Proceedings of the 1st International Conference on Natural Resources Engineering & Technology 2006
24-25th July 2006; Putrajaya, Malaysia, 500-509
External Mass Transfer Model for a Recirculated Packed-Bed Batch
Reactor on the Hydrolysis of Palm Olein Using Immobilized Lipase
Chew Yin Hoon∗, Lee Chew Tin
Department of Bioprocess Engineering, Faculty of Chemical and Natural Resources Engineering,
Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia.
Abstract
The application of immobilized enzyme in organic synthesis is gaining popularity as it offers
advantages over conventional chemical reactions. A recirculated packed-bed batch reactor
(RPBBR) can be used for immobilized enzyme systems. However, external mass transfer
limitation is significant in an RPBBR, especially at large scales. This study investigated the
external mass transfer coefficients in an RPBBR. The effect of mass flow rate, one of the key
parameters affecting the external mass transfer resistance, was considered. The hydrolysis of
palm olein using immobilized lipase was used as a case study. A mass transfer correlation
model of the form JD = K Ren-1 was developed based on the literatures. The Colburn factor, JD,
which is a function of Reynolds and Schmidt numbers, can be related to the external mass
transfer coefficient, km. The values of K and n were determined by conducting experimental
work in the RPBBR at different mass flow rates. It was found that the values of K and n are
0.056 and 1, respectively. Since the average mass transfer coefficients can be correlated in
terms of dimensionless groups which characterize the flow conditions, this model can be used
for the design of reactors, particularly scaling-up.
Keywords: external mass transfer coefficient - recirculated packed-bed batch reactor - immobilized lipase –
hydrolysis - palm olein
1.0
Introduction
In recent years, immobilized enzymes have become a choice of interest in organic synthesis.
Immobilized enzymes offer many advantages over free enzymes as they can be recovered and
reutilized easily. Difficult separation processes can be avoided in the downstream processing
of product purification. Besides that, immobilization can sometimes provide a better
microenvironment for the activity of enzyme.
Various reactor configurations can be used for immobilized enzyme systems. Nowadays,
recirculated packed-bed batch reactor (RPBBR) with single column or multicolumn packedbed reactor is used commercially [1]. An RPBBR is shown in Figure 1. It consists of a fixed
bed reactor with recycling system.
∗
Corresponding author: Tel.: +6012-4597367, Email address: cyinhoon@yahoo.com
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Proceedings of the 1st International Conference on Natural Resources Engineering & Technology 2006
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C=C2(t)
C=C(x,t)
z=H
Reservoir
Packed-bed
column
z=0
C=C1(t)
C=C1(t)
Peristaltic pump
Figure 1
Schematic representation of an RPBBR [2].
An RPBBR enables enzyme reusability. The reactor construction is simple and it requires
minimum start-up operation. Since the enzymes are enclosed in the reactor, enzymes
recovery between batches is avoided. Therefore, risk of contamination and handling losses
can be minimized. A faster reaction rate can also be achieved due to the high immobilizedlipase concentration in the reactor.
Most of the time, industrial practice involves large-scale reactor where mass transfer
limitations are very significant. Therefore, a correlation model is important to estimate the
mass transfer coefficient at different scales and operating parameters, to predict reactor
performance and to aid scaling up besides overcoming other engineering constraints.
In order to develop an external mass transfer correlation model for an RPBBR, the hydrolysis
of palm olein using immobilized lipase was used as a case study here. The hydrolysis reaction
was conducted in an organic-aqueous phase. An organic-aqueous system was selected over a
free-solvent system to reduce the viscosity of palm olein. Furthermore, the addition of solvent
enables the concentration of substrates to be determined instead of taking the volumetric ratio
of the substrates.
N-hexane was selected as the organic solvent due to its ability to dissolve most oils, fatty
acids and derivatives of fatty acids. No surfactant or emulsifier was used in this study to ease
downstream separation.
1.1
Development of a Mass Transfer Model
In a reactor packed with enzymes immobilized in a porous matrix, two transport processes
occur. The first process is the transfer of the substrate from the bulk liquid phase to the
surface of immobilized biocatalyst. The second process is the simultaneous diffusion and
reaction of the substrate within the biocatalyst particles.
