SCIENCE CHINA Technological Sciences • Article •
May 2015 Vol.58 No.5: 935–942 doi: 10.1007/s11431-015-5819-y
Thermodynamic models based on Pitzer-NRTL and Pitzer-Margules equations for the extraction of tungstic acid with primary amine N1923 LIN Xiao1,3, NING PengGe1,3*, XU WeiFeng1,3, CAO HongBin1,3 & ZHANG Yi1,2,3 1
Research Centre for Process Pollution Control of Beijing, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China; 2 National Engineering Laboratory for Hydrometallurgical Cleaner Production Technology, Chinese Academy of Sciences, Beijing 100190, China; 3 Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China Received December 27, 2014; accepted March 20, 2015; published online April 20, 2015
The thermodynamic model of the extraction of W with primary amine under near neutral conditions is reported in this paper. The activity coefficients of the nonelectrolytes in organic phase are calculated by the Margules and NRTL equations which are based on previously tested liquid-liquid extraction equilibrium data in combination with mass balances and charge balance formula. The activity coefficients of the electrolytes in aqueous phase are calculated by the Pitzer equation. The thermodynamic model of the extraction of W by a primary amine is constructed from the calculated activity coefficients of electrolytes and nonelectrolytes. The extraction of W using primary amine is also predicated, and the data is compared to the calculated results of the thermodynamic model. It is concluded that Margules equation proves to be suitable and reliable for calculating the activity coefficients of nonelectrolytes in complex organic phase systems. primary amine extraction, separation of Mo from W, thermodynamic, model parameters Citation:
Lin X, Ning P G, Xu W F, et al. Thermodynamic models based on Pitzer-NRTL and Pitzer-Margules equations for the extraction of tungstic acid with primary amine N1923. Sci China Tech Sci, 2015, 58: 935942, doi: 10.1007/s11431-015-5819-y
1 Introduction Tungsten is a rare, noble metal that has certain properties applicable in many fields, especially in defense and high technology areas. Tungsten is commonly associated with some metals [1,2], specifically molybdenum. Both elements exhibit great similarity in atomic structure, ionic radius, et al., which results in great difficulty of separation due to the strong lanthanide contraction [3]. The quantity of Tungsten is limited on the Earth; thus, the separation of tungsten and molybdenum is highly important in extractive hydrometal*Corresponding author (email:
[email protected].) © Science China Press and Springer-Verlag Berlin Heidelberg 2015
lurgy. These separations are usually based on aqueous solution chemistry, which relies on differences in the composition, aqueous species, and coordination ability with other ions. Separation methods, such as precipitation [4,5], ion exchange [6], adsorption methods [7], and extraction [8,9], have been explored and applied in industrial productions. Ion floatation and liquid membrane separation have also been reported as new and improved separation methods. Extraction is one of the most promising separation methods due to its great success in generating high purity products as well as being easy to operate [10,11]. Recently, the use of a primary amine to extract and separate tungsten and molybdenum under near neutral conditions has attracted much attention. Yu [12] reported on the mechanism and impact tech.scichina.com link.springer.com
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factors of the separation of tungsten and molybdenum via a primary amine. A primary amine can efficiently separate W from the high Mo-low W system under neutral and weak alkaline conditions, where the removal yield of W can reach 90% through the 4-stage cross-current extraction. The extracted complex of primary amine (RNH2) extraction of W forms a structure of (RNH2)4·(H2WO4)3 as demonstrated by the slope, saturated capacity, and molar series methods. Our report [8] discusses the detailed research of using a primary amine to extract and separate Mo and W in order to obtain high purities of sodium molybdate and sodium tungstate. The experimental results demonstrate that the primary amine is suitable for a high Mo-low W solution in which the W/Mo mass ratio in the extraction raffinate can reach 2.876×105 through the 2-stage, cross-current extraction. These results are in agreement with Chinese standards that state in which the ratio of W in sodium molybdate is lower than 0.0001. The complexity of the aqueous solution chemistry of W and Mo [13,14] usually lead to the formation of various homopolymolybdate ions or miscellaneous polyacid ions under acidic conditions [15,16]. Such conditions increase the difficulty of separating Mo and W. There are few reports concerning the thermodynamic data of W/Mo [17] and the extraction system of W/Mo using a primary amine. A previous study [18] reported on the activity coefficients of the ions and ions in aqueous and organic phase that were calculated using Pitzer equations. Various interaction energy coefficients of molecules-molecules and ions-molecules were also obtained in the study. However, a certain error occurred between the predicated and obtained results for the extraction of W via the primary amine. Although the experiment was successful, the calculation process requires much improvement. In this work, the activity coefficients of nonelectrolytes in organic phase are obtained from the Margules and NRTL equations. These equations are used in conjunction with various equilibrium data of liquid-liquid extraction of W with primary amine and also combined with mass balances and charge balance formulas. Additionally, the Pitzer equation is used to obtain the activity coefficients of electrolytes in aqueous phase. Considering a thermodynamic model of tungsten extraction with a primary amine has been established, this work is aimed to achieve improved predication of the effect a primary amine has on the extraction of W.
