Rate of the vegetable oil extraction with supercritical CO2—I. Modelling of extraction curves

Chemical Engineering Science, Rimed in Great Britain.

Vol. 49, lb.

ooo9-zmwl 36.00 + 0.00 8 1993 Pergnmon Pras Ltd

3, pp. 40%414.1994.

RATE OF THE SUPERCRITICAL

VEGETABLE OIL EXTRACTION WITH C02--I. MODELLING OF EXTRACTION CURVES H. SOVOVA

Institute of Chemical Process Fundamentals,

Academy of Sciences of the Czech Republic, 16502 Prague 6, Czech Republic

(First received 15 March 1993, accepted in revised form 22 July 1993) Abstract-During the extraction from milled vegetable material, the easily accessible solute from the cells opened by milling is extracted first, and the slower extraction of the solute protected by the cell walls follows. Mathematical models based on the assumption of plug flow of supercritical solvent through a fixed bed of milled material were published for both extraction periods. A new model with analytical solution was developed on the basis of these models. Extraction parameters can be evaluated by comparison of extraction curves calculated by the model with experimentaldata.

INTRODUCTION

The extraction of vegetable oils using supercritical carbon dioxide has been studied as a potential alternative to the current extraction methods. The interest in this application of supercritical extraction was evoked by the rapidly escalating costs and uncertain availability of petroleum solvents in the early 198Os, and also be potential health- and safety-related problems of both hydrocarbon and chlorinated hydrocarbon solvents. Comparing the composition of extracts, Friedrich et al. (1982) found that the soybean oil extracted with CO2 was lighter in colour and contained less iron and about one-tenth the phosphorus of hexane-extracted crude oil. Extraction of the rapeseed oil with supercritical carbon dioxide was investi’gated by several groups of workers (Brunner, 1984; Bunzenberger et al., 1984; Lack, 1985; Lee et al., 1986). The mass product nature of oil seed makes a continuous supercritical extraction essential if operation is to become economic relative to the conventional hexane extraction. However, at present only batch processing is possible, although several attempts have been made to design a plant in which seeds are transported continuously into, through and out of a pressure vessel (Eggers et al., 1985). On the other hand, the advantages of supercritical fluid extraction prevail when smaller amounts of materials yielding highquality products are processed. One example is the extraction of oils containing polyunsaturated fatty acids, especially y-linolenic acid, from seeds (Brunner et al., 1987). As the labile unsaturated acids are protected by inert atmosphere of CO2 and relatively low extraction temperature, quality of the product is superior to that of hexane-extracted oil. A reliable and simple mass transfer model is necessary to design extraction plant and determine the optimum operating conditions. Several models of supercritical carbon dioxide extraction from ground seeds have been published which describe extraction rate using either mass transfer coefficient in the sol-

vent phase (Lack, 1985; Lee et al., 1986; Cygnarowicz et nl., 1992) or mass transfer coefficient in the solid phase (Pekhov and Goncharenko, 1968). In the present work, equations of these models are compared and combined into a new model containing both mass transfer coefficients. MATHEMATICAL MODELS OF EXTRACTION Fixed-bed

extractor

This model describes a situation when solvent flows axially with superficial velocity U through a bed of milled plant material in a cylindrical extractor. The solvent is solute-free at the entrance of the extractor, and the temperature and pressure are regarded as constants. The solid bed is homogeneous with respect to both the particle size and the initial distribution of solute. The solute is deposited in plant cells and protected by cell walls. However, a part of the walls has been broken open by milling, so that a part of the solute is directly exposed to the solvent. The mass of the solute contained initially in the solid phase, 0, consists of the mass of easily accessible solute, P, and of the mass of inaccessible solute inside the solidphase particles, K: O=P+K.

(1)

Mass of the solute-free solid phase, N, remains constant during the extraction. Amounts of solute are related to this quantity so that the initial concentrations are x(t=O)=x,,=O/N=x,+x,=PfN+K/N.

(2)

Height of the bed of particles is H and its void fraction is E. Axial distance along the bed is h. The material balances for an element of bed are given by

-Ps(l

ay+

PE z

-E)g=J(X,Y) PU

aY z

@a) =

J(x, y).

H. SovovA

410

continuously during the extraction:

The first term in the fluid-phase balance is often neglected and a set of equations

.J(x, y) = k/a&y,

x0 - xlc 1

- y)exp

ln(O.OO1)z

-h(l-E)$=J(x,Y)

(8)

(3b) = Jk

PU g

Both extraction periods were represented by this expression. Equations (3a) with boundary conditions (4) were solved by numerical integration. Pekhov and Goncharenko (1968) described the slow extraction period using the expression with a solid-phase mass transfer coefficient, k,:

Y)

is solved. The boundary conditions are

x(h, t = 0) = XiJ

(4)

Y(h = 0, t) = 0.

