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Mass and heat transfer analysis in fructose concentration by osmotic distillation process using hollow fibre module
Journal of Food Engineering 78 (2007) 126–135 www.elsevier.com/locate/jfoodeng
Mass and heat transfer analysis in fructose concentration by osmotic distillation process using hollow fibre module R. Thanedgunbaworn a, R. Jiraratananon a b
a,*
, M.H. Nguyen
b
Department of Chemical Engineering, King Mongkuts University of Technology Thonburi, Toongkru, Bangkok 10140, Thailand Centre for Advanced Food Research, University of Western Sydney, Bld M8, Locked bag 1797, Penrith, NSW 1797, Australia Received 6 June 2005; accepted 17 September 2005 Available online 14 November 2005
Abstract Osmotic distillation process was carried out on a hollow fibre membrane module using fructose solutions and clarified grape juice as feeds. The influence of operating parameters such as feed and brine flow velocities, feed concentration, and temperature, on the osmotic distillation flux was studied. For the experimental conditions employed, the water flux varied from 0.58 kg m2 h1 to 2.02 kg m2 h1. Temperature and feed concentration had significant effect on flux. On the contrary, feed and brine velocities had little effect on flux. The increase of feed and brine velocities or change of the hydrodynamic conditions also enhanced flux. The concentration polarization at high flow velocities can be neglected. In this work, the value of temperature polarization was small and the polarization coefficient H was estimated. It was found that temperature polarization reduced the driving force for mass transfer approximately 5–6%. However, this phenomenon affected the transport resistance of the system. The concentration and temperature polarization can be reduced by operating the process at high Reynolds number and low temperature. The transport resistance was affected by changing of operating condition such as feed velocity and temperature. The major transport resistance of the process was in the membrane. 2005 Elsevier Ltd. All rights reserved. Keywords: Concentration polarization; Fructose solution; Hollow fibre; Osmotic distillation; Polarization coefficient; Temperature polarization
1. Introduction The advantages of the concentration of the liquid foodstuffs include the reduction in packaging, storage, transport cost and prevention of deterioration by microorganisms. For these reasons, many concentration techniques have been developed and used for the food industries. They include evaporative concentration, freeze concentration, and membrane processes such as reverse osmosis (RO) and ultrafiltration (UF). Recently, the new alternative membrane process has been developed and it is called osmotic distillation (OD). Osmotic distillation, a low energy concentration process, is a membrane contactor technique in which the porous hydrophobic membrane separates two aqueous solutions *
Corresponding author. Tel.: +66 2 470 9222; fax: +66 2 428 3534. E-mail address: [email protected] (R. Jiraratananon).
0260-8774/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2005.09.023
and prevents penetration of the aqueous solution into the pore. One surface of membrane is contacted with dilute aqueous solution and the opposing surface is contacted with concentrated salt solution as the stripping solution. The separation by OD is based on the activity difference or the vapour pressure difference between the feed solution and the brine causing the water vapor to transfer from the dilute solution to the stripping solution. The OD process can be operated at room temperature and atmospheric pressure, which avoids the degradation of heat-sensitive components and some loss of volatile components of the liquid foodstuffs (Kunz, Benhabiles, & Ben-Aim, 1996). In addition, this process can concentrate the solutions to a very high concentration (60–70Brix) (Bailey, Barbe, Hogen, Johnson, & Sheng, 2000; Vaillant et al., 2001). From these advantages, OD process has been widely investigated by many researchers. However, the major disadvantage of OD process is low fluxes. In order to improve the
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127
Nomenclature aw cp C dp D h DHv J k kT K M P P* ri ro R T U v
water activity heat capacity (J kg1 K1) concentration (%w/w) pore diameter (lm) diffusion coefficient (m2 s1) liquid heat transfer coefficient (W m2 K1) latent heat of vaporization (J kg1) mass vapour flux (kg m2 h1) mass transfer coefficient (m s1) thermal conductivity (W m1 K1) transport coefficient (kg m2 h1 Pa1) molecular weight (kg mol1) pressure (Pa) saturation vapour pressure (Pa) internal radius of the fibre (mm) external radius of the fibre (mm) universal gas constant (8.314 J K1 mol1) temperature (C, K) overall heat transfer coefficient (W m2 K1) fluid velocity (m s1)
Dimensionless numbers Gz Graetz Nu Nusselt
OD flux, it is necessary to understand the mass transfer phenomenon and the effect of operating conditions involved in the system. There are limited studies on mass and heat transfer phenomena in OD in the literatures (Alves & Coelhoso, 2004; Celere & Gostoli, 2002; Courel, Dornier, Rios, & Reynes, 2000; Sheng, Johnson, & Lefebvre, 1991). Sheng et al. (1991) proposed the models for predicting flux and juice concentration using various operating parameters. The analysis of heat and mass transfer phenomena in osmotic distillation in plate and frame module was also proposed by Celere and Gostoli (2002). Asymmetric porous membrane was applied for the experiments on osmotic distillation of pure water to investigate mass transfer resistances and phenomena (Courel, Dornier, Rios, et al., 2000). Although mass transfer is an important phenomenon of the OD system, the heat transfer also plays an important role in the process. It was reported that the temperature polarization phenomena affected the driving force of OD system resulting in the water flux reduction (Alves & Coelhoso, 2004; Gostoli, 1999). However, for the osmotic distillation in a stirred cell, the magnitude of temperature polarization was reported to be small (Alves & Coelhoso, 2004). The aim of this paper is to study the effect of operating conditions such as feed and brine velocities, feed concentration, and bulk temperature on flux. The fructose solutions are chosen for this study because fructose is the main sugar found in fruit juices. In addition, the experiments were also
Pr Re Sc Sh
Prandtl Reynolds Schmidt Sherwood
Greek letters d membrane thickness (m) e membrane porosity q fluid density (kg m3) l fluid viscosity (Pa s) H polarization coefficient / packing density Subscripts A air b bulk f feed m membrane s salt w water 1 membrane location at the feed side 2 membrane location at the brine side
carried out using clarified grape juice as feed. In osmotic distillation process, the concentration and temperature polarization affect the OD performance and these polarizations are influenced by the operating conditions which must be investigated to avoid the undesirable effect. Therefore, the characteristics of concentration and temperature polarization in OD are included in this study. This work also attempted to estimate the transport resistance of membrane, feed and brine boundary layers. 2. Theory 2.1. Mass transfer The principle of OD is depicted in Fig. 1. The mass transfer mechanism of water vapor through the hydrophobic membrane includes three consecutive steps: (1) evaporation of water at a membrane pore entry: (2) diffusion or convective transport of water vapor through the membrane pore; and (3) condensation of water vapor on the brine-side at the pore exit. Evaporation of water vapour at the membrane pore entrance results in the build up of feed concentration at the membrane surface (Cf,m). On the other hand, condensation of water vapour into the brine permeate also gives rise to the difference in brine concentrations. This phenomenon is called concentration polarization (CP). The existence of the boundary layers due to the concentration polarization at each side of the
128
R. Thanedgunbaworn et al. / Journal of Food Engineering 78 (2007) 126–135 Membrane
Dilute feed solution
Ts ,m
T f ,b
where k is the mass transfer coefficient (m s1); k = DAB/d, and DAB is the diffusion coefficient. The coefficients, kf and ks, can be obtained by the experiment or estimated by the empirical correlation as the following:
Osmotic solution Ts ,b
T f ,m
C s ,b Pw,1
Pw, 2
Sh ¼ AðRea Scb Þ
C s ,m
in which,
C f ,m
C f ,b
1/Kf
Flux 1/Km
Sh ¼
kd h DAB
Re ¼
vd h q l
and
Sc ¼
l qDAB
ð8Þ
1/Ks
Water vapour flux
Fig. 1. Concentration and temperature profiles in osmotic distillation.
