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J. of Supercritical Fluids 39 (2006) 30–39

Supercritical CO2 extraction of nutmeg oil: Experiments and modeling

Siti Machmudah a, Anny Sulaswatty b, Mitsuru Sasaki a, Motonobu Goto a,∗, Tsutomu Hirose a

a Department of Applied Chemistry and Biochemistry, Kumamoto University, Kurokami 2-39-1, Kumamoto 860-8555, Japanb Research Centre for Chemistry, Indonesian Institute of Sciences, Kawasan Puspiptek-Serpong 15314 Tangerang, Banten, Indonesia

Received 1 June 2005; accepted 10 January 2006

bstract

Nutmeg oil was extracted from nutmeg seed at pressures of 15–20 MPa and temperatures of 313–323 K with supercritical CO2. The effects ofeparation parameters such as temperature, pressure, CO2 flow rate and particle size on the extraction rate of nutmeg oil were observed. Brokennd intact cells (BIC) model combined with discontinuous phase equilibrium between fluid phase and solid phase, and shrinking core modelere selected to describe the extraction process. For BIC model, the initial fraction solute in broken cell to total solute in the ground particle

, dimensionless transition concentration X and partition coefficient K were used as fitting parameters. For shrinking core model, two effective

c

iffusivities De were used as fitting parameters. The best fitting of De1 was from 4.33 × 10−9 to 7.69 × 10−8 m2/s and De2 was from 1.90 × 10−9 to.20 × 10−8 m2/s. From comparison of experimental data and models calculation, the shrinking core model could describe the experimental dataell for all extraction conditions, while the BIC model could only describe the data at lower extraction yields well.2006 Elsevier B.V. All rights reserved.

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eywords: Supercritical CO2 extraction; Nutmeg oil; Shrinking core model; B

. Introduction

Nutmeg is obtained from seeds of myristica fragrans, a treeultivated in tropical regions. The amount of the seed oil variesith origin, soil and climate. Spricigo et al. [1] reported a steamistillation of ground nutmeg yielded 6.9 wt.% essential oil.bout 80% of the essential oil was composed of terpenes such

s �, � and �-pinene, sabinene, limonene and 4-terpineol. Othermportant components are safrol, elimicin, eugenol and myris-icin, of which the last one is responsible for the characteristicroma of nutmeg. However, in spite of the low oil content, theharacteristic composition of nutmeg oil makes it a valuableroduct for food, cosmetic and pharmaceutical industries. There-ore, an improved process for its extraction would be of industrialnterest.

Nutmeg is also characterized by high fatty oil content.ccording to Spricigo et al. [1], fatty oil was coextracted during

he extraction of nutmeg essential oil with liquid carbon dioxide.

he essential oil was higher in the extract samples collected at

he beginning of the process, but gradually more fatty oil ratherhan essential oil was extracted.

∗ Corresponding author.E-mail address: mgoto@kumamoto-u.ac.jp (M. Goto).

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896-8446/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.supflu.2006.01.007

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Supercritical fluid extraction (SCFE) is a powerful techniquen separation processes. Several investigations have been maden recent years on probable industrial applications of the SCFEhich offer some advantages over the conventional methods,

specially in the areas of food, pharmaceutical, chemical and oilndustries [2,3]. Extraction of essential oils using supercriticalarbon dioxide (SC-CO2) from herbs and spices has been con-idered as a possible applied field of the SCFE because of lowperating temperature, no contamination of product by usualolvents and lower physical plant area space requirements.

Although high pressure equipment is more expensive thanhat of conventional separation processes, the operating cost issually lower, and hence the total costs are comparable if the pro-ess is carried out at optimum conditions and sufficient extractorolume [4]. It is important to model the SCFE of the essential oilo obtain access to optimum operating conditions. The mathe-

atical modeling of experimental data of SCFE has the objectivef determining parameters for process design, such as equipmentimensions, solvent flow rate, and particle size, to make possiblehe prediction of the viability of SCFE processes on an industrialcale, through the simulation of overall extraction curves [5].

Mathematical models proposed are generally based on dif-erential mass balance integration. These models are basedn mass transfer mechanisms and equilibrium relationships.hrinking core model is the model which describes the situ-

