Modelling of Supercritical Fluid Extraction from Plant Materials

1
Modelling of Supercritical Fluid Extraction from
Plant Materials

• H. Sovová
• Institute of Chemical Process Fundamentals
• Prague, Czech Republic

2
Contents

• Diffusion from intact seed
• Effect of material pre-treatment
• Mass flux
• Phase equilibrium in the presence of matrix
• Flow patterns
• Two extraction periods
• Examples of extraction kinetics
• More on mass transfer resistance
• Conclusions

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Extraction from plant materials
Extractor
Separator
cooling
heating
High-pressure pump
4
Single intact particle (seed)

• What happens in the extractor? Let us start from
  a single solid particle. Mass transfer rate to
  the particle surface is

y
y
x
x
5
Single intact particle (seed)
y

• As internal mass transfer resistance in dry plant
  tissue is extremely high, extraction rate will be
  very low and fluid phase concentration y will be
  close to 0.
• Due to the excellent mass transfer properties of
  supercritical solvent, the concentrations at
  interface y and x will be negligible.

y
x
x
6
Single intact particle (seed)

• Thus,

y
y
x
and after integration from x x0 at t 0 we
obtain
x
xu
xu
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Single intact particle diffusivity

• Approximate relationships between the
  characteristic diffusion time ts l/ks, the
  characteristic particle dimension l and the
  effective diffusivity De for different particle
  geometries Villermaux, J. Chromatogr. 406 (1987)
  11

m 3/5 for spheres, 1/2 for cylinders, and 1/3
for slabs
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Hot-ball model

• sphere, Ficks 2nd law

x0
x
Bartle et al., J. Supercrit. Fluid 3 (1990) 143
9
Single sphere
e/xu
10
Material pretreatment

• necessity to disintegrate the plant material

11
Material pretreatment

• necessity to disintegrate the plant material
  (exception essential oil from glandular hairs)
• effects on diffusion path, interfacial area,
  walls of the cavities containing the solute
• consequences concentrations depend on local
  position in the extractor, the solution at the
  extractor outlet is almost saturated (exception
  short extractor/differential bed)

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Mass flux from disintegrated material j

• j kfa0(c - c) kfa0rf(y - y)
• j ksa0(cs - cs) ksa0rs(x x)
• for y Kx
  j ka0rf (Kx - y)

y
y
x
x
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Matrix effect on phase equilibrium y y(x)

• Decrease in solid phase concentration in the
  course of extraction
• Different types of equilibrium isotherms

a) linear equilibrium - typical for essential
oils from plants solute-matrix
interaction partition coefficient
K Reverchon, J. Supercrit. Fluids 10 (1997)
1 del Valle et al., Ind. Eng. Chem. Res. 39
(2000) 4720
y
y Kx
x
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Matrix effect on phase equilibrium y y(x)
y
y
y ys for x gt 0, y 0 for x 0
x
x
c) Langmuir isotherm dynamic equilibrium
adsorption-desorption Di Giovanni et al., J.
Chrom. A 919 (2001) 1
b) solute solubility ys - typical for
fatty oils no solute-matrix interaction Lee
et al., J. Am.Oil Chem. Soc. 63 (1986) 921
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Matrix effect on phase equilibrium y y(x)
y
y
x
x
e) combined - unfavourable equilibrium Perrut
et al., Ind. Eng. Chem. Res. 36 (1997) 430
d) BET isotherm Goto et al., J. Chem. Eng. Japan
31 (1998) 171
16
Flow patterns
axial dispersion series of mixers
natural convection
plug flow
channeling
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Mass balance for plug flow extractor
e void fraction u interstitial velocity
u
x
xdx
18
Mass balance for stirred extractor(s)
tr residence time
n number of stirrers for i 1,2,...,n
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Solid phase concentration profiles for plug flow
inert matrix

• Pure solvent enters from the left
• Profiles in broken cells the higher kfa0, the
  closer to step function
• Profiles in intact cells flat, controlled by
  small ksa0
• t 0, 5, 10, 15, 20

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Extraction curve for plug flow inert matrix

• Initial period straight line (concentration
  decreases only inside the bed, not yet at the
  extractor outlet)
• Transition to final section is sharp
• Final period curved line is controlled by
  internal mass transfer resistance

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Solid-phase concentration profiles for plug flow
linear equilibrium

