Applicability Assessment of Subcritical Flux Operation in Crossflow Microfiltration with a Concentration Polarization Model

Applicability Assessment of Subcritical Flux Operation in Crossflow Microfiltration with a Concentration Polarization Model Suhan Kim 1 and Heekyung Park 2 Abstract: In the process of crossflow microfiltration, a deposit of cake layer tends to form on the membrane, which usually controls the performance of filtration. However it is found that there exists a condition under which no deposit of cake layer is made. This condition is called the subcritical flux condition and the maximum flux in the condition here is called the critical flux. Which means, it is a flux below which a decline of flux with time due to the deposit of cake layer does not occur. This study develops a concentration polarization model to predict the critical flux condition and to study about its characteristics. The model is verified with experimental results. For the model, the concept of effective particle diameter is introduced to find a representative size of various particles in relation to diffusive properties of particles. The modeling and the experimental results include that the critical flux condition can be determined by the use of effective particle diameter and the ratio of initial permeate flux to crossflow velocity. This study also finds that the subcritical flux operation is limited for the real world application because of the limitation to increasing crossflow velocity and its sensitivity to the change of feed composition. DOI: 10.1061/ASCE0733-93722002128:4335 CE Database keywords: Crossflow; Filtration; Models; Sub critical flow. Introduction Critical Flux in Microfiltration Microfiltration MF is a pressure driven process using microporous membrane as a separating media. It is used to filter the suspensions containing colloidal or fine particles with linear dimensions in the range of 0.02 to 10 m. Most of the pollutants in water and wastewater fall in this size range and will-be efficiently removed by MF. The MF process can be operated by either crossflow or deadend flow configuration. Crossflow microfiltration CFMF is known to be advantageous over deadend flow because its high shear tangential to membrane surface sweeps deposited particles away toward the filter exit Belfort et al. 1994. However, in practice, suspended particles were transported to the membrane surface by permeate flow due to the imposed pressure drop during CFMF, and a cake layer is formed by these particles. The cake layer formed on membrane surface induces membrane permeate flux decline. This is one of the major problems in pressure-driven membrane processes. Over the decades, many studies have been carried out to overcome this flux decline problem in CFMF, which are mainly looking at modifications of 1 Dept. of Civil Engineering, Korea Advanced Institute of Science and Technology KAIST, Taejon, Korea. 2 Dept. of Civil Engineering, Korea Advanced Institute of Science and Technology KAIST, Taejon, Korea. Note. Associate Editor: Makram T. Suidan. Discussion open until September 1, 2002. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and possible publication on November 23, 1999; approved on October 17, 2001. This paper is part of the Journal of Environmental Engineering, Vol. 128, No. 4, April 1, 2002. ASCE, ISSN 0733-9372/2002/4-335 340/$8.00$.50 per page. the membrane, the feed, and fluids dynamics in the membrane modules. The fluid dynamics approach focuses on the design of the membrane modules and optimization of the operating conditions. Especially for the microfiltration of particulate suspensions, efforts have mainly concentrated on modifying the fluid dynamics in membrane module Kwon 1998. The concept of critical flux has been recently introduced with a number of experimental evidences. The concept of critical flux proposed by Field et al. 1995 and Howell 1995 is as follows: Critical flux is the flux below which a decline of flux with time does not occur and the value of critical flux depends on the hydrodynamics and probably also on the other variables. Operation below the critical flux is called subcritical flux operation or clean nonfouling operation. Several researchers have tried to find out about the characteristics of critical flux. As discussed above, Field et al. 1995 and Howell 1995 proposed the concept of critical flux. Ghayeny et al. 1996 described critical flux operation to optimize flux through the MF membrane as a pretreatment to reverse osmosis. Chen et al. 1997 studied the transition from concentration polarization to cake formation with critical flux as a standard. As the flux increases over the critical flux, the colloids in the polarized layer form a consolidated cake structure that is slow to depolarize and which reduces the flux. Li et al. 1998 carried out direct observation of particle deposition on the membrane surface and observed the particle deposition in the subcritical flux microfiltration. Below the critical flux, the particle deposition is negligible; near the critical flux the particle deposition is significant; and above the critical flux, particle layer forms on the membrane surface. Defrance et al. 1999 applied critical flux to membrane bioreactor. They stated that; the constant flux procedure below the critical flux avoids overfouling of the membrane in the initial stage and is more advantageous for membrane bioreactor operation. Kwon et al. 1998, Huisman et al. 1999, and Madaeni JOURNAL OF ENVIRONMENTAL ENGINEERING / APRIL 2002 / 335

