# Modelling Faecal Sludge Dewatering Processes in Drying Beds Based on the Results from Tete, Mozambique

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Model Development

#### 2.1.1. Theoretical Overview of the Sludge Dewatering Processes of Drying Beds

#### Drainage Process

#### Evaporation

#### 2.1.2. Model Scope and Key Assumptions

- Sludge is considered heterogeneous, with solid and fluid phases. The water mass in the sludge is present in free, interstitial, adsorbed and intracellular fractions.
- Air is considered to be an ideal gas with a constant composition that flows perpendicularly to the SDB with a certain temperature (${T}_{air}$), wind speed (${\omega}_{g}$) and relative humidity ($HR$).
- Drying beds are subject to atmospheric pressure and temperature.
- During SDB loading, the influence of the settling velocity on the drainage process is neglectable.
- Sludge solids are deposited over the entire surface of the filter medium, forming a homogeneous porous layer with a constant permeability.
- The effect of biochemical transformations that may occur throughout the dewatering process is neglected both in the sludge and inside the filter medium.
- Drainage processes start after the cake is formed, corresponding with the intermediate phase.
- The energy available for the drainage is constant.
- The mass of solids remains constant as evaporation occurs.
- Evaporation occurs from the interfacial area of the sludge layer, neglecting the transfer of mass and energy through the side walls and through the bottom of the drying beds.

#### 2.1.3. Mathematical Formulation of the Sludge Dewatering Process

#### Initial Water Mass

#### Precipitated Water Mass

#### Drained Water Mass

#### Evaporated Water Mass

- (a)
- turbulent regime ($5\times {10}^{5}<{\mathrm{R}}_{\mathrm{e}}<\infty $; $0.8<{\mathrm{S}}_{\mathrm{c}}<\infty $):

- (b)
- laminar regime ($0<{\mathrm{R}}_{\mathrm{e}}\le 5\times {10}^{5}$; $0<{\mathrm{S}}_{\mathrm{c}}<\infty $):

_{1}reflecting the effect of the interfacial layer.

#### 2.2. Pilot Facility

^{2}of area and was installed on a brick base at approximately 0.5 m from the ground (Figure 4). This setting avoided contact with the ground and the significant heat changes that could result from it. In addition, it allowed the installation of a plastic container underneath the SDB to collect and quantify the drained water.

_{m}is the thickness of the filter medium (m), h is the height difference between the constant level N and the discharge height H (m), A is the bed section area (m

^{2}), Q is the flow rate (m

^{3}/s), V is the water volume (m

^{3}) and t is the time elapsed for filling a given volume (s). The experimental procedure is described in detail in [27]. The results indicated a mean K value of 4 × 10

^{−4}m/s for the three SDB units.

## 3. Experimental Results

## 4. Discussion of the Experimental Results

#### 4.1. Sludge Field Capacity

#### 4.2. Total Drainage Time

#### 4.3. Filter Medium Resistance

_{m}) was estimated from Equation (11) based on the results of the hydraulic conductivity tests carried out, as described in Section 2.2. The value found corresponded with about 1% of the total resistance.

#### 4.4. Cake Specific Resistance

#### 4.5. Mass Transfer Coefficient

^{2}.

## 5. Conclusions

_{d}(the empirical constant reflecting the resistance to the water flow) in Equation (6), two empirical parameters, K

_{d1}and K

_{d2}, may be considered. These would reflect, respectively, the cake resistance during the intermediate phase and the cake resistance during the final drainage phase (being t

_{d1}and t

_{d2}, respectively, the time of completing the intermediate phase and the time to complete the drainage process). The field studies should be planned considering those purposes.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**Sludge moisture content evolution (TH_Real) and water losses due to drainage (TH_Drenagem) for tests ENS01 to ENS06.

