## Abstract

This study uses computational fluid dynamics (CFD) models for an improved performance of secondary settling tanks, taking as a case study the wastewater treatment plant (WWTP) of Souk-Ahras City, Northeastern Algeria. Unlike previous studies, which focused primarily on simulations of real-time clarifiers by independent measures, this study combines differentoperating criteria and geometric standards on clarifiers to estimate the ultimate capacity of secondary sedimentation tanks (SST). Numerical simulations were performed toassess the SST hydraulic performance under different conditions in order to (i) eliminate vortex zones; (ii) optimize the surface overflow rate (SOR) and predict sludge blanket height (SBH), and finally, (iii) estimate SST ultimate capacity. Based on the current configuration of the SST of Souk-Ahras WWTP, its hydraulic treatment capacity was found to be 49,000 m^{3}/d. The results obtained, which were validated by field observations, showed that optimizing the different parameters yields a significantly improved SST performance. Furthermore, the tests consideredwere shown to be satisfactorily correlated with SOR. Validation using the receiver operating characteristic (ROC) curve analysis yielded anarea under curve (AUC) value of 90%, implying thereby a reasonably good performance. Indeed, optimization resulted in increased solidremoval efficiency and increased SOR to 1.4 m.h^{−1} (compared to 0.8 m.h^{−1} in literature) without overflow beyond the SBH.

## HIGHLIGHTS

Secondary settling tanks (SST) may be achieved with a surface overflow rate (SOR) of 1.4 m·h

^{−1}, which exceeds the guide value for conventional configurations (0.8 m·h^{−1}).Computational fluid dynamics (CFD) was shown to be an interesting method for optimization of the capacity of circular SSTs.

The characterization of sludge settling is necessary to determine sedimentation velocities and evaluate purification efficiency.

## ABBREVIATIONS

- CFD
Computational fluid dynamics

- 2D
Two-dimensional

- SBH
Sludge blanket height

- SST
Secondary settling tank

- WWTP
Wastewater treatment plant

- SOR
Surface overflow rate

- ESS
Effluent suspended solids

*Q*_{r}Recycling flow rate

*Q*_{w}Waste flow rates

- HRT
Hydraulic residence time

- SS
Suspended solid

- BOD
Biochemical oxygen demand

- COD
Chemical oxygen demand

*R*Radius

*V*_{c}Corrected volume

- SVI
Sludge volume index

## SYMBOLS

*U*;*V*(m s^{−1})The components of the mean velocity over time in all directions

*p*(Pa)Pressure

*ρ*(kg m^{−3})Density of the fluid-solid mixture

*g*(m s^{−2})Acceleration due to gravity

*ν*_{t}(kg m^{−1}s^{−1})Eddy viscosity

*S*_{u}and*S*_{v}(Pa)The pressure forces acting on the fluid in the vertical and radial directions, respectively

*k*(m^{2}s^{−2})The turbulent kinetic energy

*ε*(m^{2}s^{−3})Turbulent kinetic energy dissipation rate

*ρ*_{p}(kg m^{−3})Density of dry particles

*ρ*_{r}(kg m^{−3})Reference density (clear water)

*X*(g/l)Concentration of suspended solids (SS)

*V*_{s}(m s^{−1})Speed of the particle settling

*ν*_{sy}(m s^{−1})Swirl effect of SS in the

*y*direction*D*_{h}(m)Diameter of the inlet pipe

- Re
_{D}_{h} Reynolds Number based on the hydraulic diameter

*μ*(Pa s)_{c}Dynamic viscosity

*V*(m/s)Average flow velocity

*r*(m)Radial coordinate

## INTRODUCTION

Increasing the performance of secondary settling tanks (SSTs) in wastewater treatment plants (WWTPs) is of paramount importance. Nevertheless, biological processes in SSTs are delicate and sometimes difficult to control (Dairi *et al.* 2021). They may cause unforeseen situations, which impose costly interventions for the reorganization of the system (for example, phenomena of swelling of sludge in secondary sedimentation, or poisoning of biomass). However, the proper functioning of the activated sludge biological process goes beyond the liquid–solid separation phase (Gnirss *et al.* 1996; Cho *et al.* 2007), responsible for the separating of sludge from the aeration tanks by decantation. The settling of this sludge in a SST, also known as secondary clarifier or secondary sedimentation tank, is very slow and sensitive to different operating conditions. Its hydraulic design is therefore important and can in many cases be optimized. For this reason, dynamic simulation techniques have become a support in the design phases of new stations and in the renovation of existing WWTPs, and a tool for monitoring and evaluating the effectiveness of management choices.

