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Influence of inclination on gas-sparged cross-flow ultrafiltration through an inorganic tubular membrane
Journal of Membrane Science 196 (2002) 103–110
Influence of inclination on gas-sparged cross-flow ultrafiltration through an inorganic tubular membrane Tung-Wen Cheng∗ Department of Chemical Engineering, Tamkang University, Tamsui, Taipei 251, Taiwan, ROC Received 22 March 2001; received in revised form 29 June 2001; accepted 9 July 2001
Abstract The effect of membrane inclination on the flux of single-phase or gas–liquid two-phase ultrafiltration in a tubular membrane has been investigated. Experimental result shows that membrane inclination has a significant enhancement on the flux of two-phase ultrafiltration operated at slug flow pattern. As the angle of inclination from the horizontal increases, the flux increases, reaches a maximum, and then decreases. The flux may be enhanced more than 1.5 when the membrane is inclined from 0 to 50◦ . The flux enhancement due to membrane inclination increases with increasing the gas velocity, the feed concentration, and the transmembrane pressure, while it decreases with increasing the liquid velocity. The optimal inclination angle of the membrane in a slug-flow ultrafiltration is close to 50◦ . An equation for determining the optimal inclination angle was also proposed in this work. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Ultrafiltration; Inorganic membrane; Concentration polarization; Membrane inclination; Flux enhancement
1. Introduction Ultrafiltration is a pressure-driven membrane separation process. The working pressure is usually in the range of 100–1000 kPa. This pressure provides the driving potential to force the solvent or the lower molecular weight solutes through the membrane while the larger molecules are rejected by the membrane. The concentration of rejected solute on the membrane surface is always higher than that in the bulk solution. This is the so-called concentration polarization phenomenon, which results in fouling and solute adsorption on the membrane as well as a flux decline. The ultrafiltration is usually operated in the cross-flow type in order to decrease the accumulation of the rejected solute on the membrane surface. Recently, membrane ∗ Tel.: +886-2-262-19554; fax: +886-2-262-09887. E-mail address: [email protected] (T.-W. Cheng).
ultrafiltration has been applied in a wide variety of fields, such as drinking water supply, food industry, biotechnology, treatment of industrial effluent or oil emulsion wastewater, and medical therapeutics. The performance of an ultrafiltration process is dominated by the phenomena of concentration polarization and membrane fouling. Gas–liquid two-phase flow as well as other techniques such as centrifugal force, pulsatile flow, turbulence promoter, secondary flow, etc., have been devised for decreasing concentration polarization and fouling in order to increase the permeate flux [1]. In general, the method of gas–liquid two-phase flow is a simple and economical technique and is able to enhance permeate flux effectively in membrane filtration [1–7]. The introduction of air slugs into the liquid stream increases turbulence on the membrane surface and suppresses the formation of the concentration boundary layer, leading to an enhancement in the flux of the filtration process.
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T.-W. Cheng / Journal of Membrane Science 196 (2002) 103–110
Nomenclature C E J JH JV uG uL V VG VG,H VG,V
feed concentration (kg/m3 ) flux enhancement permeate flux (m3 /m2 s) permeate flux of horizontal membrane (m3 /m2 s) permeate flux of vertical membrane (m3 /m2 s) superficial gas velocity (m/s) superficial liquid velocity (m/s) flow velocity cross the membrane (m/s) velocity of gas bubble (m/s) velocity of gas bubble in horizontal tube (m/s) velocity of gas bubble in vertical tube (m/s)
Greek letters ε average error between predictions and experimental data Pi feed transmembrane pressure (Pa) θ inclination angle (◦ ) θm optimal inclination angle (◦ ) The influence of gas slugs on the flux enhancement depends on the resistance of the concentration polarization layer in the single liquid-phase ultrafiltration [1]. When the resistance of the polarization layer is large, i.e. the system is operated under the conditions of low liquid velocity, high transmembrane pressure or high feed concentration, a low gas flow rate cannot effectively disturb the concentration polarization layer. Thus, a certain threshold of gas velocity is required to disturb this layer. Beyond the critical gas velocity, gas slugs can enhance the permeate flux significantly. Therefore, the same permeate flux obtained in single liquid-phase ultrafiltration with a higher liquid velocity can be achieved with a lower liquid velocity by introducing a moderate velocity of gas slugs. The gas–liquid two-phase flow pattern in the membrane is an important factor in determining the performance of an air-sparging ultrafiltration system. The slug-flow pattern was thought to be the best flow regime for increasing permeate flux [4]. Effects of slug flow on the flux of ultrafiltration in a hollow-fiber
membrane and in a tubular membrane module were studied, respectively, by Cabassud et al. [6] and Mercier et al. [7]. For filtration at the slug flow, the membrane surface is alternately submitted to positive and negative shear stresses. The successive and unstable stresses were expected to prevent filtered particles from settling on the membrane surface and then enhancing the filtration mass transfer [6,7]. Experimental results of microfiltration [8] also showed that slug flow pattern is better than bubble flow pattern in enhancing the permeate flux. The model for calculating the mass transfer coefficients and the permeate fluxes in slug flow ultrafiltration was proposed by Ghosh and Cui [9]. In the model, the region near a gas slug is divided into three zones: falling film zone, wake zone, and liquid slug zone. Mercier-Bonin et al. [10] showed that the flux enhancement in the slug flow is related to the increase in the wall shear stress as well as to other phenomena: such as intermittency, reversal of the wall shear stress, instantaneous pressure variations, and the enhanced local mixing. It has been reported that the permeate flux for the upward flow in the vertically mounted membrane is about 10–20% higher than that in the horizontally installed membrane [3]. The experimental results [11] also showed that when the single liquid-phase ultrafiltration with a flat membrane channel cell was used with various orientations, the natural convection instability will enhance the flux at a unstable gravitational orientation (i.e. membrane above the flow channel). Some studies [12–15] showed that the rise velocity of a slug bubble in the tube with an inclination angle is larger than the rise velocity in a vertical or in a horizontal tube. Due to the higher rise velocity of the bubble in the inclined tube, the mass transfer for the two-phase flow in an inclined tube is higher than that in a vertical one [16], and the heat transfer in an inclined tube is higher than that in a horizontal one [17]. A pioneer study [18] on the flux behavior of ultrafiltration within an inclined tubular membrane shows that the flux usually keeps increasing as the inclination angle changes from 0 (horizontal) to 30 and 45◦ , then decreasing as the angle increases to 60 and 90◦ (vertical). This result implies that an optimal inclination angle exists in the ultrafiltration operation for obtaining the maximum permeate flux. In this study,
T.-W. Cheng / Journal of Membrane Science 196 (2002) 103–110
more experiments of the ultrafiltration under various inclinations, especially between 45 and 60◦ , have been conducted in order to investigate the optimal inclination of the ultrafiltration system. The flux enhancement due to membrane inclination was discussed systemically under various operating parameters, such as liquid flow rate, gas flow rate, feed concentration, transmembrane pressure, etc. Finally, an equation for calculating the flux in an inclined-membrane ultrafiltration system and hence determining the optimal inclination angle was proposed.
