Environ. Sci. Technol. 2000, 34, 3767-3773
Mechanisms and Parameters Affecting Flux Decline in Cross-Flow Microfiltration and Ultrafiltration of Colloids MIAOMIAO ZHANG AND LIANFA SONG* Department of Civil Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Flux decline in cross-flow membrane filtration of colloids under various conditions is systematically investigated. By comparing theoretical predictions with experimental measurements, it is demonstrated that the permeate flux in cross-flow filtration is controlled by the dynamic process of cake formation and growth. The permeate flux declines with time when the cake layer grows, whereas it attains steady state as the cake layer reaches the equilibrium thickness. The effects of parameters, such as applied pressure, shear rate, feed concentration, and particle size, on flux decline are also investigated. The time for a crossflow filtration process to reach steady state is demonstrated to be generally proportional to (i) applied pressure (∆P); (ii) minus one-third power of feed concentration (c0-1/3); (iii) minus two-third power of shear rate (γ-2/3); and (iv) tenthird power of particle size (ap10/3). It is also experimentally shown in this study that the fouling of large particles is more severe than that of small particles. Though the initial flux decline rate is greater for small particles, the permeate flux declines over a much longer period and has a lower steady-state value for large particles.
Introduction Applications of membrane technology in water and wastewater treatment have been growing steadily in recent years (1). Microfiltration and ultrafiltration are effective processes for removal of organic matter, colloids, and suspended particles in water and wastewater. The use of membrane processes in place of the traditional disinfection processes can maintain a high removal efficiency of pathogens and avoid producing the disinfection-byproducts (DBPs) (2). Studies have also been conducted on the use of microfiltration in biological wastewater treatment to eliminate the settling tank and to achieve a better separation (3). Furthermore, micro- and ultrafiltration processes, because of their high efficiency and stable performance in removing colloidal particles, have shown high potential to become one popular pretreatment method for reverse osmosis processes in water industries (4, 5). Permeate flux in micro- and ultrafiltration processes decreases with time as the retained particles accumulate on membrane surface. This phenomenon is called membrane fouling. Membrane fouling can severely reduce the efficiency of the membrane process and makes it less competitive in * Corresponding author phone: (852)2358 7885; fax: (852)2358 1534; e-mail:
[email protected]. 10.1021/es990475u CCC: $19.00 Published on Web 08/02/2000
2000 American Chemical Society
many applications. Consequently, the understanding of the mechanisms and parameters that affect membrane fouling remains as a focus of membrane study for the last 2 decades. Investigations on flux decline in cross-flow filtration were extensively reported in the literature (6-12). Tarleton and Wakeman attempted to provide a comprehensive picture of particle fouling in a series of papers (13-15). The effects of suspension properties, process parameters, and membrane morphology on permeate flux decline in microfiltration were systematically investigated and summarized. Elimelech and co-workers (16, 17) demonstrated the effects of colloidal interactions on particle fouling in ultrafiltration. Recently, Chellem et al. (18) reported their theoretical and experimental study on colloidal fouling of membranes in a pilot water treatment plant. These studies greatly advanced our knowledge about flux decline in cross-flow membrane processes. However, the mechanisms of membrane fouling and the effect of key process parameters on fouling dynamics are still not clear or quite controversial (13). Recently, Song (19) developed a mechanistic model for fouling dynamics in cross-flow micro- and ultrafiltration processes. In this model, flux decline was considered as a result of the dynamic process of cake formation and growth in the filtration channel. The model was able to predict the time-dependent flux of a membrane process and the time for the process to reach steady state, which are two important parameters in the design and operation of membrane systems. In a follow-up study (20), ultrafiltration experiments were conducted in a rectangular channel with uniform spherical silica colloids. Preliminary experimental supports to the theory were obtained. In this paper, flux decline in micro- and ultrafiltration is further studied by comparing theoretical predictions with measurements from filtration experiments of model colloidal suspensions. The effects of various parameters, such as applied pressure, feed particle concentration, shear rate, and particle size, on flux decline are systematically investigated. The experiments conducted in this investigation demonstrate that the effects of these parameters on colloidal fouling in cross-flow filtration can be correctly predicted with the newly developed theory.
