vapour–liquid equilibrium of propionic acid+caproic acid, isobutyric acid+caproic acid, valeric...

Accepted Manuscript

Title: Vapour-liquid Equilibrium of Propionic Acid + CaproicAcid, Isobutyric Acid + Caproic Acid, Valeric Acid + CaproicAcid and Caproic Acid + Enanthoic Acid Binary Mixtures

Author: Alex Hlengwere Samuel A. Iwarere ParamespriNaidoo J. David Raal Deresh Ramjugernath

PII: S0378-3812(14)00246-5DOI: http://dx.doi.org/doi:10.1016/j.fluid.2014.04.026Reference: FLUID 10087

To appear in: Fluid Phase Equilibria

Received date: 20-1-2014Revised date: 9-4-2014Accepted date: 25-4-2014

Please cite this article as: A. Hlengwere, S.A. Iwarere, P. Naidoo, J.D. Raal,D. Ramjugernath, Vapour-liquid Equilibrium of Propionic Acid + Caproic Acid,Isobutyric Acid + Caproic Acid, Valeric Acid + Caproic Acid and CaproicAcid + Enanthoic Acid Binary Mixtures, Fluid Phase Equilibria (2014),http://dx.doi.org/10.1016/j.fluid.2014.04.026

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http://dx.doi.org/doi:10.1016/j.fluid.2014.04.026

http://dx.doi.org/10.1016/j.fluid.2014.04.026

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Vapour-liquid Equilibrium of Propionic Acid + Caproic Acid, Isobutyric Acid + Caproic Acid, Valeric Acid + Caproic Acid and Caproic Acid + Enanthoic Acid Binary Mixtures

Alex Hlengwere, Samuel A. Iwarere, Paramespri Naidoo, J. David Raal, Deresh Ramjugernath*

Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Durban 4041, South Africa.

Abstract

Isothermal vapour-liquid equilibrium data (VLE) were measured for propionic acid + caproic acid, isobutyric acid + caproic acid, valeric acid + caproic acid, and caproic acid + enanthoic acid at several temperatures. A refined glass recirculating still with a packed equilibrium chamber and a vacuum-insulated, centrally located Cottrell pump was used for the measurements. Using the chemical theory for the vapour phase, true species concentrations (zi) were calculated for the monomers and dimers and from these liquid-phase activity coefficients by the methods of Prausnitz et al.[J.M. Prausnitz, T.F. Anderson, E.A. Grens, C.A. Eckert, R. Hsieh, J.P. O’Connell, Computer Calculations for Multicomponent Vapor-Liquid and Liquid-Liquid Equilibrium, Prentice- Hall, New Jersey, 1980], based on corresponding states theory and the Lewis fugacity rule for species fugacities. Rigorous tests showed the thermodynamic consistencies to be unusually high for all data sets. All systems showed positive deviations from Raoult’s law and were satisfactorily modelled with the NRTL equation.

Keywords: Activity coefficient; Carboxylic acid; Chemical theory; Fugacity coefficient; Vapour–liquid equilibria

*Corresponding author: E-mail: [email protected], Tel: +27 (0)31 2603128

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1. Introduction

The SASOL oil-from- coal industry produces a considerable array of chemicals in addition to fuels including a substantial stream of mixed carboxylic acids. For process design, accurate VLE data are required for still unmeasured systems and the results must be presented in useful form based on activity coefficient models with temperature dependent parameters. Activity coefficients must be calculated by solving for the true species concentrations by complex procedures which require knowledge of association constants (Ki). Calculation of vapour phase fugacity coefficients requires in addition, association parameters (ɳ), radii of gyration (RD) and dipole moments (µ). Some of these constants were not available in literature and require estimation as discussed further below. In view of the uncertainty in some of these parameter values (particularly the association constants), it is advisable to test thermodynamic consistency, which requires that both liquid and vapour concentrations be measured. Dynamic equilibrium stills with a packed equilibrium chamber are suitable for this purpose for systems of moderate relative volatility (as in the present study) since equilibrium can be achieved (as it must) in a single pass. [For systems of high relative volatility achievement of equilibrium is more difficult and may be complicated by substantial rate-dependent temperature gradients in the packed section or along the thermometer well in simpler apparatus]. As will be seen from the data and analyses below, equipment choice and computational procedures were well justified as confirmed by the unusually high thermodynamic consistencies found for all systems.

2. Experimental Section

2.1 Materials. All the chemicals used were purchased from Fluka. They were used without further purification since chromatographic analyses and refractive index checks showed no significant impurities. The results are shown in Table1.

