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SCOTT A.C. PITBLADO R.M. and BARTON G.W. A mathematical model of a zinc electrowinning cell.APCOM 87. Proceedings of the Twentieth International Symposium on the Application of Computers andMathematics in the Mineral Industries. Volume 2: Metallurgy. Johannesburg SAIMM 1987. pp. 51- 62

A Mathematical Model of a Zinc Electrowinning CellA.C. SCOTT R.M. PITBLADO and G.W. BARTON

University o Sydney N.S. W. Australia

A detailed fundamental model of a zinc electrowinning cell has been developedand validated for both steady state and dynamic simulations. This model wasused to investigate the effects of a range of operating variables and to findtheir optimum values. As well as providing useful design information for aplanned upgrading of the EZ refinery more generally it demonstrates thepotential benefits to the minerals industry of the applications of modern CADflowsheeting techniques. The SPEEDUP equation oriented CAD package wasfound most suitable for this task as the user can easily generate models specific

to his site with any number of components and mixture properties.

ntroductionFlowsheet s imu la t ion models are now

wide ly used in t he pe t r ochemi ca l sindus t r y and i n c r e a s i n g l y so in t hemi ne r a l s indus t r y . Such models can-beused f o r t he des i gn of new pr ocessesas we l l as op t imiza t ion of e x i s t i n gones . In t he f i e l d of e lec t rowinning ,the equa t i ons t ha t desc r ibe t hee l e c t r o l y t i c c e l l s have of ten beenou t l ined 1 - 1 o but have r a r e ly beenapp l i ed to s p e c i f i c i n d u s t r i a lproces ses . One excep t i on i s t h a t ofBrysonl l who developed a s i m p l i f i e dequa t i on s e t f o r mode l l ing t he z ince l ec t rowinn ing p roces s .

This paper o u t l i n e s t ~ developmento f a d e t a i l e d fundamental model o ft he z inc e lec t rowinning process . Themodel con ta ins the most ex tens iveequa t i on s e t yet publ i shed . Numer icals o l u t i o n was ach ieved using t heSPEEDUP f lowsheet ing package fo r bo ths t eady s t a t e and dynamics imu la t ions 1 2 . A wide range of

exper iments were c a r r i e d out tov a l i d a t e both t he e l ec t r owi nn i ng andc e l l hydrodynamic equat ion s e t s .

This example demons t ra te s t heex i s t ence and s u i t a b i l i t y ofnumer ica l t oo l s capable o f so l v i ngthe complex equa t i on s e t s found inminera l c i r c u i t s . Deta i l edmechan i s t i c models are a p r e r e q u i s i t efo r pr ope r p r ocess des i gn , con t r o land o p t i m i s a t i o n exe r c i s e s .

Zinc electrowinning principlesAt the EZ Risdon p l a n t in Tasmaniaz inc ores a re r oa s ted , d i s so lved in

su lphur i c ac id and then h i gh l ypur i f i ed . M e t a l l i c z inc i s won fromt he p u r i f i e d z i nc su l pha t e s o l u t i o nby e l e c t r o l y s i s using aluminiumcathodes and l e ad anodes 1 3 .

The ca t hod i c ha l f r eac t ions withs t anda r d po te n t i a l s are :Zn 2 + + 2e- Zn s ) E:=-0 .763 V

2 g) E:= 0.00 V 2MATHEMATICAL MODEL OF A ZINC ELECTROWINNING CELL 51


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The anodic ha l f r eac t ions are2H + + 2e- + O 2 ( g )

-1 .229V 3

= - 1 .2 0 8 V ( 4 )Genera l ly , 90 of the cathodic

curren t i s used in the product ion ofz inc by r eac t ion I ) , and 99 of theanodic cu r ren t i s used by r eac t ion

3). Combining r eac t ions 1) and 3)gives the ove r a l l des i r ed r eac t ion :

= - 1 .9 9 2 VThe ~ a j o r var i ab les tha t a f f e c t

these r eac t ions are :- Zn 2+ concentra t ion

concentra t ion- curren t densi ty- t empera ture .

5

These, the re fore , are the keyvar i ab les t ha t must be consideredwhen developing the mathemat icalmodel. As each of these i s in tu rndependent on severa l o the r var iab les ,the re su l t ing s imula t ion model hasmany equa t ions . The e f fec t of each ofthe major v a r i a b l e s has beeni nves t iga ted in a se r ie s ofexperiments under taken in order toobta in e lec t rochemica l da ta for usein model development 14 .

Addi t ives and impur i t i e s apa r tfrom magnesium, manganese andammonium ions) were not model led. Thee f f e c t s of these could be inc luded a ta l a t e r s tage in the modeldevelopment cons i s t en t with anexper imenta l program to va l ida tenecessary equa t ions .

