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Predicting Stationary Permeate Flux in the Ultrafiltration of Apple Juice
Lebensm.-Wiss. u.-Technol., 29, 587–592 (1996)
Predicting Stationary Permeate Flux in the Ultrafiltration of Apple Juice Diana T. Constenla and Jorge E. Lozano Plapiqui (Uns - Conicet), 12 de Octubre 1842, 8000 Bahia Blanca (Argentina) (Received December 19, 1994; accepted March 27, 1995)
Stationary permeate flux was studied in the hollow fibre ultrafiltration of apple juice. The effect of flow velocity (Q = 10, 12.5 and 15 L/min) and volume concentration ratio (VCR = 1, 1.5, 2 and 5) was determined over the 0–1.6 kg/cm2 range of transmembrane pressure. The flux showed an asymptotic behaviour and proved to be pressure-independent at a value that increased with Q and VCR. Flux also showed a hysteresis loop during the up and down curve with transmembrane pressure. Film theory, surface renewal approach (SRM) and resistance-in-series model were used to analyse the experimental results. Fitting of experimental data to the Leveque laminar flow model was acceptable in the mass transfer-controlled region. Semi-empirical SRM concept appropriately describes the entire pressure-flux behaviour observed during the ultrafiltration of apple juice. ©1996 Academic Press Limited
Introduction The application of ultrafiltration (UF) as an alternative to conventional processes for clarification of apple juice was demonstrated by Heatherbell et al. (1). However, the acceptance of UF in the fruit processing industry is not yet complete, because there are problems with the operation and fouling of membranes. During ultrafiltration two fluid streams are generated: the ultrafiltrated solids-free juice (permeate), and the retentate, with variable content of insoluble solids, dissolved macromolecules and colloidal particles. Analysis of the nature of permeate flux and rejection in ultrafiltration has become of primary importance. The permeate flux (J) in the ultrafiltration of apple juice is affected by the membrane properties, the juice properties and the operating conditions (recirculating flow, transmembrane pressure, temperature, etc.). The main driving force of ultrafiltration is the transmembrane pressure, which is a difference in pressures at both sides of the membrane and in the case of hollow fibre UF systems can be defined as: ∆PTM =
( P +2 P ) – P i
o
ext
Eqn [1]
where Pi = pressure at the inlet of the fibre; Po = outlet pressure; and Pext = pressure on the permeate side. In practice, the J values obtained with apple juice are much less than those obtained with water only. It is well known (2) that the transmembrane pressure-permeate flux characteristic for ultrafiltration shows at lower values of pressure (1st region) a linear dependence of J with ∆PTM, while at higher pressures (2nd region) the permeate flux approaches a limiting value (Jlim) inde0023-6438/96/070587 + 06$25.00/0
pendent of further increase in pressure. The last situation is assumed to be controlled by mass transfer. A number of phenomena have been suggested to account for the flux decline during ultrafiltration, including osmotic pressure, resistance of gel layer, concentration polarization boundary layer, plugging of pores due to fouling, etc. Concentration polarization is defined as a localized increase in concentration of rejected solutes at the membrane surface due to convective transport of solutes. Flux decline due to this phenomenon can be reduced by increasing flow velocity on the membrane. Permeate flux results from the difference between a convective flux from the bulk of the juice to the membrane and a counter diffusive flux or outflow by which solute is transferred back into the bulk of the fluid. Therefore, the value of J is strongly dependent on hydrodynamical conditions in the membrane vicinity. Traditionally correlations of J with ∆PTM and VCR, the volume concentration ratio, have been determined by parameter fitting of the experimental data. VCR is defined as the initial volume divided by retentate volume at any time. Since the polynomial functions have no physical basis, a large number of experimental data is needed for determination of J.
Film theory One of the simplest theories for modelling flux in the 2nd region is the film theory (FT). This model needs less experimental data for determination of the involved parameters. Several models for the mass transport in membranes have been developed. A review has been given by (3). The solution of the differential equation ©1996 Academic Press Limited
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lwt/vol. 29 (1996) No. 7
for the boundary layer which gives the equation for permeate flux has been described by Rautembach and Albrech (4): J = k ln
(C
Cg – Cper b
– Cper
of the total permeate flux. According to this surface renewal theory the value of J may be written as: J = (Ji – Jf)
)
Eqn [2]
where J = flux; k = D/δbl is the mass transfer coefficient; D = diffusion coefficient; δbl = boundary layer thickness; Cb = bulk concentration of rejected macromolecules (mainly pectin); Cg = gel concentration; and Cper = solute concentration in permeate. To determine k some empirical correlations based on Bird and Steward heat– mass transfer analogy can be used (5,6) Sh = A' Reα Scβ
η = Kγn–1
Eqn [4]
Jlim =
Sh =
Re =
Sc =
Eqn [5]
D
8 dhv2–nρret
( 6nn+ 2 )
K
dh1–nvn–1K 6n + 2
(
8rretD
n
)
n
Eqn [6]
n
Eqn [7]
where ρret = retentate density; v = fluid velocity; and dh = hydraulic diameter. During ultrafiltration of apple juice Cper is many times lower than Cb and Cg. Then Eqn [2] can be simplified to:
