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Experimental investigation and modeling of phase equilibria for Cu-Bi and Cu-Bi-Sb alloys in vacuum distillation
Fluid Phase Equilibria 490 (2019) 86e91
Contents lists available at ScienceDirect
Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Experimental investigation and modeling of phase equilibria for Cu-Bi and Cu-Bi-Sb alloys in vacuum distillation Yuhu Chen b, c, Bin Yang c, Baoqiang Xu a, b, c, HongWei Yang a, b, c, * a
The State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Kunming, 650093, PR China b Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming, 650093, PR China c National Engineering Laboratory for Vacuum Metallurgy, Kunming University of Science and Technology, Kunming, 650093, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 December 2018 Received in revised form 1 March 2019 Accepted 4 March 2019 Available online 7 March 2019
The measurements of vapor-liquid equilibrium (VLE) for Cu-Bi and Cu-Bi-Sb alloys in vacuum distillation were performed. We calculated the VLE diagrams of Cu-Bi and Cu-Bi-Sb alloys at 10 Pa by Wilson equation only using binary parameters. Thermodynamic consistency tests of experimental data for the binary and ternary systems were discussed using the Van Ness method. The calculated results are in good agreement with the experimental data. The VLE data can be used for designing the purification process and phase separation of crude copper in vacuum metallurgy. © 2019 Elsevier B.V. All rights reserved.
Keywords: Cu-based alloys Vaporeliquid equilibria Thermodynamic properties Vacuum distillation
1. Introduction With the continuous mining of copper, the components of copper ore become more and more complex. A large number of complex copper alloys and low grade crude copper are produced in the process of smelting of copper and recovering copper secondary resource. There are many disadvantages such as long process, environmental issues when separating metal impurity from copper alloys by traditional incineration process and hydrometallurgical approach. Due to its short flow process, pollution-free, and high metal recovery advantages, vacuum distillation technology has been widely used in the separation and purification of crude metal [1]. Lots of work have been done on the separation and purification of crude metal by vacuum distillation. The rates of removal of bismuth, arsenic, and antimony were measured over temperature and pressure ranges of 1450e1610 K and 3e30 Pa, respectively [2]. It is shown that, at typical concentrations of these elements in copper, monatomic evaporation is the predominant evaporation
* Corresponding author. The State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Kunming, 650093, PR China. E-mail address: [email protected] (H. Yang). https://doi.org/10.1016/j.fluid.2019.03.003 0378-3812/© 2019 Elsevier B.V. All rights reserved.
mechanism. Removal of bismuth from liquid copper was studied over a range of pressures [3]. The results revealed there is a negligible effect of oxygen and sulphur. Bismuth removal from copper sulphide was slower than from copper. Yang and co-workers developed a novel technique to remove As and Sb contents from Cu-As-Sb multi-component alloy by sulfuration and distillation in vacuum [4]. It indicated that sulfuration is possible to considerably improve the vacuum distillation of Cu-As-Sb alloy. Yi addressed extraction of As and Sb by vacuum distillation from a variety of CuNi alloys containing As and Sb impurities [5]. The results manifested that temperature and time of distillation strongly affect the extraction rates of As and Sb. For instance, coexistence of As and Sb in stable Cu3As and Cu5As2 compounds accounted for incomplete evaporation of As below 1473 K. Fully decomposition of Cu3As and Cu5As2 was responsible for complete evaporation of As above 1474 K. Allaire carried out vacuum -refining experiments on copper matte melts [6]. After 40e60 min of treatment, lead elimination was between 70 and 96 pct., bismuth elimination was between 88 and 98 pct., arsenic, elimination was between 60 and 93 pct. and antimony elimination was between 40 and 92 pct. Recently, it is reported that the vapor-liquid equilibrium (VLE) theory can be used to guide vacuum distillation of alloys [7]. The VLE data are always required for the separation of an alloy such as in design of the distillation process.
Y. Chen et al. / Fluid Phase Equilibria 490 (2019) 86e91
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In our previous work, vacuum distillation experiment for Cu-Sb alloy was performed [8]. In the present study, VLE data of Bi-Sb and Bi-Cu-Sb systems under vacuum condition have been measured. The calculated T-x diagrams for Bi-Sb and Bi-Cu-Sb systems by the Wilson equation were compared with experiment. The thermodynamic consistency of the experimental VLE data was checked out by means of the Van Ness test. 2. Experimental 2.1. Materials Fig. 1. Schematic of apparatus for vacuum distillation equilibrium experiments.
Bismuth (99.99 wt %), copper (99.99 wt %) and antimony (99.99 wt %) were obtained from Hebei Guantai Metal Material Co., Ltd., China. Twelve alloys were prepared for the experimental study with compositions as listed in Table 1. 2.2. Apparatus and procedure The experimental apparatus includes distillation apparatus, condensing apparatus, heating apparatus and calorimeter apparatus as shown in Fig. 1. A vertical vacuum furnace (Kunming Diboo Technology Co., Ltd.) was used which the schematic diagram is shown in Fig. 2. In this furnace, a crucible-coil assembly was positioned the center of a water-cooled vacuum chamber which inner diameter 0.22 m, out diameter 0.27 m and 0.2 m depth. The distance between the crucible and the condensation plate is 0.01 m. The temperature was regulated by control system, and the stable heating can be provided by adjusting the current. The maximum temperature of the furnace can be heated to 1773 K. Temperature was obtained with Pt-100 probes connecting to a digital temperature meter (ANTHONE LU-900 M) with a measurement error of less than 0.2 K. Pressure was measured by a stand McLeod Gauge (Shanghai Shuangyu Electronics Co., Ltd., PM-4) with error range less than 0.1 Pa. First of all, the prepared alloy 70 g was placed in a high purity graphite crucible (99.998 wt % C) with an inner diameter of 0.04 m and a depth of 0.04 m. Then the crucible was placed in the vacuum furnace. The pressure was maintained at 10 Pa by turning on the vacuum pump. The temperature was heated to the preset value. In the process of distillation, element evaporates from the surface of melt and condenses rapidly on the condenser. The experiment of VLE was carried out in a closed vessel, and the entire chamber was sealed after being pumped to the specified pressure. It is regarded as a closed system during the entire distillation process. We hypothesized that the distillation processes will approach to a stable level with the extension of time. It will be maintained long enough time to ensure the stability of the system during the experiment. The components of distillation product
Table 1 Chemical composition of Cu-Bi and Cu-Bi-Sb alloys with different composition. Sample No.