52

odel developmentEquat ions have been developed to

model the e f f e c t s of the 7 majorspec ies pr e sen t in the e l e c t r o l y t e ofthe EZ r e f ine ry a t Risdon. These are

NH4+. The equat ion se t for theseseven spec ies can be div ided i n tofour main sec t ions , which wi l l beexamined in tu rn :1) Mass balance equat ions2) Energy balance equat ions3) Elec t rochemica l equat ions4) Conduct iv i ty and dens i ty

cor re la t ions .Mass balance equations

Each of the seven chemicali s def ined by a mass balance

spec iesof the

form :[INPUTl+[GENERATIONl-[CONSUMPTIONl

-[OUTPUTl = [ACCUMULATIONl 6)The INPUT i s the product of thevolumetr ic f lowra te of feed to thec e l l and the concentra t ion of thespec ies in the feed. The GENERATIONte rm def ines any r eac t ions where on2of the chemical spec ies i s produced.H i s produced a t the anode byr eac t ion 2) . The consumption termdescr ibes any r eac t ions which consumeone of the chemical species . Zn 2+,H+, H20 and Mn2+ are a l l consumed.Zn 2+ and H20 are consumed by r eac t ion5) while H and Mn2+ are consumed bys ide r eac t ions 2) and 4 ) . TheOUTPUT te rm acpounts fo r the amountof each spec ies leav ing the system.There are two ou tpu t s , the overf lowof the spent so lu t ion and l o ss due toevapora t ion . I t i s assumed t ha t wateri s l o s t through e v a p o r a t ~ o n and t h i si s model led using a modif ied Antoineequat ion for ac id ic so lu t ions .ACCUMULATION i s the t ime der iva t ive

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de f in ing the r a t e of change of massof each spec ie s . At s teady s t a t e t hed e r i v a t i v e equal s zero .

nergy balance equationsThe energy balance of a system can

a l so be determined analogous ly toequat ion (6) . The INPUT te rm de f inesthe amount of energy en te r ing t hesystem. Energy en te r s bo th in t hefeed s t r eam and as e l e c t r i c a l energy.The OUTPUT def ines energy l eav ing t hesystem with the e x i t s t ream. TheCONSUMPTION t e rm de f ine s anyendothermic processes . This inc ludesthe overa l l hea t of r eac t ion and t hehea t of evapora t ion . The GENERATIONt e rm i s not r equ i r ed for t he z incc e l l s ince no exothermic r eac t ionsoccur . Equa t ion (6) can now bew r i t t e n more sp e c i f i c a l l y as :Hf + He + Hl + Hr + Hevap - Hd

= [ACCUMULATION) 7 )Hl accoun ts for t he hea t l o s t t o theatmosphere through conduc t ion andr a d i a t i on .

lectrochemical equationsEach c e l l must mainta in e l e c t r i c a ln e u t r a l i t y :x n ( j ) . C ( j )j = 1where n( j )

ot he charge ofcomponent j

8 )

C j ) t he concentra t ion ofcomponent j (mol/I )

I t i s neces sa ry to cons ider boththe thermodynamics and k i n e t i c s ofthe e l e c t r o l y t i c process . Theequ i l ib r ium p o t e n t i a l of each spec iesi s given by a thermodynamic equat ion ,the Nerns t equat ion

E e j) = E:- j ) + R. T . 1 n [ _a =..o_ _j_)]n ( j ) . F a r ( j ) 9 )

where Ee( j ) equ i l ib r ium po te n t i a l( vo l t s )a c t i v i t y of theox id i sed and reducedspec ies of component j .

Ac t iv i t i e s should be employed int h i s equat ion as er ro r s can r e su l t i fconcentra t ions are used. The a c t i v i t yof a spec i e s i s r e l a t e d to i t sconcentra t ion by equat ion (10) .

ao ( j ) l o ( j ) Co ( j )a r j )

,; here I a c t i v i t y c oe f f i c i e n t ofcomponent j

( 1 0 )

The dr iv ing force or overpo ten t i a lfor each spec ies can t hen bedesc r ibed as the d i f f e r ence betweenthe working e lec t rode po te n t i a l E,and t he equ i l i b r ium po te n t i a l .

7)(j) E - Ee( j ) 11 )where 7)(j) = overpo ten t i a l (vo l t s )The k ine t i c s are more complex and anumber of equat ions have beenproposed. The most use f u l i s t heTafe l equa t ion which in i t s ca thodicform i s ;

[Cd j ) . z ( j ) .F.T)(j)]i j ) =i 0 j ) . exp R.T (12 )

where i ( j ) = cu r r en t produced by t her educ t ion o f component j (A/m2).

