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# Modeling First Flush and Particle Destabilization: Implications for Design and Operation of Stormwater BMPs

Joohyon Kang

2005

## UNIVERSITY OF CALIFORNIA Los Angeles

Modeling First Flush and Particle Destabilization: Implications for Design and Operation of Stormwater BMPs

A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Civil Engineering

by

Joohyon Kang

2005

## The dissertation of Joohyon Kang is approved.

Richard F. Ambrose

Jennifer A. Jay

Keith D. Stolzenbach

ii

## To my parents and brother

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Chapter 1. Introduction / 1 Chapter 2. Backgound and Literature Review / 5
2.1 CHARACTERISTICS OF URBAN RUNOFF / 5 2.1.1 Pollutants sources in Urban Runoff / 6 2.1.2 Pollutant Buildup and Washoff / 8 2.1.3 First Flush Phenomena / 13 2.2 MODELS FOR STORMWATER RUNOFF / 17 2.2.1 Water Quantity Models / 18 2.2.2 Water Quality Models / 19 2.2.3 Numerical Solutions for Partial Differential Equations / 20 2.3 PARTICLE REMOVAL IN STORMWATER RUNOFF / 24 2.3.1 Particle Settling in Highway Runoff / 24 2.3.2 Particle Destabilization / 27

## Chapter 3. Model Development / 30

MODEL EQUATIONS / 30 3.1.1 Kinematic Wave Equation / 32 3.1.2 Diffusion wave equation / 33 3.1.3 Infiltration / 34 3.1.4 Pollutant Transport / 35 3.1.5 Pollutant Erosion from a Plane Surface / 35 3.2 NUMERICAL SOLUTIONS / 38 3.2.1 Method of Characteristics for 1-D Flow / 38 3.2.2 Characteristics Averaging Method for Radial Flow / 39 3.2.3 Stability and Convergence in Numerical Solutions / 41 3.3 PARAMETER ESTIMATION / 48 3.1

## Chpater 4. Methodology for Highway Runoff Coagulation/Flocculation / 50

4.1 4.2 4.3 4.4 PREPARATION OF RUNOFF SAMPLE / 50 MIXING TESTS / 51 PROTOCOLS FOR JAR TESTS / 51 WATER QUALITY MEASUREMENTS / 53

## Chapter 5. First Flush Simulation / 54

5.1 PARAMETER ESTIMATION IN 1-D HIGHWAY RUNOFF MODEL / 54 5.1.1 Flow Calculation / 54 5.1.2 Calibration of Water Quality Parameters / 62

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5.1.3 Pollutant Buildup / 63 FIRST FLUSH SIMULATIONS IN 1-D FLOW / 66 5.2.1 Maximum MFF Ratio and Optimum Watershed Length / 66 5.2.2 Evaluation of Affecting Factors / 68 5.3 RADIAL FLOW SIMULATION / 77 5.4 DESIGN IMPLICATIONS / 81 5.4.1 MFF Ratio as a Design Parameter / 82 5.4.2 BMP design for Highway Runoff / 88 5.4.3 BMP Design for Parking Lots / 90 5.4.4 Potential Improvement of BMP Performance by Optimal Design / 92 5.2

## Chapter 6. Particle Destabilization in Highway Runoff / 95

6.1 PARTICLE AGGREGATION OVER TIME / 95 6.2 LOW DOSE FLOCCULATION / 98 6.3 SWEEP FLOC COAGULATION / 100 6.4 FLOCCULATION WITH CATIONIC POLYMER / 104 6.5 REMOVAL OF DISSOLVED HEAVY METALS / 108 6.6 DISCUSSION / 112

Chpater 7. Conclusion / 114 Appendix A. Site Descriptions / 118 Appendix B. Numerical Tests for Radial Flow Problem / 120 Appendix C. Measured and Simulated Polluto-graphs / 130 Appendix D. Regressions for Buildup / 139 Appendix E. Program Codes (MATLAB) / 141 Appendix F. Calculation of Metal Removal Efficiency / 151 REFERENCES / 152

List of Figures
FIGURE 2.1 FIGURE 2.2 FIGURE 3.1 FIGURE 3.2 FIGURE 3.3 FIGURE 3.4 FIGURE 3.5 FIGURE 3.6 FIGURE 3.7 FIGURE 3.8 FIGURE 3.9 FIGURE 3.10 FIGURE 5.1 FIGURE 5.2 FIGURE 5.3 FIGURE 5.4 FIGURE 5.5 FIGURE 5.6 FIGURE 5.7 FIGURE 5.8 FIGURE 5.9 FIGURE 5.10 FIGURE 5.11 FIGURE 5.12 FIGURE 5.13 Definition of mass first flush ratio / 15 Hydrograph with TSS, turbidity, conductivity and PSD for site 2, event 1/7/05 / 25 Concept of 1-D flow model for highway runoff / 31 Two-phase washoff of the pollutants / 37 Procedure of the node value calculation in MOC / 39 Characteristics averaging Interior points / 40 Calculated outflow using different values of t with different xo / 43 Water depth profile at t = 70 min using different values of t with xo = 1m / 44 Calculated outflow using different values of xo with t = 1/8 min / 45 Water depth profile at t = 70 min using different values of xo with t = 1/8 min / 45 Outflow concentration profiles calculated for the same storm event using different values of x with t =1/8 min / 46 Mass profiles along the distance at t = 30 min calculated for the same storm event using different values of x with t =1/8 min / 46 Measured and simulated runoff volumes with different values of pavement hydraulic conductivity / 55 Measured and simulated peak flows with different values of pavement hydraulic conductivity / 57 Runoff coefficients with respect to the total rainfall volume at Kp = 10-5 cm/sec / 58 Measured and calculated hydrographs and polluto-graphs / 61 Regressions for COD buildup using different curve forms / 64 MFF changes with different watershed lengths at I = 3 mm/hr and T = 3 hr / 67 Maximum MFF20, optimum watershed length, and watershed length at MFF20 = 2.5 / 68 MFF10 and MFF20 with respect to the watershed length for different rainfall intensities and durations / 70 MFF10 and MFF20 with respect to the watershed length for different slopes / 71 MFF10 and MFF20 with respect to the watershed length for different values of pavement hydraulic conductivity / 72 MFF10 and MFF20 with respect to the watershed length for different values of mb,so / 74 MFF10 and MFF20 with respect to the watershed for different erosion coefficients of short-term pollutant source / 75 MFF10 and MFF20 with respect to the watershed for different erosion rates of longterm pollutant source / 76

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FIGURE 5.14 MFF10 and MFF20 with respect to the watershed length for different inlet radius in the radial flow / 79 FIGURE 5.15 Maximum MFF ratio and optimum watershed length in the radial flow simulation in Figure 5.14 / 80 FIGURE 5.16 Mass distribution on the converging watershed / 81 FIGURE 5.17 Contours of the optimal watershed length for maximum MFF20 as a function of rainfall intensity and duration for different values of mb,so at So = 0.02 and Kp = 10-5 cm/sec / 84 FIGURE 5.18 Contours of the maximum MFF20 as a function of rainfall intensity and duration for different values of mb,so at So = 0.02 and Kp = 10-5 cm/sec / 85 FIGURE 5.19 Contours of the maximum watershed length at MFF20 = 2.5 as a function of rainfall intensity and duration for different values of mb,so at So = 0.02 and Kp = 10-5 cm/sec / 87 FIGURE 5.20 Contours of the maximum watershed length at MFF20 = 2.5 as a function of rainfall intensity and duration for different slopes at mb,so = 1.0 g/m2 and Kp = 10-5 cm/sec / 88 FIGURE 5.21 Collection system design in the highway runoff BMPs / 89 FIGURE 5.22 Different inlet location and watershed length in a square type watershed / 91 FIGURE 5.23 Determination of design watershed length based on a MFF20 curve for Cu / 93 FIGURE 6.1 TSS and TDS changes over time from the observation of natural aggregation on 2/6/05 / 97 FIGURE 6.2 PSD changes over time on 2/6/05 / 98 FIGURE 6.3 Turbidity changes in the samples in low dose coagulation: (a) Alum; (b) Ferric chloride / 99 FIGURE 6.4 Turbidity removal from sweep floc coagulation / 102 FIGURE 6.5 Optimum coagulant dose and initial conductivity / 103 FIGURE 6.6 Turbidity and ZP changes after adding same serious of amounts for alum and ferric chloride on 3/18/05 / 103 FIGURE 6.7 ZP changes in the sample after adding two different molecular weight polyDADMACs on 2/6/05 / 104 FIGURE 6.8 Optimum polymer dose and initial sample conductivity / 105 FIGURE 6.9 Effect of mixing time on the turbidity removal with and without polymer on 1/28/05 / 105 FIGURE 6.10 Effect of alum addition on the mixing time using polymer coagulation on 1/28/05 / 107 FIGURE 6.11 PSD changes with different molecular weight polymers on 2/11/05 / 107 FIGURE 6.12 Dissolved metal concentrations in the treated runoff from different coagulation/flocculation tests on 3/18/05 / 109 FIGURE 6.13 Coagulation results with different polymer doses at alum = 8 mg/L on 4/28/05 / 110 FIGURE 6.14 Coagulation results with different polymer doses at alum = 16 mg/L on 4/28/05 / 111

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List of Tables
TABLE 2.1 Metal Concentrations for Different Particle Size Ranges / 7 TABLE 2.2 Quantitative Definitions of First Flush in the Stormwater Runoff from Different Researchers / 14 TABLE 2.3 Deterministic Studies for Pollutant Washoff Simulation / 21 TABLE 2.4 FDMs used for the Overland Flow Calculation / 22 TABLE 3.1 Model Equations and Numerical Schemes / 31 TABLE 3.2 Summary of Storm Events Used for the Estimation of Water Quality Parameters / 49 TABLE 4.1 Characteristics of 1 hr Composite Samples from Site 2 / 50 TABLE 4.2 Protocols for the Coagulation / Flocculation Tests / 52 TABLE 5.1 Input Parameters for the Flow Calculation / 58 TABLE 5.2 Calibrated Parameters for Site 3 / 62 TABLE 5.3 Buildup Equations Fitted by Different Curve Forms for COD, Conductivity, Zn and Cu / 63 TABLE 5.4 Comparison of Buildup Equations / 65 TABLE 5.5 Qualitative Relationship between MFF20 and Design factors / 82 TABLE 5.6 Design Factors Applied in the MFF Simulations / 83 TABLE 5.7 Performances of BMPs with Different Designs / 94

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ACKNOWLEDMENTS

I am deeply grateful to my advisor, Prof. Stenstrom, M.K., who has constantly given me inspiration in the research as well as physical supports. He has always been a model of what a scholar ought to be. Also, it is pleasant duty to express special thanks to Dr. Lau, S.-L. and Dr. Li, Y.-X. at UCLA. This dissertation would not have been completed without their contribution. Finally, I would like to thank Caltrans (California Department of Transportation) for funding the stormwater monitoring project.

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VITA September 6, 1971 1996 Born, Pusan, Korea B.S., Civil and Environmental Engineering Korea University Seoul, Korea M.S., Civil and Environmental Engineering Korea University Seoul, Korea Staff, Water and Wastewater Treatment Project Team LG Engineering and Construction Corporation Seoul, Korea Graduate Student Researcher University of California, Los Angeles

1998

1998-2001

2002-05

PUBLICATION AND PRESENTATIONS Kang, J.-H. (1998). Nutrient removal in wastewater using supernatant of septage as an external carbon source, Masters thesis, Dept. of Civil and Environmental Engineering, Korea University, Seoul, Korea, Feb. Kang, J.-H., Li, Y., Lau, S., Kayhanian, M., and Stenstrom, M.K. (2005). Application of particle size distribution in highway runoff: Optimization of settling tank design to remove particles, Proceedings of the 4th south pacific conference on stormwater and aquatic resource protection, Auchland, New Zealand.

## ABSTRACT OF THE DISSERTATION

Modeling First Flush and Particle Destabilization: Implications for Design and Operation of Highway Stormwater BMPs

by

Joohyon Kang Doctor of Philosophy in Civil Engineering University of California, Los Angeles, 2005 Professor Michael K. Stenstrom, Chair

First flush, which describes a greater pollutant discharge rate in the earlier part of a storm event, is an important phenomenon to understand pollutant washoff behavior of stormwater runoff and to establish appropriate best management practices (BMPs). A number of partially successful efforts have been made to reveal the relationship between first flush and the factors involved in the physical processes, including the characteristics of the rainfall and the watershed.

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In this study, a deterministic model was developed to predict the mass first flush (MFF) and to utilize it for better design of BMPs focusing on treating the first flush. The model used the kinematic wave equation to calculate flow. For the water quality calculation, the mass transport equation and erosion equation were used with the concept of two different sources of pollutant mass. The model parameters were calibrated by a parameter estimation procedure using three years monitoring data from a highway runoff site. The MFF simulation results showed that there exists an optimum watershed size to maximize MFF and by maximizing MFF, BMPs can improve overall reduction of pollutant mass. Contours of watershed length, developed using MFF simulations for different conditions of rainfall and watershed geometry, can be used to design runoff collection system of a BMP for highways and parking lots. Another aspect of BMP design is how to enhance pollutant removal efficiency. Although most stormwater BMPs use gravity settling to remove particulates, particles in highway runoff are generally too small to be removed effectively. Therefore, additional means to destabilize particles are required. Alum, ferric chloride and cationic polymers were evaluated to destabilize particle in the runoff. Alum or ferric chloride alone was not successful due to large dose requirement and sludge production. A small dose addition of polymer followed by a long period of gentle mixing was successful. The required dose for polymer and coagulant were proportional to the initial conductivity of the runoff and therefore, unattended operation in the field might be possible by controlling the dose based on the initial conductivity.

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Chapter 1

Introduction

Non-point source (NPS) pollution such as urban stormwater runoff is receiving considerable attention because it has been identified as a major pollutant source, impairing receiving water bodies (Furumai et al., 2002). In the United States, the Clean Water Act (CWA) was amended by Congress in 1987 for the United States Environmental Protection Agency (USEPA) to establish phased National Pollutant Discharge Elimination System (NPDES) for stormwater discharges, to address permit applications, regulatory guidance and management and treatment requirements Under the CWA, California Department of Transportation (Caltrans) also instituted a statewide stormwater program in an effort to control stormwater pollution from the transportation facilities including highways in the State of California. Urbanized landuses generate significantly greater pollutant loads as well as high peak flow and flow volume than undeveloped landuse, causing contamination and flood risk in ecosystems. Highway runoff readily transports heavy metals, oil and grease and other

toxic compounds that are accumulated during dry periods (Roger et al., 1998; Furumai et al., 2002; Lau and Stenstrom, 2005). To mitigate this problem, selection of appropriate controlling strategies, which are referred to as best management practices (BMPs), is essential. BMPs encompass all possible methods including public education, regulatory procedures and treatment facilities. A treatment facility is classified as a structural BMP and has been a preferred approach among BMPs because educational or regulatory methods are institutionally difficult (Kim, 2002). Most structural BMPs adapt physical and chemical mechanisms such as sedimentation and filtration to remove pollutants. In theses treatment systems, particle removal mechanisms play an important role, determining overall efficiency of pollutant removal. Suspended solids in urban runoff are composed of relatively fine particles, providing high surface to volume ratio for adsorption of reactive organics and metals on surface or within pores (Characklis and Wiesner, 1997; Roger et al., 1998; Sansalone et al., 1998). Particles in the highway runoff are unexpectedly stable in the solution because particles density and shape are heterogeneous. Therefore, particle destabilization processes are required (Kang et al., 2005). Characterizing pollutant washoff behavior is also crucial for design and operation of BMPs. Pollutant washoff is generally characterized by the first flush, a popularly used concept to indicate the high discharge of constituent mass or concentration in the early part of the runoff volume (Geiger, 1987). First flush is frequently observed in the runoff of the urbanized area including highly impervious landuses such as highways and parking lots. Therefore, characterizing first flush phenomena has been an important goal in the

stormwater pollution studies to establish better treatment strategies. First flush is strongly associated with the hydraulic condition that depends on meteorological and geometrical characteristics of the watershed. Numerous efforts have been made to reveal the relationship between the pollutant washoff behavior and associated factors including rainfall intensity, flow rate, watershed area and bed slope (Gupta and Saul, 1996; Deletic and Maksimovic, 1998; Cristina and Sansalone, 2003a; Taebi and Droste, 2004). However, no clear relationships among those factors have been yet verified.

Research Objectives This research is composed of two main categories: Mass first flush (MFF) simulation using deterministic models for the stormwater runoff and experimental studies on particle destabilization using coagulation and flocculation. The first objective of this study is to explore the first flush behavior quantitatively and qualitatively as a function of major factors that are related to the physical processes occurring during runoff using deterministic runoff models. The kinematic wave and diffusive wave theories were used to calculate flow depth and velocity. In addition, erosion and transport equations were coupled with water quantity solutions from the wave equations. The model was calibrated using three years monitored concentration data using an optimization technique to solve the inverse problem. Using the calibrated model, a series of simulations was performed, exploring design relationships in order to develop a design tool to maximize first flush from small watersheds.

The second goal was to develop ways of increasing particle size in the runoff from highway sites. A series of coagulation and flocculation studies of highway runoff were performed to remove particles and associated pollutants. Various kinds of particle removal mechanisms including sweep floc coagulation and charge neutralization were tested using different coagulants and operating conditions. The goal of this study was to suggest the appropriate strategies for the particle destabilization in highway runoff.

Organization of Dissertation The dissertation is organized into seven chapters. Chapter 2 introduces background and pervious work on the mathematical models for urban runoff as well as previous particle destabilization studies. Chapter 3 describes model development and calculation methods. Chapter 4 discusses the protocols for the coagulation and flocculation tests. Chapter 5 provides the results of model verification, first flush simulation with discussion of the implications for practice. Chapter 6 presents the results of coagulation and flocculation tests. Finally, chapter 7 concludes the dissertation with summary on the induced results and those applications.

Chapter 2

## 2.1 CHARACTERISTICS OF URBAN RUNOFF

Non-point source pollution has long been recognized for its potential to degrade surface waters in the United States. The 1972 Amendments to the Clean Water Act recognized non-point source pollution under its 208 requirements. Early work was limited mostly to planning for non-point source management and identified agricultural runoff as being different and requiring alternative management strategies than point sources such as municipal and industrial wastewaters. Highways and streets were among the first to be investigated as non-point source pollutants very early in Sartor and Boyd (1972). Other early research included the Nationwide Urban Runoff Program (U.S. EPA, 1983) which addressed different types of landuse. The first work in our laboratory investigated transportation land use such as parking lots and commercial as sources of oil and grease (Stenstrom et al. 1984).

2.1.1 Pollutants sources in Urban Runoff Heavy Metals. Urban stormwater runoff is known to be the largest contribution of

metals to the local receiving water bodies (Characklis and Wiesner, 1997). The Metals from anthropogenic sources include As, Pb, Na, Zn, Ba, Cd, Fe and Cr whereas Al, Ca, Mg, Sr, Hg and Mn are usually from natural sources (Zartman et al., 2001). The chemical nature and source of the individual metals lead to different partitioning between solid and liquid. Particulate metals in the urban runoff are typically associated with organic matter from the tire wear, pavement surface wear and dust from exhausted pipes as well as minerals from soil, pavement and sources in the watershed (Roger et al., 1998). A pollutants partition between solid and liquid phases is of concern because particulate fraction plays an important role in determining BMP efficiency. Hunter et al. (1981) reported that approximately 50% of total metals in stormwater were associated with particles. Characklis and Wiesner (1997) concluded that Zn exists mainly in the dissolved phase up to 80% of total concentration, while Fe is usually combined with coarse materials. Roger et al. (1998) stated that Pb and Zn were often found in the sediments from motorways and Zn was associated with the fine particles (< 50 m). Furumai et al. (2002) stated that the particulate fractions accounted for 55 ~ 89%, 56 ~ 89% and 79 ~ 96% of total load of Zn, Cu and Pb, respectively, in highway runoff. Pb concentrations are declining in urban runoff because of elimination of lead in the gasoline (Furumai et al., 2002; Characklis and Wiesner, 1997). A large fraction of a particulate metal is usually associated with fine particles as shown in Table 2.1 (Li et al., 2005b).

