The effects of certain variables on the current efficiency and power consumption of a .... volume was 800 ml and thus the maximum change in electrolyte volume.
Hydrometallurgy, 1 (1975) 183--203 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
INTERACTIONS OF VARIABLES WINNING OF COPPER*
IN THE FLUIDISED-BED
ELECTRO-
A.J. MONHEMIUS**
Department of Metallurgy and Materials Science, Imperial College, London (Great Britain) and P.L.N. COSTA
CEPED, Centre for Research and Development, Salvador, Bahia (Brazil) (Received June 9th, 1975)
ABSTRACT Monhemius, A.J. and Costa, P.L.N., 1975. Interactions of variables in the fluidised-bed electrowinning of copper. Hydrometallurgy, 1: 183--203. The effects of certain variables on the current efficiency and power consumption of a small fluidised-bed electrowinning cell treating dilute copper sulphate solutions have been studied. A factorial experimental design in two levels has been used to investigate the effects of cell current, sulphuric acid concentration, temperature and the presence of iron in the electrolyte, and the results have been analysed by the Yates technique. It is shown that an increase in temperature and the presence of iron in solution both decrease the current efficiency, while an increase in the cell current increases the current efficiency, for conditions where the cathode is n o t polarized with respect to copper ions. Significant interaction effects on the current efficiency are shown to exist for the case of cell current and iron concentration and for cell current and temperature. These main effects and interactions can be accounted for by a model in which three simultaneous reduction reactions occur at the cathode involving cupric ions, ferric ions and oxygen, with the latter two occurring at their diffusion limited rates. Significant main effects on the power consumption of the cell are shown to exist for cell current, iron concentration and acid concentration. Increasing either of the former two variables increases the power consumption whereas an increase in the latter causes a marked decrease in power consumption, and significant interactions occur between cell current and iron concentration and cell current and acid concentration. An increase in temperature is shown to lead to an increase in the a m o u n t of metal deposited on the feeder electrode. The paper concludes with a discussion of the application of fluidised-bed cathodes to the recovery of copper by electrowinning from various types of solutions.
* A short report of this work was presented at the 3rd National Meeting of Minerals Treatment, Federal University of Minas Gerais, Belo Horizonte, Brazil, 22--24 May 1975. **Present address: COPPE, Post Graduate School of Engineering, Federal University o f Rio de Janeiro, Caixa Postal 1191, 20000 Rio de Janeiro, Brazil.
184
INTRODUCTION The use of fluidised-bed cathodes for the electrowinning of copper from dilute solutions is attracting increasing interest. The t r e a t m e n t of such solutions in conventional electrowinning cells is u n e c o n o m i c because of the high p o w e r c o n s u m p t i o n due to excessive hydrogen evolution at the cathode caused b y concentration polarization. By using a fluidised-bed cathode, in which particles of copper are fluidised b y an upward flow of electrolyte through the bed, the metal concentration level at which the onset of concentration polarization c o m m e n c e s is considerably reduced and thus the treatment of dilute copper solutions, in principle, becomes feasible. The fluidised-bed electrolytic cell was developed by Backhurst and coworkers (1969) and applied originally to electrochemical synthesis and fuel cells (Berent et al., 1969). The application of this t y p e of cell to copper electrowinning was studied b y Flett (1971, 1972) and the development of commercial sized fluidised-bed cells for copper electrowinning was described b y Wilkinson and Haines (1972). In essence, the fluidised-bed electrowinning cell consists of a bed of copper particles which is fluidised b y an upward flow of electrolyte. The whole bed is made cathodic b y a " f e e d e r " electrode inserted into the bed and the cell is c o m p l e t e d by an inert anode immersed in the electrolyte. In some cell designs, the anode is separated from the cathode b y an ion-exchange membrane. F r o m the electrochemical point-of-view, the fluidised-bed cathode differs from the conventional planar cathode in t w o main respects. Firstly, as the c a t h o d e is a bed of particles, it has a very large surface-area to volume ratio. Thus, for any given cell current, the current density at the cathode surface is very low -- in the case of copper, typically one to t w o orders of magnitude lower than in conventional electrowinning cells. Secondly, a very high degree of agitation exists within the bed which reduces the Nernst diffusion layer and increases the limiting diffusion currents. Both these effects reduce the problem of concentration polarization and, under favorable conditions, make it possible to electrowin copper d o w n to parts-per-million concentrations w i t h o u t loss of current efficiency. Hence the possibility of the direct electrowinning of metal from dilute copper-bearing solutions, such as d u m p leach liquors, w i t h o u t the need for prior concentration by, for example, solvent extraction. The object of this work was to study the changes in the current efficiency and p o w e r c o n s u m p t i o n of a small laboratory scale fluidised-bed cell during the t r e a t m e n t of dilute copper solutions (2 g/1 Cu). The effects of the following variables were investigated: cell current, sulphuric acid concentration, temperature and the presence of iron in the solution. In order to study both the main effects and also the interactions of these variables, a factorial experimental design in t w o levels was used. A statistical analysis of the results of the factorial experiment was carried o u t to obtain the significant main effects and interactions of the variables. From these results, a physical model of the processes occurring in the fluidised-bed cathode was developed.
185 EXPERIMENTAL The cell, illustrated in Figure 1, was made from a cylinder of acrylic with an internal diameter of 4.4 cm and a length of 20 cm. The bed of particles was supported b y a porous glass plate, through which the electrolyte was p u m p e d from a reservoir to fluidise the bed. After passing through the cell, the electrolyte flowed back to the reservoir. Circulation in the system was maintained b y the use o f a peristaltic pump, and the electrolyte was held within + 3°C of the predetermined temperature b y a thermostated heating mantle around the reservoir.
