g L1)KE extraction mass transfer coefcient (h1)KS stripping mass transfer coefcient (h1)Qai aqueous mixer inlet owrate (m3 h1)QAL aqueous owrate in slow ow branch in settler (m3 h1)Qam aqueous mixer outlet owrate (m3 h1)QAUi aqueous owrate in ith CSTR outlet in fast ow branch

in settler (m3 h1)Qoi organic mixer inlet owrate (m3 h1)QOL organic owrate in slow ow branch in settler (m3 h1)Qom organic mixer outlet owrate (m3 h1)QOUi organic owrate in ith CSTR outlet in fast ow branch in

settler (m3 h1)VAL1 aqueous volume of rst CholetteCloutier unit (m3)VAL2 aqueous volume of second CholetteCloutier unit (m3)Vam aqueous volume in mixer (m3)VAUi aqueous volume of ith CSTR (m3)VOL1 organic volume of rst CholetteCloutier unit (m3)VOL2 organic volume of second CholetteCloutier unit (m3)Vom organic volume in mixer (m3)VOUi organic volume of ith CSTR (m3)VS settler volume (m3)X* aqueous equilibrium copper concentration (g L1)Xi aqueous inlet copper concentration (g L1)XaL1 aqueous copper concentration in active zone of rst

CholetteCloutier unit (g L1)XbL1 aqueous copper concentration in dead zone of rst Cho-

letteCloutier unit (g L1)

Fig. 1. Typical LXSXEW copper plant.XaL2 aqueous copper concentration in active zone of secondCholetteCloutier unit (g L1)

XbL2 aqueous copper concentration in dead zone of secondCholetteCloutier unit (g L1)

Xm aqueous copper concentration in mixer (g L1)XP time delayed aqueous copper concentration in slow

ow branch (g L1)XST aqueous equilibrium copper concentration in stripping

stage (g L1)XUi aqueous copper concentration in ith CSTR in fast ow

branch in settler (g L1)

eering 22 (2009) 13501358 1351predictions of the steady states of a test SXEW plant. The mixerwas modelled as an ideal continuous stirred tank reactor, hereinaf-ter, CSTR, and the settler as two compartments in parallel, an idealplug ow and an ideal CSTR. Using a more elaborated steady statemodel, Pinto et al. (2004) improved the conguration of an SX Cuplant applying multi-objective optimization. They included chem-ical reaction kinetics and a non-ideal hydrodynamics in the mixersettler units. Then a multi-variable optimizing objective functionwas dened that considered equipment geometry, residence timeand agitator speeds, among other design parameters. The optimi-zation yielded the optimum unit and plant design, which can beapplied for the design of new plants, or for improving existing de-signs. In spite of being extremely useful in SX plant design, thatmodel cannot be used to develop and test control systems.

Only dynamic models are useful to design control strategies bysimulation. Most of these models presented in the literature

Y* organic equilibrium copper concentration (g L1)Yi organic inlet copper concentration (g L1)YaL1 organic copper concentration in active zone of rst Cho-

letteCloutier unit (g L1)YbL1 organic copper concentration in dead zone of rst Cho-

letteCloutier unit (g L1)YaL2 organic copper concentration in active zone of second

CholetteCloutier unit (g L1)YbL2 organic copper concentration in dead zone of second

CholetteCloutier unit (g L1)Ym organic copper concentration in mixer (g L1)YP time delayed organic copper concentration in slow ow

branch (g L1)YST organic equilibrium copper concentration in extraction

stage (g L1)YUi organic copper concentration in ith CSTR in fast ow

branch in settler (g L1)eE extraction stage organic copper concentration steady

state gradient (g L1)eS stripping stage aqueous copper concentration steady

state gradient (g L1)gE extraction efciency coefcientgS stripping efciency coefcientuA fraction of aqueous solution owing by slow ow

