11

th

International Conference on Urban Drainage, Edinbu rgh, Scotland, UK, 2008

Zawilski and Sakson

1

Modelling of detention-sedimentation basins for stormwater

treatment using SWMM software

M.Zawilski

1*

, G.Sakson

1

1

Department of Environmental Engineering, Technical University of Lodz

Al.Politechniki 6, 90-924 Lodz, Poland

*Corresponding author, e-mail: mrkzaw@p.lodz.pl

ABSTRACT

In the paper, application of the model for total su spended solids removal with the use of

SWMM software is analysed. Two types of kinetics we re checked: first order and second

order. In the SWMM model two types of detention-sed imentation tank were input: a single

completely stirred reactor and a reactor of the same mixing conditions but divided into four

subsequent parts. The model was calibrated according to field investigations of a real tank.

The modelling results show a good accordance of the modelled and measured parameters,

especially of the outflow TSS load. The best result s were obtained for the single CSTR and

the second order kinetics. The proposed model is se nsitive to changes of decay rate constant.

Removal of TSS depends also on the tank area and ou tflow intensity. However, these changes

are essential for intense storm events. Despite some simplifications, the SWMM model can be

used for practical calculations.

KEYWORDS

Detention tanks; total suspended solids; sedimentat ion; urban drainage; SWMM software.

INTRODUCTION

Detention-sedimentation basins are frequently used for stormwater treatment prior to its

draining into natural waters. The random character of rainfall events and unsteady flow

conditions make it difficult to evaluate the technological effect of such facilities. It is well-

known that elimination of suspended solids is essential for stormwater treatment and allows

for elimination of other pollutants (like heavy met als and organic contaminants) associated

with suspended solids.

In detention-sedimentation basins, various processes occur: detention of water as a

consequence of throttling of the outflow, flocculat ion and sedimentation of (mainly mineral)

particles, resuspension of sediments, flotation of oils, light particles and so on. In practical

engineering analyses, there is an urgent need to ev aluate the efficiency of such tanks

depending on their size, hydraulic loading, pollutant level of influent stormwater and other

factors. Long-term computer simulation is one of techniques used for this purpose. A

detention tank usually is an element of sewerage ne twork and often is situated at the outlet of

a main stormwater sewer. The tank receives all the catchment runoff and depending of the

tank size (area, active depth) a removal of certain portion of incoming load of suspended

solids is possible. So far, several original simple and sophisticated models for such tanks have

been elaborated. However, the popular SWMM software can be used for this purpose but the

Modelling of detention-sedimentation basins

2

user should introduce a treatment function. In the paper, a proposal for using such SWMM

option is presented. The proposed algorithm resulte d from own investigation of a real tank.

METHODS

The principle of detention-sedimentation tanks is c apturing storm runoff together with

transported pollutant load. Usually, this can be ac hieved by installation of a throttling device

or a regulator at the tank bottom end. Capturing of inflow or pollutant load from a certain

period (for instance the whole year) may be a basic design criterion (Vaes and Berlamont,

2004; Birch et al., 2006; Calabro and Viviani, 2006). Another option is limiting the annual

volume or load input from a catchment into receivin g water body. Computer modelling is an

effective method for assessing the technological ef ficiency of stormwater detention-

sedimentation tanks situated at outlets from urban catchments.

Models of detention-sedimentation tanks

The functioning of the detention-sedimentation tank can be described either as a hydraulic or

a technological efficiency (i.e. reducing the flow, volume of stormwater or the pollutant load).

Long-term simulations can be used for this purpose. Having a well-calibrated model for

calculation of runoff, stormwater flow and load fro m a catchment, it is necessary to introduce

certain treatment efficiency formula for a possible tank.