-ELECTROLYTE OUT
EL
POROUS PLATE
ELECTROLYTE IN
Fig.1. The fluidised-bed electrowinning cell.
Electrical c o n t a c t with the fluidised bed was made by a copper feeder electrode made in the shape of a flat spiral. The anode was a disc of lead with the lower surface made slightly convex to prevent the accumulation of oxygen bubbles under it. Energy was supplied to the electrodes at constant current from a D.C. p o w e r supply. The cell voltage was accurately measured b y a voltmeter c o n n e c t e d across the electrodes and a recorder was used to follow changes in voltage during each experiment. Due to the difficulty of obtaining suitable copper particles, the bed consisted of nominal 0.5 m m glass spheres, coated with copper. The initial coating was carried o u t by vacuum evaporation of copper on to the surface of the spheres. The volume of spheres used in the bed was 30 cm 3. The
186
specific surface area of the bed was calculated to be approximately 90 cm2/cm 3 assuming uniform s m o o t h spheres. The current efficiency was determined b y atomic absorption analysis of the copper concentration of samples of electrolyte withdrawn from the system every five minutes. Each experiment was run for 30 minutes. However, in some of the runs, where the conditions used led to a rapid depletion o f the copper in the electrolyte, the experiment was stopped at the onset of hydrogen evolution in the bed. This was necessary because the hydrogen evolution upset the fluidisation of the bed and particles of copper tended to be swept o u t of the cell by the electrolyte flow. During each experiment o f 30 minutes, seven samples of 3 ml were taken. The initial total electrolyte volume was 800 ml and thus the m a x i m u m change in electrolyte volume during an experiment was approximately 2.5%. Before and after each experiment, the cathode feeder electrode was weighed in order to determine the percentage of copper deposited on the feeder electrode instead of on the copper particles. Initial experiments were carried o u t to determine the o p t i m u m electrode positions and bed expansion. These were found to be as follows: cathode feeder electrode 1 cm from the porous plate; anode 1 cm from the t o p of the bed in the expanded condition; height of fixed bed 2 cm with an expansion of 25 % when fluidised. These conditions were maintained t h r o u g h o u t the whole series of experiments of the factorial design.
Factorial design In order to study b o t h the main effects of the chosen variables and also any possible interactions, a factorial experiment in t w o levels was carried o u t The variables studied were cell current, sulphuric acid concentration, iron concentration and temperature, each at two levels. The levels chosen are shown in Table 1. The initial copper concentration in the electrolyte was 2 g/1 for all experiments. In those experiments where iron was present in the electrolyte, it was initially in the ferric state, although it was rapidly reduced to the ferrous state due to the dissolution of copper from the cathode, as discussed later. TABLE 1 M i n i m u m and m a x i m u m level o f variables Factor
Variable
Min
Max
Units
A B C D
Cell c u r r e n t Fe c o n c e n t r a t i o n H2SO 4 concentration Temperature
2 0 10 30
4 2 100 50
A g/1 g/l °C
187
TABLE 2 Experimental conditions Tr e a t m en t code
Current (A)
Fe (g/l)
H2SO4 (g/l)
Temp. (°C)
1 a b ab c ac bc abc d ad bd abd cd acd bcd abcd
2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4
0 0 2 2 0 0 2 2 0 0 2 2 0 0 2 2
10 10 10 10 100 100 100 100 10 10 10 10 100 100 100 100
30 30 30 30 30 30 30 30 50 50 50 50 50 50 50 50
The total number of combinations of four factors at two levels is 24 , i.e., 16, and this is the number of experiments required for the full factorial design. The sixteen combinations of levels used, plus the code given to each experiment, are shown in Table 2. In order to be able to estimate the experimental error, each experiment was duplicated, giving a total of 32 experiments. To avoid systematic errors, the order of execution of the experiments was randomised using a standard procedure involving the use of a table of random numbers (Duckworth, 1968).
Collection of data For those experiments in which the electrolyte did not contain iron, it was found that there was a linear decrease in the copper concentration of the electrolyte with time during the whole run or until the visible onset of hydrogen evolution. A linear regression analysis was used to fit the best line to the experimental data to give the rate of deposition and then the current efficiency was calculated by applying Faraday's law. When ferric iron was present in the electrolyte, the copper concentration rose initially due to dissolution of copper from the cathode particles by the following reaction: 2 Fe 3+ + Cu-~ 2 Fe2÷ + Cu2÷ This reaction was complete within approximately five minutes from the start of the run. Thereafter the copper concentration decreased linearly.