2. Experiment The operated experimental set-up was described in a previous work [18]. This gas–liquid two-phase ultrafiltration system is operated in an inorganic tubular membrane module. The membrane medium used was a 15 kDa MWCO tubular ZrO2 /carbon membrane (M2 type, Tech-Sep) with 40.0 cm length, 6.0 mm internal diameter, and 75.4 cm2 effective membrane area. The tested solute was dextran T500 (Pharmacia) which was more than 99% retained by the membrane used. The solvent was distilled water. The inclination angles, θ , of the ultrafiltration column in this experimental work included 0, 30, 45, 50, 55, 60, and 90◦ . The superficial liquid velocities, uL , were 0.168, 0.336, and 0.672 m/s; and the superficial gas velocities, uG , were 0.04–0.32 m/s. According to the velocities, the value of air injection ratio, defined as uG /(uG + uL ), varies from 0.06 to 0.66. The feed transmembrane pressures, Pi , were 50–300 kPa. The feed concentrations were 4.0–16.0 kg/m3 , and the feed solution temperature was kept at 30◦ C by a thermostat. During the operation, the permeate and retentate are recycled into the feed tank in order to maintain a constant feed concentration. The flux ordinarily reaches steady state within 30 min. In the experiments, because the pressure drop along the membrane module is small, the feed transmembrane pressure is treated as the mean transmembrane pressure. After each experiment, the membrane was cleaned by high circulation and backflushing with 10% NaOH and 10% HNO3 aqueous solutions and pure water. The cleaning procedure was repeated until the original water flux had been restored.
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3. Results and discussion 3.1. Flow pattern The diameter of hollow fiber or tubular ultrafiltration membrane is usually in the order of millimeters. The flow regime of gas–liquid two-phase flow in a small diameter tube is different from that in a large diameter tube [19]. Barnea et al. [20] investigated the flow patterns of gas–liquid two-phase flow in small diameter tubes (4–12 mm). Their results showed that slug flow exists in the range of uG < 5.0 m/s and uL < 1.0 m/s for 4–12 mm vertical tubes and in the range of uG < 5.0 m/s and 0.1 m/s < uL < 1.0 m/s for 4–8 mm horizontal tubes. It is notable that when uG < 1.0 m/s, the liquid slug in the tube is free of entrained gas bubbles, contrary to what is observed in tubes of larger diameters. The observations of Laborie et al. [21] also indicate that the two-phase flow in vertical capillaries of 1–4 mm i.d. is slug flow when the air injection ratio varies between 0.17 and 0.67, and the liquid slug contains no small dispersed bubbles. With a vertical tube of 7 mm i.d., the slug flow regime was obtained when the injection ratio was between 0.25 and 0.9, while the bubble flow regime are obtained when the ratio is lower than 0.25 [8]. In this work, the diameter of the membrane tube used is 6.0 mm and the injection ratio is comprised between 0.06 and 0.66. Although, the effect of inclination on the gas–liquid flow pattern in a small diameter tube is still unknown and lacking in the current literature. According to the result of Vera et al. [8], the slug flow regime is assumed in the present tube when the air injection ratio is larger than 0.25. 3.2. Effect of inclination on flux of single-phase ultrafiltration Fig. 1 is the plot of permeate fluxes versus inclination angles for single liquid-phase ultrafiltration at various transmembrane pressures and feed velocities. As shown in the figure, the permeate flux increases with the increase in the transmembrane pressure as well as in the cross-flow velocity on the membrane. It also shows that the permeate flux varies slightly with the change in inclination angle. For example, at 100 kPa transmembrane pressure and 0.168 m/s liquid velocity, the fluxes are (2.23, 2.61 and 2.32) × 10−6 m3 /m2 s,
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Fig. 1. Permeate fluxes vs. inclination angles for liquid ultrafiltration under various transmembrane pressures.
Fig. 2. Permeate fluxes vs. inclination angles for liquid ultrafiltration under various feed concentrations.
respectively, for inclination angles of 0, 45 and 90◦ . The measurement accuracy of the experimental flux has been checked for confirming the influence of inclination on the flux. The flux of the operation with a 45◦ inclination is found to be the highest among those inclinations, and the flux of the vertical membrane operation is slightly higher than that in the horizontally installed membrane. The flux enhancement is between 1.10 and 1.17 as the membrane inclined from horizontal to 45◦ under those operating conditions. Fig. 2 is the plot of permeate fluxes versus inclination angles for various feed concentrations. As presented in the figure, the permeate flux decreases with the increase in feed concentration, and the membrane inclination affected slightly on the flux too. The flux with a 45◦ inclination is still the highest, however, the flux enhancement is small, between 1.10 and 1.16, under presented conditions. In the present liquid-phase ultrafiltration, the variation of inclination angle influences insignificantly on the flux. Tilting the membrane may induce a natural convection effect, and hence disturb the concentration polarization layer and enhance the permeate flux, however, the natural convection instability is important at a lower cross-flow velocity in which the forced convection is relatively weak [11]. The critical cross-flow velocity is about 0.1 m/s. In present single-phase ultrafiltration, the cross-flow velocity is
higher than 0.1 m/s, therefore, the effect of tilting the membrane on the permeate flux is not significant. 3.3. Effect of inclination on flux of two-phase ultrafiltration 3.3.1. Effect of velocities Fig. 3 represents the relationship between permeate fluxes and inclination angles under various gas velocities. The superficial liquid velocity was 0.168 m/s and the superficial gas velocity varied from 0.04
Fig. 3. Permeate fluxes vs. inclination angles under various gas velocities: uL = 0.672 m/s.
