VaporâLiquid Equilibria for Three Binary Systems of N

Article pubs.acs.org/jced

Vapor−Liquid Equilibria for Three Binary Systems of N‑Methylethanolamine, N‑Methyldiethanolamine, and Ethylene Glycol at P = (40.0, 30.0, and 20.0) kPa Changsheng Yang,* Yang Feng, Bing Cheng, Ping Zhang, Zhenli Qin, Hao Zeng, and Feizhong Sun Key Laboratory for Green Chemical Technology of State Education Ministry, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, People’s Republic of China ABSTRACT: The isobaric vapor−liquid equilibrium (VLE) data of {Nmethylethanolamine + N-methyldiethanolamine (MDEA), N-methylethanolamine + ethylene glycol, ethylene glycol + MDEA} at P = (40.0, 30.0, and 20.0) kPa were investigated in this work. All of the VLE data of the three binary systems were verified to be thermodynamically consistent by both Herington area test and Van Ness point test. At the same time, the universal quasichemical (UNIQUAC), nonrandom twoliquid (NRTL), Wilson, and Margules activity coefficient equations were chosen to correlate the experimental results, deriving the coefficient parameters and estimating the standard error values. The correlation values showed that estimated data reached a good agreement with the experimental data in this study.

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INTRODUCTION As the most common chemical absorbent, alkanolamines are used to remove carbon dioxide from effluents of industries, which are using fossil energy or natural gas reservoirs.1,2 They are always drawing researchers’ attention along with the development of large-scale industries and the strict requirements of environmental improvement. For enhanced understanding and awareness, the physical and chemical properties of alkanolamines2 need to be studied to improve the separation process and to establish specific condition of residual removal. In this present work, our interest focuses on the vapor−liquid phase equilibrium under three reduced pressures for the mixtures containing N-methyldiethanolamine (MDEA), Nmethylethanolamine (MMEA), and ethylene glycol. MDEA is a widely used solvent and absorbent, especially in chemical absorption.3 As is reported in several papers, the currently dominant technology to remove carbon dioxide (CO2) and hydrogen sulfide (H2S) from natural gas and the absorption and stripping process of liquefied petroleum gas (LPG) is carried on with alkanolamines,4 such as MMEA, MDEA, N,N-diethylethanolamine,5 and diethanolamine.6,7 MMEA is also acted as a solvent in absorbing the acid gases, together with its analogues, such as ethanolamine and dimethylethanolamine.6 Meanwhile, it is a useful intermediate in the preparation of chemical products, including polymers and pharmaceuticals. The separation of alkanolamine mixtures using vacuum distillation is commonly encountered in chemical industries. MDEA and MMEA can be synthesized from the chemical reaction between ethylene oxide (EO) and monomethylamine (MMA).8,9 In recent years, some chemical plants are gradually inclined to produce MDEA and MMEA, using EO and MMA (containing water as an impurity) as organic chemical raw materials in the synthesis reaction. Others even use methyl© 2013 American Chemical Society

amine aqueous solution. So in the synthesis process, there are several byproducts mixed in the products apart from the major products, for example, ethylene glycol (EG). In this work, the impurity EG is also an important chemical material that can be used for manufacturing polymer ester and antifreezer. It is presently prepared by EO hydrolysis reaction or ethylene epoxide hydration in industry.10 To get highly purified products and further study the dynamic theory of absorbing acid gases, it is essential to receive a good understanding of the phase equilibrium data based on the separation and purification process.6 Fundamental knowledge of vapor−liquid equilibrium (VLE) data under reduced pressures is very useful in designing the separation process, such as distillation and extractive distillation. Simultaneously, the chemical engineering data bank needs to be updated and improved with new experimental data to fit the model parameters. However, there are hardly any VLE data involved in literature for the separation of MMEA, MDEA, and EG. Thereupon, this work focused on the isobaric (vapor + liquid) equilibrium data of {MMEA + MDEA, MMEA + EG, EG + MDEA} at (40.0, 30.0, and 20.0) kPa. It aimed at providing basic references and equilibrium data for industrial production. All of the VLE data were tested and verified for thermodynamic consistency test by the Herington area test and Van Ness point test. Four activity coefficient models, universal quasichemical activity coefficient (UNIQUAC), nonrandom two-liquid (NRTL), Wilson, and Margules were chosen to correlate the experimental data of the three binary systems. Received: April 16, 2013 Accepted: July 5, 2013 Published: July 17, 2013 2272