( CC )
J = k ln
g
Eqn [8]
b
J = Jf +
(
∆PTM Rm
Eqn [9]
s α Rm *
+ Jf
Eqn [10]
s/α*
) ( s/α + ∆PTM )
– Jf
*
Eqn [11]
Resistance-in-series model (RSM) Another approach to predict the flux of permeate is the resistance-in-series model. The resistance term may be thought of as separate additive resistances in series. The membrane resistance is a property of the mechanical and chemical structure of the membrane material. The gel resistance will depend upon the extent of polarization, and the physical properties of both the gel layer and the permeate which must pass across it. J =
∆PTM R'm + Rg + Rbl
Eqn [12]
where R'm = intrinsic resistance of the membrane; Rg = gel resistance; and Rbl = boundary layer resistance. Chiang and Cheryan (8) considered that Rp = Rg + Rbl is a function of pressure (Rp = φ∆PTM) and Eqn [12] can be rewritten as: J =
Surface renewal theory (SRT) It was found that the film model frequently underestimates the values of the permeate flux. To improve the model Koltuniewicz (2) added to J a correction factor that takes into account the lateral migration of macromolecules from the membrane to the bulk of the feed stream. This lateral migration originated by the forces involved in the laminar flow and the roughness of the membrane surface is responsible for instability of the concentration polarization layer and the increases
+ Jf
where Rm is the membrane resistance to flux. Eqn [10] may be used to determine s experimentally. Rm can also easily be determined experimentally using water as solvent. All other parameters must be determined empirically. It is also possible to estimate flux J for a given rate of surface renewal s and constant Q and VCR, in this way:
where η is the apparent viscosity; K is the consistency coefficient; γ is the shear rate; and n is the flow behaviour index. Dimensionless numbers included in Eqn [3] must then be modified to account for this rheological behaviour: kdh
s+A
where Ji and Jf are the initial and final flux, respectively; A was defined as the rate of flux decline and s the rate of surface renewal. Koltuniewicz (2) also proposed that in the case of ultrafiltration with a limiting permeate flux, as during apple juice clarification, A is proportional to the transmembrane pressure (A = α* ∆PTM) and Jlim can be obtained from Eqn [10] as:
Eqn [3]
where Sh, Re and Sc are the Sherwood, Reynolds and Schmidt number, respectively, and the parameters A’, α and β will depend on flux conditions and geometry of the system. It is well known that undepectinized fruit juices are pseudoplastic in nature (7) and their rheological behaviour can be described by the well-known power law:
s
∆PTM R'm + φ ∆PTM
Eqn [13]
where φ, the resistance index, is a constant for a particular membrane–solute combination. When ∆PTM is low, the value of J is controlled by the membrane resistance. On the other hand, when ∆PTM is large, the permeate flux approaches 1/φ. The objectives of this study are to determine the stationary permeate flux of apple juice through a hollow fibre membrane module; to study the effect of operating parameters such as pressure, recirculating
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lwt/vol. 29 (1996) No. 7
flow rate and feed concentration on limiting flux; and to verify the application of accepted predictive models. Temperature is often constant in industrial membrane processes. Therefore, in this work the determination of J is made at constant temperature.
Table 1 50 °C
Power law constants for apple juice retentate at
VCR
K×103(Pa·s)
n
0.710 1.427 2.341 11.33
1.00 0.99 0.98 0.93
1 1.5 2 5
Materials and Methods Apple fruit (variety Red Delicious) was sorted, washed and crushed in a Model N°6 Fitz Mill Comminutor (Fitzpatrick Co., Chicago, Ill, U.S.A.). Juice was produced by pressing in a hydraulic press followed by screening through a 100 µm stainless steel mesh and pasteurized at 95 °C during 1 min in a pilot equipment. Samples were stored at –20 °C until analysed.
Determination of density Density was determined by pycnometry. The pycnometer of 50 mL capacity was calibrated with distilled water at 50 °C. A minimum of four consecutive replicates per sample with a reproducibility better than 0.3% were averaged.
Determination of apparent viscosity A model RMS-605s Rheometrics Spectrometer (Rheometric Inc., Piscataway, NJ, U.S.A.) was used to measure shear stress vs. shear rate of the apple juice retentate at different VCR values. A 5 cm diameter 0.1 rad cone-and-plate geometry was employed. The gap between the cone and plate was set to reasonably ensure no obstruction due to pulp particles. Moreover, when oscillation or perturbation during shear stress vs. shear rate was observed the sample was discarded. All tests were conducted at 50 ± 0.5 °C with a humidity and temperature air-controlled chamber. The effect of shear rate on shear stress was directly acquired with a personal computer through a data acquisition system and fitted to Eqn [2] using the SYSTAT/NONLIN programme. Experimental determinations were performed in duplicate.
L/min) and four VCR values (1, 1.5, 2 and 5) were tested in the range ∆PTM = 0–1.6 kg/cm2.
Results and Discussion Properties of apple juice retentate Density of apple juice retentate at 50 °C resulted in ρret = 1.0359 g/cm3 (r2 = 0.994), practically independent of VCR. Table 1 gives the values of power law constants K and n experimentally obtained at different VCR. It can be observed that apple juice showed some deviations from Newtonian behaviour even at 50 °C.