T.-W. Cheng / Journal of Membrane Science 196 (2002) 103–110
to 0.16 m/s. The flux is enhanced by the introduction of gas slugs even with a low gas velocity (e.g. uG = 0.04 m/s), with the flux seeming to approach a limiting value as the gas velocity further increases. It is noticeable that the inclination does not influence the flux at 0 and 0.04 m/s gas velocity, that is, without sparging and at 0.19 air injection ratio that corresponds to bubble flow regime [8]. A dramatic enhancement in flux by tilting the membrane occurs as the gas velocity is above 0.08 m/s that corresponds to slug flow regime. The inclination angle influences the flux with a maximum obtained at 45◦ . The effect of inclination on flux under various liquid flow rates is shown in Fig. 4, where the gas velocity was 0.08 m/s and transmembrane pressure was 200 kPa. The flux enhancements at 45◦ inclination angle are 1.51, 1.20 and 1.18, respectively, for uL = 0.168, 0.336 and 0.672 m/s. Increasing liquid velocity will weaken the natural convection as well as the effect of inclination on the flux. However, it shows that the flux for uL = 0.168 m/s with a 45◦ inclination is higher than that of a uL = 0.336 m/s using a horizontally or vertically installed membrane. The method of tilting membrane can be used for enhancing the flux of gas-sparged ultrafiltration operated at a lower liquid velocity in order to reduce energy consumption or to recover the solutes which are mechanicalsensitive.
Fig. 4. Permeate fluxes vs. inclination angles under various liquid velocities: uG = 0.08 m/s.
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Fig. 5. Permeate fluxes vs. inclination angles under various feed concentrations and gas velocities: uL = 0.168 m/s.
3.3.2. Effect of feed concentration The effect of inclination on flux under various feed concentrations was shown in Fig. 5. The superficial liquid velocity was 0.168 m/s. At low gas velocity uG = 0.04 m/s, shown as the solid points in the figure, the flux enhancements are 1.18 and 1.20 for feed concentrations of 8.0 and 16.0 kg/m3 , respectively. For high gas velocity uG = 0.16 m/s, the flux enhancements are 1.18, 1.43 and 1.44, respectively, for feed concentrations of 4.0, 8.0 and 16.0 kg/m3 . These results show that flux enhancement increases with the increase in feed concentration. For a higher feed concentration, the extent of concentration polarization is more severe, so that the effect of inclination on disturbing the polarization layer is significant; hence the flux enhancement is larger for a concentrated feed. 3.3.3. Effect of transmembrane pressure Data for inspecting the effect of inclination under various transmembrane pressures were shown in Fig. 6. The applied transmembrane pressure varied from 100 to 300 kPa. At low pressure, the effect of inclination on flux enhancement is slight. When applied pressure increases up to 200 kPa or more, the flux significantly increases as the installation of membrane changes from the horizontal to vertical or other inclinations. These results imply that flux enhancement increases with the increase in transmembrane pressure. The flux enhancement reaches 1.46
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The correlation equation for the velocity of a gas bubble in an inclined tube, VG , can be expressed as [13] VG = VG,H cos θ + VG,V sin θ
(1)
where VG,H and VG,V are the velocities of the gas bubble measured at horizontal and vertical orientations, respectively. In ultrafiltration, the permeate flux usually increases with the flow velocity cross the membrane as J = aVb
Fig. 6. Permeate fluxes vs. inclination angles under various transmembrane pressures: uL = 0.168 m/s; uG = 0.16 m/s.
when operated at 300 kPa transmembrane pressure. The extent of concentration polarization phenomenon usually is severe at high transmembrane pressure. Inclination in the membrane will disturb the concentration polarization layer, especially if operated at higher transmembrane pressure. 3.4. Optimal inclination angle The experimental data, as shown in Fig. 3, show that the flux enhancement may grow up to 1.51 when the membrane is inclined from 0 to 45◦ . The enhancement in flux is achieved due to the natural convection instability, which is induced by inclining the ultrafiltration column. Especially, this effect is more significant in the case of lower liquid velocity [18]. The other factor for heightening the enhancement is the increase in forced convection or cross-flow velocity in an inclined slug-flow system. The gas slug velocity in the inclined tube is faster than that in the vertical tube, and the vertical one is faster than the horizontal [12–14]. Therefore, due to the higher bubble velocity as well as the cross-flow velocity, the permeate flux in the inclined system is larger than that in the vertical one, and the flux in the vertical system is larger than that in horizontal one. The experimental data also show that the optimal inclination angle of the membrane for ultrafiltration exists in the range between 45 and 60◦ .
(2)
where a and b are determined parameters, and V is the tangential liquid velocity in liquid-phase ultrafiltration or the mean flow velocity (=uG + uL ) in two-phase ultrafiltration. For slug flow in a small tube, the relationship between the gas bubble velocity and the mean flow velocity can be expressed as follows: VG = cV
(3)
where the value of the parameter c is between 1.0 and 1.2 [22]. Values of a and b, in Eq. (2), depend on the flow pattern in the tube. For single liquid-phase ultrafiltration, b is 0.8 for turbulent flow and is 0.33 for laminar flow [23]. For slug flow ultrafiltration, the model proposed by Ghosh and Cui [9] indicated that in the falling film zone, b is 0.8; in the wake zone, b also is 0.8; and in liquid slug zone, b is 0.8 for turbulent flow and is 0.33 for laminar flow. The flux calculated by the model agreed reasonably well with their experimental data. It also showed that the mass transfer in the liquid slug zone is more than an order of magnitude lower than that in the falling film zone or in the wake zone. Therefore, 0.8 is a reasonable value for b for the slug flow ultrafiltration system. Combination of Eqs. (1)–(3) and let b = 0.8, the equation for relating ultrafiltration flux with inclination angle was obtained as J = (JH1.25 cos θ + JV1.25 sin θ)0.8
(4)
where JH and JV are the fluxes measured at horizontal and vertical orientations, respectively. More experiments for measuring the fluxes with inclination angles between 45 and 60◦ were conducted. Figs. 7 and 8 show the experimental results of 4 and 16 kg/m3 feed concentration, respectively, in the condition of
T.-W. Cheng / Journal of Membrane Science 196 (2002) 103–110
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where N is the number of the experimental data, are <3%. Further, the optimal inclination angle (θ m ) of an inclined-membrane ultrafiltration can be also derived from Eq. (4) and expressed as θm = tan−1
Fig. 7. Optimal inclination angles for membrane ultrafiltration: C = 4.0 kg/m3 ; the solid lines are the predictions of Eq. (4).
