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LIX 64N system
Hydrometallurgy, 4 (1979) 109--124 109 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
THE MODELLING OF EQUILIBRIUM DATA FOR THE LIQUID--LIQUID EXTRACTION OF METALS P A R T III. A N I M P R O V E D C H E M I C A L M O D E L F O R T H E C O P P E R / L I X 64N SYSTEM
R.J. WHEWELL and M.A. HUGHES
Schools of Chemical Engineering, University of Bradford, Bradford, BD7 1DP (U.K.) (Received May 19th, 1978; in revised form July 28th, 1978)
ABSTRACT Whewell, R.J. and Hughes, M.A., 1979. The modelling of equilibrium data for the liquid-liquid extraction of metals. III. An improved chemical model for the copper/LIX 64N system. Hydrometallurgy, 4: 109--124. New data are presented for the copper sulphate--sulphuric acid/LIX 64N--Escald 100 solvent extraction system, and it is shown that these data do not exhibit the anomalous features of Robinson's (1971) results. The data are modelled using equations based on the thermodynamics of the Cu 2÷, CuSO 4, H÷, HSO,-, SO42- aqueous system and the HR, (HR)n, CuR~ organic system (where HR represents the active ~-hydroxyoxime in LIX 64N). Although the values of the two aqueous and the two organic equilibrium constants cannot be held to have thermodynamic significance, the best models are capable of predicting the organic copper concentrations of the 86 data points at four different concentrations of LIX 64N (5--50 vol.%) from the aqueous phase analyses with average errors as low as 7%. Isotherms for desired aqueous feedstocks and desired concentrations of our batch of LIX 64N in Escaid 100 at 25--26°C can be calculated.
INTRODUCTION In t h e earlier papers o f this series ( F o r r e s t and H u g h e s 1975a, 1 9 7 5 b ) , a n u m b e r o f possible a p p r o a c h e s t o equilibrium m o d e l f o r m u l a t i o n were discussed, and m o d e l s b o t h c h e m i c a l and empirical p r e s e n t e d f o r t h e c o p p e r / L I X 6 4 N s y s t e m based o n t h e d a t a o f R o b i n s o n and P a y n t e r ( 1 9 7 1 ) . T h e simple c h e m i c a l m o d e l simulated o n l y individual c o n s t a n t acid i s o t h e r m s o f the s y s t e m , giving an average e r r o r o f 7.3% in t h e i s o t h e r m s or o f 5% a f t e r empirical m o d i f i c a t i o n . The o n e or t w o p a r a m e t e r s h o w e v e r d i f f e r e d f r o m i s o t h e r m t o i s o t h e r m even at a given c o n c e n t r a t i o n o f L I X 64N. T h e empirical m o d e l , based o n a p o l y n o m i a l e q u a t i o n , q u a n t i f i e d t h e e q u i l i b r i u m surface f o r 20 vol.% L I X 6 4 N in Escaid in t w o sections w i t h 6 and 10 p a r a m e t e r s respectively, giving an average e r r o r o f 6%. The usefulness o f this t y p e o f m o d e l in interpolation o f equilibrium d a t a has been d e m o n s t r a t e d in s u b s e q u e n t c o n f i d e n t i a l c o n t r a c t w o r k at B r a d f o r d . It m u s t , h o w e v e r , be stressed t h a t t h e m o d e l can be used o n l y f o r i n t e r p o l a t i o n , and
110
not for extrapolative prediction; the values of the parameters have of course, no fundamental significance. The w o r k described in this paper is a continuation of the chemical approach to modelling, in which more sophisticated chemical forms are adopted for the equations. The model is designed to achieve a substantial reduction in the number of parameters involved in the equation b y comparison with the empirical model, and to enable some conclusions to be drawn concerning the chemistry of the system. Two anomalous features of Robinson and Paynter's (1971) data, discussed below, dictated the need to remeasure the equilibrium data to be modelled. While concentrating on the 10% and 20% solutions of LIX 64N in Escaid 100 which have hitherto been of commercial importance, some data for 5% and 50% LIX 64N have been included so that the effect of LIX 64N concentration could be better studied. EXPERIMENTAL
Reagents. LIX 64N (General Mills Inc., batch number 1D1502) and Escaid 100 (Essochem Europe Inc., batch number TK649) were supplied b y N.C.C.M. and were used w i t h o u t pretreatment. Aqueous phases were made up from stock solutions of copper sulphate and sulphuric acid (B.D.H. AnalaR) which had previously been analysed. The remaining reagents were of AnalaR quality; only water distilled from an all glass still was used.
Equilibration experiments were carried o u t in conical flasks on a laboratory shaker at 25--26°C. Since shaking for 15--30 minutes produced samples n o t wholly equilibrated, a total of at least 12 hours shaking was allowe.d for each test. The phases were separated and analysed; it was demonstrated that centrifugation of the phases to complete their clarification was unnecessary in these experiments.
Analyses. Organic copper concentrations were determined by stripping with 20% nitric acid and atomic absorption spectrophotometry, as described by Whewell et al. (1975). Aqueous copper concentrations were similarly determined b y dilution and atomic absorption spectrophotometry, and were confirmed in many cases b y iodometric titration (Vogel, 1961) with a precision better than 2%. Aqueous sulphuric acid concentrations were measured b y titration with sodium hydroxide solution, discontinuing the titration before precipitate started to appear. The use of an extrapolative plot due to Gran (1952) in the pH range of approximately 3.3 (below which HSO4- formation is apparent) to 4.3 (above which CuOH ÷ formation is apparent) enabled the concentration of sulphuric acid to be calculated with a precision better than 1%.
111
RESULTS T h e equilibrium d a t a are s h o w n in Tables 1--4, t o g e t h e r with t w o c h e c k s o f self-consistency. T h e " c o p p e r b a l a n c e " is given b y [Cu] aq + p h a s e ratio × [Cu] org, and s h o u l d equal t h e c o p p e r feed c o n c e n t r a t i o n ; the " a c i d b a l a n c e " is [H~SO4] aq + ( 9 8 . 0 8 / 6 3 . 5 4 ) X [Cu] aq and s h o u l d equal t h a t o f t h e a q u e o u s feed. T h e acid balances are generally c o r r e c t t o a b o u t 2%, t h e c o p p e r balances to 3%, with the organic c o p p e r c o n c e n t r a t i o n t h e least precise o f t h e three analyses. O n e t y p i c a l i s o t h e r m f r o m R o b i n s o n ' s ( 1 9 7 1 ) studies is s h o w n in Fig. 1 f o r c o m p a r i s o n with o u r c o r r e s p o n d i n g isotherm. Direct c o m p a r i s o n is o p e n to q u e s t i o n since d i f f e r e n t b a t c h e s o f L I X 6 4 N were used in t h e t w o studies. H o w TABLE1 Equilibrium isotherm for 5 vol.% LIX 64N in Escaid 100 at 25--26°C Phase ratio org:aqueous
aqueous copper concn, (g dm-s)
aqueous sulphuric acid concn, (g dm -3)
organic copper concn. (g dm -3)
Aqueous feed 5.17 g dm -3 copper, 5.01 g dm -s sulphuric acid (acid balance 13.00 g dm -s) 90:10 70:30 50:50 30:70 10:90
1.55 3.55 4.30 4.78 5.08
CuJ org [gdm-'}
10.63 7.81 6.38 5.68 5.19
I "
4
0.389 0.756 0.895 0.965 1.015
..Cr "'Q ....A
,d"/..~ j t"
z /"
/"
z / z / //
,P,'
g;x
z '
i
,
/.
,,'¢ / o
[CuJaq (ga~ s) ~.
,~
,5I
Fig. 1. Comparison of the equilibrium data of Robinson (/") with the data of this work (o); aqueous feed 5 g d m -3 copper, 1 g dm -s sulphuric acid, organic feed 20 vol.% LIX 64N in Escaid 100. The dotted lines are arbitrary smooth curves.
112
TABLE 2 E q u i l i b r i u m i s o t h e r m s for 10 vol.% L I X 6 4 N in Escaid 1 0 0 a t 2 5 - - 2 6 ° C Phase r a t i o org:aqueous
aqueous copper concn,
aqueous sulphuric acid c o n c n ,
organic copper concn.
(g dm-3)
(g dm -3)
(g dm-3)
A q u e o u s feed 1.5 g d m -3 c o p p e r (acid b a l a n c e 2.32 g d m -3 ) 90:10 80:20 70:30 40:60 30:70 20:80 10:90
0.0075 0.018 0.038 0.262 0.528 0.87 1.22
2.451 2.400 2.343 1.960 1.560 1.000 0.475
0.166 0,367 0.612 1.84 2,16 2.44 2.54
A q u e o u s feed 3.0 g d m -3 c o p p e r (acid b a l a n c e 4 . 6 3 g d m - 3 ) 90:10 80:20 70:30 60:40 40:60 30:70 20:80 10:90
0.058 0.160 0.306 0.568 1.41 1.94 2.33 2.65
4.54 4.34 4.20 3.70 2.47 1.71 1.06 0.49
0.32 0.70 1.13 1.56 2.38 2.46 2.73 2.78
A q u e o u s feed 5.0 g d m - 3 c o p p e r , 1.0 g d m -3 s u l p h u r i c acid (acid b a l a n c e 8.72 g d m - a ) 90:10 80:20 70:30 60:40 40:60 30:70 20:80 10:90
0.334 0.805 1.41 2.10 3.41 3.85 4.28 4.70
8.37 7.64 6.74 5.58 3.47 2.69 1.99 1.47
0.50 1.01 1.46 1.90 2.33 2.47 2.57 2.67
A q u e o u s f e e d 6.0 g d m -3 c o p p e r , 2.0 g d m - 3 s u l p h u r i c acid (acid b a l a n c e 1 1 . 2 6 g d m - 3 ) 90:10 80:20 70:30 60:40 40:60 30:70 20:80 10:90
0.63 1.46 2.25 3.05 4.45 4.96 5.33 5.72
10.56 9.24 7.97 6.66 4.53 3.71 3.03 2.49
0.57 1.12 1.54 1.92 2.32 2.42 2.58 2.49
113
TABLE 3 Equilibrium isotherms for 20 vol.% L I X 64N in Escaid 100 at 2 5 - - 2 6 ° C Phase ratio org: aqueous
aqueous copper concn,
aqueous sulphuric acid concn,
organic copper concn.
