# A Computational Fluid Dynamics Simulation Model of Sediment Deposition in a Storage Reservoir Subject to Water Withdrawal

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Site Description

^{9}m

^{3}, including 2.95 × 10

^{9}m

^{3}as dead storage. The main inflow and sediment load that feeds the Mosul Dam reservoir is the Tigris River. In addition, there are ten seasonal valleys on both sides of the reservoir adding flow and sediment load, which makes the reservoir flow regime more complex (Figure 1), the topography, Digital Elevation Model (DEM) of the area was also shown in the figure. The average annual sediment load that was delivered to the Mosul Dam reservoir during the period 1986–2011 is about 48 × 10

^{6}m

^{3}[25].

^{3}/s, and it works between the 5 m head at 305 m a.s.l (minimum reservoir operation level) to 30 m at normal reservoir operation level (330 m a.s.l). The main component of the station is the intake sediment trap; its dimensions about 150 m long and 80 m wide at the base, 100 m wide with sides. The geometry and elevations of the sediment trapping basin is shown in Figure 3. The intake structure consists of three rectangular tunnels of 3 × 3.5 m for each, which changes to a circular section 3.5 m in diameter; the final main part is the central pumping station [21]. This plant suffers from sediment being deposited into the sediment trap basin inside the intake and suction pipes, which leads to a reduction in the pumping rate and plant efficiency. The contribution of the valleys’ flow and withdrawal of flow towards the pumping plant makes the flow regime more complicated, especially near these locations. It is difficult and inefficient to study and analyse such cases using a 1-D model. Only a 2-D or a 3-D model can simulate such cases. To acquire more details on the flow and sediment transport distribution and concentration in all directions along the flow path, a 3-D model was applied in this study.

## 3. Computational Fluid Dynamics Model

^{3})$;P$ is the dynamic pressure (M/L

^{2}/T)$;{\delta}_{ij}$ is the kronecker delta, which is equal to 1 if i equals j and 0 if not; and $\overline{{v}_{i}}\overline{{v}_{j}}$ is the Reynolds stress. The Reynolds stress has been modelled with eddy viscosity and the standard k–ε model in the following form [14]:

^{3}/L

^{3}; $t$ is the time (T); ${\omega}_{i}$ is the fall velocity of particle size i (L/T); $\Gamma $ is the coefficient of diffusion; and ${F}_{R,i}$ is the pickup rate of sediment size i, due to erosion.

^{3}/L

^{3}), $\tau $ is the bed shear stress (M/L/T

^{2}), ${\tau}_{c}$ is the critical bed shear stress of the sediment particle movement (M/L/T

^{2}), ${D}_{i}$ is the ith sediment particle diameter (L), ${\rho}_{s}$ is the sediment density (M/L

^{3}), and $\nu $ is the kinematic viscosity coefficient (L

^{2}/T).

_{R}) for a certain particle size i can be defined by the following equation [30]:

## 4. Data and Model Setup

^{3}[25], was considered for model validation.

^{2}at the normal water level), and long simulation period (25 years). These large grids can be rationalized due to wide reservoir sections (ranged from 3 to 12 km at the normal operation level), so that there is not big variation in bed level within the considered grid size. Furthermore, a previous study [14] applied the same SSIIM model, and indicated that considering fine cells sizes of the geometry did not give appreciable changes in the results, so the computational time was multiplied. However, for the area of greatest interest neighboring the intake, a nested block was added. The nested block was represented by 45 cells in the streamwise (x) direction, 22 cells in the transversal (y) direction, and a maximum of 10 cells in the vertical direction (z). A total of 990 cells represent the horizontal layer of the area near the intake, and 10 vertical cells were used to identify the flow depth. The grid dimensions are 10 × 10 m, which covers an area of 99 × 10

^{3}m

^{2}.

