Supercritical Fluid Science and Technology - American Chemical

Chapter 8

Vapor-Liquid Equilibria of Fatty Acid Esters in Supercritical Fluids 1

1

1

2

M . Zou , S. B.Lim ,S. S. H. Rizvi , and John A. Zollweg 1

Downloaded by UNIV LAVAL on April 5, 2016 | http://pubs.acs.org Publication Date: August 29, 1989 | doi: 10.1021/bk-1989-0406.ch008

2

Institute of Food Science, Cornell University, Ithaca, NY 14853 School of Chemical Engineering, Cornell University, Ithaca, NY 14853

Several cubic equations of state such as Redlich-Kwong, Soave-Redlich-Kwong, and Peng-Robinson have been used to calculate vapor-liquid equilibria of fatty acid esters in supercritical fluids. Comparisons are made with experimental data on n-butanol, n-octane, methyl oleate, and methyl linoleate in carbon dioxide and methyl oleate in ethane. Two cubic equations of state with a nonquadratic mixing rule were successful in modeling the experimental data.

In recent years, a great deal o f i n t e r e s t has been paid to s u p e r c r i t i c a l f l u i d e x t r a c t i o n (SFE) processes. They are e s p e c i a l l y s u i t a b l e f o r the separation o f substances with low v o l a t i l i t y which decompose before reaching t h e i r normal b o i l i n g points. These processes are based on the phenomenon that the d i s s o l v i n g power o f a solvent, as a f i r s t approximation, changes greatly with i t s density. One o f the recent major advances made i n solvent e x t r a c t i o n i s the a p p l i c a t i o n of s u p e r c r i t i c a l carbon dioxide (SC-CO2) i n the food and beverage industry f o r the e x t r a c t i o n and concentration of natural products and f l a v o r i n g s ( 1 - 2 ) . Several actual or p o t e n t i a l commercial applications o f t h i s method include the extraction o f fragrances and f l a v o r s from l i q u i d s , decaffeination of coffee beans, deodorization of o i l s , e x t r a c t i o n o f o i l seeds, f r a c t i o n a t i o n of highly unsaturated methyl esters derived from f i s h o i l t r i g l y c e r i d e s , and separation of organic materials from water. A d d i t i o n a l l y , there i s increasing i n t e r e s t i n separating and rearranging the f a t t y acids o f food materials to formulate new products. However, i n order to e s t a b l i s h commercial SFE processes which involve vapor phase extraction, i t i s important to have r e l i a b l e equilibrium data and methods f o r p r e d i c t i n g phase equilibrium behavior. 0097-6156/89/0406-0098$06.00A)

© 1989 American Chemical Society

Johnston and Penninger; Supercritical Fluid Science and Technology ACS Symposium Series; American Chemical Society: Washington, DC, 1989.


8. ZOU ET AL.

99

Vapor-Liquid Equilibria ofFatty Acid Esters

For s o l i d s o l u b i l i t i e s i n SC-fluids, numerous experimental data are reported i n the l i t e r a t u r e Q ) . At moderate pressure, equilibrium s o l u b i l i t i e s can be c a l c u l a t e d from the truncated v i r i a l equation o f state since r e l i a b l e methods are a v a i l a b l e f o r estimating v i r i a l c o e f f i c i e n t s f o r such mixtures; at higher pressure, the Peng-Robinson (PR) equation o f state represents the s o l u b i l i t y behavior quite w e l l . The Soave-Redlich-Kwong (SRK) equation o f state as w e l l as other simple cubic equations o f state would give comparable r e s u l t s . In the case o f s u p e r c r i t i c a l f l u i d - l i q u i d e q u i l i b r i a , i t i s p a r t i c u l a r l y d i f f i c u l t to adapt the t r a d i t i o n a l cubic equations o f state to systems containing components which have high molecular weight and are r e l a t i v e l y n o n - v o l a t i l e . The a d d i t i o n a l complexity i n the equilibrium c a l c u l a t i o n s introduced by the solvent d i s s o l v i n g i n the solute makes these c a l c u l a t i o n s much more d i f f i c u l t . The objective o f the present paper i s to describe the behavior o f s u p e r c r i t i c a l f l u i d - l i q u i d mixtures by using simple equations o f state (EOS) with d i f f e r e n t mixing r u l e s . Experimental The apparatus and methods are described i n d e t a i l i n the previous paper (4) and elsewhere (5-6). I t i s o f the dual r e c i r c u l a t i o n type and i s comprised, i n part, of a c e n t r a l pressure v e s s e l through which both l i q u i d and vapor phases are continuously r e c i r c u l a t e d . Samples o f the l i q u i d and vapor phases are removed from the c i r c u l a t i o n loops and analyzed by gas chromatography. The uncertainty i n measured compositions i s 0.02 mole f r a c t i o n f o r the l i q u i d and 0.001 f o r the vapor. The densities o f the samples are determined by f i r s t c a l i b r a t i n g the sampling system using pure materials, and then using the integrated peak areas on the gas chromâtοgraph to determine the t o t a l quantity of material i n each sample. The c a l i b r a t i o n curve i s s l i g h t l y nonlinear. In order to obtain good r e s u l t s , separate sampling valves are used f o r taking the l i q u i d and vapor samples so as to prevent cross-contamination o f samples. Measured phase equilibrium data are shown i n Table I. The manufacturer's stated mole percent p u r i t i e s o f the compounds were 99.98 f o r carbon dioxide (MG Industries) and 99.0 f o r methyl l l n o l e a t e (Sigma Products). Vapor-Liquid Equilibrium c a l c u l a t i o n :

