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145
DOI: 10.31577/ahs-2020-0021.02.0018
Volume 21, No. 2, 2020, 145 – 151
ACTA HYDROLOGICA
SLOVACA
IMPACT OF ROUGHNESS CHANGES ON CONTAMINANT
TRANSPORT IN SEWERS
Marek Sokáč*, Yvetta Velísková
The paper deals with question how the bed sediment or deposits impact transport processes in conditions of flow with low
velocity and water depth. This is often a problem especially in case of flow in sewer network. For this reason, there were
performed several tests in laboratory flume having the shape of a pipe with circular cross-section. To simulate
the hydraulic condition in sewer pipe with sediments and deposits, some sand was inserted in the pipe with various layer
thickness and granularity. It was used a sand of fraction 0.6–1.2 mm. In total, 4 sets of experiments with different layer
thickness were performed: with layer thickness of 0 mm (no sediments), 8.5 mm (3.4% of the pipe diameter), 25 mm
(10%) and 35 mm (14%) of sand sediment. For each thickness of the sediment layer a set of tracer experiment was
performed with different discharges ranging approximately (0.14–2.5) l s-1. Results of the tracer experiments show, that
the value of the longitudinal dispersion coefficient Dx in the hydraulic conditions of circular sewer pipe with sediment and
deposits decreases when the Reynolds number is decreasing too. The value of Dx reaches its minimal value in the range
of the Reynolds number between 4500 up to 10 000. With Reynolds number below this range the value of Dx start to rise.
KEY WORDS: contaminant transport, longitudinal dispersion, bed sediment, roughness, sewers
Introduction
Flowing water in any natural conditions is connected
with substances transport. This process consists basically
of advection and dispersion. Substances transport is due
primarily to advection, but there are many situations in
which dispersion plays an important role and cannot be
neglected. Knowledge of the rate at which substances
disperse in streams is essential to stream management
especially if the carried substance is toxic and means
contamination for the stream.
Predicting of pollution spread is important for
the environmental protection. In the field of water quality
modelling, several authors (Chapra, 1997; Fischer et al.,
1979; Graf, 1998; Runkel and Broshears, 1991;
Marsalek, et al., 2004; Meddah, et al., 2015) presented
different approaches to understand and interpret the basic
concept of water quality problems. In a case an accidental
discharge in a stream, the prediction of the pollutant
transport is crucial in effective and rapid decision-
making. On the other hand, in the case of an illegal
release of a toxic substance, the determination of
the source of the pollution is even more complicated,
since it is an inverse task with a high degree of
uncertainty. A way to solve that can be finding a simple,
precise, a reduced computational time and a minimum
input data consuming solution – equation. But in natural
condition dispersion process is impacted by several
hydrodynamic parameters of flow. One of them is
occurrence of bottom sediment which changes
the roughness. This effect can be significant especially at
low speeds and water depths. These conditions often
occur in sewer networks.
This paper describes partial results of the research of
the influence of bottom deposits in a circular pipeline in
laboratory conditions to the value of longitudinal
dispersion coefficient as a parameter of dispersion rate.
Theoretical background
Dispersion is a combination of molecular and turbulent
diffusion, advection and shear (Meddah, et al., 2015). It
is created by the non-uniformity of velocity fields related
to the different characteristics of the stream such as
geometry, roughness, and kinematics. The dispersion
zones are usually (Rutherford, 1994): the initial mixing
zone, the mid-field mixing zone and the „far” field zone,
where dispersion is considered longitudinal and one-
dimensional in the flow direction. In the mathematical
models, the effect of dispersion is accounted by means of
the dispersion coefficient, for the evaluation of which
several procedures are proposed, supported by
experimental studies.
One-dimensional advection-dispersion equation (ADE)
describes the mixing and transport phenomena, where
the following assumptions are considered:
Acta Hydrologica Slovaca, Volume 21, No. 2, 2020, 145 – 151
146
Vertical and transversal dispersions are very small;
The pollutant is completely miscible in water;
Chemical reactions between the pollutant and its
environment are absent;
The overall mass of pollutant is maintained during
transport.
The form of this equation is then as follows:
(1)
where
C – substance concentration [kg m−3];
vx – fluid velocity in longitudinal direction [m s−1];
Dx – dispersion coefficient in the longitudinal direction
[m2 s−1];
t – time [s];
Ms – express the substance sources or sinks [kg m−3 s−1];
x – distance in the longitudinal direction [m].
