I n d . Eng. Chem. Res. 1989,28, 284-288
284 a = G / G o = (s/s0)‘
(16)
where the subscript o refers to the corresponding MSMPR operation values and the nonsubscripted variables to DDO operation. Given MSMPR operation values (Go, lo)and kinetic exponents (i, j , a), eq 11 can be solved iteratively for a for selected values of R and XF. In the Yk terms, x1 may be replaced by xF/a. Once a is evaluated, all other ratios can be calculated directly. The results can be expressed in terms of the independent variables i, j , a, R, and xF. For high-yield (class 11) systems, lo 1 and a is not involved, so only the variables i, j , R, and X F are needed. If desired, eq 11 can be programmed simply for iterative solution in a computer. (f) Optimum Values. The values of XF giving maximum values of the mass mean size and Sauter mean size can be obtained by differentiating eq 12 and 13 (and eq 11). Note that aYk/dx, = Yk-1 - Yk (17)
-
c0,
The resulting equations may be solved iteratively. (g) Clear Liquor Advance. For clear liquor advance, xF = 0 (and x1 = 0). Hence, Yk = Rk. With eq 11, this gives
(l/lo)’-’ = [ (1 - () / (1 - l,,)](3+i)”R3+’ which can be solved for the recovery, l.
(18)
Literature Cited Chang, J. C. S.; Brna, T. G. Gypsum Crystallization for Limestone FGD. Chem. Eng. Prog. 1986 (Nov), 51. Hulburt, H. H.; Stephango, D. G . Design Models for Continuous Crystallizers with Double Draw-Off. CEP Symp. Ser. 1969, 65(95), 50. Randolph, A. D.; Larson, M. A. Theory of Particulate Processes, 2nd ed.; Academic Press: New York, 1988. Randolph, A. D.; Vaden, D. E.; Stewart, D. Improved Crystal Size Distribution of Gypsum from Flue Gas Desulfurization Liquors. Chem. Eng. Symp. Ser. 1984, 80(240), 110. Receiued f o r review April 28, 1988 Revised manuscript received November 18, 1988 Accepted December 13, 1988
Chemical Model for Copper Extraction from Acidic Sulfate Solutions by Hydroxy Oximes Jerzy Piotrowicz,? Mariusz B. Bogacki,’ Stanidaw Wasylkiewicz,’ and Jan Szymanowski*,’ Wroclaw Technical University, Wybrzeie Wyspi0Askiego 27, 50-370, Wroclaw, Poland, and Poznafi Technical University, P1. Sklodowskiej-Curie 2, 60-965 Poznari, Poland
Chemical models for copper extraction from acidic sulfate solutions by hydroxy oximes are presented. Extraction constants and hydroxy oxime dimerization constants are calculated. They demonstrate that hydroxy oxime dimerization in the organic phase can be neglected for hydroxy oxime concentrations up to 20%. Copper extraction from acidic sulfate solutions by commercial hydroxy oxime extractants was discussed in several independent papers. Forrest and Hughes (1975a,b), Hughes et al. (1975), and Robinson and Paynter (1971) discussed empiric and semiempiric models and proposed to use them to correlate equilibrium copper concentration in the organic phase with its equilibrium concentration in the aqueous phase. Szymanowski and Jeszka (1985) used a similar approach to compare simple multistage and countercurrent multistage copper extraction by “pure” isolated fractions of 2-hydroxy-5-nonylbenzaldehydeoxime and 2-hydroxy-5-nonylbenzophenone oxime. Szymanowski and Atamadczuk (1982) used the modified Couchy distribution to model the extraction of copper by pure individual hydroxy oximes from very dilute acidic sulfate solutions. Piotrowicz and Wasylkiewicz (1986) proposed recently the chemical approach, in which activity coefficients of inorganic species present in the aqueous phase were calculated according to the modification of the Pitzer method (Wasylkiewicz, 1988). The aim of this work is to model the extraction of copper from acidic sulfate solutions by “pure” isolation fractions of 2-hydroxy-5-nonylbenzaldehyde oxime and 2-hydroxy5-nonylbenzophenone oxime and to discuss hydroxy oxime association in the organic phase during extraction.
* Author to whom
*
correspondence should be addressed. Wrodaw Technical University. PoznaA Technical liniversity.