## Metal Concentrations for Different Particle Size Ranges (Li et al.,

Size Heavy Metal Concentration (g/g) Sampling and References Ranges Experimental Al Cd Cr Cu Fe Ni Pb Zn Methods (m) Urban stormwater suspension 0.45-2 2894 29267 199 13540 Morquecho 2-10 4668 18508 868 13641 and Pitt 2003, Manually 10-45 735 26221 229 1559 Birmingham collected samples; and 45-106 1312 14615 226 2076 Wet sieving Tuscaloosa, 106-250 2137 21730 375 3486 Alabama >250 50 28604 117 266 Highway runoff sediments 25-38 16.8 364 265 1189 38-45 17.2 353 236 996 Sansalone 45-63 17.3 364 266 1027 Manually and 63-75 16.3 333 258 1057 collected from Buchberger trough; 75-150 15 312 248 1014 1997b, 150-250 9.2 204 195 574 Drying at 110C- Cincinnati, Sieving 250-425 8 78 65 325 Ohio 425-850 9.5 48 53 314 850-2000 9.7 45 37 259 Manually <50 60000 350 420 230 1570 4370 Roger et al. collected from 50-100 45000 400 250 250 1480 1700 1998, collection Hrault 100-200 38000 410 200 220 1550 1100 channel; region, 200-500 35500 150 100 220 850 930 Wet sievingFrance 500-1000 37500 140 50 220 460 930 Drying at 105C Street sweeping <75 470 410 German and 75-125 270 230 Svensson Vacuuming; 2002, 125-250 340 190 Sieving Jnkping, 250-500 200 120 Sweden 500-1000 50 70 <43 5 46 220 65 350 960 Lau and 43-100 5 58 230 50 300 805 Stenstrom Vacuuming; 2004, Air Drying100-250 2 38 230 40 210 500 Los Angeles, Sieving 250-841 na 12 240 5 44 150 California Average 1 28 238 25 142 360

Organics and Nutrients. Polynuclear aromatic hydrocarbons (PAHs) and microorganisms such as fecal coliforms and pathogens are of concern because of their potential toxicity to human health and ecosystems. PAHs are usually combined with the other organic matter (Schueler, 1987) and the origins of PAHs in urban runoff are usually pavement leaching, tire abrasion, automobiles combustion processes and lubricating oils (Latimer et al., 1990; Takada et al., 1991; Ngabe et al., 2000; Krein and Schorer, 2000; Kamalakkannan et al., 2004). Atmospheric deposition and regional air pollution emission is also a significant PAH source (Herricks, 1995). Urban runoff also carries significant amount of nutrients such as nitrogen and phosphorous (Abustan et al., 1998). Nutrients sources include fertilizer applied to the yards, roof runoff, various household chemicals and street runoff. Vaze et al. (2002) performed an experimental study of pollutant accumulation on urban road surfaces and found that majority of total phosphorous and nitrogen in the solid samples was associated with particles less than 50 m in diameter. Borst and Selvakumar (2003) found large concentrations of fecal coliforms and pathogens in urban runoff. Microorganisms are self-suspended or absorbed to suspended particles, and prefer particles that are larger than 30 m in diameter (Schillinger and Gannon, 1985).

2.1.2 Pollutant Buildup and Washoff A variety of pollutants originating from vehicles, atmospheric deposition and pavement degradation are accumulated in the dry season and washed out during the next storm

event. The two stages, pollutant accumulation and emission, are referred to as buildup and washoff. Understanding the behavior of buildup and washoff is important to predict pollutant load emissions and establish treatment strategy. Most of buildup/washoff studies have adapted empirical approaches based on analysis of large databases because the physical and chemical processes involved in buildup and washoff are complicated and difficult to generalize.

Buildup. Landuse type is considered an important factor that determines the buildup characteristics for pollutants from different sources and having varying characteristic such as particle size, portioning between particulate and liquid phases and density. Sartor and Boyd (1972) monitored pollutant buildup in the ten US cities to identify the types and characteristics of pollutants accumulating on streets and reported that the buildup of solids, COD and heavy metals is strongly associated with landuses. The buildup mass in industrial areas was the largest among three different landuses: residential, industrial and commercial. Manning et al. (1977) performed field measurements of accumulated pollutants in the four different landuses (i.e. single family residential, multi family residential, commercial and industrial) and calculated relative fractions of organics, nutrients and heavy metals in the total solids. Many researchers have tried to develop appropriate mathematical expressions for buildup. Among several types of buildup formulas, exponential and Michaelis-Menton types have been common because the upper limit of mass accumulation is clearly defined in the formulas. A linear-type buildup formula is sometimes preferred because the

formulation and calculations are simple (Barb et al., 1995). Buildup formulas are typically site specific but include the antecedent dry days (ADD) as a common variable. Other parameters such as atmospheric deposition, traffic load, street sweeping, biological degradation and wind speed can be incorporated in a buildup formula as positive or negative affecting factors (James and Shivalingaiah , 1985). Shahbeen (1975) particularly emphasized the contribution of traffic loading by assigning the dust and dirt (DD) production per vehicle as 800-1200 mg/axle-km travel.

Washoff.

## The physical processes involved in washoff are erosion and transport.

During a storm, pollutants accumulated on the watershed are exposed to the energy of flow and rainfall, initiating pollutant mobilization. In urban runoff, the mass deficiency on the impervious surface results in relatively high washoff rate at the beginning of the storm. This phenomenon is called first flush and will be discussed in a separate section of this chapter. Lacking theoretical studies, constituent washoff might be described utilizing the erosion and transport theories developed for sediment. Sediment transport by water flow is typically classified into two different modes of discharge: bed load and suspended load discharges. The commencement of particle mobilization is usually estimated by the ratio of the shear velocity of the flow, u*, to the settling velocity of the particle, w (Graf, 1998). Most prediction models for the bed load discharge are based on the empirical or semiempirical formulas, most of which are functions of bed shear stress, b. A conventional empirical formula for bed load discharge is Duboys equation:

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q b = b ( b c )

(2.1)

where qb is the bed load transport in lb/sec-ft, is the coefficient for a given bed, b is the bed shear stress (= hS), is the specific weight of fluid, h is the flow depth, S is the channel slope, and c is the critical bed shear stress to cause movement of the bed. Conventional prediction methods for the suspended load discharge involve the shear velocity and boundary conditions, which depend on the concentration of bed load discharge. A theoretical equation (Rouse, 1938; Einstein, 1950) gives the vertical distribution of concentration of suspended solids for 2-D flow as follows:

Cy

D y a = Ca y D a

(2.2)

with

z=

w u*

(2.3)

where Cy is the concentration at a distance y above the streambed, Ca is the concentration at a distance a above the streambed, D is the flow depth, w is the fall velocity of the particles, is the turbulence constant (Karman constant), and u* is the shear velocity (= gRS , where R = hydraulic radius). Most of the theories on the bed load and suspended load discharges were developed for the non-cohesive sediment, which is larger than 20 m in diameter. Cohesive sediment particles, which are less than 20m in diameter, are subject to the van der Waals attractive force and the double layer repulsive force. It can be therefore assumed that particles are transported as suspended load rather than as bed load (Deletic,

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2001). For the mobilization of cohesive sediment, critical boundary shear stress should be exerted, which is proportional to the plastic yield strength . Mehta (1994) suggested the following equation for the erosion rate from consolidated cohesive bed:
E=M

b s s

(2.4)

where E is the erosion rate, b and s are the bed shear stress and shear strength, respectively, and M is the constant for a given bed. Zhang et al. (2002) investigated the effects of flow rate, flow depth and slope gradient on the soil detachment rate. According to their experiments using an artificial channel, the detachment rate could be estimated by the power function of flow rate and bed slope. For overland flow caused by excess rainfall (i.e. Hotonian overland flow) such as stormwater runoff, rainfall energy also influences on pollutant erosion. Gabet and Dunne (2003) described the relationship between the rain power and sediment detachment in the hill slope area using the following equation:
= R A(h, d )

(2.5)

where is the sediment detachment rate (g m-2 s-1), and are empirical constants,

A(h, d) is the attenuation function (0 ~ 1), R is the rain power (W m-2), h is the flow depth,
and d is the raindrop diameter.

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2.1.3 First Flush Phenomena The first flush is defined as the emission of a greater fraction of constituent mass or higher concentration in the early part of the runoff volume (Geiger, 1987). The first flush phenomenon is frequently observed in the runoff of small, highly impervious urbanized areas, such as highways and parking lots (Sansalone and Cristina, 2004). Characterizing the first flush phenomena is important to establish treatment strategies. If a large portion of pollutant mass is contained in the first portion of the runoff, a BMP that is optimized to treat the first portion may be economically advantageous. The first flush phenomenon is strongly related to hydraulic conditions. A number of efforts have been performed to determine the relationship between pollutant washoff behavior and rainfall intensity, flow rate, watershed area or bed slope, using statistical analysis of empirical observations. Unfortunately no clear, general relationships among have been found. Because no consensual definition of first flush has yet been established, different criteria are used according to the researchers as summarized in table 2.2. Among several criteria for occurring of first flush, a criterion proposed by Geiger (1987) is common, which suggests that the occurrence of a first flush when the initial slope of the curve of the normalized cumulative mass emission with respect to the normalized cumulative runoff volume is greater than 45%. In order to quantify the high initial pollutant load of the first flush, Ma et al. (2002) suggested a concept of mass first flush (MFF) ratio as depicted in Figure 2.1. Figure 2.1

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can be created by plotting normalized discharged mass versus normalized runoff volume using the following equation:

y = x

t1

C (t )Q(t ) dt / M

t1

Q (t )dt / V

t1

C (t )Q(t ) dt / Q(t )
0

t1

M /V

(2.6)

where C(t) is pollutant concentration (M/L3), Q(t) is stormwater flow discharged at time t (L3/T), M is total pollutant mass (M), V is total flow volume (L3), and t1 is elapsed time (T). The existence of a mass first flush can be determined if the plotted line lies above the

TABLE 2.2

## Different Researchers Quantitative Definition or Criteria for FF Reference

Initial slope of normalized cumulative mass emission plotted against normalized cumulative runoff volume > 45% 40 ~ 60% of the pollutant load in the initial 25% of the runoff volume 80% of pollutant load in the first 30% of the runoff volume

## Geiger (1987) Vorreiter and Hickey (1994) Saget et al. (1996)

Gupta and Saul (1996) Maximum gap between normalized cumulative mass emission and corresponding normalized cumulative runoff volume during a storm event Generalized quantitative definition of mass first flush using the ratio of mass washoff fraction to the runoff volume fraction (Mass First Flush ratio, MFF) Particle number first flush (PNFF) ratio defining particle first flush, which is an extension of the MFF ratio developed by Ma et al. (2002) Ma et al. (2002)

Li et al. (2005a)

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## 0.8 Mass Flush Fraction

0.6

MFF20=0.6/0.2=3.0

0.4

MFF10=0.4/0.1=4.0

0.2

FIGURE 2.1

## Definition of mass first flush ratio

straight line indicating the proportional mass delivery according to the amount of runoff volume. The intersection of the a vertical line at a specific normalized volume and the mass line is used to calculate the MFFn, by dividing the normalized mass at same normalized volume, designated as n, which is expressed as a percentage from 0 to 100%. Therefore, the MFF10 and MFF20 for the constituent at 10% and 20% of the runoff volume are respectively calculated as 3.0 and 4.0 in the Figure 2.1. First flush phenomena might or might not be observed depending on meteorological and geometrical characteristics of the watershed. Generally, small size watersheds with high imperviousness tend to show strong first flush (Ma et al., 2002). There have been numerous studies to establish the relationship between first flush phenomena and associated parameters such as watershed types, rainfall characteristics and other factors

15

(Gupta and Saul, 1996; Charneneau and Barrette, 1998; Deletic and Maksimovic, 1998; Taebi and Droste, 2004; Cristina and Sansalone, 2003a; Lee et al., 2003). Gupta and Saul (1996) conducted correlation studies in the combined sewer system and reported that total suspended solids (TSS) load in the first flush was well correlated with rainfall intensity, storm duration and ADD whereas mean concentration of the first flush was not. Deletic and Maksimovic (1998) performed statistical analysis using monitored data from paved road runoff and concluded that washoff TSS load were merely influenced by ADD as opposed to the conductivity. Taebi and Droste (2004) examined the runoff from an urbanized landuse in Iran and stated that first flush load of total solids (TS) and chemical oxygen demand (COD) were not closely related to the characteristics of rainfall-runoff. Meanwhile, Cristina and Sansalone (2003a) observed the high first flush effect in masslimited high runoff volume events compared to the flow-limited low runoff volume events. Lee et al. (2003) investigated the first flush of organics, nutrients and iron from four different landuses (i.e. apartments, commercial, single residential and mixed area) and proposed polynomial equations to represent first flush, which were site and event specific. As shown from the proceeding discussion, no consensus exists for hydrodynamic behavior of pollutant washoff, and therefore no clear methodology for quantifying the first flush exists.

16

## 2.2 MODELS FOR STORMWATER RUNOFF

Stormwater model is basically composed of water quantity and water quality models. A water quantity model calculates runoff volume or flow rate resulting from excess rainfall, which is used for the flood control. The pollutant concentration or mass load in the runoff is estimated by a water quality model. Accurate water quantity calculation is prerequisite for the water quality calculation because most water quality models include hydrologic or hydraulic factors as independent variables (Zoppou, 2001). There exist various kinds of mathematical models for water quantity and water quality from simple empirical models to complex deterministic models. Empirical or regression models are frequently adapted because they are mathematically simple and thus require less calculation efforts. Those models are limited in application because they are valid only for specific sites or events. Development of fast computing technology makes it easier to utilize a complicated deterministic model for the accurate solution of temporal and spatial varying water quantity and quality. A deterministic stormwater model usually includes several components in the governing equations: rainfall-runoff, pollutant buildup, erosion, transport and sink/source of the pollutants mass such as settling or biodegradation. Complexity of the model depends on the mathematical expressions of those components in the model. Some of those components can be neglected or simplified according to their relative importance.

17

## 2.2.1 Water Quantity Models

One of the simplest water quantity models is the rational formula, which calculates the runoff volume. However, the simulation of temporal and spatial flow behavior can be performed by deterministic models such as the Saint-Venant system of equations and their simplifications. The Saint-Venant equations are composed of two conservative laws and have been popularly used for the open channel flow problems (Graf, 1998). Shallow water flow can be also described by these equations. One-dimensional form considering uniform rainfall and infiltration are written on a unit width basis as follows (Singh, 1996): Continuity equation:
h + (uh) = I f t x

(2.7)

Momentum equation:

u 1 2 + u + gh = g ( S0 S f ) t x 2

(2.8)

where h is flow depth (L), u is local mean velocity (L/T), I is rainfall intensity (L/T), f is infiltration rate (L/T), g is gravitational acceleration, x is space coordinate in the flow direction (L), t is time (T), S0 is bed slope, and Sf is frictional slope. It is sometimes more convenient to use the reduced form of above equations (i.e. the kinematic wave and diffusive wave equations) in the simulation of sheet flow over plane surfaces by neglecting local acceleration, convective acceleration or pressure force effects. The kinematic wave equation has been a preferred modeling equation in the calculation of

18

surface runoff because the calculation is simple and accurate (Tomanovic and Maksmovic, 1996; Deletic, 2001; Singh, 2002a, 2002b; Jaber and Mohtar, 2002; Haque, 2002; Cristina and Sansalone, 2003b). The diffusion wave equation can be applied where the hydraulic diffusivity plays a major role such as a watershed with a very mild slope (Ponce and Klabunde, 1999).

2.2.2 Water Quality Models As opposed to the water quantity model, the history of water quality models for the stormwater runoff is relatively short. Due to limited knowledge on the involving mechanisms in the pollutant washoff, the majority of the model equations that have been used are based on the empirical or statistical approaches. One of the simplest models (Grottker, 1987) is the exponential equation representing emission rate of pollutants as follows:
Pt = Pe k2Vt 1

(2.9)

where Pt is load remaining on the watershed after time t from the beginning of the runoff event (kg), P1 is initial load (kg), k2 is washoff coefficient (mm-1), and Vt is total runoff to time t. The exponential-type equations have been used to approximate greater washoff at the begging of a storm. Regression models relate water quality parameters with selected factors considered to be important using simple linear, simple linear, semi-log, log-log transformations. These models have been popularly used to estimate event mean concentrations and total load of the pollutant. However, regression models are limited in

19

use because those models are only site-specifically valid (Zoppou, 2001). Despite of this limitation, empirical and regression models are still popularly used because the calculations are simple. Several researchers have focused on deterministic models addressing transport and erosion mechanisms of pollutants in the overland flow system (Tomanovic and Maksimovic, 1996; Singh, 2002a, 2002b). A deterministic model requires comparatively larger calculation efforts because spatial and time varying water quantity and quality equations are integrated. Table 2.3 summaries several previous works on the deterministic models for pollutant washoff. Singh (2002a, 2002b) performed simulation for hydrology and pollutant transport over the plane surfaces using hyperbolic equations. He investigated solute discharge patterns for different locations in a watershed, rainfall duration as well as hydraulic conditions. More recently, Deng et al. (2005) simulated first flush of salt in a flume using fractional kinetic theory in the transport equation to consider heavy tail effect in pollutant washoff.

## 2.2.3 Numerical Solutions for Partial Differential Equations

Finite difference methods (FDMs) have been widely used because this approach is conceptually easier and efficient in geometrically simple problems as opposed to finite element methods (FEMs). Most problems for water resources and mass transport are generally modeled by hyperbolic or parabolic partial differential equations, which can be effectively solved using various numerical schemes including explicit and implicit methods. Explicit schemes require less laborious program codes while implicit schemes

20

## TABLE 2.3 Deterministic Studies for Pollutant Washoff Simulation a

Domain Asphalt surface Target Species Suspended solid Hydraulics 1-D Kinematic wave equation
h t + ( uh ) x = I f, u = S /nh
2/3

M t

Sink/Source

References
u c
u

= b1 ME k (1 e

hm / h

0, )+ b M (
2

c )

1.5

u > c

## Tomanovic and Maksimovic (1996) Stuck et al. (2001)

Agricultural Area

## 1-D St. Venant equations:

B H t Q t + gA + Q x H x + x ( Qv ) + g Q Q C AR
2

= 0,

dC SS dt

wsed C SS z

0, + (v 0, ( v
2

v vc
2

v c ) C EM z

, v > vc v vc

= 0

dC EM dt

= wsed C SS +

v c ) C EM ,

v > vc

Solute

2

w t

= kShw

21

Solute

w t

= kShw

Sediment

## 1-D Kinematic wave equation

( hq s / q ) t

q s x

= D

( hq s / q ) x
2

s qs

Particle Deposition = s q s

a

Salt

## 1-D Kinematic wave equation

C t

+u

C x

= D

C x
F

+ EC s

(I f ) h

C s = C 0 exp( t )

## Deng et al. (2005)

M-amount of sediments on the surface (g/m2), u-total shear stress (Pa), c-Shieldss critical shear stress (Pa), Ek-kinetic energy of rain drops per unit area [J/m2s], hm-penetration depth (m), hflow depth (m), b1 and b2-coefficients, B-cross-sectional storage width (m), H-water surface elevation (m), x-longitudinal distance (m), t-time (s), Q-flow (m3/s), g-acceleration due to gravity (m/s2), A-cross-sectional area (m2), -flow non-uniformity correction factor, v-mean velocity over cross-sectional area (m/s), w-mass of pollutant per unit surface area (g/m2), k-washoff rate constant (1/m/s), S-bottom slope, C-constituent concentration (gm-3), D-dispersion coefficient (m2/s), -erosion coefficient (s/m2), CEM-surface concentration of erodible mass for each event (g/m2), CSS-volumetric concentration of suspended solids (g/m3), vc-critical velocity for erosion (m/s), wsed-sedimentation velocity (m/s), z-channel depth (m), , u-velocity of the flow (m/s), Irainfall intensity (m/s), f-infiltration rate (m/s), Cs-pollutant concentration on the fractal surface (g/m3), E-transfer coefficient of pollutant, F-fractor, C0-initial value for Cs (g/m3), -decay coefficient (1/s), qs-sediment loading rate (g/m/s), s-trapping efficiency (1/m).

allow larger time step without losing stability of the solution. Table 2.4 shows different FDMs adapted in solving overland flow problem by several researchers. One of the important aspects in the numerical calculation is convergence of the solution. The convergence condition for a finite difference scheme for hyperbolic equations such as the kinemetic wave equation is defined by the well-known CourantFriedrichs-Lewy (CFL) condition as follows:
t 1 x c

or

CN =

ct 1 x

(2.10)

where c is celerity (L/T), t is time step (T), x is grid size and CN is the Courant number.

