PARTICLE FILTRATION FOR WASTEWATER IRRIGATION

By Avner Adin1 and Menachem Elimelech2

ABSTRACT: Conventional water filtration methods cannot be generalized for use in direct wastewater filtration for drip (trickle) irrigation systems. Effluents from an oxidation ponds-reservoir system and from an activated sludge plant were fil­tered through granular beds and filter screens, for the purpose of evaluating particle filterability. The granular beds remove particles larger than 10 (j,m with an effi­ciency of 40 to 85%, depending on the existence of surface straining and effluent type, whereas smaller particles (1-2 .̂m in size) are hardly removed, suggesting that minimum transport theory applies. The removal ratio for all particles measured increases with grain size and with bed depth, and decreases with filtration velocity, affecting the lower particle size range more. Filter screens clog very rapidly even though they remove only about 1-2% of the total suspended solids (TSS). Both turbidity and TSS are inferior to particle size distribution measurements for filter-ability evaluation of wastewater effluents.

INTRODUCTION

Clogging of emitters in drip (trickle) irrigation sytems using treated waste­water effluents is primarily attributable to suspended matter in the water (Adin 1978; Bucks et al. 1982; Dasberg and Bresler 1985). Suspended solids cause rapid pressure drops and flow disturbances in screen filters commonly used for the protection of sensitive appurtenances (Adin and Alon 1986). Granular deep-bed filtration is a means of major importance for the removal of suspended matter to cope with these problems. In conventional water treatment by granular filters, removal of suspended solids is usually im­proved by the use of a finer medium, a deeper filter bed, or a lower filtration rate, while headloss buildup is increased by a finer medium, a deeper filter bed, or a higher filtration rate (Ives 1980; Ives and Sholji 1965). In filtration of wastewater effluents, however, these relationships may not hold. Depar­tures from these generalizations have been reported during the last fifteen years in works in the literature dealing with wastewater filtration.

The purpose of this work was to study the filterability properties of sec­ondary effluents used for irrigation. The filtration was direct and without chemical pretreatment, as is commonly practiced in agriculture. Pilot ex­periments with both granular and screen filters were carried out in the lab­oratory with two types of secondary effluents. Emphasis was placed on par­ticle size distribution (PSD) measurements and analysis for better evaluation of the results.

'Assoc. Prof., Human Envir. Sci. Div., Graduate School of Appl. Sci. and Tech., The Hebrew Univ. of Jerusalem, 91904 Jerusalem, Israel.

2Doctoral student, Dept. of Geography and Envir. Engrg., Johns Hopkins Univ., Baltimore, Maryland 21218; formerly, M.S. Student, Human Envir. Sci., The He­brew Univ. of Jerusalem, Israel.

Note. Discussion open until November 1, 1989. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on July 10, 1987. This paper is part of the Journal of Irrigation and Drainage Engineering, Vol. 115, No. 3, June, 1989. ©ASCE, ISSN 0733-9437/89/0003-0474/$1.00 + $.15 per page. Paper No. 23593.

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WASTEWATER FILTRATION

Characteristics of Suspended Solids There is a large variability in the concentration and properties of the sus­

pended solids in secondary effluents, depending on the treatment applied prior to the filtration system. Tebbutt (1971) reported that the concentration of suspended solids in effluents may change by a factor of 2 within an hour. Biological floes from secondary effluents appeal- to be stronger and more resistant to sheer forces than are chemical floes found in water treatment, whereas floes in chlorinated effluents are smaller, lighter, and more fragile than those in unchlorinated effluents (Hsiung 1980). Tchobanoglous and Eliassen (1970) found that'PSD in an activated sludge effluent was bimodal. They also found that the relationship between turbidity and gravimetric total suspended solids (TSS) data was linear up to 14 NTU and became curvilinear for larger values of turbidity.