Equa t ion (12) r e l a t e s t heoverpo ten t i a l f o r each spec i e s to t her a t e of r eac t ion expressed in termsof cu r r en t dens i ty . I t assumes t ha tt he r a te determining s tep i s thecharge t r a n s f e r a t t he e lec t r odesu r f ace and not the mass t r a n s f e r ofthe spec ies to t he sur face . For boththe r eac t ions in which gas i sevolved, hydrogen a t t he cathode( r eac t ion (2 and oxygen a t theanode ( r eac t ion ( 3 , t he charge

MATHEMATICAL MODEL OF A ZINC ELECTROWINNING CELL 53


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t r an s f e r k i n e t i c s are slow and theassumpt ions of the Tafe l equa t ion areva l id .

For the z inc r eac t ion , an equa t ionder ived by Bard and Faulkner 1 5 whichi ncorpora t es both Tafe l kine t i c s andmass t r an s f e r e f f ec t s was found to bemore sUi tab lei j ) = i 1 j )-i j ) ) / i 1 j ) ) . i 0 j )

. exp a j ) . z j ) . F. 7 j ) / R . T) )where i 1 j ) = l imi t ing c u r re n tdens i ty .The l i m i t i n g c u r re n t dens i ty i sgiven by :

13 )

14 )where m = mass t r an s f e r c o e f f i c i e n t .

The exchange c u r re n t dens i ty i o j ) ,i s an impor tan t kine t i cc h a r a c t e r i s t i c of an e l ec t ront r an s f e r process . A dynamice q u i l ib r iu m e x i s t s a t . the surfacewhen there i s no n e t c u r re n t or ne tchemical change in the ce l l . The r a t eof reduc t ion of each spec ies equalsthe r a t e of oxida t ion . This r a t eexpressed in terms of c u r re n t dens i tyi s i o j ) . Ple t che r 1 6 def ines theexchange cur ren t dens i ty as :

l-a j) )i o j ) = n . F . k : j ) . [ao j ) ] 15)The r a t e constan t , k ~ is s t rong ly

dependent on t empera ture . AnArrhenius equa t ion i s a p p ro p r ia t e .k : j ) = A o j ) .e x p - e j ) / R . T ) ) 16 )where Ao j )=frequency fac to r m/sec)

e j ) =ac t iva t ion energy J/mole)The r e l a t i o n s h i p between the r a t e

of r e a c t i o n expressed in terms ofcharge t r an s f e r or c u r re n t ) andmoles per second i s given by theFaraday equa t ion ;A. i l j ) = r j ) . F .L U n j ) ) 17)

The t o t a l current pass ing through54

an elec t rode i s the sum of thec u r re n t s of a l l the r eac t ionsoccur r ing on i t s sur face .

xi t o t a l ) = E i j ) 18)j 1The overa l l c e l l vol tage i sca l cu l a t ed by summing the vol tage

drops of the e l ec t rodes and acrossthe so lu t ion between the e l ec t rodes .

19 )E, i s a measured cor rec t ion term to

al low fo r vo l tage l os ses across thebusbars and con tac t s , and g e n e ra l lyequals 0.1 to 0.2 vo l t s .

The f i n a l e le c t ro c h e mic a l equat ionsemployed are those desc r ib ing thec u r re n t e f f i c i e n c y and the t o t a lenergy used by the p rocess

CE

P 81974 .VCEConductivity and density correlationsonductivity

20 )

21 )

The c o n d u c t iv i ty of the so lu t ionhas a s i g n i f i can t e f f ec t on the ce l lvol tage and t he re fore on powerconsumption. A fundamenta lmechanis t i c model was viewed asunnecessary and a s impler cor re la t ion Happroach was adopted in whichc o n d u c t iv i ty i s dete rmined byca lcu la t ing the dev ia t i on from as tandard so lu t ion .Cond = 32.0+B T-308)+0.20 H z S0 4 -110)

-0 .17 C*-82) 22)where; HZ S0 4 and C are in g / land B a c id / t e mp e ra tu re c o e f f i c i e n t

o . 0028 H z SO 4 )Contr ibu t ions of the cat ions are

equated to z inc based on t h e i r i o n icMETALLURGY SIMULATION ND CONTROL


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charge . Experimental work has shownt h i s assumpt ion to be co r rec t for therange of c ~ n c e n t r t i o n s encounteredin a z inc e l ec t ro ly t i c ce l l .C 65.4(Zn+Mn+Mg+0.5(NH 4 (23)where concentra t ions are in mol / l

ensity correlationDensi ty was inc luded in the model

pr imar i ly to s tudy i t s value as av a r i a b l e t ha t can be used for c e l lcon t ro l . Cor r e la t ions were obta inedfo r both a c i d i c and neut r a lso lu t ions .Po f ) = 1000+2.25(Zn)+4.36(Mg)+2.41(Mn)+3.22(NH 4 ) (24)Pots ) = 1000+2.18(Zn)+0.56(H 2 S0 4 )