188
B e c a u s e o f this e f f e c t , t h e c u r r e n t e f f i c i e n c i e s f o r e x p e r i m e n t s in w h i c h i r o n was p r e s e n t w e r e c a l c u l a t e d f r o m d a t a c o l l e c t e d b e t w e e n t h e 1 0 t h a n d 3 0 t h m i n u t e s o f t h e e x p e r i m e n t s . T h e rise in c o p p e r c o n c e n t r a t i o n c a u s e d b y t h e d i s s o l u t i o n r e a c t i o n a b o v e was a l w a y s a p p r o x i m a t e l y 1 g/1. Since t h e solut i o n s initially c o n t a i n e d 2 g/1 ferric iron, it was c o n c l u d e d t h a t t h e e q u i l i b r i u m f o r t h e a b o v e r e a c t i o n lay well t o t h e r i g h t a n d t h a t m o s t o f t h e i r o n was r e d u c e d t o t h e f e r r o u s state. T h u s results given f o r e x p e r i m e n t s in w h i c h i r o n was p r e s e n t , r e f e r t o s o l u t i o n s in w h i c h t h e b u l k o f t h e i r o n is p r e s e n t in t h e ferrous state, with a steady-state condition occurring for the oxidation-reduction reactions of iron at the electrodes. T h e cell v o l t a g e was f o u n d t o d e p e n d s t r o n g l y o n t h e c o m b i n a t i o n o f variables used. H o w e v e r , f o r a n y p a r t i c u l a r r u n , t h e cell v o l t a g e r e m a i n e d p r a c t i c a l l y c o n s t a n t t h r o u g h o u t a n d so t h e a v e r a g e v a l u e o f t h e cell v o l t a g e o f e a c h e x p e r i m e n t was u s e d t o c a l c u l a t e t h e p o w e r c o n s u m p t i o n f o r t h a t e x p e r iment. RESULTS T h e c o m p l e t e set o f results f o r t h e f a c t o r i a l e x p e r i m e n t is given in T a b l e 3, w h i c h c o n t a i n s t h e c u r r e n t e f f i c i e n c y , t h e p o w e r c o n s u m p t i o n , t h e average cell v o l t a g e , a n d also t h e p e r c e n t a g e o f m e t a l d e p o s i t e d o n t h e f e e d e r elect r o d e f o r e a c h t r e a t m e n t c o m b i n a t i o n . T h e results are given in pairs since e v e r y e x p e r i m e n t was d u p l i c a t e d . TABLE 3 Results Treatment code
Current efficiency (%)
Power consumption (kWh/kg Cu)
Av. cell voltage
1 a b ab c ac bc abc d ad bd abd cd acd bcd abcd
74.12 74.16 54.00 63.56 78.10 81.44 55.60 67.94 69.19 77.82 40.78 60.62 62.39 79.44 39.51 66.55
7.06 12.34 8.43 12.01 3.13 3.78 4.02 4.91 7.13 9.65 11.17 11.97 3.65 3.82 6.80 4.18
6.20 10.85 5.40 9.05 2.90 3.65 2.65 3.95 5.85 8.90 5.40 8.60 2.70 3.60 2.85 5.30
78.96 72.23 51.55 64.94 74.12 83.01 53.13 66.08 67.94 68.59 45.50 59.36 57.42 75.79 37.06 58.22
6.63 11.56 9.16 11.63 2.95 3.76 4.12 4.27 6.46 11.07 9.82 11.44 3.52 3.56 6.14 5.07
% Cu on feeder 6.20 9.90 5.60 8.95 2.60 3.70 2.60 3.35 5.20 9.00 5.30 8.05 2.40 3.20 2.70 3.50
2.0 2.2 0.0 0.4 2.0 1.7 1.1 4.0 6.5 2.3 5.2 5.7 4.3 3.8 32.0 3.6
0.7 0.9 0.1 0.5 1.0 1.0 0.0 0.3 1.4 3.8 3.7 2.8 3.8 2.0 9.8 5.5
189
Factorial analysis Estimates of the main effects and interactions of the variables on the current efficiency and p o w e r c o n s u m p t i o n were obtained b y a Yates analysis of the data (Yates, 1937; Duckworth, 1968). This was done b y a c o m p u t e r programme which also calculated the statistical consistency and significance of the results. The consistency was tested b y means of the F-ratio, i.e. the ratio b e t w e e n variances, and the significance b y the " t " value, i.e., the normalised standard deviation. The mean differences obtained from the Yates analysis and the t-values o f these mean differences are given in Table 4. A certain a m o u n t o f inhomogeneity of variance was demonstrated by the F-ratios since, for the current efficiency, four of the results were significant at the 10% level. This indicates that for these four results, the variance of the response changes b e t w e e n the two chosen levels of the variables. In the case of the p o w e r consumption, three of the results showed F-ratios significant at the 10% level. The t-test for the statistical significance of the responses depends on the h o m o g e n e i t y o f variance. However, moderate amounts of inhomogeneity can be tolerated (Duckworth, 1968, p.190), particularly for results which have highly significant t-values, i.e., 99% or greater. The t-value at the 99% significance level for this factorial design is 2.92. Thus all results TABLE4 M e a n d i f f e r e n c e s a n d t-values o f e x p e r i m e n t a l results Treatment code
1 a b ab c ac bc abc d ad bd abd cd acd bcd abcd
Effect
Mean total A B AB C AC BC ABC D AD BD ABD CD ACD BCD ABCD
Mean differences a
t-values
CE (%)
PC ( k W h / k g )
CE
PC
128.69 11.27 --18.14 4.99 0.78 3.87 --0.31 --1.76 --7.92 4.55 --0.73 --0.34 --2.46 1.21 0.75 0.31
14.03 1.59 1.52 --0.78 --5.65 --1.63 --0.20 0.33 0.31 --0.75 0.60 0.21 0.32 0.09 --0.20 --0.14
-10.65 --17.14 4.72 0.74 3.65 --0.29 --1.66 --7.48 4.30 --0.69 --0.32 --2.32 1.14 0.71 0.29
9.41 8.97 --4.59 --33.36 --9.61 --1.15 1.94 1.83 --4.41 3.56 --1.22 1,91 0.54 1.19 --0.82
aCE = C u r r e n t e f f i c i e n c y ; PC = p o w e r c o n s u m p t i o n .
190
given in Table 4 having a t-value greater than 2.92 are considered to be statistically significant. In the case of current efficiency, three main effects A, B, and D (i.e., cell current, iron concentration and temperature) and three interactions AB, AC and AD may be seen to be statistically significant, according to the above criterion. However one of these interactions, AC, the interaction b e t w e e n cell current and acid concentration, contains a factor C, the acid concentration, whose main effect on the response is n o t significant. Thus it is unlikely that an interaction involving the factor acid concentration will be physically meaningful. Accordingly AC was excluded from the significant interactions. In the case of the p o w e r consumption, the significant main effects are A, B and C (i.e. cell current, iron concentration and acid concentration) and interactions AB and AC. Interactions AD and BD, although statistically significant, were excluded because t h e y involve the non significant factor D (temperature).
