# Effect of Aluminium Salt Dosing on Activated Sludge Settleability Indicators: A New Settleability Model Development

^{*}

## Abstract

**:**

^{3+}) for the chemical precipitation of phosphates in wastewater treatment plants due to growing stricter regulatory requirements for wastewater effluent release to the environment. The modelling of the settleability of the resultant Al

^{3+}sludge in present engineering practice for design and optimisation are still based on conventional sludge settleability models. This paper describes a novel activated sludge settleability model which is designed to analyse the effects of Al

^{3+}dosing on activated sludge settleability indicators, zone settling velocity (ZSV), and stirred specific volume index (SSVI). The impact of Al

^{3+}dosing concentrations on ZSV and SSVI of full scale activated sludge plant were analysed in the laboratory over a three years’ period and the exponential form of the Vesilind equation was optimised and validated to include alum chemical dosing parameters. The proposed model equation was found to effectively describe the settleability of Al

^{3+}dosed sludge for dosing concentrations range of 0 to 100 mg/L.

## 1. Introduction

^{3+}) are increasingly being used for the precipitation of phosphates from wastewater [1,2,3]. Their use is more common in activated sludge plants (ASP) [4,5].

- ZSV = zone settling velocity (m/h)
- X = activated sludge concentration (g/L)
- ${\mathrm{v}}_{0}$ = sludge settleability constant (m/h)
- k = sludge settleability constant (L/g).

^{3+}dosing on activated sludge settleability indicators. The proposed new model equation will address the limitation of Pitman and White model for the modelling of the settleability of CDAS.

## 2. Materials and Methods

#### 2.1. Sludge Sampling and Analysis

#### 2.2. Settlometer Tests

#### 2.3. Data Analysis

^{2}(coefficient of determination), residual plot, probability plot and interval plot was used to validate how the ZSV model fits the ZSV experimental data.

## 3. Model Development and Model Validity for Al^{3+} Dosed Sludge

^{3}due to the limit of measurement and because there is no interaction with the sludge particles and settling velocity will be a function of individual floc properties and also, since no clear relationship with the concentration of the activated sludge particle exists at low sludge concentration. This challenge was resolved by other researchers by utilising Vesilind functions in different ways to determine the settling process at low concentration namely; modelling directly the functions Takacs´ et al. [26]; Dupont and Dahl [47] and defining particles with different velocities Dupont and Henze [48]; Lyn et al. [49]; Otterpohl and Freund [50]; and Mazzolani et al. [51]. Previous studies also reported the investigation of their own data from unit processes in South Africa Smollen and Ekama [52] and numerous activated sludge processes Pitman [43] and [44]; Tuntoolavest and Grady [53]; and concluded that Vesilind’s equation gave a better description of the actual settling performance of activated sludge. Following a further result from research conducted by Catunda et al. [54,55], rearranging Equations (3) to (5) will make it possible to express k and ${\mathrm{v}}_{0}$ as a function of SSVI which can be expressed as

^{3+}dosed sludge. Also, the results as previously reported [19] showed that the ZSV increased, while SSVI decreased with increasing concentrations of Al

^{3+}salt up to <100 mg/L. Beyond this concentration the sludge settleability disintegrated due mainly to surface charge reversal.

^{3+}used (0 to 250 mg/L), a non-linear representation of ZSV and SSVI as a function of Al

^{3+}dosing concentrations were observed as presented in Figure 2 and Figure 3. It was additionally represented using the rate of change of ZSV and SSVI (Figure 4 and Figure 5). This provided a basis for the modification of the conventional empirical model of ZSV (Equation (1)) to include a new Al

^{3+}dosing parameter. It further demonstrated that Al

^{3+}dosing concentrations had a non-linear correlation with ZSV and SSVI.

^{3+}dosed sludge as mentioned earlier and applying linear regression to the linearized form of the Vesilind equation to obtain a new expression in Equation (9).

^{3+}dosing concentration for the average data from the various batch test is shown in Figure 6. The negative of the gradient of each linear regression for the batch test is the Vesilind k value while the intercept is the Vesilind ${\mathrm{v}}_{0}$ parameter. However, because we are modelling an Al

^{3+}dosed sludge, then Vesilind ${\mathrm{v}}_{0}$ and k expression becomes re-defined as ${\mathrm{ZSV}}_{0}$ and ${\mathrm{K}}_{\mathrm{d}}$ for Al

^{3+}dosed sludge. There is a relationship between Al

^{3+}dosing concentration and ZSV which was not accounted for in the conventional Vesilind model equation in Equation (1). To express this, it was achieved by the transformation of data in the Vesilind exponential relationship and back tracking to calculate the values of the Vesilind exponential constant parameter. Hence, the ZSV was plotted against the Al

^{3+}dosing concentration on a natural log to a linear scale (Figure 6) and the Vesilind coefficient was Al (${\mathrm{K}}_{\mathrm{d}}$= −0.0045 and ${\mathrm{ZSV}}_{0}$ = 1.576 m/h). It can be inferred that the calculated ${\mathrm{ZSV}}_{0}$ and ${\mathrm{K}}_{\mathrm{d}}$ parthe ameter for Al

^{3+}dosed sludge from the graph of ln ZSV against Al

^{3+}concentrations is a function of the dosing concentrations.