membrane result in the reduction of driving force for mass transfer. The basic equation to describe the water vapour transport in OD system relates between the flux (J) and the water vapour pressure difference across the membrane (Pw,1 Pw,2): J ¼ K m ðP w;1 P w;2 Þ
ð1Þ
where Km is the membrane transport coefficient which is also referred to as the membrane permeability. The water vapor pressure is a function of temperature and is related to the activity of the solution by P w ¼ P w aw
ð2Þ P w
where Pw is the water vapor pressure, is the vapor pressure of pure water, and aw represents the water activity in the solutions. However, the vapour–liquid interfaces conditions are not accessible. Thus, the alternative mass transfer model is given by Eq. (3): J ¼ KDP w;b
ð7Þ
ð3Þ
where DPw,b is the water vapour pressure difference corresponding to the bulk concentration of the liquid compartments. K is the overall transport coefficient (kg m2 h1 Pa1) of the system and is given by Eq. (4). 1 1 1 1 þ þ ð4Þ K¼ Kf Km Ks where 1/Kf, 1/Km, and 1/Ks are the transport resistances of feed boundary layer, membrane, and of permeate boundary layer, respectively. Owing to the concentration process, the concentration difference between bulk and membrane surface locations is created and induces a diffusion of solute. According to Ficks law and mass balance across the boundary layers, the relationship between bulk concentration (Ci,b) and concentration at membrane surface (Ci,m), i = f for feed and s for brine side, is given by C f;m ¼ C f;b expðJ =qw k f Þ
ð5Þ
C s;m ¼ C s;b expðJ =qw k s Þ
ð6Þ
where A, a, and b are constants, q is the density, l is the viscosity of the fluid, v is the velocity. dh is the hydraulic diameter which is also called the characteristic diameter of the flow channel. For a flow inside the pipe, dh equals to the diameter of the pipe. However, for a flow in noncircular channel, the hydrodynamic diameter can be determined by dh = 4S/P where S is the cross-sectional area and P is the wetted perimeter of the flow channel. The hollow fibre module was employed in this work. The configuration of hollow fibre module is similar to the shell and tube heat exchanger. Therefore, mass transfer at the two sides of the hollow fibre module are distinguished as tube side and shell side. 2.1.1. Mass transfer at the tube side In case that the solution flows inside the fibre, the mass transfer coefficient can be estimated by many equations (Gawronski & Wrzesinska, 2000; Skelland, 1974; Viegas et al., 1998). For the Graetz number (Gz) larger than 400, the mass transfer coefficient is given by Leveque (Gawronski & Wrzesinska, 2000; Skelland, 1974): 1=3 dh Sh ¼ 1:615 ðRe ScÞ1=3 ð9Þ L Viegas et al. (1998) proposed the correlation for Re < 34 and Gz < 65. The correlation is 1=3 1:01 d h Sh ¼ 0:2Re Sc ð10Þ L 2.1.2. Mass transfer at the shell side Mass transfer at the shell side of the hollow fibre module is different from the mass transfer at the tube side owing to the packing of the fibres in the shell. Gawronski and Wrzesinska (2000) concluded that the Sherwood number of the shell side strongly depended on the fibre packing density (/). Lipnizki and Field (2001) compared and discussed the differences of the correlations which were taken from the literature. It was concluded that for the correlations proposed by Gawronski and Wrzesinska (2000), Prasad and Sirkar (1988), Costello, Fane, Hogan, and Schofield (1993), the Sherwood number decreased with increasing packing density. However, Wu and Chen (2000) observed that the Sherwood number decreased by increasing packing density until the packing density reached about 55%, beyond that point the Sherwood number increased with
R. Thanedgunbaworn et al. / Journal of Food Engineering 78 (2007) 126–135
the packing density. In this work, the correlation of Costello et al. (1993) was chosen because constrains of the equation correspond with our experimental condition. The correlation is as follows: Sh ¼ ð0:53 0:58/ÞRe
0:53
Sc
0:33
ð11Þ
2.2. Heat transfer Even though OD is essentially a mass transfer process, heat transfer is also concerned. The temperature difference is created due to the evaporation at the feed side and condensation at the brine side and this reduces the vapor pressure difference across the membrane, resulting in the driving force decay. The temperature profile is showed in Fig. 1. Steady state heat transfer considerations of the system is given by Eq. (12) and the overall heat transfer coefficient (U) of the OD process is given by Eq. (13). Q ¼ U DT b ¼ hf ðT f;b T f;m Þ ¼ J DH v þ hm ðT f;m T s;m Þ ¼ hs ðT s;m T s;b Þ 1 1 1 1 U¼ þ þ hf hm þ ðJDH v Þ=DT m hs
ð12Þ ð13Þ
where Q is the total heat transferred across the membrane, J is the flux and DHv is the latent heat of vaporization, hf and hs represent the heat transfer coefficients of the feed and permeate thermal boundary layers, and hm is the heat transfer coefficient of the membrane. Therefore hf(Tf,b Tf,m) and hs(Ts,m Ts,b) represent the heat flux through the boundary layers. The heat transfer in the membrane is given by the convective heat flux, JDHv, and the conductive contribution related to the temperature difference, hm(Tf,m Ts,m). From Eq. (12), the temperatures at the membrane surfaces can be evaluated by the following equations: hm ðT s þ ðhf =hs ÞT f Þ þ hf T f N DH v hm þ hf ð1 þ hm =hs Þ hm ðT f þ ðhs =hf ÞT s Þ þ hs T s þ N DH v ¼ hm þ hs ð1 þ hm =hf Þ
T f;m ¼
ð14Þ
T s;m
ð15Þ
The heat transfer coefficient of the membrane (hm) can be evaluated through the thermal conductivity of the membrane, k Tm . Therefore, hm for a cylindrical geometry based on the internal surface can be approximated as (Bui, Nguyen, & Muller, 2005; Gostoli, 1999): hm ¼
e k TA þ ð1 eÞk Tpolymer k Tm ¼ ri lnðro =ri Þ ri lnðro =ri Þ
ð16Þ
where k Tpolymer and k TA are the thermal conductivities of the polymer and of the air, respectively, e is the porosity of the membrane, and ri, ro are the internal and external radius of the fibres. Furthermore, the liquid heat transfer coefficients can be estimated by empirical correlations of dimensionless numbers, Nusselt (Nu), Reynolds (Re), and Prandtl (Pr) numbers.
b2
Nu ¼ b1 Re Pr with Nu ¼
b3
hd h kT
lb lm
129
b4
and
ð17Þ Pr ¼
lcp kT
ð18Þ
where bi are coefficients of the correlation, kT is the thermal conductivity, and cp is the heat capacity. In the case of the hollow fibre module with the co-current flow, there are the concentrations and temperatures change along the module. However, the flux in OD process is very small compared with the flow rates. Hence, it can be assumed that the concentrations of the two streams are constant along the module (Gostoli, 1999). This assumption can be checked by considering the mass and energy balance analysis. Using the experimental conditions of this work, it was found that the concentration change along the module can be estimated in the order of 0.2%. Moreover, according to the energy balance equations of the both feed and brine streams, the outlet temperatures of the two streams can be evaluated. For this work, it was found that the value of outlet temperature is very close to the inlet value, a temperature change of 0.03–0.09 C was observed. Therefore, the inlet temperature will be used as the bulk temperature in order to determine the temperature at the membrane surface and temperature polarization in this study. The temperature polarization reduces the driving force for the mass transfer through the membrane. Its effect on flux was studied (Alves & Coelhoso, 2004; Gostoli, 1999) and the polarization coefficient (H) was introduced to represent the fraction of the driving force really effective for the mass transfer through the membrane. Thus, the flux can be estimated by J ¼ K m DP w;m ¼ HK m DP w;b
ð19Þ
Thus, the polarization coefficient H can be estimated by using Eq. (20). H¼
DP w;m DP w;b
ð20Þ
From the experiments, the flux data were obtained. Eqs. (5) and (6) are used to determine the feed and brine concentration at the membrane surface, and was also used to estimate the concentration polarization ratio. The mass transfer coefficients within feed and brine boundary layer can be estimated by Eqs. (9) and (11), respectively. The heat transfer coefficients are estimated by mass and heat transfer analogy using Eqs. (9) and (11). 3. Experimental The experiments were performed with fructose solutions and clarified Chardonnay grape juice (ultrafiltration permeate) as feeds. Fructose solutions were prepared with Fructose (C6H12O6) powder of 99.6% purity (Chem-supply Pty. Ltd., Australia) and distilled water. Brine solution was prepared from CaCl2 Æ 2H2O, analytical grade (Chemsupply Pty. Ltd., Australia) to obtain a fixed concentration
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of 43% (w/w). The concentrations of feeds and brine solutions were determined by a refractometer. A hydrometer (Townson & Mercer (T&M) Pty. Ltd.) was used to determine the density of solutions. However, the properties of fructose and calcium chloride solutions were checked by comparing with the data from the CRC handbook Lide (2001). The hollow fibre membrane was polyvinylidenefluoride (PVDF) supplied by Memcor Australia (South Windsor, New South Wales, Australia). The main characteristics of the fibres are 0.660 mm internal diameter, 170 lm thickness, 0.2 lm pore diameter and 64% porosity, as specified by the supplier. The specifications of the hollow fibre modules used in the experiment are illustrated in Table 1. The membrane was cleaned after use by thoroughly flushing the system with distilled water through the feed side without recycling. Subsequently, NaOH solution (1%w/w) was circulated for 1 h at 45 C. Finally, the system was rinsed with distilled water without recycling for 10 min and then the liquid was discharged from the system. For the brine side, the membrane was flushed with 4 l of distilled water. The experimental setup is depicted in Fig. 2. The membrane module was installed in a vertical position. The feed and brine solutions were fed into the module by the peristaltic pumps (Easy-Load Masterflex model 7518-00). Circulation of both feed and brine was co-current with upward flow direction. The feed solution was circulated inside the
fibres whereas the brine solution was circulated in the shell side of the module. The brine tank of 5 l was large enough to maintain a nearly constant concentration during the experiment. The water baths with the temperature control were used to control the feed and brine temperatures. The water flux was obtained by measuring the feed volume over a 15 min in the pipette connected to the feed tank. The operating parameters, the feed flow velocity (vf), the brine flow velocity (vs), the feed concentration (Cf), and the temperature (T) were studied in this work. In order to study the effect of feed flow velocity, the experiments were performed using equal inlet temperatures of feed and brine at 25, 35, and 45 C. The feed flow velocity was varied from 0.1 to 0.5 m s1, while maintaining a constant feed concentration of 45%w/w and brine flow velocity of 0.4 m s1. The brine flow velocity was varied from 0.1 to 0.5 m s1 for studying the effect of brine flow velocity. The feed concentration was varied from 35 to 55%w/w and the temperature was varied from 25 to 55 C in order to study the effect of feed concentration and temperature on flux, respectively. For the experiment with the clarified grape juice, the concentration of grape juice was 45Brix and experimental methods were the same as the case of fructose solution.
