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Experimental investigations of cake characteristics in crossflow microfiltration
Chemical Engineering Science 54 (1999) 4023}4030
Experimental investigations of cake characteristics in cross#ow micro"ltration M. Hamachi , M. Mietton-Peuchot * Laboratoire de Ge& nie Chimique, CNRS/UMR 5503, 18 Chemin de la loge, 31078 Toulouse, France Universite& Victor Segalen Bordeaux 2, Faculte& d+Oenologie, 351 cours de la libe& ration, 33405 Talence Cedex, France Received 19 June 1998; accepted 3 February 1999
Abstract The fundamental analysis of deposit characteristics requires the knowledge of a size key that is di$cult to obtain in cross#ow "ltration, which is the geometric characterization of the deposit and most especially its thickness. The measurement in situ of this size with an optical captor which will not alter the characteristics of the deposit allows to have complete information on deposit characteristics. The e!ects of di!erent operating parameters on permeability, resistance, porosity and compressibility are discussed and lead to that the initial layers of the deposit constitute the determining resistance. The deposit is not homogeneous and the compressibility coe$cient depends on concentration. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Cross#ow micro"ltration; Membrane; Bentonite suspension; Permeability; Deposit resistance; Porosity; Cake thickness
1. Introduction During cross#ow micro"ltration of bentonite suspension, retained particles lead to modi"cations in the structure and properties of the "ltering medium. So, the increase in deposit thickness translates, at "rst, into a quick drop in permeate #ux, which will then stabilise after several minutes thanks to the forces of shear stress. This drop in #ux is attributable, according to several authors (Ficher and Raasch, 1986; Lu and Ju, 1989), to "ne particles, which are less likely to be swept away by the shear stress: such particles accumulate on the membrane and bring about a reduced porosity. These authors thus show the existence of a selective phenomenon of particles deposition during cross#ow micro"ltration. An experimental study of Rushton et al. (1980) concerning fragments of calcium salts and magnesium carbonates shows that for a concentration superior to a certain threshold value, the speci"c resistance will fall with decreased concentration. The authors assume that increased concentration will lead to increased frequency of particles adding to the deposit. Moreover, the density of the deposit is seen in terms of an arrangement of
*Correspondig author. Tel.: (33) 05.56.84.64.95.
particles, which can only come about if the number of particles arriving simultaneously at the deposit layer, yet build-up, is limited. The decrease in speci"c resistance, when the concentration is increased, is put down to a disordering in the arrangement of particles during the deposit constitution, thus leading to greater porosity. Various other studies are based on the concept of particle arrangement within the deposit; the conclusions which these studies reach are all the more questionable as they are sometimes contradictory. These contradictions may be put down to the di!erence in particle types and the various di!erent operating conditions underlying each experiment. All these latter studies reveal a lack of knowledge about deposit structure. To better understand the mechanisms of membrane fouling, the direct measurement of deposit thickness (Hamachi and Mietton Peuchot, 1996) allows the analysis of bentonite deposit structure as a function of operating conditions.
2. Materials and methods The experiments are carried out using a conventional cross#ow micro"ltration pilot, together with a laser device to measure deposit thickness (Fig. 1).
0009-2509/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 9 ) 0 0 1 0 1 - 3
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M. Hamachi, M. Mietton-Peuchot/Chemical Engineering Science 54 (1999) 4023}4030
2.1. Crossyow microxltration system The #ow rate within the "ltration loop is maintained by the centrifugal pump (P) and determined by the #owmeter (D). The heat exchanger (E) placed between the feedtank (R) and the "ltering module allows regulation of the suspension temperature to 20$23C. The gates (V1) and (V2) allow the regulation and adjustment of transmembrane pressure, indicated by the average value of the two manometers (M1) and (M2). The instantaneous "ltrate #ux is estimated using the accumulated mass, continuously measured by means of the Sartorius scales (Ba). The deposit measuring process requires the use of a rigid tubular membrane with an external skin, and a suspension which prevent internal fouling so the deposit may be more accurately characterised. So, we use a membrane with pore diameters less than the smallest particles present in the suspension. The tubular membrane (T1-70) provided by SCT-US Filter (France) has an external alumina skin, a nominal pore size of 0.2 lm and an inner diameter of 6 mm. The length of the module is 25 cm. The permeate #ux with water is about 3m/mh at 10 Pa. The suspension of Volclay SPV bentonite used is prepared using distilled water, "ltered to 30 lm 24 hours before the experiment, so that all variation in particle size is avoided. Furthermore, it is subjected to ultrasonics in order to make sure that particles are well dispersed in the suspension. A particle distribution analysis using Malvern granulometer identi"ed a range of particles sizes from 0.77 to 7.54 lm centered around 2.45 lm. 2.2. Deposit thickness measurement technique The measurement technique of the deposit thickness is based on the use of He}Ne laser beam and an optical captor, it relies on the absorption of light by the deposit. The laser beam is focussed tangentially onto the membrane surface, the image of the focal point is then picked up on the photomultiplier, which allows immediate measurement of the signal. The formation of the deposit on the membrane surface translates into an absorption of light. The variation of the intensity of the signal corresponds directly to the deposit thickness through a calibration curve which is recorded at the beginning of the experiment. This calibration curve links the signal fading to the displacement of the membrane, so during the deposit formation we assume that the deposit thickness is equivalent to the displacement. In plotting each experimental value against this curve, the total thickness of the deposit may be determined at any time (Hamachi and Mietton Peuchot, 1996). The luminous intensity of the focal point, as well as that of the initial laser beam (a reference signal) are provided respectively by the photomultiplier and the photocell. These two operational parameters are simulta-
neously recorded by the system designed for monitoring experimental data. 2.3. Operating parameters The transmembrane pressures examined, 110, 160 and 210 kPa, correspond to the order of pressures likely to be encountered for water treatment, and the average cross#ow velocities studied are between 0.055 and 0.552 m/s. The corresponding Reynolds numbers and the #ow rate nature are presented in Table 1. The concentration of the solution is set at between 0.05 and 0.375 g/l, beyond which the measurement of deposit thickness is made di$cult by the turbidity of the solution.