## TABLE 2.4 Numerical Scheme

FDMs used for the Overland Flow Calculation Classification Flow Equation Reference

Lax-Wendroff

Explicit

Kinematic wave

Singh (2002), Moramarco and Singh (2002), Cristina and Sansalone (2003) Henderson et al. (1964)

## Method of Characteristics Preiss-Manns 4 Point Implicit MacCormack

Kinematic wave

Implicit

Kinematic wave

Deletic (2001)

Explicit

Saint-Venant

Fennema and Chaudhry (1986), Fiedler and Ramirez (2000) Fennema et al. (1994)

## Alternating Direction Explicit

Explicit

Diffusion wave

22

Convergence does not always guaranty accuracy of the solution. Numerical schemes often suffer from unfavorable Noise, which means spurious oscillations in space or time, resulting in erroneous solutions. Oscillatory solutions are introduced from inappropriate time step and grid size, sudden change in boundary conditions, initial noise and numerical dispersion (Wood, 1993). In the shallow water problem, oscillation control is exceedingly challenging due to non-linear nature of the governing partial differential equations (Govindaraju et al., 1988). A smoothing operator is often required to attenuate oscillation in the numerical solution of the non-linear partial differential equations such as those of fluid dynamics (Shapiro, 1975). Fiedler and Ramirez (2000) claimed that additional oscillation control is needed for the overland flow simulation with extreme hydraulic conductivity and spatial variance. Sometimes a damping term such as artificial viscosity is introduced in the governing equation to smooth 2x oscillation (Fennema and Chaudhry, 1990, 1986; Fiedler and Ramirez, 2000). The method of characteristics (MOC) is oscillation free and thus produces a very accurate solution because the characteristics trace the disturbance trajectories. This scheme, however, needs extra effort to interpolate the solution at the required points because the resulting matrix of grid points is non-uniformly spaced.

23

## 2.3 PARTICLE REMOVAL IN STORMWATER RUNOFF

Performance of a stormwater BMP is primarily determined by the particle removal efficiency because a great portion of pollutant mass is associated with particles (Pettersson, 1998). Most BMPs cannot remove soluble pollutants. A widely used particle removal mechanism for stormwater BMPs is gravity settling due its low cost and simplicity of operation and maintenance, as compared to other methods such as filtration (Aldheimer and Bennerstedt, 2003). A settling tank is a common stormwater BMP and uses gravity settling to remove pollutants. Its performance is a function of particle settling velocity, hydrologic and hydraulic conditions (Jacopin et al., 1999, 2001; Persson and Wittgren, 2003; Guo, 2004). There have been several studies to determine the settling profile of the stormwater particles to optimize the design and operation of a settling tank (Aiguier et al., 1996, 1998; Li et al., 2005b). However, majority of the stormwater particles are fine particles (Li et al., 2005a), which are stable in the water column and thus additional efforts to destabilize particles are sometimes required.

## 2.3.1 Particle Settling in Highway Runoff

A particles terminal settling velocity depends on its size, shape, density, and is influenced by the liquid characteristics, such as temperature and viscosity. Particle size distribution (PSD) monitored in our three highway sites (see Appendix A) showed that 97% of particles were less than 30 m in diameter (Li, et al., 2005a), which makes small

24

## Intensity (mm/ hr)

250

0 8
Site 2 01/ 07/05 Flow Intensity TSS 5h 8h

120

TSS (mg/ L)

1h

45 min 2 h 0 min

40 0

Turbidity (NTU)

## 80 60 40 20 0 20 15 10 5 0 0 200 Time (min)

Turbidity Conductivity

2000 1000 0

400

600

## dN/ dlogDp (#mL/ / m)

160000000 120000000 80000000 40000000 0 40000000 30000000 20000000 10000000 0 0.1 1 10 Particle Diameter Dp (m) 100
45 min 30 min 1h

## dN/ dlogDp (# mL/ / m)

2h 15 min 0 min 5h 3h 6h 4h 8h 7h

FIGURE 2.2

Hydrograph with TSS, turbidity, conductivity and PSD for site 2, event

1/7/05

25

## Conductivity (umho/ cm)

Flow (L/ s)

16

80

particle removal extremely important in BMP design. Figure 2.2 shows the typical PSD of a series of grab samples collected through a storm event. Turbidity, TSS, specific conductivity are also shown, and additional information about measuring techniques and more events are available elsewhere (Li, et al., 2005a). Li et al. (2005b) performed simulations for the removal efficiencies of the particles and associated pollutants for the entire 2002-2003 wet year using particle settling velocities calculated with Newtons and Stokes law. Spherical particles corresponding to the measured PSD and having a uniform density 2.6 g/cm3 were assumed. Continuous flow clarifiers with volumes sized to contain 1.6 mm to 26 mm of rainfall were simulated and were able to remove 75% to 92% of the particles between 2 and 1000 m, respectively. The clarifier could remove only 3% to 29% of particles between 2 and 10 m and was able to remove only 13% to 72% of particles between 2 and 25 m. A series of settling column tests with fresh stormwater samples showed much less removal than predicted, which suggests that settling velocities of smaller particles are much lower than calculated by Newtons and Stokes law with the stated assumptions. The difference is hypothesized to be caused by a distribution of densities and deviation from spherical shape. These results support anecdotal observations of poor performance of BMPs using sedimentation for removing smaller particles (Stenstrom and Kayhanian, 2005). It is unfortunate that the smaller particles are not removed since they routinely have higher concentrations of heavy metals and PAHs than the larger particles (Sansalone and Buchberger, 1997; Roger, et al., 1998; German and Svensson, 2002; Morquecho and Pitt, 2003; Lau and Stenstrom, 2004). It is clear that using sedimentation for smaller particle

26

removal will require some type of particle destabilization in order to increase particle size and improve settling velocity. This is challenging because stormwater BMPs usually operate unattended in many locations. In addition, managing coagulation/flocculation systems will be difficult.

## Particles in the aqueous system naturally

aggregate due to the collision between particles resulting from Brownian diffusion, fluid shear and differential settling (McAnally and Mehta, 2000; Perigault et al., 2000; Li et al., 2005a). Microbiological activities such as degradation or polymer production change surface properties to enhance particle aggregation (Milligan and Loring, 1997; Krishnappan et al., 1999). Kranck and Milligan (1991) stated that gravitational settling and particle aggregation play an important role for the deposition of fine sediment in the ocean. However, colloidal particles are generally very stable in the solution by equilibrating between the gravitational force, van der Waals attractive force and columbic repulsive force. The stability of particles retards their natural aggregation. It is thus necessary to destabilize particles and thereby accelerate particle aggregation rate to separate fine particles from the solution easily.

## Destabilization of dispersed particles in

aqueous systems can be achieved by several different mechanisms. The formation of deltas in estuaries is a common example of the double layer compression mechanism.

27

Engineered systems, however, typically use coagulants and coagulant aids for colloid destabilization involving either charge neutralization, bridging, sweep floc, or a combination of those mechanisms. Among the metal ions, Al3+ and Fe3+ are commonly used in the water and wastewater treatment. Depending on their dosage and water characteristics, Al3+, Fe3+, and their hydrolysis products neutralize the negatively charged particles (stoichiometric destabilization) or precipitate as amorphous forms to enmesh colloidal particles (sweep floc coagulation) (Summ and OMelia, 1968). Natural and synthetic polymers have been used as a flocculating aid in water and wastewater treatment systems for many years. Cationic polymers are used to reduce the repulsive force between particles, both by neutralization and bridging mechanisms. Polymers bridge two or more particles by attaching themselves to the available sites on the particles. Anionic polymers are commonly used to flocculate negatively charged particles via bridging. Both bridging and neutralization mechanisms can fail with excessive concentrations of polymer. Restabilization resulting from charge reversal can easily occur.

## In stormwater treatment, coagulation and

flocculation have proposed as methods for enhancing colloid destabilization. Polyaluminum chloride (PACl) has frequently been employed because its low acidity is advantageous for weakly buffered stormwater. Heinzmann (1994) has shown that the mixture of PACl and cationic polymer (polyacrilamide) was effective in the filtration system of urban stormwater. Annadurai, et al. (2003) investigated the efficiency of PACl

28

to treat high turbidity stormwater (1,650 NTU). They stated that a high dose of PACl (>100 mg/L) is preferable to generate large flocs for easy solid-liquid separation (i.e., bridging). The California Department of Transportation (Caltrans) has recently conducted comprehensive coagulation studies using PACl along with polymer and ballast sand as coagulant aids to remove the turbidity and phosphorus in stormwater entering Lake Tahoe (Johnston and Patel, 2004). From the pilot plant tests, Johnston and Patel (2004) reported that the optimum dose of PACl ranged from 75 to 100 mg/L. Trejo-Gaytan et al. (2005) conducted a low dose coagulation study using several classes of coagulants to treat runoff into the Lake Tahoe. They tested new types of coagulants, which are prehydrolized aluminum salts with and without silica, sulfate and organic polymers and controlled the doses using inline particle surface charge detector. From their three phase coagulation study, PACl modified with silica or sulfate were most effective to obtain lower than 20 NTU under different conditions of initial water turbidity, temperature, mixing intensity and settling time.

29

Chapter 3

Model Development

## 3.1 MODEL EQUATIONS

Because a highway is a longitudinally extended structure, highway runoff is simplified as 1-D flow problem in the longitudinal direction. Figure 3.1 conceptualizes the translation of 2-D problem into 1-D problem for the highway runoff simulation. The arrows in the 2D domain show the vectors indicating real flow direction in the highway. In the simulation, a large arrow in 1-D domain is assumed to represent the velocity vectors in the corresponding section of 2-D domain. Table 3.1 summaries the model equations and numerical schemes that were used in this study. The kinematic wave equation is used to calculate 1-D flow with a steep bed slope (~ 2%). For the radial flow simulation, the diffusion wave equation was used to consider the effect of backwater diffusion near the downstream where water mass accumulates. Non-oscillatory solutions for water depth and velocity are essential to

30

2-D Domain

1-D Domain

FIGURE 3.1

## Concept of 1-D flow model for highway runoff

TABLE 3.1

Model Equations and Numerical Schemes Models 1-D Flow Kinematic wave equation Hyperbolic Method of characteristics (MOC) Advection-diffusion equation Parabolic Crank-Nicolson method Radial Flow Diffusion wave equation Parabolic Characteristics averaging method (CAM) Advection-diffusion equation Parabolic Crank-Nicolson method

## Governing equation Equation type Numerical scheme

Water quality Governing equation (Mass transport model) Equation type Numerical scheme

31

obtain accurate solutions for the mass transport equation. Therefore, the method of characteristics (MOC) and characteristics averaging method (CAM) were considered appropriate schemes to solve the kinematic wave and diffusion wave equations, which are hyperbolic and near-hyperbolic partial differential equations, respectively.

3.1.1 Kinematic Wave Equation The kinematic wave equation is derived by simplifying equation (2.8). Neglecting the terms on the left hand side (i.e. the terms of acceleration, gravity and pressure force), Equation (2.8) is reduced to

S f = S0

(3.1)

Mannings equation and equation (3.1) are plugged into equation (2.7), resulting in the kinematic wave equation as follows:
h h + mh m 1 =I f t x

(3.2)

with

c = mhm1 = mu, = S0 / n

(3.3)

where c is celerity (L/T), m is constant (=5/3), n is Mannings roughness coefficient. The initial and boundary conditions for the overland flow can be reasonably assumed as (Singh, 1996)
h(0, t ) = 0, h( x, 0) = 0, 0t T 0 xL

(3.4) (3.5)

32

## where T is storm duration and L is length of overland flow plane.

3.1.2 Diffusion wave equation The diffusion wave equation is also a simplification of the Saint-Venant equations. Equation (2.8) is reduced to equation (3.6) by ignoring acceleration and gravity force terms:
S f = S0 h H = x x

(3.6)

where H is water level above a datum (L). By substituting equation (3.6) and the Mannings equation, Equation (2.7) yields a parabolic equation, called the diffusion wave equation as follows:

H H = K t x x

+I f

(3.7)

or

h 5 h K 2 h = u + 2 + I f 3 x 2 x t

(3.8)

with

K=

h5/ 3 n Sf

(3.9)

Radial flow can be also dealt with as a 1-D flow that includes additional lateral flow resulting from convergence of flow area to the downstream. Considering the tapering width in the flow direction, radial flow equation is derived from equation (3.8) as follows:

33

h 5 h K 2 h hu = u + 2 + +I f t 3 x 2 x L x

(3.10)

3.1.3 Infiltration Although paved area such as highway and parking lots are classified as impervious landuses, infiltration, albeit small, inevitably occurs. In this study, 10-cm-thick asphalt pavement is assumed to approximate the infiltration through the bed surface. Introducing Darcys law of permeability, infiltration rate can be expressed as
h + Tp p p h pp h f = K p = K p = K p Tp z Tp Kp

(3.11)

where Kp is hydraulic conductivity of the pavement (L/T), z is distance in the vertical direction (L), Tp is thickness of the pavement layer (L), pp is pressure head under the pavement layer (L). Hydraulic conductivity of asphalt pavement has been reported in the range of 10-5 to 10-3 cm/sec (Allen, 2003; Bowders et al., 2003). By assuming the pavement is asphalt supported by well draining materials such as gravel, the pressure head under the pavement layer (pp) becomes zero and equation (3.11) is reduced to a linear function of water flow depth (h) as

f =

(3.12)

## where the unit of the infiltration rate is [cm/sec].

34

3.1.4

Pollutant Transport

The conventional advection-dispersion equation (ADE) is used for the mass pollutant transport calculation. Ignoring mass transfer through infiltration, the ADE is expressed as

mw mw = D ( u mw ) E t x x x
where mw is pollutant mass in the water of the unit area (M/L2) and D is dispersion coefficient (L2/T) and E is pollutant erosion rate from the bed surface (M/L2/T).

(3.13)

The dispersion coefficient can be calculated using the equation developed for the open channel flow (Elder, 1956) as follows:

D = 6.0hu* ,
where u* is friction velocity (L/T).

u*

ghS0

(3.14)

3.1.5 Pollutant Erosion from a Plane Surface Pollutant erosion rate is generally assumed as a first order reaction in terms of mass available on the bed surface (Singh, 1996; Tomanovic and Maksimovic, 1996). The erosion coefficient of solutes or cohesive particles is typically related to the bed shear stress, which is reasonably correlated with mean flow velocity (Chien and Wan, 1999). Therefore, the erosion equation can be basically formulated as
E= dmb = u 2 mb dt

(3.15)

35

where mb is mass available on the bed surface (M/L2) and is erosion coefficient (T/L2). However, equation (3.15) can not properly reflect polluto-graphs obtained from the monitoring data. Figure 3.2 displays an example of polluto-graph showing typical washoff behavior of COD, DOC and Oil and Grease. At the beginning of a storm, a pollutant is discharged with a considerably high concentration (phase I), declining to a low level in a short time followed by a prolonged residual concentration (phase II) to the storm end. This washoff behavior will be defined as two-phase washoff in this study. Two-phase washoff was observed in the washoff of most of the measured constituents except suspended solids (SS). To model this phenomenon, two pollutant sources having different erosion rates were introduced: the short-term source and long-term source. The short-term source represents pollutant mass accumulated during antecedent dry period before a storm. Pollutants from the short-term source are easily detached from the surface under even small flow energy because they are on the outmost layer of the pollutant mass. In contrast, pollutants from the long-term source are not directly exposed to the flow shear or protected by the bed roughness; as a result, through the repeated storm events, survived pollutant is solidified on the surface and acts as a permanent pollutant source in the impervious watershed. Considering the terms for two different pollutant sources, equation (3.15) can be modified as follows:

E=

dmb ,t dt

dmb, s dt

dmb,l dt

= s u 2 mb , s l u 2 mb,l

(3.16)

36

800

2500
UCLA3, 11/07/02 Flow Rate Rainfall (in) COD DOC O il & Grease

160

2000 600

Phase I

400

COD (mg/L)

1500 80 1000

200 500

40

Phase II

FIGURE 3.2

## Two-phase washoff of the pollutants

where mb,t is total pollutant mass, mb,s is pollutant mass from the short-term source, mb,l is pollutant mass from the long-term source and s, l are constants. The following relationships are valid if mb,l is large and l is assumed to be negligibly small:

dmb ,l dt
where l is constant.

0, l mb ,l = l '

(3.17)

By plugging equation (3.17) into equation (3.16), the erosion equation can be simplified as

E=

dmb ,t dt

dmb , s dt

= s u 2 mb , s l 'u 2

(3.18)

37

Now, s and l are defined as erosion coefficients of pollutant mass from the short-term source and long-term source, respectively.

## 3.2 NUMERICAL SOLUTIONS

Model equations were calculated using FDMs as summarized in Table 3.1. The kinematic wave equation was solved by the method of characteristics (MOC) to avoid oscillatory solutions. Due to the near hyperbolic nature of the diffusion wave equation of this study, characteristics averaging method (CAM), was used for the radial flow problem. Mass transport equation is calculated using Crank-Nicolson method (C-N), which is a common method for parabolic differential equations.

3.2.1 Method of Characteristics for 1-D Flow In the kinematic wave equation, the equation of characteristic curve can be obtained by calculating the determinant of the coefficient matrix as follows:
h 5 = c = h2 / 3 t 3

(3.19)

Figure 3.3 illustrates the calculation procedure of node values using MOC. The destination of characteristic curve to the next time level at each node is determined explicitly using equation (3.19). For example, knowing the position (x1, t1) and value (h1) of point X1, the position (x2, t2) and value (h2) of point X2 can be calculated as follows:

38

Interpolation

## FIGURE 3.3 Procedure of the node value calculation in MOC

5 ( x2 , t2 ) = ( x1 + x1 , t1 + t ) = ( x1 + h12 / 3t , t1 + t ) 3

(3.20)

h2 = h1 + I (t1 ) t

(3.21)

where I (t1) is rainfall intensity at t = t1. Starting with an evenly distributed node set at t = 0, the distance between nodes are disturbed as the calculation continues. The nodal values of the resulting nonhomogeneous node set should finally be interpolated, obtaining a homogeneous node set.

3.2.2

## Characteristics Averaging Method for Radial Flow

CAM is a modification of C-N to solve the near-hyperbolic equation of 1-D problems (Stenstrom, 1996). This method uses six node values to diagonally average the derivative terms as shown in Figure 3.4.

39

i+1 n+1

n i-2 i-1 i

## old time level, known new time level, unknown

Characteristics averaging Interior points (Stenstrom, 1996)

FIGURE 3.4

## The diffusion wave equation can be formulated as follows:

K 5u n +1 K 5u n 1 1 + hi 1 hi 2 2 t 4x 6x 2 t 4 x 6 x 5u n +1 5u n K K 1 1 + + + = + + hi hi 1 2 2 2t 2x 6x 2 t 2 x 6 x K n +1 K n + h h 2 i 1 2 i2 4x 4x
n hin1/ 2uin1/ 2 I in1/ 2 fi 1/ 2 + + 2 L xi 1/ 2

(3.22)

where i is node number and n is time step. In equation (3.22), K, u, I and f are assumed constants within a time step and determined at time n. This assumption is valid for the implicit methods (Wasantha Lal, 1998). A set of equations composed of equation (3.22) for each node can be constructed as a tri-diagonal matrix, which is solved using the Thomas algorithm (Von Rosenberg, 1969).

40

## 3.2.3 Stability and Convergence in Numerical Solutions

It is difficult to establish rigorous stability criteria for the grid size (x) and time step (t) because the overland flow equations are nonlinear (Fieldeler and Ramirez, 2000). MOC and implicit schemes are used for the stability of numerical solution in this study. However, numerical sensitivity tests to determine appropriate x and t were necessary to insure that an accurate solution was obtained.