dx.doi.org/10.1021/je400373d | J. Chem. Eng. Data 2013, 58, 2272−2279

Journal of Chemical & Engineering Data

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EXPERIMENTAL SECTION Materials. MDEA (≥ 0.995, mass fraction purity) and EG (≥ 0.998, mass fraction purity) were purchased from Tianjin Guangfu Fine Chemical Research Institute, China; the mass fractions of impurities of water in MDEA and diethylene glycol in EG were less than 0.005 and 0.002, respectively. They were both used without further purification. MMEA (≥ 0.950, mass fraction purity) was purchased from Shanghai Canto Chemical Co. Ltd., China. We gave it a further purification in a distillation column at atmospheric pressure. The purity of the distilled MMEA was tested to be higher than 0.999 (mass fraction) with gas chromatography (GC) analysis. Apparatus and Procedures. The VLE data were measured in modified Rose−Williams still.11,28 This still can ensure intensive mixing of the vapor and liquid phases by letting both phases circulate continuously and achieving phase equilibrium. Equilibrium was achieved when a stable vapor temperature was obtained for at least 30 min. The system pressures were regulated by a vacuum pump and a buffer tank. We used a U-shaped differential manometer connected with the vacuum pump to measure pressures correctly, with a fluctuation within 0.13 kPa. A precision mercury thermometer was used to measure the equilibrium temperature, with the uncertainty of u(T) = 0.1 K. In addition, a condenser with ethanol as coolant was used to convert the vapor phase into liquid phase quickly, whose working temperature was T = (265.15 to 272.15) K. We also tied several Teflon tapes to instrument interfaces to reduce the systematic error. Some insulation measurements were adopted. Previous works already calibrated the reliability of the experimental system.11−14,28 Analysis. The equilibrium components of liquid and vapor (cooled to liquid) phases were analyzed by a BFRL SP-2100A GC. The FID was used with a SE-54 capillary column (30 m × 0.32 mm × 0.5 μm), and the N2000 chromatography station was used to treat the GC response peaks. The flow velocities of H2 and air were 30 mL·min−1 and 300 mL·min−1, respectively. For the three binary systems of {MMEA + MDEA}, {MMEA + EG}, and {EG + MDEA}, the column, injector, and detector temperatures were kept at T = (458.15, 498.15, and 528.15) K, T = (393.15, 458.15, and 508.15) K, and T = (453.15, 513.15, and 548.15) K, respectively. The nitrogen of high purity (0.99999, mass fraction) acted as the carrier gas; its flow rate was 30 mL·min−1, and the precolumn pressure was 0.05 MPa. The injection volume was 0.4 μL. The three pure substances of the vapor pressures were measured by our modified Rose− Williams still,11 and the comparison between experimental boiling temperatures of the pure substances and the literature ones is shown in Table 1. Calibration analyses using gravimetrically prepared standard solutions were carried out to convert the peak area ratios to mole fractions of the sample. Three or four analyses were performed for each sample to

obtain a mean mass fraction value with repeatability better than 0.1 %. To ensure the accuracy, each sample was analyzed at least three times; the uncertainties of the mole fractions were kept within ± 0.005.