The main effects of the variables The main effects of the four variables on the current efficiency (CE) are shown in Table 5 together with their mean differences given b y the Yates analysis. The mean differences are obtained b y averaging all the results with the particular variable at its low level and subtracting this from the average of all the results with the variable at its high level. Thus the mean differences TABLE5 M a i n e f f e c t s of variables o n c u r r e n t e f f i c i e n c y Variable
Influence a
Cell c u r r e n t , A Iron conc., B H~SO4 c o n c . , C Temperature, D
At Bt Ct Dt
CEt CE~ CE n o c h a n g e CE$
M e a n d i f f e r e n c e (%) +11.27 --18.14 +0.76 --7.92
a t = I n c r e a s e s ; ~ = decreases.
give a quantitative estimate of the average change in the current efficiency caused b y raising the particular variable from its low level to its high level, and enable the magnitude of the influences to be compared. The main effects o f the variables and the mean differences on the p o w e r c o n s u m p t i o n of the cell are given in Table 6.
Interactions between variables As indicated above, certain two-factor interactions were considered to be b o t h statistically and physically significant. A reverse Yates analysis was
191
TABLE 6 Main effects of variables on power consumption Variable
Influence a
Mean difference (kWh/kg)
Cell current, A Iron conc., B H~SO4 conc., C Temperature, D
At Bt Ct Dt
+1.59 +1.52 --5.65 +0.31
PCt PCt PC~ PC no change
at = Increases; $ = decreases.
carried out to obtain the mean values at the high and low levels of each com. bination of variables. The significant interactions with respect to current efficiency are shown in Tables 7 and 8 and with respect to p o w e r consumption in Tables 9 and 10. In order to clarify the meaning of these tables of interactions, Table 7, which deals with the interaction b e t w e e n cell current and iron concentration, will be examined in detail as an example. In this table, the upper figure in the left-hand column, 70.28%, is the mean of the results of the four t r e a t m e n t combinations in which both cell current and iron concentration were at their low levels, i.e. treatments (1), c, d and cd T AB LE 7 The interaction effect of cell current and iron concentration on current efficiency (%) Cell current (A)
Fe concentration (g/l) 0
ACE
2
2 4
70.28 76.56
47.14 63.41
aCE
+6.28
+16.27
--23.14 --13.15
TABLE 8 The interaction effect of cell current and temperature on current efficiency (%) Cell current (A)
Temperature (°C) 30
ACE
50
2 4
64.95 71.67
52.47 68.30
aCE
+6.72
+15.83
--12.48 --3.37
192
TABLE 9 The interaction effect of cell current and iron concentration on power consumption (kWh/kg) Cell current
Fe concentration (g/l)
APC
(A) 0 2 4 5PC
2 5.06 7.44
7.37 8.18
+2.38
+0.81
+2.31 +0.74
TA B L E 10 The interaction effect of cell current and acidity on power consumption (kWh/kg) Cell current
H2SO4 concentration (g/l)
APC
(A) 10 2 4
8.23 11.46
~PC
+3.23
I00 4.20 4.17
--4.03 --7.29
--0.03
(see Table 2). Similarly the lower figure in the left-hand column, 76.56%, is the mean of the results of the four treatment combinations in which iron was held at its low level b u t the cell current was at its high level, i.e. treatments a, ac, ad and acd. The difference of these means (ACE) is +6.28% and this is the average change in current efficiency at the low level of iron caused by raising the cell current from the low to the high level. The upper and lower figures in the right-hand column are the means of treatments (b, bc, bd, bcd) and (ab, abc, abd, abcd) respectively. The difference of these means is +16.27% and this is the average change in current efficiency at the high level of iron caused b y raising the cell current. The fact that these two mean differences (~ CE for the columns) are different shows that there is an interaction b e t w e e n the t w o variables, since the improvement in current efficiency caused by raising the cell current is greater in the presence of iron than in its absence. Similarly the values of ACE for the rows (--23.14% and --13.15%) show that the detrimental effect of iron on the current efficiency is more marked at the low value of cell current than at the high value. The other tables of interactions given in Tables 8--10 are derived similarly. The main value of these tables is that t h e y give a quantitative estimate of the magnitudes of the significant interactions.
