Measurement and Modeling of VaporâLiquid Equilibria for the

Article pubs.acs.org/jced

Measurement and Modeling of Vapor−Liquid Equilibria for the Octane + Sulfuric Acid + Water + Ethanol System Geng Li and Zhibao Li* Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China ABSTRACT: Octane was considered to be a potential entrainer for the recovery of spent sulfuric acid by heterogeneous azeotropic distillation. The vapor−liquid equilibria (VLE) data were determined for octane + ethanol, octane + water + ethanol, and octane + sulfuric acid + water + ethanol systems at (30, 60, 90, and 101.3) kPa using the ebulliometric method. The VLE data were used to regress the electrolyte nonrandom two-liquid interaction parameters with the help of Aspen Plus for pairs: C8H18−C2H6O, C8H18−H2O, H2SO4−C2H6O, C2H6O−[H3O]+:[HSO4]−, C2H6O−[H3O]+:[SO4]2−, C8H18−[H3O]+:[HSO4]−, and C8H18−[H3O]+:[SO4]2−. The correlation fitted the experimental data well for all the systems. The maximum absolute deviation and average absolute deviation for temperature for the systems are 0.86 K and 0.26 K, respectively.

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NRTL) model.18−21 Que et al.22 developed a thermodynamic model for the sulfuric acid + water + sulfur trioxide system over the whole concentration range from pure water to pure sulfuric acid to pure sulfur trioxide by the use of the symmetric electrolyte NRTL activity coefficient model. Excellent matches between model correlations and available literature data are achieved. The aim of this paper is to measure the VLE data for the system containing octane + sulfuric acid + water + ethanol at the pressures of (30, 60, 90, and 101.3) kPa by the quasi-static ebulliometric method. A thermodynamic model for the system is then developed on the basis of the electrolyte NRTL model with the help of Aspen Plus. The electrolyte NRTL parameters for the following pairs are obtained by regressing the experimental VLE data, namely, pairs of C8H18−C2H6O, C8H18−H2O, H2SO4− C2H6O, C2H6O−[H3O]+:[HSO4]−, C2H6O−[H3O]+:[SO4]2−, C8H18−[H3O]+:[HSO4]−, and C8H18−[H3O]+:[SO4]2−. The VLE data and the parameters will provide the information for the enrichment of spent sulfuric acid by heterogeneous azeotropic distillation.

INTRODUCTION Most recently, a new method for the recovery of waste sulfuric acid generated from the titanium dioxide (TiO2) industry by heterogeneous azeotropic distillation was proposed in our previous work.1 In this process butyl acetate was chosen as the entrainer due to its large capacity to carry water. Unfortunately, it was found that butyl acetate was partially decomposed when sulfuric acid was present at the operation temperature. This reminds us that much more work in the screening of other entrainers should be done. On the basis of the rules for entrainer selection,2,3 potential entrainers should on one hand form a minimum-boiling azeotrope with water and on the other hand be very stable in the sulfuric acid system. Some hydrocarbons and ethers, including octane, isooctane, cyclohexane, heptane, di-npropyl ether, and diisopropyl ether, etc.,4−6 are considered to be attractive potential entrainers. To select a suitable entrainer and design the heterogeneous azeotropic distillation process proposed by the authors, more phase equilibria data for sulfuric acid + water system are required. In this work, the VLE for the octane + sulfuric acid + water + ethanol system were investigated. Boublikova and Lu,7 Janaszewski et al.,8 Hongo et al.,9 Hiaki et al.,10 and Hull et al.,11 determined the isothermal vapor−liquid equilibria (VLE) data of ethanol + octane at different temperatures, and Hiaki et al.12 also measured the VLE data for ethanol + octane at 101.3 kPa. Although the isobaric VLE data of water + octane at atmospheric pressure was given by Tu et al.,13 larger uncertainty of measurement was observed due to the extreme immiscibility for the system. However, the addition of ethanol enables us to accurately measure the boiling points within a wider miscible region.14 Then the binary parameters for C8H18−H2O can be obtained by correlating the VLE data for the octane + water + ethanol system. Sulfuric acid containing systems have been studied extensively over the years. Some widely referenced activity coefficient models in the literatures include the Pitzer model,15 the extended UNIQUAC model,16 the OLI mixed-solvent electrolyte (MSE) model,17 and the electrolyte nonrandom two-liquid (electrolyte © XXXX American Chemical Society