3. Results and discussion 3.1. Ewect of diwerent operating conditions The increase in deposit thickness as a function of volume "ltered is linear in the "rst phase of the process, before reaching a level where it stabilises, starting from a certain volume of "ltrate as a function of cross#ow velocity (Fig. 2). For cross#ow velocities less than 0.193 m/s, deposit stabilisation doesn't start to occur until reaching a volume of "ltrate of around 350 l/m. Despite the presence of a cross#ow velocity, the evolution of the deposit thickness is linked to the "ltrate #ux, i.e. the #ux of particles carried to the membrane by convection. During the initial phase, the cross#ow velocity has little e!ect on deposit build-up: in e!ect, this factor will only begin to be felt after a volume of "ltrate of around 100 l/m. The deposit thickness and the permeate #ux plotted against time, with a constant concentration and cross#ow velocity, show that the increase of pressure (110 to 210 kPa), causes more important deposit thickness (Fig. 3). This aspect becomes ever more apparent when the "ltration time is lengthened. Even if the thickness of the deposit grows with pressure, the evolution of #ux remains almost the same, and tends towards identical values (20 l/mh). This would therefore imply that the deposit structure should evolve according to transmembrane pressure. The e!ect of concentration on deposit thickness evolution (Fig. 4), at a "xed pressure and cross#ow velocity, shows that for an identical volume of "ltrate, the greater the concentration, the more pronounced the deposit becomes. For a weak concentration (0.05 g/l), the deposit build-up is very slow (thickness less than 80 lm) compared to higher concentrations (thickness until 500 lm) and its development seems to be linear. Furthermore, it is observed (Hamachi, 1997) that over time the permeate #ux and the deposit thickness always tend towards constant values in a state of equilibrium.
M. Hamachi, M. Mietton-Peuchot/Chemical Engineering Science 54 (1999) 4023}4030
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Fig. 1. Filtration pilot (M1, M2: manometers; V1, V2, V3, V4: gates; D: #owmeter; R: feedtank; Ba: scale; P: pump; E: heat exchanger); Laser measuring device (PM: Photomultiplier; PC: Photocell; LM: Glass strip).
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Table 1 Cross#ow velocities and corresponding Reynolds numbers Flow rate regime
Laminar
Cross#ow velocities (m/s) Re
0.055 660
Turbulent 0.11 1300
0.19 2300
0.30 3600
0.41 5000
0.55 6600
Fig. 2. E!ect of cross#ow velocity on deposit build-up as a function of cumulative volume (DP"110 kPa; c"0.375 g/l).
Fig. 4. E!ect of concentration on deposit build-up as a function of cumulative volume (u"0.055 m/s; DP"110 kPa).
Fig. 3. E!ect of transmembrane pressure on deposit build-up and permeate #ux (u"0.11 m/s; c"0.375 g/l).
Fig. 5. Evolution of the product of deposit thickness and permeate #ux values for di!erent cross#ow velocities (DP"110 kPa; c"0.05 g/l).
This important "nding led us, "rst, to focus on deposit permeability.
As the permeate #ux (J) and the thickness of the cake (ep ) tend towards a limit, the product (J;ep ) also E E inevitably tends towards a limit value. For a constant concentration and pressure, all the various curves converge towards the same limit point, whatever the cross#ow velocity (Fig. 5). Moreover, as over time the deposit resistance becomes preponderant in proportion to the membrane resistance (R ), the latter may be negliged in comparison to the cake K thickness, thus giving us, after simpli"cation
3.2. Deposit structure analysis 3.2.1. Permeability at the equilibrium Darcy's law is related to the hydraulic resistance. In our case, this resistance is the sum of the initial membrane resistance (R ) and the deposit resistance (R ). The K E permeate #ux may be written as DP J" . k(R #R ) E K
B J;ep " DP. E k
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Table 2 Permeability as a function of concentration and pressure C (g/l)
DP (kPa)
J;ep E (;10\/3600 m/s)
B (m)
0.375
110 160 210
6482 7666 8239
1.637E!17 1.331E!17 1.089E!17
0.25
110 160 210
5276 7084 7198
1.332E!17 1.230E!17 0.952E!17
0.05
110
5150
1.300E!17 Fig. 6. Evolution of the permeate #ux as a function of deposit thickness for various concentrations (u"0.055 m/s; DP"110 kPa).
Given that the viscosity of the suspension and the transmembrane pressure are constant, the permeability of the deposit must also be constant, whatever the cross#ow velocity, for a constant pressure and concentration. For each of the pressures and concentrations tested, the product of the limit of permeate #ux and the limit of deposit thickness is set out in Table 2, as well as the corresponding permeability in each case. The permeability of the deposit drops systematically as transmembrane pressure increases (for a given concentration), this may be attributable to compressibility of the deposit or fouling of the deposit with "ne particles due to higher volumes "ltered at high pressures. This explains the evolution of the permeate #ux as a function of deposit thickness, linked to pressure (Fig. 3). Moreover, the permeability drops with concentration. Fig. 6 shows that for the same deposit thickness, the permeate #ux is all the greater with more signi"cant concentrations. One reason for this could be that suspensions at weak concentrations contain fewer large particles and thus their deposits are less permeable. This leads us back to the hypothesis of Rjimati and Grasmick (1991), who report that increased concentration is accompanied by increase in the proportion of larger particles to the detriment of smaller ones. 3.2.2. Deposit resistance during xltration The knowledge of #ow rates and thickness of deposit during "ltration allows to calculate the resistance for di!erent deposit thicknesses. Following the Darcy law, the total resistance (R ) of the porous medium is the sum R of the resistance of the membrane (R ) and that of the K deposit (R ) E DP R "R #R " . R K E kJ The resistance of the clean membrane being known, and assuming that particles are being retained only at the surface of the membrane (size of smallest particle: 0.77 lm, membrane pore size: 0.2 lm), we can deter-
Fig. 7. Deposit resistance variation as a function of its thickness for various concentrations (u"0.055 m/s; DP"110 kPa).
