# Dry Weather Channel Impacts on Wet Weather Combined Sewer Overflow Pollution Rates

## Abstract

Settling solids upstream of a combined sewer overflow (CSO) have led to an undesirable odour issue in warm temperatures and elevated environmental pollutant loading during the first flush period of wet weather events. Several strategies exist to ameliorate the solids discharged during the first flush period of an overflow event, with one strategy being the use of a dry weather channel (DWC). A DWC is a collection system design feature that can be used to limit and reduce solids deposition within the collection system, by maintaining higher forward flow velocities during low flow while reducing the settleable surface area within the collection system for solids accumulation. This paper describes how we employed a first order solids transport model from Willems (2009) to represent the settling and washoff rates within the collection system in conjunction with the P8 urban catchment model from Walker (1990) to model the influent mass rate from overland flow. The model was subsequently refined to incorporate the concept of uniform settling on the wetted surfaces within the collection system. When comparing the existing system to the proposed system, modeling results at the CSO outflow point suggest that a DWC could reduce the solids discharged from the CSO by approximately 25% annually.

## 1 Overview

Aging combined sewer systems with assigned outflow structures can be large contributors to environmental pollutant loading during wet weather events. Typically, the most environmentally disruptive part of a combined sewer overflow is the first flush phase, where settled solids from normal dry weather sedimentation are sheared off the walls of the conduits and land surfaces due to elevated flow turbulence and higher velocities. In the context of this work, the term *first flush* is used to specifically describe the fate and transport of the solids within the collection system during the initial rainfall; it does not describe the solids transport overland which could be entering the collection system. From a hydrologic standpoint, it is debatable whether first flush exists or not (Hager 2001).

Within the collection system, larger diameter conduits tend to suffer more from sedimentation due to non-fully developed flow regimes, low forward flow velocities (i.e. ≤2.0 ft/sec, 0.6 m/s; Sonnen 1977; Ten State Standards 2004), shallow depths, and increased wet perimeter lengths. Several methodologies exist to reduce the impacts of combined sewer overflows (CSOs) and sanitary sewer overflows (SSOs) during wet weather events, such as: storm water separation; surface and subsurface storage facilities; and employing real-time controls to direct and regulate system flows. More creative approaches exist which focus on water quality improvement and dry weather flow sedimentation reduction, in turn leading to a decreased first flush mass flux of contaminants. Dry weather channels (DWCs) can be used as a passive technology aimed at the reduction of solids mass accumulation by increasing the dry weather flow depth and forward flow velocity, and subsequently decreasing the wet perimeter length (Sonnen 1977). A DWC was successfully implemented along a storage tank invert in Switzerland to re-suspend and convey solids during the final portion of a wet weather event (Perdek 1998).

The Metropolitan Sewer District of Greater Cincinnati is proposing to incorporate a 5 639 ft (1 719 m) DWC into one of its existing arch type sewers that currently suffers from odour issues. The main goal of the DWC is to mitigate the odour issues by decreasing the solids deposition during dry weather flow. In an attempt to quantify the unrealized benefits (i.e. the impacts on CSO outflow pollution rates during wet weather events) a modeling project was initiated to try to determine the minimum benefit the proposed DWC could impose on annual solids settling and solids outflow.

The objectives of this study were to:

- Repurpose an existing model and estimate mass transport parameters for the total suspended solids (TSS) buildup and washoff rates from within the collection system, using data collected from previous wet weather events;
- Apply the solids model to the existing system wide storm water management modeled flow rates using the typical year rainfall period; and
- Apply the water quality model using the proposed conditions, including the incorporation of a DWC, to assess the local reduction of solids accumulation within the sewer.

## 2 Background

This section describes the site details and the analysis of solids settling therein.