Relatively simple analytical solution of Eq. (1) can be
obtained by using various mathematical approaches. One
of the most used approach is the general solution of
the ADE by (Socolofsky and Jirka, 2005), and eventually
by (Fischer et al., 1979; Martin and McCutcheon, 1998),
and it could be written as
(2)
where
M – substance mass [kg];
A – cross-sectional area of the stream [m2];
f – unknown function (“similarity solution “).
Other symbols meanings are the same as in the previous
equation. The most-used one-dimensional analytical
solution of the equation (2) for simplified conditions and
immediate solute input has the form (Martin and
McCutcheon, 1998)
(3)
where
vx – velocity of water flow in x direction of flow [m s−1].
Unfortunately, the analytical solution used in Eq. (3) is
based on the assumption of symmetrical substance
spreading up- and downstream (Gauss distribution) and
thus it does not take into account the temporary storage
zones (dead zones) (Weitbrecht, 2004; Gualtieri, 2008;
Valentine & Wood, 1977; 1979) or other singularities
influencing substance spreading. Use of this approxi-
mation in streams with large presence of those singu-
larities can be problematic. Because of this, we used in
our research also alternative formulation of the one-
dimensional analytic solution of the ADE based on
the assumption of asymmetrical substance spreading.
This alternative solution is based on the Gumbel statis-
tical distribution and it has the form (Sokáč et al., 2019):
(4)
where
Dx,G – dispersion coefficient in the longitudinal direction
[m2 s−1] used in the Gumbel distribution model.
Materials and Methods
The experiments were performed in the hydraulic labo-
ratory of the WUT (Warsaw University of Technology).
In aim to simulate the hydraulic conditions of a real
sewer, experiments were conducted in a hydraulic flume
with form of the pipe with circular cross-section.
The inner diameter of the pipe was 250 mm, length was
12 m, slope of the pipe was 0.5 % (5 ‰). The pipe mate-
rial was transparent plastic; every 2 m there were holes at
the top of the pipe, enabling the access into the pipe
(measuring devices, sediment insertion and retrieval). At
the pipe inlet there was a storage tank with water inlet in
the bottom part of the storage tank. After the water level
rises above the pipe bottom, water starts to flow into
the circular pipe. At the downstream end of the pipe was
a free outfall into another storage tank with outflow in
the tank bed (Fig. 1).
A drinking water was used for all the experiments,
without recirculation, so there was no problem with
the tracer background concentration increase. The inflow
into the system was regulated with a lever valve; using
this device it was very difficult to set up the same
discharge in the experiments. Because of this, in all
the experiments the discharge was measured individually
for each individual experiment, using a simple volu-
metric method below the water free outfall in the down-
stream storage tank.
To simulate the hydraulic condition in sewer pipe with
sediments and deposits, some sand was inserted in
the pipe with various layer thickness and granularity. It
was used a commercially available sand of fraction 0.6–
1.2 mm; coarser material – fine gravel – was spread on
the bottom of the sand layer to create hydraulic condi-
tions similar to the real sewer pipes. After each insertion
the sand was spread and finely compacted; then water
was discharged approximately 20 minutes through
the pipe to saturate the sand layer and to naturally form
the top of the sand layer. To stabilise the velocity and to
prevent the water level drop connected with sand out-
wash, it was necessary to form a small weir at the end of
the pipe.
In total, 4 sets of hydraulic experiments were performed
with layer thickness of 0 mm (no sediments), 8.5 mm of
sand sediment (3.4% of the pipe diameter), 25 mm (10%)
and 35 mm (14%) of sand sediment. The layer thickness
was measured with a portable calliper at the locations of
the openings in the experimental circular flume with
accuracy of 0.1 mm. For each thickness of the sand layer
sediment a set of tracer experiment was performed with
different discharges ranging approximately from
0.14 l s- 1 up to 2.5 l s-1. The upper discharge limit was set
up individually for each experiment and with respect
the sand wash-out.
The dispersion (tracer) experiments were performed
Sokáč, M., Velísková, Y.: Impact of roughness changes on contaminant transport in sewers
147
using the Rhodamine and the salt as tracers, for the con-
centration measurement there were used a fluorometric
and a conductivity probe. The fluorometric probe (Turner
designs, Inc.) has declared mini-mum detection limit 0.01
ppb and linear range 0–1000 ppb (linearity 0.99 R2).
The conductivity probe has a detection range from
1 µS cm-1 up to 1000 mS cm-1, manufacturer (WTW)
typically declares the accuracy for the probes of this type
±0.5% of measured value. The probes were placed at
the pipe end, approximately 200 mm prior the weir at
the pipe end. Tracers were dosed manually at the pipe
beginning.
