Modelling and simulation of countercurrent fractional extraction with supercritical solvents

Modelling Rev Cdn Therm (1997) 0 Elsevier, Paris

and simulation

of countercurrent

fractional

extraction

with supercritical

solvents

36, 93-98

Modelling and simulation of countercurrent fractional extraction with supercritical solvents Andreas lnstitut

fiir

Technische

Chrisochoou,

Thermodynamik Pfaffenwaldring

Karl Stephan *

und Therm&he 9, D-70550

(Received 2 1 November

Verfahrenstechnik, Stuttgart, Germany

1996; accepted

20 January

Universittit

Stuttgart,

1997)

- Fractionating fluid mixtures by supercritical fluid extraction has received increasing attention within the last few years. In this paper, a simulation model of a countercurrent fractional extraction column operated with supercritical fluids is presented. The model is based on ideal separation stages and incorporates the equation of state due to Redlich-Kwong and Soave for describing phase equilibria. Simulation studies were performed on the separation of a binary feed using supercritical carbon dioxide as extraction solvent. The system is also used when treating a reaction mixture from an enzymatic conversion effected in supercritical carbon dioxide. To achieve a symmetric fractionation with equal purities in both top and bottom product flow of the column, the reflux ratio has to be set to a distinct ‘optimal’ value. All other column parameters remaining unchanged, the optimal reflux ratio increases as the solvent flow is increased. As a consequence, product purities also increase. Summary

Supercritical fluids state / Redlich-Kwong

/

fractional extraction and Soave

Resume - Modklisation supercritiques. L’inte’rEt

et

/ countercurrent

simulation

de

column

I’extraction

/

modelling

fractionhe

/

simulation

/

phase

g contre-courant

equilibria

utilisant

/

equation

des

of

solvants

le fractionnement de mtlanges @ides par extraction supercritique a augment6 au tours des dernikres anne’es. Un mode/e de simulation d’une colonne d’extraction fractionne’e d contre-courant utilisant un solvant supercritique est pre’sente’ dans cet article. Le modtile est base’ sur la notion d’ktages thioriques et utilise I’tquation d’e’tat de Redlich-Kwong et Soave pour de’crire /es iquilibres entre phases. La simulation de la siparation d’un flux d’alimentation binaire d /‘aide du dioxyde de carbone comme solvant supercritique a e’tL rialise’e. Le milange ttudie’ intervient lors de /a se’paration du produit d’une riaction enzymatique qui s’effectue egalement dans le dioxyde de carbone supercritique. Afin d’obtenir un fractionnement symttrique caracttrise par des puretLs tgales en te^te et en pied de la colonne, une valeur < du reflux doit etre diterminie. Le reflux optimal augmente avec le flux de solvant, /es autres paramatres de la colonne restant inchange’s. Par consdquent, la puretL des produits augmente igalement.

fluides equation

pour

suoercritiaues . / extraction &tat / Redlich-Kwong

fractionnke et Soave

/ colonne

A contre-courant

Nomenclature a b c cw E F 7% N

parameter in the SRK equation ofstate......................... parameter in the SRK equation of&ate......................... total number of mixture components binary interaction parameter (Huron-Vidal) .. . . . . extract flow rate. feed tlow rate. . . parameter in the SRK equation of state (Soave) total number of stages

n ni mG.MPa.mol-2 m3.mol-l

P P

Q q E

kPa.m3.mol-’ mol.s-’ mol.s-’

r L T V v 2 X1

* Correspondance

and reprints

Y

/

modelisation

/ simulation

/ kquilibres

mole number . . . . .. . . parameter in the SRK equation of state (Soave) top product flow . . . . pressure........................ bottom product flow. . .. product purity universal gas constant. . . raffinate flow rate . . . reflux ratio solvent flow rate. temperature.................... waste flow...................... molar volume................... liquid mole fraction liquid mole fraction on a solvent-free basis gaseous mole fraction

de

phases

/

mol mol.s-l MPa mol.s-l J.mol-l.K-’ mo1.sl mol.s-l K mob-l m”.mol-l

93

A Chrisochoou,

mole fraction solvent-free basis total mole fraction

gaseous

Y*

z

on a

Greek symbols

clz.J binary interaction parameter (Huron-Vidal) 9’ fugacity coefficient (raffinate phase) 9” fugacity coefficient (extract phase) Subscripts

critical state extract phase feed component i component j stage j top product bottom product raffinate phase