## Solutions for 1-D Flow.

The model domain size and input conditions used for the

## numerical sensitivity tests are shown bellow:

Rainfall intensity = 6 mm/hr Rainfall duration = 1 hr Pavement hydraulic conductivity (Kp) = 0 cm/sec Slope = 0.02 Watershed length (WL) = 244 m

Different values of t were evaluated for a given initial x (xo) in MOC (x changes as MOC procedure proceeds). Figure 3.5 (a) and (b) show the outflow as a function of time calculated using six different values of t with 1 m and 2 m of xo, respectively. As t decreases, the solution converges to be an accurate solution. Large t produces overestimated solution, resulting from the error in the calculated position due to the linear assumption for the non-linear characteristics curve. Figure 3.6 shows the water

41

depth profile along the distance at t = 70 min using different values of t for a given xo. In the water depth profile shown in Figure 3.6, a sudden change in water depth indicates the wave propagation. Smaller t decreases the height of wave that moves along the distance during the t, providing better resolution in the water depth profile. From the results in Figure 3.5 and 3.6, 1/8 min was chosen for t to achieve sufficiently high accuracy in the solutions. Effect of grid size was also tested. Figure 3.7 is the outflow profile over time using different values of xo at t = 1/8 min and Figure 3.8 is the water depth profile along the distance at t = 70 min under the same conditions for xo and t. According to those figures, different values of xo from 1 to 4 m make little difference in the solution of MOC. The numerical solutions from C-N were also investigated to determine an appropriate grid size for the mass calculation in the 1-D flow model. Figure 3.9 is the pollutant concentration in the outflow with respect to time using different x from 1 to 6.1 m at t = 1/8 and Figure 3.10 is the profile of mass in the water along the distance using the same conditions for x and t. As shown in these figures, different grid sizes within the tested range make little change in calculated concentration of the outflow although 2 m or larger x causes slight oscillation in the spatial mass profile for a given time. According to the numerical tests performed above, smaller x and t produce more accurate solutions for both MOC and C-N. Due to small grid size and time step, however, the computing time might be prohibitively long. In this study, the values of x = 1 m and t = 1/8 min were considered satisfactory. Occasionally, x larger than 1 m was also

42

x 10

-4

(a)

20

40

60 time(min)

80

100

120

4.5 4 3.5 3
qout (m2/sec)

x 10

-4

(b)

20

40

60 time(min)

80

100

120

FIGURE 3.5

## Calculated outflow using different values of t with different xo: (a)

xo = 1 m; (b) xo = 2 m

used to reduce computing time without losing accuracy of the solution for the mass emission when the simulated watershed was longer than 1,000 m.

43

1.2

x 10

-3

0.8

h(m)

0.6

0.4

0.2

50

200

250

x 10

-4

h(m)

10

20

30 distance(m)

40

50

60

FIGURE 3.6

1m

44

x 10

-4

20

40

60 time(min)

80

100

120

FIGURE 3.7

1.4

x 10

-3

1.2

0.8
h(m)

0.6

0.4

0.2

50

200

250

FIGURE 3.8

1/8 min

45

700

600

500

## dx=1 dx=2 dx=4 dx=6.1

Cout(mg/L)

400

300

200

100

20

40

60 time(min)

80

100

120

FIGURE 3.9

Outflow concentration profiles calculated for the same storm event using

## 0.35 0.3 0.25

mass in the water(g)

50

## 100 150 distance(m)

200

250

FIGURE 3.10

Mass profiles along the distance at t = 30 min calculated for the same

## storm event using different values of x with t =1/8 min

46

Solutions for Radial Flow. Using the same inputs for rainfall, slope and pavement

hydraulic conductivity with those of the numerical tests for 1-D flow, four different watershed dimensions were tested as follows:

WL = 50 m, ro = 1 m WL = 50 m, ro = 5 m WL = 100 m, ro = 1 m WL = 100 m, ro = 5 m

where WL is length of converging-type watershed and ro is the inlet radius. Tested ranges for x and t are 0.05 ~ 0.5 m and 1 ~ 1/32 min, respectively. By investigating the numerical solutions from the tests, following criteria were experimentally obtained.

CAM - 1/8 min or smaller t is required to obtain non-oscillatory solution - x should be less than 1/10 ~ 1/20 of ro for the accurate outflow calculation

C-N - 1/8 min or smaller t is required to obtain accurate and non-oscillatory solution - x were to be less than 0.5 m to avoid 2x oscillation

Allowable size of x proportionally decreases as the inlet dimension decreases; as a result, extremely long computing time would be required for the solution of a watershed that has large WL and small ro. In this case, the variable grid size might be useful. That is, the model domain can be discretized finer in the downstream domain than in the upstream domain. However, homogeneous grid sizes were used in this study because the

47

simulated watershed lengths were sufficiently short (1 ~200 m). The details results of the numerical tests can be found in Appendix B.

## 3.3 PARAMETER ESTIMATION

The model parameters were calibrated using measured runoff and pollutant concentration data obtained from selected storm events in site 3 (7-203) during 2000~2003 (see Appendix A). 22 storm events were used for the water quantity calculation and 12 storm events among them were selected for the water quality parameter calibration. The monitoring data used for these calibrations were selected based on the data availability for the constituent concentrations. Hydrologic characteristics of 12 storm events for the water quality parameter calibration are summarized in Table 3.2. The calibrated model parameters were the initial value of mb,s (mb,so), s and l. A non-linear least-squares solver (i.e. lscurvefit) in the MATLAB toolbox was used to minimize equation (3.23) as the objective function.

(C
i

i ,cal

Ci ,obs ) 2

(3.23)

where Ci,cal and Ci,obs are the calculated and observed concentrations for ith grab sample, respectively.

48

Date

## Average Rainfall Intensity (mm/hr)

1/10/2001 2/19/2001 2/24/2001 3/4/2001 11/24/2001 12/20/2001 1/27/2002 2/17/2002 3/17/2002 12/19/2002 2/11/2003 3/15/2003

127.0 7.1 14.5 11.9 29.7 12.2 24.6 7.4 10.4 32.5 20.1 123.2

14.6 6.9 14.2 3.7 4.6 12.7 8.6 2.0 1.4 10.4 15.6 21.7

2.0 5.3 1.0 4.0 11.6 6.3 27.1 20.3 10.7 3.1 44.1 11.7

3.8 128.8 2.0 10.7 7.4 2.0 16.3 24.6 4.6 40.6 9.7 1.5

8.70 1.03 1.02 3.22 6.46 0.96 2.86 3.70 7.43 3.22 1.29 5.68

49

Chapter 4

## 4.1 PREPARATION OF RUNOFF SAMPLE

Multiple composite samples were collected during the first hour of runoff from site 2 (see Appendix A for site details) during the 2004-2005 storm season. One-hour composites were selected because this time is generally equal to the time of the first flush. Samples were returned to the laboratory within 1 hour and a series of jar tests were performed using different coagulants and mixing strategies. Table 4.1 shows a brief summary showing the range of sample characteristics. TABLE 4.1 Parameter pH Temp ( C) Turbidity (NTU) EC (S) ZP (mV)
o

Characteristics of 1 hr Composite Samples from Site 2 Range of Untreated Composite Samples 6.3 ~ 7.1 13.2 ~ 19.8 51 ~ 197 141 ~ 1,014 -46.54 ~ -26.54

50

## 4.2 MIXING TESTS

Natural aggregation of the particles was investigated using runoff sample. Two 4 L bottles of runoff sample were prepared and labeled no mixing and mixing respectively. The bottle labeled no mixing was kept quiescent and the other labeled mixing was stirred by a magnetic bar exerting collision between particles to accelerate aggregation. The stirring speed of the magnetic bar was set to be as low as possible in order to minimize the breakup the particle flocs. The observation was performed for 385 hours in the normal temperature (20 C). Samples were taken from each bottle (mixing and no mixing) and TSS, TDS and PSD were analyzed at 0, 24, 40.8, 76, 96, 240 and 385 hr, respectively.

## 4.3 PROTOCOLS FOR JAR TESTS

The jar tests were divided into three different experimental regimes: low dose coagulation, sweep floc coagulation and flocculation using organic polymers. In the low dose coagulation, relatively small doses of alum or ferric chloride were applied and then slowly mixed for 4 to 8 hours. These procedures were intended to investigate the effect of metal ions on neutralizing and aggregating negatively charged particles in the water. The second regime used higher doses to produce sweep floc coagulation. The high alum or ferric chloride dosage formed a sweep floc enmeshing the colloidal particles. Optimum dose for each coagulant was estimated based on turbidity

51

removal. pHs were always adjusted to 7 both in low dose and sweep floc coagulation tests. Finally, a more extensive series of flocculation tests were performed using cationic organic polymers. Polydiallyldimethylammonuim chlorides (polyDADMACs) with different molecular weights (Table 4.2) were used. Long periods of slow mixing were provided after 1minute of rapid mixing to allow sufficient contact time for particle aggregation. The general procedures of each coagulation/flocculation test are shown in Table 4.2.

## TABLE 4.2 Experimental Regime Low dose coagulation

Protocols for the Coagulation / Flocculation Tests Rapid Mixing 1min 100 rpm Slow Mixing

Settling

Coagulant

## 4~8 hr 16~20 hr PolyDADMAC HMW: 400,000-500.000 5~10 rpm

MMW: 200,000350,000 LMW: 100,000-200,000

52

## 4.4 WATER QUALITY MEASUREMENTS

Turbidity, zeta potential (ZP) and particle size distribution (PSD) were the major parameters measured in the tests. Particle ZP was measured with ZetaPlus (Brookhaven Instruments Corp., Holtsville, New York). Water samples were diluted with de-ionized (DI) water before measured when they contained too high turbidity for measurement. Dilution with DI water was compared with samples diluted with filtered stormwater using 0.1m filter and were not significantly different, showing that pre-dilution with DI water does not significantly alter the measured ZP of the particles. PSD was measured with AccuSizer 780 Optical Particle Sizer module (Nicomp Particle Sizing Systems, Santa Barbra, California). The light scattering/extinction sensor attached on the AccuSizer can measure the particle number in the solution in different size range from 0.5 m to 400 m. Detail procedures for the PSD measurement are described in Li et al. (2005a).

53

Chapter 5

## 5.1 PARAMETER ESTIMATION IN 1-D HIGHWAY RUNOFF MODEL

5.1.1 Flow Calculation The modeled highway site (site 3) was selected for modeling and considered as a 1-D catchment with 178 m in length. The measured rainfall data were used as the input rainfall and were assumed homogeneous along the distance. Flow was calculated on the basis of unit width and then multiplied by the site width (21.9 m) to be compared with the measured flow data. A value of 0.11 was used for Mannings roughness coefficient (n) assuming that the pavement surface is made of smooth asphalt or concrete. It is necessary to estimate a representative hydraulic conductivity of the pavement (Kp). Three different values of Kp (i.e. 510-4, 10-5, and 210-5 cm/sec) were evaluated using 22 storm events data. Figure 5.1 shows the calculated and measured runoff volumes with values of R2 for different Kp. As shown in the figure, the flow model predicts runoff

54

3

(a)

400

300 R = 0.983
2

200

100 0 500

(b)

400

300 R = 0.988
2

200

100 0
500

(c)

400

300 R = 0.982
2

200

100

3

500

FIGURE 5.1

## Measured and simulated runoff volumes with different values of

pavement hydraulic conductivity: (a) 510-6 cm/sec; (b) 10-5 cm/sec; (c) 210-5 cm/sec

55

volume very well with R2 larger than 0.980 and 10-5 cm/sec was the best value of Kp (R2 = 0.989). Figure 5.2 compares the calculated and measured peak flow rates using the same plotting format with Figure 5.1. As opposed to the runoff volume calculation, calculated peak flows results were more scattered when compared to the measured peak flows. Despite this scattered correlation, Figure 5.2 suggested that peak flow can reasonably be simulated in the evaluated range of Kp (510-4 ~ 210-5 cm/sec) and R2 ranged from 0.437 to 0.440. Considering the results in Figure 5.1 and 5.2, 10-5 cm/sec was chosen as the best site-representative value of Kp. Figure 5.3 shows the measured and calculated runoff coefficients with respect to the total rainfall volume at Kp = 10-5 cm/sec. Both the measured and calculated runoff coefficients ranged from 0.60 ~ 0.96 and generally increased as the total rainfall increased. This demonstrates that the site infiltration can be reasonably modeled by Darcys permeability theory. Figure 5.4 contains the hydrographs for three different storm events. As can be seen, the 1-D runoff model can closely simulate the measured flow in peak flow rate, peak flow time and hydrodynamic flow patterns. More hydrographs can be found in Appendix C. Based on the flow simulations described above, the parameters for the flow calculation were determined and summarized in Table 5.1. These parameters were used in the subsequent mass transport calculation.

56

(a)

0.03

0.02

0.01 0 0.05

R = 0.437

(b)
0.04

0.03

0.02

0.01 0

R = 0.439

(c)

0.03

0.02

0.01

3

0.05

FIGURE 5.2

## Measured and simulated peak flows with different values of pavement

hydraulic conductivity: (a) 510-6 cm/sec; (b) 10-5 cm/sec; (c) 210-5 cm/sec

57

## 0.8 Runoff Coefficient

0.6

0.4

0.2

Measured Calculated

## Runoff coefficients with respect to the total rainfall volume at Kp = 10-5

TABLE 5.1

Input Parameters for the Flow Calculation Parameter Values 178 21.9 0.02 0.011 10-5

Input Parameters Watershed Length, WL (m) Watershed Width, W (m) Slope in the Longitudinal Direction, S0 Mannings Coefficient, n Hydraulic conductivity of the Pavement, Kp (cm/sec)

58

800
1/10/01 Rainfall Intensity Measured Flow Calculated Flow Measured COD Calculated COD Measured Cond. Calculated Cond.

400

600
COD (mg/L)

300

400

200

200

100

200

400

600

800

1000

Time (min)

800
1/10/01 Rainfall Intensity M easured Flow Calculated Flow M easured CO D Calculated COD M easured Cond. Calculated Cond.

160

600
Total Zn (ug/L)

120

400

80

200

40

200

400

600

800

1000

Time (min)

## (a) Storm event on 1/10/2001

59

Total Cu (ug/L)

Conductivity (mmho/Cm)

1200

800

800

400

400

## 0 0 50 100 150 200 250 Time (min)

2000
3/4/01 Rainfall Intensity Measured Flow Calculated Flow Measured COD Calculated COD Measured Cond. Calculated Cond.

500

1600

400

1200

300

800

200

400

100

## (b) Storm event on 3/4/2001

60

Total Cu (ug/L)

Total Zn (ug/L)

Conductivity (mmho/Cm)

COD (mg/L)

3/4/01 Rainfall Intensity Measured Flow Calculated Flow Measured COD Calculated COD Measured Cond. Calculated Cond.

1200

4000
1/27/02 Rainfall Intensity Meas ured Flow Calculated Flow Meas ured COD Calculated COD Meas ured Cond. Calculated Cond.

2000

1600

1200

2000
800

1000
400

## 200 Time (min)

400

600

5000
1/27/02 Rainfall Intensity Measured Flow Calculated Flow Measured COD Calculated COD

1000

4000

800

3000

Measured Cond .
Calculated Cond.

600

2000

400

1000

200

## 200 Time (min)

400

600

(c) Storm event on 1/27/2002 FIGURE 5.4 Measured and calculated hydrographs and polluto-graphs

61

Total Cu (ug/L)

Total Zn (ug/L)

Conductivity (mmho/Cm)

5.1.2 Calibration of Water Quality Parameters Calculated concentrations were fitted with measured concentrations to calibrate the model parameters (mb,so, s and l ) for COD, conductivity, Zn and Cu, respectively. Before minimizing the sum of square errors between measured and calculated concentrations, the calibrated parameters were constrained to reasonable values by observing the measured and calculated concentration curves. Table 5.2 provides the calibrated parameters for four different constituents. s ranged from 0.87 to 1.10 sec/m2, without large variance among constituents. l, however, widely varies from one constituent to another. mb,so was different for individual storm events due to different ADD, which was as predicted. Concentrations for each constituent were calculated using calibrated parameters and plotted with measured concentrations as illustrated in Figure 5.4. This figure provides polluto-graphs for three storm events on 1/10/2001, 3/4/2001 and 1/27/2002, respectively.

## TABLE 5.2 Parameters COD Conductivity Zn Cu

a

Calibrated Parameters for Site 3 a mb,so (g/m2) 0.10 ~ 1.18 0.10 ~ 0.55 0.05 ~ 1.46 0.05 ~ 0.29

s (sec/m2)
1.09 (0.6 ~ 1.2) 0.99 (0.4 ~ 1.2) 0.87 (0.4 ~ 1.2) 0.88 (0.4 ~ 1.2)

l (gsec/m4) 0.0024 (0.001 ~ 0.004) 0.0027 (0.002 ~ 0.004) 0.0073 (0.004 ~ 0.014) 0.0016 (0.001 ~ 0.0028)

Average values with lower and upper boundaries in parentheses mb,so -Initial pollutant mass from the short-term sources

62

As can be seen, two-phase washoff phenomenon (high concentration first flush followed by prolonged emission in a low concentration level) was well simulated. A quick rise in the calculated concentration sometimes occurs at the end of rainfall as observed in Figure 4.3(a) and (b). This is due to the reduced dilution caused by the flow decrease. More polluto-graphs for the other storm events can be found in Appendix C.

5.1.3 Pollutant Buildup Using calibrated mb,so values for each storm event, buildup equations were obtained as shown in Figure 5.5. This figure illustrates COD buildup as a function of ADD, showing the plots of calibrated values of mb,so fitted with four different curve forms using the least-square method. In the same manner, buildup formulas for the other constituents can be also obtained and presented in Table 5.3. Regressions for conductivity, Zn and Cu are provided in Appendix D.

TABLE 5.3

a

## t - Antecedent dry days (days)

63

1.8 1.6 1.4 1.2 mb,o (g/m2) s 1 0.8 0.6 0.4 0.2 0 Linear Power Exponential Michaelis-Menton

10

15 Time(days)

20

25

30

FIGURE 5.5

## Regressions for COD buildup using different curve forms

Table 5.4 compares buildup formulas suggested by different researchers for urban landuses. Buildup mass of total solids (TS) for 30 days of ADD is calculated using each formula and compared in 4th and 5th columns of Table 5.4. Because a buildup formula for solid was not available in this study, The COD buildup formula was used and calculated COD mass was converted into the equivalent TS mass using the factor of 46,120 mgCOD/kgTS, reported for urban landuses by Manning et al. (1977). Table 5.4 implies that the solid accumulation estimated from this study (416 gTS/m) is reasonably well matched with that from Sartors formula (427 gTS/curb m) that represents 95% of TS accumulated across the street width. Tomanovics and Kims formulas slightly underestimated the total because their studies were only for suspended fraction of TS.

64

TABLE 5.4

Comparison of Buildup Equations Equivalent solid mass accumulation for 30 days of References ADD mass/length mass/area
TS (lb / curb mi ) = t 0.00187 + 0.000601t

Application

Pollutant

Formula a

Industrial landuse

TS

427 gTS/m

Sartor et al. (1972) Tomanovic and Maksimovic (1996) Kim (2002) This study (Exponential type)

TSS

7.4 gTSS/m2

TSS

416 gTS/m b

8.9 gTSS/m2

Highway

COD

## COD( g / m2 ) = 1.29(1 e0.088t )

26.0 gTS/m2 c

b, c

t - Antecedent dry days (days) calculated using the ratio of 46,120 mgCOD/kgTS reported by Manning et al. (1977)

## 5.2 FIRST FLUSH SIMULATIONS IN 1-D FLOW

All the MFF simulations in this study were based on the calibrated parameters (i.e. mb,so,

s and l) for COD. MFF10 and MFF20 were selected as the representative MFF ratios.
MFF was basically investigated as a function of watershed length (WL) under different conditions in rainfall intensity, rainfall duration, slope, pavement hydraulic conductivity, initial mass and erosion coefficients. Constant rainfall intensity was assumed for the input rainfall in the model equation. Different types of rainfall such as triangular or sinusoidal shaped rainfall patterns were remained for the future work.

5.2.1 Maximum MFF Ratio and Optimum Watershed Length The MFF ratios (i.e. MFF10 and MFF20) calculated for various watershed lengths (WLs) were investigated and it was found that there exists an optimum watershed length (WLopt) that maximizes MFF10 or MFF20 in the range of 1 to 10,000 m. Figure 5.6 illustrates the MFF changes for different WLs. In this figure, both MFF10 and MFF20 are maximized at a 50 m-long-watershed. This demonstrates that neither of extremely small and large watersheds yields high MFFn (e.g. MFF10, MFF20). In a small watershed, rainfall water rapidly flushes out without forming sufficiently high flow rate; as a result, pollutants are not well mobilized due to lack of flow energy. In a very large watershed, pollutants travel a long distance, resulting in retardation of mass emission although large flow energy effectively erodes pollutants out of the surface. MFF can be even inversed (MFFn < 1.0) in an extremely large watershed (e.g. WL > 5,000 m in the Figure 5.6).

66

20
0.8 Normalized Cumulative Mass

100

10

5
0.6

0 50
00 10

50 00
0 0.2

0.4

0.2

Number = Watershed Length (m) 0 0.4 0.6 Normalized Cumulative Flow 0.8 1

FIGURE 5.6 hr

## MFF changes with different watershed lengths at I = 3 mm/hr and T = 3

Figure 5.7 illustrates how the maximum MFF ratio (MFFn,max) and optimum watershed length (WLopt) can be obtained from a MFF simulation. Because MFFn is calculated at discrete points of WL, calculated values of MFFn at those points are interpolated to produce a continuous function. A scalar-minimization solver (i.e. fminbnd) in the MATLAB toolbox was used to calculate maximum MFF10 (MFF10,max), maximum MFF20 (MFF20,max) and WLopt from the non-linear continuous function obtained by interpolation. To calculate WL at a certain MFFn value, a function solver (i.e. fzero) in the MATLAB was used. In Figure 5.7, MFF20,max, WLopt, and WL at MFF20 = 2.5 are calculated as 4.2, 30 and 550 m, respectively.