Each tracer experiment (for each combination of the layer
thickness and discharge) was repeated five times. The da-
ta were measured in one second interval and they were
saved automatically in the storage unit of the corres-
ponding measuring device.
During evaluation of the measured data we noticed, that
the fluorometric probe responded better to the concen-
tration changes, its response time was minimal, whereas
the conductivity probe had the response time about 2–3
secs. Moreover, the measured values were probably time-
averaged by the device software. Because of this, we used
only the measured data from the fluorometric probe in
the evaluation process.
Results and discussion
Five tracer experiments, measured for the same discharge
and deposit layer thickness, form one dataset. The exam-
ple of such dataset is on the Fig. 2. Each measured tracer
experiment was evaluated to determine the dispersion
parameters according the Eq. (3) and Eq. (4). For
the numeric evaluation, the statistical approach was used.
The best approximation between measured and modelled
data, i.e. the optimal set of dispersion parameters was
determined searching the minimal root square mean error
(RMSE). For the numeric optimisation procedure,
the built-in function Solver in MS Excel environment
was used.
The dispersion parameters, evaluated from five tracer
experiments were averaged. The complete results are
shown in Table 1. Graphical evaluation of the experiment
results can be seen on the Fig. 3, 4, 5 and 6.
Fig. 1. Hydraulic scheme of the experimental device.
Fig. 2. Example of a dataset (a) and detail of a single experiment concentration time-
course (b).
12 m
Upstream
storage tank
Downstream
storage tank
Circular pipe DN 250 mm
Water inflow
Water outflow
0
10
20
30
40
50
60
70
0100 200 300 400 500 600 700
RFUB [-]
time [sec]
0
10
20
30
40
50
60
70
525 527 529 531 533 535 537 539 541 543 545
RFUB [-]
time [sec]
a)
b)
Acta Hydrologica Slovaca, Volume 21, No. 2, 2020, 145 – 151
148
Table 1. Results of the tracer experiments
sediment
Dataset Nr.
Water
depth
Discharge
Velocity
Dx
Dx,G
[-]
[mm]
[l s-1]
[m s-1]
[m2 s−1]
[m2 s−1]
sediment 0 mm
37
10.4
0.145
0.211
0.011
0.016
38
15.5
0.422
0.293
0.008
0.013
11
19.6
0.505
0.324
0.008
0.014
12
24
0.839
0.361
0.008
0.013
13
29.6
1.170
0.385
0.009
0.015
14
34.4
1.628
0.397
0.011
0.018
15
40.3
2.237
0.458
0.014
0.023
sediment 8.5
mm
20
7.7
0.147
0.181
0.015
0.026
20.1
16.6
0.410
0.232
0.010
0.016
21
20.6
0.589
0.270
0.008
0.014
22
24.7
0.799
0.306
0.008
0.013
23
30.7
1.114
0.343
0.008
0.013
sediment 25
mm
28
5.9
0.140
0.157
0.021
0.038
24
14.3
0.392
0.181
0.013
0.022
25
18.1
0.600
0.220
0.008
0.013
26
20.2
0.794
0.260
0.007
0.012
27
24.6
1.227
0.330
0.007
0.013
sediment 35 mm
31
9.1
0.141
0.084
0.044
0.072
32
14.2
0.410
0.155
0.015
0.024
33
18.2
0.633
0.188
0.010
0.017
34
21.1
0.876
0.224
0.008
0.014
35
25.6
1.280
0.270
0.009
0.015
36
30.2
2.070
0.370
0.012
0.021
Fig. 3. Results of tracer experiments (Dx vs discharge Q).
From these figures it can be seen that the course of all
evaluated dependencies is the same. The only difference
is in the values of the dispersion coefficients: the values
determined by using the Gaussian distribution are
generally smaller than the values of the coefficient
according to the distribution by Gumbel.
Interestingly, results of the tracer experiments also show
that the value of the dispersion coefficient in the hydrau-
lic conditions of circular sewer pipe with sediment and
deposits reaches its minimal value in certain range of
velocities (discharges), which are definitely not close to
the minimal velocity. We assume that this phenomenon
0.0000
0.0050
0.0100
0.0150
0.0200
0.0250
0.0300
0.0350
0.0400
0.0450
0.0500
0.000 0.500 1.000 1.500 2.000 2.500
Dx [m2.s-1]
Q [l.s-1]
sediment 0 mm
sediment 8.5 mm
sediment 25 mm
sediment 35 mm
Sokáč, M., Velísková, Y.: Impact of roughness changes on contaminant transport in sewers
149
Fig. 4. Results of tracer experiments (Dx, G vs discharge Q).