193 DISCUSSION
The effects of the variables on the current efficiency Examination of Table 5 shows t h a t an increase in the cell current from 2 A to 4 A causes a marked increase in the current efficiency. A similar p h e n o m e n o n was n o t e d by Flett (1971) who attributed it to a slow redissolution of cathode copper by the acid electrolyte, the redissolution being more evident at low current densities, since the rate of electrodeposition is low. He suggested that, since increasing the current density increases the rate of deposition, whereas the redissolution rate remains constant, the overall effect is to increase the current efficiency. However in a later paper (Flett, 1972) he discounted this theory, but was unable to offer an alternative explanation. It will be shown t h a t the effect can be adequately accounted for in terms of a series of simultaneously occurring cathode reactions. The presence of 2 g/1 of iron in the electrolyte has a markedly deleterious effect on the current efficiency. This effect can be attributed to ferric iron, f o r m e d by oxidation at the anode, being reduced at the cathode. Wilkinson and Haines (1972), who worked with a cell in which the fluidised cathode was separated from the anode by an ion-exchange membrane, noted t h a t in the presence of iron, the current efficiency was lowered until all the iron was in the ferrous state. Thereafter, the current efficiency returned to normal values. In Wilkinson's cell, reoxidation of iron at the anode was n o t possible, due to the presence of the membrane, whereas in the present work, continuous oxidation--reduction of iron could occur; since there was no membrane separating the electrodes. The factorial analysis shows that an interaction occurred between the cell current and the iron concentration. From Table 7, it m a y be seen t h a t the increase in current efficiency with cell current is considerably greater in the presence of iron in the electrolyte than in its absence. Also the detrimental effect o f iron on the current efficiency is greater when the cell current is low. Changing the acid concentration from 10 g/1 to 100 g/1 had no significant effect on the current efficiency, whereas a significant decrease occurred on raising the temperature from 30 to 50°C (Table 5). An interaction between temperature and cell current was observed, as shown in Table 8. The increase in current efficiency with cell current is greater at the higher temperature and the detrimental effect of temperature decreases as the cell current is increased. A physical interpretation of the effects of the variables on the current efficiency m a y be made on the assumption t h a t the following three reactions are the main processes occurring at the cathode, under conditions where the c a t h o d e is n o t polarized with respect to copper ions: Cu :÷ + 2e -* Cu
(1)
Fe 3* + e ~ Fe 2+
(2) (3)
O: + 4H ÷ + 4e -~ 2H20
194 The total c u r r e n t density at the cathode, it, will thus be the sum of the current densities of the above reactions: it = icu + iFe + io~ Only reaction (1) leads to the deposition of copper on the cathode and so the current efficiency for copper deposition ( C E ) is given by: C E = iCu/i t = 1 -- (iFe
+ io 2)~it
(4)
Ferric ions will be reduced as rapidly as t h e y can diffuse to the cathode surface (Andersen et al., 1973) and so iFe will be limited by the rate o f diffusion of ferric ions, i.e., iFe will be the limiting diffusion current density, i~e. Similarly, io2 will be limited by the diffusion of oxygen to the cathode and so io~ can be replaced by the limiting diffusion current density for oxygen, -$ ~O~. Under normal electrowinning conditions, the consumption of current by reduction of oxygen is negligible because of the very low solubility of oxygen in aqueous solutions. However, in the present study, the total current densities used are m u c h lower than in normal electrowinning practice, at least one order of magnitude lower, and so the relative effect of oxygen will be greater. Also the intense agitation occurring in the fluidised-bed means that the Nernst diffusion layer around the cathode particles will be very thin. This will tend to maximise i*O5 (and, of course, i~e ). Thus it is reasonable to assume that the limiting current density for oxygen reduction will make a small but significant contribution to the total current density. Some evidence for this is that, even in the absence of iron in the electrolyte, the m a x i m u m current efficiency that was achieved in any of the factorial experiments was 82% (see Table 3), indicating that at least 18% of the current was being consumed by other reactions, the major contributor being presumably the reduction of oxygen. Thus equation (4) m a y be rewritten as: C E = 1 - - (i~e + i~)2)/i t
(5)
where i~e and i*O2 are the limiting current densities for Fe 3÷ and 02, respectively. Equation (5) shows t h a t the current efficiency for copper deposition will be affected by changes in the total current density, it, and also by any variables which change the limiting current densities of Fe 3÷ and 02. The limiting diffusion current density for an ion is given by: i* = n F D C / 5
where n is the valency of the ion, C is its concentration in the bulk solution and D its diffusion coefficient; F is the Faraday and 5 is the thickness of the Nernst diffusion layer. Hence the main factors in an electrowinning system which affect i* are the concentration of the ion in solution, the temperature, since this will affect, mainly, the diffusion coefficient, and the agitation, which will affect 5. In the present work, the latter factor, agitation, is consid-
195
ered to be constant since the same conditions of electrolyte flow and fluidisedbed expansion were used t h r o u g h o u t the series of experiments. Thus the t w o main factors affecting the limiting current densities to be considered here are the electrolyte compositions and the temperature. For conditions of constant t e m p e r a t u r e and electrolyte composition, the effect on the current efficiency of a change in the cell current from a value it(L) t o it(H) may be obtained from equation (5):
ACE(T, comp) = C E ( H ) - - CE(L) = (i~e + i*O~)(1/it(L) -- 1/it(H))
(6)
Similarly, at constant cell current, a change in the limiting current of either iron and/or oxygen from value (1) to value (2), caused by a change in either the temperature or electrolyte composition, will result in a change in the current efficiency given by: ACE(curr, T or comp) = [(i'Ve + tO=)l -- (i e + i~)~)2] /it (7) The values of A C E given b y the interaction b e t w e e n cell current and iron concentration, shown in Table 7, enable estimates of the value of i'o2 a n d i~e to be made, since for the A CE value obtained at zero iron concentration, i~e must be zero. Thus from equation (6) at zero iron: •*
ACE( T, comp) = i~) 2(1/it(L) - - 1/it(H) ) • 0.063 = i~2(1/0.74 -- 1/1.48) • i*O2 = 0.09 m A / c m 2 The values of it used above, 0.74 and 1.48 m A / c m 2, were calculated b y averaging the applied cell current (2 A and 4 A, respectively) over the total surface area of the particles in the bed, calculated to be 2700 cm 2, assuming uniform s m o o t h spheres. The value of i*O~ given b y the calculation is the limiting diffusion current density for oxygen reduction averaged b e t w e e n 30 and 50°C, and also averaged over solutions containing 10 g/1 acid and 100 g/1 acid. Having obtained i*O~, the value of i~e can be calculated from the interaction observed in the presence of iron given in Table 7. Again using equation
