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Fluid Phase Equilibria 289 (2010) 80–89

Contents lists available at ScienceDirect

Fluid Phase Equilibria

journa l homepage: www.e lsev ier .com/ locate / f lu id

etermination of vapour–liquid and vapour–liquid–liquid equilibrium of thehloroform–water and trichloroethylene–water binary mixtures

u-Sheng Hu ∗

nstitute of Nuclear Energy and New Energy Technology, Tsinghua University, Beijing, 102201, China

r t i c l e i n f o

rticle history:eceived 9 August 2009eceived in revised form 3 November 2009ccepted 5 November 2009vailable online 13 November 2009

eywords:etermination

a b s t r a c t

The vapour–liquid equilibrium (VLE) and vapour–liquid–liquid equilibrium (VLLE) data are the basis forthe design of distillation columns for the recovery or removal of residual extractant such as chloro-form from wastewater. In this study, a new dynamic condensate-circulation still was designed and usedfor determination of VLE and VLLE of chloroform–water and trichloroethylene–water binary systemsat 101.3 kPa. The phase diagrams of equilibrated vapour-phase composition versus overall liquid-phasecomposition y1–x1 (where subscript 1 references organic component in the binary system) and equi-librated temperature versus vapour-phase or overall liquid-phase composition T–x1(y1) were plotted

apour–liquid equilibriumapour–liquid–liquid equilibriumhloroform–waterrichloroethylene–water

by using the VLE and VLLE data and the data on mutual solubility. The experimental results showedthat the two binary systems used have highly non-ideality and form heteroazeotropes, and their het-eroazeotrope points are (t = 55.8 ◦C, x1 = y1 = 0.856) for chloroform–water and (t = 73.9 ◦C, x1 = y1 = 0.716)for trichloroethylene–water system. The activity coefficients of the component acted as solvent are ingeneral, while the activity coefficients of the component acted as solute are very high in the equilibrated

of the) acti

liquid phase. Correlation(non-random two liquids

. Introduction

N,N-Dimethylfomamide (DMF) is widely used as a solvent inanneries and as a vesicant in the manufacture of polyurethane.oth of these processes produce large quantities of wastewaterontaining DMF. It is now commercially important to treat theseaste streams to remove and recover the DMF with the joint bene-ts of reducing the chemical oxygen demand (COD) of the wastetream and reuse of the recovered DMF. Historically the wastetream has been treated by direct distillation. This process hasany disadvantages, it consumes large amounts of energy due to

he high latent heat of vapourisation of the water, it is difficult toreat the wastewaters containing low concentrations of DMF, andhe DMF can be hydrolysed to form dimethylamine and methylcid during the distillation that cause secondary pollution of thenvironment.

The author of this paper has recently developed a new alter-ative technique [1] that involves the extraction of DMF firstly

rom the wastewater using chloroform as the extractant, followedy distillation of HCCl3 from the extracted solvent for separationnd recovery of DMF and HCCl3. This new process has many sig-ificant merits, such as a lower energy consumption due to the

∗ Tel.: +86 10 89796088; fax: +86 10 89791464.E-mail address: huhusheng123@tom.com.

378-3812/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.fluid.2009.11.006

VLE and VLLE data respectively for the two binary systems with the NRTLvity coefficient model gave satisfactory results.

© 2009 Elsevier B.V. All rights reserved.

low latent heat of vapourisation of chloroform (one-ninth thatof water), and little or no hydrolysis of DMF during distillationsince hardly any water is present in the extracted solvent, fur-ther, this method is suitable for the treatment of wastewaterscontaining low concentrations of DMF. However, since chloroformis slightly soluble in water (approximately 0.8 wt%), its recoveryfrom the extraction raffinate is important. Since there is a largedifference between the vapour pressure of chloroform and watervapour, they are likely to form a binary azeotrope when heatingthe raffinate, hence, distillation is the preferred method for therecovery of chloroform from wastewater. However, in the litera-ture the VLE (vapour–liquid equilibrium) data for the HCCl3–H2Obinary system, which form the basis for the design of a distil-lation column that is used for the recovery of chloroform fromwastewater, are incomplete. Gmehling and Onken compiled a largeamount of VLE data for many aqueous-organic systems, but nodata are available for the CHCl3–H2O binary system. Leighton andCalo [2] reported the distribution coefficients of chloroform in anair–water system over the temperature range of 0–30 ◦C; Turner etal. [3] comprehensively reviewed and measured the vapour–liquidpartition coefficients and activity coefficients of several organic

compounds, including chloroform and trichloroethylene in waterover the temperature range of 15–60 and 15–47 ◦C, respectively,but there are no extant VLE data available over the temperaturerange of 60–100 ◦C for chloroform–water system and 47–100 ◦C fortrichloroethylene–water system.

quilibria 289 (2010) 80–89 81

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Fig. 1. apparatus for determining the vapour–liquid–liquid equilibrium. 1: Voltageregulator; 2: electric heater (Cotrell pump); 3: separation–equilibrium chamber forvapour phase and liquid phase; 4 and 7: electromagnetic stirrer; 5: mixing cham-ber; 6: thermostatic water bath; 8 and 11: condenser; 9: precision thermometer; 10:three-way valve for sampling condensate from vapour phase; 12: separation cham-