Fig. 2. Problem domain in cylindrical format Fig. 1. Mass transfer of crossflow microfiltration et al. 1999 studied factors influencing critical flux. They said that since it depends on particle size and crossflow velocity, the critical flux becomes higher for higher crossflow velocity and for larger particles. As an extension of these above studies, this study tried to mathematically simulate the concept of critical flux using concentration polarization model. This model enables us to study the effects of crossflow velocity, permeate flux, and particle size on the critical flux quantitatively and assess the applicability of subcritical flux operation. Three Mass Transfer Mechanisms in Crossflow Microfiltration In the membrane module of CFMF, mass transfer can be well explained by Fig. 1 which divides mass transfer in membrane module into three mechanisms; convective, backdiffusive, and axial mass transfer. As well known, convective mass transfer means that particles move from bulk suspension to the membrane surface while backdiffusive mass transfer means vice versa. Axial mass transfer means that particles move with crossflow of bulk suspension. As flux, J, increases, convective mass transfer becomes dominant, and as particle diffusivity increases, backdiffusive mass transfer increases. Axial mass transfer increases with the increase of crossflow velocity. The particle diffusivity is expressed by diffusion coefficient as shown in Eq. 1 Lee 1997 D eff D m D s kt 6a 0.03a2 (1a) u (1b) r where D eff effective diffusion coefficient m 2 /s; D m molecular diffusion coefficient m 2 /s; D s shear induced diffusion coefficient m 2 /s; kboltzmann constant (1.38 10 23 J/K); Tabsolute temperature K; viscosity 1.00510 7 kg/m s in 2 C; aparticle radius m; shear rate /s; ulateral crossflow velocity m/s; and rradial axis of membrane module m; refer to Fig. 2. In the case of particle with a size of over 0.1 m, D eff is approximately equal to D s. This means the diffusivity of particles larger than 0.1 m in size is proportional to shear rate. Also shear rate is generally increased with the increase of crossflow velocity. Therefore backdiffusive mass transfer becomes dominant as the crossflow velocity increases. Due to selective permeability of membrane, some particles are accumulated in the vicinity of membrane and concentration polarization occurs. Concentration polarization means particle accumulation on membrane surface where the particle concentration is much higher than that of bulk feed solution. Since the CFMF operation started, the concentration polarization effect has become larger and flux has decreased with time until a steady state reaches. At the steady state, no more deposition occurs because three mass transfers in CFMF are balanced together. The concentration polarization effect becomes small when axial and backdiffusive mass transfers are dominant over convective mass transfer. If the concentration polarization effect at a steady state is small enough to sustain initial flux, there is no stagnant cake above the membrane surface. This filtration operation is called the subcritical flux operation. Consequently, the subcritical flux operation is a steady state flux operation in which the concentration polarization effect is too small for particle deposition to occur. In Fig. 1, x cr indicates the length where no particle deposition occurs and L is the whole length of the membrane. It is said that the critical flux condition is established for filtration, when x cr reaches L. Methods and Materials Prediction of Critical Flux Condition In this study, a concentration polarization CP model is used to find the subcritical flux condition. The CP model includes three mass transfer mechanisms in CFMF and it can evaluate if a certain condition, usually consisting of particle radius, crossflow velocity and transmembrane pressure satisfies the subcritical flux condition. Its modeling procedure consists of the following four steps: 1 formulation of the mass balance equation, 2 determination of a velocity distribution in a membrane module given, 3 finding a concentration distribution in the membrane module by solving the mass balance equation, and 4 confirming if the mass balance calculated from the concentration distribution satisfies. Fig. 2 is used for model development, which simplifies a tubular membrane module and shows a problem domain in cylindrical format. C 0 is the particle concentration, J the permeate flux, L the membrane length, x the horizontal axis, r the cylindrical axis, and R the radius. As a first step, a mass balance equation, boundary conditions and related assumptions are developed as follows. The membrane module used for this study is a tubular module and Eq. 2a is a mass balance equation for tubular membrane module Ma et al. 1985 336 / JOURNAL OF ENVIRONMENTAL ENGINEERING / APRIL 2002

