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Experiment and model for the surface tension of carbonated MEA–MDEA aqueous solutions
Fluid Phase Equilibria 337 (2013) 83–88
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Experiment and model for the surface tension of carbonated MEA–MDEA aqueous solutions Dong Fu ∗ , Lin Wei, SongTao Liu School of Environmental Science and Engineering, North China Electric Power University, Baoding 071003, China
a r t i c l e
i n f o
Article history: Received 14 May 2012 Received in revised form 7 October 2012 Accepted 16 October 2012 Available online 23 October 2012 Keywords: Surface tension MEA–MDEA aqueous solution CO2 loading
a b s t r a c t Surface tensions of CO2 unloaded and CO2 loaded MEA–MDEA aqueous solutions were measured by using the BZY-1 surface tension meter, which employs the Wilhemy plate principle. For CO2 unloaded solutions, the temperatures ranged from 293.15 to 333.15 K, and the mass fractions of MEA (wMEA ) and MDEA (wMDEA ) respectively ranged from 0.05 to 0.20, and 0.05 to 0.45. For CO2 loaded solutions, the temperatures ranged from 293.15 to 323.15 K, and wMEA and wMDEA respectively ranged from 0.05 to 0.10 and 0.30 to 0.45. The uncertainty of the surface tensions is ±0.1 mN m−1 . A model was proposed to correlate the surface tensions of both CO2 loaded and CO2 unloaded solutions. For CO2 unloaded MEA–MDEA solutions, with 3 adjustable parameters as input, the average relative deviation (ARD) between experiments and calculations is 1.63%. For CO2 loaded MEA–MDEA solutions, with 5 adjustable parameters as input, ARD is 1.76%. The temperature, mass fractions of amines and CO2 loading dependence of the surface tensions were demonstrated on the basis of experiments and calculations. © 2012 Elsevier B.V. All rights reserved.
1. Introduction In recent decades, atmospheric levels of CO2 have increased rapidly due to the utilization of great amount of fossil fuel. The reduction of CO2 emissions became a global issue [1,2]. Aqueous solutions of alkanolamines like monoethanolamine (MEA) and Nmethyldiethanolamine (MDEA) are widely used for the removal of CO2 from a variety of gas streams [3–8]. Among the alkanolamines series, MDEA takes the advantages of high resistance to thermal and chemical degradation, low solution vapor pressure (minimum solvent loss during regeneration), and low enthalpy of absorption (low energy requirement for regeneration). However, compared with other amines like MEA, an MDEA aqueous solution has a lower absorption rate. Adding small amounts of MEA to an aqueous solution of MDEA has found widespread application in the removal of CO2 . The mixtures of MEA and MDEA preserve the high rate of the reaction of MEA with CO2 , and the low enthalpy of the reaction of MDEA with CO2 , hence lead to higher absorption rates in the absorber column, yet lower heat of regeneration in the stripper section [5,6]. Surface tensions of aqueous solutions are required when designing or simulating an absorption column for CO2 absorption
∗ Corresponding author. Tel.: +86 312 7522037. E-mail address: [email protected] (D. Fu). 0378-3812/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fluid.2012.10.013
associated with chemical reactions. Until now, there are some experiments concerning the surface tensions of aqueous solutions containing MEA and MDEA [9–16]. In particular, Vazquez et al. [12] and Alvarez et al. [15] systematically measured the surface tensions of MEA aqueous solutions and MDEA aqueous solutions at temperatures from 298.15 to 323.15 K. They also measured the surface tensions of MEA–MDEA aqueous solutions at temperatures from 298.15 to 323.15 K, with the total mass fraction of amines wMEA + wMDEA = 0.5. However, the surface tensions of MEA–MDEA aqueous solutions at relatively low mass fractions of amines, e.g., wMEA + wMDEA = 0.2, 0.3 and 0.4 are rare. Moreover, the surface tensions of carbonated MEA–MDEA aqueous solutions have been rarely reported, and due to the lack of the experiments and theoretical models, the effects of mass fraction of amines, temperatures and CO2 loading have not been well documented by far. To demonstrate the temperature, mass fraction of amines and CO2 loading dependence of the surface tensions, the surface tensions of CO2 unloaded (temperature ranging from 293.15 to 333.15 K, wMEA and wMDEA respectively ranging from 0.05 to 0.20, and 0.05 to 0.45) and CO2 loaded (temperature ranging from 293.15 to 323.15 K, wMEA and wMDEA respectively ranging from 0.05 to 0.10 and 0.30 to 0.45, CO2 loading ranging from 0.1 to 0.5) MEA–MDEA aqueous solutions were measured by using the BZY-1 surface tension meter, which employs the Wilhemy plate principle. A model was proposed to correlate the surface tensions of both CO2 unloaded and CO2 loaded solutions.
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D. Fu et al. / Fluid Phase Equilibria 337 (2013) 83–88
Table 1 Sample description. Chemical
CAS No.