(g d m -3)
(g dm -3 )
(g d m -3)
A q u e o u s feed 1.5 g d m -3 copper (acid balance 2.32 g dm -3) 90:10 80:20 70:30 60:40 40:60 30:70 10:90
0.0027 0.0067 0.014 0.023 0.070 0.146 0.925
2.263 2.257 2.265 2.297 2.225 2.117 0.895
0.168 0.376 0.643 0.978 2.02 2.96 4.77
A q u e o u s feed 3.0 g dm -3 c o p p e r (acid balance 4.63 g dm -3) 90:10 80:20 70:30 60:40 40:60 30:70 20:80 10:90
0.022 0.057 0.121 0.202 0.645 1.13 1.74 2.40
4.55 4.48 4.43 4.31 3.70 2.95 1.99 0.96
0.334 0.751 1.24 1.77 3.59 4.39 5.08 5.43
A q u e o u s feed 3.0 g d m -3 copper, 2.0 g dm -3 sulphuric acid (acid balance 6.63 g dm -3) 90:10 70:30 60:40 40:60 30:70 10:90
0.045 0.216 0.358 0.864 1.31 2.47
6.54 6.21 6.13 5.29 4.62 2.85
0.329 1.20 1.72 3.05 3.79 4.96
A q u e o u s feed 5.0 g d m -3 copper, 1.0 g d m -3 sulphuric acid (acid balance 8.72 g d m -3) 90:10 80:20 70:30 60:40 40:60 30:70 20:80 10:90
0.151 0.370 0.645 1.03 2.19 3,00 3.76 4,44
8.34 8.02 7.72 7.12 5.28 4.16 2.94 1.91
0.536 1.17 1.86 2.50 3.94 4.54 5.02 5.16
114
TABLE 3 (continued) Phase r a t i o org:aqueous
aqueous copper concn,
aqueous sulphuric acid concn,
organic copper cone.n.
(g d m -3)
(g d m -~)
(g dm -3)
A q u e o u s feed 6.0 g dm -3 copper, 2.0 g d m -3 sulphuric acid (acid balance 11.26 g d m -3) 90:10 80:20 70:30 60:40 40:60 30:70 20:80 10:90
0.287 0.70 1.12 1.72 3.19 4.05 4.62 5.32
10.78 10.08 9.78 8.58 6.45 5.11 4.01 2.96
0.612 1.30 1.91 2.57 4.03 4.36 4.84 5.15
A q u e o u s feed 9.0 g dm -3 copper, 1.5 g d m -3 sulphuric acid (acid balance 15.39 g d m -3) 90:10 80:20 60:40 30:70
0.74 1.61 3.65 6.82
14.09 12.83 9.82 4.87
0.93 1.77 3.36 4.52
A q u e o u s feed 3.0 g d m -3 copper, 12.0 g d m -3 sulphuric acid (acid balance 16.62 g dm -3) 90:10 60:40 20:80
0.36 1.19 2.44
15.88 14.67 12.89
0.303 1.13 2.15
TABLE 4 Equilibrium i s o t h e r m for 50 vol.% L I X 64N in Escaid 100 at 2 5 - - 2 6 ° C Phase r a t i o org:aqueous
aqueous copper concn,
aqueous sulphuric acid concn,
organic copper concn.
(g d m -3 )
(g d m -3)
(g dm -3)
A q u e o u s feed 6.0 g d m -3 copper, 2.0 g d m -3 sulphuric acid (acid balance 11.26 g d m -a) 90:10 80:20 70:30 50:50 30:70 20:80 10:90
0.125 0.295 0.503 1.09 2.27 3.36 4.60
10.94 10.74 10.43 9.54 7.66 6.11 4.13
0.65 1.45 2.38 4.89 8.55 10.54 12.59
115
ever, Robinson's isotherm shows a distinct S-shaped character between the origin and the first data point. Our data are shifted in a direction corresponding to completion of equilibration and the S-shaped characteristic has disappeared. It therefore seems likely that Robinson's data come from solutions not entirely at equilibrium. Our experiments in which shaking was carried o u t for only 15--30 minutes gave an S-shaped isotherm, and it m a y be that the degree of extraction of copper after only a short time is of relevance in plant design. It is clear, however, that for chemical studies of the system complete equilibration is essential. A second feature of Robinson's results, c o m m e n t e d u p o n b y Forrest and Hughes (1975b), is the " d i p " in the isotherms at high copper concentration and low aqueous acid concentration. This dip is not evident in our new data. MODELLING Introduction
In order to model the system chemically it is necessary to define a route for the transfer of copper from aqueous to organic phases. This route is a feasible part of the thermodynamic cycle, b u t need not necessarily represent the true mechanism of the reaction. Complexation of copper with oxime (eqns. 1--3) is taken to occur in the aqueous phase, +
HRaq -~ Haq + Raq
(1)
2+ + Raq--CUaq ~ CuRaq +
(2)
+
CURaq + Raq ~- CuR2 aq
(3)
(where H R represents the active ~-hydroxyoxime in LIX 64N). Conventional stability constants can be defined for these reactions, and partition coefficients for the distribution of single uncharged species between the aqueous and organic phases. HRaq ~ HRorg
(4)
CuR2 aq ~ CuR2 org
(5)
The organic phase is complicated b y oxime aggregation (Whewell et al., 1977), nHRorg ~- (HR)n org
(6)
and the aqueous phase by the formation of sulphate complexes or ion pairs (Whewell and Hughes, 1976). 2+ Cuaq + SO~aq ~ CuSO4 aq
(7)
naq + SO42aq ~ HSO4-aq
(8)
116
For the t w o phase system at equilibrium it is possible to draw up mass balance equations for each of the known total concentrations of copper, acid, oxime and sulphate in each phase. The major species are u n d o u b t e d l y Cu 2÷, H ÷, CuSO4, HSO~, SO~- (aqueous) and CuRs, HR, (HR)n (organic). By comparison, the minor species (such as aqueous species which include an oxime molecule) have no real effect in the mass balance equations. It is therefore possible to treat the system with four simplified mass balance equations (9) to (12), L = l + [CuSO4] + [HSO~]
aqueous
(9)
B = b + [CuSO4]
aqueous
(10)
H=h+
aqueous
(11)
organic
(12)
[HSO~]
R = [HR] + 2[CUR2] + ~n [(HR)n]
where L, B and H are the total aqueous concentrations at equilibrium of sulphate, copper and total analytical proton; the respective free concentrations in the aqueous phase are l, b and h. R is the total concentration of active oxime in the organic phase. Concentrations L and R are conserved throughout the extraction process; B and H alter as ion exchange occurs. This simplification offers substantial economies in calculation, arising from: (a) the separate treatment of the two phases, (b) the justifiable neglect to the charged species R - and CuR +, existing at low contribution in the aqueous phase only and contributing negligibly to the mass balances, and (c) the possibility of treating eqns. (1) to (5) as a single process Cu aq + 2HRorg ~- CuR2 ore + 2Haq
(13)
with only one parameter ~ = [Cu] org h 2 [HR] -2org b - ' (14) necessary to quantify organic phase copper complexation. Study of the constituent equilibria, eqns. (1) to (5), has been initiated (Preston and Whewell, 1977; Foakes et al., 1978), because of their potential importance in kinetic performance.