J(x < xk, y) = kSaop,(x - x +)m”.

The easily accessible solute which surmounts only the diffusion resistance in the solvent is extracted first. When the solid-phase concentration decreases to xlr. mass transfer is retarded by the diffusion in the solid phase: J(x >

xk, y) ’

J(x

As the extractor was represented by a mixer in their model, the concentrations were not space-dependent. The term m” denoted the effect of solvent-to-solid feed ratio on the mass transfer rate and its value approached unity for most plant materials tested. Moreover, as the solid-phase diffusion resistance was much larger than the resistance in the supercritical phase, the interfacial concentration x+ could be neglected in comparison with the concentration inside particles x and eq. (9a) became

(5)

< Xkr y).

The concentration profiles in the solid and solvent phases are calculated from eqs (3a) or (3b) by integration after substituting for the rate of mass transfer J(x,Y). Extraction curve is determined as H x(h, t)dh. (6) e(t) = e(q = Qt) = x0 - (l/H) s0

J(x d Xk. Y) = k.UoP.X.

Rate of mass transfer Several expressions for mass transfer rate during the supercritical fluid extraction are listed in Table 1. If the easily accessible solute crosses the interfacial boundary fast enough to keep the solvent at the boundary saturated, the mass transfer rate is J(x > %Y) = k@op(Y,

r = X/Xkr

z=k/aoh

1 -Y/Y.,

y=

u

(10) k,aopy.

T= (1

Lee et al. (1986) used this relation when modelling the fast extraction period. Equations (3a) and (7) with boundary conditions (4) were rearranged and solved numerically using the method of characteristics. Brunner (1984) and Lack (1985) also described the mass transfer rate in the fast period by eq. (7). In combination with eqs (3b) and (4) they obtained an analytical solution which is given further. Cygnarowicz-Provost et al. (1992) substituted for the mass transfer rate in eqs (3a) an empirical relation with the right-hand side of eq. (7) multiplied by a coefficient which was equal to unity for x = x0 and diminished

- E)P,Xlr f

into eq. (3b) with boundary conditions (4) yields a set of equations

ar ay -=_= aT a2 r(z,

T

=

0)

- J*(r, Y) r.

=

(11)

Y(z = 0,T) = 1 where J*(r,

Y) = J(x.Y)l%-aopY,J.

Table 1. Mass transfer rate Reference Lee

et al.

Cygnarowicz

k,noP(Yr

Y) kfady,

Lack (1985)

This work

-

x0

et al. (1992)

Pekhov and Goncharenko

J(x < Xt, Y)

J(x > %Y)

(1986)

k@op(Y, (1968)

- Y)

k/a&Y.

Pb)

Model with analytical solution Introducing dimensionless variables

(7)

- Y)-

(94

- y)exp

[

-

x

ln(O.~l) x _ x 0

k

1

k+,P(Yr k,aopBx

- Y)

- Y)x/~t

(12)

Rate of the vegetable

For the fast-extraction into

oil extraction

period, eq. (7) is transformed

J*(r > 1, Y) = Y.

Y) =f(r)Y,

j-‘(I > 1) = 1, j-(r < 1) < 1. (14)

Substituting for J* from eq. (14) into eqs (1 I), elimination of Y in these equations and their integration yields the equation 1 at j=j=s+r=r0

fm = r. -

ar

7n =

-rm +

1 1 + ~~exp (r&Z) -1n k 1 + 7m (19)

The easily accessible solute becomes exhausted at the solvent entrance at the time T,,,, when a transition period between the fast and slow extraction begins. In this period, the easily accessible solute is still extracted in one section of the fixed bed, while the extraction from the inside of particles takes place in the other section. The coordinate of the boundary between both sections is z _ &r,expCW

v-

kro

- dl I.0- 1

- 1

for z’DI< t < 5. .

