Application of the LCVM model to systems containing organic compounds and supercritical carbon dioxide

88

The Journal of Supercritical Fluids, 1996,9, 88-98

Application of the LCVM Model to Systems Containing Organic Compounds and Supercritical Carbon Dioxide lakovos V. Yakoumis, Konstantinos Kontogeorgis, Philippos Coutsikos, Dimitrios Tassios*

Vlachos, Georgios M. Nikolaos S. Kalospiros,

and

Laboratory of Thermodynamics and Transport Phenomena, Department of Chemical Engineering, National Technical University of Athens, 9, Heroon Polytechniou St., Zografou Campus, 15780 Athens, Greece

Fragiskos

N. Kolisis

Biosystems Technology Laboratory, Department of Chemical Engineering, National Technical University of Athens, 9, Heroon Polytechniou St., Zogra fou Campus, 15780 Athens, Greece Received October 25, 1995; accepted in revised form January 29, 1996

A recently developed equation of state-excess Gibbs free energy (EOWGE) model with the LCVM (linear combination of Vidal and Michelsen) mixing rule, capable of successful VLE prediction in asymmetric systems is applied to the prediction of solubilities of alkenes, ethers, acids, alcohols, and esters in supercritical carbon dioxide. Considering the experimental uncertainties, excellent correlation of binary data and satisfactory prediction of ternary and multicomponent equilibria are obtained in most casesover a wide range of temperature, pressure, and system asymmetry. These promising results render the LCVM model a useful tool for the preliminary design of processesinvolving mixtures with organic compounds and super-critical carbon dioxide. Keywords:

equation of state, EOS/GE model, solubility, vapor-liquid equilibria, carbon dioxide, biotechnology

1.

INTRODUCTION In recent years, enzyme-catalyzed reactions in supercritical gases have received much attention. Many enzymes maintain their catalytic activity in micro aqueous, that is nearly anhydrous environments. This discovery, made in mid-1980s, has considerably widened the potential use of biocatalysts in non-conventional media such as supercritical gases.’ In particular, supercritical carbon dioxide has an attractive combination of properties for industrial use and it has received the most attention (It is non-toxic, non-flammable, it has low viscosity, surface tension, cost, and high diffusivity). A crucial parameter for the effective design of processesfor enzyme-catalyzed reactions and for product separations is the solubility of substrates and reaction products in supercritical carbon dioxide, and the dependence of sol0896-8446/96/0902-0088$7.50/O

ubility on temperature and pressure. Consequently, the objective of this study is the use of cubic equations of state (EOS) in the prediction of solubilities of liquid organics, especially of acids, alcohols, and esters in supercritical carbon dioxide. Cubic EOS with conventional van der Waals one fluid mixing rules have been extensively used in the correlation of vapor-liquid equilibrium (VLE) data. Usually, (at least) two interaction parameters are required for polar and asymmetric mixtures. However, in the recent years cubic EOS became predictive tools even for mixtures with polar components through the development of the socalled EOS@ models. Several such models have been developed recently: VidaL2 MHVl and MHV2 (Modified Huron-Vidal firstand second-order approximations) (Michelsen3 Dahl and 0 1996 PRA Press

The Journal of Supercritical Fluids, Vol. 9, No. 2, 1996 Michelsen4), PSRK (Predictive Soave-Redlich Kwong model by Holderbraum and Gmehling5), Wong and Sandler,6 and LCVM (Linear Combination of Vidal and Michelsen rules by Boukouvalas et al.7). The main feature in the development of these models is to obtain a mixing rule for the attractive term parameter, a, of the EOS setting the expression for GE obtained from the EOS equal to the GE from an existing activity coefficient model, like the classical models of UNIFAC, ASOG, and NRTL. In the case of the Vidal model, this matching was postulated at infinite pressure. On the other hand, MHVl, MHV2, and PSRK are simThis pler versions of a model proposed by Michelsen.* group of models is based on matching the excess Gibbs free-energies at zero pressure. Recently, Coniglio et al.9 developed a modified MHVl model suitable for mixtures of carbon dioxide with acids and esters. The LCVM model is, as denoted by its acronym, a linear combination of the mixing rules of the Vidal and MHVI models, developed so as to give satisfactory bubble point pressure predictions for a variety of systems. The LCVM model is of empirical origin and has no specified reference pressure, but it possesses many good features in calculating phase equilibria including several extreme cases (infinite dilution activity coefficients, Henry constants and soiid-gas equilibria), as will be explained later. Finally, the Wong-Sandler model is probably theoretically the soundest among these models, but, unfortunately, it has not been extended to systems with carbon dioxide so far. J All the models mentioned above, except the one proposed by Vidal, have been successfully applied to the prediction of high-pressure, high-temperature vapor-liquid equilibrium, mostly for systems with components that do not differ appreciably in size (symmetric systems). The modified MHVl model by Coniglio et al. has been applied to a limited number of asymmetric systems (C02esters, acids). Most other models (e.g., MHV2, WongSandler) are shown to have problems for asymmetric systems.10-*2 On the other hand, it has been demonstrated in a series of recent publications that the LCVM model is capable of satisfactory predictions for both, symmetric and asymmetric systems and for a great variety of systems, including carbon dioxide and other supercritical fluids with heavy alkanes, alkane solutions, etc.7*11+13,14 The good performance of LCVM is extended to infinite dilution activity coefficients6* and Henry constants.69 Since most of the systems of interest to the present study contain highmolecular-weight alkenes, carboxylic acids, alcohols or esters with supercritical carbon dioxide, and are thus highly asymmetric, the LCVM model was chosen for the prediction of solubilities of such compounds in supercritical carbon dioxide. The LCVM model is briefly presented in the next section. In addition to the above, LCVM has been previously used with success in the prediction of solubilities of liquid and solid aromatic compounds in supercritical