H.-S. Hu / Fluid Phase E

In this study, the VLE and VLLE (vapour–liquid–liquid equi-ibrium) data at 55–100 ◦C for a CHCl3–H2O binary system and

utual-solubility data are investigated in detail. In addition, theLE and VLLE data at 74–100 ◦C for the trichloroethylene–waterystem are also investigated in detail, because the trichloroethy-ene is probably as candidate of extractant for extracting DMF from

aste water and recovery of the extractant from its extraction raf-nate is required. Moreover, the trichloroethylene is widely used

or rinsing metal parts, thus recovery or removal of it by distillationrom rinsing wastewater is again required. The composition of thequilibrated liquid phases and vapour phase and boiling points ofhe liquid at 101.3 kPa for the two binary systems were measured,urther, phase diagrams of equilibrated vapour-phase compositionersus liquid-phase composition (y–x) and the equilibrated tem-erature versus composition of the vapour or liquid phase (T–x(y))ere plotted. In addition, the isobaric VLE and VLLE data were cor-

elated with the NRTL activity coefficient model.

. Experimental

The VLE data are often determined using a best-known Othmertill or Othmer-type still (e.g., Gilmont and Conti still) [4], as wells a modified Scatchard still [5] or a Raal still [6]. These stills haveottrell pump feature that can ensure a intimate contact betweenapour and liquid phase, however, they are not suitable for deter-ination of the VLLE data because there is no a electromagnetic

tirring equipped with in the still where there are two liquid layersince the system determined is partial miscible, thus no a good mix-ng and intimate contact between two liquid phases is ensured. Thellis equilibrium still, similar to a condensate-circulating Kortüm-ype still [4] is also used for obtaining the VLE data, but they aregain not suitable for determination of the VLLE data, because theyave no Cottrell pump although they may have electromagnetictirring in the still, moreover, their condensate-samplers are soeep that they can deposit and accumulate a certain amounts ofhe heavier liquid phase there (the condensate generally formswo liquid phases if the system measured is partial miscible) dur-ng the condensate reflows back to the still, hence, the samplesrom those concave sampler do not represent the true composi-ions of vapour phase being in equilibrium with liquids. In order to

easuring the VLLE data, Haddad and Edmister [5] used a specifi-ally designed Hands and Norman equilibrium still for the systemshose condensate forms two liquid phases. However, the Hands

nd Norman still lacked a Cottrell pump that guaranteed an intenseapour–liquid-phase exchange.

In this study, based on the consideration of overcoming or elim-nating the above still’s drawbacks, a new condensate-circulatingtill is designed, as shown in Fig. 1. This still is an all glass one.he heating tube(2), whose outer surface is winded with the elec-rical resistance wire, acts as a Cottrell pump, that ensures anntimate contact between vapour and liquid phases. When heat-ng the tube(2), an equilibrium mixture of liquid and vapour areischarged out from the top outlet of the tube, and the vapoureparates from liquid and enters the condenser(8), and the liquids spurted to the opposite wall inside the separation-equilibriumhamber(3) and quickly spreads into the liquid membrane alonghe inside wall and flows downward reaching the bottom of thequilibrium chamber(3), in where there is electromagnetic stir-ing for strongly mixing the two liquid phases thus the equilibriumetween the two liquid phases is quickly reached. The outer surfacef the equilibrium chamber(3) is lagged with insulating material

o as to prevent the mixture from fractionation. The condensate inhe form of two-liquid phases from condenser(8) and liquid fromeparation-equilibrium chamber(3) are adequately mixed and uni-orm dispersed even emulsified in the mixing chamber(5) beforehey enter the heating tube(2). The bottom of chamber(5) is specif-

ber for two-liquid-phase samples; 13: pressure transducer; 14: valve for dischargeof liquid; 15: buffer tank; 16: two-stage cylinder pressure regulator; 17: high pure(grade #5) nitrogen cylinder; 18: valve to vacuum system; 19: three-way valve forsampling liquids.

ically designed to be an plane inclined by a slope of 20◦, thisstructure is of great advantage to emulsification of the two liquidphases so as to ensure the stability of the temperature in the equi-librium chamber(3). The sampler(10) equips with a 3-port valve,through which the condensate (one or two liquid phases) flows viaa reflowing pipe back to the still without accumulating any heav-ier liquid phase (organic) in the sampler. When sampling vapouris needed, the 3-port valve is conducted to the right-hand out-let thus the condensate is diverted into a cone-shaped tube withgraduations of 0.01 ml, then the tube is placed in a centrifuger forphase-separation. Similarly, when sampling liquid is needed, theliquid in the separation-equilibrium chamber(3) is diverted in asmall amount by the 3-port valve(19) into the sample-separationchamber(12), where the temperature is controlled by the waterbath at the same temperature as that of separation-equilibriumchamber(3) for separation of two-liquid-phase samples, then theliquid samples are taken from the sample-separation chamber(12)using a syringe.