^{3+}dosing concentration (Figure 7). The gradient and intercept of the curves accounted for the coefficient for Al ($\mathrm{gradient}$ = 0.0072 and $\mathrm{intercept}$ = 64.78 mL/g).

#### 3.1. New Model Calibration to Include Al^{3+} Dosing Parameter

^{3+}sludge. The approach is to check whether the new model fits the experimental batch test results. The exponential form of the Vesilind equation (Equation (1)) can be optimised to include chemical dosing parameter by investigating a new model equation for settling velocity. The investigated ZSVo and ${\mathrm{K}}_{\mathrm{d}}$ parameter for Al

^{3+}dosed sludge from the graph of ln ZSV against dosed MLSS concentration (${X}_{d}$) and Al

^{3+}dosing concentration (mg/L) (Figure 6 and Figure 7) shows linearised and exponential correlation between ZSV and SSVI with Al

^{3+}dosing concentrations. The new empirical model for settling velocity for an Al

^{3+}dosed activated sludge can take the form of a decay equation (A = ${\mathrm{A}}_{\mathrm{o}}{\mathrm{e}}^{-\mathsf{\lambda}\mathrm{t}}$) (Equation (10)) that obeys the exponential law of decay

- A = Activity (the number of unstable nuclei remaining), Bq
- ${\mathrm{A}}_{\mathrm{o}}$ = Original number of unstable nuclei, Bq
- e = Constant = 2.718
- λ = Decay constant, ${\mathrm{s}}^{-1}$
- t = time, s

- ZSV = Actual settling velocity (m/h)
- (${\mathrm{ZSV}}_{\mathrm{O}}$)
_{Al}= Maximum settling velocity (m/h) for Al^{3+}dosed sludge - (${\mathrm{K}}_{\mathrm{d}}$)
_{Al}= Empirical Al^{3+}dosed sludge settling parameter relating to sludge compaction - (${\mathrm{C}}_{\mathrm{O}}$)
_{Al}= Empirical Al^{3+}dosing constant related to stokes settling velocity - (${\mathrm{C}}_{\mathrm{K}}$)
_{Al}= Empirical Al^{3+}dosing constant related sludge compaction - (${\mathrm{D}}_{\mathrm{C}}$)
_{Al}= Al^{3+}dosing concentration (mg/L) - (X) = Al
^{3+}dosed MLSS concentration (mg/L)

^{3+}dosed sludge expression (Equation (11)) and conventional decay equation becomes vital. The version of terms in Equation (10) compared with Equation (11) is as follows; ${\mathrm{A}}_{\mathrm{o}}$ = $({\mathrm{C}}_{\mathrm{O}}{\mathrm{D}}_{\mathrm{C}}$ + ${\mathrm{ZSV}}_{\mathrm{O}}$), λ = $\left({\mathrm{K}}_{\mathrm{d}}-{\mathrm{C}}_{\mathrm{K}}{\mathrm{D}}_{\mathrm{C}}\right)$ and t = x. This shows below that applying the additive rule with e as a common factor in Equation (11), then Equation (12) can be expressed as

^{3+}dosed activated sludge model.

^{3+}dosed sludge (${\mathrm{ZSV}}_{\mathrm{O}}$, ${\mathrm{K}}_{\mathrm{d}},{\mathrm{C}}_{\mathrm{O}}$, and ${\mathrm{C}}_{\mathrm{K}}$) to predict the ZSV experimental data. Therefore, once a linear relationship is established between Z and X (Z = P − QX), the value of the Al

^{3+}dosed settleability constants ($ZS{V}_{O}$, ${\mathrm{K}}_{\mathrm{d}},{\mathrm{C}}_{\mathrm{O}}$, and ${\mathrm{C}}_{\mathrm{K}}$) can be evaluated and the experimental value of ZSV and dosing concentrations (${\mathrm{D}}_{\mathrm{C}}$) without performing a ZSV batch experiment. A new expression ((17) and (18)) was obtained from Equation (16) for calculating the value of ${\mathrm{D}}_{\mathrm{C}}$ as it relates to aluminium when the four constants (${\mathrm{ZSV}}_{\mathrm{O}}$, ${\mathrm{K}}_{\mathrm{d}},{\mathrm{C}}_{\mathrm{O}}$, and ${\mathrm{C}}_{\mathrm{K}}$) for aluminium dosed sludge are known.

^{2}) was close to 1 (Figure 6). This suggests that the exponential function in Equation (11) was suitable to model the Al

^{3+}dosed activated sludge settleability process (ZSV).