Application of the LCVM Model

89

CO;!.t5 The same authors also tested the applicability of the LCVM model and of the t-mPR EOS (a modified translated version of the Peng-Robinson EOS developed by Magoulas and Tassiost6) with conventional mixing rules to the correlation of solubilities of aromatic hydrocarbons in supercritical C02. The results with LCVM were generally satisfactory, comparable with those using two parameter conventional mixing rules. The remainder of the paper is organised as follows: In the next section, a short overview of the LCVM model is given. Then, we present the data base used and the procedure for the evaluation of the LCVM interaction parameters for the pairs of groups containing COz. These groups are not available in the Original UNIFAC interaction parameter table.17 Correlation and prediction results for binary and multicomponent systems are presented and discussed next. We close with our conclusions. 2.

THE LCVM MODEL The LCVM model is an equation of state-excess Gibbs free energy model, that is, it uses a cubic EOS coupled with a GE model for the mixing rule of the attractive parameter. A short presentation of the cubic EOS employed and of the mixing rule are given in this section. 2.1. The Cubic Equation of State. The cubic EOS is a translated (and modified) version of the Peng-Robinson EOS (t-mPR) recently proposed by Magoulas and Tassios16 p=--

RT V+t-b

a (V+t)(V+t+b)+b(V+t-b)

(1)

where a = 0.45724 Ff(r,) c b=0.0778% PC

(3)

R is the ideal gas constant, T, and P, are the critical temperature and critical pressure of the compound, respectively. The translation factor t, is given by a generalized (with respect to o) and temperature dependent equation and is introduced in order to improve the saturated volume predictions. TheAT,) equation follows for nonpolar compounds (COZ, alkenes, ethers) a Soave-type expression as a function of only the reduced temperature and the acentric factor.

90

Yakoumis et al.

The Journal

TABLE l Critical Properties (T,, P,), Normal Boiling Points (Tb) and Acentric Factors (w) for the Compounds Used in this Study

of Supercritical

Mathias-Copeman Compounds Compound

Carbon Dioxide Acetic acid Laurie acid Palmitic acid Stearic acid Oleic acid Linoleic acid Arachidic acid Methyl myristate Methyl palmitate Methyl stearate Methyl oleate Methyl linoleate Ethyl stearate Ethyl oleate Ethyl linoleate EPA ethyl ester DHA ethyl ester Methyl benzoate Methanol Ethanol 1-Propanol 2-Propanol 1-butanol I-Pentanol 2-Methyl-1-pentanol I-Octanol 1-Decanol 1-Dodecanol I-Hexadecanol I-Octadecanol 1,8-Octanediol Propene 1 -Butene 1-Hexene 1-Heptene 1-Hexadecene Dimethyl ether Diethyl ether Methyl-t-butyl ether Dibutyl ether

304.2 592.7 743.2 782.3 803.7 792.6 792.2 808.6 736.1 759.1 779.6 778.8 778.3 783.5 782.9 782.4 794.8 801.9 693.0 512.6 513.9 536.7 508.3 562.9 586.2 582.0 652.5 690.0 721.0 759.1 776.4 700.4 364.2 419.6 504.0 537.3 722.0 400.1 466.7 497.1 579.9

73.82 57.86 18.68 14.68 13.26 13.55 13.84 12.10 15.36 13.81 12.55 12.80 13.07 12.00 12.23 12.47 12.08 11.30 35.90 80.97 61.48 51.70 47.62 44.13 38.80 34.00 28.60 23.70 19.30 16.18 14.58 28.57 46.13 40.20 3 1.40 28.30 14.80 53.70 36.38 34.30 24.46

0.2276 0.4604 0.8524 0.9992 1.0676 1.0584 1.0489 1.1329 0.8163 0.8914 0.9630 0.9530 0.9429 0.9975 0.9879 0.9780 1.0168 1.1237 0.42 11 0.5560 0.6371 0.6279 0.6650 0.5945 0.5938 0.7262 0.5944 0.6134 0.6393 0.7729 0.8410 1.0889 0.1424 0.1867 0.2800 0.3310 0.7319 0.2036 0.2846 0.2674 0.4768

Acetic acid Laurie acid Palmitic acid Stearic acid Oleic acid Linoleic acid Arachidic acid Methyl myristate Methyl palmitate Methyl stearate Methyl oleate Methyl linoleate Ethyl stearate Ethyl oleate Ethyl linoleate EPA ethyl ester DHA ethyl ester Methyl benzoate Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 1-Pentanol 2-Methyl-1-pentanol 1-Octanol 1-Decanol 1-Dodecanol 1-Hexadecanol 1-Octadecanol Dimethyl ether Diethyl ether Methyl-t-butyl ether Dibutyl ether

319.0 571.9 622.3 648.1 637.7 635.8 660.0 572.7 600.3 625.4 623.2 621.2 632.6 630.7 628.8 642.5 657.3 472.7 337.9 351.4 370.4 355.4 390.8 411.0 421.2 468.4 503.4 535.0 585.2 608.2 536.5 225.5 266.9 336.6 366.7 558.0 248.3 307.6 328.4 413.5

m = 0.384401+ 1.5227~ - 0.2138080~

- 0.0001976~~.