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Chinese Academy of Sciences. The molar mass of N1923 is 310.30 g/mol. Dilute sulfuric acid was prepared with concentrated sulfuric acid (95%–98%, Sinopharm Chemical Reagent Co., Ltd., China) and ultra-pure water, homemade. All reagents were used without further purification. 2.2
Experimental apparatus
The apparatus included an electronic balance ML104 (Mettler Toledo, Switzerland) with an accuracy of ±0.0001 g, a pH meter Delta 320 (Mettler, Switzerland) with an accuracy of ±0.01, Thermostat DC-0510 (Ningbo ScientzBiotechnology Poltroon Technologies Inc., China) with an accuracy of ±0.1°C, magnetic agitator 84-1A (Shanghai SileInstrument Co., Ltd. China), a 50 mL self-made jacketed equilibrium still, pipette tube, PTFE separating funnel, beaker, and pipette gun. The analytical instruments used were an OPTIMA 5300DV inductively couple plasma-optical emission spectrometer (ICP-OES, Perkin-Elmer, USA) and ion chromatograph DX-500 (Dionex, USA). The experimental setup is shown in Figure 1, and includes a thermostat, magnetic stirrer, equilibrium still, and rubber pipe. 2.3
Experimental procedure
The extraction equilibrium method is as follows. Various concentrations of Na2WO4 aqueous solutions and primary amine solution were first prepared. The initial pH of aqueous solution of tungsten was adjusted to a desired value using dilute sulfuric acid, which was recorded as the initial value. Samples containing equal volumes of 10 mL of an aqueous phase and organic phase were first placed in the equilibrium vessel at 293.15 K for 10 min by pipette, rigorously stirred for 1 hr at rates of 1030 r/min, and allowed to settle for more than 1 hr. Thereafter, samples were transferred into the PTFE separating funnel. After phase disengagement, the aqueous phase was separated, and the equilibrium pH
2 Experiments 2.1
Materials
Sodium tungstate dehydrate (analytical grade) and toluene (analytical grade) were obtained from Beijing Chemical Works, China. The primary amine N1923, (C19–C23) secondary alkyl primary amine, with a purity of 98%, was purchased from Shanghai Institute of Organic Chemistry,
Figure 1
Apparatus for the liquid-liquid extraction equilibrium.
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was measured using a pH meter. Analytical methods: the aqueous solution and raffinate were first diluted followed by analysis of the W concentration by ICP-OES with power of 1.3 kW, assistant gas flow of 0.2 L/min, cooling air flow of 15 L/min, and carrier gas flow of 0.8 L/min. The active wavelength used for tungsten analysis was 207.912 nm. The concentration of SO42 in aqueous solution was determined by ion chromatography with eluent conditions of 1.1 g/L NaOH, eluent flow rate of 1 mL/min, AC11 detection column, ED50 detector, and 100 mA suppressor. 2.4
Models
2.4.1 Chemical equilibrium Ning et al. [8] reported that when the initial mass concentration of W is less than 1.0 g/L and the equilibrium pH of the aqueous phase is approximately 7.00, the composition proportion of a complex molecule can be determined by the slope method. The chemical equilibrium reaction is described as follows: H 2 WO 4 RNH 2org. 2H + +WO 24 RNH org. 2 K
(1)
where RNH2 is primary amine N1923, and org. is the organic phase. The corresponding thermodynamic equilibrium constant, K, is expressed as:
K
aHorg. 2 WO4 RNH 2 org. aH2 aWO 2 aRNH 2 4
=
mHorg. Horg. 2 WO 4 RNH 2 2 WO 4 RNH 2 org. org. RNH aH2 mWO 2 WO 2 mRNH 2 2 4
,
(2)
4
where ai is activity of species i, mi is molality of species i, and i is activity coefficient of species i. 2.4.2 Mass and charge balance Before the extraction process, dilute sulfuric acid was added to the feed solution to adjust the initial pH of the aqueous phase. The entire process is described by the following equilibria reactions.
