
Hydraulic Design of Sand Filters

Detention Volume, P_{o}, Drain Time T_{d} in hours 
Suggested Percent Removal  R_{D} 

Detention 
Retention 

48 
60 
90 
24 
55 
85 
12 
50 
80 
6 
40 
75 
3 
30 
70 
1 
20 
50 
Table 1. Suggested Removal Rates by Retention and Detention Upstream of a Media Filter
For Cases 1 and 2 defined in Figure 2 the concentration of TSS leaving the filter facility can be estimated using Equation 4.
(4)
In which,
E_{sfr }= the change in suspended solids concentration through the filter in mg/l
R_{T }= total system's average percent removal rate of TSS (95% recommended)
R_{D }= the percent removal rate for the retention or detention basin upstream of the filter bed from Table 1
For Case 3 the above analysis needs to be modified. The water column that is above the filter's surface receives no pretreatment and all the TSS in this water is subject to removal by the filter. Thus, for Case 3 reduction in the EMC of TSS by the filter installation can be expressed by
(5)
In which,
r_{R }= [A_{R} / (A_{R}+A_{f})], ratio of the retention basin's surface area to the total system's surface area (When all detention storage is above the filter, r_{R} = 0 and all the TSS load is removed by the filter)
A_{R }= surface area of the retention pond's permanent pool in square feet
A_{f }= surface area of the filter bed in square feet
The classic relationship for water percolating through uniform soil media, such as sand, breaks down for a slow sand filter when fine sediment accumulates on top of its surface. Field observation and laboratory tests (Neufeld, 1996; Urbonas et al., 1996b) show that the flowthrough rate for a sand filter (and other media as well) quickly becomes a function of the sediment being accumulated on the filter's surface. This relationship for a sand filter (i.e., Figure 3) appears to be not sensitive to the hydraulic surcharge on the filter's surface and can be expressed by Equation 6.
(6)
In which,
k_{ }= empirical flowthrough constant (see Figure 3)
c = empirical exponential decay constant (see Figure 3)
L_{m }= TSS load accumulated on the filter's surface in pounds per square foot
Figure 3: Flowthroughrate of sand filter as a function of TSS removal.
Recognizing that not all runoff during any given year will pass through the filter installation, the average annual load removed by the filter facility can be expressed by Equation 7.
(7)
In which,
L_{afr }= average annual TSS load removed by the filter in pounds
b = the fraction of all average annual runoff volumes that is treated by the filter facility (i.e., not bypassed)
The fraction of all runoff volume from the tributary area that will be treated through the filter facility is, in part, a function of the WQCV upstream of the filter. Depending on whether the basin is bypassed or overtopped will also determine the amount of treatment provided to the excess volumes during large storms. If the maximized capture volume is provided, approximately 80% to 90% of all runoff volume can be treated by the filter installation. If, however, the mean capture volume is used, approximately 65% to 70% of the total annual runoff volume will be fully processed through the filter.
The filter will also need to be maintained to stay in operation. The contaminated and clogged layers will need to be removed and replaced with new media and eventually (say after five to ten surface cleanings) the entire media filter will need to be replaced. Equation 8 can be used to estimate the TSS load removed by each square foot of the filter during each maintenance cycle.
(8)
In which,
L_{m }= average TSS load removed by each square foot of the filter during each maintenance cycle in pounds per square foot per maintenance cycle
m = number of times per year the filter is cleaned and reconditioned. Use a fraction (i.e., 0.5) if more than one year between cleanings
A_{fm }= surface area of the filter based on annual TSS load removed in square feet
Equation 8 can be rearranged to estimate the filter's area based on TSS removed.
(9)
Equation 10 can be used to estimate this area based on the desired drain time of WQCV.
(10)
In which,
Q = the design flowthrough rate through the sand filter's surface in inches/hour
T_{d }= the time it takes volume P_{o} to drain out at rate q in hours
A_{fh }= surface area of the filter based on hydraulic sizing in square feet
The designer now has to find the filter area that comes close to satisfying both conditions and the following design procedure to accomplish this:
