Journal of Food Engineering 159 (2015) 76–85
Contents lists available at ScienceDirect
Journal of Food Engineering
journal homepage: www.elsevier.com/locate/jfoodeng
Mathematical modeling of transport phenomena and quality changes
of fish sauce undergoing electrodialysis desalination
Kuson Bawornruttanaboonya a, Sakamon Devahastin a,⇑, Tipaporn Yoovidhya a, Nathamol Chindapan b
a
b
Department of Food Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi, 126 Pracha u-tid Road, Tungkru, Bangkok 10140, Thailand
Department of Food Technology, Faculty of Science, Siam University, 38 Phetkasem Road, Phasicharoen, Bangkok 10160, Thailand
a r t i c l e
i n f o
Article history:
Received 27 October 2014
Received in revised form 4 March 2015
Accepted 10 March 2015
Available online 21 March 2015
Keywords:
Amino nitrogen
Aroma
Color
Nernst–Planck equation
Salt concentration
Osmosis
Water flux
a b s t r a c t
Despite many existing attempts on modeling electrodialysis (ED) desalination, no work has so far
modeled the effect of water transport due to osmosis across the membranes on the quality changes of
such a highly concentrated product as fish sauce during the desalination. In this study, a model taking
into account the effect of water transport due to the osmotic pressure and electric potential is proposed.
Coupled mass and momentum transport equations, along with appropriate initial and boundary
conditions, were numerically solved using the finite element method through COMSOL Multiphysics™
version 4.3. The predictability of the model was compared with that of the model neglecting water
transport. The model was capable of predicting the evolutions of the salt concentration and volume as well
as the quality changes, in terms of the total nitrogen concentration, total amino nitrogen concentration,
total aroma concentration and total change of color, of fish sauce undergoing ED desalination at both
laboratory and pilot scales. The model was validated against the experimental results and noted to
satisfactorily predict the evolutions of the salt concentration as well as volume of the diluate (fish sauce)
and concentrate solutions at both scales; quality changes were also well predicted. The effect of
neglecting the water transport during ED on the various predicted values was also illustrated. When
water transport was not considered, the evolutions of the salt concentration of both the diluate and
concentrate solutions as well as the changes of all quality attributes were not adequately predicted.
Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction
Fish sauce is a popular condiment and is used to prepare a wide
variety of dishes in both Thai and other Asian cuisines. Despite its
desirable flavor and aroma characteristics, fish sauce contains a
high level of salt (sodium chloride), typically in the range of 20–
25% (w/w). A high intake of sodium is well recognized to result
in higher risks of hypertension and cardiovascular diseases (Ajani
et al., 2005). In order to reduce the sodium content of fish sauce,
electrodialysis (ED) desalination is an alternative that has recently
been investigated (Chindapan et al., 2009). Some important characteristics of fish sauce are nevertheless unavoidably affected by the
ED. These include such important quality attributes as the total
nitrogen and total amino nitrogen concentrations as well as aroma
and color (Chindapan et al., 2009, 2011).
A capability to model and hence optimize the ED desalination
process to obtain fish sauce with acceptable salt content and quality is desired. Only a few related studies are so far available,
⇑ Corresponding author. Tel.: +66 2 470 9244; fax: +66 2 470 9240.
E-mail address:
[email protected] (S. Devahastin).
http://dx.doi.org/10.1016/j.jfoodeng.2015.03.014
0260-8774/Ó 2015 Elsevier Ltd. All rights reserved.
however. Chindapan et al. (2013) employed artificial neural network (ANN) to predict selected quality changes of fish sauce during
ED desalination; the process was then optimized via the use of
multi-objective optimization using genetic algorithm (MOGA).
Although satisfactory predictions were noted, the model relies
rather heavily on the training data and is therefore limited. Only
the effects of the applied voltage and residual salt concentration
are also included in the model. A desirable model should indeed
take into account the effects of other important parameters,
including the stack construction, flow rates of diluate and concentrate streams and number of ED cell pairs (Lee et al., 2002; Ortiz
et al., 2005; Tsiakis and Papageorgiou, 2005; Nikbakht et al.,
2007; Fidaleo et al., 2012).
Despite many attempts on modeling ED desalination, none
exists to explain the effect of water transport due to osmosis across
the membranes on the quality changes of fish sauce (or similar
products) during the desalination. It is noted that the effect of
water transport would become significant when desalinating such
a highly concentrated solution as fish sauce. Although some
models do include the osmosis term and hence are capable of
predicting the water transport across the membranes during ED
77
K. Bawornruttanaboonya et al. / Journal of Food Engineering 159 (2015) 76–85
desalination, no attempts have been made to employ such a term to
explain the quality changes of the diluate (Bailly et al., 2001; Fidaleo
and Moresi, 2010, 2011; Rohman et al., 2010; Fidaleo et al., 2013).
In this work, a model based on the conservation equations of
mass and momentum along with Nernst–Planck equation, taking
into account the effect of water transport due to the osmotic
pressure and electric potential is proposed to predict the changes
in the salt concentration and volume of fish sauce undergoing ED
desalination in a batch recirculation mode. Kinetic model is used
in conjunction with the transport model to predict the changes
in the fish sauce quality. The model was validated against the
laboratory-scale and pilot-scale experimental results. The considered
parameters include the initial ion concentrations, flow rates of the
diluate and concentrate streams, applied voltage and membrane
characteristics. The effect of neglecting the water transport during
ED on the predicted values was also illustrated.