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When T=293.15 K, Ks is 0.01234. The equilibrium constant Ks can be described according to eq. (2):
Ks
aH aSO2
=
4
aHSO
aH mSO2 SO2 4
4
mHSO HSO
4
4
mSO2 SO2 4
4
mHSO HSO 4
=
4
Ks . aH
(10)
Because the equilibrium pH of the raffinate is close to 7.00 and the aqueous phase is relatively dilute, the value of SO2 HSO can be considered 1 after phase equilibrium 4
4
under neutral conditions. The molality of SO42 is nearly 1234500 times as much as that of HSO4 after calculating eq. (10). It is worth noting that the anion HSO4 can be ignored after phase equilibrium since the molality of SO42 is far greater than the molality of HSO4. Similarly, the primary (K1) and secondary (K2) ionization constants of tungstic acid obtained from the literature are 104.6 and 103.5, respectively. The concentrations of HWO4 are far less than that of WO42 under phase equilibrium; therefore, WO4 is considered the dominant ion. Additionally, the ions of H+ and OH− are minimal and can also be ignored when the pH value of the raffinate is close to 7.00. As discussed above, only the ions of Na+, SO42, and WO42 should be considered in the equilibrium aqueous phase. As for the organic phase, the complex H2WO4·RNH2, extractant (N1923), and diluent (toluene) need to be acknowledged. The mass balances and charge balance equations are as follows:
mNa+ 2 mWO2
4
mH2 WO4 RNH2 C7 H8 mWO2
initial
,
H 2 SO 4 H + +HSO 4
(4)
mH2 WO4 RNH2 mRNH2 mRNH2
Ks H + +SO 42 HSO 4
(5)
2 mSO2 2 mWO2 mNa+ .
K1 H + +HWO 4 H 2 WO 4
(6)
K2 H + +WO 24 HWO 4
(7)
4
2825.2 . T
(8)
4
4
initial
(11)
(12)
,
(13)
mWO2 H2 O ,
(3)
ln K s = 14.0321+
(9)
Eq. (9) transforms into:
Na 2 WO 4 2Na + +WO24
The secondary ionization thermodynamic equilibrium constant of sulfuric acid, Ks, can be calculated by the semi-empirical formula (eq. (8)).
.
4
4
initial
(14)
The density of water and toluene at 273.15 K in eqs. (2)–(12) is 0.9982 and 0.8670 kg/L respectively. 2.4.3 Pitzer model in the electrolyte aqueous solution In this work, the activity coefficients in the electrolyte aqueous solution were obtained from the Pitzer model [19–21]. The activity coefficient, or activity formula, of WO42, SO42, Na+, H+, and activity calculation formula of solvent H2O are expressed as:
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I 2 ln 1 b I 1 b I b
ln WO 4 A 2 4
(0) 2mNa WO +
mWO mNa 2 4
2 + 4 ,Na
(1) 2 WO 2 ,Na + 4
2I
(1) 4 WO 2 ,Na + 4
+
mSO2 mNa + 4
2I 2 (1) 4 SO ,Na 2 4
2I 2
+
1 1 I exp I
1 1 I 2 I 2 exp I
1 1 I 2 I 2 exp I ,
(15) where A is the Debye-Hückel constant of water, I represents the ionic strength and b is Pitzer parameter which is a fixed constant (b=1.2).
ln aH2 O
mNa+ mSO2 mWO2 4
1000
4
M
,
H2 O
(16)
(17)
2.4.4 Nonelectrolyte organic phase model The activity coefficients of H2WO4·RNH2, N1923 (RNH2), and toluene (C7H8) are described by f1, f2, and f3 respectively. (I) Margules models [22] 2-Suffix formula ln f1 A12 x22 A13 x32 +(A12 A13 A23 ) x2 x3 ,
(18)
ln f 2 A x A x +(A12 A23 A13 ) x1 x3 ,
(19)
ln f3 A x A x +(A13 A23 A12 ) x1 x2 ,
(20)
2 13 1
2 23 3
2 23 2
3-Suffix formula
ln f1 x22 A12 2 x1 A21 A12 x32 A13 2 x1 A31 A13 x2 x3 A21 A13 A32 2 x1 A31 A13 2 x3 A32 A23 C (1 2 x1 ) ,
(21)
ln f 2 x32 A23 2 x2 A32 A23 x12 A21 2 x2 A12 A21 x1 x3 A32 A21 A12 2 x2 A12 A21 2 x1 A13 A31 C (1 2 x2 ) ,
(22)
ln f3 x12 A31 2 x3 A13 A31 x22 A32 2 x3 A23 A32 x1 x2 A13 A32 A21 2 x3 A23 A32 2 x2 A21 A12 C (1 2 x3 ) ,
m1 , m1 m2 m3
(25)
x3
m3 . m1 m2 m3
(26)
(II) NRTL model [22] The activity coefficients of the organic complexes including H2WO4·RNH2, N1923(RNH2) and toluene (C7H8) are described as follows, and the i, j, k represent any compound among H2WO4·RNH2, RNH2 and C7H8. ln i
ji
G ji x j
j
G
x
j
k
l li Gli xl Gij x j k Gki xk ij k Gkj xk
G ji exp ji ji ,
(23)
(24)
,
(27)
(28)
where Gji is the excess Gibbs free energy and x stands for mole fraction.