mine the resistance of the deposit at any moment R "R !R . The evolutions of the deposit resistance E R K as a function of thickness, for di!erent concentrations, are presented in Fig. 7 and show that deposit resistance grows as concentration drops. This con"rms the remark on the permeability mentioned above. As a function of cross#ow velocity of the suspension, and according to deposit thickness, resistance tends to increase with velocity over an initial period, and then to decrease again after a velocity of 0.193 m/s has been reached (Fig. 8). The resistance of the deposit is increasingly signi"cant as its thickness grows, whatever the cross#ow velocity. For a given thickness of deposit, the resistance grows with pressure, this growth becoming all the more signi"cant for greater thicknesses (Fig. 9). Previous studies concerning frontal "ltrations of clay have shown the compressibility of the cakes when the pressure is increased (Yim, 1984). Considering the bentonite deposit formed during cross#ow "ltration, we can assume that the increase of deposit resistance observed is mainly due to the compressibility.
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Fig. 8. Deposit resistance variation at a given thickness as a function of cross#ow velocity (*P"110 kPa; c"0.25 g/l).
Fig. 9. Deposit resistance variation at a given thickness as a function of transmembrane pressure (u"0.193 m/s; c"0.375 g/l).
3.2.3. Specixc resistance and compressibility of the deposit Available literature contains several di!erent studies relating to how operating conditions may a!ect speci"c resistance of deposits during cross#ow micro"ltration. The in#uence of pressure, through compression of deposit, is not disputed in these studies. By means of a speci"c experimental device Murase et al. (1988) have determined speci"c resistance values (a) for kaolin suspensions, these being in full agreement with standard "ltration theory and dependent on the transmembrane pressure. This is given under the form: a"A DP@. In our case, speci"c resistances for the bentonite deposits may be estimated using the relation: a"R S /M , E K E where the mass of the deposit (M ) is calculated by E M "p.ep .l.(ep #2R)(1!e)o . E E E @ Fig. 10 shows, for two concentrations, the relationship linking a and DP, and displays the way in which speci"c resistance depends upon transmembrane pressure. Furthermore, it would seem that the compressibility coe$cient depends upon concentration: it is higher as the
Fig. 10. E!ect of concentration on speci"c resistance as a function of transmembrane pressure.
concentration increases, this coe$cient values varies from 0.54 to 0.73 for the concentrations of 0.25 and 0.375 g/l respectively. Even though during experimentation the constant &&A'' varies, it nevertheless maintains the same order of size. The in#uence of concentration on the compressibility coe$cient may be due to the very signi"cant deposit thicknesses produced at higher concentrations: the measurement of deposit thickness become more precise and so the perceived role of compressibility becomes more obvious. As it has been shown above that the initial deposit is made up of "ne particles, the subsequent deposit having a lower hydraulic resistance and seeming to be homogeneous, it is probable that the initial deposit will stay the same under all test conditions. The "nal deposit having a di!erent thickness, the proportions of "ne and larger particles are not therefore the same. This might explain the di!erence encountered in compressibility coe$cient. For a concentration of 0.375 g/l, the estimated compressibility coe$cient is slightly lower than that given by Chloe et al. (1986) or Gourgues (1991) (Table 3). In contrast, for a concentration of 0.25 g/l, this coe$cient is very di!erent from that given by the cited authors. The compressibility coe$cient for bentonite recently reported by Murase et al. (1995) obtained through a relationship of the type: a"a #a .DP@ seems too high with regard to the scale of pressures in action, all the more so as the average diameter of bentonite particles (2.2 lm) used for their experiments is of roughly the same order as the bentonite used in this study (2.45 lm). The working pressure signi"cantly in#uences the compressibility coe$cient and con"rms the kaolin example, according to values published by Murase et al. in both 1995 and 1988, for varying pressures (Table 3). 3.2.4. Deposit porosity Knowing the size of particles and the permeability of the deposit, the Carman}Kozeny equation allows to
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M. Hamachi, M. Mietton-Peuchot/Chemical Engineering Science 54 (1999) 4023}4030 Table 3 Comparison of compressibility coe$cients Authors
Particles
Pressure range (kPa)
Compressibility coe$cient
Chloe et al. (1986) Murase et al. (1988) Gourgues (1991) Murase et al. (1995)
Bentonite Kaolin Bentonite Bentonite Kaolin Bentonite
50}500 981}6860 25}150 10}60 50}400 110}210
0.84 0.88 0.83 0.96 0.46 0.54}0.73
Hamachi (1997)
Fig. 11. Deposit porosity variation as a function of its thickness for di!erent cross#ow velocities (DP"210 kPa; c"0.375 g/l).
Fig. 12. Deposit porosity variation as a function of transmembrane pressure for di!erent cross#ow velocities (c"0.375 g/l; ep"200 lm).
determine the theoretical porosity of the deposit using experimental values and taking into account thickness of deposit and permeate #ux.
ity) as a function of h . Between 3 and 7, the variation in I this constant gives more-or-less the same average porosity, varying between 8.5 and 11%, and is comparable to values given in existing literature (Table 4). The calculated average porosity corresponds to that suggested by Bourden (1990), who use the cake "ltration theory. The porosity of 80}95% reported by Wandelt (1993) corresponds to the porosity of a dry deposit.
