Vapor–liquid equilibria for the system 1-propanol+n-hexane near the critical region

Fluid Phase Equilibria 220 (2004) 41–46

Vapor–liquid equilibria for the system 1-propanol + n-hexane near the critical region Byung Chul Oh a , Youngdae Kim a , Hun Yong Shin b , Hwayong Kim a,∗ a

School of Chemical Engineering, Institute of Chemical Processes, Seoul National University, Shilim-dong, Kwanak-gu, Seoul 151-744, South Korea b Department of Chemical Engineering, Seoul National University of Technology, Seoul 139-743, South Korea Received 3 October 2003; accepted 5 December 2003 Available online 8 May 2004

Abstract Vapor–liquid equilibria and critical point data for the system 1-propanol + n-hexane at 483.15, 493.15, 503.15 and 513.15 K are reported. The critical pressures determined from the critical opalescence of the mixture were compared with published data for the system 2-propanol + n-hexane. Phase behavior measurements were made in a modified circulating type apparatus with a view cell. These mixtures are highly nonideal because of the hydrogen bonding of 1-propanol. Modeling of the experimental data has been performed using the multi-fluid nonrandom lattice fluid with hydrogen-bonding (MF-NLF-HB) equation of state and the Peng–Robinson–Stryjek–Vera (PRSV) equation of state with Wong–Sandler mixing rule. The critical points and the critical locus were also calculated. © 2003 Elsevier B.V. All rights reserved. Keywords: Vapor–liquid equilibria; Critical point; n-Hexane; 1-Propanol; Lattice equation of state

1. Introduction Vapor–liquid equilibria (VLE) and critical point data are of great significance in various industrial fields; design, simulation and optimization of processes. Phase equilibrium of alkane + alkanol systems have been extensively investigated at low pressures, but only a few data are available at elevated temperature and pressure [1,2]. Furthermore, near the critical region, VLE measurements for polar and nonpolar mixtures are especially important because the properties of such mixtures cannot be predicted from the pure component values. Seo et al. [3] measured the VLE data for the system 2-propanol + n-hexane by a circulating method, and Deák et al. [4] measured the VLE data for the system 1-propanol+ n-butane by the static nonanalytic method. In this work, we have measured vapor–liquid equilibrium data for the 1-propanol + n-hexane system. The most common chemical effect encountered in alcohol solutions is that due to the hydrogen bond. Therefore, modeling mixtures containing alcohols was difficult quantitatively. In this paper VLE correlations for the sys∗

Corresponding author. Tel.: +82-2-880-7604; fax: +82-2-888-6695. E-mail address: [email protected] (H. Kim).

0378-3812/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2003.12.004

tem 1-propanol + n-hexane were carried out using a PRSV [5] with Wong–Sandler mixing rules [6] and MF-NLF-HB [7]. The MF-NLF-HB EOS was recently proposed by the present authors based on the nonrandom lattice-fluid theory combined with the effect of hydrogen bonding. Finally, we predicted critical loci for the system n-hexane + 1-propanol and 2-propanol.

2. Experimental 2.1. Chemicals 1-Propanol was supplied by Aldrich with a minimum purity of 99.5%. n-Hexane was supplied by Fluka with a minimum purity of 99.5% (GC) and stored over a molecular sieve. We kept the chemicals at a slightly higher temperature than the boiling temperature of each chemical for degassing before use. 2.2. Apparatus and procedure We carried out experiments using the modified apparatus of Seo et al. [8]. As shown in Fig. 1, the sampling box

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B.C. Oh et al. / Fluid Phase Equilibria 220 (2004) 41–46

Fig. 1. Schematic diagram of the experimental apparatus. TT, thermometer; PT, pressure transducer; PG, pressure gauge.