Purity (in mass fraction %)
MEA
141-43-5
99.4
MDEA
105-59-9
99.5
2. Experimental 2.1. Materials Both MEA and MDEA were purchased from HuaXin Chemical Co. The sample description is shown in Table 1. They were used without further purification. Aqueous solutions of MEA–MDEA were prepared by adding doubly distilled water. 2.2. Apparatus and procedure The surface tension was measured by using the BZY-1 surface tension meter produced by Shanghai Hengping Instrument Factory. BZY-1 meter employs the Wilhemy plate principle, i.e., the maximum tensile force competing with the surface tension is measured when the bottom edge of platinum parallel to the interface and just touches it. The measurement ranges for temperature and surface tensions are respectively 268.15–383.15 K and 0.1–400.0 mN m−1 . The sensitivity, repeatability and uncertainty are respectively 0.1 mN m−1 , 0.1 mN m−1 , and 0.1 mN m−1 . The size-volume of the different samples used in BZY-1 meter is 20 ml. During the experiments, the copper pan in the host of the BZY-1 meter is connected with the thermostatic bath (CH-1006, uncertainty ±0.1 K). Via the circulation of the water, the temperature of the water in the copper pan is kept the same as that in the thermostatic bath, hence the temperature readings in the surface tension measuring cell may be regulated within 0.1 K. The aqueous solution is put into the solution container immersed in the copper pan and its temperature can be measured by a thermocouple. The scale reading of the thermocouple has been well calibrated by a mercury thermometer (uncertainty ±0.05 K). To verify the reliability of the equipment, the surface tensions of deionized water, pure MEA and pure MDEA were measured at 298.15 K and 318.15 K and compared with experimental values from previous reports [12,15]. The relative deviations are shown in Table 2. The surface tensions of both deionized water and pure amines were measured three times with standard deviation less than 0.3%, indicating that the experimental equipment is reliable. The carbonated MEA–MDEA aqueous solutions were prepared according to the methods mentioned in the work of Amundsen et al. [17], Weiland et al. [20] and Fu et al. [21,22]: CO2 -unloaded MEA–MDEA aqueous solution (in the preparation of aqueous solutions, the uncertainty of the electronic balance is ±0.1 mg) was put into a volumetric flask immersed in the thermostatic bath with a built-in stirrer for uniform temperature distribution. The bath temperature was regulated within 0.1 K. CO2 from a high-pressure tank was inlet into the volumetric flask at certain temperatures (CO2 pressure is 1 atm). Once the carbonated solution was prepared, varying proportions of the unloaded and loaded solutions
Molecular mass (Da)
Density (g cm−3 )
61.09
298.15 K
1.0003 [17]
119.16
303.15 K 323.15 K
1.0337 [18] 1.0250 [19]
were mixed together to produce a set of samples having a fixed MEA/MDEA-to-water ratio but with varying CO2 loading. CO2 loading, ˛, is defined as ˛ = nCO2 /(nMEA + nMDEA ), in which nCO2 is the mole of loaded CO2 , nMEA and nMDEA are respectively the mole of MEA and MDEA in the unloaded aqueous solutions. It is worth noting that CO2 loading is expected to be a major uncertainty in the experiment. In this work, carbonated solution was prepared at non-equilibrium conditions, under which the thermodynamic equilibrium (saturated absorption, corresponding to maximum CO2 loading, ˛max ) cannot be achieved. The surface tension was measured in an open measuring cell. It refers to the liquid (aqueous solution)–vapor (air + water vapor and amines vapor) surface tension, and different to the surface tension measured at equilibrium state (closed system, with equilibrium liquid phase and vapor phase). However, under low pressures, as the density of the vapor phase is too small, no matter using Wilhemy plate principle or drop-volume method, the contribution of vapor phase to the surface tension is very small. Hence the surface tensions presented in this work are very close to those measured at equilibrium state. The key is that certain amount of CO2 will escape when loaded solution is mixed with unloaded solution and put into the open measuring cell. Moreover, atmospheric CO2 and humidity have some effects on CO2 loading and solution concentration. To estimate the uncertainty of CO2 loadings, we selected 2 diluted samples (as shown in Table 4, T = 313.15 K, wMEA = 0.05, wMDEA = 0.35, ˛ = 0.2 and 0.4) and determined the CO2 loadings using the analysis method based on the precipitation of BaCO3 [17,20]. The obtained CO2 loading ˛ are respectively 0.198 and 0.394, indicating that the real values of CO2 loading may be lower than those list in Table 4, however, as documented by Amundsen et al. [17] and Weiland et al. [20], the uncertainty of CO2 loading is less than 2%. 3. Results and discussion Surface tensions of CO2 unloaded MEA–MDEA aqueous solutions at different temperatures and different mass fraction of amines are shown in Table 3. Some of the experimental data are compared with the work of Vazquez et al. [12] and Alvarez et al. [15]. The average relative deviations between our results and those from the work of Vazquez et al. [12] and Alvarez et al. [15] are respectively 0.81% and 0.33%. Surface tensions of the CO2 loaded MEA–MDEA aqueous solutions at series of temperatures, mass fraction of amines and CO2 loadings are shown in Table 4. Besides experimental measurements, models that can calculate the surface tensions of concerned systems are also important. By far, some equations have been proposed for modeling the surface tensions of amine aqueous solutions, in particular, Alvarez et al. [15] correlated the experimental data of MEA–MDEA aqueous solutions with high accuracy. However, due to the complexity of the
Table 2 Surface tension (␥/mN m−1 ) of pure water, MEA and MDEA and the relative deviations (RD) between the experiments from this work and those from literatures [12,15]. Components
298.2 K exp
Water MEA MDEA
72.0 48.9 38.6
318.2 K lit 72.0 [12,15] 49.0 [12] 38.9 [15]
RD%
exp
0.0 0.2 0.8
69.0 45.5 37.0
lit 68.8 [12,15] 45.7 [12] 37.2 [15]
RD% 0.3 0.4 0.5
D. Fu et al. / Fluid Phase Equilibria 337 (2013) 83–88
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Table 3 Surface tensions of MEA–MDEA aqueous solutions at different mass fractions (wMEA , wMDEA ) and temperatures. wMEA
0.05
0.10
0.15
0.20
a b
wMDEA
␥/(mN m−1 ) T/K = 293.2
T/K = 298.2
T/K = 303.2
T/K = 308.2
T/K = 313.2
T/K = 318.2
T/K = 323.2
T/K = 328.2
T/K = 333.2
0.15 0.25 0.35 0.45
60.3 56.1 53.1 50.9
59.5 55.4 52.3 50.0
58.4 54.2 51.1 48.9
57.9 53.5 50.4 48.2
56.9 52.5 49.4 47.2
56.1 51.6 48.5 46.3
55.1 50.6 47.4 45.4
54.5 49.7 46.6 44.3
53.2 48.6 45.7 43.4
0.10 0.20 0.30 0.40
61.5 57.3 54.3 51.7
60.9 56.5 53.6 51.0 50.83a
59.8 55.4 52.4 49.9 50.25a
59.1 54.8 51.8 49.2 49.51a
58.1 53.7 50.7 48.2 48.75a
57.3 52.9 49.9 47.3 48.28a
56.5 51.9 48.8 46.3 47.20a
55.5 51.1 48.0 45.4
54.6 50.0 46.6 44.3
0.05 0.15 0.25 0.35
62.6 58.5 55.4 52.7
61.8 57.8 54.6 51.9
60.7 56.5 53.6 50.8
60.2 55.7 52.8 50.1
59.4 55.2 52.1 49.2
58.5 54.4 51.3 48.3
57.7 53.3 50.2 47.4
57.0 52.5 49.3 46.6
56.0 51.4 48.3 45.5
0.00
63.7
61.2 61.06b 57.2 54.3 51.0 50.80a
60.5 60.17b 55.8 52.7 50.1 49.99a
59.5 59.49b 55.0 52.1 49.3 49.54a
58.4 58.09b 54.4 51.2 48.4 49.00a
57.0
59.6 56.4 53.5
62.1 61.84b 57.9 54.3 51.7 51.60a
58.1
0.10 0.20 0.30
62.8 62.63b 58.8 55.5 52.6 52.40a
53.5 50.3 47.5
52.2 49.3 46.4
From Ref. [15]. From Ref. [12].