^{3+}dosed activated sludge can be derived from the new empirical Al

^{3+}dosed activated sludge model for settling velocity in Equation (11). The K and Vo parameter calculated from the expression in Catunda et al. [54] in Equations (6) and (7) becomes re-written as ZSVo and ${\mathrm{k}}_{\mathrm{d}}$ parameter for Al

^{3+}dosed sludge computed in Equations (19) and (20)

- ${\mathrm{K}}_{\mathrm{d}}$ = Empirical aluminium dosed activated sludge settling parameter related to sludge compaction (L/g)
- ${\mathrm{ZSV}}_{0}$ = Maximum settling velocity for Al
^{3+}dosed activated sludge related to stokes settling velocity (m/h)

^{3+}dosed SSVI, Equations (19) and (20), was compared with the existing Pitman [43] and White [36] expression in Equation (2) {$\frac{{\mathrm{V}}_{0}}{\mathrm{K}}$ = 68 × e

^{(−0.016 × SSVI}

_{3.5}

^{)}} and the Equation (2) can be re-written in the form of ZSVo and ${\mathrm{K}}_{\mathrm{d}}$ parameter as

^{3+}dosing on SSVI using the experimental data in the batch test conducted showed that the coefficient of determination (R

^{2}) was close to 1 (0.986) (Figure 7). This suggests that the linearized expression in Equation (22) was suitable to model the impact of Al

^{3+}dosing on activated sludge settleability (SSVI) process.

#### 3.2. Validation of Novel Model for Impact of Al^{3+} Dosing on ZSV and SSVI

#### Novel ZSV Model

^{3+}dosed sludge expressed in Equation (21) (ZSV = $({\mathrm{C}}_{\mathrm{O}}{\mathrm{D}}_{\mathrm{C}}$ + ${\mathrm{ZSV}}_{\mathrm{O}}$) ${\mathrm{e}}^{-\left({\mathrm{K}}_{\mathrm{d}}-{\mathrm{C}}_{\mathrm{K}}{\mathrm{D}}_{\mathrm{C}}\right)\mathrm{X}}$) and its linear approximation is ln (ZSV) = ln (${\mathrm{C}}_{\mathrm{O}}{\mathrm{D}}_{\mathrm{C}}$ + ${\mathrm{ZSV}}_{\mathrm{O}}$) – (${\mathrm{K}}_{\mathrm{d}}-{\mathrm{C}}_{\mathrm{K}}{\mathrm{D}}_{\mathrm{C}}$) X. The experimental data of five batches of settling velocity tests were classified into two groups. The first group (Figure 1, Figure 2, Figure 3, Figure 4 and Figure 5) were used to develop the model while the second group (Table 1 and Table 2 and Figure 8 and Figure 9) are used to validate the model. The model was validated using two approaches namely; Solver optimization tool and Minitab 17. Although, the batch settling test measurements revealed ZSV as a linear representation (sludge height as a function of time) (Figure 1), on the contrary a non-linear representation was observed in Figure 2 and Figure 3 showing ZSV and SSVI as a function of Al

^{3+}dosing concentration. The transformation of the data of the parameter in the conventional Vesilind equation further allows the inclusion of a new Al

^{3+}dosing parameter (${\mathrm{D}}_{\mathrm{C}}$) in the existing Pitman and White model [36,43] in Equation (2) and Catunda et al. [54] in Equations (6) and (7) which are both in agreement with the Vesilind (1968) expression.

^{2}) was 0.993 in Table 1, shows that the difference between the observed experimental value and the model predicted values are small and unbiased. The interval plot (Figure 8) shows that at 95% CI, the mean value of ZSV model and experimental is significant as the 95% confidence interval bar do not overlap.

^{−0.016 × SSVI}

_{3.5}} and substituting into the new alum dosed activated sludge model for settling velocity in Equation (11).

#### 3.3. Summary and Perspectives

^{3+}dosing concentrations on the settleability of activated sludge. The ZSV and SSVI model equations will find applications in the design and optimisation of FSTs for the solids separation of Al

^{3+}dosed activated sludge plants. They are valid for Al

^{3+}concentrations in the range of 0 to100 mg/L. High surface charges associated with higher concentrations of Al

^{3+}, causes a general disintegration of the activated sludge floc structure as previously reported [19]. This will result in the Al

^{3+}dosed sludge not fitting the proposed equation at concentrations higher than the stated range.

## 4. Conclusions

^{3+}dosing concentrations on activated sludge settleability indicators; zone settling velocity (ZSV) and stirred specific volume index (SSVI) using linear transformation of polynomials and exponential functions to achieve replication of a non-linear correlation between the Al

^{3+}dosing concentrations and settleability indicators (ZSV and SSVI). The new empirical model that describes the relationship between Al

^{3+}dosing concentrations and the ZSV and SSVI were further validated using non-linear parameterization. The results showed that the settleability indicators of Al

^{3+}dosed sludges can be described by the proposed equations which showed a good fit to the experimental data within a dose range of between 0 to <100 mg/L of Al

^{3+}. The new model equations will find application in the water industry for the modelling and optimization of Al

^{3+}dosed activated plants.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Al | Aluminium |

ASP | Activated sludge plant |

CI | Confidence interval |

CDAS | Chemically dosed activated sludge |

${C}_{O}$ | Empirical chemical dosing constant related to stokes settling velocity |

