3

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Measurement and modelling of the ternary phase equilibria for high

pressure carbon dioxide–ethanol–water mixtures

Nicola E. Durling, Owen J. Catchpole

∗

, Stephen J. Tallon, John B. Grey

Integrated Bioactive Technologies, Industrial Research Limited, Graceﬁeld Road, P.O. Box 31-310, Lower Hutt, New Zealand Received 2 July 2006; received in revised form 12 December 2006; accepted 21 December 2006

Available online 5 January 2007

Abstract

A continuous flow apparatus for measuring the phase equilibria of liquids in CO2is presented. Phase equilibrium measurements have been made

on the ternary system CO2–EtOH–H2O at 313 K and pressures of 100–300 bar, and comparisons have been made with literature data where possible.

Ethanol partition coefficients, selectivities and loadings for the CO2–EtOH–H2O system at 313 K and pressures of 100–300 bar are reported. Binary

data from the literature and ternary CO2–EtOH–H2O equilibrium measurements from this work were compared with results predicted using the

Peng–Robinson equation of state with quadratic and Wong–Sandler mixing rules. The phase behaviour of the ternary systems was predicted more accurately with the Wong–Sandler mixing rules than with the quadratic mixing rules.

Keywords: High pressure; Equilibria; Ethanol; Water; Carbon dioxide

1. Introduction

The vapour–liquid equilibrium of the ternary system CO2–EtOH–H2O is of relevance to the extraction of ethanol

from fermentation broths [1–3], dealcoholisation of bever-ages [4] and flavour enrichment of fruit juices [5] and wine

[6]. Phase equilibria data for CO2–EtOH–H2O have

previ-ously been determined at pressures up to 200 bar [2,7–13]. As far as the authors are aware there is no experimental data to date at 313 K and pressures from 200 to 300 bar

for the CO2–EtOH–H2O ternary system, which are common

experimental conditions for supercritical extraction, supercrit-ical antisolvent, chemsupercrit-ical reaction and many other processes

[14–15].

Catchpole et al.[16]compared the fractionation of lipids in a static mixer and a packed column using supercritical CO2. Their

results indicated that a static mixer could be used in conjunction with an effective separator for the rapid measurement of phase equilibrium data. Recent work by Fonseca et al.[17]and Ruivo et al.[18]utilised these findings and used a static mixer to measure

∗_{Corresponding author. Tel.: +64 4 9313138; fax: +64 4 9313055.} E-mail address:o.catchpole@irl.cri.nz(O.J. Catchpole).

the phase equilibria for ternary mixtures of essential oils and methyl oleate + squalene, respectively at supercritical conditions with CO2. The use of a static mixer gave numerous advantages

over typical phase equilibria measurement techniques including lower capital costs, rapid attainment of equilibrium conditions and compared to static methods, larger amounts of solute are available for analysis.

The Peng–Robinson equation of state (PR EOS) [19] has

been used to model the phase equilibrium behaviour of a large number of systems at supercritical conditions. It has been successfully applied to the CO2–EtOH, CO2–H2O and

EtOH–H2O binary systems[12,20–22], but its application to the

CO2–EtOH–H2O ternary system has not been thoroughly

stud-ied and accuracy is found to be highly dependant on the mixing rules and the interaction parameters used in the mixing rules

[12,20].

In this work we utilise a simple, continuous flow exper-imental method for determining phase equilibrium data for the CO2–EtOH–H2O system and report experimental

measure-ments at 313 K and pressures of 100, 200 and 300 bar. Measured and published data are modelled using the PR EOS with two mix-ing rules; the quadratic mixmix-ing rules for both the attractive and repulsive parameters[12], and the Wong–Sandler mixing rules

[23].

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2. Experimental

2.1. Apparatus and method

A schematic diagram of the experimental apparatus con-structed for the measurement of the phase equilibria between liquids and CO2, and in this work CO2–EtOH–H2O, is shown

inFig. 1. The apparatus was continuous flow for both CO2and

liquids. Liquid CO2 from the CO2cylinder flowed through a

needle valve (NV1) and two glycol chilled heat exchangers. The subcooled CO2was then compressed by an air driven diaphragm

pump (DC1) and delivered to the vessel V1 via a buffer vessel (BV). The pressure in V1 was controlled by a back pressure regulator (BPR). When the desired pressure (100–300 bar) was reached, the two valves (MV and NV4) between the vessels V1 and V2 were then opened to allow pressurisation of vessel V2. When the pressure in vessel V2 reached approximately 30 bar the venting valve PRV was opened. The metering valve (MV) and the venting valve (PRV) were tuned to stabilise the flow through the apparatus. The exiting CO2stream flowed through