(6): 0.163 = (/Fe "* + 0 . 0 9 ) (1/0.74 -- 1/1.48) •". i~e = 0 . 1 5 m A / c m 2
Similarly this is the limiting diffusion current density for reduction of Fe 3÷, averaged b e t w e e n 30 and 50°C and 10 and 100 g/1 acid. It is an implicit assumption in the above calculation that the presence of iron in the electrolyte does n o t alter the limiting diffusion current density for oxygen. Having obtained values f o r i~e and i*O~, equation (7) may be used to calculate the theoretical effect on the current efficiency of adding 2 g/1 Fe to the electrolyte at the t w o levels of cell current used, i.e. the mean differences b e t w e e n the rows in Table 7. Thus from equation (7):
196 ACE(curt, T) = [(0 + 0.09) -- (0.15 + 0.09)I/it At a cell current of 2 A, it ~ 0.74 m A / c m :, thus A C E = --0.2, i.e. --20%. Similarly at a cell current of 4 A, A C E = --10%. It m a y be seen that these values are in reasonable agreement with the experimental values o f - - 2 3 . 1 % and --13.4%, respectively. The calculated values of the limiting diffusion currents i*o~and i~e m a y also be used to estimate theoretical values for some of the main effects of the variables on the current efficiency. Thus the theoretical main effect of cell current should be given by equation (6). However, the experimental value of this main effect, given by the Yates analysis, is a value averaged over all solutions used, i.e. solutions both with and without iron. Since the t e r m (i~e + i*O: ) of equation (6) differs for these two types of solutions, an average value of this term has to be used. Because of the balanced nature of the experimental design employed, in which half of the experiments contained iron in solution and the other half did not, the required average value is simply given by [(0 + i* ) + (i~e + i~) )]/2. Substitut the values of i~) and i~e calculated above, a value o~'b.17 is obtair]ed. Thus from equation ~6), the theoretical main effect of cell current is: A C E ( T , comp) = 0.17 (1/0.74 -- 1/1.48) = +0.115. In percentage terms, the value is +11.5%, which agrees with the experimental value of +11.3%, given in Table 5. The main effect of the variable, iron concentration, should be given by equation (7). However the cell current, it, appears in this equation. The value given by the Yates analysis for the main effect of iron is a value averaged over both levels of cell current used in the factorial design. Thus to estimate the theoretical main effect of iron, equation (7) is used to calculate A C E at a cell current of both 2 A and 4 A, the values being, respectively, ACE(2 A) = --20% and ACE{4 A) = --10%. The average of these two values is --15% and this is the theoretical main effect of iron. The experimental value, also given in Table 5, is --18.1%. The main effect of changing the acid concentration on the current efficiency should be zero according to equations (6) and (7) assuming that changes in the acid concentration do not appreciably alter the limiting currents of iron and oxygen. This is in agreement with the experimental results which showed the main effect of the acid concentration to be non-significant. The theoretical main effect of temperature cannot be quantitatively estimated from the available data since it is not possible to separate the individual values of the limiting current densities at the two temperatures used in the series of experiments. The major influence of temperature in the system under consideration will be to increase the diffusion coefficients of the ions. This will lead to an increase in the limiting diffusion current densities of iron and oxygen. Thus it m a y be seen qualitatively from equation (7) that, as the temperature is raised, the function in the square brackets will b e c o m e negative. Hence increasing the temperature should lead to a decrease in the current efficiency, in agreement with the experimental observation of the main effect
197
(Table 5). Also the interaction between cell current and temperature shown in Table 8 is in qualitative agreement with equations (6) and (7). Equation (6) applies to the difference between the means in the columns of Table 8. Since t h e t e r m ( i ~ e + i*05) in equation (6) will be greater at 50°C than at 30°C, ACE at 50°C should be greater than ACE at 30°C, in agreement with Table 8. Equation (7) applies to the difference between the means in the rows of Table 8 and it may be seen that as it increases ACE should become less negative, again in qualitative agreement with Table 8. To summarise this discussion, the numerical values of the mean differences due to the main effects and interactions given by the Yates analysis of the experimental data are compared with the theoretical values calculated or inferred using equations (6) and (7) in Table 11. It may be seen that the proposed model for the processes occurring at the cathode, namely the three reactions given in equations (1), (2) and (3), with reactions (2) and (3) occurring at their limiting rates, clearly predicts the direction of change of the current efficiency for all the main effects and interactions, and in view of the approximate nature of the calculations, the numerical agreement between the estimated and observed values is considered to be satisfactory. Thus the model is considered to be a reasonable approximation of the processes occurring in the fluidised-bed cathode. It should be noted that the main uncertainty in the calculations given above is due to the values assigned to it, since the true total surface area of T A B LE 11 Comparison of the estimated and observed mean differences due to the main effects and interactions o f the variables Mean differences (%) Estimated a
Observed
Main effects Cell current Iron concentration Acid concentration Temperature
+11.5 --15.0 0 --x
+11.3 --18.1 +0.8 (Not significant) --7.9
Interactions Iron concentration with cell current at 2 A Iron concentration with cell current at 4 A Temperature with cell current at 2 A Temperature with cell current at 4 A Cell current with temperature at 30°C Cell current with temperature at 50°C
--20.0 --10.0 --Y --y +z +Z
--23.1 --13.4 --12.5 --3.4 +6.7 +15.8
aValues designated by letters cannot be estimated numerically from the available data, However, the model predicts that Y > y and Z > z.
198 the fluidised-bed is n o t known. However this uncertainty does n o t affect the estimated mean difference values given in Table 11, since, in the algebraic manipulations o f equations {6) and (7) required to arrive at these values, the it values always cancel. It is only the ratio of the levels of it used that is important. This ratio is o f course, independent of the surface area of the bed and depends only on the values of the applied cell current (2 A and 4 A in the present work). The only results given above which do depend on the absolute values of i t a r e the estimates of i~e and i~) 2 and so these results should be considered only as very approximate values of the limiting current densities.