2. Materials and methods
Fish sauce obtained from a local distributor was desalinated
using both the laboratory-scale and pilot-scale ED systems. The
fish sauce contained 38.8% (w/w) total soluble solids, of which
about 65% and 32% were sodium chloride and total proteins,
respectively (Chindapan et al., 2009). The details of the ED system
set-ups and experimental procedures are those of Chindapan et al.
(2009) and Jundee et al. (2012). A summary of the basic system and
operating information is given in Table 1. The fractions of the total
current carried by the sodium ion and chloride ion are known as
the transport number. The values of the transport numbers are
from the specifications of the anion- and cation-exchange
membranes. The applied voltages at the laboratory scale were 6,
7 and 8 V; the pilot-scale system was operated only at 6 V. The
upper voltage limit was the highest voltage that provided the current density of not higher than 16 A, which is the recommended
maximum current by the membrane manufacturer.
3.1. Model description and assumptions
The assumed geometry of an ED cell pair consists of a diluate
compartment, a concentrate compartment, a cation-exchange
membrane, an anion-exchange membrane as well as inlets and
outlets for the diluate and concentrate streams. The ED geometry
was drawn using COMSOL Multiphysics™ version 4.3 (Comsol
AB, Stockholm, Sweden) and is shown in Fig. 1.
The following assumptions are made:
Electroneutrality during the ED desalination process.
Diffusivities and mobilities of cation and anion are functions of
the ion concentrations.
Resistance of the membranes is a function of both the salt concentration and time.
Current densities of the ions are assumed to be equal to the current density of the solutions at the interface of the membranes.
Density and viscosity of the fish sauce are functions of the salt
concentration and were estimated from the data of Chindapan
et al. (2009).
Transport number of anion is equal to the transport number of
cation.
Incompressible laminar flow.
No chemical reactions.
3.2. Mass transfer phenomenon
The conservation equation that can be used to describe the
mass transfer in either a diluate or concentrate compartment
consists of the transient term, convection term and flux term.
The equation, in terms of the molar concentration of sodium ion
(cation), which is equal to the salt concentration, is shown in
lc
ldil
la
3. Mathematical model development
The model is developed based on two-dimensional transport
phenomena. The effects of the initial ion concentrations, flow rates
of the diluate and concentrate streams, applied voltage and
membrane characteristics are included in the model.
Table 1
A summary of basic system and operating information.
1 2
Parameter
Lab-scale
Pilot-scale
Initial volume of diluate (L)
Initial salt concentration of diluate (% w/w)
Initial salt concentration of concentrate (% w/w)
Volumetric flow rates of diluate and concentrate
per compartment pair (Q, m3/s)
Volumetric flow rate of electrolyte (m3/s)
Thickness of anion and cation-exchange
membranes (la and lc, mm)
Width of diluate and concentrate compartments
(ldil and lconc, mm)
Membrane size (mm2)
Compartment length (L, mm)
Number of compartment pairs (N,
dimensionless)
Total effective membrane surface area (Aeff, m2)
Transport number of anion and cation-exchange
membranes (ta and tc, dimensionless)
Cross-sectional area of diluate and concentrate
compartments (A, m2)
Transport number of water (tw, dimensionless)
Constant for membrane transport by osmosis
(Lw, mol m2 s1 Pa1)
1
25
1
1.11 106
100
25
1
6 106
4.44 106
0.5
6.67 105
0.5
0.5
0.5
110 110
80
5
300 500
400
50
0.064
0.93
10
0.93
4 105
1.25 104
7.5
6 1010
7.5
8 109
3
4 5
L
Y
X
lconc
2
Fig. 1. A schematic diagram of ED compartment pair: 1, 5 = half concentrate
compartments (lconc/2 = 0.25 mm), 2 = cation exchange membrane (lc = 0.5 mm),
3 = diluate compartment (ldil = 0.5 mm), 4 = anion exchange membrane (la = 0.5
mm). Compartment lengths (L) of laboratory-scale and pilot-scale systems were
80 mm and 400 mm, respectively.
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K. Bawornruttanaboonya et al. / Journal of Food Engineering 159 (2015) 76–85
Eq. (1). The equation describing the water transport, in terms of the
molar concentration of water, is given in Eq. (2).
@C þ
@C þ
@C þ
þu
þv
¼ ðr jþ Þ
@t
@x
@y
ð1Þ
@C w
@C w
@C w
þu
þv
¼ ðr jw Þ
@t
@x
@y
ð2Þ
where C+ is the molar concentration of sodium ion (mol m3), Cw is
the molar concentration of water, u is the bulk flow velocity in the
x-direction (m s1), v is the bulk flow velocity in the y-direction
(Q/A, m s1) and j+ and jw are, respectively, the total molar fluxes
of sodium ion and water molecules in the flow channels (mol m2
s1). Q is the volumetric flow rate per cell pair (m3 s1) and A is
the cross-sectional area of each flow compartment (m2).