(5)

However for polar compounds (alcohols, acids, esters), the Mathias-Copeman23 equation with component specific

constants

(obtained

from

vapor

pressure

1.19794 1.49932 I .76697 1.71243 1.71271 1.67612 1.86135 1.5817 1.6610 1.7383 1.7340 1.7098 1.8082 1.7956 1.7825 1.8040 1.9642 1.18624 1.2240 1.2062 1.0656 1.10525 0.9 1805 1.1355 1.23767 1.3354 1.1423 1.25278 1.66445 1.4013 0.67124 0.84166 0.748782 1.073294

the

c2

c3

-1.241967 0.132745 -0.87978 1 0.09765 1 1.28208 1 1.499946 0.787478 -0.842390 -0.705430 -0.586910 -0.674530 -0.539180 -0.92 1080 -0.905430 -0.887850 -0.576780 -0.92863 -1.951413 -0.273495 0.789830 1.614770 1.837749 2.445210 0.279793 1.540299 -1.907881 0.299890 -0.456273 -2.431791 1.285258 0.070523 -0.500041 0.150900 -0.293 192

1.506926 1.420256 3.529730 1.869709 - 1.967284 -2.392585 - 1.077648 1.476600 1.183200 0.938200 1.199600 0.882370 1.449080 1.434930 1.416800 0.898450 1.521140 4.325466 -0.398234 -2.308420 -2.942920 -3.853776 -4.118070 0.996500 -4.171926 7.028472 1.682867 3.544573 7.55702 1 -0.521033 -0.152003 1.318113 -0.068678 0.972619

6)

where

+0.03461603

Vol. 9, No. 2, 1996

TABLE II Equation Constants for Involved in this Study Cl

Compound

Fluids,

data) is

The critical properties and the constants of eq 6 are presented for the compounds used in this work in Tables I and II. 2.2. The LCVM Mixing Rule (Boukouvalas et al.‘). Application of any EOS for mixtures requires mixing rules for the energy and the covolume parameters. In the case of the LCVM model which is originally suggested by Boukouvalas used for the mixture

et al.,’ the linear mixing rule is covolume parameter b, while the mixing rule for the EOS attractive-term parameter a (in terms of the dimensionless parameter a! = a/bRT) is a linear combination of the ones by Vida12 and Michelsen* a=;la,+(l-qa,

(7)

The Journal of Supercritical Fluids, Vol. 9, No. 2, 1996

Application of the LCVM Model

91

where 1 GE a, =?iz%RT+

c

Yiai

(8)

and a,=~[[GE/RT]+Cyiln(b/b,)]+Cyia,

(9)

In these equations, yi is the mole fraction of the component i in the mixture. The subscript i denotes pure-component properties of the component i. The GE model employed in the LCVM model is the original UNIFAC equation.t7*‘* Boukouvalas et al.’ suggest that il = 0.36, a value which yields good results for a number of asymmetric systems (e.g., C02-alkanes, ethane-alkanes, etc.). The &value of LCVM depends on the GE model used and the value il = 0.36 is recommended for use with the original UNIFAC model. Other a-values should be used if other Gn models are chosen. Equation 7 combines the Vidal (infinite reference pressure) and Michelsen-MHVl (zero reference pressure) mixing rules. Consequently, the LCVM model has no specified reference pressure although we should mention that the MHVl model is not rigorously a zero-reference pressure model since it does not reproduce the GE model (Kalospiros et al . 67). Furthermore, the use of the UNIFAC table (obtained from low pressure VLE data) in combination with the LCVM model cannot be justified theoretically. However, the obtained results in a series of recent publications mentioned before in this section clearly justified the use of LCVM as an empirical, yet highly successful model. 3. DATA BASE AND PARAMETER EVALUATION 3.1. Pure Component Properties. a. Critical Properties and Acentric Factor. The Tb, T,, P,, and w values of the compounds considered in this study are given in Table I. The values for the critical properties and acentric factor for CO*, alkenes, ethers, methyl benzoate, and 2-methyl-1-pentanol are experimental taken from the DIPPR Data Compilation,r9 while those for acetic acid are from Ambrose and Ghiassee.20 The same properties for the other alcohols (up to 1-dodecanol) were obtained from the recent measurements by Teja et a1.21 For all the other compounds (l,S-octanediol, heavy alcohols, acids and esters, dibutyl-ether) no experimental critical properties are available. They are, thus, estimated using the group-contribution method of Ambrose,22 with the boiling point taken from the AMP method, as modified by Coniglio et a1.9 (see below). Preliminary results of an investigation carried out in our laboratory show that - among most existing property estimation methods - the one of

