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Material balance and current efficiency in electrowinning
Hydrometallurgy, 2 (1976) 35--50 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
35
MATERIAL BALANCE AND CURRENT EFFICIENCY IN ELECTROWINNING
W.W. HARVEY* EIC Corporation, 55 Chapel Street, Newton, Mass. 02158 (U.S.A.) (Received October 17th, 1975) ABSTRACT
Harvey, W.W., 1976. Material balance and current efficiency in electrowinning. Hydrometallurgy, 2: 35--50. A process variable in addition to the current efficiency is required in order to obtain exact correlation among current, electrolyte flow, and concentration changes in electrowinning. To this end, a volume efficiency has been defined and incorporated into a formulation for estimating the separate contributions to observed current efficiencies. In Part I, expressions are presented which enable the response of the electrowinning system to changes in infiuent to be accurately predicted. The formulation developed is practical, and its use is illustrated by actual examples. Part II presents a somewhat idealized treatment, in that very precise and accurate chemical analyses would be required in order to obtain a reliable estimation of the relative rates of competing electrode reactions. PART I MATERIAL BALANCE IN ELECTROWINNING Introduction E a r l y in o n e ' s i n v o l v e m e n t in p r a c t i c a l e l e c t r o w i n n i n g , t h e i n a b i l i t y t o rec o n c i l e c o n c e n t r a t i o n c h a n g e w i t h c u r r e n t a n d f l o w c a n be a s o u r c e o f frust r a t i o n . Of c o u r s e , an e f f e c t i v e c u r r e n t e f f i c i e n c y m a y be so d e f i n e d t o give t h e d e s i r e d r e s u l t , b u t i t will d i f f e r t o s o m e d e g r e e f r o m t h e a c t u a l , m e a s u r e d current efficiency. On further examination of the problem, one can become r e a s s u r e d t h a t t h e e l e c t r o w i n n i n g p r o c e s s is, i n d e e d , c a p a b l e o f p r e c i s e a n d r a t i o n a l c o n t r o l . In o r d e r t o e x t e n d t h i s c o n t r o l b e y o n d t h e p r o d u c t i o n o f electrowon metal to include the composition of effluent electrolyte, which will g e n e r a l l y be r e c o n s t i t u t e d a n d r e c y c l e d b a c k t o e l e c t r o w i n n i n g , it is n e c e s s a r y t o t a k e a c c o u n t o f t h e v o l u m e c h a n g e s i n h e r e n t in e l e c t r o w i n n i n g . T h e a u t h o r ' s a p p r o a c h t o a m a t e r i a l - b a l a n c e d e s c r i p t i o n o f t h e p r o c e s s is developed below. *Formerly, Ledgemont Laboratory, Kennecott Copper Corporation, Lexington, Massachusetts 02173, U.S.A.
6
C o n c e p t s attd definitiolts
For present purposes it will be useful to treat electrowinning as a batch operation. The treatment also encompasses continuous operation, ~he time interval between each stage then being determined by the times at which the deposit is weighed and the electrolyte sampled. The expressions obtained in Part I may be recast into continuous notation by consistent application of time derivatives. How this may be done is shown in Part II, which focusses on the formulation of the several electrochemical factors determining cathodic efficiency in copper electrowinning from a leach electrolyte containing appreciable iron. w, 9 depGsiteci
t c '° g/~ M 2+
'
1 5w, 9
"lost" Fig.1. C o m p o n e n t s o f material balance for metal in e l e c t r o w i n n i n g .
In accordance with the conservation diagram for the metal being electrowon (Fig. 1), the following identifications are made: V' = volume of electro, lyte entering the cell in time t; V " = volume of electrolyte exiting the cell in time t; c', c " = respective concentrations of the metal ions; q = electrochemical equivalence factor, e.g., A h/g; c = fractional cathodic current efficiency. The weight of metal deposited in time t is w
= - - /J q 0
(1~
e I dt
where I is the instantaneous cell current. The overall current efficiency for the period of observation is
c.E.
:-
loo w/-" Iq
f
x dt = l o o wq/ t
o
where < I > is the time-average cell current. There are a number of inherent physical and t h e r m o d y n a m i c factors in electrowinning which combine to make V ' ~: V " and w ~t V ' c ' - - V " c "
The second of the two inequalities defines a weight decrement, 5 w, which
(3)
37 includes the resultant of errors in the measurement of volume and concentration as well as metal value actually lost from the system. The factors that come to mind and an indication of which quantities, A V and 5 w, t h e y affect are given in Table 1. It is important to recognize t h a t tidying up an electrowinning operation, whether laboratory or commercial, may only reduce but cannot eliminate the majority of these factors. That fact appreciated, one can then concentrate on the business of accounting for their effects in a manner to permit realization of precise process control. TABLE1 F a c t o r s c o n t r i b u t i n g t o v o l u m e c h a n g e a n d m e t a l loss in e l e c t r o w i n n i n g Factor
AV
5w
Factor
AV
5w
E v a p o r a t i o n losses Generation of mist Sampling and bleedoff Spatter and leakage Misc. t r a n s f e r l o s s e s
× x × X x
-× × × x
Dragout (on pulling) Temperature change Partial v o l u m e c h a n g e Cell i n v e n t o r y c h a n g e (if n o t i n c l u d e d in m a t e r i a l
X x × -× -x x balance)
As is indicated at the b o t t o m right of Table 1, one has the option of considering the electrolyte in the cell as having its steady-state composition and volume. The actual changes which do occur (changes in concentration, displacement of solution by anodically generated oxygen and by the growing deposit, etc.) then become lumped into the measured volume change and weight decrement. If a complete inventory is attempted, it is well to keep in mind that in the electrowinning of nickel, copper or zinc, for example, the loss in system mass associated with anodically evolved oxygen is about 25 percent of the mass of metal deposited. A useful comprehensive formulation of material balance in electrowinning can be derived by defining an operational volume efficiency, V.E.(%) as follows: V.E.
w = V'c'--V"c"--Sw
i.e., V.E. = 100
H
(4)
~ 100 \V'--+ V " c "
(5)
~ V'(c'---c ) 100 + V'c"
The approximation shown in eqn. (5) is permissible on the basis that the second term in parentheses is small in comparison to the first (In practice, w sometimes has a negative sign, depending upon analytical and inventory measurement errors). The "volume efficiency" is, thus, seen to consist of two components, viz., the ratio of effluent to influent electrolyte volumes plus the ratio of apparent metal loss to metal contained in the electrolyte
exiting the cell. Provided that bleed-off, if any, is not counted as loss from the system, the volume efficiency is also given approximately by the ratio o.~~ effluent to influent electrolyte flow rates. Either way of describing volume efficiency, it will be found to differ sufficiently from 100 percent to have an effect on concentration changes in electrowinning. Use o f V.E. a n d C.E.
From the above definitions and relationships, the change in concentration of the metal being deposited is given by --Ac = c'--c"
-
100
w
c'
V E v'
(100
v:E:
--1
)
(6)
Equation (6) includes the current efficiency implicitly through the equivalence w
C.E. < I > t .............. V' 100q V'
C.E.
(7)
100qv
where v is the time-average influent flow rate, V ' / t . It is obvious that --~c may n o t he equated to w / V ' , the ratio of metal deposited to the volume of electrolyte entering the cell during the given interval of time, unless the volume efficiency is precisely 100%. Rather, for a given value of V.E., the concentration decrease is linear in C . E . The dependence of --Ac on V.E. for a given value of C.E. is also (approximately) linear, but of greater magnitude as illustrated by the numerical example of Table 2. Note that if V.E. were 100%, a one percent decrease in current efficiency would reduce the target concentration change, or " b i t e " , by only 0.1 g/1. TABLE 2 Calculated variation of --Ac with V.E.: c' = 45 g/l and w / V ' -'- 10 g/1 V.E. (%) --zxc (g/l)
99 9.65
98 9.29
97 8.92
96 8.54
In some metallurgical operations of which etectrowinning is a step, it is desirable to produce a specified metal concentration in the effluent electrolyte being recycled. In t h a t case, if the production of cathode and, hence, the electrolysis current are to be fixed, the flow rate must be adjusted to the concentration of the cell feed. Specifically, since C.E. lOOq
t V'
V.E. - c'
100
c "
(8)
39
the desired flow rate is v =
C.E./q lOOc'--c"V.E.