Fig. 5. Results of tracer experiments (Dx vs velocity).
can be caused due to specific hydrodynamic condition of
the flow, which varies at shallow depths. However, this
assumption needs to be further analysed.
In this study, we have tried to define the point with
the minimum value of the dispersion coefficient, which
has been not easy. One of the possible ways can be
definition based on the Reynolds number, eventually
based on geometric characteristics of the streambed (e.g.
depth / width ratio).
In our case we have observed some dependency between
the Reynolds number and the minimal value of
the dispersion coefficient: the minimal values of
the longitudinal dispersion coefficient occur for both
applied distribution in the Reynolds number range from
4500 up to 10000 (Fig. 7 and 8).
Conclusions
The aim of this paper was to present the partial results of
the study concerning dispersion processes in water flows
with low velocity and occurrence of sediments or
deposits. These results were obtained from the analysis
of data from experiments in laboratory conditions. In this
analysis there were used values of the longitudinal
dispersion coefficient as a characteristic of mixing rate of
flowing water. There were used two ways of their
determination: by using Gaussian and Gumbel statistical
distribution. These parameters were compared or put in
the dependency with values of discharges and velocities
in the various thicknesses of bed sediments conditions.
Obtained values of the longitudinal dispersion coefficient
0.0000
0.0100
0.0200
0.0300
0.0400
0.0500
0.0600
0.0700
0.0800
0.000 0.500 1.000 1.500 2.000 2.500 3.000 3.500
GUMBEL Dx [m2.s-1 ]
Q [l.s-1]
sediment 0 mm
sediment 8.5 mm
sediment 25 mm
sediment 35 mm
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0.045
0.050
0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
Dx [m2.s-1]
v [m.s-1]
sediment 0 mm
sediment 8.5 mm
sediment 25 mm
sediment 35 mm
Acta Hydrologica Slovaca, Volume 21, No. 2, 2020, 145 – 151
150
have had a similar course of mentioned dependencies in
both cases of used distributions, only values determined
by using the Gaussian distribution are generally smaller
than the values of the coefficient according to
the distribution by Gumbel distribution. Results of
the tracer experiments also have showed, that the value
of the longitudinal dispersion coefficient in the hydraulic
conditions of circular sewer pipe with sediment and
deposits reaches its minimal value not in or close to
the minimal velocity. Trying to define the point with
the minimum value of this coefficient, we used
the Reynolds number Re and analysed dependency of Re
and Dx, eventually Dx,G . Results of analysis have showed
that minimal values of the longitudinal dispersion
coefficient occur in the Reynolds number range (4500–
10000).
Fig. 6. Results of tracer experiments (Dx,G vs velocity).
Fig. 7. Results of tracer experiments (Dx vs Re).
0.0000
0.0100
0.0200
0.0300
0.0400
0.0500
0.0600
0.0700
0.0800
0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500
GUMBEL Dx [m2.s-1]
v [m.s-1]
sediment 0 mm
sediment 8.5 mm
sediment 25 mm
sediment 35 mm
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0.045
0.050
- 2 000 4 000 6 000 8 000 10 000 12 000 14 000 16 000 18 000 20 000
Dx [m2.s-1]
Re [-]
sediment 0 mm
sediment 8.5 mm
sediment 25 mm
sediment 35 mm
Sokáč, M., Velísková, Y.: Impact of roughness changes on contaminant transport in sewers
151
Fig. 8. Results of tracer experiments (Dx,G vs Re).
Acknowledgment
This work was supported by the Scientific Grant Agency
VEGA–grant number VEGA 2/0085/20, and by
the project H2020–“SYSTEM”, grant agreement No.
787128.
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Doc. Ing. Marek Sokáč, PhD. (*corresponding author, e-mail: sokac@uh.savba.sk)
Ing. Yvetta Velísková, PhD.
Institute of Hydrology SAS
Dúbravská cesta 9
84104 Bratislava
Slovak Republic
0.000
0.010
0.020
0.030
0.040
0.050
0.060
0.070
0.080
- 2 000 4 000 6 000 8 000 10 000 12 000 14 000 16 000 18 000 20 000
GUMBEL Dx [m2.s-1]
Re [-]
sediment 0 mm
sediment 8.5 mm
sediment 25 mm
sediment 35 mm