Example 1. At a commercial site in Denver the media filter will be preceded by an upstream extended detention basin. The known site conditions are:Example 1. At a commercial site in Denver the media filter will be preceded by an upstream extended detention basin. The known site conditions are:
Step 1:
Tributary Area, A_{c }= 1.5 acres
Expected EMC of TSS, E_{s }= 225 mg/l
Average storm depth, P_{6 }= 0.43 inches
Average number of runoff storms per year, n = 30
Catchment's total imperviousness, I_{a }= 85%
Step 2: Using Equation 2 find its runoff coefficient:
C = 0.66
Using Equation 3 calculate the annual TSS load from the catchment:
L_{a }= 651 lbs
Step 3: Since the filter will be preceded by an upstream extended detention basin, we have Case 1 configuration. The WQCV will drain in 12 hours.
Step 4: Using T_{d} = 12 hours, Table 1 suggests R_{D }= 50%. Assuming 95% overall removal rate for the detentionfilter system, estimate using Equation 4 the reduction in TSS produced by the filter itself.
E_{sfr} = 101 mg/l
Step 5: Using Equation 7 estimate the average annual TSS load removal by the filter.
L_{afr} = 263 lbs
Step 6: Determine the filter's annual maintenance frequency. Assume m = 1 (i.e., once per year).
Step 7: To keep the size of the filter small while not imposing a very frequent maintenance schedule we choose to design the filter to drain at approximately 2.0 inches per hour. This means L_{m} = 0.32 pound/square foot in Figure 3.
Step 8: Using T_{d} = 12 hours and C = 0.66 from Step 2 and a from Figure 1 in Equation 1, find the maximized WQCV:
P_{o} = 0.32 watershed inches = (1720 ft^{3})
Step 9: Using Equations 9 and 10:
A_{fm} = 822 ft^{2}
A_{fh} = 871 ft^{2}
Step 10: The two areas are within 20% of each other. Choose the larger of the two.
A_{f }= 870 sq. ft. (after rounding off)
Example 2Example 2. Same as Example 1 except use a filter inlet, namely Case 3, with r_{R} = 0.5.
Steps 1 through 3 are the same as in Example 1.
Step 4: Using Equation 5 for a "retention basin" with a 12hour drain time find:
E_{sfr} = 124 mg/l
Step 5: Using Equation 7 we find
L_{afr} = 322 lbs
Step 6: Assume m = 1.
Step 7: Using the same reasons stated in Example 1 we find: L_{m}=0.32 lbs/ sq. ft.
Step 8: Same as in Example 1 @ T_{d} = 12 hrs.: P_{o}=0.32 inches (1,720 cu. ft.)
Step 9: Using Equations 9 and 10:
A_{fm} = 1006 ft^{2}
A_{fh} = 871 ft^{2}
Step 10: The two are within 20% of each other. Use the larger of the two.
A_{f} = 1,000 ft^{2} (after rounding off)
Figure 4 illustrates two cases during larger storms, namely overflow of the excess and the bypass of the excess. To make a valid assessment of the average annual EMC for any constituent reaching receiving waters, to flowweight the concentrations of the effluent and the excess runoff from all the storms that occur, on the average, any given year. For Case 1 shown in Figure 4 this is given by Equation 11.
Figure 4  Stormwater Runofff Connection Arrangements for a Filter System.
(11)
and for Case 2 by Equation 12
(12)
In which,
E_{c }= average annual EMC downstream of the filter facility, in mg/l
E_{i }= average annual EMC in the runoff inflow to the WQCV, in mg/l
E_{f }= average annual concentration in the filter's effluent, in mg/l
r_{pf} = fraction of the average annual runoff volume that flows through the filter
k_{B} = fraction of the original EMC in the runoff that remains in the water after overflows
k_{T} = coefficient of the EMC that represent the post "firstflush" fraction of the average EMC in stormwater runoff
If the maximized coefficients in Figure 1 are used, one can expect r_{p } = 0.8 to 0.9. If, however, the runoff from the mean storm is used, one can expect r_{pf} = 0.65 to 0.7.
Currently it is not possible to suggest definitive values for k_{D} and k_{T}, which coefficients depend on the constituent being considered and the actual design. However, a literature review by the author suggests the following tentative ranges for TSS:
k_{D }= 0.3 to 0.5 k_{T} = 0.7 to 0.9
Table 2 summarizes, after screening out the outliers, the findings of filter tests at four cities in the United States, namely, Alexandria, VA; Austin, TX; Anchorage, AK; and Lakewood, CO. Data for the first three were consolidated by Bell et al. (1996) and the data for the Lakewood site were obtained by the Urban Drainage and Flood Control District in 1995. Note the high variability in the influent concentrations for all constituents and that the ratios between the high and the low concentrations are significantly less for the effluent. The variability in the influent quality accounts for most of the range in the reported removal percentages.
Constituent  In or Out  Concentration mg/l 
Percent Removed 