branch in settleruJ fraction of organic solution owing by slow ow branch

in settlerk1A aqueous exchange rate between zones in rst Cholette

Cloutier unitk1O organic exchange rate between zones in rst Cholette

Cloutier unitk2A aqueous exchange rate between zones in second Cho-

letteCloutier unitk2O organic exchange rate between zones in second Cho-

letteCloutier unit

include simple thermodynamics and rate expressions, where mostof the complexity is lumped into the hydrodynamics of the settler.An example of this is the mixersettler cascade model for rareearths of Wichterlov and Rod (1999). Here, the hydrodynamicswere modelled as a series of CSTRs. However, this model is not thatuseful to design control systems since it is too simple, not able toreproduce the complex dynamics observed in real plants. Wilkin-son and Ingham (1983) and Ingham et al. (2007) modelled the mix-er as a CSTR, but included entrainment factors in the outletstreams. Furthermore, the settler was modelled as two parallelcompartments, just as in the Aminian model. Although this is an

outlet loaded organic solution (LO) from the extraction stage, is

Mass transfer in the settler is signicantly lower than in themixer, therefore mass transfer is considered only in the mixer

concentrations in the aqueous and organic phases in the mixer,

1352 C.M. Moreno et al. /Minerals Enginmixed in the stripping stage with the lean electrolyte (LE) streamcoming from the electrowinning process. Since there is a differentpH in the stripping stage, copper transfers now from the organicphase to the aqueous phase. Then, the outlet aqueous stream fromthe stripping stage, rich electrolyte (RE), goes to the electrowinningstage, where copper is extracted in cathodes, bringing the leanelectrolyte back to the loop.

In this work we developed a general dynamic model for mixersettlers and t it to two different units, one in the multi-unitsextraction stage and the other in the multi-units stripping stageof an SX process of a LXSXEW copper plant from Molymet S.A.,similar to that shown in Fig. 1. Although, this plant, with an annualproduction of 1 million lb of copper, is rather small compared toother industrial mining facilities.improvement over Wichterlov and Rod model, no comparisonwith industrial data has been presented so far. Komulainen et al.(2006) presented a dynamic model of a SX Cu process calibratedwith plant data, however, the settler is modelled simply as a delay.Hence, even though the model described the SX process dynamicswell, it will probably be difcult to t that model to other plantswith more complex behaviour.

Here, we present a exible SXCu unit model, able to reproducethe complex dynamics observed on any stage at any industrialplant. The model includes McCabeThiele specic diagrams andcomplex settler hydrodynamics. The model considers variablesnormally measured at industrial facilities and simulates the dy-namic response of copper concentrations in both phases in the out-let streams.

2. Process model

Fig. 1 (Jackson, 1986) describes a standard LXSXEW industrialplant. Leaching (LX) is the rst stage, where copper is extracted bywashing the ore with an acid aqueous solution (SX rafnate). Theoutlet stream of LX, the pregnant liquid solution (PLS), is the inletstream to the rst stage of the SX process (extraction). In this stage,the PLS stream is mixed with the barren organic solution (BO), i.e.,the outlet stream of the second SX stage (stripping), to selectivelytransfer copper from the aqueous phase to the organic phase. TheFig. 2. Flow diagram of a mixersettler unit.respectively, KE and KS are the copper mass transfer coefcients inthe extraction and stripping units (subindex E stands for extractionand S for stripping).

XS and YE are pseudo-equilibrium copper concentrations de-

ned by empirical equilibrium isotherms (X* or Y*) and extractionefciencies (gE or gS) (Wilkinson and Ingham, 1983).

YE 1 gEYi gEY 7XS 1 gSXi gSX 8

2.1.2. Settler balancesA non-ideal ow (see Fig. 3) for both phases was used to model

the hydrodynamics in this tank (Ingham et al., 2007). The basicmodel assumes that the solution is split into two streams, one thatmoves fast (fraction 1 u) and the other that moves slowly (frac-tion u). The fast moving stream, represented by the upper branch(Wilkinson and Ingham, 1983). Equilibrium isotherms dene composition gradients for masstransfer (Steiner and Hartland, 1983).

Perfect mixer (Wilkinson and Ingham, 1983). Entrainments only occur in the settler (Aminian et al., 1998). Settler modelled with non-ideal hydrodynamics (Ingham et al.,2007).

Constant density.

