Envlron. Sci. Technol. 1983, 27, 1099-1 107
Solids Accumulation during Deep Bed Filtration James R. Hunt,‘ Bor-Chlh Hwang,? and Laura M. McDowell-Boyer*
Environmental Resources Engineering, Department of Civil Engineering, University of California, Berkeley, California 94720
A series of pilot plant experiments provide data on particle accumulation and increasing hydraulic gradients within packed beds. For two medium sizes and three filtration velocities, increased hydraulic gradients normalized by clean-bed gradients all follow the same dependence on u, the mass of solids deposited per filter volume. For u less than 4 g/L, the normalized gradient goes as u2/3. Particle accumulation ceases when solids have accumulated to only 15 g/L, which corresponds to less than 2% of the pore space occupied by deposited solids. After the mass of retained solids reaches a steady-state value, the hydraulic gradients continue to increase. Quantitative models can be fitted to these observations, but only if the accumulated particles form a porous deposit that decreases in porosity as particles accumulate. The processes causing this porous deposit to decrease in porosity could be internal filtration caused by flow through the deposit or consolidation caused by hydrodynamic forces.
Introduction Particle removal within granular filters is important in water treatment processes and in purifying groundwater aquifers of pathogens and other colloidal contaminants. The actual design and operation of filters has been largely empirical because there is no fundamental understanding of filter performance once particles accumulate within pore spaces. There has been extensive theoretical and experimental work on the initial deposition rate of particles onto clean porous media as reviewed by Spielman ( I ) and Tien and Payatakes (2). When there is no electrostatic repulsion between the suspended particles and the media surfaces, experimental results and predictive theories for clean media are in good agreement. Under conditions of electrostatic repulsion between particles and clean-filter media, available theories are not predictive (1,3,4). As particles accumulate, clean-media conditions cease to exist, and the accumulated deposit alters further particle deposition and fluid flow. Added collector surfaces can improve particle deposition, but the deposit causes a decrease in permeability which is reflected in increasing hydraulic gradients under constant flow conditions. The available models for particle accumulation are empirical, and such models are not predictive under new conditions ( 5 , 6 ) . For this reason, filter performance is estimated in practice through extensive pilot plant experiments. In order to improve the predictability of filter performance, it is necessary to improve our understanding of the mechanisms underlying the filtration process. Following a brief review of previous work by others on modeling particle retention in filters, data from a set of pilot plant experiments are reviewed. This data set allows a dynamic, depth-dependent analysis of the coupled processes in+ Present address: Environmental Engineering Department (V7), China Steel Corp., P.O. Box 47-29, Hsiao Kang, Kaohsiung 81233, Taiwan, Republic of China. Present address: Oak Ridge National Laboratory, Grand Junction Office, P.O. Box 2567, Grand Junction, CO 81502.
*
0013-936X/93/0927-1099$04.00/0
0 1993 American Chemical Soclety
volved in deep-bed filtration. Models that incorporate mechanisms not usually considered during deep-bed filtration are proposed to represent the data.
Filtration Models The usual starting point of filtration modeling is a phenomenologicalapproach first used by Iwasaki (7) based on a mass balance relationship for a plug flow reactor
eb at
-d!? az
where u is the specific deposit (or mass accumulated per bed volume), C is the suspended solids concentration, t is time, U is filtration or darcy velocity, and z is filter bed depth. Camp (8)has provided a careful analysis of filter performance based on this approach. Another approach to analyzing the dynamic filtration process, or clogging, is to model deposition and erosion as separate rate processes similar to adsorption (9-12). This approach had no physical justification but is adopted for mathematical convenience because there is very little fundamental understanding of particle release when flow and solution conditions remain fixed (13). As particles accumulate, the filter’s permeability is reduced, and under constant flow conditions, the hydraulic gradient increases. Tien (ref 6,p 29)provides a summary of empirical models for hydraulic gradients that are of the form