a volumetric gas flow totaliser (GFT1) and a rotameter (RM). The temperature of the vessels V1 and V2 was maintained by

using a heated water bath. Once a steady flow of CO2 was

attained, the liquid feed of ethanol + water (which was placed on a balance), was fed into vessel V1 via a piston pump. The high pressure liquid then met with the CO2stream at a T-junction

just before the static mixer inlet. The CO2and liquid feed stream

were thoroughly mixed in the static mixer to reach vapour–liquid equilibrium (VLE) at the outlet of the mixer. The vessel V1 was then used to separate the two phases in equilibrium. The liquid phase collects at the base of V1, and was drained manually via SV1 into vessel V3, up to a pressure of 20 bar. Here the CO2

previously dissolved in the liquid phase exits the top of V3 and is measured by its flow through a volumetric GFT2 attached. The remaining liquid in V3 is collected through SV3, and the accu-mulated mass of liquid recorded. The temperature of the liquid phase being collected was monitored between the valve SV1 and vessel V3. The liquid/CO2interface was easily monitored

by a sharp decrease in temperature. The temperature monitoring was used to ensure that only the liquid phase was collected, and that the vessel V1 did not overflow. Oversampling of the liquid phase was also indicated by a rapid increase in pressure in the vessel V3.

The gas phase exits the top of vessel V1 and the dissolved liquid solutes are collected in vessel V2 due to the decrease in pressure between the two vessels. The liquid solutes were col-lected from the base of V2 via valve SV2 and the accumulated mass of liquid was recorded. The CO2in the gas phase was

mea-sured via its flow through the volumetric GFT1. The separator V2 was operated at 30 bar to try and minimise any loss of dis-solved liquid with the flow of gaseous CO2. The mole fraction

of ethanol and water in the gas phase were assumed to follow

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the perfect gas law, so the loss of ethanol and water could be estimated using the known flow rate of CO2and the literature

vapour pressure of ethanol and water[24]. The loss of water was shown to be negligible. The ethanol loss was added to the mass of ethanol and water recovered in V2 to obtain the final composi-tion. A mass balance was also performed over each experiment, and also during the experiment to see if any additional phases may have occurred. An intermediate phase results in accumula-tion inside V1, and eventually overflows into the gas phase. The mass balance for ethanol and water was found to agree within ±2%.

During operation, the collection valves at the base of the two vessels V1 and V2 were opened at regular 10 min intervals and the recovered liquids weighed. For all conditions used in this work a period of no more than 20 min was needed to achieve equilibrium conditions. The experiments were typically carried out over 60–90 min. The densities of the recovered liquids from V1 and V2 were measured and used to calculate the amount of ethanol and water in the samples (see Section2.3).

2.2. Materials

Mixtures ranging from 89 wt.% ethanol (Barwell Pacific, 99.8%) to 0 wt.% ethanol were used as liquid feeds. Liquid CO2

was supplied by BOC (New Zealand, 99%). 2.3. Density measurements

One milliliter samples of the collected liquids from V1 and V2 were withdrawn using a Gilson calibrated pipette and weighed. The average mass of 10 measurements was used to calculate the density of the liquid and the standard devia-tion in the measurements was found to vary by no more than ±0.008 g cm−3_{. The temperature of the liquid samples was also}

recorded. Standard solutions ranging from 99.8 wt.% ethanol to 0 wt.% ethanol were made and the densities measured using this method. The measured densities of these standard solutions, at the recorded temperature, were then compared to published data of densities of known ethanol wt.% in ethanol/water mixtures

[25]. Agreement between standard solutions and published data

was within±2 ethanol wt.%. The density method was further

verified by carrying out Karl–Fischer analysis on all standard solutions and 20 randomly selected samples. The wt.% of water calculated from Karl–Fischer analysis and the density method were in good agreement and varied by no more than±1.3 wt.% for all analysed samples.

3. Thermodynamic models

3.1. Peng–Robinson equation of state

The Peng–Robinson equation of state (PR EOS) is used in this work to predict the phase equilibria of the ternary sys-tem CO2–EtOH–H2O at 313 K and 100, 200 and 300 bar. The

PR EOS has been used to model the phase equilibrium of a large number of systems at supercritical conditions includ-ing the binary systems CO2–EtOH, CO2–H2O and EtOH–H2O

[12,20–23]. The PR EOS is given by[19]

P = _{v − b}RT −_{v(v + b) + b(v − b)}a(T ) (1)

Eq.(1)can be rearranged into the following form

Z3_{− Z}2

(1− B) + Z(A − 3B2− 2B) − AB + B2+ B3= 0

(2) For a mixture, the fugacity coefficient, ϕ, can be calculated ln(ϕi)= 1 bm _∂nb m ∂ni (Z− 1) − ln(Z − B) − A 2√2B × 1 am _∂n₂_a m ∂ni −_b1 m _∂nb m ∂ni ln Z + 2.414B Z − 0.414B (3) where bmand amare evaluated using appropriate mixing rules.