2.1.1. Mixer balancesApplying total mass balances (see Fig. 2) to both, aqueous and

organic phases in the mixer tank, yield,

dVAmdt

QAi QAm QOm VAm VOm VAm 1

dVOmdt

QOi QAm QOm VAm VOm VOm 2

copper balances differ if the tank is in an extraction or in a strippingstage. For an extraction unit,

dXmdt

QAiVAm

Xi Xm KEYE Ym 3dYmdt

QOiVOm

Yi Ym KEYE Ym 4

and for a stripping unit,

dXmdt

QAiVAm

Xi Xm KSXS Xm 5dYmdt

QOiVOm

Yi Ym KSXS Xm: 6

In these equations, QAi and QOi are the aqueous (subindex A) and or-ganic (subindex O) mixer inlet owrates, VAm and VOm are the aque-ous and organic volumes in the mixer, Xm and Ym are the copper2.1. Mass balances

The model was obtained by applying independent copper andtotal mass balances on the mixer and the settler (Fig. 2) underthe following assumptions:

eering 22 (2009) 13501358(subindex U) in Fig. 3, is modelled by N perfectly mixed tanks con-nected in series. Then, in the upper branch, the aqueous phase cop-per balances are,

QA1,X1

VUAN

a1AVL1A

XL A

QAL1

X AQAL1

b1

X

a2AVL2A

A

QAUN

XUN

ode

ngineering 22 (2009) 13501358 1353i 1dXUidt

1uAQAmVAUi

Xm XUi 9i 2 . . .NdXUidt

QAUi1VAUi

XUi1 XUi 10

and the organic phase copper balances are,

i 1dYUidt

1uOQOmVOUi

Ym YUi 11i 2 . . .NdYUidt

QOUi1VOUi

YUi1 YUi 12

In turn, the slowly moving stream, represented by the lowerbranch in Fig. 3 (subindex L), is modelled as a plug ow tank in ser-ies with two CholetteCloutier units (Aminian et al., 1998). Each ofthese consists of two perfectly mixed zones, an active (top) and adead one (bottom). Total and copper balances for both phases inthe plug ow tank are,

QALt uAQAmHt sAL 13

(1-A1) QAm1

Xm1

QAm1,Xm1

VUA1

QAL1

XP1

1AQAL1

A1QAm1Xm1

AL

Fig. 3. Hydrodynamic model of aqueous solution in the settler; the hydrodynamic mcopper concentrations Y instead of X.

C.M. Moreno et al. /Minerals EXPt XmHt sAL 14QOLt uOQOmHt sOL 15YPt YmHt sOL 16

Here, H is the Heaviside step function, which represents a timedelay. Copper balances for both phases in the two CholetteClou-tier units are given by,

dXaL1dt

QALa1AVAL1

XP k1AXbL1 1 k1AXaL1

17

dXbL1dt

k1AQALb1AVAL1

XaL1 XbL1

18

dXaL2dt

QAL1a2AVAL2

XaL1 k2AXbL2 1 k2AXaL2

19

dXbL2dt

k2AQAL1b2AVAL2

XaL2 XbL2

20

dYaL1dt

QOLa1OVOL1

YP k1OYbL1 1 k1OYaL1

21

dYbL1dt

k1OQOLb1OVOL1

YaL1 YbL1

22dYaL2dt

QOL1a2OVOL2

YaL1 k2OYbL2 1 k2OYaL2

23

dYbL2dt

k2OQOL1b2OVOL2

YaL2 YbL2

24

Therefore, the nal copper concentration at the exit of the set-tler is a weighted sum of both outlet branches,

X uAXaL2 1uAXUN 25Y uOYaL2 1uOYUN 26In these equations, a stands for active zone, b stands for dead zoneand k stands for exchange rate between zones.

2.2. Constitutive equations

2.2.1. EquilibriumThe equilibrium isotherm in an extraction unit (see Eq. (7)) is

given by (Komulainen et al., 2006),

Y AX

X B 27

A and B are empirical coefcients tted with process measurementsand extractant manufacturer data as follows:

1 L2xL1A

1AQAL1AVL1A

L1B

XL2

b2AVL2A

XL2B

1AQAL1

l for the organic solution is the same, but with sub-indexes O instead of A, andA a ML 28

B 10pH b

PLS

MLcd Cu2h i

PLS f Cu2

h iBO

29

where ML is the maximum load (g L1) of Cu in the organic stream(extractant manufacturer data), and pH and [Cu+2] are daily aver-aged off-line measured values. In these equations, a, b, c, d and fare tting parameters (see Table 1).