${C}_{K}$ | Empirical chemical dosing constant related sludge compaction |

DF | Degree of freedom |

DSVI | Diluted sludge volume index, mL/g |

${D}_{C}$ | Aluminium dosing concentration (mg/L) |

ESS | Effluent suspended solid |

EPS | Extracellular polymeric substances |

EN | Effluent nitrogen |

EP | Effluent phosphorus (EP) |

FST | Final settling tank |

F | F-test statistics |

FFT | Full flow treatment |

H | Sludge height, cm |

k | Vesilind sludge settleablity constant |

K | Dick and Young sludge settleability constant |

${k}_{d}$ | Empirical settling parameter relating to sludge compaction |

MLD | Mega litres per day |

MLSS | Mixed liquor suspended solids, g/L |

R^{2} | Coefficient of determination |

SSVI | Stirred specific volume Index, mL/g |

SVI | Sludge volume index, mL/g |

SS | Suspended colids |

SSD | Sum of squared deviation |

${v}_{0}$ | Vesilind sludge parameter related to settling velocity (m/h) |

${V}_{0}$ | Dick and Young sludge parameter related to settling velocity (m/h) |

WWTP | Wastewater treatment plant |

WRc | Water Research Council |

X | Activated sludge concentration, g/L |

${X}_{d}$ | Alum dosed MLSS concentration, g/L |

α | Significance level |

ZSV_{O} | Maximum zone settling velocity (m/h) |

ZSV | Actual zone settling velocity (m/h) |

## References

- Wilfert, P.; Kumar, P.S.; Korving, L.; Witkamp, G.J.; van Loosdrecht, M.C.M. The relevance of phosphorus and iron chemistry to the recovery of phosphorus from wastewater: A review. Environ. Sci. Technol.
**2015**, 49, 9400–9414. [Google Scholar] [CrossRef] - Haandel, A.C.V.; Lubbe, J.G.M.V. Handbook of Biological Wastewater Treatment: Design and Optimisation of Activated Sludge System, 2nd ed.; IWA Publishing: London, UK, 2012. [Google Scholar]
- Ojo, P.; Ifelebuegu, A.O. The Impact of Alum on the Bulking of a Full scale Activated Sludge Plant. Environ. Eng.
**2016**, 3, 53–57. [Google Scholar] - Zou, J.; Zhang, L.; Wang, L.; Li, Y. Enhancing phosphorus release from waste activated sludge containing ferric or aluminium phosphates by EDTA addition during anaerobic fermentation process. Chemosphere
**2017**, 171, 601–608. [Google Scholar] [CrossRef] [PubMed] - Ge, J.; Meng, X.; Song, Y.; Terracciano, A. Effect of phosphate releasing in activated sludge on phosphorus removal from municipal wastewater. Environ. Sci.
**2018**, 67, 216–223. [Google Scholar] [CrossRef] [PubMed] - Xu, G.; Yin, F.; Xu, Y.; Yu, H. A force-based mechanistic model for describing activated sludge settling process. Water Res.
**2017**, 127, 118–126. [Google Scholar] [CrossRef] - Li, B.; Stenstrom, M.K. Dynamic one-dimensional modelling of secondary settling tanks and design impacts of sizing decisions. Water Res. J.
**2014**, 50, 160–170. [Google Scholar] [CrossRef] - François, P.; Locatelli, F.; Laurent, J.; Bekkour, K. Experimental study of activated sludge batch settling velocity profile. Flow Measur. Instrum. J.
**2016**, 48, 112–117. [Google Scholar] [CrossRef] - Heikal, H.A.M.; El Baz, A.R.; El-Hafiz, A.A.; Farghaly, S.M. Study the Performance of Circular Clarifier in Existing Potable Water Treatment Plant by Computational Fluid Dynamics; International Water Resources Association: Paris, France, 2017. [Google Scholar]
- Zhang, D.J.; Li, Z.L.; Lu, P.L.; Zhang, T.; Xua, D.Y. A method for characterizing the complete settling process of activated sludge. Water Res.
**2006**, 40, 2637–2644. [Google Scholar] [CrossRef] [PubMed] - Mancell-Egala, W.A.S.K.; Kinnear, D.J.; Jones, K.L.; Clippeleir, H.D.; Takacs, I.; Murthy, S.N. Limit of stokesian settling concentration characterizes sludge settling velocity. Water Res.
**2016**, 90, 100–110. [Google Scholar] [CrossRef] - Ramin, E.; Wagner, D.S.; Yde, L.; Binning, P.J.; Rasmussen, M.R.; Mikkelsen, P.S.; Plosz, B.G. A new settling velocity model to describe secondary sedimentation. Water Res.
**2014**, 55, 447–458. [Google Scholar] [CrossRef] - Ekama, G.A.; Barnard, J.L.; Gunthert, F.W.; Krebs, P.; McCorquadale, J.A.; Parker, D.S.; Wahlberg, E.J. Secondary Settling Tanks, Theory, Modelling, Design and Operation; Scientific Report No 6; International Association of Water Quality (IAWQ): London, UK, 1997. [Google Scholar]
- Tchobanoglous, G.; Burton, F.L.; Stensel, H.D. Wastewater Engineering: Treatment and Reuse, 4th ed.; McGraw-Hill Science: New York, NY, USA, 2003. [Google Scholar]