Figure 1. Percentage deviation between experimental and estimated vapor pressuresfor stearic acid. The methods used are the AMP equation as modified by Coniglio et aIg and the group contribution method of Tu.~~ Experimental vaporpressuredata are from Ashour et a1.24

Ambrose seems the most reliable (at least for low to medium molecular weight compounds) and, therefore, this method is used in this work. 6. Estimation of Constants for the Mathias-Copeman Equation. It is well-known that the Soave equation for the energy parameter yields satisfactory vapor pressures for nonpolar and slightly polar compounds (e.g., alkanes, 1-alkenes, some ethers). However, for strongly polar and hydrogen-bonding compounds (esters, acids, alcohols) the Mathias-Copeman equation23 for the temperature correction of the pure-component attractive-term parameter of the t-mPR EOS should be used. This equation requires three compoundspecific constants, cl, c2, and c3, which are obtained by regressing experimental vapor-pressure data. In the case of alcohols, ethers, and methyl benzoate these data are taken from the DIPPR Data Compilation*9 and the compound-specific constants are given in Table II. The Mathias-Copeman constants for four carboxylic acids, namely caproic, lauric, palmitic, and stearic have been estimated using the experimental vapor-pressure data compiled by Ashour et a1.24 Unfortunately, no reliable experimental vapor-pressure data over extended temperature ranges are available for the remaining carboxylic acids and for all the esters of interest to this study. For this reason, three methods for vapor-pressure estimation have been compared: . . .

The DIPPR Correlation (Daubert and Dannert9) A recently developed group-contribution method by Twu= The Abrams-Massaldi-Prausnitz (AMP) equation as modified for acids and esters by Coniglio et a1.,9 which has the following algebraic form: lnP=A+B/T+ClnT+DT+ET2

(10)

where the five constants A, B, C, D, and E are expressed in terms of three compound-specific parameters: the van

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The Journal of Supercritical Fluids, Vol. 9, No. 2, 1996

TABLE llla References of Experimental Data for the Systems Used in the Parameter Estimation CO*-solute

Reference of Experimental Data

Propene 1-Butene 1-Hexane 1-Heptene Dimethyl ether Diethyl ether Methyl-t-butyl ether Methanol Ethanol n-Propanol n-Butanol n-Pentanol n-decanol

(341, (35) (34), (36) (371, 381, (39) (38) (4% (41) (42) (43) (4% (4% (461, 47) (44), (451, (48) (44) (48) (49) (50) (51) (27) (261, (27) (29) (27) (52) (52) (52) (52) (53) (53) (53) (54), (55)

n-dodecanol

Laurie acid Palmitic acid Oleic acid Arachidic acid Methyl

myristate

Methyl palmitate Methyl stearate Methyl oleate Ethyl stearate Ethyl oleate Ethyl linoleate Methyl benzoate

TABLE lllb References of Experimental Data Systems Not Used in the Parameter CO*-solute

Reference of Experimental Data

Dibutyl ether EPA ethyl ester DHA ethyl ester 1-Hexadecene Acetic acid Laurie acid Oleic acid Linoleic acid

(56) (53) (53) (57) (58)

(26) (31) (31) (51) (59) (59)

1,8-Octanediol 1-Hexadecanol

1-Octadecanol Propanol-2

(60)

2-Methyl- 1-pentanol 1-Octanol Oleic acid-Linoleic

(50) (50), (61)

acid

Methyl oleate-Methyl linoleate Methyl oleate-Oleic acid 1-Dodecanol-Laurie acid Hexadecane-1 -Dodecanol n-Hexane-Stearic

for the Estimation

acid-Oleic

acid

(62) (62) (63) (64) (65)

(66)

der Waals volume (VW), the E, parameter which reflects the strength of the intermolecular forces, and the s parameter which reflects the shape, size, and flexibility of the molecule. Figure 1 presents an evaluation of these methods for stearic acid. It seems that the AMP equation gives the best overall performance and it was, therefore, used for the estimation of the Mathias-Copeman constants for those carboxylic acids and esters for which no experimental vapor pressure were available. The corresponding constants are given in Table II. 3.2. Estimation of Interaction Parameters. The Gn equation implemented in the LCVM mode1 is Original UNIFAC. l8 The interaction parameters used in this work for the pairs not including CO* are temperature-independent and they are taken from a recent revision of the UNIFAC tab1e.17 In activity coefficient models like UNIFAC, the interaction parameters for the pairs of groups containing CO2 (and other gases) are not available. Therefore, the application of the LCVM model to systems containing CO;! with organic compounds, like esters, ethers, alcohols, and acids, requires several parameters which have to be estimated. The group-parameters estimated in this work for the LCVM mode1 are: COz-OH (and CO*-methanol), CO*-COOH, CO+H2COO, CO;?CH*O, C02-CO0 (for aromatic esters), and CO+H=CH using the database shown in Table IIIa. Table IIIb presents the database for the systems used for prediction, that is, the binary systems not included in the database as well as the multicomponent systems considered here (Note that the parameter C02-CH2 is taken from Boukouvalas et a1.7). Like what is common practice in most EOS/GE models, linear temperature dependent UNIFAC interaction parameters are used in this work in the LCVM mode1 for the gas-containing mixtures Yg = exp

Aii + Bti x(T-298.15) T

1 (11)

with Tin K. Note that if Bii is set equal to zero, the result is the original UNIFAC model. The CO;! UNIFAC group volume (R) and surface area (Q) parameters, are the ones used by Boukouvalas et a1.7: R = 1.296 and Q = 1.261. The group-interaction parameters Aii and Bv are determined using the database of Table IIIa. Bubble-point pressure calculations are performed by minimizing simultaneously the percentage error in pressure and the absolute error in vapor phase mole fraction. These parameters are shown in Table IV. 4.