C

E F i

j j Q’ R

1

n

INTRODUCTION

Within the past two decades, the extraction with supercritical fluids (SFE) has become established in industrial use as a separation technique for winning low-volume specialty products rather than commodity chemicals. These are, in general, highvalue-added materials which are neither to be processed by distillation (because of low volatility or heat-sensitivity) nor to be treated with organic solvents (eg, due to purity requirements for consumer products). Most SFE applications are found in food, pharmaceutical and cosmetics branches, such as the decaffeination of coffee beans, the extraction of natural flavours or the purification of vitamins. A recent overview on industrial SFE use is given, for example, by Krukonis et al (1994). Recent years have seen a rising interest in separating complex fluid mixtures by SFE. Here, the separation problem shifts away from gaining a single product from a feed mixture towards fractionating a binary (or multicomponent) mixture into two pure substances (or fractions). This type of extraction is termed fractional extraction fulfilling the same task as fractional distillation. Fractional extraction of fluids is usually performed in continuous countercurrent columns with extract reflux (Pratt, 1991). Countercurrent extraction with supercritical fluids has been investigated for quite a long time. But former studies were dedicated mainly to experimental investigations of ‘classical’ countercurrent columns, ie, without reflux (eg Peter et al, 1978 and 1986). Within the last few years work on fractional extraction with supercritical fluids has been published by numerous researchers, with an emphasis on experimental investigations. Saure and Brunner (1994) studied the separation of tocopherols in a laboratory column. Riha and Brunner (1994) used a similar setup for separating fatty acids and also 94

K Stephan

performed some basic modelling and simulation of the process. Based on phase equilibrium data, Staby and Mollerup (1993) outlined the scheme of a complex SFE process employing several columns in order to fractionate a mixture of fish oils. Chrisochoou and Schaber (1996) presented a flow scheme for separating fluid mixtures encountered in enzymatic reactions. In this paper, we want to present a simulation model of a fractional extraction column with a (single) supercritical solvent. It employs the traditional concept of ideal separation stages and incorporates a cubic equation of state for calculating phase equilibria.

2

n

MODELLING

AND

SIMULATION

Figure la shows the schematic Ilow scheme of a countercurrent extraction column with extract reflux. A feed F containing the components A and B is to be separated by means of a solvent flow L into two product flows: a top product P that carries, besides the solvent S, the ‘light’ (ie, higher soluble) component in high purity and a bottom product Q made up of S and the ‘heavy’ (ie, lower soluble) component B. The feed F is introduced at about mid-height into the column, thus dividing it in an enrichment section and a stripping section. In Figure lb the model structure of a staged column is shown. The solvent flow L, usually consisting of pure solvent S, enters the bottom of the column. It is led in countercurrent to the

F z,,r

Fig 1. Fractional extraction column. (a) Basic flow scheme. (b) Equilibrium-stage model. Fig 1. Colonne d’extraction fractionnCe. (a) Schema proc6dC. (b) Modele d’ktages d’kquilibre.

Modelling

and

simulation

of countercurrent

fractional

descending raffmate phase which finally yields the bottom product Q. The extract phase leaving the feed stage f is further enriched with component B in the column’s upper section. In order to maintain countercurrent flow a raffinate-type phase (ie, poor in S) has to be fed into the top of the column. To this effect, the extract phase leaving the enrichment section is flashed in the separator at a lower pressure and/or temperature to yield a waste flow V = El almost entirely made up of solvent S, and a raffinate phase RI. Part of the latter is refluxed into the column, the remainder is withdrawn as top product P. In modelling, the following assumptions are made: a) The process is treated as a continuous steadystate operation. b) The column is made up of theoretical stages, ie, the extract and raffinate phases leaving each stage are in phase equilibrium. Homogeneity and perfect partitioning of the phases are also provided. c) Pressure p and temperature t are the same on every column stage j = 2,. . . , N. Only the separator j = 1 is operated at different conditions pl, Tl. (Energy balances are disregarded.) d) The reflux ratio r, defined as -RI - P Rl

r=

+

= Rjx,,, + E,y,,,

E,+IY,,,+I

i=l,...,C,

j #

1,2,f>N

(2)