Theoretical Analyses The theoretical analysis below is mainly based on a recent work on colloidal fouling in cross-flow filtration (19), in which flux decline is manipulated as a result of the formation and growth of a cake layer on the membrane surface. The intention of this section is to introduce the key concepts of the theory and to highlight the equations that are relevant to the experimental investigations. These who are interested in the detailed derivation of the theory are encouraged to refer to the original work on the theory (19). Critical Pressure for Cake Formation. In cross-flow micro- and ultrafiltration, colloids in suspension are brought to the membrane surface by permeate flux, and, as a result, a concentration polarization layer forms in the vicinity of membrane surface. The development of the concentration polarization layer reduces the effective pressure for permeate because there is a pressure drop across it. The deduction of the effective pressure by concentration polarization can also be understood in terms of the buildup of osmotic pressure. Elimelech and Bhattachajee (21) recently showed that the pressure drop across the concentration polarization layer was equal to the osmotic pressure with respect to the wall colloidal concentration. The pressure drop on the concenVOL. 34, NO. 17, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
9
3767
TABLE 1. Critical Pressure for Different Particle Radii particle radius critical pressure particle radius critical pressure (m) (Pa) (m) (Pa) 1.00 × 10-9 2.51 × 10-9 6.31 × 10-9 1.58 × 10-8 3.98 × 10-8 1.00 × 10-7
1.08 × 10+7 6.81 × 10+5 4.30 × 10+4 2.71 × 10+3 1.71 × 10+2 1.08 × 10+1
2.51 × 10-7 6.31 × 10-7 1.58 × 10-6 3.98 × 10-6 1.00 × 10-5
6.81 × 10-1 4.30 × 10-2 2.71 × 10-3 1.71 × 10-4 1.08 × 10-5
tration polarization layer grows as concentration polarization develops. There is a critical pressure (or maximum osmotic pressure) for colloidal suspensions of a given particle size (7, 8). Only a concentration polarization layer exists over the membrane surface if the applied pressure is smaller than the critical pressure. When the applied pressure is greater than the critical pressure, a layer of densely packed colloids, the so-called cake layer, will form on the membrane surface. The critical pressure for suspensions of uniform spherical colloids is determined with
∆Pc )
3kTNFC
(1)
4πap3
where ∆Pc is the critical pressure, k is the Boltzmann constant, T is the absolute temperature, ap is the particle radius, and NFC is the critical filtration number. The critical filtration number is a function of cake density cg (8). Table 1 lists the critical pressures for different colloid sizes when the critical filtration number is assumed to be 11 (correspondingly, cg ) 0.52). It can be seen from Table 1 that the critical pressures are very small for large particles. A cake layer is expected to form in most micro- and ultrafiltration processes because these processes are usually operated under pressures way above the critical pressures. Cake Layer Growth. The cake layer in a membrane process usually takes a period of time to grow to the equilibrium thickness because of the limited supply of retained particles by the permeate flow. Sometimes, the time for the cake layer to reach the equilibrium thickness can be quite long for extremely diluted suspensions. It is the slow growth of cake layer thickness that causes the gradual decline of permeate flux in the membrane filtration process. To describe cake growth more precisely, the cake layer in a cross-flow channel is divided into two regions, namely the equilibrium and nonequilibrium regions (19). In the equilibrium region, the cake thickness is a function of location, which does not change with time,
δeq (x) )
( )
∆P - ∆Pc 3xc0 rc 2D2γcg
1/3
(2)
where δeq (x) is the equilibrium cake thickness at location x, ∆P is the applied pressure, rc is the specific resistance of the cake, c0 is the feed colloid concentration, D is the colloid diffusion coefficient, and γ is the shear rate. In writing eq 2, the membrane resistance is assumed much smaller than the cake resistance and c0 , cg. These assumptions are true for most practically used micro- and ultrafiltration processes. For suspensions of uniform spherical particles, the specific cake resistance rc and colloidal diffusion coefficient D can be determined, respectively, with the Carman-Kozeny equation
rc ) 3768
9
45µ(1 - )2 2 3
ap
(3)
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 34, NO. 17, 2000
FIGURE 1. A schematic description of cake layer growth in crossflow filtration channel. and Einstein-Stokes’ law
kT 6πµap
D)
(4)
