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Modeling and simulation sedimentation process using finite difference method

  • Mohammed Abed Naser EMAIL logo and Khalid Adel Abdulrazzaq
Published/Copyright: May 31, 2022

Abstract

The goal of this research is to develop a numerical model that can be used to simulate the sedimentation process under two scenarios: first, the flocculation unit is on duty, and second, the flocculation unit is out of commission. The general equation of flow and sediment transport were solved using the finite difference method, then coded using Matlab software. The result of this study was: the difference in removal efficiency between the coded model and operational model for each particle size dataset was very close, with a difference value of +3.01%, indicating that the model can be used to predict the removal efficiency of a rectangular sedimentation basin. The study also revealed that the critical particle size was 0.01 mm, which means that most particles with diameters larger than 0.01 mm settled due to physical force, while most particles with diameters smaller than 0.01 mm settled due to flocculation process. At 10 m from the inlet zone, the removal efficiency was more than 60% of the total removal rate, indicating that increasing basin length is not a cost-effective way to improve removal efficiency. The influence of the flocculation process appears at particle sizes smaller than 0.01 mm, which is a small percentage (10%) of sieve analysis test. When the percentage reaches 20%, the difference in accumulative removal efficiency rises from +3.57% to 11.1% at the AL-Muthana sedimentation unit.

1 Introduction

Sedimentation basins are one of the most important units of a water treatment plant (WTP), with the goal of removing the greatest amount of suspended solids in the water by passing it through a sedimentation basin in a specific amount of time [1]. The presence of suspended solids in water has a negative impact on water quality and its uses because it provides suitable conditions for the absorption of biological and chemical substances. These conditions provide microorganisms with a barrier against the chemical effect of chlorine, and the removal of these substances is an important process that receives a lot of attention in WTPs [2]. The concept of sedimentation process is based on the idea that if the weight of the suspended particles in water was greater than the buoyancy force, the particles would fall freely to the bottom of the basin and if the weight force was insufficient to achieve free settling, in this case the flocculation process would appear to improve the sedimentation process by flocculating the collided particles to form a large mass [3].

Since the nature of water is variable in terms of properties, the mathematical modeling process provides a good alternative for observing the dynamic behavior of water in sedimentation basins and predicting the performance of treatment units by describing flow patterns based on momentum and continuity equations and then these models are tested using simulation tools [4]. Simulating the operation of a real-world process or system over time is known as a simulation where the models are required for simulations in which the model represents the key characteristics or behaviors of the selected system or process, whereas the simulation represents the model’s evolution over time [5]. Due to the importance of the sedimentation process, many numerical models have been developed to simulate the sedimentation process, providing a better understanding of flow characteristics and sediment transport, as well as studying the factors that affect the sedimentation process by solving flow governing equations using the finite element method and the finite difference method [6]. The goal of this research is to create a numerical model that can be used to simulate sedimentation and flocculation units and predict removal efficiency using the finite difference method and Matlab software.

2 Materials and methods

  • The Leibniz integral rule was used to derive the main equations governing the flow process.

    Depth-averaged continuity flow equation:

    (1) h u x + h t = 0 .

    Depth-averaged momentum flow equation:

    (2) 1 2 g u 2 x + h x + u 2 g h C 2 = 0 .

    Sediment transport equation:

    (3) ε z s z z b = β ω ( s s ) .

    Sediment carrying capacity

    (4) s = k u 3 h ω m .

    Sediment continuity equation:

    (5) s x h u = β ω ( s s ) = ρ d z s t .

  • The finite differential method was used to solve the unknown limits in momentum and sediment transport equations using Taylor series.

  • The experimental model’s results were compared to the results of an operating model using the same data and conditions [7].

  • The simulation process was applied on the sedimentation unit of Al-Muthanna WTP using two scenarios; the first flocculation unit is operational, while the second is not.

  • Operational and coded models’ data.

Table 1 and Figure 1 listed the input data of operating model and definition sketch of operation model that come from ref. [7], while the input data of operating model of AL-Muthana WTP were same except for the basin dimensions which were: length: L = 46 m, width: B = 11 m, longitudinal slope 0.01%, total tank elevation = 4.5 m, tank elevation at bottom: zg = 2 m, actual water depth: h = 2 m, manning coefficient: n = 0.012 and flow rate for one basin was 0.231  m 3 / s .