- Jung, K.W.; Hwang, M.J.; Ahn, K.H.; Ok, Y.S. Kinetic study on phosphate removal from aqueous solution by biochar derived from peanut shell as renewable adsorptive media. Int. J. Environ. Sci. Technol.
**2015**, 12, 3363–3372. [Google Scholar] [CrossRef] [Green Version] - Ghawi, A.G.; Kris, J. A Computational Fluid Dynamics Model of Flow and Settling in Sedimentation Tanks. Appl. Comput. Fluid Dyn. J.
**2012**, 2, 19–34. [Google Scholar] - Ghawi, A.G.; Kris, J. Improvement Performance of Secondary Clarifiers by a Computational Fluid Dynamics Model. Slovak J. Civ. Eng.
**2011**, 19, 1–11. [Google Scholar] [CrossRef] - WEF-Water Environment Federation. Clarifier Design WEF Manual of Practice No. FD-8, 2nd ed.; McGraw-Hill: New York, NY, USA, 2005; Available online: http://www.assettler.com/COKTURME%20TANKLARI%20TASARIMI.pdf> (accessed on 20 May 2015).
- Ojo, P.; Ifelebuegu, A.O. The Impact of Aluminium Salt for Chemical Phosphorus Removal on the Settleability of Activated Sludge. Environments
**2018**, 5, 88. [Google Scholar] [CrossRef] - Wilen, B.M.; Jin, B.; Lant, P. The influence of key constituents in activated sludge on surface and flocculating properties. Water Res.
**2003**, 37, 127–2139. [Google Scholar] [CrossRef] - Kynch, G.J. A theory of sedimentation. Trans. Faraday Soc.
**1952**, 148, 166–176. [Google Scholar] [CrossRef] - Li, B.; Stenstrom, M.K. Research advances and challenges in one-dimensional modelling of secondary settling Tanks: A critical review. Water Res. J.
**2014**, 65, 40–63. [Google Scholar] [CrossRef] - Torfs, E.; Balemans, S.; Locatelli, F.; Diehl, S.; Bürger, R.; Laurent, J.; François, P.; Nopens, I. On constitutive functions for hindered settling velocity in 1-D settler models: Selection of appropriate model structure. Water Res.
**2017**, 110, 38–47. [Google Scholar] [CrossRef] - Vesilind, P.A. Theoretical considerations: Design of prototype thickeners from batch settling tests. J. Water Sew. Works
**1968**, 115, 302–307. [Google Scholar] - Dick, R.I.; Young, K.W. Analysis of thickening performance of final settling tanks. In Proceedings of the 27th Industrial Waste Conference, Lafayette, IN, USA, 2–4 May 1972. [Google Scholar]
- Takács, I.; Patry, G.G.; Nolasco, D. A dynamic model of the clarification-thickening process. Water Res. J.
**1991**, 25, 1263–1271. [Google Scholar] [CrossRef] - Dupont, R.; Dahl, C. A one-dimensional model for a secondary settling tank including density current and short-circuiting. Water Sci. Technol.
**1995**, 31, 215–224. [Google Scholar] [CrossRef] - Cho, S.; Colin, F.; Sardin, M.; Prost, C. Settling velocity model of activated sludge. Water Res. J.
**1993**, 27, 1237–1242. [Google Scholar] [CrossRef] - Zhang, Y.; Grassia, P.; Martin, A.; Usher, S.P.; Scales, P.J. Designing thickeners by matching hindered settling and gelled suspension zones in the presence of aggregate densification. Chem. Eng. Sci.
**2015**, 134, 297–307. [Google Scholar] [CrossRef] [Green Version] - Guyonvarch, E.; Ramin, E.; Kulahci, M.; Plosz, B.G. ICFD: Interpreted Computational Fluid Dynamics—Degeneration of CFD to one-dimensional advection-dispersion models using statistical experimental design—The secondary clarifier. Water Res.
**2015**, 83, 396–411. [Google Scholar] [CrossRef] [PubMed] - Bürger, R.; Diehl, S.; Faras, S.; Nopens, I.; Torfs, E. A consistent modelling methodology for secondary settling tanks: A reliable numerical method. Water Sci. Technol.
**2013**, 68, 192–208. [Google Scholar] [CrossRef] [PubMed] - De Clercq, J. Batch and Continuous Settling of Activated Sludge: In-depth Monitoring and 1D Compression Modelling. Ph.D. Thesis, Ghent University, Ghent, Belgium, 2006. [Google Scholar]
- De Clercq, J.G.U.; Nopens, I.G.U.; Defrancq, J.; Vanrolleghem, P. Extending and calibrating a mechanistic hindered and compression settling model for activated sludge using in-depth batch experiments. Water Res. J.