PSD data for aqueous particulates larger than 1 u.m in many freshwater and wastewater systems are known to be modeled with the following two-parameter power law distribution function (Kavanaugh et al. 1980):

in which TV = particle number density; dp = particle size; and A, p = em­pirical constants. The exponent provides an estimate of particulates contri­bution by size to the total particulate number, the surface area, the volume, and the light scattering coefficient. Removal mechanisms of particulates in granular beds are markedly affected by the particle size. Yao et al. (1971) showed that particles of 1-2 u,m in size have minimal opportunity for re­moval, since transport mechanisms of these particles within the filter bed are less efficient.

Effect of Filtration Rate Fitzpatrick and Swanson (1980) found that TSS removal efficiency and

filtration rate were inversely related. Tchobanoglous and Eliassen (1970) have shown that the filtration rate had little effect on TSS removal. According to Tebbutt (1971) and Bench et al (1981), increasing the filtration rate does not appear to reduce the removal of TSS. In secondary effluent filtration, filtrate quality is less dependent on filtration rate and influent suspended solids concentration compared to water treatment (Baumann and Cleasby 1974).

Effect of Grain Size and Depth The size of filter media has a little effect on TSS removal, but does sig­

nificantly affect head-loss build-up (Baumann and Huang 1974). Tebbutt (1971) found that suspended solids could be removed independently of media grain size in the range of 1.0-2.5 mm, but there was some evidence of suspended solids breakthrough for larger media. Tchobanoglous and Eliassen (1970) concluded that removal of suspended solids in secondary activated sludge effluent is primarily a function of the bed grain size, showing a significant improvement in TSS removal with finer media. Small media filters (0.45-0.55 mm) are actually surface-straining devices, resulting with an exponen­tial head-loss buildup and uneconomical filter runs (Bench et al. 1981). In filtration of secondary effluents media of at least 1.2 mm effective grain

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size are required and coarser media are preferred if appropriate backwash is to be provided. Increased media depth may not compensate for coarser media in achieving filtrate quality (Baumann and Cleasby 1974).

EXPERIMENTAL

Filtration Equipment The experimental equipment used for the pilot-scale filtration studies com­

prised a feeding system and filter columns. The effluents were poured into a feeding tank in which they were pumped by a small centrifugal pump to a constant head tank to maintain an available head of 2.0 m above the filter beds. Three 55-mm diameter Plexiglass columns were operated simulta­neously so that studies could be carried out on the same feed. The' trans­parent columns allowed visual observation of the suspended solids that ac­cumulated in the bed during the filtration experiments. The filters were operated at a constant flow rate in the conventional downward direction. The flow rate, measured by a flowmeter, was adjusted manually by a valve connected to the outlet of each filter column. Head-loss development was measured using piezometer tubes connected to the outlet and inlet of each filter. Grab samples for PSD and TSS monitoring were taken just before a significant head loss (5 kPa) was reached. The filter columns were 0.6 m long, and the bed depth varied from 0.15 to 0.45 m to allow room for expansion during backwash. When screen filtration experiments were conducted, the filter col­umns were replaced by 45-mm diameter screen-filter devices. The granular media were uniform local sands of 0.70, 0.84, and 1.20 mm effective grain size, with uniformity coefficients of 1.28, 1.23, and 1.21, respectively. The screen filters were of 80 and 130 |Jim polyester media, commonly used in irrigation systems.

Laboratory Apparatus A HIAC/ROYCO PC-320 multichannel particle-size analyzer was used

for measuring PSD. HIAC sensors operate on the light blockage principle and can commonly measure particles larger than 1 |xm. Particle counts were carried out using 1-60 |xm and occasionally 5-300 (xm HIAC sensors. From 1-26 u-m, measurements were taken at intervals of 1 u,m, while the 26 to 60 (jum size range was taken as one interval. Influent and filtrate quality were also monitored by turbidity measurements with a HACH 2100A turbidimeter and by gravimetric determination of suspended solids.

Wastewater Effluents Two kinds of secondary effluents were used in this investigation: (1) Ef­

fluents from an open, deep reservoir (Naan Reservoir) that stores stabili­zation ponds effluents (effluent storage in open, deep reservoirs is commonly used in Israel to enable collection of effluents during the winter for irrigation in the dry summer season); and (2) secondary effluent from a conventional activated sludge plant (Ein-Kerem Treatment Plant of Jerusalem).