4. Results and discussion 4.1. The effect of operating conditions on flux, concentration, and temperature polarization
Table 1 Specifications of the hollow fibre module Module
Value
Number of fibres Total length of module (mm) Total effective length (mm) Effective area (cm2) Cross-section flow area of the fibre side (mm2) Cross-section flow area of the shell side (mm2)
35 250 180 130.63 11.97 16.69
4.1.1. Effect of feed velocity The effect of feed velocity on the flux was studied at different bulk temperatures. The results, shown in Fig. 3, indicate that increasing of feed velocity (vf) improved fluxes and it makes the flux appear 8.5% increase as the feed velocity increase from 0.1 to 0.2 m s1. Moreover, the flux was higher at high temperature because the water vapour
Fig. 2. Osmotic distillation experimental setup: (1) hollow fibre module, (2) thermometer, (3) pipette, (4) pressure gauge, (5) flowmeter.
R. Thanedgunbaworn et al. / Journal of Food Engineering 78 (2007) 126–135
131
1.0300
1.80 45 o C
1.60
25 °C
1.0250
35 °C
35 o C Cf,m /C f,b
25 o C
1.00
45 °C
1.0200
35
1.20
22
Flux (kg/m .h)
1.40
0.80
1.0150 1.0100
0.60
1.0050
0.40 Fructose Grape Juice
0.20
1.0000 0
50
0.00 0
0.1
0.2
0.3 0.4 v f (m/s)
0.5
0.6
Fig. 3. Effect of feed cross-section flow velocity (vf, m s ) on flux rate at the conditions: Cf = 45%w/w, Cs = 43%w/w, vs = 0.4 m s1, and at different bulk temperatures: Comparison between fructose solution and Chardonnay white grape juice (45Brix).
150
Re
0.7
1
100
Fig. 4. Influence of Reynolds number and bulk temperature (Tb) on fructose concentration gradient.
0.9994 25 °C 35 °C 45 °C
pressure, the driving force of the process, increases with the temperature. For the experiment with the clarified grape juice, the concentration of grape juice was 45Brix. The experimental results for the grape juice were the same as the case of fructose solution. The results may be explained by the similarity in physical properties, viscosity and density, between fructose and UF permeate grape juice. The effect of ultrafiltration on the subsequent concentration of grape juice by osmotic distillation was studied by Bailey et al. (2000). It was reported that the UF permeate concentrated to 59Brix had fermentable sugars content (glucose + fructose) of 60%w/w. It was also showed that UF resulted in a small increase in juice surface tension, thus reducing membrane wetting. In this work, the experimental results with fructose solution can be used for the juice concentration process due to the similar features between fructose solution and UF permeate grape juice as mentioned. The feed velocity from 0.1 to 0.5 m s1 corresponds with Reynolds numbers (Re) of 12.37–116.23. In order to estimate the concentration polarization (CP) at the feed side, the feed concentration at the membrane surface (Cf,m) and mass transfer coefficient of the feed boundary layer (kf) were evaluated using Eqs. (5) and (9), respectively. The mass transfer coefficients of the feed boundary layer ranged from 1.27 · 105 to 2.96 · 105 m s1, using the properties of fructose solution for calculation. The increase of feed velocity resulted in higher shear stress along the membrane surface and, consequently, there was less concentration polarization (Fig. 4) such that flux was increased. Moreover, Fig. 4 indicates the value of CP ratio (Cf,m/Cf,b) increased with the bulk temperature (Tb). The evaporation rate of water at the membrane surface increased with temperature and, consequently feed concentration was high at the membrane surface. Therefore, the concentration polarization can be reduced by operating
Tf,m /Tf,b
0.9992 0.9990 0.9988 0.9986 0.9984 0.9982 0
50
100
150
Re Fig. 5. Influence of Reynolds number and bulk temperature (Tb) on radial temperature profile within the boundary layer at the feed side.
the OD process at high Reynolds numbers and low temperatures. The influence of the hydrodynamic condition (Re) and the temperature on temperature polarization (TP) is shown in Fig. 5. Firstly, heat transfer was studied in order to evaluate the membrane surface temperatures (see Eqs. (14) and (15)). The heat transfer coefficients within the feed boundary layer were estimated by mass and heat transfer analogy using Eq. (9), as the following: 1=3 dh 1=3 Nu ¼ 1:615 ðRe PrÞ ð21Þ L The heat transfer coefficient of the feed side (hf) varied between 1208 and 2069 W m2 K1. From Fig. 5, the value of TP ratio (Tf,m/Tf,b) increased (close to 1) with increasing Re. The meaning is TP decreased with increasing Re. This result can be explained by the correlation between Reynolds number and heat transfer coefficient (hf). The increase of Reynolds number resulted in the enhancement of hf within feed boundary layer and consequently, the TP decreased. Hence, TP can be decreased by operating the process at high Re and low Tb. In order to evaluate
R. Thanedgunbaworn et al. / Journal of Food Engineering 78 (2007) 126–135
4.1.2. Effect of brine velocity The brine flow velocity (vs) was varied from 0.1 to 0.5 m s1 corresponding to the Reynolds numbers of 7.00– 54.09. The effect of brine velocity on flux is shown in Fig. 6. The increase of OD flux was attributed to the increase of brine velocity at any operating temperature due to higher shear rates along the membrane surface of the brine side. For the experiment with grape juice, fluxes also increased with brine velocity for all bulk temperatures considered. The boundary layer mass transfer coefficient of the brine side (ks) was evaluated by Eq. (11) because the experimental conditions in this study corresponded with the conditions of the correlation. It was found that ks varied between 1.15 · 105 and 3.15 · 105 m s1, using the properties of brine solution for calculation. The values of concentration polarization depend on the physical properties of the solution and the hydrodynamic conditions. Hence, the influence of Re and bulk temperature (Tb) on the concentration polarization on the brine side was studied and shown in Fig. 7. The values of Cs,m/Cs,b decreased, which indicates that CP increased, with decreasing Re and with increasing Tb. Concentration polarization increased with the temperature because the condensation of water vapour was high at higher temperature and, consequently, the brine concentration difference within the boundary layer was enhanced. Fig. 8 shows the influence of Re and temperature on temperature polarization (TP) of the brine side. TP 1.80 1.60
Flux (Kg/m2.h)
1.40 1.20 1.00 0.80 0.60 0.40 Fructose Grape Juice
0.20 0.00 0
0.1
0.2
0.3 0.4 vs (m/s)
0.5
0.6
0.7
Fig. 6. The effect of brine velocity (vs, m s1) on flux rate at the conditions: Cf = 45%w/w, Cs = 43%w/w, vf = 0.4 m s1, and at different bulk temperatures; Comparison between fructose solution and Chardonnay red grape juice (45Brix).
0.9950 0.9900
Cs,m /Cs,b
the effect of TP on the flux, the polarization coefficient (H) was calculated using Eq. (20). The value of DP w;b was determined by using the water activity at the membrane surface instead of the bulk water activity in order to avoid the concentration polarization effects. The value of H in this work was 0.94 indicating that temperature polarization reduced the driving force for mass transfer through the membrane in the order of 6%. However, this effect can be reduced by choosing the appropriate operating condition for the system studied.
0.9850 0.9800 0.9750
25 °C 35 °C
0.9700
45 °C
0.9650 0
10
20
30
40
50
60
Re
Fig. 7. Influence of Re and bulk temperature (Tb) on brine (CaCl2) concentration gradient.
1.0012 25 °C 35 °C 45 °C
1.0010
Ts,m / Ts,b
132
1.0008 1.0006 1.0004 1.0002 1.0000 0
10
20
30
40
50
60
Re Fig. 8. Influence of Re and Tb on temperature profile within the boundary layer at the brine side.
decreased with increasing Re. Moreover, temperatures affected the concentration profile within brine boundary layer. The existence of TP within the brine boundary layer resulted in the driving force decay. The polarization coefficient H value was 0.95. 4.1.3. Effect of feed concentration The effect of feed concentration on flux for fructose solution is presented in Fig. 9. The feed concentration was varied from 35 to 55%w/w and vf was adjusted between 0.1 and 0.3 m s1 in order to maintain the Re of feed solution at a constant value of 18. The flux was measured for various feed concentrations, which corresponded to different water activities. It can be seen that the effect of feed concentration on flux using fructose solution and grape juice was similar. Moreover, the water flux decreased by 12% as the feed concentration increased from 35 to 40%w/w. Since the water vapour pressure is the driving force of OD process and it relates to the water activity, therefore, the increase of feed concentration reduced the water activity and flux. The calculations of CP and TP ratio revealed that both concentration and temperature polarization decreased with
R. Thanedgunbaworn et al. / Journal of Food Engineering 78 (2007) 126–135
increasing feed concentration. This result can be explained to be due to the decrease of driving force. In the other words, the evaporation rate of water at the membrane surface decreased with increasing feed concentration. The values of polarization coefficient (H) increased with feed concentration and was in the range of 0.94–0.96. 4.1.4. Effect of temperature The effect of temperature on OD flux was studied in the range of 25–55 C and was demonstrated in Fig. 10. The Reynolds numbers (Re) were maintained constant (±10%) for the range of temperatures tested. Flux increased 20% with increasing bulk temperature from 25 to 35 C. There was the exponential relationship between the temperatures and driving force of the process. The effect of temperature was mainly due to the increase of the water vapour pressure and reduction of solution viscosity. Additionally, high temperatures give more kinetic energy to water vapour to transport through the membrane, hence flux was increased. The mass transfer coefficients of the feed and brine boundary layers (kf and ks) are presented in Table 2. These values were calculated from
1.00
0.9600
0.90
Flux (Kg/m2.h)
0.9200
0.70 0.60
0.9000
0.50 0.8800
0.40 0.30
Flux : fructose
0.20
Flux : juice
0.10
aw
0.8600
Water activity (aw)
0.9400
0.80
0.8400
0.00
0.8200 35
40
45
50
55
Feed concentration (%w/w)
Fig. 9. Effect of feed concentration (Cf) on OD flux: comparison between fructose solution and UF permeate grape juice. Cs = 43%w/w, vs = 0.4 m s1, and Tb = 25 C.