+ 4 . 3 6 Mg ) + 2 . 4 1 Mn ) + 3 . 22 NH 4) (25)Both cor re la t ions have been t e s t e dover a wide range of condi t ions asmight be found a t EZ, Risdon.

ell mixing characteristicsAccura te f u l l - s c a l e model l ing of a

z inc e lec t rowinning c e l l required adescr ip t ion of the c e l lhydrodynamics. Rawling and Coste l lo 1 7conducted a de t a i l e d s tudy of acopper r e f ine ry c e l l and proposed amodel cons i s t ing of four volumee lements . Brysonl l used a s implermodel which cons i s ted of a wel l mixedr eg ion with a bypass f r ac t ion of 0.1.

Tracer t e s t s c a r r i e d out on th reei ndus t r i a l c e l l s a t Risdon ind ica tedt ha t a model cons i s t ing of two wel lmixed tanks was appr op r ia te f igu r e1) . In l i ne with phys ica lcons ide r a t ions the volume of the toptank , vt , was t aken as the volume ofthe e l e c t r o l y t e in the e lec t rodereg ion . The volume of the bot tomt ank , Vb, was t ha t between the bot tomo f the e lec t rodes and the top of themanganese dioxide mud (which s e t t l e s

Top cstr

" ' ~ i l l r l l l l l l - n_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Spent

Bottom cstrMnd; mud

SpentF eed

Top cstr

R

- - -+ Bottom cstr

FIGURE 1. Top) Diagram of a zinc electrowinning cellBottom) Model representationa t the bot tom of the tank) .

The bes t fit was obta ined when1) All the feed went to the bot tomtank.

2) No e l e c t r o l y t e from thebot tom t ank by-passed the t optank. This ind ica ted t ha t thefeed en te r ing the reg ion underthe e lec t r odes was drawn up i n tothe e lec t rode reg ion and did notpass s t r a i gh t through the ce l l .

3) A moderate value of R, ther e c i r c u l a t i on between t op andbot tom tanks was used. Thevalues t ha t gave bes t fit aregiven in t a b l e 1).

The i n t e r na l r e c i r c u l a t i on pa t t e r nof a c e l l was not only dr iven by f eedf low r a t e but a l so by the l a rgeamount of r i s i ng bubbles between thee lec t rodes . I f the cu r r en t dens i tywas reduced , the amount of bubbl ing

MATHEMATICAL MODEL OF A ZINC ELECTROWINNING CELL 55


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TABLE 1Reci rcu la t ion Rate, R, with in anElectrowinninq Cell

The 3 c e l l s s tud ied were a t the EZRefinery, Risdon.

1s t ce l l inCascade un i t3rd ce l l inCascade un i tRec i r cu la t ingce l l

Cel l feed R{L/min)r a t e L/min)

6.0 5418.0 40

l l 8 145

would decrease , and t he re fo re R therec i rcu la t ion parameter would beexpected to decrease . Fur therd e ta i l s of t h i s work are presen ted byShewring 1 8 .

SPEEDUP modellingBarton and Pitb lado 1 9 showed the re

are only a few genera l purposecomputer aided des ign CAD) too ls fo rthe minerals process ing indust ry .This i s in s ign i f i can t cont r as t tothe chemicals and pet rochemicalsindus t r ie s which have severa lPROCESS, FLOWPACK FLOWTRAN ASPEN,SPEEDUP). Par t of the reason i s themore pred ic tab le performance ofchemical plan t equipment s incechemical proper t i e s and process uni toperat ions , al though complicated, canbe wel l s imulated. Mineralsf lowsheets are much more in f luencedby the feed ore proper t i e s and manyuni t opera t ions a re s i t e spec i f i c ,thus genera l i sed packages are l e s susefu l .

There are a number of f lowsheet CADa r c h i t e c tu r e s in use. Rosen 2 0 reviewsthe impor tant f ea tu res of the var ioustypes , inc luding the two most56

important - sequen t i a l modular andequat ion or i en ted . The sequen t i a lmodular s t ruc ture i s the most commonand in many r espec t s i s s imi la r to anautomated manual ca lcu la t ionprocedure . Because of i t s f ixed ,ca lcu la t ion s t ruc ture , a sequen t i a lmodular package i s i n e f f i c i en t formany f lowsheet problems. The equat ionor i en ted a r c h i t e c tu r e as descr ibed byShacham e t a l 21 i s more e f f i c i en t .Perk ins 1 2 discusses the SPEEDUP CADf lowsheet program, one of the f i r s tequat ion or i en ted packages. SPEEDUP

Simulat ion Package for theEvalua t ion and Evolu t ionary Design ofUnsteady Processes) was developed a tImper ia l College, London, over anumber of years . I t i s a powerfultoo l for the so lu t ion of minera lsf lowsheet problems, both s teady s t a t eand dynamic.