S. Machmudah et al. / J. of Supercritical Fluids 39 (2006) 30–39 31

Nomenclature

a model’s constant (vR2/DeL)ap interfacial area per unit volume of bed (m−1)b model’s constant (ys/x0)B model’s constant (ρfε/ρs(1 − ε))Bi Biot number (kfR/De)dp particle diameter (m)De effective intraparticle diffusivity (m2/s)De1 effective intraparticle diffusivity of lighter

component (m2/s)De2 effective intraparticle diffusivity of heavier

component (m2/s)DL axial dispersion coefficient (m2/s)D12 binary diffusivity of solute and solvent (m2/s)E dimensionless extraction yield (F/Nxi)f initial fraction solute in broken cell to total solute

in the ground particleF extract (kg)G model’s constant (ksap/(1 − ε))kf film mass transfer coefficient in fluid phase (m/s)ks film mass transfer coefficient in solid phase (m/s)K partition coefficientK̄ partition constant in the dimensionless model

equation (Kx10/y0)L bed length (m)N solid charge in the extractor (kg)Pe Peclet number (Lv/DL)r radial coordinaterc critical radius of core (m)R particle radius (m)S solvent flow rate (kg/s)t time (s)v interstitial fluid velocity (m/s)x concentration of solid phase (kg solute/kg

insoluble solid)xc transition concentration (kg solute/kg insoluble

solid)xi solute fraction in untreated solute (kg solute/kg

insoluble solid)x0 initial solute in ground particle (kg solute/kg

insoluble solid)x1 concentration of solid phase with broken cells (kg

solute/kg insoluble solid)x10 initial concentration of solid phase with broken

cells (kg solute/kg insoluble solid)x2 concentration of solid phase with intact

cells (kg solute/kg insoluble solid)x20 initial concentration of solid phase with intact

cells (kg solute/kg insoluble solid)X dimensionless concentration of solid phase

(x/x0)Xc dimensionless transition concentration (xc/x10)X1 dimensionless concentration in broken cells

(x1/x10)

X2 dimensionless concentration in intact cells(x2/x10)

X̄ average value of Xy concentration of fluid phase (kg solute/kg solvent)yi concentration of fluid phase in pores (kg solute/kg

solvent)ys solubility (kg solute/kg solvent)y0 initial concentration of fluid phase (kg solute/kg

solvent)y* equilibrium fluid phase concentration

(kg solute/kg solvent)Y dimensionless fluid phase concentration (y/y0)Yi dimensionless concentration of fluid phase in

pores (yi/y0)Y* dimensionless equilibrium fluid phase

concentration (y*/y0)z axial coordinate in extractorZ dimensionless axial distance (z/L)

Greek lettersε bed voidageθ dimensionless time (vt/L)ξ dimensionless radial coordinate (r/R)ξc dimensionless radius of core (rc/R)ρc density of overall seed (kg/m3)ρf density of fluid (kg/m3)ρs density of insoluble solids in the seeds (kg/m3)τ dimensionless time (Det/R2)Φ initial solute distribution between solvent and

broken cells (ρfεy0/ρs(1 − ε)fx10)ψe dimensionless external mass transfer resistance

(εv/kfapL)ψ dimensionless internal mass transfer resistance

apstsdasm2ltvp

wi[d

i((1 − ε)v/ksapL)

tion of irreversible desorption followed by diffusion in theorous solid through the pores. This model assumes that theolute inside the particle is located within a core that shrinks ashe solute is extracted. Shrinking core model has been used inolid–fluid reaction [6] and successfully applied to experimentalata for �-carotene extraction [7], oil extraction from root [8]nd seed [9–11]. Liquid carbon dioxide extraction of nutmegeed oil has been modeled by Spricigo et al. [11], however theodel was only applied to one extraction condition (9 MPa and

96 K). They considered extraction of essential oil without theipid (pseudo-single compound), and its extraction was assumedo be independent of the extraction of lipid. In their model,arious effective diffusion coefficients were used as fittingarameter.

The concept of broken and intact cells (BIC) model firstly

as introduced by Sovova [12]. BIC model has been applied

n extraction of essential oil from seed by some researchers12–21]. The advantage of this model is the use of realisticescriptions of the biological material structure. The structure

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2 S. Machmudah et al. / J. of Su

f biological material, where the solute deposited is in vari-us types of cavities (vacuoles, glands, and others) contained inarenchyma cells [22] that are called cells. Two regions are dis-inguished in the particle. Close to the surface there is a regionf broken cells whose walls have been damaged by mechani-al pre-treatment, and particle core contains intact cells. Massransfer resistance of cell walls is high and therefore there is aarge difference in diffusion rates from both regions; the initialast extraction from broken cells is followed by much slowerxtraction from intact cells. Reverchon et al. [16–18,20] usedcanning electron microscope (SEM) to observe broken cellsn particle surface. They were able to calculate the volumetricatio of broken to intact cell ratio and thus reduce the number ofodel parameters evaluated from extraction curves. The concept

f BIC was combined with equilibrium relationship for eitherree solute [12,14] or solute interacting with matrix [15,19]. Bothypes of equilibrium were also assumed to occur simultaneously,he free solute in broken cells and the interacting solute in intactells [16–20]. BIC model was also combined with discontinu-us equilibrium between the fluid phase and the solid phase withroken cells [21].