2.5
Flux (Kg/m2.h)
2.0 1.5 y = 0.4232e0.0283x R 2 = 0.9893
1.0 0.5 0.0
20
30
40 Temperature (oC)
50
60
Fig. 10. OD flux dependence upon temperature (Tb); at the conditions Cf = 45%w/w and Cs = 43%w/w.
133
Table 2 Values of the mass transfer coefficients, kf and ks, estimated from Eqs. (9) and (11) for different operating temperatures Temperature (C)
kf (·105 m s1)
ks (·105 m s1)
25 35 45 55
2.01 2.16 2.18 2.44
2.69 2.60 2.81 2.60
Eqs. (9) and (11) which do not take into account the effect of temperature polarization. Both kf and ks slightly increased with temperature (at constant Re) and increased with velocity (at specific temperature) as generally found. 4.2. Transport resistances In order to improve flux, it is necessary to compare the resistance of the feed boundary layer with the resistance of the permeate boundary layer, and the resistance of the membrane. Most researches on osmotic distillation process were carried out using pure water as feed and did not take into account the effect of temperature polarization (Alves & Coelhoso, 2004; Courel, Dornier, Herry, Rios, & Reynes, 2000; Courel, Dornier, Rios, et al., 2000). In the present work, the effect of temperature polarization has been included in the calculations. Therefore, it is more appropriate in defining 1/Km, 1/Kf, and 1/Ks as transport resistances in which both concentration and temperature polarization have been taken into account. From the calculation, the temperature drops across the feed and brine boundary layers, ((Tf,b Tf,m) and (Ts,m Ts,b)), ranged 0.1–0.6 C. With the purpose of calculating the individual resistance, the vapour pressure at each point (see Fig. 1) which is the function of both composition and temperature must be known. The results in Table 3 indicate that at a certain temperature the transport resistances of the feed side (1/Kf) decreased with increasing feed velocity due to the enhancement of kf while the transport resistances of the brine side were approximately constant. On the other hand, the transport resistance of the membrane (1/Km), which is also affected by both heat and mass transfer across the membrane, decreased with increasing feed velocity due to a slight increase of (Pw,1 Pw,2) and more pronounced increase of flux (see Eq. (1)). In other words, the membrane permeability increased with feed velocity because both concentration and temperature polarization were influenced by the Reynolds number (see Figs. 4 and 5). The comparison of transport resistances in percentages revealed that the membrane transport resistance was relatively constant and was the major resistance of the system. This corresponds with previous works (Alves & Coelhoso, 2004; Courel, Dornier, Rios, et al., 2000). Table 4 depicts that all transport resistances increased with temperature due to the enhancement of both concentration and temperature polarization at higher temperatures. Therefore, the values of K, the total transport coefficients (see Eq. (4)) decreased with increasing
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Table 3 Transport resistances (1/K) of the individual compartment at different feed velocities and temperatures with a constant velocity in the brine side Feed velocity (m s1)
1/Km (Pa m2 h kg1)
1/Kf (Pa m2 h kg1)
At 25 C vf = 0.1 = 0.2 = 0.3 = 0.4 = 0.5
2.5 · 103 2.3 · 103 2.2 · 103 2.2 · 103 2.1 · 103
76.49 63.57 56.86 52.45 49.23
At 35 C vf = 0.1 = 0.2 = 0.3 = 0.4 = 0.5
3.3 · 103 3.2 · 103 2.9 · 103 2.8 · 103 2.7 · 103
At 45 C vf = 0.1 = 0.2 = 0.3 = 0.4 = 0.5
3.4 · 103 3.3 · 103 3.2 · 103 3.1 · 103 3.1 · 103
1/Ks (Pa m2 h kg1)
1/Km (%)
1/Kf (%)
1/Ks (%)
48.20 48.65 48.89 49.06 49.18
95.28 95.39 95.49 95.50 95.40
2.90 2.61 2.43 2.32 2.30
1.82 2.00 2.09 2.17 2.30
123.55 102.80 91.96 84.86 79.67
79.16 79.90 80.32 80.59 80.78
94.21 94.62 94.37 94.36 94.39
3.53 3.03 3.01 2.89 2.79
2.26 2.35 2.63 2.75 2.83
191.98 159.92 143.17 132.17 124.13
125.09 126.27 126.90 127.32 127.63
91.39 91.99 92.14 92.31 92.40
5.22 4.48 4.16 3.92 3.75
3.40 3.53 3.69 3.77 3.85
Table 4 The effect of temperature on resistances Temperature (C)
1/Km (Pa m2 h kg1)
1/Kf (Pa m2 h kg1)
1/Ks (Pa m2 h kg1)
1/Km (%)
1/Kf (%)
1/Ks (%)
25 35 45 55
2.04 · 103 2.89 · 103 3.29 · 103 3.93 · 103
52.89 91.96 159.92 238.84
43.65 80.24 125.96 222.87
95.49 94.37 91.99 89.49
2.47 3.01 4.47 5.43
2.04 2.63 3.53 5.07
Reynolds numbers at feed and brine side were maintained constant at 54.20 ± 7.71 and 39.12 ± 4.15, respectively.
temperature. The enhancement of flux at high temperature, therefore, resulted from the exponential increase of DPw (see Eq. (3)) which influenced flux more than the reduction of K. Consideration of the percentages of transport resistances in Table 4 would reveal a better understanding of the results, i.e., the contribution of membrane transport resistance was less significant at higher temperature. The membrane permeability (Km) was reported to be temperature dependent (Schofield, Fane, & Fell, 1990) in which the trend is dependent upon the gas diffusion mechanisms in the membrane pores. 5. Conclusions In order to present the importance of the operating parameters on the performance of osmotic distillation (OD) process, the effect of several parameters on osmotic distillation flux namely feed and brine velocity, feed concentration, and operating temperature were studied. The OD fluxes in this study ranged from 0.58 kg m2 h1 to 2.02 kg m2 h1. The experimental results showed that temperature and feed concentration had significant effect on the flux. Flux increased with temperature since water vapour pressure is the function with temperature according to Antoine equation. It can be concluded that the flux was affected by the feed concentration via the water activity of
feed solution. In this study, feed and brine velocity had little effect on the flux. However, the increase of feed and brine velocity or the hydrodynamic conditions can cause the OD flux enhancement. The concentration and temperature polarization effects were evaluated. The minimum and maximum temperature differences between both sides of the membrane were 0.31 C (vf = 0.4 m s1, vs = 0.3 m s1, and Tb = 25 C) and 0.87 C (vf = 0.2 m s1, vs = 0.3 m s1, and Tb = 55 C), respectively. In this study, the polarization coefficient which indicates the effect of temperature polarization on the driving force was about 0.95. It means that temperature polarization reduced the driving force for mass transfer about 5%. The concentration and temperature polarization can be reduced by operating process at high Re and low temperature. In this work, the transport coefficients (K) and the transport resistances (1/K) were defined. Kf and Ks are different from the mass transfer coefficients (kf, ks) in both units and physical meaning. In other words, all transport resistances (1/Ki) are neither the mass transfer resistance nor the heat transfer resistance but, they are resistances coupled by the effect of both heat and mass transfer and are appropriate in describing the system with simultaneous heat and mass transfer such as membrane distillation and osmotic distillation.