The key f ea tu res of SPEEDUP t ha tmake t a t t r a c t i v e for minera lsf lowsheet s imula t ion a re :- t can s imula te dynamic response as

well as s teady s t a t e ;- opera t ion i s i n t e r a c t i ve and

f lowsheet changes are easy;f lowsheet opt imisat ions should bep ar t i cu l a r ly e f f i c i en t ;

- s i t e s pe c i f i c models can eas i ly begenera ted by user s , e i th e r asequat ions or as subrout ines ;

- any combinat ion of a rb i t r a ryspec i f ica t ions may be made, so longas they are f e a s ib l e ;equat ions may be expressed in anyform and order ;

- t provides a s u i t e ofs t a t e -o f - th e - a r t numerical methodsto solve the f lowsheet .SPEEDUP co l l ec t s t oge ther the fu l l

se t of def in ing equat ions for a l lMETALLURGY SIMULATION AND CONTROL


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un i t opera t ions , which need not be inany c a l c u l a t i o n sequence . Thec o l l e c t e d equat ions form a s e t inwhich the t o t a l number of equat ionsi s M and var i ab les N. For any r e a lf lowshee t , N always exceeds M andprovides for N-M s pe c i f i c a t i ons . Oncethe N-M s pe c i f i c a t i ons are made, thef lowsheet problem reduces to anumer ica l one of M simul taneousequat ions in M unknowns, and inpr inc ip l e a so lu t ion may be obta inedby s tandard means. With t h i sapproach, the types of s p e c i f i c a t i o n s

feed s t reams, parameter s e tc ) areunimpor tant , so long as they a re a l li ndependent . Thus des ign c lassproblems are so lved with equal easeto performance problems.

odel calibrationPi l o t p lan t sca le experiments were

c a r r i e d out in two 10 litr ce l l seach conta in ing two aluminiumca thodes and th r ee s i l ve r - l e a d anodes(0.75 Ag). Each cathode had animmersed sur face a rea of 590 cm 2 . Theadd i t ion of f r e sh feed e l e c t r o ly t e tothe c e l l s was con t ro l l ed in order toma in t a in a cons tan t c e l l a c id i t y .Cel l t empera ture was a l so con t r o l l ed .The c e l l s were wel l ins t rumented inorder to ob ta in the data required formodel c a l i b r a t i on . Experimentalmeasurements were cont inuous lyrecorded by a 30 poin t char t r ecorderand a PDP 11/23 computer. The e f f e c t sof each of the major var i ab les - z incconcen t r a t ion , a c id concen t r a tion ,t empera ture , cu r ren t dens i ty anddepos i t ion t ime - were i nves t iga tedone a t a t ime, while a l l o the rv a r i a b l e s were held cons tan t , in ahigh pur i t y i n d u s t r i a l e l e c t r o ly t e 1 4 .

Cal ib ra t ion of a number of themodel parameter s was car r ied out bycomparing model r e su l t s with theexper imenta l r e su l t s . The sum of thesquares of the e r r o r s for bothcu r r en t e f f i c i e n c y and cathodeoverpo ten t i a l were ca lcu la t ed foreach se t of parameters t e s t e d . These t of parameter s t ha t gave the bes tfit werea zn) 0 .4a H+) 0.5

k ~ z n ) 2.69 X 10- 4 cm/sec a t 35 Ck:(H+) 3.08 x 10- 1 2 cm/sec a t 35 C

These a r e with in t ~ range ofvalues repor ted by Bard 2 2 . The valueused f o r the charge t r a n s f e r number,z, f o r z inc depos i t ion was 2. Tbiswas recommended by Parsons 2 3 andconf irmed by Tafe l s lope experimentsconducted in the exper imenta l c e l l s .

The mass t r a ns f e r c oe f f i c i e n t wasobta ined us ing the same method ast ha t r epo r ted by E t t e l e t a l 2 4 wherea t r a c e impur i ty was depos i ted on thee lec t r ode sur face . Copper, the t r a c eimpur i ty se l ec t ed , was t e s t e d a t f ived i f f e r e n t l e v e l s between 0.05 mg/land 2.6 mg/ l . A value of 9 x 10- 4cm/sec was obta ined .

The electrowinning modelA f u l l y c a l i b r a t e d z inc

e lec t rowinning c e l l model capable ofboth s t eady s t a t e and dynamics imu la t ions has been developed f o ruse in op t imisa t ion and i n d u s t r i a lcase s tud ies . The model, cons i s t ingof 200 var i ab les and 121 equa t ions ,r ep resen t s a s ubs t a n t i a l numer ica lproblem as many of the equat ions areh ighly non- l inea r .

