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MEASUREMENT AND MODELLING OF MASS TRANSFER RATES OF

EXTRACTION OF USEFUL COMPONENTS FROM SELECTED HERBS ANDALGAE USING SUPERCRITICAL CARBON DIOXIDE AS SOLVENT

1995

Lars Schlieper


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Table of contents 2

3.1.4 Details of the used equipment ............................................................49

3.1.4.1 Pressure vessels used in the apparatus.................................49

3.1.4.2 Air driven pump...................................................................53

3.1.4.3 Bursting discs ......................................................................53

3.1.4.4 The thermocouples and pressure transducers ......................54

3.1.4.5 The valves and connecting piping .......................................54

3.1.4.6 The collectors ......................................................................54

3.2 General operating procedure.............................................................................55

3.2.1 Preliminary Procedures.......................................................................56

3.2.1.1 Charging the Extractor.........................................................56

3.2.1.2 Other steps taken before operation ......................................57

3.2.2 Start-up procedure ..............................................................................573.2.3 Shut down procedure..........................................................................58

4 Results and conclusions ...................................................................................................60

4.1 Results...............................................................................................................60

4.1.1 Introduction to the tables of results and diagrams..............................61

4.1.2 Tables of Results and their graphical representation..........................63

4.1.3 Components present in the extracts....................................................84

4.1.4 Supplementary observations made during the experiments ...............88

4.2 Discussion of the results for the algae Spirulina...............................................89

4.2.1. Discussing of the extraction of "oily" solute from the algae

Spirulina.............................................................................................89

4.2.2. Discussion of the extraction of water from the algae Spirulina .........90

4.3 Discussion of the results for the herbs Thymus zygis, Origanum virens

and Rosemarinus officinalis..............................................................................91

4.3.1 Discussion of the extraction of "oily" solute from the herbs..............91

4.3.2. Discussion of the water of extraction from the herbs Thyme,

Oregano and Rosemary. .....................................................................93

4.3.3 Overall mass balance obtained in the herb extraction

experiments ........................................................................................94

5. Experiments for the determination of bed and particle properties...................................95

5.1 Determination of the particle diameter .............................................................97

5.2 Determination of the bed voidage and particle density.....................................99

5.3 Determination of initial amount of water and solute ........................................100

5.3.1 Determination of initial content of "oily" solute in the samples ........100


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Index 4

Index

Parameter : Definition : Explanation : unit :

Ab db/4 bed cross section area m

ap interfacial area per unit volume m-1

C bulk fluid concentration kg/msolvent

C* solubility concentration of solute in solvent kg/msolvent

Cexit bed exit fluid concentration kg/msolvent

Cinlet bed inlet fluid concentration kg/msolvent

Co outlet hydraulic fluid pressure (air drive pump) bar

Cp fluid phase particle concentration kg/msolvent

Cp0 fluid phase particle initial concentration kg/msolvent

Cps fluid phase particle surface concentration kg/msolvent

C average bulk fluid concentration kg/msolventCp average fluid phase particle concentration kg/msolvent

D diffusion coefficient m/s

D12 binary diffusion coefficient m/s

Dax axial dispersion coefficient m/s

Dc

self diffusivity at the critical point m/s

db bed diameter m

De,De,De,De effective diffusivity m/s

DR compression ratio (air drive pump) -

F surface area factor -

Gr Grashof number -

j material flux kg/(m*s)

K equilibrium constant -

K volumetric partition coefficient -

ka absorption constant 1/s

kf external mass transfer coefficient m/s

kf mass transfer coefficient m/s

kp over all mass transfer coefficient m/s

L bed height m

msolute,0 initial mass solute present in the sample kg

msolute,extracted mass of solute extracted kg

msolute,present mass of extractable solute present in the sample kg

mparticle,solute,present mass of solute extracted form one particle kg

np number of particles in the bed -


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Index 5

P pressure bar

Pc critical pressure bar

Pai supply air drive pressure (air drive pump) bar

Pe Peclet number -

Pi inlet hydraulic fluid pressure (air drive pump) bar

Pro exhaust air pressure (air drive pump) bar

q solid phase particle concentration kg/msolid

q ration of the solid phase particle concentration -

q0 solid phase particle initial concentration kg/msolid

q average solid phase particle concentration kg/msolid

q0 q initial average solid phase particle concentration kg/msolidq

p solid phase particle concentration kg/mparticle

R particle radius m

r particle radius co-ordinate m

RR reaction - extraction rate kg/(m*s)

Re Reynolds number -

S mass transfer surface m

Sc Schmidt number -

Sh Sherwood number -

Ssphere

4R surface of a sphere m

T temperature K

Tc critical temperature K

Tr reduced temperature -

t time s

t time s

ti internal diffusion time s

Ui bUs interstitial velocity m/s

Us superficial velocity m/s

Vb L Ab bed volume m

Vbf fluid bed volume m

Vp particle volume m

Vpf fluid volume inside the particle m

Vsphere 4R/3 volume of a sphere m

V molar volume m/mol

w(t) yield of solute extracted -

x Cp/Cp0 dimensionless concentration -

z bed height co-ordinate m

z bed height co-ordinate m


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1. Introduction 7

1. Introduction

For several decades there has been considerable industrial and academic interest in the

fundamentals as well as the potential applications of supercritical fluids (SCF). They may be used, for

example, as extractive solvents, in the separation of multicomponent mixtures. The extraction takes

place at temperatures and pressures exceeding the critical values of the solvent. The separation

process is possible because of differences in the specific interactions between the various mixture

components (solute) and the supercritical fluid (solvent). Scientists and engineers have been aware of

this experimental fact for more then one hundred years [1]. Today there is very substantial interest in

the possibilities of using these solvents on a commercial scale more extensively than in the past.

Connected with this development compressed carbon dioxide is the solvent receiving most attention .

The interest is largely stimulated by increasing concern about the state of the environment and onincreasing demands of customers for the use of "natural" solvents in the food industry. These facts

have accelerated the rate of research in this field.

The main object of the work described in this thesis is to measure transfer rates of components

from natural products into supercritical carbon dioxide. The work involves the determination of mass

transfer data from packed beds of particulate solids consisting of the herbs Rosemary, Thyme and

Oregano as well as the algae Spirulina. The experimental data are compared with mathematical mass

transfer models using diffusion and film mass transfer coefficients.

This thesis is intended to make a contribution to the understanding of the mechanisms involved in

packed bed mass transfer into supercritical solvents, with a view to facilitating the design and

development of industrial scale processes.


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1. Introduction 8

1.1 General principles of supercritical fluid extraction

When the pressure is raised, a gas, such as carbon dioxide either liquefies or acquires a density

approaching that of the liquid. For example, at a temperatures up to 31.06 C (the critical temperature)

carbon dioxide can be liquefied by raising the pressure ( figure 1.1). At the critical point, the

properties of the vapour and liquid phase merge. At the critical point (CP), for a pure fluid :

eq. (1.1)

P

V

P

VT T

=

=

2

20 at P = Pcand T = Tc

The region around the critical point (say 1.4 > T/Tc > 0.9 and 5 > P/Pc>1.0) is called the near

critical region. In this region the pressure/volume isotherms shows that small changes in pressure canproduce quite large changes in density.

The physical properties of near critical fluids are intermediate between those of gases and liquids

at ambient conditions. Fluid density approaches that of a liquid at high pressures, whilst viscosity is

an order of magnitude greater than a gas, and self diffusion coefficients 10-100 times less than that of

a gas. In figure () the density of carbon dioxide as a function of pressure and temperature is

illustrated.

1.2 The solvent properties of supercritical carbon dioxide

The solvent power of compressed carbon dioxide depends on a number of factors. The density is

the property of major importance. Figure 1.1 shows lines of constant density drawn as a third

dimension on the Pressure/Temperature diagram of carbon dioxide. In the near-critical region, the

density of the solvent is comparatively strongly pressure and temperature dependent and any slight

changes in temperature or pressure lead to substantial changes in density. Since solvent power is a

function of density, these diagrams provide a qualitative representation of the solvent power of carbon

dioxide as a function of pressure and temperature. For example, in the region marked as being suitable

for near-critical extraction on figure 1.1, carbon dioxide has medium solvent power. A further

increase in pressure in this temperature range will lead to an increase in the density of carbon dioxide

which in effect will result in an improved solvent power. The largest density changes and hence the

widest range of solvent power is obtained in the supercritical area above the critical point. The area

around the critical point is interesting for process development because of the large density changes

which result from small isothermal pressure changes or small isobaric temperature changes.