Aqueous phase treatment Equations (9) to (11) are identical to those used in our earlier work (Whewell and Hughes, 1976). It is thus possible with t w o parameters
~i = [CuSO4]b-' f-1 ~ 500
(15)
K H = [HSO~] h -1 /-1 ~ 130
(16)
to determine h for the equilibrated aqueous phases of known B, L and H,
117
preferably for 1.1 ~< pH ~< 2.1. The concentration units used throughout the calculation are mol dm -3 . In the original treatment activities were equated to concentrations w i t h o u t control of ionic strength, and the model developed to calculate pH values from values of B, L and H. Its use here is thus entirely justified. Values of b calculated from eqns. (9) to (11), (15) and (16) are however less certain, and it is likely that the calculated values of biB are underestimated b y a factor of around two b y comparison with calculations from N~is~inen's (1949) work. Trends in the calculated values of b are expected to be more representative of trends in the true copper ion activity than are those in values of B. On these grounds alone, the t w o phase model is based on b rather than on B. The first stage of modelling is therefore the calculation of h and b for the equilibrated aqueous phase, solving an equation cubic in h b y Newton's m e t h o d with an initial estimate of h = 0.5 H. It is then possible to obtain y, where (17)
y = bh -2 Organic phase treatment
Some slope analysis (Stary, 1964) was carried o u t on the results of the 20 vol.% LIX 64N experiments. Data B, h were interpolated b y smooth curves at constant values of [Cu] org and hence at constant [HR] org. Plots of log(D = [Cu] org/B) against log h were straight lines of gradient - 2 . 0 + 0.15, thus confirming the generally accepted CuR2 stoichiometry of the organic phase species. However, eqns. (13) and (14) also predict DVFDhv ~ [HR] org
(18)
A graph of ~ against total LIX concentration u n b o u n d to copper shows significant deviation from the expected straight line at higher LIX concentrations, such that [HR] org ( [ u n b o u n d LIX]. This finding confirms the oxime aggregation reported recently (Hummelstedt, 1977; Whewell et al., 1977) and shown in eq. (6). In modelling eqn. (6) we have continued our practice of allowing only one parameter to express aggregatinn, and have found three forms of eqn. (6) to be of interest: 2HR ~- H2R2
K22 = [H2R2] [ H R ] - 2
dimer
4 H R ~ H4R,
K44 = [H4R4] [ H R ] - 4
tetramer (20)
HR-~ H2R2 ~ H3R3 ~ . . . H n R n Kn = [HnRn] [ H n - I R n - I ] - ' [ H R ] - I
series
Equation (19) is suggested b y the w o r k of Price and Tumilty (1975), b u t was shown b y Whewell et al. (1977) to be inadequate to describe the vapour phase behaviour of solutions of purified oximes in dry n-heptane. Equations (20) and (21) were suggested b y the latter study, b u t the reported values of parameters appropriate to purified oximes are n o t applicable to these studies of reagents as received.
(19)
(21)
118
Optimisation
Concentrations were in mol dm -3 throughout. From values of y = bh - 2 for the aqueous phases, values of [Cu] org were calculated using eqn. (12) with varying values of/~2 (eqn. 14) and aggregation constant (eqn. 19, 20 or 21). The total oxime concentration R was at first allowed to vary slightly in the optimisation but later a fixed value of R corresponding to a 5.7 g dm -3 ultimate load of copper in 20 vol.% LIX 64N was adopted as consistent with our previous work. Values of the two parameters being varied were accepted when V A = ~ ( [ C u ] org, calc - [ C u ] org, expt ) 2 or Up = ~ { ( [ C u ] org, calc - [ C u ] org, e x p t ) / [ C u ] org, expt )2
were minimised; UA is the sum of squared absolute errors and Up of percentage errors in the calculated organic copper concentrations, and no additional weighting factors are included. Our experimental strategy therefore biases the results somewhat in favour of the commercially important region (10--20 vol.%) of LIX 64N concentration. Any local minima are readily avoided by the grid search m e t h o d of optimisation used, and this m e t h o d allows checking during optimisation to ensure that small improvements in the overall fit are n o t being achieved at the expense of large systematic errors in fitting the extreme (5 or 50 vol.%) concentrations of LIX 64N. The Up criterion is more in accordance with the expected errors in [Cu] org,expt than is UA, and was used by Forrest and Hughes (1975b), but the UA criterion is attractive when results biased towards high concentrations of extracted copper are required. Although the errors in [Cu] org,expt are probably the largest of the three analytical errors, a rigorous expression would require an additional weighting factor to take account of expected errors in y. EVALUATION OF THE MODELS Dimer model
Equation (12) becomes R = x + 2/~2 Yx2 + 2K22 x2
(22)
where x = [HR] org- The organic copper concentration is given by [Cu] org,ealc = ~2 Yx 2
(23)
Data R, y at trial values of ~2, K22 enable values of x and so of [Cu] org,ealc to be obtained for each experimental point. Although satisfactory fitting could be obtained for any given concentration of LIX 64N, the values of the parameters giving the best fit tended to vary systematically with LIX concentration. The best results that could be obtained gave an overall root mean square percentage deviation of 9.8% on 86 experimental points with/32 = 36 and K22 =
119
15, or an overall root mean square absolute deviation of 0.128 g dm -3 with ~2 = 31 and K n = 15. For individual concentrations of LIX 64N other values would be chosen, e.g. ~2 = 17 and K2~ = 5 for 20 vol.% LIX 64N, which gives poorer (0.197 g dm -3 or 11.6%) overall fitting. Tetramer
model
Equation (12) becomes R = x + 2 ~ 2 y x 2 + 4K44x 4
(24)
and eqn. (23) applies. Equation (24) is readily solved for x by Newton's m e t h o d using the arbitrary initial estimate x = 0.01R. The fits obtained were more satisfactory than for the dimer model, and there was no systematic variation in the o p t i m u m parameters with LIX concentration. The two minimisation criteria UA and Up gave slightly differing optima, as shown on Table 5. The effectiveness of the modelling can be shown in two ways. First a theoretical isotherm can be constructed from feed concentration data, phase ratio and the parameters. A set of isotherms for 20 vol.% LIX 64N is shown in Fig. 2, where the experimental data can be compared with isotherms for ~2 = 13, K44 = 160 (the best model giving 7.1% average error) and ~2 = 11, K44 = 160 (giving the lowest absolute error of 0.149 g dm -3 copper). A second check of effectiveness is a plot of [Cu] org,calc against [Cu] org,expt, which should appear as a straight line of unit gradient. Such plots for ~2 = 13, K44 = 160 revealed systematic overestimation of organic copper concentration above 3 g d m -3, whereas/~2 = 11, K44 = 160 gave systematic underestimation of those points below 1.5 g dm -3. The plot for/~2 = 12, K44 = 160 shown in Fig. 3 gives a good compromise between these two differently defined optima. Series model
Equation (12) is now R = 2~2yx 2 + ( x + 2 K n x 2 + 3 K n 2 x 3 + . ..) TABLE
5
T e t r a m e r m o d e l -- best values of the parameters T h e e r r o r s q u o t e d are r o o t m e a n s q u a r e v a l u e s f o r t h e 86 d a t a p o i n t s
~2
K44
Percentage error
Absolute error (g d m -3 )
11 12 13
160 160 160
11.0 8.2 7.1
0.149 0.152 0.184
120
5
[Cu] org ( g dm-~) [Cu] org calc (g dm ~)
/ /f. . , Y
4
;
-
I
A/
~ /
2
-3
[Cu]aq ( gdm-3)
m)
O O Fig. 2. I s o t h e r m s f o r 20 vol.% L I X 6 4 N e q u i l i b r a t e d w i t h various a q u e o u s phases. T h e e x p e r i m e n t a l p o i n t s are t h o s e in T a b l e 3; t h e i s o t h e r m s d r a w n are c a l c u l a t e d f r o m 13: = 13, K44 = 1 6 0 ( c o n t i n u o u s lines) a n d f r o m 132 = 11, K44 = 160 ( d o t t e d lines). Fig. 3. P l o t o f o r g a n i c c o p p e r c o n c e n t r a t i o n c a l c u l a t e d f r o m 132 = 12, K4, = 1 6 0 against t h e experimentally determined concentrations.
or for a series mathematically infinite but in practice including only around six significant terms, R = 2/]2yx 2 + x/(1
- Knx) 2
(25)
Again eqn. (23)*applies and eqn. (25) can be solved for x by Newton's m e t h o d with an initial estimate of x = 0.01R. Much the same pattern as for the tetramer model emerges, as shown in Table 6, and the isotherms calculated for the best percentage model (/]2 = 21, K n = 4 , with 6.7% average error) and for the best absolute error model (/]2 = 15, K n = 3, with 0.120 g dm -3 average error) are barely different from the respective optima of the tetramer model. The same systematic deviations are seen in the plots of calculated against experimental organic copper concentration, and again the intermediate model (/]2 = 18, K n = 3.5) has advantages by comparison with the formally defined optima. This model is represented in Figure 4. TABLE6 Series m o d e l - - b e s t values o f t h e p a r a m e t e r s The e r r o r s q u o t e d are r o o t m e a n s q u a r e values for t h e 86 d a t a p o i n t s 132
K n
Percentage error
Absolute error
(g d m - 3 ) 15 18 21
3 3.5 4
9.7 7.5 6.7
0.120 0.134 0.159
121
[Cu]orcjcole l gdm-3)
,
~
"
./
.e
4
2
!
/,
o'
[Cu]orgc x p t
r
( g dm-~)
~
~,
Fig. 4. Plot of organic copper concentration calculated from/~2 = 18, experimentally determined concentrations.
Kn =
3.5 against the
CONCLUSIONS
The models outlined above offer average errors in the calculated organic copper concentration as l o w as 7%, and span a wider range of LIX 64N concentrations than has been modelled previously. Aqueous phase properties are calculated with two parameters for which optimum values have been determined in previous work, and a further two parameters are added in this treatment to express extraction and organic phase properties. A shortening of the calculation can be achieved by the use of a graph such as Figure 5. Since [Cu] org,ealc is a function solely of the total LIX concentration,
40 35
6 4
~
1
5
3 2
I©
I
5 bh~ 2
j
0
ool
o.os
o.I
os
i-o
s
io
5o
Fig. 5. D e p e n d e n c e of organic phase copper concentration o n y = bh -2 for various concentrations of L I X 6 4 N in Escaid; calculated f r o m f12 = 18, K n = 3.5.