For the v a p o r - l i q u i d equilibrium c a l c u l a t i o n s , a t the equilibrium state the f u g a c i t i e s f o r a l l species i must be the same i n a l l phases, namely fi

v

- fi

L

or

* i

v

L

y

i

- *t χι

(1)

where f£ i s the fugacity and φι i s the fugacity c o e f f i c i e n t . To c a l c u l a t e fugacity c o e f f i c i e n t s , equations of state which are


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SUPERCRITICAL FLUID SCIENCE A N D T E C H N O L O G Y

Table I Experimental Data Carbon dioxide (1)/Methyl linoleate(2) at 343.15K


Pressure (bar)

l i q u i d volume Vapor volume l yi ( l i q u i d phase) (vapor phase) (cnr/g-mol) (cnr/g-mol) x

21.3 35.5 53.6 71.9 88.4 95.8 140.3

0.29 0.43 0.48 0.56 0.58 0.55 0.62

295 220 209 207 193 180 189

0.9989 1.0000 0.9987 0.9987 0.9987 0.9996 0.9989

1022 567 345 235 177 150 90

v a l i d f o r both the vapor phase mixture and the l i q u i d phase mixture were used (2). Cubic equations of state (EOS) such as the Redlich-Kwong (RK), Soave-Redlich-Kwong and Peng-Robinson equations of state have become important tools i n the area of phase equilibrium modeling, e s p e c i a l l y f o r systems at pressures close to or above the c r i t i c a l pressure of one or more of these system components. The functional form of the Soave-Redlich-Kwong and Peng-Robinson equations o f state can be represented i n a general manner as shown i n Equation 2: 2

ρ - RT/(v-b) - a/O^+uvb+wb )

(2)

where u and w are numerical constants. For the Soave-RedlichKwong equation o f state, u - 1, w - 0; f o r the Peng-Robinson equation of state, u - 2, w - -1. For simple mixtures, the parameters a and b are related to the pure component parameters and composition through the following mixing r u l e s : nn a - ΣΣ X £ X4 ai4 (3) ij nn b - ΣΣ x X4 b (4) ij In these equations, a j ^ and b^£ are parameters corresponding to pure components; while a j j and b j j (1*3) are c a l l e d the unlike i n t e r a c t i o n parameters. I t has been customary to r e l a t e the unlike i n t e r a c t i o n parameters to the pure component parameters by combining rules, such as the following: m

m

a

t

i 1

a

ij - (aii jj)

l / 2

k

d- ij)


(5)

8.

ZOUETAL.

b

i j - 0>ii+bjj)/2

(6)

In Equation 5, k j j i s c a l l e d a binary i n t e r a c t i o n parameter. I t i s calculated from experimental binary phase equilibrium data on a given isotherm by regression. For the calculations presented i n t h i s paper, we f i r s t elected to use three simple cubic equations of state: PR-EOS; SRKEOS; and RK-E0S. For the pure components, c r i t i c a l properties (P , T ) and P i t z e r ' s acentric factor (ω) are needed to obtain a^ and bj[. C r i t i c a l properties have been measured f o r most o f the low molecular weight components and are reported by Reid e t a l . (8). For biomaterials that are thermally unstable and decompose before reaching the c r i t i c a l temperature, several estimation techniques are a v a i l a b l e . We have used the Lydersen group contributions method (fi). Other techniques a v a i l a b l e f o r p r e d i c t i n g c r i t i c a l properties have been reviewed and evaluated by Spencer and Daubert (2) and Brunner and Hederer (1Q). I t i s also possible to determine the EOS parameters from r e a d i l y measurable data such as vapor pressure, and l i q u i d molar volume instead of c r i t i c a l properties (H). We used the Lydersen method to get pure component parameters because the vapor compositions we obtained were i n closer agreement with experiment than those we got from pure component parameters derived by Brunner's method. The c r i t i c a l properties we used f o r the systems we studied are summarized i n Table I I . c