### 2.1 Site Details

Figure 1 illustrates where the study site is within Hamiltion County, Ohio and Figure 2 depicts a site map of the combined sewer system which encompasses the extent of the proposed DWC. The contributing watershed is roughly 1 300 acres (526 ha) with a typical peak dry weather flow (DWF) of 1.64 MGD (4 303 L/min). The land usage is primarily residential, with a population of ~12 000, but also includes light commercial areas. The basin is predominantly comprised of ~20.8 mi (33 km) of vitrified clay pipe and concrete. Branches of the collection system all converge to an arch type trunk main that is 15 ft (4.6 m) wide and 11 ft (3.4 m) tall. Dry weather flow is directed to a 24 in. (62 cm) interceptor immediately upstream of the CSO structure. The average DWF TSS concentration is 168 mg/L. Along the main trunk line there is a long history of odour complaints.

Figure 1 Study site location within the service area of the Metropolitan Sewer District of Greater Cincinnati

Figure 2 Local collection system studied, highlighting the proposed dry weather channel plan; the bold conduits are those that fail the minimum DWF tractive force solids settling test (Bizier 2007).

### 2.2 Analysis of Solids Settling

A solids settling quantitative analysis was conducted based on a methodology commonly employed (from Bizier 2007) for sanitary sewer design by testing for tractive force. The test compares the shear of a fluid vs the shear force required to keep the maximum design particle moving during minimum DWF. In our work, the test was conducted to give qualitative insight into the occurrence of settling within this reach of the collection system. As suggested by Bizier (2007), the typical design particle for sanitary flow is 1 mm since grit found in wastewater is typically <1 mm.

An analysis of the existing collection system was conducted based on minimum DWF modeled rates for all of the conduits (model described later). The analysis compared the shear stress of flowing water within a conduit (known as tractive force) and the resisting shear stress of the design particle. According to Bizier (2007) the tractive force for a conduit can be determined by Equation 1:

(1) |

where:

γ |
= | specific weight of water, |

R_{h} |
= | hydraulic radius, and |

S |
= | slope. |

Equation 2 is used to determine the shear stress required to move the 1 mm design particle:

(2) |

where:

k |
= | 0.0181, and |

d |
= | design particle diameter (Bizier 2007). |

A conduit fails the test if the DWF minimum shear stress is less than the shear stress of the design particle.

Conducting the analysis for each of the conduits within the local collection system model, it was concluded that ~62% of the conduits fail the tractive force test as illustrated in Figure 3. Based on *settleable* surface area alone, ~65% of the system conduit’s surface area (flow width at minimum DWF multiplied by the conduit length) was susceptible to settling which was ultimately determined to be ~2 acres (0.8 ha) of settling area. Referring to Figure 2, the bold conduits are those conduits that likely suffer from solids deposition based on the tractive force test. Moreover, almost the entire main trunk (proposed site for the DWC) suffers from settling. Understanding that the combined sewer system is highly susceptible to solids deposition during DWF, and as a conservative practice, uniform settling was assumed for the extent of the collection system for the minimum DWF.

Figure 3 The Tractive Force test (Bizier 2007) for the collection system model at minimum DWF using a 1 mm design particle.

## 3 Data Collection

For this study, in an effort to develop the water quality mass transport model, flow monitoring combined with TSS sampling was conducted. The following subsections describe the flow monitoring and TSS sampling during wet weather events and the dry weather flow.

### 3.1 Flow Data Collection

Three flow monitors were installed at strategic locations to gather data for comparison with the storm water management model as shown in Figure 4: two in the main arch type trunk line (Sigma 920 and Sigma 910) and one within the interceptor (Sigma 910). The monitors installed in the arch type conduit were used exclusively for wet weather, whereas the monitor within the interceptor was used continuously for dry and wet weather analysis. Flow monitoring was collected on a 5 min time step interval.

Figure 4 Local map of flow monitoring and TSS sampling locations.

### 3.2 Total Suspended Solids Sampling

The following paragraphs describe the two genres of TSS sampling conducted for DWF and for a series of wet weather events. The sampling effort, which was part of a related project and documented in Black and Veatch (2011), is summarized in the following section.

