Prediction of Flux and Aroma Compounds ... - ACS Publications

Ind. Eng. Chem. Res. 2001, 40, 4925-4934

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Prediction of Flux and Aroma Compounds Rejection in a Reverse Osmosis Concentration of Apple Juice Model Solutions Silvia A Ä lvarez, Francisco A. Riera,* Ricardo A Ä lvarez, and Jose´ Coca Department of Chemical Engineering and Environmental Technology, University of Oviedo, C/Julia´ n Claverıá, 8, 33 006 Oviedo, Spain

The aim of this work was to predict the rejection of aroma compounds and permeate flux during the reverse osmosis concentration of model solutions simulating apple juice. For the concentration, the MSCB2521 R99 spiral-wound membrane (Separem SpA, Biella, Italy) was used. The preferential sorption-capillary flow model was employed for this purpose. Water and aqueous solutions of apple juice aroma were used to determine the parameters included in the model. Then, the model was tested with aqueous solutions of glucose and aroma compounds. Experiments were performed at different transmembrane pressures (1.5-3.5 MPa), feed flow rates (200-600 L/h; Reynolds numbers ) 51-190), temperatures (15-30 °C), and glucose concentrations (9.1-17.0 °Brix). Good agreement between experimental and estimated data was observed for most of the aroma compounds and operating conditions used. 1. Introduction Apple juice, like other fruit juices, is usually concentrated to reduce packaging, storage, and transportation costs. Reverse osmosis (RO) is a membrane process that can be used to preconcentrate the juice and presents several advantages over the conventional concentration methods evaporation and freezing. As the process is carried out at low temperatures, minimum thermal damage is caused. Other advantages include lower capital and operating costs.1,2 After the first work on the concentration of apple juice published by Merson and Morgan,3 several papers have followed.2,4-10 These papers have mainly focused on the measurement of permeate flux using different types of membranes and operating conditions with only a few also involving measurements of flavor retention. Polyamide membranes (PA) were found to perform better in terms of both flux and flavor retention than cellulose acetate (CA) membranes. The modeling perspective has received less attention. The success of RO for fruit juice concentration depends on the adequate retention of flavor components that can permeate the membrane.7 Merson et al.4 concluded that the major factor concerning the quality of the final products is the retention of flavor components, as these compounds affect the organoleptic properties such as odor and flavor. Retention of these components during the RO process is related to the type of membranes and the operating conditions used. The composition of apple juice depends on the variety, origin, and growing conditions of the apples; the quality of the fruit at the time of processing; the processing procedures; and the storage technique. The major components of apple juice are sugars. Other components include acids, nitrogen compounds, polyphenols, minerals, and vitamins.11 Apple juice aroma is caused by the blend of many compounds rather than the presence of one particular component. Three groups of compounds can be found * Corresponding author. Tel.: + 34 8 5103438. Fax: + 34 8 5103434. E-mail: [email protected].

in apple flavors: esters, aldehydes, and alcohols, with esters being reported as the most important ones. The major compounds thought to be responsible for apple flavor are ethyl butanoate, ethyl-2-methyl butanoate, trans-2-hexenal, and hexanal. Some authors have correlated the quality of juice flavors negatively with the presence of ethanol and ethyl acetate.12,13 Several works have been published on the modelization of the RO process.14 The preferential sorptioncapillary flow model was developed by Sourirajan et al. and has been successfully applied to several CA and PA membranes.15-18 The aim of this work was to predict permeate flux and aroma compounds rejection in the RO concentration of aqueous solutions simulating apple juice. 2. Materials and Methods 2.1. Feed Solutions. In the first step, aqueous solutions of aroma compounds were used to perform the experiments. Eleven of the main identified apple aroma components were selected. These components were ethyl acetate, ethyl butanoate, ethyl-2-methyl butanoate, isopentyl acetate, hexyl acetate, hexanal, trans-2-hexenal, butanol, isobutanol, isopentanol, and hexanol. Experiments were conducted with single and mixed aroma compound solutions. Two different concentrations, shown in Table 1, were considered. Concentration A was much higher than the concentration of the individual aromas in real apple juice, taking into account their solubilities in water.19,20 Thus, errors in the analytical determination of the aroma compounds in the permeate stream were reduced. Concentration B is similar to the concentration of the aromas in real apple juice.11 The compounds were selected after the analytical characterization of several samples of apple juice and apple juice aroma concentrates obtained from an industrial multiple effect evaporator was performed.21 Samples were supplied by Valle, Ballina, and Fernańdez, S.A. (Villaviciosa, Spain). As sugars are the main components of apple juice, in the second step of this work, aqueous solutions of