RESULTS AND DISCUSSION The correlation results obtained from the parameter estimation are briefly presented in Tables V-IX for the

The Journal of Supercritical Fluids, Vol. 9, No. 2, 1996

UNIFAC

Interaction

i

a The UNIFAC

Parameters

Application of the LCVM Model

TABLE IV for the LCVM

Model,

Determined

in This

Study

j

T 6)

Aij

Aji

Bij

Bji

CH=CH CH,O OH CH,OH COOH cc00 COO CHza

252-343 273-386 313-453 298-478 3 13-473 298-343 313-393 273-423

55.7 -45.7 87.1 283.8 938.5 1009.7 168.6 110.6

48.6 -55.8 471.8 33.8 -190.0 -256.4 -31.7 116.7

-0.279 0.434 3.927 0.032 -1.688 1.078 -2.676 0.500

-0.034 0.490 2.588 0.024 -0.806 -1.567 6.977 -0.9110

interaction

parameters for this pair of groups were taken from Boukouvalas

TABLE V Vapor-Liquid Equilibrium Correlation LCVM Model for C02-Alkene

co*-

NDP

Propene I-Butene 1-Hexene 1-Heptene

52 54 92 24

T G-3 253-283 273-318 303-343 303-343

Results with Systems

AP (%I Ay* 1000

Vapor-Liquid

Absolute Absolute

4.5-60 3.1-74 9.9-94 10-73

2.8 2.6 8.7 7.0

7.5 13.2 7.3 3.2

5.3

7.8

TABLE VI Equilibrium Correlation Model for Cot-Ether

coz-

Dimethyl ether Diethyl ether Methyl-t-butyl ether

NDP

169 18 44

T (K) 273-386 298-313 310-338

Total

various types of systems considered in this study. Typical examples are shown in Figures 2 and 4. Finally, Table X presents prediction results for binary systems not included in the parameter estimation, while Table XI shows predictions for multicomponent systems containing CO2 and esters, acids, alcohols, and alkenes. Typical examples of prediction with the LCVM model is shown in Figures 3 and 5. The overall performance of the model is satisfactory for both the binary and the multicomponent systems. The following remarks summarize our conclusions:

Ay* lo3

AP (%)

average percent deviation deviation in solubility.

in bubble-point

Results with Systems

et al.’

the

P (bar)

Total

93

pressure.

the LCVM

P (bar)

AP @J)

Ay*103

4-80 7-73 5-91

1.0 7.4 5.8

13.5 5.2 6.0

4.7

8.2

0) CO*-Alkenes. Very satisfactory correlation is achieved. The prediction for the system containing 1-hexadecene - not included in the parameter estimation - is particularly gratifying, considering especially that only phase equilibrium data up to CO*-1-heptene were used in the estimation of the parameter. (ii) COP-Ethers. Only few experimental data were available in the literature for the estimation of this parameter. Both the correlation results and the prediction for CO.+-butyl ether, not included in the parameter estimation, are satisfactory.

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Vapor-Liquid

cozMethanol Ethanol 1 -Propanol I-Butanol 1 -Pentanol 1 -Decanol 1 -Dodecanol

Equilibrium Model for

TABLE VII Correlation CO*-Alcohol

NDP 48 57 19 28 22 15 9

T (K) 298-478 313-337 313-333 315-337 315-337 348-453 393

Results with Systems P (b=)

AP (%)

Ay*103

4.4- 163 5.1-109 5.2-108 46-l 18 52-120 10-50 loo-275

6.4 5.2 5.0 9.6 11.4 14.9 6.2

13.7 4.1 2.7 2.9 1.4 0.3 3.6

8.7

2.5

Total

Vapor-Liquid

TABLE VIII Equilibrium Correlation Results with Model for CO*-Acid Systems

co*-

NDP

Laurie acid Palmitic acid*’ Palmitic acidz6 Oleic acid Arachidic acid

15 15 4 17 15

T WI

P (bar)

373-473 373-473 353-373 313-333 373-473

IO-50 10-50 136-306 33-312 10-50

Total

Vapor-Liquid

the LCVM

TABLE IX Equilibrium Correlation Model for CO*-Ester

co,-

NDP

Methyl myristate Methyl palmitate Methyl stearate Methyl oleate Ethyl stearate Ethyl oleate Ethyl linoleate Methyl benzoate