was closely attached in the rear of the convection oven. The sampling box was maintained the same temperature as the convection oven. The accuracy of the temperature measuring system is ±0.03 K in the range 373–673 K, as specified by the manufacturer, and the accuracy of the pressure transducer is ±0.1% on specification and ±0.05% after calibration by the Korea Testing Laboratory. The cell was installed with the especially designed quartz sight glasses. Details of cell apparatus were given in our previous work [3]. Two circulation pumps mixed the chemicals of both phases sufficiently because the liquid was circulated from the liquid phase to the vapor phase and the vapor phase was circulated reversely. When the cell reached the equilibrium, the samples were taken from the circulation lines. The samples are

transported to the gas chromatography (GC) on-line, so no samples were discarded. Fig. 2 shows the sampling loop diagram. We devised an alternative sampling procedure for high pressure and high temperature sampling valve. Three three-way needle valves with graphite yarn packing (Autoclave Engineers, 10V2075) could replace one six-port sampling valve. The transfer circuit between the sampling box and GC was heated to prevent condensation. The loop was evacuated after sampling in order to eliminate the resident carrier gas causing the error in pressure measurement. The critical pressures were determined from critical opalescence of the mixture. In the case of pressure near the critical points of the mixture, we had observed phase behavior while feeding a small quantity of samples using liquid charging pump. The liquid and vapor samples were simultaneously analyzed by on-line gas chromatography (GC). In GC, two sets of TCD and Porapak Q packing column were used. The total volume of equilibrium cell is 100 cm3 and the sampling volume of each valve was large, about 0.05 ml. All sampling of 0.05 ml were transferred into GC. So, the GC columns were specially manufactured from 316 stainless steel tube of 0.95 cm o.d. and 85 cm long. A total of 13.5 g of packing material was used for each column.

3. Experimental results

Fig. 2. Schematic diagram of the sampling loop.

The isothermal vapor–liquid equilibrium data for n-hexane + 1-propanol were measured at 483.15, 493.15, 503.15 and 513.15 K (Fig. 3). These data are listed in Table 1. We could determined the critical points for this system at 503.15 and 513.15 K. The critical mole fractions

B.C. Oh et al. / Fluid Phase Equilibria 220 (2004) 41–46

43

Table 1 Experimental vapor–liquid equilibrium data for n-hexane (1) + 1-propanol (2) P (bar)

x1

y1

T = 483.15 K 20.88 21.38 22.05 24.85 26.75 27.35 27.58 27.71 27.15 25.96 23.29 21.71 21.27

0.000 0.015 0.035 0.146 0.322 0.401 0.450 0.519 0.642 0.730 0.904 0.981 1.000

0.000 0.038 0.065 0.248 0.371 0.432 0.471 0.515 0.613 0.681 0.859 0.961 1.000

T = 493.15 K 25.07 26.00 28.00 30.82 31.81 32.12 32.15 31.60 31.06 29.87 29.25 28.22 26.20 24.51

0.000 0.029 0.096 0.247 0.354 0.421 0.473 0.619 0.684 0.759 0.807 0.852 0.942 1.000

0.000 0.054 0.155 0.319 0.406 0.441 0.494 0.592 0.647 0.727 0.756 0.808 0.913 1.000

T = 503.15 K 30.09 31.97 34.47 36.34 37.18 37.54 37.75 37.88 37.58 37.05 34.07 33.33 32.74 31.90 29.64 28.24

0.000 0.061 0.179 0.291 0.362 0.404 0.432 0.495 0.541 0.599 0.786 0.829 0.853 0.888 0.954 1.000

0.000 0.103 0.224 0.325 0.385 0.421 0.449 0.502 0.533 CP CP 0.814 0.835 0.864 0.935 1.000

T = 513.15 K 35.54 37.14 40.40 42.12 43.13 43.32 43.40

0.000 0.034 0.134 0.238 0.300 0.312 0.319

0.000 0.064 0.181 0.265 0.307 0.317 CP

Critical point (CP).