Sedimentation of suspended solid particles was reco gnised as the main technological process

for traditional and also modern sediment trap devic es (Phipps et al., 2005). Removing of

turbidity of stormwater is especially difficult (Ha n and Mun, 2007). However, the

sedimentation process occur in non-standard conditi ons, for instance in comparison with

typical primary settling tanks used in wastewater t reatment plants. The main difference is

unsteady inflow, outflow and active volume which ma ke impossible a direct application of

known simple sedimentation models for typical clari fiers. Additionally, inflow and (in

consequence) outflow pollutant concentration are hi ghly variable in time as well as a flow

turbulence undergo rapid changes, especially in rea l tanks of non-ideal shapes (Vaes, 1998).

Models for describing objects are formulated with s ome simplifications. For instance,

Takamatsu et al. (2006) assumed the plug-flow inside the tank which made possible

adaptation of the known Camp theory of particle mov ement in the tank active volume. If a

particle settling velocity distribution is known, t his theory makes possible calculating

technological effect as a portion of removed load o f solid particles in relation to the inflow

load. Other assumptions take non-ideal flow conditi ons, i.e. longitudinal mixing into

consideration (Jensen, 2005). This effect, as known, can be modelled as a flow through a

completely stirred tank reactors (CSTRs) in series and usually few (4-10) such reactors can be

assumed. This model, however, does not allow for de tailed calculating of particle trajectories

during settling process and a kinetic model for pol lutant removal has to be applied instead.

Nonetheless, such models may give satisfactory resu lts (Zawilski, 1997; Person et al.,

1999;Wong et al., 2002).

EPA SWMM model for treatment facilities

EPA SWMM (Stormwater Management Model) is the widel y known and free software used

for modelling of sewerage systems. Among others, it contains a procedure for modelling the

technological effect taking place at any node of a sewer network. The node can be declared as

a storage unit with an assumed treatment function w hich the option can serve for modelling

detention-sedimentation facilities. The user, howe ver, should input his own formula (or a set

of formulas) calculating the removal efficiency usi ng some standard technological parameters.

Some general hints for the algorithm are known only. Basically, a treatment function for the

11

th

International Conference on Urban Drainage, Edinbu rgh, Scotland, UK, 2008

Zawilski and Sakson

3

pollutant concentration (C) in a stream entering th e tank can be used. The following process

variables may be used in the formula:

FLOW for flow rate into node (in user-defined flow units )

DEPTH for water depth above node invert (ft or m)

AREA for node surface area (ft

2

or m

2

)

DT for routing time step (sec)

HRT for hydraulic residence time (hours)

Also, a fractional removal (R) of some other tracer pollutants (usually associated with TSS)

can be formulated. In this case a simple proportional formula type R= a×R(TSS) is proposed.

It is logical that the used treatment formula should be verified according to investigations of a

pilot or real object.

Proposed treatment formula

First of all, it was checked whether a reasonable simple formula for a single CSTR can be

applied. Formally, the process of static sedimentation can be modeled using first order kinetic.

However, as it was stated earlier for the investigated real tank, also other phenomena affect

the sedimentation efficiency:

· characteristics of inflowing TSS strongly depends on rainfall intensity; there is a strong

correlation between TSS concentration and settling velocity distribution, i.e. smaller TSS

concentration always is correlated with smaller settling velocities and vice-versa

(Zawilski, 1996, 1998). However, only a crude relationship can be derived from real data

because of random variation of TSS composition transported from the catchment after

each rainfall event,

· As it was proved earlier, a certain portion of TSS of low settling velocity cannot be

removed during dynamic conditions with variable water level inside the tank (Takamatsu

et al., 2006),

· Turbulence of flow may have greater influence on removal of particles of low settling

velocity.

Therefore the influence of TSS concentration cannot be ignored as it dominates the kinetics

especially for low concentration inflows. Similar relationship was found for settling tanks at

wastewater treatment plants (Lessard and Beck, 1988).