Table 4 Surface tensions of carbonated MEA–MDEA aqueous solutions at different temperatures, mass fractions (wMEA , wMDEA ) and CO2 loadings (˛). wMEA
wMDEA
/(mN m−1 ) ˛ = 0.1
˛ = 0.2
˛ = 0.3
˛ = 0.4
˛ = 0.5
293.2
0.05 0.05 0.05 0.10 0.10 0.10
0.35 0.40 0.45 0.30 0.35 0.40
53.5 52.1 51.4 53.9 52.5 51.2
54.0 52.9 51.7 54.2 53.0 51.7
54.8 53.8 52.4 55.2 54.0 52.5
56.2 54.8 53.4 56.5 55.4 53.3
57.9 56.5 54.4 58.1 57.1 54.6
303.2
0.05 0.05 0.05 0.10 0.10 0.10
0.35 0.40 0.45 0.30 0.35 0.40
51.9 50.8 49.4 52.0 50.7 49.9
52.3 50.9 49.6 52.6 51.2 50.2
52.8 51.5 50.3 53.4 52.0 50.4
53.4 52.4 50.8 54.4 52.7 51.0
54.2 53.2 51.5 55.5 53.5 51.9
313.2
0.05 0.05 0.05 0.10 0.10 0.10
0.35 0.40 0.45 0.30 0.35 0.40
49.7 48.1 47.0 50.0 48.4 47.4
49.9 48.1 47.1 50.4 48.5 47.4
50.0 48.2 47.2 50.7 48.5 47.6
50.2 48.5 47.3 50.8 48.6 47.7
50.3 48.8 47.9 51.2 48.9 48.1
323.2
0.05 0.05 0.05 0.10 0.10 0.10
0.35 0.40 0.45 0.30 0.35 0.40
47.2 45.3 43.3 48.1 46.4 44.1
47.5 45.6 43.3 48.2 46.6 44.2
47.5 46.0 43.8 48.6 46.6 44.5
47.9 46.5 44.4 48.9 46.9 45.1
48.0 47.1 44.9 49.1 47.2 45.4
T/K
amine aqueous solutions, equations that simultaneously take the CO2 loading, amine concentration and temperature dependence into account are rare [21,22]. Moreover, for the carbonated systems, due to the great variety of ions, the application of advanced approaches like density gradient theory [23–28] to such systems is very difficult. In this work, the surface tension of CO2 unloaded MEA–MDEA aqueous solutions is formulated as following: aq = 0 + in which
0
and
= x1 x2 G12 + x1 x3 G13 + x2 x3 G23
(3)
where the subscripts 1, 2 and 3 stand for MEA, MDEA and water, respectively. xi is the mole fraction of component i in the aqueous solution, i is the surface tension of pure component i, which can be expressed as a function of temperature by fitting to the experimental data [12,15]. Gij is expressed as the function of T and mass fractions of amines:
(1) are expressed as:
0 = x1 1 + x2 2 + x3 3
(2)
2 G13 = (a13 + b13 wMEA + c13 wMEA )T
(4)
2 G13 = (a13 + b13 wMEA + c13 wMEA )T
(5)
D. Fu et al. / Fluid Phase Equilibria 337 (2013) 83–88
80
80
60
70
/(mN m-1)
/(mN m-1)
86
40
60
50
20
40 0.0
0 280
300
320
T/K Fig. 1. Comparison of the calculations with experimental data from Refs. [12,15]. Symbols: experimental data; lines: calculated results. Main plot: temperature dependence of the surface tensions of MEA–MDEA aqueous solutions at different concentrations, (䊉) wMEA = 0.5, wMDEA = 0.0; () wMEA = 0.4, wMDEA = 0.1; () wMEA = 0.3, wMDEA = 0.2; () wMEA = 0.2, wMDEA = 0.3; () wMEA = 0.1, wMDEA = 0.4; () wMEA = 0.0, wMDEA = 0.5. Insert plots: concentration dependence of the surface tensions of MEA aqueous solutions and MDEA aqueous solutions at different temperatures, (䊉) 298.15 K; () 303.15 K; () 308.15 K; () 313.15 K; () 318.15 K; and () 323.15 K.
G12 =
a12 + b12
w
MEA
+ wMDEA 2
+ c12
w
MEA
+ wMDEA 2
2 T (6)
The model parameters aij , bij and cij can be obtained by fitting to the experimental data. The objective function (the average relative deviation, ARD) is defined as:
n
ARD (%) =
i=1
[1 − cal / exp ] n
× 100
(7)
where the superscripts ‘exp’ and ‘cal’ respectively stand for the experimental and calculated data, n is the data numbers. The model parameters for MEA aqueous solutions, a13 = 17.90, b13 = −47.10 and c13 = −9.40, are regressed from the experiments present in the work of Vazquez et al. [12] with ARD = 0.64%. Similarly, a23 = −1.74, b23 = 3.19 and c23 = −1.58 are regressed from the experiments present in the work of Alvarez et al. [15] with ARD = 2.06%. Compared with the correlation for MEA aqueous solutions, the correlation for MDEA aqueous solutions is also good, but we find when the mass fraction of MDEA is low, in particular, wMDEA = 0.05 and 0.1, the model significantly overestimates the surface tensions. Once a13 , b13 , c13 , a23 , b23 and c23 are obtained, to model the surface tensions of CO2 unloaded MEA–MDEA aqueous solutions, there are only three parameters, a12 , b12 and c12 , need to be determined. Using the experimental data listed in Table 3, we obtained a12 = −0.57, b12 = 1.05 and c12 = −0.55, with ARD = 1.63%. Fig. 1 shows the temperature dependence of the surface tensions of MDEA–MEA aqueous solutions at different concentrations, and the comparison with the experimental data from Refs. [12,15]. One finds from this figure that at each amine concentration, the surface tensions decrease with increasing temperature. At relatively low
0.1
0.2
0.3
0.4
0.5
wMDEA
340
Fig. 2. Concentration dependence of the surface tensions of MEA–MDEA aqueous solutions at different temperatures, in the cases of wMEA = 0.05 and 0.1 (insert plot). Symbols: experimental data in this work, (䊉) 293.15 K; () 303.15 K; () 313.15 K; () 323.15 K; () 333.15 K. Lines: calculated results.
