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Experimental investigation and calculation of vapor–liquid equilibria for Cu–Pb binary alloy in vacuum distillation
Fluid Phase Equilibria 405 (2015) 68–72
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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 calculation of vapor–liquid equilibria for Cu–Pb binary alloy in vacuum distillation Cheng Zhangb , WenLong Jiangc, Bin Yangc, DaChun Liuc , BaoQiang Xuc , HongWei Yanga,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 18 April 2015 Received in revised form 18 July 2015 Accepted 23 July 2015 Available online 29 July 2015
In this study, vacuum distillation experiments of high-lead crude copper were performed under the vapor pressure 5 Pa. The content of lead in crude copper was reduced from 15% to less than 0.01% in a single stage distillation process with residual vapor pressures of below 10 Pa, distillation temperatures of 1423 K and distillation times of 60 min. The vapor–liquid equilibrium (VLE) phase diagrams of Cu–Pb binary alloy in vacuum distillation were calculated using the Wilson equation. Thermodynamic experimental data taken from literature were used for calculating Wilson equation temperature dependent interaction parameters. The calculations give a satisfactory accuracy with the experimental data for separation of Cu–Pb alloy in vacuum distillation. The results indicate that VLE phase diagrams under vacuum obtained by this method are reliable for predicting the process of vacuum distillation for Cu–Pb alloy. The VLE phase diagrams of alloys will have significant benefits for the industrial production of vacuum metallurgy especially for the process of multistage distillation in the vacuum furnace. ã 2015 Elsevier B.V. All rights reserved.
Keywords: Vacuum distillation VLE phase diagram Cu–Pb alloy Wilson equation Thermodynamic properties
1. Introduction The use of vacuum distillation for separating various elements from nonferrous alloys have been very successful and is expanding rapidly, largely due to its ability to achieve high metal recovery, low impurities in recovered metal, simplified flow sheet, good environmental protection, low operation costs and simple equipment [1,2]. Small-scale vacuum distillation experiments to purify the Pb contaminated alloys have been investigated in previous work and have reported good separation effects [3–5]. There is an increasing need to consider phase diagrams for vapor–liquid phase with the development of vacuum metallurgy. In our previous works [6,7], we only calculated the separation coefficients and vapor–liquid equilibrium composition of Pb-based alloys in vacuum distillation. However, the vapor–liquid equilibrium composition curve cannot provide an intuitive and convenient way to analyze the product component dependence of temperature or pressure in the design of vacuum distillation experiment. A
* Corresponding author at: The State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Kunming 650093, PR China. [73_TD$IF]Tel.: +86 13987157570. E-mail address: [email protected] (H. Yang). http://dx.doi.org/10.1016/j.fluid.2015.07.043 0378-3812/ ã 2015 Elsevier B.V. All rights reserved.
firm knowledge of the VLE relationships is a prerequisite to predict the process of vacuum distillation [8,9]. Crude copper usually contains lead as an impurity, the conventional separation method cannot be used when the lead is high. In this work, vacuum distillation of high-lead crude copper was investigated with vapor pressures ranging from 5 to 10 Pa. The VLE phase diagrams such as temperature-composition (T-x) and pressure-composition (P-x) curves of Cu–Pb alloy under vacuum are obtained based on the VLE calculation and the Wilson equation. The VLE phase diagrams can provide an intuitive way to predict the VLE relationships of alloy system under vacuum distillation continuously. The present work is available for obtaining the VLE phase diagrams of alloys which will bring an efficient and reliable way to analyze and predict the VLE data of alloys in vacuum distillation, especially for the process of multistage distillation in the vacuum furnace. 2. Experimental procedure The Cu–Pb alloy for the experiment was prepared from high purity metals using Pb and Cu with a purity of 99.99% and the content of Pb in Cu–Pb alloy is 15%. The information of experimental sample for the Cu–Pb alloy is listed in Table 1.
C. Zhang et al. / Fluid Phase Equilibria 405 (2015) 68–72
69
Table 1 The information of experimental sample for the Cu–Pb alloy. Chemical name
Source
Initial mole fraction purity
Purification method
Final mole fraction purity
Analysis method
Copper Lead
Yunnan tin company
0.85 0.15
Vacuum distillation
0.9982 0.0016
Gas–liquid chromatography Atomic absorption spectroscopy
Small-scale vacuum distillation experiments for Cu–Pb alloy were carried out in the vertical vacuum furnace in this work and the internal structure schematic diagram is shown in Fig. 1. Vacuum degree in the furnace were at the range of 5 10 Pa during the experiment. In the furnace, 50 g Cu–Pb alloy was placed in graphite crucible to be heated and melted after the vacuum degree reached to 5 Pa. With the temperature rising to a certain degree, lead and copper in liquid alloy will evaporate from the melt and solidified rapidly on the condenser. Melting temperatures of each experiment during this investigation were 1223 K, 1273 K, 1323 K, 1373 K and 1423 K, respectively. The relationship between distillation time and composition of distillation product has been investigated in our previous works [10] and the composition of distillation product started to approach a stable level when the time exceeds 30 minutes under 10 25 Pa and 1373 K. In other words, the stable level of composition of distillation product is the phase equilibrium of Cu–Pb system under some specified pressure and temperature. On this basis, 60 min was selected as the final distillation time in this work which allows the system to approach the phase equilibrium sufficiently. In addition, it can also minimizes the mass loss during experiment with increasing distillation time and reduce any errors associated the data that we obtained. The samples were collected from the volatile and residue, and then remelted, respectively, to determine the average components of the samples. The experimental data of the vapor-liquid phase equilibria for the Pb content in residuum (liquid phase) and volatiles (vapor phase) are listed in Table 2.