Taking this into consideration, two types of kinetic reactions for inflow TSS concentration

were checked:

· First order kinetic

in

kc

dt

dc

= (1)

· Second order kinetic

2

in

kc

dt

dc

= (2)

These kinetic equations result in following formulas for pollutant removal:

· First order kinetic

HRT)kEXP(1R

×

=

(3)

Modelling of detention-sedimentation basins

4

· Second order kinetic

HRTkc1

HRTkc

R

in

in

×+

×

= (4)

where hydraulic residence time HRT is assumed as a driving parameter.

A dependence of settling velocity on TSS concentration was stated earlier by the author and

considered for the first-order kinetics (Zawilski 1996). A correction in the formula for TSS

removal efficiency was proposed. In this paper, a similar attitude for formula (3) is applied,

resulting in the following expression:

×=

n

1000

TSS

HRTkEXP1R (5)

In other words, in this corrected formula low TSS concentration causes the same effect as

shortening of HRT. The above formula (5) can be called the improved first order kinetic. In

the SWMM algorithm, HRT is represented by the instantaneous volume divided by outflow

intensity. The outflow intensity can be obtained from the water balance (as it will be

described later).

Additionally, the model for 4 CSTR in series was checked, too. This option was supposed to

give better fitting to measured data as it represents longitudinal mixing of the tank content

better. For this purpose, a series of four sub-tanks were input. The sub-tanks, each of 25%

area of the total area were connected with short virtual channels of big dimensions in order to

avoid artificial throttling effects. Outflow was modeled with the input of outlet characteristics

from the last tank only. Inflow was input to the first tank in series. For each of the sub-tanks

the same kinetic equation was assumed but the decay rate k could be different in comparison

with a single CSTR and should be adjusted separately.

Description of the research object

Lodz city (central Poland) was equipped with a separate sewerage system in the city districts

outside the centre where still the combined system is operated. The stormwater separate

outlets direct runoff into local urban rivers. Therefore, some of the outlets were equipped with

detention-sedimentation tanks in order to remove most of stormwater pollutants prior to their

diverting into receiving waters. One of the biggest tanks was built in 1970s at the outlet of a

sewer serving for a 300 ha urban catchment. The geometrical parameters of the tank are given

in Table 1.

Table 1. Geometrical parameters of the investigated tank

Category Unit

Value

Bottom area m

2

4233

Minimum water depth m 0.16

Water level area increase m

2

m

depth 477

Crest height of emergency overflow

above bottom level

m 1.52

Inflow channel

(long.slope 7%)

m

2.60 1.60

Outflow pipes (29) mm 100

Box filter length m 2G20

Box filter width m 0.5

11

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International Conference on Urban Drainage, Edinburgh, Scotland, UK, 2008

Zawilski and Sakson

5

The open triangular tank is situated at a local urban river. During first years of functioning,

outflow from the tank was taking place through 29 pipes of 100 mm diameter. Afterwards, a

special filter as an open-work box made from bricks filled with wood-wool was constructed

few meters in front of the end wall (Fig.1). The role of the filter is retaining oils. The filter,

however, functions as a ponding device because of its significant flow resistance. In the

middle of the box filter a concrete wall with small openings at the tank bottom was

constructed (Fig.1). The inlet to the tank was constructed as a short open channel with the

slope of 7%. This allows avoiding of backwater in the inlet rectangular sewer. The tank

collects sediments which are removed from the bottom once a year, usually at the end of the

year (November-December) when no frequent storms over the catchment are observed.

Figure.1. Scheme of the investigated tank

Experimental data

The investigations were performed on the basis of older but still valuable measurements made

for the five years research campaign in 1987-1991 (Table 2). The general results were

already presented (Zawilski 1996).

Inflow measurements were carried out with the use of a limnigraph situated in the side well at

the last segment of the inflow sewer. Simultaneously, water depth in the tank was measured

with the time interval depending on the water level variations. During the research period,

Modelling of detention-sedimentation basins

6

activating of the emergency overflow was observed only once but not for an investigated run.

Also, in most cases the receiving water level was well below the tank bottom level.