xCu
xSb
xBi
1# 2# 3# 4# 5# 6# 7# 8# 9# 10# 11# 12#
0.70 0.90 0.80 0.70 0.60 0.60 0.60 0.50 0.40 0.30 0.20 0.10
e 0.05 0.10 0.15 0.30 0.10 0.20 0.25 0.30 0.35 0.40 0.45
0.30 0.05 0.10 0.15 0.10 0.30 0.20 0.25 0.30 0.35 0.40 0.45
Fig. 2. Schematic diagram of the internal structure of the vertical vacuum furnace: 1 furnace lid; 2 furnace body; 3 furnace bottom; 4 electrode; 5 condensation plate; 6 observation hole; 7 heat preservation cover; 8 heating unit; 9 graphite evaporator.
approach to a stable level with the extension of time, which means that the system reaches the vapor-liquid equilibrium. The state was regarded as the vapor-liquid phase equilibrium state when the vapor-liquid phase reached the limit of separation. The mole fractions of volatile and residue were measured when the system is cooled to room temperature. The equilibrium compositions were analyzed by atomic absorption spectrometry and volumetric method with an atomic absorption spectrophotometer (WFX-320 Atomic Absorption Spectrophotometer, supplied by Beijing Rayleigh Analytical Instrument Co., Ltd.) and Potentiometric titration (848 Titrino plus, supplied by Metrohm), respectively. The limit of detection is 0.01 mg/ml. Then, the uncertainty of mole fraction is ±0.0001. 3. Method 3.1. Theory of VLE For a vapor-liquid binary system, the phase equilibrium criterion [9] is that the equality of fugacity in vapor and liquid phase
f vi ¼ f li ði ¼ 1; 2Þ
(1)
Where and represent the fugacity of species i in the vapor phase and liquid phase. Usually, the liquid phase is not an ideal solution. The pressure is not high so that the vapor phase can be considered as an ideal gas, as a result
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Y. Chen et al. / Fluid Phase Equilibria 490 (2019) 86e91
xi gi ðxi ; T; PÞP *i ðTÞ ¼ yi P
(2)
Where xi and yi are the mole fraction of species i in the liquid phase and vapor phase, respectively; P *i ðTÞ is saturation pressure of a pure liquid i, gi is activity coefficient of species i in terms of temperature, respectively. T and P are the temperature and pressure of the system, respectively. For a binary system,
P ¼ P *i gi xi þ P *j gj xj ¼ P *i gi xi þ P *j gj ð1 xi Þ
(3)
xi þ xj ¼ yi þ yj ¼ 1
(4)
Then xi and yi are solved by Eqs. (2) and (4):
xi ¼
P P *j gj P *i gi
(5)
P *j gj
0
0
Aij ¼
vi 0 vj
Aij vi vj
! T0 T
(12)
For a i-j-k ternary system, the activity coefficient of component i can be expressed by Wilson equation:
lngi ¼ 1 ln xi þ xj Aji þ xk Aki
xi xi þ xj Aji þ xk Aki
Aij xj Aik xk xi Aij þ xj þ xk Akj xi Aik þ xj Ajk þ xk
(13)
Prediction of ternary VLE can be calculated using the Wilson equation with binary parameters. The parameters of the Wilson equation for the Cu-Bi, Cu-Sb and Bi-Sb systems were obtained by fitting experimental activities of components taken from literature [16] are shown in Table 3. 3.3. Thermodynamic consistency test
yi ¼
P *i gi xi
(6)
P
3.2. Wilson equation Wilson proposed an expression for activity coefficient which has been used successfully to describe the vaporeliquid equilibrium relationship [10e14]. For a binary system, it presents
lngi ¼ ln xi þ xj Aij þ xj
Aij Aji xi þ xj Aij xj þ xi Aji
lngj ¼ ln xj þ xi Aji xi
Aij Aji xi þ xj Aij xj þ xi Aji
! (7) ! (8)
Thermodynamic consistency test has been frequently used for vapor-liquid equilibrium data for binary and ternary mixtures. The consistency of the thermodynamic results was checked by the Van Ness test [17,18] for the VLE experimental values for the two systems. The yðMADÞ values are calculated by the following Eq. (14)
yðMADÞ ¼
n 1X exp 100yi ycal i n i¼1
(14)
Where yðMADÞ means absolute deviation; n is the number of experimental points; yexp means experimental data; ycal means i i predicted values. The Van Ness method performs a point-by-point test on experimental data of different concentrations so that unreliable data points can be eliminated. 4. Results and discussion
Where xi and xj are the mole fraction of components i and j, where Aij and Aji are binary interaction parameters. Aij and Aji expressed by
Aij ¼
vj exp lij lii RT vi
(9)
Aji ¼
vi exp lji ljj RT vj
(10)
Where vi and vj are the molar volumes of components i and j show in Table 2 which can be seen as a functions of temperature [15]; lii , ljj and lij (lij ¼ lji ) are the interaction energies i-i, j-j, and i-j pairs, respectively. For Wilson equation, ðlji lii Þ and ðlij ljj Þ were considered 0 0 independent of temperature. Therefore, values of Aji and Aij at other temperature T 0 can be obtained as follows: 0