[(Fig._1)TD$IG]
Table 2 Experimental values of mole fraction xPb and yPb at temperature T, pressure P for the Cu–Pb alloy in vacuum distillation.a Experiment condition
Content of Pb (mole fraction)
Temperature (K)
Pressure (Pa) Time (min) xPb
yPb
1223 1273 1323 1373 1423
5 5 5 5 5
0.999022 0.997066 0.993500 0.988018 0.981629
60 60 60 60 60
0.005367 0.002886 0.000834 0.000308 0.000015
a Standard uncertainties u are uðTÞ ¼ 5K,uðPÞ ¼ 2Pa, uðxÞ ¼ 0:000002, and uðyÞ ¼ 0:000002.
Considering the high temperatures and low vapor pressure during the experiment, the experimental VLE data we collected by this method will bring some certain deviations from ideal condition. They are mainly rising from the following aspects. The purity of the distillation products are both high ranging from 0.98 to 1, the deviations caused by the mass loss will be magnified in the final results. What's more, during the process of temperature rising to a certain degree, there will have be some mass metal evaporated from the liquid phase and the system vacuum degree will be outside the range of 10 15 Pa during this heating time. All the factors above are unavoidable so far. 3. Method 3.1. VLE calculation For the rare case of a low-pressure and ideal mixture system, Raoult’s law applies to indicate the relationship of VLE which is expressed as [11,12] xi Pi ðTÞ ¼ yi P
(1)
where xi and yi are the mole fraction of species i in the liquid phase and vapor phase, respectively; T is the temperature; Pi and P are the saturation pressure of species i and the pressure of the system, respectively, in terms of temperature. Due to most of the liquid solutions for alloy systems cannot be considered as ideal, Raoult’s law will give highly inaccurate results. For these systems under vacuum, the liquid phase is not an ideal solution but the pressure is low enough so that the vapor phase behaves as an ideal gas. In this case, the deviations are taken into account by incorporating a correction factor, g , into Raoult’s law to quantitatively consider the deviations from ideality. Therefore, Raoult’s law can be modified as xi g i ðxi ; T; PÞPi ðTÞ ¼ yi P
(2)
where g i is activity coefficient of species i in terms of temperature, pressure and the mole fraction of species i. For a binary alloy system i-j,
Fig. 1. Schematic diagram of the internal structure of the vertical vacuum furnace: 1 furnace lid; 2 furnace body; 3 furnace bottom; 4 electrode; 5 cold plate; 6 observation door; 7 heat holding cover; 8 heating unit; 9 graphite evaporator.
xi þ xj ¼ 1; yi þ yj ¼ 1
(3)
P ¼ xi g i Pi þ xj g j Pj ¼ xi g i Pi þ ð1 xi Þg j Pj
(4)
70
C. Zhang et al. / Fluid Phase Equilibria 405 (2015) 68–72
Then xi and yi are solved by Eqs. (3) and (4): xi ¼
yi ¼
g
P g j Pj i Pi
g
(5)
j Pj
xi g P
i Pi
(6)
Aij ¼
lij ljj vi exp vj RT
(11)
where vi and vj are the molar volumes of components i and j which are written as a functions of temperature, lii , ljj and lij lij ¼ lji , which are the interaction energies i–i, j–j, and i–j pairs, respectively. 4. Results and discussion
3.2. Wilson equation Activity coefficient of component in liquid phase is one of the key roles in VLE phase diagram calculation. To obtain VLE from calculation, thermodynamic models are efficient methods and the Wilson equation is considered to be one of the most successful models [13,14]. According to the well-known Wilson equation [15], the excess Gibbs energy GE of a multicomponent solution is given as 0 1 X X GE ¼ xi ln@1 xj Aji A RT i j
(7)
where R is the gas constant, and T the absolute temperature, xi is the mole fraction of component i and Aji is a positive adjustable parameter (Aii ¼ Ajj ¼ 1). For a binary mixture i-j, the respective activity coefficients of component i and j are: Aji Aij (8) lng i ¼ ln xi þ xj Aji þ xj xi þ xj Aji xj þ xi Aij lng j ¼ ln xj þ xi Aij þ xi
Aij Aji xj þ xi Aij xi þ xj Aji
The Wilson parameters Aji and Aij are expressed by: vj lji lii Aji ¼ exp RT vi
(9)
The Wilson parameters Aji and Aij can be obtained by the Newton–Raphson methodology if experimental activity coefficients are known. The experimental data of Cu–Pb system [16] were used for fitting the Wilson parameters using Eqs. (8) and (9). The calculated results of Aji and Aij for the Cu–Pb system at 1473 K are 0.398 and 0.218, respectively. Substituting the parameters Aji and Aij into Eqs. (8) and (9), the activity coefficients of components of Cu–Pb alloy can be calculated as shown in Fig. 2. It can be seen from Fig. 2 that the calculated values are in good agreement with the experimental data [16] which are also listed in Table 3. For comparing with experimental data, the average relative error is given by m ai;cal ai;exp 100X S¼ j j m i¼1 ai;exp
(12)
and the average standard error is expressed by " S¼
m 1X ða ai;exp Þ2 m i¼1 i;cal
#12 (13)
where ai;exp is the activity of experimental data and ai;cal is the calculated result using the Wilson equation, respectively. m is the number of data points. If we assume that lji lii and lij ljj in Eqs. (10) and (11) are independent of temperature T, the values of A0ji and A0ij at other
(10)
temperature T 0 should be calculated as follows: A0ji ¼
[(Fig._2)TD$IG]
A0ij ¼
v0j v0i
Aji vj =vi
T0 T
(14)
T v0i Aij T0 v0j vi =vj
(15)
Table 3 Comparison between the calculated values via Eqs. (8) and (9) and the experimental data [16] of Cu–Pb alloy at 1473 K. xPb 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 S Fig. 2. Comparison of the predicted activities of the Wilson equation (lines) with experimental data (symbols) of Cu–Pb alloy at 1473 K.