In this work, SC-CO2 extraction of nutmeg seed oil was per-ormed at various pressures, temperatures, particle sizes andO2 flow rates. In addition, the BIC model combined withiscontinuous equilibrium relationship and the shrinking coreodel were applied to describe the extraction process based on

he experimental data.

. Experimental

Nutmeg seeds imported from India were obtained fromakasagoyakugyo Co., Japan. Nutmeg seeds were ground bycoffee grinder and sieved into several grades of particle size

0.556, 0.688, and 2.117 mm). Grinding was performed justefore extraction and within a time of 5 s in order to preventeating of nutmeg.

Schematic diagram of the experimental apparatus is shown in

ig. 1. The apparatus was provided by AKICO Co., Japan. Nut-eg oil was extracted with SC-CO2 in a semi-continuous flow

xtractor. Initially, about 50 g of nutmeg was placed in the extrac-or of 20 cm height, 7 cm inside diameter and 500 ml capacity.

•

Fig. 1. Schematic diagram of

itical Fluids 39 (2006) 30–39

iquid CO2 from a cylinder with siphon attachment was passedhrough a chiller kept at 262 K and compressed to the operatingressure by a high pressure pump. Compressed CO2 was flowednto the extractor placed in the heating bath that was maintainedt the operating temperature. The exit fluid from the extractoras expanded to a pressurized separator at 2.5 MPa and 273 K byack pressure regulator (BPR) 1 and then expanded to ambientressure by BPR 2. The pressure in the extractor was controlledy BPR 1, while the pressure in the separator was controlled byPR 2. CO2 flow rate was measured by flow meter and dry gaseter. Oil extracted was collected from the pressurized separa-

or at every 10–30 min for 90–300 min and weighed immediatelyfter collection. Extractions were carried out at temperatures of13, 318, and 323 K, pressures of 10, 15 and 20 MPa, and CO2ow rates of 2.78 × 10−5, 8.33 × 10−5 and 1.39 × 10−4 m3/sased on the CO2 exiting the separator at room temperature and.1 MPa.

Analysis of nutmeg seed oil was performed by a GC/MSHewlett Packard 6890 series) coupled with a mass selectiveetector (J&W Scientific, Agilent Tech., USA), with capil-ary column (HP 5 MS, 5%, Phenyl Methyl Siloxane, Capil-ary 30.0 m × 250 �m × 0.25 �m nominal). Injector tempera-ure was 523 K. The oven temperature program was 323–343 Kt rate of 3 K/min and 343–473 K at rate of 10 K/min. The carrieras was He and sample volume injected was 1 �l. The analysisas replicated two times to check reproducibility. Compound

dentification was performed by data base and auto integratederiodically.

. Mathematical model

.1. Broken and intact cells (BIC) model

The BIC model was developed using the following assump-ions:

The solute is assumed to be homogeneously distributed in

untreated particles that arranged as packed bed in the extrac-tor.The particles contain broken cells near the surface and intactcells in the core. The volumetric fraction of broken cells in

experimental apparatus.

percritical Fluids 39 (2006) 30–39 33

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S. Machmudah et al. / J. of Su

the particles is f (0 < f < 1). Their initial proportion was deter-mined by

x0 = x1(t = 0) + x2(t = 0) (1)

x1(t = 0) = fx0 (2)

where x1 is the concentration of solid phase with broken cellsand x2 is the concentration of solid phase with intact cells.The solute from broken cells is transferred directly to thefluid phase, while the solute from intact cells diffuses first tobroken cells and then to the fluid phase. Mass transfer frombroken cells to the solvent is characterized by fluid phase masstransfer coefficient (kf) that is by several orders of magnitudelarger than the solid phase mass transfer coefficient (ks) relatedto the diffusion from intact cells to broken cells.The extraction bed characteristics, void fraction and surfacearea, are not affected by the reduction in the solid mass duringthe extraction, and fluid density is not affected by the solutedissolved in the solvent.Equilibrium between the fluid phase and the solid phase withbroken cells is established before the extraction starts, whilethe concentration in the intact cells is equal to the originalconcentration in the untreated material.

Mass balance per unit volume of extraction bed is writtenor plug flow, thus the axial dispersion is neglected. It consistsf equations for the solute in the fluid phase, solid phase withroken cells, and solid phase with intact cells.