1 de ep E , B" E" 36h (1!e) R I E where h is the Kozeny constant (taken as equal to 5) and I d the Sauter diameter (d "1.63 lm). E E Generally, the porosity of the bentonite deposit tends to increase with thickness (Fig. 11), due to a selective deposition of the particles. At the beginning of the "ltration process, the deposit is made up of "ner particles provoking the rapid decrease in permeate #ux (Fig. 6). The "ne particles create deposits with a great resistance. Gradually the thickeness of the deposit increased with larger particles, con"rming the observations of Ficher (1987). However, the average porosity seems to be stabilised as thickness increases. For di!erent cross#ow velocities of the suspension, Fig. 12 shows the decrease of the porosity as the transmembrane pressure increases. The in#uence of cross#ow velocity on the porosity seems limited. The average porosity, calculated using the Carman} Kozeny equation, is around 10% for a constant h "5. I Applying this value of h for an average porosity of the I deposit, one can study the sensitivity of this factor (poros-
4. Conclusion The analysis of the deposit characteristics for bentonite allows better understanding of the mechanisms of membrane surface fouling, through measurements of deposit thicknesses. The evolution of the deposit thickness as a function of cumulative volume shows that despite the presence of a cross#ow velocity, the deposit is directly linked to the convective #ux of matter bringing to the membrane. The initial layers of bentonite deposit constitute the higher resistance, and even if the deposit continues to grow, any further decrease in the permeate #ux is limited. The deposit formed is not homogeneous and its permeability tends towards a constant value, whatever the cross#ow velocity, for a given pressure and concentration. The in#uence of concentration may lead to
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M. Hamachi, M. Mietton-Peuchot/Chemical Engineering Science 54 (1999) 4023}4030
Table 4 Comparison of porosity Authors
Particles
Pressure (kPa)
Porosity
Bourden (1990) Blake et al. (1992) Wandelt (1993)
Bentonite Latex Bentonite Latex Bentonite
85}185 200 30}125 30}125 110}210
10% 36% 80}95% 30}40% 10%
Hamachi (1997)
increased permeability. The deposit is compressible, and the compressibility coe$cient depends on concentration, varying from 0.54 to 0.73. Carman}Kozeny equation allows the bentonite cake porosity to be determined, for which the calculated average value (10%) corresponds to that given in previous literature in this "eld.
Notation A B c d E ep E ep K h I J l M E R S K
constant deposit permeability, m suspension concentration, kg/m the Sauter diameter, m deposit thickness, m thickness of the membrane "ltering layer, m Kozeny constant permeate #ux, l/h m useful length of membrane, m deposit mass, kg membrane radius, m surface area of the membrane, m
Greek letters a b DP k o @ e
speci"c resistance of the deposit, m/kg compressibility coe$cient transmembrane pressure, Pa dynamic viscosity of water, kg/m s volumic mass of the swollen bentonite, kg/m cake porosity
References Blake, N.J., Cumming, I.W., & Streat, M. (1992). Prediction of steady state cross#ow "ltration using a force balance model. Journal of Membrane Science, 68, 205}216.
Bourden, S. (1990). CaracteH risation par capteur optique de l'eH volution spatio-temporelle du deH po( t formeH lors de la "ltration sur "bre creuse. The% se de doctorat, INP Toulouse, France. Chloe, T.B., Masse, P., Verdier, A., & Clifton, M.J. (1986). Flux decline in batch ultra"ltration: concentration, polarization and cake formation. Journal of Membrane Science, 26, 1}15. Ficher, E. (1987). Untersuchungen zum Trennprozess bei der Querstrom"ltratio. Dissertation, TU Karlsruhe. Ficher, E., & Raasch, J. (1986). Model tests of the particle deposition at the "lter medium. In Proceeding of the 4th World Filtration Congress, Belgium, 11}17 November 1986. Gourgues, C. (1991). Ultra"ltration de suspensions de bentonite par des "bres creuses: production d'eau potable. The% se de doctorat, UPS Toulouse, France. Hamachi, M. (1997). Mesure dynamique de l'eH paisseur du deH po( t a` l'aide d'un capteur optique et modeH lisation par reH seau de neurones de la micro"ltration tangentielle de suspensions. The% se de doctorat, INP Toulouse, France. Hamachi, M., & Mietton Peuchot, M. (1996). Dynamic measurement of deposit thickness on inorganic membrane. In Proceedings of the 4th International Conference on Inorganic Membranes, Gatlinburg, Tennessee, U.S.A. Lu, W., & Ju, S.C. (1989). Selective particle deposition in cross#ow "ltration. Separation of Science and ¹echnology, 24, 517}540 Murase, T., Iwata, M., Kato, I., Lee, W.D., & Shirato, M. (1988). Determination of speci"c resistance of highly compressed cake by use expression data. Journal of Chemical Engineering of Japan, 21 (2), 204}206. Murase, T., Ohn, T., & Kimata, K. (1995). Filtrate #ux in cross#ow micro"ltration of dilute suspension forming a highly compressed fouling cake layer. Journal of Membrane Science, 108, 121}128. Rjimati, E., & Grasmick, A. (1991). Micro"ltration tangentielle d'une suspension de bentonite. Entropie, 163, 23}30. Rushton, A., Hosseini, M., & Hassan, I. (1980). The e!ect of velocity and concentration on "lter cake resistance. Journal of Separation Proceedings ¹echnology, 1 (3), 34}41. Wandelt, B. (1993). Analyse de la formation des deH po( ts de particules lors d'un proceH deH d'ultra"ltration tangentielle. Visualisation par imagerie a` reH sonance magneH tique nucleH aire. The% se de doctorat, INP Toulouse, France. Yim, S.S. (1984). Filtration sur ga( teau compressible. The% se de doctorat, INP Toulouse, France.