Only an equat ion or i en tedMATHEMATICAL MODEL OF A ZINC ELECTROWINNING CELL 57


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f lowshee t ing package (such asSPEEDUP) r ep resen t s a f eas ib l eso lu t ion method to such a problem.

Model resultsSteady state simulation

A s e r i e s of runs were car r ied outto determine an approximate optimumopera t ing condi t ion for a high pur i t yfeed e l e c t r o l y t e of 160 g / l Zn. Thee f f e c t s of 1) zinc and ac idconcent ra t ion i 2) t empera ture i 3)cu r r en t dens i ty were assessed withr espec t to curren t ef f ic iency andpower consumption.The SPEEDUP package i s pa r t i c u l a r l ywell s u i t e d to t h i s type of ana lys i ss ince the se t of spec i f i ed var i ab lescan e a s i l y be changed withouta l t e r i ng the problem s t ruc ture . Others imula t ion packages would bes t ruc tured for a pa r t i c u l a r se t ofs pe c i f i c a t i ons and any o the r se tcould only be achieved, i f a t a l l bya cos t ly and i n e f f i c i en t se t ofi t e r a t i v e ca lcu la t ions .Zinc and acid concentration

The model was run a t a number ofc e l l a c i d i t i e s in the range 80-200g / l H2 S0 4 , for a cons tan t ce l ltemperature of 35 C. Figure (2)demonstra tes t ha t the lowest powerusage wi l l be achieved a t 150 g / lH2 S0 4 . This corresponds to a spentz inc concen t r a t ion of 65 g / l Ata c i d i t i e s above 180 g / l the powerconsumption r i s e s sharp ly due to therap id dec l ine in cu r r en t ef f i c i ency .Temperature

The nex t se t of s imula t ions wererun a t a cons tan t c e l l a c id i t y of 160g / l H2 S0 4 and curren t densi ty of 500A/m2. Cell t empera tures in the range35-45 C were i nves t iga ted . Figure (3)58

98

96

90

88Zn in cell gil)

110 91 72 53 3580 120 160 260

Acidity in cell (g/l)

3300

2NQ)

3200 ,9;;;...c:i:::,3100 .::.90,a;::l'::ou3000 1;;;:o0...2900

FIGURE 2. Effect of acidity and zinc concentration

97

96

93

Zn in feed 160 g/l temp. 35C,-current density5 Alm2

2960

29402N...;;;;

2920 l:J-.::o2900 Ra; l'::ou2880 1;;;:o0...

2850

92L--L__ __ __ ~ 7 ~ 7 ~ ~ ~ 2 8 4 032 36 40 44Temperature 0 C)

FIGURE 3. Effect of temperatureZn in feed 160 g/l cell acidity 160 gll H,S04 currentdensity 500 A/m2METALLURGY: SIMULATION AND CONTROL


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demonstra tes t ha t the powerconsumption dropped from 2950kW-hrs / t Zn to 2860 kW-hrs/ t Zn , dueto the smal l r i s e in currente f f i c i e n c y and a drop in c e l l vol tagecaused by i n c re a se d so lu t ionconduct iv i ty . At presen t mosti n d u s t r i a l p l a n t s do not opera teabove 40 C due to problems with theadd i t i on reagen ts . However, once t h i sproblem i s overcome, power sav ingsw i l l be poss ib l e by i n c re a s in g thec e l l t empera ture .Current density

Figure (4) demonstra tes t h a tcur ren t dens i ty has a la rge e f f ec t onpower consumpt ion due to the i n c re a sein IR vol tage ac ross the so lu t ion asthe cur ren t i s inc reased . The powerconsumpt ion inc reased l i n ea r l y a t ar a t e of 80 kW-hrs/ t Zn per 100 A/m2Unfor tuna te ly however by reduc ingcur ren t dens i ty the p roduc t ion r a t e

;> .u

97

96

5 950SCl)cCl);::: 94U

3200

3100

'23000 :;:'c::

2900 Cl)00..

2800

~ ~ ~ ~ ~ ~ ~ ~ 2 7 0 0200 400 600Current density, A m2

FIGURE 4. Effect of current densityZn in feed 160 g/J, cell acidity 160 g/J, temp. 35C

i s a l so reduced. New cel l roomsovercome t h i s problem by havingcathodes of l a rg e r surface a rea . Thesame produc t ion r a t e can be obta ineda t lower c u r re n t d e n s i t i e s andt he re fore lower power consumpt ion .The new Cominco ce l lhouse tookadvantage of t h i s concept by reduc ingcurrent dens i ty from 600-700 A/m2 to400 A/m2 and i nc reas ing cathode s i zefrom 1 m2 to 3m 2 2 5Dynamic simul tion

A dynamic s imula t ion fo r a c e l l ina cascade u n i t of the Risdon ce l l roomwas performed to demonst ra t e ~ huncontro l led response to a s t e pchange. The feed f lowra te wasdecreased from 0.09 l i s to 0.07 l i s .Figure (5) i l l u s t r a t e s the responseof zinc concen tra t ion in the c e l l andcurrent e f f i c iency with r e spec t tot ime. The current e f f i c i e n c y took 40

70 .