3.2. Mixing rules

In this work two common types of mixing rules have been applied, (1) quadratic mixing rules (VW) and (2) Wong–Sandler mixing rules (WS).

(1) Quadratic mixing rules

The quadratic (van der Waals) one-fluid mixing rules are:

am= i j xixjaij (4) bm= i j xixjbij (5)

where x is the mole fraction of component in that phase, aij and bij are cross parameters and are determined by the

standard combining rules:

aij = (aiaj)(1− kij) (6)

bij =bi+ bj

2 (1− lij) (7)

where i= j, k is the attraction interaction parameter between component i and j and l is the repulsion interaction parameter between component i and j, which are characteristic of each binary pair.

Yao et al.[12]modified the bijcross parameter to:

bij = (bibj)(1− lij) (8)

The adjustable parameters kijand lijfor each binary system,

CO2–EtOH, CO2–H2O and EtOH–H2O, were obtained by

using the PR EOS with VW mixing rules to fit experimental data from the literature. In parameter regression, the inter-action parameters were calculated using both a composition and a fugacity objective function as shown in Eqs.(9)and

(10), respectively.

Fmin=

i

(xli,exp− xli,calc)2+ (yi,expv − yvi,calc)2

(9)

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and Fmin= i (fiv− fil)2 (10) where f is the fugacity. In the fugacity minimisation objec-tive function Eq.(10), the fugacities for the vapour and liquid phase were calculated from the EOS using the experimen-tal liquid and vapour phase mole fractions, and the binary parameters were then adjusted to minimise the difference between the liquid and vapour phase fugacities. The calcu-lation procedure is simpler than the mole fraction objective function Eq. (9), as iteration is not required to calculate the predicted mole fractions. The calculated phase compo-sitions at constant temperature and pressure are obtained under the constraints of the phase equilibrium conditions

_x

i = 1 andyi= 1 and for Eq.(9)f_il= f_iv.

The average absolute percentage deviation (AAPD) is given by AAPD= 100 N xexp− xcalc xexp (11) and is used to compare the calculated results from the PR EOS with traditional VW mixing rules and modified Yao mixing rules to experimental data.

(2) Wong–Sandler mixing rules

In the WS mixing rule[23], the molar excess Helmholtz free energy at infinite pressure calculated from an EOS (A_-E,EOS_∞ ) is equated to the same property calculated from the NRTL excess free energy model (A_-E_∞). The WS mixing rules are: am RT =Q D 1− D (12) bm= Q 1− D (13)

where Q and D are defined as:

Q = i j xixj b − _RTa ij (14) and D = i xi_bai iRT + AE ∞ CRT (15)

where xiis the mole fraction of component i in that phase

and C is a constant depending on the EOS. The NRTL model

[26]was used for A_-E_∞/RT :

AE ∞ RT = i xi jxjτjigji kxkgki (16) with gij = exp(−αijτij) (αij= αji) (17)

The parameter αij is related to the randomness of the

mix-ture and is reported to be 0.3 for the CO2–EtOH[27]and

EtOH–H2O[23,28]systems and 0.4 for the CO2–H2O

sys-tem[29], and τjiare binary interaction parameters from the

NRTL model. In Eq.(14), the cross second virial coefficient can be calculated using:

b −_RTa ij= bi+ bj 2 − √aiiajj RT (1− kij) (18)

kijis a second virial coefficient binary interaction parameter,

which increases as the asymmetry of the system increases. The adjustable interaction parameters for each binary sys-tem, CO2–EtOH, CO2–H2O and EtOH–H2O, were obtained

from the literature [23,27–29] or determined from the

respective binary data using the PR EOS with WS mixing rules by minimising the objective functions given in Eqs.

(9)and(10).

The AAPD defined in Eq.(11)is used to compare the

calculated results from the PR EOS with WS mixing rules to experimental data.