0.12 m/s gas velocity, 0.168 m/s liquid velocity and a varying transmembrane pressure from 100 to 300 kPa. These experimental data show that the flux with a 50◦ inclination is higher than the flux with a 45◦ inclination. The predictions of Eq. (4) were also plotted in Figs. 7 and 8. The predictions agree well with the experimental data. Average errors between the experimental data and predictions, defined as follows: n=N |Jpre,n − Jexp,n |/Jexp,n ε = n=1 (5) N
JV JH
1.25 (6)
The optimal inclination angle can be determined from the values of JV and JH . The calculated values of θ m by using Eq. (6) and the experimental data of JV and JH under various operating conditions are listed in Table 1. For the two-phase ultrafiltration system operated at 0.168 m/s liquid velocity, whose flux is sensitive to the change in inclination angle, the optimal inclination angle is a bit over 50◦ , as shown in Table 1(a). These predictions of θ m agree well with the experimental measurements as shown in Figs. 7 and 8. When the system was operated at a higher liquid velocity (uL = 0.672 m/s), the calculated optimal inclination angles, listed in Table 1(b), are smaller than but close to 50◦ . Based on the present wide range operating conditions, the optimal inclination angle of a two-phase slug flow ultrafiltration system is close to 50◦ . The optimal angle is slightly affected by the flow velocities of liquid and gas, and is less sensitive to the transmembrane pressure and feed concentration. Table 1 Optimal inclination angles of membrane in the two-phase ultrafiltration Pi (kPa) uG (m/s) C = 4.0 kg/m3
C = 8.0 kg/m3 C = 16.0 kg/m3
0.08
0.12
0.08
0.08
0.12
52◦ 51◦ 51◦
50◦ 51◦ 51◦
50◦ 51◦ 51◦
52◦ 53◦ 53◦
(a) uL = 0.168 m/s 100 50◦ 200 51◦ 300 51◦
Fig. 8. Optimal inclination angles for membrane ultrafiltration: C = 16.0 kg/m3 ; the solid lines are the predictions of Eq. (4).
C = 4.0 kg/m3
C = 8.0 kg/m3 C = 16.0 kg/m3
0.08
0.16
0.16
0.08
0.16
46◦ 47◦ 48◦
48◦ 48◦ 48◦
48◦ 47◦ 47◦
48◦ 47◦ 48◦
(b) uL = 0.672 m/s 100 48◦ 200 47◦ 300 48◦
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4. Conclusions The effect of the inclination on the permeate flux of ultrafiltration was studied and discussed based on various operating parameters, such as superficial liquid velocity, superficial gas velocity, feed concentration and transmembrane pressure. The experiments were carried out in a tubular ceramic membrane module by using dextran T500 as tested solute. Inclination effectively enhances the flux of ultrafiltration at slug flow regime, while its influence is insignificant for liquid-phase ultrafiltration or at bubble flow regime. In the slug-flow ultrafiltration, the flux enhancement by inclining the membrane increases with increasing gas velocity, feed concentration, and transmembrane pressure, while it decreases with increasing liquid velocity. The flux may be enhanced more than 1.5 when the membrane is inclined from 0 to 50◦ . A model was also proposed for estimating the ultrafiltration flux in an inclined membrane system and determining the optimal inclination angle for maximum flux. The flux calculated from the correlation equation agrees very well with the experimental data. The optimal inclination angle of the membrane in a slug-flow ultrafiltration is close to 50◦ .
Acknowledgements The author wishes to express his appreciation to the National Science Council of Taiwan, ROC for financial aid. References [1] T.-W. Cheng, H.M. Yeh, C.T. Gau, Enhancement of permeate flux by gas slugs for cross-flow ultrafiltration in tubular membrane module, Sep. Sci. Technol. 33 (1998) 2295. [2] C.K. Lee, W.G. Chang, Y.H. Ju, Air slugs entrapped cross-flow filtration of bacterial suspensions, Biotechnol. Bioeng. 41 (1993) 525. [3] Z.F. Cui, K.I.T. Wright, Gas–liquid two-phase cross-flow utrafiltration of BSA and dextran solution, J. Membr. Sci. 90 (1994) 183. [4] M. Mercier, C. Fonade, C. Lafforgue-Delorme, Influence of the flow regime on the efficiency of a gas–liquid two-phase medium filtration, Biotechnol. Tech. 9 (1995) 853.