The TSS concentration was determined in grab samples taken: - at the inlet at the lowest point

of the inflow channel (where strong turbulence of flowing stormwater is observed), -at the

outlet at the middle of the filter wall for samples taken from below 20 cm depth; if the active

depth was less than about 40 cm, samples were taken from the outflow opening in the wall.

Table 2. Characteristics of investigated runoff events

Inflow Rainfall

Run

Q

max

(m

3

/s)

TSS

max

(g/m

3

)

C

w

#

(g/m

3

)

V

(m

3

)

L

TSS

(kg)

h

(mm)

t

(min)

i

mean

(mm/h)

1

5.11 1900 1044 10061 10507

7.98 22 21.76

2

3.40 1326 294 5902 1736

7.39 26 17.05

3

0.69 1230 699 2571 1796

10.26 430 1.44

4

3.64 5875 933 5528 5158

6.56 135 2.91

5

1.58 3105 2486 2972 7388

3.78 124 1.83

6

0.13 640 195 5904 1149

- - 1.1*

7

0.23 164 83 9216 761

13.94 1493 0.58

8

0.59 916 639 1856 1186

3.49 62 3.38

9

1.91 2257 549 3488 1916

5.53 40 8.31

10

0.29 296 89 3325 296

7.64 306 1.51

11

0.19 503 183 1041 191

2.31 323 0.43

# TSS concentration weighted by flow for the whole event

* snowmelt event; intensity of equivalent rainfall caused the same average outflow

The effect of the wood-wool filter was not investigated although apart from oils it is likely

able to capture some portion of fine suspended solids.

For the SWMM implementation, the obtained flow, depth and TSS measurements were input

into text files using the necessary format.

RESULTS

Calibration of SWMM model

For all measured runs, separate calculations were carried out in order to adjust model

parameters. At first, for each run outflow characteristics were found. The outflow from the

tank as the flow through the wood-wool filter was not measurable in details. However, its

value can be determined from the water balance:

dt

dV

QQ

inout

= (6)

This equation was solved twice: - with the use of the SWMM procedure as fitting the outflow

parameters (see below) so that the measured and calculated water level in the tank were in

close agreement, and for control with the use of own calculation procedure numerically

determining values of dV/dt for any time point.

The SWMM formula for outflow intensity is:

B

out

hAQ ×= (7)

11

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International Conference on Urban Drainage, Edinburgh, Scotland, UK, 2008

Zawilski and Sakson

7

This formula was checked for its applicability and satisfactory results were obtained (Figure

2). However, the outflow parameter A had to be adjusted for each run independently and

turned out to be much greater after the periodical exchange of wood-wool in comparison with

the periods of partly clogged material. During few months of filter functioning, the parameter

A was gradually decreasing from 3.0 to 0.3. The value of parameter B was around 2.8.

For the calibration of TSS removal model, several computation runs were carried out for

different values of kinetic coefficients. The main optimisation fitting criterion was the

correlation between the measured and modelled outflow TSS load. This relationship was

assumed as linear:

meas

out

mod

out

LaL ×= (8)

with ideal fitting for a=1 and R

2

=1.

It was stated that the pure first order kinetics (Equation 3) gives wrong model results.

All calculations were made for the time step of 30 seconds. This parameter proved to be

essential for model results to some extent, decreasing the outflow TSS load with a decreasing

of time step. However, this effect was not studied in detail since input of very short time steps

results in a substantial increase of calculation time. This would be very unfavorable in the

case of simultaneous modeling the runoff from a catchment, flow in sewer networks and

treatment in the tank.

One run had to be rejected from the whole experimental set. For this run, a considerable

scouring of TSS from the tank bottom was detected. Unfortunately, this effect cannot be

directly modeled as the SWMM removal formula allows for positive reduction of pollutant

only. During the rejected run, the maximum inflow was equal to 5 m

3

/s and was reached soon

after a very intense rainfall and with a corresponding rapid increase of the inflow.

The results of calibration are presented in Table 3.