Numerous decantation models, used to study flow fields and solids distribution in an SST, are available in the literature (Ekama 1997). Uni-dimensional (1D) models are the mostly used (Laikari 1989; Takács *et al.* 1991; Dupont & Henze 1992; Härtel & Pöpel 1992; Otterpohl & Freund 1992; Jeppsson 1996; Watts *et al.* 1996; Chancelier *et al.* 1997; Printemps *et al.* 2004). They treat the different sedimentation zones with the appropriate equations in homogeneous horizontal layers along a vertical axis.

More sophisticated modeling techniques, notably computational fluid dynamics (CFD), have been applied for clarifiers in order to overcome certain limitations of conventional modeling methods. Indeed, the use of CFD models for design and operation is an innovative technique intended to improve SST performance. It enables optimization of configuration, sludge blanket height (SBH), and surface overflow rates. CFD models offer a thorough understanding of the fluid dynamics and mixing patterns in SSTs, which is important for their optimum design and operation. They also make it feasible to test different operating scenarios and assess various SST configurations, which enables wastewater engineers to locate and resolve any blockages in the treatment process.

Larsen (1977) was the pioneer in applying CFD to simulate the hydrodynamics in settling tanks and set the framework for future CFD settling tank research. SST modeling technique is presented in the form of a grid or mesh with a set of cells. Using the continuity equation and the concentration of solids, all chemical and biological reactions are marked for each cell in the grid. This would imply that flow in any particular cell depends on what happens in the neighboring cells and on the borders of the basin.

The use of CFD models in SST design and operation provides a number of benefits, including:

- (1)
Improved SST performance: CFD models may enhance SST performance by optimizing surface overflow rates and SBH management, which results in increased clarifier efficiency and better overall treatment performance.

- (2)
Reduced operational expenses: CFD models may reduce operational costs and increase the sustainability of WWTPs by limiting energy consumption and reducing the need for manual adjustments.

- (3)
Enhanced treatment capacity: CFD models improve treatment capacity by optimizing SST designs, enabling WWTPs to handle higher volumes of wastewater more effectively.

During the past 30 years, CFD models have been developed and used to analyze the impact of hydrodynamics and the arrangement of internal features on the performance of SSTs. These models (i) consider different physical characteristics, such as the effects of turbulence and density currents, which would improve our knowledge of SSTs (Adams & Rodi 1990; Wells & LaLiberte 1998; Jayanti & Narayanan 2004), (ii) incorporate a mathematical structure in order to better describe turbulence mechanisms and buoyant flow modeling components (Adams & Rodi 1990; Bretscher *et al.* 1992; Lakehal *et al.* 1999; Griborio 2004), and (iii) rapidly converge to the optimum solution of the specified differential equations (Imam *et al.* 1983; Abdel-Gawad & McCorquodale 1984).

Compared to experimental studies, CFD simulations usually require lower cost and shorter time. To qualitatively examine the turbulence flow in the SST, however, early research often relied on basic turbulence models like the constant eddy viscosity model and the mixing length theory model due to the restricted computational speed and storage (Imam *et al.* 1983; Krebs 1991; Krebs *et al.* 1992, 1995). In sedimentation basins, in spite of relatively low flow velocities compared to other processes, turbulent flows, associated with high Reynolds numbers, may occur. Turbulence effects, created in the clarifier, can be represented by a variety of turbulence models, ranging from simple equations (Valioulis & List 1984; Krebs *et al.* 1995) to more complex differential equation models, such as k-ε model (Stamou *et al.* 1989; Dahl *et al.* 1994).