In general, the density of carbon dioxide normally decreases with increase in temperature at

constant pressure and so does its solvent power. This factor tends to lead to a decrease in the


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1. Introduction 9

solubility of a given solute with isobaric increase in temperature. On the other hand, the vapour

pressure of the solute increases with temperature and this factor tends to increase its solubility.

Depending on the relative intensity of these competing effects the solubility will either increase or

decrease as the temperature is raised at constant pressure.

Since solubility increases with increase in density entail increasing solubility, extraction takes

place at high solvent density, and separation of solute from the SCF at low density.

Carbon dioxide is a low molecular weight non polar solvent, and is therefore a good solvent for

low molecular weight, low polarity compounds. The solubility's of components in this solvent

decrease with increasing molecular weight (i.e. increasing molecular size) and decreasing vapour

pressure. They decrease also with increasing polarity.

For example, high polar compounds such as the sugar or the proteins are virtually insoluble. On

the other hand low polarity compounds, such as essential oils, with a molecular weight of about 300

or less, dissolve well. The list below shows some commonly components, and the extent to which

they dissolve in supercritical carbon dioxide

highly soluble or completely miscible :

- Oxygenated organic compounds of low to medium molar masses such as ketones, esters, alcohols,

ethers and aldehydes

- Essential oils

slightly soluble (1wt% at 250bar, 50C) :

- Fatty acids and their glycerides

- Water

virtually insoluble :

- Fruit acids

- Sugars

- Amino acids

- Proteins

- Most inorganic salts


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1. Introduction 10

temperature ( oC )

-80 -60 -40 -20 0 20 40 60 80 100

press

ure

(bar)

0

50

100

150

200

250

300

350

400

450Tc: 31.06 oC

Melting line

Solid

Gas

Liquid

TP

CP Pc: 73.8 bar

1200 1100 1000 900

800

700

600

500

400

300

200

100

Sublimation line

Boiling

line

Supercritical

fluid extraction

Extraxtion with liquid CO2 at high pressur

Near critical

liquid extraction

density (g/dm3)

Figure 1.1 P.T. diagram of CO2with the density (kg/m) as third dimension


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1. Introduction 11

1.3 Advantages of SCF extraction over other separation processes

The motivation for the development of SCF technology as a viable separations technique

(specially using carbon dioxide as solvent) results from :

- The lower energy cost in SCF extraction in comparison with most other separation techniques, such

as distillation.

- The fact that virtually no solvent residue is left in the product.

- Because of the diffusivity and viscosity behaviour of SC solvents it is anticipated that they give

better penetration into pores and matrices, and hence encourage and more efficient extraction from

fixed beds than normal liquid solvents do.

- It is easily possible to recycle the solvent- The solvent does not react with the product or equipment.

- The extraction can take place at low temperature, which is important for heat sensitive components.

- The solvent is non flammable and nontoxic, which is very important for the food industry.

- In same cases (as in the decaffeination of coffee or the extraction of essential oils) carbon dioxide

has a very large capacity for the solute of interest. This minimises the ratio amount of solvent

required to process a given mass of raw material.

1.4 Compressed carbon dioxide extraction of useful compounds from natural

products.

A large body of experimental data for the solubility and extractability of natural products in

compressed carbon dioxide is available. Many commercial processes are well established like hops

extraction or decaffeinating coffee and tea. Existing and proposed extraction operations can be

generally classified into the following main application areas :

- extraction of edible oils, fats and waxes, with or without fractionation

- extraction of alkaloids from vegetable matter, particularly the decaffeination of coffee and tea

- extraction of flavours, spices and essential oils, particularly the extraction of hops

- purification of contaminated materials, such as production of pesticide free extracts or de-

alcoholisation of wines and beers

Useful ingredients such as try-gliceride, fatty-acid, oleic acid and vitamin E can be extracted from

natural oils from plants such as soybean oil, hop oil, corn oil, wheat germ oil, lemon oil and

sunflower.


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1. Introduction 12

Some of the application of dense carbon dioxide extraction on a commercial scale are shown in the

table below :

Firm Application Throughput Date of Start-

up

SKW Trotsberg AG

(Trotsberg, Germany)

tea decaffeination 6,000 t/y 1988

Kraft General Food

(Houston, US)

coffee decaffeination 200,000 t/y 1988

Philip Morris Cos. Inc.

(Chester, US)

removal of nicotine from

tobacco

US Hop Extraction Crop

(Yakima, US)

hop extraction 4,400-8,800 t/y 1990

Camilli Albert & Laloue

(Grass, US)

extraction of flavour

essences from plants

1989

Flavex GmbH

(Rehlingen, Germany)

extraction of aroma and

cosmetic components from

plant material

220 - 3,650 t/y

One of the first commercial process for the decaffeination of coffee using carbon dioxide as the

compressed solvent came into operation in 1979 and since then the separation technique offered by

near and supercritical fluid technology have taken a growing niche in the food processing and

pharmaceutical industries.

Many probable future application have not been commercialised yet and are the subject of present

research and publications. Useful essential oils for instance are contained in some plants and herbs

such as Rosemary, Thyme and Oregano (tables 4.13-4.16). Many are already extracted on acommercial scale [4] for use in perfumes and flavourings. However there is scope for future

development in the isolation of individual compounds. Rosemary for example contains the

antioxidants Rosmanol and Carnosol [2]. Other useful components such as fatty acids and -carotine

are found in algae [3]


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1. Introduction 13

1.5 Scope of this work

The importance of a good understanding of mass transfer rates in the design of commercial

equipment as well as the desirability of developing improved methods of extracting natural

components from plant material has been stressed in the previous section.

Part of the present studies consist in examining and quantifying mass transfer from packed beds of

plant material using supercritical carbon dioxide as the solvent.

In chapter 2 of this thesis mathematical mass transfer models are presented. This chapter includes also

a discussion of the extraction mechanism and the parameters which control the mass transfer process.

The equipment used for measuring mass transfer rates is described in chapter 3 and the results of

the extraction tests on the herbs Rosemary , Thyme and Oregano as well as on Spirulina algae aredescribed in chapter 4.

In the last part of the thesis the experimental data are compared with selected mass transfer models

using the effective diffusion coefficient as an adjusting parameter.


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2. Mass transfer in packed beds 14

2. Mass transfer in packed beds

The extraction of natural products from solid matrices in packed beds forms the basis of most

present-day commercial scale supercritical fluid extractions. Despite this fact a better understanding

of the basic phenomena which control the process of supercritical extraction is still required. There

have been many reports about measuring and modelling the rates of mass transfer from beds of

organic material. Most studies have been concentrated on the extract quality, and the influence of the

operating parameters pressure and temperature on the yield of extract, its quality and is solubility in

the solvent.

In the experiments carried out in this work and also in the mathematical models in the sections

below , we are concerned with a packed bed of porous particles, through which is passed a stream ofsolvent. The concentration of solute Cexit at the outlet of the bed of extractable material in general

varies with the time or the degree of extraction (figures 2.1 and 2.3). Factors which influence the

extraction process include the following :

- temperature and pressure

- solvent flow rate

- pure component properties of the solvent and the solute. These include density, viscosity and self

diffusivity.

- interactions between the solvent and the solute molecules. These determine the phase equilibrium of

the system and diffusions coefficients.

- properties of the individual particles and the bed. These properties include the particle size and

particle distribution, particle porosity and bed voidage.

These properties determine, among other things, the nature of the solute flow through the bed

(including the axial diffusivity) and the ratio of the effective diffusivity of the dissolved solute inside

the pores of particles.