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The results of transport resistance study led to the conclusions that the transport resistances were affected by the operating parameters. The membrane transport resistance was the major resistance controlling the permeation flux while the boundary layer resistances were much lower with those of feed boundary layer were higher than the brine side boundary layer. Acknowledgements The authors would like to thank The Thailand Research Fund and The Royal Golden Jubilee Ph.D. Program for financial support and the Centre for Advanced Food Research of the University of Western Sydney for supplying facilities and assistance. References Alves, V. D., & Coelhoso, I. M. (2004). Effect of membrane characteristics on mass and heat transfer in the osmotic evaporation process. Journal of Membrane Science, 228, 159–167. Bailey, A. F. G., Barbe, A. M., Hogen, P. A., Johnson, R. A., & Sheng, J. (2000). The effect of ultrafiltration on the subsequent concentration of grape juice by osmotic distillation. Journal of Membrane Science, 164, 195–204. Bui, A. V., Nguyen, M. H., & Muller, J. (2005). Characterisation of the polarization in osmotic distillation of glucose solutions in hollow fibre module. Journal of Food Engineering, 68, 391–402. Celere, M., & Gostoli, C. (2002). The heat and mass transfer phenomena in osmotic membrane distillation. Desalination, 147, 133–138. Costello, M. J., Fane, A. G., Hogan, P. A., & Schofield, R. W. (1993). The effect of shell side hydrodynamics on the performance of axial flow hollow fibre modules. Journal of Membrane Science, 80, 1–11. Courel, M., Dornier, M., Herry, J. M., Rios, G. M., & Reynes, M. (2000). Effect of operating conditions on water transport during the concen-
135
tration of sucrose solutions by osmotic distillation. Journal of Membrane Science, 170, 281–289. Courel, M., Dornier, M., Rios, G. M., & Reynes, M. (2000). Modelling of water transport in osmotic distillation using asymmetric membrane. Journal of Membrane Science, 173, 107–122. Gawronski, R., & Wrzesinska, B. (2000). Kinetics of solvent extraction in hollow-fiber contactors. Journal of Membrane Science, 168, 213–222. Gostoli, C. (1999). Thermal effects in osmotic distillation. Journal of Membrane Science, 163, 75–91. Kunz, W., Benhabiles, A., & Ben-Aim, R. (1996). Osmotic evaporation through macroporous hydrophobic membranes: a survey of current research and applications. Journal of Membrane Science, 121, 25–36. Lide, D. R. (2001). CRC handbook of chemistry and physics (2000–2001) (81st ed.). USA: CRC Press. Lipnizki, F., & Field, R. W. (2001). Mass transfer performance for hollow fibre modules with shell-side axial feed flow: using an engineering approach to develop a framework. Journal of Membrane Science, 193, 195–208. Prasad, R., & Sirkar, K. K. (1988). Dispersion-free solvent extraction with microporous hollow-fiber modules. AIChE Journal, 34, 177–188. Schofield, R. W., Fane, A. G., & Fell, C. J. D. (1990). Gas and vapour transport through microporous membranes. I. Knudsen–Poiseuille transition. Journal of Membrane Science, 53, 159–171. Sheng, J., Johnson, R. A., & Lefebvre, M. S. (1991). Mass and heat transfer mechanisms in the osmotic distillation process. Desalination, 80, 113–121. Skelland, A. H. P. (1974). Diffusion mass transfer. New York: Wiley. Vaillant, F., Jeanton, E., Dornier, M., OBrien, G. M., Reynes, M., & Decloux, M. (2001). Concentration of passion fruit juice on an industrial pilot scale using osmotic evaporation. Journal of Food Engineering, 47, 195–202. Viegas, R. M. C., Rodriguez, M., Luque, S., Alvarez, J. R., Coelhoso, I. M., & Crespo, J. P. S. G. (1998). Mass transfer correlations in membrane extraction: analysis of Wilson-plot methodology. Journal of Membrane Science, 145, 129–142. Wu, J., & Chen, V. (2000). Shell-side mass transfer performance of randomly packed hollow fiber modules. Journal of Membrane Science, 172, 59–74.
Mass and heat transfer analysis in fructose concentration by osmotic distillation process using hollow fibre module R. Thanedgunbaworn a, R. Jiraratananon a b
a,*
, M.H. Nguyen
b
Department of Chemical Engineering, King Mongkuts University of Technology Thonburi, Toongkru, Bangkok 10140, Thailand Centre for Advanced Food Research, University of Western Sydney, Bld M8, Locked bag 1797, Penrith, NSW 1797, Australia Received 6 June 2005; accepted 17 September 2005 Available online 14 November 2005
Abstract Osmotic distillation process was carried out on a hollow fibre membrane module using fructose solutions and clarified grape juice as feeds. The influence of operating parameters such as feed and brine flow velocities, feed concentration, and temperature, on the osmotic distillation flux was studied. For the experimental conditions employed, the water flux varied from 0.58 kg m2 h1 to 2.02 kg m2 h1. Temperature and feed concentration had significant effect on flux. On the contrary, feed and brine velocities had little effect on flux. The increase of feed and brine velocities or change of the hydrodynamic conditions also enhanced flux. The concentration polarization at high flow velocities can be neglected. In this work, the value of temperature polarization was small and the polarization coefficient H was estimated. It was found that temperature polarization reduced the driving force for mass transfer approximately 5–6%. However, this phenomenon affected the transport resistance of the system. The concentration and temperature polarization can be reduced by operating the process at high Reynolds number and low temperature. The transport resistance was affected by changing of operating condition such as feed velocity and temperature. The major transport resistance of the process was in the membrane. 2005 Elsevier Ltd. All rights reserved. Keywords: Concentration polarization; Fructose solution; Hollow fibre; Osmotic distillation; Polarization coefficient; Temperature polarization
1. Introduction The advantages of the concentration of the liquid foodstuffs include the reduction in packaging, storage, transport cost and prevention of deterioration by microorganisms. For these reasons, many concentration techniques have been developed and used for the food industries. They include evaporative concentration, freeze concentration, and membrane processes such as reverse osmosis (RO) and ultrafiltration (UF). Recently, the new alternative membrane process has been developed and it is called osmotic distillation (OD). Osmotic distillation, a low energy concentration process, is a membrane contactor technique in which the porous hydrophobic membrane separates two aqueous solutions *
Corresponding author. Tel.: +66 2 470 9222; fax: +66 2 428 3534. E-mail address: [email protected] (R. Jiraratananon).
0260-8774/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2005.09.023
and prevents penetration of the aqueous solution into the pore. One surface of membrane is contacted with dilute aqueous solution and the opposing surface is contacted with concentrated salt solution as the stripping solution. The separation by OD is based on the activity difference or the vapour pressure difference between the feed solution and the brine causing the water vapor to transfer from the dilute solution to the stripping solution. The OD process can be operated at room temperature and atmospheric pressure, which avoids the degradation of heat-sensitive components and some loss of volatile components of the liquid foodstuffs (Kunz, Benhabiles, & Ben-Aim, 1996). In addition, this process can concentrate the solutions to a very high concentration (60–70Brix) (Bailey, Barbe, Hogen, Johnson, & Sheng, 2000; Vaillant et al., 2001). From these advantages, OD process has been widely investigated by many researchers. However, the major disadvantage of OD process is low fluxes. In order to improve the
R. Thanedgunbaworn et al. / Journal of Food Engineering 78 (2007) 126–135
127
Nomenclature aw cp C dp D h DHv J k kT K M P P* ri ro R T U v
water activity heat capacity (J kg1 K1) concentration (%w/w) pore diameter (lm) diffusion coefficient (m2 s1) liquid heat transfer coefficient (W m2 K1) latent heat of vaporization (J kg1) mass vapour flux (kg m2 h1) mass transfer coefficient (m s1) thermal conductivity (W m1 K1) transport coefficient (kg m2 h1 Pa1) molecular weight (kg mol1) pressure (Pa) saturation vapour pressure (Pa) internal radius of the fibre (mm) external radius of the fibre (mm) universal gas constant (8.314 J K1 mol1) temperature (C, K) overall heat transfer coefficient (W m2 K1) fluid velocity (m s1)
Dimensionless numbers Gz Graetz Nu Nusselt
OD flux, it is necessary to understand the mass transfer phenomenon and the effect of operating conditions involved in the system. There are limited studies on mass and heat transfer phenomena in OD in the literatures (Alves & Coelhoso, 2004; Celere & Gostoli, 2002; Courel, Dornier, Rios, & Reynes, 2000; Sheng, Johnson, & Lefebvre, 1991). Sheng et al. (1991) proposed the models for predicting flux and juice concentration using various operating parameters. The analysis of heat and mass transfer phenomena in osmotic distillation in plate and frame module was also proposed by Celere and Gostoli (2002). Asymmetric porous membrane was applied for the experiments on osmotic distillation of pure water to investigate mass transfer resistances and phenomena (Courel, Dornier, Rios, et al., 2000). Although mass transfer is an important phenomenon of the OD system, the heat transfer also plays an important role in the process. It was reported that the temperature polarization phenomena affected the driving force of OD system resulting in the water flux reduction (Alves & Coelhoso, 2004; Gostoli, 1999). However, for the osmotic distillation in a stirred cell, the magnitude of temperature polarization was reported to be small (Alves & Coelhoso, 2004). The aim of this paper is to study the effect of operating conditions such as feed and brine velocities, feed concentration, and bulk temperature on flux. The fructose solutions are chosen for this study because fructose is the main sugar found in fruit juices. In addition, the experiments were also
Pr Re Sc Sh
Prandtl Reynolds Schmidt Sherwood
Greek letters d membrane thickness (m) e membrane porosity q fluid density (kg m3) l fluid viscosity (Pa s) H polarization coefficient / packing density Subscripts A air b bulk f feed m membrane s salt w water 1 membrane location at the feed side 2 membrane location at the brine side
carried out using clarified grape juice as feed. In osmotic distillation process, the concentration and temperature polarization affect the OD performance and these polarizations are influenced by the operating conditions which must be investigated to avoid the undesirable effect. Therefore, the characteristics of concentration and temperature polarization in OD are included in this study. This work also attempted to estimate the transport resistance of membrane, feed and brine boundary layers. 2. Theory 2.1. Mass transfer The principle of OD is depicted in Fig. 1. The mass transfer mechanism of water vapor through the hydrophobic membrane includes three consecutive steps: (1) evaporation of water at a membrane pore entry: (2) diffusion or convective transport of water vapor through the membrane pore; and (3) condensation of water vapor on the brine-side at the pore exit. Evaporation of water vapour at the membrane pore entrance results in the build up of feed concentration at the membrane surface (Cf,m). On the other hand, condensation of water vapour into the brine permeate also gives rise to the difference in brine concentrations. This phenomenon is called concentration polarization (CP). The existence of the boundary layers due to the concentration polarization at each side of the
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R. Thanedgunbaworn et al. / Journal of Food Engineering 78 (2007) 126–135 Membrane
Dilute feed solution
Ts ,m
T f ,b
where k is the mass transfer coefficient (m s1); k = DAB/d, and DAB is the diffusion coefficient. The coefficients, kf and ks, can be obtained by the experiment or estimated by the empirical correlation as the following:
Osmotic solution Ts ,b
T f ,m
C s ,b Pw,1
Pw, 2
Sh ¼ AðRea Scb Þ
C s ,m
in which,
C f ,m
C f ,b
1/Kf
Flux 1/Km
Sh ¼
kd h DAB
Re ¼
vd h q l
and
Sc ¼
l qDAB
ð8Þ
1/Ks
Water vapour flux
Fig. 1. Concentration and temperature profiles in osmotic distillation.