(9)
The following numerical example may be helpful. Consider that copper is to be electrowon to 35.0 g/1 at 183 A/m 2 (17 ASF) and that the electrowinning cell contains 40 cathodes of area 2.0 m 2 each. The cell current is, then, 14,640 A. If the feed to the cell contains 45.0 g/1 Cu (0.8436 A h/g) and the current efficiency is 98% ( " c l e a n " electrolyte and positive positioning of cathode blanks and insoluble anodes), the electrolyte flow rate appropriate to a volume efficiency of 97% is v=
98 × 14,640 0.8436 × 1105
= 1539 1/h (6.78 gal/min)
As illustration t h a t the foregoing considerations are not hypothetical, some pertinent results of actual pilot-scale electrowinning will be given. Electrodes were of commercial size but numerically equivalent to about one tenth the total cathode area of the preceding example. The two trial runs consisted of several stages of electrolysis (Table 3). At the conclusion of each trial run, C.E. and V.E. were determined from overall metal and solution inventory according to Eqns. (2) and (8). These directly measured quantities are designated 'actual' in the Table. During the first trial, the assumed values of C.E. and V.E. were n o t sufficiently close to their subsequently measured actual values to achieve the tarTABLE 3
Typical c o p p e r e l e c t r o w i n n i n g results ( t a r g e t c " = 35.0 g/l) A s s u m e d values c ' (g/l)
C.E. (%)
V.E. (%)
c"(g/1)
lsttrial 44.49 44.62 44.96
98 99 99
100 98 98
35,28 35.40 35.29
actual: 2nd trial 44.75 44.86 45.26 46.00
actual:
97.98
97.22
98 98 98 98
97 97 97 97.5
97.68
97.53
( 3 5 . 3 3 avg.)
35.30 34.99 34.75 34.80 ( 3 4 . 9 6 avg.)
40
get 35.0 g/l copper concentration in the cell effluent. By having measured current and volume efficiencies between trials, it was subsequently possible to bring the copper content of combined cell effluent very close to the desired value, in spite of variations in Uhe concentration of the feed to the cell. If copper deposited and concentration change had been reconciled empiri cally through the use of an apparent (i.e., calculated on the erroneous basis --V' Ac = w) current efficiency, that quantity would have had to be assigned a value of a b o u t 8 8 - 8 9 % . The discrepancy between actual and apparent current efficiency renders this approach not only less than satisfying in terms of possible reflection on performance, but requires the use of two current efficiencies, one for deposit weight and one for concentration changes, in process control and data analysis. Acid production in electrowinning
All of the physical and thermodynamic factors enumerated in Table 1, plus possible source terms of electrochemical nature, influence the material balance for acid. Intrinsically, therefore, the ratio of increase in acid concentration to decrease in metal concentration will deviate from the corresponding ratio of equivalent weights. With reference to the conservation diagram (Fig.2) for acid, assumed to be H2SO4, the weight of acid produced relative to that of metal electrowon is accurately described by WH2SO 4 _
(C.E.) a q
W
C.E. qa
(10)
where (C.E.)a is the overall current efficiency for acid production and qa is the electrochemical equivalence factor for H2SO4 (in copper electrowinning, q/qa = 1.544). The precise formulation o f - - A [HzSO4]/A[M :+ ] is given by the ratio of V " A [ H : S O 4 ] = wH~SO~ + ( V ' - - V " ) [H:SO4 ] '--SWH2SO"
(11)
to - - V " A [ M 2÷] = w - - ( V ' - - V " ) [M2÷] ' + 5w
wH2SO4, g lbY cellieacti°ns
"lost" Fig.2. C o m p o n e n t s o f m a t e r i a l b a l a n c e for acid in e l e e t r o w i n n i n g .
(12)
41
In eqns. (11) a n d (12) t h e s e c o n d t e r m t o t h e right o f t h e equals sign norm a l l y e x c e e d s t h e t h i r d in m a g n i t u d e , so t h a t t h e e x p e r i m e n t a l o b s e r v a t i o n t h a t - - A [H2SO4 ] / A [M 2÷ ] a p p r e c i a b l y e x c e e d s w H 2 S O 4 / w is n o t indicative o f p o o r p r o c e s s c o n t r o l . V a r i a n c e s as large as 10 p e r c e n t f r o m t h e s t o i c h i o m e t r i c r a t i o are n o t unusual. I t m a y be h e l p f u l t o list t h e c h e m i c a l c h a n g e s t h a t a f f e c t t h e overall curr e n t e f f i c i e n c y f o r acid p r o d u c t i o n in e l e c t r o w i n n i n g . T h e a n o d i c r e a c t i o n s (3. t h r o u g h 6.) listed in T a b l e 4 are all c h a r a c t e r i z e d b y a r a t i o o f h y d r o g e n ions t o e l e c t r o n s d i f f e r e n t f r o m u n i t y . T h e p r i n c i p a l a n o d i c r e a c t i o n is, o f course, H 2 0 -~ 1 / 2 O~. + 2 H ÷ + 2 e-
(13)
or, in acidic s u l f a t e e l e c t r o l y t e , H 2 0 + 2 SO~- -* 1 / 2 02 + 2 HSO4 + 2 e -
(13)'
T h e f o r m a t i o n o f lead s u l f a t e ( R e a c t i o n 5.) decreases t h e a n o d i c y i e l d o f h y d r o g e n ion w h e t h e r t h e sulfate is f o r m e d d i r e c t l y or s u b s e q u e n t l y u p o n self-discharge o f t h e a n o d e ; t h e f o r m a t i o n o f P b O or PbO2 d o e s n o t a f f e c t t h e y i e l d o f acid. O x i d a t i o n o f s u l f a t e t o p e r o x y d i s u l f a t e ( R e a c t i o n 4.) also decreases the a m o u n t o f acid p r o d u c e d in t h e cell, if d e c o m p o s i t i o n o f t h e p e r o x y d i s u l f a t e d o e s n o t o c c u r b e f o r e or d u r i n g analysis f o r h y d r o g e n ion. Zinc e l e c t r o w i n n i n g e l e c t r o l y t e a n d s o m e v a t leach leach s o l u t i o n s f o r c o p p e r e l e c t r o w i n n i n g c o n t a i n m a n g a n e s e . O x i d a t i o n o f m a n g a n e s e ion at t h e a n o d e as in R e a c t i o n 6 , in d i s t i n c t i o n t o t h e o t h e r r e a c t i o n s listed in T a b l e 4, adds t o the a n o d i c p r o d u c t i o n o f acid. TABLE4 Reactions affecting acid production in electrowinning 1.2 H ÷ + 2 e- ~ H~ (at cathode, if Ni, Zn, etc.) 2. 1/2 02 + 2 H ÷ + 2 e- ~ H:O (at cathode and in volume) 3. 2 Fe: ~ ~ 2 Fe ~* + 2 e- (at anode-- see text) 4. 2S(~4- - S~O~:- + 2 e- (at anode) 5. Pb + SO~2- -~ PbSO~ + 2 e- (at anode) 6. Mn 2÷ + 2 H~O ~ MnO~ + 4 H ÷ + 2 e- (at anode) T h e p r e s e n c e o f a p p r e c i a b l e iron in the e l e c t r o l y t e c a n be a large f a c t o r in t h e acid balance. As is well k n o w n , iron can also h a v e a significant d o w n w a r d e f f e c t o n c a t h o d i c c u r r e n t e f f i c i e n c y . E x a m p l e s are given in t h e s e c t i o n to follow. Possible c a t h o d i c r e a c t i o n s t h a t a f f e c t (viz., decrease) acid p r o d u c t i o n in e l e c t r o w i n n i n g are h y d r o g e n e v o l u t i o n ( R e a c t i o n 1.) a n d r e d u c t i o n o f a q u e o u s o x y g e n . H y d r o g e n e v o l u t i o n is usually n o t significant f o r c o p p e r e l e c t r o w i n ning. T h e l o w s o l u b i l i t y o f o x y g e n , f o r t u n a t e l y , generally limits t h e i n f l u e n c e o f t h e a c i d - c o n s u m i n g R e a c t i o n 2. t o e f f e c t s o f a f e w p e r c e n t in m a g n i t u d e .
12
Current efficiency in the presence of iron Lest it be inferred t h a t quantitative prediction of current efficiency in practical electrowinning is within the present state of the science, some examples will be given of the effect of iron in a vat leach electrolyte. The results reported were obtained in collaboration with L. Hsueh [1]. In addition to about 18 g/1 of total iron, the electrolyte contained comparable concentrations of aluminum and magnesium (~ 17 g/l A1 and ~ 12 g/1 Mg), Effluent copper concentrations are shown in Fig.3, where cathode current efficiency is plotted against reciprocal current density. CURRENT DENSITY, ASF 75 r
100
90-
>~J
z ill
80-
i i1 u_
50 40 '"r 1
30 r
AIR AGITATION ~k Present
25 w
~
Mode
20 v
'
~
15 I
NORMAL PRACTICE (~ 20 g/i Cu)
~
_4
(~ 10 g/I Cu) ~
~
._.
LU
z
70-
iii
rr {J
Earlier Mode (~ 20 g/I Cu}
60-
5C
0
I 0.01
I 0.02
l 0.03
I 0.04
I 0.05
1 0.06
i 0.07
1.08
RECIPROCAL CURRENT DENSITY Fig. 3. Current efficiency in copper electrowinning from vat leach electrolyte.