To classify the extraction process, it is first necessary to have a look at typical forms for the

variation of bed exit concentration Cexit(t) fractional extraction with time w(t), which have been

published in the literature. Cexit(t) and w(t) are inter-related by the equation :

eq. (2.1) w t m t

m

m t

m

solute

solute

solute extracted

solute

( )( ) ( )

,

,

,

= =10 0


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eq. (2.2) m t C t

U t Adtsolute extracted

exit

s b

, ( )( )

( )=

where

msolute,extracted(t) mass of solute extracted from the sample at time t [kg]

msoltue,0 initial mass of solute in the sample [kg]

Generally, two types of variation of Cexit(t) and w(t) with time have been observed in practice. These

are shown in figure 2.1.

Figure 2.1 Different forms for the variation of bed outlet concentration and degree of extraction.

In the first type, a steady - state situation develops in the early stages of the extraction with a near

constant value of Cexit , followed by an unsteady state period in which the concentration decreases

with time. Examples of this type include the extraction or natural oils from crushed seed such as rape

seed and the extraction of hops.

There is no such initial period in the second type. An unsteady situation prevails throughout and

Cexitfalls progressively as extraction proceeds. Examples that fall into this category are the extraction

of caffeine from coffee beans and peanut oil from peanuts.


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2.1 The mathematics of mass transfer models

If existing mass transfer rate data are to be extended or scale up calculations have to be carried out

with regard to optimising the costs of the process, it is useful to obtain mathematical models of the

mass transfer process. A first subdivision of the models is possible on the basis of figure 2.1. The

models can be classified into :

- steady state models, these represent the first stage of the type I curves shown in figure 2.1/I.

and

- unsteady state models, these are required to represent the type II curves shown in figure 2.1/II and

also the last stage of the type I curves of figure 2.1/I.

For the further development of the models it is now necessary to identify the principal steps taking

place during the extraction process. The mechanism of the extraction of solutes from porous

structures into a near critical solvent can in general be described as taking place in five steps [5].

1. Transport solvent molecules from bulk solvent to the particle surface through the boundary layer

adjacent to the particle surface.

2. Transport solvent molecules from the particle surface to interior of particle by diffusion in fluid

filled pores

3. solubilisation or reaction of the solute with the solvent at the pore particle surface

4. Transport solvent molecules from interior of particle to particle surface by diffusion through

porous network

5. Transport solvent molecules from particle surface to bulk solvent through the stagnant film

An additional division particularly of the unsteady state models can be made by simplifying or

neglecting different steps of the extraction process given in points 1 to 5 above.

One simplification can be made when the solute concentration in the pores approaches a maximum

(equilibrium) value, so that the limits of solubility are approaches at the outlet from the extraction

vessel. The models which have been developed to represent the behaviour of this type of system relate

the rate of mass transfer to a concentration driving force (C-C*). C is the concentration of solute in

the bulk solvent at a given point in the bed and C* is the maximum (equilibrium) concentration

possible. Typical examples could be the extraction of vegetable oil from seeds like peanuts, rape or

sunflower seeds.

These models usually suppose plug flow through a cylindrical bed of particles. In this case the

concentration C of solvent stream is a function of time and bed height C(t,Z). Due to this fact these

models are called "plug flow models".


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Contrasting with this situation, there are cases where the solute to be extracted is present in the

solid in low amount so that its concentration on the fluid side is always negligible and far from the

equilibrium conditions. In such process it is valid to assume that the mass transfer process is identical

in each of the individual particles in the bed. This is the case in the extraction of essential oils from

vegetables like ginger and vanilla.

Because of the equality of all particles in a homogeneous bed, these models describe only the

variation of the concentration of one single particle. A common particle geometry used is a sphere.

For this reason these models are often called "single sphere models"

However, the division into these two groups of models (single sphere and plug flow models) is not

always a sharp one, as many combinations are possible.In the following sections the mathematical development of several of these models is described

and examples are given for which kind of extraction process they were used in previous experiments

of other scientists.


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2.2 General particle phase mass balance.

The transport of solute (at low concentration) in or out of the particle is assumed to take place by

diffusion through a network of pores as described in step 1 to 5. The diffusion is described in terms of

an effective pore diffusion coefficient, as the pore diameter considerably vary. The solute distribution

is assumed to be radially symmetric. Then the pore fluid solute mass balance can be written for an

annulus of the spherical particle (as shown in figure 2.2) as follows :

Figure 2.2 Porous particle

eq. (2.3) ( ) ( )4 4 4 42 2 2 2

r r

C

tr j r j RR r r p

p

rr r r

=

+( )

where j is given by [6] :

eq. (2.4) j DC

re f

p= ,

In these equations, which are applicable equally to extraction or adsorption operations ,

r distance of annulus from centre of particle [m]

p particle porosity [-]

Cp concentration of solute in pore fluid in annulus [kg/m]


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j flux of solute into interior of particle expressed

as mass transported by pore diffusion (and

sometimes by mass flow also) per unit time

perunit area [kg/s]

RR rate at which solute leaves the pore space and

attaches to the surrounding solid, expressed as

mass solute transported per unit time per unit

volume ofannulus [kg/(s*m)]

4 2

r r

C

tp

p

r

rate at which mass of solute enclosed in pore

space within the annulus increases with time. [kg/s]

( )4 2r jr

rate at which solute enters annulus at r by

transport along the pores [kg/s]

( )4 2r jr r+

rate at which solute enters annulus at r+r by

transport along the pores [kg/s]

RR r r( )4 2 rate at which solute leaves the surface of the

solid and enters the pore space within the

annulus [kg/s]

On dividing through by 4r, equation (2.3) becomes, in the limit as r0 :

eq. (2.5)

p

p

e

p

C

t r

r DC

r

rRR=

12

2

The intra particle mass transfer rate per unit volume of particle is given by :

eq. (2.6) RR q

tp=

where

q` concentration of solute in solid phase expressed

as mass of solute per unit mass of solid [kg/m]


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The rate at which material enters (or leaves) the solid particle would be expected to depend on the

relative concentration of solute in the pore fluid and the surrounding solid. This belief is embodied in

the so-called "solid phase mass balance equation" according to which

eq. (2.7)

q

tf C qp= ( , )

where

q concentration of solute in solid phase expressed

as mass of solute per unit volume of solid material [kg/m]

( q = q` p(1/(1-p) )

A common formulation for the solid phase balance of the particle is to regard the transport of

solute from the solid to the pore fluid as being a first order reaction with respect to q :

eq. (2.8)

=

q

tk

q

KCa p

To solve equation 2.5 with 2.6 it is necessary to specify initial and boundary conditions. Usually

the conditions specified in eq.(2.9) to (2.12) are need :

eq. (2.9) ( )

= D

C

rk C Ce

p

f ps

for r = R at all t

eq. (2.10)

C

r

p

= 0 for r = 0 and all t

eq. (2.11) C Cp p= 0 for t = 0, 0 r R

eq. (2.12) q q= 0 for t = 0, 0 r R

where

De effective diffusivity [m/s]

C concentration of solute in the bulk fluid phase

surrounding the particle [kg/m]

Cps concentration of solute in the pore space at the

surface of the particle [kg/m]

kf film mass transfer coefficient [m/s]


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R particle radius [m]

Average concentrations for the solid and interior fluid phases within the particles can be obtained

using the equations ;

eq. (2.13) qR

r q r dr

R

= 3

44

3

2

0

( )

eq. (2.14) CR

r C r dr p p

R

= 3

44

3

2

0

( )

whereq average of concentration q [kg/m]

Cp average of concentration Cp [kg/m]


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2.3 General fluid phase mass balance

After the above analysis of the extraction process of a single particle, it is now important to

formulate a description of the bed. The concentration C of solute in the fluid phase at height z in a bed

of particulate material depends on the rate of mass transfer from the particles at height z, the fluid

flow rate and extent of mixing.

Equation 2.15 (below) is obtained by taking a mass balance about a height element z of bed . In

obtaining the equation it is assumed that the solute concentration C and average velocity of the bulk

fluid are uniform across the bed at any given bed height and also that the superficial velocity (U s) and

fluid density are independent of z. The model developed in equation 2.15 is not a pure "plug flow"

model since it allows axial dispersion.