67

10 00 0

5
MFF20,max = 4.2

MFF

20

3
2.5

2
WLMFF
20=2.5

= 550 m

1
WLopt = 30 m

10

100

1000

10

## Watershed Length (m)

Maximum MFF20, optimum watershed length, and watershed length at

## FIGURE 5.7 MFF20 = 2.5

5.2.2 Evaluation of Affecting Factors Rainfall Intensity (I) and Duration (T).
Six hypothetical rainfalls with different

rainfall intensity and duration were simulated and calculated values of MFF10 and MFF20 were plotted as functions of WL in Figure 5.8. As can be seen, MFF10,max and MFF20,max occur at different WLs for each rainfall simulated. This is because different combinations of rainfall intensity and duration change hydraulic conditions, resulting in different emission rates of pollutants. Higher rainfall intensity and longer duration produce larger MFFn and smaller WLopt. As the watershed becomes longer, both MFF10 and MFF20 approach 1 or less. Storm events with the same total rainfall volume (e.g. rainfall 1 and 5,

68

or rainfall 2 and 6) showed similar curves in both cases of MFF10 and MFF20, which implies total rainfall volume might be useful as a potential indicator for estimating MFFn, max (e.g. MFF10, max, MFF20, max).

Slope (S0) and Infiltration Rate (f). The effects of slope and infiltration rate were
estimated using rainfall 1 (I = 3 mm/hr and T = 3 hr). Figure 5.9 displays the effect of the bed slope on MFF10 and MFF20 for different WLs. As the slope increases, WLopt tends to be shorter. MFF10, max and MFF20, max proportionally increase as the slope increases although the increments were insignificant in the simulated range of slope (0.01 ~ 0.06). MFF10,max was more sensitive than MFF20,max to slope change. Figure 5.10 shows MFF10 and MFF20 with respect to WL for three different values of Kp ranging from 10-5 to 510-5 cm/sec. Corresponding runoff coefficients were also displayed in the figure. As can be seen, smaller Kp produces larger MFF10 and MFF20, and requires smaller WL for MFFn, max. MFF10, max and MFF20, max also decrease as Kp increases. High infiltration rate reduces net precipitation, thereby retarding pollutant erosion rate because of lower flow energy. In the long watershed range (WL > 300 m), the curves of MFF10 and MFF20 under different infiltration rate become closer. That is, MFF10 and MFF20 are less sensitive to the infiltration rate in a large watershed.

69

8 7 6 5 MFF10 4 3 2 1 0
8 7 6 5 MFF20 4 3 2 1 0 1 10 100 Watershed length (m)
o 2

Rainfall 1: I=3.00mm/hr, T=3hr Rainfall 2: I=1.50mm/hr, T=3hr Rainfall 3: I=0.75mm/hr, T=3hr Rainfall 4: I=3.00mm/hr, T=6hr Rainfall 5: I=1.50mm/hr, T=6hr Rainfall 6: I=0.75mm/hr, T=6hr

1000

10

## So=0.02, Kp=10 cm/sec, mb,s =0.5g/m

-5

FIGURE 5.8

MFF10 and MFF20 with respect to the watershed length for different

## rainfall intensities and durations

70

8 7 6 5 MFF10 4 3 2 1 0 8
7 6 MFF20 5 4 3 2 1 0 1 10 100 Watershed Length (m) 1000 10
4

## So = 0.01 So = 0.02 So = 0.04 So = 0.06

FIGURE 5.9

MFF10 and MFF20 with respect to the watershed length for different

## slopes (I = 3 mm/hr and T = 3 hr)

71

8 7 6 5 MFF10 4 3 2 1 0

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 1 Runoff Coeff.

8 7 6 5 MFF20 4 3 2 1 0 1 10 100 1000 Watershed lenth (m) Kp1, RC Kp2, RC Kp3, RC Kp1=10 cm/sec
-5

4

0.2

## Kp2=2.5x10 cm/sec Kp3=5x10 cm/sec

-5

-5

FIGURE 5.10

MFF10 and MFF20 with respect to the watershed length for different

72

Runoff Coeff.

## Different values of mb,so

were simulated as a function of WLs in Figure 5.11. As can be seen, larger mb,so yield greater MFF ratios and larger WLopt for MFF10, max or MFF20, max. Accumulated mass per unit distance strongly affects the MFF ratios in large watersheds. In contrast, the differences among the values of MFF10 or MFF20 for different values of mb,so were small in a very small watershed (WL < 10 m). With mb,so larger than 1g/m2, there was little change in the curves of MFF ratio. In this case, short-term source becomes the dominant pollutant source, so that the total mass emission rate is primarily controlled by s, not the absolute amount of total pollutant mass. As the ADD increases, the short-term pollutant accumulation approaches to maximum capacity. Therefore, the relationship between MFF and ADD becomes weaker as the ADD becomes longer because of limited mass accumulation as well as domination of the short-term source in the total pollutant mass. Figure 5.11 also implies MFF10 is more sensitive to the initial mass than MFF20. The pollutant erosion coefficients were also evaluated. Figure 5.12 shows the simulation results of MFF10 and MFF20 using two different values of erosion coefficient of the short-term source (s). As shown in the figure, higher s produces greater MFF ratios whereas the MFF10, max and MFF20, max are obtained at shorter WLs. MFFn might be hardly influenced by changing s in a relatively long watershed because the values of MFF10 or MFF20 for s = 1 and s = 0.5 are similar in watersheds longer than around 1,000 m.

73

4 o 2

## mb,s = 0.1 g/m mb,s = 0.5 g/m mb,s = 1.0 g/m

o o

FIGURE 5.11

MFF10 and MFF20 with respect to the watershed length for different

## values of mb,so (I = 3 mm/hr and T = 3 hr)

74

8 7 6 5 MFF10 4 3 2 1 0

4 2

## es = 0.5 sec/m 2 es = 1.0 sec/m

FIGURE 5.12

MFF10 and MFF20 with respect to the watershed for different erosion

## coefficients of short-term pollutant source (I = 3 mm/hr and T = 3 hr)

75

10

MFF10

8 7 6 5 MFF20 4 3 2 1 0 1 10

2 2 2

4 4 4 4

## 100 1000 Watershed length (m)

10

FIGURE 5.13

MFF10 and MFF20 with respect to the watershed for different erosion

## rates of long-term pollutant source (I = 3 mm/hr and T = 3 hr)

Figure 5.13 shows the effect of the erosion coefficient of the short-term source (l). The MFF ratios are very sensitive to the change of l in the long watershed range, and

76

relatively insensitive to s. For shorter watersheds, the opposite sensitivities are observed. As l increased from 0.001 to 0.004 gsec/m4 (this is estimated range for l in the parameter estimation study previously performed in section 5.1.2), WLopt, and WL at MFF20 = 2.5 decreased by ln(WL) 0.7 for both values of mb,so. However, decreases in

MFF20, max, were relatively small. The sensitivity value of WL for l change (ln(WL)/l 233) may be considered in determining a design watershed length

(WLdes) although more sensitivity studies will be required to establish the relationship among parameters. As discussed above, the relative importance between pollutants from short-term and long-term sources strongly depends on mb,so, s and l, which determines the characteristics of MFF.

Irregular geometry can change MFF characteristics by converging or diverging water flow. To investigate the effect of geometry in 2-D watersheds, 2-D flow simulation is required, which is more complicated in numerical formulation and solution. However, the radial flow model, as a simple case of the 2-D flow model, can be used to obtain basic characteristics of the flow in a converging type watershed (converging flow). Converging flows are commonly observed in 2-D watersheds such as a parking lot as well as a large watershed that has a small number of inlets. A radial flow simulation will provide

77

fundamental information on MFF behavior in 2-D watersheds. The diffusion wave equation was used for the flow simulation because a strong effect of hydraulic diffusivity is predicted near the downstream where great volume of water accumulates. Simulated I and T were 3 mm/hr and 3 hr respectively. Values of 0.02 and 0.5 were used for S0 and mb,so, respectively, for all radial flow simulations. Because the degree of flow converging depends on the ratio of the watershed length (WL = watershed radius inlet radius) to the inlet radius (ro), the effect of flow converging was investigated using different values for WL and ro. Simulated WL ranged from 1 to 200 m with different of ros (i.e. 1, 5, 10 and 100 m). Watersheds longer than 200 m were not simulated because too much computing time was required. Figure 5.14 shows the curves for MFF10 and MFF20 with respect to WL for different ros. There were no significant differences in the WLopt, MFF10, max and MFF20, max between each simulation. Figure 5.15 more clearly shows the maximum MFF ratios and corresponding values of WLopt shown in Figure 5.14. As ro increases, MFF10 or MFF20 also increases although the rate of increase is small and WLopt is little changed. Lower MFF in the converging flow is due to the tapering distribution of pollutant mass in the flow direction (Figure 5.16). Figure 5.16 illustrates the mass distribution in a converging watershed. Assuming the mass accumulation per unit area is constant, the total mass in a discrete zone becomes larger as the distance of that discrete zone to the downstream boundary becomes longer. That is, less pollutant mass is available for the erosion although flow velocity is much higher near the downstream than the upstream. As a result, the accumulated pollutant

78

8 7 6 5 MFF10 4 3 2 1 0 8
7 6 5 MFF20 4 3 2 1 0 1 10 100 1000 Watershed length (m)
So=0.02, Kp=10 cm/sec, mb,s =0.5g/m I=3mm/hr, T=3hr
-5 o 2

## ro=1m ro=5m ro=10m ro=100m

FIGURE 5.14

MFF10 and MFF20 with respect to the watershed length for different

79

## 7.1 7 MFF10, max 6.9 6.8 6.7 6.6 6.5

4.2 4.1 4 MFF20, max 3.9 3.8 3.7 3.6 3.5 3.4 1 10 ro (m) MFF20, max WLopt

## 60 50 40 30 MFF10, max WLopt 20 10 0

40 35 30 WLopt 25 20 15 10 5 0 100

FIGURE 5.15

Maximum MFF ratio and optimum watershed length in the radial flow

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WLopt

Mass/Area

Total Mass

WL

FIGURE 5.16

## Mass distribution on the converging watershed

mass near the downstream is exhausted rapidly whereas the erosion of pollutant mass is comparatively less in the upstream area, where more pollutant mass is accumulated compared to the downstream. This uneven mass distribution affects on the MFF ratios but the difference was minimal when viewed as a whole.

## 5.4 DESIGN IMPLICATIONS

The 1-D highway runoff model developed in this study can be utilized for the BMP design in two ways. First, treatment capacity and operating conditions of a BMP can be determined using the runoff quantity and quality predicted by the model. Second, through simulation using various conditions, the best condition to obtain a desired MFF can be found and applied for designing storm-drain inlets and collection pipes. This studys focus is mainly on the collection system design described as the second purpose above.

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## 5.4.1 MFF Ratio as a Design Parameter

Although many alternative choices for MFF ratio exist for a design parameter, MFF20 was considered an appropriate design parameter because the MFF simulation results (Figure 5.8 ~ Figure 5.13) shows that MFF20 is comparatively less sensitive to the varying conditions and thereby allows more robust design than designs using MFF10. A proper criterion should be established to use MFF20 as a design parameter because the design watershed length (WLdes) is determined by the design MFF20 (MFF20, des). If a designer needs to maximize the pollutant mass to be treated in a BMP, MFF20, max can be used as a design criterion (i.e. MFF20, des = MFF20, max). MFF20, des can be also purposely adjusted to a lower level for more cost-effective design (e.g. MFF20, des = 2.5 < MFF20, max). The MFF simulations from Figure 5.8 to Figure 5.13 provide a qualitative relationship between the MFF ratio and affecting factors as summarized in Table 5.5.

TABLE 5.5

Qualitative Relationship between MFF20 and Design factors MFF20, max Increase Increase Increase Decrease Increase Increase Decrease WLopt Shorten Shorten Shorten Lengthen Lengthen Shorten Shorten

Design Factors to be Increased Rainfall Intensity Rainfall Duration Slope Infiltration Rate ADD Erosion coefficient for short-term source Erosion coefficient for long-term source

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This qualitative result might be useful for screening before undertaking the full BMP design procedure. A universal design procedure will not be possible because of site specific conditions, due to the diversity in slope, rainfall and available mass of pollutant. Comprehensive MFF simulations under various conditions of slope, rainfall and initial mass of the pollutant were conducted to generate a design tool for determining the watershed length. Table 5.6 shows the ranges of design factors that were used in the MFF simulations. Figure 5.17 shows contours of WLopt as a function of rainfall intensity and duration for different mb,so values at S0 = 0.02. Similarly, contours of MFF20, max corresponding to the WLopt were also constructed as shown in Figure 5.18. These two figures contain contours for four different values of mb,so (i.e. 0.1, 0.5, 1.0 and 1.5 g/m2). Simulated rainfall intensity and duration were in the ranges of 1.2 ~ 12.0 mm/hr and 1 ~ 12 hr,

TABLE 5.6

Design Factors Applied in the MFF Simulations Simulated Values 1.2 ~ 12.0 1 ~ 12 0.01 ~ 0.06 0.1 ~ 1.5 10-5 1.09 0.0024

s (sec/m2)
l (gsec/m4)

83

5
10

(a)
5
10

(b)
30

8.4 7.2
20

20

5
5

40

6.0 4.8

10

2
10
5

30

30
40

20

50
5

20

40
30

10
20
40

10
30

5
60

10
20

50

10

70
10

50

20

20

(c)
2

(d)

30

10

30

## 9.6 8.4 7.2 6.0 4.8 3.6 2.4

70

1.2

80

5 70 60 0

60

20

70

FIGURE 5.17

function of rainfall intensity and duration for different values of mb,so at So = 0.02 and Kp = 10-5 cm/sec: (a) mb,so = 0.1 g/m2; (b) mb,so = 0.5 g/m2; (c) mb,so = 1.0 g/m2; (d) mb,so = 1.5 g/m2

respectively, based on the rainfall data in site 3 (7-203). These contours can be used to decide the inlet location in highways or parking lots for a given characteristics of weather and watershed.

40

40 50

5
2

10

20

20

50
30
40

10
5

30
5

50

40

10
20

60 50

20
30 40

10
10

30

10 40

20 30 40

60
80

50 70

30

20
40

10

11

12 1

60

50

10

11

30

12

84

12.0
3.6

(a)

3. 4

4.3 8

(b)

4.2

4.3

3.4
4.2

## 6.0 4.8 3.6

4.3

3.2
3 8 2..6 2

2.4 1.2 12.0 10.8 Rainfall Intensity (mm/hr) 9.6 8.4 7.2 6.0 4.8 3.6

3. 4

4.3
4.2
4

3.5 3

4.3

4. 55

(c)

(d)
4.6 4
4. 6

4.5

4.5

4.5 5

4.5

4. 5

4.6

4. 5

2.4 1.2

4. 5

4. 6
4.6

FIGURE 5.18

duration for different values of mb,so at So = 0.02 and Kp = 10-5 cm/sec: (a) mb,so = 0.1 g/m2; (b) mb,so = 0.5 g/m2; (c) mb,so = 1.0 g/m2; (d) mb,so = 1.5 g/m2

According to the contours in Figure 5.17, the values of WLopt are less than 100 m for the entire range of the rainfall considered. If MFF20, max is a design criterion, the inlets should be installed at intervals of less than 100 m along the highway, which might result in undesirably high construction costs. For economic purpose, the design criteria for MFF20 (MFF20, des) might be lowered to allow a longer WLdes. All aspects including costs and water quality should be therefore considered to determine MFF20, des.

3. 5

3.5

4.5

10

11

12 1

10

11

12

## Contours of the maximum MFF20 as a function of rainfall intensity and

85

The broad peak of simulated MFF ratios implies a wide range of lengths to obtain high or favorable MFF20 ratios. For example, the MFF20 curve for rainfall 1 in the Figure 5.8 shows that 2.5 or larger MFF20 can be obtained at any WL between 2 and 400 m. This wide range of allowable WL provides a designer the alternative choices for WLdes. A strategy in determining WLdes can be selecting a value between WLopt and the WL at a required MFF20, which is the upper limit of allowable WL (i.e. the maximum WL among WLs yielding MFF20s larger than a required value). Figure 5.19 illustrates contours of the maximum WL at MFF20 = 2.5 (if MFF20, max < 2.5, MFF20, max was used in the contours), which means 50% of the total mass washoff is in the first 20% of the runoff volume. A designer can select a value as a WLdes between the WLopt from Figure 5.17 and the maximum WL from Figure 5.19. Figure 5.20 contains contours for four different slopes at mb,so = 1.0 g/m2. This figure can be used for the watershed with slope ranged from 0.01 to 0.06. 1.0 g/m2 of mb,so corresponds to 17 days of ADD based on the COD buildup estimated earlier. In this manner, the design contour sets for possible conditions of slope and initial mass might be prepared and utilized as a design tool for installing storm-drain inlets.

86

12.0 10.8 Rainfall Intensity (mm/hr) 9.6 8.4 7.2 6.0 4.8
14 0 12 0
80 10 0

(a)
0 30

(b)
0 10

20

60 80

20 0

40

20

0 20

10 0

60

0 30

0 40

40
20

## 3.6 2.4 1.2 12.0 10.8

0 10 80

20 0
40 0
50 0

10 0

30 0
30 0

10 0

80

60

40

20

20 0

40 0

16 0 18 0

12 0 14 0

10 0

80

60

40
60

60 0

30 0 40 0 50 0 60 0 70 0

0 20

50 0

40 0

40 0

80 0

(c)
600

20 0

(d)

0 20

60 0

0 40

## 8.4 7.2 6.0 4.8 3.6 2.4

0 20

60 0

9.6

80 0

60 0

20 0 60 0

20 0

0 40

20 0 40 0

80 0
10 00

40 0

600

800

40 0
600

0 60
80 0
0 10 0

60 0

40 0

40 0

60 0
80 0

40 0

60 0
1000 1200
80 0

80 0 10 0 0 12 0 0 14 00

60 0

1.2

10

11

12 1

80 10 00 0 12 00 1400 1600

0 12 0

0 20

0 80 0 60

00 10

FIGURE 5.19

function of rainfall intensity and duration for different values of mb,so at So = 0.02 and Kp = 10-5 cm/sec: (a) mb,so = 0.1 g/m2; (b) mb,so = 0.5 g/m2; (c) mb,so = 1.0 g/m2; (d) mb,so = 1.5 g/m2

0 40

0 80

10

11

12

87

600

20 0

60 0

40 0

(a)

(b)

40 0

0 20

0 20

60 0
0 40

7.2
40 0
20 0

20 0

0 40

80 0

40 0
80 0

600

600
60 0
0 40

0 60

0 60
40 0
60 0
80 0

20 0
60 0

40 0
40 0

10 00
80 0

60 0

80 0
80 0

60 0
10 00 80 0

0 60 0 40

00 12

10 00

00 10

0 20

0 80

1200

(c)
0 10

(d)

20 0

40 0

20 0

0 10

30 0

40 0

9.6 8.4

0 30

0 20

0 10

500

## 7.2 6.0 4.8

10 0
50 0

50 0

0 20

40 0

60 0

0 30

30 0

0 40

20 0
50 0 60 0
40 0
30 0

10 0

70 0

3.6
60 0 50 040 0 0 30

20 0
60 0 50 0 0 40 0 0 3

50 0

20 0

0 60

40 0

30 0
20 0

800

2.4 1.2

70 0 80 0 90 0 1000

50 60 00

40 0

90 0

70 0 80 0

30 0 50 60 00

70 0

800
900

60 0

50 0

40 0

30 0
60 0 50 0

80 0 70 0

40 0

10

11

12 1

10

11

12

## Rainfall Duration (hr)

FIGURE 5.20 Contours of the maximum watershed length at MFF20 = 2.5 as a function of rainfall intensity and duration for different slopes at mb,so = 1.0 g/m2 and Kp = 10-5 cm/sec: (a) So = 0.01; (b) So = 0.02; (c) So = 0.04; (d) So = 0.06

## 5.4.2 BMP design for Highway Runoff

For treating MFF of highway runoff, the location and number of storm-drain inlets can be adjusted based on the WLdes for a given rainfall and slope condition of the catchment. Figure 5.21 illustrates conceptual design of collection system in the highway runoff BMPs. Inlet 1 and inlet 2 can be located based on the L1 and L2, which are determined

88

Highway

Inlet 1

L1

Inlet 2

L2

Inlet 3

BMP 1

BMP 2

## Catchment Area for BMP 1 Collection Pipe Flow Direction

Inlet BMP

FIGURE 5.21

as WLs to generate a required MFF ratio (e.g. MFF20, max). To determine a WL, the contours previously described can be used. The collection pipes can be designed to ensure rapid delivery of the runoff, minimizing attenuation of combined MFF ratio. For example, when a designer needs to determine WL (i.e. L1 or L2 in Figure 5.21) for site 3, the contours in Figure 5.17 and Figure 5.19 can be used because the bed slope is 0.02. The ellipse in the Figure 5.19(c) shows the region corresponding to the mean values of observed rainfall intensity and duration (I = 3.8 mm/hr, T = 8.2 hr) surrounded by 1 standard deviation that were observed using three years monitoring data at site 3. Although an alternative design rainfall can be chosen inside the ellipse area, the mean values are selected in this design example. The design value of mb,so is set to 1.0 g/m2 assuming 17 days of ADD, which is three years average during wet season in this site. Therefore, Figure 5.17(c) and Figure 5.19(c) can be used for these design conditions.