= -f(r)

which has analytical solution for f(r) = 1. For the slow-extraction period, Lack integrated eq. (15) with various forms of function f(r) numerically, He also published an analytical solution for f(r) = r. This solution will be presented here in a more general form with the functionf(r) extended by a constant k d 1: f(r > 1) = 1, J(r < 1) = kr. Concentration

1,

Z = kfaoH/V.

with boundary condition ar(2 = 0,r)

411

CO*-I

where

(13)

In the slow-extraction period, Lack (1985) assumed the dimensionless mass transfer rate to be a product of Y and a function f(r): J*(r,

with supercritical

The boundary passes through the bed until it reaches its end with dimensionless coordinate Z at the time r,. Examples of the concentration profiles computed by eqs (18)-(20) are given in Figs 1 and 2. The profile of the normalized concentration in the solvent phase is

(17)

profile in the solid phase is for z c T, for t,z, J-0

1) exp (- r&z))

(18)

for t,,,<~-~~~,z
and for rab

1.8 1.6 1.2 Q < 1.0 ‘;;’ 0.8 0.6 0.4 0.2 0.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Z Fig.

1.

Solid-phase

concentration

(20)

profiles with time interval AT = 1 according

to eq. (18): r0 = 2; k = 1.

412 2.0 f1.8 -

1.4

1.2 c N" 1.0 =

0.8 0.6

I

I

I

I

I

I

I

I

Fig. 2. Solid-phase concentration profiles with time interval Ar = 1 according to eq. (18): rD = 2; k = 0.2.

c

exp(-

-

for z < z,

4

for rm G z < r., z > z,

exp [k(r,,, - 7)1)

r~expCk(r- 41 + TO exp [k(r - T,)I- 11

for r, < 7 CT.,

(21)

z G z,,, and for T > 2.

and the extraction curve is given by the relation

(xirlZ)Cl e =

(xr/Z)

[T -

i x0 - &/kZ)

-

for T -z 7,

exp( - Z)l rr. exp (z, -

for 7, d 7 < 7. (22)

Z)]

In { 1 + [exp (r,kZ)

-

l] exp [k(7,- r)]/ro} for ‘5 & 1..

Several extraction curves calculated by means of eq. (22) are depicted in Fig. 3.

Though the extraction in the second period is controlled by diffusion in the solid phase, the coefficient k, is missing in the expression for mass transfer rate

I 0

1

2

3

4

5 z

6

7

9

(22) (-) (29) (- - - -). r0=2,A:Z=0.5,k=1,B:Z=1,k=0.2,C:Z=2.k=0.04.

Fig. 3. Extraction curves according to extended Lack’s model-q.

combined model-eq.

8

10 and according to

Rate of the vegetable oil extraction with supercritical CO,-1 according parameter

to the Lack’s model. The purpose of the _k is to introduce the solid-phase mass

transfer coefficient into j(r) from eq. (17) with

the model.

Substitution

for (23)

k = k,p,x,l(k,pyr)

into eq. (14) yields, after rearrangement, the mass transfer rate in the second extraction period J(x

d xkr y) = k,aop,xY

(24)

which differs from eq. (9b) used by Pekhov and Goncharenko (1968) only by the dimensionless concentration Y. Both models are equal when Y = 1. During the extraction of inaccessible material, Y is at its minimum when z = T. and z = Z, as follows from eq. (21). At this point, the ratio of the driving force

qy,C1 - exp(

413

both models is small and diminishes with decreasing the value of the product kZ, which is directly proportional to the solid-phase mass transfer coefficient k,. The extended Lack’s model is therefore adequate to describe the course of the supercritical fluid extraction from milled vegetable material which has small k. in consequence of the large diffusion resistance of the cell walls. EXTRACTION

CURVE

AS A FUNCTION

For evaluation of experimental data, extraction curve should be expressed in terms of real time or amount of the solvent consumed. Equation (22) was therefore rearranged to yield the amount of extract as a function of the specific amount of solvent q, concentrations x0, xlr and y,, and parameters Z, W:

- Z)l

for

calculated according is

yv,

(1 + Cexp

( Wxdy,)

by the Lack’s mode1 to the driving force to the model of Pekhov and Goncharenko

?I) =

exp(

r. +

-rokZ)

1

-

> 1-

kZ.

7”)

Q

e(7)L/e(~)pG

<

1

for 5 > tm.

(26)

r(z, 7”) =

f-0

1 + r,exp[r,k(Z

qm = (x0 -

The next course of extraction Pekhov and Goncharenko: r(z, t) = r(z, r,)exp

is modelled

[ - k(T -

7”)]

according

profile

yields the last part of the

L

In

xexp[-kk(s--r.)J

r-0 r,+

exp(-

r&Z)

fort>?.

-

xf:xp

(~%h’r)

xO exp [w(q - %)I - Xk x0 - Xl

Z = k,aoplC4(l

W = kSao/[cj(l

(32)

’

(33)

- E)PJ

(34)

-

E)] = kZy,/x,.