101

Vapor-Liquid Equilibria of Fatty Acid Esters

c

Table I I C r i t i c a l Properties and P i t z e r ' s Acentric Factor f o r the Working Materials Component Carbon dioxide Ethane n-Butanol η-Octane Methyl oleate Methyl l i n o l e a t e

T /K 304 305 562 568 785 786

c

P /bar

.2 .4 .93 .8 .99 .88

73. 82 48..84 44. 12 24..82 12..83 13..06

ω

c

0. 225 0. 098 0. 59 0. 394 0. 9835 0. 9869

The binary i n t e r a c t i o n parameter, k j j , i s i n i t i a l l y assumed to be zero, and a modification of the Levenberg-Marquardt algorithm (MINPACK) i s applied to minimize the sum o f the squares given by Equation (1). This c a l c u l a t i o n was applied to the following systems a t the indicated temperatures: e

Carbon dioxide (l)/n-Butanol(2) a t 40 C and 110°C (1£) Carbon dioxide (l)/n-0ctane(2) a t 40°C and 110 C (11) Carbon dioxide(1)/Methyl oleate(2) a t 40 C and 70 C (4) Ethane(1)/Methyl oleate(2) at 40 C and 70 C ( i ) Carbon dioxide(1)/Methyl l i n o l e a t e ( 2 ) a t 70°C ( t h i s work) e

e

e

e

e


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SUPERCRITICAL FLUID SCIENCE AND

TECHNOLOGY

The optimum binary i n t e r a c t i o n parameters are shown i n Table I I I . An example of the r e s u l t s i s shown i n Figure 1 f o r the PR-EOS applied to carbon dioxide/methyl oleate at 70 C. Comparing the r e s u l t s of those three simple equations of state, the RedlichKwong equation of state gave the poorest p r e d i c t i o n . There has been c r i t i c i s m directed toward the oversimplicity of the cubic equation form, e s p e c i a l l y i n the modeling of s u p e r c r i t i c a l v a p o r - l i q u i d equilibrium. Nevertheless, t h i s representation does describe at l e a s t q u a l i t a t i v e l y a l l the important c h a r a c t e r i s t i c s of vapor-liquid equilibrium behavior. A l t e r n a t i v e equations of state have been suggested, but none have been widely used and tested. Also, other EOS are s i g n i f i c a n t l y more complex and b r i n g with them additional parameters which must be evaluated by regression from experimental data. I t i s our opinion that the key to success i n employing the cubic equations of state at high pressure to model phase equilibrium with s u p e r c r i t i c a l f l u i d s i s i n the choice of the mixing and combining rules and i n keeping the EOS i n the simplest form with the fewest i n t e r a c t i o n parameters. A number of suggestions f o r the improvement of mixing rules, some of which show promise, have evolved from recent work i n t h i s area (13-16). Based on s t a t i s t i c a l mechanical theory, the following mixing rules have been derived (17):


e

σ

3

3

- ΣΣ X£ Xj a j 4 ij . nn ctr - ΣΣ X£ xj €£j crjj

(7)

3

(8)

where €£j i s the i n t e r a c t i o n energy parameter between molecule i and j , and a j j i s the intermolecular i n t e r a c t i o n distance between the two molecules. Knowing that the c o e f f i c i e n t s a and b of the cubic equations of state are proportional to € and σ according to the following expressions, a a N

0

b α N

0

ea σ

3

(9)

3

(10)

where N i s Avogadro's number, one can derive the mixing rules f o r the cubic equations of state (17-18). Q

Redlich-Kwong: 2

a - (ΣΣ X i xj > ij b - ΣΣ X i X J b y a i j

J

J

3

1

3

3

2

b i j ' } ' /{ΣΣ ij J

1

X

i

xj b y } ' J

2

J


(11)

ZOU ET AL.