+ o2a2+ 03u3+ ...) i = io (1 + (2) where i is the hydraulic gradient, io is the clean-bed hydraulic gradient, and the p’s are empirical coefficients. Empirical models for the hydraulic gradient are necessary because completely theoretical models are not predictive without parameter adjustments. Ojha and Graham (14) note that the resulting parameters for the empirical models cannot be generalized to other conditions. Tien (ref 6,p 336)also summarizes empirical expressionsfor the pressure drop during aerosol filtration where the correlations are of the form ( P - Po)/Po= .a@ (3) where Po and P are the pressure drops under clean and clogging conditions, respectively, and the Ps are parameters. The parameter ,152 covered the range 0.76-1.42but was filter-depth and velocity dependent. A more mechanistic approach to particle accumulation has followed from the work of Yao et al. (15) using models developed for aerosol filtration. O’Melia and Ali (16) assumed that deposited particles can act as additional collectors for subsequent particle removal. Their model for filter ripening has an autocatalytic characteristic requiring recursion equations to describe the spatial and temporal distribution of filtration efficiencyand head loss. Nevertheless, deposit saturation is not considered in their model, and the model is restricted to a monodisperse suspension. Vigneswaran and Tulachan (17)extended the O’Melia and Ali formulation to include a maximum limit Environ. Scl. Technol., Vol. 27,
No. 6, 1993 1099
on particle deposition to describe the entire filtration cycle. The model contains five separate parameters that were dependent on filtration velocity, medium and particle sizes, and coagulant along with two other parameters that were held constant. Tien et al. (18)modeled the entire filtration operation as two stages: the first one is dominated by a uniform coating of the collectors, and the second stage is simulated by a constriction of pore opening. The attempt to account for deposit morphology transition at two extremes was partially satisfactory. Subsequent work by Chiang and Tien (19, 20) extended the modeling efforts but found that the observed increase in hydraulic gradient was an order of magnitude greater than the models predicted. Recently, Darby and Lawler (21)and Darby et al. (22) made simultaneous measurements of head loss and particle size distributions in different layers of filters as particles accumulated. They argued that both floc formation and detachment mechanisms were responsible for their observed filter behavior but offered no mechanistic model. Theories for particle removal by deep-bed filters are not sufficiently advanced for the sole use in treatment plant design, and pilot plant studies are almost always conducted to obtain data on filter performance for the specific suspension of solids, coagulant, mixing conditions, media characteristics, and filtration velocity. These data are usually collected over large depth or infrequent time intervals and, thus, may not identify the location of particle retention. The following section discusses the experimental system developed by Wright (23) for his studies on filter performance. The experimental procedures are improved over previous efforts, and the resulting data are sufficiently detailed to provide insight into the processes responsible for permeability reduction.
Experimental Methods and Data Analysis The pilot plant filtration system adopted by Wright (23) provides for control of flow rate, background elec-
trolyte concentration, clay dose, coagulant dose, and rapid mixing of coagulant with the suspension in a centrifugal pump. An inert salt and bicarbonate for pH buffering were added to reproduce conditions likely encountered in waters using alum [Alz(S04)~16H~OI as a coagulant. Tap water was deionized and then dosed with a concentrated feed solution to give 50 mg/L KC1,42 mg/L NaHC03, and 30 mg/L kaolin powder (food grade, Mallinckrodt Chemical Works). Particle destabilization was achieved by the addition of alum at the suction side of a centrifugal pump at an optimum dose of 10 mg/L that was determined from jar tests. The clay and alum feeds were both controlled by a multiple head pump so that a stoichiometry was maintained between coagulant dose and clay concentration. This alum dose produces 2.5 mg/L aluminum hydroxide, and while the pH of the suspension was not reported, it is estimated to be 7 for this closed system. The destabilized suspension was introduced 41 cm above the filter media in a 10.2-cm i.d. filter column as illustrated in Figure 1. The flow rate into the filter column was constant throughout all the filter runs, and variations in flow through the media were achieved by adjusting a flow controller at the bottom of the filter column. Excess suspension flowed upward to a constant head tank and was removed from the system. This arrangement achieved a constant physical and chemical environment for the 1100
Envlron. Sci. Technol., Vol. 27, No. 6, 1993
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CONSTANT HEAD TANK
DESFABILIZED KAOLIN SOLLITION
FILTER COLUMN
METER
To WASTE
Figure 1. Pllot plant filter flow scheme used by Wright (23).