0
Aji ¼
vj 0
vi
Aji vj vi
!TT0 (11)
4.1. Cu-Bi system The vapor-liquid equilibrium of Cu-Bi system were measured at 10 Pa. Experimental VLE values of the Cu-Bi system between 1150 k and 1550 k are shown in Table 4. It shows that Bi can be mostly removed from crude Cu. The content of Cu in the liquid phase reached more than 0.9999 mol fraction with residual vapor pressure at 10 Pa and distillation temperature of 1550 K. The calculated activities by the Wilson equation are shown by solid lines in Fig. 3. The results are compared with literature data, and a good agreement is obtained. Calculation based on the Wilson
Table 3 Calculated parameters of the Wilson equation for Cu-Bi, Cu-Sb and Bi-Sb systems. i-j
T/K
Aij
Aji
Cu-Bi Cu-Sb Bi-Sb
1400 1375 950
0.4556 0.3465 0.9459
0.6791 8.2472 0.8857
Table 2 The related parameters of Cu, Bi and Sb [15]. i
Vapor pressure equation (Pa)
Cu
lgðP * Þ
Bi
lgðP * Þ ¼ 10400T 1 1:26lgT þ 10:23 (T ¼ 544e1837 K)
Sb
lgðP * Þ ¼ 6500T 1 þ 4:25 (T ¼ 904e1860 K)
¼
17520T 1
1:21lgT þ 13:21 (T ¼ 1356e3200 K)
vmi (cm3 =mol) 7:94½1 þ 1:00 104 ðT 1356Þ 20:8½1 þ 1:17 104 ðT 544Þ 18:8½1 þ 1:3 104 ðT 904Þ
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Table 4 Experimental VLE data for the Cu-Bi binary alloy system at 10 Pa. T=K
Time/min
xCu;exp
xCu;cal
yCu;exp
yCu;cal
1150 1200 1250 1300 1350 1400 1450 1500 1550
360 330 300 270 240 210 180 150 120
0.9707 0.9933 0.9990 0.9838 0.9921 0.9997 0.9982 0.9990 0.9999
0.6153 0.8047 0.9037 0.9514 0.9745 0.9861 0.9922 0.9956 0.9976
0.0014 0.0064 0.0018 0.0025 0.0004 0.0106 0.0268 0.0832 0.1218
0.0000 0.0001 0.0003 0.0012 0.0036 0.0101 0.0264 0.0653 0.1443
equation and experimental vapor-liquid equilibrium for Cu-Bi system are compared in Fig. 4. It can be observed that the trend of the experimental points and the VLE phase diagram is consistent with the change of temperature. However, there is a relatively large deviation between the experimental data and the theoretical calculation value in the liquid phase when the temperature is below 1300 K.
Fig. 4. Comparison of the predicted VLE of calculation (lines) with experimental data (symbols) of Cu-Bi alloy at 10 Pa.
4.2. Cu-Bi-Sb system In order to check reliability when the Wilson equation extends to the ternary system, substituting the Wilson parameters of Cu-Bi, Cu-Sb and Bi-Sb binary systems into Eq. (13), the activities of Bi in liquid Cu-Bi-Sb alloys were obtained. Fig. 5 indicates that there is satisfactory agreement between the calculated values and experimental data [19] for the Cu-Bi-Sb ternary system. It denotes that the Wilson equation can be extended successfully to ternary system only using binary parameters. The experimental VLE data of Cu-Bi-Sb ternary system at 10 Pa and 1400 K are shown in Table 5. The vapor curves for Cu-Bi-Sb ternary system at 1500 K and 1600 K were plotted using the Wilson equation which shown in Fig. 6. It can be seen that the content of Bi in the liquid phase with different compositions ternary alloy samples can reach up to 0.0272 mol fraction. The liquid composition indicates that Bi can be separated from Cu-Bi-Sb ternary alloy by the vacuum distillation. The content of Cu in vapor phase less than 0.0084 mol fraction. The vapor composition indicates that Bi and Sb are the more volatile components than Cu. The test results for thermodynamic consistency of VLE data for the binary and ternary systems are listed in Table 6. It means that the VLE data of
Fig. 5. Comparison of the predicted activities by the Wilson equation (line) with experimental data [19] (symbols) for the Cu-Bi-Sb system at 1373 K.
Cu-Bi and Cu-Bi-Sb systems are reliable. Due to the content of Bi is much higher than Sb in vapor phase. Bi should be easy to evaporate from crude copper. In the purification of crude copper by vacuum distillation, the following factors may lead to the deviations: (1) Bismuth will evaporate into the vapor phase as the vacuum distillation
Table 5 Experimental VLE data for the Cu-Bi-Sb ternary alloy system at 10 Pa.
Fig. 3. Comparison of the predicted activities of Wilson equation (lines) with experimental data [16] (symbols) for the Cu-Bi system at 1400 K.
Sample No.