#### Dry Weather Sampling

Dry weather TSS sampling was conducted to determine the DWF mass rate signature. All DWF grab samples were collected from within the interceptor near the dry weather flow monitoring site. Samples were hand collected every two hours over a ~24 h period from 10:19 on 2011 06 06 to 08:51 on 2011 06 07. DWF samples were collected based on systematic-judgemental sampling which the plan considered the diurnal flows to determine the best times to collect the samples, according to Keith (1990). Considering that DWF patterns and subsequent water quality is *predictable* under normal diurnal flow conditions, the sampling time step used for this analysis was aimed at catching the maximum and minimum TSS mass rates.

#### Wet Weather Sampling

The wet weather event sampling included 8 events (from 2010 11 24 to 2011 01 18), shown in Table 1 below. A 14 bottle capacity auto-sampler (ISCO Avalanche) was used for the sampling collection. The sampler was programmed to draw samples in aliquots after >1 in. (2.5 cm) flow passed over the outflow structure weir. The aliquots collected were 1 L, set to collect over 20 min periods that were divided into four 250 mL draws on 5 min intervals.

The WWF sampling procedure was inherently different than the DWF considering the WWF were 20 min composite samples and the DWF were grab samples. Similarly, the WWF sampling plan was also classified as systematic–judgemental sampling according to Keith (1990). Compared to DWF, WWF has significant variability over time. The sampling method was aimed at understanding the rate of change in mass rate over time, hence, samples were collected in smaller time steps. The 20 min aliquot sampling method was used to provide a clearer picture of the temporal changes in the water quality over time. It is understood that the difference in practice between the DWF and WWF sampling methods could introduce some variability. As described later, the DWF samples were used as model inputs, whereas, the WWF samples were used to calibrate the model transport parameters.

Table 1 Event sampling schedule.

Evt # | Start | # Samples | Peak Conc., mg/L | Antecedent Dry Time, h |

1 | 2010 11 24 | 23 | 443 | 30.7 |

2 | 2010 11 25 | 4 | 79 | 5.5 |

3 | 2010 11 29 | 14 | 684 | 92.3 |

4 | 2010 11 30 | 14 | 35 | 3.92 |

5 | 2010 12 11 | 14 | 900 | 166.1 |

6 | 2010 12 30 | 15 | 850 | 212.8 |

7 | 2010 12 31 | 4 | 1 290 | 29.3 |

8 | 2011 01 18 | 26 | 970 | 396 |

Evt # | Peak Flow, MGD (kL/min) | Vol., MG (kL) | Peak Intensity, in./hr (cm/hr) | Rainfall Vol., in. (cm) |

1 | 84 (220) | 16 (42) | 0.35 (0.89) | 0.90 (2.27) |

2 | 114 (299) | 49 (128) | 0.70 (1.78) | 2.61 (6.64) |

3 | 131 (345) | 19 (50) | 0.41 (1.04) | 1.09 (2.78) |

4 | 120 (314) | 15 (40) | 0.61 (1.55) | 0.81 (2.05) |

5 | 32 (84) | 12 (32) | 0.26 (0.67) | 0.47 (1.18) |

6 | 21 (56) | 6 (17) | 0.18 (0.46) | 0.32 (0.81) |

7 | 48 (126) | 8 (20) | 0.036 (0.09) | 0.01 (0.0254) |

8 | 38 (101) | 8 (21) | 0.20 (0.51) | 0.48 (1.22) |

### 3.3 TSS Sample Results

Figure 5 illustrates a plot showing the total mass from individual wet weather events compared to the wet weather event antecedent dry time.

Figure 5 Individual wet weather event cumulative mass compared to event antecedent dry time.

A first order decay regression showed that the total mass below and above ground seemed to reach an asymptotic phase of ~3 600 kg. The event on 2010 12 31 was excluded due to incomplete sampling as the event water quality tail was not completely captured. The plot suggests a general correlation between the antecedent dry time and the mass that accumulates both above ground and within the collection system. Considering that the sampling method offered no way to distinguish where the mass was coming from, the plot aims to bolster the concept that mass accumulation could be asymptotic within the collection system.

## 4 Modeling

The following subsection describes the hydraulic and water quality modeling and the associated parameter estimation.