Extractants and Extraction Conditions Extractant syntheses were described previously (Szymanowski and Jeszka, 1985). The ratio of E to Z isomers in 2-hydroxy-5-nonylbenzophenone oxime (11)was 5.9; in 2-hydroxy-5-nonylbenzaldehyde oxime (I),Z isomer was not found. Extraction data were obtained at 18-20 “C for different hydroxy oxime concentrations and different initial concentrations of sulfuric acid in an aqueous phase. The oximes’ concentrations were approximately equal to 5%, lo%, 15%, and 20%, while the amount of sulfuric acid added to the aqueous phase vriried from 0 to 50 g dm-3 for 2-hydroxy-5-nonylbenzophenoneoxime and from 0 to 200 g dm-3 for 2-hydroxy-5-nonylbenzaldehyde oxime. The equilibrium copper concentrations in the aqueous phase varied from 0 to 30 g dm-3. Results In a previous paper (Szymanowski and Jeszka, 1985), different polynomials were used to match experimental data and to correlate the equilibrium copper concentration in the organic phase with the equilibrium copper concentration in the aqueous phase and the initial concentration of sulfuric acid. Simultaneously, appropriate polynomials correlating the equilibrium sulfuric acid concentration with its initial concentration in the aqueous layer and with the equilibrium copper concentration in the organic phase were derived. These polynomials were statistically significant a t a probability level of 1.0000, and their correlation
0888-5885/89/2628-0284$01.50/00 1989 American Chemical Society
Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989 285 coefficients were equal to 0.967-0.999. However, although these polynomials can be well matched to the experimental data, they have no physical meaning and they can only be used to discuss some technological problems, e.g., numbers of extraction stages in countercurrent multistage extraction. If they are used, it is impossible to estimate the basic extraction parameters such as the extraction constant and the dimerization constant. Extraction of copper by hydroxy oximes can be described as follows:
+ 2RH0 =
CUR^,^
+ 2H+,
:
0.50
L
01
0.25
0.00 0.0
(%R*)o(aH+2)w
(2)
(acuz+)w(aRH2) 0
(3)
11.3 (0.387)
The dimerization constant in the organic phase can be expressed as
15.0 (0.514)
[RHlo2[c~2+lw
2RHo = (RH)2,0
(4) (5)
Thus, the total concentration of hydroxy oxime can be calculated as the sum of its monomer, dimer, and complex concentrations: [RHlt = [RHIO + 2[(RH),IO
+ 2[CuR210
(6)
The concentrations in the aqueous phase can be neglected as a result of very small solubilities of hydroxy oxime and its copper complex in the aqueous phase. When eq 3 , 5 , and 6 are solved, the following expression for complex concentration in the organic phase is obtained
+ 4(2K,x[Cu2+]w/[H+]w2 + 2Kd)[RH]t)''2 - 1 \ 2
I
(71 I"
The constants Kex and Kd can be calculated by the least-squares method: n
It was also assumed that the total concentration of hydroxy oxime can differ from the analytical one, and due to this, the concentration can be also computed from the model (eq 7). According to Whewell and Hughes (1976), the composition of the aqueous phase containing sulfuric acid and copper sulfate can be described by the following dissociation reactions:
H2S04= H+ + HSO, HS04- = H+
20.0 (0.685)
0 (0.0) 10 (0.102) 20 (0.204) 50 (0.510) 0 (0.0) 10 (0.102) 20 (0.204) 50 (0.510) 0 (0.0) 10 (0.102) 20 (0.204) 50 (0.510) 0 (0.0) 10 (0.102) 20 (0.204) 50 (0.510)
0.157
0.355
0.471
0.628
+
CuS04 = Cu2++ S042+
(9)
K = 130
p
= 500
(10) (11)
-
0.8
1.0
85 95 140 120 130 160 140 200 83
0.026 0.002 0.024 0.009 0.139 0.638 0.345 1.849 0.002
140 84 140 53 81 65
1.153 18.871 1.667 0.042 0.458 0.282
The appropriate equilibrium constants for reactions 10 and 11 must be considered. They were taken from the work of Whewell and Hughes (1976). If the expressions for equilibrium constants of reactions 10 and 11 and the mass balance equations (eq 12-14) for copper, hydrogen, and sulfate are solved,
+ [CUSO4], [S0d2-]t = [S042-]w + [HSO,-], + [CuS04lw [CU2+], = [CU2+],
rr-.,2+1
(1
0.6
Table I. Estimated Values of Model Parameters (Oxime I) concn sulfuric acid, oxime, % [RH],,,, Kd, dm-3 g dm-3 (mol (mol dm-3) mol dm-3 K.. mol-' dm-3) 5.0 (0.171)
~C~R2I,~H+1W2
0.4
Figure 1. Composition of the aqueous phase.