Different studies (Larsen 1977; Krebs 1991; Takás *et al.* 1991; Ekama 1997; Patziger *et al.* 2005; Bürger *et al.* 2011) dealt with the analysis of the performance of clarifiers, taking into account various constraints, including: (i) the geometry of the basins, (ii) the mass balance applied, and (iii) the hydrodynamic flow. Larsen (1977) presented the application of CFD for secondary settling in Sweden to show that the most important flow characteristic is the presence of density currents. These latter are mainly related to the differences in density of both phases present in the basins.

Other CFD models, based on sedimentation theory, were presented following the work of Larsen (1977). However, only a few of these models take density currents from the combination of flux with the transport equations of solid matter via a static equation. This combination, which is essential for the proper modeling of the flow in clarifiers, was first presented by Adams & Stamou (1988) and DeVantier & Larock (1987). Adams & Stamou (1987) applied the finite difference method, using the two-dimensional model in one of the sedimentation basins studied by Larsen (1977) to demonstrate the effect of including a buoyancy force term in the flow field. Without this term, the flow showed unidirectional behavior throughout the clarifier.

The effect of non-uniformity of solid particles was considered in the models of Zhou & McCorquodale (1992) and Lyn *et al.* (1992) through the double exponential speed equation of Takács *et al.* (1991). Lyn *et al.* (1992) applied the method proposed by Stamou *et al.* (1989) using a sedimentation rate corresponding to the different classes of sedimentation. Both models showed that (i) the flux field can be significantly changed by small differences in density and (ii) the non-uniformity of the materials to be decanted is critical to predict the displacement efficiency.

Rodi (1980) modeled the behavior of turbulent flow based on Navier–Stokes equations using the k-ε turbulence model. The latter confirms that the actual performance of the clarifier is strongly influenced by hydrodynamic and physical effects of both solid–liquid phases. Another study was developed by Szalai *et al.* (1994) using (CFD) to detect the height of the sludge bed and the swirl, where the results obtained were compared with the measurements of McCorquodale (1976). Griborio (2004) presented the importance of CFD techniques in predicting the performance of circular clarifiers of different geometric configurations.

The method usually adopted to simulate SSTs relied basically on real-time observation and control to characterize sludge settling and compare the efficiency of clarification under restricted conditions. Unlike previous studies, which focused primarily on simulations of real-time clarifiers by independent criteria, this study proposes a two-dimensional CFD model that combines operating criteria (SOR, SBH) and other geometric criteria on clarifiers and suggests improved surface overflow rate (SOR) to estimate the SST ultimate capacity. Indeed, one of the primary challenges in designing and operating circular clarifiers in WWTPs is to achieve high performance without exceeding the SOR limit. This is particularly crucial when design criteria rely solely on input speed.

This study is interested in making the best possible choices in terms of the design of future SST and optimizing the limit capacity of these structures for existing installations. We, therefore, seek to provide the WWTP managers with integrated information on how to optimize the operation of WWTP. CFD simulations are considered to optimize the design of circular clarifiers in the Souk-Ahras WWTP, Northeastern Algeria, under various tests and to explore the SOR limit, with the aim of preventing overflow beyond the secondary clarifier's boundary. This optimization approach in clarifiers is important for efficient and effective wastewater treatment. It maximizes clarification efficiency, prevents short-circuiting, reduces maintenance costs, and improves settling characteristics. Moreover, simulations are used to improve the treatment capacity of the Souk-Ahras WWTP, taking into account future extensions in terms of new inter-communal connections and transfers while respecting environmental standards for wastewater effluent disposal.

CFD simulations are also considered to ensure that the SST geometry does not present a risk of settling sludge at a SOR exceeding 0.8 m h^{−1}. In fact, this SOR value, recommended in several research studies for conventional SST design, may be exceeded in the case study of Souk-Ahras WWTP, characterized by particular operating conditions. It is important to note at this stage that SOR plays a critical role in controlling the SBH, which refers to the depth of settled solids at the bottom of the clarifier. This parameter (SBH) is a key indicator of clarifier performance and needs to be optimized. Indeed, a high SBH reflects poor settling and reduced effluent quality while a low value may be associated with a loss of solids and reduced treatment efficiency.

## MATERIAL AND METHODS

Field campaigns were conducted by the InfraRes Laboratory research team of the University of Souk-Ahras to gather information from the public water and sanitation service. In addition, bibliographic and web graphic searches were carried out. Data were also collected from the National Sanitation Office via written documents, operating data sheets, and official reports.