### 4.1 Hydraulic Modeling

The collection system’s hydraulic conditions were modeled and compared to the monitored data using PCSWMM–SWMM5 (James et al. 2010). Over a period of 10 y the model has been expanded and recalibrated. For this project, model comparisons were performed using a set of wet weather events from November, 2010 to January, 2011 and determined to be adequate for the purposes of this project. Ultimately, modeled flow data time series were used as inputs to support the water quality modeling as discussed in the following sections. Three simulations were conducted with the hydraulic network: a dry weather flow analysis; a continuous simulation with rain series input during the special sampling period from November, 2010 to January, 2011; and finally, a simulation for the 1970 typical year rain series.

### 4.2 Water Quality Modeling

The overall system water quality model can be likened to a theoretical tank where mass can accumulate within the tank and be mechanically removed. The point of the system that was modeled was immediately upstream of the CSO and interceptor inlet (see Figure 4). The following model includes mass rates entering and leaving the sewer system, but most importantly, mass accumulating on the conduit walls during DWF. Equation 3 represents the overall mass rate equation for the TSS water quality model.

(3) |

where:

dM/_{out} dt |
= | modeled mass rate at the point leaving the system immediately upstream of the CSO and interceptor inlet, |

dM/_{in} dt |
= | mass rate entering the system from overland and sanitary flow, and |

dM/_{wall} dt |
= | modeled mass rate leaving the system immediately upstream of the CSO and interceptor inlet. |

#### Influent Mass Rate (*dM*_{in} /*dt*)

_{in}

To support the modeling of mass accumulation within the sewer system, the system influent mass rate was disaggregated from a lumped time series input to DWF influent mass rate and wet weather flow influent mass rate as shown in Equation 4.

(4) |

where:

dM /_{in,DWF}dt |
= | DWF influent mass rate (Q * _{dwf}C), and_{TSS,DWF} |

dM /_{in,over}dt |
= | overland flow mass rate (Q * _{over}C)._{TSS,over} |

The 24 h DWF TSS sampled concentrations (*C _{TSS,DWF}*), described in Section 2.2, were multiplied by the respective hydraulic model DWF rates (

*Q*) from within the interceptor giving an influent TSS mass rate time series for the overall system.

_{dwf}The overland flow mass rate was represented using another modeling application known as the P8 model (*Program for Predicting Pollution Particle Passage through Pits, Puddles and Ponds Urban Catchment Model*, Walker 1990). The P8 model was developed based on data from the United States Environmental Protection Agency’s Nationwide Urban Runoff Program (NURP 1983). An overland flow hydraulic and water quality model was developed in SWMM using the P8 model initial conditions, which incorporated the land use features to determine a time series of overland TSS concentrations (*C _{TSS,over}*) that contributed to the overland mass rate into the collection system (

*dM*/

_{in,over}*dt*). The overland flow hydraulic and water quality model took into account the impervious and pervious areas separately.

The stormwater TSS buildup and washoff parameters were added to the SWMM model of the combined sewer system for the impervious and pervious portions of the area contributing to the CSO. These parameters were set to be equivalent to the calibrated parameters presented in the *P8 Urban Catchment Model Program Documentation Version 1.1* which were calibrated to the median TSS event mean concentration (EMC) from the National Urban Runoff Program (Walker 1990).

As described in the P8 program documentation, the impervious area buildup and wash-off parameters were set to the following: TSS accumulation rate = 8.75 lbs/acre-day (9.81 kg/ha-day), TSS accumulation decay rate = 0.25 1/day, washoff exponent = 2, and washoff coefficient = 20.

The pervious area buildup and wash-off parameters in SWMM were determined by a trial and error process in which the parameters were modified until they produced an effluent TSS concentration of 500 mg/L when the runoff rate from contributing catchment had reached 1 in./h (2.54 cm/h), which is consistent with the P8 model methodology. The buildup of TSS on the pervious area was set to be large enough so that the TSS on the pervious area did not limit the discharge of TSS from the system. For pervious areas the washoff coefficient and exponent were estimated to be 14.25 and 2 respectively. The runoff P8 TSS concentrations from the overland flow model (*C _{TSS,over} *) were multiplied by the corresponding modeled flow rates (

*Q*) giving a final time series vector for

_{over}*dM*/

_{in,over }*dt*.