membrane result in the reduction of driving force for mass transfer. The basic equation to describe the water vapour transport in OD system relates between the flux (J) and the water vapour pressure difference across the membrane (Pw,1 Pw,2): J ¼ K m ðP w;1 P w;2 Þ
ð1Þ
where Km is the membrane transport coefficient which is also referred to as the membrane permeability. The water vapor pressure is a function of temperature and is related to the activity of the solution by P w ¼ P w aw
ð2Þ P w
where Pw is the water vapor pressure, is the vapor pressure of pure water, and aw represents the water activity in the solutions. However, the vapour–liquid interfaces conditions are not accessible. Thus, the alternative mass transfer model is given by Eq. (3): J ¼ KDP w;b
ð7Þ
ð3Þ
where DPw,b is the water vapour pressure difference corresponding to the bulk concentration of the liquid compartments. K is the overall transport coefficient (kg m2 h1 Pa1) of the system and is given by Eq. (4). 1 1 1 1 þ þ ð4Þ K¼ Kf Km Ks where 1/Kf, 1/Km, and 1/Ks are the transport resistances of feed boundary layer, membrane, and of permeate boundary layer, respectively. Owing to the concentration process, the concentration difference between bulk and membrane surface locations is created and induces a diffusion of solute. According to Ficks law and mass balance across the boundary layers, the relationship between bulk concentration (Ci,b) and concentration at membrane surface (Ci,m), i = f for feed and s for brine side, is given by C f;m ¼ C f;b expðJ =qw k f Þ
ð5Þ
C s;m ¼ C s;b expðJ =qw k s Þ
ð6Þ
where A, a, and b are constants, q is the density, l is the viscosity of the fluid, v is the velocity. dh is the hydraulic diameter which is also called the characteristic diameter of the flow channel. For a flow inside the pipe, dh equals to the diameter of the pipe. However, for a flow in noncircular channel, the hydrodynamic diameter can be determined by dh = 4S/P where S is the cross-sectional area and P is the wetted perimeter of the flow channel. The hollow fibre module was employed in this work. The configuration of hollow fibre module is similar to the shell and tube heat exchanger. Therefore, mass transfer at the two sides of the hollow fibre module are distinguished as tube side and shell side. 2.1.1. Mass transfer at the tube side In case that the solution flows inside the fibre, the mass transfer coefficient can be estimated by many equations (Gawronski & Wrzesinska, 2000; Skelland, 1974; Viegas et al., 1998). For the Graetz number (Gz) larger than 400, the mass transfer coefficient is given by Leveque (Gawronski & Wrzesinska, 2000; Skelland, 1974): 1=3 dh Sh ¼ 1:615 ðRe ScÞ1=3 ð9Þ L Viegas et al. (1998) proposed the correlation for Re < 34 and Gz < 65. The correlation is 1=3 1:01 d h Sh ¼ 0:2Re Sc ð10Þ L 2.1.2. Mass transfer at the shell side Mass transfer at the shell side of the hollow fibre module is different from the mass transfer at the tube side owing to the packing of the fibres in the shell. Gawronski and Wrzesinska (2000) concluded that the Sherwood number of the shell side strongly depended on the fibre packing density (/). Lipnizki and Field (2001) compared and discussed the differences of the correlations which were taken from the literature. It was concluded that for the correlations proposed by Gawronski and Wrzesinska (2000), Prasad and Sirkar (1988), Costello, Fane, Hogan, and Schofield (1993), the Sherwood number decreased with increasing packing density. However, Wu and Chen (2000) observed that the Sherwood number decreased by increasing packing density until the packing density reached about 55%, beyond that point the Sherwood number increased with
R. Thanedgunbaworn et al. / Journal of Food Engineering 78 (2007) 126–135
the packing density. In this work, the correlation of Costello et al. (1993) was chosen because constrains of the equation correspond with our experimental condition. The correlation is as follows: Sh ¼ ð0:53 0:58/ÞRe
0:53
Sc
0:33
ð11Þ
2.2. Heat transfer Even though OD is essentially a mass transfer process, heat transfer is also concerned. The temperature difference is created due to the evaporation at the feed side and condensation at the brine side and this reduces the vapor pressure difference across the membrane, resulting in the driving force decay. The temperature profile is showed in Fig. 1. Steady state heat transfer considerations of the system is given by Eq. (12) and the overall heat transfer coefficient (U) of the OD process is given by Eq. (13). Q ¼ U DT b ¼ hf ðT f;b T f;m Þ ¼ J DH v þ hm ðT f;m T s;m Þ ¼ hs ðT s;m T s;b Þ 1 1 1 1 U¼ þ þ hf hm þ ðJDH v Þ=DT m hs
ð12Þ ð13Þ
where Q is the total heat transferred across the membrane, J is the flux and DHv is the latent heat of vaporization, hf and hs represent the heat transfer coefficients of the feed and permeate thermal boundary layers, and hm is the heat transfer coefficient of the membrane. Therefore hf(Tf,b Tf,m) and hs(Ts,m Ts,b) represent the heat flux through the boundary layers. The heat transfer in the membrane is given by the convective heat flux, JDHv, and the conductive contribution related to the temperature difference, hm(Tf,m Ts,m). From Eq. (12), the temperatures at the membrane surfaces can be evaluated by the following equations: hm ðT s þ ðhf =hs ÞT f Þ þ hf T f N DH v hm þ hf ð1 þ hm =hs Þ hm ðT f þ ðhs =hf ÞT s Þ þ hs T s þ N DH v ¼ hm þ hs ð1 þ hm =hf Þ
T f;m ¼
ð14Þ
T s;m
ð15Þ
The heat transfer coefficient of the membrane (hm) can be evaluated through the thermal conductivity of the membrane, k Tm . Therefore, hm for a cylindrical geometry based on the internal surface can be approximated as (Bui, Nguyen, & Muller, 2005; Gostoli, 1999): hm ¼
e k TA þ ð1 eÞk Tpolymer k Tm ¼ ri lnðro =ri Þ ri lnðro =ri Þ
ð16Þ
where k Tpolymer and k TA are the thermal conductivities of the polymer and of the air, respectively, e is the porosity of the membrane, and ri, ro are the internal and external radius of the fibres. Furthermore, the liquid heat transfer coefficients can be estimated by empirical correlations of dimensionless numbers, Nusselt (Nu), Reynolds (Re), and Prandtl (Pr) numbers.
b2
Nu ¼ b1 Re Pr with Nu ¼
b3
hd h kT
lb lm
129
b4
and
ð17Þ Pr ¼
lcp kT
ð18Þ
where bi are coefficients of the correlation, kT is the thermal conductivity, and cp is the heat capacity. In the case of the hollow fibre module with the co-current flow, there are the concentrations and temperatures change along the module. However, the flux in OD process is very small compared with the flow rates. Hence, it can be assumed that the concentrations of the two streams are constant along the module (Gostoli, 1999). This assumption can be checked by considering the mass and energy balance analysis. Using the experimental conditions of this work, it was found that the concentration change along the module can be estimated in the order of 0.2%. Moreover, according to the energy balance equations of the both feed and brine streams, the outlet temperatures of the two streams can be evaluated. For this work, it was found that the value of outlet temperature is very close to the inlet value, a temperature change of 0.03–0.09 C was observed. Therefore, the inlet temperature will be used as the bulk temperature in order to determine the temperature at the membrane surface and temperature polarization in this study. The temperature polarization reduces the driving force for the mass transfer through the membrane. Its effect on flux was studied (Alves & Coelhoso, 2004; Gostoli, 1999) and the polarization coefficient (H) was introduced to represent the fraction of the driving force really effective for the mass transfer through the membrane. Thus, the flux can be estimated by J ¼ K m DP w;m ¼ HK m DP w;b
ð19Þ
Thus, the polarization coefficient H can be estimated by using Eq. (20). H¼
DP w;m DP w;b
ð20Þ
From the experiments, the flux data were obtained. Eqs. (5) and (6) are used to determine the feed and brine concentration at the membrane surface, and was also used to estimate the concentration polarization ratio. The mass transfer coefficients within feed and brine boundary layer can be estimated by Eqs. (9) and (11), respectively. The heat transfer coefficients are estimated by mass and heat transfer analogy using Eqs. (9) and (11). 3. Experimental The experiments were performed with fructose solutions and clarified Chardonnay grape juice (ultrafiltration permeate) as feeds. Fructose solutions were prepared with Fructose (C6H12O6) powder of 99.6% purity (Chem-supply Pty. Ltd., Australia) and distilled water. Brine solution was prepared from CaCl2 Æ 2H2O, analytical grade (Chemsupply Pty. Ltd., Australia) to obtain a fixed concentration
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of 43% (w/w). The concentrations of feeds and brine solutions were determined by a refractometer. A hydrometer (Townson & Mercer (T&M) Pty. Ltd.) was used to determine the density of solutions. However, the properties of fructose and calcium chloride solutions were checked by comparing with the data from the CRC handbook Lide (2001). The hollow fibre membrane was polyvinylidenefluoride (PVDF) supplied by Memcor Australia (South Windsor, New South Wales, Australia). The main characteristics of the fibres are 0.660 mm internal diameter, 170 lm thickness, 0.2 lm pore diameter and 64% porosity, as specified by the supplier. The specifications of the hollow fibre modules used in the experiment are illustrated in Table 1. The membrane was cleaned after use by thoroughly flushing the system with distilled water through the feed side without recycling. Subsequently, NaOH solution (1%w/w) was circulated for 1 h at 45 C. Finally, the system was rinsed with distilled water without recycling for 10 min and then the liquid was discharged from the system. For the brine side, the membrane was flushed with 4 l of distilled water. The experimental setup is depicted in Fig. 2. The membrane module was installed in a vertical position. The feed and brine solutions were fed into the module by the peristaltic pumps (Easy-Load Masterflex model 7518-00). Circulation of both feed and brine was co-current with upward flow direction. The feed solution was circulated inside the
fibres whereas the brine solution was circulated in the shell side of the module. The brine tank of 5 l was large enough to maintain a nearly constant concentration during the experiment. The water baths with the temperature control were used to control the feed and brine temperatures. The water flux was obtained by measuring the feed volume over a 15 min in the pipette connected to the feed tank. The operating parameters, the feed flow velocity (vf), the brine flow velocity (vs), the feed concentration (Cf), and the temperature (T) were studied in this work. In order to study the effect of feed flow velocity, the experiments were performed using equal inlet temperatures of feed and brine at 25, 35, and 45 C. The feed flow velocity was varied from 0.1 to 0.5 m s1, while maintaining a constant feed concentration of 45%w/w and brine flow velocity of 0.4 m s1. The brine flow velocity was varied from 0.1 to 0.5 m s1 for studying the effect of brine flow velocity. The feed concentration was varied from 35 to 55%w/w and the temperature was varied from 25 to 55 C in order to study the effect of feed concentration and temperature on flux, respectively. For the experiment with the clarified grape juice, the concentration of grape juice was 45Brix and experimental methods were the same as the case of fructose solution.