Table 1

Data form operational model [7]

Data input Data description Value
Coefficient n Mining coefficient reference 0.011
k Represents the flow’s ability to carry sediment 0.01
k 1 Empirical coefficient 0.513
k 2 Empirical coefficient 0.008
nd Between 1.8 and 2.0 empirical exponent 1.9
dr Represents a reference diameter ranging from 0.011 to 0.022. 0.022
r Empirical exponent between 3 and 5 4.65
S P 1.5
B The ratio of deposited material at tank bottom to the remaining matter in the flow 1.2
t Time interval 65 (s)
x Space interval 0.1 (m)
Dimensions B Tank width 3 (m)
L Tank length 30 (m)
h Tank elevation 4 (m)
H Actual water depth 2 (m)
zg Tank elevation at bottom 2 (m)
Flow characteristics Q Influent discharge to units 0.088 (m3/s)
S Influent suspended solid concentration 0.5 (kg/m3)
ρ s Dry sediment mass density 1,200 (kg/m3)
ρ w Water mass density 1,000 (kg/m3)
Group D (mm) Partial settling velocity (m/s) PSD%
1 <0.0052 0.0000095 2
2 0.0052–0.01 0.0000536 8
3 0.01–0.026 0.000299 17
4 0.026–0.05 0.00134 22
5 0.05–0. 12 0.00536 20
6 0. 12–0. 26 0.0172 14
7 0. 26–0.52 0.0404 11
8 0.52–1 0.0828 6
Figure 1 
               Definition sketch [7].
Figure 1

Definition sketch [7].

3 Results and discussion

Depending on the previous steps, the removal efficiency of the rectangular sediment basin was predicted using Matlab software in which the flow and design characteristics represent the main influence factor to build this model. The applied part consisted of: first ensuring the accuracy of the model’s work by comparing with an operational model, and second simulating the sedimentation unit of AL-Muthanna WTP to predict the removal efficiency with and without flocculation unit. This model will aid researchers in predicting the removal efficiency and amount of sludge generated in the rectangular sedimentation basins.

Table 2 and Figures 25 list the results of comparison in removal efficiency between coded model and operational model for each dataset of particle size and the results were very close with small difference indicating that the models can be used to predict the removal efficiency of rectangular sedimentation basin, so that the total accumulative removal efficiency for these models were 73.76 and 76.77%, respectively.

Table 2

Removal efficiency for each particle size of operational and coded models with and without flocculation unit

Data Particle size (mm) RE operation (%) RE develop (%) RE with floc.
1 <0.005 1.03 1.135 17.69
2 0.005–0.01 6.4 6.36 25.67
3 0.01–0.025 30.76 30.73 31.26
4 0.025–0.05 80.69 80.87 82.15
5 0.05–0.1 99.86 99.87 99.89
6 0.1–0.25 100 100 100
7 0.25–0.5 100 100 100
8 0.5–1 100 100 100
Total 73.76% 74.5% 76.77%
Figure 2 
               Accumulative removal efficiency with flocculation process for coded model.
Figure 2

Accumulative removal efficiency with flocculation process for coded model.

Figure 3 
               Removal efficiency for each particle size with flocculation process for coded model.
Figure 3

Removal efficiency for each particle size with flocculation process for coded model.

Figure 4 
               Accumulative removal efficiency without flocculation process for coded model.
Figure 4

Accumulative removal efficiency without flocculation process for coded model.

Figure 5 
               Removal efficiency for each particle size without flocculation process for coded model.
Figure 5

Removal efficiency for each particle size without flocculation process for coded model.