The total molar flux of sodium ion depends on the diffusion due
to concentration gradient as well as on the migration due to electric potential gradient and convection due to bulk movement in the
cross flow direction (x-direction in Fig. 1). The total molar flux (j+)
can then be described by Eq. (3). For the total molar flux of water,
electric potential gradient is neglected as shown in Eq. (4).
jþ ¼ ½Dþ rC þ ½zþ Ftþ C þ r£ þ ½C þ u
ð3Þ
jw ¼ ½Dw rC w þ ½C w u
ð4Þ
where z+ is the valence number of sodium ion (z+ = 1), t+ is the
mobility of sodium ion (m2 s1 V1), D+ is the diffusivity of sodium
ion (m2 s1), F is the Faraday constant (C mol1) and r£ is the electric potential gradient (V m1). Eq. (3) is indeed the well-known
Nernst–Planck equation, in which the first, second and third terms
on the right-hand side represent the contributions of the fluxes
from diffusion, migration and convection, respectively. Eqs. (3),
(4) can be substituted into Eqs. (1), (2) to yield, respectively:
@C þ
@C þ
@C þ
þu
þv
¼ ½Dþ rC þ þ ½zþ Ftþ C þ r£ ½C þ u
@t
@x
@y
ð5Þ
@C w
@C w
@C w
þu
þv
¼ ½Dw rC w ½C w u
@t
@x
@y
ð6Þ
The initial and boundary conditions needed to solve Eqs. (5) and (6)
are as follows:
Initial conditions (at t = 0):
Diluate compartment:
Outlet boundary conditions
Diluate compartment:
C þ;dil ¼ C þ;out;dil
ð11Þ
C w;dil ¼ C w;out;dil
ð12Þ
Concentrate compartment:
C þ;conc ¼ C þ;out;conc
ð13Þ
C w;conc ¼ C w;out;conc
ð14Þ
Potential boundary conditions
At far left side of the cell pair, the electric potential is:
£¼0
ð15Þ
At far right side of the cell pair, the electric potential is:
£¼
Applied voltage
Number of cell pairs
ð16Þ
At the surface of an anion-exchange membrane and a cation-exchange membrane, the electric potential is:
£m;a ¼ £m;c ¼
RT
Cþ
ln
F
C þ;c
ð17Þ
where R is the gas constant (8.314 J mol1 K1), T is the absolute
temperature (303.15 K) and C+,c is the cation concentration inside
a cation-exchange membrane (mol m3). Cation concentration
inside the cation exchange membrane was assumed to be equal
to the fixed ion concentration of 1000 mol m3 (McKetta, 1993).
For the ED geometry in Fig. 1, the fluxes of sodium ion (J+) and
water molecules (Jw) across each membrane can be represented by
Eqs. (18), (19). The difference in the osmotic pressure between the
diluate and concentrate compartments can be calculated using Eqs.
(20), (21) (Sagiv et al., 2014).
Jþ ¼
iþ tþ
F
Jw ¼
iþ tw
þ L w Dp
F
ð18Þ
ð19Þ
Dp ¼ pdil pconc
ð20Þ
p ¼ 4260 þ 0:7C 2þ
ð21Þ
where i+ is the current density of sodium ion (A m2) and t+ is the
ionic transport number in cation-exchange membranes. Lw is the
empirical constant for membrane transport by osmosis
(mol m2 s1 Pa1), Dp is the difference in osmotic pressure (Pa)
C+,dil, Cw,dil = initial concentration
£dil ¼ 0
Concentrate compartment:
and C þ (mol m3) is the average sodium ion concentration.
P
The current density in Eq. (18) is defined as i = F zJ. The summation of valence of ions in this model is that of sodium ion and
that of chloride ion. Using Eq. (3) the current density of the ions
in a dilute aqueous solution can be written as:
C+,conc, Cw,conc = initial concentration
£conc ¼ 0
Membrane domain:
£m ¼ 0
iþ ¼ F2 r£z2þ tþ C þ Fzþ Dþ rC þ þ Fuzþ
Boundary conditions:
Inlet boundary conditions
Diluate compartment : C þ;in;dil ¼ C þ;out;dil
ð7Þ
C w;in;dil ¼ C w;out;dil
ð8Þ
Concentrate compartment:
C þ;in;conc ¼ C þ;out;conc
ð9Þ
C w;in;conc ¼ C w;out;conc
ð10Þ
ð22Þ
At the membrane interface, the current density in the solutions
is assumed to be equal to the current density of the membrane
at the interface. The current density of the membrane is
assumed to be a function of the membrane conductivity (rm)
and electric potential gradient as shown in Eq. (23). The electric
potential at the surface of both a cation-exchange membrane
and an anion-exchange membrane can be calculated from Eq.
(17).
iþ;m ¼ rm r£
ð23Þ
K. Bawornruttanaboonya et al. / Journal of Food Engineering 159 (2015) 76–85
Volume variation in the diluate or concentrate compartment is
affected by both the salt and water transfer as expressed by
Eqs. (24), (25).
dV dil
dnsalt;dil
dnw;dil
¼
M salt þ
Mw
dt
dt
dt
dV conc
¼
dt
ð24Þ
dnsalt;conc
dnw;conc
M salt þ
Mw
dt
dt
ð25Þ
where Vdil and Vconc are the volumes of the solutions (m3) in
the diluate and concentrate compartments; nsalt,dil and nsalt,conc
are the number of moles of salt in the diluate and concentrate
compartments; Msalt and Mw are the molecular weights of salt
and water. The number of moles of salt can be calculated by
Eqs. (26), (27), while the number of moles of water can be expressed
by Eqs. (28), (29).
dC salt;dil
V dil;0
dt
!
dC salt;conc
V conc;0
dt
dnsalt;conc
¼
dt
!
dC w;dil
V dil;0
dt
dnw;dil
¼
dt
V dil;0
V conc;0
!
¼
dC salt;conc
dt
¼
dnsalt;conc
dt
ð37Þ
ð26Þ
tþ ¼ 5 1012 þ ð3 1015 ÞC salt þ ð1 1018 ÞC 2salt
ð38Þ
ð27Þ
where D+ and Dw are the mass diffusivities of sodium ion and water
in fish sauce; the ranges of the diffusivities for cation and for water
are 1.0 107 to 2.0 108 m2 s1 and 5.0 107 to 1.0 107
(m2 s1), respectively. t+ is the mobility of sodium ion in fish sauce,
which is in the range of 3.6 1011 to 5.6 1012 (m2 s1 V1).