^{3}/s to 90 m

^{3}/s. Meanwhile, the reservoir water level ranged between about 332 m a.s.l and 300 m a.s.l. The daily assessment of surface runoff and carried sediment loads were also considered for the different watershed valleys, which were represented as separate blocks connected to the main reservoir. Based on a grain size distribution analysis of samples that were taken from different locations of the study area, previous samples that have been analysed in [35,36]. In addition, the surface soil and runoff sediment load analysis [21], as well as the main river sediment load distribution [37], the range of the considered grain size distribution and fall velocity for all sediment inflow groups is shown in Table 1. The particles’ fall velocities were calculated based on the formula presented by Ponce [38]. The fraction of each size is dependent on the size of the sediment load distribution of the reflected block. As a sample of the fraction of the sediment sizes, the fractions of the measured sediment sizes for the main river flow (Block 1) are shown in Table 1. The empirical formula presented by van Raijn [39] was used to assess the roughness of the reservoir bed based on the size distribution of the bed material’s particles.

## 5. Model Validation

^{3}; this value represents about 9% of the total reservoir storage capacity. Furthermore, the average value of the sediment trap efficiency for the simulated period was about 92%. This simulated trapped sediment (1.04 km

^{3}) indicates a good model performance for a long period of simulation compared to measured values (1.14 km

^{3}[25]). The main difference is due to neglecting bed load particles larger than 0.45 mm, which was done to reduce the number of considered particles sizes in the simulation to 11, in order to decrease the simulation’s running time and increase the computational capacity. The considered maximum limit of the particle sizes is based on the maximum particle size carried as bed load and suspended load by the main watercourses around the reservoir, which is 0.4 mm [21], while the median grain size diameter, d

_{50}value of the bed load particles is 12.4 mm [25]. An underestimation of the deposited sediment may also be attributed to an assessment of the sediment inflow of the main flow river based on the created sediment rating curve, as well as the load carried by watercourses around the reservoir; this was assessed based on the simulated values by the SWAT model. The other important variable that was considered for model validation is the suspended load measurement near the intake structure. The second measured values used for model validation were the sediment concentration measurements in [21] at different depths in the reservoir near the intake at two different times, as shown in Table 2. The PBIAS between the measured and simulated sediment concentration was −3.6% (less than ± 10%), indicating very good model performance [41]. Furthermore, the paired t-test value was 0.43 (less than the tabulated value (2) at a 0.05 probability level), indicating that there is no significant difference.

## 6. Model Sensitivity to Grid Size and Time Steps

## 7. Results and Discussion

^{3}of the left bank soil of the Mosul Dam Reservoir were eroded during the flood wave of 1988, and that the right bank river section is characterized by a steep slope. The values of the considered statistical criteria (percent bias and t-test) are used to evaluate the deposited sediment depths in the selected sections, as shown in Table 4.

^{2}) (Figure 5a) was 5.2 m. In comparison with the simulated values, the sediment depth deposition at the intake ranged from 3.1 m to 4.9 m, while the average value for the whole the area was 4.5 m. The sediment depth measurements at different points in the trapping basin were compared with the simulated values. The results indicate that the PBIAS between the measured and observed values is 3.6% (less than 10%), while the t-test value is 1.41, less than the critical tabulated values at a 0.05 probability level. This indicates that there is no significant difference between the observed and simulated values. The deposited sediment volume in the considered area, shown in Figure 5a,b, are 0.111 × 10

^{6}m

^{3}and 0.096 × 10

^{6}m

^{3}for the observed and simulated values, respectively.

## 8. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The topography (Digital Elevation Model (DEM)) of the Mosul Dam reservoir surrounded by the main valleys.

**Figure 3.**Geometry and elevations of the simulated sediment trap basin of the Mosul Dam pumping station in 1986.

**Figure 4.**Measured and simulated bed levels for the four selected sections, as follows: (

**a**) section 1, (

**b**) section 2, (

**c**) section 3, and (

**d**) section 4.

**Figure 5.**(

**a**) Measured sediment elevations in the sediment trap basin in February 2001 (based on measured values [21]); (

**b**) Simulated sediment elevations in the sediment trap basin in February 2001 (sediment simulations in intakes with multiblock option (SSIIM2)).