10.1021/ie010087c CCC: $20.00 © 2001 American Chemical Society Published on Web 10/10/2001

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Ind. Eng. Chem. Res., Vol. 40, No. 22, 2001

Table 1. Some Properties of the Selected Aroma Compounds and Their Concentrations in the Model Solutions

compound ethyl acetate ethyl butanoate ethyl-2-methyl butanoate isopentyl acetate hexyl acetate trans-2-hexenal hexanal isobutanol butanol isopentanol hexanol a

concentration molecular solubility (ppm) weight at 25 °C A B (kg/kmol) (wt %) 150 100 100 100 30 130 80 200 200 200 150

50 15 7 17 10 70 15 20 20 15 30

88.11 116.16 130.19 130.19 144.22 98.14 100.2 74.12 74.12 88.15 102.18

7.43 0.60 sls 2.8 slsa 8.02 7.35 2.67 0.57

sls ) slightly soluble.

glucose and aromas were used to simulate apple juice. The concentration of glucose was set between 9.1 and 17.0 °Brix, and the concentrations of the aroma compounds are shown in Table 1 ( column B). 2.2. Equipment. Experiments were performed in a RO unit specially built for this process. The main components of the RO system are a 26-L feed tank, a CAT piston pump (model 311, 5.5 HP, CAT Pumps, Minneapolis, MN) with a maximum velocity of 2.95 m/s and a maximum operating pressure of 5.5 MPa, an MSCB 2521 R99 spiral-wound membrane module supplied by Separem SpA (Biella, Italy), a rotameter located in the retentate line, and a temperature and pressure control system. The RO module consists of a spiral-wound aromatic polyamide membrane with a total effective area of 1.03 m2 and a typical NaCl rejection of 99.2% (at a transmembrane pressure of 1.5 MPa, temperature of 25 °C, and NaCl concentration of 3500 ppm). Permeate and retentate streams were recycled back to the feed tank. Experiments were carried out at pressures from 1.5 to 3.5 MPa, temperatures from 15 to 30 °C, and feed flow rates between 200 and 600 L/h. The permeate flux was measured gravimetrically. The equipment was cleaned in place with a 0.2% commercial P3 Ultrasil 10 (Henkel Corporation, Cincinnati, OH) solution at a pressure of 0.5 MPa and a temperature of 35-40 °C and rinsed with distilled water for about 15-20 min. The flux of distilled water at a transmembrane pressure of 1.5 MPa and a temperature of 25 °C was measured before each experiment. 2.3. Analytical Methods. The concentrations of the aroma compounds were analyzed in the permeate, retentate, and feed streams by gas chromatography. Analyses were made with a Konik 3000 gas chromatograph (Miami, FL) equipped with a flame ionization detector, a Spectra-Physics SP4290 integrator (SpectraPhysics, Mountain View, CA), and a CTCA2000S liquid autosampler (CTC Analytics, Carrboro, NC). A Supelcowax 10 fused-silica capillary column (Supelco Inc., Bellefonte, PA) with dimensions of 60 m × 0.25 mm i.d. was used for the analysis. Helium was employed as the carrier gas at a flow rate of 2.0 mL/min using a 100:1 split ratio. The temperature ramp was programmed from 55 to 93 °C at a rate of 2 °C/min and then from 93 to 110 °C at a rate of 10 °C/min, with an initial hold of 2 min and a final hold of 3 min. The injector and detector were set at 190 and 200 °C, respectively. Samples of 1-µL volumes were injected into the gas

chromatograph, and 1-pentanol was used as the internal standard.21 The glucose concentration was measured by an Abbe refractometer (Sibuya Optical, Tokyo, Japan). 3. The Model To predict the permeate flux and the rejection of the aroma compounds, the preferential sorption-capillary flow model was applied. The model, as described by Sourirajan et al.,15-18 assumes that all transport through the membrane takes place through the “pores” in the membrane skin layer. This mechanism defines a pore as any space between two nonbonded material entities in the membrane matrix through which mass transport can occur. It also assumes that water is preferentially adsorbed onto the pore walls and that solute is rejected at the surface for physicochemical reasons. The equations describing the solute and solvent fluxes are

NA )

DAM (C - CA3) Kδ A2

(1)

NB ) A(∆P - ∆Π)

(2)

where NA and NB are the fluxes of solute and solvent, respectively, through the membrane; A is the solvent permeability of the membrane; ∆P is the pressure difference across the membrane; ∆Π is the osmotic pressure difference at the two sides of the membrane; CA2 and CA3 are the solute concentrations on the membrane surface at the feed side and at the permeate side, respectively; and DAM/Kδ is the solute transport parameter, which is usually unknown. To predict the concentration of solute on the membrane surface at the feed side, the film theory was used