During experiment, the reflow rate of the condensate fromvapour phase is controlled by manual operation of the voltageregulator(1) for adjusting electric-heating power applied. The abso-lute pressure of the system is controlled at 101.3 kPa by manualoperating carefully the two-stage cylinder pressure regulator(16)installed on the top of the cylinder(17) for controlling the flowrate of high pure (grade #5) nitrogen applied into the buffer tank(10-l) (15), and the pressure is measured by a pressure transducer(KLP800-AK, Guang Zhou Kun Lun automatic control equipmentCo.)(13) with a digital-display unit (CH6/A-H(s)RTB1). The pressuremeasurement device was checked by measuring the normal boilingpoint of water. The system temperature is measured by a precision

◦

glass thermometer(9) with scale of 0–50 or 50–100 C. The uncer-tainties of pressure and temperature measured are p{+0.1

−0.1 kPa and

t{+0.05−0.15

◦C, respectively.The concentrations of chloroform in the aqueous phase and

trichloroethylene in aqueous phase are determined using a colori-

8 Equilib

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2 H.-S. Hu / Fluid Phase

etric method [7] with a visible light spectrophotometer (model22, Shang Hai Heng Ping Scientific Instrument Co.). The uncer-ainty of measurement of composition (x1) with this kind of analysiss x1{+0.000008

−0.000012 mol fraction.The concentrations of water in the organic phase are deter-

ined using a volumetric Karl Fischer titration method [8] withKF-II automated titration system (Shang Hai Bao Shan Jing

ong Electronic Instrument Co.). The uncertainty of measurementf composition (x2) is x2{+0.00010

−0.00016 mol fraction. The uncertaintyf measurement of vapour composition (y1) is estimated to be1{+0.0015

−0.0025 mol fraction.All of the chemical reagents used such as Carl-Fischer reagent,

aOH and pyridine are of analytic purity (Bei Jing Chemical Regento.). The fresh chloroform (analytic purity, purity ≥99.0 wt%, H2O.03 wt%, stabilizer-ethyl alcohol 0.3–1.0 wt%) is washed two timesefore being used with deionised water (1000 ml water per 100 mlhloroform) for removal of the stabilizer-ethyl alcohol. After wash-ng, the concentration of ethyl alcohol is less than 0.01 wt%.he trichloroethylene (purity ≥99.9 wt%, H2O 0.004 wt%) is alsof analytic purity. The deionised water (electrolytic conductivity.01 mS/m) is used throughout the experiment.

. Results and discussion

.1. Vapour–liquid and vapour–liquid–liquid equilibrium data

The density data of pure liquid components used in this paperre taken from the literature [9,10] and regressed against each others functions of temperature expressed as the following Eqs. (1)–(3)ith regression coefficient R2 = 1, 0.999 and 0.9984, respectively.

able 1omparison of the results correlated with experimental measured (for chloroform(1)–wa

Equilibrium temperature, t (◦C) Experimental values

x1a y1

61.2 1.00000 1.00061.0 0.99859 0.98259.0 0.99625 0.95157.0 0.99209 0.90056.0 0.98796 0.87155.8 0.95701 0.85555.8 0.81035 0.86055.8 0.56031 0.86055.8 0.34415 0.84955.8 0.18360 0.86055.8 0.08791 0.84955.8 0.02438 0.86055.8 0.00691 0.855 156.0 0.00136 0.854 756.5 0.00122 0.842 857.0 0.00117 0.838 862.0 0.00076 0.820 1063.0 0.00056 0.805 1369.0 0.00046 0.754 1271.0 0.00038 0.736 1475.0 0.00031 0.710 1576.0 0.00025 0.688 1778.0 0.00018 0.647 2082.0 0.00015 0.619 2184.0 0.00012 0.577 2390.0 0.00011 0.472 1893.0 0.00008 0.439 2294.0 0.00006 0.338 2297.0 0.00005 0.165 1298.0 0.00003 0.095 1099.0 0.00002 0.012 2

100 0.00000 0.000

a x1 is the overall liquid-phase composition.

ria 289 (2010) 80–89

The relative errors between reproduced density data and originalones are very small, e.g., less than 0.2% for Eq. (1), and less than 0.06%for Eq. (2). The reproduced density data from these equations arealso consistent with (for Eqs. (1) and (3)) or considerably better than(for Eq. (2)) those calculated using the modified Rackett equation[11].

�1 = −0.0019T2 − 0.7139T + 1860.7 (for chloroform) (1)

�2 = −0.0035T2 + 1.8659T + 755.43 (for water) (2)

�1 = −0.005T2 + 1.6504T + 1403 (for trichloroethylene) (3)

where the subscripts 1 and 2 refer to organic component andwater, respectively, the �i denotes the density of pure liquid i (unit:kg/m3), and T is the system temperature (unit: K).

The density of each single-liquid phase (aqueous or organic) canbe calculated by the following Eqs. (4) and (5) [12]:

�aq = ϕaq1 �1 + (1 − ϕaq

1 )�2 (4)

�org = ϕorg1 �1 + (1 − ϕorg

1 )�2 (5)

where ϕaq1 and ϕorg

1 are the volume fractions of organic componentin aqueous and in organic phase, respectively. The relative errors ofdensity of each single-liquid phase between calculated and exper-imental measured by a Li volumetric flask (250 ml,whose top hasan outlet tube with graduation 0.1 ml) are less than 0.07% for the

two binary systems used in the experiment.

The data on the isobaric VLE for chloroform–water andtrichloroethylene–water systems in the entire concentration rangeof x1 are given in Tables 1 and 2, respectively, where t is the boil-ing point (◦C) of the liquid mixture; and y1 is the mole fraction of

ter(2) system).