Temperature K
xCu;exp
xSb;exp
yCu ;exp
ySb;exp
yCu;cal
2# 3# 4# 5# 6# 7# 8# 9# 10# 11# 12#
1400 1400 1400 1400 1400 1400 1400 1400 1400 1400 1400
0.9311 0.8148 0.7191 0.6205 0.7733 0.6404 0.6320 0.6379 0.6611 0.6467 0.6243
0.0651 0.1642 0.2731 0.3637 0.2203 0.3324 0.3613 0.3535 0.3315 0.3470 0.3658
0.0084 0.0060 0.0013 0.0005 0.0036 0.0012 0.0010 0.0014 0.0001 0.0000 0.0000
0.0201 0.0601 0.0605 0.3844 0.0187 0.1512 0.3215 0.2076 0.3445 0.3613 0.3580
0.0101 0.0086 0.0068 0.0043 0.0043 0.0043 0.0027 0.0013 0.0003 0.0001 0.0000
90
Y. Chen et al. / Fluid Phase Equilibria 490 (2019) 86e91
Fig. 6. VLE of the Cu-Bi-Sb alloy at 10 Pa 1400 K. Vapor curves at 1500 K and 1600 K using the Wilson equation (dash lines).
Table 6 Thermodynamic consistency test of VLE results. system
yðMADÞ;Cu
Result
Cu-Bi Cu-Bi-Sb
0.61 0.18
pass pass
progresses. Due to the decrease of bismuth, the ratio of copper to bismuth in the liquid phase changes, which causes the melting point temperature of the alloy to be lower than 1350 K. It will affect the experimental results. (2) Copper at intermediate phase zone (vapor phase þ liquid phase) may return to the liquid phase which will cause the copper in the liquid phase to be higher than the calculated value during the cooling process. So, there are large deviations exist in the liquid phase. (3) For a ternary system, only binary interactions between atoms are considered, the atomic interactions of multicomponent systems are neglected when use Wilson equation to calculate. It also affects the calculation accuracy of VLE. (4) In the calculation process of VLE, vapor phase is assumed to be an ideal gas, which has a certain small deviation from the actual situation. (5) The lack of an efficient apparatus to measure VLE data of alloy melts under high temperature and low pressure. Owing to the difficulty of vacuum condition, the accurate experimental data of the alloy system are not easy to get. In this work, static method was used for determination of VLE data for Cu-Bi and Cu-Bi-Sb systems. (6) In our previous work [8], since Cu3Sb phase is formed in the liquid phase. It demonstrated that the bonding force between copper and antimony is strong. Antimony cannot be completely separated from the crude copper alloy. The interaction between copper and antimony makes the Cu-Bi-Sb ternary alloy more complicated. Since the results in the vapor phase are more accurate than in the liquid phase. Thermodynamic consistency tests of experimental data in the vapor phase for the binary and ternary systems were checked using the Van Ness method. Usually, there has not yet been a thermodynamic consistency test rigorously applied to VLE data nor does there exist a set of data that is known a priori to be absolutely accurate. Hence, the approximations that have been
replaced by some of the rigorous expressions in these tests as well as the potential for experimental error. In order to facilitate the test and eliminate the residual diagram, the average absolute deviation is used as the criterion. The experimental data are considered to be thermodynamic consistent if the mean absolute deviation is less than 1. 5. Conclusion In this work, the isobaric VLE data for Cu-Bi and Cu-Bi-Sb systems were measured at 10 Pa. The experimental results indicated that Bi and Sb can be separated successfully from Cu by vacuum distillation. Furthermore, the VLE experimental values for binary and ternary systems passed the consistency test of thermodynamics using the Van Ness method. The activity of component Bi of Cu-Bi-Sb ternary system were calculated by sub-binary interaction parameters. The VLE phase diagrams of Cu-Bi and Cu-Bi-Sb systems in vacuum distillation were modeled based on the Wilson equation. This study provides a theoretical basis for the separation of Bi and Sb from crude copper. It is reasonable that VLE phase diagram can be applied to the process of crude copper purification by vacuum distillation. Acknowledgements This work has been founded by the Fund of National Natural Science Foundation of China under Grant Nos. 51764031 and U1502271, the Science and Technological Talent Cultivation Plan of Yunnan Province under Grant No. 2017HB009 and the National Key Research and Development Program of China under Grant No. 2016YFC0400404. References [1] Y.N. Dai, Vacuum Metallurgy of Nonferrous Metals, Metallurgical Industry Press, Beijing, 2009. [2] R. Harris, Mater. Trans., JIM 15 (2) (1984) 251e257. [3] R. Bryan, D.M. Pollard, G.M. Willis, Aust. Jpn. Extr. Metall. Symp. (1980) 439e448. [4] X.K. Yang, B. Yang, H. Xiong, B.Q. Xu, Y.N. Dai, D.C. Liu, Chin. J. Vac. Sci. Technol.