u c x v 1 r D r c boundary conditions: c r D 2 c r r 2 rr0 c vcd r r 0 rr 0 (2a) (2b) (2c) cc 0 at membrane inlet (2d) where ux-direction velocity m/s; vr-direction velocity m/s; cconcentration; and D r diffusion coefficient m 2 /s in r direction. In Eq. 2a, the first term in the left-hand side indicates axial mass transfer, the second term convective mass transfer, and the term in the right-hand side backdiffusive mass transfer. In order to develop a concentration polarization model, three boundary conditions and four basic assumptions are needed. The three boundary conditions are as follows. The concentration difference at r 0 center of membrane is zero because of symmetry see Eq. 2b, the mass transfer at rr membrane surface is zero because particles cannot permeate membrane see Eq. 2c, and the concentration is uniform before the feed flows into the membrane inlet see Eq. 2d. Four assumptions are as follows: 1. Crossflow of suspension is laminar and viscous; 2. In subcritical flux condition, flux decline does not occur. This in turn indicates that the velocity distribution in the subcritical flux condition does not change with time; 3. Particles are sphere and their sizes are larger than the membrane pore size; 4. Particles are lifted from the membrane surface by shear induced diffusion only and the effect of surface charge is insignificant because the radii of particles used in this study are over than 1 m Kwon 1998. For determining pressure and velocity distribution in the tubular membrane module, which is the second step of the modeling procedure, Eqs. 3a 3e are used Brian 1965; Kleinstreuer et al. 1983; Bouchard et al. 1994 Transmembrane pressuren/m 2 ): Permeate fluxm/s): PxP0 f ru avg 0x r 2 v p x Px R m (3a) (3b) Average crossflow velocitym/s): u avg xu avg 0 2 R 0 xv p xdx (3c) x-direction velocity distributionm/s): r-direction velocity distributionm/s): ux,r2u avg x vx,rv p x 1 R r 2 2 R r R r 3 (3d) (3e) where P(x)transmembrane pressure TMP distribution in x direction; f r friction factor of membrane; u avg (x)average crossflow velocity distribution in x direction; and v p (x)permeate flux distribution. In the third step, a concentration distribution in the module is calculated by solving Eqs. 2a 2d using the finite difference method FDM. The velocity distribution and diffusion coefficient obtained from Eqs. 3a 3e and Eqs. 1a and 1b, respectively, are used for it r r 0 u cda 0 u cda for all x (4) x xx0 It is important to check the mass calculation from the concentration distribution at the final step if it is balanced. We calculate a mass at every slice in x direction from the concentration distribution obtained in the third step. Since FDM is used, the problem domain is divided into many slices in x and r direction to form grids. We then compare it to the total mass at the module inlet. If their difference is less than 1% at all slices, a concentration distribution obtained in the third step is said to satisfy mass balance. For this, we use Eq. 4 and an assumption that particles do not penetrate membrane assumption 3. If mass balance is satisfied, then this case of particle size, crossflow velocity, and initial permeate flux is determined to be in the subcritical flux condition. But if not, it is determined that the real velocity distribution differs from the theoretical velocity distribution Eqs. 3a 3e because of flux decline induced by particle deposition and that the case is not considered in the subcritical flux condition. In addition, we check if the Reynolds number R is less than or equal to 2000, just to make sure that the laminar flow condition in the tubular module is established assumption1. Fig. 3 illustrates the procedure to see if a certain condition particle size, crossflow velocity, and TMP satisfies the subcritical flux condition, using the CP model and procedure described above. Among the subcritical flux conditions searched by the CP model, the critical flux condition is defined as the highest flux condition per unit crossflow velocity. Experiments In order to verify use of the CP model for prediction of the critical and/or subcritical flux condition, experiments are conducted as described below. A hollow fiber MF membrane of polysulfone SKM-103 model, Korea is used, whose pore sizes are 0.01 0.1 m, effective surface area 0.06 m 2, length 36 cm, and inner diameter 0.8 mm. The schematic diagram of the microfiltration setup used in this study is shown in Fig. 4. Suspensions stirred are JOURNAL OF ENVIRONMENTAL ENGINEERING / APRIL 2002 / 337

range of 0.66 2.33 m/s. So, the values of Re in this study are less than 1850, satisfying the laminar flow condition. In order to find the critical flux condition, we have observed the change of permeate flux for the first 30 min of the experiment, since flux decline in CFMF typically occurs in early filtration time at such a concentration of 500 mg/l. If flux decline does not occur at all during the observation time, the suspension concentration at the end of the observation time is measured to see if it is the same with that of the beginning of the observation time. The same suspension concentrations at both times indicate that no particle has disappeared from the suspension during the experiment. If the two conditions, no flux decline and no difference in suspension concentrations during the