Flux characteristics Figures 1 and 2 show the variation of J with ∆PTM as a function of both concentration (VCR = 1, 1.5, 2 and 5) and recirculating flow rate (Q = 10, 12.5 and 15 L/min), respectively. Pressure independence (2nd region) was observed to occur at a higher pressure at higher recirculating velocities. The point at which the pressure independence is evident is considered as the optimum transmembrane pressure (∆PTMO). Table 2 lists both Jlim and ∆PTMO values obtained at different VCR and Q. The reduction of Jlim with Q can be associated with a reduction in the boundary layer due to an increase in the turbulence. On the other hand, the optimal ∆PTM values resulted practically independent of VCR at flow velocities higher than 10 L/min. Results also indicate 80.00 T=50°C, PC=50 000 ds, Qr=10 l/min
Ultrafiltration unit A pilot scale UF unit (Amicon model DC50P) with a single hollow fibre cartridge was used. The membranes were made of polysulfone with a normal molecular weight cut-off of 50,000. The unit had a 40 L storage tank, sanitary stainless steel pump and pipes, a flow reversing valve, pressure control and permeate and retentate streams flow meters. The unit was operated in batch mode and process parameters were: initial juice volume (Vo) = 27 L; temperature = 50 °C. This temperature is usual at the apple juice industry for alternative pectinolitic enzyme treatment, viscosity reduction and reduction of risk of contamination during UF treatment. During a run both permeate and retentate were recycled back to the feed tank to keep VCR constant. Three flow rates (Q = 10, 12.5 and 15
J (L/(h·m2))
60.00
40.00
20.00
0
0.40
0.80 ∆PMT (kg/cm2)
1.20
1.60
Fig. 1 Effect of transmembrane pressure and volume concentration ratio on permeate flux at 50 °C. (Untreated juice was 12°Brix) (j, VCR = 1; s, VCR = 1.5; d, VCR = 2; n, VCR = 5)
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80.00
10 T=50°C, PC=50 000 ds, VCR=1
60.00 Sh Sc–1/3
J (L/(h·m2))
Leveque solution
40.00
1
Eqn{14]
20.00
0.40
0
0.80 ∆PMT (kg/cm2)
102
0
1.60
1.20
103
104
Re
Fig. 2 Effect of transmembrane pressure and feed stream flow rate on permeate flux at 50 °C. (Untreated juice was 12°Brix) (j, Qr = 10 L/min; s, Qr = 12.5 L/min; d, Qr = 15.0 L/min)
Fig. 3 Mass transfer correlation for ultrafiltration of apple juice. Full line represents the behaviour predicted according to the Leveque equation. Dotted line represents Eqn [14]. Points are experimental results
that regardless of the operating conditions or the retentate concentration the reduction of the transmembrane pressure from the maximum to the minimum is translated in a hysteresis effect in the permeate flux, attributable to the consolidation of the gel layer (9,10). Similar effects have been observed during the UF of other liquid foods (11,12). The area enclosed by the hysteresis loop was greater at lower Q and VCR values.
with the Leveque solution (6). As Fig. 3 shows the Leveque solution fits the results quite well (hardly over predicted the experimental fluxes) suggesting that the velocity and concentration profile assumed were appropriate.
Sh = 0.149 Re0.336 Sc0.329
Eqn [14]
In the hollow fibre system used in this study, the length of the concentration profile entrance region is much greater than the channel length, indicating the concentration profile is still developing during flow down the channel (6). For laminar flow systems, if velocity profile is fully developed but concentration boundary layer is developing along the fibre, the Leveque solution of Eqn [3] can be used with A’ = 1.86; α = 1/3 and β = 1/3 (13). Figure 3 compares Eqn [14] and experimental results
80.00
60.00 J (L/(h·m2))
Film theory To evaluate the film model, the calculated values of log Sh were fitted vs. log Re and log Sc by multiple linear regression, resulting:
Surface renewal model The characteristic resistance of the membrane was calculated from the water flux variation with ∆PTM. With this Rm value (Rm = 6.366 3 105 Pa.h/m) and the final flux Jf (determined from the flux decline with time at constant Q and VCR), both the ratio s/α* and Jlim were calculated (Table 3). These experimental data were finally fitted to Eqn [11] and plotted in Fig. 4. The points shown in the figure represent actual experi-
Table 2 Values of limiting flux and optimal transmembrane pressures at various conditions Q (L/min) 10.0 12.5 15.0 ∆PTMO (kg/cm2) 10.0 12.5 15.0
Jlim
20.00
VCR 1.0
(L/hm2)
40.00
58.0 66.0 72.0 0.80 1.38 1.45
1.5
2.0
3.0
5.0
54.3 48.7 44.0 39.3 57.3 52.7 48.7 42.7 59.3 54.0 50.7 44.0 0.95 1.10 1.22 1.25 1.40 1.40 1.38 1.40 1.48 1.46 1.40 1.42
0
0.40
0.80 ∆PMT (kg/cm2)
1.20
1.60
Fig. 4 Comparison of experimental permeate flux data (points) as a function of transmembrane pressure with those predicted from the SRM model (full line; Eqn [11]), at various VCR values. (d, VCR = 1; j, VCR = 1.5; s, VCR = 2; r, VCR = 5)
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lwt/vol. 29 (1996) No. 7
Table 3 Parameters of the surface renewal model, Eqn [11] Q (L/min)
VCR
s/a* 10–4Pa
Jlim (L/m2.h)
Standard error
10.0 10.0 10.0 10.0 10.0 12.5 15.0
1.0 1.5 2.0 3.0 5.0 1.0 1.0
4.591 4.090 3.365 3.266 2.835 4.610 4.169
72.07 64.22 52.83 51.29 44.51 88.76 90.96
2.162 3.165 2.252 1.855 0.843 1.893 1.686
mental data. An excellent agreement exists between experimental data and the surface model predictions.
Resistance-in-series approach Theoretically this model could predict J throughout the range of transmembrane pressures. Table 4 lists the R'm; φ and φ ∆PTM values. Clearly R'm and φ ∆PTM are of the same order of magnitude. Therefore, simplification proposed by Chiang and Cheryan (8) to the resistance-in-series model, represented by Eqn [13], resulted in a poor fitting of experimental data (Fig. 5). It was also found that there was a definite correlation between the resistance R'm and VCR, as follows: R'm = 0.010935 + 0.007182ln(VCR) Eqn [15] r2 = 0.993 The increasing nature of R'm regarding VCR suggests continuous formation of fouling with ∆PTM. On the contrary, during UF of other solutions Chiang and 80.00 T=50°C, PC=50 000 ds, Qr=10 l/min
Cheryan (8) claimed independence of R'm with operating parameters.