4. Results and discussion

4.1. Phase equilibria results

To test the reliability of the experimental method and

proce-dure the VLE for the CO2–EtOH–H2O system was measured

at 313 K and 100 bar, as experimental data at these conditions has been reported in the literature[2,7,11]. The measured data are shown inTable 1, andFig. 2shows the comparison of our data with that of Lim et al.[11], Horizoe et al. [2]and de la Ossa et al.[7]at 313 K and 100 bar. The CO2composition of

the liquid phase is not reported by Horizoe et al. or de la Ossa et al. and cannot be compared to our data. The work by Lim et al., Horizoe et al. and de la Ossa does not cover such a wide composition range as the results shown here, but at comparable compositions, and within the experimental error of each data set, good agreement between measured results from this work and the literature was achieved. The results give confidence that equilibrium, rather than steady state was achieved. It is possible that additional phases could occur, especially in the region near

Fig. 2. Comparison between phase equilibria data measured in this work and that of Lim et al.[11], Horizoe et al.[2]and de la Ossa et al.[7]for the CO2–EtOH–H2O system at 313 K and 100 bar.

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Table 1

Mole fraction phase equilibrium data for the CO2–EtOH–H2O system at 313 K Pressure

(bar)

Ethanol in feed (wt.%)

Liquid:CO2 mass flow ratio

Liquid phase Gaseous phase KEtOH

(Eq.(1))

Selectivity (Eq.(2))

Loading (Eq.(3)) CO2 Ethanol Water CO2 Ethanol Water

100 89 0.345 0.5635 0.3282 0.1083 0.6825 0.2534 0.0641 0.772 1.30 38.82 87 0.289 0.4275 0.3890 0.1835 0.8441 0.1347 0.0212 0.346 3.00 16.68 87 0.120 0.3200 0.3815 0.2985 0.8938 0.0911 0.0151 0.239 4.72 10.66 81 0.122 0.2230 0.3632 0.4138 0.9223 0.0626 0.0151 0.172 4.72 7.10 81 0.125 0.1756 0.3364 0.4880 0.9246 0.0607 0.0147 0.180 5.99 6.86 61 0.126 0.1407 0.3114 0.5479 0.9378 0.0527 0.0095 0.169 9.76 5.87 76 0.182 0.0952 0.2728 0.6320 0.9453 0.0450 0.0097 0.165 10.75 4.98 76 0.095 0.0651 0.2312 0.7037 0.9415 0.0481 0.0104 0.208 14.08 5.34 47 0.308 0.0577 0.1909 0.7514 0.9609 0.0310 0.0081 0.162 15.06 3.37 47 0.140 0.0505 0.1558 0.7937 0.9688 0.0243 0.0069 0.156 17.94 2.62 27 0.330 0.0343 0.0945 0.8712 0.9792 0.0153 0.0055 0.162 25.65 1.63 27 0.149 0.0335 0.0777 0.8888 0.9820 0.0138 0.0042 0.178 37.58 1.47 200 89 0.672 0.5637 0.3161 0.1202 0.689 0.2363 0.0747 0.748 1.20 35.86 80 0.659 0.4189 0.3726 0.2085 0.7415 0.2014 0.0571 0.541 1.97 28.40 80 0.498 0.3457 0.3778 0.2765 0.7883 0.1663 0.0454 0.440 2.68 22.06 80 0.388 0.3160 0.3799 0.3041 0.8428 0.1225 0.0347 0.322 2.83 15.20 80 0.304 0.2776 0.3655 0.3569 0.8525 0.1177 0.0298 0.322 3.86 14.44 65 0.464 0.2110 0.3254 0.4636 0.8671 0.0962 0.0367 0.296 3.74 11.60 80 0.222 0.1911 0.3055 0.5034 0.8962 0.0795 0.0243 0.260 5.39 9.27 80 0.179 0.1752 0.2918 0.5330 0.9138 0.0689 0.0173 0.236 7.27 7.88 65 0.464 0.1624 0.2740 0.5636 0.9249 0.0600 0.0151 0.219 8.17 6.78 69 0.150 0.1208 0.2285 0.6507 0.9282 0.0530 0.0188 0.232 8.03 5.97 47 0.230 0.0924 0.1668 0.7408 0.9542 0.0374 0.0084 0.224 19.77 4.10 47 0.125 0.0871 0.1463 0.7666 0.9669 0.0277 0.0054 0.189 26.88 2.99 44 0.356 0.0827 0.1310 0.7863 0.9673 0.0239 0.0088 0.182 16.30 2.58 47 0.118 0.0501 0.0800 0.8699 0.9720 0.0200 0.0080 0.250 27.18 2.15 300 80 0.800 0.5216 0.3200 0.1584 0.6247 0.2607 0.1146 0.815 1.13 43.63 80 0.566 0.4250 0.3517 0.2233 0.6792 0.2244 0.0964 0.638 1.49 34.54 80 0.318 0.3350 0.3487 0.3163 0.6949 0.2094 0.0957 0.601 1.98 31.50 80 0.256 0.2801 0.3378 0.3821 0.7052 0.2056 0.0892 0.609 2.61 30.48 80 0.225 0.2578 0.3228 0.4194 0.8278 0.1239 0.0483 0.384 3.33 15.65 69 0.547 0.2089 0.2988 0.4923 0.8484 0.1110 0.0406 0.371 4.50 13.68 68 0.330 0.1590 0.2546 0.5864 0.8830 0.0868 0.0302 0.341 6.62 10.28 63 0.465 0.1459 0.2441 0.6100 0.8877 0.0849 0.0274 0.348 7.74 10.00 65 0.345 0.1318 0.2217 0.6465 0.8877 0.0786 0.0337 0.355 6.80 9.26 68 0.235 0.1184 0.1980 0.6836 0.9002 0.0706 0.0292 0.357 8.35 8.20 47 0.141 0.0841 0.1218 0.7941 0.9625 0.0222 0.0153 0.182 9.46 2.41 47 0.049 0.0691 0.0725 0.8584 0.9747 0.0138 0.0115 0.190 14.21 1.48