NA + NB ) kAC1 ln

(

)

XA2 - XA3 XA1 - XA3

(3)

where kA is the mass transfer coefficient; C1 is the molar density of the bulk solution; and XA1, XA2, and XA3 are the mole fractions of the solute in the bulk solution, on the membrane surface at the feed side, and in the permeate, respectively. As the concentration of the aroma compounds in the feed solution is very low, NA can be neglected in eq 3. The mole fraction of solute in the permeate can be calculated as

XA3 )

NA NA ≈ NA + NB NB

(4)

The rejection of the aroma compounds (R) can be determined from the expression

(

R (%) ) 1 -

)

CA3 × 100 CA1

(5)

According to the Kimura-Sourirajan analysis, using eqs 1-4 and a set of experimental data on the pure-water permeation rate, product rate, and solute rejection, it is possible to calculate A, CA2, DAM/Kδ, and kA. In our research, however, kA has been estimated using Schock and Miquel’s correlation, which was established for spiral-wound modules and Reynolds numbers in the range of 100 < Re < 100022

Ind. Eng. Chem. Res., Vol. 40, No. 22, 2001 4927

Figure 1. Water flux versus transmembrane pressure at different temperatures (Q ) 400 L/h).

Sh ) 0.065Re0.875 Sc0.25

(6)

where Sh is the Sherwood number (kAdh/DA), Re is the Reynolds number (dhvF/µ), and Sc is the Schmidt number (µ/FDA). kA is the mass transfer coefficient for species A, dh is the equivalent hydraulic diameter, DA is the diffusion coefficient for species A, v is the tangential flow velocity, F is the solution density, and µ is the solution viscosity. The hydraulic diameter was reported by the membrane supplier to have a value of 0.96 mm. The diffusion coefficients of the aroma compounds were obtained from the literature.23-25 For those compounds whose diffusion coefficients were not available, the empirical equation of Wilke and Chang was used26

DAB )

117.3 × 10-8(ΦMB)0.5T µVbp,A0.6

(7)

where DAB is the diffusion coefficient of solute A in solvent B expressed in m2/s, MB is the molecular weight of the solvent (kg/kmol), T is the absolute temperature (K), µ is the viscosity of the solution [kg/(m s)], Vbp,A is the molal volume of the solute at its normal boiling point (m3/kmol), and Φ is an associated parameter of the solvent, whose value is 2.6 for water. The tangential flow velocity can be expressed as

v ) Q/S

(8)

where Q is the feed flow rate and S is the effective area tangential to the feed flow, which can be calculated from the membrane leaf width (b) and the spacer thickness (h) and porosity () using10

S ) bh

(9)

In a previous work,10 the solute transport parameter (DAM/Kδ) for each compound was estimated using correlations from the literature.18 However, relatively high divergences between predicted and experimental data were found. Thus, in this study, DAM/Kδ was experimentally determined for each of the aroma compounds. Aqueous solutions of the aroma compounds were used for this purpose. On the other hand, the pure-water permeability coefficient, A, was estimated from experiments with distilled water.

The membrane used in this work has an effective surface of 1.03 m2. As this is quite a large membrane area in relation to the batch volume treated, the permeate rate is not small compared to the feed rate. Thus, the retentate concentration and flow rate are different from the feed concentration and flow rate. Average values of the feed concentration and feed flow rate have been considered throughout this work. 3.1. Estimation of Pure-Water Permeability. To obtain the pure-water permeability coefficient, A, experiments with distilled water were conducted at different transmembrane pressures. The flux was plotted versus the transmembrane pressure, and a linear relationship was found (Figure 1). For pure water, the osmotic pressure difference (∆Π) is equal to 0, and according to eq 2, the slope of the straight line obtained is A. This coefficient has been found to be independent of transmembrane pressure, contrary to the findings of Dickson et al., who indicated that A decreases with increasing transmembrane pressure for different films of PA membranes.17,18 Figure 1 also shows the influence of temperature on A. A set of experiments was also carried out at different feed flow rates (Figure 2). It was observed that permeability slightly decreased with feed flow rate. This effect can be explained by the increase in pressure drop through the feed channel that occurs with increasing flow rate, thus reducing the driving force for permeation. This effect was taken into account as the transmembrane pressure (∆P) was estimated by means of the equation

∆P )

Pi + Ps - P3 2

(10)

where Pi and Ps are, respectively, the pressures at the inlet and outlet of the membrane module at the feed side and P3 is the pressure at the permeate side. However, the variation of the pressure inside the module is probably not linear. Some authors have proposed several equations to estimate the pressure drop in spiral-wound modules.22,27 Equation 11 shows the influence of temperature and feed flow rate on permeability within the range of operating conditions considered in this research

AQ,T ) 32.186

Q (25T ) (400 ) 0.62

-0.1447

(11)

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Figure 2. Water flux versus transmembrane pressure at different feed flows (T ) 25 °C).