Table 3 and Figures 6 and 7 list the removal rate of each particle size and accumulative removal efficiency of AL-Muthana WTP sedimentation basin with two scenario: First, the flocculation unit was on duty, with accumulative rate of 86.28%, and second, the flocculation unit was out of service with accumulative rate of 82.72% in which the influence of flocculation unit on removal efficiency for each dataset of particle size of 0.005–0.01 mm was very effective. So this stage appears the important in the flocculation process to improve settling of the colloidal particles. Therefore, the range of removal efficiency at these diameters was 34.14–47.03% at first approach (flocculation unit on duty) and 2.455–13.14% at second approach (flocculation unit out of service). The flocculation unit improves the sedimentation process by converting colloidal particles that cannot settle naturally to floc that can fall freely due to physical forces [8]. The table also shows that the 0.01 mm diameter represents the critical particle size, which means that most of the particles with diameters greater than 0.01 mm settled due to physical force, while most of the particles with diameters less than .01 mm settled due to the flocculation process.

Table 3

Two scenarios of AL-Muthana WTP removal efficiency

Data set Particle size (mm) Particle size disruption (%) Removal efficiency without flocculation unit (%) Removal efficiency (coded model) with flocculation (%)
1 <0.005 2 2.455 34.14
2 0.005–0.01 8 13.14 47.03
3 0.01–0.025 17 54.46 55.2
4 0.025–0.05 22 97.09 97.51
5 0.05–0.1 20 100 100
6 0.1–0.25 14 100 100
7 0.25–0.5 11 100 100
8 0.5–1 6 100 100
Total accumulative 2 82.72 86.28
Figure 6 
               Removal efficiency for each particle size of AL-Muthana sedimentation unit with flocculation process.
Figure 6

Removal efficiency for each particle size of AL-Muthana sedimentation unit with flocculation process.

Figure 7 
               Removal efficiency for each particle size of AL-Muthana sedimentation basin without flocculation process.
Figure 7

Removal efficiency for each particle size of AL-Muthana sedimentation basin without flocculation process.

Figure 8 depicts the relationship between accumulative removal rate and tank length with and without flocculation process in which the accumulative removal efficiency at 10 m from inlet zone was achieved to be more than 60% of the total accumulative removal rate which means that increasing the basin length is not a cost-effective way to improve the removal efficiency, this was consistent with the researcher’s findings [9].

Figure 8 
               Difference in accumulative removal efficiency between first and second scenarios.
Figure 8

Difference in accumulative removal efficiency between first and second scenarios.

The figure also shows that the difference between the accumulative removal efficiency for first and second scenarios was +3.56% which represents a small value because the influence of flocculation process appears at dataset of particle size of 0.01 mm in which these data have small percentage (10%) of total particle size disruption of sieve analysis test, therefore the difference in removal rate was small. When the percentage of these particle size disruption rises to 20% as a result of sieve analysis test, the difference in accumulative removal efficiency between the scenarios will be raised [10]. In other words, because the concentration of the suspended materials with diameters of 0.01 mm was very low at influent raw water, the difference in removal efficiency between the scenarios was small; however, when the percentage of these particles in the coming flow is high, the effect of the flocculation process will be visible due to the large difference in removal percentage [11].

4 Conclusion

  1. The difference in accumulative removal efficiency between coded and operational models was very close, with values of +3.01% and +0.74% in cases of flocculation unit on duty and flocculation unit off duty, respectively, indicating that the model can be used to predict removal rate at rectangular sedimentation units.

  2. The accumulative removal efficiency at 10 m from the inlet zone was achieved to be more than 60% of the total accumulative removal rate of AL-Muthana sedimentation basin that means increasing basin length is not a cost-effective way to improve the removal efficiency.

  3. The 0.01 mm diameter represents the critical particle size, which means that most of the particles with diameters greater than 0.01 mm settled due to physical force, while most of the particles with diameters less than 0.01 mm settled due to the flocculation process.

  4. The difference in accumulative removal efficiency between the first and second scenarios of the AL-Muthana WTP sedimentation unit was +3.56% which is a small value because the influence of the flocculation process appears at particle sizes smaller than 0.01 mm, which is a small percentage (10%) of sieve analysis test. When the percentage reaches 20%, the difference in accumulative removal efficiency rises to 11.1%.

  1. Funding information: The authors state no funding involved.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: Authors state no conflict of interest.

References

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Received: 2022-02-19
Revised: 2022-03-21
Accepted: 2022-04-07
Published Online: 2022-05-31

© 2022 Mohammed Abed Naser and Khalid Adel Abdulrazzaq, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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