2.2 Apparatus and procedure. The glass recirculating still, with a packed equilibrium chamber and centrally-located, vacuum-insulated Cottrell tube, has been used previously for acid systems by Sewnarain et al.[1], Clifford et al.[2], and also by Joseph et al.[3] for highly non-ideal alcohol-hydrocarbon systems. A detailed description of the apparatus has been given by Joseph et al.[3]. Temperatures were measured with a grade A Pt-100 sensor, with signals transmitted to a PC through an HP 34401A multimeter. The calculated combined uncertainty in the reported temperature is 0.1 K. Pressure was monitored with a SENSOTEC Super THE pressure transducer with a claimed accuracy of 0.05% of full-scale. The transducer showed excellent long-term stability. It was calibrated using a mercury manometer together with a VAISALA electronic barometer model PTB100A. The latter has a claimed uncertainty of 0.15 hPa at a 95% confidence level. The calculated combined uncertainty in the reported pressure is 0.2 kPa. Temperature calibration was done chemically using high-purity cyclohexane and n-decane for the low- and high-temperature regions respectively. Vapour and liquid samples were analysed on a

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Varian 3300 GC with flame ionization (FID) detector. Accuracy was estimated at ±0.002 mole fraction throughout the composition range since relative volatilities were comparatively modest. The GC area ratio method [4] was used.

3. Analysis of Associating Systems

Liquid phase activity coefficients are required for process equipment design and simulation since they can be fitted to an appropriate correlating equation. The formation of strongly hydrogen-bonded complexes (principally dimers) in the vapour phase makes the latter highly non-ideal and necessitates the use of complex specialised computational procedures. In a previous study of VLE in acid mixtures [2] chemical theory was applied to find the concentrations of the true species A1, A2, B1, B2 and AB in the vapour phase. It was however assumed that the above species formed an ideal mixture since the acids studied did not differ appreciably in molecular size. In the present study, this was considered too limiting and the computational procedures described by Prausnitz et al. [5], which accounts for non-ideality of the species mixture in the gas phase were implemented.

For a mixture of two carboxylic acids A and B, reversible vapour phase dimerization reactions are assumed as follows:

212 AA ⇔ (1)

212 BB ⇔ (2)

ABBA ⇔+ 11 (3)

The chemical equilibrium constants indicated in the above equations are defined as follows:

21

2

A

AAA P

KΖΖ

= (4a)

21

2

B

BBB P

KΖΖ

= (4b)

11 BA

ABAB P

KΖΖ

Ζ= (4c)

ΖAB are the true species mole fractions. As shown by Vawdrey et al. [6], the dimer fraction decreases with increasing temperature and increases with increasing pressure. The Vawdrey et al. [6] studies were based on extensive density functional theory (DFT) computations following procedures developed by Wohlbach and Sandler [7]. In particular, they found trimer and higher oligomer mole fractions in the vapour phase, for

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acetic acid, to be negligible, contrary to some earlier speculations. In larger acids such as those used in the present study, oligomers above the dimer would be even less significant at low pressures and only equations (1) to (3) were considered relevant. The formation of dimers and higher oligomers in the vapour phase has been discussed by Tsonopoulos and Prausnitz [8], Vawdrey et al. [6], and Appelblat [9].

Monomer concentrations in the vapour phase, zA1 and zB1 can be calculated by the iterative procedures of Prausnitz et al.[5] or by the simultaneous solution of two symmetrical quadratic equations, as used by Clifford et al. [2] and by Tamir and Wisniak [10]. It is readily shown that the species concentrations are related to the vapour phase stoichiometric (i.e. measured) mole fractions yA, yB by:

ABBA

ABAAA ZZZ

ZZy

+++++Ζ

=22

21

12

(5)

ABBA

ABBBB ZZZ

ZZy+++++Ζ

=22

21

12 (6)

Substitution of the equilibrium relationships (Eqs (4)) then produces the following equations for the species concentrations [2]:

0)1()1( 11211

21 =++−++ BBAABBBBAAABAA yZPZKPZKyZZyPK (7)

0)1()1( 11211

21 =++−++ ABAABAAABBBABB yZPZKPZKyZZyPK (8)

For the same values of the equilibrium constants, the two procedures produced the same species concentrations, as they should. The true fugacity coefficients of species A, ΦA*, were computed using the Lewis fugacity rule and second virial coefficients as detailed in Prausnitz et al. [5]. The equations and procedures are complex and will not be detailed here. The procedures require critical constants as well as values for the dipole moment, association parameter, and the radius of gyration. The values used for the five acids are given in Table 2 together with source information. Association parameters for the C4 to C7 acids were not found in literature, but were assumed to be the same as that for propionic acid, following the suggestion by Prausnitz et al. [5]. No dipole moment could be found for heptanoic acid in frequently cited references, but an estimate was obtained from a polynomial fit to the known values for C1, C3 , and C5, acids, based on an interesting observation of trends for odd and even numbered (C atom) acids by Vawdrey et al.[6]. Values for the association equilibrium constants from various sources can differ considerably as shown for valeric acid at two temperatures in Table 3. The values used in this study were calculated as proposed by Prausnitz et al. [5] based on values for Bij