Figure 3. Rejection of the aroma compounds in individual and mixed solute solutions (concentration A in Table 1; pressure ) 3.5 MPa; temperature ) 25 °C; feed flow ) 600 L/h).

where A is the permeability in L/(h m2 MPa), T is the temperature in °C, and Q is the feed flow rate in L/h. 3.2. Estimation of DAM/Kδ. Aqueous solutions of aroma compounds were used to estimate the value of DAM/Kδ for each compound. Experiments were conducted with mixed and individual aroma compound solutions to check for any interaction between the compounds that could affect their permeabilities through the membrane. Experiments were performed at different concentrations, temperatures, transmembrane pressures, and feed flow rates to determine the effect of these variables on DAM/Kδ. As the concentration of the aroma compounds in the solutions was very low, the physicochemical properties of the feed, permeate, and retentate were considered to be equal to those of water at the same temperature, and the osmotic pressure difference at the two sides of the membrane (∆Π) was overlooked. From the experiments, data on NB, NA, and XA3 at different operating conditions were obtained. The value of NB for these diluted solutions was very similar to NB for pure water, although it was slightly lower for several

runs. Using eq 1, the value of DAM/Kδ for each aroma compound was determined. Figure 3 compares the experimental data on the rejection of the aroma compounds at 25 °C, 3.5 MPa, and 600 L/h when aqueous solutions of individual as well as mixed aroma compounds were used as feeds. Similar rejections can be observed in the two cases. Therefore, it can be concluded that, within the range of concentrations considered here, there are no interactions among the aroma compounds that considerably affect their rejection. Then, the effect of operating variables on DAM/Kδ was studied. As feed flow directly affects the concentration of solute on the membrane surface (CA2),the effect of feed flow on DAM/Kδ was considered to be due to its effect on CA2. Therefore, the variables studied were transmembrane pressure, concentration, and temperature. Figure 4 shows the influence of the transmembrane pressure and concentration on DAM/Kδ at 25 °C for ethyl butanoate and hexanol. No important effect of these two variables on DAM/Kδ was observed. Similar results were obtained for the rest of the aroma compounds. Thus,


Figure 4. Influence of transmembrane pressure and concentration on DAM/Kδ at 25 °C.

Figure 5. Influence of temperature on DAM/Kδ. Table 2. Experimental Values of DAM/Kδ at 25 °C compound

DAM/Kδ at 25 °C (cm/s × 104)

ethyl acetate trans-2-hexenal hexanal butanol ethyl butanoate hexyl acetate hexanol isopentyl acetate isobutanol isopentanol ethyl-2-metil butanoate

4.818 4.574 2.084 1.905 1.739 1.564 1.556 0.387 0.302 0.297 0.223

DAM/Kδ was considered to be independent of pressure and concentration within the range of operating conditions studied. The slight dispersion of the experimental values of DAM/Kδ is due to the errors of the analytical method, as the concentration of the aroma compounds in the permeate stream is very low. The value of DAM/Kδ for each compound at 25 °C, as reported in Table 2, was determined as the mean of the values obtained at different concentrations and transmembrane pressures. The values of DAM/Kδ at other temperatures were also calculated as the means of the values at different concentrations and pressures. Figure 5 displays the

value of DAM/Kδ thus obtained as a function of temperature for ethyl butanoate and hexanol. We observed that this parameter increases exponentially with temperature

DAM R exp(aT) Kδ

(12)

This parameter was referred to a temperature of 25 °C; thus

( ) ( ) DAM DAM ) Kδ Kδ

ref

ea(T-Tref)

(13)

We note that the values of parameter a were very similar for all of the compounds. The mean value was 0.098, the standard deviation for this mean being equal to 0.07. Therefore, the value of DAM/Kδ for each compound at any temperature can be determined from its value at 25 °C using eq 14, which is valid for the temperature range considered (15 e T e 30 °C)

( ) ( ) DAM DAM ) Kδ Kδ

ref

e0.098(T-Tref)

(14)

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3.3. Application of the Model to Synthetic Solutions Simulating Apple Juice. In this section, the procedure followed to predict the flux and aroma compounds rejection when apple juice model solutions (glucose + aromas) were used as the feed is described. According to the preferential sorption-capillary flow model, the solvent flux through the membrane is defined by eq 2. The osmotic pressure difference between the two sides of the membrane (∆Π) can be calculated from the solute concentrations on the two sides of the membrane (CA2 and CA3). As the aroma compound concentrations are very low, their effect on the osmotic pressure is negligible. Therefore, the osmotic pressure has been considered as being due only to the different concentrations of glucose on the two sides of the membrane