According to the film-theory, there is a presence of a fictitious laminar film next to the
boundary of any surface in contact with a flowing fluid [3]. Therefore, when fluid flows
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Proceedings of the 1st International Conference on Natural Resources Engineering & Technology 2006
24-25th July 2006; Putrajaya, Malaysia, 500-509
through a bed of particles, a near stagnant film of fluid is present on the surface of the
particles where the fluid velocity is very low. In such regions around the exterior of particles,
the substrate needs to be transported. This transport takes place primarily by molecular
diffusion and it is called external mass transfer.
Murugesan and Sheeja [4] reported that in a co-current packed-bed reactor with up-flow
mode of operation, the formation of surface film on the immobilized beads relatively reduces
the observed rate of the reaction. Cooney [5], Nath and Chand [6] also found evidences of
external film effects leading to convective mass transfer and therefore influences the reaction
rates in immobilized packed-bed reactors.
Aksu and Bülbül [7]’s investigation of external mass transfer on phenol removal by
immobilized cell shows that the external mass transfer rate and observed biodegradation
reaction rate are affected by flow rate. In their experimental results, the pseudo first-order
biodegradation rate constants increase while the phenol uptakes decrease with increasing
flow rates. This is due to inefficient residence times between living cells and phenol at high
flow rates, where the space time in the column is too short and the solute does not have
enough time to diffuse into the pores of the particles. Other factors affecting the external
mass transfer rate include substrate concentration, biomass quantity, and particle size.
In this study, the mass transfer model was developed based on the model developed by Aksu
and Bülbül [7]. A few assumptions have been made during the development of this model as
follows:
¾ The reaction follows a first-order rate (this is especially true at low substrate
concentrations)
¾ The immobilized enzyme particles are spherical
¾ The packed-bed column has a plug flow with no axial dispersion
¾ The enzyme activity throughout the particle is uniform
1.2
Apparent Reaction Rate
A material balance for palm olein (substrate) in the packed-bed column was first developed
as shown in equation (1).
(
HQ dC
)
x 6 x 10-2 = -r
W dz
(1)
where r is the reaction (substrate consumption) rate (mg g-1 h-1), Q the volumetric flow rate
(ml min-1), H the height of the column (cm), W the total amount of immobilized enzyme
particles (g), and dC/dz the concentration gradient along the column length (mg l-1 cm-1).
Since a first-order reaction rate was assumed, the relation between the apparent reaction rate
and bulk substrate (palm olein) concentration in the column is given as:
(2)
r = kp C
-1 -1
where kp is the apparent first-order reaction rate constant (l g h ) or the observed reaction
rate constant and C is the bulk substrate concentration (mg l-1). Combining equation (1) and
(2) gives:
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Proceedings of the 1st International Conference on Natural Resources Engineering & Technology 2006
24-25th July 2006; Putrajaya, Malaysia, 500-509
(
HQ dC
)
x 6 x 10-2 = - kpC
W dz
(3)
Equation (4) is found by integrating equation (3) using boundary conditions at z = 0 of C =
Cin, and at z = H of C = Cout.
ln (
C in
W
) = kp x (103/60)
C out
Q
(4)
where Cin is the column inlet substrate (palm olein) concentration (mg l-1) and Cout is the
column outlet substrate (palm olein) concentration (mg l-1). The concentration at the outlet of
the packed-bed is therefore given by:
Cout = Cine-N
(5)
with N defined as
N=
W
kp x (103/60)
Q
(6)
Equation (5) only gives the relation between the inlet and outlet concentration of palm olein
in the packed-bed column every time the fluid flows through the column. Since a recycling
system is involved, the inlet concentration to the column changes for every cycle. Therefore,
an overall mass balance for an RPBBR as developed by Mutlu and Gökmen [2] is as follows.