the critical point for CO2/ethanol, and not be visually observed

using a continuous flow method. Such phases can be observed experimentally either by mass balance discrepancies during the experiment (accumulation of a middle phase in the phase separa-tion vessel), or by a sudden change in composisepara-tion of the extract, when a middle phase has overflowed out of the phase separation vessel. No discrepancies in mass or composition were observed which would indicate more than two phases being present.

The experimental conditions and measured data for the VLE of CO2–EtOH–H2O system at 313 K and 200 and 300 bar are

also shown inTable 1. The phase compositions reported here are mean values for 3 different samples taken at different time intervals after equilibrium was attained (typically 30–35, 35–40 and 40–45 min), where the variation is found to be no more than±0.008 mole fraction in the liquid phase and ±0.002 mole fraction in the gaseous phase.

The phase equilibrium data for the CO2–EtOH–H2O system

at 313 K and 100, 200 and 300 bar are shown inFig. 3. As the

Fig. 3. Phase equilibria data for the CO2–EtOH–H2O system at 313 K and various pressures.

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pressure increases at constant temperature the size of the single phase region of the ternary diagram increases.

4.2. Partition coefﬁcients

The ethanol partition coefficients, K, between the CO2rich

phase and the water rich phase were calculated using Eq.(19), where y and x are the mole fractions of ethanol in the gaseous and liquid phases, respectively.

Ki= y_xi

i (19)

On comparison with published data at 100 bar and similar com-positions, the K results in this work are found to be in good agreement with those calculated from the data by Lim et al.[11]

and de la Ossa et al.[7]. The K values in this work at 200 bar are also in good agreement with those calculated from the data of de la Ossa et al.[7]at 200 bar. There is no data in the literature at higher pressures. At a given ethanol content in the feed and flow rate ratio, ethanol K values are found to increase with increasing pressure as shown inTable 1.

4.3. Selectivity and loading

For a separation based process the solvent selectivity and ethanol loading in the extract (gaseous) phase are of key impor-tance. The solvent selectivity of ethanol between the liquid and gaseous phases is obtained from the ratio of the partition coef-ficients (see Eq.(19)) of ethanol and water:

Selectivity= KEtOH Kwater

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Fig. 4 shows the experimental selectivity values calculated in this work in CO2at 313 K. For comparison the results of Lim

et al.[11]at 100 bar and de la Ossa et al.[7]at 100 and 200 bar are also shown. The solvent selectivity is seen to decrease with increasing ethanol concentration in the liquid phase at each pres-sure. Also, the selectivity decreases with increasing pressure at a given ethanol concentration in the liquid phase.

Fig. 4. Solvent selectivity for the CO2–EtOH–H2O ternary system at 313 K.

Fig. 5. Ethanol loading in the ternary CO2–EtOH–H2O system at 313 K.

At 100 bar, over the ethanol concentration range comparable to the data of Lim et al.[11]the selectivities in this work are found to be similar. However, the selectivities reported here and by Lim et al.[11]are lower than those reported by de la Ossa et al.[7]. The pressure dependency of the selectivity results from this work agrees with that of Lim et al.[11]and de la Ossa et al.[7]but is different from Kuk and Montagna[30]who found that as the pressure increases at a given ethanol concentration the selectivity increases.