Low 
High 
Mean 
Low 
High 
MCR* 

TSS  In  12 
884 
160 

Out  4 
40 
16 
8% 
96% 
8094% 

TP  In  0.05 
1.4 
0.52 

Out  0.035 
0.14 
0.11 
5% 
92% 
5075% 

TN  In  2.4 
30 
8.0 

Out  1.6 
8.2 
3.8 
(130)% 
84% 
3050% 

TKN  In  0.4 
28 
3.8 

Out  0.2 
2.9 
1.1 
0% 
90% 
6075% 

TC_{u}  In  0.030 
0.135 
0.06 

Out  0.016 
0.035 
0.025 
0% 
71% 
2040% 

TZ_{n} 
In  0.04 
0.89 
0.20 

Out  0.008 
0.059 
0.033 
50% 
98% 
8090% 

*MCR  Most Common Data Range 
Table 2. Field Measured Performance Ranges of Sand Filters
In Example 1 an extended detention basin was used upstream of the filter. It is relatively easy to design this arrangement so that all runoff will pass through the detention basin and the excess runoff will overtop the pond. Let's further assume that k_{D} = 0.35 and k_{T} = 0.75 and as a first order estimate assume that 80% of the average annual runoff volume will pass through the basin and the filter. Using an average effluent TSS concentration of 16 mg/l (Table 2), the average annual EMC of TSS downstream of the filter installation is:
E_{c} = 25 mg/l
Comparing this to the average EMC for TSS in stormwater runoff at that site (i.e., 225 mg/l), this installation will have 82% average annual removal efficiency for TSS.
The author wishes to acknowledge the support of the Urban Drainage and Flood Control District and City of Lakewood in the building and testing of this test filter installation. Many thanks to L. Scott Tucker, the District’s Executive Director, for his continuing support of scientific exploration.
The author is also grateful to John Doerfer, Richard Ommert, Curtis Neufeld, Jerry Goldman, Chris Jacobson, Warren Bell, Richard Horner, Betty Rushton, Eugene D. Driscoll, Jonathan E. Jones, Jiri Marsalek, Bill Pisano, William P. Ruzzo, George Chang and James C.Y. Guo for their help, support and/or review and comments on the original paper and to Galene Bushor for sorting through and making sense of the author's handwritten manuscripts.
Bell, W., Stokes, L., Gavan, L.J. and Nguyen, T. 1996 (undated). Assessment of the Pollutant Removal Efficiencies of Delaware Sand Filter BMPs. City of Alexandria, Department of Transportation and Environmental Services, Alexandria, VA.
Driscoll, E.D., Palhegyi, G.E., Strecker, E.W. and Shelley, P.E. 1989. Analysis of Storm Events Characteristics for Selected Rainfall Gauges Throughout the United States. U.S. Environmental Protection Agency, Washington, D.C.
EPA. 1983. Results of the Nationwide Urban Runoff Program, Final Report. U.S. Environmental Protection Agency, NTIS PB8418552, Washington D.C.
Guo, J.C.Y. and Urbonas, B. 1996. "Maximized Detention Volume Determined by Runoff Capture Ratio," J. Water Resources Planning and Management. Jan/Feb, p. 3339, American Society of Civil Engineers, Reston, VA.
Neufeld, C.Y. 1996. "An Investigation of Different Media for Filtration of Stormwater." Masters Thesis, Department of Civil Engineering, University of Colorado at Denver, Denver, Colorado.
Urbonas, B. R., and Ruzzo, W. 1986. "Standardization of Detention Pond Design for Phosphorus Removal," Urban Runoff Pollution. NATO ASI Series Vol. G10, SpringerVerlag, Berlin.
Urbonas, B., Roesner, L.A., and Guo, C.Y., L.S. 1996a. "Hydrology for Optimal Sizing of Urban Runoff Treatment Control Systems," Water Quality International. International Association for Water Quality, London, England.
Urbonas, B.R., Doerfer, J.T. and Tucker, L.S. 1996b. "Stormwater Sand Filtration: A Solution or a Problem?" APWA Reporter. American Public Works Association, Washington, DC.