Figure 2.3 Bed of particles streamed by the solvent

eq. (2.15)

( ) ( ) ( )A z C

tU A C U A C A D

C

zA D

C

zS k C C b b s b z s b z z b ax

z

b ax

z z

f ps

= +

+

++


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where

Ab cross section area of the bed [m]

b bed voidage [-]

Dax axial dispersion coefficient [m/s]

S surface area of particles exposed to flowing

solvent in volume element Abz [m]

Cps solute concentration at the pore surface [kg/m]

A z C

tb b

rate at which mass of solute in the bulk fluid

within the volume element Abz increases with

time. [kg/s]

( )U A Cs b r rate at which solute would enter the volume

element at z under "plug flow" [kg/s]

( )U A Cs b r r+ rate at which solute would leaves the volume

element at z+z under "plug flow" [kg/s]

A D

C

zb ax

r

rate at which solute leaves the volume element

by axial dispersion. [kg/s]

A D C

zb ax

r r

+

rate at which solute enters the volume element

by axial dispersion. [kg/s]

( )S k C C f ps rate at which solute from the particles enters the

bulk solvent. [kg/s]

In the limity case, where z0, the fist and second pairs of terms on the right hand side of

equation 2.15 may be expressed as

+

U A C

zz

s b

z z

and D C

zz

ax

z z

2

2

+

respectively.

Equation 2.16 below is obtained by making these substitutions in equation 2.15, then dividing through

by Abz and since z tend to zero with dS/dz for S/z.

eq. (2.16) ( )

b s ax

b

f ps

C

tU

C

zD

C

z

dS

A dzk C C= + +

2

2


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For spherical particles the interfacial area per unit volume of bed a dS

A dzp

b

= can be written as :

eq. (2.17) aV

Sd

pb

sphere

sphereb

p

=

= ( ) ( )1 6 1

where

Ssphere surface area of a sphere [m

Vsphere volume of a sphere [m]

dp particle diameter of the sphere [m]

The initial conditions for these plug flow equation are :

eq. (2.16) C = 0 for z = 0

eq. (2.17)

C

z

= 0 for z = 0

eq. (2.18) C = 0 1 for t = 0 , 0 z L

Equation (2.16) and (2.5) are the final working equations for the chapters below. The equations are

for a single component which is extracted by a solute. An extension to multi-component mixtures can

be made by formulating corresponding equations for the other components and assuming parallel and

non interacting processes.

Another possibility is to use the exactly same number of equations as above but to substitute

parameters which are representative of the overall properties and components of the system.

1These initial condition assume, that no extraction take place, during "start-up" period as the extractor pressure israised to its operating value while the first solvent enters the extractor. If the residence time at the beginning of

process is short in relation to the extraction time, this assumption is justified.


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2.3.1 The axial dispersion coefficient

The axial dispersion coefficient Dax is a measure of the extent of back-mixing as the fluid traverses

the packed bed. The dispersion coefficient may take any value from zero to infinity, where zero

represents no mixing or plug flow and infinity represents perfect mixing. Dispersion coefficients are

generally expressed in the Peclet number Pe which is correlated as a function of the Reynolds number

Re and the Schmidt number Sc.

eq. (2.19) Pe f Sc= (Re, )

with

eq (2.20) Re=d Up s

eq. (2.21) ScD

=

12

eq. (2.22) Ped U

D

p

ax

=

In the above equations, and are the fluid density and viscosity respectively, other symbols are

as before.

2.3.2 The effective diffusivity

The effective diffusivity De describes the influence of the porous network on the diffusion inside

the particle. It depends on the form of the pore structure. This may consist, for example of

monodisperse pores, bidisperse (macro and micro) pores or there may be a random distribution of

pore size. The effective diffusivity is not generally easily predicted and because of this many authors

define a tortuosity factor e, which is fitted empirically to the data.

eq. (2.23) DD

e

p

e

=

12

The effective Diffusivity is used as an adjustable parameter which can be estimated if the pore

structure of the solid is known, or calculated by fitting the experimental results to the model

prediction.

Wakao and Smith [7] have suggested the following simple equation for estimating De:

eq. (2.24) D De p=2

12


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Goto et al. use a comparable definition for the extraction of lignin from wood chips [8] :

eq. (2.25) D Dep

p

=

212

2.3.3 Film mass transfer coefficients

The resistance to mass transfer of solute from the surface of a particle in a packed bed of particles

to the fluid phase is described in terms of an external film mass transfer coefficient. Mass transfer of

solute from the particle surface takes place by diffusion and / or natural convection. The concentrationof the solute in the fluid at the particle surface is Cps. (When the particle consists only of soluble

material the concentration at the particle surface is assumed to be the equilibrium concentration).

The solute concentration C in the film of fluid immediately adjacent to the particle, decreases with

distance normal to the surface until the bulk or average concentration in the fluid is reached. If it is

assumed that the mass transfer coefficient is not a function of concentration or bed co-ordinates, the

local mass transfer coefficient becomes the average mass transfer coefficient kf, which is used in

equation (2.16).

Many theories exist for predicting the film transfer coefficient i.e. "Penetration Theory" or

"Boundary Layer Theory"[9]. In practice the coefficient is usually predicted from correlation's using

dimensionless numbers, which have been developed from mass transfer studies using gases and

liquids at near ambient conditions. These correlation's are in general of the form :

eq. (2.26) Sh f Sc Gr b= (Re, , , )

with

eq. (2.27) Shk d

D

f p=12

For forced convection is the influence of the Grashof number Gr, which is only significant under

condition of free and natural condition negligible. The prediction of kf at near-critical conditions

requires an accurate value of the diffusion coefficient in the film surrounding the particle. In case of a

binary mixture the binary diffusion coefficient D12 , at the same temperature and pressure as kf, is

used.


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A number of dimensionless correlation's have been published in the literature covering wide

ranges of Re, Sc and Sh. Only some two will be mentioned here. These are given by equations (2.28)

and (2.29) below.

eq. (2.28) Sh Sc= 0 82 0 661

3. ( Re ).

for 3 < Sc < 11 and 1 < Re < 70

Equation (2.28) was derived empirically from determinations of mass transfer rates in packed beds

was found by Catchpole et al. They used benzonic acid as solute and near critical carbon dioxide as

solvent [10,36].

eq. (2.29) Sh Sc= 0 38 0 831

3. (Re ).

Equation (2.29) was derived empirically from measurements of mass transfer rates made by Tan et

al. using the -naphthol/carbon dioxide system. The bulk diffusivity under the conditions studied was

about 1*10-6m/s [11].

2.4 Simplifications and solutions of the fluid mass balance equation

A rigorous analytical solution of pair of differential equations (2.5) and (2.16) is not possible, and

their solution by numerical methods is difficult. Consequently many simplifications and

approximations are employed in the models found in the literature. As mentioned in section 2.1 one

group of models called "single sphere models" consider primarily the mass balance equation of the

particle (eq.(2.5)) while the other group the "plug flow models" examine equation (2.16) in more

details. This last group of models is now explained.


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2.5 Plug flow and dispersed flow models

In order to use the fluid phase mass balance equation (2.16), an assumption concerning Cps must

be made to eliminate the particle mass balance equation. Different possibilities are conceivable and

should be mentioned .

The disadvantage of this approach is that all information about the interior particle processes is

lost. One possible route is to write the overall particle mass balance in the simplified form [12]:

eq. (2.30) ( ) ( )1 =

b

p

f p ps

q

tk a C C

Equation (2.30) is a "steady state" result only exactly for

Cp/

t = 0. q

p

is the mass of solute in

solid phase per unit volume of particle.

Glueckauf's [13] linear driving force approximation is proposed for the change in average particle

phase concentration with time :

eq. (2.31) ( ) ( )115

2 =

b

p eps

q

t

D

RC C

*

Where C*is the equilibrium concentration of the solute in the solvent. Equation (2.30) and (2.31)

can be combined and lead to :

eq. (2.32) ( ) ( )1 =

b

p

p p

q

tk a C C

*

eq. (2.33) kk

R k

D

p

f

f

e

=

+

1

5

The overall mass transfer coefficient kp is here a combination of the intra particle diffusion and the

external mass transfer effects and can be used in the fluid mass balance equation instead of kf. A very

similar formulation was suggested from Tomida at al. [14] and used by Goto et al. [15,16]. By

definition kp(C*-C) = kf(CPS-C) a new simplificated fluid phase mass balance equation (eq. 2.16) can

be rewritten as :

eq. (2.33) ( )

C

t

U C

z

D C

z

a kC C

iax

b

p p

b

= + + 2

2

*


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A common assumption, which is made to solve equation (2.32) and (2.33), is that C* is

proportional to q p. An alternative assumption, especially for the steady state models, is to consider

that C* stays at a constant level.