When conforming to normal practice, in a pilot electrowinning cell employing full-size electrodes, data points were obtained t h a t could reasonably be said to lie on a straight line intersecting the ordinate at C.E. = 100%. At least, their locations are compatible with mass-transport limited reduction of ferric ion at the cathode. This explanation presupposes t h a t a steady-state concentration of ferric ion is maintained in the volume and that the contribution of migration is small by comparison. Both assumptions are reasonable and, indeed, the first has been verified experimentally [2]. Now, however, when mass transport becomes strongly enhanced by air agitation [3, 4], t h e same model no longer appears to apply. The range and reliability of the current efficiency data are n o t adequate to permit confident conclusions concerning the curvature of the lines (Fig.3), but cathodic cur-
43 rent efficiencies for the earlier mode [5] of air agitation appear to extrapolate to a current efficiency on the ordinate measurably less than 100%. On the other hand, the points obtained by the present technique [6] (closer spacing, convection baffles) lie on a much steeper curve (Fig.3). A possibly more useful manner of plotting results of this nature is as current density of copper deposition against total cathodic current density. When this is done (Fig.4), the two sets of air-agitation data fit reasonably well on straight lines. Cathodic current efficiency is given by the ratio of i Cu2. to total cathodic current density, i. What can be predicted with assurance is that below a certain current density, which is greater for greater mass transport in the electrolyte, there would be no net deposition of copper. A more detailed study would doubtless turn up some interesting and useful generalizations and lead to a better understanding of the interaction of the competing reactions of ferric and cupric ion reduction at the cathode. Recently, Quraishi and Fahidy [7] have made a useful contribution in this direction. 50
PRESENT
40
(1.2
30 iCu2+, ASF
PREVIOUS (2.3 in.) /
2O lO
=///
,,~
// / / /
0
/
0
~
1
l
I
l
I
10
20
30
40
50
60
CURRENT DENSITY, ASF Fig.4. Air-agitation data replotted density.
as c u r r e n t d e n s i t y o f c o p p e r d e p o s i t i o n vs. t o t a l c u r r e n t
In Part II, expressions are derived by means of which it is possible, in principle, to estimate the separate rates of competing cathodic and anodic reactions. :The case considered is copper electrowinning, with Fe 2+ and Fe 3+ as the only extraneous electroactive solute species.
P A R T II C U R R E N T E F F I C I E N C Y IN C O P P E R E L E C T R O W I N N I N G
Introduction In a typical copper electrowinning operation, several reactions contribute directly or indirectly to lowered efficiency of cathodic copper deposition. If flows and concentration differences could be measured with sufficient accuracy, it would be possible in some cases to obtain good estimates of the separate contributions to observed current efficiencies. The approach is to formulate mass balances for the electroactive species and to supplement these equations, if required, with an appropriate electroneutrality condition.
General considerations With reference to the depicted fluid-flow diagram of an electrowinning operation (Fig.5), the following definitions and conventions will be utilized: cl = concentration of solute species i in the cell feed: mass per unit volume; ci" = concentration of solute species i in the partially decopperized effluent; u' = flow rate of electrolyte fed to the cell, or block of cells; u " = flow rate of electrolyte discharged from the cell, or block of cells. Both v' and u" are to be construed as being measured exclusive of any electrolyte recirculation which may be applied within the electrowinning system; that is, to the extent t h a t the losses subsequently enumerated may be neglected, u '~ v " ~ u, the flow-through rate. Where the flow rates are n o t sensibly constant during the period of measurement, use of time-average values, e.g.,
ft vdt (integrating flowmeter), is indicated -
t
-
0
Several mechanisms contribute to a loss of solution volume. The first of these is evaporation of solvent, which we shall express as the rate of the equivalent volume decrease of the electrolyte, L v . As noted above, electrolyte is directly lost by dragout, splashing, misting, leakage, sampling and bleed-off, if any. The total rate of direct loss of electrolyte will be represented by L.
Evaporation I Loss c'Feed ~ - ]
Effluent
oLL , Bleed
Fig. 5.
off
45
N o t e t h a t t h e l o s s L V l e a d s t o a n i n c r e a s e i n t h e c o n c e n t r a t i o n s o f all s o l u t e s , whereas the loss L has a less perceptible effect on concentrations. A d d i t i o n a l f a c t o r s c o n t r i b u t e t o a c h a n g e in v o l u m e d u r i n g e l e c t r o w i n n i n g a n d h e n c e t o a d i f f e r e n c e i n t h e e l e c t r o l y t e f l o w r a t e s v' a n d v " . T h e n e t e f f e c t o f t h e s e f a c t o r s , d e n o t e d as 2~, w i l l i n c l u d e , in p a r t i c u l a r , c h a n g e s d u e t o d i f ferences in temperature and chemical composition attending passage through the cell. Within the stated definitions and conventions, the conservation of fluid volume may be written
v " = v' + 2 - - L - - L v
(1)
I n t h e f o l l o w i n g t r e a t m e n t , i t will b e a s s u m e d t h a t t h e r e is n o i n t e n t i o n a l b l e e d - o f f , s o t h a t E a n d L will b e r e l a t i v e l y s m a l l , b u t n o t n e g l i g i b l e q u a n t i ties.
C o n c e n t r a t i o n changes b r o u g h t a b o u t by c h e m i c a l and e l e c t r o c h e m i c a l reactions As a s p e c i f i c a n d c o m m o n e x a m p l e o f a n e l e c t r o w i n n i n g c e l l f e e d , t h e e l e c t r o l y t e will b e c o n s i d e r e d t o i n c l u d e s u l f u r i c a c i d , a n d c o p p e r a n d i r o n as t h e i r s u l f a t e s , t o g e t h e r w i t h s o m ~ i n e r t c a t i o n s s u c h as a l u m i n u m a n d i n e r t a n i o n s s u c h as p h o s p h a t e a n d o n l y m i n o r a m o u n t s o f o r g a n i c s o l u t e s . In our example, the electroactive solute species present at significant concent r a t i o n l e v e l s a r e C u 2÷, F e :÷, F e 3+ a n d O : ( a q . ) ; s e e T a b l e 5. TABLE5 Chemical and electrochemical changes in electrowinning example Change
Rate
Changes originating at cathodes 1. Cu 2÷ + 2 e - ~ Cu 2. C u + 2 H ÷ + l / 2 0 ~ ( a q . ) ~ Cu 2. + H:O 3. C u + 2 Fe 3÷~ Cu 2÷ + 2 F e ~+
cathodic deposition of Cu corrosion of Cu by 02 (a,q.)* corrosion of Cu by Fe 3÷
I r~ r3
Changes occurring in the volume 4. 1/20~(aq.) + 2 Fe 2. + 2 H ÷ ~ 2 Fe 3. + H20
oxidation of Fe 2+ by O 2 (aq.)
r,
Changes originating at anodes 5. H - O ~ 2 H÷ + 1/2 O2 + 2 e 6. 2 F e 2 . ~ 2 F e 3. + 2 e -
anodic O~ evolution anodic oxidation of Fe 2÷
fI (l--f)/
*Reactions 2. and 3. could equally well have been written as the cathodic reduction of O2(aq. ) and Fe 3÷, respectively, thus subtracting from the cathodic current which would otherwise go into the reduction of Cu 2.. However, the distinction would be largely a formal o n e and, besides, the indicated reactions take place whether or not current is flowing, although not necessarily at the same rates.
46 The corrosion rates r~ and r3 are expressed as mass of copper dissolved per unit time; the rate r4 will relate to the mass of ferric iron produced in unit time by Reaction 4. The current I is here the effective electrolysis cur-~ rent, i.e., exclusive of stray or parasitic currents. On the average, the fraction f of the anodic current goes i n t o oxygen evolution (Reaction 5.) at the insoluble anodes and the remaining fraction 1--f into anodic oxidation of ferrous ion (Reaction 6.). The use of the time-average current, i.e., ] t
f t Idt, is m a n d a t o r y whenever the current cannot be held sensibly constant 0 during the period of measurement*.
Material balances
The symbol M will be used to denote the formula weight of a chemical species, and F represents the Faraday constant. It is, of course, assumed that M, F and I are expressed in consistent units. Copper balance The mass balance equation
Mcu c'v'
influx
2F
I
+
r2
cathodic corrosion deposition by O2(aq.)