ð29Þ
C salt;conc
dV conc
dt
ð30Þ
ð31Þ
Continuity and Navier–Stokes equations are used to
describe the laminar momentum transport in either a diluate or
concentrate compartment. The equations are written only in the
y-direction because it is assumed that there is no bulk flow in
the x-direction.
@v
¼0
@y
@v
@v
þv
@t
@y
ð32Þ
¼
Mass diffusivity (D) and mobility (t) of the ions in the fish sauce
at any position in the computational domain were obtained by fitting the simulated results to the laboratory-scale experimental
data at an applied voltage of 6 V. The obtained empirical constants
were then applied to predict the experimental data at other
conditions; the predictions were made at both the laboratory scale
and pilot scale. Mass diffusivity and mobility are again assumed to
be only a function of the salt concentration. The mass diffusivity
and mobility of the ions are described by Eqs. (36)–(38).
Dw ¼ 9 108 þ ð9 1011 ÞC salt þ ð1 1015 ÞC 2salt
3.3. Momentum transfer phenomenon
q
ð35Þ
3.5. Kinetic model development
dnsalt;dil
dV dil
C salt;dil
dt
dt
!
l ¼ 0:0015 þ ð5 108 ÞC salt þ ð5 1011 ÞC 2salt
ð36Þ
Finally, prediction of the salt concentration (mol m3), which must
take into account the effect of osmosis in the diluate and concentrate compartments, is expressed by the first-order differential
equation represented in Eqs. (30), (31).
dC salt;dil
dt
ð34Þ
ð28Þ
!
dC w;conc
V conc;0
dt
dnw;conc
¼
dt
q ¼ 1074:5 þ ð0:0384ÞC salt
Dþ ¼ 2 108 þ ð5 1011 ÞC salt þ ð9 1015 ÞC 2salt
!
dnsalt;dil
¼
dt
79
@p
@2v @2v
þl
þ
@y
@x2 @y2
!
ð33Þ
The quality changes of fish sauce, in terms of the total nitrogen
concentration, total amino nitrogen concentration, total aroma
concentration and total color change, are modeled using the
first-order kinetic equation shown in Eq. (39).
d½A
¼ k½A
dt
ð39Þ
where [A] represents the concentration of a component of interest, k
is the rate constant (s1), which is estimated from the Arrhenius
equation shown in Eq. (40). k0 is noted to be a function of the salt
concentration (Csalt,dil) and water concentration (Cw,dil) as shown
in Eq. (41).
Ea
k ¼ k0 eRT
ð40Þ
k0 ¼ a1 þ a2 C salt;dil þ a3 C 2salt;dil þ a4 C w;dil þ a5 C 2w;dil
ð41Þ
where Ea is the activation energy (J mol1), R is the gas constant
(J mol1 K1), T is the absolute temperature of the fish sauce during
ED (K), a1 ; a2 ; a3 ; a4 ; and a5 are the empirically derived constants.
The constants in Eqs. (40), (41) were obtained by fitting the
corresponding simulated data to the laboratory-scale experimental
results at 6 V. The results are shown in Tables 2 and 3. All model
parameters were indeed obtained by fitting the corresponding
simulated data to the laboratory-scale experimental results at 6 V;
the resulting parameters were then used to predict the laboratoryscale results at 6, 7 and 8 V as well as the pilot-scale results at 6 V.
3.6. Model implementation
where q is the density of the fish sauce (kg m3), p is the pressure
(Pa) and l is the dynamic viscosity of the fish sauce (Pa s).
3.4. Parameters estimation
The physical properties (density and viscosity) of the fish sauce
are assumed to be only a function of the salt concentration
(mol m3). The density and viscosity of the fish sauce at any
position in the computation domain are as described by
Chindapan et al. (2009).
The model equations, along with the initial and boundary conditions, were solved using COMSOL Multiphysics™ version 4.3
(Comsol AB, Stockholm, Sweden). The software is based on the
control-volume finite element method. The elements were of uniform size and suffered no expansion/contraction. The convergence
criteria were simple tolerance, which was set in the program.
Different mesh elements were tested to obtain mesh-independent solutions. At an applied voltage of 8 V, which represents the
highest electric potential tested in this work, the differences in
80
K. Bawornruttanaboonya et al. / Journal of Food Engineering 159 (2015) 76–85
Table 2
Constants of model with water transport consideration.
nitrogen concentration
amino nitrogen concentration
aroma concentration
change of color (DE⁄)
a2
6
7.0 10
1.0 105
3.5 105
1.2 105
a3
9
2.4 10
2.0 109
1 1010
2.5 109
the average salt concentration at the diluate compartment outlet
between using 47,780 and 75,530 elements were negligible.
Therefore, 47,780 elements were used in all simulations.
4. Results and discussion
To assess the predictability of the proposed model, the
simulated results were compared with both the laboratory-scale
experimental results of Chindapan et al. (2009, 2011) and pilotscale experimental results of Jundee et al. (2012). The simulated
and laboratory-scale experimental results were compared at the
applied voltages of 6, 7 and 8 V. On the other hand, comparison
between the simulated and pilot-scale experimental results was
made only at 6 V. It is noted again that the diffusivity, mobility
of sodium ion as well as membrane resistance were fitted only to
the laboratory-scale experimental results at 6 V. The membrane
resistance of the pilot-scale system was fitted to the pilot-scale
experimental data at 6 V.