D, the dimerization contribution to the second virial coefficient:

RTB

RTPBRTPBRTPB

PK ij

Dij

Fjj

Fii

Fij

ji

ijij

)2()/exp()/exp(

)/exp(

11

δ−−=

ΖΖ

Ζ= (9)

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with the Kronecker delta, δij equals 0 when i ≠ j and 1 when i = j.

The K values are shown in Table 4 as constants in the equation:

)()(ln 1

KTB

AkPaK ΚΚ

− += (10)

The K values obtained were generally close to those from the Design Institute for Physical Properties (DIPPR) data [11].

To calculate the cross-coefficient KAB, the relationship mentioned by Christian [12] and Prausnitz et al. [5] was used on the basis that at equilibrium, ½ A1 + ½ B1 = AB, thus

BBAAAB KKK 2= (11)

Activity coefficients were calculated by taking into account dimerization in the liquid phase after the values calculated from Eq. (12) were not consistent for gamma 1 (γ1).

satii

iii Px

Py

1

Φ=γ (12)

with Φi given by:

i

iii y

*ΦΖ=Φ (13)

PsatA1 is the vapour pressure of monomer A1.

In the iterative calculation procedure, the estimated total pressure (P0) and the vapour composition yi were calculated iteratively from:

∑ Φ=

i i

satiii Px

P 10

γ (14)

and ∑ Φ

Φ=

ii

satiii

isat

iiii PPx

PPxy

01

01

//

γγ

(15)

to small residual values (e.g. ǀP0 –Pǀ ≤ ϵ with ϵ = 10-4 ).

4. Experimental Results

Measured isothermal VLE data and the calculated activity coefficients are shown in Tables 5 to 12 for propionic acid (1) + caproic acid (2), isobutyric acid (1) + caproic acid (2), valeric acid (1) + caproic acid (2) and caproic acid (1) + enanthoic acid (2)

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respectively. Also included in these tables are the species monomer concentrations zA1, zB1 calculated as discussed above, and the vapour phase correction factors Ф, defined by yi = xiγiPi1

sat/PФ where y and x are measured mole fractions.

Illustrated P-x-y plots are shown for propionic acid + caproic acid at 408.15 K and 413.15 K in Figure 1, and for valeric acid + caproic acid in Figures 2 and 3 at the indicated temperatures. Activity coefficient plots are shown in Figures 4 and 5 for isobutyric acid + caproic acid and for caproic acid + enanthoic acid at the indicated temperatures. An example of the plot for the area test of consistency is shown in Figure 6 for valeric acid + caproic acid at 423.15 K, with the direct test of thermodynamic consistency for the same valeric acid + caproic acid at 423.15 K shown in Figure 7.

5. Discussion

Liquid phase activity coefficients, calculated by the complex procedures discussed above showed positive deviations from Raoult’s law for all systems at all temperatures. The data were satisfactorily fitted to the NRTL equation, with the correlating constants and residuals shown in Table 13. In view of the uncertainties introduced into the activity coefficients by substantial discrepancies in available data or procedures for the equilibrium constants Kij, it is advisable to test thermodynamic consistency. This was done for all systems using the area test and the much more rigorous direct test of Van Ness [13] in which activity coefficients are calculated from experimental values and compared with predicted values evaluated from calculated vapor compositions (yi ) and pressures (P), determined as described above. Results for the area test, Table 13, showed very low residuals and suggest that the data are not inconsistent. The rms residuals δln(γA/γB) for the Van Ness [13] direct test are shown in the last column of Table 13. The residuals are remarkably small with five of the eight data sets surpassing the “highest consistency” (index 1 out of 10). The other three sets are only marginally outside and fall into the next highest category, index 2. It is interesting to note that procedures such as those of Clifford et al.[2], and Tamir and Wisniak [10] in which the vapour phase was considered an ideal mixture of species, gave unrealistic activity coefficients.

6. Conclusions

Eight isothermal VLE sets are presented for four binary carboxylic acid combinations from propionic acid to enanthoic (heptanoic) acid. Activity coefficients were calculated by the methods of Prausnitz et al. [5], which involved solving for the true species concentrations in the vapour phase (zij) and correlations for the second virial coefficient by corresponding states methods. Species fugacity coefficients were computed using the Lewis fugacity rule, i.e., the vapour phase was assumed to be a non-ideal mixture of species. Association constants, required as functions of temperature in the calculations, were computed from the dimerization contribution to the second virial coefficient as

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detailed by Prausnitz et al. [5] and were close to those reported in the DIPPR[11]. The remarkably good thermodynamic consistencies obtained (appreciably better than those of other similar studies [2, 10]) confirmed the suitability of the experimental equipment and the computational procedures used.