temperatures, the calculations match the experiments very satisfactorily, however, with the increase of the temperatures, ARD increases. Also shown in this figure is the concentration dependence of the surface tensions of MEA aqueous solutions and MDEA aqueous solutions at different temperatures. From the insert figures one finds that the proposed model accurately describes both the temperature and concentration dependence of the surface tensions of MEA aqueous solutions, while it fails to correctly capture such dependence for MDEA aqueous solutions when the mass fraction is low. Figs. 2 and 3 show the concentration dependence of the surface tensions of MEA–MDEA aqueous solutions at different temperatures, and the comparison with the experimental data from this work. One finds from these figures that at a given temperature, the surface tensions decrease with the increase of amine concentration. The decreasing surface tension is mainly due to increasing MDEA concentration, since MDEA has a lower surface tension than MEA at any given temperature. The proposed model correctly captures both the temperature and concentration dependence of the surface tensions and the calculation agrees well with the experimental data. The surface tension of carbonated MEA–MDEA aqueous solutions is expressed as [22]: = aq + ion
(8)
ion
where stands for the contribution from ions, which may be empirically formulated as [22]: ion =
d1 ˛ + d2 ˛2 d3 /[(wMEA + wMDEA )/2] − T T
2
(9)
In the calculation of the surface tensions of carbonated MEA–MDEA aqueous solutions, one firstly needs to determine the mass fractions of MEA and MDEA in the carbonated solutions so that aq can be obtained. In the previous work [22], we determined the conversion rates of MDEA and PZ on the basis of the ‘shuttle’ mechanism [29,30], and modeled the surface tension of carbonated MDEA–PZ aqueous solutions satisfactorily. However, the ‘shuttle’ mechanism for carbonated MEA–MDEA aqueous solutions is not
D. Fu et al. / Fluid Phase Equilibria 337 (2013) 83–88
87
50
70
48
/(mN m-1)
/(mN m-1)
60
46
50
44
40 0.0
0.1
0.2
0.3
0.4
0.5
wMDEA Fig. 3. Concentration dependence of the surface tensions of MEA–MDEA aqueous solutions at different temperatures, in the cases of wMEA = 0.15 and 0.2 (insert plot). Symbols: experimental data in this work, (䊉) 293.15 K; () 303.15 K; () 313.15 K; () 323.15 K; () 333.15 K. Lines: calculated results.
well known. In this work, the conversion rates of MEA and MDEA, ˛MEA and ˛MDEA , are empirically expressed as: ˛MEA =
d4 ˛ ; T
˛MDEA =
d5 ˛ T
(10)
The adjustable parameters d1 , d2 , d3 , d4 and d5 can be regressed by fitting to the experimental data listed in Table 4. In the fitting procedure, the object function is the same as that in Eq. (7). The optimized values are: d1 = −121.11, d2 = −129.96, d3 = −0.64, d4 = 52.58 and d5 = 391.08. The ARD is 1.76%.
54
/(mN m-1)
52
50
0.2
0.3
0.4
0.5
Fig. 5. CO2 loading dependence of the surface tension of carbonated MEA–MDEA aqueous solutions at 323.15 K. wMEA = 0.05. (䊉) wMDEA = 0.35; () wMDEA = 0.40; () wMDEA = 0.45. Lines: calculated results.
Fig. 4 shows the temperature dependence of the surface tensions of carbonated MEA–MDEA aqueous solutions, indicating that at given amine concentration and given CO2 loading, the surface tensions decrease with the increase of temperature. Fig. 5 shows the CO2 loading dependence of the surface tensions of carbonated MEA–MDEA aqueous solutions. At given temperature, the surface tensions increase with increasing CO2 loading. At given temperature, given MEA concentration and given CO2 loading, the surface tension decreases with the increase of MDEA concentration. It is worth noting that although the ARD is of small value, both Figs. 4 and 5 show that the deviation between the experiment and calculation is distinguishable. The deviation mainly comes from the uncertainty of the determination of residual MEA and MDEA concentrations. As the ‘shuttle’ mechanism for carbonated MEA–MDEA aqueous solutions is not well known, the residual MEA and MDEA concentrations cannot be satisfactorily determined by using the empirically expressed Eq. (10), hence the proposed model can only quantitatively capture the temperature, amine concentration and CO2 loading dependence of the surface tensions of carbonated MEA–MDEA aqueous solutions.
4. Summary In this study, the surface tensions of CO2 loaded and CO2 unloaded MEA–MDEA aqueous solutions were measured and a model was proposed to calculate the surface tensions. The temperature, amine concentration and CO2 loading dependence of the surface tensions were demonstrated. Our results showed that:
48
46 290
42 0.1
300
310
320
330
T/K Fig. 4. Temperature dependence of the surface tension of carbonated MEA–MDEA aqueous solutions at different CO2 loading. wMEA = 0.05 and wMDEA = 0.35. (䊉) ˛ = 0.1, () ˛ = 0.2, () ˛ = 0.3, () ˛ = 0.4, () ˛ = 0.5. Lines: calculated results.
(1) For both the unloaded and loaded MEA–MDEA aqueous solutions, the increase of amine concentration and temperature tends to decrease the surface tensions. (2) For unloaded MEA–MDEA aqueous solutions, at a given temperature, the decreasing surface tension is mainly due to increasing MDEA concentration, since MDEA has a lower surface tension than MEA at any given temperature.
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D. Fu et al. / Fluid Phase Equilibria 337 (2013) 83–88
(3) For the CO2 loaded MEA–MDEA aqueous solutions, the increase of CO2 loading tends to increase the surface tensions at given amine concentration. List of symbols
a, b, c, d T w x
adjustable parameters absolute temperature (K) mass fraction mole fraction
Greek letters ˛ CO2 loading surface tension (mN m−1 ) Superscripts 1 MEA 2 MDEA 3 water Subscripts aq aqueous solutions cal calculated results exp experimental results ion contribution from ions
Acknowledgments The authors appreciate the financial support from the National Natural Science Foundation of China (Nos. 21276072 and 21076070), the Natural Science Funds for Distinguished Young Scholar of Hebei Province (No. B2012502076), and the Fundamental Research Funds for the Central Universities (Nos. 11MG53 and 11ZG10).