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RESULTS AND DISCUSSION Measurement Results. The VLE data for three binary systems of (MMEA + MDEA, MMEA + EG, EG + MDEA) at P = (40.0, 30.0, and 20.0) kPa are presented in Tables 2 to 4, respectively. x1 represents the mole fraction of the liquid phase; y1 represents the mole fraction of the vapor phase. The vapor Table 2. VLE Data and Calculated Activity Coefficient (γ) for the Three Binary Systems at 40.0 kPaa T/K 405.45 407.51 409.22 412.81 417.32 420.65 424.55 430.98 433.08 438.98 444.80 450.34 460.96 488.14 405.48 406.46 407.35 408.15 409.57 410.83 412.60 415.15 417.97 421.40 427.20 433.27 436.39 441.70 441.66 443.12 444.69 446.18 450.10 453.35 457.25 461.06 464.06 467.31 472.82 478.36 488.17

Table 1. Boiling Points (T) of Three Pure Compounds at 101.33 kPaa Tb/K compound

exptl

lit.

ref

MDEA MMEA EG

520.28 431.20 470.47

520.15 431.15 470.45

24 24 5

x1

y1

γ1

MMEA (1) + MDEA (2) 1.000 1.000 0.999 0.926 0.995 0.993 0.864 0.990 0.994 0.760 0.986 0.986 0.640 0.972 0.981 0.562 0.960 0.982 0.480 0.947 0.990 0.362 0.915 1.021 0.328 0.903 1.037 0.246 0.867 1.098 0.181 0.812 1.164 0.136 0.762 1.227 0.074 0.630 1.364 0.000 0.000 MMEA (1) + EG (2) 1.000 1.000 0.998 0.949 0.992 1.006 0.906 0.979 1.005 0.876 0.972 0.995 0.795 0.948 1.001 0.730 0.927 1.011 0.681 0.903 1.017 0.563 0.851 1.022 0.466 0.784 1.031 0.371 0.711 1.037 0.251 0.581 1.059 0.122 0.356 1.074 0.076 0.249 1.064 0.000 0.000 EG (1) + MDEA (2) 1.000 1.000 1.007 0.953 0.998 1.001 0.898 0.983 0.992 0.853 0.976 0.985 0.742 0.947 0.963 0.658 0.912 0.940 0.569 0.869 0.913 0.485 0.808 0.883 0.429 0.766 0.861 0.363 0.693 0.834 0.261 0.561 0.796 0.166 0.402 0.762 0.000 0.000

γ2

1.472 1.477 1.001 1.094 1.111 1.051 1.053 1.048 1.012 1.050 1.022 1.005 1.007

0.792 0.956 1.199 1.120 1.075 1.030 1.041 0.999 0.990 0.989 0.991 0.995 1.004

0.208 0.765 0.708 0.768 0.853 0.874 0.934 0.923 0.969 0.988 0.991 1.004

a

a

Uncertainties u are u(T) = 0.1 K, u(P) = 0.13 kPa, and u(x, y) = 0.005.

Uncertainties u are u(T) = 0.1 K. 2273



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Table 3. VLE Data and Calculated Activity Coefficient (γ) for the Three Binary Systems at 30.0 kPaa T/K 397.95 400.04 401.82 405.37 410.48 412.88 416.44 423.15 425.07 429.83 436.77 442.53 455.68 479.40 397.89 398.99 399.94 400.58 402.42 403.66 404.95 407.87 410.75 413.43 419.50 425.62 427.89 433.71 433.66 434.91 436.10 437.83 441.07 444.25 448.26 451.44 453.47 456.47 461.93 468.10 479.37

x1

y1

γ1


Table 4. VLE Data and Calculated Activity Coefficient (γ) for the Three Binary Systems at 20.0 kPaa

γ2

T/K

1.147 1.664 1.151 1.103 1.121 1.067 1.074 1.047 1.044 1.044 1.029 1.009 1.001

388.04 389.92 391.97 395.23 399.05 402.18 405.77 411.95 413.97 418.83 424.84 431.53 445.30 467.34

0.987 0.838 0.852 0.920 1.022 0.992 0.986 0.996 1.003 0.996 1.005 1.003 1.000

388.00 389.03 389.82 390.40 392.14 393.76 394.70 397.97 400.54 404.08 408.60 415.06 417.71 422.80

0.106 1.093 1.051 0.953 0.969 0.960 0.959 0.946 0.997 0.997 0.999 1.005

422.75 423.98 425.32 426.92 430.37 433.63 437.92 441.00 443.03 446.06 451.50 457.08 467.40

a Uncertainties u are u(T) = 0.1 K, u(P) = 0.13 kPa, and u(x, y) = 0.005.