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EXPERIMENTAL SECTION Experimental Materials. The ethanol and sulfuric acid used in the experiments were analytical grade and supplied by Beijing Chemical Plant with mass fraction purities of 0.995 and 0.95−0.98, respectively. The octane was supplied by Sinapharm Chemical Reagent Co., Ltd. with minimum mass fraction purity of 0.98. All were used without further purification. The deionized water produced in the local laboratory was used in the experiments. Experimental Apparatus. The boiling points of the systems were determined by the quasi-static ebulliometric

Received: March 11, 2013 Accepted: June 3, 2013

A

dx.doi.org/10.1021/je400238j | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

method.23 The schematic diagram of the experimental apparatus was presented in detail in previous publications.1,24 The boiling points were measured by two calibrated microthermometers. The total temperature uncertainty was considered to be ± 0.15 K, including a reading error of ± 0.05 K and an error of ± 0.10 K for the nonimmersed stem correction. This temperature variation may cause an uncertainty of ± 0.6 kPa for pressure. The vapor phases were cooled with glycol solution at 273 K to minimize the loss. On the basis of the holdup on the inner face of the ebulliometer, the fluctuation of feed composition of liquid phase in mole fraction was considered to be within ± 0.002.24 Experimental Procedure. The experimental procedure was as follows:23 The deionized water and the mixture with a known composition were charged into separate ebulliometers. The composition of mixture was obtained gravimetrically by a digital balance (model JA5003) with an uncertainty of ± 0.001 g. The system pressure was carefully adjusted until the desired water temperature was reached when the equilibrium was achieved. The boiling point of the mixture was recorded and then the measurement was executed again at a higher water temperature. The Antoine equation25 of pure water was used to determine the system pressures of (30, 60, 90, and 101.3) kPa by controlling corresponding water temperatures at (342.35, 359.15, 369.85 and 373.15) K, respectively. The Antoine equation constants are listed in Table 1. The experimental apparatus and procedure

reactions. For the octane + sulfuric acid + water + ethanol system, the electrolyte NRTL model embedded in the Aspen Plus (Version 2006) was selected and the main dissociation reactions are summarized in eqs 3 to 5.

a

A

B

C

octane water ethanol

13.9346 16.3872 8.1122

3123.13 3885.70 1592.864

209.635 230.170 226.184

(4)

2H 2O ↔ H3O+ + OH−

(5)

(6)

j

The electrolyte NRTL model contains two contributions:27 one is the long-range ion−ion interactions represented by the Pitzer−Debye−Hückel model and Born equation, and one is the local interaction described by the nonrandom two-liquid (NRTL) theory.28 The excess Gibbs energy model is expressed as follows: Gm*E G*E,PDH G*E,Born G*E ,lc = m + m + m RT RT RT RT

(7)

which leads to ln γi* = ln γi*PDH + ln γi*Born + ln γi*lc

(8)

where Gm*E is molar excess Gibbs energy, and γi is the activity coefficient of species i in the liquid phase. The superscripted asterisk (∗) is used to denote an unsymmetrical reference state, PDH, Born, and lc mean Pitzer−Debye−Hückel, Born, and local composition, respectively. The expression for the Pitzer−Debye−Hückel equation is given by29

were verified by measuring VLE data for the butyl acetate + cyclohexane binary system and comparing experimental data with literature.23

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THERMODYNAMIC MODELING FRAMEWORK Vapor−Liquid Equilibria. General equilibrium relationship for vapor−liquid can be expressed as follows:26

⎛ 1000 ⎞1/2 PDH * ln γi = −⎜ ⎟ Aφ ⎝ MB ⎠ ⎡⎛ 2z 2 ⎞ z 2I1/2 − 2Ix3/2 ⎤ ⎥ × ⎢⎜ i ⎟ln(1 + ρIx1/2) + i x ⎢⎣⎝ ρ ⎠ 1 + ρIx1/2 ⎥⎦