### WWTP operating mode

*Q*

_{r}) and extraction flow rates (

*Q*

_{w}) of 8,000 and 730 m

^{3}d

^{−1}, respectively, which were adopted based on the present operation mode. It is important to note at this stage that an appropriate mass budget shall be attributed to the system to ensure an optimal activated sludge operation.

### Construction of geometry and mesh

### The numerical model

This is the most delicate part because it conditions the quality and relevance of the results. The solved equations are those of the conservation of mass and momentum coupled with equations describing turbulence processes. The functioning of the clarifier is conditioned by a continuous phase (water) and another dispersed phase (sludge diluted in water). The literature shows that the volume fraction of sludge in such structures rarely exceeds, on average, 10%. The Eulerian-Eulerian model was chosen to solve the continuity equation of mass, water and sludge velocities, and that related to the volume fraction of sludge. It considers that both phases are continued and interact with each other via the terms of interfacial exchanges. This model requires local data to correctly choose the closure models, with very important calculation times, because it solves the same number of equations for both water and sludge.

In this Eulerian approach, Fluent offers three models of turbulence (laminar, k-ε, Reynolds stress). The standard turbulence model k-ε is used in this study to develop a CFD model validated against a large number of *in-situ* measurements in Souk-Ahras WWTP. In a recent study, Ganjare & Patwardhan (2019) showed, through CFD simulations, that predictions based on k-ε models, are better than those of k-ω models for rectangular and circular settling basins. This approach makes it possible to examine several aspects, such as the correct configuration, the height of the sludge bed and the surface hydraulic head. In circular secondary clarifiers, the dominant hydrodynamic process is located in the vertical plane (radial direction). This process can be reasonably studied by an axisymmetric CFD approach, which reduces the number of cells, the computation time, and the required computation capacity (Bürger *et al.* 2011).

*U*(m s

^{−1}) and

*V*(m s

^{−1}) are the components of the mean velocity over time in all directions,

*p*(pa) is the general pressure minus the hydrostatic pressure at the reference density,

*ρ*and ρ

_{r}(kg m

^{−3}) is the fluid density,

*g*(m s

^{−2}) is the acceleration due to gravity,

*ν*

_{t}(kg m

^{−1}s

^{−1}) is the eddy viscosity,

*S*

_{u}and

*S*

_{v}(Pa) are other terms of stress (Krebs 1991).

*k*(m

^{2}/s

^{2}) and its dissipation rate

*ε*(m

^{2}/s

^{3}).

*k*and

*ε*. The effect of the concentration of SS on the density of the mixture is indicated in Equation (5), where

*X*is the concentration of SS,

*ρ*

_{p}is the density of dry particles,

*ρ*

_{r}is the reference density (clear water), and

*ρ*is the density of the fluid-solid mixture:

In which *X* is the concentration of suspended solids (SS), *ν*_{sr} is the swirl effect of SS in the *r* direction, *ν*_{sy} is the swirl effect of SS in the *y* direction, and *V*_{s} (m s^{−1}) is the particle settling speed, which is determined as a function of the local concentration expressed by the settling function. Cutting-edge research studies (Eshtiaghi *et al.* 2013; Ratkovich *et al.* 2013) clearly indicate that the settling of sludge under Newton's law in the SS concentration may reach 6–8 g/l.

### Boundary conditions

The effluent entry is simulated by a speed condition, represented by a uniform speed over the entire entrance section. In turbulent conditions, two other parameters are required: (i) the hydraulic diameter, calculated for the circular inlet section, *D*_{h} = diameter of the inlet pipe; (ii) the turbulent intensity, calculated by the formula: *I* = 0.16. (Re_{D}_{h})^{−1/8}, where Re_{D}_{h} is the Reynolds Number based on the hydraulic diameter , in which is the density of water, is its dynamic viscosity, and *V* is the average velocity of the fluid.

The boundary conditions are given as follows: (i) the walls of the clarifier, the inlet pipe, and the Clifford are represented by a non-slip condition (solid wall); (ii) the section of the supply pipe is represented by an inlet condition; (iii) the overflow is represented by an exit condition; and (iv) the free surface of the clarifier is represented by a plane of symmetry. Finally, the last step consists in a numerical resolution of the equations.