x1

γ1

y1

γ2


2.556 1.694 1.079 1.072 1.104 1.124 1.066 1.057 1.044 1.034 1.025 1.002 1.004

0.665 0.915 0.900 0.929 0.919 0.990 0.958 1.016 0.988 0.994 0.998 0.995 1.003

0.110 1.099 1.035 0.844 0.890 0.954 0.929 0.926 0.982 0.990 1.000 0.999

a Uncertainties u are u(T) = 0.1 K, u(P) = 0.13 kPa, and u(x, y) = 0.005.

Table 5. Antonine Equation Parameters of Pure Components Used in This Study

pressures of three pure components were calculated from the Antoine equations, which were presented in Table 5 together with the Antoine equation parameters. All of the experimental data passed the thermodynamic consistency test well, including the semiempirical method (area test) suggested by Herington for isobaric binary VLE data15 and the Van Ness point test (point test) modified by Fredenslund et al.16 The tests were exactly applicable to verify the quality of the experimental values. Just as Herington proposed, the experimental data were proved to be thermodynamically consistent, when the value of |D−J| was less than 10.

compound

A

B

C

ref

MMEAa EGb

17.1700 8.0908

4778.20 2088.94

−51.00 −67.70

6 24

a Antoine equation: ln(psi /Pa) = A − B/[(T/K) + C]. blog(psi /mmHg) = A − B/[(T/K) + C].

D=

2274

(area + ) − (area − ) ·100 (area + ) + (area − )

(1)



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Table 8. Critical Properties (Tc, Pc, Zc), Molecule Volume Parameters r, and Area Parameters q for the UNIQUAC Model

Table 6. Results of Thermodynamic Consistency Tests for the Three Binary Systems system

P/kPa

area testa

D−J

point testb

|Δy1|av

MMEA + MDEA

40.0 30.0 20.0 40.0 30.0 20.0 40.0 30.0 20.0

8.546 2.925 −8.706 7.897 6.052 4.322 8.111 9.150 9.161

+ + + + + + + + +

0.002 0.002 0.001 0.004 0.004 0.004 0.002 0.003 0.003

+ + + + + + + + +

MMEA + EG

EG + MDEA

a

MDEA MMEA EG e

∑ (Py1cal

+ Py2cal − P)

678.00 630.00c 645.00c c

Reference 24.

d

3880 5220d 8573e

Reference 29.

g12−g22/J·mol−1 g21−g11/J·mol−1 AADT/K AADy1 g12−g11/J·mol−1 g21−g22/J·mol−1 AADT/K AADy1

(3)

A12 A21 AADT/K AADy1 a

(4)

30.0 kPa

UNIQUAC Parameters −2263.00 −2163.10 3755.30 3571.20 0.06 0.05 0.002 0.002 NRTL Parameters −3602.20 −3403.70 6483.60 6106.70 0.17 0.15 0.005 0.005 Wilson Parameters 6372.60 5999.10 −3625.30 −3457.50 0.13 0.24 0.009 0.009 Margules Parameters 0.4212 0.4191 −0.0812 −0.0552 0.15 0.13 0.005 0.005

g12−g22/J·mol−1 g21−g11/J·mol−1 AADT/K AADy1

A nonlinear optimization method was used to minimize the following objective function: F=

4.268 2.908d 2.248b

40.0 kPa

(2)

k=4

Pc/kPa c

d

Zc 0.254d 0.252d 0.262e

Reference 30.

Table 9. Parameters for the UNIQUAC, NRTL, Wilson, and Margules Equations and AADT/K and AADy1 for {MMEA (1) + MDEA (2)} at p = (40.0, 30.0, and 20.0) kPaa

where Tmax and Tmin are the maximum and minimum temperatures of the system. |D−J|max for the three binary systems were 8.706, 7.897, and 9.161, respectively. Researchers Gmehling and Onken17 suggested that the VLE data were internally consistent, if the absolute average deviation in vapor mole fractions is less than or equal to about 0.01. For the point-to-point test of Van Ness et al., we used a fourparameter Legendre polynomial for the excess Gibbs free energy: k GE = x1(1 − x1)∑ ak Lk (x1) RT

b

Tc/K a

4.94410 3.31246d 2.40800b

Reference 25. Reference 10.

where the values of (area+) and (area−) are sourced from the ln(γ1/γ2) − x1 diagram.

g=

q a

a

Reference 12. bReference 15.