∆Π ) Π(Cg2) - Π(Cg3)

(15)

where the subscript g refers to glucose. On the other hand, as the rejection of glucose by the membrane is very high, its concentration in the permeate (Cg3) is very low and can be neglected in eq 15. To calculate the osmotic pressure as a function of glucose concentration an empirical equation proposed by Kimura et al. was used28

RT (1000 - Cg)/Mw - 2Cg/Mg ln Πg ) Vw (1000 - Cg)/Mw - Cg/Mg

(16)

where R and T are the universal gas constant and temperature, respectively; Vw is the molar volume of pure water (18.07 m3/kmol); and Mw and Mg are the molecular weights of water and glucose, respectively. The concentration of glucose on the membrane surface was determined by the film theory (eq 3)

Cg2 ) Cg1 exp

( ) NB kgC1

(17)

Equation 6 was employed to estimate the mass transfer coefficient of glucose in the concentration polarization boundary layer (kg). To apply this equation, the density (F) and viscosity (µ) of the solution in the boundary layer must be known. As the aroma compounds concentration is very low, the solution was considered as an aqueous solution of glucose. The values of F and µ were estimated using two equations proposed by Kimura et al.28 for aqueous glucose solutions

F)

100 (100 - C)Fw + νC

ln

2.41C µ ) µw 100 - C

(18) (19)

where Fw and µw are the density and viscosity of water, respectively; ν is the partial specific volume of glucose (0.626 × 10-3 m3/kg); and C is the concentration of glucose in the boundary layer, which was considered to be the mean between the feed concentration (Cg1) and the concentration on the membrane surface (Cg2). In these equations, C is expressed in weight percent. The equations can be used in concentration ranges up to 58 wt % with an error of ( 0.2%. The diffusion coefficient of glucose in the boundary layer was estimated using

the equation reported by Gladden and Dole28 for aqueous glucose and sucrose solutions

Dg ) Dog(µw/µ)0.45

(20)

where Dg and Dog are the diffusion coefficients of glucose in the boundary layer and in a very dilute solution, respectively. The value of Dog from the literature28 at 25 °C is 6.9 × 10-10 m2/s. Its value at other temperatures was determined by eq 7. To estimate the values of kg, F, µ, and Dg in the boundary layer, the concentration of glucose on the membrane surface, Cg2, must be known. Therefore, to predict the value of the permeate flux, NB, it is necessary to simultaneously solve not only eqs 2, 16, and 17, but also eqs 6 and 18-20. The procedure followed to predict the permeate flux can be seen in Figure 6. The model was also applied to predict the rejection of each of the aroma compounds. According to the model, the flux of each compound through the membrane is described by eq 1

NA )

DAM DAM (C - CA3) ) (C X - C3XA3) (1) Kδ A2 Kδ 2 A2

where the subscript A refers to each of the aroma compounds in the model solution; C2 and C3 are the molar densities of the model solution on the membrane surface and in the permeate, respectively; and XA2 and XA3 are the molar fractions of the aroma compounds on the membrane surface and in the permeate, respectively. The molar density C2 was estimated from the literature29 as a function of the glucose concentration on the membrane surface (Cg2). The molar density of the permeate was considered to be equal to that of the water at the same temperature. The solute transport parameters for all of the aroma compounds at 25 °C are displayed in Table 2. Their values at other temperatures were estimated using eq 14. The molar fractions of the aroma compounds in the permeate stream were calculated using eq 4, and their molar fractions on the membrane surface were determined using eq 3

( )

XA2 ) XA3 + (XA1 - XA3) exp

NB k AC 1

(21)

where NB is the previously determined permeate flux, C1 is the molar density of the feed, and XA1 is the molar fraction of the aroma compounds in the feed. To estimate the mass transfer coefficient of each aroma compound, the same equation as previously indicated for glucose (eq 6) was used. From data reported by Chandrasekaran and King,31 the diffusion coefficients of the aroma compounds in the concentration polarization boundary layer can be described by

log

( )

DA ) 4.61 log Cw - 8.04 DoA

(22)

where DA and D0A are the diffusion coefficients of the aroma compounds in the boundary layer and in a dilute aqueous solution at 25 °C, respectively, and CW is the concentration of water in the boundary layer in mol/L. This is an empirical equation that is valid for estimating the diffusivities of dilute organic compounds in aqueous


Figure 6. Procedure followed to estimate permeate flux.