Y. Chen et al. / Fluid Phase Equilibria 490 (2019) 86e91 33 (1) (2013) 82e87. [5] J.F. Yi, D.C. Liu, B. Yang, H. Xiong, L.X. Kong, Y.N. Dai, Chin. J. Vac. Sci. Technol. 35 (3) (2015) 338e343. [6] A. Allaire, R. Harris, Mater. Trans., JIM 20 (6) (1989) 793e804. [7] H.W. Yang, C. Zhang, B. Yang, L.X. Kong, B.Q. Xu, D.C. Liu, Vacuum 119 (2015) 179e184. [8] Y.H. Chen, H.W. Yang, in: 4rd International Conference on Environmental Science and Material Application, Earth and Environmental Science, 2018 (2019). (In press). [9] C.D. Maranas, C.M. Mcdonald, S.T. Harding, C.A. Floudas, Comput. Chem. Eng. 20 (1996) S413eS418. [10] G.M. Wilson, J. Am. Chem. Soc. 86 (1964) 127e130. [11] S.K. Ghosh, S.J. Chopra, Ind. Eng. Chem. 14 (3) (1975) 304e308. [12] N. Sllverman, D. Tassios, Ind. Eng. Chem. Process Des. Dev. 23 (3) (1984)
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586e589. [13] K. Kurihara, T. Oshita, O.A. Kenji, K. Kojima, J. Chem. Eng. Data 48 (1) (2003) 102e106. [14] Y.H. Song, P.H. Wei, J. Song, H. Huang, J.Q. Li, J. Chem. Thermodyn. 110 (2017) 237e242. [15] T. Iida, R.I.L. Guthrie, The Physical Properties of Liquid Metals, Clarendon Press, Oxford, 1988. €rnstein, Springer-Verlag, Berlin, 1993. [16] H. Landolt, R. Bo [17] J.W. Kang, V. Diky, R.D. Chirico, J.W. Magee, C.D. Muzny, I.M. Abdulagatov, A.F. Kazakov, M. Frenkel, J. Chem. Eng. Data 55 (9) (2010) 3631e3640. [18] P.L. Jackson, R.A. Wilsak, Fluid Phase Equilib. 103 (2) (1995) 155e197. [19] D. Zivkovi c, D. Mini c, D. Manasijevi c, A. Kostov, N. Talijan, L. Balanovi c, Zivkovi A. Mitovski, Z. c, J. Min. Metall. Sect. B Metall. 46 (1) (2010) 105e111. B.
Contents lists available at ScienceDirect
Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Experimental investigation and modeling of phase equilibria for Cu-Bi and Cu-Bi-Sb alloys in vacuum distillation Yuhu Chen b, c, Bin Yang c, Baoqiang Xu a, b, c, HongWei Yang a, b, c, * a
The State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Kunming, 650093, PR China b Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming, 650093, PR China c National Engineering Laboratory for Vacuum Metallurgy, Kunming University of Science and Technology, Kunming, 650093, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 December 2018 Received in revised form 1 March 2019 Accepted 4 March 2019 Available online 7 March 2019
The measurements of vapor-liquid equilibrium (VLE) for Cu-Bi and Cu-Bi-Sb alloys in vacuum distillation were performed. We calculated the VLE diagrams of Cu-Bi and Cu-Bi-Sb alloys at 10 Pa by Wilson equation only using binary parameters. Thermodynamic consistency tests of experimental data for the binary and ternary systems were discussed using the Van Ness method. The calculated results are in good agreement with the experimental data. The VLE data can be used for designing the purification process and phase separation of crude copper in vacuum metallurgy. © 2019 Elsevier B.V. All rights reserved.
Keywords: Cu-based alloys Vaporeliquid equilibria Thermodynamic properties Vacuum distillation
1. Introduction With the continuous mining of copper, the components of copper ore become more and more complex. A large number of complex copper alloys and low grade crude copper are produced in the process of smelting of copper and recovering copper secondary resource. There are many disadvantages such as long process, environmental issues when separating metal impurity from copper alloys by traditional incineration process and hydrometallurgical approach. Due to its short flow process, pollution-free, and high metal recovery advantages, vacuum distillation technology has been widely used in the separation and purification of crude metal [1]. Lots of work have been done on the separation and purification of crude metal by vacuum distillation. The rates of removal of bismuth, arsenic, and antimony were measured over temperature and pressure ranges of 1450e1610 K and 3e30 Pa, respectively [2]. It is shown that, at typical concentrations of these elements in copper, monatomic evaporation is the predominant evaporation
* Corresponding author. The State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Kunming, 650093, PR China. E-mail address: [email protected] (H. Yang). https://doi.org/10.1016/j.fluid.2019.03.003 0378-3812/© 2019 Elsevier B.V. All rights reserved.
mechanism. Removal of bismuth from liquid copper was studied over a range of pressures [3]. The results revealed there is a negligible effect of oxygen and sulphur. Bismuth removal from copper sulphide was slower than from copper. Yang and co-workers developed a novel technique to remove As and Sb contents from Cu-As-Sb multi-component alloy by sulfuration and distillation in vacuum [4]. It indicated that sulfuration is possible to considerably improve the vacuum distillation of Cu-As-Sb alloy. Yi addressed extraction of As and Sb by vacuum distillation from a variety of CuNi alloys containing As and Sb impurities [5]. The results manifested that temperature and time of distillation strongly affect the extraction rates of As and Sb. For instance, coexistence of As and Sb in stable Cu3As and Cu5As2 compounds accounted for incomplete evaporation of As below 1473 K. Fully decomposition of Cu3As and Cu5As2 was responsible for complete evaporation of As above 1474 K. Allaire carried out vacuum -refining experiments on copper matte melts [6]. After 40e60 min of treatment, lead elimination was between 70 and 96 pct., bismuth elimination was between 88 and 98 pct., arsenic, elimination was between 60 and 93 pct. and antimony elimination was between 40 and 92 pct. Recently, it is reported that the vapor-liquid equilibrium (VLE) theory can be used to guide vacuum distillation of alloys [7]. The VLE data are always required for the separation of an alloy such as in design of the distillation process.
Y. Chen et al. / Fluid Phase Equilibria 490 (2019) 86e91
87
In our previous work, vacuum distillation experiment for Cu-Sb alloy was performed [8]. In the present study, VLE data of Bi-Sb and Bi-Cu-Sb systems under vacuum condition have been measured. The calculated T-x diagrams for Bi-Sb and Bi-Cu-Sb systems by the Wilson equation were compared with experiment. The thermodynamic consistency of the experimental VLE data was checked out by means of the Van Ness test. 2. Experimental 2.1. Materials Fig. 1. Schematic of apparatus for vacuum distillation equilibrium experiments.