**2008**, 42, 781–791. [Google Scholar] [CrossRef] - Schuler, A.J.; Jang, H. Causes of variable biomass density and its effects on settleability in full-scale biological wastewater treatment systems. Environ. Sci. Technol.
**2007**, 41, 1675–1681. [Google Scholar] [CrossRef] - Schuler, A.J.; Jang, H. Microsphere addition for the study of biomass properties and density effects on settleability in biological wastewater treatment systems. Water Res.
**2007**, 41, 2163–2170. [Google Scholar] [CrossRef] - White, Settling of Activated Sludge, Technical Report TR11; WRC: Stevanhage, UK, 1975.
- MCR-Process & Technology 2008 Stiro-Settlometer. Available online: http://www.mcrpt.com/english/pdf/manuel_stiro.pdf > (accessed on 10 February 2014).
- Schuler, A.J.; Jang, H. Density effects on activated sludge zone settling velocities. Water Res. J.
**2007**, 41, 1814–1822. [Google Scholar] [CrossRef] - Vaerenbergh, E.V. Numerical computation of secondary settler area using batch settling data. Tribune Cebedeau
**1980**, 33, 369–374. [Google Scholar] - Wahlberg, E.J.; Keinath, T.M. Development of settling flux curves using SVI. J. Water Pollut. Control Fed.
**1988**, 60, 2095–2100. [Google Scholar] [CrossRef] - Giokas, D.; Diagger, G.T.; Sperling, M.V.; Kim, Y.; Paraskevas, A. Comparison and evaluation of empirical zone settling velocity parameters based on sludge volume index using unified settling characteristics database. J. Water Res.
**2003**, 37, 3821–3836. [Google Scholar] [CrossRef] - Daigger, G.T. Development of refined clarifier operating diagrams using an updated settling characteristics database. J. Water Environ. Res.
**1995**, 67, 95–100. [Google Scholar] [CrossRef] - Pitman, A.R. Settling properties of extended aeration sludge. J. Water Pollut. Control Fed.
**1980**, 52, 524–536. [Google Scholar] - Pitman, A.R. Operation of biological nutrient removal plants: In Theory, Design and Operation of Nutrient Removal Activated Sludge Processes; Water Research Commission: Pretoria, South Africa, 1984. [Google Scholar]
- Ekama, G.A.; Marais, G.V.R. Sludge Settleability and Secondary Settling and Design Procedures. Water Pollut. Control
**1986**, 87, 101–113. [Google Scholar] - Koopman, B.; Cadee, K. Prediction of thickening capacity using diluted sludge volume index. Water Res.
**1983**, 17, 1427–1431. [Google Scholar] [CrossRef] - Lakehal, D.; Krebs, P.; Krijgsman, J.; Rodi, W. Computing shear flow and sludge blanket in secondary clarifiers. J. Hydraul. Eng.
**1999**, 125, 253–262. [Google Scholar] [CrossRef] - Dupont, R.; Henze, M. Modelling of the secondary clarifier combined with the activated sludge model no. 1. Water Sci. Technol.
**1992**, 25, 285–300. [Google Scholar] [CrossRef] - Lyn, D.A.; Stamou, A.I.; Rodi, W. Density currents and shear induced flocculation in sedimentation tanks. Hydraul. Eng.
**1992**, 118, 849–867. [Google Scholar] [CrossRef] - Otterpohl, R.; Freund, M. Dynamic models for clarifiers of activated sludge plants with dry and wet weather flows. Water Sci. Technol.
**1992**, 26, 1391–1400. [Google Scholar] [CrossRef] - Mazzolani, G.; Pirozzi, F.; d’Antonoi, G. A generalized settling approach in the numerical modelling of sedimentation tanks. Water Sci. Technol.
**1998**, 38, 95–102. [Google Scholar] [CrossRef] - Smollen, M.; Ekama, G.A. Comparison of empirical settling velocity equations in flux theory for secondary settling tanks: South Africa. Water Sci. Technol.
**1984**, 10, 175–184. [Google Scholar] - Tuntoolavest, M.; Grady, C.P.L.J. Effect of activated sludge operational conditions on sludge thickening characteristics. Water Pollut. Control Fed.
**1980**, 54, 1112–1117. [Google Scholar] - Catunda, P.F.C.; Van Haandel, A.C.; Araujo, L.S.; Vilar, A. Determination of the Settleability of Activated Sludge; The 15th Congress of the Brazilian Sanitary Engineering Organisation: Belem, Brazil, 1989. [Google Scholar]
- Catunda, P.F.C.; Van Haandel, A.C. Activated sludge settling-part I: Experimental determination of settling characteristics. Water
**1992**, 18, 165–172. [Google Scholar] - Bürger, R.; Careaga, J.; Diehl, S.; Ryan, M.; Zambrano, J. Estimating the hindered-settling flux function from a batch test in a cone. Chem. Eng. Sci.
**2018**, 192, 244–253. [Google Scholar] [CrossRef]