Experimental investigations of cake characteristics in cross#ow micro"ltration M. Hamachi , M. Mietton-Peuchot * Laboratoire de Ge& nie Chimique, CNRS/UMR 5503, 18 Chemin de la loge, 31078 Toulouse, France Universite& Victor Segalen Bordeaux 2, Faculte& d+Oenologie, 351 cours de la libe& ration, 33405 Talence Cedex, France Received 19 June 1998; accepted 3 February 1999
Abstract The fundamental analysis of deposit characteristics requires the knowledge of a size key that is di$cult to obtain in cross#ow "ltration, which is the geometric characterization of the deposit and most especially its thickness. The measurement in situ of this size with an optical captor which will not alter the characteristics of the deposit allows to have complete information on deposit characteristics. The e!ects of di!erent operating parameters on permeability, resistance, porosity and compressibility are discussed and lead to that the initial layers of the deposit constitute the determining resistance. The deposit is not homogeneous and the compressibility coe$cient depends on concentration. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Cross#ow micro"ltration; Membrane; Bentonite suspension; Permeability; Deposit resistance; Porosity; Cake thickness
1. Introduction During cross#ow micro"ltration of bentonite suspension, retained particles lead to modi"cations in the structure and properties of the "ltering medium. So, the increase in deposit thickness translates, at "rst, into a quick drop in permeate #ux, which will then stabilise after several minutes thanks to the forces of shear stress. This drop in #ux is attributable, according to several authors (Ficher and Raasch, 1986; Lu and Ju, 1989), to "ne particles, which are less likely to be swept away by the shear stress: such particles accumulate on the membrane and bring about a reduced porosity. These authors thus show the existence of a selective phenomenon of particles deposition during cross#ow micro"ltration. An experimental study of Rushton et al. (1980) concerning fragments of calcium salts and magnesium carbonates shows that for a concentration superior to a certain threshold value, the speci"c resistance will fall with decreased concentration. The authors assume that increased concentration will lead to increased frequency of particles adding to the deposit. Moreover, the density of the deposit is seen in terms of an arrangement of
*Correspondig author. Tel.: (33) 05.56.84.64.95.
particles, which can only come about if the number of particles arriving simultaneously at the deposit layer, yet build-up, is limited. The decrease in speci"c resistance, when the concentration is increased, is put down to a disordering in the arrangement of particles during the deposit constitution, thus leading to greater porosity. Various other studies are based on the concept of particle arrangement within the deposit; the conclusions which these studies reach are all the more questionable as they are sometimes contradictory. These contradictions may be put down to the di!erence in particle types and the various di!erent operating conditions underlying each experiment. All these latter studies reveal a lack of knowledge about deposit structure. To better understand the mechanisms of membrane fouling, the direct measurement of deposit thickness (Hamachi and Mietton Peuchot, 1996) allows the analysis of bentonite deposit structure as a function of operating conditions.
2. Materials and methods The experiments are carried out using a conventional cross#ow micro"ltration pilot, together with a laser device to measure deposit thickness (Fig. 1).
0009-2509/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 9 ) 0 0 1 0 1 - 3
4024
M. Hamachi, M. Mietton-Peuchot/Chemical Engineering Science 54 (1999) 4023}4030
2.1. Crossyow microxltration system The #ow rate within the "ltration loop is maintained by the centrifugal pump (P) and determined by the #owmeter (D). The heat exchanger (E) placed between the feedtank (R) and the "ltering module allows regulation of the suspension temperature to 20$23C. The gates (V1) and (V2) allow the regulation and adjustment of transmembrane pressure, indicated by the average value of the two manometers (M1) and (M2). The instantaneous "ltrate #ux is estimated using the accumulated mass, continuously measured by means of the Sartorius scales (Ba). The deposit measuring process requires the use of a rigid tubular membrane with an external skin, and a suspension which prevent internal fouling so the deposit may be more accurately characterised. So, we use a membrane with pore diameters less than the smallest particles present in the suspension. The tubular membrane (T1-70) provided by SCT-US Filter (France) has an external alumina skin, a nominal pore size of 0.2 lm and an inner diameter of 6 mm. The length of the module is 25 cm. The permeate #ux with water is about 3m/mh at 10 Pa. The suspension of Volclay SPV bentonite used is prepared using distilled water, "ltered to 30 lm 24 hours before the experiment, so that all variation in particle size is avoided. Furthermore, it is subjected to ultrasonics in order to make sure that particles are well dispersed in the suspension. A particle distribution analysis using Malvern granulometer identi"ed a range of particles sizes from 0.77 to 7.54 lm centered around 2.45 lm. 2.2. Deposit thickness measurement technique The measurement technique of the deposit thickness is based on the use of He}Ne laser beam and an optical captor, it relies on the absorption of light by the deposit. The laser beam is focussed tangentially onto the membrane surface, the image of the focal point is then picked up on the photomultiplier, which allows immediate measurement of the signal. The formation of the deposit on the membrane surface translates into an absorption of light. The variation of the intensity of the signal corresponds directly to the deposit thickness through a calibration curve which is recorded at the beginning of the experiment. This calibration curve links the signal fading to the displacement of the membrane, so during the deposit formation we assume that the deposit thickness is equivalent to the displacement. In plotting each experimental value against this curve, the total thickness of the deposit may be determined at any time (Hamachi and Mietton Peuchot, 1996). The luminous intensity of the focal point, as well as that of the initial laser beam (a reference signal) are provided respectively by the photomultiplier and the photocell. These two operational parameters are simulta-
neously recorded by the system designed for monitoring experimental data. 2.3. Operating parameters The transmembrane pressures examined, 110, 160 and 210 kPa, correspond to the order of pressures likely to be encountered for water treatment, and the average cross#ow velocities studied are between 0.055 and 0.552 m/s. The corresponding Reynolds numbers and the #ow rate nature are presented in Table 1. The concentration of the solution is set at between 0.05 and 0.375 g/l, beyond which the measurement of deposit thickness is made di$cult by the turbidity of the solution.