(1)

where P is the system pressure, yi is the vapor phase mole fraction of component i, φi is the vapor phase fugacity coefficient of component i, xi is the liquid phase mole fraction of component i, γi is the liquid phase activity coefficient for component i in the liquid phase, Psi is the vapor pressure of pure component i at the system temperature T, calculated by the Antoine equation using the parameters listed in Table 1, φsi is the vapor fugacity coefficient of pure component i at T and Psi , and θsi is the Poynting pressure correction from Psi to P. The Poynting pressure correction θsi , φi, and φsi could be reasonably assumed to be unity at low equilibrium pressures, and then eq 1 can be simplified to Pyi = xiγiPiS

HSO−4 + H 2O ↔ SO24− + H3O+

⎛ ∂(n GE /RT ) ⎞ total ⎟ ln γi = ⎜ ∂ni ⎝ ⎠T , P , n

Antoine equation: log(psi /kPa) = A − B /[(T − 273.15)/K + C].

Pyi φi = xiγiPiSφiSθiS

(3)

The dissociation constants of eqs 3 and 4 are taken from the literature,22 and dissociation constant of water is taken from the Aspen Plus default databank. Activity Coefficient Model. The activity coefficient is a thermodynamic state function, accounts for nonideality (excess properties) of an electrolyte solution, and is derived from the excess Gibbs free energy of the solution:

Table 1. Antoine Equationa Constants of the Pure Components25 component

H 2SO4 + H 2O ↔ HSO−4 + H3O+

(9)

where MB is molecular weight of the solvent B, Aφ is Debye− Hückel parameter, zi is charge number of ion i, ρ is “closest approach” parameter, and Ix is ionic strength (mole fraction scale). The expression for the activity coefficient of Born equation is as follows:27

ln γi*Born =

(2)

2 Q e2 ⎛ 1 1 ⎞ zi −2 ⎟ 10 ⎜ − 2kT ⎝ ε εw ⎠ ri

(10)

where Qe is electron charge, εw is the dielectric constant of water, and ri is the Born radius.

Dissociation Reactions. Thermodynamic modeling of electrolyte solutions requires proper representation of chemical B



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In a multicomponent solution, the local composition activity coefficients equation for cation, anion, and molecular components are given by the following: 1 ln γ *lc = zc c

Table 2. Isobaric Experimental Boiling Points for Temperature T, Pressure p, and Mole Fraction x for the Binary System Octane (1) + Ethanol (2)a

⎛

Xa ′ ⎞ ∑k XkGk c,a ′ cτk c,a ′ c ⎟⎟ ⎝ ∑a ″ Xa ″ ⎠ ∑k XkGk c,a ′ c

T/K

∑ ⎜⎜ a′

+∑ B

∑ XG τ ⎞ XBGcB ⎛ ⎜⎜τcB − k k k B k B ⎟⎟ ∑k XkGk B ⎝ ∑k XkGk B ⎠ ⎛

+

Xc ′ ⎞ XaGca,c ′ a ⎟⎟ ⎝ ∑c ″ Xc ″ ⎠ ∑k XkGk a,c ′ a

∑ ∑ ⎜⎜ c′

a

⎛ ∑ XkGk a,c ′ aτk a,c ′ a ⎞ ⎟⎟ × ⎜⎜τca,c ′ a − k ∑k XkGk a,c ′ a ⎠ ⎝ 1 ln γ *lc = za a

(11)