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Experiment and model for the surface tension of carbonated MEA–MDEA aqueous solutions Dong Fu ∗ , Lin Wei, SongTao Liu School of Environmental Science and Engineering, North China Electric Power University, Baoding 071003, China
a r t i c l e
i n f o
Article history: Received 14 May 2012 Received in revised form 7 October 2012 Accepted 16 October 2012 Available online 23 October 2012 Keywords: Surface tension MEA–MDEA aqueous solution CO2 loading
a b s t r a c t Surface tensions of CO2 unloaded and CO2 loaded MEA–MDEA aqueous solutions were measured by using the BZY-1 surface tension meter, which employs the Wilhemy plate principle. For CO2 unloaded solutions, the temperatures ranged from 293.15 to 333.15 K, and the mass fractions of MEA (wMEA ) and MDEA (wMDEA ) respectively ranged from 0.05 to 0.20, and 0.05 to 0.45. For CO2 loaded solutions, the temperatures ranged from 293.15 to 323.15 K, and wMEA and wMDEA respectively ranged from 0.05 to 0.10 and 0.30 to 0.45. The uncertainty of the surface tensions is ±0.1 mN m−1 . A model was proposed to correlate the surface tensions of both CO2 loaded and CO2 unloaded solutions. For CO2 unloaded MEA–MDEA solutions, with 3 adjustable parameters as input, the average relative deviation (ARD) between experiments and calculations is 1.63%. For CO2 loaded MEA–MDEA solutions, with 5 adjustable parameters as input, ARD is 1.76%. The temperature, mass fractions of amines and CO2 loading dependence of the surface tensions were demonstrated on the basis of experiments and calculations. © 2012 Elsevier B.V. All rights reserved.
1. Introduction In recent decades, atmospheric levels of CO2 have increased rapidly due to the utilization of great amount of fossil fuel. The reduction of CO2 emissions became a global issue [1,2]. Aqueous solutions of alkanolamines like monoethanolamine (MEA) and Nmethyldiethanolamine (MDEA) are widely used for the removal of CO2 from a variety of gas streams [3–8]. Among the alkanolamines series, MDEA takes the advantages of high resistance to thermal and chemical degradation, low solution vapor pressure (minimum solvent loss during regeneration), and low enthalpy of absorption (low energy requirement for regeneration). However, compared with other amines like MEA, an MDEA aqueous solution has a lower absorption rate. Adding small amounts of MEA to an aqueous solution of MDEA has found widespread application in the removal of CO2 . The mixtures of MEA and MDEA preserve the high rate of the reaction of MEA with CO2 , and the low enthalpy of the reaction of MDEA with CO2 , hence lead to higher absorption rates in the absorber column, yet lower heat of regeneration in the stripper section [5,6]. Surface tensions of aqueous solutions are required when designing or simulating an absorption column for CO2 absorption
∗ Corresponding author. Tel.: +86 312 7522037. E-mail address: [email protected] (D. Fu). 0378-3812/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fluid.2012.10.013
associated with chemical reactions. Until now, there are some experiments concerning the surface tensions of aqueous solutions containing MEA and MDEA [9–16]. In particular, Vazquez et al. [12] and Alvarez et al. [15] systematically measured the surface tensions of MEA aqueous solutions and MDEA aqueous solutions at temperatures from 298.15 to 323.15 K. They also measured the surface tensions of MEA–MDEA aqueous solutions at temperatures from 298.15 to 323.15 K, with the total mass fraction of amines wMEA + wMDEA = 0.5. However, the surface tensions of MEA–MDEA aqueous solutions at relatively low mass fractions of amines, e.g., wMEA + wMDEA = 0.2, 0.3 and 0.4 are rare. Moreover, the surface tensions of carbonated MEA–MDEA aqueous solutions have been rarely reported, and due to the lack of the experiments and theoretical models, the effects of mass fraction of amines, temperatures and CO2 loading have not been well documented by far. To demonstrate the temperature, mass fraction of amines and CO2 loading dependence of the surface tensions, the surface tensions of CO2 unloaded (temperature ranging from 293.15 to 333.15 K, wMEA and wMDEA respectively ranging from 0.05 to 0.20, and 0.05 to 0.45) and CO2 loaded (temperature ranging from 293.15 to 323.15 K, wMEA and wMDEA respectively ranging from 0.05 to 0.10 and 0.30 to 0.45, CO2 loading ranging from 0.1 to 0.5) MEA–MDEA aqueous solutions were measured by using the BZY-1 surface tension meter, which employs the Wilhemy plate principle. A model was proposed to correlate the surface tensions of both CO2 unloaded and CO2 loaded solutions.
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D. Fu et al. / Fluid Phase Equilibria 337 (2013) 83–88
Table 1 Sample description. Chemical
CAS No.