In fluid phase:

fε

(∂y

∂t+ v

∂y

∂z

)= kfapρf(y

∗ − y) (3)

In solid phase with broken cells:

ρs(1 − ε)∂x1

∂t= ksapρs(x2 − x1) − kfapρf(y

∗ − y) (4)

In solid phase with intact cells:

1 − f )ρs(1 − ε)∂x2

∂t= −ksapρs(x2 − x1) (5)

The extraction is calculated as

= S

∫ t

0y|z=L dt (6)

The initial and boundary conditions are

y|t=0 = y0 = y∗; x1|t=0 = x10; x2|t=0 = x20 = xi;

y|z=0 = 0;dy

dz

∣∣∣∣z=L

= 0 (7)

Phase equilibrium between the fluid phase and the solid phaseith broken cells is given by the discontinuous equilibrium func-

ion depicted in Fig. 2 which is proposed by Perrut et al. [23].he discontinuity occurs at transition concentration, xc, which

s equal to matrix capacity for interaction with the solute. Atolid phase concentration lower than xc, all solute interacts with

Fig. 2. Equilibrium curve according to Perrut et al. [23].

atrix and phase equilibrium is determined by partition coef-cient, K. At the concentration higher than xc, the solid phaseontains also free solute whose equilibrium fluid phase concen-ration is equal to the solubility, ys:

y∗ = ys for x1 > xc; y∗ = Kx1 for x1 ≤ xc,

where Kxc < ys (8)

The model equations are transformed into dimensionlessorm using dimensionless variables:

Z = z

L; θ = vt

L; Y = y

y0; X1 = x1

x10;

X2 = x1

x10; Y∗ = y∗

y0; Xc = xc

x10(9)

Dimensionless model equations with initial and boundaryonditions are:

∂Y

∂θ+ ∂Y

∂Z= 1

Ψe(Y∗ − Y ) (10)

∂X1

∂θ= 1

Ψif(X2 −X1) − Φ

Ψe(Y∗ − Y ) (11)

∂X2

∂θ= − 1

Ψi(1 − f )(X2 −X1) (12)

= F

Nxi= Φf

1 +Φ

∫ θ

0Y |z=1 dθ (13)

Y |θ=0 = 1; X1|θ=0 = 1; X2|θ=0 = 1 +Φ;

Y |Z=0 = 0;∂Y

∂Z

∣∣∣∣Z=1

= 0 (14)

here

i = (1 − ε)v

ksapL; Ψe = εv

kfapL; Φ = ρfεy0

ρs(1 − ε)fx10

Dimensionless equilibrium relations are:

Y∗ = 1 forX1 > Xc; Y∗ = K̄X1 forX1 ≤ Xc,

where K̄ = Kx10

y0(15)

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4 S. Machmudah et al. / J. of Su

.2. Shrinking core model

The shrinking core model was adopted from Goto et al. [9].o derive the shrinking core model, the following criteria aressumed. The solvent flows axially with interstitial velocity, v,hrough a packed bed in a cylindrical extractor of height, z. Theystem is isothermal and isobaric. The physical properties of theC fluid are constant during extraction. Extraction is irreversibleesorption and radial dispersion is neglected. Axial dispersionas neglected to simplify the analysis; although it may influen-

ial in some cases. Based on the assumptions and consideringxial dispersion, the dimensionless material balances in the fluidhase and solid phase are described as:

In fluid phase:

∂Y

∂τ+ a

∂Y

∂Z= a

Pe

∂2Y

∂Z2 − 1 − ε

ε3Bi[Y − Yi(1)] (16)

In solid phase:

∂X̄

∂τ= 3Bib[Y − Yi(1)] (17)

Dimensionless diffusion in outer region:

1

ξ2

∂

∂ξ

[ξ2 ∂Yi

∂ξ

]= 0 (18)

Solid phase solute exists within the core:

¯ = ξ3c (19)

Dimensionless boundary conditions are given as follows. Athe core boundary, the concentration in the fluid phase is at itsaturated value:

i = 1 at ξ = ξc (20)

Diffusion flux at the outer surface of a particle is equal to theass transfer through external film:

∂Yi

∂ξ

)ξ=1

= Bi[Y − Yi(1)] (21)

Dimensionless initial conditions are given as follows:

= 0 at τ = 0; ξc = 1 at τ = 0 (22)

Dimensionless Danckwert’s boundary conditions at the inletnd exit of extractor are given by

− 1

Pe

∂Y

∂Z= 0 atZ = 0;

∂Y

∂Z= 0 atZ = 1 (23)

The following equations were derived by rearranging Eqs.16)–(23):

∂Y ∂Y a ∂2Y 1 − ε 3Bi(Y − 1)

∂τ+ a

∂Z=Pe ∂Z

−ε 1 − Bi(1 − 1/ξc)

(24)

∂ξc

∂τ= bBi(Y − 1)

ξc[1 − Bi(1 − 1/ξc)](25)

ar

x

itical Fluids 39 (2006) 30–39

The yield that is cumulative amount of extract up to time θ isiven by

ield = εab

1 − ε

∫ τ

0Y dτ (26)

The differential equations (Eqs. (24) and (25)) coupled withoundary and initial conditions were solved numerically byrank Nicholson’s method and tridiagonal matrix, and compu-

ational programming using Visual Basic. Extraction curve wasescribed as yield versus time.