122
the above parameters, and y = bh -2, the single line graph of [Cu] org,calc against logl0(y) is sufficient to represent all equilibria (at least in the range tested) of the copper sulphate--sulphuric acid/LIX 64N--Escaid 100 system at a given concentration of LIX 64N. As with/31 and K~ H, it is dubious to attach thermodynamic significance to the parameters/32 and K44 or Kn. Loss of this significance is inevitable through the use of the calculated free copper ion concentration in the aqueous phase, although better data might n o w be obtained b y the use of a copper ion selective electrode to measure b directly. There is still some uncertainty attached to the nature of the aggregated species in the organic phase, and the use of oversimplified one parameter representations of aggregation inevitably conceals the complexity of the system. It is however clear that the tetramer and series models give a significantly better description of the extraction system than does the dimer model. This important conclusion emphasises the significance of aggregatior in commercial oxime systems. An operation to be discouraged is the calculation of oxime m o n o m e r concentrations from the values of K44 and K n obtained here. We have deliberately avoided discussion of "errors" in the values of the parameters, in order to avoid any suggestion that we have measured stability constants as such. A further reason for uncertainty in the values of the parameters is the shape of the surfaces of UA and Up as a function of the t w o parameters f12 and K44 (or Kn ); a c o n t o u r map shows a long diagonal trough which would enable ratios of the parameters to be determined quite precisely b u t forces absolute values to remain nncertain. Until copper ion activity in the aqueous phase is measured directly and incorporated into the model, it will not be possible to extend the model to encompass aqueous counterions other than sulphate. Equilibrium experiments carried o u t in Bradford with copper perchlorate/perchloric acid phases, for example, gives organic copper concentrations lower than predicted by the model when all of the aqueous copper and proton are taken to be uncomplexed. A more effective rationalisation of the counterion effect has been published by Cognet and Renon (1977). Spink and Okuhara (1974) included a CuA2 • HA species in their organic phase model for Kelex 100 (where HA represents the active extractant molecule). A species of this t y p e is a likely adduct in the LIX 64N system, b u t unlike (HR)n there is no evidence independent of the model to confirm its existence in the LIX system. The difficult nature of the minimisation surfaces of UA and Up preclude the incorporation of a third parameter. It:is indeed surprising that Spink and Okuhara are able to q u o t e with such precision five parameters determined for each of their Kelex-diluent systems, in particular when the values of the parameters rely on the inclusion of CuA ÷, CuA2 and CuA2 -HA species in the aqueous phase mass balance. A referee has drawn to our attention a paper by Hoh and Bautista (1978) in which a chemical model is described for a dilute solution of LIX 65N in toluene The model is constructed on a similar basis to ours, with an improved calculation of free copper(II) ion concentration b u t unfortunately no consideration
123
of the bisulphate equilibrium. Aggregation in the organic phase is not included in the model, an appropriate omission provided that the model is restricted to dilute solution work. The use of the model with the data of Spink and Okuhara (1974) shows that these data can be interpreted more simply than suggested by the original authors. Unfortunately the application of Hoh and Bautista's model to the LIX 65N data raises a number of questions, particularly with respect to the assumption that their sample of LIX 65N as received contains 100% active oxime. It would also be interesting to have fuller details of the authors' calculation of the free sulphate concentrations in the aqueous phase and of the values of ionic strength. An application of our model to these data involves a substantial extrapolation beyond the range of concentrations studied by us, but accepting the data B, H from the authors' Table III and incorporating a purity factor of 36.4% appropriate to our batch of LIX 65N, it is possible to obtain partial fitting using our models. Thus for the tetramer model the values of the parameters 92 = 12 and K44 = 160 were used, but were modified in the calculation by a factor Q (explained in the following paper) to allow for the exchange of an Escaid 100 diluent for toluene. In this case the guestimated value of log Q = 0.35 × (98.5/80) = 0.43. The results showed an excellent agreement between the [Cu] org values (material balance) of Hoh and Bautista and the calculated [Cu] org values for the " p H = 4 " data with a root mean square deviation of 0.00040 mol dm -3 (7.8%) compared with 0.00108 mol dm -3 from the authors' calculation. For the " p H = 3" data the fit was poorer (0.00097 mol dm -3, originating largely from the first two points) and for " p H = 2" the model gave systematically high calculated values. If we permitted ourselves to use three separate values of 92, as did Hoh and Bautista, then we could u n d o u b t e d l y achieve three satisfactory fits. Bauer and Chapman (1976) proposed an alternative m e t h o d of allowing for alterations in the " a c t i v i t y " of the organic phase containing Kelex 100. In place of our complex equilibria they define organic and aqueous phase activity coefficients in terms of defensible chemical equations and fit two parameters to each. The overall model is based on an equilibrium constant similar to our /32, the value of which in a particular case is derived from a six parameter equation (two parameters for each of the activity expressions and two for the temperature dependence). Standard errors of 9% were obtained for the model produced. In applying such a treatment to the LIX system, it would be expected that the same activity relationships could be applied to the aqueous sulphate system, but that as in the case of our model there is no theoretical basis for direct extension to other aqueous counterions. The authors state that a much more complicated expression would be required for the organic phase activity coefficient in systems (such as copper/LIX 64N) in which dimer or polymer formation occur. Our t r e a t m e n t of the organic phase goes some way towards meeting these problems of quantifying its equilibrium behaviour.
124
ACKNOWLEDGEMENTS
The authors wish to thank Nchanga Consolidated Copper Mines of Zambia for the financial support of this project, and Mrs. M. Paul and Miss M. Medley for carrying out much o f the experimental work.
REFERENCES Bauer, G.L. and Chapman, T.W., 1976. Measurement and correlation of solvent extraction equilibria. The extraction of copper b y Kelex 100. Met. Trans., 7B: 519--527. Cognet, M.-C. and Renon, H., 1977. Influence of aqueous phase composition upon copper extraction by cationic extractants: A thermodynamic interpretation. Hydrometallurgy, 2: 305--314. Foakes, H.J., Preston, J.S. and Whewell, R.J., 1978. Aqueous phase solubilities and partition data for commercial copper extractants. Anal. Chim. Acta, 97: 349--356. Forrest, C. and Hughes, M.A., 1975a. The modelling of equilibrium data for the liquid-liquid extraction of metals. I. A survey of existing models. Hydrometallurgy, 1: 25--37. Forrest, C. and Hughes, M.A., 1975b. The modelling of equilibrium data for the liquid-liquid extraction of metals. II. Models for the copper/LIX 64N and chromate/Aliquat 336 systems. HydrometaUurgy, 1 : 139--154. Gran, G., 1952. Determination of the equivalence point in potentiometric titrations, II. Analyst, 77: 661--671. Hoh, Y.-C. and Bautista, R.G., 1978. Chemically based model to predict distribution coefficients in the Cu--LIX 65N and Cu--Kelex 100 Systems. Met. Trans., 9B: 69--75. Hummelstedt, L., 1977. Reagents particularly suited for metal extraction from sulphate media: Recent developments. Proc. Int. Solvent Extraction Conf. (ISEC'77), Toronto, Paper 5c. N~is~nen, R., 1949. Spectrophotometric study on complex formation between cupric and sulphate ions. Acta Chem. Scand., 3: 179--189. Preston, J.S. and Whewell, R.J., 1977. Purification and acid--base properties of hydroxyoxime extractants for copper. J. Inorg. Nucl. Chem., 39: 1675--1678. Price, R. and Tumilty, J.A., 1975. An interpretation of some aspects of solvent extraction as related to the extraction of copper using o-hydroxyaryloximes. Inst. Chem. Eng. Symp. Set., No. 42, Institution of Chemical Engineers, London, Paper 18. Robinson, C.G. and Paynter, J.C., 1971. Optimisation of the design of a countercurrent liquid--liquid extraction plant using LIX 64N. Proc. Int. Solvent Extraction Conf. (ISEC '71), Society of Chemical Industry, London, II: 1416--1428. Spink, D.R. and Okuhara, D.N., 1974. The effect of diluents on the extraction of tracer level copper by an alkyl hydroxyquinoline (Kelex 100). Proc. Int. Solvent Extraction Conf. (ISEC '74), Society of Chemical Industry, London, 3: 2527--2540. Stary, J., 1964. The Solvent Extraction of Metal Chelates, Pergamon, London. Vogel, A.I., 1961. A T e x t b o o k of Quantitative Inorganic Analysis, Longmans, London, 3rd edition, 1216 pp. Whewell, R.J. and Hughes, M.A., 1976. Interpretation of pH measurements in solutions containing sulphuric acid and copper sulphate. J. Inorg. Nucl. Chem., 38: 180--181. Whewell, R.J., Hughes, M.A. and Hanson, C., 1975. The kinetics of the solvent extraction of copper(II) with LIX reagents. I. Single drop experiments. J. Inorg. Nucl. Chem,, 37: 2303--2307. Whewell, R.J., Hughes, M.A. and Hanson, C., 1977. Aspects of the kinetics and mechanism of the extraction of copper with hydroxyoximes. Proc. Int. Solvent Extraction Conf. (ISEC '77), Toronto, Paper 4a.