⎛

Xc ′ ⎞ ∑k XkGk c,c ′ aτk c,c ′ a ⎟⎟ ⎝ ∑c ″ Xc ″ ⎠ ∑k XkGk c,c ′ a

∑ ⎜⎜ c

+∑ B

∑ XG τ ⎞ XBmGaB ⎛ ⎜⎜τaB − k k k B k B ⎟⎟ ∑k XkGk B ⎝ ∑k XkGk B ⎠ ⎛

+

Xa ′ ⎞ XcGac,a ′ c ⎟⎟ ⎝ ∑a ″ Xa ″ ⎠ ∑k XkGk c,a ′ c

∑ ∑ ⎜⎜ a′

c

⎛ ∑ XkGk c,a ′ cτk c,a ′ c ⎞ ⎟⎟ × ⎜⎜τac,a ′ c − k ∑k XkGk c,a ′ c ⎠ ⎝ ln γBlc =

∑j XjGjBτjB ∑k XkGk B

+

∑ B′

(12)

x1

30 kPa

60 kPa

90 kPa

101.3 kPa

0.0000 0.0270 0.0520 0.1002 0.1425 0.1676 0.2099 0.2421 0.2778 0.3379 0.4074 0.4449 0.4836 0.5292 0.5741 0.6434 0.6835 0.7347 0.8110 0.8400 0.9080 0.9542 1.0000

323.46 322.56 322.10 321.70 321.60 321.60 321.60 321.65 321.65 321.75 321.85 321.90 322.00 322.10 322.26 322.36 322.56 322.76 323.73 323.86 326.13 331.63 359.76

338.72 337.91 337.35 337.00 336.89 336.89 336.89 337.00 337.05 337.15 337.30 337.40 337.50 337.60 337.81 338.01 338.26 338.62 339.43 339.98 342.27 348.36 380.43

348.56 347.75 347.29 346.93 346.83 346.83 346.88 346.93 347.04 347.24 347.34 347.44 347.59 347.75 348.00 348.20 348.61 348.97 350.19 350.75 353.54 361.39 394.09

351.51 350.69 350.34 349.98 349.88 349.93 349.98 350.03 350.14 350.29 350.39 350.54 350.69 350.85 351.10 351.30 351.71 352.02 353.34 353.90 357.16 366.08 398.49

a

Standard uncertainties u are u(T) = 0.15 K, u(p) = 0.6 kPa, and u(x) = 0.002.

∑ XG τ ⎞ XB ′G BB ′ ⎛ ⎜⎜τBB ′ − k k k B ′ k B ′ ⎟⎟ ∑k XkGk B ′ ⎠ ∑k XkGk B ′ ⎝

⎛ X ⎞ XcG Bc,a ′ c ⎛ ⎞ ∑ XG τ a′ ⎟ ⎜⎜τBc,a ′ c − k k k c,a ′ c k c,a ′ c ⎟⎟ + ∑ ∑ ⎜⎜ ⎟ ∑ ∑ ∑ XG ⎠ c a ′ ⎝ a ″ X a ″ ⎠ k Xk Gk c,a ′ c ⎝ k k k c,a ′ c ⎛

+

⎞ ∑ XG τ Xc ′ ⎞ XaG Ba,c ′ a ⎛ ⎟⎟ ⎜⎜τBa,c ′ a − k k k a,c ′ a k a,c ′ a ⎟⎟ ∑k XkGk a,c ′ a ⎠ ⎝ ∑c ″ Xc ″ ⎠ ∑k XkGk a,c ′ a ⎝

∑ ∑ ⎜⎜ a

c′

(13)

where ln Gk a,c ′ a = −τk a,c ′ aα

τcB = τaB = τca,B ;

(14)

τBc = τBa = τB,ca ;

τBc,ac = τBa,ca = τB,ca

(15)

where a means anion, c means cation, B means solvent, j and k can be any species (a, c, or B), and Xj = xjZj is the effective mole fraction of species j. α and τ are nonrandomness factor and energy parameter, respectively. Normally, the value of α is 0.2 for molecule−electrolyte and 0.3 for molecule−molecule.30 The energy parameters τ can be assumed to be temperature-dependent as follows:27 Molecule−molecule binary parameters: τB,B′ = C B,B′ +

Figure 1. Isobaric VLE diagram for octane (1) + ethanol (2) binary system. □, 30 kPa; ○, 60 kPa; Δ, 90 kPa; ▽, 101.3 kPa; ◊, Hiaki et al.;12 , (T−x), ---, (T−y), electrolyte NRTL equation.