Figure 7. Experimental (symbols) and predicted (lines) permeate fluxes at different feed flow rates and glucose concentrations.

solutions of sugars (glucose, fructose, and sucrose individually as well as mixed). The diffusion coefficients at other temperatures were determined using eq 7. Solving the system formed by eqs 1, 4, and 21, the values of NA, XA2, and XA3 for each aroma compound were obtained. Finally, rejection was calculated by eq 5. 4. Results and Discussion Experiments with apple juice model solutions were carried out at different feed flow velocities (200-600 L/h) and glucose concentrations (9.1-17.0 °Brix). The corresponding Reynolds numbers ranged between 51 and 190. The temperature was set at 25 °C, and the

transmembrane pressure was 3.5 MPa for all runs. The permeate flux and aroma compounds rejection were measured. Experimental results for both variables were compared with the data predicted by the model. Figure 7 displays the permeate flux as a function of the feed flow rate at different concentrations. The lines represent the values predicted by the model, and the symbols indicate the experimental values. It can be observed that the permeate flux increases with feed flow rate. This is due to the reduction of concentration polarization with feed flow rate because of the better mixing in the high-pressure channel. This result is contrary to those obtained with water (no solutes), where flux decreased with feed flow rate because of a

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Figure 8. Experimental (symbols) and predicted (lines) rejection at different feed flow rates and glucose concentrations (T ) 25 °C; ∆P ) 3.5 MPa).

Figure 9. Comparison between experimental and predicted rejections for the aroma compounds at 9.1 °Brix glucose concentration, 25 °C, 3.5 MPa, and 600 L/h.

pressure drop effect, as explained in section 3.1. In the case of glucose solutions, the influence of feed flow rate on concentration polarization is higher than its influence on pressure drop, and hence, the flux increases with this variable. On the other hand, the permeate flux decreased with glucose concentration because of the increase in osmotic pressure. The positive effect of feed flow rate on flux is reduced as the concentration increases because of an exponential increase of osmotic pressure with concentration. Good agreement between the experimental and calculated flux values was observed except for the results obtained at the 200 L/h feed flow rate. At this flow rate, the model predicts lower fluxes than were found experimentally. The reason for the discrepancy could be that, operating at 200 L/h, the permeate flow is not negligible

compared to the feed flow. Therefore, the feed concentration and flow change from the inlet to the outlet of the membrane. Average values of the two parameters were considered for the calculations. However, the variations of the two variables inside the module are not known and are probably not linear. This effect is less important for the other feed flow rates considered (400 and 600 L/h), where the difference between the experimental and calculated permeate fluxes was lower than 6.5%. The best fit was obtained at 400 L/h. Figure 8 compares the experimental and predicted rejections for ethyl acetate and isopentanol, which are the compounds that show the best and worst agreement, respectively, between the experimental and calculated values. We can observe that rejection increases with feed flow rate but decreases with concentration. As the


feed flow rate rises, the solute concentration on the membrane surface falls, and hence, the aroma compound permeation decreases. Moreover, as the solvent flux increases with feed flow rate, the ratio NB/NA increases, as does the rejection. However, the rejection decreases with increasing glucose concentration. A rise in the feed concentration involves an increase in the viscosity and density of the solution on the membrane surface. Thus, the mass transfer coefficients of the aroma compounds are lower, and their concentrations on the membrane surface as well as their permeations increase. As the solvent flux decreases with glucose concentration, the relationship NB/NA, and hence the rejection, also decreases with this variable. It can also be observed that the worst agreement between the experimental and predicted data was obtained at high glucose concentrations. A possible source of error is the estimation of diffusivity using eq 22. Diffusivity estimation is, according to several authors, the weakest part of mathematical models.9 On the other hand, the errors of the analytical methods increase with glucose concentration. Figure 9 compares the experimental and estimated rejections for the aroma compounds selected in this research at 9.1 °Brix, 25 °C, 3.5 MPa, and 600 L/h. The model fits well with the experimental data for all of the aroma compounds and experimental conditions studied. Differences between experimental and calculated rejections were around 5% for most cases. The discrepancy was very low (0-3%) for the compounds that showed the highest rejection (95-99%). The compounds with the lowest rejections (ethyl acetate and trans-2-hexenal) presented the highest divergence, which, for certain operating conditions, was as high as 15%. Rejection increases in the following order: ethyl acetate ≈ trans-2-hexenal < butanol ≈ hexanal ≈ ethyl butanoate ≈ hexyl acetate ≈ hexanol < isopentyl acetate < isobutanol < isopentanol < ethyl-2-methyl butanoate, which is related to the values of the solute transport parameters of the aroma compounds. The higher the value of DAM/Kδ, the lower the rejection. The discrepancies between the experimental and calculated data can be explained as the result of the various approximations considered throughout the analysis. Moreover, membrane fouling was not taken into consideration. This effect could make the predictions more difficult. Fouling decreases the permeation through the membrane, so that a new resistance due to this phenomenon could be considered. The effects of fouling on the reverse osmosis process can be found in the literature.31,32 5. Conclusions The preferential sorption-capillary flow model describes reasonably well the experimental data on permeate flux and aroma compounds rejection during the reverse osmosis concentration of apple juice model solutions using the MSCB 2521 R99 membrane (Separem SpA, Biella, Italy). The permeability of the membrane and the solute transport parameters were determined from experiments with water and with aqueous solutions of apple juice aroma compounds, respectively. The permeate flux and rejection were observed to increase with feed flow rate and to decrease with glucose concentration. The predicted flux was accurate to within 5% for most of the operating conditions studied. The worst results were noted for the experiments at the 200