60Q- ~

9u50.S:::Cl) :::0 .9;::::

"'" ~l)C 92 :::Cl)Cl) 40 g;::: 0U uu.S90 N30

88

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 2 0o 20 40 60Time hours)

FIGURE 5. Zinc concentration and current efficiency vs timeMATHEMATICAL MODEL OF A ZINC ELECTROWINNING CELL 59

i'i


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hours to f a l l with in 0.5 of the news teady- s ta te value. Not only can themodel s imula te s tep changes such asthe above example, but a lso pulses ,s ine wave d is tu r bances and rampinputs .

ConclusionTo date the use of f lowshee t ing

models in the minera ls indus t r y hasbeen l imi t ed . A new genera t ion ofequat ion or i en ted CAD packages (suchas SPEEDUP) now provides t oo l ss u i t a b l e for the s teady s t a t e anddynamic s imula t ion of complex minera lprocesses .

A s teady s t a t e and dynamic model ofa zinc e lec t rowinning c e l l has beendeveloped based on a fundamentalmechanis t ic model us ing the SPEEDUPpackage. This i s the most de t a i l e dmodel yet publ ished . An extens ive se tof experiments has been car r ied outto c a l i b r a t e the model which conta insonly four f ixed parameters out of 121equat ions and 200 var iab les . Themodel has been used for s teady s t a t eop t imisa t ion of z inc c e l l opera t ionsand for dynamic ana lys i s of feedvar ia t ions for con t ro l sys temj u s t i f i ca t i o n .

AcknowledgementsThe authors of t h i s paper wouldl ike to thank the Elec t ro ly t i c Zinc

Company of Aust ra l as i a fo r t h e i rf inanc ia l suppor t .

SymbolsA Elec trode Surface

areaAo(j) Frequency f ac tor

(Arrhenius eqn.) (m/sec)ao j ) Ac t iv i ty of the

oxid ised spec ies (moles / I )6

a r j ) Act iv i ty of thereduced spec ies (moles / I )

b I n t e r - e l e c t r ode gap m)C(j) Concent ra t ion in

bulk so lu t ion (moles / I )CE Current Eff i c i ency ( )cond Conduct iv i ty (s/m)E Working e lec t rode

po t e n t i a l vol t s )Ee j ) Equi l ibr ium

e j

F

Hevap

Hd

i j )

po t e n t i a l vol t s )Standard equi l ib r iumpo t e n t i a l vol t s )Act iva t ion energy(Arrhenius eqn. ) (J /mole)Anode P o te n t i a l vo l t s )Cathode P o te n t i a l vol t s )Voltage l o sses in busbarand contac ts vo l t s )Faraday cons tan t (c /mole)Heat f low of feeds t ream J / s )E l e c t r i c a l energy J / s )Energy l o ssesTota l hea t ofr eac t ionsHeat ofevapora t ionHeat f low ofdischarge s t reamCurrent dens i ty

J / s )

J / s )

J / s)

j s)(A/m 2 )

i t o t a l T o t a l curren tdens i ty A/m2 )i 1 j ) Mass t r a n s f e r l im i t i ngcu r ren t dens i ty (A/m2)Current dens i ty fo rz inc deposi t ionreac t ion A/m2 )

k : j ) Standard r a t econs tan t (m/sec)

n j ) Ion ic chargeP Power consumpt ion(kW-hrs/ t ZnR Gas cons tan t (J/mole.K)

METALLURGY SIMULATION ND CONTROL


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V

TemperatureCel l vo l tage

K )(vo l t s )

Z ( j ) Charge t r a n s f e r numbera j) Transfe r c oe f f i c i e n tlo j) Act iv i ty c oe f f i c i e n t of

oxid ised spec iesIr j) Act iv i ty c oe f f i c i e n t of

reduced spec iesOverpoten t ia l (vo l t s )

f Densi ty of feed (neu t ra l )e l e c t r o l y t e g / l )

s Densi ty of spent (acid ic)e l e c t r o l y t e g / l )

eferences1. PICKETT D.J. Elec t rochemica lr eac tor des ign . AmsterdamElsev ie r Sc i e n t i f i c Publ i sh ingCompany 1977.