Purity (in mass fraction %)
MEA
141-43-5
99.4
MDEA
105-59-9
99.5
2. Experimental 2.1. Materials Both MEA and MDEA were purchased from HuaXin Chemical Co. The sample description is shown in Table 1. They were used without further purification. Aqueous solutions of MEA–MDEA were prepared by adding doubly distilled water. 2.2. Apparatus and procedure The surface tension was measured by using the BZY-1 surface tension meter produced by Shanghai Hengping Instrument Factory. BZY-1 meter employs the Wilhemy plate principle, i.e., the maximum tensile force competing with the surface tension is measured when the bottom edge of platinum parallel to the interface and just touches it. The measurement ranges for temperature and surface tensions are respectively 268.15–383.15 K and 0.1–400.0 mN m−1 . The sensitivity, repeatability and uncertainty are respectively 0.1 mN m−1 , 0.1 mN m−1 , and 0.1 mN m−1 . The size-volume of the different samples used in BZY-1 meter is 20 ml. During the experiments, the copper pan in the host of the BZY-1 meter is connected with the thermostatic bath (CH-1006, uncertainty ±0.1 K). Via the circulation of the water, the temperature of the water in the copper pan is kept the same as that in the thermostatic bath, hence the temperature readings in the surface tension measuring cell may be regulated within 0.1 K. The aqueous solution is put into the solution container immersed in the copper pan and its temperature can be measured by a thermocouple. The scale reading of the thermocouple has been well calibrated by a mercury thermometer (uncertainty ±0.05 K). To verify the reliability of the equipment, the surface tensions of deionized water, pure MEA and pure MDEA were measured at 298.15 K and 318.15 K and compared with experimental values from previous reports [12,15]. The relative deviations are shown in Table 2. The surface tensions of both deionized water and pure amines were measured three times with standard deviation less than 0.3%, indicating that the experimental equipment is reliable. The carbonated MEA–MDEA aqueous solutions were prepared according to the methods mentioned in the work of Amundsen et al. [17], Weiland et al. [20] and Fu et al. [21,22]: CO2 -unloaded MEA–MDEA aqueous solution (in the preparation of aqueous solutions, the uncertainty of the electronic balance is ±0.1 mg) was put into a volumetric flask immersed in the thermostatic bath with a built-in stirrer for uniform temperature distribution. The bath temperature was regulated within 0.1 K. CO2 from a high-pressure tank was inlet into the volumetric flask at certain temperatures (CO2 pressure is 1 atm). Once the carbonated solution was prepared, varying proportions of the unloaded and loaded solutions
Molecular mass (Da)
Density (g cm−3 )
61.09
298.15 K
1.0003 [17]
119.16
303.15 K 323.15 K
1.0337 [18] 1.0250 [19]
were mixed together to produce a set of samples having a fixed MEA/MDEA-to-water ratio but with varying CO2 loading. CO2 loading, ˛, is defined as ˛ = nCO2 /(nMEA + nMDEA ), in which nCO2 is the mole of loaded CO2 , nMEA and nMDEA are respectively the mole of MEA and MDEA in the unloaded aqueous solutions. It is worth noting that CO2 loading is expected to be a major uncertainty in the experiment. In this work, carbonated solution was prepared at non-equilibrium conditions, under which the thermodynamic equilibrium (saturated absorption, corresponding to maximum CO2 loading, ˛max ) cannot be achieved. The surface tension was measured in an open measuring cell. It refers to the liquid (aqueous solution)–vapor (air + water vapor and amines vapor) surface tension, and different to the surface tension measured at equilibrium state (closed system, with equilibrium liquid phase and vapor phase). However, under low pressures, as the density of the vapor phase is too small, no matter using Wilhemy plate principle or drop-volume method, the contribution of vapor phase to the surface tension is very small. Hence the surface tensions presented in this work are very close to those measured at equilibrium state. The key is that certain amount of CO2 will escape when loaded solution is mixed with unloaded solution and put into the open measuring cell. Moreover, atmospheric CO2 and humidity have some effects on CO2 loading and solution concentration. To estimate the uncertainty of CO2 loadings, we selected 2 diluted samples (as shown in Table 4, T = 313.15 K, wMEA = 0.05, wMDEA = 0.35, ˛ = 0.2 and 0.4) and determined the CO2 loadings using the analysis method based on the precipitation of BaCO3 [17,20]. The obtained CO2 loading ˛ are respectively 0.198 and 0.394, indicating that the real values of CO2 loading may be lower than those list in Table 4, however, as documented by Amundsen et al. [17] and Weiland et al. [20], the uncertainty of CO2 loading is less than 2%. 3. Results and discussion Surface tensions of CO2 unloaded MEA–MDEA aqueous solutions at different temperatures and different mass fraction of amines are shown in Table 3. Some of the experimental data are compared with the work of Vazquez et al. [12] and Alvarez et al. [15]. The average relative deviations between our results and those from the work of Vazquez et al. [12] and Alvarez et al. [15] are respectively 0.81% and 0.33%. Surface tensions of the CO2 loaded MEA–MDEA aqueous solutions at series of temperatures, mass fraction of amines and CO2 loadings are shown in Table 4. Besides experimental measurements, models that can calculate the surface tensions of concerned systems are also important. By far, some equations have been proposed for modeling the surface tensions of amine aqueous solutions, in particular, Alvarez et al. [15] correlated the experimental data of MEA–MDEA aqueous solutions with high accuracy. However, due to the complexity of the
Table 2 Surface tension (␥/mN m−1 ) of pure water, MEA and MDEA and the relative deviations (RD) between the experiments from this work and those from literatures [12,15]. Components
298.2 K exp
Water MEA MDEA
72.0 48.9 38.6
318.2 K lit 72.0 [12,15] 49.0 [12] 38.9 [15]
RD%
exp
0.0 0.2 0.8
69.0 45.5 37.0
lit 68.8 [12,15] 45.7 [12] 37.2 [15]
RD% 0.3 0.4 0.5
D. Fu et al. / Fluid Phase Equilibria 337 (2013) 83–88
85
Table 3 Surface tensions of MEA–MDEA aqueous solutions at different mass fractions (wMEA , wMDEA ) and temperatures. wMEA
0.05
0.10
0.15
0.20
a b
wMDEA
␥/(mN m−1 ) T/K = 293.2
T/K = 298.2
T/K = 303.2
T/K = 308.2
T/K = 313.2
T/K = 318.2
T/K = 323.2
T/K = 328.2
T/K = 333.2
0.15 0.25 0.35 0.45
60.3 56.1 53.1 50.9
59.5 55.4 52.3 50.0
58.4 54.2 51.1 48.9
57.9 53.5 50.4 48.2
56.9 52.5 49.4 47.2
56.1 51.6 48.5 46.3
55.1 50.6 47.4 45.4
54.5 49.7 46.6 44.3
53.2 48.6 45.7 43.4
0.10 0.20 0.30 0.40
61.5 57.3 54.3 51.7
60.9 56.5 53.6 51.0 50.83a
59.8 55.4 52.4 49.9 50.25a
59.1 54.8 51.8 49.2 49.51a
58.1 53.7 50.7 48.2 48.75a
57.3 52.9 49.9 47.3 48.28a
56.5 51.9 48.8 46.3 47.20a
55.5 51.1 48.0 45.4
54.6 50.0 46.6 44.3
0.05 0.15 0.25 0.35
62.6 58.5 55.4 52.7
61.8 57.8 54.6 51.9
60.7 56.5 53.6 50.8
60.2 55.7 52.8 50.1
59.4 55.2 52.1 49.2
58.5 54.4 51.3 48.3
57.7 53.3 50.2 47.4
57.0 52.5 49.3 46.6
56.0 51.4 48.3 45.5
0.00
63.7
61.2 61.06b 57.2 54.3 51.0 50.80a
60.5 60.17b 55.8 52.7 50.1 49.99a
59.5 59.49b 55.0 52.1 49.3 49.54a
58.4 58.09b 54.4 51.2 48.4 49.00a
57.0
59.6 56.4 53.5
62.1 61.84b 57.9 54.3 51.7 51.60a
58.1
0.10 0.20 0.30
62.8 62.63b 58.8 55.5 52.6 52.40a
53.5 50.3 47.5
52.2 49.3 46.4
From Ref. [15]. From Ref. [12].