Table 1Isotherm tting parameters.

Parameters Values

a 0.99b 1.02c 1.01d 35.15f 27.15g 0.11h 444.49m 0.10n 0.81p 8.91

Similarly, for the stripping isotherm (see Eq. (8)) (Komulainenet al., 2006),

Y C X D 30C g ML 31

D h vol:%m

H2SO4 nLE p 32

where vol.% is the % v/v of reactant in the organic and [H2SO4]LE isthe free acidity of the lean electrolyte (g L1); g, h,m, n and p are t-ting parameters (see Table 1). Variables involved in Eqs. (28)(32)were measured from common shift samples in the laboratory bychromatography (see Table 2). Fig. 4a shows daily averages of calcu-lated isotherm parameters A, B, C and D. Further details regardingtting isotherm parameters are given in Appendix A.

2.2.2. Mass transferIn this study, the extraction rate is modelled by a mass transfer

expression obtained from the interface theory (Jackson, 1986),

KE QAiVAmXi XmYE Ym

QAiVAm

Xi XmeE

33

KS QOiVOmYi YmXS Xm

QOiVOm

Yi YmeS

34

In these equations, the steady state copper concentration gradients(eE YST Ym for an extraction unit and eE XST Xm for a strip-ping unit) are tting parameters (Komulainen et al., 2006). Copperconcentrations in Eqs. (33) and (34) (Xi, Yi, Xm, Ym) were measured

in the laboratory by chromatography from shift samples (see Table2). Fig. 4b shows daily averages of calculated KE and KS coefcients.

2.2.3. EfcienciesEfciencies for both, extraction and stripping units, are dened

by,

gE eE Ym Yi

Y Yi 35

gS eS Xm Xi

X Xi 36

Table 2Measured variables in LXSXEW copper plant.

Measured variables Sampling time (h) Symbols

InputsAqueous inlet owrate 1 Qai[Cu+2] aqueous inlet 1 XiOrganic inlet owrate 1 Qoi[Cu+2] organic inlet 1 YiMixer volume 1 VmSettler volume 1 VspH of PLS 1 pHPLSFree acidity of the lean electrolyte 1 [H2SO4]LE

OutputsVolumes of phases in mixer (i = A, O) 1 VimFlowrates at mixer exit (i = A, O) 1 Qim[Cu+2] in aqueous phase at mixer exit 1 Xm[Cu+2] in organic phase at mixer exit 1 Ym

1.2

es

(a)

672 840 1008 1176 1344t (h) E S

672 840 1008 1176 1344

1354 C.M. Moreno et al. /Minerals Engineering 22 (2009) 13501358-1.2

-0.4

0.4

0 168 336 504

Scal

ed v

alu

-1.20

-0.20

0.80

1.80

0 168 336 504

K (s

cale

d)

(b)

-0.60

-0.30

0.00

0.30

0 168 336 504

(sc

aled

)

(c)Fig. 4. Calculated model parameters: (a) Isotherm param672 840 1008 1176 1344

t (h) A B C Dt (h) E S

eters. (b) Mass transfer coefcients. (c) Efciencies.

In the mixers, Ym and Xm are the outlet copper concentrations, Yiand Xi are the inlet concentrations, and Y* and X* are the equilib-rium concentrations. Fitting parameters, eE1 and eS1, were set bytrial and error to minimize the sum of squared errors between sim-ulated and measured outlet copper concentrations. Note that anefciency 1 means that the respective steady state copper concen-tration gradient is 0; hence, YE Y or XS X. Fig. 4c shows dailyaveraged calculated efciencies. In these calculations, copper con-centration values averaged every 8 h in the laboratory by chroma-tography, were used. Nomenclature provides a completedescription of the symbols used.