where is the cake porosity, and µ is the fluid viscosity. The nonequilibrium region occurs downstream of the equilibrium region. The cake layer in this region is of uniform thickness δ(t), which is a function of time,
δ(t) )
c0 cg
∫ ν(τ)dτ t
(5)
0
and v(t) is given by
ν(τ) )
[
(∆P - ∆Pc) 2rc(∆P - ∆Pc) c0 1+ t Rm cg R 2 m
]
-1/2
(6)
where Rm is the membrane resistance. While the cake layer thickness grows in the nonequilibrium region, the equilibrium region expands as the front of the equilibrium region progresses downstream. The location of the front at any time, X(t), is given by
X(t) ) 4.81(D2γ)
() ( c0 cg
1/2
rc t ∆P - ∆Pc
)
3/2
(7)
The cake layer growth in cross-flow filtration channel is schematically illustrated in Figure 1. Time to Steady State and Average Flux. When the front of the equilibrium region moves to the end of the filtration channel, the cake layer in the entire channel reaches the equilibrium thickness and will no longer change with time. The filtration system then is said to have reached steady state. The time needed to reach steady state is calculated by
tss ) 0.351
( ) () ( L D2 γ
2/3
cg c0
1/3
)
∆P - ∆Pc rc
(8)
With the knowledge of the location of the front of the equilibrium region, the average permeate flux at any time can be simply calculated with weighted averaging method. When t < tss, the average permeate flux over the whole channel is
V(t) )
[
1.31 cg 2 D γX(t)2 L c0
]
1/3
+
[L - X(t)] ν(t) L
(9)
When t g tss, the filtration system reaches steady state and the permeate flux becomes a constant, i.e.,
( )
V ) 1.31
cgD2γ c 0L
1/3
(10)
FIGURE 2. Schematic diagram of cross-flow ultrafiltration experiment setup.
Equation 10 reveals that the average permeate flux at steady state is unaffected by the applied pressure. Therefore, the steady-state flux is actually the limiting flux of the filtration system (20). Affecting Factors. From above theoretical analyses of the cross-flow filtration, it can be seen that the performance of cross-flow filtration is strongly affected by many parameters, such as applied pressure, shear rate, feed colloid concentration, and particles size. If the particles can be regarded as rigid spheres, the cake concentration cg and the specific resistance rc will be pressure independent. If the pressure is further assumed to be much higher than the critical pressure, then we have the following simple correlations between the time to steady state and affecting factors: (1) The time to steady state is proportional to the applied pressure, i.e., tss ∝ ∆P. (2) The time to reach steady state is inversely proportional to the cubic root of feed concentration, i.e., tss ∝ c0-1/3. (3) The time to steady state is inversely proportional to the two-third power of shear rate, i.e., tss ∝ γ--2/3. (4) The time to steady state is proportional to the ten-third power of article size, i.e., tss ∝ ap10/3. These simple rules may provide significant insights for design and operation of cross-flow membrane filtration. However, the above points are theoretical derivations, and experimental supports are needed.
A schematic diagram of the laboratory-scale, cross-flow membrane filtration system is shown in Figure 2. The colloidal suspension is stored in a 5-L reservoir and circulated by a peristaltic pump (Cole-Palmer Instrument Co., Niles, IL) through the membrane module. A damper is connected with the pump to eliminate fluctuations in pressure and flow rate. The feed flow rate is measured by a flow meter ranging from 0 to 2.0 L/min. The applied pressure is controlled with a needle valve on the outlet side of the membrane module. The pressure is monitored with two digital pressure gauges (PSI-TRONIX, Tulare, CA) at both ends of the membrane module. The difference between the readings of these two meters is usually less than 0.2 psi, and the average value of the two gauges is taken as the applied pressure on the membrane. Another reservoir is used to hold deionized water for establishing flow field and washing the membrane before and after each experiment. Permeate flux from the membrane system is weighted with an electronic balance and automatically recorded with a computer at predetermined time intervals. Permeate fluxes of pure water through the membrane are measured under different applied pressures, and the fluxes are nearly constant at each pressure. From the flux data, the membrane resistance Rm can be calculated from the following equation
Experiments Colloidal Suspensions. Two suspensions of silica colloids (P50 and P0L, Nissan Chemicals, Japan) are used as model colloids in the membrane filtration experiments. According to the manufacturer, the particles are uniform spheres with a size deviation