S ð%Þ
aPb;exp
aCu;exp
aPb;cal
aCu;cal
g Pb;exp
g Cu;exp
g Pb;cal
g Cu;cal
0.450 0.610 0.661 0.678 0.694 0.720 0.762 0.824 0.905
0.922 0.877 0.855 0.844 0.828 0.791 0.709 0.557 0.319
0.446 0.592 0.661 0.703 0.738 0.772 0.810 0.856 0.916 0.032 3.645
0.928 0.886 0.855 0.826 0.794 0.752 0.687 0.579 0.384 0.030 4.504
4.504 3.050 2.203 1.696 1.387 1.199 1.089 1.030 1.005
1.024 1.097 1.222 1.406 1.657 1.977 2.362 2.785 3.189
4.473 2.963 2.203 1.760 1.477 1.288 1.158 1.071 1.018
1.031 1.108 1.222 1.378 1.590 1.881 2.292 2.899 3.855
C. Zhang et al. / Fluid Phase Equilibria 405 (2015) 68–72
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Table 4 Saturated vapor pressure experimental equations of Cu and Pb in liquid stated [17,18]. i
Vapor pressure equation (mm Hg)
Temperature (K)
Cu
lgðp =atmÞ ¼ 5:849 16415T 1
505 2875
Pb
lgðp =atmÞ ¼ 4:911 9701T
0
0
1
Substituting the parameters Aji and Aij at different temperatures into Eqs. (8) and (9), the activity coefficients g i and g j can be calculated at corresponding temperatures. T-x diagram for Cu–Pb binary alloy system can be obtained by substituting the corresponding g Cu , g Pb , P, pCu and pPb at different temperatures into Eqs. (5) and (6), and the content of Pb in vapor and liquid phase can then be obtained. The saturated vapor pressure of Cu and Pb can be calculated by the saturated vapor equations shown in Table 4 [17,18]. This is done by an iterative procedures by varying xPb to obtain an approximate temperature until the system pressure P, fixed by g Cu and g Pb , equals the vacuum degree we set. The calculation for P-x diagram is somewhat similar to T-x diagram. For the system temperature, T, it is a constant and we can get g Cu and g Pb from Eqs. (8) and (9) by setting a series of values for xPb . Then substituting these values into Eq. (4), the system pressure P can be obtained, respectively, and yPb can be obtained from Eq. (6). Finally, P-x phase diagram for Cu–Pb binary alloy system can be generated with xPb , yPb and P. T-x diagram for Cu–Pb under 5 10 Pa with experimental data (1223 1423 K) is shown in Fig. 3(a) and P-x diagram for Cu–Pb at 1200 1600 K is shown in Fig. 3(b).
601 2022
V mi cm3 =mol h i 7:94 1 þ 1:0 104 ðT 1356Þ h i 19:42 1 þ 1:24 104 ðT 600Þ
Fig. 3(a) shows that the distillation temperature increases with increasing system pressure. And when the temperature falls below 1300 K, the content of Cu left in liquid phase under 5 Pa is much higher than 10 Pa which indicates that low pressures have a positive effect on the separation of Pb and Cu. What is more, the content of Cu in vapor phase increases with the temperature. This is because there will be more Cu evaporating into vapor phase than Pb at higher temperatures. The T-x curve of 5 Pa, where the temperatures ranges from 1200 to 1300 K, indicates that the vapor and liquid product reaches the rich point at the same temperature, which corresponds to the content of Pb in vapor range from 0.9999 to 0.9984 and the content of Cu in liquid range from 0.9982 to 0.9972. This temperature range can separate Pb and Cu at high purity. Similarly, from the P-x diagram of Cu–Pb shown in Fig. 3(b), we can achieve the same results. According to the VLE phase diagrams, we can predict an optimizing experimental condition of the vacuum process. For example, based on the T-x phase diagram, if the purity of Cu we wanted is higher than 0.9999, then the distillation temperature at 5 Pa must not be lower than 1548.3 K while the content of Pb in vapor phase will be less than 0.7113. A multistage distillation process is needed in order to obtain Pb of high purity. The specific
[(Fig._3)TD$IG]
Fig. 3. Phase diagrams of Cu–Pb alloy: (a) T-x curves from 5 to 10 Pa; (b) P-x curves at 1200 K, 1400 K and 1600 K.