L/h feed flow. The predicted values of the aroma compounds rejection were accurate to within 5% for most of the compounds and experimental conditions used. The best results were obtained for the compounds showing the highest rejections (discrepancies between experimental and calculated rejection lower than 3%). The worst agreement was seen for high glucose concentrations. The proposed model is able to predict the influence of operating conditions (feed flow rate and concentration) on the permeate flux and aroma compounds rejection. Therefore, operating conditions can be selected to optimize both variables. Further work is needed to determine whether the model also predicts the effects of other operating conditions (pressure and temperature) and to apply it to different types of membranes and feed solutions. List of Symbols A ) solvent permeability of the membrane, kmol/(s m2 MPa) a ) parameter in eq 12 b ) membrane leaf width, m C ) concentration, kmol/m3 D ) diffusion coefficient, m2/s DAM/Kδ ) solute transport parameter, m/s dh ) equivalent hydraulic diameter, m h ) spacer thickness, m J ) flux through the membrane, m/s k ) mass transfer coefficient, m/s M ) molecular weight, kg/kmol N ) flux through the membrane, kmol/(s m2) ∆P ) transmembrane pressure, MPa Q ) feed flow rate, m3/s R ) rejection, % R ) universal gas constant, MPa m3/(K kmol) Re ) Reynolds number S ) effective area tangential to the feed flow, m2 Sc ) Schmidt number Sh ) Sherwood number T ) absolute temperature, K v ) tangential flow velocity, m/s V ) molal volume, m3/kmol X ) mole fraction Greek Letters ) porosity of the spacer Φ ) associated parameter of the solvent in the equation of Wilke and Chang µ ) solution viscosity, kg/(m s) ∆Π ) osmotic pressure difference at the two sides of the membrane, MPa F ) solution density, kg/m3 ν ) partial specific volume of glucose, m3/kg Subscripts A ) solute B ) solvent bp ) boiling point g ) glucose i ) inlet of the membrane module M ) membrane o ) very dilute solution ref ) reference s ) outlet of the membrane module w ) water 1 ) bulk solution 2 ) membrane surface at feed side 3 ) permeate

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Acknowledgment This work was supported by the EU (European Union) through the AAIR project PL94-1931 and by the MEC (Ministerio de Educacioń y Ciencia, Spain). The authors also thank the apple processing factory Valle, Ballina, and Fernańdez, S.A. for the apple juice and apple aroma concentrate supplied. Literature Cited (1) Rao, M. A. Concentration of Apple Juice. In Processed Apple Products; Downing, D. L., Ed.; Van Nostrand Reinhold: New York, 1989. (2) Sheu, M. J.; Wiley: R. C. Preconcentration of Apple Juice by Reverse Osmosis. J. Food Sci. 1983, 48, 422. (3) Merson, R. L.; Morgan, J. A. I. Juice Concentration by Reverse Osmosis. Food Technol. 1968, 22, 631. (4) Baxter, A. G.; Bednas, M. E.; Matsuura, T.; Sourirajan, S. Reverse Osmosis Concentration of Flavor Components in Apple Juice and Grape Juice Waters. Chem. Eng. Commun. 1980, 4, 471. (5) Pepper, D.; Orchard, A. C. J.; Merry, A. J. Concentration of Tomato Juice and Other Fruit Juices by Reverse Osmosis. Desalination 1985, 53, 157. (6) Chua, H. T.; Rao, M. A.; Acree, T. E.; Cunningham, D. G. Reverse Osmosis Concentration of Apple Juice: Flux and Flavor Retention by Cellulose Acetate and Polyamide Membranes. J. Food Process Eng. 1987, 9, 231. (7) Walter, J. B. Reverse Osmosis Concentration of Juice Products with Improved Flavor. U.S. Patent 4959237, Sep 25, 1990. (8) Scott, K. Handbook of Industrial Membranes; Elsevier: Oxford, U.K., 1995. (9) A Ä lvarez, V.; A Ä lvarez, S.; Riera, F. A.; AÄ lvarez, R. Permeate Flux Prediction in Apple Juice Concentration by Reverse Osmosis. J. Membr. Sci. 1997, 127, 25. (10) A Ä lvarez, S.; Riera, F. A.; A Ä lvarez, R.; Coca, J. Permeation of Apple Juice Aroma Compounds in Reverse Osmosis. Sep. Purif. Technol. 1998, 14, 209. (11) Lea, A. G. J. Apple Juice. In Production and Packaging of Noncarbonated Fruit Juices and Fruit Beverages; Hicks, D., Ed.; Blackie and Son: New York, 1990. (12) Flath, R. A.; Black, D. R.; Guadagni, D. G.; McFadden, W. H.; Schultz, T. H. Identification and Organoleptic Evaluation of Compounds in Delicious Apple Essence. J. Agr. Food Chem. 1967, 15, 29. (13) Durr, P.; Rothlin, H. Development of a Synthetic Apple Juice Odor. Lebensm.-Wiss. Technol. 1981, 14, 313. (14) Soltanieh, M.; Gill, W. N. Review of Reverse Osmosis Membrane and Transport Models. Chem. Eng. Commun. 1981, 12, 279.