Fig. 3. Comparison of measured data with correlation values by MF-NLF-HB EOS and PRSV-WS EOS for n-hexane (1) + 1-propanol (2). Experimental data: (䊊) 483.15 K; (䊐) 493.15 K; () 503.15 K; (䉫) 513.15 K; (䊉) experimental critical points; (– – –) calculated by PRSV-WS EOS; (—) calculated by MF-NLF-HB EOS.

of n-hexane were 0.599 and 0.786 at 503.15 and 0.319 at 513.15 K, respectively. In Fig. 4, the P–T projection of the critical locus indicates three critical points. This system shows type I fluid phase behavior according to the

Fig. 4. Vapor–liquid equilibria for the system n-hexane + 1-propanol. Vapor pressure curves (—): (1) n-hexane; (2) 1-propanol; (3) azeotrope line ((䊉) experimental critical points; (䊐) azeotrope points from this work; (䊊) pure vapor pressure points from this work; () pure component critical points [21]; (· · ·) interpolation curve of experimental data).

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  xi qi and rM = xi ri . ri and qi where β = 1/kT, qM = are the segment number and the surface area parameters and they related by zq i = ri (z − 2) + 2. ρ is the system density defined by ρ = ρi , where ρi = Ni ri /Nr and Nr = N0 +  r . The overall surface area fraction is defined by θ = N i i  θi , where θi = Ni qi /Nq and Nq = N0 + Ni qi . N0 and Ni are the number of vacant sites and molecules of species i. The fraction of hydrogen bonds, υHB , and the fraction of zero hydrogen bonds, υHB0 , in system was reported by Park et al. [16] as follows: M N HB HB0 i j (Nij − Nij ) c υHB − υHB0 = (2) i=1 ri Ni

Fig. 5. Vapor–liquid equilibria for the systems n-hexane + 1-propanol and n-hexane + 2-propanol. Vapor pressure curves (—): (1) n-hexane; (2) 1-propanol; (3) 2-propanol ((䊉) experimental critical points; (䊊) Seo et al. [3]; () pure component critical points [21]. Critical points calculation: (4) n-hexane + 1-propanol; (5) n-hexane + 2-propanol. (· · ·) interpolation curve of experimental data).

classification of van Konynenburg and Scott [9]. This type of critical locus, shown in Fig. 4, is usually associated with the occurrence of a positive azeotrope extending up to the critical line [10]. In the P–T projection, the azeotropic line is tangential to the critical locus but dose not meet it at the temperature minimum. Also the azeotrope pressure at 503.15 K, 37.88 bar is higher than the critical pressure, 37.05 bar at this temperature. This system shows absolute azeotropy. In Fig. 5, the critical curve of the system n-hexane + 1-propanol is compared with the critical curve of the system n-hexane + 2-propanol [3]. 4. Correlation

In the original derivation, Veytsman first counted the number of distribution of loosely connected pairs. These pairs can be hydrogen, if sites of pairs are sitting adjacent to each other and then reacted with the accompanying free energy change. Thus, the zero hydrogen-bonding free energy corresponds to two sites of a pair physically occupying adjacent sites without forming hydrogen bonds (i.e. AHB ij = 0). The nonrandomness factor τ ji is defined as: τji = exp{β(εji − εij )}

(3)

where εji is the absolute value of the interaction energy between species j and i. We set the coordination number, z, at 10 and the unit lattice cell volume, VH , at 9.75 cm3 mol−1 . Other expressions such as chemical potential necessary for phase equilibria calculation are available elsewhere [7]. Two molecular energy and size parameters were fitted to the saturated liquid density and vapor pressure data. They were correlated by the following equations as function of temperature:     ε11 T0 = Ea + Eb (T − T0 ) + Ec T ln + T − T0 (4) k T     T0 (5) r1 = Ra + Rb (T − T0 ) + Rc T ln + T − T0 T where T0 = 298.15 K is a reference temperature. The EOS has one binary interaction parameter λ12 for each binary system which is defined by:

4.1. MF-NLF-HB EOS The MF-NLF-HB EOS proposed by the present authors based on the two-liquid approximation of the Guggenheim combinatory [11] of the lattice-hole theory [12–14] was extended for hydrogen-bonding systems. Under the fundamental assumption that the intermolecular forces are divided into physical and chemical forces, generalized Veytsman’s statistics [15,16] for hydrogen-bonding theory was combined with the nonrandom lattice-fluid theory. The pressure explicit form of the EOS is given by:
    1 qM z P= ln 1 + − 1 ρ − ln(1 − ρ) βVH 2 rM   c τ0i z θ i c −1 (1) − (υHB − υHB0 )ρ + 2 k=0 θk τ0k i=1

ε12 = (ε11 ε22 )1/2 (1 − λ12 )

(6)

where λ12 is determined by experimental data fitting and may be temperature dependent. 4.2. PRSV-WS EOS The modified Peng–Robinson equation of state suggested by Stryjek and Vera [5] was used: p=

a(T) RT − v − b v2 + 2bv − b2

(7)

where a(T) =

0.457235α(T)R2 Tc2 , pc

b=

0.077796RTc pc

(8)

B.C. Oh et al. / Fluid Phase Equilibria 220 (2004) 41–46

α = [1 + κ(1 − TR0.5 )]2 , κ = κ0 + κ1 (1 + TR0.5 )(0.7 − TR )

(9)

κ0 = 0.378893 + 1.4897153ω − 0.17131848ω2 + 0.0196544ω

3

(10)

The parameter κ1 is an adjustable parameter characteristic for each pure compound. The correlation values, κ1 , provided by Stryjek and Vera were used for n-hexane and 1-propanol. The Wong–Sandler mixing rule [6] for the evaluation of the parameter a, b was used. In case of the PRSV equation of state:   i j xi xj (b − (a/RT))ij  bm = (11) 1 − i xi (ai /bi RT) − (AE∞ /CRT) am = bm

 i

ai AE xi + ∞ bi C



√ 1 with C = √ ln( 2 − 1) 2 (12)

The combining rule used was: 

b−

aj  a 1  ai  bi − = + bj − (1 − λij ) RT ij 2 RT RT (13)

The NRTL activity coefficient model [17] given below was used in the equations above: n n  AE∞ j=1 xj Gji δji xi n with Gji = exp(−αji δji ) (14) = RT k=1 xk Gkj i=1

where δji =

gji RT

(15)

4.3. VLE correlation The binary VLE reported in this work were correlated using the PRSV equation of state with Wong and Sandler mixing rules and MF-NLF-HB. The energy and size parameters of the pure n-hexane and 1-propanol for the MF-NLF-HB model were reported in previous works [7]. Estimated values of the coefficient for Eqs. (4) and (5) are summarized in Table 2 for the pure chemicals. The objective function to

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Table 3 Binary interaction parameters and average absolute deviation for the equilibrium data T (K)

Model

λ12

AADPa

AADYb

483.15

PRSV-WS MF-NLF-HB

0.1312 0.0267

0.679 0.652

0.039 0.009

493.15

PRSV-WS MF-NLF-HB

0.1188 0.0285

0.499 0.420

0.040 0.013

503.15

PRSV-WS MF-NLF-HB

0.1233 0.0332

0.433 0.697

0.028 0.016

PRSV-WS 0.1516 0.313 MF-NLF-HB 0.0375 0.345 N cal exp exp AADP = (100/nT ) i |Pi − Pi |/Pi .  cal exp exp AADY = (1/nT ) N i |yi − yi |/yi .