89

That is, a designer can select a value for WLdes between 8 m and 400 m, which can be read in Figure 5.17(c) and Figure 5.19(c) as the lower and upper boundaries of the WL, respectively.

## 5.4.3 BMP Design for Parking Lots

The concepts of design MFF ratio and watershed length can be also applied for the design of simple-geometric 2-D watersheds such as parking lots, which is known as a non-point pollutant source in urban landuses (Sonstrom et al, 2002). Although the dimension of the parking lots is generally determined by the site conditions, a typical geometry is a simple rectangle. Therefore, rectangular-type watersheds will be discussed in this study. For accurate MFF simulation for complex 2-D geometry, 2-D flow model might be necessary. 2-D flow can be characterized by the flow path and degree of flow convergence. From the case study of radial flow performed in the section 5.3, a dominant impacting factor on the MFF ratio is the watershed length (flow distance) rather than flow converging because little change in the curves of MFF ratio was observed in the radial flow compared to the 1-D flow. Therefore, MFF simulation of 1-D flow can be also applicable in BMPs for parking lots. In a rectangular watershed, flow path is determined by slope and inlet location. Therefore, the design concerning is how to locate inlets and slope in order to make the runoff flow a required distance for design MFF ratio (i.e. WLdes).

90

Inlet

(a) WL =

L L ~ 2 2

(b) WL = L ~ 2 L

(c) WL =

L 5 L ~ 2 2

(d) WL =

L ~L 2

(e) WL =

L 5 L ~ 2 2

(f) WL =

L L ~ 2 2

FIGURE 5.22

## Different inlet location and watershed length in a square type watershed

Degree of slope is one of the important factors that determine WLdes. If the catchment dimension is too small, relatively steeper slope can be used for smaller WLdes in order to meat the criteria for MFF ratio. On the contrary, if the catchment dimension is large, lower slope can be used. Number and location of the inlets can be also adjusted under a fixed degree of slope to satisfy WLdes. Figure 5.22 shows how the flow direction and flow distance can be changed with different inlet locations in a given square type catchment

91

area. Slope directions were assumed to be always toward the location of inlets. The arrows represent the flow direction and WLs (flow distances) were calculated for six different cases from case (a) to (f). Case (a) and (f) are equivalent in terms of WL but have different numbers and locations of inlets. Case (a) is a better design than case (f) for the economic point of view because case (a) has fewer inlets. Similarly, case (c) and (e) are also equivalent watersheds for the same reason. Case (a), (b) and (c) containing only one inlet, have different WLs depending on the inlet location. According to the required MFF ratio, different strategies can be adapted in selecting the number and location of the inlets in a catchment area.

## 5.4.4 Potential Improvement of BMP Performance by Optimal Design

This section discusses the potential improvement of pollutant removal efficiency that can be obtained from different inlet designs for site 3. The design follows the procedure already described in the section 5.4.2. The evaluated pollutant for this discussion is Cu instead of COD because Cu is one of the most frequently observed and has relatively large emission rate among heavy metals in the highway runoff. The mb,so for Cu at ADD = 17 days was calculated as 0.23 g/m2 using the buildup formula provided in Table 5.3. Referring Table 5.2, s and l for Cu were 0.88 sec/m2 and 0.0016 gsec/m4), respectively. Using those design parameters and design rainfall intensity and duration (I = 3.8 mm/hr, T = 8.2 hr), the MFF20 curve for Cu can be obtained by the model simulation as shown in Figure 5.23 (Of course, contours of WL can be used instead if they are available). As shown in the figure, four different values of

92

4
3.2 3 2.7

MFF20

2 2.2 1
WL1=7 m WL3=89m WL2=45m WL4=178m

0 1 10 100

1000

FIGURE 5.23 Cu

## Determination of design watershed length based on a MFF20 curve for

WL were evaluated for WLdes (WL1 = 7 m, WL2 = 45 m, WL3 = 89 m and WL4 = 178 m). WL1 was selected as WLopt and the other WLs were selected based on different numbers of storm-drain inlets to be installed. The removal efficiency of Cu is evaluated for those different design conditions of storm-drain inlets with and without polymer addition. The removal efficiency with polymer addition was estimated based on the results of particle destabilization study described in Chapter 6 and Appendix F. Table 5.7 summarizes the final evaluation results assuming only 20% of total runoff was treated and removal efficiency of dissolved Cu is zero. There was little improvement in Cu removal using only gravity settling by maximizing MFF ratio because the settling efficiency is very low. As the removal efficiency increases, there is greater value in capturing the first flush. For

93

example, the removal efficiency increases from 16.4% to 30.2% by maximizing the first flush using only 24-hour settling. If polymer flocculation used, the absolute particle removal efficiency increases to 37.2%, and maximizing the first flush increases the overall efficiency to 67.6%.The optimum inlet design provides greater benefit with more efficient particle removal processes.

TABLE 5.7

## Performances of BMPs with Different Designs WLdes

Parameter Evaluated Number of Inlets Design MFF20 Removal Efficiencies of Particulate Cu a 24h Gravity Settling 72h Gravity Settling

## WL4 (178 m) 1 2.2 16.4% 16.8% 37.2%

67.6% 54.1% Flocculation with Polymer (12h Settling) a It is assumed that only 20% of total runoff is treated

94

Chapter 6

## 6.1 PARTICLE AGGREGATION OVER TIME

Throughout the course of the experimental program, small changes in runoff samples were noted as storage time increased. By measuring the PSD, Li et al (2005a) was able to quantify the differences and develop a sampling protocol that avoided PSD change during storage. The natural aggregation of particles during sample storage is a problem for quantifying stormwater quality, but can be an advantage for BMP development. Increases in particle size generally improve settling and filtration performance. To understand the magnitude of the changes in TDS and TSS, a series of experiments were performed to monitor changes over time. Figure 6.1 shows the result of one experiment and displays the concentration changes for TSS and TDS in the runoff water with respect to the time. The sample was collected on 2/6/05 and shows results with and

95

without slow mixing. Slow mixing was provided by a magnetic stirring bar operating at 100 rpm and providing a G factor of 9.3/s. TSS concentration increased by about 30% and TDS concentrations decreased by about 10% of initial values during the first 100 hr for both mixed and unmixed samples. No significant changes in the concentration of TSS and TDS were observed after 240 hrs. In the mixed sample, TSS increased rapidly within 50 hrs and plateaued at about 300 mg/L after 100 hrs. The unmixed sample showed similar trends but required longer time to reach steady state. Steady state concentration of TSS in the unmixed sample was a little bit higher than that of mixed sample, although there are too few data points to evaluate significance. This might be because unmixed sample is free from fluid shear or agitation that would cause particle breakup. The decrease of TDS in the mixed and unmixed samples might imply that a portion of dissolved solid transforms to the suspended solid through aggregation. The increase in TSS does not balance the decrease in TDS, and this might be due to the definition of dissolved solids, which are defined as less than 0.45 m, as opposed to being truly dissolved. Figure 6.2 compares the PSD changes over time in the mixed and unmixed samples. The number of smaller particles decreased dramatically over time and larger particles increased in number. The particle change was more rapid in the mixed sample than unmixed sample. In the unmixed sample, there was an increase in particles smaller than 1 m up to 48 hours and then a decrease with most particles disappearing after 264 h. Particles larger than 10 m generally increased. For the mixed sample, changes in PSD occurred much more rapidly. The number of smaller particles at 24 and 48 hours was

96

320 300 280 TSS, TDS (mg/L) 260 240 220 200 180 0 50 100 150 200 250 Time (hr) 300 350 400 TSS-no mixing TSS-mixing TDS-no mixing TDS-mixing

FIGURE 6.1

TSS and TDS changes over time from the observation of natural

aggregation on 2/6/05

nearly the same as the original number and then decreased until 264 hours. The increase in small particles that occurred in the sample without mixing either did not occur with the mixed sample or occurred so rapidly that it was not observed (no observations were made between 0 and 24 hours). This experiment demonstrates that the particles in highway runoff naturally aggregate over time and mixing can increase aggregation rate. However, the time required for the particle aggregation might not be sufficiently short for the practical application. As a result, additional efforts for destabilizing particles are needed.

97

7 7 7 7 7 7 6

## 1.5 10 No mixing (0.5 ~ 30 m) dN/dLogDp (#/mL/m)

No mixing (5 ~ 100 m)
5

1 10

5 10

(a)

7 7 7 7 7 7 6

1.5 10

1.5 10 1 10 5 10

1 10

5 10

## 10 Particle Diameter, D (m)

100

(b)

FIGURE 6.2

PSD changes over time on 2/6/05: (a) Without mixing; (b) With mixing

## 6.2 LOW DOSE FLOCCULATION

The first series of experiments used low dosages of coagulants to avoid pH changes that might occur with the low alkalinity runoff and to avoid the expense of high coagulant dose and resulting sludge production. Figure 6.3 shows the turbidity removals in the low

98

10

15
2

20
4 3

25

30

35

200

100

50

## 4hr mixing 8hr mixing 12hr settling

0 0 5 10 15 20 25
3

30

35

40

## FIGURE 6.3 Ferric chloride

Turbidity changes in the samples in low dose coagulation: (a) Alum; (b)

99

dose coagulation tests for two different storm events using alum and ferric chloride. In these tests, alum or ferric chloride was added in varying amounts up to 40 mg/L, which were did not produce sweep floc. Figure 4.25 shows that in low dosages, neither coagulant is able to produce settable particles but instead forms pin flocs, increasing turbidity. Settable particles were never produced even though extended periods of slow mixing were investigated. This conditioning might have been useful for granular media filtration, but was not investigated.

## 6.3 SWEEP FLOC COAGULATION

Figure 6.4 shows the results of turbidity removal using sweep floc coagulation with alum and ferric chloride respectively. Each storm event had a different optimum dose and the range was from approximately 40 to 500 mg/l. Optimum dose was defined as the minimum coagulant concentration required to produce less than 5 NTU. The optimum does was plotted as a function of specific conductivity in Figure 6.5, showing that the optimum does is proportional to the initial conductivity. This relationship is not due to changing electro chemical properties with conductivity, but from the higher concentrations of dissolved and colloidal material, which consume more coagulants for destabilization. Han, et al., (2004) found that initial turbidity is related to dilution of the stormwater, with more heavily contaminated stormwater having higher initial conductivity. Other parameters such as TSS might be better indicators of coagulant

100

does, but conductivity can be easily measured in real-time, allowing it to be used for control. This result suggests that an automatic controller could use sample conductivity to adjust coagulant dose. Figure 6.6 shows the turbidity and ZP changes as a function of alum and ferric chloride does. For both alum and ferric chloride, the isoelectrical point of ZP could not be obtained, and sweep floc was routinely observed at -20 to -10 mV ZP. Alum was slightly more effective than ferric chloride in terms of turbidity removal and ZP reduction (all experiments performed at pH 7). The higher efficiency of alum over ferric chloride may result from its wider optimum pH range. One test was performed to evaluate the impact of ionic strength on coagulation efficiency. Sodium chloride (NaCl) was added over the range of 10,000 to 50,000 mg/L in a series of jar tests. No significant drop in turbidity was observed in this range of salt concentration. However, at 30,000 mg/l NaCl the required alum or ferric chloride concentration was reduced to approximately 25% of the dose required without salt.

101

(a) Sweep Floc Coagulation with Alum 200 10/16/04 10/26/04 11/7/04 1/28/05 3/18/05

Turbidity (NTU)

150

100

50

## 0 0 100 200 300 Al (SO ) (mg/L)

2 4 3

400

500

(b) Sweep Floc Coagulation with Ferric Chloride 300 250 Turbidity (NTU) 200 150 100 50 00 50 100 150
3

200

250

300

FeCl (mg/L)

## FIGURE 6.4 chloride

Turbidity removal from sweep floc coagulation: (a) Alum; (b) Ferric

102

300 Optimum Dose of Coagulant (mg/L) 250 200 150 100 Alum 50 Ferric Chloride 0 0 200 400 600 800 1000 1200 Initial Conductivity (uS)

FIGURE 6.5

## 350 300 Turbidity (NTU) 250 200 150 100 50 0 0

ZP with Alum ZP with Ferric Chloride Turbidity with Alum Turbidity with Ferric Chloride

50

100

150

200

## Coagulant Dose (mg/L)

FIGURE 6.6

Turbidity and ZP changes after adding same serious of amounts for alum

103

## 6.4 FLOCCULATION WITH CATIONIC POLYMER

Figure 6.7 shows the ZP changes as a function of polymer dose for two different molecular weight polyDADMACs. Both polymers were equally effective in reducing the ZP. Figure 6.8 shows the isoelectric point as a function of initial conductivity, which is similar to the previous results showing optimum alum or ferric chloride dose related to initial conductivity. Figure 6.9 shows the effect of mixing time on the turbidity removal with and without polymer. As can be seen, at least six hours were needed to reduce turbidity to less than 5 NTU after particles were destabilized. An extended mixing period might be required for particle aggregation and sedimentation even though the isoelectric point is reached by adding polymers.

0 -5

HMW LM W

FIGURE 6.7

## ZP changes in the sample after adding two different molecular weight

104

40 Optimum Polymer Dose (mg/L) 35 30 25 20 15 10 5 0 0 100 200 300 400 500 600 Initial Conductivity (uS)

FIGURE 6.8

## 100 No mixing Mixing Mixing with Polymer (HMW)

80 Turbidity (NTU)

60

40

20

0 0 4 8 12 16 Time elapsed(hr) 20 24

## FIGURE 6.9 on 1/28/05

Effect of mixing time on the turbidity removal with and without polymer

105

Figure 6.10 shows the effect of alum addition on the mixing time in the flocculation using the polymer on 1/28/05. Turbidity removals are displayed with slow mixing and after settling for different alum doses from 2.6 to 15.4 mg/L with 8 mg/L polymer dose, which was the optimum dose for this storm event. As more alum was added, shorter mixing time was required to reduce the turbidity in the supernatant. As a result, mixing time required for the flocculation by combining polymer and other coagulants such as alum or ferric chloride can be reduced. Figure 6.11 shows that particle sizes were dramatically increased after coagulation. The vertical axis shows the relative decrease in the number of particles in a given size range, which is shown on the horizontal axis. Relative decrease is calculated relative to the initial particle concentrations. The various lines show a time series from just after rapid mixing to 8 hours and the final line shows the particle concentration after sedimentation. The graph shows that the relative number of smaller particles in the 2-3 m to 20-30 m ranges increases rapidly after dosage and initial mixing. This is direct evidence for particle aggregation. After settling the numbers of particles is much lower in all size ranges. The 12 hr settling line can also be though of as removal efficiency. The low, medium (not shown) and high molecular weight polymers produced similar results.

106

## 70 60 Turbidity (NTU) 50 40 30 20 10 0 2.6 5.1 7.7

2 4 3

10min Slow mix & 40min Set 1hr Slow mix & 20min Set 2hr Slow mix & 20min Set 4hr Slow mix & 20min Set 12hr Set

10.3

12.8

15.4

Al (SO ) (mg/L)

FIGURE 6.10

## on 1/28/05 (polymer concentration was fixed at 8 mg/L)

Relative Decrease in Particle Number (%)
100

-100

-200

-300

-400

Rap. mix 1hr mix 2hr mix 4hr mix 8hr mix 12hr set.

-500 0.5-2 2-3 3-5 5-7 7-10 10-20 20-30 30-5050-100 0.5-2 2-3 3-5 5-7 7-10 10-20 20-30 30-5050-100

107

## 6.5 REMOVAL OF DISSOLVED HEAVY METALS

Figure 6.12 displays the dissolved phase concentrations of seven species of heavy metals in the treated water from sweep floc coagulation with alum, ferric chloride and flocculation with polymer on 3/18/05. Figure 6.12(a) and (b) show that dissolved heavy metals except Ni can be reduced in proportion to the amount of alum or ferric chloride added. The removal efficiencies of dissolved Cr, As, Cd, As, Cu were over 50% at the sweep floc regimes of alum and ferric chloride. Dissolved Zn dramatically declined with the addition of alum or ferric chloride, and the maximum removal efficiency was over 85%. The spike of dissolved Pb at 50 mg/L of ferric chloride (Figure 4.12(b)) was probably due to sample contamination. PolyDADMAC was not effective in removing dissolved heavy metals as revealed in Figure 4.12(c) although dissolved Cr and Pb were selectively removed to some extent. Dissolved Ni could not be removed in both sweep floc coagulation and flocculation with polymer. Figure 6.13 and 6.14 show turbidity, zeta potential, concentration and removal efficiency of dissolved metals in the treated runoff with combined polymer and alum dose at 8 and 16 mg/L. As can be seen, combinations of polymer and alum effectively remove turbidity with short mixing time (~10 min). Dissolved Pb was removed up to 60% with comparatively large amount of polymer (polyDADMAC > 6 mg/L). Dissolved As was removed up to 40% at alum = 16 mg/L. This removal may have been due to precipitation or it could be a result of aggregation of particles less than 0.45 m. Metals adsorbed to particles less than 0.45 mm will be classified as suspended by the analytical methods. In no cases did the combination of polymer and alum achieve remarkable removal high removal of dissolved heavy metals.