+
r3
corrosion by Fe 3÷
--
EL
solution loss
=
c " v " (2)
effluent
details the net rate of removal of Cu 2÷ from the system, as mass of copper per unit time. In eqn. (2), ~ is the mean copper c o n t e n t of the solution which is lost. Use will be made of the fact that ~ is intermediate in value between c' and c " On collecting terms in the concentration and utilizing eqn. (1), we may write c " v " - - c ' v ' + ~-L= ( c " - - c ' ) v ' - - c " ( L v - - ~ ) + ( ~ - - c " ) L
(3)
Now, while the third term on the right of eqn. (3) may be neglected in comparison to the first two terms (unless there is an unusual loss of electrolyte), in general it will not be feasible to neglect the second term. For whereas, for example, LV might be only a percent or less of v', the difference c'--.c" for Cu 2÷ might be of the order of 2 5 percent of c " ; the contribution E could also be of significant magnitude. Therefore, we shall retain the term c " ( L v - 2 ~ ) and denote it by c " 5 . T h e change in concentration of a given solute on passage through the cell, c " - - c ' , will be denoted Ac, as before. The increment 5 might be estimated from an observed change in total electrolyte volume, combined with m e a s u r e d t e m p e r a t u r e s a n d d e n s i t i e s . *If this condition applies, some inaccuracy in extracted values of f will result, since f will
1 t not be independent of I, and one should then write f[ =t f fldt. 0
47 More straightforward methods of calculating ~ are indicated below. Accordingly, l i k e / , v and concentrations, 5 will be considered to be susceptible to measurement. The collected concentration terms then become, in the case of cupric ion, v' Accu2+--c"cu2+
Equation (2) may be recast as v'ACCu2+-
Mcu C"cu2+6 + - - I 2F
= r2 + r3
(4)
Measured copper concentrations are seen to be linearly related to the unknown quantities rz and r3, whose magnitudes we wish to determine. The weight gain* w of the cathodes can also be used to evaluate the sum of r2 and r 3 : MCu w -
t f o
2F
Idt--(r2
(5)
+r3)t
Unfortunately, relations (4) and (5) give the same information, and it will be seen necessary to employ three additional relations to evaluate r2 and r3 separately. However, if the copper concentrations are measured with good accuracy (titration or electrogravimetry), the incremental rate of electrolyte volume change (exclusive of evaporation), 5, may be calculated in principle by combining eqns. (4) and (5). Hydrogen
balance
In what follows, the quantity c H + is intended to represent the hydrogen ion concentration as measured by the so-called "free acid", which includ.es in addition to H+(aq.) the hydrogen which is combined with sulfate as HSO~, the first hydrogen of the species H3PO4, if present, etc. MH c'v'
H÷ influx
+
--
2MH fI
--
MH --
F anodic 02 evolution
Mc u r2 Cu corrosion by 02 (aq.)
r4
--
EL
=
c"v"
MF e volume oxisolution effluent dation of Fe 2+ loss H÷
(6)
or MHI v ACH+--C"H+6 = - -
F
f--
2M H - r2
MH
Mcu
MFe
r4
Le. assuming that physical detachement o f portions o f the deposit does not occur.
(7)
4~
Iron balance
C U
+
Fe 3+ influx
MFe 2MFe ..... (1--f)I . . . . . . . . r~ + F Mcu anodic oxiCu corrosion dation of Fe :÷ by Fe 3÷
r4
--
~L
=
(8!
c"v"
volume oxi- solution effluent dation of Fe 2÷ loss Fe 3.
or t
,,
V ACFe3+--c Fe.~+~
MFe
F
MFeJ 2MFe -. . . . . f . . . . . r3 + r4 F Mcu
I -
(9)
Because of the reciprocal variations of the ferrous and ferric ion concentrations (Reactions 3., 4. and 6.), a mass balance for Fe 2÷ provides no new information, yielding MFe MFe I 2MFe v' ACFe2÷ - - C " F e 2 +5 + . . . . . I = + - f + .... r3--r4 F F Mcu
(10)
However, if Fe 2÷ and Fe 3. concentrations can be measured with good accuracy, the sum of eqns. (9) and (10) may be used as an alternate metals for estimating 5. Except for a small term in 5, the total iron concentration, CFe2. + CFe3÷, may be treated as the concentration of a single, indifferent (i.e., n o t electroactive) chemical species. Sulfate
balance
Actually, what is derived here applies equally to all indifferent species. Sulfate is singled out because changes in total sulfate concentration can be measured with greater accuracy than for most of the other inactive solutes. Material balance gives, simply 0 = c'v'--~L--c"v"
~ (c"--c')v'--c"
5
(11)
The approximation implied in eqn. (11) is quite close, since c and c " will be nearly equal. Thus, the increment 8 may be estimated from a measured change
in the concentration of indifferent electrolyte. For total sulfate, including both HSO~ and SO~- species, 5 = V'ACso ~-(total)/C" SO~-(total) Evaluation
of the unknown
(12)
quantities
In terms of the quantities n o t susceptible to direct measurement, f, r2, r3 and r4, linear relations of the following form have been formulated: Ac Cu2÷ = ~ ( r : , ra)
(4 ')
ACH* = • (f, r2, r4)
(7')
ACFeS+ = 7(f, r3,/'4)
(9')
49 The requisite supplementary relationship for obtaining solutions for any one of the unknowns is obtained by utilizing the electroneutrality condition Zzi[Si] = 0
(13)
where z i is the charge on the solute species Si, the molar concentration [Si] -= ci/Mi, and the sum extends over all solute species in the electrolyte. Some simplification ensues when making use of the requirement of charge conservation in the alternate form GziA[Si] = 0
(14)
since, now, ionic species for which the change in concentration is of a low order of magnitude need not be included in the summation. Thus, an equation such as 2A[Cu ~+] + A [ H ÷] + 3A[Fe 3÷] + 2A[Fe 2+] + 3A[AP ÷] + etc. = 2A [SO~-(total)] +3A [po43-(total)] + etc.
(15)
where A[A~ 3÷]
5 -
v'
/I
/I
C A~~+ 5 C SO~-(total) , A[SO42-(total)] - , etc. MA~ v MSO,
(16)
can be combined with eqns. (4), (7), (9) and either eqn. (5), (10) or (12) to yield (conveniently, by computer) values of f, r2, r3, r4 and 5 from measured concentrations and parameters. Equation (1 5) is seen to be correct as written when [H ÷] is interpreted as the free acid concentration, as previously stipulated. Thus, the primitive equation of electroneutrality equivalent to eqn. (1 5) would have the term A [H+(aq.)] on the left in place of A[H ÷] and the terms 2A[SO42-] + A [HS(F4 ] + A [H~POj] on the right. But A [H +] is obtained by adding A [HSO4-] + A [H3PO4]to A [H+(aq.)] ; adding the same terms to the right of the primitive equation results in eqn. (15). The ability to make effective use of the foregoing material-balance analysis depends critically upon the capabilities of the measurement techniques. Under the most favorable circumstances when fluid flow, electric current and pertinent concentrations can be accurately measured, and the quantities f, r~, r3, and r4 have non-negligible values, it should be possible to estimate the separate contributions of 02 (aq.) and Fe 3÷ to cathode corrosion and of Fe 2÷ to the anode reaction. ACKNOWLEDGEMENT The author is pleased to acknowledge the useful input of Dr. L. Hsueh, particularly for evaluating by c o m p u t e r calculations the degree of precision required in chemical analysis in order to realize the objectives set forth in Part II.
50
A talk based on the contents of this paper was given at the 67th Annual Meeting of the AICHE, Washington, D.C., December 2, 1974. REFERENCES
1 W.W. Harvey and L. Hsueh, Copper electrowinning from vat leach electrolyte, C I M Bulletin, 69 (April) (1976) 109--119. 2 T.N. Andersen, C.N. Wright and K.J. Richards, Important electrochemical aspects of e]ectrowinning copper from acid leach solutions. International Symposium on Hydrometallurgy, published by AIME, N e w York, 1973, pp. 171--202. 3 N. Ibl, Stofftransport bei der Elektrolyse mit Gasrnhrung, Chemic Ing. Tech., 43 (1971) 202--215. 4 V.A. Ettet, B.V. Tilak and A.S. Gendron, Measurement of cathode mass transfer coefficients in electrowinning cells, J. Electrochem. Soc., 121 (1974) 867--872. For more recent papers by the Inco group on the same subject, see: Can. J. Chem. Eng., 53 (February) (1975) 36--40; Metall. Trans., 6B (March) (1975) 31--36; Chem. and Ind: 9 (3 May) (1975) 376--377. 5 W.W. Harvey, A.H. Miguel, P. Larson and LS. Servi, Application of air agitation in electrolytic decopperization, Trans. Instn. Min. Metall. (Sect. C: Mineral Process. Extr. Metall.) 84 (1975) 11--17 6 W.W. Harvey, M.R. Randlett and K.I. Bangerskis, Elevated current density electro* winning of superior quality copper from high-acid electrolyte, Trans. Instn. Min. Metall. (Sect. C: Mineral Process. Extr. Metall.), 84 (1975)210--220. 7 M.S. Quraishi and T.Z. Fahidy, Chemistry and Industry, 3 May 1975, 377---378.