where ca means electrolyte (cation−anion), Tref is reference temperature (273.15 K), and αij, Cij, Dij, and Eij are adjustable parameters. The electrolyte NRTL model incorporated in Aspen Plus (version 2006) was used in the correlation, and the following objective function was minimized to obtain the optimal parameters values by fitting the experimental boiling point data on the basis of maximum likelihood principle:27

DB,B′ (16)

T

Electrolyte−molecule pair parameters: τca,B = Cca,B +

Dca,B T

⎡ (T ref − T ) ⎛ T ⎞⎤ + Eca,B⎢ + ln⎜ ref ⎟⎥ ⎝ T ⎠⎦ T ⎣ (17) C



Article

Table 3. The Electrolyte NRTL Interaction Parametersa Used in This Work

a

no.

component i

component j

C

D

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

H2O C2H6O C8H18 C2H6O C8H18 H2O H2SO4 C2H6O H2SO4 H3O+:HSO4 H2SO4 H3O+:SO42 H2O H3O+:HSO4 H2O H3O+:SO42 C2H6O H3O+:HSO4 C2H6O H3O+:SO42 C8H18 H3O+:HSO4 C8H18 H3O+:SO42

C2H6O H2O C2H6O C8H18 H2O C8H18 C2H6O H2SO4 H3O+:HSO4 H2SO4 H3O+:SO42 H2SO4 H3O+:HSO4 H2O H3O+:SO42 H2O H3O+:HSO4 C2H6O H3O+:SO42 C2H6O H3O+:HSO4 C8H18 H3O:SO42 C8H18

3.6220 −0.9223 −0.0168 −2.1242 −4.8065 −0.6096 −2.3854 −0.3568 12.9920 −2.9810 8.0000 −4.0000 6.3620 −3.7490 8.0000 −4.0000 6.8540 −5.3237 8.0000 −4.0000 −48.5243 16.8868 8.0000 −4.0000

−636.7260 284.2856 698.4643 1350.5125 2877.2482 2792.0132 246.3705 −4280.9401 −1732.9000 −162.3000 0.0000 0.0000 1958.2000 −583.2000 0.0000 0.0000 −14.8637 573.0786

E

−30.1260 0.8060

55.5145 84.4520

1215.2812 36.2590

−4.5990 4.4720

76.7735 −1.8791

αij 0.30 0.30 0.4832 0.4832 0.2356 0.2356 0.30 0.30 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20

Parameters (no. 1, 2, and 9 to 16) from AspenPlus data bank, (no. 3 to 8, 17 to 24) obtained in this work.

Table 4. Azeotropic Compositions and Temperatures for Octane (1) + Ethanol (2) Binary System at (30, 60, 90, and 101.3) kPa

a

p/kPa

30

60

90

101.3

101.3a

x1 (AZ) T (AZ)/K

0.1576 321.45

0.1487 336.93

0.1413 346.85

0.1378 349.88

0.137a 349.76a

Taken from ref 12.

FOB

⎡ ⎛ exp ⎛ pexp − pcal ⎞2 cal ⎞2 ⎢ ⎜ Ti − Ti ⎟ i i ⎟ = ∑ ⎢f1 ⎜ ⎟ + f2 ⎜⎜ ⎟ σ σ ⎠ T P ⎝ ⎠ i ⎣ ⎝ ⎛ z exp − z cal ⎞2 ⎤ i ⎟⎟ ⎥ + f3 ⎜⎜ i σ ⎝ ⎠ ⎥⎦ Z

(18)

where σ is standard deviation (0.1 K for temperature, 0.1 % for pressure, and 1 % for the feed composition z), f is weight factor, z is the feed composition, exp and cal mean experimental data and calculated result, respectively.