13 13 18 25 15 22 20 35

313-343 313-343 313-343 313-343 313-333 313-333 313-333 313-393

Total

(iii) CO,A/coho/s. This parameter has been estimated based on extensive phase equilibrium data. The correlation errors in bubble-point pressure are typically in the range of 4-10% and the ones in the solubility between 15-35%, depending on the system and the temperature. Typical examples are shown in Figures 2 and 3 for the systems CO*-methanol at 352.6 K, and CO*-1-octanol at 348.15 K. Notice the good results obtained, especially

AFJ(%)

Ay*103

8.0 7.2 12.6 5.8 5.0

0.4 0.1 5.5 2.1 0.1

7.7

1.6

Results with Systems

T 09 75-160 81-183 81-197 87-200 79-183 81-186 80-170 30-145

the LCVM

the LCVM

AP (%)

Ay* lo3

14.1 1.5 5.7 4.1 4.2 7.3 9.8 3.0

2.3 0.9 1.6 1.1 2.3 2.7 4.1 0.6

6.2

1.9

for the 1-octanol system, which was not included in the parameter estimation. Predictions for more asymmetric systems (COz-1-hexadecanol and COz-1,8-octanediol) are also very satisfactory. A typical example is shown in Figure 5 for the mixture CO*-1-hexadecanol at 473 K. This overall good performance indicates that the LCVM model can successfully describe with the same set of interaction parameters COz-containing systems with both

The Journal of Supercritical Fluids, Vol. 9, No. 2, 1996 1 ,

Application of the LCVM Model

low- and high-molecular-weight compounds. This point was previously made in the case of COz-n-alkanes by Boukouvalas et a1.7

I

Pressure

(iv) COTAcids. The data base used in the estimation of this interaction parameter includes acids from six up to twenty carbon atoms as well as one acid (oleic) with a double bond. We found it necessary to include at least one system with an unsaturated acid into the parameter estimation in order to describe successfully mixtures with oleic, linoleic, and other unsaturated acids which are very important in practical applications, especially those related to biotechnology. The correlation results are very satisfactory (especially at high solubilities and pressures), while very good predictions are obtained for the systems CO*-acetic acid and CO*-linoleic acid (flash calculations), which are not included in the parameter estimation. The predictions are not satisfactory for the high pressure data of the system C02-lauric acid (Bharath et al.26) which was not used in the parameter estimation. On the contrary,

(bar)

Figure 2. Solubility of methanol in CO, at 352.6 K with the LCVM model.

Prediction of Vapor-Liquid Used in the Parameter co*-

T 6)

P (bar)

AP (%)

Ay* lo3

15 22 16 22 21 15 15 16 17 14 9 9 8 10

314-531 312-366 317-355 328-453 348-453 373-573 373-573 393.2 293-333 333-353 313-333 313-333 313-333 313-333

9-52 11-143 59-l 14 10-170 10-190 10-51 10-51 loo-980 6-70 53-277 138-276 138-276 75-132 go-174

8.7 7.3 10.8 11.0 12.8 9.4 7.9 15.8 11.5 71.5 19.3 23.9

1.6 2.1 10.8 8.0 3.6 7.5 4.3 2.6

Laurie acid Oleic acid Linoleic acid EPA ethyl ester DHA ethyl ester

Prediction

of Vapor-Liquid with

Methyl oleate-Methyl linoleate Methyl oleate-Oleic acid Oleic acid-Linoleic acid 1-Dodecanol-Laurie acid Hexadecane-1-Dodecanol n-Hexane-Steak acid-Oleic acid Absolute

deviation

7.0 1.0 1.2 2.9 2.1

TABLE XI Equilibria for Multi-Component the LCVM Model

T (K)

co*-

Ay*lOOO -

TABLE X Equilibria for Binary Systems Not Estimation with the LCVM Model

NDP

1-Hexadecene Dibutyl ether 2-Propanol 2-Methyl- 1-pentanol I-Octanol 1-Hexadecanol 1-Octadecanol 1,8-Octanediol Acetic acid

95

313.15 - 333.15 313.15 313.15 - 333.15 393 353.2 375.15

Systems

P (bat)

Al’(%)

Ay*103

47 - 210 45 - 262 59 - 287 100 - 317 100 - 223 151-259

6.8 7.3 29.1 7.6 7.0 13.1

5.9 3.5 4.5 4.0 3.2 3.5

in the mole fraction of CO2 in the vapor phase.

96

Yakoumis et al.

The Journal of Supercritical Fluids, Vol. 9, No. 2, 1996

“oooo ~

exp. data LCVM

0 mole

fraction

of

co2

5. Prediction of vapor-liquid equilibrium of CO,1-hexadecanolmixture at 473 K with the LCVM model.

Figure

Solubility of n-octanol in CO, at 348.15 K with the LCVM model.

Figure 250

3.

1

Figure 4. Description of vapor-liquid equilibrium of CO,-methylpalmitate mixture at 343.15 K with the LCVM model.

the correlation for the low pressure data of the same system measured by Yau et a1.27 is excellent. We have not been able so far to detect the reasons for this discrepancy. (V) COTEsters. The correlation results are excellent for both the methyl and the ethyl esters included in the parameter estimation, especially at pressures higher than the CO2 critical pressure. The results are less satisfactory for CO2 with ethyl eicosapentanoate (EPA) and ethyl docosahexanoate (DHA) esters, although this could be attributed to the critical properties and the vapor pressures of these two heavy and highly unsaturated ethyl esters.