The ethanol loading (g/100 g) is obtained from the mass ratio of ethanol and CO2in the gaseous phase:

Loading= 104.55 _y EtOH yCO2 (21)

Fig. 5shows the ethanol loading obtained in this work at 313 K and 100, 200 and 300 bar. The ethanol loading increases with increasing ethanol concentration in the liquid phase and increas-ing pressure.Fig. 5also shows the loading data from Lim et al.

[11]and de la Ossa[7]. Loadings at high ethanol contents in the liquid phase are not reported by either author. However, at comparable ethanol contents in the liquid phase and 100 bar the ethanol loadings from this work are slightly lower than those obtained by Lim et al.[11], but are in good agreement with the loadings of de la Ossa et al.[7]. At 200 bar there is good agree-ment between the experiagree-mental loadings calculated from this work and those of de la Ossa et al.[7].

The loading results from this work at 100, 200 and 300 bar increase with increasing pressure. It was found earlier that the partition coefficient also increases with increasing pressure.

Fig. 6is a plot of loading/K against the mole fraction of ethanol in the liquid phase on a CO2free basis. A linear correlation of

y = 96.9761x (R2_{= 0.9921)}

(22) is observed which is independent of pressure up to an ethanol molar concentration of 0.5 in the liquid phase.

A solvent free representation of the vapour phase equilib-rium for the CO2–EtOH–H2O ternary system at 313 K is shown

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Fig. 6. Correlation between ethanol loading/K in the ternary CO2–EtOH–H2O system at 313 K.

not concentrated above the atmospheric azeotropic composition, ymax, of 89.4 mol%. The highest attainable ethanol concentration

decreases as the system pressure increases, which is consis-tent with a decrease in the ethanol selectivity as the pressure is increased, as seen inFig. 4. The data at all pressures can be fitted to the equation

yEtOH = ymax(1− e−cxEtOH) (23)

where yEtOHis the mole fraction of ethanol in the gaseous phase

on a CO2free basis, ymaxthe maximum mole fraction of ethanol

in the gaseous phase that can be attained, xEtOH the mole

frac-tion of ethanol in the liquid phase on a CO2free basis and c is

a gaseous phase constant which is a function of pressure. The predicted data for each pressure using Eq.(23)is also shown in Fig. 7. The predicted values of ymax and c decrease with

increasing pressure. The ymaxvalues are 0.82, 0.75 and 0.72 and

the c values are 28.2, 24.7 and 16.6 for 100, 200 and 300 bar, respectively.

Fig. 7. Solvent free representation of the ternary CO2–EtOH–H2O system at 313 K.

4.4. Modelling the phase equilibria of binary systems with the PR EOS

4.4.1. The CO2–EtOH system

The adjustable parameters for the standard VW, Yao and WS mixing rules were used in the PR EOS to model the phase equilibrium data for the CO2–EtOH[31]system at 313 K and

pressures from 9 to 79 bar. The results for each mixing rule and objective function are shown inTable 2, along with the average absolute percentage deviation (AAPD) in the liquid and gaseous phases. The AAPD in the liquid and gaseous phases did not vary significantly between the two objective functions for the VW and Yao mixing rules, however, the objective function has a greater influence on the AAPD when using the WS mixing rules. The experimental and calculated values using the fugacity objective function are compared inFig. 8.

4.4.2. The CO2–H2O system

The adjustable parameters for the standard VW, Yao and WS mixing rules were used in the PR EOS to model the phase equi-librium data for the CO2–H2O [32,33] system at 313 K and

pressures from 75 to 400 bar. The results for each mixing rule and objective function are shown in Table 2, along with the average absolute percentage deviation (AAPD) in the liquid and gaseous phases. The experimental and calculated values using the fugacity objective function are compared inFig. 9. All mix-ing rules and objective functions gave good results in the liquid and gaseous phases, but the predicted results begin to deviate from the literature data at low pressures.

4.4.3. The EtOH–H2O system

The adjustable parameters for the standard VW, Yao and WS mixing rules were used in the PR EOS to model the phase equilibrium data for the EtOH–H2O[34]system at 313 K and

pressures from 0.1 to 0.78 bar. The results for each mixing rule and objective function are shown in Table 2, along with the average absolute percentage deviation (AAPD) in the liquid and gaseous phases. The experimental and calculated values

Fig. 8. Comparison of experimental and calculated vapour–liquid equilibria for the CO2–EtOH system at 313 K.