THE MODELLING OF EQUILIBRIUM DATA FOR THE LIQUID--LIQUID EXTRACTION OF METALS P A R T III. A N I M P R O V E D C H E M I C A L M O D E L F O R T H E C O P P E R / L I X 64N SYSTEM
R.J. WHEWELL and M.A. HUGHES
Schools of Chemical Engineering, University of Bradford, Bradford, BD7 1DP (U.K.) (Received May 19th, 1978; in revised form July 28th, 1978)
ABSTRACT Whewell, R.J. and Hughes, M.A., 1979. The modelling of equilibrium data for the liquid-liquid extraction of metals. III. An improved chemical model for the copper/LIX 64N system. Hydrometallurgy, 4: 109--124. New data are presented for the copper sulphate--sulphuric acid/LIX 64N--Escald 100 solvent extraction system, and it is shown that these data do not exhibit the anomalous features of Robinson's (1971) results. The data are modelled using equations based on the thermodynamics of the Cu 2÷, CuSO 4, H÷, HSO,-, SO42- aqueous system and the HR, (HR)n, CuR~ organic system (where HR represents the active ~-hydroxyoxime in LIX 64N). Although the values of the two aqueous and the two organic equilibrium constants cannot be held to have thermodynamic significance, the best models are capable of predicting the organic copper concentrations of the 86 data points at four different concentrations of LIX 64N (5--50 vol.%) from the aqueous phase analyses with average errors as low as 7%. Isotherms for desired aqueous feedstocks and desired concentrations of our batch of LIX 64N in Escaid 100 at 25--26°C can be calculated.
INTRODUCTION In t h e earlier papers o f this series ( F o r r e s t and H u g h e s 1975a, 1 9 7 5 b ) , a n u m b e r o f possible a p p r o a c h e s t o equilibrium m o d e l f o r m u l a t i o n were discussed, and m o d e l s b o t h c h e m i c a l and empirical p r e s e n t e d f o r t h e c o p p e r / L I X 6 4 N s y s t e m based o n t h e d a t a o f R o b i n s o n and P a y n t e r ( 1 9 7 1 ) . T h e simple c h e m i c a l m o d e l simulated o n l y individual c o n s t a n t acid i s o t h e r m s o f the s y s t e m , giving an average e r r o r o f 7.3% in t h e i s o t h e r m s or o f 5% a f t e r empirical m o d i f i c a t i o n . The o n e or t w o p a r a m e t e r s h o w e v e r d i f f e r e d f r o m i s o t h e r m t o i s o t h e r m even at a given c o n c e n t r a t i o n o f L I X 64N. T h e empirical m o d e l , based o n a p o l y n o m i a l e q u a t i o n , q u a n t i f i e d t h e e q u i l i b r i u m surface f o r 20 vol.% L I X 6 4 N in Escaid in t w o sections w i t h 6 and 10 p a r a m e t e r s respectively, giving an average e r r o r o f 6%. The usefulness o f this t y p e o f m o d e l in interpolation o f equilibrium d a t a has been d e m o n s t r a t e d in s u b s e q u e n t c o n f i d e n t i a l c o n t r a c t w o r k at B r a d f o r d . It m u s t , h o w e v e r , be stressed t h a t t h e m o d e l can be used o n l y f o r i n t e r p o l a t i o n , and
110
not for extrapolative prediction; the values of the parameters have of course, no fundamental significance. The w o r k described in this paper is a continuation of the chemical approach to modelling, in which more sophisticated chemical forms are adopted for the equations. The model is designed to achieve a substantial reduction in the number of parameters involved in the equation b y comparison with the empirical model, and to enable some conclusions to be drawn concerning the chemistry of the system. Two anomalous features of Robinson and Paynter's (1971) data, discussed below, dictated the need to remeasure the equilibrium data to be modelled. While concentrating on the 10% and 20% solutions of LIX 64N in Escaid 100 which have hitherto been of commercial importance, some data for 5% and 50% LIX 64N have been included so that the effect of LIX 64N concentration could be better studied. EXPERIMENTAL
Reagents. LIX 64N (General Mills Inc., batch number 1D1502) and Escaid 100 (Essochem Europe Inc., batch number TK649) were supplied b y N.C.C.M. and were used w i t h o u t pretreatment. Aqueous phases were made up from stock solutions of copper sulphate and sulphuric acid (B.D.H. AnalaR) which had previously been analysed. The remaining reagents were of AnalaR quality; only water distilled from an all glass still was used.
Equilibration experiments were carried o u t in conical flasks on a laboratory shaker at 25--26°C. Since shaking for 15--30 minutes produced samples n o t wholly equilibrated, a total of at least 12 hours shaking was allowe.d for each test. The phases were separated and analysed; it was demonstrated that centrifugation of the phases to complete their clarification was unnecessary in these experiments.
Analyses. Organic copper concentrations were determined by stripping with 20% nitric acid and atomic absorption spectrophotometry, as described by Whewell et al. (1975). Aqueous copper concentrations were similarly determined b y dilution and atomic absorption spectrophotometry, and were confirmed in many cases b y iodometric titration (Vogel, 1961) with a precision better than 2%. Aqueous sulphuric acid concentrations were measured b y titration with sodium hydroxide solution, discontinuing the titration before precipitate started to appear. The use of an extrapolative plot due to Gran (1952) in the pH range of approximately 3.3 (below which HSO4- formation is apparent) to 4.3 (above which CuOH ÷ formation is apparent) enabled the concentration of sulphuric acid to be calculated with a precision better than 1%.
111
RESULTS T h e equilibrium d a t a are s h o w n in Tables 1--4, t o g e t h e r with t w o c h e c k s o f self-consistency. T h e " c o p p e r b a l a n c e " is given b y [Cu] aq + p h a s e ratio × [Cu] org, and s h o u l d equal t h e c o p p e r feed c o n c e n t r a t i o n ; the " a c i d b a l a n c e " is [H~SO4] aq + ( 9 8 . 0 8 / 6 3 . 5 4 ) X [Cu] aq and s h o u l d equal t h a t o f t h e a q u e o u s feed. T h e acid balances are generally c o r r e c t t o a b o u t 2%, t h e c o p p e r balances to 3%, with the organic c o p p e r c o n c e n t r a t i o n t h e least precise o f t h e three analyses. O n e t y p i c a l i s o t h e r m f r o m R o b i n s o n ' s ( 1 9 7 1 ) studies is s h o w n in Fig. 1 f o r c o m p a r i s o n with o u r c o r r e s p o n d i n g isotherm. Direct c o m p a r i s o n is o p e n to q u e s t i o n since d i f f e r e n t b a t c h e s o f L I X 6 4 N were used in t h e t w o studies. H o w TABLE1 Equilibrium isotherm for 5 vol.% LIX 64N in Escaid 100 at 25--26°C Phase ratio org:aqueous
aqueous copper concn, (g dm-s)
aqueous sulphuric acid concn, (g dm -3)
organic copper concn. (g dm -3)
Aqueous feed 5.17 g dm -3 copper, 5.01 g dm -s sulphuric acid (acid balance 13.00 g dm -s) 90:10 70:30 50:50 30:70 10:90
1.55 3.55 4.30 4.78 5.08
CuJ org [gdm-'}
10.63 7.81 6.38 5.68 5.19
I "
4
0.389 0.756 0.895 0.965 1.015
..Cr "'Q ....A
,d"/..~ j t"
z /"
/"
z / z / //
,P,'
g;x
z '
i
,
/.
,,'¢ / o
[CuJaq (ga~ s) ~.
,~
,5I
Fig. 1. Comparison of the equilibrium data of Robinson (/") with the data of this work (o); aqueous feed 5 g d m -3 copper, 1 g dm -s sulphuric acid, organic feed 20 vol.% LIX 64N in Escaid 100. The dotted lines are arbitrary smooth curves.
112
TABLE 2 E q u i l i b r i u m i s o t h e r m s for 10 vol.% L I X 6 4 N in Escaid 1 0 0 a t 2 5 - - 2 6 ° C Phase r a t i o org:aqueous
aqueous copper concn,
aqueous sulphuric acid c o n c n ,
organic copper concn.
(g dm-3)
(g dm -3)
(g dm-3)
A q u e o u s feed 1.5 g d m -3 c o p p e r (acid b a l a n c e 2.32 g d m -3 ) 90:10 80:20 70:30 40:60 30:70 20:80 10:90
0.0075 0.018 0.038 0.262 0.528 0.87 1.22
2.451 2.400 2.343 1.960 1.560 1.000 0.475
0.166 0,367 0.612 1.84 2,16 2.44 2.54
A q u e o u s feed 3.0 g d m -3 c o p p e r (acid b a l a n c e 4 . 6 3 g d m - 3 ) 90:10 80:20 70:30 60:40 40:60 30:70 20:80 10:90
0.058 0.160 0.306 0.568 1.41 1.94 2.33 2.65
4.54 4.34 4.20 3.70 2.47 1.71 1.06 0.49
0.32 0.70 1.13 1.56 2.38 2.46 2.73 2.78
A q u e o u s feed 5.0 g d m - 3 c o p p e r , 1.0 g d m -3 s u l p h u r i c acid (acid b a l a n c e 8.72 g d m - a ) 90:10 80:20 70:30 60:40 40:60 30:70 20:80 10:90
0.334 0.805 1.41 2.10 3.41 3.85 4.28 4.70
8.37 7.64 6.74 5.58 3.47 2.69 1.99 1.47
0.50 1.01 1.46 1.90 2.33 2.47 2.57 2.67
A q u e o u s f e e d 6.0 g d m -3 c o p p e r , 2.0 g d m - 3 s u l p h u r i c acid (acid b a l a n c e 1 1 . 2 6 g d m - 3 ) 90:10 80:20 70:30 60:40 40:60 30:70 20:80 10:90
0.63 1.46 2.25 3.05 4.45 4.96 5.33 5.72
10.56 9.24 7.97 6.66 4.53 3.71 3.03 2.49
0.57 1.12 1.54 1.92 2.32 2.42 2.58 2.49
113
TABLE 3 Equilibrium isotherms for 20 vol.% L I X 64N in Escaid 100 at 2 5 - - 2 6 ° C Phase ratio org: aqueous
aqueous copper concn,
aqueous sulphuric acid concn,
organic copper concn.