RESULTS

The results presented in this paper include: (1) PSD analysis and turbid­ity—TSS relationship; (2) granular filtration experiments; and (3) screen fil-

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Parlicie Diameter (/jm)

1-5 5-10 10-15 15-20 20-25 25-60 Size Range (/im)

FIG. 1. PSD by Size Range in Wastewater Reservoir Effluents: (a) Continuous Distribution; {b) Distribution by Intervals

S 60

c o

n

M 20 Q

I . 1 I r- 1

1-5 5-10 10-15 15-20 20-25 25-60 Size Range iprn)

FIG. 2. PSD by Size Range Intervals in Activated Sludge Plant Effluent

tration experiments. Due to the large amount of experimental data, only rep­resentative results obtained in this study will be presented.

Particle-Size Distribution The particle size characterization was mainly concentrated in the 1-25 |jim

range, since this was the range where filtration was expected to be inde­pendent of interstitial straining mechanisms. Particle-number distributions of the secondary effluents are presented in Figs. 1 and 2. The bloc intervals in the figures were obtained by summation of l-|xm interval measurements. This presentation method is preferable to a continuous curve, since it enables one more easily to discern which filtration mechanism prevails for each range. As shown, PSD in the reservoir effluent is dominated by very fine particles (1-5 (xm), whereas the activated sludge effluent contains a greater percent­age of larger particles.

Regarding TSS removal and filter pore volume reduction, it is more im­portant that the particle volume distributions PVD be known, rather than PSD. The volume of particles at each l-u,m size interval, in the size range of 1-26 |xm, was calculated from the particle number distribution as follows:

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_ 30

.2 20

Dis

trit

o -

1-5 5-10 10-15 15-20 20-26 Size Range (/jm)

FIG. 3. PVD by Size Range Intervals in Wastewater Reservoir Effluent

aS 60 c o

=> 40

"in o 20

o

> 1

-5 5-10 10-15 15-2020-26 Size Range (pm)

FIG. 4. PVD by Size Range Intervals in Activated Sludge Plant Effluent

AV, = AM - dl (2)

where AV, = volume contribution by particles in the range of i to i + 1 u,m; AiV,- = number of particles in this corresponding size range; and dp = log­arithmic average of this size range. The logarithmic average is given by

dp = dpi+1 dpi

In dpH,

(3)

where dpi and dpi+l are the lower and upper limits of the l-(xm interval. Figs. 3 and 4 depict the PVD in the effluents by intervals, obtained by

summation of adjacent l-|xm intervals. It can be observed that in the 1-26 u,m range, the volume of particles in the activated sludge effluent is con­trolled by the larger particles, while in the reservoir effluent, fine particles of 1-10 u,m make a notable contribution to the total volume of particles. It can be expected, then, that the removal efficiency in terms of suspended solids will be higher in the activated sludge effluent since the chance for removal of suspended solids in direct granular filtration increases markedly with particle size.

Linearization of the distribution function in Eq. 1 yields

In-dN

d(dp) = - p i n dp + In A (4)

Least-square fits of the PSD data to Eq. 4 yielded good results, as shown

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0 1 2 3 4 5 LogedP(/jm)

FIG. 5. PSD Fitness to Power-Law Function Model: Open Circles Effluent, Filled Circles = Activated Sludge Effluent

Reservoir

in Fig. 5, with correlation coefficients of 0.98 and 0.99 for the reservoir effluent and the activated sludge effluent, respectively. As described by Ka-vanaugh et al. (1980) and Lawler et al. (1980), the very low value of the exponent (3 in Eq. 1 for the activated sludge effluent, i.e., 1.6, indicates that the total particle volume is dominated by the larger particles, whereas the exponent value of 3.2 for the reservoir effluent indicates that the mag­nitude of the total amount and the total surface area of the particles, as well

90

80

70

„ 60 \ |? 50

01 40 1-

30

20

1 0

0

-

-

0 1

10

o y i

0

1 r 1 T

i i i

20 30 40 Turbidity (NTU)

1 50

FIG. 6. TSS—Turbidity Relationship for Activated Sludge Effluent

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as the light-scattering properties, are controlled by very fine particles in­cluding submicron particles, which were not measured.