ji ij 0.2 .
(29)
The mole fractions of each substance in organic phases are expressed as:
xi
mi . mi
(30)
i
2.4.5 Methods of model solution The unknown parameters are solved by the nonlinear optimization method. GAMS (General Algebraic Modeling System) is used to program and accurately solve the models. This system is a computer numerical analysis commercial software, or a high-level modeling system designed for mathematical programming and optimization, solving linear, nonlinear, and mixed-integer optimization problems that are tailored for complex, large-scale modeling applications. Target function F is defined as eq. (31) during the modeling process. AARDWO2 is defined as the model error of eq. 4
(32), which is the average absolute relative deviation of WO4 in raffinate . cal. exp. mWO 2 – m WO24 4 Target function: min F = exp. mWO i 1 2 4 n
where fi represents the activity coefficient of species I and Aij is the terminal parameter in Margules model. The mole fractions of organic phases are expressed as:
x1
m2 , m1 m2 m3
ki k
aH+ 10 – pH .
2 12 1
x2
2
,
cal. exp. 1 n mWO24 – mWO24 , AARD WO2 = exp. 4 n i 1 mWO 2
(31)
(32)
4
where exp and cal correspond to the experimental data and calculated data respectively.
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illustrate, the extraction percentages of W decrease by reducing pH value, which is consistent with previous literature research. The experiments are completed and represented by dots in the Figure 2, which are used to verify the prediction results from models. The lines in the figures are the results of the predictions. The experimental results agree well with the predicated results at low equilibrium pH range, but large deviation occurs at high equilibrium pH range. Since the model was established at low equilibrium pH range.
Results and discussion
3.1
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Liquid-Liquid phase equilibrium data
The data agrees with previous literature [14] and listed in Table 1. 3.2 Pitzer-Margules model of primary amine extraction of W
3.2.1 Results of model solution The parameters concluded by the 2-suffix Margules model are listed in Table 2. The parameters calculated by the 3-suffix Margules model are listed in Table 3. As for the table results, the AARD from the 2-suffix Margules model is more larger than the results from the 3-suffix Margules model. The binary interaction parameters, Aij from the 3-suffix Margules model, are double the values from the 2-suffix Margules model and up to 106 larger, which is not reasonable. The 2-suffix Margules model is taken into consideration in the model analyzing process while ignoring the 3-suffix Margules model.
3.3 Pitzer-NRTL model of primary amine extraction of W
3.3.1 Solution of model The parameters of the model calculated by nonlinear solver in GAMS are listed in Table 4. The calculated value from the Pitzer-NRTL model and experiments of AARDWO2 is 4
13.38%, which is the same as the results from the PitzerMargules (2-suffix) model. The calculated thermodynamic equilibrium constant is also consistent with the PitzerMargules (2-suffix) model.
3.2.2 Model predicated results New Pitzer-Margules models are used to predict the effect of equilibrium pH on the extraction of W with the fixed initial concentration of extract N1923 and W. As Figure 2
3.3.2 Model predicated results A line represents the predicated results in Figure 2, whereas the experiments results are represented as dots. The predicated
Table 1 Experimental data for the extraction of W by primary amine N1923 diluted in toluene at 293.15 K (phase ratio: O/A=1, equilibrium time: 1 h, standing time: 1 h)
m WO24
Note:
initial
(103 mol kg1)
m org. RNH 2
(103 mol kg1)
initial
Initial pH
m exp. WO24
res.