Acknowledgements

This work is based upon research supported by the South African Research Chairs Initiative of the Department of Science and Technology and National Research Foundation.

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Nomenclature

A component 1 in a binary carboxylic acid mixture

A′ Antoine vapour pressure equation constant

AK constant in the chemical equilibrium constant equation; Eq. (10)

A1, A2 monomer and dimer of component 1

AB heterodimer in a binary carboxylic acid mixture

B component 2 in a binary carboxylic acid mixture

B′ Antoine vapour pressure equation constant

BFAA, BF

BB free contribution to the second virial coefficients of components A and B

BDAB dimerization contribution to the second virial coefficient of heterodimer AB

BK constant in the chemical equilibrium constant equation; Eq. (10)

B1, B2 monomer and dimer of component 2

C′ Antoine vapour pressure equation constant

(gij-gii) energy parameters in the NRTL equation (J/mol)

KAB vapour-phase chemical equilibrium constant for heterodimer (kPa−1)

KAA, KBB vapour-phase chemical equilibrium constant for components A and B (kPa−1)

P system pressure (kPa)

Pc critical pressure (kPa)

PsatA1, Psat

B1 saturated vapor pressures for the carboxylic acid monomers, A1 and B1 (kPa)

R universal gas constant (J/mol K)

RMS root mean square

T temperature (K)

Tc critical temperature (K)

xA, xB measured liquid-phase mole fractions of components A and B

yA, yB measured vapour-phase mole fractions of components A and B

Greek letters

αij nonrandomness parameter in the NRTL equation (dimensionless)

δ residual (e.g. δP, δy)

δij Kronecker delta (ij = components 1 and 2)

ε tolerance in bubble-point iteration scheme

γi liquid-phase activity coefficients for the species i with (i = A, B); Eq. (12)

ΦA,ΦB vapour-phase correction factor for components A and B

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ΦA*,ΦB* true fugacity coefficients for components A and B (based on Lewis fugacity

rule)

ZA1, Z B1 mole fraction of monomers A1, B1 in the vapour phase

ZA2, Z B2 mole fraction of dimers A2, B2 in the vapour phase

ZAB mole fraction of heterodimer AB in the vapour phase

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References [1] R. Sewnarain, J.D. Raal, D. Ramjugernath, J. Chem. Eng. Data 47 (2002) 603–607. [2] S.L. Clifford, D. Ramjugernath, J.D. Raal, Fluid Phase Equilibr. 237 (2005) 89–99. [3] M. Joseph, J.D. Raal, D. Ramjugernath, Fluid Phase Equilibr. 182 (2001) 157–176. [4] J.D. Raal, A.L. Mühlbauer, Phase Equilibria: Measurement and Computation, Taylor and Francis, Bristol, PA, 1998. [5] J.M. Prausnitz, T.F. Anderson, E.A. Grens, C.A. Eckert, R. Hseih, J.P. O’Connell, Computer Calculations for Multicomponent Vapour–Liquid and Liquid–Liquid Equilibria, Prentice- Hall, Englewood Cliffs, NJ, 1980. [6] A.C. Vawdrey, J.L. Oscarson, R.L. Rowley, W.V. Wilding, Fluid Phase Equilibr. 222–223 (2004) 239–245. [7] J. P.Wohlbach, S. I. Sandler, AIChE. J. 43 (1997) 1589-1596. [7] J. P.Wohlbach, S. I. Sandler, AIChE. J. 43 (1997) 1597-1604. [8] C. Tsonopoulos, J.M. Prausnitz, Chem. Eng. J. 1 (1970) 273–278. [9] A. Apelblat, J. Molec. Liquids 130 (2007) 133-162. [10] A. Tamir, J. Wisniak, Chem. Eng. Sci. 30 (1975) 335–342. [11] T.T. Shih, D.K. Jones, Experimental Results from the Design Institute for Physical Property Data: Phase Equilibria and Pure Component Properties Part II, AIChE Symposium Series No. 271, vol. 85, AIChE, 1989. [12] S.D. Christian, J. Phys. Chem. 61 (1957) 1441–1442. [13] H. C Van Ness, Pure Appl. Chem. 67 (1995) 859-872. [14] R. C Weast, M. J. Astle, W. H. Beyer, Handbook of Chemistry and Physics, 64th ed., CRC Press, London, 1983 -1984. [15] Dortmund Data Bank Software Purchased 2011. [16] J. Gmehling, U. Onken, P. Grenzheuser, Vapour–Liquid Equilibrium Data Collection: Carboxylic Acids, Anhydrides, Esters, Chemistry Data Series, 1:5 DECHEMA, 1982. [17] J.G. Hayden, J. P. O’Connell, Ind. Eng. Chem. Proc. Des. Dev. 14 (1975) 209-215. [18] A.L. McClellan, Tables of Experimental Dipoles, W.H. Freeman, San Francisco, 1963. [19] B.E Poling, J.M. Prausnitz, J.P. O'Connell, The Properties of Gases and Liquids, 5th ed., McGraw-Hill: New York, 2001.