Turbidity—TSS Relationship Turbidity measurements have long been used in water treatment for mea­

suring filter efficiency. In wastewater treatment, however, TSS measure­ments are commonly used to evaluate particulate matter removal. It was necessary to search for a rapid field test that could be used to monitor the filtration process effectively. Turbidity measurement was chosen because of the ease with which it could be used in the field. However, effluent from the reservoir failed to prove a linear relationship between turbidity and TSS measurements. The correlation coefficient of 0.17 is very poor, presumably due to the variable nature of the colloidal particulates that significantly affect the light-scattering properties of the suspension and contribute relatively little to the mass concentration. On the other hand, activated sludge effluent showed a reasonably good linear relationship (correlation coefficient 0.96) between turbidity and TSS measurements, as shown in Fig. 6 (slope 2.81, intercept -11.31), indicating the feasibility of using turbidity to monitor the quality of this type of effluent, at least at that particular range.

RESULTS OF GRANULAR FILTRATION EXPERIMENTS

Reservoir Effluent Filtration The effect of filtration rate on head-loss development for a 0.7-mm media

sand bed is shown in Fig. 7. The head-loss curves show the characteristic exponential form, indicating that surface removal predominated. At a given head loss, water production per unit area decreased with an increase in the filtration rate. The raw water contained a few very large particles, clearly observed through the transparent column, which quickly clogged the media surface, forming a dark layer. Filter runs were very short due to the rapid head-loss development: 80 min for the low filtration rate (2.2 L/m2/s) and only 30 min for the higher rate (4.4 L/m2/s).

Fig. 8 presents particle-removal efficiency as a function of particle size for the same conditions previously mentioned. Better removal efficiency of particles at the lower filtration rate for all particle sizes was observed. The difference in percentage became smaller as particle size increased. Removal efficiency was at a minimum for the size range of 1-2 (xm, while it increased significantly with increase in particle size up to 9-10 jjim. At the higher filtration rate, an instantaneous phenomenon of more particles in the filtrate than in the effluent was observed in the size range of 1-3 u.m. Particles larger than 10 \im were removed with a constant removal efficiency of about 80%, most probably by the layer formed on the medium surface.

Although significant removal of large particles was noted, the removal efficiency in terms of concentration of suspended solids was very low, about 20% at a filtration rate of 3.25 gpm/sq ft (2.2 L/m2/s) and only 10% at 6.50 gpm/sq ft (4.4 L/m2/s). Actually, a continuous and steady TSS and turbidity breakthrough was observed during each filtration run. The effect of media grain size on particulate removal for the reservoir effluent was also studied, with interesting results: larger grain sizes clearly showed better re­moval efficiency of very fine particles (1-10 |xm). For particles larger than 10 (Jim (up to 60 u,m), there was no difference in the rate of particle removal.

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2 4 6 8 10 12

Filtrate Volume (m3/m2)

FIG. 7. Head-Loss Development During Filtration of Wastewater Reservoir Ef­fluents for Different Rates: v, = 3.25 gpm/sq ft (2.2 L/m7s); v2 = 6.50 gpm/sq ft (4.4 L/m2/s); Effective Grain Size = 0.7 mm; Bed Depth = 150 mm; TSS of In­coming Effluent = 104 mg/L

IOO

50

5 IO 15 Particle Diameter (/ jm)

20 25

FIG. 8. Removal Ratio versus Particle Size for Different Filtration Rates: Waste­water Reservoir Effluents; v, = 3.25 gpm/sq ft (2.2 L/m2/s); v2 = 6.50 gpm/sq ft (4.4 L/m2/s); Effective Grain Size = 0.7 mm, Bed Depth = 150 mm; TSS of In­coming Effluent = 104 mg/L

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*-s - 6 0 o > o if. 50 rr ^ 4 0 H i i i 1 1