If we neglect activity coefficients in both phases, then Kex =
0.2
m d e frnction o f copper sulfnte mole fraction of sulfuric acid
(1)
where RH stands for hydroxy oxime and subscripts w and o denote water and organic phases, respectively. The equilibrium extraction constant can be expressed as follows: Kex =
0.15 C
(12)
(13)
concentrations of various species present in the aqueous phase can be calculated (Figure 1). The obtained results demonstrate that the actual copper(I1) ion concentration is significantly lower from the analytical concentration calculated from the added copper sulfate. By use of the calculated values of copper and hydrogen ion concentrations, the constants Kexand Kd and the total concentrations of hydroxy oxime were computed for model 7 (Table I). Various values of the extraction constant were obtained for each set of sulfuric acid and hydroxy oxime concentrations. They differ significantly as these concentrations of sulfuric acid and hydroxy oxime are changed, probably due to the neglection of the appropriate activity coefficients. Dimerization constants are low, and in the most considered cases, their confidence limits contain zero (Figure 2). Due to this, computing was repeated assuming Kd = 0 (Table 11). The obtained values of the extraction constant decrease as the concentrations of sulfuric acid and hydroxy oxime increase. They are statistically different, and it was impossible to calculate general constants for various sulfuric acid concentrations and/or hydroxy oxime concentrations. The estimated values of hydroxy oxime
286 Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989 K, t
400
16
0
12
,
0.8
200
04
00
1
80
160
240
0
320, Lex
I
1
70
LO
60
Figure 2. Confidence regions for model parameters KO,and Kd for various significance levels (a = 0.99,0.975,0.95,0.90). Figure 4. Relation 17 for 2-hydroxy-5-nonylbenzophenone oxime (5%). LO
I
5
10
[&lJS -2
0
Figure 5. Relation 17 for 2-hydroxy-5-nonylbenzophenone oxime (207 0 ) .
2
[c.s0J/[/[yso,]'
Figure 3. Deviations from ideality in the aqueous phase: (1,X) mol dm-3; (2,0 ) [HzS04]= 25 X mol dm-3; [H2S04]= 6 X (3, A) [HzS04]= 2.5 mol dm-3.
concentration are lower by 6-1l% from the analytical concentrations obtained from the weights used to prepare organic phases. Similar results were obtained as the extraction data for 2-hydroxy-5-nonylbenzophenone oxime were considered. To obtain a more general model, activity coefficients in the aqueous phase were further considered. In this case, the activity coefficients in the organic phase were only neglected, ( U C ~ ~ J =, [CUR,],, and URH = [RH], and acug+f aH+,was expressed as a. Thus, Kex = [CuR,Io/[RHI,2a
Figure 6. Relation 17 for 2-hydroxy-5-nonylbenzaldehyde oxime (5%).
(15)
If expressions for dimer and complex concentrations obtained from eq 5 and 15 are introduced into eq 6, the following relation is obtained 0.5
(16) which can be further rearranged to the following linear relation 1 [CUR210
2 2KD [RHItU = K,x[RHl*
Kex-0.5a0.5
+ ~RHI,[CuR210
(17)
The variables [CUR,], and a can differ for various initial concentrations of copper and hydrogen ions in the aqueous phase for the constant total hydroxy oxime concentration in the organic phase, while the extraction and dimerization constants should be approximately constant. Parameter a depends upon the concentration of copper sulfate and sulfuric acid in the aqueous phase and must
'
1
I
,I
I
Figure 7. Relation 17 for 2-hydroxy-5-nonylbenzaldehyde oxime (2070 ).