108

3.5 dCr, dAs, dCd, dPb (ug/L) 3 2.5 2 1.5 1 0.5 0 0 50 100 150 200 Al (SO ) (mg/L)
2 4 3

600 dNi, dCu, dZn (ug/L) dCr dAs dCd dPb 500 400 300 200 100 0 0 50 100 150 200 Al (SO ) (mg/L)
2 4 3

## dNi dCu dZn

250

250

(a)
6 dCr, dAs, dCd, dPb (ug/L) dNi, Cu, Zn (ug/L) 5 4 3 2 1 0 0 50 100 150 FeCl (mg/L)
3

600 dCr dAs dCd dPb 500 400 300 200 100 200 250 0 0 50 100 150 FeCl (mg/L)
3

## dNi dCu dZn

200

250

(b)
3.5 dCr, dAs, dCd, dPb (ug/L) 3 2.5 2 1.5 1 0.5 0 0 10 20 30 40 DADMAC, HMW (mg/L) 50 dNi, dCu, dZn (ug/L) dCr dAs dCd dPb 800 700 600 500 400 300 200 100 0 0 10 20 30 40 DADMAC, HMW (mg/L) 50 dNi dCu dZn

(c)

FIGURE 6.12 Dissolved metal concentrations in the treated runoff from different coagulation/flocculation tests on 3/18/05: (a) Sweep floc coagulation with alum; (b) Sweep floc coagulation with ferric chloride; (c) Flocculation with polymer

109

## 45 40 35 Turb (NTU) ZP (mv) 30 25 20 15 10 5 0 2 4 6 8 DADMAC, HMW (mg/L) 10 Turb (NTU)

-5 -10 -15 -20 -25 -30 -35 -40 0 2 4 6 8 DADMAC, HMW (mg/L) 10 ZP (mv)

(a)
2 dCr, dAs, dCd, dPb (ug/L) 300 250 200 150 100 50 0 0 2 4 6 8 DADMAC, HMW (mg/L) 10 dNi dCu dZn

0.5

## 2 4 6 8 DADMAC, HMW (mg/L)

10

(b)
100 Removal Efficiency (%) dCr, dAs, dCd, dPb 80 60 40 20 0 -20 -40 0 2 4 6 8 DADMAC, HMW (mg/L) 10 dCr dAs dCd dPb 100 Removal Efficiency (%) dNi, dCu, dZn 80 60 40 20 0 -20 -40 0 2 4 6 8 DADMAC, HMW (mg/L) 10 dNi dCu dZn

(c) FIGURE 6.13 Coagulation results with different polymer doses at alum = 8 mg/L on

4/28/05: (a) Turbidity and zeta potential; (b) Concentrations of dissolved metals; (c) Removal efficiencies of dissolved metals

110

## 2 4 6 8 DADMAC, HMW (mg/L)

10

(a)
2 dCr, dAs, dCd, dPb (ug/L) dCr dAs dCd dPb 300 250 dNi, dCu, dZn (ug/L) 200 150 100 50 0 0 2 4 6 8 DADMAC, HMW (mg/L) 10 dNi dCu dZn

1.5

0.5

## 2 4 6 8 DADMAC, HMW (mg/L)

10

(b)
100 Removal Efficiency (%) dCr, dAs, dCd, dPb 80 60 40 20 0 dCr dAs dCd dPb 100 Removal Efficiency (%) dNi, dCu, dZn 80 60 40 20 0 -20 -40 0 2 4 6 8 DADMAC, HMW (mg/L) 10 dNi dCu dZn

## -20 -40 0 2 4 6 8 DADMAC, HMW (mg/L) 10

(c) FIGURE 6.14 Coagulation results with different polymer doses at alum = 16 mg/L on

4/28/05: (a) Turbidity and zeta potential; (b) Concentrations of dissolved metals; (c) Removal efficiencies of dissolved metals

111

6.6 DISCUSSION
Coagulation can greatly increase particle sizes in stormwater runoff, which will make sedimentation BMPs much more efficient, especially for small particle removal. Li, et al. (2005b) proposed a two-compartment sedimentation tank with a first compartment to hold the initial runoff volume (first flush) for an extended period of time and a second compartment to treat the rest as a continuous flow clarifier. By holding the first flush and treating the remaining volume in a continuous flow clarifier, the two-compartment settling tank removed both small and large particles in stormwater runoff. This concept can be extended using coagulation and flocculation. Based upon the results from particle settling experiments, only 27.1% and 27.5% particle mass reductions were possible for in settling basins with 24 and 72 hr retention times, respectively, using a storage tank designed to capture a 26 mm rainfall. In contrast, 90% of total particle mass was removed by providing 8 hr slow mixing and 4 hr settling with polymer addition. Removal efficiencies of heavy metals were also evaluated utilizing the particle removal efficiency and metal-particle mass ratio reported by Morquecho and Pitt (2003) (refer to Table 2.1). The suspended solids reduction with polymer addition can reduce approximately 85% of particulate Cu and Zn, which correspond to the total removal efficiencies of 35% and 23% for Cu and Zn, respectively (see Appendix F). Jar testing using metal salts was ineffective in removing particles at low concentrations and required high dosages well into the sweep floc regime for efficient

112

particle removal. The need for sweep floc increases costs due to coagulant cost and excess sludge production. In addition, the acidic nature of both metal salts will require neutralization, as well as further increase costs. A cationic polymer was effective in coagulating the stormwater runoff at low dosages and did not modify the pH. Additional mixing was necessary to effect efficient particle aggregation. The addition of small amounts of alum (2 to 15 mg/L) reduced the mixing time as well as dissolved heavy metals and suggests that a regime using polymer, followed by alum, is a good way to destabilize particles and enhance heavy metal removal in highway runoff. BMPs in the field need unattended operation, as well as robustness because pollutant concentration in the highway runoff always changes as a function of rainfall characteristics, antecedent dry days, average daily traffic, and other factors. Therefore, runoff concentration is different for each storm event and BMPs must be able to cope with a range of influent concentrations and flow rates without special controls. A combination of cationic polymer with small amounts of alum and sufficient mixing time should enable effective colloid removal without close monitoring of dosages. Unattended polymer addition (automatic) to the first compartment can be also easily achieved by using the initial conductivity of the runoff and the fixed compartment volume. Unattended polymer addition to the continuous flow compartment needs further investigation due to the dynamic runoff retention time. Further studies on particle change with different mixing periods with polymer addition are on-going in our laboratory.

113

Chapter 7

Conclusion

This dissertation developed a methodology for design and operation of best management practices (BMPs) for paved landuses such as highways and parking lots. To take the economic advantage of treating first flush, the MFF ratio can be maximized by means of adjusting the number and location of the storm-drain inlets, thereby changing the watershed length (i. e. catchment size). The developed 1-D model can be utilized to determine the watershed length to obtain the minimum required MFF ratio. In addition, the coagulation experiments revealed more efficient operating conditions for treating first flush in a settling basin, a common stormwater BMP.

Mass First Flush Modeling Highway runoff was modeled as 1-D flow problem using the kinematic wave equation coupled with mass transport and erosion equation. The model parameters were calibrated using three years monitoring data obtained from a highway site in west Los Angeles.

114

Calibrated parameters were initial mass and erosion equation coefficients developed by introducing two different pollutant source terms. Using the developed model, MFF simulations were performed. Through the first flush modeling study, the following conclusions are made: 1. The results from parameter estimation in 1-D model showed that there was no significant variations among the erosion coefficients for short-term sources for COD, conductivity, Zn and Cu. The initial mass and erosion rates of the longterm sources showed large differences among those constituents. 2. Different types of buildup formulas were fitted with calibrated initial mass and exponential and Michaelis-Menton type curves were useful to predict pollutant mass in a stormwater runoff. 3. The qualitative relationship between MFF and affecting factors such as rainfall intensity, duration, infiltration rate, slope, initial mass, erosion coefficients and watershed length were obtained using the developed 1-D model. 4. Mass first flush simulations showed that extremely short watershed lengths cannot develop sufficient flow energy for pollutant mobilization, and only low MFF can be observed. Extremely long watersheds also cannot achieve high MFF ratios due to long transport time. Therefore, it is necessary to optimize the size of catchment area so that the maximum MFF ratio can be captured by the BMPs. 5. Contours of watershed length constructed by MFF simulations using different conditions of weather and watershed geometry can be used in determining

115

location and number of storm-drain inlets for the BMPs for highway runoff. Those contours are also applicable for the BMP design of simple 2-D structures with converging flow (radial flow) such as parking lots. Converging flow is common in 2-D watersheds and does not significantly change the mass first flush behavior that is observed in 1-D flow. 6. Although the MFF ratio may be maximized, improvement of pollutant removal cannot be guarantied unless effective particle removal is obtained using additional particle destabilization process.

Coagulation/Flocculation This research has shown that highway runoff can be effectively coagulated with a combination of metal salts (alum and ferric chloride) and organic cationic polymers. The following conclusions are made: 1. Alum or ferric chloride alone cannot effectively coagulate highway runoff at low concentrations (< 40 mg/L), suggesting that bridging and charge neutralization are not effective mechanisms for this application. 2. Alum and ferric chloride at high doses produced sweep floc that removed turbidity and suspended solids to low concentrations (< 5 NTU). Unfortunately the sludge production and the need for pH control limit this application. Alum appeared to be slightly more effective that ferric chloride. The dissolved

116

concentrations of As, Cu, Cr, Cd, Pb, and Zn were reduced by as much as 50% during these experiments. Dissolved Ni concentration was unchanged. 3. Small dosages (< 10 mg/L) of an organic polymer in three different molecular weights were useful in obtaining the isoelectric point. Gentle mixing (G ~ 2.6/s) over extended periods (~ 8 hrs) was effective in producing low effluent turbidity. Dissolved Pb concentration was reduced by 50% but other metal concentrations were unchanged. 4. The addition of alum (~8 mg/L) after optimal polymer dosing reduced mixing time by 50%. 5. Optimal dosage of metal salts and polymer was proportional to the initial conductivity of the runoff. 6. The removal of dissolved metals, with the possible exception of Pb, occurred only with high concentrations of metal salts. This suggests that removal occurred because of precipitation of truly dissolved metals, as opposed to removal of small particles (< 0.45 m) that are classified as dissolved due to the working definition of soluble and particulate phases. Further research is necessary to validate this work at larger scale and over a range of conditions to provide a robust and unattended operation.

117

Appendix A

Site Descriptions

Figure A.1 shows the map of three monitoring sites located in west Los Angeles, near UCLA campus. The catchments areas ranged from 3,900 to 16,900 m2. Traffic loadings are over 269,000 vehicles per day in annual average daily traffic (AADT) and the average rainfall is approximately 330 mm. All sites were equipped with 950 Flow Meters (American Sigma, Loveland, Colorado), tipping bucket rain gauges and composite auto samplers. Site details are provided in Table A.1. Model parameters were calculated using the rainfall and flow data from site 3 (7-203), which was chosen as an ideal model domain because the site is geometrically simple and meteorologically homogeneous. Site 3 is 21.6-m-wide and 178-m-long rectangular-shape chachment. The average slope is 0.02 with little local variation and there exits only one storm-drain inlet located on the freeway shoulder at the south-most end of the site. The coagulation experiment was focused on site 2. Site 2 is the largest among the monitoring sites, producing enough runoff volume for the experiment in the first one hour of the storm.

118

101
Ventur a Blvd

405

## Getty Center Brentwood

et Suns
1

Beverly Hills
Site 2 (7-202) UCLA Westwood

Blvd

## Santa Monica Bay

a re ic hi ils on W M ta 10 an S

vd Bl

vd Bl

## FIGURE A.1 Location of monitoring sites for highway runoff

TABLE A.1 Summary Description of Sampling Sites Site No. Location Freeway / Post Miles HWY 101 PM 17 FW 405 PM 34 Area (h) 1.28 1.69 0.39 AADT (vehicle/day) 328,000 269,000 322,000 Imperviousness (%) 100 95 100

1 (7-201) Eastbound US 101 2 (7-202) 3 (7-203) I-405 Freeway and Sepulveda Blvd

119

Appendix B

## Numerical Tests for Radial Flow Problem

A.1 CAM: WL = 50 m, ro = 1 m

FIGURE A.1 Numerical solutions for the outflow depth using different values of t with x = 0.5 m

120

(a)

(b) FIGURE A.2 Numerical solutions for the outflow using different values of x with t = 1/16 min: (a) depth; (b) flow rate

121

FIGURE A.3 Numerical solutions for the water depth profile along the distance using different values of x with t = 1/16 at t = 70 min

122

FIGURE A.4 Numerical solutions for the outflow depth using different values of t with x = 0.05 m

123

A.2 CAM: WL = 50 m, ro = 5 m

FIGURE A.5 Numerical solutions for the outflow depth using different values of t with x = 0.5 m

124

(a)

(b) FIGURE A.6 Numerical solutions for the outflow using different values of x with t = 1/16 min: (a) depth; (b) flow rate

125

## A.3 CAM: WL = 100 m, ro = 1 m

(a)

(b) FIGURE A.7 Numerical solutions for the outflow using different values of x with t = 1/16 min: (a) depth; (b) flow rate

126

## A.4 CAM: WL = 100 m, ro = 5 m

FIGURE A.8 Numerical solutions for the outflow depth using different values of t with x = 0.1 m

127

(a)

(b) FIGURE A.9 Numerical solutions for the outflow using different values of x with t = 1/16 min: (a) depth; (b) flow rate

128

A.5 C-N: WL = 50 m, ro = 1 m

FIGURE A.10

Numerical solutions for the mass in the water along the distance using

FIGURE A.11

129

Appendix C

## Measured and Simulated Polluto-graphs

2000
2/19/01
Rainfall Intensity Measured Flow Calculated Fl ow Measured COD Calculated COD Measured Cond. Calculated Cond.

1200

Total Cu (ug/L)

COD (mg/L)

1200 800

## 0 0 100 200 300 400 500 Time (min)

1600
2/19/01
Rainfall Intensity Measured Flow Calculated Flow Measured COD Calculated COD Measured Cond. Calculated Cond.

800

1200

600

Total Zn (ug/L)

800

400

400

200

100

200

300

400

500

Time (min)

## FIGURE C.1 Storm event on 2/19/01

130

800
2/24/01
Ra infall Intensity Measur ed Flow Ca lculated Flow Measur ed COD Ca lculated COD Measur ed Cond. Ca lculated Cond.

800

400

400

200

200

## 0 0 200 400 600 800 1000 Time (min)

800
2/24/01
Rainfall Intensity Measured Flow Calculated Flow Measured COD Calculated COD Measured Cond. Calculated Cond.

300

400

200

1000

## FIGURE C.2 Storm event on 2/24/01

131

Conductivity (mmho/Cm)

600

600

COD (mg/L)

3000
11/24/01
Rainfall Intensity Measur ed Flow Calculated Flow Measur ed COD Calculated COD Measur ed Cond. Calculated Cond.

1600

800

1000 400

## 0 0 100 200 Time (min) 3000 300 400

800

11/24/01
Rainfall Intensity Measured Flow Calculated Flow Measured COD Calculated COD Measured Cond. Calculated Cond.

400

1000 200

## FIGURE C.3 Storm event on 11/24/01

132

Conductivity (mmho/Cm)

1200

600
12/20/01
Rainfall Intensity Measured Flow Calculated Flow Measured COD Calculated COD Measured Cond. Calculated Cond.

400

200

200 100

## 0 0 40 80 Time (min) 800

12/20/01
Ra infall Intensity Measured Flow Ca lculated Flow Measured COD Ca lculated COD Measured Cond. Ca lculated Cond.

0 120 160

160

400

80

200

40

## FIGURE C.4 Storm event on 12/20/01

133

Conductivity (mmho/Cm)

300

4000
2/17/02
Rainfall Intensity Measured Flow Calculated Flow Measured COD Calculated COD Measured Cond. Calculated Cond.

2000

Total Cu (ug/L)

3000

COD (mg/L)

1000 400

## 0 0 40 80 120 160 200 Time (min)

3000
2/17/02
Rainfall Intensity Measured Flow Calculated Flow Measured COD Calculated COD Measured Cond. Calculated Cond.

800

600

400

1000 200

## FIGURE C.5 Storm event on 2/17/02

134

3000
3/17/02
Rainfall Intensity Measured Flow Calcula ted Flow Measured CO D Calcula ted COD Measured Cond. Calcula ted Cond.

1200

## 2000 COD (mg/L)

800

1000

400

0 0 40 80 Time (min)
2000
3/17/02
Rainfall Intensity Measured Flow Calculated Flow Measured COD Calculated COD Measured Cond. Calculated Cond.

0 120 160

400

1600

Total Zn (ug/L)

100 400

## FIGURE C.6 Storm event on 3/17/02

135

Conductivity (mmho/Cm)

800
12/19/02
Rainfall Intensity Measured Flow Calculated Flow Measured COD Calculated CO D Measured Cond. Calculated Cond.

600

400

400

200 200

## 0 0 100 200 300 400 500 Time (min)

600
12/19/02
Rainfall Intensity Measured Flow Calculated Flow Measured COD Calculated COD Measured Cond. Calculated Cond.

160

80

200 40

## FIGURE C.7 Storm event on 12/19/02

136

Conductivity (mmho/Cm)

600

COD (mg/L)

2000

2000

2/11/03

1600

COD (mg/L)

1200

1200

800

800

400

400

## 0 0 200 400 600 800 1000 Time (min)

3000
2/11/03
Rainfall Intensity Measured Flow Calculated Flow Measured COD Calculated COD Measured Cond. Calculated Cond.

600

1000

## FIGURE C.8 Storm event on 2/11/03

137

Conductivity (mmho/Cm)

Rainfall Intensity Measured Flow Calculated Flow Measured COD Calculated COD Measured Cond. Calculated Cond.

1600

800
3/15/03
Rainfall Intensity Measur ed Flow Calculated Flow Measur ed COD Calculated COD Measur ed Cond. Calculated Cond.

500

400
Conductivity (mmho/Cm)

600

COD (mg/L)

200 100

138

Appendix D

## Regressions for Buildup

0.9 0.8 0.7 0.6 mo (102xmmho) b,s 0.5 0.4 0.3 0.2 0.1 0 Linear Power Exponential Michelis-Menton

10

15 Time(days)

20

25

30

## FIGURE D.1 Regression for conductivity buildup

139

1.8 1.6 1.4 1.2 mo (g/m2) b,s 1 0.8 0.6 0.4 0.2 0 Linear Power Exponential Michelis-Menton

10

15 Time(days)

20

25

30

## FIGURE D.2 Regression for Zn buildup

0.4 0.35 0.3 0.25 mo (g/m2) b,s 0.2 0.15 0.1 0.05 0 Linear Power Exponential Michelis-Menton

10

15 Time(days)

20

25

30

140

Appendix E

## Program Codes (MATLAB)

Data matrices in the Input mat file input: flow, rainfall and corresponding time vectors conc: times and concentrations of constituents in the grab samples metal: concentrations of heavy metals in the grab samples

%=====================================================% % PARAMETER OPTIMIZATION FOR 1-D FREEWAY RUNOFF MODEL % %=====================================================% close all; clear all; tic, % Input Data (Rainfall, Pollutant Conc.) load 021901s3.mat % data for Feb.19,2001 in site3 rain=input(:,2); % rainfall data [cm/min] flow_m=1/60*input(:,3); % measured flow [m3/min]->[m3/sec] tc=conc(:,1); % time for grab samle [min] [tnn,ff]=size(tc); tc_m=tc(2:tnn-1); c_m=conc(2:tnn-1,7); % measured conc of a pollutant % Watershed Dimension (Site3, L=244m, W=16m) [nt,ff]=size(rain); xmax=178; tmax=nt-1; dx=2; dt=1/8; % Grid Size, Time Step mc=0.011 ; % manning's coeff nx=int32(xmax/dx+1); % Grid number sx=0.02; % Slope in the flow direction % Initializing matrices h=zeros(nx,nt); h1=zeros(nx,2); di=zeros(nx,2); hi=h; v1=h; hi_=h1; hout=zeros(tmax,1); v=h; q=h; vi=v;

141

## % Minimum infiltration [m/min] % Infiltration rate with water depth [m]

% SUBPROGRAM 1 : Solution for Kinematic Wave Equation % Method of Characteristics tv=[0:tmax]; n=2; t=0; while n<nt % Time vector % index of time vector % Real time in min

t=t+dt; % real time xx=1; % index for x grid x_cum=0; % distance from x=0 while x_cum < xmax xx=xx+1; p=interp1(tv,rain,t,'linear'); if t==dt; h1(xx,2)=max(0,p*dt/100-(is*h1(xx-1,1)+imin)*dt); di(xx,2)=dx*(xx-1); else if xx==2; h1(xx,2)=max(0,p*dt/100-(is*h1(xx-1,1)+imin)*dt); di(xx,2)=dx; else c=alpha*m*h1(xx-1)^(m-1); if c==0; h1(xx,2)=max(0,p*dt/100-(is*h1(xx-1,1)+imin)*dt); di(xx,2)=di(xx,1); else h1(xx,2)=max(0,h1(xx-1,1)+p*dt/100- ... (is*h1(xx-1,1)+imin)*dt); di(xx,2)=di(xx-1,1)+c*dt*60; end end end x_cum=di(xx,2); end % generation of velocity field based on the homogeneous node set dis=di(1:xx,2); hig=h1(1:xx,2); xxi=[0:dx:xmax]; hi_=(interp1(dis,hig,xxi,'linear'))'; %rainfall vector v1=alpha*hi_.^(m-1); % saving solution at required time if fix(t)==t n=fix(t)+1; % vector index hi(:,n)=hi_; vi(:,n)=v1; end

142

h1(:,1)=h1(:,2); di(:,1)=di(:,2); end for n=2:nt hout(n)=hi(nx,n); vout(n)=alpha*hout(n)^(m-1); qout(n)=vout(n)*hout(n); end % Generating velocity and water depth vectors for water quality calc. nxx=nx-1; % number of cells hi2=zeros(nxx,nt); vi2=zeros(nxx,nt); for n=1:nt for i=1:nxx hi2(i,n)=(hi(i,n)+hi(i+1,n))/2; vi2(i,n)=alpha*hi2(i,n)^(m-1); end end

% SUBPROGRAM 2 : Estimation of Parameters for Water Quality % Transport Equation is calculated by C-N method % Optimization tool box ("laqcurvefit") ko=[0.7 0.002 0.5]; % initial guess lb=[0.6 0.001 0.3]; % lower boundary ub=[1.2 0.005 1]; % upper boundary options=optimset('MaxFunEvals',100); [k,resnorm]=lsqcurvefit(@washoff4,ko,tc_m,c_m,lb,ub,options,... vi2,hi2,rain,nt,nxx,xmax,dt,dx,... tmax,tv,alpha,m,sx,qout)