0.7 0.8 0.9 1.0 I.I

Grain Size (mm) 1.2

FIG. 9. TSS Removal versus Filter Grain Size for Activated Sludge Effluent: In­coming TSS = 138 mg/L; v = 3.1 gpm/sq ft (2.1 L/m2/s); Experimental Bed Depth = 400 mm

Activated Sludge Effluent Removal efficiency in terms of TSS concentration increased with media

grain size (see Fig. 9). This finding was confirmed by PSD measurements in influent and filtrate. Fig. 10 describes the removal efficiency of particles as a function of particle size ranges for the three media investigated. The rate of head-loss buildup was much higher for the finer media, although there was some evidence of surface removal in the coarsest medium.

The effect of filtration rate on TSS removal was investigated by four ex­perimental series with filtration rates ranging from 0.8 L/m2/s up to 6.0 L/m2/s. The results are presented in Fig. 11, suggesting a linear increase in TSS removal with a decrease in filtration rate at this range. The average slope of all series was the same, indicating an improvement of about 2% in TSS removal with a decrease of 1 m/hr in filtration rate. As can also ob­served in Fig. 11, the percentage of TSS removal increases with the con­centration of TSS in the influent. The difference in removal efficiency be­tween series a, b, and c, d at the same filtration rate (2.1 L/m2/s) and close

o5 80 "o | 60 CD

to _a> o t 20 o Q_

0

-

-

_ "1.2 mm

_0.84mm

0.7 mm

1

J

1-5 5-10 10-15 15-20 20-25 25-60 Size Range (jum)

FIG. 10. Particle Removal by Size Range Intervals for Different Filter Grain Sizes: Activated Sludge Effluent, TSS = 138 mg/L; v = 3.1 gpm/sq ft (2.1 L/m2/s); Bed Depth = 400 mm

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"o > o ir

CC

C/)

\-

60

fin

4 0

30

20

10

1 2 3 4 5 6 7

Fi l trat ion Ve loc i t y ( l /m 2 / s )

FIG. 11. Effect of Filtration Rate on TSS Removal: Activated Sludge Effluent; Ef­fective Grain Size = 1.2 mm; Bed Depth = 300 mm; Triangles and Circles Rep­resent Two Different Series of Experiments

TSS values was due to changes in the nature of the suspended matter in the secondary effluents of the treatment plant during the four-week period be­tween these experiments.

SCREEN FILTRATION EXPERIMENTS

Reservoir Effluent Experiments with the reservoir effluents showed that screen filters with

130 am of polyester media were clogged after a short period of time (1/2 hr) at a filtration rate of 6.6 L/m2/s. The immediate clogging was caused by a very few large particles, which formed a compressed cake on the screen. TSS removal by the 130 am screen was no more than 2%. A phenomenon of more particles (15-20 am in size) leaving the screen was observed, point­ing out a possible detachment mechanism, as previously reported by Adin and Alon (1986). This rapid clogging emphasized the need for pretreatment of the effluent before its use.

Activated Sludge Effluent Screen filtration experiments were performed with the activated sludge

effluent, using polyester screens of 80 and 130 am with different filtration rates. It was found that water production per unit area of filter screen de­creased with an increase in filtration rate due to rapid head-loss buildup, indicating that clogging was enhanced by higher filtration rates. TSS re­moval was found to be less than 1% and in some cases a negative value was obtained. Since negative removal is impossible, it may be accounted for as experimental error in gravimetric determination of suspended solids or as an

J I I L

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20

o 15 a. -*: in tft O _l

•g 10 a) I

5

fegt?T-o--or-o~o--0--0-i-u I I 0 50 100 150

Filtrate Volume (m3/m2)

FIG. 12. Head-Loss Development in Screen Filters with and without Pretreat-ment by Granular Filter of 1.2 mm Grain Size, 2.1 L/m2/s Rate and 0.45 m Depth; TSS = 66-70 mg/L; v = 9.7 gpm/sq ft (6.6 L/m2/s); Full Line = without Pretreat-ment; Dashed Line = with Pretreatment

instantaneous negative value resulting from particles breakdown. The effect of pretreatment by granular filtration on screen filter runs was radical. Fig. 12 describes the head-loss development in such a case (80 and 130 |j,m of polyester screens). As shown, the rate of head-loss buildup was significantly decreased by pretreatment with granular filtration.