(g d m -3)
(g dm -3 )
(g d m -3)
A q u e o u s feed 1.5 g d m -3 copper (acid balance 2.32 g dm -3) 90:10 80:20 70:30 60:40 40:60 30:70 10:90
0.0027 0.0067 0.014 0.023 0.070 0.146 0.925
2.263 2.257 2.265 2.297 2.225 2.117 0.895
0.168 0.376 0.643 0.978 2.02 2.96 4.77
A q u e o u s feed 3.0 g dm -3 c o p p e r (acid balance 4.63 g dm -3) 90:10 80:20 70:30 60:40 40:60 30:70 20:80 10:90
0.022 0.057 0.121 0.202 0.645 1.13 1.74 2.40
4.55 4.48 4.43 4.31 3.70 2.95 1.99 0.96
0.334 0.751 1.24 1.77 3.59 4.39 5.08 5.43
A q u e o u s feed 3.0 g d m -3 copper, 2.0 g dm -3 sulphuric acid (acid balance 6.63 g dm -3) 90:10 70:30 60:40 40:60 30:70 10:90
0.045 0.216 0.358 0.864 1.31 2.47
6.54 6.21 6.13 5.29 4.62 2.85
0.329 1.20 1.72 3.05 3.79 4.96
A q u e o u s feed 5.0 g d m -3 copper, 1.0 g d m -3 sulphuric acid (acid balance 8.72 g d m -3) 90:10 80:20 70:30 60:40 40:60 30:70 20:80 10:90
0.151 0.370 0.645 1.03 2.19 3,00 3.76 4,44
8.34 8.02 7.72 7.12 5.28 4.16 2.94 1.91
0.536 1.17 1.86 2.50 3.94 4.54 5.02 5.16
114
TABLE 3 (continued) Phase r a t i o org:aqueous
aqueous copper concn,
aqueous sulphuric acid concn,
organic copper cone.n.
(g d m -3)
(g d m -~)
(g dm -3)
A q u e o u s feed 6.0 g dm -3 copper, 2.0 g d m -3 sulphuric acid (acid balance 11.26 g d m -3) 90:10 80:20 70:30 60:40 40:60 30:70 20:80 10:90
0.287 0.70 1.12 1.72 3.19 4.05 4.62 5.32
10.78 10.08 9.78 8.58 6.45 5.11 4.01 2.96
0.612 1.30 1.91 2.57 4.03 4.36 4.84 5.15
A q u e o u s feed 9.0 g dm -3 copper, 1.5 g d m -3 sulphuric acid (acid balance 15.39 g d m -3) 90:10 80:20 60:40 30:70
0.74 1.61 3.65 6.82
14.09 12.83 9.82 4.87
0.93 1.77 3.36 4.52
A q u e o u s feed 3.0 g d m -3 copper, 12.0 g d m -3 sulphuric acid (acid balance 16.62 g dm -3) 90:10 60:40 20:80
0.36 1.19 2.44
15.88 14.67 12.89
0.303 1.13 2.15
TABLE 4 Equilibrium i s o t h e r m for 50 vol.% L I X 64N in Escaid 100 at 2 5 - - 2 6 ° C Phase r a t i o org:aqueous
aqueous copper concn,
aqueous sulphuric acid concn,
organic copper concn.
(g d m -3 )
(g d m -3)
(g dm -3)
A q u e o u s feed 6.0 g d m -3 copper, 2.0 g d m -3 sulphuric acid (acid balance 11.26 g d m -a) 90:10 80:20 70:30 50:50 30:70 20:80 10:90
0.125 0.295 0.503 1.09 2.27 3.36 4.60
10.94 10.74 10.43 9.54 7.66 6.11 4.13
0.65 1.45 2.38 4.89 8.55 10.54 12.59
115
ever, Robinson's isotherm shows a distinct S-shaped character between the origin and the first data point. Our data are shifted in a direction corresponding to completion of equilibration and the S-shaped characteristic has disappeared. It therefore seems likely that Robinson's data come from solutions not entirely at equilibrium. Our experiments in which shaking was carried o u t for only 15--30 minutes gave an S-shaped isotherm, and it m a y be that the degree of extraction of copper after only a short time is of relevance in plant design. It is clear, however, that for chemical studies of the system complete equilibration is essential. A second feature of Robinson's results, c o m m e n t e d u p o n b y Forrest and Hughes (1975b), is the " d i p " in the isotherms at high copper concentration and low aqueous acid concentration. This dip is not evident in our new data. MODELLING Introduction
In order to model the system chemically it is necessary to define a route for the transfer of copper from aqueous to organic phases. This route is a feasible part of the thermodynamic cycle, b u t need not necessarily represent the true mechanism of the reaction. Complexation of copper with oxime (eqns. 1--3) is taken to occur in the aqueous phase, +
HRaq -~ Haq + Raq
(1)
2+ + Raq--CUaq ~ CuRaq +
(2)
+
CURaq + Raq ~- CuR2 aq
(3)
(where H R represents the active ~-hydroxyoxime in LIX 64N). Conventional stability constants can be defined for these reactions, and partition coefficients for the distribution of single uncharged species between the aqueous and organic phases. HRaq ~ HRorg
(4)
CuR2 aq ~ CuR2 org
(5)
The organic phase is complicated b y oxime aggregation (Whewell et al., 1977), nHRorg ~- (HR)n org
(6)
and the aqueous phase by the formation of sulphate complexes or ion pairs (Whewell and Hughes, 1976). 2+ Cuaq + SO~aq ~ CuSO4 aq
(7)
naq + SO42aq ~ HSO4-aq
(8)
116
For the t w o phase system at equilibrium it is possible to draw up mass balance equations for each of the known total concentrations of copper, acid, oxime and sulphate in each phase. The major species are u n d o u b t e d l y Cu 2÷, H ÷, CuSO4, HSO~, SO~- (aqueous) and CuRs, HR, (HR)n (organic). By comparison, the minor species (such as aqueous species which include an oxime molecule) have no real effect in the mass balance equations. It is therefore possible to treat the system with four simplified mass balance equations (9) to (12), L = l + [CuSO4] + [HSO~]
aqueous
(9)
B = b + [CuSO4]
aqueous
(10)
H=h+
aqueous
(11)
organic
(12)
[HSO~]
R = [HR] + 2[CUR2] + ~n [(HR)n]
where L, B and H are the total aqueous concentrations at equilibrium of sulphate, copper and total analytical proton; the respective free concentrations in the aqueous phase are l, b and h. R is the total concentration of active oxime in the organic phase. Concentrations L and R are conserved throughout the extraction process; B and H alter as ion exchange occurs. This simplification offers substantial economies in calculation, arising from: (a) the separate treatment of the two phases, (b) the justifiable neglect to the charged species R - and CuR +, existing at low contribution in the aqueous phase only and contributing negligibly to the mass balances, and (c) the possibility of treating eqns. (1) to (5) as a single process Cu aq + 2HRorg ~- CuR2 ore + 2Haq
(13)
with only one parameter ~ = [Cu] org h 2 [HR] -2org b - ' (14) necessary to quantify organic phase copper complexation. Study of the constituent equilibria, eqns. (1) to (5), has been initiated (Preston and Whewell, 1977; Foakes et al., 1978), because of their potential importance in kinetic performance.