Simulations were performed with Simulink software, usingcalculated model parameters (shown in Fig. 4) updated daily, inputvariables (shown in Fig. 5) measured hourly, and main modelparameters (see Table 3) which were xed during the whole sim-ulation run (56 days). Flowrates and pH were measured on-line

with magnetic owmeters (Siemens MAG 3100) and standardpH-meters, respectively. Copper and acid concentrations weremeasured in the laboratory by chromatography. In the actual pro-cess at Molymet S.A., inlet copper concentration standard devia-tions ranged between 1 and 2 g L1, owrates between 0.03 and0.3 m3 h1, and pH varied between 0.8 and 1.8. To keep conden-tiality, no further process details can be disclosed.

3. Results and discussion

First, a parameter sensitivity analysis was carried out to aidmodel calibration. After calibration, i.e., setting model parametersat xed values, simulations were compared with measured outputsof the actual process, shown in Fig. 6. The same analysis was car-ried out for both extraction and stripping units.

-4.8

0.0

4.8

9.6

0 168 336 504 672 840 1008 1176 1344t (h) PLS LE

(a)

-2.8

-1.4

0.0

1.4

0 168 336 504 672 840 1008 1176 1344

Y(sc

aled

)

t (h) BO LO

(b)

-0.08

0.08

A(s

cale

d)

t

(c)

t (

X (s

cale

d)

C.M. Moreno et al. /Minerals Engineering 22 (2009) 13501358 1355-0.40

-0.24

0 168 336 504

Q

-0.03

-0.01

0.01

0.03

0 168 336 504

QO

(sca

led)

(d)Fig. 5. Scaled measured input variables: (a) Copper concentration in aqueous inlet streamOrganic inlet owrate.672 840 1008 1176 1344h) BO LO672 840 1008 1176 1344 (h) PLS LEs. (b) Copper concentration in organic inlet streams. (c) Aqueous inlet owrate. (d)

Table 3Model parameters for extraction unit (E) and stripping unit (S). Sub-indexes A and O stand for aqueous and organic phases, respectively. CC stands for CholetteCloutier units.

Parameters Symbols Nominal values (E) Nominal values (S) Units

Fitting parametersFraction of plug ow in lower branch f 0.3 0.4 Steady state concentration gradient eE 0.7 1.9 g L1

Fraction going through lower branch (i = A, O) ui 0.8 0.9 Fraction in CC units active zones (i = 1, 2; j = A, O) aij 0.6 0.7 Exchange rate between CC zones (i = A, O; j = 1, 2) kij 1.8 1.3 Number of upper branch CSTR tanks N 2.0 2.0

Calculated from tting parameters (see Appendix A)Upper branch CSTR volume (i = A, O; j = 1, N) ViUj 5.3 2.7 m3

Plug ow residence time (i = A, O) sLi 0.9 1.3 hVolume of CC units (i = A, O; j = 1, 2) ViLj 14.2 14.3 m3

Fraction of dead volume in CC units (i = 1, 2; j = A, O) bij 0.4 0.3

-0.90

0.10

1.10

2.10

0 168 336 504 672 840 1008 1176 1344

t (h) Simulated-E Measured-E

(a)

-0.35

0.05

0.45

0.85

0 168 336 504 672 840 1008 1176 1344t (h) Simulated Measured

(b)

-0.90

0.10

1.10

2.10

0 168 336 504 672 840 1008 1176 1344

t (h) Simulated-S Measured-S

(c)

-1.00

-0.60

-0.20

0.20

0 168 336 504 672 840 1008 1176 1344t (h) Simulated-S Measured-S

(d)

X (s

cale

d)Y

(sca

led)

X (s

cale

d)Y

(sca

led)

Fig. 6. Simulated vs. measured output variables: (a) Copper concentration in aqueous extraction outlet stream. (b) Copper concentration in organic extraction outlet stream.(c) Copper concentration in aqueous stripping outlet stream. (d) Copper concentration in organic stripping outlet stream.

1356 C.M. Moreno et al. /Minerals Engineering 22 (2009) 13501358

6t

settl

ngin3.1. Sensitivity analysis

The impact of changing model parameters in the simulation ofoutput variables was assessed. We were particularly interested indetecting high impact parameters that could then be used to tthe model to reproduce actual process outputs. Starting from anominal case, dened by arbitrarily assigned values of input vari-ables and model parameters, the model was simulated severaltimes applying one step change at a time in a given parameter.By trial and error, we found that for both units (extraction andstripping), the split fractions, us, and steady state copper concen-tration gradients, es, were high impact parameters. Therefore, theywere used to calibrate the model for the extraction and the strip-ping units, running a large number of trial and error simulations.The rest of model parameters, since they did not affect much sim-ulation results, were dened after few simulations. The nal modelparameter values are given in Table 3.