[(Fig._4)TD$IG]
Fig. 4. Enlarged part of Fig. 3. (a): (a) xPb range from 0.000–0.010; (b) xPb range from 0.980–1.000.
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C. Zhang et al. / Fluid Phase Equilibria 405 (2015) 68–72
temperature for every stage of multistage distillation can be also predicted quantitatively by the T-x phase diagram. To have a better comparison between the experimental and calculations, Fig. 4(a) and (b) shows an enlarged segment of Fig. 3. (a) with xPb ranging from 0.000 to 0.010 and 0.980 to 1.000, respectively. We can obviously find that the calculated VLE phase diagrams of Cu–Pb binary alloy system by this method are in reasonable agreement with the experimental data. In other words, the VLE phase diagrams we obtained by this method are available for analyzing and predicting the process of vacuum distillation for Cu–Pb alloy. However, there is still some deviations between the calculations and experimental data which mainly arise from the mass loss during the experiment and the deviation of the experimental conditions away from the ideal equilibrium state. The Wilson equation that we adopted during calculations will also bring some certain errors. 5. Conclusions In this work, the experiment of vacuum distillation of Cu–Pb binary alloy was performed. The present experimental results indicate that Pb can be satisfactorily removed from crude copper. It is helpful in controlling the elimination of lead from crude copper or copper from crude lead by vacuum distillation. The Wilson equation provides a good representation of excess Gibbs energies for Cu–Pb alloy system. The VLE phase diagrams of Cu–Pb alloy system in vacuum distillation were calculated based on VLE calculation and Wilson equation. The agreement of the VLE phase diagrams with the experimental data indicates that the calculation method of VLE is reliable for the process of vacuum distillation of alloys. The VLE phase diagrams can be used to predict the separation degree and the products composition quantitatively for vacuum metallurgy. From temperature-composition (T-x) and pressure-composition (P-x) phase diagrams, we can set the processing conditions according to the purity of products. This will provide an efficient and convenient way to guide the process of vacuum metallurgy.
Acknowledgements The authors acknowledge the funding provided through the Fund of [74_TD$IF]5National Natural Science Foundation of China under Grant Nos. 51364018 and u1202271, the Applied Fundamental Research Foundation of Yunnan Province under Grant Nos. 2012FB126 and 2013FZ033, the Program for Innovative Research Team in University of Ministry of Education of China under Grant No. IRT1250, and the Key Areas Innovation Team of Ministry of Science and Technology of China under Grant No. 2014RA4018. References [1] O. Winkler, R. Bakish, Vacuum Metallurgy, Elsevier London, UK, 1971. [2] Y.N. Dai, Vacuum Metallurgy of Nonferrous Metals, Metallurgical Industry Press, Beijing, 2009 (in Chinese). [3] Y.N. Dai, Trans. Nonferrous Met. Soc. China 9 (1977) 24–30. [4] Y.N. Dai, Non-ferrous Metal 32 (1980) 73–79. [5] G.B. Jia, B. Yang, D.C. Liu, Trans. Nonferrous Met. Soc. China 23 (2013) 1822–1831. [6] H.W. Yang, B. Yang, B.Q. Xu, D.C. Liu, D.P. Tao, Vacuum 86 (2012) 1296–1299. [7] H.W. Yang, B.Q. Xu, B. Yang, W.H. Ma, D.P. Tao, Fluid Phase Equilib. 314 (2012) 78–81. [8] S.M. Walas, Phase Equilibria in Chemical Engineering, Butterworth Boston, 1985. [9] A. Tamir, J. Wisniak, Chem. Eng. Sci. 30 (1975) 335–342. [10] J.J. Chen, W.L. Jiang, B. Yang, D.C. Liu, Y.N. Dai, Chin. J. Vac. Sci. Technol. 33 (2013) 490–495. [11] H. Orbey, S.I. Sandler, Modeling Vapor–liquid Equilibria: Cubic Equations of State and Their Mixing Rules, Cambridge University Press, 1998. [12] L. Theodore, F. Ricci, T. Vanvliet, Thermodynamics for the Practicing Engineer, John Wiley and Sons, 2009. [13] S. Govindaswamy, A. Andiappan, S. Lakshmanan, J. Chem. Eng. Data 21 (1976) 366–369. [14] INAGATA, J. Chem. Eng. Jpn. 6 (1973) 18–30. [15] G.M. Wilson, J. Am. Chem. Soc. 86 (1964) 127–130. [16] H. Landolt, R. Börnstein, Phase Equilibria Crystallographic and Thermodynamic Data of Binary Alloys, Springer-Verlag, 1993. [17] O. Kubaschewski, C.B. Alcock, Metallurgical Thermochemistry (Revised and Enlarged), 5th ed., Pergamon Press, Oxford, 1979. [18] T. Iida, R.I. Guthrie, The Physical Properties of Liquid Metals, Clarendon Press, Walton Street, Oxford OX 2 6 DP, UK, 1988.