.3. Model parameters

Models parameters were evaluated using existing correlationsnd available data. Parameters including in the models are asollow. The values initial concentrations y0 and x0 were required.n the cases studied, the first part of the extraction yield curve isinear. As pointed out by some authors, this means that the soluteoncentration in the solvent at the exit of the system reached thequilibrium value. In this case, the initial oil concentration inhe fluid, y0, can be evaluated from the experimental plot of theil yield as a function of the mass of solvent flown, ms:

0 = me

ms= me

m0

m0

ms= yield

ms/m0(27)

here me is the mass of the extracted oil and m0 is the initial massf seed. The last term of Eq. (27) is the slope of the linear sectionf the extraction yield curve. For the hypothesis that exhaustedeeds are free of solute, the initial mass of the oil available in theolid can be assumed to be equal to the asymptotic value of theass of oil extracted, me∞. With yield∞ being the asymptotic

ield, the expression becomes:

0 = me∞m0 −me∞

= yield∞1 − yield∞

(28)

The overall mass balance also defines the relationshipetween the density of the insoluble solids in the seeds ρs andhe overall seed density ρc:

sx0 = ρcyield∞ (29)

Because the simulation starts after the equilibrium, the initialoncentrations in the solid phases given by Eq. (1) should behanged to appropriate values limited by the mass balance ofhe closed extractor:

0 = x1(t = 0) + x2(t = 0) + By(t = 0) (30)

= ρfε

ρs(1 − ε)(31)

For the sake of simplicity, the diffusion of essential oil fromhe intact cells in the time t < 0 was neglected. Eq. (32) reduceso the relation between x1(t=0) and y(t=0):

x0 = x1(t = 0) + By(t = 0) (32)

nd the initial mass fraction of essential oil inside the intact cellsemains:

2(t = 0) = (1 − f )x0

percritical Fluids 39 (2006) 30–39 35

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Table 1Composition of nutmeg oil extracted at pressure of 15 MPa, particle size of0.556 mm and CO2 flow rate of 1.39 × 10−4 m3/s

Retention time (min) Component Peak area (%)

4.64 Bicyclo[3.1.0]hex-2-ene 1.014.80 �-Pinene 8.375.98 �-Phellandrene 19.226.03 �-Pinene 7.556.52 �-Myrcene 1.247.31 2-Carene 0.907.62 Benzene 0.927.73 �-Limonene 4.818.92 3-Carene 1.699.31 Camphene 1.079.93 Cyclohexene 0.72

10.32 2-Cyclohexene-1-ol 1.1610.45 Linalyl butanoate 0.5612.25 3-Cyclohexene-1-ol 4.0212.58 3-Cyclohexene-1-methanol 0.8413.72 1,6-Octadien-3-ol 0.9314.32 1,3-Benzodioxole 2.7115.20 �-Cubebene 0.5515.59 Copaene 1.2216.10 1,2-Dimethoxy-4-(2-propene) 3.6717.70 Myristicin 31.5511

ap

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utwcomponent with higher molecular weight (terpene derivativesand myristicin), where both components homogeneously dis-tributed over the core, two De were used as fitting parameter.

Table 2Initial concentrations in BIC model

P (MPa) T (K) y0 x0

10 313 0.021 0.058

S. Machmudah et al. / J. of Su

The external mass transfer coefficient was obtained by equa-ion expressed by King and Bott [3]:

f = 0.82

(D12

dp

)[Re0.66Sc1/3] (33)

here D12 is the binary diffusivity of solute and solvent, whichas calculated by:

12 = 23/2D11R

X, ρr = 2.5 (34)

11 = DcTr(ρ1/3r − 0.4358ρr)

0.5642ρr, 0.4 ≤ ρr ≤ 2.5 (35)

= (1 + (Vc2/Vc1)1/3)2

(1 +M1/M2)1/2 (36)

here Dc is the self diffusion coefficient of the solvent at theritical point, Tr and ρr the reduced temperature and density,espectively, Vc1 and Vc2 the critical volumes of components 1nd 2, and M1 and M2 are their molecular weights.

For nutmeg oil (cyclic solute), R is given by

= 0.664X0.17 (37)

The external volumetric mass transfer coefficient kfap wasalculated by Eq. (33), where ap is surface area of the particlesontained in unit volume of bed:

p = 6(1 − ε)

dp(38)

The internal volumetric mass transfer coefficient ksap wasbtained by equation expressed by Sovova et al. [13]:

= ksap

1 − ε(39)

The value of G ranged from 1.6 × 10−4 s−1, for black pepper,o 2 × 10−3 s−1, for mace/nutmeg.