NRTL mode Region

�1 �2 �t �y1

1.0 0.0 0

VLE1.0 62.3 −12.3 0.0041.0 69.5 −13.3 0.0031.0 74.1 −13.9 −0.0061.0 65.7 −13.9 −0.0061.1 21.0 −11.7 0.053

VLLE

1.3 4.6 −12.1 0.0401.8 2.0 −13.2 0.0783.0 1.4 −17.3 0.1765.6 1.1 −21.8 0.303

11.6 1.0 −22.2 0.30542.2 0.9 −4.9 0.06447.9 0.9 20.9 −0.09145.2 0.9 24.3 −0.100

VLE

04.2 0.9 22.9 −0.10723.2 1.0 22.5 −0.10943.5 0.8 16.6 −0.08454.0 0.9 7.7 −0.03778.8 0.8 7.3 −0.03407.8 0.8 3.8 0.00902.2 0.8 1.7 0.06572.6 0.8 −2.6 0.13088.2 0.8 −5.9 0.19333.6 0.8 −4.6 0.22647.9 0.8 −5.3 0.25154.1 0.8 −0.6 0.18025.9 0.7 −0.3 0.22375.2 0.8 −1.1 0.17650.1 0.9 1.0 0.03057.9 1.0 0.7 0.00462.7 1.0 0.3 −0.034

1.0 0.0 0.000

Standard deviation SDR (�y1) 0.138

H.-S. Hu / Fluid Phase Equilibria 289 (2010) 80–89 83

Table 2Comparison of the results correlated with experimental measured (for trichloroethylene(1)–water(2) system).

Equilibrium temperature, t (◦C) Experimental values NRTL mode Region

x1a y1 �1 �2 �t �y1

87.1 1.00000 1.000 1.0 0.0 0.000

VLE

84.5 0.99919 0.976 1.1 53.9 −1.0 0.01682.0 0.99785 0.935 1.1 60.1 −1.4 0.03079.5 0.99680 0.879 1.1 82.7 −2.5 0.01077.0 0.99548 0.830 1.1 91.0 −3.5 −0.00273.9 0.99287 0.727 1.1 106.5 −4.6 −0.05174.0 0.94610 0.706 1.1 15.0 −0.5 0.036

VLLE

74.0 0.77109 0.706 1.4 3.5 −3.0 −0.05274.0 0.61474 0.714 1.8 2.0 −3.4 −0.01174.0 0.29263 0.722 3.7 1.1 −7.9 0.20073.8 0.15059 0.737 7.4 0.9 −11.1 0.33874.0 0.07062 0.710 15.2 0.9 −10.8 0.30973.6 0.01932 0.718 56.8 0.8 6.1 −0.00973.6 0.00924 0.718 118.7 0.8 23.9 −0.16573.6 0.00019 0.718 5728.7 0.8 7.2 −0.017

VLE

74.0 0.00018 0.715 5988.7 0.8 5.6 0.00375.0 0.00017 0.713 5981.8 0.8 5.6 0.01477.0 0.00017 0.690 5668.5 0.8 6.3 0.00878.0 0.00016 0.677 5480.5 0.7 6.9 0.00279.0 0.00016 0.670 5304.3 0.7 7.6 −0.00180.0 0.00015 0.640 5162.4 0.8 7.2 −0.01181.8 0.00013 0.586 5450.3 0.8 4.0 0.01583.8 0.00011 0.530 5208.7 0.9 3.5 0.00585.0 0.00009 0.466 5745.4 0.9 0.1 0.03888.0 0.00008 0.375 4706.8 1.0 1.5 −0.01789.4 0.00007 0.306 4110.2 1.0 1.4 −0.05192.5 0.00006 0.252 3525.1 1.0 3.0 −0.06795.0 0.00004 0.167 3119.9 1.0 2.3 −0.06497.0 0.00002 0.090 3163.2 1.0 0.6 −0.03098.0 0.00001 0.035 3654.3 1.0 −0.8 −0.00699.5 0.00001 0.025 3026.1 1.0 0.5 −0.008

100.0 0.00000 0.000 1.0 0.0 0.000

oopxofr

TC

a x1 is the overall liquid-phase composition.

rganic component in the vapour phase being in equilibrium withne or two liquids; and x1 is total mole fraction of organic com-

onent in the equilibrated liquid phase with one or two liquids,1 = (1 − ˇ)xaq

1 + ˇxorg1 , where the ˇ is phase split, is the fraction

f the organic phase in the total liquids; xaq1 and xorg

1 are moleractions of organic component in aqueous and in organic phase,espectively. It can be seen from Table 1 for chloroform–water sys-

able 3orrelation of VLLE data with NRTL equations (for chloroform(1)–water(2) system).

x1a

0.95701 0.81035 0.56031 0.34415 0.1

texp (◦C) 55.80 55.80 55.80 55.80 55.xaq

1,exp = 0.00130 0.00132 0.00133 0.00136 0.0xorg

1,exp = 0.9930 0.9927 0.9927 0.9927 0.9y1,exp = 0.855 0.860 0.860 0.849 0.8�aq

1,exp = 785.72 779.14 770.27 744.14 880�aq

2,exp = 0.90 0.87 0.87 0.93 0.8�org

1,exp = 1.03 1.04 1.04 1.02 1.0�org

2,exp = 128.76 119.81 119.81 128.52 94.�aq

1,calc= 844.80 845.42 845.84 846.48 837

�aq2,calc

= 1.00 1.00 1.00 1.00 1.0�org

1,calc= 1.00 1.00 1.00 1.00 1.0

�org2,calc

= 116.61 114.28 114.28 114.28 98.�xaq

1 =�xorg

1 =�taq =�torg

�yaq1 =

�yorg1 =

a x1 is the overall liquid-phase composition.