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 calculation of vapor–liquid equilibria for Cu–Pb binary alloy in vacuum distillation Cheng Zhangb , WenLong Jiangc, Bin Yangc, DaChun Liuc , BaoQiang Xuc , HongWei Yanga,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 18 April 2015 Received in revised form 18 July 2015 Accepted 23 July 2015 Available online 29 July 2015
In this study, vacuum distillation experiments of high-lead crude copper were performed under the vapor pressure 5 Pa. The content of lead in crude copper was reduced from 15% to less than 0.01% in a single stage distillation process with residual vapor pressures of below 10 Pa, distillation temperatures of 1423 K and distillation times of 60 min. The vapor–liquid equilibrium (VLE) phase diagrams of Cu–Pb binary alloy in vacuum distillation were calculated using the Wilson equation. Thermodynamic experimental data taken from literature were used for calculating Wilson equation temperature dependent interaction parameters. The calculations give a satisfactory accuracy with the experimental data for separation of Cu–Pb alloy in vacuum distillation. The results indicate that VLE phase diagrams under vacuum obtained by this method are reliable for predicting the process of vacuum distillation for Cu–Pb alloy. The VLE phase diagrams of alloys will have significant benefits for the industrial production of vacuum metallurgy especially for the process of multistage distillation in the vacuum furnace. ã 2015 Elsevier B.V. All rights reserved.
Keywords: Vacuum distillation VLE phase diagram Cu–Pb alloy Wilson equation Thermodynamic properties
1. Introduction The use of vacuum distillation for separating various elements from nonferrous alloys have been very successful and is expanding rapidly, largely due to its ability to achieve high metal recovery, low impurities in recovered metal, simplified flow sheet, good environmental protection, low operation costs and simple equipment [1,2]. Small-scale vacuum distillation experiments to purify the Pb contaminated alloys have been investigated in previous work and have reported good separation effects [3–5]. There is an increasing need to consider phase diagrams for vapor–liquid phase with the development of vacuum metallurgy. In our previous works [6,7], we only calculated the separation coefficients and vapor–liquid equilibrium composition of Pb-based alloys in vacuum distillation. However, the vapor–liquid equilibrium composition curve cannot provide an intuitive and convenient way to analyze the product component dependence of temperature or pressure in the design of vacuum distillation experiment. A
* Corresponding author at: The State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Kunming 650093, PR China. [73_TD$IF]Tel.: +86 13987157570. E-mail address: [email protected] (H. Yang). http://dx.doi.org/10.1016/j.fluid.2015.07.043 0378-3812/ ã 2015 Elsevier B.V. All rights reserved.
firm knowledge of the VLE relationships is a prerequisite to predict the process of vacuum distillation [8,9]. Crude copper usually contains lead as an impurity, the conventional separation method cannot be used when the lead is high. In this work, vacuum distillation of high-lead crude copper was investigated with vapor pressures ranging from 5 to 10 Pa. The VLE phase diagrams such as temperature-composition (T-x) and pressure-composition (P-x) curves of Cu–Pb alloy under vacuum are obtained based on the VLE calculation and the Wilson equation. The VLE phase diagrams can provide an intuitive way to predict the VLE relationships of alloy system under vacuum distillation continuously. The present work is available for obtaining the VLE phase diagrams of alloys which will bring an efficient and reliable way to analyze and predict the VLE data of alloys in vacuum distillation, especially for the process of multistage distillation in the vacuum furnace. 2. Experimental procedure The Cu–Pb alloy for the experiment was prepared from high purity metals using Pb and Cu with a purity of 99.99% and the content of Pb in Cu–Pb alloy is 15%. The information of experimental sample for the Cu–Pb alloy is listed in Table 1.
C. Zhang et al. / Fluid Phase Equilibria 405 (2015) 68–72
69
Table 1 The information of experimental sample for the Cu–Pb alloy. Chemical name
Source
Initial mole fraction purity
Purification method
Final mole fraction purity
Analysis method
Copper Lead
Yunnan tin company
0.85 0.15
Vacuum distillation
0.9982 0.0016
Gas–liquid chromatography Atomic absorption spectroscopy
Small-scale vacuum distillation experiments for Cu–Pb alloy were carried out in the vertical vacuum furnace in this work and the internal structure schematic diagram is shown in Fig. 1. Vacuum degree in the furnace were at the range of 5 10 Pa during the experiment. In the furnace, 50 g Cu–Pb alloy was placed in graphite crucible to be heated and melted after the vacuum degree reached to 5 Pa. With the temperature rising to a certain degree, lead and copper in liquid alloy will evaporate from the melt and solidified rapidly on the condenser. Melting temperatures of each experiment during this investigation were 1223 K, 1273 K, 1323 K, 1373 K and 1423 K, respectively. The relationship between distillation time and composition of distillation product has been investigated in our previous works [10] and the composition of distillation product started to approach a stable level when the time exceeds 30 minutes under 10 25 Pa and 1373 K. In other words, the stable level of composition of distillation product is the phase equilibrium of Cu–Pb system under some specified pressure and temperature. On this basis, 60 min was selected as the final distillation time in this work which allows the system to approach the phase equilibrium sufficiently. In addition, it can also minimizes the mass loss during experiment with increasing distillation time and reduce any errors associated the data that we obtained. The samples were collected from the volatile and residue, and then remelted, respectively, to determine the average components of the samples. The experimental data of the vapor-liquid phase equilibria for the Pb content in residuum (liquid phase) and volatiles (vapor phase) are listed in Table 2.