Axial dispersion coefficient was given by correlation ofunazukuri et al. [24] for εReSc > 0.3:

εDL

D12= 1.317(εReSc)1.392 (40)

. Results and discussions

In this study, the effects of temperature, pressure, SC-CO2ow rate and particle size of nutmeg seed on the extractionield were investigated and the experimental and model resultsere compared. Nutmeg oil extracted was golden-brown liquid

nd considered to be essential oil. The composition of nutmegil extracted analyzed by GC–MS is summarized in Table 1.utmeg oil extracted contained terpene hydrocarbons (such ashellandrene, pinene, camphene, myrcene, limonene, carene and

amphene), terpene derivatives (such as linalyl butanoate, �-ubebene, copaene, asarone and anthrone) and myristicin ashe main components. The composition of terpene hydrocar-ons, terpene derivatives and myristicin were 44.85%, 7.23%,

1

2

8.05 Asarone 2.998.70 Anthrone 1.91

nd 31.55%, respectively. Based on the oil composition, soluteroperties were estimated using Yoneda method [25].

In BIC model, the initial fraction solute in broken cell tootal solute in the ground particle f, dimensionless transitiononcentration Xc and partition coefficient K were used as fittingarameters. The initial concentrations, y0 and x0, and the valuesf fitting parameters are summarized in Tables 2 and 3, respec-ively. The discontinuous equilibrium curve for every extractionondition could be displayed. Fig. 3 shows the equilibrium curveor various extraction pressures. Xc and K values increased withncreasing pressure. It expected that Xc and K values mightlso describe the solubility of solvent, where it increased withncreasing pressure.

In the shrinking core model, the effective diffusivity, De wassed as fitting parameter. With assumption that the core con-ains lighter components, i.e. component with lower moleculareight (terpene hydrocarbons), and heavier components, i.e.

5 313 0.024 0.058318 0.011 0.058323 0.009 0.058

0 313 0.082 0.058

36 S. Machmudah et al. / J. of Supercritical Fluids 39 (2006) 30–39

Table 3Values of fitting parameters in BIC model and SCM

BIC model SCM model

F Xc K De1 (m2/s) De2 (m2/s)

Particle size dp (mm) 0.556 0.48 0.2 0.3 6.09 × 10−9 2.80 × 10−9

0.688 0.45 0.3 0.2 6.20 × 10−9 2.82 × 10−9

2.117 0.4 0.4 0.1 7.69 × 10−8 3.20 × 10−8

Pressure P (MPa) 10 0.48 0.35 0.15 6.92 × 10−9 3.00 × 10−9

15 0.48 0.55 0.2 4.94 × 10−9 2.00 × 10−9

20 0.48 0.81 0.4 4.33 × 10−9 1.90 × 10−9

Temperature T (K) 313 0.45 0.77 0.3 5.03 × 10−9 2.30 × 10−9

318 0.45 0.75 0.2 6.72 × 10−9 2.70 × 10−9

323 0.45 0.7 0.1 6.20 × 10−9 2.82 × 10−9

Solvent flow rate S (m3/s) 2.78 × 10−5 0.45 0.6 0.2 4.94 × 10−9 2.00 × 10−9

8.33 × 10−5 0.45 0.6 0.2 4.94 × 10−9 2.00 × 10−9

1.39 × 10−4 0.45 0.6 0.2 4.94 × 10−9 2.00 × 10−9

Table 4Calculated parameters in shrinking core model

dp (mm) ρc (kg/m3) ε P (MPa) T (K) v (m/s) kf (m/s) DL (m2/s)

0.688 1312 0.86 15 313 0.03614 7.14 × 10−4 6.99 × 10−4

318 7.72 × 10−4 6.72 × 10−4

323 8.39 × 10−4 6.44 × 10−4

0.556 1187 0.84 10 313 9.97 × 10−4 4.52 × 10−4

15 7.68 × 10−4 5.16 × 10−4

20 6.87 × 10−4 5.43 × 10−4

0.688 1312 0.86 15 323 0.02166 6.44 × 10−4 2.33 × 10−4

2.117 1636 0.89 5.99 × 10−4 3.16 × 10−4

−3 −4

0

F

F

y

w

.556 1187 0.84 15

urthermore Eqs. (24)–(26) were modified into:

∂Yi

∂τ+ a

∂Yi

∂Z= a

Pe

∂2Yi

∂Z− 1 − ε

ε

3Bii(Yi − 1)

1 − Bii(1 − 1/ξci)(41)

∂ξci

∂τ= biBii(Yi − 1)