Table 3. Results of calibration of the SWMM model

Type of tank Improved first order kinetics

(formula (5))

Second order kinetics

(formula (4))

Single CSTR k = 0.42; n =2

a = 1.007

R

2

= 0.91

k = 0.0011

a = 0.978

R

2

= 0.97

Four CSTRs k = 0.98; n = 2

a = 1.015

R

2

= 0.92

k = 0.00085

a = 1.002

R

2

= 0.92

In Figure 2 some modelling results are presented. Surprisingly, the best results were obtained

for a single CSTR and assumption of four CSTRs in series did not improve the general fitting.

This result can be explained as following: the SWMM model is able to predict the removal of

the total TSS load from a single event and a series of events. However, simplified calculation

formula for pollutant removal cannot describe outflow pollutographs ideally. Especially, the

TSS concentration is underestimated in its late part, i.e. the concentration tail is not

represented and the TSS level decreases to zero. Most of the TSS load is being removed

during first phases of the tank filling when it works in a manner similar to a single CSTR. The

later rest of TSS load is not decisive for the result.

Modelling of detention-sedimentation basins

8

Modelling of COD concentration and load

The COD parameter is one of most important ones for evaluating of the influence of

stormwater on receiving waters. This parameter can be modelled in similar way like TSS.

However, it would be necessary to gather a COD database similar to that of TSS and to

calibrate the model. Other simplified method is using the relationship between the two

parameters. The relationship can serve for recalculating of COD from TSS at the outlet of the

tank. For the investigated catchment and the tank, the following relationship was found:

70TSS2.08COD

0.66

+×= (9)

in which the value 70 represents the average soluble fraction of COD (non-degradable in the

tank). The formula is valid both for the inflow, as and the outflow COD, therefore can be

applied in the SWMM removal model. The relationship may be input as the treatment formula

for any node downstream of the tank.

Figure 2. Examples of modelling results for run no.4. Water depth and outflow TSS with

dots as measurement data (above), inflow - outflow discharge and inflow - outflow TSS

(below).

11

th

International Conference on Urban Drainage, Edinburgh, Scotland, UK, 2008

Zawilski and Sakson

9

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7

Multiplication factor for tank bottom area

Percentage of outflow TSS load

Run 1

Run 7

Sensitivity analysis of the model

For the purpose of evaluation of the model, a sensitivity analysis was made. The analysis was

carried out for the single tank, second-order model and the best fitted decay rate k=0.0011

was taken as a base value.

Figure 3. Sensitivity analysis of the model for the decay rate

Figure 4. Effect of hydraulic loading and outflow discharge onto outflow TSS load

From Figure 3 it can be concluded that the model is very sensitive to changes of decay rate

constant. Therefore, the decay coefficient should be determined in field tests, possibly with

the use of a real or pilot installation.

Removal of TSS depends also on the tank area and outflow intensity (Figure 4). However, the

appropriate changes of TSS load are essential for intense storm events. For weak rainfalls, the

efficiency of the tank is usually poor; therefore the effect of the tank area and outflow

discharge is relatively less.

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.0005 0.001 0.0015 0.002 0.0025

Decay rate constant

Fitting coefficient

70

80

90

100

110

120

130

0 0.5 1 1.5 2 2.5

Outflow coefficient

Percentage of outflow TSS load

Run 1

Run 7

Modelling of detention-sedimentation basins

10

CONCLUSIONS

The SWMM model proved to be able to predict TSS removal in detention-sedimentation

tanks properly. However, it is necessary to use a proper formula for TSS removal and to

determine kinetic coefficients. For the investigated real tank, the second order kinetics and

single CSTR reactor turned out to be the best model option. Alternatively, the first order

kinetics with a correction for TSS concentration can be used. In both cases, best results were

obtained for modelling the TSS outflow load, the TSS outflow pollutographs are modelled

with a less precision. For further practical use of the removal model a credible and not

complicated test methodology for determining the decay rate of TSS removal in dynamic flow

conditions should be elaborated.

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