be computed separately. The method proposed by Wasylkiewicz (1988), who modified the Pitzer method for strong electrolytes (Pitzer and Kim, 1974),was used. The dissociation reactions (eq 9-11) were considered. Data given in Figure 3 demonstrate important deviations from ideality in the aqueous phase. These deviations increase as the sulfuric acid concentration increases, e.g., curves 3 and 1. Curves 1 and 2 are typical for extraction conditions, while curve 3 is typical for stripping. Thus,
Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989 287 Table 11. Estimated Values of Model Parameters (Oxime I, Kd = 0) concn
0.U
~
oxime, ’70 (mol dm”) 5.0 (0.171)
11.3 (0.387)
15.0 (0.514)
20.0 (0.685)
sulfuric acid, g dm-3 (mol dm-3) 0 (0.0) 10 (0.102) 20 (0.204) 50 (0.510) 0 (0.0) 10 (0.102) 20 (0.204) 50 (0.510) 0 (0.0) 10 (0.102) 20 (0.204) 50 (0.510) 0 (0.0) 10 (0.102) 20 (0.204) 50 (0.510)
032
[RH],,,, mol dm” 0.143
Kex 350 120 60 49 210 130
0.352
45 290 110 71 48 190 110 69 43
0.482
0.635
77
- .
a
3
.% 0.10
008 0.06
OlYI
-
0132
0 0
I
I1
A 0.056 f 0.11 -0.044 f 0.046 0.100 f 0.040 0.037 f 0.034 2.5 f 5.5 -6.05 f 1.7 0.14 f 1.5 -3.7 f 8.7
0.50 f 0.07 0.39 f 0.08 0.13 f 0.06 0.19 f 0.06 5.3 f 0.3 4.5 f 5.0 2.5 f 3.1 3.8 f 1.8
in the whole investigated region of sulfuric acid and copper sulfate concentrations, the nonideality of the aqueous phase must be taken under consideration. Relation 17 is demonstrated in exemplary Figure 4-7. Deviations from the straight line increase as ( a / CUR^]^)^.^ increases. The experimental data are somewhat scattered, but the regression coefficients can be still calculated with acceptable errors (Table 111). The average errors (mAand mg)of regression coefficients A and B were calculated from
mA =
s,
CXi2 i
nCxi2- (CxJ2 i
m B = S,
(18)
i
n nCx: - (CxJ2 i
0
,
.m
030
0.20
‘ D
m
Figure 8. Relation 21 for 2-hydroxy-5-nonylbenzophenone oxime.
,
- 11 s
B
0 0
0 0
0
OdO
20%
a .
;,
a
d
oxime concn. % ~ _ _ _ 5 11.3 15 20 5 10 15 20
0
001
0.25
oxime
-
oo
0
0.30
Table 111. Regression Coefficients for
I
15 */e
-
0.20
0.15
.. a
. ,
8
a
%o.oR
11.3%
a
a
0
t
1 .
0.10 L 0 0
0.05
I
0
I
I 1
0
I
O
2
I
3
0
v-mx
Figure 9. Relation 21 for 2-hydroxy-5-nonylbenzaldehyde oxime. Table IV. Extraction and Dimerization Constants oxime [RH],..,, mol dm-’ K.. Kd, dm3 mol-’ 240 f 50 -0.7 + 3.3 I 0.135 f 0.04 90 f 10 -1.2 + 0.0 0.332 f 0.10 0.424 f 0.022 60 f 10 0.6 + 2.2 50 f 10 0.0 + 1.2 0.568 f 0.030 -1.1 + 5.8 I1 0.077 f 0.004 14.0 f 4.0 0.208 f 0.008 4.1 f 0.7 -2.6 + -2.3 0.262 f 0.010 1.8 f 0.3 -0.3 + 0.4
merization must be neglected. In such a case,
i
where S, = ( s / ( n- 2)]0.5,s is the sum of square errors, and n is the number of experimental data. Regressioh coefficient A for all selected concentrations of hydroxy oximes is near zero. In some cases, even negative values for this coefficient were obtained. This all suggests that under studied extraction conditions the dimerization of hydroxy oximes is not an important parameter. Thus, the conclusion is the same as in the case of the simplified model discussed in the first part of this work. The values of the dimerization and extraction constants can be estimated from the obtained regression coefficients, introducing appropriate values of the total hydroxy oxime concentration. These values can be taken from the weights of hydroxy oximes used to prepare organic phases and the content of the E isomer, or they can be estimated from the extraction data. In this last case, the hydroxy oxime di-
Introducing the hydroxy oxime concentration in the organic phase from eq 15 and rearranging gives the following linear relation: 1 [CUR,], = 0.5[RH], - -[ C U R ~ ] ? ~ U - ”(21) .~ 2 ~ ~ ~ 4 . 5
The deviations from the straight lines are quite significant (Figures 8 and 9), although the linear character of the obtained relationships is observed. However, the correlation coefficients are relatively low and near 0.9. The values of the estimated hydroxy oxime total concentration and extraction constant as well as the estimated values of the dimerization constant are given in Table IV. They demonstrate that the model discussed does not consider interactions in the organic phase between hydroxy