ξci[1 − Bii(1 − 1/ξci)](42)

ig. 3. Discontinuous equilibrium curve for various extraction pressures.

hefb43dmmuT

esflthwad

2.14 × 10 5.78 × 10313 0.02166 5.48 × 10−4 2.53 × 10−4

0.00723 2.65 × 10−4 5.49 × 10−5

ield = εaibi

1 − ε

∫ τ

0Yi dτ (43)

here i = 1, 2.Because the lighter components are depleted faster than the

eavier components, De1 > De2 may be used for computing invery condition [10]. As initial guesses, values of De, equationrom Wakao and Smith [26], ε2D12, were used. The model coulde adjusted to the experimental data with values of De1 from.33 × 10−9 to 7.69 × 10−8 m2/s and De2 from 1.90 × 10−9 to.20 × 10−8 m2/s. The values of De for every operating con-ition are listed in Table 3. Apparent solubility used in theodel calculation was similar with the value of y0 in the BICodel. The calculation result of parameters and calculated val-

es of dimensionless parameters in this model are displayed inables 4 and 5, respectively.

Predicted concentration profile in fluid phase as function ofxtractor height for BIC model and shrinking core model arehown in Figs. 4 and 5, respectively. Solute concentration inuid phase decreased with increasing extraction time. Initially,

he solute easily dissolved in the fluid phase along the extractor

eight. Solute in particles placed in the bottom of the extractoras removed first following the next position. For comparison

t the same time, in the BIC model, the solute was very easy toissolve in the fluid phase and was quickly removed from particle

S. Machmudah et al. / J. of Supercritical Fluids 39 (2006) 30–39 37

Table 5Calculated values of dimensionless parameters in shrinking core model

dp (mm) P (MPa) T (K) v (m/s) Bi1 Bi2 a1 a2 Pe

0.688 15 313 0.03614 48.8 107 4.25 9.30 10.3318 47.8 98.4 3.85 7.92 10.8323 46.6 102 3.45 7.58 11.2

0.556 10 313 40.1 92.4 2.02 4.65 16.015 43.2 107 2.83 6.98 14.020 44.1 101 3.22 7.35 13.3

0.556 15 323 0.02166 31.4 68.2 1.37 2.99 18.50.688 33.2 73.1 2.07 4.54 13.72.117 20.556 15 313 0.02166 3

0.00723 1

Fo

ppsflsar

Fo

Topd

4

aflFTcatr

mdidescribe experimental data well at lower temperatures (313 K).

ig. 4. Predicted concentration profile as function of extractor height as functionf extractor height for BIC model.

hase, which suggested that the fluid easily penetrated into thearticle, even for particles placed at the top of the bed. Theolute from intact cells was easily dissolved in the fluid. Then,

uid transferred to the broken cells and more easily dissolvedolute in the cells. In other words, equilibrium was easily reachedccording to the BIC model. In the SCM model, equilibrium waseached slowly, even for particles placed at the bottom of the bed.

ig. 5. Predicted concentration profile as function of extractor height as functionf extractor height for shrinking core model.

Tii

Fco

9.5 70.9 1.58 3.79 7.500.8 72.5 1.69 3.98 17.14.9 35.1 0.565 1.33 26.3

his can be attributed to the solute that was placed in the coref particle, and thus the fluid could not easily disperse into thearticle and had to penetrate through the pore into the core toissolve the solute.

.1. Effect of temperature

The effect of temperature on extraction yield for both modelst a pressure of 15 MPa, particle size of 0.556 mm and CO2ow rate of 1.39 × 10−4 m3/s is shown in Fig. 6. As shown inig. 6, extraction yield increased with decreasing temperature.his can be understood from the decrease in temperature thatauses an increase in solubility or solvent density. In addition,t this condition, the change of solvent density is more effectivehan that of solute vapor pressure. Consequently, the extractionate increased with decrease in temperature.

As shown in Fig. 6 both models could describe the experi-ental data. For comparison of the models to the experimental

ata, the shrinking core model had good agreement with exper-mental data for all conditions, but the BIC model could not

his might be due to the use of more than one fitting parametersn the BIC model. Some difficulties were encountered in provid-ng initial guess values of the parameters. Thus, it is important

ig. 6. Effect of temperature on extraction yield with comparison to modelalculation at pressure of 15 MPa, particle size of 0.556 mm and CO2 flow ratef 1.39 × 10−4 m3/s.