35
MATERIAL BALANCE AND CURRENT EFFICIENCY IN ELECTROWINNING
W.W. HARVEY* EIC Corporation, 55 Chapel Street, Newton, Mass. 02158 (U.S.A.) (Received October 17th, 1975) ABSTRACT
Harvey, W.W., 1976. Material balance and current efficiency in electrowinning. Hydrometallurgy, 2: 35--50. A process variable in addition to the current efficiency is required in order to obtain exact correlation among current, electrolyte flow, and concentration changes in electrowinning. To this end, a volume efficiency has been defined and incorporated into a formulation for estimating the separate contributions to observed current efficiencies. In Part I, expressions are presented which enable the response of the electrowinning system to changes in infiuent to be accurately predicted. The formulation developed is practical, and its use is illustrated by actual examples. Part II presents a somewhat idealized treatment, in that very precise and accurate chemical analyses would be required in order to obtain a reliable estimation of the relative rates of competing electrode reactions. PART I MATERIAL BALANCE IN ELECTROWINNING Introduction E a r l y in o n e ' s i n v o l v e m e n t in p r a c t i c a l e l e c t r o w i n n i n g , t h e i n a b i l i t y t o rec o n c i l e c o n c e n t r a t i o n c h a n g e w i t h c u r r e n t a n d f l o w c a n be a s o u r c e o f frust r a t i o n . Of c o u r s e , an e f f e c t i v e c u r r e n t e f f i c i e n c y m a y be so d e f i n e d t o give t h e d e s i r e d r e s u l t , b u t i t will d i f f e r t o s o m e d e g r e e f r o m t h e a c t u a l , m e a s u r e d current efficiency. On further examination of the problem, one can become r e a s s u r e d t h a t t h e e l e c t r o w i n n i n g p r o c e s s is, i n d e e d , c a p a b l e o f p r e c i s e a n d r a t i o n a l c o n t r o l . In o r d e r t o e x t e n d t h i s c o n t r o l b e y o n d t h e p r o d u c t i o n o f electrowon metal to include the composition of effluent electrolyte, which will g e n e r a l l y be r e c o n s t i t u t e d a n d r e c y c l e d b a c k t o e l e c t r o w i n n i n g , it is n e c e s s a r y t o t a k e a c c o u n t o f t h e v o l u m e c h a n g e s i n h e r e n t in e l e c t r o w i n n i n g . T h e a u t h o r ' s a p p r o a c h t o a m a t e r i a l - b a l a n c e d e s c r i p t i o n o f t h e p r o c e s s is developed below. *Formerly, Ledgemont Laboratory, Kennecott Copper Corporation, Lexington, Massachusetts 02173, U.S.A.
6
C o n c e p t s attd definitiolts
For present purposes it will be useful to treat electrowinning as a batch operation. The treatment also encompasses continuous operation, ~he time interval between each stage then being determined by the times at which the deposit is weighed and the electrolyte sampled. The expressions obtained in Part I may be recast into continuous notation by consistent application of time derivatives. How this may be done is shown in Part II, which focusses on the formulation of the several electrochemical factors determining cathodic efficiency in copper electrowinning from a leach electrolyte containing appreciable iron. w, 9 depGsiteci
t c '° g/~ M 2+
'
1 5w, 9
"lost" Fig.1. C o m p o n e n t s o f material balance for metal in e l e c t r o w i n n i n g .
In accordance with the conservation diagram for the metal being electrowon (Fig. 1), the following identifications are made: V' = volume of electro, lyte entering the cell in time t; V " = volume of electrolyte exiting the cell in time t; c', c " = respective concentrations of the metal ions; q = electrochemical equivalence factor, e.g., A h/g; c = fractional cathodic current efficiency. The weight of metal deposited in time t is w
= - - /J q 0
(1~
e I dt
where I is the instantaneous cell current. The overall current efficiency for the period of observation is
c.E.
:-
loo w/-" Iq
f
x dt = l o o wq/ t
o
where < I > is the time-average cell current. There are a number of inherent physical and t h e r m o d y n a m i c factors in electrowinning which combine to make V ' ~: V " and w ~t V ' c ' - - V " c "
The second of the two inequalities defines a weight decrement, 5 w, which
(3)
37 includes the resultant of errors in the measurement of volume and concentration as well as metal value actually lost from the system. The factors that come to mind and an indication of which quantities, A V and 5 w, t h e y affect are given in Table 1. It is important to recognize t h a t tidying up an electrowinning operation, whether laboratory or commercial, may only reduce but cannot eliminate the majority of these factors. That fact appreciated, one can then concentrate on the business of accounting for their effects in a manner to permit realization of precise process control. TABLE1 F a c t o r s c o n t r i b u t i n g t o v o l u m e c h a n g e a n d m e t a l loss in e l e c t r o w i n n i n g Factor
AV
5w
Factor
AV
5w
E v a p o r a t i o n losses Generation of mist Sampling and bleedoff Spatter and leakage Misc. t r a n s f e r l o s s e s
× x × X x
-× × × x
Dragout (on pulling) Temperature change Partial v o l u m e c h a n g e Cell i n v e n t o r y c h a n g e (if n o t i n c l u d e d in m a t e r i a l
X x × -× -x x balance)
As is indicated at the b o t t o m right of Table 1, one has the option of considering the electrolyte in the cell as having its steady-state composition and volume. The actual changes which do occur (changes in concentration, displacement of solution by anodically generated oxygen and by the growing deposit, etc.) then become lumped into the measured volume change and weight decrement. If a complete inventory is attempted, it is well to keep in mind that in the electrowinning of nickel, copper or zinc, for example, the loss in system mass associated with anodically evolved oxygen is about 25 percent of the mass of metal deposited. A useful comprehensive formulation of material balance in electrowinning can be derived by defining an operational volume efficiency, V.E.(%) as follows: V.E.
w = V'c'--V"c"--Sw
i.e., V.E. = 100
H
(4)
~ 100 \V'--+ V " c "
(5)
~ V'(c'---c ) 100 + V'c"
The approximation shown in eqn. (5) is permissible on the basis that the second term in parentheses is small in comparison to the first (In practice, w sometimes has a negative sign, depending upon analytical and inventory measurement errors). The "volume efficiency" is, thus, seen to consist of two components, viz., the ratio of effluent to influent electrolyte volumes plus the ratio of apparent metal loss to metal contained in the electrolyte
exiting the cell. Provided that bleed-off, if any, is not counted as loss from the system, the volume efficiency is also given approximately by the ratio o.~~ effluent to influent electrolyte flow rates. Either way of describing volume efficiency, it will be found to differ sufficiently from 100 percent to have an effect on concentration changes in electrowinning. Use o f V.E. a n d C.E.
From the above definitions and relationships, the change in concentration of the metal being deposited is given by --Ac = c'--c"
-
100
w
c'
V E v'
(100
v:E:
--1
)
(6)
Equation (6) includes the current efficiency implicitly through the equivalence w
C.E. < I > t .............. V' 100q V'
C.E.
(7)
100qv
where v is the time-average influent flow rate, V ' / t . It is obvious that --~c may n o t he equated to w / V ' , the ratio of metal deposited to the volume of electrolyte entering the cell during the given interval of time, unless the volume efficiency is precisely 100%. Rather, for a given value of V.E., the concentration decrease is linear in C . E . The dependence of --Ac on V.E. for a given value of C.E. is also (approximately) linear, but of greater magnitude as illustrated by the numerical example of Table 2. Note that if V.E. were 100%, a one percent decrease in current efficiency would reduce the target concentration change, or " b i t e " , by only 0.1 g/1. TABLE 2 Calculated variation of --Ac with V.E.: c' = 45 g/l and w / V ' -'- 10 g/1 V.E. (%) --zxc (g/l)
99 9.65
98 9.29
97 8.92
96 8.54
In some metallurgical operations of which etectrowinning is a step, it is desirable to produce a specified metal concentration in the effluent electrolyte being recycled. In t h a t case, if the production of cathode and, hence, the electrolysis current are to be fixed, the flow rate must be adjusted to the concentration of the cell feed. Specifically, since C.E. lOOq
t V'
V.E. - c'
100
c "
(8)
39
the desired flow rate is v =
C.E./q lOOc'--c"V.E.