INTERPRETATION

Filtration through porous media is a process which is based in principle on the capture of particles, rather than on removal of masses of solids. The main tool for evaluation of filter performance in wastewater filtration prac­tice has been the removal ratio of TSS and/or turbidity. The aforementioned results clearly demonstrate that removal of particles of different sizes may be affected by the type of wastewater and the physical parameters of the filtration system. Besides the importance of studying PSD in filtration for better understanding of filtration mechanisms, the PSD analysis may enable a better choice of filter and its operational conditions for pretreatment before use with operational units such as drip irrigation systems.

Both PSD measurements of the wastewater effluents and filtered water were adequately described using a power-law distribution function. Particle measurements in the range of 5-300 |xm produced no evidence of bimodal distribution of the particle sizes, as previously reported by Tchobanoglus and Eliassen (1970). Logarithmic linearization of the function enables the de-

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termination of the (3 factor, which provides some predictions as to the rel­ative contribution of different particle sizes to the total surface area and vol­ume of the particles.

The comparison of filter-removal efficiency of reservoir particles for dif­ferent filtration rates as a function of particle size showed a lower efficiency for the higher rate, probably due to the higher hydrodynamic shear forces developed in the bed, affecting particularly the smaller particle range. The tendency of the removal curves toward a minimal efficiency in the 1-2 (Jim range (Fig. 8) supports the experimental and theoretical works of other in­vestigators (Habibian and O'Melia 1975; Yao et al. 1971), which pointed to a minimal particle transport efficiency in between the range where gravity and interception mechanisms and diffusion mechanism dominate. However, no information based on direct particle-size measurements was gathered about the behavior of submicron particles in the filter bed.

The instantaneous phenomenon occasionally observed, in which more par­ticles appeared in the filtrate than in the original filter influent, may be at­tributable to shear forces that develop in the bed, causing the breakdown of aggregates and colonies of algae into single cells or the rupture of small particles from biological floes. The observation that larger grain sizes re­moved fine particles better than small grain sizes for both types of effluents tested contradicts transport and filtration theories (Yao et al. 1971). This is still a matter for further research.

In this study, screen filters were evaluated for their filtration and clogging potential and for the effect on clogging of pretreatment by granular media filtration. It is suggested that screen filters can be used to develop a prelim­inary test for determining the clogging potential of different types of water. One should bear in mind, though, that by no means does a screen-filter test simulate a deep-bed granular media filter, since their removal mechanisms are principally different.

CONCLUSIONS

1. Filterability of wastewater effluents can be effectively evaluated using PSD measurements in the following ways: (1) Calculations of removal ratios of dif­ferent particle sizes for different design variables; (2) computation of particle volume distribution according to particle size ranges; and (3) determination of the p factor value from the power law distribution function. This value, when larger than 3.0, suggests lower filtration efficiency.

2. More than 90% of the particles in the reservoir effluents within the range detected were smaller than 10 (xm; these particles constituted a large part of the total solids volume. In the activated sludge effluents, the contribution of the small particles to the total volume was considerably smaller than that of the larger particles. The particulate removal efficiency through granular beds in­creased with filter grain size and decreased with filtration velocity (especially valid for the lower particle size range).

3. The removal ratio of particles larger than 10 u,m in direct granular filtration of the effluents studied was relatively large, while smaller particles were hardly removed; removal efficiency tended towards a minimum in the 1-2 u,m size range.

4. Good linear correlation was found between turbidity and TSS measure-

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ments for the activated sludge secondary effluent. However, no correlation ex­isted for the reservoir wastewater, possibly due to the variable nature of the colloidal particles. PSD measurements are more informative than turbidity and TSS measurements for the purpose of filterability and clogging studies.

5. Screen filters performed very poorly—their removal efficiency was about 1%, which was sufficient to cause surface clogging. However, screen filters may provide a basis for the development of a clogging index that would help in de­fining the clogging potential of different types of water.