first 30 min of the experiment, are satisfied, the subcritical flux condition is achieved. The critical flux in an experiment is also found by following a procedure similar to the procedure with the CP model see Fig. 3. Results and Discussion Fig. 3. Procedure of finding critical flux condition delivered from a feed tank to membrane by a variable speed tubing pump. The suspensions for experiments are made, using CaCO 3 mean particle diameter 21.53 m, Kaolin 4.11 m, bentonite 6.25 m, bentoniteii 47.23 m and MgOH) 2 (6.03 m), respectively. Their concentration is kept 500 mg/l. Here bentoniteii means bentonite retained on a 26 m sieve. Both the permeate and retentate lines are returned to the feed tank to maintain constant inlet condition and to check mass balance condition of the system. The pressure in membrane is controlled by two valves in permeate and retentate line and transmembrane pressure is calculated using pressures at membrane inlet and outlet Eq. 5 P tm P inp out (5) 2 where P tm transmembrane pressure; P in membrane inlet pressure; and P out membrane outlet pressure. The experiment is carried out in the room temperature. The crossflow velocity is in a Fig. 4. Schematic of microfiltration system Concept of Effective Particle Diameter In order to simulate the wet experiments with the CP model, a representative particle size must be introduced because the CP model is for a suspension of particles of a single size while the suspensions for the wet experiment have particles of various sizes. A representative particle size for a set of various sizes of particles here is called as effective particle diameter. Effective particle diameter is calculated using Eqs. 6a and 6b Effective particle diameter N i w i a i w i 1/D i 1/a i 2 that is w i k/a i 2, k is const (6a) w i N i k N i /a i 2 1 that is k1/ N i /a i 2 (6b) where a i ith size of particle in diameter; N i percentage of particles whose size belong to a i ; and w i weight for the ith particle size which reflects the diffusivity of the particles of ith size. The larger the effect on the concentration polarization gets, the weight gets larger also. When the diffusion coefficient gets smaller, the effect on the concentration polarization gets smaller. Therefore the weight is inversely proportional to diffusion coefficient. Since diffusion coefficients of the particles whose sizes are over 0.1 m are approximately proportional to the square of particle diameter Lee 1997 and since particles used in this study have diameters over 0.1 m, the weight is thus inversely proportional to the particle diameter. Using Eqs. 6a and 6b, the effective particle diameters of CaCO 3, kaolin, bentonite, bentoniteii, and MgOH) 2 are calculated to be 3.46, 2.53, 2.92, 3.80, and 2.85 m. Table 1 shows an example calculation of the effective particle diameter for the case of CaCO 3. Particle size distribution in suspension needs to be measured for these calculations and the PAMAS-2120 is used for the measurement. The samples are kept under the upper concentration limit 200,000 particles/ml for the accurate measurement PAMAS 1992. As shown in Table 1, smaller particles have larger weights than the larger ones. So the effective particle diameter is more affected by the portion of small particles whose sizes are less than several micrometers. This explains that the effective particle diameter of CaCO 3 is 3.46 m, despite of its mean diameter of 21.53 m. It is attributed to the fact that small particles are more in percentage than larger particles. 338 / JOURNAL OF ENVIRONMENTAL ENGINEERING / APRIL 2002

Table 1. Calculation of Effective Particle Diameter for Case of CaCO 3 Particle size range m Average size per each size range, a i m Percentage of particle, N i (%) Weighted factor, w i a N i w i a i m b 1.53 2.0 1.765 5.45 9.725 0.935 2.02 3.0 2.51 4.51 4.809 0.544 3.09 3.9 3.495 2.33 2.48 0.202 3.98 5.0 4.49 5.00 1.5 0.337 5.01 6.9 5.955 5.06 0.854 0.257 6.99 9.6 8.295 5.89 0.44 0.215 9.69 15.0 12.345 11.12 0.199 0.273 15.0 20.4 17.7 14.38 0.0967 0.246 20.49 29.9 25.195 22.07 0.0477 0.265 29.9 40.1 35 12.57 0.0247 0.109 40.1 49.5 44.8 6.89 0.0151 0.047 49.5 74.1 61.8 3.56 0.0079 0.017 74.1 99.0 86.55 1.06 0.004 0.004 99.0 162.0 130.5 0.11 0.0018 0.003 Effective particle diameter N i w i a i m3.46 a 1 2 (/ 2 ). b. Effect of Crossflow Velocity on Critical Flux Condition Fig. 5 shows the critical fluxes at a range of crossflow velocity. The wet experiment results of CaCO 3 and the CP modeling results with an effective particle diameter of CaCO 3 are shown together. We can summarize these results as follows: 1. Both of the results are close enough to say that the CP model and procedure developed in this study can predict the critical flux and subcritical flux conditions well; 2. It is shown that the critical flux condition is linearly related to crossflow velocity. This indicates that the critical flux condition can be described as the ratio of permeate flux to crossflow velocity for the kinds of suspensions considered in this study. For example, if crossflow velocity becomes double then the value of critical flux becomes double. Effect of Particle Size on Critical Flux Condition In addition to the linear relationship, it is also found that the particle