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Table 1. Refractive Indices and Purities of Chemicals Used in this Study.

Reagent Refractive Index

a (293.15 K) GC (Peak Area %) Min. Purity (Mass %)

b

Exp Ref [14]

Propionic Acid 1.3812 1.3810 99.6 ≥99.5

Isobutyric Acid 1.3931 1.3930 99.3 ≥99.5 Valeric Acid 1.4082 1.4085 99.2 ≥99.0 Caproic Acid 1.4150 1.4163 98.1 ≥99.0 Enanthoic Acid 1.4172 1.4170 99.1 ≥99.0 a Refractive index at 293.15 K, U(nD) = 0.0004

b as stated by the supplier

Table(s)

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Table 2. Physical Properties for the Pure Components Used in this Study.

Pure Component Property

Propionic

Acid Isobutyric Acid

Valeric

Acid

Caproic

Acid

Enanthoic

Acid

Tc /K [15] 604 605 639.9 663 679

Pc / kPa [15] 4333.00 3698.36 3624.46 3201.87 2877.63

Dipole Moment /debye [18,19 ] 1.76 1.30 1.81 1.2 1.65

Association Parameter [5] 4.5 4.5 4.5 4.5 4.5

Radius of Gyration /Å [5] 2.682 3.115 3.541 4.4 4.8

A′ [15] 16.3841 14.7739 15.6157 16.0924 15.6868

B′ [15] 4442.38 3340.48 4092.15 4499.90 4364.92

C′ [15] 236.430 175.712 186.600 186.507 171.398

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Table 3. Vapour-phase chemical equilibrium constants from different literature for valeric acid.

Kii (kPa-1

)

Aii Bii Literature source 423.15 K 433.15 K

-19.0355 6221.6 DIPPR [11] 0.01314 0.00935

-23.0374 6891.6 Gmehling et al. [16] 0.00877 0.00602

-18.5860 7614.0 Vawdrey et al. [6] 0.00546 0.00360

Hayden & O'Connell approach [17] 0.01269 0.00862

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Table 4. Vapour-phase chemical equilibrium constants obtained for the studied acid mixtures.

Kii (kPa-1

) at different temperatures

Components 403.15 K 408.15 K 413.15 K 423.15 K 433.15 K 443.15 K

Propionic Acid 0.02693 0.02168 0.01755 - - -

Isobutyric Acid - 0.02358 - 0.01270 - -

Valeric Acid - - - 0.01269 0.00862 -

Caproic Acid 0.02898 0.02338 0.01895 0.01265 0.00862 0.00599

Enanthoic Acid - - - - - 0.00636

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Table 5. Vapour-liquid equilibrium dataa for propionic acid (1) + caproic acid (2) at 403.15 K.

P (kPa) x1 y1 zA1 zB1 γ1 γ2 Φ1 Φ2

6.55 0.000 0.000

9.84 0.090 0.383 0.3143 0.5009 1.4587 1.0029 0.8207 0.8116

13.17 0.167 0.563 0.4405 0.3373 1.3899 1.0102 0.7824 0.7716

16.01 0.211 0.652 0.4918 0.2585 1.3541 1.0165 0.7544 0.7425

19.95 0.287 0.735 0.5297 0.1877 1.2975 1.0312 0.7208 0.7079

24.58 0.359 0.793 0.5449 0.1395 1.2493 1.0503 0.6873 0.6736

27.69 0.416 0.826 0.5514 0.1138 1.2144 1.0695 0.6676 0.6536

34.01 0.535 0.868 0.5494 0.0817 1.1501 1.1247 0.6331 0.6185

40.33 0.647 0.907 0.5477 0.0548 1.0988 1.2033 0.6040 0.5892

45.85 0.731 0.931 0.5417 0.0392 1.0657 1.2897 0.5820 0.5670

59.06 0.889 0.979 0.5272 0.0110 1.0170 1.5975 0.5387 0.5236

63.19 0.937 0.987 0.5202 0.0067 1.0068 1.7853 0.5273 0.5122

69.02 0.985 0.996 0.5101 0.0020 1.0005 2.1142 0.5124 0.4974

70.88 1.000 1.000 a

Expanded uncertainties (k = 2): U(T) = 0.1 K, U(P) = 0.2 kPa, U(x,y) = 0.002

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Table 6. Vapour-liquid equilibrium dataa for propionic acid (1) + caproic acid (2) at 408.15 K.