suspension among filter runs at different filtration velocities and medium sizes. The destabilized suspension had a 1.6-min flow time following the mixing pump before entering the filter column. The estimated shear rate in this part of the piping system is about 20 s-l. On entering the filter column, flow times to the filter media varied from 4.7 min at a 0.145 cm/s filtration velocity to 1.2 min at a 0.554 cm/s filtration velocity. The fluid shear rate in the open filter column under these conditions is expected to be much less than the shear within the inlet piping system. Two narrowly sized sands were used by Wright as filter media along with three flow rates. The fine sand had a geometric mean size of 0.54 mm with a range of 0.4950.589 mm and a porosity of 0.40. The coarse media was 1.29 mm in geometric mean size distributed over 1.191.40 mm with a reported porosity of 0.44. Filtration velocities of 0.145 and 0.279 cm/s were examined in the fine media and 0.145,0.279, and 0.554 cm/s in the coarse media. Experiments were conducted repeatedly on the same media. Prior to an experiment, the filter column was fluidized by upward flow of clean tap water to remove any solids, achieve thermal equilibrium, and remove trapped air bubbles. The filter column had sampling and manometer ports installed to measure suspended solids concentration and hydraulic head at 20-30-min intervals for up to 300 min. The fine medium column had ports located at 0.63, 3.2, 5.7, 8.3, 13.3, 21, and 31 cm below the surface, and the coarse medium ports were at depths of 1.27,3.8,6.4,8.9, 14,22, and 32 cm. Manometer ports from above the filter and at the seven locations within the filter were connected to tubes mounted vertically, and water heights were visually recorded. Suspension samples were obtained with a motor-driven syringe sampler. The sampler uniformly withdrew 30 mL vola through 0.32-cm diameter tubing over an 8-min time period. The effective sampler face velocity inside the filter was 0.41 cm/s, nearly isokinetic with the actual fluid velocity inside the clean-mediumpores (0.36-1.4 cm/s). Suspended solids concentrations are reported as mass of solids that would be retained on a 0.2-pm filter. The sample volumes were limited to 30 mL each, and this precluded accurate analysis using filtration for all samples. Instead, samples were analyzed by the amount of light
scattered by the suspended solids. To eliminate any differences in light scattering by variations in aggregate size distributions between samples, the clay-aluminum hydroxide aggregates were dispersed by dissolving the coagulant with a few drops of nitric acid and then shaking the samples by hand prior to pouring the sample into a 5-cm spectrophotometer cell. Sample absorbance was linearly related to suspended solids concentration using a calibration curve developed from 0.2-pm Nucleopore filtration of the clay-aluminum hydroxide suspension prior to acidification. This procedure allowed rapid measurement of suspended solids concentration to less than 1mg/ L. The experimental data consist of a time series of solids concentration and hydraulic head both above the filters and at seven sampling depths. The data were used to calculate specific deposits and hydraulic gradients at various depths and times within the filters. The specific deposit at a given depth zj and time t is equal to the integral of eq 1, the mass balance expression: (4) Since the raw data consisted of concentration at discrete depths and times, the integral was approximated numerically as a sum a(zj,t ) =
-.E(-)acaz
At
(5)
zj
where the concentration gradient at a depth zj was approximated by the average gradient over the time interval t - At to t
and At is the time between samples. The concentration gradient at depth zj and time t was approximated as (7) The accuracy of the approximations indicated in eqs 5-7 could not be verified directly because the specific deposit a t the end of the experiment was not determined independently by analysis of back-washed particles; yet, an overall mass balance is used to check the validity of the estimation method. The inflow solid mass, Mi,,, is calculated by integrating over the mass flow rate up to the time, T,that the experiment was terminated
Mi, = $,’AUC,(t) d t where A is the filter column cross-sectional area, and C,(t) is the influent solids concentration. The mass leaving the filter column, Mout,at depth L, is also calculated as
Mout= JTAUC,(t) d t
(9)
where CL(t)is the solids concentration at the deepest depth, L. Since the influent solids concentration was nearly constant and suspended solids concentration in the bottom sampling port was low and slowly varying with time, accurate calculations of mass in and mass out are possible. At the end of each experiment, the calculated specific deposit over the column can be integrated to arrive at
total mass retained:
For all five experiments conducted by Wright, the solid mass influent to the filter was within 5% of the calculated mass accumulated on the filter plus the measured mass in the effluent. This indicates acceptable numerical procedures for calculating the deposited mass. The hydraulic gradient at depth Zj and time t was calculated as
where h(zj, t ) is the hydraulic head at depth zj and time t.