[5] Z.F. Cui, K.I.T. Wright, Flux enhancements with gas sparging in downwards cross-flow ultrafiltration: performance and mechanism, J. Membr. Sci. 117 (1996) 109. [6] C. Cabassud, S. Laborie, J.M. Laine, How slug flow can improve ultrafiltration flux in organic hollow fibers, J. Membr. Sci. 128 (1997) 93. [7] M. Mercier, C. Fonade, C. Lafforgue-Delorme, How slug flow can enhance the ultrafiltration flux in mineral tubular membranes, J. Membr. Sci. 128 (1997) 103. [8] L. Vera, R. Villarroel, S. Delgado, S. Elmaleh, Enhancing microfiltration through an inorganic tubular membrane by gas sparging, J. Membr. Sci. 165 (2000) 47. [9] R. Ghosh, Z.F. Cui, Mass transfer in gas-sparged ultrafiltration: upward slug flow in tubular membranes, J. Membr. Sci. 162 (1999) 91. [10] M. Mercier-Bonin, C. Maranges, C. Lafforgue, C. Fonade, Hydrodynamics of slug flow applied to cross-flow filtration in narrow tubes, AIChE J. 46 (2000) 476. [11] K.H. Youm, A.G. Fane, D.E. Wiley, Effects of natural convection instability on membrane performance in dead-end and cross-flow ultrafiltration, J. Membr. Sci. 116 (1996) 229. [12] G.B. Wallis, One-Dimensional Two-Phase Flow, McGrawHill, New York, 1969, pp. 304–307. [13] K.H. Bendiksen, An experimental investigation of the motion of long bubbles in inclined tubes, Int. J. Multiphase Flow 10 (1984) 467. [14] M.E. Weber, A. Alarie, M.E. Ryan, Velocities of extended bubbles in inclined tubes, Chem. Eng. Sci. 41 (1986) 2235. [15] P.S. Carew, N.H. Thomas, A.B. Johnson, A physically based correlation for the effects of power law rheology and inclination on slug bubble rise velocity, Int. J. Multiphase Flow 21 (1995) 1091. [16] K.D.P. Nigam, A.B. Pandit, K. Niranjan, Effect of angle of inclination on liquid-phase controlled mass transfer from a gas slug, Chem. Eng. Sci. 50 (1995) 289. [17] G. Hetsroni, J.H. Yi, B.G. Hu, A. Mosyak, L.P. Yarin, G. Ziskind, Heat transfer in intermittent air–water flows — Part II. Upward inclined tube, Int. J. Multiphase Flow 24 (1998) 189. [18] T.-W. Cheng, H.M. Yeh, J.H. Wu, Effects of gas slugs and inclination angle on the ultrafiltration flux in tubular membrane module, J. Membr. Sci. 158 (1999) 223. [19] B. Lowry, M. Kawaji, Adiabatic vertical two-phase flow in narrow flow channels, AIChE Symp. Ser. 84 (1988) 133. [20] D. Barnea, Y. Luninski, Y. Taitel, Flow pattern in horizontal and vertical two-phase flow in small diameter pipes, Can. J. Chem. Eng. 61 (1983) 617. [21] S. Laborie, C. Cabassud, L. Durand-Bourlier, J.M. Laine, Characterisation of gas–liquid two-phase flow inside capillaries, Chem. Eng. Sci. 54 (1999) 5723. [22] K. Mishima, T. Hibiki, Some characteristics of air–water twophase flow in small diameter vertical tubes, Int. J. Multiphase Flow 22 (1996) 703. [23] T.-W. Cheng, H.M. Yeh, C.T. Gau, Resistance analyses for ultrafiltration in tubular membrane module, Sep. Sci. Technol. 32 (1997) 2623.
Influence of inclination on gas-sparged cross-flow ultrafiltration through an inorganic tubular membrane Tung-Wen Cheng∗ Department of Chemical Engineering, Tamkang University, Tamsui, Taipei 251, Taiwan, ROC Received 22 March 2001; received in revised form 29 June 2001; accepted 9 July 2001
Abstract The effect of membrane inclination on the flux of single-phase or gas–liquid two-phase ultrafiltration in a tubular membrane has been investigated. Experimental result shows that membrane inclination has a significant enhancement on the flux of two-phase ultrafiltration operated at slug flow pattern. As the angle of inclination from the horizontal increases, the flux increases, reaches a maximum, and then decreases. The flux may be enhanced more than 1.5 when the membrane is inclined from 0 to 50◦ . The flux enhancement due to membrane inclination increases with increasing the gas velocity, the feed concentration, and the transmembrane pressure, while it decreases with increasing the liquid velocity. The optimal inclination angle of the membrane in a slug-flow ultrafiltration is close to 50◦ . An equation for determining the optimal inclination angle was also proposed in this work. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Ultrafiltration; Inorganic membrane; Concentration polarization; Membrane inclination; Flux enhancement
1. Introduction Ultrafiltration is a pressure-driven membrane separation process. The working pressure is usually in the range of 100–1000 kPa. This pressure provides the driving potential to force the solvent or the lower molecular weight solutes through the membrane while the larger molecules are rejected by the membrane. The concentration of rejected solute on the membrane surface is always higher than that in the bulk solution. This is the so-called concentration polarization phenomenon, which results in fouling and solute adsorption on the membrane as well as a flux decline. The ultrafiltration is usually operated in the cross-flow type in order to decrease the accumulation of the rejected solute on the membrane surface. Recently, membrane ∗ Tel.: +886-2-262-19554; fax: +886-2-262-09887. E-mail address: [email protected] (T.-W. Cheng).
ultrafiltration has been applied in a wide variety of fields, such as drinking water supply, food industry, biotechnology, treatment of industrial effluent or oil emulsion wastewater, and medical therapeutics. The performance of an ultrafiltration process is dominated by the phenomena of concentration polarization and membrane fouling. Gas–liquid two-phase flow as well as other techniques such as centrifugal force, pulsatile flow, turbulence promoter, secondary flow, etc., have been devised for decreasing concentration polarization and fouling in order to increase the permeate flux [1]. In general, the method of gas–liquid two-phase flow is a simple and economical technique and is able to enhance permeate flux effectively in membrane filtration [1–7]. The introduction of air slugs into the liquid stream increases turbulence on the membrane surface and suppresses the formation of the concentration boundary layer, leading to an enhancement in the flux of the filtration process.