ACKNOWLEDGMENT

This work was mainly supported by a grant from the Robert Szold Institute for Applied Science.

APPENDIX I. REFERENCES

Adin, A. (1978). "Problems and advanced methods in filtration for low rate appli­cators." Proc, Int. Conf. on Water Systems and Applications, Israel Ctr. of Water­works Appliances, Tel Aviv, Israel, V-3.

Adin, A., and Alon, G. (1986). "Mechanisms and process parameters of filter screens." J. Irrig. and Drain. Engrg., ASCE, 112(4), 293-304.

Baumann, E. R., and Cleasby, J. L. (1974). "Wastewater filtration: Design consid­erations." Technology Transfer, Series No. EPA-625/4-74-007a, Envir. Protection Agcy.

Baumann, E. R., and Huang, J. Y. C. (1974). "Granular filters for tertiary waste­water treatment." J. Water Pollution Control Fed., 46(8), 1958-1973.

Bench, B. L., et al. (1981). "Evaluation of wastewater filtration." Water Quality Series, No. UWRL/Q-81/01, Utah Water Res. Lab.

Bucks, D. A., Nakayama, F. S., and Warrick, A. W. (1982). "Principles, practices and potentialities of trickle irrigation." Advances in Irrigation, D. Hillel, ed., 1, Academic Press, San Diego, Calif., 219-298.

Dasberg, S., and Bresler, E. (1985). Drip irrigation manual, Int. Irrig. Information Ctr., Volcani Ctr. for Agric. Res., Beit-Dagan, Israel.

Fitzpatrick, J. A., and Swanson, R. (1980). "Evaluation of full-scale tertiary waste­water filters." EPA-600/2-80-005, Envir. Protection Agency.

Habibian, M. T., and O'Melia, C. R. (1975). "Particles, polymers and performance in filtration." J. Envir. Engrg. Div., ASCE, 101(4), 567-583.

Hsiung, K. I. (1980). "Chlorine effect on secondary effluent filtration." J. Envir. Engrg. Div., ASCE, 106(3), 649-654.

Ives, K. J. (1980). "Deep bed filtration: Theory and practice." Filtration and Sep­aration, 17(2), 157-166.

Ives, K. J., and Sholji, I. (1965). "Research variables affecting filtration." J. Envir. Engrg. Div., ASCE, 91(4), 1-18.

Kavanaugh, M. C , et al. (1980). "Use of particle size distribution measurement for selection and control of solid/liquid separation processes." Particles in Water, M. C. Kavanaugh and J. O. Luckie, eds., Advances in Chem. Series, Amer. Chem. Soc, Washington, D.C., 305-328.

Lawler, D. F., O'Melia, C. R., andTobiason, J. E. (1980). "Integral water treatment plant design." Particles in Water, M. C. Kavanaugh and J. O. Luckie, eds., Ad­vances in Chem. Series, Amer. Chem. Soc, Washington, D.C., 353-388.

Tchobanoglous, G., and Eliassen, R. (1970). "Filtration of treated sewage effluent." J. Sanitary Engrg. Div., ASCE, 96(2), 243-265.

Tebbutt, H. Y. (1971). "An investigation into tertiary treatment by rapid sand fil­tration." Water Res., 5(3), 81-92.

Yao, K. M., Habibian, M. T., and O'Melia, C. R. (1971). "Water and wastewater filtration: Concepts and applications." Envir. Sci. and Tech., 5(11), 1105-1112.

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APPENDIX II. NOTATION

The following symbols are used in this paper:

A C

Co dp

H N

NTU AN,

PSD PVD

r t

TSS V

Ay, P

am

= = = = = = = = = = = = = = = = =

empirical constant related to PSD; concentration; initial concentration; particle size; head loss; particle number density; Nephelometric Turbidity Units number of particles in the size range of i to i particle size distribution; particle volume distribution; correlation coefficient; filtration time; total suspended solids; filtration velocity/rate; volume contribution by TV, particles; empirical factor related to PSD; and micrometer.

+ 1 am;

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