38 S. Machmudah et al. / J. of Supercritical Fluids 39 (2006) 30–39

Fl1

tcy

4

to1r

smitwcsntmtiensfda

4

fayi

Fc0

ntsma

is

4

eFtsratio of broken cells to intact cells, reducing mass transfer resis-tance, leaving the essential oil more accessible to the solvent,and consequently, increasing the extraction yield. The reductionin extraction yield with increasing particle size indicates that oil

ig. 7. Effect of pressure on extraction yield with comparison to model calcu-ation at temperature of 313 K, particle size of 0.556 mm and CO2 flow rate of.39 × 10−4 m3/s.

o minimize the fitting parameter. Besides that, the initial con-entration of solute in solid, x0, should be based on maximumield of experimental result for every condition.

.2. Effect of pressure

The effect of pressure on extraction yield with comparisono both models calculation has been studied at a temperaturef 313 K, particle size of 0.556 mm and CO2 flow rate of.39 × 10−4 m3/s. The corresponding extraction yield data iseported in Fig. 7.

Extraction yield dramatically increased with increasing pres-ure, especially at higher pressures. At constant temperature, theass transfer coefficient decreased but solubility of nutmeg oil

ncreased with increasing pressure (Tables 2 and 4). At the sameime, internal and external mass transfer resistances increasedith decreasing mass transfer coefficient. For this reason, super-

ritical CO2 did not disperse into the solid particles easily (alsoee Fig. 5). The result of increasing saturation concentration ofutmeg oil in fluid phase showed a positive effect on the extrac-ion process. On the contrary, increasing internal and external

ass transfer resistances showed a negative effect. At constantemperature (T = 313 K), extraction yield increased with increas-ng pressure. This behavior can be explained by the positiveffects on the extraction process that apparently overcame theegative effects at increasing pressures. At this condition, thehrinking core model could describe the experimental data wellor all conditions, while the BIC model only could describe theata at lower pressures. For the BIC model, larger errors resultedt higher extraction yield.

.3. Effect of CO2 flow rate

Fig. 8 shows the effect of CO2 flow rate on the extraction yield

or both models at temperature of 313 K, pressure of 15 MPand particle size of 0.556 mm. As shown in Fig. 8, extractionield slightly increased with an increase in CO2 flow rate. Thencreasing CO2 flow rate generally caused an increase in the

Fc8

ig. 8. Effect of CO2 flow rate on the extraction yield with comparison to modelalculation at temperature of 313 K, pressure of 15 MPa and particle size of.556 mm.

umber of CO2 molecules per unit volume to enter the extractor,hus increasing inter-molecular interaction between CO2 and theolute, thus increasing the solute dissolution. For this condition,ass transfer was influenced by the increasing CO2 flow rate

nd the intraparticle diffusion resistance was dominant.In Fig. 8, SCM model more satisfactorily described the exper-

mental data than the BIC model. As explained above, BIC modelatisfactorily described the data for lower extraction yields.

.4. Effect of particle size

The effect of particle size (2.117, 0.688, and 0.556 mm) onxtraction yield for both models is shown in Fig. 9. As shown inig. 9, a reduction in extraction yield for an increase in par-

icle size could be observed. The grinding process increasesurface area and may disrupt the cell walls and increase the

ig. 9. Effect of particle size on extraction yield with comparison to modelalculation at temperature of 323 K, pressure of 15 MPa and CO2 flow rate of.33 × 10−5 m3/s.

percri

wsrct

stpkp

5

CCybwmmflmdwyopa

A

2

R

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

169–175.

S. Machmudah et al. / J. of Su

as not transported through the unbroken cell walls, and onlyurface oil was removed. Spricigo et al. [1] obtained similaresults for extraction of nutmeg oil using liquid CO2. They con-luded that liquid CO2 was not able to reach all of the oil insidehe cells; only the exposed oil was extracted.

Although both models could describe the experimental data,hrinking core model had better agreement with the data thanhe BIC model. The BIC model could describe the data for largerarticle sizes. The model could also explain that amount of bro-en cells in the surface of particles increased with decreasingarticle sizes (see Table 3 for values of f).

. Conclusion

Oil from nutmeg seed was extracted by using supercriticalO2 as a solvent to observe the effects of temperature, pressure,O2 flow rate and particle size on the extraction yield. Extractionield increased with decreasing temperature and particle size,ut increased with increasing pressure and slightly increasedith an increase in CO2 flow rate. Furthermore, the experi-ental data were compared with shrinking core model and BICodel combined with discontinuous phase equilibrium betweenuid phase and solid phase. From the comparison of experi-ental data and models calculation, shrinking core model could

escribe the experimental data well for all extraction conditions,hile BIC model only could describe well for lower extractionield. For BIC model, the best fitting parameters was dependentn extraction condition. For shrinking core model, the best fittingarameters of De1 was from 4.33 × 10−9 to 7.69 × 10−8 m2/snd De2 was from 1.90 × 10−9 to 3.20 × 10−8 m2/s.

cknowledgment

This work was partly supported by Kumamoto University1st century COE Program “Pulsed Power Science”.

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