On the feed stage, the entering feed flow also has to be accounted for: F&F

+ Rf-lxz.f-1

+

Ef+lyi,f+l

=

Rfx,,f

+ I3jyz.f

i=l,...,C

Balances on the remaining

(3)

stages give:

E2y,.2 = RIX,.~ + Ely,,l

i = 1,.

with

supercritical

and the phase equilibrium I P2.3xi.3 =

I,

i=

(Pi,jYw

solvents

conditions j = l,...,N

l,...,C,

(9)

The fugacity coefficients cp: and cp:’ are calculated using the cubic equation of state proposed by Redlich and Kwong (1949) and modified by Soave (1972 and 1979) (SRK equation). The SRK equation is employed in the following form: ‘=

RT -V-b

- I$+

(10)

b)

with a = a(x, or yzrT,T~.,,~c,l.,mZ,~z,~z,,C,,,C~~)

(11)

b = b(x, or yz, Tc.z, pm)

(12)

The SRK equation requires parameters specific for the mixture of substances treated. These are the critical data Tc,i,p,,z and the Soave parameters m,, 72%.To account for interactions between the mixture components the binary interaction parameters at31 Ctj, C,, proposed by Huron and Vidal(l979) are applied. The variables of the exiting (product) flows are calculated as:

O
is controlled externally. For calculating the unknown variables Rz.3. Et,3,xt,i, ~2.3 a set of N(2C + 2) equations is required. Component material balances on every stage, excepted for the feed, the separator, the top and the bottom stages, yield: Rj--1xw1

extraction

P = (1 - r)Rl, &=RN% V = El:

X,,P

=

x2.1

x,,Q = 5t.N Yz,V = Yz,l

(13) (14) (15)

The model equations were implemented in a FORTRAN simulation program where they were solved iteratively by means of a numerical subroutine called NLEQlB, developped by Nowak and Weimann (1992) especially for treating non-linear, numerically sensitive problems. All simulation parameters, such as feed flow F, stage number N or the substances treated are fixed in a single input file. Substances data are stored in separate files. The program delivers all of the N(2 C + 2) state variables prepared in different output formats. Some of them can be processed by graphics utilities for depicting flow and concentration profiles of the column.

,C

(4) rRlx,,l

+ EsY,.~ = R2xt.2 + E2y2,2

i=

l,...,C

(5) RN-I&.N-I

+ LYLL

=

RNG,N

+EN'&,N

i=

3

n

SIMULATION

RESULTS

l,...,C

(6) The above relationships comprise NC equations leaving another N (C + 2) yet to be determined. They are obtained from j = l,...,N

(7)

j =

(8)

i=l c c ZZl

Yi,j

= 1

l,...,N

In the following, fractionating a binary mixture of cu-cyano m-phenoxybenzyl alcohol (XAl) and cy-cyano m-phenoxybenzyl acetate (XAc) is investigated, using supercritical carbon dioxide as extraction solvent. XAl is an important starting material for the synthesis of pyrethroid insecticides and can be obtained from XAc via enzymatic catalyzed transesterification in supercritical carbon dioxide (Chrisochoou et al, 1995). Separating the product XAl from the amount of non-converted substrate XAc is 95

A Chrisochoou,

K Stephan

the final-and decisive-step in treating the reaction mixture. For regarding the separation process, it is convenient to introduce solvent-free molar fractions, defined as: i#S

(16)

This enables a ternary system S-A-B to be treated as pseudo-binary A-B in an equilibrium selectivity diagram (Stevens and Pratt, 1992). There, the solvent-free molar fractions of the higher soluble component of the extract phase y: are plotted versus the same quantities of the raffinate phase xi. Figure 2 shows the phase equilibrium of the ternary COZ-XAl-XAc at 313.15 K and 15 MPa as calculated with the SRK model. The required model parameters were determined in previous work on the phase equilibria of the ternary system (Chrisochoou et al, 1997). They are summarized in tables I and II. For the conditions given in Figure 2, the equilibrium curve extends, without any interruption, from the lower left hand of the diagram to the upper right hand corner, thereby running exclusively above the diagram diagonal. Thus, it can be concluded that it is possible to achieve a complete separation of XAl and XAc at the given conditions (Crisochoou and Sehaber, 1996). TABLE I / TABLEAU I Pure substance parameters of the SRK model Parametres des composes purs du modele SRK