Conclusions The stationary flux of permeate during UF of apple juice was studied. Limiting flux, hysteresis loop and membrane resistance were determined over a wide range of transmembrane pressures, feed rates and concentrations. In particular, the limiting flux was analysed on the basis of three approaches: the film theory, the surface renewal concept and the resistancein-series model. The results of this study revealed that limiting flux of apple juice in hollow fibre can be adequately described using classical laminar flow mass transfer models. The film theory was, by definition, meaningful only during the 2nd region (mass control region). On the contrary, the semi-empirical model based on the modification of the membrane surface due to lateral migration was successfully extended over the total range of pressures. The resistance-in-series model failed to simulate flux of apple juice under the conditions used in this work.
J (L/(h·m2))
60.00
Nomenclature
VCR=1 VCR=1.5
40.00
A A' Cb
VCR=2 VCR=5
20.00
0
0.50
1.00 ∆PMT (kg/cm2)
2.00
1.50
Fig. 5 Comparison of permeate flux between experimental and calculated values using Chiang and Cheryan (8) model (full lines; Eqn [13]). (d, VCR = 1; j, VCR = 1.5; s, VCR = 2; r, VCR = 5)
Cg Cper D dh J Ji Jf Jlim k
rate of flux decline (s–1) constant in the dimensionless Eqn [3] bulk concentration of rejected macromolecules (g/100g) gel concentration (g/100g) solute concentration in permeate (g/100g) diffusion coefficient (m2/s) hydraulic diameter (m) flux (L/(m2·h) initial flux (L/(m2·h) final flux (L/(m2·h) limiting permeate flux (L/(m2·h) mass transfer coefficient (m/s)
Table 4 Values of intrinsic resistance (R'm); resistance index (φ) and (φ*∆PTM) product of the resistance-in-series model VCR ×10–6
R'm φ φ×∆PTM×10–6
(Pa·h/m) (m2.h/L) (Pa·h/m)
1.0
1.5
2.0
3.0
5.0
1.079 0.0172 3.037
1.314 0.0184 3.249
1.609 0.0205 3.620
1.815 0.0227 4.008
2.105 0.0254 4.486
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K n Pi Po Pext Rbl Re Rg Rm R’m s Sc Sh v VCR
consistency coefficient in power law viscosity model (Pa·sn) flow behaviour index in power law viscosity model (dimensionless) pressure at the inlet of the fibre (Pa) pressure at the outlet of the fibre (Pa) pressure on the permeate side (Pa) boundary layer resistance of the membrane (Pa·h/m) Reynold number (dimensionless) gel resistance of the membrane (Pa·h/m) Characteristic resistance of the membrane (Pa·h/m) Intrinsic resistance of the membrane, Eqn [12] (Pa·h/m) rate of surface renewal (s–1) Schmidt number (dimensionless) Sherwood number (dimensionless) fluid velocity (m/s) volume concentration ratio
Greek letters α, β constants in dimensionless Eqn [3] α* constant as defined by Eqn [10] boundary layer thickness (m) δbl φ constant as defined by Eqn [12] η apparent viscosity (Pa·sn) ρret retentate density (kg/m3) γ shear rate (s–1) ∆PTM transmembrane pressure (Pa) ∆PTMo optimum transmembrane pressure (Pa)
References 1 HEATHERBELL, D. A., SHORT, J. L. AND STAUEBI, P. Apple juice clarification by ultrafiltration. Confructa, 22, 157–169 (1977) 2 KOLTUNIEWICZ, A. Predicting permeate flux in ultrafiltration on the basis of surface renewal concept. Journal of Membrane Science, 68, 107–118 (1992) 3 SOLTANIEH, M. AND GILL, W. N. Review of reverse osmosis membranes and transport models. Chemical Engineering Communications, 12, 279–287 (1981) 4 RAUTEMBACH, R. AND ALBRECHT, R. Membrane Processes, 2nd Edn. New York: John Wiley & Sons, p. 78 (1989) 5 GEKAS, V. AND HALLSTROMM, B. Mass transfer in the membrane concentration polarization layer under turbulent cross flow. I. Critical literature review and adaptation of existing Sherwood correlations to membrane operations. Journal of Membrane Science, 30, 153–162 (1987) 6 CHIANG, B. H. AND CHERYAN, M. Modelling of hollow fibre ultrafiltration of skim milk under mass-transfer limiting conditions. Journal of Food Engineering, 6, 241–255 (1987) 7 SARAVACOS, G. D. Effect of temperature on viscosity of fruit juices and purees. Journal of Food Science, 35, 122–125 (1970) 8 CHIANG, B. H. AND CHERYAN, M. Ultrafiltration of skimmilk in hollow fibres. Journal of Food Science, 51, 340–344 (1986) 9 MICHAELS, A. New Separation Technique for the CPI. Chemical Engineering Progress, 64, 31–36 (1968) 10 OMOSAIYE, O., CHERYAN, M. AND MATTHEWS, M. Removal of oligosaccharides from soybean water extracts by ultrafiltration. Journal Food Science, 43, 354–358 (1978) 11 FENTON-MAY, R. L., HILL, C. G. AND AMUNDSON, C. H. Use of Ultrafiltration/Reverse Osmosis systems for the concentration and fractionation of whey. Journal of Food Science, 36, 14 (1971) 12 CHERYAN, M. AND SCHLESSER, J. Performance of hollow fibre system for ultrafiltration of aqueous extracts soybeans. Lebensmittel-Wissenschaft und-Technologie, 11, 65–69 (1977) 13 CHERYAN, M. Ultrafiltration Handbook. Lancaster, Pennsylvania: Technomic Publishing Company, Inc., pp. 85–87 (1986)
592
Predicting Stationary Permeate Flux in the Ultrafiltration of Apple Juice Diana T. Constenla and Jorge E. Lozano Plapiqui (Uns - Conicet), 12 de Octubre 1842, 8000 Bahia Blanca (Argentina) (Received December 19, 1994; accepted March 27, 1995)