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Nomenclature C E J JH JV uG uL V VG VG,H VG,V
feed concentration (kg/m3 ) flux enhancement permeate flux (m3 /m2 s) permeate flux of horizontal membrane (m3 /m2 s) permeate flux of vertical membrane (m3 /m2 s) superficial gas velocity (m/s) superficial liquid velocity (m/s) flow velocity cross the membrane (m/s) velocity of gas bubble (m/s) velocity of gas bubble in horizontal tube (m/s) velocity of gas bubble in vertical tube (m/s)
Greek letters ε average error between predictions and experimental data Pi feed transmembrane pressure (Pa) θ inclination angle (◦ ) θm optimal inclination angle (◦ ) The influence of gas slugs on the flux enhancement depends on the resistance of the concentration polarization layer in the single liquid-phase ultrafiltration [1]. When the resistance of the polarization layer is large, i.e. the system is operated under the conditions of low liquid velocity, high transmembrane pressure or high feed concentration, a low gas flow rate cannot effectively disturb the concentration polarization layer. Thus, a certain threshold of gas velocity is required to disturb this layer. Beyond the critical gas velocity, gas slugs can enhance the permeate flux significantly. Therefore, the same permeate flux obtained in single liquid-phase ultrafiltration with a higher liquid velocity can be achieved with a lower liquid velocity by introducing a moderate velocity of gas slugs. The gas–liquid two-phase flow pattern in the membrane is an important factor in determining the performance of an air-sparging ultrafiltration system. The slug-flow pattern was thought to be the best flow regime for increasing permeate flux [4]. Effects of slug flow on the flux of ultrafiltration in a hollow-fiber
membrane and in a tubular membrane module were studied, respectively, by Cabassud et al. [6] and Mercier et al. [7]. For filtration at the slug flow, the membrane surface is alternately submitted to positive and negative shear stresses. The successive and unstable stresses were expected to prevent filtered particles from settling on the membrane surface and then enhancing the filtration mass transfer [6,7]. Experimental results of microfiltration [8] also showed that slug flow pattern is better than bubble flow pattern in enhancing the permeate flux. The model for calculating the mass transfer coefficients and the permeate fluxes in slug flow ultrafiltration was proposed by Ghosh and Cui [9]. In the model, the region near a gas slug is divided into three zones: falling film zone, wake zone, and liquid slug zone. Mercier-Bonin et al. [10] showed that the flux enhancement in the slug flow is related to the increase in the wall shear stress as well as to other phenomena: such as intermittency, reversal of the wall shear stress, instantaneous pressure variations, and the enhanced local mixing. It has been reported that the permeate flux for the upward flow in the vertically mounted membrane is about 10–20% higher than that in the horizontally installed membrane [3]. The experimental results [11] also showed that when the single liquid-phase ultrafiltration with a flat membrane channel cell was used with various orientations, the natural convection instability will enhance the flux at a unstable gravitational orientation (i.e. membrane above the flow channel). Some studies [12–15] showed that the rise velocity of a slug bubble in the tube with an inclination angle is larger than the rise velocity in a vertical or in a horizontal tube. Due to the higher rise velocity of the bubble in the inclined tube, the mass transfer for the two-phase flow in an inclined tube is higher than that in a vertical one [16], and the heat transfer in an inclined tube is higher than that in a horizontal one [17]. A pioneer study [18] on the flux behavior of ultrafiltration within an inclined tubular membrane shows that the flux usually keeps increasing as the inclination angle changes from 0 (horizontal) to 30 and 45◦ , then decreasing as the angle increases to 60 and 90◦ (vertical). This result implies that an optimal inclination angle exists in the ultrafiltration operation for obtaining the maximum permeate flux. In this study,
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more experiments of the ultrafiltration under various inclinations, especially between 45 and 60◦ , have been conducted in order to investigate the optimal inclination of the ultrafiltration system. The flux enhancement due to membrane inclination was discussed systemically under various operating parameters, such as liquid flow rate, gas flow rate, feed concentration, transmembrane pressure, etc. Finally, an equation for calculating the flux in an inclined-membrane ultrafiltration system and hence determining the optimal inclination angle was proposed.
2. Experiment The operated experimental set-up was described in a previous work [18]. This gas–liquid two-phase ultrafiltration system is operated in an inorganic tubular membrane module. The membrane medium used was a 15 kDa MWCO tubular ZrO2 /carbon membrane (M2 type, Tech-Sep) with 40.0 cm length, 6.0 mm internal diameter, and 75.4 cm2 effective membrane area. The tested solute was dextran T500 (Pharmacia) which was more than 99% retained by the membrane used. The solvent was distilled water. The inclination angles, θ , of the ultrafiltration column in this experimental work included 0, 30, 45, 50, 55, 60, and 90◦ . The superficial liquid velocities, uL , were 0.168, 0.336, and 0.672 m/s; and the superficial gas velocities, uG , were 0.04–0.32 m/s. According to the velocities, the value of air injection ratio, defined as uG /(uG + uL ), varies from 0.06 to 0.66. The feed transmembrane pressures, Pi , were 50–300 kPa. The feed concentrations were 4.0–16.0 kg/m3 , and the feed solution temperature was kept at 30◦ C by a thermostat. During the operation, the permeate and retentate are recycled into the feed tank in order to maintain a constant feed concentration. The flux ordinarily reaches steady state within 30 min. In the experiments, because the pressure drop along the membrane module is small, the feed transmembrane pressure is treated as the mean transmembrane pressure. After each experiment, the membrane was cleaned by high circulation and backflushing with 10% NaOH and 10% HNO3 aqueous solutions and pure water. The cleaning procedure was repeated until the original water flux had been restored.
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3. Results and discussion 3.1. Flow pattern The diameter of hollow fiber or tubular ultrafiltration membrane is usually in the order of millimeters. The flow regime of gas–liquid two-phase flow in a small diameter tube is different from that in a large diameter tube [19]. Barnea et al. [20] investigated the flow patterns of gas–liquid two-phase flow in small diameter tubes (4–12 mm). Their results showed that slug flow exists in the range of uG < 5.0 m/s and uL < 1.0 m/s for 4–12 mm vertical tubes and in the range of uG < 5.0 m/s and 0.1 m/s < uL < 1.0 m/s for 4–8 mm horizontal tubes. It is notable that when uG < 1.0 m/s, the liquid slug in the tube is free of entrained gas bubbles, contrary to what is observed in tubes of larger diameters. The observations of Laborie et al. [21] also indicate that the two-phase flow in vertical capillaries of 1–4 mm i.d. is slug flow when the air injection ratio varies between 0.17 and 0.67, and the liquid slug contains no small dispersed bubbles. With a vertical tube of 7 mm i.d., the slug flow regime was obtained when the injection ratio was between 0.25 and 0.9, while the bubble flow regime are obtained when the ratio is lower than 0.25 [8]. In this work, the diameter of the membrane tube used is 6.0 mm and the injection ratio is comprised between 0.06 and 0.66. Although, the effect of inclination on the gas–liquid flow pattern in a small diameter tube is still unknown and lacking in the current literature. According to the result of Vera et al. [8], the slug flow regime is assumed in the present tube when the air injection ratio is larger than 0.25. 3.2. Effect of inclination on flux of single-phase ultrafiltration Fig. 1 is the plot of permeate fluxes versus inclination angles for single liquid-phase ultrafiltration at various transmembrane pressures and feed velocities. As shown in the figure, the permeate flux increases with the increase in the transmembrane pressure as well as in the cross-flow velocity on the membrane. It also shows that the permeate flux varies slightly with the change in inclination angle. For example, at 100 kPa transmembrane pressure and 0.168 m/s liquid velocity, the fluxes are (2.23, 2.61 and 2.32) × 10−6 m3 /m2 s,
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Fig. 1. Permeate fluxes vs. inclination angles for liquid ultrafiltration under various transmembrane pressures.