4.1. Salt concentration evolution
In the diluate compartment, fish sauce with an initial salt
concentration of 25% (w/w) was desalinated in the laboratory-scale
ED system until the salt content of either 22%, 18%, 14%, 10%, 6% or
2% (w/w) had been reached (Chindapan et al., 2009). The time
to obtain the above predetermined salt concentrations was
obtained from the rate of salt removal data shown in Fig. 2. The
rate of salt removal was higher at a higher applied voltage because
of the higher driving force in terms of the electric potential
gradient.
In the concentrate compartment, concentrate solution with an
initial concentration of 1% (w/w) received salt from the diluate
compartment. The salt concentration of the concentrate solution
continuously increased until the end of the process as shown in
Fig. 3. The rate of salt concentration increase was only marginally
higher at a higher applied voltage. The model considering water
transport was able to predict the salt concentration evolution of
the diluate and concentrate solutions during ED at 6, 7 and 8 V well
with R2 0.99 as shown in Figs. 2(a) and 3(a), whereas the model
neglecting the water transport could not well predict the salt
concentration evolution of both solutions. When water transport
was not taken into account, the model over predicted the
salt concentration of the diluate solution and under predicted the
salt concentration of the concentrate solution as shown in
Figs. 2(b) and 3(b). This is because the water transport, which
was due to osmosis, especially at a lower electric potential, led to
a decrease in the salt concentration of the diluate solution and
an increase in the salt concentration of the concentrate solution.
At higher voltages (7 and 8 V) the effect of water transport inclusion in the model was smaller. This is probably because higher
voltages led to excess current generation, which could result in
the transfer of other ion species besides sodium and chloride ions
(Chindapan et al., 2009). This in turn led to reduced current efficiency and hence the smaller differences between the salt removal
rates at the higher voltages.
a4
1.0 10
0
0
0
30
Salt concentration (%, w/w)
Total
Total
Total
Total
a1
12
a5
Ea
15
0
0
0
0
1.0 10
4.5 1015
1.0 1015
0
(a)
0
0
0
14.4
Lab scale 6 V
Predicted 6 V
Lab scale 7 V
Predicted 7 V
Lab scale 8 V
Predicted 8 V
25
20
15
10
5
0
0
100
200
300
400
500
600
700
Time (minute)
30
Salt concentration (%, w/w)
[A]
(b)
Lab scale 6 V
Predicted 6 V
Lab scalte 7 V
Predicted 7 V
Lab scale 8 V
Predicted 8 V
25
20
15
10
5
0
0
100
200
300
400
500
600
700
Time (minute)
Fig. 2. Comparison between simulated and laboratory-scale experimental salt
concentration evolution of diluate solution. (a) With water transport consideration
and (b) without water transport consideration. Salt concentration (% w/w) was
calculated by the following equation: Csalt (% w/w) = [Csalt (mol m3) M.W. of
salt]/[10 density].
Moreover, the simulated evolution of the salt concentration
when water transport was not taken into account was almost linear as shown in Figs. 2(b) and 3(b). This is because the simulated
volume of both the diluate and concentrate solutions would
remain constant throughout the whole ED process, which was
indeed unrealistic.
At the pilot-scale fish sauce was desalinated at 6 V until the salt
content reached 18%, 16% or 14% (w/w) (Jundee et al., 2012).
Similar to the laboratory-scale results, while the salt concentration
of the diluate solution decreased, the salt concentration of the concentrate solution increased as shown in Fig. 4(a) and (b). The model
with water transport consideration was again capable of predicting
the salt concentration evolution at the pilot scale despite the fact
that the necessary model parameters were obtained via the
laboratory-scale data. On the other hand, the model without water
transport consideration could not predict the salt concentration
evolution of both solutions. The model neglecting water transport
81
K. Bawornruttanaboonya et al. / Journal of Food Engineering 159 (2015) 76–85
30
(a)
Salt concentration (%, w/w)
Salt concentration (%, w/w)
14
12
10
8
Lab scale 6 V
Predicted 6 V
Lab scale 7 V
Predicted 7 V
Lab scale 8 V
Predicted 8 V
6
4
2
0
0
100
200
300
400
500
600
(a)
Pilot scale 6 V
25
Predicted
20
Predicted without
water transport
15
10
5
0
700
0
100
200
Time (minute)
10
8
Lab scale 6 V
Predicted 6 V
Lab scale 7 V
Predicted 7 V
Lab scale 8 V
Predicted 8 V
6
4
2
0
0
100
400
500
600
25
(b)
Salt concentration (%, w/w)
Salt concentration (%, w/w)
14
12
300
Time (minute)
200
300
400
500
600
700
Time (minute)
Fig. 3. Comparison between simulated and laboratory-scale experimental salt
concentration evolution of concentrate solution. (a) With water transport
consideration and (b) without water transport consideration. Salt concentration
(% w/w) was calculated by the following equation: Csalt (% w/w) = [Csalt (mol m3)
M.W. of salt]/[10 density].
over predicted the salt concentration of the diluate solution and
under predicted the salt concentration of the concentrate solution
as mentioned earlier. Linear evolution of the salt concentration
was again observed when no water transport consideration was
assumed.
4.2. Diluate volume evolution
Fig. 5(a) shows a comparison between the simulated and
experimental evolutions of the volume of the fish sauce (diluate)
undergoing laboratory-scale ED at 6, 7 and 8 V. During an initial
period of ED, an increase in the diluate volume was observed
when the salt concentration was reduced from 25% to 17%
(w/w) at 6 V and from 25% to 21% at 7 V. This observation is
ascribed to the high water transport from the concentrate compartment to the diluate compartment due to the high osmotic
pressure difference between the two compartments. At the salt
concentrations below 17% and 21% (w/w), on the other hand, a
decrease in the volume of the diluate solution was observed,
not only because of the salt removal but also the losses of water
molecules along with the sodium and chloride ions, probably as a
result of both electric potential and osmotic pressure differences.