Standard deviation SDR (�y1) 0.101

tem that, in the range of x1 from 0.0013 to 0.9880, the boiling point tmaintains a constant (55.8 ◦C), and the y1 also maintains a constant

(0.856), so this x1 range is a invariant region with respect to temper-ature and vapour composition. In fact, this x1 range corresponds toa two-liquid-phase region, i.e., a three-phase (one vapour phaseand two liquid phases, denoted by VLL)-coexistence region, theother ranges correspond to single-liquid-phase regions, i.e., within

Averaged

8360 0.08791 0.02438 0.00691

80 55.80 55.80 55.80 55.800117 0.00106 0.00130 0.00135 0.00127908 0.9908 0.9895 0.9920 0.991860 0.849 0.860 0.855 0.856.82 957.75 788.27 756.62 807.84

7 0.93 0.87 0.90 0.894 1.02 1.04 1.03 1.0330 101.15 82.60 112.67 110.95.10 826.59 844.93 846.21 842.17

0 1.00 1.00 1.00 1.000 1.00 1.00 1.00 1.0027 98.27 89.17 107.88 106.63

4.71E−06−0.00021.33−0.790.00065602−0.0012239

84 H.-S. Hu / Fluid Phase Equilibria 289 (2010) 80–89

x1af

vvx

vuFtpaatix

Fig. 2. (a–c) y1–x1 phase diagrams for chloroform(1)–water(2) system.

1 from 0.0 to 0.0013 is an aqueous phase; within x1 from 0.988 to.0 is an organic phase. The similar results are observed in Table 2,nd the invariant region is the range of x1 from 0.00019 to 0.9929or trichloroethylene–water system.

In order to further clearly describe the changing laws of theariables, such as equilibrium temperature, equilibrated liquid andapour compositions varying with the overall liquid composition1, the equilibrium phase diagrams are plotted in this study.

At a constant total pressure of 101.3 kPa, the equilibratedapour-phase compositions (y1) and the corresponding overall liq-id composition (x1) form the y1–x1 phase diagram, shown inig. 2. Fig. 2(b) and (c) are close-up views of specific regions ofhe phase diagram shown in Fig. 2(a). It can be seen from thelot for chloroform–water system that, the y1 increases sharplys x1 increases from 0 to 0.0013, after which it maintains almost

constant 0.856 when x1 varies in a wide range from 0.0013

o 0.988. This implies the formation of the azeotrope when x1s in the range of 0.0013–0.988, with the azeotropic composition1 = y1 = 0.856. The x1 values 0.0–0.0013 and 0.988–1.0 correspond

Fig. 3. (a–c) y1–x1 phase diagrams for trichloroethylene(1)–water(2) system.

to single-liquid-phase regions, i.e., the aqueous phase and organicphase, respectively. The similar result is observed in Fig. 3 for thetrichloroethylene–water system, i.e., the values of y1 remain a con-stant of 0.716 as x1 varies from 0.00019 to 0.9929.

Fig. 4(a) shows the phase diagram of equilibrated tempera-ture versus compositions, T–x1(y1), at a constant total pressure of101.3 kPa. Fig. 4(b) and (c) are close-up views of specific regionsof the phase diagram shown in Fig. 4(a). It can be seen from Fig. 4that there exists a lowest-temperature point C on the dew-pointcurve at y1 = 0.856 (t = 55.8 ◦C), which corresponds to equilibratedliquid-phase compositions point A (x1 = 0.0013, t = 55.8 ◦C) on theleft-branch of boiling-point curve and point B (x1 = 0.988, t = 55.8 ◦C)on the right-branch of boiling-point curve. This implies that theCHCl3–H2O binary system shows strong positive deviations fromRaoult’s law. The point C is just the azeotropic point. The pointsA and B on the boiling-point curves are called turning points, thevalues of which are depended on the solubilities of chloroformin aqueous phase and water in organic phase at azeotropic tem-perature of 55.8 ◦C, respectively. The range of x1 0.0013–0.988corresponds to a three-phase (VLL)-coexistence region and the

other ranges correspond to regions where a single liquid and vapourcoexist. In the VLL-coexistence region, with x1 increasing from0.0013 to 0.988, the boiling points keep at 55.8 ◦C, so the so-calledazeotropic curve is a perfectly horizontal straight line; in addi-

H.-S. Hu / Fluid Phase Equilibria 289 (2010) 80–89 85

Fb

tttdhp

tht(

ctep

vts

ig. 4. (a–c) T–x1(y1) phase diagrams at 101.3 kPa for chloroform(1)–water(2)inary system.

ion, y1 maintains almost a constant 0.856 (also see Table 3) inhe three-phase-coexistence region. According to the Gibbs rule, inhe three-phase (VLL)-coexistence region the numbers of freedomegrees is 0 (invariant system), i.e., the azeotropic curve must be aorizontal straight line, and y1 must be a constant. Therefore, thesehase diagrams for binary system are in accord with the Gibbs rule.

The similar situations are observed in Fig. 5 for therichloroethylene–water system. The azeotropic curve is also aorizontal straight line with the turning point A (x1 = 0.00019,= 73.9 ◦C), B (x1 = 0.9929, t = 73.9 ◦C) and azeotropic point Cy1 = 0.716, t = 73.9 ◦C).

In each phase diagram, Figs. 4 and 5, except for a dew-pointurve, boiling-point curves and azeotropic-point curves, there arewo mutual-solubility curves (binodal curves). The solubility ofither organic component in aqueous phase or water in organichase slightly increases as the temperature increases.