(9)
The following numerical example may be helpful. Consider that copper is to be electrowon to 35.0 g/1 at 183 A/m 2 (17 ASF) and that the electrowinning cell contains 40 cathodes of area 2.0 m 2 each. The cell current is, then, 14,640 A. If the feed to the cell contains 45.0 g/1 Cu (0.8436 A h/g) and the current efficiency is 98% ( " c l e a n " electrolyte and positive positioning of cathode blanks and insoluble anodes), the electrolyte flow rate appropriate to a volume efficiency of 97% is v=
98 × 14,640 0.8436 × 1105
= 1539 1/h (6.78 gal/min)
As illustration t h a t the foregoing considerations are not hypothetical, some pertinent results of actual pilot-scale electrowinning will be given. Electrodes were of commercial size but numerically equivalent to about one tenth the total cathode area of the preceding example. The two trial runs consisted of several stages of electrolysis (Table 3). At the conclusion of each trial run, C.E. and V.E. were determined from overall metal and solution inventory according to Eqns. (2) and (8). These directly measured quantities are designated 'actual' in the Table. During the first trial, the assumed values of C.E. and V.E. were n o t sufficiently close to their subsequently measured actual values to achieve the tarTABLE 3
Typical c o p p e r e l e c t r o w i n n i n g results ( t a r g e t c " = 35.0 g/l) A s s u m e d values c ' (g/l)
C.E. (%)
V.E. (%)
c"(g/1)
lsttrial 44.49 44.62 44.96
98 99 99
100 98 98
35,28 35.40 35.29
actual: 2nd trial 44.75 44.86 45.26 46.00
actual:
97.98
97.22
98 98 98 98
97 97 97 97.5
97.68
97.53
( 3 5 . 3 3 avg.)
35.30 34.99 34.75 34.80 ( 3 4 . 9 6 avg.)
40
get 35.0 g/l copper concentration in the cell effluent. By having measured current and volume efficiencies between trials, it was subsequently possible to bring the copper content of combined cell effluent very close to the desired value, in spite of variations in Uhe concentration of the feed to the cell. If copper deposited and concentration change had been reconciled empiri cally through the use of an apparent (i.e., calculated on the erroneous basis --V' Ac = w) current efficiency, that quantity would have had to be assigned a value of a b o u t 8 8 - 8 9 % . The discrepancy between actual and apparent current efficiency renders this approach not only less than satisfying in terms of possible reflection on performance, but requires the use of two current efficiencies, one for deposit weight and one for concentration changes, in process control and data analysis. Acid production in electrowinning
All of the physical and thermodynamic factors enumerated in Table 1, plus possible source terms of electrochemical nature, influence the material balance for acid. Intrinsically, therefore, the ratio of increase in acid concentration to decrease in metal concentration will deviate from the corresponding ratio of equivalent weights. With reference to the conservation diagram (Fig.2) for acid, assumed to be H2SO4, the weight of acid produced relative to that of metal electrowon is accurately described by WH2SO 4 _
(C.E.) a q
W
C.E. qa
(10)
where (C.E.)a is the overall current efficiency for acid production and qa is the electrochemical equivalence factor for H2SO4 (in copper electrowinning, q/qa = 1.544). The precise formulation o f - - A [HzSO4]/A[M :+ ] is given by the ratio of V " A [ H : S O 4 ] = wH~SO~ + ( V ' - - V " ) [H:SO4 ] '--SWH2SO"
(11)
to - - V " A [ M 2÷] = w - - ( V ' - - V " ) [M2÷] ' + 5w
wH2SO4, g lbY cellieacti°ns
"lost" Fig.2. C o m p o n e n t s o f m a t e r i a l b a l a n c e for acid in e l e e t r o w i n n i n g .
(12)
41
In eqns. (11) a n d (12) t h e s e c o n d t e r m t o t h e right o f t h e equals sign norm a l l y e x c e e d s t h e t h i r d in m a g n i t u d e , so t h a t t h e e x p e r i m e n t a l o b s e r v a t i o n t h a t - - A [H2SO4 ] / A [M 2÷ ] a p p r e c i a b l y e x c e e d s w H 2 S O 4 / w is n o t indicative o f p o o r p r o c e s s c o n t r o l . V a r i a n c e s as large as 10 p e r c e n t f r o m t h e s t o i c h i o m e t r i c r a t i o are n o t unusual. I t m a y be h e l p f u l t o list t h e c h e m i c a l c h a n g e s t h a t a f f e c t t h e overall curr e n t e f f i c i e n c y f o r acid p r o d u c t i o n in e l e c t r o w i n n i n g . T h e a n o d i c r e a c t i o n s (3. t h r o u g h 6.) listed in T a b l e 4 are all c h a r a c t e r i z e d b y a r a t i o o f h y d r o g e n ions t o e l e c t r o n s d i f f e r e n t f r o m u n i t y . T h e p r i n c i p a l a n o d i c r e a c t i o n is, o f course, H 2 0 -~ 1 / 2 O~. + 2 H ÷ + 2 e-
(13)
or, in acidic s u l f a t e e l e c t r o l y t e , H 2 0 + 2 SO~- -* 1 / 2 02 + 2 HSO4 + 2 e -
(13)'
T h e f o r m a t i o n o f lead s u l f a t e ( R e a c t i o n 5.) decreases t h e a n o d i c y i e l d o f h y d r o g e n ion w h e t h e r t h e sulfate is f o r m e d d i r e c t l y or s u b s e q u e n t l y u p o n self-discharge o f t h e a n o d e ; t h e f o r m a t i o n o f P b O or PbO2 d o e s n o t a f f e c t t h e y i e l d o f acid. O x i d a t i o n o f s u l f a t e t o p e r o x y d i s u l f a t e ( R e a c t i o n 4.) also decreases the a m o u n t o f acid p r o d u c e d in t h e cell, if d e c o m p o s i t i o n o f t h e p e r o x y d i s u l f a t e d o e s n o t o c c u r b e f o r e or d u r i n g analysis f o r h y d r o g e n ion. Zinc e l e c t r o w i n n i n g e l e c t r o l y t e a n d s o m e v a t leach leach s o l u t i o n s f o r c o p p e r e l e c t r o w i n n i n g c o n t a i n m a n g a n e s e . O x i d a t i o n o f m a n g a n e s e ion at t h e a n o d e as in R e a c t i o n 6 , in d i s t i n c t i o n t o t h e o t h e r r e a c t i o n s listed in T a b l e 4, adds t o the a n o d i c p r o d u c t i o n o f acid. TABLE4 Reactions affecting acid production in electrowinning 1.2 H ÷ + 2 e- ~ H~ (at cathode, if Ni, Zn, etc.) 2. 1/2 02 + 2 H ÷ + 2 e- ~ H:O (at cathode and in volume) 3. 2 Fe: ~ ~ 2 Fe ~* + 2 e- (at anode-- see text) 4. 2S(~4- - S~O~:- + 2 e- (at anode) 5. Pb + SO~2- -~ PbSO~ + 2 e- (at anode) 6. Mn 2÷ + 2 H~O ~ MnO~ + 4 H ÷ + 2 e- (at anode) T h e p r e s e n c e o f a p p r e c i a b l e iron in the e l e c t r o l y t e c a n be a large f a c t o r in t h e acid balance. As is well k n o w n , iron can also h a v e a significant d o w n w a r d e f f e c t o n c a t h o d i c c u r r e n t e f f i c i e n c y . E x a m p l e s are given in t h e s e c t i o n to follow. Possible c a t h o d i c r e a c t i o n s t h a t a f f e c t (viz., decrease) acid p r o d u c t i o n in e l e c t r o w i n n i n g are h y d r o g e n e v o l u t i o n ( R e a c t i o n 1.) a n d r e d u c t i o n o f a q u e o u s o x y g e n . H y d r o g e n e v o l u t i o n is usually n o t significant f o r c o p p e r e l e c t r o w i n ning. T h e l o w s o l u b i l i t y o f o x y g e n , f o r t u n a t e l y , generally limits t h e i n f l u e n c e o f t h e a c i d - c o n s u m i n g R e a c t i o n 2. t o e f f e c t s o f a f e w p e r c e n t in m a g n i t u d e .
12
Current efficiency in the presence of iron Lest it be inferred t h a t quantitative prediction of current efficiency in practical electrowinning is within the present state of the science, some examples will be given of the effect of iron in a vat leach electrolyte. The results reported were obtained in collaboration with L. Hsueh [1]. In addition to about 18 g/1 of total iron, the electrolyte contained comparable concentrations of aluminum and magnesium (~ 17 g/l A1 and ~ 12 g/1 Mg), Effluent copper concentrations are shown in Fig.3, where cathode current efficiency is plotted against reciprocal current density. CURRENT DENSITY, ASF 75 r
100
90-
>~J
z ill
80-
i i1 u_
50 40 '"r 1
30 r
AIR AGITATION ~k Present
25 w
~
Mode
20 v
'
~
15 I
NORMAL PRACTICE (~ 20 g/i Cu)
~
_4
(~ 10 g/I Cu) ~
~
._.
LU
z
70-
iii
rr {J
Earlier Mode (~ 20 g/I Cu}
60-
5C
0
I 0.01
I 0.02
l 0.03
I 0.04
I 0.05
1 0.06
i 0.07
1.08
RECIPROCAL CURRENT DENSITY Fig. 3. Current efficiency in copper electrowinning from vat leach electrolyte.