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Table 2

Calculated adjustable parameters and AAPD for binary systems using quadratic and Wong–Sandler mixing rules and two objective functions (OF)

OF Parameters CO2(1)–EtOH(2) CO2(1)–H2O(3) EtOH(2)–H2O(3)

Quadratic mixing rule at 313 K

Composition kij 0.0967 0.263 0.0257 lij −0.000966 0.216 0.131 x 2.39 1.02 3.06 y 15.49 3.93 1.56 Ref. [31] [32,33] [34] Fugacity kij 0.083000 0.262 0.105 lij −0.0143 0.215 0.207 x 2.21 1.02 1.52 y 15.50 3.98 1.43 Ref. [31] [32,33] [34]

Wong–Sandler mixing rule at 313 K

Composition αij 0.30 0.40 0.30 kij 0.257 0.254 0.594 τij 7.19 5.22 2.63 τji 0.258 2.75 −1.29 x 0.39 2.27 0.85 y 9.21 3.34 0.70 Ref. [27,31] [29,32,33] [23,28,34] Fugacity αij 0.30 0.40 0.30 kij 0.346 0.236 0.425 τij 3.53 5.40 0.568 τji −0.365 2.82 0.208 x 0.89 2.27 0.48 y 7.94 4.02 0.30 Ref. [27,31] [29,32,33] [23,28,34]

Yao mixing rules at 313 K

Composition kij 0.112 0.263 0.128 lij −0.0516 0.204 0.121 x 0.76 1.02 0.52 y 9.41 3.95 0.33 Ref. [31] [32,33] [34] Fugacity kij 0.0830 0.262 0.126 lij −0.0787 0.204 0.0771 x 0.75 1.02 1.68 y 8.90 3.97 0.99 Ref. [31] [32,33] [34]

x = (100/N){|xexp− xcalc|/xexp|}, y = (100/N)

{|yexp− ycalc|/yexp|}.

Fig. 9. Comparison of experimental and calculated vapour–liquid equilibria for the CO2–H2O system at 313 K.

using the fugacity objective function are compared inFig. 10. The VW mixing rule with both objective functions has good predictive capabilities for this binary system in the liquid and gaseous phases, however the Yao and WS mixing rules with both objective functions display even better predictive capabilities. 4.5. Modelling the phase equilibria of the ternary system with the PR EOS

Using the binary interaction parameters for the standard VW, Yao and WS mixing rules shown inTable 2, the phase equilib-rium of the ternary system CO2–EtOH–H2O at 313 K and 100,

200 and 300 bar was estimated and compared with experimental data collected in this work. A comparison between experimental and calculated results (PR EOS using VW, WS and Yao mixing rules with the fugacity objective function) for this ternary sys-tem at 313 K and 100, 200 and 300 bar are shown inFigs. 11–13, respectively. Experimental data reported in the literature is also

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Table 3

Average absolute percentage deviations of predicted and experimental data for the ternary system CO2–EtOH–H2O at 313 K

Pressure (bar) Quadratic mixing rules Wong–Sandler mixing rules Yao mixing rules

x y x y x y Composition error 100 7.59 20.03 4.55 20.00 11.88 19.82 200 9.45 17.60 3.51 12.45 12.10 18.62 300 10.09 24.14 4.17 19.35 12.60 25.01 Fugacity error 100 11.42 19.94 4.32 16.60 11.71 32.14 200 11.77 17.99 1.94 12.37 11.91 19.35 300 12.20 24.74 1.97 11.27 11.99 30.10

Fig. 10. Comparison of experimental and calculated vapour–liquid equilibria for the EtOH–H2O system at 313 K.

shown[2,7,11]. The AAPD between experimental and predicted liquid and gaseous phases, for each mixing rule and objective function, are given inTable 3at each pressure.

The liquid phase AAPD using the VW mixing rules increases as the pressure increases with both objective functions. The gaseous phase AAPD is much greater than that in the liquid phase and this pressure dependency is not observed. The composition objective function gives improved liquid phase predictions but

Fig. 11. Comparison between experimental and calculated phase equilibrium values for the ternary system CO2–EtOH–H2O at 313 K and 100 bar.

the gaseous phase predictions do not vary significantly between the two objective functions. The AAPD in the liquid and gaseous phases for the WS mixing rules is consistently lower than those using the VW mixing rules at each pressure and with each objective function. Application of the Yao mixing rules to the experimental data reported in this work gave improved AAPD for the binary systems compared to the VW mixing rules, and showed similar or improved AAPD compared to the WS mixing rules.

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Even though the VW and Yao mixing rules gave good corre-lations for all the binary systems, it is not possible to reproduce this for the ternary phase equilibria data (Table 3). At all pres-sures studied in this work the WS mixing rules in the PR EOS model predict the phase behaviour of the ternary system more accurately. Also, the AAPD in both the liquid and gaseous phases using the WS mixing rules is lower at all pressures when employ-ing the fugacity objective function. Excellent predictions are observed in the liquid phase even at concentrations close to the critical point.