### Convergence of calculations

^{−3}for the residuals, as recommended by Rameshwaran

*et al.*(2013). However, convergence is not solely determined by the residuals. Another criterion used to represent convergence was the evolution of the flow velocity and pressure fields as iterations progressed. When these fields no longer changed significantly, it indicated that the calculation had converged (Figure 5).

## RESULTS AND DISCUSSION

This section presents the results obtained by the numerical simulation for the clarifier of the Souk-Ahras WWTP, following the characterization of the physical properties (viscosity, density, and diameter of flocks) for water and sludge. Water properties include: viscosity = 10^{−3} Pa s, density = 1,000 kg m^{−3} while sludge properties include: viscosity = 1.53.10^{−3} Pa s, density = 1,005.3 kg m^{−3}, and diameter of flocks = 0.89 mm. As for the clarifier, it is of a traditional configuration: Clifford plunging into the sludge blanket.

*Q*

_{in}= 10,000 m

^{3}d

^{−1},

*Q*

_{r}= 730 m

^{3}d

^{−1};

*X*

_{o}= 3.8 g/l) conditions. Figure 6 illustrates how extensive turbulent zones with turbulent kinetic energies greater than 0.004 m

^{2}s

^{−2}are caused by the extraordinarily high velocity components in the inflow near field. As soon as the effluent reaches the Clifford area, the intensity decreases: the Clifford dissipates part of the turbulent kinetic energy of the fluid. Then, part of the effluent is reaspirated in this area under the effect of a vortex. The other part is directed toward the central axis. Several low intensity recirculation loops are created within the clarifier. These circulation regions and turbulence intensity in the sedimentation tank are the result of the absence of a proper baffle at the inlet (Krebs

*et al.*1995). In addition, the radius of the tank is not exceeded by the length of the density current (

*R*/

*R*

_{0}> 1) in order to prevent contacting the SST boundary. A reasonably good performance and a high effluent quality are the end outcomes, with an effluent SS content of around 0.04 g/l. Each vector's length is proportional to the model's estimate of the velocity at the relevant grid point and corresponds to the 0.03 m/s scale shown in Figure 4.

The hydrodynamics of the clarifier and sludge behavior in both vertical and horizontal directions may be represented by the findings of the CFD simulation. Figure 7 shows the SBH and sludge concentration inside the clarifier. The sludge is concentrated at the bottom of the clarifier, the highest volume fractions being located in the sludge pit and on the slope of the slab. There is no discontinuity in the volume fraction of the sludge between the Clifford and the sludge pit. The sludge blanket is almost horizontal.

^{3}).

### Model calibration and validation

Table 1 shows the difference between simulated and measured sludge blanket heights, estimated to be around 17%. The CFD simulations showed that the dynamics of the SBH can be accurately represented by applying the same operating conditions to the Souk-Ahras WWTP clarifier. Although there is a subsequent response to the prediction of SBH peaks, it can be seen that the simulated average sludge bed heights are quite similar to the corresponding measured values.

Simulated (m) sludge blanket height (SBH) . | Measured (m) sludge blanket height (SBH) . | Deviation (%) . |
---|---|---|

1.65 | 2 | 17 |

Simulated (m) sludge blanket height (SBH) . | Measured (m) sludge blanket height (SBH) . | Deviation (%) . |
---|---|---|

1.65 | 2 | 17 |

### Secondary settling tanks configuration and optimization

Understanding the effects of each parameter on the performance of the clarifier may be achieved by a thorough description and sensitivity analysis of the various settings. There are various methods that can be used to evaluate the impact of different parameters and variables on the clarifier model. These include local sensitivity analysis, global sensitivity analysis, and variance-based sensitivity analysis. Each of these methods has its own advantages and limitations, and the choice of method will depend on the specific objectives of the modeling study. The effects of the most important parameters governing SST operation are listed below:

✓ The SOR affects both the thickness of the sludge blanket and the settling velocity of the particles; it is a crucial factor in the design and operation of SSTs. Relatively high surface overflow rates may shorten settling times while exceeding a particular threshold can result in carryover and inefficient settling.