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RESULTS AND DISCUSSION Binary System. The VLE for octane + ethanol binary system at (30, 60, 90, and 101.3) kPa were determined and listed in Table 2. As illustrated in Figure 1, the measurement covered a temperature range from (321 to 399) K, and the minimumboiling azeotropes were found in this system at all experimental pressures. The VLE data were used to correlate the C8H18− C2H6O binary parameters, which were listed in Table 3. The correlation fitted the experimental data well, and the average absolute deviation (AAD) and the maximum absolute deviation (MAD) of temperature between correlated and experimental were of 0.10 and 0.52 K, respectively. The comparisons between the experimental data, correlated values, and literature12 data which are thermodynamically consistent were also shown in

Figure 2. Isobaric VLE diagram for octane (1) + water (2) + ethanol (3) ternary systems. x2/x3 = 0.0749: ■, 30 kPa; ●, 60 kPa; ▲, 90 kPa; ▼, 101.3 kPa. x2/x3 = 0.0337: □, 30 kPa; ○, 60 kPa; Δ, 90 kPa; ▽, 101.3 kPa; , electrolyte NRTL equation.

Figure 1. The experimental results of pure components are consistent with the literature data12 at 101.3 kPa with absolute deviations of 0.07 K for ethanol and 0.31 K for octane. The correlated results agree with the literature data quite well with the AAD for vapor phase mole fraction and temperature of 0.0047 D



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Table 5. Isobaric Experimental Boiling Points for Temperature T, Pressure p, and Mole Fraction x for the Ternary System Octane (1) + Water (2) + Ethanol (3)a T/K x1

x2

30 kPa

60 kPa

90 kPa

101.3 kPa

348.46 347.24 346.53 346.22 346.17 346.12 345.82 345.77 345.72 346.02 346.22 346.43 346.83 348.86 350.69 355.27 394.60

351.41 350.24 349.53 349.47 349.27 349.17 348.97 348.97 348.97 349.27 349.47 349.58 349.88 352.02 353.80 359.09 398.74

348.47 347.25 346.69 346.39 346.34 346.29 346.24 346.24 346.34 346.74 347.19 347.75 349.78 351.81 358.23 394.60

351.42 350.30 349.84 349.44 349.44 349.34 349.34 349.34 349.49 349.84 350.24 350.90 352.93 355.27 362.51 398.74

x2/x3 = 0.0749 0.0000 0.0260 0.0529 0.0902 0.0928 0.1316 0.2122 0.4006 0.4631 0.6433 0.6886 0.6996 0.7922 0.8876 0.9174 0.9451 1.0000

0.0697 0.0679 0.0660 0.0634 0.0632 0.0605 0.0549 0.0418 0.0374 0.0249 0.0217 0.0209 0.0145 0.0078 0.0058 0.0038 0.0000

0.0000 0.0304 0.0541 0.0960 0.1386 0.2141 0.3034 0.4135 0.5232 0.6147 0.6962 0.7900 0.8841 0.9146 0.9486 1.0000

0.0326 0.0316 0.0308 0.0295 0.0281 0.0256 0.0227 0.0191 0.0155 0.0126 0.0099 0.0068 0.0038 0.0028 0.0017 0.0000

323.46 338.62 322.20 337.40 321.54 336.79 320.93 336.39 321.14 336.34 320.99 336.19 320.63 335.88 320.58 335.78 320.58 335.68 320.63 336.03 320.73 336.14 320.99 336.39 321.14 336.79 321.95 338.57 323.53 340.04 326.17 343.28 360.06 380.94 x2/x3 = 0.0337 323.46 338.63 322.10 337.41 321.65 337.01 321.09 336.50 321.09 336.40 320.99 336.30 320.93 336.25 320.93 336.30 321.04 336.45 321.09 336.60 321.39 337.00 321.60 337.50 322.76 339.02 324.06 341.35 327.59 346.02 360.06 380.94

Figure 3. Isobaric VLE diagram for sulfuric acid (1) + water (2) + ethanol (3) ternary system. x1/x2 = 0.0431:1 ○, 30 kPa; ●, 60 kPa; ☆, 90 kPa. x1/x2 = 0.1334:1 Δ, 30 kPa; ▲, 60 kPa; ▽, 90 kPa. x1/x2 = 0.3222:1 □, 30 kPa; ■, 60 kPa; ◊, 90 kPa; , electrolyte NRTL equation.