For further inspecting the properties of temperature, liquid andapour compositions in the three-phase (VLL)-coexistence region,he data on the isobaric VLLE for the two binary systems are pre-ented in Tables 3 and 4, respectively. It can be seen from these

Fig. 5. (a–c) T–x1(y1) phase diagrams at 101.3 kPa for trichloroethylene(1)–water(2)binary system.

tables that the equilibrium temperature texp, equilibrated twoliquid-phase compositions xaq

1,exp and xorg1,exp, and vapour compo-

sitions y1,exp all maintain almost constant when x1 varies in thethree-phase (VLL)-coexistence region. This further proves theseVLL-coexistence regions are “invariant regions”.

3.2. Activity coefficient of liquid-phase components

Under the normal or negative pressure, the condition ofvapour–liquid equilibrium can be expressed as Eq. (6) below [13]:

pyi = psi xi�i (6)

where p is the total pressure (unit: kPa) of system, psiis the saturated

vapour pressure (unit: kPa) of pure liquid component i; x1 is theoverall composition of component i in the liquid mixture; �1 is the

activity coefficient of component i in liquid mixture. Eq. (6) can bewritten as,

�i = pyi

psixi

(7)

86 H.-S. Hu / Fluid Phase Equilibria 289 (2010) 80–89

Table 4Correlation of VLLE data with NRTL equations (for trichloroethylene(1)–water(2) system).

x1a Averaged

0.94610 0.77109 0.61474 0.29263 0.15059 0.07062 0.01932 0.00924

texp (◦C) 74.00 74.00 74.00 74.00 73.80 74.00 73.60 73.60 73.88xaq

1,exp = 0.00018 0.00018 0.00018 0.00022 0.00018 0.00016 0.00022 0.00017 0.00018xorg

1,exp = 0.9927 0.9933 0.9930 0.9927 0.9933 0.9933 0.9929 0.9927 0.9930y1,exp = 0.706 0.706 0.714 0.722 0.737 0.710 0.718 0.718 0.716�aq

1,exp = 6055.03 6035.22 6084.67 4974.55 6383.92 6780.17 4953.96 6395.70 5957.90�aq

2,exp = 0.81 0.81 0.78 0.76 0.73 0.79 0.78 0.78 0.78�org

1,exp = 1.07 1.07 1.09 1.10 1.13 1.08 1.11 1.11 1.09�org

2,exp = 110.04 119.98 111.51 103.92 108.26 118.30 109.93 106.54 111.06�aq

1,calc= 7062.89 7075.80 7090.35 8055.57 7049.50 6669.44 8128.84 6978.31 7263.84

�aq2,calc

= 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00�org

1,calc= 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

�org2,calc

= 96.56 99.37 97.96 96.56 99.37 99.37 97.60 96.57 97.92�xaq

1 = −1.50E−06�xorg

1 = −0.0010�taq = 6.16

wk

l

l

l

u(oaofcxSE

TC

�torg

�yaq1 =

�yorg1 =

a x1 is the overall liquid-phase composition.

The saturated vapour pressures of pure organic component andater were calculated from the Antoine equations (8)–(10) (ps

i:

Pa), respectively [14],

og ps1 = 5.9629 − 1106.94

t + 218.55(for chloroform) (8)

og ps2 = 7.07396 − 1657.46

t + 227.02(for water) (9)

og ps3 = 3.153 − 1315.3

t + 230.0(for trichloroethylene) (10)

The activity coefficients of organic component and water in liq-id phase, denoted by �1 and �2, respectively, calculated using Eq.7). It can be seen from Fig. 6 (Fig. 6(b) and (c) are close-up viewsf specific regions of the phase diagram shown in Fig. 6(a)) as wells from Table 1 (for chloroform–water system) that in the rangef x1 = 0.0013–0.988, �1 and �2 are ordinary values, but when x1

alls in the single-liquid-phase region the activity coefficients of theomponent acted as solute are very high, e.g., �1 = 750–2300 when1 is near the endpoint (x1 < 0.0013) of horizontal coordinated axis.ince all the activity coefficients are obtained by calculated usingq. (7) from the overall liquid composition x1, in Fig. 6 the values

able 5omparison the data from this work with the literatures (for system A: chloroform(1)–w

System Temp. (◦C) Partition coefficient, K1 = y1/x1

A 25 202A 25 200A 35 280A 35 296A 60 960A 60 950B 35 990B 35 940

System Temp. (◦C) Solubility of organic compound in water

A 20 8200A 20 8400B 25 1000B 25 1140

System Temp. (◦C) Solubility of water in organic compound

A 25 0.093A 25 0.097B 25 0.033B 25 0.032

−3.000.00700.0072

of �1 and �1 corresponding to the range of x1 = 0.0013–0.988 (two-liquid-phase region) are only apparent ones, i.e., the dashed linescorrespond to two-liquid phases, so the plotted values by dashedlines have no physical significance there.

The similar situations are observed for thetrichloroethylene–water system. In Table 2, the activity coef-ficients of the component acted as solute are very high, e.g.,�1 = 3000–5980 when x1 is less than 0.00019; and the values of �1and �2 corresponding to the range of x1 from 0.00019 to 0.9929have no physical significance because this range corresponds totwo-liquid phase.

The true values of activity coefficients of component i in aque-ous phase and in organic phase in two-liquid-phase region, �aq

i,exp

and �orgi,exp, are calculated using Eqs. (11) and (12) after experimen-

tally measuring the compositions of two liquid and vapour phases,respectively. These values calculated for the two systems are tabu-

lated in Tables 3 and 4, respectively.

�aqi,exp = pyi,exp

psixaq

i,exp

(11)

ater(2); B: trichloroethylene(1)–water(2)).