A similar formulation can be obtained by assuming that the concentration of the solute in the fluid

at the particle surface Cps (equation (2.16)) is equal to the solubility concentration C* of the solute in

the solvent. This would be exactly true, for example for a non porous particle which consists only of

soluble material.

eq. (2.34) ( )

C

tU

C

z

D C

z

a kC Ci

ax

b

p f

b

= + + 2

2

*

The only difference between these two equations is in the definition of the mass transfer

coefficient. However, this small difference can be important. Both equations are used in the literature

to develop mass transfer models.

2.5.1 Steady state models

When steady state extraction occurs the fluid phase concentration at a given bed height does not

change with time. This is predicted to occur when variations in concentration within the particles can

be neglected, so that the surface concentration Cps of solute stays at a constant level. Physically the

solute concentration in the particles would be anticipated to be evenly distributed for sufficiently

small particles and the particle phase concentration of solute is high and the solubility in the fluid

phase is low. This ensures that the particle surface is not rapidly depleted of solute.

Solid matrices for which steady state extraction behaviour has been observed over the initial

period of extraction (figure 2.1/I) include ground oil seeds [17,37,38,39] , spices [18] and ground

seeds containing alkaloids

2.5.1.1 The steady state dispersed flow model

This model represents an easy solution of equation (2.34) and often was used to back calculate the

mass transfer coefficient out of experimental results. Catchpole [19] for instance used it for the

determination of dimensionless relationship of equation (2.28).

At steady state

Ct

= 0 and with kf, ap, Dax, C* constant up the bed, equation (2.34) becomes an

ordinary second order differential equation of the form :


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eq. (2.42) q qk a C t

ef p

b

k a z

U

f p

b i=

01

*

( )

The yield of extracted solute w(t) is the same as in equation (2.38). This equation was used by

Chami [20] to simulate the rate of extraction from ground rape seed oil. The extraction of oil from

ground rape seed shows a concentration profile as it is presented in figure 2.1/I. Respect this fact

equation (2.40) and (2.38) are good depiction for the first constant period.

Chami established a surface area factor F as it was used by many other workers to fit the data to

the experimental results. The argumentation is that not all parts of the surface of the particle are

exposed to mass transfer. This effect can be represented by defining the effective surface area per unit

volume :

eq. (2.43) aa

Fe

p=

By using ae instead of ap (geometrical surface area) Chami calculated a surface area factor F =

0.02 ( page 156 ) for his configuration.

An other way to adapt the measured data to model equation (2.40) should be suggested here.

Instead of changing ap the model can be enlarged to consider also the internal mass transfer processes

of the particle. Therefore bulk fluid mass balance equation (2.33) is simplified in the same way as it

was done with equation (2.34). This leads to a nearly same formulation of equation (2.42) with the

difference that kpis used. Than it is possible to interpretate the Chami's results as particles which are

influence by their porous structure. As it was mentioned in chapter 2.4 the over all mass transfer kp

contain the effective diffusivity Deand can be used as the adjustment parameter or can be calculated

out of equation (2.23) - (2.25).


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2.5.2 Unsteady state plug flow models

Considering the fact that the steady state models just describe the first steady phase of the

concentration profile in figure 2.1/I , new models must be developed to describe the second unsteady

state. To reach this aim the back mixing term in bulk fluid mass balance equation (2.33) is neglected.

eq. (2.44) ( )

C

tU

C

z

a kC Ci

p p

b

= + *

2.5.2.1 Unsteady plug flow model

Catchpole [12] shows, together with equation (2.44), two different possible solution for this

system of differential equation. It is assumed that solubility concentration C*is constant and does not

change with time ( see introduction of chapter 2.4). In this model the rate of mass transfer is then

limited by the equilibrium solubility.

Unsteady plug flow model I

To obtain the final working equations, it was assumed that the solids concentration profile with

bed height z could be approximated by step change, with q= 0 as the prior the step and q q= 0as the

following step. Solving equation (2.44) and (2.32) according to this assumption gives :

eq. (2.45) C z C e B z Ze( )

*= 1

eq. (2.46) Z LB

e e G t eB L G B L= + +

11ln

eq. (2.47) w t Z

L

e( )=

with

Bk a

U

p p

b i

=

G C U

q

i b

b

=

*

( )

0 1


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Unsteady plug flow model II

No assumptions were made regarding to the solids concentration profile. The fluid phase

concentration is again given by equation (2.44) and (2.32), but with Ze and w(t) given by equation

(2.48) to (2.49).

eq. (2.48) Z G tG B

e= 1

for t (G B)-1

Ze= 0 for t (G B)-1

eq. (2.49) w t GL

tG B

e B L Ze( )= 1 for 0


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eq. (2.50)

C

z

C

L=

Making these substitutions, the fluid phase mass balance over an element of extractor height dzcan be written as :

eq. (2.51)

b

sb

C

t

U C

L

q

t= ( )1

The particle mass balance (eq. 2.30) now represents internal mass transfer only. (external mass

transfer is neglected) :

eq. (2.52)

q

t

a kq q

p f

b

s=

( )

( )1

To solve equations 2.51 and 2.52 the phase equilibrium condition (eq. 2.53) is required :

eq. (2.53) C K qs=

K' is the volumetric partition coefficient of the extract between solid and fluid phase at

equilibrium. The term k'fap/(1-b) in equation (2.52) is constant and has the dimension of reciprocaltime. Therefore, it can be represented in term of a characteristic time , 1/t i, where ti is the internal

diffusion time. Using the initial condition :

eq. (2.54) q q= 0 for t = 0

and neglecting the accumulation of the extract in the fluid phase in equation (2.51) (

C

t= 0 ) , the

following solution can be obtained :

eq. (2.55) q t q e

K t

L

UK tb

si

( )

( )

=

+

0

1

When diffusion and phase equilibrium influence the extraction rate, both phenomena have to be

considered in equation (2.55). If internal diffusion is the only limiting factor for mass transfer, the

term K' ti is some orders of magnitude higher than (1-) L/Us. and the latter term can be neglected

giving :


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eq. (2.56) q t q e

t

ti( ) =

0

with the normalised extraction yield :

eq. (2.57) w tq q

q( ) =

0

0

Villermaux [22] showed the equivalence between the diffusion time ti and the effective diffusion

coefficient Defor different particle geometries. He proposed the relationship :

eq. (2.58) tV

A Di

p

p e=

2

where

Vp particle volume [m]

Ap particle surface area [m]

correction parameter [-]

In the case of spherical particles of radius R, equation 2.58 becomes :

eq. (2.59) tD

Ri

e

=

3

5 3

2

Reverchon et al. [21] use this model to represent the extraction of essential oils from basil. They

use equations (2.56) and (2.57) to model the experimental data. In this case K ranges from 0.13 to

0.24 for a solvent density equal to 622 kg/m. Bastos et al. [23] used the same functions to simulate

the extraction of essential oils and waxes from Basil, Marjoram and Rosemary.

This model belongs to a group of equations which are good for the simulation of extraction yields

of the type shown in figure 2.1/II. A group of models which also describe this kind of extraction yield

are the "single sphere models and which are described in the chapter below.


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2.6 Single sphere models

When intraparticle or internal diffusion control the mass transfer process, it is opportune to start

modelling by considering mass transfer between a single particle and the supercritical solvent and

then extend the results to the whole bed. Although typical vegetable particles do not all conform to

these assumptions, it seems to be a good start to model the mass transfer. Many other models, for a

spherical particles were developed under different assumptions.

M. Goto et al. [24] developed a model for isothermal, irreversible chemical reactions in particles

when both internal and external mass transfer resistance are present.

For the case where the reactant is a solid (or a non diffusing adsorbed species on the solid) and the

reaction products diffuse out of the particle ( e.g. during an extraction or desorption process), heformulated a mass balance for the fluid phase inside the pores of the particle, which is identical to

equation (2.5). He assumed a first-order reaction RR = Krq , for the nondiffusing reactant and solved

the differential equation system analytically.