✓ Sludge blanket height: The height of the sludge blanket is another crucial factor that affects SST effectiveness. The retention duration can be extended and the settling efficiency improved by raising the height of the sludge blanket. However, if the height of the sludge blanket is too high, particles may be transported into the effluent and impair treatment efficiency. The ideal range of this parameter for a certain WWTP may be determined with the use of a sensitivity analysis of the SBH.

✓ Input speed: The input speed governs the flow rate of the wastewater entering the clarifier. Sensitivity analysis of this parameter can help to optimize the performance of the clarifier by identifying the optimal flow rate to achieve the desired level of treatment performance. A higher input speed can reduce settling time but can also cause turbulence and affect the settling efficiency.

✓ Floor slope: The floor slope is another crucial factor that affects the clarifier's flow pattern and settling effectiveness. The optimal slope shall result in the required degree of clarifier efficiency. A high slope can improve settling efficiency and flow velocity, but it may also short-circuit and result in poor treatment performance.

In **Test 1**, the immersion (height) of the Clifford was increased from 2.40 to 3.40 m, the SBH was reduced compared to the reference case (2 to 1.20 m), with a very large dilution under the Clifford and up to the sludge pit: the strong jet drives the sludge poured laterally and out of the pit. The percentage (1.66%) shows a volume (96.28 m^{3}) occupied by the settled sludge compared to the total volume of the structure (Test 1A). The effluent reaches the Clifford area, where two vortices are created. The jet splits into two parts. One part is circled in the Clifford area, and the other part descends directly downward. Several recirculation loops are created within the clarifier (Test 1B).

In **Test 2**, the diameter of the Clifford increased from 3.7 to 6.5 m, which resulted in a higher sludge concentration at the bottom of the clarifier compared to Test 1. The sludge veil did not change in appearance compared to the reference case. This test showed that the settled sludge volume represents 11.25% of the volume of the structure (652.5 m^{3}) (Test 2A). Two existing vortices were noticed in the banks of the Clifford. Several recirculation loops occurred within the structure (Test 2B).

In **Test 3**, the Clifford diameter was reduced from 3.70 to 2 m. This yielded an SBH of 2.3 m, with a percentage of 23% and a volume of 1,334 m^{3} occupied by the settled sludge compared to the total volume of the structure (Test 3A). The effluent leaves in a horizontal direction and rises immediately toward the free surface (Test 3B).

In **Test 4**, we aimed to test the behavior of the clarifier by minimizing the input speed to 0.1 m/s. The test illustrates the speed field in the structure. The decrease in the input speed induced a low velocity within the Clifford; the effluent takes a vertical direction directly toward the sludge pit and an increase in SBH (2.2 m) was detected. Moreover, the percentage was 25% and the volume occupied by the settled sludge compared to the total volume of the structure was 1,450 m^{3} (Test 4A). The decrease in the input speed induced a low speed within the Clifford; the effluent takes a vertical direction directly toward the sludge pit (Test 4B).

In **Test 5**, the slope of the raft was reduced and therefore the water height at the periphery increased: we went from 10% and 3 m to 5% and 4 m compared to the initial configuration. The sludge veil did not change in appearance compared to the reference case, with significant dilution under the Clifford. This last test gave a fractionation percentage (22%) and a volume occupied by the settled sludge is worth (1,276 m^{3}) (Test 5A). This disturbance induced several recirculation loops within the structure (Test 5B).

Sludge characteristics affect its accumulation in the clarifier. Rapid particle settling caused by a high mineral content results in a layer of undigested sludge at the bottom with a high concentration of sludge. This would imply that the compression feature is not in use. The rheological model was shown to be better adapted to predict the hydrodynamics of the sludge. The experimental findings demonstrated that the sludge cover can be found on a uniform surface over the whole axis. The advantages of including the rheological model and explaining its constitutive function in a CFD model are highlighted by all of these tests. As a result, it would be feasible to evaluate the influence of geometrical characteristics and operating modes on the concentration of predicted SBH.

### Optimization of the SOR

*V*

_{c}(corrected volume) expressed in m1/1, obtained by taking the product of the sludge volume index SVI (which makes it possible to assess the aptitude of the sludge for settling) by the sludge concentration at the entrance to the settling tank (Figure 15).