• Pure solvent enters from the left
• Driving force decreases with decreasing x
• Broken cells very high kfa0 is necessary to
  approach step function
• Profiles in intact cells as for equilibrium
  solubility
• t 0, 5, 10, 15, 20

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Extraction curve for plug flowlinear equilibrium

• Initial section becomes slightly curved early
  after the start
• Smooth transition to final section
• Final section the curved line is controlled by
  internal mass transfer resistance

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Two extraction periods

• Residence time in extraction bed is proportional
  to N/Q where N solid feed (g), Q
  solvent flow (g/min)
• Normalized extraction curve e e(q) where
  e E/N, q Qt/N
• Experiment N1, N2, N1 gt N2 , Q const.

e
e
diffusion controlled
diffusion controlled
equilibrium
equilibrium
q
t
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Fatty oil from almonds Marrone et al., Chem.
Eng. Sci. 53 (1998) 3711
Experiment CO2, 40C, 35 MPa, 3 particle
sizes
Model solubility
ys 0.011 g/g, kfa0 gt 0.05 s-1
diffusion controlled - r0.75-0.58-0.33,
ksa00.8 10-5 s-1, xu 0.54 g/g almonds
25
Essential oil from fennel seed Reverchon et
al., Ind. Eng. Chem. Res. 38 (1999) 3069
Experiment CO2, 50C, 9 MPa, N0.27-0.30 kg,
3 flow rates
Model linear equilibrium
K 0.14 g/g, natural convection,
diffusion controlled -r0.60, ksa03-5 10-5 s-1,
xu 18 mg/g seed
26
Essential oil from orange peelsBerna et al., J.
Supercrit. Fluids 18 (2000) 227
Experiment CO2, 40C, 20 MPa, N0.08-0.11 kg and
1.6-2.2 kg
Model combined equilibrium
K 0.09 g/g, xt 0.05 g/g, xu
0.126 g/g matrix, nat. convection,
diffusion controlled -r0.7, ksa02.4 10-5 s-1
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More on external mass transfer
Correlations for mass transfer coefficient
kf forced convection Sh Sh(Re,
Sc) natural convection Sh Sh(Gr, Sc) effect
of solvent flow direction gravity assisted and
gravity opposed flows

• Sherwood number Sh kfl/De
• Reynolds number Re ul/n
• Schmidt number Sc n/De
• Grasshof number Gr gl3lDrfl/(rfn2)

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More on external mass transfer
forced convection Sh 2 1.1Re0.6Sc1/3 Wakao
and Funazukuri, Chem. Eng. Sci. 33 (1978)
1375 Sh 0.38Re0.83 Sc1/3 Tan et al., Chem.
Eng. J. 38 (1988) 17 Sh 0.839 Re0.667
Sc1/3 Catchpole, PhD dissertation, Univ.
Birmingham, UK , 1991
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More on intraparticle diffusion

• Importance of initial ditribution of solute in
  matrix and of the structure of matrix
• Solid particles (ks or De)
• Porous particles (porosity b, De DABb2) Goto
  et al., J. Chem. Eng. Japan 26 (1993) 401, and 31
  (1998) 171
• Shrinking core model Goto et al., J. Supercrit.
  Fluids 6 (1996) 128 Akgün et al., Ind. Eng.
  Chem. Eng. 36 (2000) 473
• Broken and intact cells Reverchon et al., Ind.
  Eng. Chem. Res. 38 (1999) 3069 Sovová, Chem.
  Eng. Sci. 49 (1994) 409

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Intraparticle diffusion shrinking core

• Increasing length of diffusion path in the pores
  between the surface of shrinking core and
  particle surface

Characteristics effective diffusivity De
y is constant in the course of
extraction recommended only when xu is
sufficiently high
31
Intraparticle diffusion broken and intact cells

• Broken walls (open cavities) near particle
  surface, intact cavities in particle core

Characteristics fraction of open cells in
particle volume r, mass transfer coefficient in
particle core ks
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Conclusions

• Supercritical solvents variable solvent power,
  excellent transport properties, tendency to
  natural convection, dryness material structure
  preserved, low permeability of cell walls
• SC-CO2 non-toxic, inert, non-polar solvent,
  relatively low solvent power solute-matrix
  interaction
• 3 aspects of SFE phase equilibrium, mass
  transfer resistance (low external m.t.r., high
  intraparticle m.t.r.), flow patterns
• 2 extraction periods equilibrium-controlled (e
  e(q)) and diffusion-controlled period (e e(t))