#### Sedimentation–Resuspension Mass Rate (*dM*_{wall} /*dt*)

_{wall}

Both Bechmann (1999) and Willems (2009) used the following model to determine the mass rate as a lumped system which included both the wet weather and sanitary mass rates. For our work the model was repurposed to represent the mass rate to and from the sewer wall exclusively. Returning to the concept that the collection system can be likened to a theoretical tank, the mass on the sewer wall can be considered the mass that accumulates and is subsequently removed from the bottom of the tank. For this modeling exercise, as described later, the sewer wall is the bottom surface area (plan view) associated with the peak DWF flow rate. For example, in a 1 m diameter conduit at peak DWF of 0.5 m, the sewer wall area considered would be 1 m multiplied by the sewer length.

The mass rate to and from the sewer wall, which was based on the following first order one dimensional model from Bechmann (1999) and Willems (2009), is:

(5) |

where:

dM /_{wall}dt |
= | mass rate to and from the sewer walls, |

= | steady-state mass sedimentation on the sewer wall, | |

M_{wall} |
= | current mass within the system adhering to surfaces (state variable), |

q |
= | current flow rate, |

= | maximum DWF flow rate, and | |

k_{a} |
= | solids settling rate. |

In the nominal case, the model performs as follows: if the current wall mass *M _{wall}* < then mass will settle, and when

*M*> then mass is removed from the sewer walls. As for the flow rate

_{wall}*q*, when

*q*< mass will settle out, and likewise when

*q*> mass will be removed. The idea that a steady state mass sedimentation within the sewer is real is assumed and accepted in this modeling practice since the sampled data dictated this value through the parameter estimation process. Furthermore, the assumption is predicated on the data presented in Figure 5 above, where an asymptotic relationship is observed. During dry weather, the model is essentially trying to reach steady state value, but the wall mass can be greater or lesser than the steady state value.

A model extension was provided by Willems (2009) to incorporate the general behaviour of mass resuspension in elevated flows. The relationships is as follows

(6) |

where:

k_{b} |
= | deposition or accumulation rate of wall mass, and |

b_{max} |
= | disaggregated into b and _{max,1}b._{max,2} |

Disaggregated into two parts, *b _{max}* was representative of the deposition and washoff maximum concentrations:

*b*for deposition concentration (i.e. when

_{max,1}*q*≤ ) and

*b*for the maximum resuspension concentration (i.e. when

_{max,2}*q*> ). Parameter

*b*is identified as a maximum resuspension concentration but in reality, this term is more of a model fitting parameter.

_{max}### 4.3 Modeling Inputs and Settling Model Parameter Estimation

From Table 1, events 1 through 7 were used to estimate parameters *k _{a}*,

*k*,

_{b}*b*,

_{max,1}*b*and . Event 8 was reserved for the water quality model validation. Hydraulic data was used from a continuous simulation performed over simulations times from 00:00 on 2010 11 17 to 11:00 on 2010 12 30 to support the settling–resuspension model parameter estimation process. The simulation start time,

_{max,2}*t*, was equal to the time at the end of a previous wet weather event where the mass accumulated on the conduit wall was assumed to be completely washed off. Therefore

_{0}*M*was set to 0.

_{0}Due to the multiple degrees of freedom to the model (i.e. *k _{a}*,

*k*,

_{b}*b*,

_{max,1}*b*and ) and the complexity of the model extension by Willems (2009), Equation 7, a Monte Carlo method of randomized inputs, was employed for the parameter estimation process. An ordinary differential equation solver was used from the Python 2.7–SciPy 0.10.1 optimization tools (The SciPy Community 2013) to solve the differential equations. For every iteration of this process each parameter was assigned a random number within the bounds of the parameter space where convergence could be achieved. Using a function minimizer search tool, from the Python 2.7–SciPy 0.10.1 optimization toolkit functions, that allowed a bounded search, trials were performed within the function in an effort to find to a minimum root mean square error (RMSE) between the model predicted effluent mass rate (