Aqueous phase treatment Equations (9) to (11) are identical to those used in our earlier work (Whewell and Hughes, 1976). It is thus possible with t w o parameters
~i = [CuSO4]b-' f-1 ~ 500
(15)
K H = [HSO~] h -1 /-1 ~ 130
(16)
to determine h for the equilibrated aqueous phases of known B, L and H,
117
preferably for 1.1 ~< pH ~< 2.1. The concentration units used throughout the calculation are mol dm -3 . In the original treatment activities were equated to concentrations w i t h o u t control of ionic strength, and the model developed to calculate pH values from values of B, L and H. Its use here is thus entirely justified. Values of b calculated from eqns. (9) to (11), (15) and (16) are however less certain, and it is likely that the calculated values of biB are underestimated b y a factor of around two b y comparison with calculations from N~is~inen's (1949) work. Trends in the calculated values of b are expected to be more representative of trends in the true copper ion activity than are those in values of B. On these grounds alone, the t w o phase model is based on b rather than on B. The first stage of modelling is therefore the calculation of h and b for the equilibrated aqueous phase, solving an equation cubic in h b y Newton's m e t h o d with an initial estimate of h = 0.5 H. It is then possible to obtain y, where (17)
y = bh -2 Organic phase treatment
Some slope analysis (Stary, 1964) was carried o u t on the results of the 20 vol.% LIX 64N experiments. Data B, h were interpolated b y smooth curves at constant values of [Cu] org and hence at constant [HR] org. Plots of log(D = [Cu] org/B) against log h were straight lines of gradient - 2 . 0 + 0.15, thus confirming the generally accepted CuR2 stoichiometry of the organic phase species. However, eqns. (13) and (14) also predict DVFDhv ~ [HR] org
(18)
A graph of ~ against total LIX concentration u n b o u n d to copper shows significant deviation from the expected straight line at higher LIX concentrations, such that [HR] org ( [ u n b o u n d LIX]. This finding confirms the oxime aggregation reported recently (Hummelstedt, 1977; Whewell et al., 1977) and shown in eq. (6). In modelling eqn. (6) we have continued our practice of allowing only one parameter to express aggregatinn, and have found three forms of eqn. (6) to be of interest: 2HR ~- H2R2
K22 = [H2R2] [ H R ] - 2
dimer
4 H R ~ H4R,
K44 = [H4R4] [ H R ] - 4
tetramer (20)
HR-~ H2R2 ~ H3R3 ~ . . . H n R n Kn = [HnRn] [ H n - I R n - I ] - ' [ H R ] - I
series
Equation (19) is suggested b y the w o r k of Price and Tumilty (1975), b u t was shown b y Whewell et al. (1977) to be inadequate to describe the vapour phase behaviour of solutions of purified oximes in dry n-heptane. Equations (20) and (21) were suggested b y the latter study, b u t the reported values of parameters appropriate to purified oximes are n o t applicable to these studies of reagents as received.
(19)
(21)
118
Optimisation
Concentrations were in mol dm -3 throughout. From values of y = bh - 2 for the aqueous phases, values of [Cu] org were calculated using eqn. (12) with varying values of/~2 (eqn. 14) and aggregation constant (eqn. 19, 20 or 21). The total oxime concentration R was at first allowed to vary slightly in the optimisation but later a fixed value of R corresponding to a 5.7 g dm -3 ultimate load of copper in 20 vol.% LIX 64N was adopted as consistent with our previous work. Values of the two parameters being varied were accepted when V A = ~ ( [ C u ] org, calc - [ C u ] org, expt ) 2 or Up = ~ { ( [ C u ] org, calc - [ C u ] org, e x p t ) / [ C u ] org, expt )2
were minimised; UA is the sum of squared absolute errors and Up of percentage errors in the calculated organic copper concentrations, and no additional weighting factors are included. Our experimental strategy therefore biases the results somewhat in favour of the commercially important region (10--20 vol.%) of LIX 64N concentration. Any local minima are readily avoided by the grid search m e t h o d of optimisation used, and this m e t h o d allows checking during optimisation to ensure that small improvements in the overall fit are n o t being achieved at the expense of large systematic errors in fitting the extreme (5 or 50 vol.%) concentrations of LIX 64N. The Up criterion is more in accordance with the expected errors in [Cu] org,expt than is UA, and was used by Forrest and Hughes (1975b), but the UA criterion is attractive when results biased towards high concentrations of extracted copper are required. Although the errors in [Cu] org,expt are probably the largest of the three analytical errors, a rigorous expression would require an additional weighting factor to take account of expected errors in y. EVALUATION OF THE MODELS Dimer model
Equation (12) becomes R = x + 2/~2 Yx2 + 2K22 x2
(22)
where x = [HR] org- The organic copper concentration is given by [Cu] org,ealc = ~2 Yx 2
(23)
Data R, y at trial values of ~2, K22 enable values of x and so of [Cu] org,ealc to be obtained for each experimental point. Although satisfactory fitting could be obtained for any given concentration of LIX 64N, the values of the parameters giving the best fit tended to vary systematically with LIX concentration. The best results that could be obtained gave an overall root mean square percentage deviation of 9.8% on 86 experimental points with/32 = 36 and K22 =
119
15, or an overall root mean square absolute deviation of 0.128 g dm -3 with ~2 = 31 and K n = 15. For individual concentrations of LIX 64N other values would be chosen, e.g. ~2 = 17 and K2~ = 5 for 20 vol.% LIX 64N, which gives poorer (0.197 g dm -3 or 11.6%) overall fitting. Tetramer
model
Equation (12) becomes R = x + 2 ~ 2 y x 2 + 4K44x 4
(24)
and eqn. (23) applies. Equation (24) is readily solved for x by Newton's m e t h o d using the arbitrary initial estimate x = 0.01R. The fits obtained were more satisfactory than for the dimer model, and there was no systematic variation in the o p t i m u m parameters with LIX concentration. The two minimisation criteria UA and Up gave slightly differing optima, as shown on Table 5. The effectiveness of the modelling can be shown in two ways. First a theoretical isotherm can be constructed from feed concentration data, phase ratio and the parameters. A set of isotherms for 20 vol.% LIX 64N is shown in Fig. 2, where the experimental data can be compared with isotherms for ~2 = 13, K44 = 160 (the best model giving 7.1% average error) and ~2 = 11, K44 = 160 (giving the lowest absolute error of 0.149 g dm -3 copper). A second check of effectiveness is a plot of [Cu] org,calc against [Cu] org,expt, which should appear as a straight line of unit gradient. Such plots for ~2 = 13, K44 = 160 revealed systematic overestimation of organic copper concentration above 3 g d m -3, whereas/~2 = 11, K44 = 160 gave systematic underestimation of those points below 1.5 g dm -3. The plot for/~2 = 12, K44 = 160 shown in Fig. 3 gives a good compromise between these two differently defined optima. Series model
Equation (12) is now R = 2~2yx 2 + ( x + 2 K n x 2 + 3 K n 2 x 3 + . ..) TABLE
5
T e t r a m e r m o d e l -- best values of the parameters T h e e r r o r s q u o t e d are r o o t m e a n s q u a r e v a l u e s f o r t h e 86 d a t a p o i n t s
~2
K44
Percentage error
Absolute error (g d m -3 )
11 12 13
160 160 160
11.0 8.2 7.1
0.149 0.152 0.184
120
5
[Cu] org ( g dm-~) [Cu] org calc (g dm ~)
/ /f. . , Y
4
;
-
I
A/
~ /
2
-3
[Cu]aq ( gdm-3)
m)
O O Fig. 2. I s o t h e r m s f o r 20 vol.% L I X 6 4 N e q u i l i b r a t e d w i t h various a q u e o u s phases. T h e e x p e r i m e n t a l p o i n t s are t h o s e in T a b l e 3; t h e i s o t h e r m s d r a w n are c a l c u l a t e d f r o m 13: = 13, K44 = 1 6 0 ( c o n t i n u o u s lines) a n d f r o m 132 = 11, K44 = 160 ( d o t t e d lines). Fig. 3. P l o t o f o r g a n i c c o p p e r c o n c e n t r a t i o n c a l c u l a t e d f r o m 132 = 12, K4, = 1 6 0 against t h e experimentally determined concentrations.
or for a series mathematically infinite but in practice including only around six significant terms, R = 2/]2yx 2 + x/(1
- Knx) 2
(25)
Again eqn. (23)*applies and eqn. (25) can be solved for x by Newton's m e t h o d with an initial estimate of x = 0.01R. Much the same pattern as for the tetramer model emerges, as shown in Table 6, and the isotherms calculated for the best percentage model (/]2 = 21, K n = 4 , with 6.7% average error) and for the best absolute error model (/]2 = 15, K n = 3, with 0.120 g dm -3 average error) are barely different from the respective optima of the tetramer model. The same systematic deviations are seen in the plots of calculated against experimental organic copper concentration, and again the intermediate model (/]2 = 18, K n = 3.5) has advantages by comparison with the formally defined optima. This model is represented in Figure 4. TABLE6 Series m o d e l - - b e s t values o f t h e p a r a m e t e r s The e r r o r s q u o t e d are r o o t m e a n s q u a r e values for t h e 86 d a t a p o i n t s 132
K n
Percentage error
Absolute error
(g d m - 3 ) 15 18 21
3 3.5 4
9.7 7.5 6.7
0.120 0.134 0.159
121
[Cu]orcjcole l gdm-3)
,
~
"
./
.e
4
2
!
/,
o'
[Cu]orgc x p t
r
( g dm-~)
~
~,
Fig. 4. Plot of organic copper concentration calculated from/~2 = 18, experimentally determined concentrations.
Kn =
3.5 against the
CONCLUSIONS
The models outlined above offer average errors in the calculated organic copper concentration as l o w as 7%, and span a wider range of LIX 64N concentrations than has been modelled previously. Aqueous phase properties are calculated with two parameters for which optimum values have been determined in previous work, and a further two parameters are added in this treatment to express extraction and organic phase properties. A shortening of the calculation can be achieved by the use of a graph such as Figure 5. Since [Cu] org,ealc is a function solely of the total LIX concentration,
40 35
6 4
~
1
5
3 2
I©
I
5 bh~ 2
j
0
ool
o.os
o.I
os
i-o
s
io
5o
Fig. 5. D e p e n d e n c e of organic phase copper concentration o n y = bh -2 for various concentrations of L I X 6 4 N in Escaid; calculated f r o m f12 = 18, K n = 3.5.