Activity coefficients, �1 Reference

857 Turner et al. [3]880 This work837 Turner et al. [3]805 This work

1120 Svetlanov et al. [15]1040 This work7600 Schoene et al. [17]7410 This work

(mg/l) Activity coefficients, �1 Reference

810 Turner et al. [3]890 This work

7300 Neely [18]8010 This work

(wt%) Activity coefficients, �2 Reference

162 Staverman [16]170 This work233 Kirk and Othmer [19]240 This work

H.-S. Hu / Fluid Phase Equilib

Fig. 6. (a–c) Experimentally obtained activity coefficients of liquid-phase compo-nents for chloroform(1)–water(2) system. The dashed and doted lines correspond totn

�

tcgiatca

gplol

optimization method as above correlation of VLE data. The condi-

he two-liquid-phase region, so the plotted values by dashed and doted lines haveo physical significance there.

orgi,exp = pyi,exp

psixorg

i,exp

(12)

It can be seen from Table 3 for chloroform–water system that inhree-phase (VLL)-equilibrium region the averaged activity coeffi-ients of the component acted as solvent, �aq

2,exp and �org1,exp, are in

eneral, to be 0.87 and 1.04, respectively; while the averaged activ-ty coefficients of the component acted as solute, �aq

1,exp and �org2,exp,

re very high, to be 807 and 110, respectively. Both equilibriumemperature texp and vapour compositions y1,exp keep at almostonstant. As for the trichloroethylene–water system, the situationsre similar to that of chloroform–water system, as shown in Table 4.

A comparison between the data collected in this study and thoseiven in the literatures is shown in Table 5. It can be seen that theartition coefficients, activity coefficients of organic compound in

iquid phase and data on solubility of organic compound in waterr water in organic compound are close to those published in theiterature [3,15–19].

ria 289 (2010) 80–89 87

3.3. Correlation of VLE and VLLE data

At first, the VLE data in entire concentration range of x1 fromTables 1 and 2 were correlated by Van Laar activity coefficientmodel [20] and Margules model [21], respectively. The resultsshowed that the plots of x1/(x1 ln �1 + x2 ln �2) versus x1/x2 andx2/(x1 ln �1 + x2 ln�2) versus x2/x1were nonlinear, and the plots ofln(�1/x2) versus x1 and of ln(�2/x1) versus x2 were also nonlinear.This implied that neither the Van Laar nor the Margules model weresuitable for correlating the VLE data obtained for the two binarysystems in the entire concentration range of x1.

Further, it has been pointed out in the literature that the NRTLmodel [22] but not the Wilson activity coefficient model [13] issuitable for correlation of the VLLE data. Therefore, the NRTL modelEqs. (13) and (14) are used to correlate the VLE data from Table 1for HCCl3–H2O binary system in entire concentration range of x1:

ln �1 = x22

[�21G2

21

(x1 + x2G21)2+ �12G12

(x2 + x1G21)2

](13)

ln �2 = x21

[�12G2

12

(x2 + x1G12)2+ �21G21

(x1 + x2G21)2

](14)

where �21 = g12−g11RT , �21 = g21−g22

RT , G12 = exp(−˛�12), G21 =exp(−˛�21).

The model interaction energy parameters g12 − g11 andg21 − g22 were obtained by minimizing the objective functionF = ∑m

k=1[(y1,exp − y1,cal)2 + (y2,exp − y2,cal)

2] using the nonlinearleast-square method. During the iterative calculation of g12 − g11and g21 − g22, the secant formula (Eq. (15)) was used for the itera-tive calculation of the boiling point t, and take the experimentalvalues texp and (texp +0.5) as the initial values of tn−1 and tn−2.For finding the other model parameter ˛, an optimization method:dimensionality-reduction method [23] were used. The results cor-related including optimized parameters ˛, g12 − g11 and g21 − g22,and corresponding differences between experimental and corre-lated (�t), (�y1) were shown in Tables 1 and 6.

tn = tn−1 − tn−1 − tn−2

H(tn−1) − H(tn−2)H(tn−1) (15)

where H(tn) =∑2

i=1yi − 1, H(tn) is a normalization function; nrefers the number of times of iteration.

It can be seen from Tables 1 and 6 that the use of the NRTLmodel for correlating the VLE data for water–chloroform binarysystem obtained from Table 1 over the entire range of overall liq-uid composition x1 yields satisfactory results; the precise valuesof ˛, g12 − g11, and g21 − g22 for NRTL model were found to be0.42, 9890.03, and 19974.4, respectively; the standard deviationSDR (�y1) was found to be 0.138.

The predicted y1 is plotted in Fig. 7. Fig. 7(b) and (c) are close-upviews of specific regions of the phase diagram shown in Fig. 7(a). Itcan be seen that in the single-phase region the predicted values ofy1 are close to the experimental ones. However, dashed line corre-sponds to two-liquid-phase region, so the plotted values of y1 bythe dashed line have no physical significance there. The true valuesof y1, as we known from Table 1, keep at almost a constant 0.856. Itis necessary for us to separate correlation of the VLLE data for thetwo-liquid-phase region from correlation of the VLE data for thesingle-liquid-phase region.

For correlating the VLLE data from Table 3 for chloroform–watersystem in the three-phase (VLL)-coexistence region, we use NRTLactivity coefficient model and take the same objective function and

tions of equilibrium among three phases (VLL) differ from aboveand are expressed as [13],

pyi = psi x

aqi

�aqi

= psi x

orgi

�orgi

(16)

88 H.-S. Hu / Fluid Phase Equilibria 289 (2010) 80–89

Table 6Parameters of the activity coefficient models.