% CALCULATION OF TRANSPORT WITH OPT. PARAMETERS k1=k(1); kp=k(2); k2=2; unit_mass0=k(3); %mass/length [g/m] m2=zeros(nxx,nt); % remaining mass in watershed [g/m] m1=m2; % mass in the solution [g/m] m2(:,1)=unit_mass0*ones(nxx,1); % [g/m] m2_2=unit_mass0*ones(nxx,2); m1_2=zeros(nxx,2); tmass_re=zeros(nt,1); tmass_re(1,1)=unit_mass0*xmax; m_emission=zeros(nt,1); h2=zeros(nxx,1); v2=h2; % adjusted for cell base calculation % Initialize tri-diagonal matrix B=zeros(nxx,nxx); e=zeros(nxx,1); Dt=dt*60; % [sec] n=1; % time vector index (@t=0) t=0; % real time while t<=tmax-dt %for n=1:nt-1 tt=fix(t); for i=1:nxx p=interp1(tv,rain,t,'linear'); % Precipitation [cm/min) if i==1

143

h2(i)=hi2(i,tt+1)-(t-tt)* ... (hi2(i,tt+1)-hi2(i,tt+2)); %interpolation h2(i+1)=hi2(i+1,tt+1)-(t-tt)* ... (hi2(i+1,tt+1)-hi2(i+1,tt+2)); v2(i)=alpha*h2(i)^(m-1); v2(i+1)=alpha*h2(i+1)^(m-1); r=k1*v2(i)^k2; % [sec-1] rc=kp*v2(i)^k2; h_p=(h2(i+1)+h2(i))/2; h_n=(h2(i)+0)/2; us_p=sqrt(9.8*h_p*sx); % [m/sec] us_n=sqrt(9.8*h_n*sx); D_p=6.0*h_p*us_p; % [m2/sec] D_n=6.0*h_n*us_n; m2_2(i,2)=m2_2(i,1)-r*m2_2(i,1)*Dt; B(i,i)=1+D_p*Dt/(2*dx^2)+D_n*Dt/(2*dx^2); B(i,i+1)=-D_p*Dt/(2*dx^2)+v2(i+1)*Dt/(4*dx); e(i,1)=(1-D_p*Dt/(2*dx^2)-D_n*Dt/(2*dx^2))*m1_2(i,1) ... +(D_p*Dt/(2*dx^2)-v2(i+1)*Dt/(4*dx))*m1_2(i+1,1) ... +r*m2_2(i,1)*Dt+rc*Dt; elseif i==nxx h2(i)=hi2(i,tt+1)-(t-tt)* ... (hi2(i,tt+1)-hi2(i,tt+2)); h2(i-1)=hi2(i-1,tt+1)-(t-tt)* ... (hi2(i-1,tt+1)-hi2(i-1,tt+2)); v2(i)=alpha*h2(i)^(m-1); v2(i-1)=alpha*h2(i-1)^(m-1); r=k1*v2(i)^k2; % [sec-1] rc=kp*v2(i)^k2; h_p=(h2(i)+h2(i))/2; h_n=(h2(i)+h2(i-1))/2; us_p=sqrt(9.8*h_p*sx); us_n=sqrt(9.8*h_n*sx); D_p=6.0*h_p*us_p; % [m2/sec] D_n=6.0*h_n*us_n; m2_2(i,2)=m2_2(i,1)-r*m2_2(i,1)*Dt; B(i,i-1)=-D_n*Dt/(2*dx^2)-v2(i-1)*Dt/(4*dx); B(i,i)=1+D_n*Dt/(2*dx^2)+v2(i)*Dt/(4*dx); e(i,1)=(D_n*Dt/(2*dx^2)+v2(i-1)*Dt/(4*dx))*m1_2(i-1,1) ... +(1-D_n*Dt/(2*dx^2)-v2(i)*Dt/(4*dx))*m1_2(i,1) ... +r*m2_2(i,1)*Dt+rc*Dt; else h2(i)=hi2(i,tt+1)-(t-tt)* ... (hi2(i,tt+1)-hi2(i,tt+2)); h2(i-1)=hi2(i-1,tt+1)-(t-tt)* ... (hi2(i-1,tt+1)-hi2(i-1,tt+2)); h2(i+1)=hi2(i+1,tt+1)-(t-tt)* ... (hi2(i+1,tt+1)-hi2(i+1,tt+2)); v2(i)=alpha*h2(i)^(m-1); v2(i-1)=alpha*h2(i-1)^(m-1); v2(i+1)=alpha*h2(i+1)^(m-1); r=k1*v2(i)^k2; % [sec-1] rc=kp*v2(i)^k2; h_p=(h2(i+1)+h2(i))/2;

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h_n=(h2(i)+h2(i-1))/2; us_p=sqrt(9.8*h_p*sx); us_n=sqrt(9.8*h_n*sx); D_p=6.0*h_p*us_p; % [m2/sec] D_n=6.0*h_n*us_n; m2_2(i,2)=m2_2(i,1)-r*m2_2(i,1)*Dt; B(i,i-1)=-D_n*Dt/(2*dx^2)-v2(i-1)*Dt/(4*dx); B(i,i)=1+D_p*Dt/(2*dx^2)+D_n*Dt/(2*dx^2); B(i,i+1)=-D_p*Dt/(2*dx^2)+v2(i+1)*Dt/(4*dx); e(i,1)=(D_n*Dt/(2*dx^2)+v2(i-1)*Dt/(4*dx))*m1_2(i-1,1) ... +(1-D_p*Dt/(2*dx^2)-D_n*Dt/(2*dx^2))*m1_2(i,1) ... +(D_p*Dt/(2*dx^2)-v2(i+1)*Dt/(4*dx))*m1_2(i+1,1) ... +r*m2_2(i,1)*Dt+rc*Dt; end end m1_2(:,2)=inv(B)*e; t=t+dt; if fix(t)==t n=n+1; % vector index m1(:,n)=m1_2(:,2); m2(:,n)=m2_2(:,2); m_emission(n)=m1_2(nxx,2)*vi2(nxx,n); end m1_2(:,1)=m1_2(:,2); m2_2(:,1)=m2_2(:,2); end % Concentration of constituent for i=1:n if qout(i)<=1e-7 % minimun flow rate for constituent transport cout(i)=0; else cout(i)=m_emission(i)/qout(i); end end % RUNOFF COEFFICIENT Total_rainfall=sum(rain)/100*xmax %[m2] Total_runoff=sum(qout)*60 Runoff_coeff=Total_runoff/Total_rainfall % MASS BALANCE (only holds for kp=0) Inital_mass=tmass_re(1,1) % [g] Mass_remaining=sum(m1(:,nt)+m2(:,nt))*dx Mass_washoff=sum(m1(nxx,:).*vi2(nxx,:))*60 Calculated_mass=Mass_remaining+Mass_washoff % PLOTS % calc for measured data time_c=conc(:,1); conc_m=conc(:,7); time_f=input(:,1); flow_m=1/60*input(:,3); c_m1=interp1(time_c,conc_m,time_f,'linear'); mass_m=c_m1.*flow_m;

145

tc=conc(:,1); [tnn,ff]=size(tc); time=[0:tmax]; figure(1) subplot(411),plot(time,rain),ylabel('p[cm/min]') subplot(412),plot(time,flow_m,time,qout*21.9,'--'),ylabel('Q[m3/sec]') subplot(413),... plot(tc(2:tnn-1),conc_m(2:tnn-1),'o',time,cout,'--') ... ,ylabel('Conc[ug/L)') subplot(414),plot(time,mass_m,time,m_emission*16,'--') ... ,ylabel('Mass[mg/sec]') xlabel('time[min]') legend('measured','simulated') % First Flush Plot % calculated tf=sum(qout); tf_m=sum(flow_m); tm=sum(m_emission); % measured cod_m=metal(:,3); cod_m_i=interp1(time_c,cod_m,time_f,'linear'); cod_mass_m=cod_m_i.*flow_m; tf_m=sum(flow_m); tm_cod_m=sum(cod_mass_m); ncf=zeros(tmax+1,1); ncm=ncf; ncf_m=ncf; ncm_cod=ncf; for i=2:tmax+1 ncf(i)=ncf(i-1)+qout(i,1)/tf; ncf_m(i)=ncf_m(i-1)+flow_m(i,1)/tf_m; ncm(i)=ncm(i-1)+m_emission(i,1)/tm; ncm_cod(i)=ncm_cod(i-1)+cod_mass_m(i,1)/tm_cod_m; end t=linspace(0,1,m); figure(2) plot(ncf_m,ncm_cu,ncf,ncm,'--'), grid,legend('Cu','Simulated') axis([0 1 0 1]), axis('square') figure(3) plot(tc(2:tnn-1),conc_m(2:tnn-1),'o',time,cout,'-'),ylabel('Conc(mg/L)') toc

146

% SOLUTION FOR TRANSPORT EQUATION % Crank-Nicolson Method function F=washoff4(k,tcm,vi2,hi2,rain,nt,nxx,xmax,dt,dx,... tmax,tv,alpha,m,sx,qout) k1=k(1); kp=k(2); k2=2; unit_mass0=k(3); %mass/length [g/m] m2=zeros(nxx,nt); % remaining mass in watershed [g/m] m1=m2; % mass in the water [g/m] m2(:,1)=unit_mass0*ones(nxx,1); % [g/m] m2_2=unit_mass0*ones(nxx,2); m1_2=zeros(nxx,2); tmass_re=zeros(nt,1); tmass_re(1,1)=unit_mass0*xmax; m_emission=zeros(nt,1); h2=zeros(nxx,1); v2=h2; % adjusted for cell base calculation % Initialize tri-diagonal matrix B=zeros(nxx,nxx); e=zeros(nxx,1); Dt=dt*60; % [sec] n=1; % time vector index (@t=0) t=0; % real time while t<=tmax-dt tt=fix(t); for i=1:nxx p=interp1(tv,rain,t,'linear'); % Precipitation [cm/min) if i==1 h2(i)=hi2(i,tt+1)-(t-tt)*(hi2(i,tt+1)-hi2(i,tt+2)); h2(i+1)=hi2(i+1,tt+1)-(t-tt)*(hi2(i+1,tt+1)-hi2(i+1,tt+2)); v2(i)=alpha*h2(i)^(m-1); v2(i+1)=alpha*h2(i+1)^(m-1); r=k1*v2(i)^k2; % [sec-1] rc=kp*v2(i)^k2; h_p=(h2(i+1)+h2(i))/2; h_n=(h2(i)+0)/2; us_p=sqrt(9.8*h_p*sx); % [m/sec] us_n=sqrt(9.8*h_n*sx); D_p=6.0*h_p*us_p; % [m2/sec] D_n=6.0*h_n*us_n; m2_2(i,2)=m2_2(i,1)-r*m2_2(i,1)*Dt; B(i,i)=1+D_p*Dt/(2*dx^2)+D_n*Dt/(2*dx^2); B(i,i+1)=-D_p*Dt/(2*dx^2)+v2(i+1)*Dt/(4*dx); e(i,1)=(1-D_p*Dt/(2*dx^2)-D_n*Dt/(2*dx^2))*m1_2(i,1) ... +(D_p*Dt/(2*dx^2)-v2(i+1)*Dt/(4*dx))*m1_2(i+1,1) ... +r*m2_2(i,1)*Dt+rc*Dt; elseif i==nxx h2(i)=hi2(i,tt+1)-(t-tt)*(hi2(i,tt+1)-hi2(i,tt+2)); h2(i-1)=hi2(i-1,tt+1)-(t-tt)*(hi2(i-1,tt+1)-hi2(i-1,tt+2)); v2(i)=alpha*h2(i)^(m-1); v2(i-1)=alpha*h2(i-1)^(m-1); r=k1*v2(i)^k2; % [sec-1] rc=kp*v2(i)^k2; h_p=(h2(i)+h2(i))/2;

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h_n=(h2(i)+h2(i-1))/2; us_p=sqrt(9.8*h_p*sx); us_n=sqrt(9.8*h_n*sx); D_p=6.0*h_p*us_p; % [m2/sec] D_n=6.0*h_n*us_n; m2_2(i,2)=m2_2(i,1)-r*m2_2(i,1)*Dt; B(i,i-1)=-D_n*Dt/(2*dx^2)-v2(i-1)*Dt/(4*dx); B(i,i)=1+D_n*Dt/(2*dx^2)+v2(i)*Dt/(4*dx); e(i,1)=(D_n*Dt/(2*dx^2)+v2(i-1)*Dt/(4*dx))*m1_2(i-1,1) ... +(1-D_n*Dt/(2*dx^2)-v2(i)*Dt/(4*dx))*m1_2(i,1) ... +r*m2_2(i,1)*Dt+rc*Dt; else h2(i)=hi2(i,tt+1)-(t-tt)*(hi2(i,tt+1)-hi2(i,tt+2)); h2(i-1)=hi2(i-1,tt+1)-(t-tt)*(hi2(i-1,tt+1)-hi2(i-1,tt+2)); h2(i+1)=hi2(i+1,tt+1)-(t-tt)*(hi2(i+1,tt+1)-hi2(i+1,tt+2)); v2(i)=alpha*h2(i)^(m-1); v2(i-1)=alpha*h2(i-1)^(m-1); v2(i+1)=alpha*h2(i+1)^(m-1); r=k1*v2(i)^k2; % [sec-1] rc=kp*v2(i)^k2; h_p=(h2(i+1)+h2(i))/2; h_n=(h2(i)+h2(i-1))/2; us_p=sqrt(9.8*h_p*sx); us_n=sqrt(9.8*h_n*sx); D_p=6.0*h_p*us_p; % [m2/sec] D_n=6.0*h_n*us_n; m2_2(i,2)=m2_2(i,1)-r*m2_2(i,1)*Dt; B(i,i-1)=-D_n*Dt/(2*dx^2)-v2(i-1)*Dt/(4*dx); B(i,i)=1+D_p*Dt/(2*dx^2)+D_n*Dt/(2*dx^2); B(i,i+1)=-D_p*Dt/(2*dx^2)+v2(i+1)*Dt/(4*dx); e(i,1)=(D_n*Dt/(2*dx^2)+v2(i-1)*Dt/(4*dx))*m1_2(i-1,1) ... +(1-D_p*Dt/(2*dx^2)-D_n*Dt/(2*dx^2))*m1_2(i,1) ... +(D_p*Dt/(2*dx^2)-v2(i+1)*Dt/(4*dx))*m1_2(i+1,1) ... +r*m2_2(i,1)*Dt+rc*Dt; end end m1_2(:,2)=inv(B)*e; t=t+dt; if fix(t)==t n=n+1; % vector index m1(:,n)=m1_2(:,2); m2(:,n)=m2_2(:,2); m_emission(n)=m1_2(nxx,2)*vi2(nxx,n); end m1_2(:,1)=m1_2(:,2); m2_2(:,1)=m2_2(:,2); end % Concentration of constituent for i=1:n if qout(i)<=1e-7 % minimun flow rate for constituent transport cout(i)=0; else cout(i)=m_emission(i)/qout(i);

148

## end end % Arbitrary function of pde solution time=[0:tmax]; F = interp1(time,cout,tcm,'linear');

%============================== % Radial Flow Simulation % %============================== % Diffusive wave theory % Characteristics averaging method close all; clear all; % Input Rainfall, [cm/min] rain=[(0.005)*ones(180,1); zeros(41,1)]; % Model domain [nt,ff]=size(rain); xmax=10; tmax=nt-1; dx=0.1; dt=1/16; mc=0.014 ; % manning's coeff nx=int32(xmax/dx+1); % grid number sx=0.02; r0=1; %[m] outlet radius % Initializing vectors h=zeros(nx,nt); h1=zeros(nx,2); hi=h; hout=zeros(nt,1); c=zeros(nx,1); v=h; q=h; vout=hout; qout=hout; alpha=(sx^0.5)/mc; m=5/3; % Infiltration parameters imin=1e-5 % [cm/sec] is=1e-6; % [cm] % Initialize tri-diagonal matrix A=zeros(nx-1,nx-1); d=zeros(nx-1,1); Dt=dt*60; tv=[0:tmax]; n=1;t=0; while t<=tmax p=interp1(tv,rain,t,'linear'); for i=2:nx c(i)=alpha*m*h1(i)^(m-1); V=(c(i)+c(i-1))/2; h_=(h1(i-1,1)+h1(i,1))/2; D=(3/5)*V*h_/(2*sx); % [m2/sec] if i==2 A(i-1,i-1)=1/(2*Dt)+V/(2*dx)+D/(dx^2); A(i-1,i)=-D/(2*dx^2); d(i-1,1)=(1/(2*Dt)-V/(2*dx)+D/(2*dx^2))*h1(i,1)... +max(0,p/6000-(is*h1(i,1)+imin)/100) ...

149

+alpha*h1(i,1)^m/(xmax+r0-(i-3/2)*dx); elseif i==nx A(i-1,i-2)=-D/(dx^2)+1/(2*Dt)-V/(2*dx); A(i-1,i-1)=1/(2*Dt)+V/(2*dx)+D/(dx^2); d(i-1,1)=(1/(2*Dt)-V/(2*dx)+D/(2*dx^2))*h1(i,1)... +(1/(2*Dt)+V/(2*dx)-D/(dx^2))*h1(i-1,1)... +(D/(2*dx^2))*h1(i-2,1)... +max(0,p/6000-(is*h1(i,1)+imin)/100) ... +alpha*h1(i,1)^m/(xmax+r0-(i-3/2)*dx); else A(i-1,i)=-D/(2*dx^2); A(i-1,i-1)=1/(2*Dt)+V/(2*dx)+D/(dx^2); A(i-1,i-2)=1/(2*Dt)-V/(2*dx)-D/(2*dx^2); d(i-1,1)=(1/(2*Dt)-V/(2*dx)+D/(2*dx^2))*h1(i,1)... +(1/(2*Dt)+V/(2*dx)-D/(dx^2))*h1(i-1,1)... +(D/(2*dx^2))*h1(i-2,1)... +max(0,p/6000-(is*h1(i,1)+imin)/100) ... +alpha*h1(i,1)^m/(xmax+r0-(i-3/2)*dx); end end h1(2:nx,2)=inv(A)*d; if fix(t)==t n=fix(t)+1; h(:,n)=h1(:,2); v(:,n)=alpha*h(:,n).^(m-1); end h1(:,1)=h1(:,2); t=t+dt; end for n=2:nt hout(n)=h(nx,n); % [m] vout(n)=alpha*hout(n)^(m-1); % [m/sec] qout(n)=vout(n)*hout(n)*r0*pi; % [m3/sec] end % Runoff coeff. Area=pi*((xmax+r0)^2-r0^2)/2; Total_rainfall=sum(rain)/100*Area %[m3] Total_runoff=sum(qout)*60 Runoff_coeff=Total_runoff/Total_rainfall

150

Appendix F

## Calculation of Metal Removal Efficiency

Particulate metal removal efficiency by 26mm design storm holding tank (for Site 2, 1.69ha, tank volume 438m3 and surface area 146m2)

## Total metal removal Pb Zn Cu Fe

28.96% 37.16% 26.27% 27.76% 8.11% 15.24% 25.48% 30.00% 38.20% 26.57% 28.36% 8.40% 15.66% 25.78% 83.81% 84.54% 90.38% 79.32% 23.47% 34.66% 87.67%

Calculaton of metal removal efficiency using polymer Particles size range 0.45-2 2-10 10-45 45-106 106-250 >250 total Particles size range 0.45-2 2-10 10-45 45-106 106-250 >250 total Measured Metal/Particl, ug/g (Morquecho) ini_vol vol after 12h Rem. Eff. Cu Fe Pb Zn 2.31E+08 3.20E+07 86.19% 2894 29267 199 13540 4.45E+08 9.12E+07 79.51% 4668 18508 868 13641 6.21E+08 2.54E+07 95.91% 735 26221 229 1559 2.15E+08 1.55E+06 99.28% 1312 14615 226 2076 0.00E+00 0.00E+00 0.00% 2137 21730 375 3486 0.00E+00 0.00E+00 0.00% 50 28604 117 266 1.51E+09 1.50E+08 90.07% Initial 12 set Pb Zn Cu Fe Pb Zn 6.8E+12 4.6E+10 3E+12 9E+10 9E+11 6.4E+09 4E+11 8.2E+12 3.9E+11 6E+12 4E+11 2E+12 7.9E+10 1E+12 1.6E+13 1.4E+11 1E+12 2E+10 7E+11 5.8E+09 4E+10 3.1E+12 4.9E+10 4E+11 2E+09 2E+10 3.5E+08 3E+09 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.4E+13 6.2E+11 1E+13 5E+11 3E+12 9.2E+10 2E+12

## Cu Fe 6.7E+11 2.08E+12 4.56E+11 2.82E+11 0 0 3.49E+12

151

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