(103 mol kg1)
Equilibrium pH
4.3513
5.8172
5.47
1.9113
6.73
4.3513
5.8172
5.47
1.8950
6.76
5.5324
5.8172
5.53
2.3282
6.70
5.5324
5.8172
5.53
2.3596
6.70
5.5324
5.8172
4.01
1.8065
6.19
5.5324
5.8172
4.01
1.7754
6.19
5.5324
12.2220
5.51
2.3173
6.93
5.5324
12.2220
5.51
2.3214
6.97
4.8254
12.2220
5.54
2.0953
6.88
4.8254
12.2220
5.54
2.1157
6.82
4.3513
12.2220
5.51
1.7969
6.93
4.3513
12.2220
5.51
1.8065
6.91
3.2737
12.2220
5.52
1.5204
6.84
3.2737
12.2220
5.52
1.4972
6.80
3.2737
12.2220
4.03
0.7793
6.68
3.2737
12.2220
4.03
0.7902
6.63
2.1307
12.2220
3.92
0.4738
6.54
2.1307
12.2220
3.92
0.4761
6.58
m WO24
initial
2 4
is the molality of WO
tration unit in mol/kg toluene.
in the residue solution. For aqueous phase, the concentration unit in mol/kg. For organic phase, the concen-
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Table 2 Pitzer-Margules (2-suffix) parameters for Na2WO4-H2SO4-primary amine N1923-toluene system at 293.15 K
i: H2WO4·RNH2 Aij 0
Na
+
,WO24
1
Na
+
,WO24
j: RNH3
409.5658
i: RNH2; j: toluene 1.1108
i: H2WO4·RNH2
j: toluene
6.4714
15.0000 48.8769
ln(K)
28.3921
AARD
13.38 %
Table 3 Pitzer-Margules (3-suffix) parameters for Na2WO4-H2SO4-primary amine N1923-toluene system at 293.15 K
i: H2WO4·RNH2
j: RNH3
i: RNH2; j: toluene
i: toluene j: H2WO4·RNH2
Aij
20328.2060
1.1243
7905.3705
Aji
1948729.994
1557.2018
0.9682
C
1950916.467
0
Na
+
,WO 24
1
Na
+
,WO24
15.0000 48.9129
ln(K)
36.0340
AARD
12.86 %
Figure 2 (a) Effect of equilibrium pH on the extraction of W, (0.6398 g/L initial W, 1.5650 g/L initial N1923); (b) Effect of initial molality of N1923 on the extraction of W, (the 0.6738 g/L initial W and constant equilibrium pH 6.54). Temperature: 293.15 K, O/A=1, equilibrium time: 1 h, standing time: 1 h. Line M1, M2——calculated using the Pitzer-Margules (2-suffix) model, line N1, N2——calculated using the Pitzer-NRTL model, dot: experimental data.
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Table 4 Pitzer-NRTL parameters for Na2WO4-H2SO4-primary amine N1923 -toluene system at 293.15 K
i: RNH2; j: toluene
i: toluene j: H2WO4·RNH2
ij
i: H2WO4·RNH2 6.0671
133.0648
6.0767
ji
22.3217
1.1111
57.5248
0
Na
+
15.000
,WO 24
1
Na
+
j: RNH3
48.8773
,WO 24
ln(K)
28.7830
AARD
13.38%
results are fairly consistent with Pitzer-Margules results. 3.4
Summary and comparison of different model results
The two established models in this paper are compared to the models in previous literature to test accuracy. The equilibrium constant of each experimental group is recalculated by the model parameters and defined as lnKcal.. The equilibrium constant of the model regression is defined as lnKreg., and the error between them is expressed as average absolute relative deviation as shown in Table 5. A summary of the organic phase model parameters, equilibrium constants of different models, model error AARDWO2 , 4
1 lnK cal. lnK reg. lnK reg. is listed in Table 5. The n differences between 1 AARDWO2 and lnK cal. lnK reg. lnK reg. 4 n of the three models are negligible according to the results. There are still large differences between these models based on the numbers of parameters and physical meanings. For example, organic Pitzer model is a semi-empirical model with non-obvious physical meaning of Pitzer parameters ; thus, it is difficult to carry deep theory analysis based on these data. The Pitzer- Margules (2-suffix) model is derived from the Scatchard-Hildebrand solution theory with obvious physical meaning of terminal parameter Aij, which can qualitatively explain the strength of interaction among various components in the organic phase and the relationship between molecule structures. The repulsive force between the different components is greater when Aij>0, which the attractive force is dominant when Aij