size is another important hydrodynamic factor affecting the critical flux condition: Fig. 6 shows the modeling and experiment results with various particle sizes to illustrate the relationship between the critical flux condition and the effective particle diameter. As shown, their relationship is almost linear in both of the results. The larger the effective particle diameter results the larger critical flux. This suggests that the increase of the effective particle diameter by reducing portions of small particles in suspensions can increase the critical flux. In addition, it is suggested that we can use the CP model and procedure for the prediction of such a relationship with reasonable accuracy. Applicability of Critical Flux Operation in Microfiltration Application of the subcritical flux operation has advantages which include cost savings in cleaning and energy. The only disadvantage is that it requires large areas of membrane because of low flux. As an example, it has been addressed that for the same conditions, the flux of the conventional CFMF is six times as large as that of the critical flux operation Kwon 1998. This disadvantage can be easily balanced off. Especially, in the large Fig. 5. Effect of crossflow velocity on critical flux condition in the case of CaCO 3 TMP range: 0.2 1.0 kgf/cm 2 for permeate flux 40 200 L/m 2 h Fig. 6. Effects of particle sizes on the critical flux condition crossflow velocity1.65 m/s TMP range: 0.3 0.75 kgf/cm 2 for permeate flux 60 150 L/m 2 h JOURNAL OF ENVIRONMENTAL ENGINEERING / APRIL 2002 / 339

scale operation cases at water treatment plant, since they allows very large modules to be installed at much low unit costs for a square meter of membrane Howell 1995. Even if so, we still think the application of the critical flux operation is limited by the following two reasons. The first reason is the limitation increasing crossflow velocity to increase critical flux. In order to overcome a problem of very low flux, we can think of increasing critical flux itself by increasing crossflow velocity since our experimental and model results shows that critical flux is a linear function of crossflow velocity. However, this option is known limited since increasing crossflow velocity definitely increases the associated energy costs, which increase sharply over a certain value of crossflow velocity Owen et al. 1995. Also, increasing crossflow velocity does not work to the small particles whose sizes are near 0.1 m since it does not increases the shear-induced diffusion to those particles very much and thus it cannot enlarge their back diffusion Lee 1997. Asa result, if there exists a certain amount of such small particles in the feed, increasing crossflow velocity cannot increase the amount of critical flux very much. The second reason is that the critical flux condition is sensitive to the change of feed composition as demonstrated in our experimental and model results. The critical flux condition is affected by effective particle diameter as demonstrated in our experimental and modeling results. The effective particle diameter can be changed by the change of feed composition. Especially the change of the population of small particles results in the large change of the effective particle diameter, which results in the large change of the critical flux. This makes it difficult to apply the subcritical flux operation to the real plant because the feed composition always changes and it will threaten the operation s stability. Summary In this study, we have constructed a modeling procedure using the concept of concentration polarization, three mass transfer mechanisms, and effective particle diameter to quantitatively estimate the effects of several factors on the critical flux. This modeling procedure here is called the CP model, just for simplicity. To verify the CP model, we carried out wet experiments with various particles. Also, we discussed about the applicability of the subcritical flux operation using our modeling and experimental results. The conclusions are summarized as follows: 1. The CP model with the use of effective particle diameter developed in this study can predict the critical flux condition. It can also predict the critical flux condition and it can be used to explain the characteristics of the critical flux condition; 2. According to the modeling and experimental results, the larger the effective particle diameter and crossflow velocity gets, the critical flux gets larger also; 3. The subcritical flux operation is limited for real world application because of the limitation to increasing crossflow velocity and its sensitivity to the change of feed composition. Acknowledgments This work was supported by Grant No. 2000-2-30900-004-3 from the Basic Research Program of the Korea Science & Engineering Foundation and the Brain Korea 21 Project. References Belfort, G., Davis, R. H., and Zydney, A. L. 1994. Review: The behavior of suspensions and macromolecular solution in crossflow microfiltration. J. Membr. Sci., 96, 1 58. Bouchard, C. R., Carreau, P. J., Matsuura, T., and Sourirjan, S. 1994. Modeling of ultrafiltration: prediction of concentration polarization effect. J. 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