No. | Particle Size (mm) | Fall Velocity (mm/s) | Fraction (%) |
---|---|---|---|

1 | 0.425 | 56.28 | 4.8 |

2 | 0.15 | 13.46 | 2.0 |

3 | 0.075 | 4.44 | 1.3 |

4 | 0.057 | 2.56 | 2.1 |

5 | 0.042 | 1.39 | 3.4 |

6 | 0.029 | 0.67 | 5.1 |

7 | 0.017 | 0.23 | 8.0 |

8 | 0.012 | 0.12 | 5.7 |

9 | 0.008 | 0.06 | 6.9 |

10 | 0.005 | 0.03 | 24.7 |

11 | 0.002 | 0.01 | 36.0 |

**Table 2.**Measured and simulated sediment concentration at different points in the front of the intake.

Point No. | Location | Date | Simulated Sediment Concentration (g/m^{3}) for Different Particles Sizes | Total Simulated Conc. (g/m ^{3}) | * Measured Conc. (g/m ^{3}) | |||
---|---|---|---|---|---|---|---|---|

0.002 (mm) | 0.005 (mm) | 0.008 (mm) | 0.012 (mm) | |||||

1 | In front of the intake (surface) | 8 February 2001 | 12.00 | 0.32 | 0.012 | 0.0007 | 12.4 | 9.5 |

2 | In front of the intake (2 m above the bed) | 8 February 2001 | 14.70 | 0.58 | 0.037 | 0.0024 | 15.4 | 17.0 |

3 | In front of the intake (near the bed) | 18 February 2001 | 17.30 | 0.92 | 0.078 | 0.0045 | 18.3 | 19.0 |

4 | In front of the intake (2 m above the bed) | 18 February 2001 | 16.80 | 0.86 | 0.071 | 0.0040 | 17.8 | 13.0 |

5 | In front of the intake (2 m below water surface) | 18 February 2001 | 15.20 | 0.64 | 0.043 | 0.0017 | 15.9 | 19.0 |

6 | In left side of the intake (2 m above the bed) | 18 February 2001 | 15.40 | 0.68 | 0.048 | 0.0021 | 16.2 | 19.0 |

7 | At 50 m front of the intake (2 m above the bed) | 18 February 2001 | 15.30 | 0.66 | 0.045 | 0.0020 | 16.0 | 20.0 |

8 | At 100 m front of the intake (2 m above the bed) | 18 February 2001 | 15.00 | 0.62 | 0.040 | 0.0015 | 15.6 | 9.0 |

9 | At 150 m front of the intake (2 m above the bed) | 18 February 2001 | 15.20 | 0.64 | 0.043 | 0.0018 | 15.9 | 13.0 |

Time Steps (s) | 7200 | 3600 | 1800 | 900 |
---|---|---|---|---|

Deposited sediment changes (%) | −0.7 | - | 3.4 | 5.9 |

**Table 4.**Measured and simulated sediment thickness at the four selected sections and the considered statistical criteria.

Section No. | Section Location Upstream of the Dam Axis (km) | Average Measured Sediment Thickness (m) | Simulated Sediment Depth (m) | Percent Bias (PBIAS, %) | t-Test Value |
---|---|---|---|---|---|

1 | 55.5 | 10.5 | 9.7 | 6.5 | 1.41 |

2 | 51.0 | 4.9 | 4.7 | 4.8 | 0.38 |

3 | 42.0 | 4.5 | 4.4 | −9.1 | 0.56 |

4 | 6.5 | 5.4 | 1.1 | 80.7 | 2.11 |

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**MDPI and ACS Style**

Mohammad, M.E.; Al-Ansari, N.; Knutsson, S.; Laue, J.
A Computational Fluid Dynamics Simulation Model of Sediment Deposition in a Storage Reservoir Subject to Water Withdrawal. *Water* **2020**, *12*, 959.
https://doi.org/10.3390/w12040959

**AMA Style**

Mohammad ME, Al-Ansari N, Knutsson S, Laue J.
A Computational Fluid Dynamics Simulation Model of Sediment Deposition in a Storage Reservoir Subject to Water Withdrawal. *Water*. 2020; 12(4):959.
https://doi.org/10.3390/w12040959

**Chicago/Turabian Style**

Mohammad, Mohammad E., Nadhir Al-Ansari, Sven Knutsson, and Jan Laue.
2020. "A Computational Fluid Dynamics Simulation Model of Sediment Deposition in a Storage Reservoir Subject to Water Withdrawal" *Water* 12, no. 4: 959.
https://doi.org/10.3390/w12040959