Table 6. Deviations (ΔT) between the Experimental Data and Electrolyte NRTL Model Regression for Octane (1) + Sulfuric Acid (2) + Water (3) + Ethanol (4) Systemsa octane + ethanol p/kPa

|ΔT|av/K

|ΔT|max/K

30 60 90 101.3 overall

0.13 0.11 0.09 0.08 0.10

0.25 0.52 0.40 0.39 0.52

sulfuric acid + water + ethanol

a

octane + water + ethanol |ΔT|av/K

|ΔT|max/K

0.20 0.48 0.19 0.48 0.18 0.48 0.18 0.55 0.19 0.55 octane + sulfuric acid + water + ethanol

p/kPa

|ΔT|av/K

|ΔT|max/K

|ΔT|av/K

|ΔT|max/K

30 60 90 101.3 overall

0.80 0.70 0.52

4.10 3.62 2.67

0.68

4.1

0.26 0.24 0.23 0.30 0.26

0.80 0.86 0.70 0.82 0.86


|ΔT| = |Tcal − Texp|; |ΔT|av = (Σin= 1|ΔT|k)/n where n is the number of data points.

and 0.17 K, respectively. The azeotropic compositions and temperatures at different pressures were also predicted and listed in Table 4. It is noted that the mole fraction of octane (x1) for the azeotropes is decreasing as pressure increases and an excellent agreement between prediction and literature12 is obtained at 101.3 kPa. Ternary Systems. The boiling points for octane + water + ethanol ternary system were measured at (30, 60, 90, and 101.3) kPa and tabulated in Table 5 and also depicted in Figure 2. The boiling points first decrease and then increase as the mole fraction of octane (x1) increases at fixed ratios of water/ethanol and they also decrease as the ratios of water/ethanol is increased. The boiling points vary merely slightly when x1 is less than 0.9, but increase dramatically when x1 is larger than 0.9. The C8H18− H2O binary parameters were obtained by regressing the boiling point data of the ternary system and demonstrated in Table 3. The regressed results were also illustrated in Figures 2 in comparison with the experimental data and the regression fitted

the experimental data quite well with the AAD (T) of 0.19 K and MAD (T) of 0.55 K. The VLE for sulfuric acid + water + ethanol ternary system from our earlier work1 were taken to correlate the interaction parameters between sulfuric acid and ethanol, namely, the electrolyte NRTL parameters for pairs H2SO4−C2H6O, C2H6O− [H3O]+:[HSO4]−, and C2H6O−[H3O]+:[SO4]2−. The comparison between correlated value and literature data were illustrated in Figure 3. As shown in Table 6, the deviations between the correlation and the literature data are 0.68 and 4.1 K for AAD (T) and MAD (T), respectively, which show a relatively good result. Quaternary System. The VLE values for octane + sulfuric acid + water + ethanol quaternary system were investigated at (30, 60, 90, and 101.3) kPa and listed in Table 7. It can be observed from Figure 4 that, at a fixed ratio of sulfuric acid/water/ ethanol, the boiling point first decreases slightly with mole fraction of octane (x1) to a minimum, then increases sharply when x1 is over 0.9, while x1 consistently increases. The quaternary

a

E



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Table 7. Isobaric Experimental Boiling Points for Temperature T, Pressure p, and Mole Fraction x for the Quaternary System Octane (1) + Sulfuric Acid (2) + Water (3) + Ethanol (4)a

Table 8. Deviations (ΔT) between the Experimental Data and MSE Model Regression for Octane (1) + Sulfuric Acid (2) + Water (3) + Ethanol (4) Systemsa octane + ethanol

T/K x1

x2

x3

30 kPa

60 kPa

90 kPa

101.3 kPa

0.0000 0.0271 0.0511 0.0952 0.1459 0.1999 0.3001 0.4232 0.5226 0.6148 0.6953 0.6968 0.7705 0.8708 0.9102 0.9512 0.9690 1.0000