When conforming to normal practice, in a pilot electrowinning cell employing full-size electrodes, data points were obtained t h a t could reasonably be said to lie on a straight line intersecting the ordinate at C.E. = 100%. At least, their locations are compatible with mass-transport limited reduction of ferric ion at the cathode. This explanation presupposes t h a t a steady-state concentration of ferric ion is maintained in the volume and that the contribution of migration is small by comparison. Both assumptions are reasonable and, indeed, the first has been verified experimentally [2]. Now, however, when mass transport becomes strongly enhanced by air agitation [3, 4], t h e same model no longer appears to apply. The range and reliability of the current efficiency data are n o t adequate to permit confident conclusions concerning the curvature of the lines (Fig.3), but cathodic cur-
43 rent efficiencies for the earlier mode [5] of air agitation appear to extrapolate to a current efficiency on the ordinate measurably less than 100%. On the other hand, the points obtained by the present technique [6] (closer spacing, convection baffles) lie on a much steeper curve (Fig.3). A possibly more useful manner of plotting results of this nature is as current density of copper deposition against total cathodic current density. When this is done (Fig.4), the two sets of air-agitation data fit reasonably well on straight lines. Cathodic current efficiency is given by the ratio of i Cu2. to total cathodic current density, i. What can be predicted with assurance is that below a certain current density, which is greater for greater mass transport in the electrolyte, there would be no net deposition of copper. A more detailed study would doubtless turn up some interesting and useful generalizations and lead to a better understanding of the interaction of the competing reactions of ferric and cupric ion reduction at the cathode. Recently, Quraishi and Fahidy [7] have made a useful contribution in this direction. 50
PRESENT
40
(1.2
30 iCu2+, ASF
PREVIOUS (2.3 in.) /
2O lO
=///
,,~
// / / /
0
/
0
~
1
l
I
l
I
10
20
30
40
50
60
CURRENT DENSITY, ASF Fig.4. Air-agitation data replotted density.
as c u r r e n t d e n s i t y o f c o p p e r d e p o s i t i o n vs. t o t a l c u r r e n t
In Part II, expressions are derived by means of which it is possible, in principle, to estimate the separate rates of competing cathodic and anodic reactions. :The case considered is copper electrowinning, with Fe 2+ and Fe 3+ as the only extraneous electroactive solute species.
P A R T II C U R R E N T E F F I C I E N C Y IN C O P P E R E L E C T R O W I N N I N G
Introduction In a typical copper electrowinning operation, several reactions contribute directly or indirectly to lowered efficiency of cathodic copper deposition. If flows and concentration differences could be measured with sufficient accuracy, it would be possible in some cases to obtain good estimates of the separate contributions to observed current efficiencies. The approach is to formulate mass balances for the electroactive species and to supplement these equations, if required, with an appropriate electroneutrality condition.
General considerations With reference to the depicted fluid-flow diagram of an electrowinning operation (Fig.5), the following definitions and conventions will be utilized: cl = concentration of solute species i in the cell feed: mass per unit volume; ci" = concentration of solute species i in the partially decopperized effluent; u' = flow rate of electrolyte fed to the cell, or block of cells; u " = flow rate of electrolyte discharged from the cell, or block of cells. Both v' and u" are to be construed as being measured exclusive of any electrolyte recirculation which may be applied within the electrowinning system; that is, to the extent t h a t the losses subsequently enumerated may be neglected, u '~ v " ~ u, the flow-through rate. Where the flow rates are n o t sensibly constant during the period of measurement, use of time-average values, e.g.,
ft vdt (integrating flowmeter), is indicated -
t
-
0
Several mechanisms contribute to a loss of solution volume. The first of these is evaporation of solvent, which we shall express as the rate of the equivalent volume decrease of the electrolyte, L v . As noted above, electrolyte is directly lost by dragout, splashing, misting, leakage, sampling and bleed-off, if any. The total rate of direct loss of electrolyte will be represented by L.
Evaporation I Loss c'Feed ~ - ]
Effluent
oLL , Bleed
Fig. 5.
off
45
N o t e t h a t t h e l o s s L V l e a d s t o a n i n c r e a s e i n t h e c o n c e n t r a t i o n s o f all s o l u t e s , whereas the loss L has a less perceptible effect on concentrations. A d d i t i o n a l f a c t o r s c o n t r i b u t e t o a c h a n g e in v o l u m e d u r i n g e l e c t r o w i n n i n g a n d h e n c e t o a d i f f e r e n c e i n t h e e l e c t r o l y t e f l o w r a t e s v' a n d v " . T h e n e t e f f e c t o f t h e s e f a c t o r s , d e n o t e d as 2~, w i l l i n c l u d e , in p a r t i c u l a r , c h a n g e s d u e t o d i f ferences in temperature and chemical composition attending passage through the cell. Within the stated definitions and conventions, the conservation of fluid volume may be written
v " = v' + 2 - - L - - L v
(1)
I n t h e f o l l o w i n g t r e a t m e n t , i t will b e a s s u m e d t h a t t h e r e is n o i n t e n t i o n a l b l e e d - o f f , s o t h a t E a n d L will b e r e l a t i v e l y s m a l l , b u t n o t n e g l i g i b l e q u a n t i ties.
C o n c e n t r a t i o n changes b r o u g h t a b o u t by c h e m i c a l and e l e c t r o c h e m i c a l reactions As a s p e c i f i c a n d c o m m o n e x a m p l e o f a n e l e c t r o w i n n i n g c e l l f e e d , t h e e l e c t r o l y t e will b e c o n s i d e r e d t o i n c l u d e s u l f u r i c a c i d , a n d c o p p e r a n d i r o n as t h e i r s u l f a t e s , t o g e t h e r w i t h s o m ~ i n e r t c a t i o n s s u c h as a l u m i n u m a n d i n e r t a n i o n s s u c h as p h o s p h a t e a n d o n l y m i n o r a m o u n t s o f o r g a n i c s o l u t e s . In our example, the electroactive solute species present at significant concent r a t i o n l e v e l s a r e C u 2÷, F e :÷, F e 3+ a n d O : ( a q . ) ; s e e T a b l e 5. TABLE5 Chemical and electrochemical changes in electrowinning example Change
Rate
Changes originating at cathodes 1. Cu 2÷ + 2 e - ~ Cu 2. C u + 2 H ÷ + l / 2 0 ~ ( a q . ) ~ Cu 2. + H:O 3. C u + 2 Fe 3÷~ Cu 2÷ + 2 F e ~+
cathodic deposition of Cu corrosion of Cu by 02 (a,q.)* corrosion of Cu by Fe 3÷
I r~ r3
Changes occurring in the volume 4. 1/20~(aq.) + 2 Fe 2. + 2 H ÷ ~ 2 Fe 3. + H20
oxidation of Fe 2+ by O 2 (aq.)
r,
Changes originating at anodes 5. H - O ~ 2 H÷ + 1/2 O2 + 2 e 6. 2 F e 2 . ~ 2 F e 3. + 2 e -
anodic O~ evolution anodic oxidation of Fe 2÷
fI (l--f)/
*Reactions 2. and 3. could equally well have been written as the cathodic reduction of O2(aq. ) and Fe 3÷, respectively, thus subtracting from the cathodic current which would otherwise go into the reduction of Cu 2.. However, the distinction would be largely a formal o n e and, besides, the indicated reactions take place whether or not current is flowing, although not necessarily at the same rates.
46 The corrosion rates r~ and r3 are expressed as mass of copper dissolved per unit time; the rate r4 will relate to the mass of ferric iron produced in unit time by Reaction 4. The current I is here the effective electrolysis cur-~ rent, i.e., exclusive of stray or parasitic currents. On the average, the fraction f of the anodic current goes i n t o oxygen evolution (Reaction 5.) at the insoluble anodes and the remaining fraction 1--f into anodic oxidation of ferrous ion (Reaction 6.). The use of the time-average current, i.e., ] t
f t Idt, is m a n d a t o r y whenever the current cannot be held sensibly constant 0 during the period of measurement*.
Material balances
The symbol M will be used to denote the formula weight of a chemical species, and F represents the Faraday constant. It is, of course, assumed that M, F and I are expressed in consistent units. Copper balance The mass balance equation
Mcu c'v'
influx
2F
I
+
r2
cathodic corrosion deposition by O2(aq.)