8.25 0.000 0.000

11.19 0.065 0.308 0.2561 0.5694 1.4520 1.0015 0.8314 0.8226

15.15 0.131 0.504 0.3996 0.3882 1.3939 1.0060 0.7930 0.7823

19.36 0.213 0.645 0.4891 0.2651 1.3295 1.0161 0.7584 0.7463

27.26 0.333 0.769 0.5426 0.1600 1.2482 1.0409 0.7057 0.6921

31.51 0.388 0.807 0.5504 0.1290 1.2154 1.0570 0.6822 0.6681

44.94 0.562 0.897 0.5583 0.0626 1.1267 1.1341 0.6226 0.6076

53.99 0.665 0.933 0.5514 0.0386 1.0839 1.2080 0.5912 0.5760

54.91 0.675 0.938 0.5516 0.0356 1.0801 1.2168 0.5883 0.5731

68.42 0.841 0.973 0.5355 0.0145 1.0266 1.4397 0.5507 0.5353

81.51 0.986 0.996 0.5186 0.0020 1.0004 1.9944 0.5210 0.5056

83.59 1.000 1.000 a


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Table 7. Vapour-liquid equilibriuma data for propionic acid (1) + caproic acid (2) at 413.15 K.


10.13 0.000 0.000

11.99 0.030 0.093 0.0788 0.7617 1.4522 1.0003 0.8476 0.8396

15.58 0.082 0.379 0.3096 0.5014 1.4065 1.0022 0.8169 0.8071

24.31 0.223 0.651 0.4921 0.2597 1.2997 1.0169 0.7560 0.7436

26.75 0.253 0.689 0.5109 0.2268 1.2797 1.0219 0.7417 0.7288

36.15 0.391 0.790 0.5483 0.1429 1.1980 1.0552 0.6943 0.6802

42.45 0.477 0.829 0.5535 0.1118 1.1545 1.0862 0.6679 0.6533

45.53 0.511 0.848 0.5563 0.0976 1.1388 1.1012 0.6562 0.6414

58.24 0.661 0.911 0.5595 0.0534 1.0780 1.1931 0.6145 0.5991

65.77 0.742 0.934 0.5542 0.0382 1.0509 1.2689 0.5937 0.5782

85.19 0.900 0.981 0.5386 0.0102 1.0111 1.5366 0.5494 0.5337

94.52 0.975 0.995 0.5287 0.0026 1.0010 1.8149 0.5318 0.5161

97.06 0.000 0.000 a


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Table 8. Vapour-liquid equilibrium dataa for isobutyric acid (1) + caproic acid (2) at 408.15 K.


8.31 0.000 0.000

12.81 0.148 0.417 0.3354 0.4696 1.3902 1.0077 0.8042 0.8053

16.45 0.264 0.547 0.4211 0.3493 1.3013 1.0251 0.7698 0.7708

20.49 0.368 0.631 0.4652 0.2725 1.2335 1.0508 0.7372 0.7381

26.91 0.498 0.745 0.5171 0.1773 1.1615 1.1003 0.6941 0.6948

28.78 0.532 0.768 0.5247 0.1587 1.1448 1.1173 0.6832 0.6838

32.86 0.594 0.811 0.5362 0.1252 1.1163 1.1542 0.6612 0.6617

37.01 0.643 0.843 0.5405 0.1008 1.0956 1.1898 0.6412 0.6416

41.42 0.704 0.880 0.5474 0.0748 1.0719 1.2446 0.6220 0.6224

44.73 0.755 0.907 0.5523 0.0567 1.0540 1.3025 0.6089 0.6092

49.06 0.810 0.940 0.5575 0.0356 1.0366 1.3828 0.5931 0.5933

54.14 0.952 0.984 0.5670 0.0092 1.0039 1.7845 0.5762 0.5763

55.34 1.000 1.000 a


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Table 9. Vapour-liquid equilibriuma data for isobutyric acid (1) + caproic acid (2) at 423.15 K.