3. Results and discussion 3.1. Ewect of diwerent operating conditions The increase in deposit thickness as a function of volume "ltered is linear in the "rst phase of the process, before reaching a level where it stabilises, starting from a certain volume of "ltrate as a function of cross#ow velocity (Fig. 2). For cross#ow velocities less than 0.193 m/s, deposit stabilisation doesn't start to occur until reaching a volume of "ltrate of around 350 l/m. Despite the presence of a cross#ow velocity, the evolution of the deposit thickness is linked to the "ltrate #ux, i.e. the #ux of particles carried to the membrane by convection. During the initial phase, the cross#ow velocity has little e!ect on deposit build-up: in e!ect, this factor will only begin to be felt after a volume of "ltrate of around 100 l/m. The deposit thickness and the permeate #ux plotted against time, with a constant concentration and cross#ow velocity, show that the increase of pressure (110 to 210 kPa), causes more important deposit thickness (Fig. 3). This aspect becomes ever more apparent when the "ltration time is lengthened. Even if the thickness of the deposit grows with pressure, the evolution of #ux remains almost the same, and tends towards identical values (20 l/mh). This would therefore imply that the deposit structure should evolve according to transmembrane pressure. The e!ect of concentration on deposit thickness evolution (Fig. 4), at a "xed pressure and cross#ow velocity, shows that for an identical volume of "ltrate, the greater the concentration, the more pronounced the deposit becomes. For a weak concentration (0.05 g/l), the deposit build-up is very slow (thickness less than 80 lm) compared to higher concentrations (thickness until 500 lm) and its development seems to be linear. Furthermore, it is observed (Hamachi, 1997) that over time the permeate #ux and the deposit thickness always tend towards constant values in a state of equilibrium.
M. Hamachi, M. Mietton-Peuchot/Chemical Engineering Science 54 (1999) 4023}4030
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Fig. 1. Filtration pilot (M1, M2: manometers; V1, V2, V3, V4: gates; D: #owmeter; R: feedtank; Ba: scale; P: pump; E: heat exchanger); Laser measuring device (PM: Photomultiplier; PC: Photocell; LM: Glass strip).
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Table 1 Cross#ow velocities and corresponding Reynolds numbers Flow rate regime
Laminar
Cross#ow velocities (m/s) Re
0.055 660
Turbulent 0.11 1300
0.19 2300
0.30 3600
0.41 5000
0.55 6600
Fig. 2. E!ect of cross#ow velocity on deposit build-up as a function of cumulative volume (DP"110 kPa; c"0.375 g/l).
Fig. 4. E!ect of concentration on deposit build-up as a function of cumulative volume (u"0.055 m/s; DP"110 kPa).
Fig. 3. E!ect of transmembrane pressure on deposit build-up and permeate #ux (u"0.11 m/s; c"0.375 g/l).
Fig. 5. Evolution of the product of deposit thickness and permeate #ux values for di!erent cross#ow velocities (DP"110 kPa; c"0.05 g/l).
This important "nding led us, "rst, to focus on deposit permeability.
As the permeate #ux (J) and the thickness of the cake (ep ) tend towards a limit, the product (J;ep ) also E E inevitably tends towards a limit value. For a constant concentration and pressure, all the various curves converge towards the same limit point, whatever the cross#ow velocity (Fig. 5). Moreover, as over time the deposit resistance becomes preponderant in proportion to the membrane resistance (R ), the latter may be negliged in comparison to the cake K thickness, thus giving us, after simpli"cation
3.2. Deposit structure analysis 3.2.1. Permeability at the equilibrium Darcy's law is related to the hydraulic resistance. In our case, this resistance is the sum of the initial membrane resistance (R ) and the deposit resistance (R ). The K E permeate #ux may be written as DP J" . k(R #R ) E K
B J;ep " DP. E k
M. Hamachi, M. Mietton-Peuchot/Chemical Engineering Science 54 (1999) 4023}4030
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Table 2 Permeability as a function of concentration and pressure C (g/l)
DP (kPa)
J;ep E (;10\/3600 m/s)
B (m)
0.375
110 160 210
6482 7666 8239
1.637E!17 1.331E!17 1.089E!17
0.25
110 160 210
5276 7084 7198
1.332E!17 1.230E!17 0.952E!17
0.05
110
5150
1.300E!17 Fig. 6. Evolution of the permeate #ux as a function of deposit thickness for various concentrations (u"0.055 m/s; DP"110 kPa).
Given that the viscosity of the suspension and the transmembrane pressure are constant, the permeability of the deposit must also be constant, whatever the cross#ow velocity, for a constant pressure and concentration. For each of the pressures and concentrations tested, the product of the limit of permeate #ux and the limit of deposit thickness is set out in Table 2, as well as the corresponding permeability in each case. The permeability of the deposit drops systematically as transmembrane pressure increases (for a given concentration), this may be attributable to compressibility of the deposit or fouling of the deposit with "ne particles due to higher volumes "ltered at high pressures. This explains the evolution of the permeate #ux as a function of deposit thickness, linked to pressure (Fig. 3). Moreover, the permeability drops with concentration. Fig. 6 shows that for the same deposit thickness, the permeate #ux is all the greater with more signi"cant concentrations. One reason for this could be that suspensions at weak concentrations contain fewer large particles and thus their deposits are less permeable. This leads us back to the hypothesis of Rjimati and Grasmick (1991), who report that increased concentration is accompanied by increase in the proportion of larger particles to the detriment of smaller ones. 3.2.2. Deposit resistance during xltration The knowledge of #ow rates and thickness of deposit during "ltration allows to calculate the resistance for di!erent deposit thicknesses. Following the Darcy law, the total resistance (R ) of the porous medium is the sum R of the resistance of the membrane (R ) and that of the K deposit (R ) E DP R "R #R " . R K E kJ The resistance of the clean membrane being known, and assuming that particles are being retained only at the surface of the membrane (size of smallest particle: 0.77 lm, membrane pore size: 0.2 lm), we can deter-
Fig. 7. Deposit resistance variation as a function of its thickness for various concentrations (u"0.055 m/s; DP"110 kPa).