Most of the settling works of low loads are currently designed on the basis of a SOR of 0.8 m h^{−1}. This velocity is only acceptable if the sludge is of good quality (SVI < 120 ml/g). Security measures usually taken in sizing the clarifiers are not sufficient. To better check the design of a clarifier, it is recommended to refer to the CEMAGREF Curve (Figure 15), giving an SOR limit of 0.8 m h^{−1} under these operating conditions. However, four ascending velocities will be tested for the current configuration of the clarifier. The goal is not to oversize the structure or to check if it can withstand heavy hydraulic loads, but to test the operation according to the chosen SOR.

The CEMAGREF curve gives an SOR limit of 0.8 m h^{−1}. However, we have well exceeded this value (1.4 m h^{−1}) without having an abrupt change in the SBH approaching the free surface. This value can be validated by an advanced experimental protocol taking into account the higher performances of other configurations.

### Optimization of the clarifier capacity

According to Medina (2019), the turbulence model has an impact on the prediction of SST capacity. Table 3 shows the relationship between flow rate, hydraulic retention time (HRT), and the removal efficiencies of SS, from which it is clear that the removal efficiency increases as HRT increases. Concerning the relationship between SOR and removal efficiencies for SS, it is evident that removal efficiency decreases as SOR increases. When it comes to the percentage of removal of SS in relation with HRT and SOR, these patterns are comparable to those seen in the conventional sedimentation tank (Ekama & Marais 2002). In addition, based on Table 3, the existing clarifier design in the WWTP can support a daily ultimate capacity of 49,000 m^{3}d^{−1}.

Q (m^{3} h^{−1})
. | HRT (hour) . | SOR (m h^{−1})
. | SS removal (%) . |
---|---|---|---|

580.8 | 9.99 | 0.4 | 97.7 |

1,161.6 | 4.99 | 0.8 | 97.1 |

2,032.8 | 2.85 | 1.4 | 96.3 |

Q (m^{3} h^{−1})
. | HRT (hour) . | SOR (m h^{−1})
. | SS removal (%) . |
---|---|---|---|

580.8 | 9.99 | 0.4 | 97.7 |

1,161.6 | 4.99 | 0.8 | 97.1 |

2,032.8 | 2.85 | 1.4 | 96.3 |

## CONCLUSIONS

This study has successfully optimized the design of circular clarifiers by modeling their hydraulic behavior via CFD simulations using the Fluent software. Simulations developed in this study provided physical data of the sludge settling and validated the model using measurements of SBH and SS profiles. Various test cases were considered, which allowed us to answer questions related to the operation of circular clarifiers.

The results obtained from this study have important practical implications for the design and operation of circular clarifiers in WWTPs. Firstly, the use of CFD simulations allows for the testing of scenarios and their interactions to help explain global phenomena observed in the activated sludge process. Secondly, there is no optimal diameter and immersion for the Clifford; design criteria should be based on input speed. Thirdly, the increase in immersion does not affect the WWTP performance. Fourthly, the floor slope and depth of the structure are crucial design elements.

This study also identified key design parameters, such as SBH, flow layer height, and effluent suspended solid concentrations, which are satisfactorily correlated with SOR, being a key design parameter in secondary decantation basins. Based on the current configuration of the SST of Souk-Ahras WWTP, its hydraulic treatment capacity was found to be 49,000 m^{3}d^{−1}. This study also showed that the SOR threshold value of 0.8 m h^{−1} recommended in the literature can be increased to 1.4 m h^{−1} without overflow beyond the SBH.

In summary, this study contributed to the optimization of circular clarifiers' design and operation, which is essential in improving the overall efficiency and reliability of WWTPs. It proposed an innovative alternative method to improve SST design and operation and therefore WWTP performance, based on CFD models. The study showed not only the practical outcome of the proposed method, but also its potential benefits and constraints, which shall help promoting the application of CFD models for the continuous improvement of wastewater treatment processes.

## CONFLICT OF INTEREST

The authors declare there is no conflict.

## REFERENCES

*Modeling Aspects of Wastewater Treatment Processes*

*Secondary Settling Tanks Modeling: Study of the Dynamics of Activated Sludge Sedimentation by Computational Fluids Dynamics*