The effects of the variables on the power consumption The main effects of the variables on the p o w e r c o n s u m p t i o n for copper deposition are given in Table 6. The overall mean value for the p o w e r consumption obtained from all the experiments in the factorial design was 7.02 kWh/kg Cu and so the magnitude of the mean differences given in Table 6 should be judged against this value. Thus it may be seen that, although an increase in the cell current has been shown to improve the current efficiency for copper deposition, it is at the expense of an increase in the p o w e r c o n s u m p t i o n of the cell. This effect is due to an increase in the cell voltage caused by larger ohmic losses at the higher current. The deleterious main effect of iron on the p o w e r consumption is directly related to the decrease in the current efficiency caused by the presence of iron, discussed in the previous section. This m a y be seen b y a comparison o f the interactions b e t w e e n cell current and iron concentration on the p o w e r c o n s u m p t i o n shown in Table 9 with the interaction of the same t w o variables on the current efficiency shown in Table 7. Bearing in mind that the addition of 2 g/1 of iron will have little effect on the average conductivity of the electrolyte and that the cell voltage will increase with the cell current, it m a y be seen that the interactions on the p o w e r c o n s u m p t i o n follow those observed on the current efficiency. Table 6 shows that an increase in temperature from 30 to 50°C has no significant effect on the p o w e r consumption. Thus it is concluded that the detrimental main effect of temperature on the current efficiency must be compensated b y a drop in cell voltage with temperature, due presumably to an increase in the conductivity of the electrolyte. Clearly the most i m p o r t a n t variable of those investigated is the acid concentration. An increase from 10 to 100 g/1 sulphuric acid causes a very marked drop in p o w e r consumption. This effect is due to the increased conductivity of the electrolyte at the high acid concentration which results in a lower cell voltage. The interaction b e t w e e n cell current and acid concentration shown in Table 10 gives further information on the effect of acid in the system. It may be seen that the decrease in p o w e r c o n s u m p t i o n due to increased acid is greater at the higher level of cell current and also that the detrimental effect
199 of increased cell current on the p o w e r c o n s u m p t i o n is n o t apparent in the higher acid solutions. These results are significant when considering the application of fluidised-bed cathodes t o t h e t r e a t m e n t of copper leach liquors and will be elaborated on in a subsequent section.
The deposition o f copper on the feeder electrode As m e n t i o n e d in the experimental section, the cathode feeder electrode was weighed before and after each experiment in order to determine the a m o u n t of metal deposited on the feeder electrode instead of on the metal particles in the bed. F r o m the p o i n t of view of industrial operation of fluidised-bed cathodes, it is obviously important to minimise metal deposition on the feeder electrode. Otherwise, over extended periods of operation, the feeder electrode would increase in size until ultimately it would upset the fluidisation of the bed. It was h o p e d that this investigation would give some indication of the effects o f the variables studied on the a m o u n t of metal deposited on the feeder. U n f o r t u n a t e l y it was found that the reproducibility of the results was very poor. This is illustrated in Table 3, which reports the percentage of metal deposited on the feeder for each pair of duplicated experiments, and it is evident that there is a wide variation in the results from replicate experiments. A Yates analysis of the data was attempted, b u t the experimental error was so large that it was not possible to have any confidence in the significance of the results of this analysis. One factor, however, clearly had a significant effect. This factor is temperature. There was no d o u b t statistically that a greater percentage of metal was deposited on the feeder in the experiments carried o u t at 50°C than those in which the temperature was 30°C.
The application o f fluidised-bed cathodes to copper electrowinning As pointed o u t in the Introduction, it has been suggested that fluidisedbed electrowinning might offer a r o u t e for the direct treatment of low-grade c o p p e r leach liquors, since copper can be electrodeposited at good current efficiencies d o w n to very low concentrations. With respect to this application of fluidised-bed cathodes, the results of this study are s o m e w h a t discouraging. A typical low-grade copper leach liquor from, say, a dump-leach operation will be low in acid, p H = 2, low in copper, ~ 1 g/l, and will probably contain at least 1--2 g/1 ferric iron. The direct electrowinning of copper using a fluidised-bed c a t h o d e from such a solution presents t w o fundamental problems. Firstly the p r o b l e m of ferric iron, which has been shown in this study t o have a very detrimental effect on the current efficiency and hence the p o w e r c o n s u m p t i o n for c o p p e r deposition. In fact at the current densities used it led to a net dissolution of c o p p e r until the iron was almost completely reduced to the ferrous state. In any industrial application, a side-by-side cell configuration, with the fluidised cathode separated from the anode b y a
200 membrane, is likely to be used. With this type of cell, the iron problem would not be as serious as in the simple plane-parallel type of cell used in the present work, since the continuous oxidation--reduction cycle of iron could not occur. Nevertheless it would still be necessary to completely reduce the iron to the ferrous state, either in situ, during copper electrolysis, or by some pre-treatment, in order for the fluidised-bed cell to operate at a good current efficiency. Whichever method is used to reduce the iron, it will constitute an operating cost for the process. The second problem which, for this application is perhaps more serious than the presence of iron in solution, is the inherently low conductivity of dilute leach liquors. This will inevitably lead to higher cell voltages and hence to higher power consumptions than those encountered in conventional electrowinning practice. The main effect of acid concentration, described earlier, showed that increasing the acid concentration of the electrolyte from 10 g/l (a value typical of dilute leach liquors) to 100 g/1 (a value closer to conventional electrowinning practice) led to a very substantial decrease in power consumption. This decrease is due mainly to the higher conductivity of the higher acid solutions with the consequent reduction in cell voltage. Thus, in spite of the good current efficiencies that can be achieved at low copper concentrations with fluidised-bed cathodes, the low conductivity of dilute leach liquors will lead to high power costs for the direct electrowinning process. This problem is further illustrated by the interaction shown in Table 10 which shows that, for the low acid solutions, the power consumption rises markedly with the cell current. Hence any attempt to improve the economics of the process by increasing the cell current to increase the rate of metal deposition is likely only to worsen the power consumption problem. Significantly, Table 10 demonstrates that this effect does not occur in the high acid solutions where, on doubling the cell current, no significant change in the power consumption is apparent. In this respect it is interesting to note that the only published data for power consumption for copper electrowinning in fluidised-bed cells in which the values are similar to those typical of conventional electrowinning are those of Flett (1971), who obtained his data using iron-free solutions 0.5 M (48 g/l) in acid. In contrast, Wilkinson and Haines (1972), using low acid solutions of pH 2--3, also free of iron, quoted values which, depending on the cell current and final copper concentration, ranged between 1.5 and almost 5 times higher than conventional practice -- the latter being typically approximately 2 kWh/kg Cu. It thus appears that the direct treatment of dilute copper leach liquors in fluidised-bed cathodes, even in the absence of ferric iron, is likely to be subject to rather high power costs which may prejudice their use for this application. For solutions which contain ferric iron, there will be the additional operating cost due to the necessity to reduce all the iron to the ferrous state. There is the possibility, however, that at least the power costs may be acceptable if the dilute leach liquor contains appreciable quantities of other dissolved salts, which increase the conductivity sufficiently to lower the cell voltages to reasonable values.