0.070 0.011

513.15 a b

fit binary interaction parameter in the MF-NLF-HB and the PRSV EOS was  NT   Pcal − Pexp 2 OF = (16) Pexp N=1

We directly used published parameters for the NRTL model obtained from the low-pressure isotherm, which are available in the DECHEMA Data Series [18]. This approach agreed with the Wong–Sandler mixing rule’s main object [6]. In this case, only one binary parameter (λij ) was regressed in Eq. (13). Thus, we set NRTL parameters, g12 = 1092.147 cal/mol, g21 = 480.674 cal/mol and α = 0.294 at whole range of temperature. For each temperature, the regressed adjustable binary interaction parameters and the percentage of the average absolute deviations between the measured and calculated pressure, AADP and the average absolute deviations of vapor composition of n-hexane, AADY are listed in Table 3. A comparison between the experimental data and the calculated phase diagram is shown in Fig. 3. Both models gave satisfactory results for this system. In this case the MF-NLF-HB was somewhat more accurate, probably because it contains a more refined description of hydrogen-bonding interaction. However, the problem of an accurate representation in the near-critical region remains as discussed by Sandler [19]. 4.4. Critical locus prediction For the critical point calculations we applied the method reported by Castier and Sandler [20]. The P–T projections of critical points calculated for the systems n-hexane + 1-propanol and 2-propanol are presented in Fig. 5 where

Table 2 Coefficient of molecular parameters for Eqs. (4) and (5) Chemicals

Ea

Eb

Ec

Ra

Rb

Rc

n-Hexane 1-Propanol

96.84253 89.39716

0.01474 0.11388

−0.03550 0.08600

11.07715 6.25494

−0.00017 0.002864

0.00391 −0.00204

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the critical loci are calculated by using 483.15 K parameters (λij = 0.1312). The predictions using fitted parameter from VLE data at 483.15 K show a little better agreement with experimental data than at other temperature. In this case n-hexane + 2-propanol system, Seo et al. reported parameters in previous work [3]. The calculation results give poor agreements. This offers a good explanation for the inaccuracy of the correlation of VLE in the near critical region.

θi κ1 λij ρ ρi τ ij

surface area fraction of component i PRSV parameter binary interaction parameter for i–j contacts total segment fraction segment fraction of component i nonrandomness factor

Superscripts cal calculated value exp experimental value HB chemical contribution by hydrogen-bonding

5. Conclusions The isothermal VLE data for the system n-hexane + 1-propanol were obtained at 483.15, 493.15, 503.15 and 513.15 K. Critical points were found at 503.15 and 513.15 K. The MF-NLF-HB EOS and PRSV EOS combined with NRTL model and Wong–Sandler mixing rules for correlating parameters resulted in a good agreement with an experimental data in the sub-critical regions. However, the prediction of critical pressure has shown a large deviation in experimental data. We also predicted critical locus for the system n-hexane + 1-propanol and 2-propanol. This system exhibited adjacent critical line because vapor pressure curves of n-hexane and 1-propanol were similar each other. The fitted parameter from VLE data near critical region gave a guidance to calculate and predict critical loci. List a AE b g Na Ni Nq Nr N0 OF P qi qM ri rM R T VH z

of symbols PRSV energy parameter excess free energy PRSV volume parameter NRTL model parameter Avogadro’s number number of molecular species  i defined by Nq = N0 + ci=1 Ni qi  defined by Nr = N0 + Nq = N0 + ci=1 Ni r number of vacant sites or holes objective function pressure (bar) surface area parameter mole fraction average of qi segment number of molecule i mole fraction average of ri universal gas constant (J mol−1 K−1 ) temperature (K) volume of unit cell (cm3 mol−1 ) lattice coordination number

Greek letters α NRTL model parameter δji NRTL parameter εij interaction energy for i–j segment contacts (J)

Acknowledgements We thank Drs. Castier and Sandler for providing the critical point calculation program. This work was supported by the BK21 project of Ministry of Education and the National Research Laboratory (NRL) Program of Korea Institute of Science and Technology Evaluation and Planning.

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