(vi) Multicomponent Phase Equilibria. Table XI presents predictions with the LCVM model for a number of multicomponent systems containing C02. The predictions are very satisfactory for most of the systems, with typical error in pressure below 10%. Only for.the system containing the two acids the error is as high as 30%. This could be due to the fact that simple group-contribution models like LCVM cannot account for the cross association between the two acids. However, much improved results are obtained for the quaternary system which also contains two acids capable of cross-association. This may be due to the presence of n-hexane (rather in large quantities). (vii) Experimental Data Evaluation. It is useful to discuss the uncertainties which may affect the accuracy of LCVM in the prediction of solubilities of organic compounds in supercritical C02. These uncertainties are mainly related to the experimental error of the phase equilibrium data as well as the lack of experimental values for the pure component properties (vapor pressures and critical properties). The latter problem has been to a certain degree eliminated in this work by using consistent and reliable method for the estimation of pure component properties whenever not experimentally available. However, the reliability of the experimental data for C02-organics poses a significant problem when assessing the accuracy of a thermodynamic model. As an example, we mention the case of C02-oleic acid and C02-linoleic acid mixtures, where experimental data have been presented by several researchers.2s32 The data measured by all the authors, with the exception of Zou et a1.,28 agree well with each other. However, Zou et al. presented data for the solubilities of oleic and linoleic acid in supercriti-