3.2. Comparing simulations with measured values

Fig. 6 shows simulated model outputs compared with plantcopper concentration measurements in both phases. It can be seenthat good agreement between simulations and measurements hasbeen achieved for both units. For the extraction unit, relative meansquared errors for the outlet stream copper concentrations were0.03% for the aqueous phase and 6.76% for the organic phase. Inturn, for the stripping unit, relative mean squared errors were0.07% for the aqueous phase and 2.89% for the organic phase. Thesedifferences in the observed errors are probably due to inherentsampling and laboratory measurements variability. For example,measurement errors in the organic phase are larger. In addition,the extraction unit shows much more variability than the strippingunit, which is expected since its feed comes directly from the heapLeaching stage. In turn, this variability is attenuated at the outlet ofthe stripping unit due to the damping effect of the mixing tanks.

-0.35

0.05

0.45

0.85

0 168 336 504

Y (s

cale

d)

Fig. 7. Comparison between our model and a simplied pure delay

C.M. Moreno et al. /Minerals EDespite this difference, the model is exible enough to reproducethe dynamics of both units well. Furthermore, we compared theperformance of our model against a simple delay model (repre-sented as a plug ow) for the settler. The simpler model performsmuch worse, yielding a relative mean square error of 15.0% for theaqueous phase (not shown) and 44.8% for the organic phase (seeFig. 7). Consequently, it is highly benecial to model the settlerwith a more complex hydrodynamic model.

Fig. 4 also shows interesting features, like the extreme variationof the estimated mass transfer coefcients and efciencies. For in-stance, the signicant drop in the efciency (see Fig. 4c) of theextraction unit can be attributed to an operational problem andmay be useful to identify its cause. Hence, the model can be renedmore by associating mass transfer and efciencies with specicoperational problems like entrainment, crud formation and vari-able phase separation times. These would be highly desirable toimprove process supervision by alerting process engineers earlier,The developed model is a relatively simple form to representnon-ideal ow in mixer settler tanks. We chose this model struc-ture since it represents a good compromise between accuracyand complexity. The main contribution of this work is to show that,with few sensitive tting parameters, the proposed model providesrealistic dynamic simulations of industrial mixersettler units.Also, the model can be calibrated with standard measurementsand information normally available in current industrial LXSXEW plants; therefore, specic dynamic models for a given indus-trial SX plant can be developed with moderate effort.

Acknowledgements

J.R.P. appreciates the support of AGAUR from the Generalitat deCatalunya through Grant 2007PIV-00017 and Ponticia Universi-dad Catlica de Chile for nancial support for a sabbatical stay atso they can take opportune corrective actions. To develop theseassociations though, exhaustive process operation and data analy-sis are necessary, after running the model in parallel with the pro-cess for long periods. It is worthwhile noting that the model has aprediction horizon of 24 h, since calculated parameters (see Fig. 4)are updated daily based on previous day laboratory data.

The model, as it is can be used to implement on-line state andparameter estimations, using for example an Extended Kalman Fil-ter. These estimations can provide further tools to improve processsupervision, and even can help to implement automatic controlstrategies. Furthermore, a dynamic model for the entire extractionSX sub-process can be developed to assess the impact of betteroperational practices or alternative automatic control strategieson process performance, before implementing them in the realplant, saving time, resources and minimizing the risk of cata-strophic events.

4. Conclusions

72 840 1008 1176 1344(h) Model Delay Real

er model. Copper concentration in extraction organic-outlet stream.eering 22 (2009) 13501358 1357Department DEnginyeria Qumica at Universitat Rovira i Virgili.C.M.M appreciates the support of Molymet S.A. for providingexperimental information and Ponticia Universidad Catlica deChile for granting a PhD scholarship. We appreciate the commentsof the anonymous referees that help us to signicantly improve thereadability of this paper.