Experimental Results Selected experimental results from the five sets of experimental conditions are presented in Figures 2 and 3. In plot A of each figure, the measured suspended solids concentration is plotted with depth for the various sample times. In plot B, the hydraulic gradient calculated from measured hydraulic heads is plotted against depth for various sample times. Plot C contains the specific deposit calculated from the concentration profiles by eq 5. Figure 2 for the 0.54-mm sand indicates very efficient solids removal in the top few centimeters as evidenced by the rapid decline in suspended solids concentration with depth. After 90 min of filtration, there is no reduction in the suspended solids concentration over the top 0.63 cm, and the top 3.2 cm no longer removes particles after 180 min. The hydraulic gradient data in plot B showscontinual gradient increases in the top 10 cm of the filter, with the topmost layers increasing more than deeper layers. The specific deposit data in plot C for this filter have a maximum accumulation of 14.5g/L in the top 0.63 cm and about 7 g/L in the second layer, over the depth interval 0.63-3.2 cm. The next two sampling intervals of 3.2-5.7 and 5.7-8.3 cm have specific deposits exceeding 7 g/L after 150 min with no evidence of reachlng another maximum value. While the specificdeposit reached depth-dependent maxima in the top two layers, the hydraulic gradient continued to increase with time in these layers. Similar behavior was noted by Camp (8) in his analysis of pilot plant filtration data. The 1.29-mm sand performance is given in Figure 3 for a filtration velocity of 0.279 cm/s. The suspended solids concentrations plotted in Figure 3A show that particle removal is occurring over the 32-cm depth of the filter. Comparing concentration profiles between 30 and 60 min shows a reduced concentration at depths of 6.4 cm and deeper, indicating some improvement in filter performance as particles accumulate. The top 1.26 cm of the filter ceases to remove particles beyond 120 min, and the top 3.8 cm no longer retains particles after 150 min. The hydraulic gradients plotted in Figure 3B continuously increase with time at all sampling depths, even the topmost intervals where no further deposition is observed. The specific deposit profiles in Figure 3C show a maximum of 3 g/L in the top 3.8 cm of the filter reached after 150 min, but greater values are found at deeper depths, and there is no apparent maximum reached yet at 8.9 cm after 210 min. Environ. Scl. Technol., Vol. 27, No. 6, 1993
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DEPTH [cml Flgure 2. Experimentaldata for 0.54-mm sand at a flltratlon veioclty of 0.279 cm/s: (A) suspended solids concentratlon; (B) hydrauilc gradlent; (C) speclflc deposlt.
The pilot plant data show dramatic increases in hydraulic gradients following the accumulation of relatively little solid material. The maximum specificdeposit is only 15 g/L of filter media. Assuming a solid density of 2.65 g/cm3 for the clay mineral and a bed porosity of 0.4, the volume occupied by solids is only 1.4% of the pore volume. At a filtration velocity of 0.279 cm/s through 0.54-mm sand, this solids deposit caused a 51-fold increase in hydraulic gradient. Others have found similar dramatic increases in hydraulic gradients with comparable specific deposits (8, 10, 14, 24). The structure of the deposited solids that can accomplish such a dramatic increase in hydraulic gradients has not been adequately appreciated or modeled. While increases in hydraulic gradients are useful in examining the hydrodynamics of filters, the fluid shear rate is an alternative measure for evaluating forces that 1102 Environ. Scl. Technol., VoI. 27, No. 6, 1993
' I 0
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90MIN 120MIN 150MIN lBOMIN 210MIN
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DEPTH [cm] Flgure 3. Experimental data for 1.29-mm sand at a flitratlon velocity of 0.279 cm/s: (A) suspended solids concentration; (e) hydraulic gradient; (C) specific deposit.
act on suspended particle aggregates and deposited solids. The relationship between the mean fluid shear rate G and the hydraulic gradient was utilized by Ives (25) in characterizing the importance of coagulation within filters with
where g is gravitational acceleration, p is porosity, and v is the kinematic viscosity of water. Table I presents the fluid shear rates calculated from eq 12 for the 0.54- and 1.29-mm filter results under clean-bed conditions and at the maximum hydraulic gradients measured. SinceWright did not report clean-bed hydraulic gradients, they were estimated from the data. For both medium sizes,the cleanbed hydraulic gradient at 0.145 cm/s is calculated from head measurements at the bottom three manometer ports
Table I. Hydraulic Gradients and Fluid Shear Rates Inside Filters 0.54-mm sand clean clogged io G imm Gmax
filtration velocity (cm/s) 0.145 0.279 0.554
0.38 0.73
110 200
22 37
790 1430
1.29-mmsand clean clogged io G imax Gmax 0.12 0.23 0.46
58 110 220
1.73 2.8 6.2
I
1003 (8-l)
220 390 820
10:
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-
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1
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