However, when the voltage was applied at 8 V, the diluate
volume continuously decreased even at the beginning of the process. Water transport due to the electric potential gradient and
water transport due to the osmotic pressure gradient are noted
to be in the opposite direction at the initial period, but to be in
the same direction toward the end of the process.
(b)
20
15
10
Pilot-scale 6 V
Predicted 6 V
5
Predicted without
water transport
0
0
100
200
300
400
500
600
Time (minute)
Fig. 4. Comparison between simulated and pilot-scale experimental salt concentration evolution of (a) diluate solution and (b) concentrate solution. Simulation
was performed with water transport consideration (—) and without water transport
consideration (). Salt concentration (% w/w) was calculated by the following
equation: Csalt (% w/w) = [Csalt (mol m3) M.W. of salt]/[10 density].
Fig. 5(b) shows that the proposed model with water transport
consideration could well predict the evolution of the diluate volume during pilot-scale ED at 6 V. The initial increase in the diluate
volume (in the range of 16–25% (w/w) salt concentration) was
noted to be more extensive at the pilot scale than at the laboratory
scale. This is probably because the electric potential gradient
across each of the cell pairs, which can be estimated from the electric potential gradient across the ED system divided by the total
number of the cell pairs, of the pilot-scale system was lower than
that of the laboratory-scale unit. Therefore, not only the ions transport from the diluate compartment to the concentrate compartment by the electric potential was lower, but the water transport
from the concentrate compartment to the diluate compartment
by osmotic pressure difference was higher when compared to the
laboratory-scale unit. Ions transport due to electric potential gradient and water transport due to osmotic pressure gradient were
noted to be in the opposite direction. Sample results are indeed
shown in Fig. 6, which illustrates the evolutions of the fluxes of salt
and water as a function of the salt concentration. During an early
stage of the process, the flux of salt was positive, indicating that
the transport of the salt was in the positive coordinate direction
(see Fig. 1). On the other hand, in the same earlier stage, the flux
of water was negative, indicating that the transport of water was
in the negative coordinate direction. Toward the end of the process,
however, the direction of the water transport was reversed. This
implies that during an early stage of the process, the transport of
water was from the concentrate to the diluate. Toward the end
82
K. Bawornruttanaboonya et al. / Journal of Food Engineering 159 (2015) 76–85
900
800
Volume of diluate (mL)
constant is described by the Arrhenius equation, while the effects
of salt and water concentrations are included in k0. The results
indicated that only DE⁄ depended on the temperature, with the
activation energy of 14.4 kJ mol1 (Tables 2 and 3).
(a)
700
600
500
Lab scale 6 V
Predicted 6 V
Lab scale 7 V
Predicted 7 V
Lab scale 8 V
Predicted 8 V
400
300
200
100
0
0
5
10
15
20
25
30
Salt concentration (%, w/w)
Volume of diluate (L)
108
(b)
106
104
102
100
98
Pilot scale 6 V
96
Predicted 6 V
94
0
5
10
15
20
25
30
4.3.1. Total nitrogen concentration evolution
Fig. 7 shows a comparison between the simulated and laboratory-scale experimental results of the total nitrogen concentration evolution; the experimental results are those of Chindapan
et al. (2009). Since the total nitrogen concentration is referred to
as the protein concentration, a decrease in the total nitrogen concentration when the salt concentration was reduced from 25% to
12% (w/w) at 6 V, from 25% to 13% (w/w) at 7 V and from 25% to
15% (w/w) at 8 V might have resulted from membrane fouling
due to protein deposits (Cros et al., 2005; Chindapan et al., 2009)
and dilution effect by water transport. This is because proteins cannot permeate through the membranes due to their larger molecular size (Sato et al., 1995). This phenomenon was observed to be
more significant at lower voltages in accordance to the increase
in the volume of the fish sauce mentioned earlier (see Fig. 5). In
contrast, a significant increase in the total nitrogen concentration
was observed when the salt concentration was reduced to less than
7.6% (w/w) at 6 V, 10.5% (w/w) at 7 V and 11.1% (w/w) at 8 V. This
is probably because of the loss of water from the diluate
compartment to the concentrate compartment by the osmotic
pressure difference and by the electric potential difference, which
became more important at a higher voltage and salt removal level.
The model considering water transport was able to predict the evolution of the total nitrogen concentration better than the model
Salt concentration (%, w/w)
10
Flux of water
Molar flux (mol⋅m-2 ⋅s-1 )
8
Flux of salt
6
4
2
2.0
Total nitrogen concentration
(g/100 mL)
Fig. 5. Comparison between simulated and predicted change in volume of diluate.
(a) Laboratory scale at 6, 7 and 8 V and (b) pilot scale at 6 V.
1.9
1.8
1.7
Lab-scale 6 V
Predicted 6 V
Lab-scale 7 V
Predicted 7 V
Predicted 8 V
Predicted 8 V
1.6
1.5
(a)
1.4
0
0
5
10
15
20
25
0
30
5
-2
10
15
20
25
30
Salt concentration (%, w/w)
-4
Salt concentration (%, w/w)
Fig. 6. Predicted fluxes of salt and water.
of the process, the transport of water was instead from the diluate
to the concentrate. Therefore, if the rate of salt removal was lower,
water would more easily diffuse into the diluate compartment.