122
the above parameters, and y = bh -2, the single line graph of [Cu] org,calc against logl0(y) is sufficient to represent all equilibria (at least in the range tested) of the copper sulphate--sulphuric acid/LIX 64N--Escaid 100 system at a given concentration of LIX 64N. As with/31 and K~ H, it is dubious to attach thermodynamic significance to the parameters/32 and K44 or Kn. Loss of this significance is inevitable through the use of the calculated free copper ion concentration in the aqueous phase, although better data might n o w be obtained b y the use of a copper ion selective electrode to measure b directly. There is still some uncertainty attached to the nature of the aggregated species in the organic phase, and the use of oversimplified one parameter representations of aggregation inevitably conceals the complexity of the system. It is however clear that the tetramer and series models give a significantly better description of the extraction system than does the dimer model. This important conclusion emphasises the significance of aggregatior in commercial oxime systems. An operation to be discouraged is the calculation of oxime m o n o m e r concentrations from the values of K44 and K n obtained here. We have deliberately avoided discussion of "errors" in the values of the parameters, in order to avoid any suggestion that we have measured stability constants as such. A further reason for uncertainty in the values of the parameters is the shape of the surfaces of UA and Up as a function of the t w o parameters f12 and K44 (or Kn ); a c o n t o u r map shows a long diagonal trough which would enable ratios of the parameters to be determined quite precisely b u t forces absolute values to remain nncertain. Until copper ion activity in the aqueous phase is measured directly and incorporated into the model, it will not be possible to extend the model to encompass aqueous counterions other than sulphate. Equilibrium experiments carried o u t in Bradford with copper perchlorate/perchloric acid phases, for example, gives organic copper concentrations lower than predicted by the model when all of the aqueous copper and proton are taken to be uncomplexed. A more effective rationalisation of the counterion effect has been published by Cognet and Renon (1977). Spink and Okuhara (1974) included a CuA2 • HA species in their organic phase model for Kelex 100 (where HA represents the active extractant molecule). A species of this t y p e is a likely adduct in the LIX 64N system, b u t unlike (HR)n there is no evidence independent of the model to confirm its existence in the LIX system. The difficult nature of the minimisation surfaces of UA and Up preclude the incorporation of a third parameter. It:is indeed surprising that Spink and Okuhara are able to q u o t e with such precision five parameters determined for each of their Kelex-diluent systems, in particular when the values of the parameters rely on the inclusion of CuA ÷, CuA2 and CuA2 -HA species in the aqueous phase mass balance. A referee has drawn to our attention a paper by Hoh and Bautista (1978) in which a chemical model is described for a dilute solution of LIX 65N in toluene The model is constructed on a similar basis to ours, with an improved calculation of free copper(II) ion concentration b u t unfortunately no consideration
123
of the bisulphate equilibrium. Aggregation in the organic phase is not included in the model, an appropriate omission provided that the model is restricted to dilute solution work. The use of the model with the data of Spink and Okuhara (1974) shows that these data can be interpreted more simply than suggested by the original authors. Unfortunately the application of Hoh and Bautista's model to the LIX 65N data raises a number of questions, particularly with respect to the assumption that their sample of LIX 65N as received contains 100% active oxime. It would also be interesting to have fuller details of the authors' calculation of the free sulphate concentrations in the aqueous phase and of the values of ionic strength. An application of our model to these data involves a substantial extrapolation beyond the range of concentrations studied by us, but accepting the data B, H from the authors' Table III and incorporating a purity factor of 36.4% appropriate to our batch of LIX 65N, it is possible to obtain partial fitting using our models. Thus for the tetramer model the values of the parameters 92 = 12 and K44 = 160 were used, but were modified in the calculation by a factor Q (explained in the following paper) to allow for the exchange of an Escaid 100 diluent for toluene. In this case the guestimated value of log Q = 0.35 × (98.5/80) = 0.43. The results showed an excellent agreement between the [Cu] org values (material balance) of Hoh and Bautista and the calculated [Cu] org values for the " p H = 4 " data with a root mean square deviation of 0.00040 mol dm -3 (7.8%) compared with 0.00108 mol dm -3 from the authors' calculation. For the " p H = 3" data the fit was poorer (0.00097 mol dm -3, originating largely from the first two points) and for " p H = 2" the model gave systematically high calculated values. If we permitted ourselves to use three separate values of 92, as did Hoh and Bautista, then we could u n d o u b t e d l y achieve three satisfactory fits. Bauer and Chapman (1976) proposed an alternative m e t h o d of allowing for alterations in the " a c t i v i t y " of the organic phase containing Kelex 100. In place of our complex equilibria they define organic and aqueous phase activity coefficients in terms of defensible chemical equations and fit two parameters to each. The overall model is based on an equilibrium constant similar to our /32, the value of which in a particular case is derived from a six parameter equation (two parameters for each of the activity expressions and two for the temperature dependence). Standard errors of 9% were obtained for the model produced. In applying such a treatment to the LIX system, it would be expected that the same activity relationships could be applied to the aqueous sulphate system, but that as in the case of our model there is no theoretical basis for direct extension to other aqueous counterions. The authors state that a much more complicated expression would be required for the organic phase activity coefficient in systems (such as copper/LIX 64N) in which dimer or polymer formation occur. Our t r e a t m e n t of the organic phase goes some way towards meeting these problems of quantifying its equilibrium behaviour.
124
ACKNOWLEDGEMENTS
The authors wish to thank Nchanga Consolidated Copper Mines of Zambia for the financial support of this project, and Mrs. M. Paul and Miss M. Medley for carrying out much o f the experimental work.
REFERENCES Bauer, G.L. and Chapman, T.W., 1976. Measurement and correlation of solvent extraction equilibria. The extraction of copper b y Kelex 100. Met. Trans., 7B: 519--527. Cognet, M.-C. and Renon, H., 1977. Influence of aqueous phase composition upon copper extraction by cationic extractants: A thermodynamic interpretation. Hydrometallurgy, 2: 305--314. Foakes, H.J., Preston, J.S. and Whewell, R.J., 1978. Aqueous phase solubilities and partition data for commercial copper extractants. Anal. Chim. Acta, 97: 349--356. Forrest, C. and Hughes, M.A., 1975a. The modelling of equilibrium data for the liquid-liquid extraction of metals. I. A survey of existing models. Hydrometallurgy, 1: 25--37. Forrest, C. and Hughes, M.A., 1975b. The modelling of equilibrium data for the liquid-liquid extraction of metals. II. Models for the copper/LIX 64N and chromate/Aliquat 336 systems. HydrometaUurgy, 1 : 139--154. Gran, G., 1952. Determination of the equivalence point in potentiometric titrations, II. Analyst, 77: 661--671. Hoh, Y.-C. and Bautista, R.G., 1978. Chemically based model to predict distribution coefficients in the Cu--LIX 65N and Cu--Kelex 100 Systems. Met. Trans., 9B: 69--75. Hummelstedt, L., 1977. Reagents particularly suited for metal extraction from sulphate media: Recent developments. Proc. Int. Solvent Extraction Conf. (ISEC'77), Toronto, Paper 5c. N~is~nen, R., 1949. Spectrophotometric study on complex formation between cupric and sulphate ions. Acta Chem. Scand., 3: 179--189. Preston, J.S. and Whewell, R.J., 1977. Purification and acid--base properties of hydroxyoxime extractants for copper. J. Inorg. Nucl. Chem., 39: 1675--1678. Price, R. and Tumilty, J.A., 1975. An interpretation of some aspects of solvent extraction as related to the extraction of copper using o-hydroxyaryloximes. Inst. Chem. Eng. Symp. Set., No. 42, Institution of Chemical Engineers, London, Paper 18. Robinson, C.G. and Paynter, J.C., 1971. Optimisation of the design of a countercurrent liquid--liquid extraction plant using LIX 64N. Proc. Int. Solvent Extraction Conf. (ISEC '71), Society of Chemical Industry, London, II: 1416--1428. Spink, D.R. and Okuhara, D.N., 1974. The effect of diluents on the extraction of tracer level copper by an alkyl hydroxyquinoline (Kelex 100). Proc. Int. Solvent Extraction Conf. (ISEC '74), Society of Chemical Industry, London, 3: 2527--2540. Stary, J., 1964. The Solvent Extraction of Metal Chelates, Pergamon, London. Vogel, A.I., 1961. A T e x t b o o k of Quantitative Inorganic Analysis, Longmans, London, 3rd edition, 1216 pp. Whewell, R.J. and Hughes, M.A., 1976. Interpretation of pH measurements in solutions containing sulphuric acid and copper sulphate. J. Inorg. Nucl. Chem., 38: 180--181. Whewell, R.J., Hughes, M.A. and Hanson, C., 1975. The kinetics of the solvent extraction of copper(II) with LIX reagents. I. Single drop experiments. J. Inorg. Nucl. Chem,, 37: 2303--2307. Whewell, R.J., Hughes, M.A. and Hanson, C., 1977. Aspects of the kinetics and mechanism of the extraction of copper with hydroxyoximes. Proc. Int. Solvent Extraction Conf. (ISEC '77), Toronto, Paper 4a.