He was able to show that the hypothesis of a parabolic concentration profile inside the particle, is a

good approximation to the exact solution.

2.6.1 Single Sphere Model I

Often the information about the kinetics of the individual processes leading to component

solubilization inside the particle is missing. In this case a solution of the problem is possible, if it is

assumed that the solute is present in the solid in low amounts and the solubility in the solvent is high.

Under these conditions all the solute can be dissolved in the fluid filled particle pores, and the kinetics

of the process is determined by the effective diffusion coefficient, which is calculated by fitting the

model to the experimental data.

Reverchon et al. [25] and Bastos et al [26] take this model for the simulation of the extraction of

essential oil and waxes from herbs such as basil, marjoram and rosemary using carbon dioxide as the

solvent.

With the above assumptions the material balance in spherical co-ordinates across an internal

particle surface of radius r, is given by Fick's first law, which is for constant density and diffusivity in

the isotropic material :

eq. (2.60) j t C Dr

r x

rpo e

( )=

12

2

where


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Cp0 initial concentration of solute in the particle

pore fluid [kg/m]

D`e effective diffusivity [m/s]

x ratio of actual and initial particle pore fluid

concentration [-]

The material flux j(t) must be equal to the transport equation on the external surface of the particle.

eq. (2.61) ( )j t k C Cf ps( )=

From equation (2.60) and the boundary condition (2.61), applying the Fourier transforms and the

heat-mass transfer analogy, the following general Solution is obtained [27] 4:

eq. (2.62)m t

AR C C e

particle solute extracted

p

pok k k

k k k

D tR

k

ek

, , ( )( )

(sin cos )

( sin )( )=

=

42 2

12

3

0

2

kis obtained by the implicit function :

eq. (2.63) k k f

e

k R

Dcot =

1

where

mparticle,solute,extracted is the extracted mass of solute form one

particle after the time t. [kg]

Equation (2.62) is a general solution of equation (2.60). The terms k depend on the boundary

conditions as given by equation (2.63). Relationship (2.62), coupled to the particular solution obtained

from eq. (2.63), enables the degree of solute extraction from a single particle to be calculated as

function of extraction time.

Moreover, it is also possible to evaluate the concentration profile of the extractable material along

the particle radius at different extraction times. For this purpose the differential material balance in a

particle can be written in equation (2.5) but without the reaction term :

4If a true diffusion coefficient is instead the analogy is only correct for a homogeneous sphere (particle) which

contains no inclusions. In this case the solution is only correct for p= 1. However the use of De is supposed tosmooth out the structural effects.


39/131


eq. (2.64 )

C

tD

r

rC

r

r

p

e

p

=

12

2

The solution of equation (2.64) with the boundary condition (2.9)-(2.11) is [27]:

eq. (2.65)C C

C Ce

r

Rr

R

p

p

k k k

k k

D tR

k

kk

ek

=

=

0 0

42 2

2

sin cos

sin

sin'

The next stage in modelling the extraction process is to extend the results obtained above, for

extraction from one particle to extraction from the whole bed. This can be done on the assumption

that all the particles in the bed behave in the same way and the concentration C does not change with

the bed co-ordinate z. The number of particles that constitute the bed np is given by:

eq. (2.66) n V

dp

b b

p

= 6 1

3

( )

On the hypothesis that all particles in the bed have the same extraction stage during the whole

process, the total amount of product extracted is (from equation (2.62)) :

eq. (2.67)

m t R C C esolute extracted pk k k

k k k

D tR

k

ek

, ( ) ( )(sin cos )

( sin )( )=

=

42 2

10

2

3

0

2

It is now possible to model the degree of extraction using the definition of the yield w(t) given by

equation (2.1). This result can be simplified by assuming that the bulk fluid concentration is zero ( C

= 0 ), which should be true for a high solvent flow rate or a high solubility in the solvent if the initial

concentration is small. Under these conditions the initial concentration Cp0can be eliminated and the

following working equations are then obtained 5:

eq. (2.68) w tm t

V C

solute extracted

b b po

( )( )

( )

,=1

5It should be remembered that equation (2.68) and (2.69) are, like (2.62) only strictly correct for a homogeneous

sphere.


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eq. (2.69) w t ek k k

k k k

D tR

k

ek

( )(sin cos )

( sin )( )

'

=

=

122 2

12

3

0

2

2.6.2 Single Sphere model II

An alternative way of solving the diffusion equation (2.64) or (2.60) is to neglect the external mass

transfer process. As in model I, the particles are regarded as solid spheres of radius R containing a

uniform initial concentration of dissolved material and immersed in a fluid in which all particles

behave in the same way. However, in model II, the surface mass transfer term does not appear and is

replaced by the boundary condition of a constant surface concentration.

eq. (2.70) C Cp ps= for r = R

The other boundary and initial conditions are equal to those given by equation (2.10) and (2.11).

The problem is again mathematically similar to that of the immersion of a hot sphere into a cold fluid

, for which the solutions in terms of diffusion are given by Crank [29] and Wong [28]:

eq. (2.71)C C

C C

R

r n

n r

Re

p p

ps p

n

n

D n t

R

e

= +

=

0

0 1

12 1

2 2

2

( )sin

The total amount of diffusing substance leaving the sphere can be written in the dimensonless form :

eq. (2.72) w tn

en

D n t

R

e

( ) = =

1 6 12 21

2 2

2

Equation (2.72) was used by Reverchon et al. [21] for the extraction of essential oils from basil

leaves; by Barcos et al. [23] for the extraction of essential oil and waxes from Basil, Marjoram and

Rosemary; by Bartle et al. [30] for extracting flavour and fragrance compounds from dried ground

rosemary and by Spiro et al. [31] for the extraction of 6-gingerol from ground sieved jamaican ginger

rhizome. All the above workers used carbon dioxide as the solvent.

However, it is important to remember that the single sphere models do not distinguish so exact

between the fluid phase and the solid phase inside the particle. Maybe to eliminate the problem of the

unknown particle voidage p. They define a particle concentration sometime as a solid phase

concentration or as a over all particle concentration. The solution of both definition is the same(equation (2.72)) because of the constant surface concentration which allowed to exclude the phase


41/131


equilibrium ship. Therefore it is also possible to use this working equation, for a higher solute

concentration than the equilibrium concentration.

The solution (2.72) is a sum of exponential decays, and at long time the later (more rapidly

decaying) terms will decrease in importance and the first exponential term (n = 1) will become

dominate. A plot of ln(1-w(t)) vs. time or carbon dioxide passed, therefore becomes linear at longer

time [30,31].

eq. (2.73) w t e

D t

R

e

( ) =

16

2

2

2

This solution looks nearly the same as the working equation (2.56),(2.57). However, this is notsurprising because the assumptions which are made are nearly the same.

2.6.3 Brief review of other solutions to the particle and bulk fluid mass balance

equations

Many other models, based on the particle and bulk fluid mass balance equations, but in which a

variety of different approximations are employed in the evaluation of the terms are given in the

literature. A short overall view of some of these models is given below.

As mentioned above Goto et al. showed that a parabolic concentration profile in the particle is a

good approximation for the diffusion process inside the particle. Moreover he assumed that axial

dispersion in the bed of particles was negligible, and that extraction from all particles in the bed took

place at the same rate so that the average bulk fluid concentration Cwas given by :

eq. (2.74) C C t z L= =( , )2

With these assumption this assumption the particle fluid phase balance (2.5) and the bulk fluid phase

equation (2.16) reduce to [32] :

eq. (2.75) ( )dC

dt

U

Lk a C C s p p p=

eq. (2.76) ( )pp p

p

dC

dt

k

RC C R=

3


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In their work on the extraction of lignin derivatives from wood chips using t-butyl alcohol as the

near critical solvent, Goto et al. found the rate of mass transfer to be limited by the reaction rate.

An analytical solution of equation (2.75) and (2.76) is feasible since the rate constant does not

change with time.