Stationary permeate flux was studied in the hollow fibre ultrafiltration of apple juice. The effect of flow velocity (Q = 10, 12.5 and 15 L/min) and volume concentration ratio (VCR = 1, 1.5, 2 and 5) was determined over the 0–1.6 kg/cm2 range of transmembrane pressure. The flux showed an asymptotic behaviour and proved to be pressure-independent at a value that increased with Q and VCR. Flux also showed a hysteresis loop during the up and down curve with transmembrane pressure. Film theory, surface renewal approach (SRM) and resistance-in-series model were used to analyse the experimental results. Fitting of experimental data to the Leveque laminar flow model was acceptable in the mass transfer-controlled region. Semi-empirical SRM concept appropriately describes the entire pressure-flux behaviour observed during the ultrafiltration of apple juice. ©1996 Academic Press Limited
Introduction The application of ultrafiltration (UF) as an alternative to conventional processes for clarification of apple juice was demonstrated by Heatherbell et al. (1). However, the acceptance of UF in the fruit processing industry is not yet complete, because there are problems with the operation and fouling of membranes. During ultrafiltration two fluid streams are generated: the ultrafiltrated solids-free juice (permeate), and the retentate, with variable content of insoluble solids, dissolved macromolecules and colloidal particles. Analysis of the nature of permeate flux and rejection in ultrafiltration has become of primary importance. The permeate flux (J) in the ultrafiltration of apple juice is affected by the membrane properties, the juice properties and the operating conditions (recirculating flow, transmembrane pressure, temperature, etc.). The main driving force of ultrafiltration is the transmembrane pressure, which is a difference in pressures at both sides of the membrane and in the case of hollow fibre UF systems can be defined as: ∆PTM =
( P +2 P ) – P i
o
ext
Eqn [1]
where Pi = pressure at the inlet of the fibre; Po = outlet pressure; and Pext = pressure on the permeate side. In practice, the J values obtained with apple juice are much less than those obtained with water only. It is well known (2) that the transmembrane pressure-permeate flux characteristic for ultrafiltration shows at lower values of pressure (1st region) a linear dependence of J with ∆PTM, while at higher pressures (2nd region) the permeate flux approaches a limiting value (Jlim) inde0023-6438/96/070587 + 06$25.00/0
pendent of further increase in pressure. The last situation is assumed to be controlled by mass transfer. A number of phenomena have been suggested to account for the flux decline during ultrafiltration, including osmotic pressure, resistance of gel layer, concentration polarization boundary layer, plugging of pores due to fouling, etc. Concentration polarization is defined as a localized increase in concentration of rejected solutes at the membrane surface due to convective transport of solutes. Flux decline due to this phenomenon can be reduced by increasing flow velocity on the membrane. Permeate flux results from the difference between a convective flux from the bulk of the juice to the membrane and a counter diffusive flux or outflow by which solute is transferred back into the bulk of the fluid. Therefore, the value of J is strongly dependent on hydrodynamical conditions in the membrane vicinity. Traditionally correlations of J with ∆PTM and VCR, the volume concentration ratio, have been determined by parameter fitting of the experimental data. VCR is defined as the initial volume divided by retentate volume at any time. Since the polynomial functions have no physical basis, a large number of experimental data is needed for determination of J.
Film theory One of the simplest theories for modelling flux in the 2nd region is the film theory (FT). This model needs less experimental data for determination of the involved parameters. Several models for the mass transport in membranes have been developed. A review has been given by (3). The solution of the differential equation ©1996 Academic Press Limited
587
lwt/vol. 29 (1996) No. 7
for the boundary layer which gives the equation for permeate flux has been described by Rautembach and Albrech (4): J = k ln
(C
Cg – Cper b
– Cper
of the total permeate flux. According to this surface renewal theory the value of J may be written as: J = (Ji – Jf)
)
Eqn [2]
where J = flux; k = D/δbl is the mass transfer coefficient; D = diffusion coefficient; δbl = boundary layer thickness; Cb = bulk concentration of rejected macromolecules (mainly pectin); Cg = gel concentration; and Cper = solute concentration in permeate. To determine k some empirical correlations based on Bird and Steward heat– mass transfer analogy can be used (5,6) Sh = A' Reα Scβ
η = Kγn–1
Eqn [4]
Jlim =
Sh =
Re =
Sc =
Eqn [5]
D
8 dhv2–nρret
( 6nn+ 2 )
K
dh1–nvn–1K 6n + 2
(
8rretD
n
)
n
Eqn [6]
n
Eqn [7]
where ρret = retentate density; v = fluid velocity; and dh = hydraulic diameter. During ultrafiltration of apple juice Cper is many times lower than Cb and Cg. Then Eqn [2] can be simplified to:
( CC )
J = k ln
g
Eqn [8]
b
J = Jf +
(
∆PTM Rm
Eqn [9]
s α Rm *
+ Jf
Eqn [10]
s/α*
) ( s/α + ∆PTM )
– Jf
*
Eqn [11]