+
r3
corrosion by Fe 3÷
--
EL
solution loss
=
c " v " (2)
effluent
details the net rate of removal of Cu 2÷ from the system, as mass of copper per unit time. In eqn. (2), ~ is the mean copper c o n t e n t of the solution which is lost. Use will be made of the fact that ~ is intermediate in value between c' and c " On collecting terms in the concentration and utilizing eqn. (1), we may write c " v " - - c ' v ' + ~-L= ( c " - - c ' ) v ' - - c " ( L v - - ~ ) + ( ~ - - c " ) L
(3)
Now, while the third term on the right of eqn. (3) may be neglected in comparison to the first two terms (unless there is an unusual loss of electrolyte), in general it will not be feasible to neglect the second term. For whereas, for example, LV might be only a percent or less of v', the difference c'--.c" for Cu 2÷ might be of the order of 2 5 percent of c " ; the contribution E could also be of significant magnitude. Therefore, we shall retain the term c " ( L v - 2 ~ ) and denote it by c " 5 . T h e change in concentration of a given solute on passage through the cell, c " - - c ' , will be denoted Ac, as before. The increment 5 might be estimated from an observed change in total electrolyte volume, combined with m e a s u r e d t e m p e r a t u r e s a n d d e n s i t i e s . *If this condition applies, some inaccuracy in extracted values of f will result, since f will
1 t not be independent of I, and one should then write f[ =t f fldt. 0
47 More straightforward methods of calculating ~ are indicated below. Accordingly, l i k e / , v and concentrations, 5 will be considered to be susceptible to measurement. The collected concentration terms then become, in the case of cupric ion, v' Accu2+--c"cu2+
Equation (2) may be recast as v'ACCu2+-
Mcu C"cu2+6 + - - I 2F
= r2 + r3
(4)
Measured copper concentrations are seen to be linearly related to the unknown quantities rz and r3, whose magnitudes we wish to determine. The weight gain* w of the cathodes can also be used to evaluate the sum of r2 and r 3 : MCu w -
t f o
2F
Idt--(r2
(5)
+r3)t
Unfortunately, relations (4) and (5) give the same information, and it will be seen necessary to employ three additional relations to evaluate r2 and r3 separately. However, if the copper concentrations are measured with good accuracy (titration or electrogravimetry), the incremental rate of electrolyte volume change (exclusive of evaporation), 5, may be calculated in principle by combining eqns. (4) and (5). Hydrogen
balance
In what follows, the quantity c H + is intended to represent the hydrogen ion concentration as measured by the so-called "free acid", which includ.es in addition to H+(aq.) the hydrogen which is combined with sulfate as HSO~, the first hydrogen of the species H3PO4, if present, etc. MH c'v'
H÷ influx
+
--
2MH fI
--
MH --
F anodic 02 evolution
Mc u r2 Cu corrosion by 02 (aq.)
r4
--
EL
=
c"v"
MF e volume oxisolution effluent dation of Fe 2+ loss H÷
(6)
or MHI v ACH+--C"H+6 = - -
F
f--
2M H - r2
MH
Mcu
MFe
r4
Le. assuming that physical detachement o f portions o f the deposit does not occur.
(7)
4~
Iron balance
C U
+
Fe 3+ influx
MFe 2MFe ..... (1--f)I . . . . . . . . r~ + F Mcu anodic oxiCu corrosion dation of Fe :÷ by Fe 3÷
r4
--
~L
=
(8!
c"v"
volume oxi- solution effluent dation of Fe 2÷ loss Fe 3.
or t
,,
V ACFe3+--c Fe.~+~
MFe
F
MFeJ 2MFe -. . . . . f . . . . . r3 + r4 F Mcu
I -
(9)
Because of the reciprocal variations of the ferrous and ferric ion concentrations (Reactions 3., 4. and 6.), a mass balance for Fe 2÷ provides no new information, yielding MFe MFe I 2MFe v' ACFe2÷ - - C " F e 2 +5 + . . . . . I = + - f + .... r3--r4 F F Mcu
(10)
However, if Fe 2÷ and Fe 3. concentrations can be measured with good accuracy, the sum of eqns. (9) and (10) may be used as an alternate metals for estimating 5. Except for a small term in 5, the total iron concentration, CFe2. + CFe3÷, may be treated as the concentration of a single, indifferent (i.e., n o t electroactive) chemical species. Sulfate
balance
Actually, what is derived here applies equally to all indifferent species. Sulfate is singled out because changes in total sulfate concentration can be measured with greater accuracy than for most of the other inactive solutes. Material balance gives, simply 0 = c'v'--~L--c"v"
~ (c"--c')v'--c"
5
(11)
The approximation implied in eqn. (11) is quite close, since c and c " will be nearly equal. Thus, the increment 8 may be estimated from a measured change
in the concentration of indifferent electrolyte. For total sulfate, including both HSO~ and SO~- species, 5 = V'ACso ~-(total)/C" SO~-(total) Evaluation
of the unknown
(12)
quantities
In terms of the quantities n o t susceptible to direct measurement, f, r2, r3 and r4, linear relations of the following form have been formulated: Ac Cu2÷ = ~ ( r : , ra)
(4 ')
ACH* = • (f, r2, r4)
(7')
ACFeS+ = 7(f, r3,/'4)
(9')
49 The requisite supplementary relationship for obtaining solutions for any one of the unknowns is obtained by utilizing the electroneutrality condition Zzi[Si] = 0
(13)
where z i is the charge on the solute species Si, the molar concentration [Si] -= ci/Mi, and the sum extends over all solute species in the electrolyte. Some simplification ensues when making use of the requirement of charge conservation in the alternate form GziA[Si] = 0
(14)
since, now, ionic species for which the change in concentration is of a low order of magnitude need not be included in the summation. Thus, an equation such as 2A[Cu ~+] + A [ H ÷] + 3A[Fe 3÷] + 2A[Fe 2+] + 3A[AP ÷] + etc. = 2A [SO~-(total)] +3A [po43-(total)] + etc.
(15)
where A[A~ 3÷]
5 -
v'
/I
/I
C A~~+ 5 C SO~-(total) , A[SO42-(total)] - , etc. MA~ v MSO,
(16)
can be combined with eqns. (4), (7), (9) and either eqn. (5), (10) or (12) to yield (conveniently, by computer) values of f, r2, r3, r4 and 5 from measured concentrations and parameters. Equation (1 5) is seen to be correct as written when [H ÷] is interpreted as the free acid concentration, as previously stipulated. Thus, the primitive equation of electroneutrality equivalent to eqn. (1 5) would have the term A [H+(aq.)] on the left in place of A[H ÷] and the terms 2A[SO42-] + A [HS(F4 ] + A [H~POj] on the right. But A [H +] is obtained by adding A [HSO4-] + A [H3PO4]to A [H+(aq.)] ; adding the same terms to the right of the primitive equation results in eqn. (15). The ability to make effective use of the foregoing material-balance analysis depends critically upon the capabilities of the measurement techniques. Under the most favorable circumstances when fluid flow, electric current and pertinent concentrations can be accurately measured, and the quantities f, r~, r3, and r4 have non-negligible values, it should be possible to estimate the separate contributions of 02 (aq.) and Fe 3÷ to cathode corrosion and of Fe 2÷ to the anode reaction. ACKNOWLEDGEMENT The author is pleased to acknowledge the useful input of Dr. L. Hsueh, particularly for evaluating by c o m p u t e r calculations the degree of precision required in chemical analysis in order to realize the objectives set forth in Part II.
50
A talk based on the contents of this paper was given at the 67th Annual Meeting of the AICHE, Washington, D.C., December 2, 1974. REFERENCES
1 W.W. Harvey and L. Hsueh, Copper electrowinning from vat leach electrolyte, C I M Bulletin, 69 (April) (1976) 109--119. 2 T.N. Andersen, C.N. Wright and K.J. Richards, Important electrochemical aspects of e]ectrowinning copper from acid leach solutions. International Symposium on Hydrometallurgy, published by AIME, N e w York, 1973, pp. 171--202. 3 N. Ibl, Stofftransport bei der Elektrolyse mit Gasrnhrung, Chemic Ing. Tech., 43 (1971) 202--215. 4 V.A. Ettet, B.V. Tilak and A.S. Gendron, Measurement of cathode mass transfer coefficients in electrowinning cells, J. Electrochem. Soc., 121 (1974) 867--872. For more recent papers by the Inco group on the same subject, see: Can. J. Chem. Eng., 53 (February) (1975) 36--40; Metall. Trans., 6B (March) (1975) 31--36; Chem. and Ind: 9 (3 May) (1975) 376--377. 5 W.W. Harvey, A.H. Miguel, P. Larson and LS. Servi, Application of air agitation in electrolytic decopperization, Trans. Instn. Min. Metall. (Sect. C: Mineral Process. Extr. Metall.) 84 (1975) 11--17 6 W.W. Harvey, M.R. Randlett and K.I. Bangerskis, Elevated current density electro* winning of superior quality copper from high-acid electrolyte, Trans. Instn. Min. Metall. (Sect. C: Mineral Process. Extr. Metall.), 84 (1975)210--220. 7 M.S. Quraishi and T.Z. Fahidy, Chemistry and Industry, 3 May 1975, 377---378.