0.0009 0.0008 0.0008 0.0008 0.0007 0.0007 0.0006 0.0005 0.0004 0.0003 0.0003 0.0003 0.0002 0.0001 0.0001 0.0000 0.0000 0.0000

0.0412 0.0401 0.0391 0.0373 0.0352 0.0330 0.0288 0.0238 0.0197 0.0159 0.0126 0.0125 0.0095 0.0053 0.0037 0.0020 0.0013 0.0000

323.56 322.36 321.80 321.39 321.19 321.19 321.19 321.19 321.29 321.44 321.60 321.60 322.10 323.53 324.95 328.31 332.59 360.06

338.62 337.55 337.05 336.59 336.44 336.49 336.49 336.54 336.59 336.95 337.30 337.30 337.91 339.63 341.35 346.73 351.51 380.94

348.56 347.44 346.93 346.53 346.27 346.32 346.32 346.43 346.53 346.93 347.34 347.24 348.00 349.78 352.02 358.13 363.23 394.60

351.46 350.34 349.83 349.48 349.27 349.22 349.27 349.37 349.68 350.14 350.54 350.39 351.20 353.24 355.48 361.90 368.43 398.74

p/kPa

|ΔT|av/K

|ΔT|max/K

30 60 90 101.3 overall

0.68 0.71 0.65 0.58 0.65

1.90 2.56 1.67 1.68 2.56

sulfuric acid + water + ethanol

octane + water + ethanol |ΔT|av/K

|ΔT|max/K

0.80 3.55 0.73 3.35 0.65 1.99 0.61 2.07 0.69 3.55 octane + sulfuric acid + water + ethanol

p/kPa

|ΔT|av/K

|ΔT|max/K

|ΔT|av/K

|ΔT|max/K

30 60 90 101.3 overall

0.62 0.69 0.57

2.89 2.93 2.47

0.63

2.93

1.28 1.21 1.05 1.12 1.17

3.85 3.46 3.16 3.21 3.85

|ΔT| = |Tcal − Texp|; |ΔT|av = (Σin= 1|ΔT|k)/n where n is the number of data points a

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CONCLUSIONS The quasi-static ebulliometric method and the apparatus herein are feasible in determining the VLE for miscible systems. Isobaric VLE data were determined at (30, 60, 90, and 101.3) kPa for the octane + ethanol, octane + water + ethanol, and octane + sulfuric acid + water + ethanol systems and the electrolyte NRTL model parameters were obtained via regression of the experimental data. The modeling results indicate that the electrolyte NRTL model, after the improvement made to it in this work, is suitable for the octane + sulfuric acid + water + ethanol system. The experimental VLE data and the new parameters obtained from experimental data provide thermodynamic data for the recovery of spent sulfuric acid by azeotropic distillation.

a


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AUTHOR INFORMATION

Corresponding Author

*Tel./Fax: +86-10-62551557. E-mail: [email protected]. Funding

The support of the National Natural Science Foundation of China (Grant No. 21076212, 21146006, and 21206165) and the National Basic Research Development Program of China (973 Program with Grant No. 2013CB632605) is gratefully acknowledged.

Figure 4. Isobaric VLE diagram for octane (1) + sulfuric acid (2) + water (3) + ethanol (4) quaternary system. □, 30 kPa; ○, 60 kPa; Δ, 90 kPa; ▽, 101.3 kPa; , electrolyte NRTL equation.

Notes

The authors declare no competing financial interest.

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boiling point data were employed to regress the electrolyte NRTL parameters for pairs of C8H18−[H3O]+:[HSO4]− and C8H18− [H3O]+:[SO4]2−, by the use of the newly regressed parameters listed in Table 3. Good agreements between model correlations and experimental data are achieved with deviations of 0.26 and 0.86 K for AAD (T) and MAD (T), respectively. We also modeled the systems with the MSE model as we did in our prior work1 as a comparison, and good results were obtained. The temperature deviations between experimental data and MSE regression were listed in Table 8. The average absolute deviations for octane + ethanol, octane + water + ethanol, and octane + sulfuric acid + water + ethanol systems are 0.65 K, 0.69 K, and 1.17 K, respectively.

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