Resistance-in-series model (RSM) Another approach to predict the flux of permeate is the resistance-in-series model. The resistance term may be thought of as separate additive resistances in series. The membrane resistance is a property of the mechanical and chemical structure of the membrane material. The gel resistance will depend upon the extent of polarization, and the physical properties of both the gel layer and the permeate which must pass across it. J =
∆PTM R'm + Rg + Rbl
Eqn [12]
where R'm = intrinsic resistance of the membrane; Rg = gel resistance; and Rbl = boundary layer resistance. Chiang and Cheryan (8) considered that Rp = Rg + Rbl is a function of pressure (Rp = φ∆PTM) and Eqn [12] can be rewritten as: J =
Surface renewal theory (SRT) It was found that the film model frequently underestimates the values of the permeate flux. To improve the model Koltuniewicz (2) added to J a correction factor that takes into account the lateral migration of macromolecules from the membrane to the bulk of the feed stream. This lateral migration originated by the forces involved in the laminar flow and the roughness of the membrane surface is responsible for instability of the concentration polarization layer and the increases
+ Jf
where Rm is the membrane resistance to flux. Eqn [10] may be used to determine s experimentally. Rm can also easily be determined experimentally using water as solvent. All other parameters must be determined empirically. It is also possible to estimate flux J for a given rate of surface renewal s and constant Q and VCR, in this way:
where η is the apparent viscosity; K is the consistency coefficient; γ is the shear rate; and n is the flow behaviour index. Dimensionless numbers included in Eqn [3] must then be modified to account for this rheological behaviour: kdh
s+A
where Ji and Jf are the initial and final flux, respectively; A was defined as the rate of flux decline and s the rate of surface renewal. Koltuniewicz (2) also proposed that in the case of ultrafiltration with a limiting permeate flux, as during apple juice clarification, A is proportional to the transmembrane pressure (A = α* ∆PTM) and Jlim can be obtained from Eqn [10] as:
Eqn [3]
where Sh, Re and Sc are the Sherwood, Reynolds and Schmidt number, respectively, and the parameters A’, α and β will depend on flux conditions and geometry of the system. It is well known that undepectinized fruit juices are pseudoplastic in nature (7) and their rheological behaviour can be described by the well-known power law:
s
∆PTM R'm + φ ∆PTM
Eqn [13]
where φ, the resistance index, is a constant for a particular membrane–solute combination. When ∆PTM is low, the value of J is controlled by the membrane resistance. On the other hand, when ∆PTM is large, the permeate flux approaches 1/φ. The objectives of this study are to determine the stationary permeate flux of apple juice through a hollow fibre membrane module; to study the effect of operating parameters such as pressure, recirculating
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flow rate and feed concentration on limiting flux; and to verify the application of accepted predictive models. Temperature is often constant in industrial membrane processes. Therefore, in this work the determination of J is made at constant temperature.
Table 1 50 °C
Power law constants for apple juice retentate at
VCR
K×103(Pa·s)
n
0.710 1.427 2.341 11.33
1.00 0.99 0.98 0.93
1 1.5 2 5
Materials and Methods Apple fruit (variety Red Delicious) was sorted, washed and crushed in a Model N°6 Fitz Mill Comminutor (Fitzpatrick Co., Chicago, Ill, U.S.A.). Juice was produced by pressing in a hydraulic press followed by screening through a 100 µm stainless steel mesh and pasteurized at 95 °C during 1 min in a pilot equipment. Samples were stored at –20 °C until analysed.
Determination of density Density was determined by pycnometry. The pycnometer of 50 mL capacity was calibrated with distilled water at 50 °C. A minimum of four consecutive replicates per sample with a reproducibility better than 0.3% were averaged.
Determination of apparent viscosity A model RMS-605s Rheometrics Spectrometer (Rheometric Inc., Piscataway, NJ, U.S.A.) was used to measure shear stress vs. shear rate of the apple juice retentate at different VCR values. A 5 cm diameter 0.1 rad cone-and-plate geometry was employed. The gap between the cone and plate was set to reasonably ensure no obstruction due to pulp particles. Moreover, when oscillation or perturbation during shear stress vs. shear rate was observed the sample was discarded. All tests were conducted at 50 ± 0.5 °C with a humidity and temperature air-controlled chamber. The effect of shear rate on shear stress was directly acquired with a personal computer through a data acquisition system and fitted to Eqn [2] using the SYSTAT/NONLIN programme. Experimental determinations were performed in duplicate.
L/min) and four VCR values (1, 1.5, 2 and 5) were tested in the range ∆PTM = 0–1.6 kg/cm2.
Results and Discussion Properties of apple juice retentate Density of apple juice retentate at 50 °C resulted in ρret = 1.0359 g/cm3 (r2 = 0.994), practically independent of VCR. Table 1 gives the values of power law constants K and n experimentally obtained at different VCR. It can be observed that apple juice showed some deviations from Newtonian behaviour even at 50 °C.