**Figure 8.**Comparison between the experimental results and the simulation results (tests EN01 to EN06).

Period | Cycle | SDB Ident. | Test Ident | Sludge Source | Initial Sludge Depth (m) |
---|---|---|---|---|---|

9 May 2017 to 7 June 2017 | 1st | LS01 LS02 LS03 | ENS01 ENS02 ENS03 | ST01 ST01 ST01 + PT01 | 0.20 0.35 0.56 |

22 June 2017 to 10 July 2017 | 2nd | LS01 | ENS04 | ST02 | 0.30 |

1 August 2017 to 17 August 2017 | 3rd | LS01 LS03 | ENS05 ENS06 | ST03 ST03 + PT01 | 0.30 0.32 |

Variable | ENS01 | ENS02 | ENS03 | ENS04 | ENS05 | ENS06 |
---|---|---|---|---|---|---|

Sludge type | ST | ST | ST + PT | ST | ST | ST + PT |

Loading date | 9 May 2017 | 9 May 2017 | 9 May 2017 | 22 June 2017 | 1 August 2017 | 1 August 2017 |

Conductivity (µS/cm) | 1528 | 1528 | 1959 | 908 | 3790 | 2740 |

Average sludge temperature (°C) | 28.8 | 28.8 | 28.5 | 27.2 | 28.0 | 23.5 |

pH | 7.8 | 7.8 | 7.5 | 6.8 | 7.6 | 8.0 |

Initial solid content (%) | 5.2 | 5.2 | 4.0 | 5.4 | 2.0 | 2.0 |

Air average temperature (°C) | 26.3 | 26.2 | 26.0 | 24.1 | 24.5 | 24.5 |

Air average humidity (%) | 63 | 62 | 62 | 66 | 64 | 64 |

Maximum solar insolation (hours/day) | 7 | 8 | 8 | 8 | 8 | 8 |

Average wind speed (km/h) | 14 | 13 | 13 | 11 | 10 | 10 |

Parameter | Unit | Determined Values |
---|---|---|

Mass transfer coefficient (${\mathrm{K}}_{\mathrm{x}}$) | kg/s/m^{2} | 0.007–0.013 |

Cake specific resistance $({\mathrm{R}}_{\mathrm{c}}$ $+{\mathrm{R}}_{\mathrm{m}}$) | m/kg | 2.3–6.6 × 10^{10} |

**Table 4.**Mean, standard deviation, variance and number of observed/modelled points for each test and for the global set of data.

ENS01 | ENS02 | ENS03 | ENS04 | ENS05 | ENS06 | Global | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Exp. | Model | Exp. | Model | Exp. | Model | Exp. | Model | Exp. | Model | Exp. | Model | Exp. | Model | |

Mean | 71.5 | 69.7 | 74.9 | 66.8 | 85.9 | 84.0 | 83.4 | 82.0 | 90.0 | 88.4 | 91.3 | 89.9 | 83.4 | 81.5 |

SD | 17.5 | 17.2 | 21.0 | 24.9 | 11.7 | 15.7 | 11.1 | 14.5 | 10.9 | 12.0 | 10.2 | 11.4 | 15.4 | 18.1 |

Var | 304.6 | 295.5 | 442.8 | 619.3 | 137.8 | 245.9 | 122.3 | 211.2 | 119.1 | 143.8 | 103.1 | 130.4 | 237.4 | 328.6 |

n | 12 | 13 | 19 | 24 | 25 | 31 | 17 | 20 | 17 | 17 | 17 | 17 | 107 | 107 |

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**MDPI and ACS Style**

Moiambo, O.; Mutevuie, R.; Ferreira, F.; Matos, J.
Modelling Faecal Sludge Dewatering Processes in Drying Beds Based on the Results from Tete, Mozambique. *Sustainability* **2021**, *13*, 8981.
https://doi.org/10.3390/su13168981

**AMA Style**

Moiambo O, Mutevuie R, Ferreira F, Matos J.
Modelling Faecal Sludge Dewatering Processes in Drying Beds Based on the Results from Tete, Mozambique. *Sustainability*. 2021; 13(16):8981.
https://doi.org/10.3390/su13168981

**Chicago/Turabian Style**

Moiambo, Osvaldo, Raúl Mutevuie, Filipa Ferreira, and José Matos.
2021. "Modelling Faecal Sludge Dewatering Processes in Drying Beds Based on the Results from Tete, Mozambique" *Sustainability* 13, no. 16: 8981.
https://doi.org/10.3390/su13168981