4. Results and discussion 4.1. The effect of operating conditions on flux, concentration, and temperature polarization
Table 1 Specifications of the hollow fibre module Module
Value
Number of fibres Total length of module (mm) Total effective length (mm) Effective area (cm2) Cross-section flow area of the fibre side (mm2) Cross-section flow area of the shell side (mm2)
35 250 180 130.63 11.97 16.69
4.1.1. Effect of feed velocity The effect of feed velocity on the flux was studied at different bulk temperatures. The results, shown in Fig. 3, indicate that increasing of feed velocity (vf) improved fluxes and it makes the flux appear 8.5% increase as the feed velocity increase from 0.1 to 0.2 m s1. Moreover, the flux was higher at high temperature because the water vapour
Fig. 2. Osmotic distillation experimental setup: (1) hollow fibre module, (2) thermometer, (3) pipette, (4) pressure gauge, (5) flowmeter.
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131
1.0300
1.80 45 o C
1.60
25 °C
1.0250
35 °C
35 o C Cf,m /C f,b
25 o C
1.00
45 °C
1.0200
35
1.20
22
Flux (kg/m .h)
1.40
0.80
1.0150 1.0100
0.60
1.0050
0.40 Fructose Grape Juice
0.20
1.0000 0
50
0.00 0
0.1
0.2
0.3 0.4 v f (m/s)
0.5
0.6
Fig. 3. Effect of feed cross-section flow velocity (vf, m s ) on flux rate at the conditions: Cf = 45%w/w, Cs = 43%w/w, vs = 0.4 m s1, and at different bulk temperatures: Comparison between fructose solution and Chardonnay white grape juice (45Brix).
150
Re
0.7
1
100
Fig. 4. Influence of Reynolds number and bulk temperature (Tb) on fructose concentration gradient.
0.9994 25 °C 35 °C 45 °C
pressure, the driving force of the process, increases with the temperature. For the experiment with the clarified grape juice, the concentration of grape juice was 45Brix. The experimental results for the grape juice were the same as the case of fructose solution. The results may be explained by the similarity in physical properties, viscosity and density, between fructose and UF permeate grape juice. The effect of ultrafiltration on the subsequent concentration of grape juice by osmotic distillation was studied by Bailey et al. (2000). It was reported that the UF permeate concentrated to 59Brix had fermentable sugars content (glucose + fructose) of 60%w/w. It was also showed that UF resulted in a small increase in juice surface tension, thus reducing membrane wetting. In this work, the experimental results with fructose solution can be used for the juice concentration process due to the similar features between fructose solution and UF permeate grape juice as mentioned. The feed velocity from 0.1 to 0.5 m s1 corresponds with Reynolds numbers (Re) of 12.37–116.23. In order to estimate the concentration polarization (CP) at the feed side, the feed concentration at the membrane surface (Cf,m) and mass transfer coefficient of the feed boundary layer (kf) were evaluated using Eqs. (5) and (9), respectively. The mass transfer coefficients of the feed boundary layer ranged from 1.27 · 105 to 2.96 · 105 m s1, using the properties of fructose solution for calculation. The increase of feed velocity resulted in higher shear stress along the membrane surface and, consequently, there was less concentration polarization (Fig. 4) such that flux was increased. Moreover, Fig. 4 indicates the value of CP ratio (Cf,m/Cf,b) increased with the bulk temperature (Tb). The evaporation rate of water at the membrane surface increased with temperature and, consequently feed concentration was high at the membrane surface. Therefore, the concentration polarization can be reduced by operating
Tf,m /Tf,b
0.9992 0.9990 0.9988 0.9986 0.9984 0.9982 0
50
100
150
Re Fig. 5. Influence of Reynolds number and bulk temperature (Tb) on radial temperature profile within the boundary layer at the feed side.
the OD process at high Reynolds numbers and low temperatures. The influence of the hydrodynamic condition (Re) and the temperature on temperature polarization (TP) is shown in Fig. 5. Firstly, heat transfer was studied in order to evaluate the membrane surface temperatures (see Eqs. (14) and (15)). The heat transfer coefficients within the feed boundary layer were estimated by mass and heat transfer analogy using Eq. (9), as the following: 1=3 dh 1=3 Nu ¼ 1:615 ðRe PrÞ ð21Þ L The heat transfer coefficient of the feed side (hf) varied between 1208 and 2069 W m2 K1. From Fig. 5, the value of TP ratio (Tf,m/Tf,b) increased (close to 1) with increasing Re. The meaning is TP decreased with increasing Re. This result can be explained by the correlation between Reynolds number and heat transfer coefficient (hf). The increase of Reynolds number resulted in the enhancement of hf within feed boundary layer and consequently, the TP decreased. Hence, TP can be decreased by operating the process at high Re and low Tb. In order to evaluate
R. Thanedgunbaworn et al. / Journal of Food Engineering 78 (2007) 126–135
4.1.2. Effect of brine velocity The brine flow velocity (vs) was varied from 0.1 to 0.5 m s1 corresponding to the Reynolds numbers of 7.00– 54.09. The effect of brine velocity on flux is shown in Fig. 6. The increase of OD flux was attributed to the increase of brine velocity at any operating temperature due to higher shear rates along the membrane surface of the brine side. For the experiment with grape juice, fluxes also increased with brine velocity for all bulk temperatures considered. The boundary layer mass transfer coefficient of the brine side (ks) was evaluated by Eq. (11) because the experimental conditions in this study corresponded with the conditions of the correlation. It was found that ks varied between 1.15 · 105 and 3.15 · 105 m s1, using the properties of brine solution for calculation. The values of concentration polarization depend on the physical properties of the solution and the hydrodynamic conditions. Hence, the influence of Re and bulk temperature (Tb) on the concentration polarization on the brine side was studied and shown in Fig. 7. The values of Cs,m/Cs,b decreased, which indicates that CP increased, with decreasing Re and with increasing Tb. Concentration polarization increased with the temperature because the condensation of water vapour was high at higher temperature and, consequently, the brine concentration difference within the boundary layer was enhanced. Fig. 8 shows the influence of Re and temperature on temperature polarization (TP) of the brine side. TP 1.80 1.60
Flux (Kg/m2.h)
1.40 1.20 1.00 0.80 0.60 0.40 Fructose Grape Juice
0.20 0.00 0
0.1
0.2
0.3 0.4 vs (m/s)
0.5
0.6
0.7
Fig. 6. The effect of brine velocity (vs, m s1) on flux rate at the conditions: Cf = 45%w/w, Cs = 43%w/w, vf = 0.4 m s1, and at different bulk temperatures; Comparison between fructose solution and Chardonnay red grape juice (45Brix).
0.9950 0.9900
Cs,m /Cs,b
the effect of TP on the flux, the polarization coefficient (H) was calculated using Eq. (20). The value of DP w;b was determined by using the water activity at the membrane surface instead of the bulk water activity in order to avoid the concentration polarization effects. The value of H in this work was 0.94 indicating that temperature polarization reduced the driving force for mass transfer through the membrane in the order of 6%. However, this effect can be reduced by choosing the appropriate operating condition for the system studied.
0.9850 0.9800 0.9750
25 °C 35 °C
0.9700
45 °C
0.9650 0
10
20
30
40
50
60
Re
Fig. 7. Influence of Re and bulk temperature (Tb) on brine (CaCl2) concentration gradient.