Appendix A. Model calibration

A.1. Equilibrium isotherm calculations

For a collection of pH, and [Cu+2]PLS values, the extractant man-ufacturer provides several McCabe diagrams, that can be used toobtain isotherm coefcients, A and B, as a correlation of these vari-ables. Additionally, plant measurements of ML, pH, [Cu+2]PLS and[Cu+2]BO (normally available at industrial facilities) were averaged

daily and, through Eqs. (28) and (29), estimated values of isothermcoefcients A^ and B^were obtained. Then, parameters a, b, c, d and fwere tted to minimize the following sum of squared differences,

MinX56i1

Ai A^ih i2

Bi B^ih i2

A1

where subindex i refers to the respective day. The tted values aregiven in Table 1.

Similarly, for a collection of [H2SO4] values, a set of McCabe dia-grams was given by the manufacturer, yielding a set of values for Cand D. Additionally, a set of plant measurements of [H2SO4]LE andvol.% were averaged daily and, through Eqs. (31) and (32), esti-mated values of isotherm coefcients C^ and D^ were obtained.Then, parameters h and p were tted to minimize the followingsum of squared differences,

MinX56i1

Ci C^ih i2

Di D^ih i2

A2

A.2. Mass transfer and efciency calculations

Mass transfer and efciency coefcients were obtained usingEqs. (33)(36). Values of eE and eS were calibrated by trial and errorafter several simulations. The nal values of eE and eS were thosethat minimized the mean squared error between the simulatedand the measured response.

A.3. Calculated parameters in Table 3

They were obtained from,

VUij VS1uN A3

sLi fuVSQimA4

VLij 1 f uVS2 A5bij 1 aij A6

References

Aminian, H., Bazin, C., Hodouin, D., 1998. Residence time distributions in SXEWequipment. International Journal of Mineral Processing, 235242.

Bergh, L.G., Yianatos, J.B., 2001. Current status and limitations of copper SX/EWplants control. Minerals Engineering 14 (9), 975985.

Ingham, J., Dunn, I.J., Heinzle, E., Prenosil, J.E., 2007. Chemical EngineeringDynamics. An Introduction to Modelling and Computer Simulation. Wiley-VCH. pp. 174183.

Jackson, E., 1986. Hydrometallurgical Extraction and Reclamation. John Wiley &Sons. pp. 109138.

Komulainen, T., Pekkala, P., Rantala, A., Jamsa-Jounela, S.L., 2006. Dynamicmodelling of an industrial copper solvent extraction process.Hydrometallurgy 81 (1), 5261.

Pinto, G.A., Durao, F.O., Fiuza, A.M.A., Guimaraes, M.M.B.L., Madureira, C.M.N., 2004.Design optimisation study of solvent extraction: chemical reaction, masstransfer and mixersettler hydrodynamics. Hydrometallurgy 74, 131147.

Steiner, L., Hartland, S., 1983. Unsteady-state extraction. In: Lo, T.C., Baird, M.H.I.,Hanson, C. (Eds.), Handbook of Solvent Extraction. John Wiley & Sons, pp. 249264.

Van Bochove, G.H., Krooshoff, G.J.P., de Loos, T.W., 2000. Modelling of liquidliquidequilibria of mixed solvent electrolyte systems using the extended electrolyteNRTL. Fluid Phase Equilibria 171, 4558.

Wichterlov, J., Rod, V., 1999. Dynamic behaviour of the mixersettler cascade.Extractive separation of the rare earths. Chemical Engineering Science, 40414051.

Wilkinson, W.L., Ingham, J., 1983. Dynamic behavior and control. In: Lo, T.C., Baird,M.H.I., Hanson, C. (Eds.), Handbook of Solvent Extraction. John Wiley & Sons, pp.853886.

1358 C.M. Moreno et al. /Minerals Engineering 22 (2009) 13501358

Dynamic modelling of copper solvent extraction mixersettler unitsIntroductionProcess modelMass balancesMixer balancesSettler balances

Constitutive equationsEquilibriumMass transferEfficiencies

Results and discussionSensitivity analysisComparing simulations with measured values

ConclusionsAcknowledgementsModel calibrationEquilibrium isotherm calculationsMass transfer and efficiency calculationsCalculated parameters in Table 3

References