**Figure 1.**Zone settling curve (ZSC) for 100 mg/L Al

^{3+}dosed MLSS (ZS = zone settling, TS = transition settling, CS = compression settling, error bars represent the standard deviation of the mean). The ZSV was obtained from the slope of the linear graph.

**Figure 2.**Impact of Al Dosing (mg/L) on ZSV (m/h) (Error bars represent standard deviation of the mean).

**Figure 3.**Impact of Al Dosing (mg/L) on SSVI (mL/g) (Error bars represent standard deviation of the mean).

**Figure 4.**Rate of Change of ZSV against aluminium dosing (error bars represent the standard deviation of the mean).

**Figure 5.**Rate of Change of SSVI against aluminium dosing (the error bars represent the standard deviation of the mean).

**Figure 6.**Natural log of ZSV against Al

^{3+}Concentration (the error bars represent the standard deviation of the mean).

**Figure 7.**ln (SSVI) against Al

^{3+}dosing concentration (the error bars represent the standard deviation of the mean).

**Figure 9.**Non-linear curve fitting of the impact of aluminium on ZSV (the bars represent the standard deviation of the mean).

Parameters | Estimated Values |
---|---|

ZSVo | 1.377 |

Co | 0.026 |

Kd | −0.02 |

Ck | −0.0023 |

DF | 36 |

lack of fit test | 30 |

SS | 1.14664 |

MS | 0.01559 |

F | 0.82 |

P-Value | 0.675 |

α | 0.05 |

R^{2} | 0.993 |

SSD | 0.334 |

^{2}—R Squared; α—significance level; CI—Confidence Interval.

MLSS (g/L) | ZSV (m/h) | ZSV Model (m/h) | Al-Dosing (mg/L) | SD | Residual | Squared Residual | Squared ZSV |
---|---|---|---|---|---|---|---|

2.50 | 0.47 | 0.37 | 0.00 | 9.77 $\times {10}^{-3}$ | 1.74 $\times {10}^{-1}$ | 3.02 $\times {10}^{-2}$ | 0.22 |

2.76 | 0.53 | 0.48 | 10.00 | 2.15 $\times {10}^{-3}$ | 7.95 $\times {10}^{-2}$ | 6.32 $\times {10}^{-3}$ | 0.28 |

2.85 | 0.59 | 0.56 | 20.00 | 6.88 $\times {10}^{-4}$ | 3.13 $\times {10}^{-2}$ | 9.82 $\times {10}^{-4}$ | 0.35 |

2.94 | 0.62 | 0.62 | 30.00 | 2.00 $\times {10}^{-6}$ | 1.98 $\times {10}^{-2}$ | 3.91 $\times {10}^{-4}$ | 0.38 |

3.04 | 0.67 | 0.66 | 40.00 | 1.04 $\times {10}^{-4}$ | 4.41 $\times {10}^{-2}$ | 1.95 $\times {10}^{-3}$ | 0.45 |

3.15 | 0.71 | 0.68 | 50.00 | 8.20 $\times {10}^{-4}$ | 4.36 $\times {10}^{-2}$ | 1.90 $\times {10}^{-3}$ | 0.50 |

3.30 | 0.62 | 0.68 | 100.00 | 4.08$\times {10}^{-3}$ | −1.09$\times {10}^{-1}$ | 1.20$\times {10}^{-2}$ | 0.38 |

3.50 | 0.56 | 0.52 | 150.00 | 1.25$\times {10}^{-3}$ | 1.28$\times {10}^{-1}$ | 1.63$\times {10}^{-2}$ | 0.31 |

2.84 | 0.41 | 0.38 | 0.00 | 1.02$\times {10}^{-3}$ | 5.77$\times {10}^{-2}$ | 3.33$\times {10}^{-3}$ | 0.17 |

2.90 | 0.46 | 0.48 | 10.00 | 5.43$\times {10}^{-4}$ | −4.23$\times {10}^{-2}$ | 1.79$\times {10}^{-3}$ | 0.21 |

2.96 | 0.52 | 0.56 | 20.00 | 1.68$\times {10}^{-3}$ | −6.53$\times {10}^{-2}$ | 4.26$\times {10}^{-3}$ | 0.27 |

3.00 | 0.56 | 0.62 | 30.00 | 3.42$\times {10}^{-3}$ | −1.25$\times {10}^{-1}$ | 1.57$\times {10}^{-2}$ | 0.31 |

3.10 | 0.62 | 0.66 | 40.00 | 1.26$\times {10}^{-3}$ | −8.79$\times {10}^{-2}$ | 7.73$\times {10}^{-3}$ | 0.38 |

3.11 | 0.67 | 0.69 | 50.00 | 2.28$\times {10}^{-4}$ | −7.38$\times {10}^{-2}$ | 5.45$\times {10}^{-3}$ | 0.45 |

3.30 | 0.55 | 0.68 | 100.00 | 1.79$\times {10}^{-2}$ | −2.29$\times {10}^{-1}$ | 5.26$\times {10}^{-2}$ | 0.30 |

3.50 | 0.51 | 0.52 | 150.00 | 2.15$\times {10}^{-4}$ | 4.75$\times {10}^{-2}$ | 2.26$\times {10}^{-3}$ | 0.26 |

2.50 | 0.47 | 0.37 | 0.00 | 9.77$\times {10}^{-3}$ | 1.74$\times {10}^{-1}$ | 3.02$\times {10}^{-2}$ | 0.22 |

2.60 | 0.50 | 0.48 | 10.00 | 2.55$\times {10}^{-4}$ | 3.16$\times {10}^{-2}$ | 9.97$\times {10}^{-4}$ | 0.25 |

2.65 | 0.53 | 0.57 | 20.00 | 1.51$\times {10}^{-3}$ | −7.48$\times {10}^{-2}$ | 5.60$\times {10}^{-3}$ | 0.28 |