Vapor—Liquid Equilibria of Fatty Acid Esters

Table I I I B i n a r y I n t e r a c t i o n Parameters f o r D i f f e r e n t Simple Cubic Equations o f S t a t e


Component Component i j Carbon dioxide

Carbon dioxide

Carbon dioxide

n-Butanol

η-Octane

Methyl oleate (MO)

EOS

Τ (C )

AAD i n

e

PR SRK RK PR SRK RK PR SRK RK PR SRK RK

40

110

40

110

PR SRK RK PR SRK RK

40

70

AAD i n

χι

yi

0.09741 0.09540 0.18257 0.07716 0.07742 0.22451

0.0042 0.0041 0.0117 0.0112 0.0117 0.0129

0.0031 0.0032 0.0172 0.0175 0.0192 0.0316

0.07806 0.08582 0.12685 0.04936 0.05997 0.18032

0.0127 0.0127 0.0146 0.0138 0.014 0.0166

0.0011 0.0015 0.0067 0.0076 0.0078 0.0185

0.02294 0.04504 0.09021 0.07644 0.08661 0.21525

0.0237 0.0231 0.0160 0.0313 0.0325 0.0234

0.0079 0.0072 0.0096 0.0014 0.0011 0.0030

Ethane

Methyl oleate (MO)

PR SRK RK PR SRK RK

40

0.00080 -0.00121 0.06519 70 - 0 . 0 0 3 3 8 -0.00571 0.12366

0.0553 0.0571 0.0483 0.0454 0.0466 0.0249

0.0041 0.0032 0.0148 0.0075 0.0072 0.0091

Carbon dioxide

Methyl linoleate

PR SRK RK

70

0.1042 0.1051 0.0863

0.0008 0.0007 0.0039

0.00397 0.01195 0.1194


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SUPERCRITICAL FLUID SCIENCE AND

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with the following combining rules: 1

ay

-

b

" 10>ii

ij

(l-kijMaj^ajj) ' 1 / 3

+ bjj

1 / 3

2

)/2]

3

Peng Robinson: a - ΣΣ i x

ij b - ΣΣ l ij c - ΣΣ i ij x


x

X

X

X

J

a

ij (13)

J bij J

c

ij

with the following combining rules: a

1 / 2

f ii aij - d - k i j ) bijl

_

—

b

b

^ ii 1

by

- U-lijMOHi '

3

Cij - (l-mij)[(ciiW3

I

j y 1

3

+ bjj ' )^] l

+

C j

3

j / )/2]

3

(14)

3

Kwak and Mansoori (12) tested these mixing rules through the p r e d i c t i o n of s o l u b i l i t y of high molecular weight s o l i d s i n s u p e r c r i t i c a l f l u i d s . They showed that these mixing rules can p r e d i c t s u p e r c r i t i c a l s o l i d s o l u b i l i t i e s more accurately than the conventional mixing rules f o r the Redlich-Kwong and Peng-Robinson equations of state. Mansoori and co-workers also tested the conformai s o l u t i o n mixing rules with other equations of state on systems containing a high molecular weight l i q u i d i n a s u p e r c r i t i c a l f l u i d mixture. They showed that the Peng-Robinson equation of state using mixing rules based on conformai solution theory can p r e d i c t the f l u i d phase equilibrium of high molecular weight l i q u i d s i n s u p e r c r i t i c a l f l u i d s more accurately than others (18.19). The Panagiotopoulos-Reid mixing rule (P & R Mixing Rule) was developed by making the normal single binary i n t e r a c t i o n parameter, k i j , composition dependent (20.21). Two binary i n t e r a c t i o n parameters k y and k j i ( k i j ^ k j i ) , are determined from regression of experimental data. The ^ e f f e c t i v e " i n t e r a c t i o n parameter between component i and j approaches k y as X i approaches zero and approaches k j i as X i approaches unity. A p p l i c a t i o n of t h i s mixing rule tor the c a l c u l a t i o n of the mixture parameter a r e s u l t s i n a cubic expression f o r the mole f r a c t i o n dependence, instead of the conventional mixing r u l e , which i s a quadratic expression f o r a . The form of the empirical modifications of the mixing rules and combining rules and the r e s u l t i n g expressions f o r the fugacity c o e f f i c i e n t i n a mixture for the case of a general cubic EOS are given below: m

m


8.

ZOUETAL.

a

a

Vapor-Liquid Equilibria ofFatty Acid Esters nn - ΣΣ X i X j a i j ij

m

- y

Supercritical Fluid Science and Technology - American Chemical

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