288 Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989
oxime molecules and the diluent molecules, which may significantly change the activity coefficients in this phase. As a result, various extraction constants were obtained for different hydroxy oxime concentrations in the organic phase, however, in comparison to the previous model, it was possible to obtain one extraction constant for various sulfuric acid concentrations. They decrease significantly as the hydroxy oxime concentration increases. The values obtained for 2-hydroxy-5-nonylbenzaldehyde oxime are approximately 10 times higher in comparison with those obtained for 2-hydroxy-5-nonylbenzophenone oxime as a result of higher extraction strength of 2-hydroxy-5nonylbenzaldehyde oxime. Lower values of the total hydroxy oxime concentration were obtained from the proposed model, in comparison with the values obtained from the weights of hydroxy oximes used to prepare organic phases. For 2-hydroxy-5nonylbenzaldehyde oxime, the ratio of these concentrations, [RHlfSt/ [RH],,, equals 78.9%, 85.8%, 82.5%, and 82.9 % for the four different concentrations considered. Almost the same values were obtained for all concentrations considered. It means a systematic error of 17.5%. For 2-hydroxy-5-nonylbenzophenoneoxime, this deviation equals approximately 32.7 %. However, as the content of the Z isomer is taken under consideration (approximately 14.5701,then the deviation is the same as for 2-hydroxy5-nonylbenzaldehyde oxime and equal to 18.2%. Very unexpected results were obtained for dimerization constants. They are approximately zero for both hydroxy oximes in the whole region of their concentrations (up to 20%). Such results are in contradiction with several previous papers summarized by Szymanowski (1984). Different values of the dimerization constants were published previously, but it was generally accepted that in aliphatic hydrocarbons they are in the range of few tens to 100 dm3 mol-l, while in aromatic hydrocarbons they do not exceed 10 dm3 mol-’. However, they were usually determined by the osmometric method under “anhydrous” conditions. Due to different contents of moisture, probably, various values of the dimerization constants were obtained by independent authors, especially in aliphatic
hydrocarbons. Activity coefficients in the aqueous phase were never considered. In this study, the dimerization constants were computed from the extraction data obtained for actual extraction systems in which both phases were saturated. Thus, water molecules dissolved in the organic phase and present a t the interface can interact with hydroxy oxime molecules. As a result, they can retard the formation of hydroxy oxime dimers. The obtained results demonstrate that extraction equilibrium data can be quite well described by the chemical models in which nonideality of the aqueous phase is taken under consideration or neglected. In such a case, dimerization of hydroxy oximes in hydrocarbons can be neglected for hydroxy oxime concentrations up to 20% as a result of water-hydroxy oxime interactions in the organic phase saturated by water and/or at the water/hydrocarbon interface occupied by adsorbed hydroxy oxime molecules.
Acknowledgment This work was supported by Polish Program CPBP 03.08. Registry No. I, 37339-32-5; 11, 59986-58-2; Cu, 7440-50-8.
Literature Cited Forrest, C.; Hughes, M. A. Hydrometallurgy 1975a, 1, 25. Forrest, C.; Hughes, M. A. Hydrometallurgy 197513, I , 139. Hughes, M. A.; Anderson, S.; Forrest, C. Int. J. Miner. Process. 1975, 2, 267. Piotrowicz, J.; Wasylkiewicz, S. Prepr. ISEC’86 1986, 2, 205. Pitzer, K. S.; Kim, J. J . Am. Chem. SOC.1974, 96, 5701. Robinson, C. G.; Paynter, J. C. Proc. ISEC‘71, SOC.Chem. Ing., London 1971, 11, 1416. Szymanowski, J. W a d . Chem. 1984,38, 371. Szymanowski, J.; Atamaiiczuk, B. Hydrometallurgy 1982, 9, 29. Szymanowski, J.; Jeszka, P. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 244. Wasylkiewicz, S. Comput. Chem. Eng. 1988, 12, 141. Whewell, R. J.; Hughes, M. A. J . Inorg. Nucl. Chem. 1976, 38, 180. Received for review April 21, 1988 Revised manuscript received October 21, 1988 Accepted November 7, 1988