(T − Tmin) J = 150· max Tmin

r

compound

20.0 kPa −2160.40 3563.80 0.07 0.002 −3488.50 6231.80 0.16 0.006 6032.00 −3490.60 0.27 0.010 0.4089 −0.0912 0.14 0.005

exp N cal exp AADT = (1/N)∑Ni=1|Tcal i − Ti |. AADy1 = (1/N)∑i=1|yi − yi |.

Table 7. Mathematical Forms of the Activity Coefficient Equations UNIQUAC

ln γi =

ϕi xi

− qi∑ li =

+

ϕ θi ⎛Z⎞ ⎜ ⎟q ln + li − i ∑ xjl j − qi ln(∑ θτ j ji) + qi ⎝2⎠ i ϕ xi j j i θτ j ij

∑j θkτkj

Z (ri − qi) − (ri − 1), 2

θi =

qixi ∑j qjxi

ϕi =

,

rx i i , ∑j rjxj

⎛ gji − gii ⎞ τji = exp⎜− ⎟ ⎝ RT ⎠ NRTL

ln γi = xj2[Aij + 2xi(Aji − Aij)],

τij =

gij − gjj RT

,

Gij = exp(− aijτij),

aij = aji Wilson

⎛ Aij Aji ⎞ ⎟ ln γi = − ln(xi + Aijxj) + xj⎜⎜ − xj + xiAji ⎟⎠ ⎝ xi + xjAij

Aij = vi = Margules

Vj Vi

⎛ gij − gii ⎞ exp⎜− ⎟ ⎝ RT ⎠

RTci τi Zci , Pci

τi = 1 + (1 − T /Tci)2/7 ,

T /Tci ≤ 0.75

ln γi = xj2[Aij + 2xi(Aji − Aij)] 2275



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Table 10. Parameters for the UNIQUAC, NRTL, Wilson, and Margules Equations and AADT/K and AADy1 for {MMEA (1) + EG (2)} at p = (40.0, 30.0, and 20.0) kPaa 40.0 kPa g12−g22/J·mol−1 g21−g11/J·mol−1 AADT/K AADy1 g12−g22/J·mol−1 g21−g11/J·mol−1 AADT/K AADy1 g12−g11/J·mol−1 g21−g22/J·mol−1 AADT/K AADy1 A12 A21 AADT/K AADy1 a

30.0 kPa

UNIQUAC Parameters 126.65 124.39 25.77 −3.31 0.10 0.06 0.005 0.004 NRTL Parameters 238.66 106.02 54.76 105.99 0.11 0.07 0.004 0.003 Wilson Parameters 110.47 177.18 370.34 253.48 0.13 0.08 0.005 0.004 Margules Parameters 0.0464 0.0671 0.1127 0.0557 0.07 0.08 0.004 0.004

20.0 kPa 61.35 13.93 0.07 0.004 49.65 49.64 0.09 0.004 25.12 250.99 0.09 0.004

Figure 1. VLE data for the system {MMEA (1) + MDEA (2)} at 40.0 kPa. ●, experimental data for T−x; ○, experimental data for T−y. , calculated data by the UNIQUAC equation for T−x−y; ···, calculated data by the NRTL equation; -·-·-, calculated data by the Wilson equation; ---, calculated data by the Margules equation. x1 and y1 are the mole fractions of MMEA in the liquid and vapor phases, respectively.