(35)

NOTATION

J J*

kr

indicated in Fig. 3 with dashed line. The difference between the extraction curves calculated according to

(xO

Similarly, parameter Wis directly proportional to the solid-phase mass transfer coefficient and inversely proportional to the specific solvent flow rate:

I (29)

+

Parameter Z is directly proportional to- the solventphase mass transfer coefficient and inversely proportional to the specific solvent flow rate:

k

xk

(31) xk

-=&In Z

h H

(28) This concentration extraction curve

ZW

to

for r > 7”

for 4 3 4”

- 411 xk/xO}

xk)/y,z

q.=q,+kln

(27)

- z)]

(30)

where

(25)

The difference between both models decreases with decreasing the solid-phase mass transfer coefficient. The models are practically equal for kZ c 0. I. The effect of Yin the mass transfer rate term of the extended Lack’s model on the last part of extraction curve is demonstrated by comparison with a combined model. In the later model, mass transfer is calculated according to the Lack’s model until the time t = z,, when the solid-phase concentration is

e=xo-iz

11 exp CWq,

-

TO

The ratio of the amounts of extract calculated according to these models must be much closer to unity than the minimum Y: Y(Z,

4 < qnl

for qm < 4 c 4.

~,Cq-q~exp&.-Z)l x0 - $ln

OF SOLVENT

AMOUNT

ks K N

specific interfacial area, L- ’ mass of extract relative to N function defining the extraction retardation by diffusion from the inside of particles axial coordinate, L height of bed, L mass transfer rate, M L- 3 T - 1 normalized mass transfer rate defined by eq. (12) parameter of extended Lack’s model solvent-phase mass transfer coefficient, LT-’ solid-phase mass transfer coefficient, LT-’ initial mass of inaccessible solute, M mass of the solute-free solid phase, M

414

H. SovovA

initial mass of solute in the solid phase, M initial mass of easily accessible solute, M ( = Q/N) specific amount of solvent mass flow rate of solvent related to N,

0 P 4

4

n PG

T-’

mass of solvent, M solid-phase concentration defined by eq. W) time, T superficial velocity of solvent, L T - 1 parameter of slow-extraction period concentration related to solute-free solid phase solid-phase concentration at interfacial boundarv solvent-phase concentration related to solute-free solvent

Q

r

I

u W x

x+ Y

solubility normalized 1101

YJ

Y

concentration

Z

kmensionless

Z

tw parameter

Greek

m

coordinte

defined by eq.

defined by eq.

of fast extraction

period

letters void fraction density of solvent,

M L- 3

density of solid phase, M L-3 dimensionless Subscripts k L

time defined by eq. (10)

:

w

REFERENCES

Bnmner, G., 1984, Mass transfer from solid material in gas extraction. Ber. Bunsenyes. Phys. Chem. 88. 887-891. Brunner, G., Forster, A. and Gehrig, M., 1987, Verfahrenzur schonenden Extraktion von olsaaten. German Patent 3542932 Al.

Bunzenberger,G., Lack, E. and Marr, R., 1984, CO,-extraction: comparison olsuper- and subcriticalconditions. Ger.

Chem. Engng 7, 25-31. Cygnarowicz-Provost, M., O’Brien, D. J., Maxwell, R. J. and Hampson, J. W., 1992, Supercritical fluid extraction of fungal lipids using mixed solvents: experiment and modeling; J. Super&t. Fluids 5, 24-30. Eggers, R., Sievers, U. and Stein, W., 1985, High pressure extraction of oil seed. J. Am. Oil them. Sot. 62, 1222-1230. Friedrich, J. P.. List, G. R. and Heakin. A. J., 1982. Petroleum-free ex&acti& of oil from sovbeans with suwrcritical CO*. J. Am. CJil them. Sot. 59,*288-292. Lack, E. A., 1985, Kriterien zur Auslegung von Anlagen fiir die Hochdruckextraktion von Naturstoffen. Ph.D. thesis, TIJ Graz. Lee, A. K. K., Bullcy, N. R., Fattori, M. and Meisen, A., 1986, Modelling of supercritical carbon dioxide extraction of canola oilseed in fixed beds. J. Am. Oil them. Sot. 63, 921-925.

easily accessible solute Lack’s model

start of the extraction from the inside of particles end of the extraction of easily accessible solute model of Pekhov and Goncharenko solute inside the particles overall initial concentration coordinate of the boundary between fast and slow extraction

Pekhov, A. V. and Goncharenko, G. K., 1968, Ekstrakcija prjanogo rastitelnogo syrja szhizhennymi gazami. Maslozhirovaja promyshlennost’ 34(10), 2629.