mine the resistance of the deposit at any moment R "R !R . The evolutions of the deposit resistance E R K as a function of thickness, for di!erent concentrations, are presented in Fig. 7 and show that deposit resistance grows as concentration drops. This con"rms the remark on the permeability mentioned above. As a function of cross#ow velocity of the suspension, and according to deposit thickness, resistance tends to increase with velocity over an initial period, and then to decrease again after a velocity of 0.193 m/s has been reached (Fig. 8). The resistance of the deposit is increasingly signi"cant as its thickness grows, whatever the cross#ow velocity. For a given thickness of deposit, the resistance grows with pressure, this growth becoming all the more signi"cant for greater thicknesses (Fig. 9). Previous studies concerning frontal "ltrations of clay have shown the compressibility of the cakes when the pressure is increased (Yim, 1984). Considering the bentonite deposit formed during cross#ow "ltration, we can assume that the increase of deposit resistance observed is mainly due to the compressibility.
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M. Hamachi, M. Mietton-Peuchot/Chemical Engineering Science 54 (1999) 4023}4030
Fig. 8. Deposit resistance variation at a given thickness as a function of cross#ow velocity (*P"110 kPa; c"0.25 g/l).
Fig. 9. Deposit resistance variation at a given thickness as a function of transmembrane pressure (u"0.193 m/s; c"0.375 g/l).
3.2.3. Specixc resistance and compressibility of the deposit Available literature contains several di!erent studies relating to how operating conditions may a!ect speci"c resistance of deposits during cross#ow micro"ltration. The in#uence of pressure, through compression of deposit, is not disputed in these studies. By means of a speci"c experimental device Murase et al. (1988) have determined speci"c resistance values (a) for kaolin suspensions, these being in full agreement with standard "ltration theory and dependent on the transmembrane pressure. This is given under the form: a"A DP@. In our case, speci"c resistances for the bentonite deposits may be estimated using the relation: a"R S /M , E K E where the mass of the deposit (M ) is calculated by E M "p.ep .l.(ep #2R)(1!e)o . E E E @ Fig. 10 shows, for two concentrations, the relationship linking a and DP, and displays the way in which speci"c resistance depends upon transmembrane pressure. Furthermore, it would seem that the compressibility coe$cient depends upon concentration: it is higher as the
Fig. 10. E!ect of concentration on speci"c resistance as a function of transmembrane pressure.
concentration increases, this coe$cient values varies from 0.54 to 0.73 for the concentrations of 0.25 and 0.375 g/l respectively. Even though during experimentation the constant &&A'' varies, it nevertheless maintains the same order of size. The in#uence of concentration on the compressibility coe$cient may be due to the very signi"cant deposit thicknesses produced at higher concentrations: the measurement of deposit thickness become more precise and so the perceived role of compressibility becomes more obvious. As it has been shown above that the initial deposit is made up of "ne particles, the subsequent deposit having a lower hydraulic resistance and seeming to be homogeneous, it is probable that the initial deposit will stay the same under all test conditions. The "nal deposit having a di!erent thickness, the proportions of "ne and larger particles are not therefore the same. This might explain the di!erence encountered in compressibility coe$cient. For a concentration of 0.375 g/l, the estimated compressibility coe$cient is slightly lower than that given by Chloe et al. (1986) or Gourgues (1991) (Table 3). In contrast, for a concentration of 0.25 g/l, this coe$cient is very di!erent from that given by the cited authors. The compressibility coe$cient for bentonite recently reported by Murase et al. (1995) obtained through a relationship of the type: a"a #a .DP@ seems too high with regard to the scale of pressures in action, all the more so as the average diameter of bentonite particles (2.2 lm) used for their experiments is of roughly the same order as the bentonite used in this study (2.45 lm). The working pressure signi"cantly in#uences the compressibility coe$cient and con"rms the kaolin example, according to values published by Murase et al. in both 1995 and 1988, for varying pressures (Table 3). 3.2.4. Deposit porosity Knowing the size of particles and the permeability of the deposit, the Carman}Kozeny equation allows to
4029
M. Hamachi, M. Mietton-Peuchot/Chemical Engineering Science 54 (1999) 4023}4030 Table 3 Comparison of compressibility coe$cients Authors
Particles
Pressure range (kPa)
Compressibility coe$cient
Chloe et al. (1986) Murase et al. (1988) Gourgues (1991) Murase et al. (1995)
Bentonite Kaolin Bentonite Bentonite Kaolin Bentonite
50}500 981}6860 25}150 10}60 50}400 110}210
0.84 0.88 0.83 0.96 0.46 0.54}0.73
Hamachi (1997)
Fig. 11. Deposit porosity variation as a function of its thickness for di!erent cross#ow velocities (DP"210 kPa; c"0.375 g/l).
Fig. 12. Deposit porosity variation as a function of transmembrane pressure for di!erent cross#ow velocities (c"0.375 g/l; ep"200 lm).
determine the theoretical porosity of the deposit using experimental values and taking into account thickness of deposit and permeate #ux.
ity) as a function of h . Between 3 and 7, the variation in I this constant gives more-or-less the same average porosity, varying between 8.5 and 11%, and is comparable to values given in existing literature (Table 4). The calculated average porosity corresponds to that suggested by Bourden (1990), who use the cake "ltration theory. The porosity of 80}95% reported by Wandelt (1993) corresponds to the porosity of a dry deposit.