0.0265 0.0316 0.09 0.004


Table 11. Parameters for the UNIQUAC, NRTL, Wilson, and Margules Equations, and AADT/K and AADy1 for the System of {EG (1) + MDEA (2)} at p = (40.0, 30.0, and 20.0) kPaa 40.0 kPa g12−g22/J·mol−1 g21−g11/J·mol−1 AADT/K AADy1 g12−g22/J·mol−1 g21−g11/J·mol−1 AADT/K AADy1 −1

g12−g11/J·mol g21−g22/J·mol−1 AADT/K AADy1 A12 A21 AADT/K AADy1 a

30.0 kPa

UNIQUAC Parameters −223.35 26.14 −27.25 −0.51 0.11 0.08 0.005 0.004 NRTL Parameters −766.28 −294.63 −835.40 −446.77 0.16 0.06 0.006 0.004 Wilson Parameters −298.43 131.75 −263.52 65.56 0.15 0.09 0.005 0.004 Margules Parameters −0.3398 −0.1872 −0.4836 −0.2058 0.07 0.06 0.002 0.004

20.0 kPa −119.72 −12.02 0.11 0.005 −598.11 −606.09 0.09 0.005

Figure 2. VLE data for the system {MMEA (1) + MDEA (2)} at 30.0 kPa. ●, experimental data for T−x; ○, experimental data for T−y. , calculated data by the UNIQUAC equation for T−x−y; ··· calculated data by the NRTL equation; -·-·-, calculated data by the Wilson equation; ---, calculated data by the Margules equation. x1 and y1 are the mole fractions of MMEA in the liquid and vapor phases, respectively.

−88.32 −199.50 0.13 0.005 −0.2769 −0.3692 0.07 0.003

optimization.22 At experimental low pressures, the behavior of vapor phase can be assumed at an ideal state. Thus, the activity coefficient of component i of the liquid phase can also be calculated. The experimental liquid-phase activity coefficient is given as follows. yp γi = i s xipi (5)


The results of thermodynamic consistency tests are presented in Table 6. It showed that the experimental points also passed the verification of the Van Ness point test and turned out to be reliable. Data Correlations. All of the VLE data were correlated by the universal quasichemical (UNIQUAC),19 nonrandom twoliquid (NRTL),18 Wilson,20 and Margules21 models. Equation 7 was used as the objective function for the parameters

where yi represents the vapor-phase mole fraction, xi is the liquid-phase mole fraction, γi is the activity coefficient of component i,23 and pis represents the vapor pressure of pure solvent i (i = 1, 2) at equilibrium temperature. For MDEA, the 2276



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Figure 3. VLE data for the system {MMEA (1) + MDEA (2)} at 20.0 kPa. ●, experimental data for T−x; ○, experimental data for T−y. , calculated data by the UNIQUAC equation for T−x−y; ···, calculated data by the NRTL equation; -·-·-, calculated data by the Wilson equation; ---, calculated data by the Margules equation. x1 and y1 are the mole fractions of MMEA in the liquid and vapor phases, respectively.

Figure 5. VLE data for the system {MMEA (1) + EG (2)} at 30.0 kPa. ●, experimental data for T−x; ○, experimental data for T−y. , calculated data by the UNIQUAC equation for T−x−y; ···, calculated data by the NRTL equation; -·-·-, calculated data by the Wilson equation; ---, calculated data by the Margules equation. x1 and y1 are the mole fractions of MMEA in the liquid and vapor phases, respectively.



vapor pressure was calculated by eq 6, the following Clausius− Clapeyron type equation.25

number, and its value is 10; gij is the interaction energy between the molecules i and j; the van der Waals volume parameters (ri) and area parameters (qi) for UNIQUAC model are listed in Table 8. For the NRTL model, the nonrandomness parameter (aij) was set to 0.3, and gij−gjj are the binary interaction energy parameters. gij−gii are the binary interaction energy parameters for the Wilson model. Aij and Aji are the Margules parameters. The corresponding parameters for the four models are given in Tables 9 to 11, respectively. The objective function OF used to regress model parameters with the least-squares method is:

7588.516 (6) T s where p is in Pa and T in K. Equation 6 originated from fitting experimental vapor pressure data in the temperature T = (413 to 513) K,26 and it is also in satisfactory agreement with the range of T = (323 to 383) K, according to a similar equation put forward by Xu et al.27 The activity coefficient equations of UNIQUAC, NRTL, and Wilson and Margules models are presented in Table 7. For UNIQUAC model, Z represents the lattice coordination ln ps = 26.13691 −

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Figure 7. VLE data for the system {EG (1) + MDEA (2)} at 40.0 kPa. ●, experimental data for T−x; ○, experimental data for T−y. , calculated data by the UNIQUAC equation for T−x−y; ···, calculated data by the NRTL equation; -·-·-, calculated data by the Wilson equation; ---, calculated data by the Margules equation. x1 and y1 are the mole fractions of EG in the liquid and vapor phases, respectively.


represent experimental and calculated, separately. N stands for the number of experimental data points. The absolute average deviations between the boiling temperatures (AADT) and vapor phase mole fractions (AADy1) at each experimental pressure are shown in Tables 9 to 11, respectively. The maximum absolute deviations |Δy1|max for the vapor phase components correlated by UNIQUAC, NRTL, and Margules models were 0.010, 0.009, and 0.009, and the maximum absolute deviations |ΔT|max were (0.37, 0.25, and 0.26) K at P = (40.0, 30.0, and 20.0) kPa, respectively. The experimental and calculated data in the form of T−x1−y1 diagrams at corresponding pressures are presented in Figures 1 to 9, respectively. It showed that there were no azeotropic behaviors observed at the three low pressures. All of these results indicated that the UNIQUAC, NRTL, and Margules models provided a good correlation for all of the experimental data of three binary systems. Otherwise, for the first system {MMEA + MDEA}, the Wilson model had a larger deviation in the vapor phase mole fraction y1 and temperature T. The maximum absolute deviations |Δy1|max were 0.021, 0.019, and 0.022, and the maximum absolute deviations |ΔT|max were (0.58, 0.50, and 0.52) K at three corresponding pressures P = (40.0, 30.0, and 20.0) kPa. All of these results demonstrated that the experimental and the calculated data of the studied systems were in good consistency.


⎛ γ − γ ⎞2 exp cal ⎟ OF = ∑ ⎜⎜ ⎟ γ ⎝ ⎠ exp

■

(7)

CONCLUSIONS In this work, the isobaric equilibrium data of three binary mixtures, {MMEA (1) + MDEA (2)}, {MMEA (1) + EG (2)}, and {EG (1) + MDEA (2)}, were studied at three reduced pressures P = (40.0, 30.0, and 20.0) kPa, using a modified still. UNIQUAC, NRTL, Wilson, and Margules models were chosen to correlate the experimental results and to obtain the interaction parameters. For the binary VLE data of the {MMEA + MDEA} system, it could be seen that UNIQUAC, NRTL, and Margules models gave a better prediction than the Wilson model. The absolute average deviation of temperature and the vapor phase components for three systems were below AADT = (0.07, 0.17, 0.27, and 0.15) K, and AADy1 = (0.002,

where γexp and γcal are the experimental and calculated activity coefficients, respectively. The absolute average deviations (AAD) of boiling temperatures and vapor phase mole fractions are used to measure the agreement between the experimental values and the calculated ones. The AAD is defined as follows. N

AAD =

1 ∑ |Uiexp − Uical| N i=1

(8)

where U indicates a variable quantity, such as temperature and vapor phase mole fraction. The superscript “exp” and “cal” 2278



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0.006, 0.10, and 0.005), respectively. All VLE data passed the semiempirical area test of Herington and the point test of Van Ness et al. The results showed the experimental data and the interaction parameters obtained in this work could be applied to the further research and the design of chemical engineering systems containing MDEA, MMEA, and EG.

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AUTHOR INFORMATION

Corresponding Author

*E-mail address: [email protected]. Fax: 02227403389. Telephone: 022-27890907. Funding

The Programme of Introducing Talents of Discipline to Universities (No. B060006) has provided great support to this work. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the anonymous reviewers for their insightful comments and would like to express our appreciation to them for helping us improve the quality of this work.

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REFERENCES

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