Referring to Figure 1.1, if the reservoir is a perfectly mixed tank, the total mass balance gives
dVres
=0
dt
(7)
where Vres is the volume of the reacting solution in the reservoir (ml). The component balance
in the reservoir gives
dC1
1
= − (C 2 − C1 )
τ
dt
(8)
where τ is the residence time (min) in the reservoir (Vres/Q), C1 the concentration of palm
olein (mg l-1) in the reservoir, and C2 the concentration (mg l-1) at the outlet of the packed-bed
column to be circulated back to the reservoir. Based on equation (5), C2 can be defined as
follows:
C2 = C1e-N
(9)
Substituting equation (9) into equation (8) gives
dC1
1
= − (C1 e − N − C1 )
τ
dt
(10)
Integrating equation (10) using boundary conditions of Vres = Vres and C1 = C0 when t = 0
gives the change of palm olein concentration in the reservoir with time as
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Proceedings of the 1st International Conference on Natural Resources Engineering & Technology 2006
24-25th July 2006; Putrajaya, Malaysia, 500-509
C1 = C0 exp[-(e-N – 1)t/τ]
(11)
Based on equation (11), a plot of ln (C1/C0) versus time will give a slope term as follows:
Slope = -
e−N − 1
τ
(12)
If a constant quantity of immobilized enzyme particles is used, the apparent reaction rate
constant, kp for each flow rate can be found from equation (6) when the value of N is known
(from the slope as shown in equation (12)). kp is the apparent rate constant which takes into
account both the reaction and mass transfer phenomena.
1.3
Apparent Reaction Rate as a Function of Reaction and Mass Transfer Limitation
The mass transfer rate of the palm olein from the bulk liquid to the surface of the
immobilized beads is proportional to the external mass transfer coefficient, area of mass
transfer and the concentration difference between the bulk and the external surface of
immobilized bead:
rm = kmam(C – Cs)
(13)
where rm is the external mass transfer rate (mg g-1 h-1), km is the external mass transfer
coefficient (cm h-1), and am is the surface area per unit weight of immobilized enzyme for
mass transfer (cm2 mg-1), while C and Cs is the substrate concentration in the bulk liquid and
at the surface of the immobilized particle (mg l-1) respectively. The value of am can be
determined using the following equation
am = 6/ρpdp
(14)
with dp as the particle diameter (cm) and ρp the particle density (mg cm-3).
The first-order reaction rate at the surface of the enzyme particle can be written as
follows:
r = kCs
(15)
where k is the surface first-order reaction rate constant (l g-1 h-1).
Since the rates of external mass transfer and reaction steps will be the same at steady state,
equations (13) and (15) are equated and rearranged to give
Cs =
k m am C
k + k m am
(16)
Substituting equation (16) into equation (15) and equating with equation (2), the effects of
reaction and mass transfer on the apparent reaction rate constant, kp is shown in equation
(17).
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Proceedings of the 1st International Conference on Natural Resources Engineering & Technology 2006
24-25th July 2006; Putrajaya, Malaysia, 500-509
kp =
kk m a m
k + k m am
(17)
or
1
1
1
= +
k p k k m am
(18)
The terms (1/k) and (1/kmam) show the contributions of reaction and external mass transfer
resistance on the kp, respectively, at constant temperature.
1.4
Mass Transfer Correlation Model
The value of k is constant as far as this particular reaction is concerned and is independent of
the operating parameter, particularly the mass flow rate and the scale of the system. However,
the external mass transfer coefficient, km changes with parameters such as flow rate, reactor
diameter and fluid properties. This in turn changes the apparent reaction rate. Therefore, a
correlation is needed so that the mass transfer coefficient can be estimated at different
operating parameters and during scale-up.
Average mass transfer coefficients between the bulk fluid and particle surface in the packedbed reactor can be correlated in terms of dimensionless groups which characterize the flow
conditions [6, 8, 9, 10]. The correlation of the external mass transfer coefficient, km, with
variables such as flow rate, reactor diameter and fluid properties can be obtained by defining
a dimensionless group as follows:
k ρ
JD = m
G
⎛ μ
⎜
⎜ ρD
f
⎝
⎞
⎟
⎟
⎠
2
3
(19)
where JD is the Colburn factor, defined in terms of Schmidt number and Reynolds number.
The Schmidt number is the term in parentheses in equation (19) as follows:
N Sc =
μ
ρD f
(20)
The symbols μ, ρ and Df are the fluid viscosity (g cm-1 min-1), density (g ml-1) and diffusivity
(cm min-1), respectively.
The Reynolds number can be defined as
Re =
d pG
μ
(21)
where dp is the particle diameter (cm).
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Proceedings of the 1st International Conference on Natural Resources Engineering & Technology 2006
24-25th July 2006; Putrajaya, Malaysia, 500-509
G is the mass flux (g cm-2 min-1) and it can be calculated using equation (22) as follows:
G=
Q
ac ε
(22)
where Q is the volumetric flow rate (ml min-1), ac the cross-sectional area of column (cm2)
and ε the void fraction in a packed-bed.