Binary systems NRTL equations Remarks

˛ g12 − g22 g21 − g11

0.03 19974.4 In the entire range of overall x1

4.51 17748.99 In VLLE equilibrium region3.62 23240.78 In the entire range of overall x1

7.8 23412.9 In VLLE equilibrium region

bptowcotsta

Fcrt

Chloroform(1)–water(2) 0.42 989Chloroform(1)–water(2) 0.45 1377Trichloroethylene(1)–water(2) 0.40 1232Trichloroethylene(1)–water(2) 0.40 1355

The results correlated are tabulated in Tables 3 and 6. It cane seen from Table 6 that the precise values of interaction energyarameters ˛, g12 − g11, and g21 − g22 for NRTL model were foundo be 0.45, 13774.51, and 17748.99, respectively. The correlationf the VLLE data using NRTL model can give satisfactory resultsith SDR (�y1) of 0.0007 and 0.001, SDR (�t) of 1.3 and 0.8 ◦C

orresponding to vapour-aqueous phase equilibrium and vapour-rganic phase equilibrium, respectively. It can be seen from Table 3

hat, the correlated activity coefficients of the component acted asolvent, �org

1,caland �aq

2,cal, are in general, to be almost 1.0, respec-

ively; while the correlated activity coefficients of the componentcted as solute, �aq

1,caland �org

2,cal, are very high, to be 842 and 106,

ig. 7. (a–c) Predicted and experimentally obtained vapour-phase compositions forhloroform(1)–water(2) system. The dashed line corresponds to two-liquid-phaseegion, so the predicted values by the dashed line have no physical significancehere.

Fig. 8. (a–c) Predicted and experimentally obtained vapour-phase compositions fortrichloroethylene(1)–water(2) system. The dashed line corresponds to two-liquid-phase region, so the predicted values by the dashed line have no physical significancethere.

respectively. That is, these correlated activity coefficients are veryclose to those of experimental ones.

The method for correlation on VLE and VLLE data fromTables 2 and 4 for trichloroethylene–water system are similar tothat of above chloroform–water system, and similar results areobtained, as shown in Tables 2, 4 and 6, respectively, and the pre-dicted y1 is plotted in Fig. 8.

4. Conclusions

It is feasible to use the new dynamic condensate-circulation stilldesigned for determination of the data on isobaric vapour–liquid

quilib

eccdimofctpasacVw

LFHGg

kmPRTtxx

x

yS

Scein

Ssao

G˛��

�

[

[[[

[

[

[

[

[

[

[

[

[[

Chinese Academy of Science in 1997. In the same year,he entered Tsinghua University and began to research the

H.-S. Hu / Fluid Phase E

quilibrium (VLE) and vapour–liquid–liquid equilibrium (VLLE) forhloroform–water and trichloroethylene–water binary partial mis-ible systems. For the two binary systems, on each T–x1(y1) phaseiagram there exists a lowest-temperature point (azeotropic point)

n the dew-point curve, this implies these systems all exhibitarked non-ideal property and strongly immiscibility. Moreover,

n each T–x1(y1) phase diagram the azeotropic-point curve is a per-ectly horizontal straight line, this implies the boiling point texp isonstant in the three-phase (VLL)-coexistence region, in addition,he VLLE data for each binary system showed that the vapour com-ositions y1,exp and the two liquid-phase composition, xaq

1 and xorg1 ,

lso remain almost constant although the overall liquid compo-ition x1 may change. The activity coefficients of the componentcted as solvent are in general, while the activity coefficients of theomponent acted as solute are very high. Both correlation of theLE data in the entire range of x1 and correlation of the VLLE dataith the NRTL activity coefficient model gave satisfactory results.

ist of symbolsobjective functionnormalization function

ij expression in NRTL equationij energy parameter (J mol−1) interaction between compo-

nent i and j in NRTL equationnumber of datatotal number of the datapressure (kPa)universal gas constant (=8.314 J mol−1 K−1)temperature in Kelvin (K)temperature in degrees Celsius (◦C)

1 total mole fraction of liquid phases component iaqi

mole fraction of liquid phase component i in aqueousphase

orgi

mole fraction of liquid phase component i in organicphase

i mole fraction of vapour-phase component iDR standard deviation

ubscriptsalc calculated data from NRTL equationxp experimental data

component inumber of times of iteration

uperscriptssaturated property

q aqueous liquid phaserg organic liquid phase

reek lettersnon-randomness parameter in NRTL equation

i activity coefficient of liquid-phase component iaqi

activity coefficient of liquid-phase component i in aque-ous phase

orgi

activity coefficient of liquid-phase component i in organicphase

ria 289 (2010) 80–89 89

�ij parameter in NRTL equation�i density of pure liquid component iϕaq

ivolume fraction of component i in aqueous phase

ϕorgi

volume fraction of component i in organic phase�aq density of aqueous phase�org density of organic phase� difference value

Acknowledgments

The author is indebted to the reviewers and professor Peter T.Cummings editor for good advices in revision of this manuscript.

References

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Hu-Sheng Hu, senior engineer, was born in 1965 in China.He held bachelor’s degree from the Science and Engineer-ing University of Kunming in 1988, and held master’sdegree from the Institute of Process and Engineering of

treatment of waste water and volatile organic compound,explored the extraction, distillation and adsorption newseparation technology. So far, he has published about 20research papers on the national and international journals.