Table 4 Surface tensions of carbonated MEA–MDEA aqueous solutions at different temperatures, mass fractions (wMEA , wMDEA ) and CO2 loadings (˛). wMEA
wMDEA
/(mN m−1 ) ˛ = 0.1
˛ = 0.2
˛ = 0.3
˛ = 0.4
˛ = 0.5
293.2
0.05 0.05 0.05 0.10 0.10 0.10
0.35 0.40 0.45 0.30 0.35 0.40
53.5 52.1 51.4 53.9 52.5 51.2
54.0 52.9 51.7 54.2 53.0 51.7
54.8 53.8 52.4 55.2 54.0 52.5
56.2 54.8 53.4 56.5 55.4 53.3
57.9 56.5 54.4 58.1 57.1 54.6
303.2
0.05 0.05 0.05 0.10 0.10 0.10
0.35 0.40 0.45 0.30 0.35 0.40
51.9 50.8 49.4 52.0 50.7 49.9
52.3 50.9 49.6 52.6 51.2 50.2
52.8 51.5 50.3 53.4 52.0 50.4
53.4 52.4 50.8 54.4 52.7 51.0
54.2 53.2 51.5 55.5 53.5 51.9
313.2
0.05 0.05 0.05 0.10 0.10 0.10
0.35 0.40 0.45 0.30 0.35 0.40
49.7 48.1 47.0 50.0 48.4 47.4
49.9 48.1 47.1 50.4 48.5 47.4
50.0 48.2 47.2 50.7 48.5 47.6
50.2 48.5 47.3 50.8 48.6 47.7
50.3 48.8 47.9 51.2 48.9 48.1
323.2
0.05 0.05 0.05 0.10 0.10 0.10
0.35 0.40 0.45 0.30 0.35 0.40
47.2 45.3 43.3 48.1 46.4 44.1
47.5 45.6 43.3 48.2 46.6 44.2
47.5 46.0 43.8 48.6 46.6 44.5
47.9 46.5 44.4 48.9 46.9 45.1
48.0 47.1 44.9 49.1 47.2 45.4
T/K
amine aqueous solutions, equations that simultaneously take the CO2 loading, amine concentration and temperature dependence into account are rare [21,22]. Moreover, for the carbonated systems, due to the great variety of ions, the application of advanced approaches like density gradient theory [23–28] to such systems is very difficult. In this work, the surface tension of CO2 unloaded MEA–MDEA aqueous solutions is formulated as following: aq = 0 + in which
0
and
= x1 x2 G12 + x1 x3 G13 + x2 x3 G23
(3)
where the subscripts 1, 2 and 3 stand for MEA, MDEA and water, respectively. xi is the mole fraction of component i in the aqueous solution, i is the surface tension of pure component i, which can be expressed as a function of temperature by fitting to the experimental data [12,15]. Gij is expressed as the function of T and mass fractions of amines:
(1) are expressed as:
0 = x1 1 + x2 2 + x3 3
(2)
2 G13 = (a13 + b13 wMEA + c13 wMEA )T
(4)
2 G13 = (a13 + b13 wMEA + c13 wMEA )T
(5)
D. Fu et al. / Fluid Phase Equilibria 337 (2013) 83–88
80
80
60
70
/(mN m-1)
/(mN m-1)
86
40
60
50
20
40 0.0
0 280
300
320
T/K Fig. 1. Comparison of the calculations with experimental data from Refs. [12,15]. Symbols: experimental data; lines: calculated results. Main plot: temperature dependence of the surface tensions of MEA–MDEA aqueous solutions at different concentrations, (䊉) wMEA = 0.5, wMDEA = 0.0; () wMEA = 0.4, wMDEA = 0.1; () wMEA = 0.3, wMDEA = 0.2; () wMEA = 0.2, wMDEA = 0.3; () wMEA = 0.1, wMDEA = 0.4; () wMEA = 0.0, wMDEA = 0.5. Insert plots: concentration dependence of the surface tensions of MEA aqueous solutions and MDEA aqueous solutions at different temperatures, (䊉) 298.15 K; () 303.15 K; () 308.15 K; () 313.15 K; () 318.15 K; and () 323.15 K.
G12 =
a12 + b12
w
MEA
+ wMDEA 2
+ c12
w
MEA
+ wMDEA 2
2 T (6)
The model parameters aij , bij and cij can be obtained by fitting to the experimental data. The objective function (the average relative deviation, ARD) is defined as:
n
ARD (%) =
i=1
[1 − cal / exp ] n
× 100
(7)
where the superscripts ‘exp’ and ‘cal’ respectively stand for the experimental and calculated data, n is the data numbers. The model parameters for MEA aqueous solutions, a13 = 17.90, b13 = −47.10 and c13 = −9.40, are regressed from the experiments present in the work of Vazquez et al. [12] with ARD = 0.64%. Similarly, a23 = −1.74, b23 = 3.19 and c23 = −1.58 are regressed from the experiments present in the work of Alvarez et al. [15] with ARD = 2.06%. Compared with the correlation for MEA aqueous solutions, the correlation for MDEA aqueous solutions is also good, but we find when the mass fraction of MDEA is low, in particular, wMDEA = 0.05 and 0.1, the model significantly overestimates the surface tensions. Once a13 , b13 , c13 , a23 , b23 and c23 are obtained, to model the surface tensions of CO2 unloaded MEA–MDEA aqueous solutions, there are only three parameters, a12 , b12 and c12 , need to be determined. Using the experimental data listed in Table 3, we obtained a12 = −0.57, b12 = 1.05 and c12 = −0.55, with ARD = 1.63%. Fig. 1 shows the temperature dependence of the surface tensions of MDEA–MEA aqueous solutions at different concentrations, and the comparison with the experimental data from Refs. [12,15]. One finds from this figure that at each amine concentration, the surface tensions decrease with increasing temperature. At relatively low
0.1
0.2
0.3
0.4
0.5
wMDEA
340
Fig. 2. Concentration dependence of the surface tensions of MEA–MDEA aqueous solutions at different temperatures, in the cases of wMEA = 0.05 and 0.1 (insert plot). Symbols: experimental data in this work, (䊉) 293.15 K; () 303.15 K; () 313.15 K; () 323.15 K; () 333.15 K. Lines: calculated results.