I MPa

T,/K

co2

7.39

XL41

2.90

XAC

2.19

304.2 844.0 853.0

Substance

r

p,

rn,

nz

0.66048

0.20537 0.55 0.52853

1.10 1.08841

TABLE II / TABLEAU II Binary interaction parameters due to Huron and Vidal Parametres d’interaction binaire d’apres Huron et Vidal

3inary :02 -xAl :02

-XAc

CA1 -xAc

C?J kPa.m”.mol-l 0.0002193 49.007 %

-0.0037602

50.127

-0.092598

0.44987

0.0 v 0.0 Fig

I

1

I

I

0.2

0.4 . xxAs

0.6

0.6

1.0

2. Equilibirum selectivity diagram of C02-XAI-XAc K and p = 15 MPa as calculated by the

T = 313,15 model. Fig

at SRK

2. Diagramme d’equilibre du melange COz-XAI-XAc a K et p = 15 MPa determine a I’aide du modele

T = 313,15 SRK.

depressurization, regarding product purities on a solvent-free basis is both appropriate and relatively simple. Therefore, the top purity 4~ is defined as the solvent-free molar fraction of the higher soluble component XAc qp = XGi4c.P and the bottom purity is identified the lower soluble component XAl:

(17)

analogously

44 = &.‘u,Q

for (18)

Figure 3 shows the product purities as simulated with different reflux ratios for a constant solvent flow of L = 210 mo1.sI. It can be seen that the top purity increases as the reflux ratio is enhanced, whereas the bottom purity behaves vice versa. The point where both curves intersect represents a ‘symmetrical’ separation of the binary XAl-XAc as both product purities are equal. This is called optimal fractionating. Here, the (common) optimal

C,,l kPa.m3.mol-’ -5.4978

i

-4.5031 0.36226

The aim of the first simulations carried out was to find out about the influence of solvent flow L and reflux ratio r on the separation performance of the column. All the other simulation parameters were fixed: feed flow: F = 1 mol.s-‘, ZCQ,F = 0.0, Zml,F

column: separator: stages: feed stage:

= ZX.&,F

= 0.5

p = 15 MPa, t = 313.15 K pl = 4 MPa, tl = 308.15 K

N =20 f = 10

Since the CO2 present in the two product flows of the column will be removed by subsequent 96

Fig

3. Simulation

for L = 210 mol.s-l purity

qp

= xL=,~;

of a countercurrent and a-,

extraction column a variable repux ratio. +J-, top bottom purity QQ = x;;A,,~.

Fig 3. Simulation dune colonne d’extraction courant pour h = 210 mol.s-1 et un taux variable. -o--, purete en t@te de colonne qp -a--, purete en pied de colonne 44 = xL~,~.

a contrede reflux = xL~,~,;

Modelling

and

simulation

of countercurrent

fractional

purity is qopt = 0.998 with a corresponding optimal reflux ratio of rapt = 0.743. Furthermore, the same type of simulation study was repeated for different solvent flows ranging from L = 150 mo1.s’ up to L = 400 mo1.sl. The couple of optimal reflux ratio and optimal purity was determined for each given flow L. Figures 4 and 5 summarize the results obtained. It can be seen that the optimal purity to be achieved grows with a higher solvent flow - provided the (optimal) reflux ratio is adjusted to higher values.

extraction

of substances treated, simulations.

solvents

and should require only few

Acknowledgement The authors want to thank Volkswagenstiftung, Hannover (Germany) for financial support of this work. REFERENCES

Chrisochoou ical fluid incurred Proc 35,

0.41 150

200

250

300 L /

4. Optimal

Fig 4. solvant.