[(Fig._1)TD$IG]
Table 2 Experimental values of mole fraction xPb and yPb at temperature T, pressure P for the Cu–Pb alloy in vacuum distillation.a Experiment condition
Content of Pb (mole fraction)
Temperature (K)
Pressure (Pa) Time (min) xPb
yPb
1223 1273 1323 1373 1423
5 5 5 5 5
0.999022 0.997066 0.993500 0.988018 0.981629
60 60 60 60 60
0.005367 0.002886 0.000834 0.000308 0.000015
a Standard uncertainties u are uðTÞ ¼ 5K,uðPÞ ¼ 2Pa, uðxÞ ¼ 0:000002, and uðyÞ ¼ 0:000002.
Considering the high temperatures and low vapor pressure during the experiment, the experimental VLE data we collected by this method will bring some certain deviations from ideal condition. They are mainly rising from the following aspects. The purity of the distillation products are both high ranging from 0.98 to 1, the deviations caused by the mass loss will be magnified in the final results. What's more, during the process of temperature rising to a certain degree, there will have be some mass metal evaporated from the liquid phase and the system vacuum degree will be outside the range of 10 15 Pa during this heating time. All the factors above are unavoidable so far. 3. Method 3.1. VLE calculation For the rare case of a low-pressure and ideal mixture system, Raoult’s law applies to indicate the relationship of VLE which is expressed as [11,12] xi Pi ðTÞ ¼ yi P
(1)
where xi and yi are the mole fraction of species i in the liquid phase and vapor phase, respectively; T is the temperature; Pi and P are the saturation pressure of species i and the pressure of the system, respectively, in terms of temperature. Due to most of the liquid solutions for alloy systems cannot be considered as ideal, Raoult’s law will give highly inaccurate results. For these systems under vacuum, the liquid phase is not an ideal solution but the pressure is low enough so that the vapor phase behaves as an ideal gas. In this case, the deviations are taken into account by incorporating a correction factor, g , into Raoult’s law to quantitatively consider the deviations from ideality. Therefore, Raoult’s law can be modified as xi g i ðxi ; T; PÞPi ðTÞ ¼ yi P
(2)
where g i is activity coefficient of species i in terms of temperature, pressure and the mole fraction of species i. For a binary alloy system i-j,
Fig. 1. Schematic diagram of the internal structure of the vertical vacuum furnace: 1 furnace lid; 2 furnace body; 3 furnace bottom; 4 electrode; 5 cold plate; 6 observation door; 7 heat holding cover; 8 heating unit; 9 graphite evaporator.
xi þ xj ¼ 1; yi þ yj ¼ 1
(3)
P ¼ xi g i Pi þ xj g j Pj ¼ xi g i Pi þ ð1 xi Þg j Pj
(4)
70
C. Zhang et al. / Fluid Phase Equilibria 405 (2015) 68–72
Then xi and yi are solved by Eqs. (3) and (4): xi ¼
yi ¼
g
P g j Pj i Pi
g
(5)
j Pj
xi g P
i Pi
(6)
Aij ¼
lij ljj vi exp vj RT
(11)
where vi and vj are the molar volumes of components i and j which are written as a functions of temperature, lii , ljj and lij lij ¼ lji , which are the interaction energies i–i, j–j, and i–j pairs, respectively. 4. Results and discussion
3.2. Wilson equation Activity coefficient of component in liquid phase is one of the key roles in VLE phase diagram calculation. To obtain VLE from calculation, thermodynamic models are efficient methods and the Wilson equation is considered to be one of the most successful models [13,14]. According to the well-known Wilson equation [15], the excess Gibbs energy GE of a multicomponent solution is given as 0 1 X X GE ¼ xi ln@1 xj Aji A RT i j
(7)
where R is the gas constant, and T the absolute temperature, xi is the mole fraction of component i and Aji is a positive adjustable parameter (Aii ¼ Ajj ¼ 1). For a binary mixture i-j, the respective activity coefficients of component i and j are: Aji Aij (8) lng i ¼ ln xi þ xj Aji þ xj xi þ xj Aji xj þ xi Aij lng j ¼ ln xj þ xi Aij þ xi
Aij Aji xj þ xi Aij xi þ xj Aji
The Wilson parameters Aji and Aij are expressed by: vj lji lii Aji ¼ exp RT vi
(9)
The Wilson parameters Aji and Aij can be obtained by the Newton–Raphson methodology if experimental activity coefficients are known. The experimental data of Cu–Pb system [16] were used for fitting the Wilson parameters using Eqs. (8) and (9). The calculated results of Aji and Aij for the Cu–Pb system at 1473 K are 0.398 and 0.218, respectively. Substituting the parameters Aji and Aij into Eqs. (8) and (9), the activity coefficients of components of Cu–Pb alloy can be calculated as shown in Fig. 2. It can be seen from Fig. 2 that the calculated values are in good agreement with the experimental data [16] which are also listed in Table 3. For comparing with experimental data, the average relative error is given by m ai;cal ai;exp 100X S¼ j j m i¼1 ai;exp
(12)
and the average standard error is expressed by " S¼
m 1X ða ai;exp Þ2 m i¼1 i;cal
#12 (13)
where ai;exp is the activity of experimental data and ai;cal is the calculated result using the Wilson equation, respectively. m is the number of data points. If we assume that lji lii and lij ljj in Eqs. (10) and (11) are independent of temperature T, the values of A0ji and A0ij at other
(10)
temperature T 0 should be calculated as follows: A0ji ¼
[(Fig._2)TD$IG]
A0ij ¼
v0j v0i
Aji vj =vi
T0 T
(14)
T v0i Aij T0 v0j vi =vj
(15)
Table 3 Comparison between the calculated values via Eqs. (8) and (9) and the experimental data [16] of Cu–Pb alloy at 1473 K. xPb 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 S Fig. 2. Comparison of the predicted activities of the Wilson equation (lines) with experimental data (symbols) of Cu–Pb alloy at 1473 K.