Flux characteristics Figures 1 and 2 show the variation of J with ∆PTM as a function of both concentration (VCR = 1, 1.5, 2 and 5) and recirculating flow rate (Q = 10, 12.5 and 15 L/min), respectively. Pressure independence (2nd region) was observed to occur at a higher pressure at higher recirculating velocities. The point at which the pressure independence is evident is considered as the optimum transmembrane pressure (∆PTMO). Table 2 lists both Jlim and ∆PTMO values obtained at different VCR and Q. The reduction of Jlim with Q can be associated with a reduction in the boundary layer due to an increase in the turbulence. On the other hand, the optimal ∆PTM values resulted practically independent of VCR at flow velocities higher than 10 L/min. Results also indicate 80.00 T=50°C, PC=50 000 ds, Qr=10 l/min
Ultrafiltration unit A pilot scale UF unit (Amicon model DC50P) with a single hollow fibre cartridge was used. The membranes were made of polysulfone with a normal molecular weight cut-off of 50,000. The unit had a 40 L storage tank, sanitary stainless steel pump and pipes, a flow reversing valve, pressure control and permeate and retentate streams flow meters. The unit was operated in batch mode and process parameters were: initial juice volume (Vo) = 27 L; temperature = 50 °C. This temperature is usual at the apple juice industry for alternative pectinolitic enzyme treatment, viscosity reduction and reduction of risk of contamination during UF treatment. During a run both permeate and retentate were recycled back to the feed tank to keep VCR constant. Three flow rates (Q = 10, 12.5 and 15
J (L/(h·m2))
60.00
40.00
20.00
0
0.40
0.80 ∆PMT (kg/cm2)
1.20
1.60
Fig. 1 Effect of transmembrane pressure and volume concentration ratio on permeate flux at 50 °C. (Untreated juice was 12°Brix) (j, VCR = 1; s, VCR = 1.5; d, VCR = 2; n, VCR = 5)
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80.00
10 T=50°C, PC=50 000 ds, VCR=1
60.00 Sh Sc–1/3
J (L/(h·m2))
Leveque solution
40.00
1
Eqn{14]
20.00
0.40
0
0.80 ∆PMT (kg/cm2)
102
0
1.60
1.20
103
104
Re
Fig. 2 Effect of transmembrane pressure and feed stream flow rate on permeate flux at 50 °C. (Untreated juice was 12°Brix) (j, Qr = 10 L/min; s, Qr = 12.5 L/min; d, Qr = 15.0 L/min)
Fig. 3 Mass transfer correlation for ultrafiltration of apple juice. Full line represents the behaviour predicted according to the Leveque equation. Dotted line represents Eqn [14]. Points are experimental results
that regardless of the operating conditions or the retentate concentration the reduction of the transmembrane pressure from the maximum to the minimum is translated in a hysteresis effect in the permeate flux, attributable to the consolidation of the gel layer (9,10). Similar effects have been observed during the UF of other liquid foods (11,12). The area enclosed by the hysteresis loop was greater at lower Q and VCR values.
with the Leveque solution (6). As Fig. 3 shows the Leveque solution fits the results quite well (hardly over predicted the experimental fluxes) suggesting that the velocity and concentration profile assumed were appropriate.
Sh = 0.149 Re0.336 Sc0.329
Eqn [14]
In the hollow fibre system used in this study, the length of the concentration profile entrance region is much greater than the channel length, indicating the concentration profile is still developing during flow down the channel (6). For laminar flow systems, if velocity profile is fully developed but concentration boundary layer is developing along the fibre, the Leveque solution of Eqn [3] can be used with A’ = 1.86; α = 1/3 and β = 1/3 (13). Figure 3 compares Eqn [14] and experimental results
80.00
60.00 J (L/(h·m2))
Film theory To evaluate the film model, the calculated values of log Sh were fitted vs. log Re and log Sc by multiple linear regression, resulting:
Surface renewal model The characteristic resistance of the membrane was calculated from the water flux variation with ∆PTM. With this Rm value (Rm = 6.366 3 105 Pa.h/m) and the final flux Jf (determined from the flux decline with time at constant Q and VCR), both the ratio s/α* and Jlim were calculated (Table 3). These experimental data were finally fitted to Eqn [11] and plotted in Fig. 4. The points shown in the figure represent actual experi-
Table 2 Values of limiting flux and optimal transmembrane pressures at various conditions Q (L/min) 10.0 12.5 15.0 ∆PTMO (kg/cm2) 10.0 12.5 15.0
Jlim
20.00
VCR 1.0
(L/hm2)
40.00
58.0 66.0 72.0 0.80 1.38 1.45
1.5
2.0
3.0
5.0
54.3 48.7 44.0 39.3 57.3 52.7 48.7 42.7 59.3 54.0 50.7 44.0 0.95 1.10 1.22 1.25 1.40 1.40 1.38 1.40 1.48 1.46 1.40 1.42
0
0.40
0.80 ∆PMT (kg/cm2)
1.20
1.60
Fig. 4 Comparison of experimental permeate flux data (points) as a function of transmembrane pressure with those predicted from the SRM model (full line; Eqn [11]), at various VCR values. (d, VCR = 1; j, VCR = 1.5; s, VCR = 2; r, VCR = 5)
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Table 3 Parameters of the surface renewal model, Eqn [11] Q (L/min)
VCR
s/a* 10–4Pa
Jlim (L/m2.h)
Standard error
10.0 10.0 10.0 10.0 10.0 12.5 15.0
1.0 1.5 2.0 3.0 5.0 1.0 1.0
4.591 4.090 3.365 3.266 2.835 4.610 4.169
72.07 64.22 52.83 51.29 44.51 88.76 90.96
2.162 3.165 2.252 1.855 0.843 1.893 1.686
mental data. An excellent agreement exists between experimental data and the surface model predictions.
Resistance-in-series approach Theoretically this model could predict J throughout the range of transmembrane pressures. Table 4 lists the R'm; φ and φ ∆PTM values. Clearly R'm and φ ∆PTM are of the same order of magnitude. Therefore, simplification proposed by Chiang and Cheryan (8) to the resistance-in-series model, represented by Eqn [13], resulted in a poor fitting of experimental data (Fig. 5). It was also found that there was a definite correlation between the resistance R'm and VCR, as follows: R'm = 0.010935 + 0.007182ln(VCR) Eqn [15] r2 = 0.993 The increasing nature of R'm regarding VCR suggests continuous formation of fouling with ∆PTM. On the contrary, during UF of other solutions Chiang and 80.00 T=50°C, PC=50 000 ds, Qr=10 l/min
Cheryan (8) claimed independence of R'm with operating parameters.