1 de ep E , B" E" 36h (1!e) R I E where h is the Kozeny constant (taken as equal to 5) and I d the Sauter diameter (d "1.63 lm). E E Generally, the porosity of the bentonite deposit tends to increase with thickness (Fig. 11), due to a selective deposition of the particles. At the beginning of the "ltration process, the deposit is made up of "ner particles provoking the rapid decrease in permeate #ux (Fig. 6). The "ne particles create deposits with a great resistance. Gradually the thickeness of the deposit increased with larger particles, con"rming the observations of Ficher (1987). However, the average porosity seems to be stabilised as thickness increases. For di!erent cross#ow velocities of the suspension, Fig. 12 shows the decrease of the porosity as the transmembrane pressure increases. The in#uence of cross#ow velocity on the porosity seems limited. The average porosity, calculated using the Carman} Kozeny equation, is around 10% for a constant h "5. I Applying this value of h for an average porosity of the I deposit, one can study the sensitivity of this factor (poros-
4. Conclusion The analysis of the deposit characteristics for bentonite allows better understanding of the mechanisms of membrane surface fouling, through measurements of deposit thicknesses. The evolution of the deposit thickness as a function of cumulative volume shows that despite the presence of a cross#ow velocity, the deposit is directly linked to the convective #ux of matter bringing to the membrane. The initial layers of bentonite deposit constitute the higher resistance, and even if the deposit continues to grow, any further decrease in the permeate #ux is limited. The deposit formed is not homogeneous and its permeability tends towards a constant value, whatever the cross#ow velocity, for a given pressure and concentration. The in#uence of concentration may lead to
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M. Hamachi, M. Mietton-Peuchot/Chemical Engineering Science 54 (1999) 4023}4030
Table 4 Comparison of porosity Authors
Particles
Pressure (kPa)
Porosity
Bourden (1990) Blake et al. (1992) Wandelt (1993)
Bentonite Latex Bentonite Latex Bentonite
85}185 200 30}125 30}125 110}210
10% 36% 80}95% 30}40% 10%
Hamachi (1997)
increased permeability. The deposit is compressible, and the compressibility coe$cient depends on concentration, varying from 0.54 to 0.73. Carman}Kozeny equation allows the bentonite cake porosity to be determined, for which the calculated average value (10%) corresponds to that given in previous literature in this "eld.
Notation A B c d E ep E ep K h I J l M E R S K
constant deposit permeability, m suspension concentration, kg/m the Sauter diameter, m deposit thickness, m thickness of the membrane "ltering layer, m Kozeny constant permeate #ux, l/h m useful length of membrane, m deposit mass, kg membrane radius, m surface area of the membrane, m
Greek letters a b DP k o @ e
speci"c resistance of the deposit, m/kg compressibility coe$cient transmembrane pressure, Pa dynamic viscosity of water, kg/m s volumic mass of the swollen bentonite, kg/m cake porosity
References Blake, N.J., Cumming, I.W., & Streat, M. (1992). Prediction of steady state cross#ow "ltration using a force balance model. Journal of Membrane Science, 68, 205}216.
Bourden, S. (1990). CaracteH risation par capteur optique de l'eH volution spatio-temporelle du deH po( t formeH lors de la "ltration sur "bre creuse. The% se de doctorat, INP Toulouse, France. Chloe, T.B., Masse, P., Verdier, A., & Clifton, M.J. (1986). Flux decline in batch ultra"ltration: concentration, polarization and cake formation. Journal of Membrane Science, 26, 1}15. Ficher, E. (1987). Untersuchungen zum Trennprozess bei der Querstrom"ltratio. Dissertation, TU Karlsruhe. Ficher, E., & Raasch, J. (1986). Model tests of the particle deposition at the "lter medium. In Proceeding of the 4th World Filtration Congress, Belgium, 11}17 November 1986. Gourgues, C. (1991). Ultra"ltration de suspensions de bentonite par des "bres creuses: production d'eau potable. The% se de doctorat, UPS Toulouse, France. Hamachi, M. (1997). Mesure dynamique de l'eH paisseur du deH po( t a` l'aide d'un capteur optique et modeH lisation par reH seau de neurones de la micro"ltration tangentielle de suspensions. The% se de doctorat, INP Toulouse, France. Hamachi, M., & Mietton Peuchot, M. (1996). Dynamic measurement of deposit thickness on inorganic membrane. In Proceedings of the 4th International Conference on Inorganic Membranes, Gatlinburg, Tennessee, U.S.A. Lu, W., & Ju, S.C. (1989). Selective particle deposition in cross#ow "ltration. Separation of Science and ¹echnology, 24, 517}540 Murase, T., Iwata, M., Kato, I., Lee, W.D., & Shirato, M. (1988). Determination of speci"c resistance of highly compressed cake by use expression data. Journal of Chemical Engineering of Japan, 21 (2), 204}206. Murase, T., Ohn, T., & Kimata, K. (1995). Filtrate #ux in cross#ow micro"ltration of dilute suspension forming a highly compressed fouling cake layer. Journal of Membrane Science, 108, 121}128. Rjimati, E., & Grasmick, A. (1991). Micro"ltration tangentielle d'une suspension de bentonite. Entropie, 163, 23}30. Rushton, A., Hosseini, M., & Hassan, I. (1980). The e!ect of velocity and concentration on "lter cake resistance. Journal of Separation Proceedings ¹echnology, 1 (3), 34}41. Wandelt, B. (1993). Analyse de la formation des deH po( ts de particules lors d'un proceH deH d'ultra"ltration tangentielle. Visualisation par imagerie a` reH sonance magneH tique nucleH aire. The% se de doctorat, INP Toulouse, France. Yim, S.S. (1984). Filtration sur ga( teau compressible. The% se de doctorat, INP Toulouse, France.