temperatures, the calculations match the experiments very satisfactorily, however, with the increase of the temperatures, ARD increases. Also shown in this figure is the concentration dependence of the surface tensions of MEA aqueous solutions and MDEA aqueous solutions at different temperatures. From the insert figures one finds that the proposed model accurately describes both the temperature and concentration dependence of the surface tensions of MEA aqueous solutions, while it fails to correctly capture such dependence for MDEA aqueous solutions when the mass fraction is low. Figs. 2 and 3 show the concentration dependence of the surface tensions of MEA–MDEA aqueous solutions at different temperatures, and the comparison with the experimental data from this work. One finds from these figures that at a given temperature, the surface tensions decrease with the increase of amine concentration. The decreasing surface tension is mainly due to increasing MDEA concentration, since MDEA has a lower surface tension than MEA at any given temperature. The proposed model correctly captures both the temperature and concentration dependence of the surface tensions and the calculation agrees well with the experimental data. The surface tension of carbonated MEA–MDEA aqueous solutions is expressed as [22]: = aq + ion
(8)
ion
where stands for the contribution from ions, which may be empirically formulated as [22]: ion =
d1 ˛ + d2 ˛2 d3 /[(wMEA + wMDEA )/2] − T T
2
(9)
In the calculation of the surface tensions of carbonated MEA–MDEA aqueous solutions, one firstly needs to determine the mass fractions of MEA and MDEA in the carbonated solutions so that aq can be obtained. In the previous work [22], we determined the conversion rates of MDEA and PZ on the basis of the ‘shuttle’ mechanism [29,30], and modeled the surface tension of carbonated MDEA–PZ aqueous solutions satisfactorily. However, the ‘shuttle’ mechanism for carbonated MEA–MDEA aqueous solutions is not
D. Fu et al. / Fluid Phase Equilibria 337 (2013) 83–88
87
50
70
48
/(mN m-1)
/(mN m-1)
60
46
50
44
40 0.0
0.1
0.2
0.3
0.4
0.5
wMDEA Fig. 3. Concentration dependence of the surface tensions of MEA–MDEA aqueous solutions at different temperatures, in the cases of wMEA = 0.15 and 0.2 (insert plot). Symbols: experimental data in this work, (䊉) 293.15 K; () 303.15 K; () 313.15 K; () 323.15 K; () 333.15 K. Lines: calculated results.
well known. In this work, the conversion rates of MEA and MDEA, ˛MEA and ˛MDEA , are empirically expressed as: ˛MEA =
d4 ˛ ; T
˛MDEA =
d5 ˛ T
(10)
The adjustable parameters d1 , d2 , d3 , d4 and d5 can be regressed by fitting to the experimental data listed in Table 4. In the fitting procedure, the object function is the same as that in Eq. (7). The optimized values are: d1 = −121.11, d2 = −129.96, d3 = −0.64, d4 = 52.58 and d5 = 391.08. The ARD is 1.76%.
54
/(mN m-1)
52
50
0.2
0.3
0.4
0.5
Fig. 5. CO2 loading dependence of the surface tension of carbonated MEA–MDEA aqueous solutions at 323.15 K. wMEA = 0.05. (䊉) wMDEA = 0.35; () wMDEA = 0.40; () wMDEA = 0.45. Lines: calculated results.
Fig. 4 shows the temperature dependence of the surface tensions of carbonated MEA–MDEA aqueous solutions, indicating that at given amine concentration and given CO2 loading, the surface tensions decrease with the increase of temperature. Fig. 5 shows the CO2 loading dependence of the surface tensions of carbonated MEA–MDEA aqueous solutions. At given temperature, the surface tensions increase with increasing CO2 loading. At given temperature, given MEA concentration and given CO2 loading, the surface tension decreases with the increase of MDEA concentration. It is worth noting that although the ARD is of small value, both Figs. 4 and 5 show that the deviation between the experiment and calculation is distinguishable. The deviation mainly comes from the uncertainty of the determination of residual MEA and MDEA concentrations. As the ‘shuttle’ mechanism for carbonated MEA–MDEA aqueous solutions is not well known, the residual MEA and MDEA concentrations cannot be satisfactorily determined by using the empirically expressed Eq. (10), hence the proposed model can only quantitatively capture the temperature, amine concentration and CO2 loading dependence of the surface tensions of carbonated MEA–MDEA aqueous solutions.
4. Summary In this study, the surface tensions of CO2 loaded and CO2 unloaded MEA–MDEA aqueous solutions were measured and a model was proposed to calculate the surface tensions. The temperature, amine concentration and CO2 loading dependence of the surface tensions were demonstrated. Our results showed that:
48
46 290
42 0.1
300
310
320
330
T/K Fig. 4. Temperature dependence of the surface tension of carbonated MEA–MDEA aqueous solutions at different CO2 loading. wMEA = 0.05 and wMDEA = 0.35. (䊉) ˛ = 0.1, () ˛ = 0.2, () ˛ = 0.3, () ˛ = 0.4, () ˛ = 0.5. Lines: calculated results.
(1) For both the unloaded and loaded MEA–MDEA aqueous solutions, the increase of amine concentration and temperature tends to decrease the surface tensions. (2) For unloaded MEA–MDEA aqueous solutions, at a given temperature, the decreasing surface tension is mainly due to increasing MDEA concentration, since MDEA has a lower surface tension than MEA at any given temperature.
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(3) For the CO2 loaded MEA–MDEA aqueous solutions, the increase of CO2 loading tends to increase the surface tensions at given amine concentration. List of symbols
a, b, c, d T w x
adjustable parameters absolute temperature (K) mass fraction mole fraction
Greek letters ˛ CO2 loading surface tension (mN m−1 ) Superscripts 1 MEA 2 MDEA 3 water Subscripts aq aqueous solutions cal calculated results exp experimental results ion contribution from ions
Acknowledgments The authors appreciate the financial support from the National Natural Science Foundation of China (Nos. 21276072 and 21076070), the Natural Science Funds for Distinguished Young Scholar of Hebei Province (No. B2012502076), and the Fundamental Research Funds for the Central Universities (Nos. 11MG53 and 11ZG10).
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