2.70 | 0.57 | 0.63 | 30.00 | 3.95$\times {10}^{-3}$ | −1.30$\times {10}^{-1}$ | 1.68$\times {10}^{-2}$ | 0.32 |

2.73 | 0.60 | 0.68 | 40.00 | 6.68$\times {10}^{-3}$ | −1.77$\times {10}^{-1}$ | 3.15$\times {10}^{-2}$ | 0.36 |

2.80 | 0.64 | 0.71 | 50.00 | 5.50$\times {10}^{-3}$ | −1.62$\times {10}^{-1}$ | 2.64$\times {10}^{-2}$ | 0.41 |

2.90 | 0.59 | 0.77 | 100.00 | 3.13$\times {10}^{-2}$ | −3.39$\times {10}^{-1}$ | 1.15$\times {10}^{-1}$ | 0.35 |

3.10 | 0.47 | 0.65 | 150.00 | 3.36$\times {10}^{-2}$ | −2.51$\times {10}^{-1}$ | 6.32$\times {10}^{-2}$ | 0.22 |

2.20 | 0.36 | 0.37 | 0.00 | 2.50$\times {10}^{-5}$ | 1.79$\times {10}^{-2}$ | 3.22$\times {10}^{-4}$ | 0.13 |

2.50 | 0.48 | 0.48 | 10.00 | 1.80$\times {10}^{-5}$ | −7.15$\times {10}^{-3}$ | 5.10$\times {10}^{-5}$ | 0.23 |

2.65 | 0.60 | 0.57 | 20.00 | 9.72$\times {10}^{-4}$ | −1.48$\times {10}^{-2}$ | 2.19$\times {10}^{-4}$ | 0.36 |

2.73 | 0.71 | 0.63 | 30.00 | 6.17$\times {10}^{-3}$ | 1.33$\times {10}^{-1}$ | 1.77$\times {10}^{-2}$ | 0.50 |

2.74 | 0.83 | 0.68 | 40.00 | 2.22$\times {10}^{-2}$ | 3.04$\times {10}^{-1}$ | 9.24$\times {10}^{-2}$ | 0.69 |

2.80 | 0.96 | 0.71 | 50.00 | 6.05$\times {10}^{-2}$ | 5.38$\times {10}^{-1}$ | 2.89$\times {10}^{-1}$ | 0.92 |

3.00 | 0.88 | 0.75 | 100.00 | 1.79$\times {10}^{-2}$ | 3.07$\times {10}^{-1}$ | 9.45$\times {10}^{-2}$ | 0.77 |

3.25 | 0.74 | 0.61 | 150.00 | 1.82$\times {10}^{-2}$ | 3.42$\times {10}^{-1}$ | 1.17$\times {10}^{-1}$ | 0.55 |

2.40 | 0.26 | 0.37 | 0.00 | 1.19$\times {10}^{-2}$ | −1.21$\times {10}^{-1}$ | 1.48$\times {10}^{-2}$ | 0.07 |

2.50 | 0.36 | 0.48 | 10.00 | 1.54$\times {10}^{-2}$ | −2.17$\times {10}^{-1}$ | 4.72$\times {10}^{-2}$ | 0.13 |

2.55 | 0.47 | 0.57 | 20.00 | 1.03$\times {10}^{-2}$ | −1.78$\times {10}^{-1}$ | 3.16$\times {10}^{-2}$ | 0.22 |

2.62 | 0.57 | 0.64 | 30.00 | 4.45$\times {10}^{-3}$ | −1.46$\times {10}^{-1}$ | 2.13$\times {10}^{-2}$ | 0.32 |

2.68 | 0.68 | 0.69 | 40.00 | 2.80$\times {10}^{-5}$ | −4.22$\times {10}^{-3}$ | 1.80$\times {10}^{-5}$ | 0.46 |

2.75 | 0.78 | 0.72 | 50.00 | 3.75$\times {10}^{-3}$ | 2.79$\times {10}^{-2}$ | 7.78$\times {10}^{-4}$ | 0.61 |

2.94 | 0.91 | 0.76 | 100.00 | 2.29$\times {10}^{-2}$ | 3.80$\times {10}^{-1}$ | 1.44$\times {10}^{-1}$ | 0.83 |

3.15 | 0.68 | 0.64 | 150.00 | 1.83$\times {10}^{-3}$ | −3.20$\times {10}^{-1}$ | 1.02$\times {10}^{-1}$ | 0.46 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ojo, P.; Ifelebuegu, A.O.
Effect of Aluminium Salt Dosing on Activated Sludge Settleability Indicators: A New Settleability Model Development. *Water* **2019**, *11*, 179.
https://doi.org/10.3390/w11010179

**AMA Style**

Ojo P, Ifelebuegu AO.
Effect of Aluminium Salt Dosing on Activated Sludge Settleability Indicators: A New Settleability Model Development. *Water*. 2019; 11(1):179.
https://doi.org/10.3390/w11010179

**Chicago/Turabian Style**

Ojo, Peter, and Augustine Osamor Ifelebuegu.
2019. "Effect of Aluminium Salt Dosing on Activated Sludge Settleability Indicators: A New Settleability Model Development" *Water* 11, no. 1: 179.
https://doi.org/10.3390/w11010179