The Journal

of Supercritical

Fluids,

Vol. 9, No. 2, 1996

0.016

‘Fl s 0.012

~~~~~ 00000 ***** 00~00

Yu et al. (1992) Foslcr el al. (1991) Zou et al. (LQQOa) Uharath et al. (lYY2)

*

l

2 0 0 2 e 0.008 0 2 h 2 2 0.004

rmm 100

150 Pressure

200 (bar)

250

300

1

:150

Figure 6. Comparison of experimental VLE data for CO,oleic acid mixture at 308.15 K, as obtained by various investigators.

cal COT of almost one order of magnitude higher (60% difference or higher) compared to the other investigators, as can be seen in Figure 6. This was also pointed out by Foster et a1.32 and Maheshwari et a1.31 For this reason, the binary data of Zou et al. were not used in the parameter estimation. Several investigators have discussed the accuracy of the available data for the C02-containing systems. For example, Spiliotis et al. l5 observed differences for the solubility of n-hexadecane in supercritical CO2 obtained from various authors, which may be larger than 100% at solubility levels in the range of 10e4 to 10e2. Finally, Yau and Tsai33 report that their experimental measurements for the solubility of phenanthrene in supercritical CO2 (mole fraction in the range 10e4to 10e2)had an uncertainty of 50%. On the other hand, some of the compounds used in this study had a relatively low purity. For example, methyl palmitate and myristate had a purity of 95% and ethyl stearate and oleate were 90% pure. Depending on the nature of the impurities, large differences in the experimental measurements may be observed. Bharath et a1.30 comparing their results with previously obtained ones, report that differences in purity of 20% may yield solubilities that differ by approximately 60%. In light of the above discussion on the experimental uncertainties of the solubility data, we conclude that in most cases studied here, the LCVM model predictions are well within the experimental uncertainty of the data. 5.

CONCLUSIONS The application of the recently proposed LCVM EOS/GE model has been extended to a number of systems with supercritical CO2 and organic compounds, like alkenes, ethers, alcohols, esters, and acids. The corresponding interaction parameters have been optimized using - to the degree possible - experimental or reliably

Application of the LCVM Model

97

estimated pure-component properties and selected phase equilibrium data. It is shown that the LCVM model can correlate (with a single temperature-dependent parameter per group) the solubilities of a variety of organic compounds (ethers, alcohols, acids, and esters), including those with large molecular weight of interest in enzymecatalyzed reactions. The results are satisfactory over extended temperature, pressure, and system asymmetry range. Furthermore, the LCVM model yields satisfactory predictions for a number of multicomponent systems, using exclusively binary group-interaction parameters. The satisfactory results obtained for this extended range of systems render the LCVM model a very useful tool for the preliminary design of separation processes, as well as of enzyme-catalyzed esterification and transesterification reaction processes. ACKNOWLEDGMENT The authors wish to thank Dr. Lucie Coniglio for useful discussions. ABBREVIATIONS AMP Abrams-Massaldi-Prausnitz equation ASGG Analytical Solution of Group Theory DHA ethyl eicosapentanoate Eos Equation of state EPA ethyl docosahexanoate LCVM Linear Combination Vidal-Michelsen mixing rules MHVl Modified Huron-Vidal mixing rule first order MHV2 Modified Huron-Vidal mixing rule second order NRTL Non-Random Two Liquid model PSRK Predictive Soave-Redlich-Kwong mixing rule t-mPR Translated-Modified Peng-Robinson VLE Vapor-Liquid Equilibria REFERENCES (1) Aaltonen, 0.; Rantakyla, R. Chemtech. 1991, 4, 240. (2) Vidal, J. Chem. Eng. Sci. 1978, 73, 787. (3) Michelsen, M. L. Fluid Phase Equil. 1990,60, 213. (4) Dahl, S.; Michelsen, M. L. AIChE .I. 1990, 36, 1829. (5) Holderbraum, T.; Gmehling, J. Fluid Phase Equil. 1991, 70, 251. (6) Wong, D. S. H.; Sandler, S. I. AZChE J. 1992, 38, 671. (7) Boukouvalas, C.; Spiliotis, N.; Coutsikos, Ph.; Tzouvaras, N.; Tassios, D. Fluid Phase Equil. 1994, 92, 75. (8) Michelsen, M. L. Fluid Phase Equil. 1990, 60, 47. (9) Coniglio, L.; Knudsen, K.; Gani, R. submitted for publication in Ind. Eng. Chem. Res. (10) Tochigi, K.; Kolar, P.; Iizumi, T.; Kojima, K. Fluid Phase Equil. 1994, 96, 215. (11) Kalospiros, N. S.; Tzouvaras, N.; Coutsikos, Ph.; Tassios, D. P. AIChE .I. 1995,41, 928. (12) Coutsikos, Ph.; Kalospiros, N. S.; Tassios, D. P. Fluid Phase Equil. 1995, 108, 59. (13) Voutsas, E. C.; Spiliotis, N.; Kalospiros, N. S.; Tassios, D. Ind. Chem. Eng. Res. 1995, 34, 681. (14) Apostolou, D. A.; Kalospiros, N. S.; Tassios, D. P. Ind. Eng. Chem. Res. 1995, 74, 948. (15) Spiliotis N.; Magoulas K.; Tassios D. Fluid Phase Equil. 1994, 102, 121. (16) Magoulas K.; Tassios D. Fluid Phase Equil. 1990.56, 119.

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Hansen, H. K.; Rasmussen, P.; Fredenslund, Aa.; Schiller, M.; Gmehling, J. SEP 9101; Institut for Kemiteknik: Lyngby, 199 1. Fredenslund, Aa.; Jones, R. L.; Prausnitz, 1. M. AIChE J. 1975, 21, 1086. Daubert, T. E.; Danner, R. P. DIPPR Data Compilation Tables of Properties of Pure Compounds; Hemisphere: New York, 1989. Ambrose, D.; Ghiassee, N. B. J. Chem. Thermodyn. 1987,19, 505. Teja, A. S.; Lee, R. J.; Rosenthal, D.; Anselme, M. Fluid Phase Equil. 1990, 56, 153. Reid, R.; Prausnitz, J.; Poling, B. The Properties of Gases and Liquids; McGraw-Hill: New York, 1987. Mathias, P. M.; Copeman, T. W. Fluid Phase Equil. 1983, IS, 91. Ashour, I.; Wennersten, R. .I. Supercrit. Fluids 1989, 2, 73. Tu, C. H. Fluid Phase Equil. 1994, 99, 105. Bharath, R.; Yamane, S.; Inomata, H.; Adschiri, T; Arai, K. Fluid Phase Equil. 1993.83, 183. Yau, J. S.; Chiang, Y. Y.; Shy, D. S.; Tsai, F. N. J. Chem. Eng. Japan 1992.25, 544. Zou, M.; Yu, Z. R.; Kashulines, P.; Rizvi, S. S.; Zollweg, J. A. J. Supercrit. Fluids 1990, 3, 23. Yu, Z. R.; Rizvi, S. S. H.; Zollweg, J. A. J. Supercrit. Fluids 1992,5, 114. Bharath, R.; Inomata, H.; Adschiri, T.; Arai, K. Fluid Phase Equil. 1992,81, 307. Maheshwari, P.; Nikolov, Z. L.; White, T. M.; Hartel, R. JAOCS 1992, 69, 1069. Foster, N. R.; Yun, S. L. J.; Ting, S. S. T. J. Supercrit. Fluids 1991, 4, 127. Yau, J. S.; Tsai, F. N. J. Chem. Eng. Data 1992, 37, 295. Nagahama, K.; Konishi, H.; Hoshino, D.; Hirata, M. J. Chem. Eng. Japan 1974, 7, 323. Ohgaki, K.; Nakai, S.; Nitta, S. Fluid Phase Equil. 1982, 8, 113. Behrens, P. K.; Sandler, S. I. J. Chem. Eng. Data 1983, 28, 52. Jennings, D. W.; Teja A. S. J. Chem. Eng. Data 1989, 34, 305. Vera, J. H.; Orbey H. J. Chem. Eng. Data 1984, 29, 269. Wagner, Z.; Wichterle I. Fluid Phase Equil. 1987, 37, 109. Tsang, C. Y.; Streett, W. B. J. Chem. Eng. Data 1981, 26, 155. Jonasson, A.; Persson, 0.; Fredenslund, Aa. J. Chem. Eng. Data 1995,40, 296. Ohgaki, K.; Katayama, T. J. Chem. Eng. Data 1975, 20, 264. Wu, G. W.; Zhang, N. W.; Zheng, X. Y.; Kubota, H.; Makita, T. J. Chem. Eng. Data 1988, 21, 25.

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