A few correlations for mass flow rates are available, varying in the dependence of the
Colburn factor, JD, on Re, as follows:
JD = K Re(n-1)
(23)
Different mass transfer conditions have different values of K and n. The value of n varies
from 0.1 to 1.0. Equating equation (19) and (23) and solving for the mass transfer coefficient
gives
⎛ K ⎞⎛ μ
k m = ⎜⎜ ⎟⎟⎜
⎝ ρ ⎠⎜⎝ ρD f
⎞
⎟
⎟
⎠
−2 / 3
⎛dp
⎜
⎜ μ
⎝
⎞
⎟
⎟
⎠
n −1
Gn
(24)
or
km = A Gn
(25)
⎛ K ⎞⎛ μ
where A = ⎜⎜ ⎟⎟⎜
⎝ ρ ⎠⎜⎝ ρD f
⎞
⎟
⎟
⎠
−2 / 3
⎛dp
⎜
⎜ μ
⎝
⎞
⎟
⎟
⎠
n −1
Substituting equation (25) into equation (18) and rearranging it leads to the following
equation:
⎛ 1
⎜
⎜k
⎝ p
⎞ ⎛ 1
⎟=⎜
⎟ ⎜ Aa
⎠ ⎝ m
⎞⎛ 1 ⎞ ⎛ 1 ⎞
⎟⎟⎜ n ⎟ + ⎜ ⎟
⎠⎝ G ⎠ ⎝ k ⎠
(26)
Equation (26) can be analyzed for different values of n ranging from 0.1 to 1.0. A straight
line of slope 1/(Aam) and intercept 1/k should be obtained if the experimentally measured
values of 1/kp versus 1/Gn for each value of n is plotted. The calculated values of A and k (the
surface first-order reaction rate constant) from the graph are then used to get the values of km
(using equation (25)) and an estimated kp (using equation (18)). A trial-and-error procedure is
repeated for all n values until the estimated value of kp matches well with the experimental kp.
2.0
Materials and Methods
The commercial immobilized lipase, Lipozyme TL IM (bead size 0.3-1.0 mm, wet bulk
density 415 kg/m3), was obtained from Novozymes. A commercial cooking oil (Seri Murni)
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was used as the source of palm olein. Oleic acid, palmitic acid and linoleic acid (GC
standard) were purchased from Sigma-Aldrich.
The batch stirred-tank reactor consisted of a water-jacketed vessel with a maximum capacity
of 50 ml and a magnetic stirrer. A water bath (Grant Instruments, Cambridge, England) was
used to maintain the temperature of the reaction mixture in the vessel. A peristaltic pump
(Masterflex, Cole-Parmer) and a thermostat XK 16/20 (16 mm ID x 20 cm length) jacketed
column from Pharmacia Biotech, Sweden was connected to the batch reactor to form a
recirculated packed-bed batch reactor (RPBBR).
The reaction mixture (15 mL of palm olein, 23 mL of n-hexane, 2 mL of water) was first
prepared and incubated at 55 0C and 200 rpm. 2 g of immobilized lipase was then packed into
the jacketed column. A time zero-sample was taken. Reaction was initiated by switching on
the peristaltic pump. Samples were taken at different time intervals and analysed for fatty
acids. Experiments were repeated at three different flow rates (0.5, 5, 20 ml min-1).
All the samples were analysed using gas chromatography. A Shimadzu GC-17A Version 3
(Kyoto, Japan) equipped with a flame-ionization detector (FID) was used. A Nukol fusedsilica capillary column (15 m length x 0.53 mm ID x 0.5 μm film thickness, Supelco, USA)
was used with nitrogen as the carrier gas. The injector and detector were set at 220 0C. The
column temperature was programmed to rise from 180 0C to 215 0C at 12 0C/min and
maintain for 4 minutes before rising again at 12 0C/min until it reaches 220 0C and stay for 2
minutes. The gas chromatography column was connected to Shimadzu CLASS-VP
Chromatography Data System software (Columbia, USA). Calibration curves for the fatty
acids were first prepared using external GC standard.
3.0
Results and Discussion
The effect of mass flow rate on the apparent rate of reaction was investigated in this study.
Table 1 shows the experimental values of kp at different flow rates, Q. According to Table 1,
the apparent first-order reaction rate constants increase with the increasing flow rates in the
range studied. As the flow rates increase, the turbulence of the flow increases and
consequently reduces the mass transfer resistance.