Bismuth (99.99 wt %), copper (99.99 wt %) and antimony (99.99 wt %) were obtained from Hebei Guantai Metal Material Co., Ltd., China. Twelve alloys were prepared for the experimental study with compositions as listed in Table 1. 2.2. Apparatus and procedure The experimental apparatus includes distillation apparatus, condensing apparatus, heating apparatus and calorimeter apparatus as shown in Fig. 1. A vertical vacuum furnace (Kunming Diboo Technology Co., Ltd.) was used which the schematic diagram is shown in Fig. 2. In this furnace, a crucible-coil assembly was positioned the center of a water-cooled vacuum chamber which inner diameter 0.22 m, out diameter 0.27 m and 0.2 m depth. The distance between the crucible and the condensation plate is 0.01 m. The temperature was regulated by control system, and the stable heating can be provided by adjusting the current. The maximum temperature of the furnace can be heated to 1773 K. Temperature was obtained with Pt-100 probes connecting to a digital temperature meter (ANTHONE LU-900 M) with a measurement error of less than 0.2 K. Pressure was measured by a stand McLeod Gauge (Shanghai Shuangyu Electronics Co., Ltd., PM-4) with error range less than 0.1 Pa. First of all, the prepared alloy 70 g was placed in a high purity graphite crucible (99.998 wt % C) with an inner diameter of 0.04 m and a depth of 0.04 m. Then the crucible was placed in the vacuum furnace. The pressure was maintained at 10 Pa by turning on the vacuum pump. The temperature was heated to the preset value. In the process of distillation, element evaporates from the surface of melt and condenses rapidly on the condenser. The experiment of VLE was carried out in a closed vessel, and the entire chamber was sealed after being pumped to the specified pressure. It is regarded as a closed system during the entire distillation process. We hypothesized that the distillation processes will approach to a stable level with the extension of time. It will be maintained long enough time to ensure the stability of the system during the experiment. The components of distillation product
Table 1 Chemical composition of Cu-Bi and Cu-Bi-Sb alloys with different composition. Sample No.
xCu
xSb
xBi
1# 2# 3# 4# 5# 6# 7# 8# 9# 10# 11# 12#
0.70 0.90 0.80 0.70 0.60 0.60 0.60 0.50 0.40 0.30 0.20 0.10
e 0.05 0.10 0.15 0.30 0.10 0.20 0.25 0.30 0.35 0.40 0.45
0.30 0.05 0.10 0.15 0.10 0.30 0.20 0.25 0.30 0.35 0.40 0.45
Fig. 2. Schematic diagram of the internal structure of the vertical vacuum furnace: 1 furnace lid; 2 furnace body; 3 furnace bottom; 4 electrode; 5 condensation plate; 6 observation hole; 7 heat preservation cover; 8 heating unit; 9 graphite evaporator.
approach to a stable level with the extension of time, which means that the system reaches the vapor-liquid equilibrium. The state was regarded as the vapor-liquid phase equilibrium state when the vapor-liquid phase reached the limit of separation. The mole fractions of volatile and residue were measured when the system is cooled to room temperature. The equilibrium compositions were analyzed by atomic absorption spectrometry and volumetric method with an atomic absorption spectrophotometer (WFX-320 Atomic Absorption Spectrophotometer, supplied by Beijing Rayleigh Analytical Instrument Co., Ltd.) and Potentiometric titration (848 Titrino plus, supplied by Metrohm), respectively. The limit of detection is 0.01 mg/ml. Then, the uncertainty of mole fraction is ±0.0001. 3. Method 3.1. Theory of VLE For a vapor-liquid binary system, the phase equilibrium criterion [9] is that the equality of fugacity in vapor and liquid phase
f vi ¼ f li ði ¼ 1; 2Þ
(1)
Where and represent the fugacity of species i in the vapor phase and liquid phase. Usually, the liquid phase is not an ideal solution. The pressure is not high so that the vapor phase can be considered as an ideal gas, as a result
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Y. Chen et al. / Fluid Phase Equilibria 490 (2019) 86e91
xi gi ðxi ; T; PÞP *i ðTÞ ¼ yi P
(2)
Where xi and yi are the mole fraction of species i in the liquid phase and vapor phase, respectively; P *i ðTÞ is saturation pressure of a pure liquid i, gi is activity coefficient of species i in terms of temperature, respectively. T and P are the temperature and pressure of the system, respectively. For a binary system,
P ¼ P *i gi xi þ P *j gj xj ¼ P *i gi xi þ P *j gj ð1 xi Þ
(3)
xi þ xj ¼ yi þ yj ¼ 1
(4)
Then xi and yi are solved by Eqs. (2) and (4):
xi ¼
P P *j gj P *i gi
(5)
P *j gj
0
0
Aij ¼
vi 0 vj
Aij vi vj
! T0 T
(12)
For a i-j-k ternary system, the activity coefficient of component i can be expressed by Wilson equation:
lngi ¼ 1 ln xi þ xj Aji þ xk Aki
xi xi þ xj Aji þ xk Aki
Aij xj Aik xk xi Aij þ xj þ xk Akj xi Aik þ xj Ajk þ xk
(13)
Prediction of ternary VLE can be calculated using the Wilson equation with binary parameters. The parameters of the Wilson equation for the Cu-Bi, Cu-Sb and Bi-Sb systems were obtained by fitting experimental activities of components taken from literature [16] are shown in Table 3. 3.3. Thermodynamic consistency test
yi ¼
P *i gi xi
(6)
P