To describe the extraction of oil from larger particles such as peanuts Catchpole et al. [33]

developed a shrinking core model. It was assumed that the solute (oil) was uniformly distributed

throughout the particle (peanut), and that the particle has no affinity for the oil. The extraction process

in thus analogous to irreversible desorption form a porous adsorbent, where the pores are initially

completely filled with solute. The process resembles the extraction of solute from a capillary. Assolute is extracted, a front between the solute and solvent-rich phases recedes down each pore towards

the centre of the particle. The solute is thus concentrated in a core of (diminishing) radius r c

It was assumed that the solute has a low solubility in the solvent system of interest and that the

extracted phase will normally be less dense than the solute- rich phase. virtually all the solute

contained within the particles will be present in the solute-rich phase, i.e. within the core. Outside the

core therefore q = 0.

The supercritical fluid extraction of Monocrotaline from Carotalaria Spectabilis using carbon

dioxide as the solvent was described be Schaeffer et al. [34]. He used the bulk fluid mass balance

(2.16) and the average particle balance (2.30) together with an equilibrium relationship and solved the

problem numerically.

A very similar suggestion was made by Espuivel [35]. She used the same system of differential

equations in analysing her data for the extraction of olive oil from olive oil husks using carbon

dioxide as the solvent. Her model was fitted to the experimental data using the mass transfer

coefficient and the equilibrium constant as adjusting parameters.


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3. The mass transfer experiments 42

3. The mass transfer experiments

3.1 Description of the experiment used

The apparatus was partly rebuilt for this work. Some parts of it had previously been used by

another student. It is suitable for studying the extraction of solid materials over a range of flow rates.

A block diagram of the apparatus is shown in figure 3.1.

Figure 3.1 Subdivision of the experiment layout

The apparatus consists essentially of solvent delivery, extraction and phase separation sections.

Carbon dioxide is the solvent in the present work. It is contacted with the bed of solid particles under

test in the extraction section and the amount of solute dissolved in it during the operation is

determined in the phase separation section. The carbon dioxide entering the extraction section is

brought to the pressure and temperature, at which the extraction is to be carried out, in the solvent

delivery section (figure 3.2). In this section the desired pressure is reached by compressing liquid

carbon dioxide from the supply cylinders using a compressed air driven pump AP1, fine control being

achieved by using a back pressure regulator BPR and compressed air used to activate the pump. The

required temperature is reached by passing the compressed carbon dioxide stream through a coil in a

temperature-controlled water bath H3. On leaving this coil the stream enters the pressure vessel used


44/131


for the extraction. This vessel and the piping leading in and out of it are contained in an temperature

controlled air bath. If consists of a stainless steel cylinder, into which a stainless steel holder can be

inserted. This holder in turn contains the glass sample holder into which the particles to be extracted

are charged.

When carrying out extraction tests of solid material, carbon dioxide from the solvent delivery

section is fed continually to the foot of the bed of particles, passes up through the bed and exits at the

top bearing solute material from the bed in solution (figure 3.3 ). Then the carbon dioxide stream

passes to the separation section (figure 3.4) where the pressure is reduced and the solute is

precipitated in a series of glass collector vessels CV. The amount of solute precipitated by a known

quantity of solvent is measured.

3.1.1 Details of the solvent delivery section

This section is designed for supplying carbon dioxide at the desired temperature and pressure to

the extraction section. It is shown in figure 3.2. Carbon dioxide in liquid form is withdrawn from

supply cylinders with "dip tubes" (Distillers MG or British Oxygen) and passes through a 15particle

removal filter F1 (Nupro, SF-4FT-15), and then through a bed of activated carbon CF to remove

moisture. The dry carbon dioxide stream then passes through a coil placed in the refrigerated bath H1,

where its temperature is reduced to between 0 and 5 C. After this, the stream splits up, because it is

used as the solvent delivery for several experiments (A,B etc.). In each case the pre-cooled carbon

dioxide is ducted to point close to the relevant equipment when it is cooled again in cooler H2 to

compensate for any worming which may have taken place over. the transport distance. It then passes

through filter F2 and enters the air-driven pump AP1 (Haskel, MCP-110) which is designed to

compress liquid of low compressibility. (To avoid cavitation in the pump it is necessary to reduce the

temperature of the carbon dioxide stream entering it to a value well below the boiling temperature at

the inlet pressure). The pump is operated by compressed air, which is manually regulated to control

the pump stroke rate, and hence the flow rate of carbon dioxide. Details of the pump are given in

section 3.1.4.2 below.

Carbon dioxide, compressed by the pump to the desired experimental pressure, then passes

through heat exchanger H3 en-route to the extraction section. This heat exchanger simply consists of a

coil immersed in a temperature controlled water bath (Grant, BE 15) maintained at a temperature

slightly (0.2C) above the extraction temperature . The water bath temperature is adjusted so that the

carbon dioxide stream leaving the water bath is brought to the desired extraction temperature. A

portion of the flow is recycled back to the cooling bath inlet via the back pressure regulator BPR (Go

Products, UP 66). The back pressure regulator acts as a relief valve which opens at just above the

extraction pressure, and closes again at the extraction pressure. The regulator operates by balancing


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the force of a partially compressed spring against the system pressure. When the pressure exceeds the

force supplied by the spring, the stem of the relief valve lifts. As the valve has a large flow coefficient

the pressure is quickly relieved, and the valve stem then reseals. The pressure can be controlled to

within 0.5 bar using this unit. The pump stroke rate is adjusted to give a carbon dioxide flow from the

pump in excess of that required further downstream, the excess being recycled via the regulator. This

procedure enables the pressure at the pump outlet to be controlled at a level which is independent of

the flow rate in the downstream parts of the apparatus. The pump outlet is protected from over

pressure by a bursting disc assembly.

Figure 3.2 Solvent delivery section


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3.1.2 Details of extraction section

The whole extraction section and parts of the solvent delivery section were set up behind a 6mm

thick steel sheet. Its purpose was to provide protection from flying debris arising from minor

explosions resulting, for example, from failure of faulty couplings. The extractor vessel was placed in

a shatter-proof "perspex" cabin, 168cm high x 92cm wide x 92cm broad.

A fan heater FH and fan MX were installed inside this cabin to heat and circulate the air within it.

The air temperature was monitored by a sensor which actuated a temperature control unit located

outside the cabin. By setting the required temperature on the control unit, the temperature could be

controlled conveniently. When the air temperature reaches the set value, the heater is automatically

turned off while the fan keeps working to ensure that the temperature within the cabin remains

approximately uniform.On entering the extraction section, the carbon dioxide stream first passes through the check valve

CV (Autoclave Engineers, TWO 4400) and 15 m particle filter F3 (Swagelok, AS-4IF-15) before

passing through the extraction vessel E1. This vessel is shown in figure 3.5 . It is provided with an

water jacket through which water at the required extraction temperature circulates. It contains the

sample holder into which a bed of the material to be extracted is charged. Mass transfer occurs as the

carbon dioxide stream passes through the bed of solid particles. The extractable components enter the

carbon dioxide stream and are carried out of this section into the separation section.

Figure 3.3 Extraction section


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3.1.3 Details of the separation section

The separation section (figure 3.4) enabled quantitative recovery to be made of solute dissolved in

the carbon dioxide leaving the extraction section. In this section, solute is precipitated from the carbon

dioxide stream by pressure-reduction and is collected in collection vessels at different temperature

and pressure, from which it is recovered and weighed. The solute-free carbon dioxide leaving these

collectors is vented from the laboratory via a flow totalyser FT1 (Alexander Wright) and a flow meter

FT2 (Rotameter Mfg. Co., Size 7X).

Figure 3.4 Separation section

Pressure reduction of the carbon dioxide stream, initially at the extraction pressure, is achieved by

passing it through pressure-reducing micro-metering valve NV1. This valve provides an intermediate

pressure reduction stage. Because the reduction in pressure is accompanied by pronounced cooling,

valve NV1 is enclosed by an electric heating tape H5, to warm the valve and the piping leading into

the "middle pressure" collector. The temperature of the heating tape H5 is adjusted to be high enough

to ensure that dry ice formation (and hence unsteady flow) is avoided. Temperature control is


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provided by a power regulator (Electrothermal MC229). The product deposited after the first

expansion is collected in a glass ampoule placed in a stainless steel pressure vessel ("middle pressure"

collector) maintained at 8 bar pressure. The carbon dioxide stream leaving this collector, now

containing the most volatile parts of the extract, passes through the heater H4 before undergoing a

further pressure decrease to atmospheric across micro-metering valve NV2. The mixture of carbon

dioxide and some solute, now enters a series of two glass collection vessels CV2 and CV3. Collector

CV2 is maintained at ambient temperature. Collectors CV3 is housed in a Dewar vessel containing a

solid carbon dioxide/acetone mixture at a nominal temperature of about -80 C. The stream leaving

valve NV2 is at about ambient temperature and ambient pressure. Solute components of low volatility

are precipitated collected in vessel CV1 and any traces still remaining collect in CV2.