Table 1 Apparent first-order reaction rate constants at various flow rates.
kp x 103 (l g-1 h-1)
6.123
21.927
26.998
Q (mL/min)
0.5
5
20
Reynolds numbers, Schmidt numbers and mass fluxes were calculated from equations 20, 21
and 22 using μ = 0.207 g cm-1min-1, ρ = 0.74 g mL-1, Df = 5.59 x 10-3 cm min-1, dp = 0.065
cm, ac = 2.01 cm2 and ε = 0.04. Plot of 1/kp against 1/Gn for n = 0.4, n = 0.6, n = 0.8 and n =
1.0 is illustrated in Figure 2.
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180
180
160
160
140
140
120
120
1/kp
1/k p
100
80
60
100
80
40
60
20
40
0
-20
20
0
0.1
0.2
0.3
0.4
0.5
0.6
0
-40
0
1/G
0.1
0.15
0.2
1/G
(a)
0.25
0.3
0.35
0.4
0.6
(b)
180
180
160
160
140
140
120
120
100
100
1/kp
1/kp
0.05
0.4
80
80
60
60
40
40
20
20
0
0
0
0.05
0.1
0.15
1/G
0.2
0.25
0
0.8
0.05
0.1
1/G
(c)
0.15
0.2
1.0
(d)
Plot of 1/kp against 1/Gn for (a) n = 0.4; (b) n = 0.6; (c) n = 0.8; (d) n = 1.0.
Figure 2
The values of k and A at different n can be obtained from the plots in Figure 2. Since the
intercept in Figure 2(a) has a negative value, it was not being further analyzed. Table 2 listed
the values of k and A for n = 0.6, n = 0.8 and n = 1.0. These values were used to calculate for
km (using equation (25)) and kp (obtained from equation (18)), which were then compared
with the experimental values of kp. The results are tabulated in Table 3.
Based on the comparison in Table 3, it is found that the calculated kp constants when n = 1.0
are quite closed to the kp constants found experimentally. The value of K when n = 1.0 is
0.056. The results of this study show that a correlation JD = 0.056 can be used to estimate the
external mass transfer coefficient during the hydrolysis of palm olein in a reactor packed with
immobilized lipase. The external mass transfer coefficient changes proportionally with the
mass flux when the Schmidt number is constant and it is independent on the Reynolds
number. As can be seen from Table 3, the external mass transfer coefficient increases when
the flow rate increases. This is because higher flow rate gives higher turbulence and thus
reduces the mass transfer resistance.
Table 2 Values of k and A calculated from the plots of 1/kp against 1/Gn at various n values.
N
0.6
0.8
1.0
k x 103 (l g-1 h-1)
65.032
36.782
30.104
508
A x 103
10.226
7.676
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Proceedings of the 1st International Conference on Natural Resources Engineering & Technology 2006
24-25th July 2006; Putrajaya, Malaysia, 500-509
Table 3 The comparison between experimental and calculated values of kp at different n values.
Experimental
Q
(mL/min)
kp x 103
(l g-1 h-1)
0.5
6.123
5
21.927
20
26.998
4.0
n = 0.6
kp x 103
km
-1
(cm h ) (l g-1 h-1)
0.03
6.163
0.12
19.132
0.28
31.811
n = 0.8
kp x 103
km
-1
(cm h ) (l g-1 h-1)
0.03
6.136
0.21
20.531
0.63
29.167
n = 1.0
kp x 103
km
-1
(cm h ) (l g-1 h-1)
0.03
6.125
0.35
21.634
1.38
27.420
Conclusions
The external mass transfer limitation in a reactor packed with immobilized enzyme has
significant effects on the overall reaction rate. This is especially true in large-scale reactors. A
mass transfer correlation model in terms of dimensionless numbers is therefore very
important in the design and simulation of reactor performance. Based on the results of this
study, a correlation model JD = 0.056 accurately predicted the experimental data for the
hydrolysis of palm olein in an RPBBR using immobilized lipase. This model is valid for the
range of flow rates used in this study. However, further studies should be carried out at a
larger range of flow rates to ensure the applicability of this model.
Acknowledgements
The authors wish to thank Vote No. 75131 for the financial support and also Chemical
Engineering Pilot Plant (CEPP), UTM for supplying some of the materials in this study.
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