201 Another possible application of fluidised-bed cells in the copper industry is as an alternative to conventional electrowinning cells for the treatment of normal electrowinning solutions. Here this new technology offers the possibility of automatic feeding and discharge of copper particles from the cells, leading to continuous operation and to the elimination of the expensive labour intensive cathode-handling operations involved in the conventional process. Since normal electrowinning liquors are generally fairly high in both acid and copper and consequently have good conductivities, the power consumption problem mentioned above is likely to be much less significant for this application. However, the problem of iron in solution will continue to be serious. Most normal copper electrowinning liquors contain at least a few grams per litre of ferric iron. This can be tolerated in conventional electrowinning cells and does not give rise to serious loss of current efficiency. The reasons for this are two-fold. Firstly, the limiting current density for iron reduction is low because the agitation in conventional cells is low and thus 5, the diffusion layer thickness, is large. Secondly, the total current density at the cathode is relatively high, typically of the order of 10--20 mA/cm 2, and so the limiting current density for iron makes only a small contribution to the total current density at the cathode. A very different situation exists within the fluidised-bed cathode, however. The intense agitation within the bed will result in an increase in the limiting current density for iron reduction, probably by at least one order of magnitude (Le Goff et al., 1969). Furthermore, for equal applied cell currents, the current density at the surface of the copper particles within the fluidisedbed, will be much less than at a planar cathode, due to the much larger total surface area of the bed. Both these effects will result in the limiting current for iron having a much greater relative contribution to the total current density. Consequently the current efficiency for copper deposition in a fluidisedbed cell will be much lower than in a conventional cell for copper solutions which contain ferric iron. Thus it is concluded that, although fluidised-bed cathodes will undoubtedly find a place in the copper extraction industry, they are perhaps not applicable to such a wide range of solutions as the early promising results might suggest. CONCLUSIONS 1. The Yates analysis of the factorial experiment showed that three of the four variables studied had a significant effect on the current efficiency of the fluidised-bed cell. 2. Increasing the temperature and the presence of iron in the electrolyte both decreased the current efficiency, while an increase in the cell current increased the current efficiency. 3. Significant interactions of the variables on the current efficiency were
202 shown to exist for the case of cell current and iron concentration and for cell current and temperature. 4. These main effects and interactions can be accounted for by a model involving three simultaneous cathode reactions; i.e. the reduction of cupric ions, the reduction of ferric ions and the reduction of oxygen, with the latter two occurring at their diffusion limited rates. 5. Significant main effects on the power c o n s u m p t i o n of the cell were established for the variables cell current, iron concentration and acid concentration. In this case the significant interactions were between cell current and iron concentration and cell current and acid concentration. 6. An increase in temperature was shown to lead to an increase in the a m o u n t of metal deposited on the feeder electrode. 7. The application of fluidised-bed cathodes to the recovery of copper from various types of solutions has been discussed. 8. Finally, it is hoped t h a t this investigation will help to demonstrate the value of statistical design in experimentation. Factorial and other statistical experimental designs are widely used in technological investigations where their power for achieving objectives such as process optimisation is well k n o w n (see, for example, Duckworth, 1968). However, as the present work and others (Villas BSas, 1973; Orofino Pinto, 1975) have shown, the same techniques can be applied to investigations of a more f u n d a m e n t a l nature and can produce much valuable information from relatively few experimental results. ACKNOWLEDGEMENTS The authors are grateful to Professor R.C. Villas B6as for m a n y invaluable discussions t h r o u g h o u t the course of this work, particularly with respect to the statistical design and analysis of the experiments.
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203 Flett, D.S., 1972. The Fluidised-Bed Electrode in Extractive Metallurgy. Chemistry and Industry, 52: 983--988. Le Golf, P., Vergnes, F., Coeurt, F. and Bordet, J., 1969. Applications of Fluidised Beds in Electrochemistry. Industrial and Engineering Chemistry, 61(10): 8--17. Orofino Pinto, C.R. and Villas BSas, R.C., 1975. Direct Leaching of Chromite Ores. Paper 31. XIth International Mineral Processing Congress, Cagliari, Italy. Villas BSas, R.C. and Balberyszski, T., 1973. A Statistical Model of Process Parameters in Electrowinning of Zinc. Paper presented at 102nd A.I.M.E. Annual Meeting and 2nd International Symposium on Hydrometallurgy, Chicago, U.S.A. Wilkinson, J.A.E. and Haines, K.P., 1972. Feasibility Study on the Electrowinning of Copper with Fluidised-Bed Electrodes. Trans. I.M.M., 81: C157--C162. Yates, F., 1937. Design and Analysis of Factorial Experiments. Imperial Bureau of Soil Science, London.