Fig. 2. Permeate fluxes vs. inclination angles for liquid ultrafiltration under various feed concentrations.
respectively, for inclination angles of 0, 45 and 90◦ . The measurement accuracy of the experimental flux has been checked for confirming the influence of inclination on the flux. The flux of the operation with a 45◦ inclination is found to be the highest among those inclinations, and the flux of the vertical membrane operation is slightly higher than that in the horizontally installed membrane. The flux enhancement is between 1.10 and 1.17 as the membrane inclined from horizontal to 45◦ under those operating conditions. Fig. 2 is the plot of permeate fluxes versus inclination angles for various feed concentrations. As presented in the figure, the permeate flux decreases with the increase in feed concentration, and the membrane inclination affected slightly on the flux too. The flux with a 45◦ inclination is still the highest, however, the flux enhancement is small, between 1.10 and 1.16, under presented conditions. In the present liquid-phase ultrafiltration, the variation of inclination angle influences insignificantly on the flux. Tilting the membrane may induce a natural convection effect, and hence disturb the concentration polarization layer and enhance the permeate flux, however, the natural convection instability is important at a lower cross-flow velocity in which the forced convection is relatively weak [11]. The critical cross-flow velocity is about 0.1 m/s. In present single-phase ultrafiltration, the cross-flow velocity is
higher than 0.1 m/s, therefore, the effect of tilting the membrane on the permeate flux is not significant. 3.3. Effect of inclination on flux of two-phase ultrafiltration 3.3.1. Effect of velocities Fig. 3 represents the relationship between permeate fluxes and inclination angles under various gas velocities. The superficial liquid velocity was 0.168 m/s and the superficial gas velocity varied from 0.04
Fig. 3. Permeate fluxes vs. inclination angles under various gas velocities: uL = 0.672 m/s.
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to 0.16 m/s. The flux is enhanced by the introduction of gas slugs even with a low gas velocity (e.g. uG = 0.04 m/s), with the flux seeming to approach a limiting value as the gas velocity further increases. It is noticeable that the inclination does not influence the flux at 0 and 0.04 m/s gas velocity, that is, without sparging and at 0.19 air injection ratio that corresponds to bubble flow regime [8]. A dramatic enhancement in flux by tilting the membrane occurs as the gas velocity is above 0.08 m/s that corresponds to slug flow regime. The inclination angle influences the flux with a maximum obtained at 45◦ . The effect of inclination on flux under various liquid flow rates is shown in Fig. 4, where the gas velocity was 0.08 m/s and transmembrane pressure was 200 kPa. The flux enhancements at 45◦ inclination angle are 1.51, 1.20 and 1.18, respectively, for uL = 0.168, 0.336 and 0.672 m/s. Increasing liquid velocity will weaken the natural convection as well as the effect of inclination on the flux. However, it shows that the flux for uL = 0.168 m/s with a 45◦ inclination is higher than that of a uL = 0.336 m/s using a horizontally or vertically installed membrane. The method of tilting membrane can be used for enhancing the flux of gas-sparged ultrafiltration operated at a lower liquid velocity in order to reduce energy consumption or to recover the solutes which are mechanicalsensitive.
Fig. 4. Permeate fluxes vs. inclination angles under various liquid velocities: uG = 0.08 m/s.
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Fig. 5. Permeate fluxes vs. inclination angles under various feed concentrations and gas velocities: uL = 0.168 m/s.
3.3.2. Effect of feed concentration The effect of inclination on flux under various feed concentrations was shown in Fig. 5. The superficial liquid velocity was 0.168 m/s. At low gas velocity uG = 0.04 m/s, shown as the solid points in the figure, the flux enhancements are 1.18 and 1.20 for feed concentrations of 8.0 and 16.0 kg/m3 , respectively. For high gas velocity uG = 0.16 m/s, the flux enhancements are 1.18, 1.43 and 1.44, respectively, for feed concentrations of 4.0, 8.0 and 16.0 kg/m3 . These results show that flux enhancement increases with the increase in feed concentration. For a higher feed concentration, the extent of concentration polarization is more severe, so that the effect of inclination on disturbing the polarization layer is significant; hence the flux enhancement is larger for a concentrated feed. 3.3.3. Effect of transmembrane pressure Data for inspecting the effect of inclination under various transmembrane pressures were shown in Fig. 6. The applied transmembrane pressure varied from 100 to 300 kPa. At low pressure, the effect of inclination on flux enhancement is slight. When applied pressure increases up to 200 kPa or more, the flux significantly increases as the installation of membrane changes from the horizontal to vertical or other inclinations. These results imply that flux enhancement increases with the increase in transmembrane pressure. The flux enhancement reaches 1.46
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The correlation equation for the velocity of a gas bubble in an inclined tube, VG , can be expressed as [13] VG = VG,H cos θ + VG,V sin θ
(1)
where VG,H and VG,V are the velocities of the gas bubble measured at horizontal and vertical orientations, respectively. In ultrafiltration, the permeate flux usually increases with the flow velocity cross the membrane as J = aVb
Fig. 6. Permeate fluxes vs. inclination angles under various transmembrane pressures: uL = 0.168 m/s; uG = 0.16 m/s.
when operated at 300 kPa transmembrane pressure. The extent of concentration polarization phenomenon usually is severe at high transmembrane pressure. Inclination in the membrane will disturb the concentration polarization layer, especially if operated at higher transmembrane pressure. 3.4. Optimal inclination angle The experimental data, as shown in Fig. 3, show that the flux enhancement may grow up to 1.51 when the membrane is inclined from 0 to 45◦ . The enhancement in flux is achieved due to the natural convection instability, which is induced by inclining the ultrafiltration column. Especially, this effect is more significant in the case of lower liquid velocity [18]. The other factor for heightening the enhancement is the increase in forced convection or cross-flow velocity in an inclined slug-flow system. The gas slug velocity in the inclined tube is faster than that in the vertical tube, and the vertical one is faster than the horizontal [12–14]. Therefore, due to the higher bubble velocity as well as the cross-flow velocity, the permeate flux in the inclined system is larger than that in the vertical one, and the flux in the vertical system is larger than that in horizontal one. The experimental data also show that the optimal inclination angle of the membrane for ultrafiltration exists in the range between 45 and 60◦ .