supercritical

Chrisochoou A, Stephan K, Winkler S, Schaber K (1995) Enzymkatalysierte Racemattrennung und Produktaufbereitung mit uberkritischem COa. Lecture at CVCJahrestagung, Strasbourg 1995. Chem Ing Tech 67, 1153

.” 0.9 I

Fig

with

Taux

repux de

reflux

ratios

350

rnOl/S

at various

optimal

I 400

pour

solvent

flows.

differents

flux

de

A, Schaber K (1996) Design of a supercritextraction process for separating mixtures in enzyme-catalyzed reactions. Chem Engng 271-282

Chrisochoou equilibria enzymatic component. Data

A, Schaber K, Stephan K (1997) Phase with supercritical carbon dioxide for the production of an enantiopure pyrethroid Submitted for publication in / Chem Engng

Huron MJ, equations equilibria Equilibria

Vidal J (1979) New mixing rules in simple of state for representing vapour-liquid of strongly non-ideal mixtures. Fluid Phase 3, 255-271

Krukonis V, Brunner C, Perrut M (1994) Industrial operations with supercritical fluids: current processes and perspectives on the future. In : Proceedings of the 3’d Int Symp Supercritical Huids, Strasbourg, vol 1, l-22

150

200

250

300 L /

Fig Fig

4

5. Optimal 5. Purete

n

purity optimale

350

400

mo1/s

at various solvent flows. pour differents flux de solvant.

CONCLUSION AND OUTLOOK

Nowak 0, Weimann L (1992) Numerical solution of nonlinear (NL) equations (EQ) especially designed for numerically sensitive problems. Explanations on the FORTRAN routine. Konrad Zuse Zentrum fur Informationstechnik, Berlin Peter S, Brunner G (1978) substances by means tercurrent processes. 746-750 Peter 5, Schneider Die Trennung Gegenstromkolonne Extraktionsmittels. Pratt

Due to the previous simulation results, solvent flow and reflux ratio of a fractional extraction column cannot be chosen independently of each other if an ‘optimal’ separation is to be achieved. Future simulations should concentrate on investigating the impact of the stage number and, especially, the operating conditions of the separator on the column’s performance. Further research will be devoted to developing a systematic approach for designing a column, ie, fixing appropriate operating conditions to attain demanded product purities. The method should be universal in that it is not related to certain types

The separation of compressed Angew Cbem

of nonvolatile gases in counInt Ed fngl 17,

M, von

Weidner E, Ziegelitz R (1986) Lecithin und Sojaol in einer mit Hilfe eines uberkritischen Chem Ing Tech 58, 148-l 49

HRC (1991) In : Handbook of so/vent Lo, MHI Baird, C Hanson, eds), Krieger Malabar, 1 5 l-1 98

extraction, Publishing

Redlich 0, Kwong JNS (1949) On the thermodynamics of solutions. V: An equation of state. Fugacities gaseous solutions. Chem Rev 44, 233-244 Riha

(TC Co,

of

V, Brunner G (1994) Separation of datty acid methyl esters by chain length and degree of saturation. A chemical engineering design analysis. Proceedings of the 3’d Int Symp Supercritical Fluids, Strasbourg, vol 2, 1994, 1 19-l 24

Saure C, Brunner C (1994) Laboratory plant for countercurrent extractions and some experiments for separation of tocochromanols. In : Proceedings of the 3’d Int Symp Supercritical Nuids, Strasbourg, vol 2, 2 1 l-2 16

97

A Chrisochoou,

Soave C (1972) Redlich-Kwong 1197-1203

Soave CS (1979) to vapour-liquid compounds.

98

Equilibrium equation

constants from a modified of state. Chem Engng Sci 27,

Application of a cubic equation equilibria of systems containing lnst Chem Eng Symp Ser 56, 1.2/1-l

of state polar .2/l 6.

K Stephan

Staby A, Mollerup J (1993) Separation of constituents of fish oil using supercritical fluids: a review of perimental solubility, extraction, and chromatographic data. Fluid Phase Equilibria 91, 349-386 Stevens CW, liquid-liquid Clarendon

ex-

Pratt HRC (1992) In : Science and practice of extraction, Vol 1, Ch 6: Plug flow analysis. Press, Oxford, 345-415