In the literature the PR EOS[12,20]has been used with seven different mixing rules to model the ternary CO2–EtOH–H2O

system, however, in most cases the equilibrium concentration is overestimated, as observed with this work for VW and Yao mixing rules. To date Yao et al.[12]using the Yao mixing rules achieved the best predictions by re-examining the CO2–EtOH–

H2O ternary data of Takishima et al. [36] and Gilbert and

Paulaitis[9]at 308 K, where satisfactory concentration predic-tions were observed in the liquid phase, even at composipredic-tions close to the critical point. The AAPD in the gaseous phase was not reported. Re-examination of this data using our PR EOS model with the values of the interaction parameters reported in the paper by Yao et al.[12]showed that the gaseous phase AAPD values were high at approximately 30%.

Other EOS approaches for modelling the CO2–EtOH–H2O

ternary system have been tried. The most commonly applied is the Patel–Teja EOS[10,11,13,35,36]. A number of different mixing rules have been applied with this EOS, which greatly influence its predictive capability. Lim et al.[11]found that the Adachi and Sugie mixing rule gave an improved prediction for the ternary phase behaviour, but the equilibrium concentrations were not estimated satisfactorily. Takishima et al.[36]used the Wilson mixing rule and reported similar findings, where the ternary phase behaviour can approximately be predicted, but equilibrium concentrations were unsatisfactory.

The group contribution[10,35,37,38]and a perturbed dipolar hard sphere EOS[7], along with a simple mathematical model based on polynomial functions[8]have also been used to pre-dict the ternary composition of the CO2–EtOH–H2O system. In

the cases where good quantitative agreement is obtained for the binary mixtures, it has not been possible to reproduce the exper-imental data for the ternary mixture over the whole composition range.

Prediction of the phase behaviour of the ternary CO2–EtOH–

H2O system was satisfactory using the PR EOS with WS mixing

rules over the whole composition range. The objective function used with the PR model and WS mixing rules was found to have an effect on its predictive capabilities with the fugacity objective function resulting in a lower AAPD in the liquid and gaseous phases.

5. Conclusions

A continuous flow apparatus employing a static mixer was used to measure the high pressure ternary phase equilibrium of CO2–EtOH–H2O at 313 K and pressures from 100 to 300 bar.

Ethanol partition coefficients, selectivities and loadings have

been calculated from the phase equilibrium data. Ethanol load-ing was found to increase with increasload-ing ethanol content in the liquid phase and also showed a pressure dependency, where loading increases with increasing pressure. Taking the pressure dependency of the partition coefficient into account when calcu-lating the loading, resulted in a linear correlation up to an ethanol molar concentration of 0.5, which is independent of pressure.

The PR EOS with quadratic and Wong–Sandler mixing rules was applied to literature data for the binary CO2–EtOH,

CO2–H2O and EtOH–H2O systems at 313 K to obtain the

adjustable parameters needed to predict the CO2–EtOH–H2O

phase equilibrium composition for the data in this work. Good correlations were obtained for the phase equilibria of the binary systems with quadratic and Wong–Sandler mixing rules. How-ever, reproducibility of experimental ternary CO2–EtOH–H2O

phase equilibrium data over the whole composition range was only possible on application of the Wong–Sandler mixing rules, where the slopes of the calculated tie lines are nearly consistent with experiment, and the calculated equilibrium concentrations were found to be similar to experimental values even as the critical point was approached.

List of symbols

a parameter of PR EOS

A aP/(RT)2

A_-E Helmholtz free energy

b parameter of PR EOS

B bP/RT

c gaseous phase constant in Eq.(23)

C equation of state constant (∼0.62323 for PR EOS)

D parameter defined by Eq.(15)

f fugacity

F objective function

g parameter defined by Eq.(17)

k binary adjustable interaction parameter

K partition coefficient

L binary adjustable interaction parameter

P pressure (Pa) defined by Eq.(1)

Q parameter defined by Eq.(14)

R gas constant (J mol−1K−1)

T absolute temperature

v molar volume (m3mol−1)

x liquid phase mole fraction

y gaseous phase mole fraction

Z compressibility factor

Greek letters

α adjustable parameter for the randomness of the mixture

ϕ fugacity coefficient

τ binary interaction parameter for the NRTL model

∞ infinite pressure Subscripts calc calculated exp experimental EtOH ethanol i, j, k component i, j, k

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m mixture

max maximum

min minimum

Superscripts

l liquid phase composition

v vapour phase composition

Acknowledgement

This work was supported by the Foundation for Research Sci-ence and Technology (Contract (C08X0305)) of New Zealand.

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