S ð%Þ
aPb;exp
aCu;exp
aPb;cal
aCu;cal
g Pb;exp
g Cu;exp
g Pb;cal
g Cu;cal
0.450 0.610 0.661 0.678 0.694 0.720 0.762 0.824 0.905
0.922 0.877 0.855 0.844 0.828 0.791 0.709 0.557 0.319
0.446 0.592 0.661 0.703 0.738 0.772 0.810 0.856 0.916 0.032 3.645
0.928 0.886 0.855 0.826 0.794 0.752 0.687 0.579 0.384 0.030 4.504
4.504 3.050 2.203 1.696 1.387 1.199 1.089 1.030 1.005
1.024 1.097 1.222 1.406 1.657 1.977 2.362 2.785 3.189
4.473 2.963 2.203 1.760 1.477 1.288 1.158 1.071 1.018
1.031 1.108 1.222 1.378 1.590 1.881 2.292 2.899 3.855
C. Zhang et al. / Fluid Phase Equilibria 405 (2015) 68–72
71
Table 4 Saturated vapor pressure experimental equations of Cu and Pb in liquid stated [17,18]. i
Vapor pressure equation (mm Hg)
Temperature (K)
Cu
lgðp =atmÞ ¼ 5:849 16415T 1
505 2875
Pb
lgðp =atmÞ ¼ 4:911 9701T
0
0
1
Substituting the parameters Aji and Aij at different temperatures into Eqs. (8) and (9), the activity coefficients g i and g j can be calculated at corresponding temperatures. T-x diagram for Cu–Pb binary alloy system can be obtained by substituting the corresponding g Cu , g Pb , P, pCu and pPb at different temperatures into Eqs. (5) and (6), and the content of Pb in vapor and liquid phase can then be obtained. The saturated vapor pressure of Cu and Pb can be calculated by the saturated vapor equations shown in Table 4 [17,18]. This is done by an iterative procedures by varying xPb to obtain an approximate temperature until the system pressure P, fixed by g Cu and g Pb , equals the vacuum degree we set. The calculation for P-x diagram is somewhat similar to T-x diagram. For the system temperature, T, it is a constant and we can get g Cu and g Pb from Eqs. (8) and (9) by setting a series of values for xPb . Then substituting these values into Eq. (4), the system pressure P can be obtained, respectively, and yPb can be obtained from Eq. (6). Finally, P-x phase diagram for Cu–Pb binary alloy system can be generated with xPb , yPb and P. T-x diagram for Cu–Pb under 5 10 Pa with experimental data (1223 1423 K) is shown in Fig. 3(a) and P-x diagram for Cu–Pb at 1200 1600 K is shown in Fig. 3(b).
601 2022
V mi cm3 =mol h i 7:94 1 þ 1:0 104 ðT 1356Þ h i 19:42 1 þ 1:24 104 ðT 600Þ
Fig. 3(a) shows that the distillation temperature increases with increasing system pressure. And when the temperature falls below 1300 K, the content of Cu left in liquid phase under 5 Pa is much higher than 10 Pa which indicates that low pressures have a positive effect on the separation of Pb and Cu. What is more, the content of Cu in vapor phase increases with the temperature. This is because there will be more Cu evaporating into vapor phase than Pb at higher temperatures. The T-x curve of 5 Pa, where the temperatures ranges from 1200 to 1300 K, indicates that the vapor and liquid product reaches the rich point at the same temperature, which corresponds to the content of Pb in vapor range from 0.9999 to 0.9984 and the content of Cu in liquid range from 0.9982 to 0.9972. This temperature range can separate Pb and Cu at high purity. Similarly, from the P-x diagram of Cu–Pb shown in Fig. 3(b), we can achieve the same results. According to the VLE phase diagrams, we can predict an optimizing experimental condition of the vacuum process. For example, based on the T-x phase diagram, if the purity of Cu we wanted is higher than 0.9999, then the distillation temperature at 5 Pa must not be lower than 1548.3 K while the content of Pb in vapor phase will be less than 0.7113. A multistage distillation process is needed in order to obtain Pb of high purity. The specific
[(Fig._3)TD$IG]
Fig. 3. Phase diagrams of Cu–Pb alloy: (a) T-x curves from 5 to 10 Pa; (b) P-x curves at 1200 K, 1400 K and 1600 K.