_{max,2}*dM*/

_{out}*dt*) from Equation 3 and the experimental sampled effluent mass rate (i.e. [(

*Q*+

_{over}*Q**

_{dwf})*C*] at corresponding sample times). The process was repeated 288 times with different random inputs for each trial. The search bounds for the individual parameters were: (minimum, maximum) for

_{TSS,sampled}*k*(4 000 min, None);

_{a}*k*(4 000 kg, None);

_{b}*b*(0 kg/L, 1);

_{max,1}*b*(0 kg/L, 1); and (1 kg, None).

_{max,2}## 5 Modeling Results for Existing Conditions

The following section describes parameterization for the sewer mass accumulation model, the results for the existing conditions, model validation, and a discussion.

### 5.1 Parameterization and Results

Table 2 provides the given wall mass model parameters as well as the results from the estimation using the first seven events enumerated in Table 1. Overall, the modeled concentrations represented the sampled data reasonably well, mimicking the mass transport behaviour within the sewer. The global RMSE from the Monte Carlo parameter estimation process reached a minimum of 6.56 kg/min (205 mg/L).

Table 2 Parameterization of given and estimated values.

Given Parameters | Value |

M_{0} |
0 kg |

4 303.7 L/min | |

Estimated Parameters | Value |

2 396.3 kg | |

k_{a} |
205 h |

k_{b} |
9 004.5 kg |

b_{max,1} |
0 mg/L |

b_{max,2} |
6 985.0 mg/L |

Figures 6 through 8 illustrate the simulation results for some select wet weather events. The first subplot in each figure presents the TSS mass rate entering the system from overland flow as well as leaving the CSO. The second subplot is the cumulative mass stored within the collection system. The third subplot is the TSS concentration. The fourth subplot is the SWMM modeled flow rate. Figures 6 and 7 illustrate the general dynamics of the model performance. As the flow begins to increase above the maximum dry weather flow rate, mass is removed from the sewer walls. For the November 24, 2010 wet weather event simulation (Figure 6), integrating to find the area under the model the model-predicted effluent mass rate gives the total wall mass before the start of the wet weather event, which is about 1 250 kg. The second subplot in Figure 6 illustrates that the total stored wall mass in the system goes to zero after the start of the wet weather. The model demonstrates the first flush effect nicely while closely achieving the sampled TSS concentrations.

Figure 6 Simulation results for 2010 11 24.

Figure 7 Simulation results for 2010 12 11.

Typically after a first flush period ended, the residual mass in the sewer would be ~0 kg. In the event of a second wet weather flow peak, the model tended to under-predict the effluent mass rate. Figure 8 illustrates the model results for two wet weather events 2 h apart on 2010 12 30. The model tends to under-predict the later of the two events since the mass on the wall was removed by the first wet weather event.

Figure 8 Simulation results for 2010 12 30.

### 5.2 Discussion

Similar to Willems’s (2009) modeled basin area of 1 217 acres (493 ha), the region upstream of CSO for our study is ~1 200 acres (486 ha) and both contain populations of ~12 000 people. Both basins act as combined collection systems for the most part and, with respect to parameterization, are similar. For parameters *k _{a}* and

*k*, Willems estimated values of 240 h and 21 600 kg respectively, and from Bechmann (1999) the

_{b}*k*equivalent variable was estimated to be 83 h. Parameters

_{a}*k*and

_{a}*k*from our study were estimated to be 205 h and 9 004.5 kg respectively.

_{b}The common parameters among each model were anticipated to be disparate likely due to a slightly different model application for this work. In general, the modeling applications provided by Bechmann (1999) and Willems (2009) were used to predict the suspended solids sedimentation and resuspension incorporating mass from both overland flow and sanitary flow. Our work attempted to disaggregate the model inputs in order to represent mass accumulation within the sewer, explicitly. The disaggregation of *dM _{in} */

*dt*led to a significantly lower estimated value of 2 396 kg, compared to 5 000 kg from Willems, given that both basins are similar in size.