15.49 0.000 0.000

20.87 0.109 0.308 0.2529 0.5686 1.3400 1.0036 0.8210 0.8214

30.98 0.287 0.555 0.4261 0.3419 1.2274 1.0256 0.7679 0.7680

35.41 0.356 0.613 0.4586 0.2897 1.1909 1.0404 0.7482 0.7482

46.00 0.500 0.726 0.5136 0.1940 1.1253 1.0856 0.7075 0.7073

51.82 0.568 0.777 0.5347 0.1536 1.0988 1.1157 0.6883 0.6880

52.28 0.568 0.781 0.5363 0.1505 1.0988 1.1157 0.6868 0.6865

63.21 0.657 0.841 0.5510 0.1042 1.0681 1.1669 0.6553 0.6549

72.00 0.736 0.886 0.5610 0.0722 1.0447 1.2280 0.6333 0.6328

80.57 0.822 0.944 0.5797 0.0344 1.0235 1.3206 0.6142 0.6135

85.19 0.931 0.975 0.5894 0.0151 1.0046 1.5129 0.6046 0.6039

88.93 1.000 1.000 a


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Table 10. Vapour-liquid equilibrium dataa for valeric acid (1) + caproic acid (2) at 423.15 K.


15.86 0.000 0.000

16.69 0.070 0.118 0.1000 0.7480 1.3687 1.0015 0.8476 0.8479

17.59 0.141 0.212 0.1785 0.6636 1.3174 1.0060 0.8417 0.8419

18.28 0.202 0.294 0.2462 0.5914 1.2774 1.0124 0.8372 0.8374

19.14 0.275 0.373 0.3103 0.5218 1.2340 1.0234 0.8318 0.8320

20.55 0.384 0.483 0.3976 0.4258 1.1770 1.0476 0.8231 0.8233

21.15 0.422 0.523 0.4287 0.3912 1.1591 1.0584 0.8195 0.8197

22.48 0.507 0.608 0.4937 0.3184 1.1224 1.0884 0.8118 0.8120

23.48 0.567 0.653 0.5265 0.2799 1.0991 1.1152 0.8062 0.8063

24.92 0.639 0.728 0.5812 0.2173 1.0739 1.1552 0.7983 0.7984

25.66 0.682 0.765 0.6078 0.1868 1.0603 1.1843 0.7943 0.7945

26.46 0.733 0.805 0.6362 0.1542 1.0455 1.2253 0.7902 0.7903

28.57 0.848 0.898 0.7001 0.0796 1.0181 1.3565 0.7795 0.7796

29.74 0.908 0.938 0.7260 0.0480 1.0077 1.4613 0.7738 0.7739

30.91 0.968 0.979 0.7523 0.0161 1.0011 1.6164 0.7683 0.7683

31.74 1.000 1.000 a


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Table 11. Vapour-liquid equilibrium dataa for valeric acid (1) + caproic acid (2) at 433.15 K.


22.33 0.000 0.000

23.29 0.031 0.049 0.0418 0.8118 1.3372 1.0003 0.8536 0.8534

25.14 0.109 0.160 0.1352 0.7099 1.2868 1.0032 0.8451 0.8449

27.03 0.184 0.278 0.2326 0.6042 1.2434 1.0091 0.8367 0.8365

28.99 0.277 0.411 0.3405 0.4880 1.1956 1.0210 0.8284 0.8281

31.17 0.414 0.533 0.4368 0.3827 1.1357 1.0492 0.8194 0.8191

32.20 0.476 0.584 0.4762 0.3392 1.1122 1.0670 0.8153 0.8150

34.74 0.591 0.691 0.5567 0.2489 1.0741 1.1106 0.8055 0.8052

35.77 0.639 0.731 0.5861 0.2157 1.0602 1.1340 0.8017 0.8013

37.53 0.709 0.789 0.6275 0.1678 1.0420 1.1753 0.7952 0.7949

38.58 0.756 0.827 0.6547 0.1369 1.0312 1.2092 0.7915 0.7911

41.14 0.847 0.888 0.6951 0.0877 1.0141 1.2948 0.7826 0.7822

42.84 0.903 0.927 0.7203 0.0567 1.0063 1.3669 0.7769 0.7765

44.14 0.940 0.969 0.7488 0.0240 1.0026 1.4273 0.7726 0.7723

45.11 1.000 1.000 a


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Table 12. Vapour-liquid equilibrium dataa for caproic acid (1) + enanthoic acid (2) at 443.15 K.