Conclusions The stationary flux of permeate during UF of apple juice was studied. Limiting flux, hysteresis loop and membrane resistance were determined over a wide range of transmembrane pressures, feed rates and concentrations. In particular, the limiting flux was analysed on the basis of three approaches: the film theory, the surface renewal concept and the resistancein-series model. The results of this study revealed that limiting flux of apple juice in hollow fibre can be adequately described using classical laminar flow mass transfer models. The film theory was, by definition, meaningful only during the 2nd region (mass control region). On the contrary, the semi-empirical model based on the modification of the membrane surface due to lateral migration was successfully extended over the total range of pressures. The resistance-in-series model failed to simulate flux of apple juice under the conditions used in this work.
J (L/(h·m2))
60.00
Nomenclature
VCR=1 VCR=1.5
40.00
A A' Cb
VCR=2 VCR=5
20.00
0
0.50
1.00 ∆PMT (kg/cm2)
2.00
1.50
Fig. 5 Comparison of permeate flux between experimental and calculated values using Chiang and Cheryan (8) model (full lines; Eqn [13]). (d, VCR = 1; j, VCR = 1.5; s, VCR = 2; r, VCR = 5)
Cg Cper D dh J Ji Jf Jlim k
rate of flux decline (s–1) constant in the dimensionless Eqn [3] bulk concentration of rejected macromolecules (g/100g) gel concentration (g/100g) solute concentration in permeate (g/100g) diffusion coefficient (m2/s) hydraulic diameter (m) flux (L/(m2·h) initial flux (L/(m2·h) final flux (L/(m2·h) limiting permeate flux (L/(m2·h) mass transfer coefficient (m/s)
Table 4 Values of intrinsic resistance (R'm); resistance index (φ) and (φ*∆PTM) product of the resistance-in-series model VCR ×10–6
R'm φ φ×∆PTM×10–6
(Pa·h/m) (m2.h/L) (Pa·h/m)
1.0
1.5
2.0
3.0
5.0
1.079 0.0172 3.037
1.314 0.0184 3.249
1.609 0.0205 3.620
1.815 0.0227 4.008
2.105 0.0254 4.486
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K n Pi Po Pext Rbl Re Rg Rm R’m s Sc Sh v VCR
consistency coefficient in power law viscosity model (Pa·sn) flow behaviour index in power law viscosity model (dimensionless) pressure at the inlet of the fibre (Pa) pressure at the outlet of the fibre (Pa) pressure on the permeate side (Pa) boundary layer resistance of the membrane (Pa·h/m) Reynold number (dimensionless) gel resistance of the membrane (Pa·h/m) Characteristic resistance of the membrane (Pa·h/m) Intrinsic resistance of the membrane, Eqn [12] (Pa·h/m) rate of surface renewal (s–1) Schmidt number (dimensionless) Sherwood number (dimensionless) fluid velocity (m/s) volume concentration ratio
Greek letters α, β constants in dimensionless Eqn [3] α* constant as defined by Eqn [10] boundary layer thickness (m) δbl φ constant as defined by Eqn [12] η apparent viscosity (Pa·sn) ρret retentate density (kg/m3) γ shear rate (s–1) ∆PTM transmembrane pressure (Pa) ∆PTMo optimum transmembrane pressure (Pa)
References 1 HEATHERBELL, D. A., SHORT, J. L. AND STAUEBI, P. Apple juice clarification by ultrafiltration. Confructa, 22, 157–169 (1977) 2 KOLTUNIEWICZ, A. Predicting permeate flux in ultrafiltration on the basis of surface renewal concept. Journal of Membrane Science, 68, 107–118 (1992) 3 SOLTANIEH, M. AND GILL, W. N. Review of reverse osmosis membranes and transport models. Chemical Engineering Communications, 12, 279–287 (1981) 4 RAUTEMBACH, R. AND ALBRECHT, R. Membrane Processes, 2nd Edn. New York: John Wiley & Sons, p. 78 (1989) 5 GEKAS, V. AND HALLSTROMM, B. Mass transfer in the membrane concentration polarization layer under turbulent cross flow. I. Critical literature review and adaptation of existing Sherwood correlations to membrane operations. Journal of Membrane Science, 30, 153–162 (1987) 6 CHIANG, B. H. AND CHERYAN, M. Modelling of hollow fibre ultrafiltration of skim milk under mass-transfer limiting conditions. Journal of Food Engineering, 6, 241–255 (1987) 7 SARAVACOS, G. D. Effect of temperature on viscosity of fruit juices and purees. Journal of Food Science, 35, 122–125 (1970) 8 CHIANG, B. H. AND CHERYAN, M. Ultrafiltration of skimmilk in hollow fibres. Journal of Food Science, 51, 340–344 (1986) 9 MICHAELS, A. New Separation Technique for the CPI. Chemical Engineering Progress, 64, 31–36 (1968) 10 OMOSAIYE, O., CHERYAN, M. AND MATTHEWS, M. Removal of oligosaccharides from soybean water extracts by ultrafiltration. Journal Food Science, 43, 354–358 (1978) 11 FENTON-MAY, R. L., HILL, C. G. AND AMUNDSON, C. H. Use of Ultrafiltration/Reverse Osmosis systems for the concentration and fractionation of whey. Journal of Food Science, 36, 14 (1971) 12 CHERYAN, M. AND SCHLESSER, J. Performance of hollow fibre system for ultrafiltration of aqueous extracts soybeans. Lebensmittel-Wissenschaft und-Technologie, 11, 65–69 (1977) 13 CHERYAN, M. Ultrafiltration Handbook. Lancaster, Pennsylvania: Technomic Publishing Company, Inc., pp. 85–87 (1986)
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