Mathematical modeling of transport phenomena and quality changes of fish sauce undergoing electrodialysis desalination

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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: sakamon.dev@kmutt.ac.th (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. 78 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. 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