1.0012 25 °C 35 °C 45 °C
1.0010
Ts,m / Ts,b
132
1.0008 1.0006 1.0004 1.0002 1.0000 0
10
20
30
40
50
60
Re Fig. 8. Influence of Re and Tb on temperature profile within the boundary layer at the brine side.
decreased with increasing Re. Moreover, temperatures affected the concentration profile within brine boundary layer. The existence of TP within the brine boundary layer resulted in the driving force decay. The polarization coefficient H value was 0.95. 4.1.3. Effect of feed concentration The effect of feed concentration on flux for fructose solution is presented in Fig. 9. The feed concentration was varied from 35 to 55%w/w and vf was adjusted between 0.1 and 0.3 m s1 in order to maintain the Re of feed solution at a constant value of 18. The flux was measured for various feed concentrations, which corresponded to different water activities. It can be seen that the effect of feed concentration on flux using fructose solution and grape juice was similar. Moreover, the water flux decreased by 12% as the feed concentration increased from 35 to 40%w/w. Since the water vapour pressure is the driving force of OD process and it relates to the water activity, therefore, the increase of feed concentration reduced the water activity and flux. The calculations of CP and TP ratio revealed that both concentration and temperature polarization decreased with
R. Thanedgunbaworn et al. / Journal of Food Engineering 78 (2007) 126–135
increasing feed concentration. This result can be explained to be due to the decrease of driving force. In the other words, the evaporation rate of water at the membrane surface decreased with increasing feed concentration. The values of polarization coefficient (H) increased with feed concentration and was in the range of 0.94–0.96. 4.1.4. Effect of temperature The effect of temperature on OD flux was studied in the range of 25–55 C and was demonstrated in Fig. 10. The Reynolds numbers (Re) were maintained constant (±10%) for the range of temperatures tested. Flux increased 20% with increasing bulk temperature from 25 to 35 C. There was the exponential relationship between the temperatures and driving force of the process. The effect of temperature was mainly due to the increase of the water vapour pressure and reduction of solution viscosity. Additionally, high temperatures give more kinetic energy to water vapour to transport through the membrane, hence flux was increased. The mass transfer coefficients of the feed and brine boundary layers (kf and ks) are presented in Table 2. These values were calculated from
1.00
0.9600
0.90
Flux (Kg/m2.h)
0.9200
0.70 0.60
0.9000
0.50 0.8800
0.40 0.30
Flux : fructose
0.20
Flux : juice
0.10
aw
0.8600
Water activity (aw)
0.9400
0.80
0.8400
0.00
0.8200 35
40
45
50
55
Feed concentration (%w/w)
Fig. 9. Effect of feed concentration (Cf) on OD flux: comparison between fructose solution and UF permeate grape juice. Cs = 43%w/w, vs = 0.4 m s1, and Tb = 25 C.
2.5
Flux (Kg/m2.h)
2.0 1.5 y = 0.4232e0.0283x R 2 = 0.9893
1.0 0.5 0.0
20
30
40 Temperature (oC)
50
60
Fig. 10. OD flux dependence upon temperature (Tb); at the conditions Cf = 45%w/w and Cs = 43%w/w.
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Table 2 Values of the mass transfer coefficients, kf and ks, estimated from Eqs. (9) and (11) for different operating temperatures Temperature (C)
kf (·105 m s1)
ks (·105 m s1)
25 35 45 55
2.01 2.16 2.18 2.44
2.69 2.60 2.81 2.60
Eqs. (9) and (11) which do not take into account the effect of temperature polarization. Both kf and ks slightly increased with temperature (at constant Re) and increased with velocity (at specific temperature) as generally found. 4.2. Transport resistances In order to improve flux, it is necessary to compare the resistance of the feed boundary layer with the resistance of the permeate boundary layer, and the resistance of the membrane. Most researches on osmotic distillation process were carried out using pure water as feed and did not take into account the effect of temperature polarization (Alves & Coelhoso, 2004; Courel, Dornier, Herry, Rios, & Reynes, 2000; Courel, Dornier, Rios, et al., 2000). In the present work, the effect of temperature polarization has been included in the calculations. Therefore, it is more appropriate in defining 1/Km, 1/Kf, and 1/Ks as transport resistances in which both concentration and temperature polarization have been taken into account. From the calculation, the temperature drops across the feed and brine boundary layers, ((Tf,b Tf,m) and (Ts,m Ts,b)), ranged 0.1–0.6 C. With the purpose of calculating the individual resistance, the vapour pressure at each point (see Fig. 1) which is the function of both composition and temperature must be known. The results in Table 3 indicate that at a certain temperature the transport resistances of the feed side (1/Kf) decreased with increasing feed velocity due to the enhancement of kf while the transport resistances of the brine side were approximately constant. On the other hand, the transport resistance of the membrane (1/Km), which is also affected by both heat and mass transfer across the membrane, decreased with increasing feed velocity due to a slight increase of (Pw,1 Pw,2) and more pronounced increase of flux (see Eq. (1)). In other words, the membrane permeability increased with feed velocity because both concentration and temperature polarization were influenced by the Reynolds number (see Figs. 4 and 5). The comparison of transport resistances in percentages revealed that the membrane transport resistance was relatively constant and was the major resistance of the system. This corresponds with previous works (Alves & Coelhoso, 2004; Courel, Dornier, Rios, et al., 2000). Table 4 depicts that all transport resistances increased with temperature due to the enhancement of both concentration and temperature polarization at higher temperatures. Therefore, the values of K, the total transport coefficients (see Eq. (4)) decreased with increasing
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Table 3 Transport resistances (1/K) of the individual compartment at different feed velocities and temperatures with a constant velocity in the brine side Feed velocity (m s1)
1/Km (Pa m2 h kg1)
1/Kf (Pa m2 h kg1)
At 25 C vf = 0.1 = 0.2 = 0.3 = 0.4 = 0.5
2.5 · 103 2.3 · 103 2.2 · 103 2.2 · 103 2.1 · 103
76.49 63.57 56.86 52.45 49.23
At 35 C vf = 0.1 = 0.2 = 0.3 = 0.4 = 0.5
3.3 · 103 3.2 · 103 2.9 · 103 2.8 · 103 2.7 · 103
At 45 C vf = 0.1 = 0.2 = 0.3 = 0.4 = 0.5
3.4 · 103 3.3 · 103 3.2 · 103 3.1 · 103 3.1 · 103
1/Ks (Pa m2 h kg1)
1/Km (%)
1/Kf (%)
1/Ks (%)
48.20 48.65 48.89 49.06 49.18
95.28 95.39 95.49 95.50 95.40
2.90 2.61 2.43 2.32 2.30
1.82 2.00 2.09 2.17 2.30
123.55 102.80 91.96 84.86 79.67
79.16 79.90 80.32 80.59 80.78
94.21 94.62 94.37 94.36 94.39
3.53 3.03 3.01 2.89 2.79
2.26 2.35 2.63 2.75 2.83
191.98 159.92 143.17 132.17 124.13
125.09 126.27 126.90 127.32 127.63
91.39 91.99 92.14 92.31 92.40
5.22 4.48 4.16 3.92 3.75
3.40 3.53 3.69 3.77 3.85
Table 4 The effect of temperature on resistances Temperature (C)
1/Km (Pa m2 h kg1)
1/Kf (Pa m2 h kg1)
1/Ks (Pa m2 h kg1)
1/Km (%)
1/Kf (%)
1/Ks (%)
25 35 45 55
2.04 · 103 2.89 · 103 3.29 · 103 3.93 · 103
52.89 91.96 159.92 238.84
43.65 80.24 125.96 222.87
95.49 94.37 91.99 89.49
2.47 3.01 4.47 5.43
2.04 2.63 3.53 5.07
Reynolds numbers at feed and brine side were maintained constant at 54.20 ± 7.71 and 39.12 ± 4.15, respectively.
temperature. The enhancement of flux at high temperature, therefore, resulted from the exponential increase of DPw (see Eq. (3)) which influenced flux more than the reduction of K. Consideration of the percentages of transport resistances in Table 4 would reveal a better understanding of the results, i.e., the contribution of membrane transport resistance was less significant at higher temperature. The membrane permeability (Km) was reported to be temperature dependent (Schofield, Fane, & Fell, 1990) in which the trend is dependent upon the gas diffusion mechanisms in the membrane pores. 5. Conclusions In order to present the importance of the operating parameters on the performance of osmotic distillation (OD) process, the effect of several parameters on osmotic distillation flux namely feed and brine velocity, feed concentration, and operating temperature were studied. The OD fluxes in this study ranged from 0.58 kg m2 h1 to 2.02 kg m2 h1. The experimental results showed that temperature and feed concentration had significant effect on the flux. Flux increased with temperature since water vapour pressure is the function with temperature according to Antoine equation. It can be concluded that the flux was affected by the feed concentration via the water activity of
feed solution. In this study, feed and brine velocity had little effect on the flux. However, the increase of feed and brine velocity or the hydrodynamic conditions can cause the OD flux enhancement. The concentration and temperature polarization effects were evaluated. The minimum and maximum temperature differences between both sides of the membrane were 0.31 C (vf = 0.4 m s1, vs = 0.3 m s1, and Tb = 25 C) and 0.87 C (vf = 0.2 m s1, vs = 0.3 m s1, and Tb = 55 C), respectively. In this study, the polarization coefficient which indicates the effect of temperature polarization on the driving force was about 0.95. It means that temperature polarization reduced the driving force for mass transfer about 5%. The concentration and temperature polarization can be reduced by operating process at high Re and low temperature. In this work, the transport coefficients (K) and the transport resistances (1/K) were defined. Kf and Ks are different from the mass transfer coefficients (kf, ks) in both units and physical meaning. In other words, all transport resistances (1/Ki) are neither the mass transfer resistance nor the heat transfer resistance but, they are resistances coupled by the effect of both heat and mass transfer and are appropriate in describing the system with simultaneous heat and mass transfer such as membrane distillation and osmotic distillation.
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