With the assumption that *–**q *≡ *q _{max,DWF}* (as discussed in Section 3.2), the objective function to minimize the error between the model predicted TSS values and the sampled TSS values led to a global minimum arriving at a

*b*, in most estimation cases to be 0 mg/L. Based on these findings, for simplicity, model predicted settling was assumed to be achieved when

_{max,1}*–*

*q*≤

*q*and when

_{max,DWF}*M*≤ . Therefore, when when

_{wall}*–*

*q*≤

*q*, the

_{max,DWF}*b*deposition concentration was set to zero, allowing the settling rate to be governed exclusively by the first term on the right hand side of Equation 5. Thus, in support of this modeling technique,

_{max,1}*b*was estimated to be zero.

_{max,1}Parameter *b _{max,2}* was estimated to be 6 985 mg/L. Compared to the literature, this estimated value is much higher than the term estimated by Willems (2009). This term is more of a model fitting parameter than one that is actually measurable. In this context, compared to the literature, our estimated

*b*is higher due to fact that the solids settling and resuspension model was used to exclusively represent sewer solids buildup and washoff, whereas previous authors modeled the complete picture of runoff and sewer. Solids buildup and washoff values in our case would be much higher since normally there is a higher amount of solids per sewer settling area compared to solids per surface area above ground.

_{max,2}The first seven events shown in Table 1 included a wide range of flow conditions and antecedent dry times which made these events strong candidates to use for the parameter estimation process. As discussed earlier, the event on 2011 01 18 was used to test the estimated water quality model parameters in parameters from Table 2. Figure 9 illustrates the model performance for the 2011 01 18 event. This event was simulated using the monitored flow data, not the modeled flow. The response from the flow monitors was much lower than the modeled flows, which could be due to higher uncertainty and spatial differences between the rainfall input and the actual rainfall (Chaubey 1999). On 2011 01 18 the mass removed from the sewer wall during the first 2 h of the wet weather event was ~950 kg. The model closely predicted the peak observed concentrations and mass rates while exhibiting the same signature.

Figure 9 Validation case simulation results for 2011 01 18.

Interestingly, the TSS sampling illustrated in Figures 6 and 8 suggests that beyond the initial flush period of the wet weather event solids concentrations tend to remain low, even during a secondary peak flow. The model suggests that, at least in this particular system, solids are completely removed from the sewer walls and overland catchment areas. Assuming complete removal is not practical since most likely the mass removed from the system has the least erosional resistance (Mannina 2010). However, observing lower TSS concentrations is possible given that the bulk of the mass is removed during the initial increase in flow during the preliminary portion of the wet weather event. Secondary increases in flow might not necessarily bode higher concentrations. A CSO water quality study conducted in Milwaukee, Wisconsin revealed similar trends between their defined first and second flush as our work but from a surface runoff or CSO perspective (Magruder et al. 2007). Among several water quality constituents, TSS concentrations were much lower during the second flush compared to the first (Soonthornnonda and Christenson 2004).

## 6 Dry Weather Channel Impact Modeling

This section describes the proposed model extension, application of the water quality model to the existing and proposed system wide models, and a discussion of the results.

### 6.1 Proposed Model Extension

The proposed model extension supports the concept that steady-state mass accumulation ( ) is a function of settleable surface area since we assumed uniform settling. Furthermore, the strategy assumed that the estimated parameters from Table 2 were appropriate for usage in a proposed modeling scenario since, conceptually, the characteristics and kinetics of the solids and the rate that solids settle does not change with any physical change in the collection system. The modeling process for this system assumed a uniform mass settling regime throughout the modeled collection system, and settling was assumed to be uniform over the sum of the surface area comprising individual corresponding conduit flow widths at peak DWF multiplied by the respective conduit lengths. The relationship of the is as follows:

(7) |

where:

= | steady-state mass settling per unit area, | |

n |
= | conduit number, |

W_{w,n} |
= | flow width corresponding to the peak DWF, and |

L_{c,n} |
= | conduit length. |

Based on this approach, was solved for using the settleable surface area from the existing collection system and the estimated from Table 2. Summing the entire collection system peak DWF flow width multiplied by each respective conduit length led to an existing settling surface area of ~131 718 ft^{2} (12 241 m^{2}). Thus was determined to be 18.2 g/ft^{2} (195.8 g/m^{2}). A supporting illustration can be seen in Figure 10.