This is indeed reflected by the higher constant for membrane
transport by osmosis (Lw) in Eq. (19); see also Table 1.
4.3. Quality evolutions
First-order kinetic model was employed to predict the
evolutions of the total nitrogen concentration, total amino nitrogen
concentration, total aroma concentration and DE⁄ of fish sauce
undergoing ED desalination. The temperature effect on the rate
Total nitrogen concentration
(g/100 mL)
2.0
-6
1.9
1.8
1.7
Lab-scale 6 V
Predicted 6 V
Lab-scale 7 V
Predicted 7 V
Predicted 8 V
Predicted 8 V
1.6
1.5
(b)
1.4
0
5
10
15
20
25
30
Salt concentration (%, w/w)
Fig. 7. Comparison between simulated and laboratory-scale experimental total
nitrogen concentration evolution. (a) With water transport consideration and (b)
without water transport consideration.
83
K. Bawornruttanaboonya et al. / Journal of Food Engineering 159 (2015) 76–85
gradients led to a significant increase in the total nitrogen
concentration.
For the pilot-scale results of Jundee et al. (2012), the total
nitrogen concentration decreased slightly when the salt concentration was reduced from 25% to 14% (w/w) as shown in Fig. 8;
this trend is similar to that of the laboratory-scale results.
Therefore, the rate constant fitted to the laboratory-scale results
at 6 V could be used to predict the pilot-scale results reasonably
well. A significant decrease in the total nitrogen concentration of
the fish sauce undergoing pilot-scale ED due to the water dilution effect was observed. This led to the model with water transport consideration predicting the total nitrogen concentration
evolution better than the model without water transport
consideration.
Table 3
Constants of model without water transport consideration.
[A]
a1
Total nitrogen
concentration
Total amino nitrogen
concentration
Total aroma concentration
Total change of color (DE⁄)
a2
8.6 10
6
1.9 10
5
3.2 10
4.0 109
5
a3
9
Ea
2.1 10
12
9
2.1 10
12
9
13
1 10
1 10
1 10
2.0 105
3 10
2.0 102
0
0
0
8.4
1.8
Total nitrogen concentration
(g/100 mL)
Pilot-scale 6 V
1.7
Predicted
1.6
Predicted without
water transport
1.5
1.4
1.3
1.2
12
14
16
18
20
22
24
26
Salt concentration (%, w/w)
Fig. 8. Comparison between simulated and pilot-scale experimental total nitrogen
concentration evolution. Simulation was performed with water transport
consideration (—) and without water transport consideration ().
neglecting the water transport effect. The under prediction was
observed at a higher voltage and salt removal level when the
water transport was not taken into account. This is because the loss
of water by the electric potential and osmotic pressure
4.3.2. Total amino nitrogen concentration evolution
Fig. 9(a–c) show a comparison between the simulated and
laboratory-scale experimental results of the total amino nitrogen
concentration evolution; the experimental results are those of
Chindapan et al. (2009). Total amino nitrogen concentration is
referred to as the concentration of amino acids existing in the fish
sauce. The model in general was able to well predict the evolution
of the total amino nitrogen concentration, except at an applied
voltage of 6 V. Although it has been reported that amino acids
can permeate across the membranes because amino acids are
ampholytes with small molecular sizes (Sato et al., 1995), the
amino nitrogen concentration in this work did not significantly
decrease during the ED. A significant increase in the total amino
nitrogen concentration was observed when the salt concentration
of the fish sauce was below 14% (w/w) at 6 V, 15.5 (w/w) at 7 V
and 17.5 (w/w) at 8 V. This is again in accordance to the decrease
in the volume as shown in Fig. 5(a). The model considering water
transport could better predict the total amino nitrogen
14
13
Total amino nitrogen
concentration (g/L)
Total amino nitrogen
concentration (g/L)
Lab-scale 6 V
Predicted
12
Predicted without
water transport
11
10
9
8
(a)
7
0
5
10
15
20
25
15
14
13
12
11
10
9
8
7
6
5
30
Lab-scale 7 V
Predicted
Predicted without
water transport
(b)
0
5
Salt concentration (%, w/w)
13
Predicted
12
Predicted without
water transport
11
10
9
8
15
20
25
30
16
Lab-scale 8 V
Total amino nitrogen
concentration (g/L)
Total amino nitrogen
concentration (g/L)
14
10
Salt concentration (%, w/w)
(c)
14
12
10
8
Pilot-scale 6 V
6
Predicted
4
2
Predicted without
water transport
(d)
0
7
0
5
10
15
20
25
Salt concentration (%, w/w)
30
12
14
16
18
20
22
24
26
Salt concentration (%, w/w)
Fig. 9. Comparison between simulated and experimental total amino nitrogen concentration evolution. Simulation was performed with water transport consideration (—)
and without water transport consideration (). (a) Laboratory scale at 6 V; (b) laboratory scale at 7 V; (c) laboratory scale at 8 V and (d) pilot scale at 6 V.
84
K. Bawornruttanaboonya et al. / Journal of Food Engineering 159 (2015) 76–85
Total aroma concentration (g/L)
2200
2000
1800
1600
1400
1200
Lab-scale 6 V
1000
Predicted
800
Predicted without
water transport
600
400
0
5
10
15
20
25
30
Salt concentration (%, w/w)
Fig. 10. Comparison between simulated and laboratory-scale experimental total
aroma concentration evolution. Simulation was performed with water transport
consideration (—) and without water transport consideration ().
concentration evolution than the model neglecting water transport. The under prediction was again observed at a higher voltage
and salt removal level when the water transport was not taken into
account.