[(Fig._4)TD$IG]
Fig. 4. Enlarged part of Fig. 3. (a): (a) xPb range from 0.000–0.010; (b) xPb range from 0.980–1.000.
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C. Zhang et al. / Fluid Phase Equilibria 405 (2015) 68–72
temperature for every stage of multistage distillation can be also predicted quantitatively by the T-x phase diagram. To have a better comparison between the experimental and calculations, Fig. 4(a) and (b) shows an enlarged segment of Fig. 3. (a) with xPb ranging from 0.000 to 0.010 and 0.980 to 1.000, respectively. We can obviously find that the calculated VLE phase diagrams of Cu–Pb binary alloy system by this method are in reasonable agreement with the experimental data. In other words, the VLE phase diagrams we obtained by this method are available for analyzing and predicting the process of vacuum distillation for Cu–Pb alloy. However, there is still some deviations between the calculations and experimental data which mainly arise from the mass loss during the experiment and the deviation of the experimental conditions away from the ideal equilibrium state. The Wilson equation that we adopted during calculations will also bring some certain errors. 5. Conclusions In this work, the experiment of vacuum distillation of Cu–Pb binary alloy was performed. The present experimental results indicate that Pb can be satisfactorily removed from crude copper. It is helpful in controlling the elimination of lead from crude copper or copper from crude lead by vacuum distillation. The Wilson equation provides a good representation of excess Gibbs energies for Cu–Pb alloy system. The VLE phase diagrams of Cu–Pb alloy system in vacuum distillation were calculated based on VLE calculation and Wilson equation. The agreement of the VLE phase diagrams with the experimental data indicates that the calculation method of VLE is reliable for the process of vacuum distillation of alloys. The VLE phase diagrams can be used to predict the separation degree and the products composition quantitatively for vacuum metallurgy. From temperature-composition (T-x) and pressure-composition (P-x) phase diagrams, we can set the processing conditions according to the purity of products. This will provide an efficient and convenient way to guide the process of vacuum metallurgy.
Acknowledgements The authors acknowledge the funding provided through the Fund of [74_TD$IF]5National Natural Science Foundation of China under Grant Nos. 51364018 and u1202271, the Applied Fundamental Research Foundation of Yunnan Province under Grant Nos. 2012FB126 and 2013FZ033, the Program for Innovative Research Team in University of Ministry of Education of China under Grant No. IRT1250, and the Key Areas Innovation Team of Ministry of Science and Technology of China under Grant No. 2014RA4018. References [1] O. Winkler, R. Bakish, Vacuum Metallurgy, Elsevier London, UK, 1971. [2] Y.N. Dai, Vacuum Metallurgy of Nonferrous Metals, Metallurgical Industry Press, Beijing, 2009 (in Chinese). [3] Y.N. Dai, Trans. Nonferrous Met. Soc. China 9 (1977) 24–30. [4] Y.N. Dai, Non-ferrous Metal 32 (1980) 73–79. [5] G.B. Jia, B. Yang, D.C. Liu, Trans. Nonferrous Met. Soc. China 23 (2013) 1822–1831. [6] H.W. Yang, B. Yang, B.Q. Xu, D.C. Liu, D.P. Tao, Vacuum 86 (2012) 1296–1299. [7] H.W. Yang, B.Q. Xu, B. Yang, W.H. Ma, D.P. Tao, Fluid Phase Equilib. 314 (2012) 78–81. [8] S.M. Walas, Phase Equilibria in Chemical Engineering, Butterworth Boston, 1985. [9] A. Tamir, J. Wisniak, Chem. Eng. Sci. 30 (1975) 335–342. [10] J.J. Chen, W.L. Jiang, B. Yang, D.C. Liu, Y.N. Dai, Chin. J. Vac. Sci. Technol. 33 (2013) 490–495. [11] H. Orbey, S.I. Sandler, Modeling Vapor–liquid Equilibria: Cubic Equations of State and Their Mixing Rules, Cambridge University Press, 1998. [12] L. Theodore, F. Ricci, T. Vanvliet, Thermodynamics for the Practicing Engineer, John Wiley and Sons, 2009. [13] S. Govindaswamy, A. Andiappan, S. Lakshmanan, J. Chem. Eng. Data 21 (1976) 366–369. [14] INAGATA, J. Chem. Eng. Jpn. 6 (1973) 18–30. [15] G.M. Wilson, J. Am. Chem. Soc. 86 (1964) 127–130. [16] H. Landolt, R. Börnstein, Phase Equilibria Crystallographic and Thermodynamic Data of Binary Alloys, Springer-Verlag, 1993. [17] O. Kubaschewski, C.B. Alcock, Metallurgical Thermochemistry (Revised and Enlarged), 5th ed., Pergamon Press, Oxford, 1979. [18] T. Iida, R.I. Guthrie, The Physical Properties of Liquid Metals, Clarendon Press, Walton Street, Oxford OX 2 6 DP, UK, 1988.