Figure 10 Supporting information for collection system settling area and the proposed DWC.

### 6.2 Simulation

Using the same Python scripts that were developed to estimate and validate the model parameters, the 1970 typical year hydraulic time series data was loaded into the solver. The proposed site for the DWC is illustrated in Figure 2. For the existing system, was used from Table 2 to determine the mass rate leaving the CSO. Equation 5 was used to determine for the proposed DWC. The proposed DWC reduces the flow width from 7.2 ft (2.2 m) to 1 ft (0.3 m) and, at a length of 5 639 ft (1 719 m), the reduction in total settling area from the collection system is 34 962 ft^{2} (3 249.2 m^{2}). The reduced settling area multiplied by led to an of 1 760 kg for the proposed DWC model.

### 6.3 Typical Year Existing and Proposed System Modeling Results

Figure 11 illustrates the results comparing the concentration time series 1 min data of the existing system typical year and the existing system with the proposed DWC.

Figure 11 Concentration comparison between the existing system and proposed system with the DWC.

From Figure 11, the results indicate that outside of normal DWF that the modeled concentrations for the system with the DWC are lower than the existing system. Overall, a reduced settling surface area reduces the amount of build-up during DWF within the collection system and subsequently sheds less mass during wet weather events. For the existing conditions based on the typical year there is an accumulation of ~64 058 kg within the collection system. Comparing these results to the proposed system with the DWC, there is a ~26.5% reduction in annual accumulating mass, giving 47 073 kg. Therefore, with the proposed DWC, model results suggest a 26.5% annual reduction of outflow solids.

### 6.4 Discussion

The assumptions leading to the results of our settling mass per area proposed model extension are likely conservative because of the uniform settling assumption. This was the best alternative to show minimal impact of a DWF since there was a lack of TSS sampling data throughout the collection system. Based on the tractive force analysis results (see Figure 3), the settling is most prevalent in the main trunk line for the proposed DWC. If the same analysis was conducted only looking at the relative reduction of surface area (34 962 ft^{2}, 3 249.2 m^{2}) within the conduits that failed the settling test (86 148 ft^{2}, 8 006 m^{2}), the results would indicate an annual settling solids outflow reduction of ~59%.

The majority of the estimated model parameters presented in Table 2, except for , are believed to be rates to describe normal municipal wastewater sedimentation. Parameter *k _{a}* can likely be used under most applications, assuming other applications have similar deposition occurrence as the collection system investigated iherein. Understanding parameter

*k*is likely to be a function of how quickly mass can be removed from the walls of the collection system, conceptually there might also be correlation between this parameter and . Similar weighting strategies to the approach for representing might be acceptable for estimating for similar systems.

_{b}## 7 Summary and Conclusions

Our work attempted to model the sedimentation and mass transport within a collection system upstream of a CSO by repurposing an existing model derived from Bechmann (1999) and expanded by Willems (2009). The effort was to support the claim that as a best available technology a DWC could reduce the quantity of sanitary solids in the annual CSO outflow. Model parameters were estimated based on seven wet weather events where TSS samples were collected. Overall the model performed best during the initial first flush phase of a wet weather event. One of the limitations to this was predicting the outflow mass rate during a secondary wet weather event (second flush).

The proposed model was modified and applied to the storm water management model upstream of the CSO, which is the proposed site of the DWC. Two separate analyses were run using the typical year time series rainfall data: (a) the existing system and (b) the existing system with the proposed DWC. Using the hydraulic data from the collection system hydraulic model as an input to the water quality model process described in this paper, the modeled results illustrated in Figure 11 suggest that the inclusion of a DWC could provide a reduction in solids during the first flush portion of wet weather events between 26.5% and ~59%.

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