(15) Kimura, S.; Sourirajan, S. Analysis of Data in Reverse Osmosis with Porous Cellulose Acetate Membranes Used. AIChE J. 1967, 13, 497. (16) Agrawal, J. P.; Sourirajan, S. Reverse Osmosis, Flow through Porous Media Symposium. Ind. Eng. Chem. 1969, 61, 62. (17) Dickson, J. M.; Matsuura, T.; Blais, P.; Sourirajan, S. Some Transport Characteristics of Aromatic Polyamide Membranes in Reverse Osmosis. J. Appl. Polym. Sci. 1976, 20, 1491. (18) Sourirajan, S.; Matsuura, T. Reverse Osmosis/Utrafı´ltration Principles; National Research Council Canada Publications: Ottawa, Canada, 1985. (19) Stephen, H.; Stephen, T. Solubilities of Inorganic and Organic Compounds; Pergamon Press: London, 1964. (20) Perry, R. H.; Green, D. Perry’s Chemical Engineers Handbook; McGraw-Hill: New York, 1984. (21) Bo¨rjesson, J.; Karlsson, H. O. E.; Tra¨gårdh, G. Pervaporation of a Model Apple Juice Aroma Solution: Comparison of Membrane Performance. J. Membr. Sci. 1996, 119, 229. (22) Schock, G.; Miquel, A. Mass Transfer and Pressure Loss in Spiral Wound Modules. Desalination 1987, 64, 339. (23) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids; McGraw-Hill: New York, 1987. (24) Frey, D. D.; King, C. J. Diffusion Coefficients of Acetates in Aqueous Sucrose Solutions. J. Chem. Eng. Data 1982, 27, 419. (25) Li, S. F. Y.; Ong, H. M. Infinite Dilution Diffusion Coefficients of Several Alcohols in Water. J. Chem. Eng. Data 1990, 35, 136. (26) Wilke, C. R.; Chang, P. Correlation of Diffusion Coefficients in Dilute Solutions. AIChE J. 1955, 1, 264. (27) Dickson, J. M.; Spencer, J.; Costa, M. L. Dilute Single and Mixed Solute Systems in Spiral Wound Reverse Osmosis Module. Part II: Experimental Data and Application of the Model. Desalination 1992, 89, 63. (28) Kimura, S.; Nakao, S.; Ikeda, S.; Watanabe, A.; Nakajima, M.; Nabetani, H. Development of a New Type of Osmometer. J. Chem. Eng. Jpn. 1992, 25, 5. (29) Weast, R. C.; Astle, M. J. CRC Handbook of Chemistry and Physics; CRC Press: Boca Raton, FL, 1981. (30) Chandrasekaran, S. K.; King, C. Multicomponent Diffusion and Vapor-Liquid Equilibria of Dilute Organic Components in Aqueous Sugar Solutions. AIChE J. 1972, 18, 513. (31) van Boxtel, A. J. B.; Otten, J. E. H.; van der Linden, H. J. L. J. Evaluation of Process Models for Fouling Control of Reverse Osmosis of Cheese Whey. J. Membr. Sci. 1991, 58, 89. (32) Bacchin, P.; Aimar, P.; Sanchez, V. Model for Colloidal Fouling of Membranes. AIChE J. 1995, 41, 368.

Received for review January 30, 2001 Revised manuscript received June 1, 2001 Accepted July 3, 2001 IE010087C