3.2. Wilson equation Wilson proposed an expression for activity coefficient which has been used successfully to describe the vaporeliquid equilibrium relationship [10e14]. For a binary system, it presents
lngi ¼ ln xi þ xj Aij þ xj
Aij Aji xi þ xj Aij xj þ xi Aji
lngj ¼ ln xj þ xi Aji xi
Aij Aji xi þ xj Aij xj þ xi Aji
! (7) ! (8)
Thermodynamic consistency test has been frequently used for vapor-liquid equilibrium data for binary and ternary mixtures. The consistency of the thermodynamic results was checked by the Van Ness test [17,18] for the VLE experimental values for the two systems. The yðMADÞ values are calculated by the following Eq. (14)
yðMADÞ ¼
n 1X exp 100yi ycal i n i¼1
(14)
Where yðMADÞ means absolute deviation; n is the number of experimental points; yexp means experimental data; ycal means i i predicted values. The Van Ness method performs a point-by-point test on experimental data of different concentrations so that unreliable data points can be eliminated. 4. Results and discussion
Where xi and xj are the mole fraction of components i and j, where Aij and Aji are binary interaction parameters. Aij and Aji expressed by
Aij ¼
vj exp lij lii RT vi
(9)
Aji ¼
vi exp lji ljj RT vj
(10)
Where vi and vj are the molar volumes of components i and j show in Table 2 which can be seen as a functions of temperature [15]; lii , ljj and lij (lij ¼ lji ) are the interaction energies i-i, j-j, and i-j pairs, respectively. For Wilson equation, ðlji lii Þ and ðlij ljj Þ were considered 0 0 independent of temperature. Therefore, values of Aji and Aij at other temperature T 0 can be obtained as follows: 0
0
Aji ¼
vj 0
vi
Aji vj vi
!TT0 (11)
4.1. Cu-Bi system The vapor-liquid equilibrium of Cu-Bi system were measured at 10 Pa. Experimental VLE values of the Cu-Bi system between 1150 k and 1550 k are shown in Table 4. It shows that Bi can be mostly removed from crude Cu. The content of Cu in the liquid phase reached more than 0.9999 mol fraction with residual vapor pressure at 10 Pa and distillation temperature of 1550 K. The calculated activities by the Wilson equation are shown by solid lines in Fig. 3. The results are compared with literature data, and a good agreement is obtained. Calculation based on the Wilson
Table 3 Calculated parameters of the Wilson equation for Cu-Bi, Cu-Sb and Bi-Sb systems. i-j
T/K
Aij
Aji
Cu-Bi Cu-Sb Bi-Sb
1400 1375 950
0.4556 0.3465 0.9459
0.6791 8.2472 0.8857
Table 2 The related parameters of Cu, Bi and Sb [15]. i
Vapor pressure equation (Pa)
Cu
lgðP * Þ
Bi
lgðP * Þ ¼ 10400T 1 1:26lgT þ 10:23 (T ¼ 544e1837 K)
Sb
lgðP * Þ ¼ 6500T 1 þ 4:25 (T ¼ 904e1860 K)
¼
17520T 1
1:21lgT þ 13:21 (T ¼ 1356e3200 K)
vmi (cm3 =mol) 7:94½1 þ 1:00 104 ðT 1356Þ 20:8½1 þ 1:17 104 ðT 544Þ 18:8½1 þ 1:3 104 ðT 904Þ
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89
Table 4 Experimental VLE data for the Cu-Bi binary alloy system at 10 Pa. T=K
Time/min
xCu;exp
xCu;cal
yCu;exp
yCu;cal
1150 1200 1250 1300 1350 1400 1450 1500 1550
360 330 300 270 240 210 180 150 120
0.9707 0.9933 0.9990 0.9838 0.9921 0.9997 0.9982 0.9990 0.9999
0.6153 0.8047 0.9037 0.9514 0.9745 0.9861 0.9922 0.9956 0.9976
0.0014 0.0064 0.0018 0.0025 0.0004 0.0106 0.0268 0.0832 0.1218
0.0000 0.0001 0.0003 0.0012 0.0036 0.0101 0.0264 0.0653 0.1443
equation and experimental vapor-liquid equilibrium for Cu-Bi system are compared in Fig. 4. It can be observed that the trend of the experimental points and the VLE phase diagram is consistent with the change of temperature. However, there is a relatively large deviation between the experimental data and the theoretical calculation value in the liquid phase when the temperature is below 1300 K.
Fig. 4. Comparison of the predicted VLE of calculation (lines) with experimental data (symbols) of Cu-Bi alloy at 10 Pa.
4.2. Cu-Bi-Sb system In order to check reliability when the Wilson equation extends to the ternary system, substituting the Wilson parameters of Cu-Bi, Cu-Sb and Bi-Sb binary systems into Eq. (13), the activities of Bi in liquid Cu-Bi-Sb alloys were obtained. Fig. 5 indicates that there is satisfactory agreement between the calculated values and experimental data [19] for the Cu-Bi-Sb ternary system. It denotes that the Wilson equation can be extended successfully to ternary system only using binary parameters. The experimental VLE data of Cu-Bi-Sb ternary system at 10 Pa and 1400 K are shown in Table 5. The vapor curves for Cu-Bi-Sb ternary system at 1500 K and 1600 K were plotted using the Wilson equation which shown in Fig. 6. It can be seen that the content of Bi in the liquid phase with different compositions ternary alloy samples can reach up to 0.0272 mol fraction. The liquid composition indicates that Bi can be separated from Cu-Bi-Sb ternary alloy by the vacuum distillation. The content of Cu in vapor phase less than 0.0084 mol fraction. The vapor composition indicates that Bi and Sb are the more volatile components than Cu. The test results for thermodynamic consistency of VLE data for the binary and ternary systems are listed in Table 6. It means that the VLE data of
Fig. 5. Comparison of the predicted activities by the Wilson equation (line) with experimental data [19] (symbols) for the Cu-Bi-Sb system at 1373 K.