At the pilot scale the total amino nitrogen concentration significantly decreased when the salt concentration was reduced from
25% to 14% (w/w) (Jundee et al., 2012). The decrease was probably
due to the dilution effect, which was more evident in the
pilot-scale system due to the lower electric potential difference
as mentioned earlier. For this reason, the model with water
transport consideration could again better predict the total amino
nitrogen concentration evolution than the model without water
transport consideration as shown in Fig. 9(d).
4.3.3. Total aroma concentration evolution
Laboratory-scale experimental total aroma concentration data
at 6 V were obtained from Chindapan et al. (2013) who defined
such a concentration as the summation of the weighted aroma
concentrations of trimethylalamine, 2,6-dimethylpyrazine, benzaldehyde, butanoic acid, 2-methylbutanoic acid, pentanoic acid,
4-methylpentanoic acid, hexanoic acid, acetic acid, and phenol.
The total aroma concentration of the fish sauce significantly
decreased upon ED desalination as shown in Fig. 10. This is
probably because of the evaporation and adsorption of the compounds on the membrane surface as well as the dilution effect at
an earlier stage of ED due to the accumulation of water as shown
in Fig. 5(a). Permeation of the aroma compounds across the membranes along with the water molecules at the later stage of ED
might also contribute to the observed phenomenon (Chindapan
et al., 2011). The model, either with or without water transport
consideration, could very well predict the total aroma
concentration evolution. This is probably because the effect of
water transport was less important on this quality attribute than
on the others. A decrease in trimethylamine, which is the most
dominant aroma compound in the fish sauce was noted to be
mainly by evaporation and not the ED (Chindapan et al., 2011).
For this reason the evolution of total aroma concentration was
not affected by the water transport across the membranes.
4.3.4. Total change of color (DE⁄) evolution
Fig. 11(a)–(c) show a comparison between the simulated and
experimental results of the total change of color of fish sauce
undergoing laboratory-scale ED at 6, 7 and 8 V; the experimental
data are again of Chindapan et al. (2009). The total change of color
of the fish sauce increased with the salt removal level. This is possibly the result of Maillard reaction, which is enhanced by an
25
25
Lab-scale 7 V
20
Prediicted
20
Predicted
15
Predicted without
water transport
15
Predicted without
water transport
ΔE*
ΔE*
Lab-scale 6 V
10
10
5
5
(a)
(b)
0
0
0
5
10
15
20
25
0
5
Salt concentration (%, w/w)
25
15
20
Lab-scale 8 V
15
20
25
Pilot-scale 6 V
18
Predicted
16
Predicted
Predicted without
water transport
14
Predicted without
water transport
ΔE*
20
ΔE*
10
Salt concentration (%, w/w)
10
12
10
8
6
5
4
(c)
0
0
(d)
2
5
10
15
20
Salt concentration (%, w/w)
25
13
14
15
16
17
18
19
20
Salt concentration (%, w/w)
Fig. 11. Comparison between simulated and experimental total change of color evolution. Simulation was performed with water transport consideration (—) and without
water transport consideration (). (a) Laboratory scale at 6 V; (b) laboratory scale at 7 V; (c) laboratory scale at 8 V and (d) pilot scale at 6 V.
K. Bawornruttanaboonya et al. / Journal of Food Engineering 159 (2015) 76–85
increase in the total nitrogen concentration (Hjalmarsson et al.,
2007) at a later stage of ED (see Fig. 7).
The kinetic model could very well predict the total change of
color of the fish sauce undergoing ED. When neglecting the effect
of water transport, however, the model could not adequately predict the total change of color of the fish sauce, especially at a higher
voltage of 8 V. This is probably because the higher voltage led to a
more extensive loss of water as shown in Fig. 5(a); extensive loss of
water led expectedly to the more extensive change of color of the
fish sauce.
Comparison between the simulated and pilot-scale experimental evolution of the total change of color is shown in Fig. 11(d). The
model considering the water transport was able to predict the evolution of the total change of color, while the model neglecting the
water transport could not predict the change. The water transport
due to osmosis led to a significant dilution of the fish sauce and
hence the more extensive change of color. The model without
water transport consideration therefore failed to capture such a
change.
5. Conclusion
A mathematical model that can be used to predict the evolutions of the salt and water concentrations as well as quality
changes of fish sauce undergoing ED desalination is proposed.
The model is based on the conservation equations of mass and
momentum along with Nernst–Planck equation to describe the
transport phenomena during the ED. Kinetic model is used in conjunction with the transport model to predict the changes of the
various quality attributes of the fish sauce during ED desalination.
All parameters of the model were fitted to the experimental laboratory-scale data at 6 V, while validation was performed at other
operating conditions. The predictability of the model was assessed
by comparing the simulated results with the experimental salt and
water concentrations as well as quality changes of the fish sauce
undergoing both laboratory-scale and pilot-scale ED. Comparison
between the simulated and experimental data revealed that the
model considering water transport was able to well predict the
evolution of the salt concentration in the diluate and concentrate
solutions as well as the change in the diluate volume in all cases.
In terms of the quality changes, the model with water transport
consideration could better predict the total nitrogen concentration,
total amino nitrogen concentration, total aroma concentration and
total change of color in all cases. Neglecting the water transport
resulted in the model not being able to predict the evolution of
the salt concentration in the diluate and concentrate solutions as
well as almost all quality attributes since in reality accumulation
of water at the earlier stage and loss of water at the later stage
of ED were observed.
85
Acknowledgement
The authors express their sincere appreciation to the Thailand
Research Fund (TRF) for supporting the study financially.
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