18.65 0.000 0.000

19.11 0.037 0.074 0.0671 0.8345 1.2772 1.0003 0.9059 0.9009

20.01 0.085 0.153 0.1381 0.7601 1.2509 1.0017 0.9022 0.8972

20.74 0.139 0.212 0.1907 0.7048 1.2234 1.0046 0.8993 0.8941

21.48 0.197 0.286 0.2564 0.6365 1.1961 1.0093 0.8964 0.8911

22.71 0.285 0.394 0.3514 0.5372 1.1587 1.0198 0.8916 0.8861

23.65 0.351 0.465 0.4130 0.4723 1.1334 1.0306 0.8880 0.8824

24.61 0.412 0.514 0.4547 0.4272 1.1121 1.0431 0.8844 0.8787

25.97 0.504 0.604 0.5313 0.3461 1.0834 1.0671 0.8793 0.8735

27.95 0.638 0.722 0.6300 0.2409 1.0485 1.1164 0.8722 0.8661

29.83 0.741 0.806 0.6980 0.1668 1.0272 1.1705 0.8657 0.8594

30.98 0.803 0.864 0.7448 0.1164 1.0169 1.2129 0.8617 0.8553

31.91 0.870 0.905 0.7774 0.0810 1.0080 1.2709 0.8586 0.8521

32.21 0.901 0.915 0.7850 0.0724 1.0049 1.3034 0.8576 0.8511

32.78 1.000 1.000 a


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Table 13. NRTL equation parameters fitted to the experimental liquid-phase activity coefficients and the

area test results for thermodynamic consistency.

T/ K α12 g12-g22 (J/mol) g21-g11 (J/mol) δP (%) δy ΔA (%) rms δln(γA/γB)

propionic acid + caproic acid

403.15 0.0672 2879.69 -2928.92 0.1772 0.0103 0.63 0.0339

408.15 0.1419 8643.90 -6215.86 0.6563 0.0243 2.51 0.0273

413.15 0.1138 2235.94 -2340.30 0.6468 0.0272 2.22 0.0206

isobutyric acid + caproic acid

408.15 0.9541 7793.37 -1867.12 0.3288 0.0486 1.90 0.0167

423.15 -0.011 7605.47 -7850.58 1.5974 0.0483 0.31 0.0339

valeric acid + caproic acid

423.15 0.0252 4951.99 -5052.37 0.2147 0.0283 0.17 0.0106

433.15 0.0068 4953.69 -4954.86 0.3268 0.0205 0.12 0.0179

caproic acid + enanthoic acid

443.15 0.3523 6343.22 -3414.51 0.3634 0.0211 1.87 0.0049

δP (kPa) = n

i

calc

ii PPn

exp1; δy =

n

i

calc

ii yyn

exp1

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Fig.1. P-x-y VLE data for propionic acid (1) + caproic acid (2) at T = 408.15 (■, experimental P-x; ◇, experimental P-y; —, calculated using chemical theory of dimerization + NRTL) and 413.15 K (●,

experimental P-x; ○, experimental P-y; ----, calculated using chemical theory of dimerization + NRTL).

Fig.2. P-x-y VLE data for valeric acid (1) + caproic acid (2) at 423.15 K (●, experimental P-x; ○,

experimental P-y; —, calculated using chemical theory of dimerization + NRTL).

0

20

40

60

80

100

120

0.0 0.2 0.4 0.6 0.8 1.0

Pre

ssu

re /

k

Pa

x1, y1

15

20

25

30

35

0.0 0.2 0.4 0.6 0.8 1.0

Pre

ssu

re /

kP

a

x1, y1

Figure(s)

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Fig.3. Experimental and calculated P-x-y VLE data for valeric acid (1) + caproic acid (2) at 433.15 K (●,

experimental P-x; ○, experimental P-y; —, calculated using chemical theory of dimerization + NRTL).

Fig. 4. Experimental liquid phase activity coefficient for isobutyric acid (1) + caproic acid (2) at 408.15 K

(●, γ2; ○, γ1)

20

25

30

35

40

45

50

0.0 0.2 0.4 0.6 0.8 1.0

Pre

ssu

re /

kP

a

x1, y1

1.0

1.2

1.4

1.6

1.8

2.0

0.0 0.2 0.4 0.6 0.8 1.0

γ1, γ

2

x1

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Fig. 5. Experimental liquid phase activity coefficient for caproic acid (1) + enanthoic acid (2) at 443.15 K

(●, γ2; ○, γ1)

Fig.6. Area test for valeric acid (1) + caproic acid (2) at 423.15 K (●, experimental; — polynomial fit)

Fig.7. Direct test for valeric acid (1) + caproic acid (2) at 423.15 K (○, calculated residuals).

1.0

1.1

1.2

1.3

1.4

1.5

1.6

0.0 0.2 0.4 0.6 0.8 1.0

γ1, γ

2

x1

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.0 0.2 0.4 0.6 0.8 1.0

ln(γ

1/γ

2)

x1

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.0 0.2 0.4 0.6 0.8 1.0

δln

(γ1/γ

2)

x1

vapour–liquid equilibrium of propionic acid+caproic acid, isobutyric acid+caproic acid, valeric...

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