(2)
where a and b are determined parameters, and V is the tangential liquid velocity in liquid-phase ultrafiltration or the mean flow velocity (=uG + uL ) in two-phase ultrafiltration. For slug flow in a small tube, the relationship between the gas bubble velocity and the mean flow velocity can be expressed as follows: VG = cV
(3)
where the value of the parameter c is between 1.0 and 1.2 [22]. Values of a and b, in Eq. (2), depend on the flow pattern in the tube. For single liquid-phase ultrafiltration, b is 0.8 for turbulent flow and is 0.33 for laminar flow [23]. For slug flow ultrafiltration, the model proposed by Ghosh and Cui [9] indicated that in the falling film zone, b is 0.8; in the wake zone, b also is 0.8; and in liquid slug zone, b is 0.8 for turbulent flow and is 0.33 for laminar flow. The flux calculated by the model agreed reasonably well with their experimental data. It also showed that the mass transfer in the liquid slug zone is more than an order of magnitude lower than that in the falling film zone or in the wake zone. Therefore, 0.8 is a reasonable value for b for the slug flow ultrafiltration system. Combination of Eqs. (1)–(3) and let b = 0.8, the equation for relating ultrafiltration flux with inclination angle was obtained as J = (JH1.25 cos θ + JV1.25 sin θ)0.8
(4)
where JH and JV are the fluxes measured at horizontal and vertical orientations, respectively. More experiments for measuring the fluxes with inclination angles between 45 and 60◦ were conducted. Figs. 7 and 8 show the experimental results of 4 and 16 kg/m3 feed concentration, respectively, in the condition of
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where N is the number of the experimental data, are <3%. Further, the optimal inclination angle (θ m ) of an inclined-membrane ultrafiltration can be also derived from Eq. (4) and expressed as θm = tan−1
Fig. 7. Optimal inclination angles for membrane ultrafiltration: C = 4.0 kg/m3 ; the solid lines are the predictions of Eq. (4).
0.12 m/s gas velocity, 0.168 m/s liquid velocity and a varying transmembrane pressure from 100 to 300 kPa. These experimental data show that the flux with a 50◦ inclination is higher than the flux with a 45◦ inclination. The predictions of Eq. (4) were also plotted in Figs. 7 and 8. The predictions agree well with the experimental data. Average errors between the experimental data and predictions, defined as follows: n=N |Jpre,n − Jexp,n |/Jexp,n ε = n=1 (5) N
JV JH
1.25 (6)
The optimal inclination angle can be determined from the values of JV and JH . The calculated values of θ m by using Eq. (6) and the experimental data of JV and JH under various operating conditions are listed in Table 1. For the two-phase ultrafiltration system operated at 0.168 m/s liquid velocity, whose flux is sensitive to the change in inclination angle, the optimal inclination angle is a bit over 50◦ , as shown in Table 1(a). These predictions of θ m agree well with the experimental measurements as shown in Figs. 7 and 8. When the system was operated at a higher liquid velocity (uL = 0.672 m/s), the calculated optimal inclination angles, listed in Table 1(b), are smaller than but close to 50◦ . Based on the present wide range operating conditions, the optimal inclination angle of a two-phase slug flow ultrafiltration system is close to 50◦ . The optimal angle is slightly affected by the flow velocities of liquid and gas, and is less sensitive to the transmembrane pressure and feed concentration. Table 1 Optimal inclination angles of membrane in the two-phase ultrafiltration Pi (kPa) uG (m/s) C = 4.0 kg/m3
C = 8.0 kg/m3 C = 16.0 kg/m3
0.08
0.12
0.08
0.08
0.12
52◦ 51◦ 51◦
50◦ 51◦ 51◦
50◦ 51◦ 51◦
52◦ 53◦ 53◦
(a) uL = 0.168 m/s 100 50◦ 200 51◦ 300 51◦
Fig. 8. Optimal inclination angles for membrane ultrafiltration: C = 16.0 kg/m3 ; the solid lines are the predictions of Eq. (4).
C = 4.0 kg/m3
C = 8.0 kg/m3 C = 16.0 kg/m3
0.08
0.16
0.16
0.08
0.16
46◦ 47◦ 48◦
48◦ 48◦ 48◦
48◦ 47◦ 47◦
48◦ 47◦ 48◦
(b) uL = 0.672 m/s 100 48◦ 200 47◦ 300 48◦
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4. Conclusions The effect of the inclination on the permeate flux of ultrafiltration was studied and discussed based on various operating parameters, such as superficial liquid velocity, superficial gas velocity, feed concentration and transmembrane pressure. The experiments were carried out in a tubular ceramic membrane module by using dextran T500 as tested solute. Inclination effectively enhances the flux of ultrafiltration at slug flow regime, while its influence is insignificant for liquid-phase ultrafiltration or at bubble flow regime. In the slug-flow ultrafiltration, the flux enhancement by inclining the membrane increases with increasing gas velocity, feed concentration, and transmembrane pressure, while it decreases with increasing liquid velocity. The flux may be enhanced more than 1.5 when the membrane is inclined from 0 to 50◦ . A model was also proposed for estimating the ultrafiltration flux in an inclined membrane system and determining the optimal inclination angle for maximum flux. The flux calculated from the correlation equation agrees very well with the experimental data. The optimal inclination angle of the membrane in a slug-flow ultrafiltration is close to 50◦ .
Acknowledgements The author wishes to express his appreciation to the National Science Council of Taiwan, ROC for financial aid. References [1] T.-W. Cheng, H.M. Yeh, C.T. Gau, Enhancement of permeate flux by gas slugs for cross-flow ultrafiltration in tubular membrane module, Sep. Sci. Technol. 33 (1998) 2295. [2] C.K. Lee, W.G. Chang, Y.H. Ju, Air slugs entrapped cross-flow filtration of bacterial suspensions, Biotechnol. Bioeng. 41 (1993) 525. [3] Z.F. Cui, K.I.T. Wright, Gas–liquid two-phase cross-flow utrafiltration of BSA and dextran solution, J. Membr. Sci. 90 (1994) 183. [4] M. Mercier, C. Fonade, C. Lafforgue-Delorme, Influence of the flow regime on the efficiency of a gas–liquid two-phase medium filtration, Biotechnol. Tech. 9 (1995) 853.
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