Cu-Bi and Cu-Bi-Sb systems are reliable. Due to the content of Bi is much higher than Sb in vapor phase. Bi should be easy to evaporate from crude copper. In the purification of crude copper by vacuum distillation, the following factors may lead to the deviations: (1) Bismuth will evaporate into the vapor phase as the vacuum distillation
Table 5 Experimental VLE data for the Cu-Bi-Sb ternary alloy system at 10 Pa.
Fig. 3. Comparison of the predicted activities of Wilson equation (lines) with experimental data [16] (symbols) for the Cu-Bi system at 1400 K.
Sample No.
Temperature K
xCu;exp
xSb;exp
yCu ;exp
ySb;exp
yCu;cal
2# 3# 4# 5# 6# 7# 8# 9# 10# 11# 12#
1400 1400 1400 1400 1400 1400 1400 1400 1400 1400 1400
0.9311 0.8148 0.7191 0.6205 0.7733 0.6404 0.6320 0.6379 0.6611 0.6467 0.6243
0.0651 0.1642 0.2731 0.3637 0.2203 0.3324 0.3613 0.3535 0.3315 0.3470 0.3658
0.0084 0.0060 0.0013 0.0005 0.0036 0.0012 0.0010 0.0014 0.0001 0.0000 0.0000
0.0201 0.0601 0.0605 0.3844 0.0187 0.1512 0.3215 0.2076 0.3445 0.3613 0.3580
0.0101 0.0086 0.0068 0.0043 0.0043 0.0043 0.0027 0.0013 0.0003 0.0001 0.0000
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Y. Chen et al. / Fluid Phase Equilibria 490 (2019) 86e91
Fig. 6. VLE of the Cu-Bi-Sb alloy at 10 Pa 1400 K. Vapor curves at 1500 K and 1600 K using the Wilson equation (dash lines).
Table 6 Thermodynamic consistency test of VLE results. system
yðMADÞ;Cu
Result
Cu-Bi Cu-Bi-Sb
0.61 0.18
pass pass
progresses. Due to the decrease of bismuth, the ratio of copper to bismuth in the liquid phase changes, which causes the melting point temperature of the alloy to be lower than 1350 K. It will affect the experimental results. (2) Copper at intermediate phase zone (vapor phase þ liquid phase) may return to the liquid phase which will cause the copper in the liquid phase to be higher than the calculated value during the cooling process. So, there are large deviations exist in the liquid phase. (3) For a ternary system, only binary interactions between atoms are considered, the atomic interactions of multicomponent systems are neglected when use Wilson equation to calculate. It also affects the calculation accuracy of VLE. (4) In the calculation process of VLE, vapor phase is assumed to be an ideal gas, which has a certain small deviation from the actual situation. (5) The lack of an efficient apparatus to measure VLE data of alloy melts under high temperature and low pressure. Owing to the difficulty of vacuum condition, the accurate experimental data of the alloy system are not easy to get. In this work, static method was used for determination of VLE data for Cu-Bi and Cu-Bi-Sb systems. (6) In our previous work [8], since Cu3Sb phase is formed in the liquid phase. It demonstrated that the bonding force between copper and antimony is strong. Antimony cannot be completely separated from the crude copper alloy. The interaction between copper and antimony makes the Cu-Bi-Sb ternary alloy more complicated. Since the results in the vapor phase are more accurate than in the liquid phase. Thermodynamic consistency tests of experimental data in the vapor phase for the binary and ternary systems were checked using the Van Ness method. Usually, there has not yet been a thermodynamic consistency test rigorously applied to VLE data nor does there exist a set of data that is known a priori to be absolutely accurate. Hence, the approximations that have been
replaced by some of the rigorous expressions in these tests as well as the potential for experimental error. In order to facilitate the test and eliminate the residual diagram, the average absolute deviation is used as the criterion. The experimental data are considered to be thermodynamic consistent if the mean absolute deviation is less than 1. 5. Conclusion In this work, the isobaric VLE data for Cu-Bi and Cu-Bi-Sb systems were measured at 10 Pa. The experimental results indicated that Bi and Sb can be separated successfully from Cu by vacuum distillation. Furthermore, the VLE experimental values for binary and ternary systems passed the consistency test of thermodynamics using the Van Ness method. The activity of component Bi of Cu-Bi-Sb ternary system were calculated by sub-binary interaction parameters. The VLE phase diagrams of Cu-Bi and Cu-Bi-Sb systems in vacuum distillation were modeled based on the Wilson equation. This study provides a theoretical basis for the separation of Bi and Sb from crude copper. It is reasonable that VLE phase diagram can be applied to the process of crude copper purification by vacuum distillation. Acknowledgements This work has been founded by the Fund of National Natural Science Foundation of China under Grant Nos. 51764031 and U1502271, the Science and Technological Talent Cultivation Plan of Yunnan Province under Grant No. 2017HB009 and the National Key Research and Development Program of China under Grant No. 2016YFC0400404. References [1] Y.N. Dai, Vacuum Metallurgy of Nonferrous Metals, Metallurgical Industry Press, Beijing, 2009. [2] R. Harris, Mater. Trans., JIM 15 (2) (1984) 251e257. [3] R. Bryan, D.M. Pollard, G.M. Willis, Aust. Jpn. Extr. Metall. Symp. (1980) 439e448. [4] X.K. Yang, B. Yang, H. Xiong, B.Q. Xu, Y.N. Dai, D.C. Liu, Chin. J. Vac. Sci. Technol.
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