The downstream collector CV3, is used to collect the more volatile components which condense

only at low temperature. These vessels will be described in detail in section 3.1.4.1 . After passingthrough these vessels, the carbon dioxide stream, now solute-free, passes through the flow totalyser

FT1 and flow meter FT2 and is then vented from the laboratory. The middle pressure collector CV1

and the glass collection vessels CV2 and CV3 are housed inside a perspex cabinet as a safety

precaution in case of breakage. Over-pressure protection is supplied by relief valve RV1 and by the

spring loaded tops to the glass vessels.

Some precipitation of solute of low volatility inevitably occurred in the tubing following NV1

prior to the collection vessel CV1. To obtain complete recovery of solute, the pipe work was washed

with suitable organic solvent stored in VC1. This was recovered and removed by evaporation. During

all the experiments described here, no solute was collected in the vessel CV2.


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3.1.4 Details of the used equipment

3.1.4.1 Pressure vessels used in the apparatus

The 500ml 0-ring closure pressure vessel AS 883 was supplied by Autoclave Engineers. It is made

of stainless steel 316 and is designed to operate under a maximum allowable working pressure (MAP)

of 450 bar. It is fixed to an iron frame and is usually not moved during the experimental period. The

vessel has a temperature controlled water jacket for the regulation of the extraction temperature. To

make the operation easy, the sample to be extracted, is charged into the glass sample holder shown in

figure 3.7 . This was placed inside a stainless steel holder, which was lowered into the extraction

vessel itself. These configuration of holders is then lowered into the appropriate extraction vessel.

The dimensions and locations of the inlet and outlet ports to the extraction vessel is shown in figure3.5 . One port is located in the bottom of the vessel, and the other three in the vessel wall near the top

of the vessel. These ports are tapped with 1/4" N.P.T. thread so that connecting piping can be screwed

into them. Two of the ports on the vessel are used to insert a pressure transducer and a thermocouple

respectively directly into the vessel. The vessel is sealed by inserting the cover with the 0-ring on it

into the vessel. Then a main nut is screwed down by inserting a rod into the hole in it. This rod is

gently tapped by hand until metal to metal contact is made. The vessel is now closed and ready for

use.

The stainless steel holder (figure 3.6) feature a removable threaded top into which screw holes

have been drilled to facilitate removal from the vessel. An 0-ring is placed between the top and main

body, to prevent carbon dioxide bypassing the sample. All 0-rings were of VITON. O-rings containing

plasticisers such as "BUNA-N" or "Nitrile" should be avoided because they are extractable.

The glass sample holder (figure 3.7) is a cylindrical reservoir with a conical movable top, equipped

with a hole for the fluid outlet and a tube at the bottom for the inlet stream. This tube is connected

with the stainless steel holder using a piece of hose as a seal. The glass sample holder has glass

sintered filters at the bottom and the top to prevent the sample from escaping. The maximum bed

height was defined by the distance between these two filters (140 mm). When smaller bed height were

used, the beds were surmounted by a pad of glass wool to prevent loos of the bed at the top. Glass

wool was also used to stabilise the glass holder inside the steel holder.


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Figure 3.5 Extractor vessel


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Figure 3.6 Stainless steel holder


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Figure 3.7 Glass sample holder


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3.1.4.2 Air driven pump

A Haskel MCP-110 air driven pump was used to compress the liquid carbon dioxide in the solvent

delivery section. To avoid contamination, a non lubricated plunger is used to compress the liquid. The

plunger is driven by compressed air, the area exposed to the compressed air being much larger than

that exposed to the high pressure fluid. The pump operates on the principle of equal forces:

The low pressure air acting on a large plunger area produces force equivalent to that produced by

high pressure carbon dioxide acting on a small plunger area. Compression occurs on the down stroke

of the piston, and suction on the up stroke. The flow rate is variable, from a maximum, at no

compression, to zero at maximum compression ratio. The compression ratio is given by equation

(3.1):

eq. (3.1) DR C P

P P

i

ai ro

=

0

where

DR compression ratio [-]

Co outlet hydraulic fluid pressure [bar]

Pi inlet hydraulic fluid pressure [bar]Pro exhaust air pressure [bar]

Pai supply air drive pressure [bar]

The pump used had a maximum compression ratio of 110 and a stroke displacement of 0.64 cm3

and was designed for a maximum working pressure of 690 bar (10,000 psi).

3.1.4.3 Bursting discs

Bursting discs are used to protect both operator and equipment. If the pressure exceeds the

maximum working pressure the disc bursts, thus relieving the pressure very quickly. Bursting discs

have the "supreme advantage" of giving instantaneous pressure relief to the system. The simplicity of

construction with no moving parts, ensures a completely sealed system and materials of construction

can be selected to give the best possible resistance to corrosion.


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3.1.4.4 The thermocouples and pressure transducers

Chromel-Alumel-thermocouples encased in 316 stainless steel sheaths were used as sensors. These

were inserted directly into the flowing streams and vessels to measure the temperature. The

temperature was indicated on a 12 point digital readout unit to provide direct readout of the

temperature at different points in the extraction system. Calibrations were performed on those

thermocouples which were located in key positions. They were found to be accurate to within 0.1 C.

Pressure in the extraction vessel was measured using pre calibrated pressure transducers (Druk

PBX 521-00, 0-700 bar gauge) and dedicated indicators (Druk DEI 260). The transducer/indicator

units are accurate to 0.5 bar.

3.1.4.5 The valves and connecting piping

The valves used were of stainless steel throughout and were manufactured by PPI (Pressure

Product Industries) and Hoke International Ltd.. The PPI valves have non-rotating stems and are used

as shut-off valves. The Hoke valves are needle valves and are placed at points where flow control is

required (NV1,NV2). Both valves are designed for a maximum working pressure of about 414 bar

(6000 psi).

The connecting piping used in parts of the equipment which are subject to high pressure is of 316

stainless steel, 6.35 mm (1/4") in outside diameter and with a wall thickness of 1.625 mm (0.064").

The maximum working pressure for this tubing is 414 bar . Some of the tubing used in parts of the

equipment which are at ambient pressure or at the pressure of the compressed air supply (maximum 9

bar (100 psi)) is made of copper or plastics, the wall thickness being appropriate to the application.

3.1.4.6 The collectors

For separating solute from the gas phase, three glass collectors are used in the separation section.

These are operated in series. As the decompressed carbon dioxide stream passes through them, its

temperature drops gradually from around ambient as it enters the first collector to below -10 C as it

leaves the final one. This arrangement has been found to provide an efficient means for collecting

virtually all extract.

The first collector CV1 has an inside diameter of 54 mm and length of 150 mm and is designed to

operate under a maximum working pressure of 35 bar. The carbon dioxide / solute stream enters the

middle pressure collector at ambient temperature and 8 bar. It flows through a down pipe into a glass


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- Interrupted flow experiments, where the same sample of material is used to obtain a sequence of data

points for given temperature, pressure and flow rate. In this type of experiment the flow of carbon

dioxide is interrupted from the flow and the amount extract collected are measured. During the period

of zero flow the extraction vessel was maintained to constant pressure and temperature. Having

measured the amount of extract collected, the experiment is continue for a further period and the

sequence is repeated.

Type first type has got the advantage that there is no stagnant period between extract measurements,

during which unwanted mass transfer take place. The second method only used in this thesis has the

advantages of greater rapidity and smaller usage of extractable material. When using this method it is

assumed that no mass transfer takes place in the stagnant periods between extract measurements. Thevalidity of this assumption requires checking for each system studied.

3.2.1 Preliminary Procedures

3.2.1.1 Charging the Extractor

At the beginning of each experiment the sample was

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