2. ALKIRE R. Model l inge lec t rochemica l systems. AIChESymposium Ser ies , vol .77 , No 2041981. pp.121-128.

3. KING C.J.H. Comments on thedes ign of e lec t rochemica l ce l l s .AIChE Symposium Ser i es . vol . 77No 204 1981. pp.46-59.

4. BENNION D.N. Modell ing andr eac tor s imula t ion . AIChESymposium Ser i es . vol . 79 No229 1983. pp. 25 - 3 6 .

5. WHITE R.E. BAIN M. and RAIBLE M.Pa r a l l e l p la t e e lec t rochemica lr eac tor model. J . Elect rochemSoc. vol . 130 No 5 1983.pp.l037-1042.

6. FLEISCHMANN M. and KELSALL G.Design model l ing and performanceof e lec t rochemica l r eac tor s .Proceedings , In te rna t iona lSymposium on Elec t rochemis t ry andMetal Process ing. Ohio 1984. pp.572-583.

7. SCOTT K. Reactor engineer ing

models of complex e lec t rochemica lr eac t ion schemes. Elec t rochimicaActa. vol .30 , No 2 1985.pp.235-244.

8. NGUYEN T.V. WALTON C.W. andWHITE R.E. A mathematical modelfor a p a r a l l e l p la t ee lec t rochemica l r eac tor . J . Elec-trochem. Soc. vol . 133 No 61986. pp.1130-1138.

9. MADER M.J. WALTON.C.W. andWhite .R.E. Pa r a l l e l p la t ee lec t rochemica l r eac tor model:Mate r ia l balance c losure and as impl i f i ca t ion . J . Elect rochemSoc. vol . 133 No 6 , 1 9 8 6 . pp.1124-1130.

10. SAVINELL R.F. Some aspec ts ofe lec t rochemica l r eac tor des ign .AIChE Symposium Ser ies . vol . 79No 229 1983. pp.13-24.

11. BRYSON A.W. Modell ing theperformance of e lec t rowinningce l l s . Hydrometal lurgy 81 ,Socie ty of Chemical Indus t rySymposium Manchester 1981.

12. PERKINS J.D. Foundat ions ofcomputer-aided chemical processdesign. Snowmass 1983.pp.309-362.

13. MANTELL.C.L. Elec t rochemica lEngineering, 4th ed i t ion . NewYork McGraw-Hill 1960. pp.210-224.

14. SCOTT A.C. BARTON G.W.PITBLADO R.M. and AULT A.R.Experimental de te rmina t ion of thef ac to r s a f f e c t i ng z ince lec t rowinning ef f ic iency . To bepubl i shed .

15. BARD A.J. and FAULKNER L.R.Elec t rochemica l methods. NewYork J . Wiley and Sons 1980.

16. PLETCHER D. I n d u s t r i a lMA THEMATICAL MODEL OF A ZINC ELECTROWINNING CELL 6


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e l ec t rochemis t ry . Chapman andHal l , 1982.

17. RAWLING J.R. and COSTELLO L.D.Mixing cha r ac t e r i s t i c s of acopper r e f i ne ry tankhouse ce l l .Journa l of Metals , May 1969.pp.49-52.

18. SHEWRING D. Tracer s tudy a.nalysisand hydrodynamic model l ing ofe lec t rowinn ing ce l l s .Undergraduate thes i s , Dept. Chem.Eng. Sydney Univers i ty , 1985.

19. BARTON G.W. and PITBLADO R.M.Simula t ion of minera l s process ingplan t s . Chemeca 84 , Melbourne1984. pp.671-676.

20. ROSEN E.M. Computer Appl ica t ionsand Chem. Eng. Assoc. Symposium.No 124 1980. p .3 .

21. SHACHAM M. MACCHIETTO S . ,STUTZMAN L.F. and BABCOCK P.

62

Equat ion or i en t ed approach toprocess f lowshee t ing . Computersand Chem. Eng. vol. 6 No 21982. pp 79-95.

22. BARD A.J. Encyclopedia ofe l ec t rochemis t ry of theelements . vol . 5 New YorkMarte l -Dekker 1976.

23. PARSONS R. Persona lcommunication 1986.

24. ETTEL V.A. TILAK B.V. andGENDRON A.S. Measurement ofcathode mass t r an s f e rcoef f i c i en t s in e lec t rowinn ingce l l s . J . Elect rochem. Soc. vol.121 No 7 1974. pp.867-872.

25. HONEY R.N. KERBY R.C. andLEGGE R.C. Zinc ce l lhouseopt imisa t ion. Zinc 85 , Symposiumon ex t r a c t i ve meta l lu rgy of zinc .Tokyo 1985. pp.349-363.

METALLURGY SIMULATION ND CONTROL

electrowinning zn 1

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