Optimal design of an activated sludge plant: theoretical analysis
 4.2k Downloads
 2 Citations
Abstract
The design procedure of an activated sludge plant consisting of an activated sludge reactor and settling tank has been theoretically analyzed assuming that (1) the Monod equation completely describes the growth kinetics of microorganisms causing the degradation of biodegradable pollutants and (2) the settling characteristics are fully described by a power law. For a given reactor height, the design parameter of the reactor (reactor volume) is reduced to the reactor area. Then the sum total area of the reactor and the settling tank is expressed as a function of activated sludge concentration X and the recycled ratio α. A procedure has been developed to calculate X_{opt}, for which the total required area of the plant is minimum for given microbiological system and recycled ratio. Mathematical relations have been derived to calculate the αrange in which X_{opt} meets the requirements of F/M ratio. Results of the analysis have been illustrated for varying X and α. Mathematical formulae have been proposed to recalculate the recycled ratio in the events, when the influent parameters differ from those assumed in the design.
Keywords
Activated sludge reactor Optimal design Optimal operation Sludge recycled ratio Settling tankList of symbols
 a
Constant in settling model (m/day)
 A_{r}
Area of the reactor (m^{2})
 A_{s}
Area of the settling tank (m^{2})
 A_{T}
Total area (m^{2})
 F/M
Food to microorganism ratio
 F_{c}
Critical solid flux in settling tank (kg/m^{2} day)
 F_{g}
Gravity solid flux in settling tank (kg/m^{2} day)
 F_{L}
Limiting solid flux in settling tank (kg/m^{2} day)
 H_{r}
Height of the activated sludge reactor (m)
 k_{d}
Endogenous decay coefficient (day^{−1})
 n
Constant in settling model
 Q_{0}
Influent wastewater flow rate (m^{3}/day)
 Q_{e}
Effluent wastewater flow rate (m^{3}/day)
 Q_{r}
Recycled wastewater flow rate (m^{3}/day)
 Q_{w}
Withdrawn wastewater flow rate (m^{3}/day)
 \( r_{\text{g}}^{\prime } \)
Net growth rate of the microorganisms (kg/m^{3} day)
 r_{su}
Substrate utilization rate (kg/m^{3} day)
 S_{0}
Influent substrate concentration (kg/m^{3})
 S
Substrate concentration in the reactor and in the settling tank (kg/m^{3})
 t
Time (days)
 v
Underflow velocity (m/day)
 V_{r}
Activated sludge reactor volume (m^{3})
 X_{0}
Activated sludge concentration in the influent (kg/m^{3})
 X
Activated sludge concentration in the reactor (kg/m^{3})
 X_{e}
Activated sludge concentration in the effluent (kg/m^{3})
 X_{r}
Activated sludge concentration in the recycled stream (kg/m^{3})
 X_{u}
Activated sludge concentration in the underflow stream (kg/m^{3})
 X_{w}
Activated sludge concentration in the waste stream (kg/m^{3})
 Y
Maximum yield coefficient (kg/kg)
 α
Sludge recycled ratio
 β
Sludge waste ratio
 θ
Hydraulic retention time (days)
Introduction
Activated sludge plant applies the microbiological process for the degradation of organic pollutants in water. The method does not require chemicals (maybe in insignificant amount). The operational cost is low as compared to the chemical method of treatment. The biodegradation process, however, is slow and the plant requires large footprint of the facilities. In recent years, highly polluting industries have been flourishing in the densely populated countries with poor economy, lowpaid working forces and liberal environmental law (in writing or in implementation). Thus, although in those countries, sometimes due to favorable atmospheric conditions, the biological method of wastewater treatment seems to be appropriate, it is hardly chosen as it demands large space. The biological treatment method is sustainable and it is the demand of the day. Therefore, some proper design and operation method has to be developed, which would find the minimum required area for an activated sludge plant and also to ensure the condition for optimal operation of an existing plant, and this requires ‘Development of comprehensive mathematical formulations for design and operation’.
Activated sludge system for biological wastewater treatment consists essentially of an activated sludge reactor and a settling tank. Reports on the analysis of the performance of the activated sludge plants based on reactor settler interaction are rather scarce. Sherrard and Kincannon (1974) proposed a correlation among the mean solid retention time, sludge recycle ratio and sludge concentration factor in secondary settling tank. Riddell et al. (1983) combined the functions of the reactor and the settling tank in order to choose permissible flow rate of an activated sludge plant. Sheintuch (1987) introduced the concept of system response for analyzing the interactions of the functions of the reactor and settling tank. But it was Cho et al. (1996) who described the reactorsettling tank interaction in very comprehensive way. They used the sludge recycle ratio and sludge waste ratio as the operating parameters and obtained the responses of the output variables such as biomass concentration in aerator, dissolved pollutant and solid concentration in the effluent. Diehl and Jeppsson (1998) presented a dynamic simulation model of an activated sludge plant. For describing the continuous sedimentation in the secondary clarifier, a onedimensional model based on nonlinear partial differential equation was proposed. The analysis of the settling process lied on vigorous mathematical treatment of the equation. The DiehlJeppsson model, however, does not correlate the dynamics of the reactor to that of the settling tank in a comprehensive way.
In the past decades much research has been conducted on the modeling and simulation of the activated sludge plants (Rigopoulos and Linke 2002; Gernaey et al. 2004; Flores et al. 2005; David et al. 2009), but comprehensive discussion on the interaction between the reactor and the settling tank is still not adequate. Instead, precise models have been proposed for the reactors (Gujer et al. 1999; Hu et al. 2003; Moulleca et al. 2011; Pholchan et al. 2010; Scuras et al. 2001) and also for the settlers (Diehl 2007; Ekama and Marais 2004; Flamant et al. 2004; Vanderhasselt and Vanrolleghem 2000; Zhang et al. 2006; Bürger et al. 2011) independently, and the performances of the units have been discussed. Patziger et al. (2012) studied the settling tank under dynamic load considering both the overall unsteady behavior and the features around the peaks, investigating the effect of various sludge return strategies as well as the inlet geometry on the performance of the tank. Thus a lot of work has been done on the problem, but comprehensive method and mathematical relations considering the reactorsettling tank interactions are yet to be developed for optimal design and operation of a wastewater treatment plant and thus to make ground for the development of computing techniques and software to serve the purpose.
The purpose of the present work is: (1) to develop a method for simultaneous design of a reactor and a settling tank constituting an activated sludge plant for an assigned performance level, (2) to develop an analytical and also graphical method for determining the range of recycle ratio and activated sludge concentration to achieve certain treatment level, (3) to work out a design method, which will ensure minimum footprint for the plant and (4) also to find the conditions of operation of an already functioning plant in the event the input parameters (influent flow rate and substrate concentration) differ from those assumed in designing. The fundamental work of Cho et al. (1996) will be taken as the basis for analysis, in which the authors studied the coupled system of reactor and the settling tank using Monod’s simple reaction kinetic model and limit flux theory. In the meantime, Pholchan et al. (2010) reported that the diversity of the microbial communities in the reactors was affected by changes in the operating parameters of the bioreactor. Tench (1994) showed that the biological treatment processes were ‘complex systems’ where many different kinds of microbes grew and interacted in a dynamic manner. The author concluded that the analysis of the treatment process would be more precise, if all the complexities concerning microorganism activities were taken into account. This paper, however, aims at describing the performance and design of the activated sludge plant in principle, when the operation of the reactor and the settling tank are described by simple equations. Thus, for the simplicity of the present analysis, it is considered that whatever changes may take place with the diversity of the microbial communities in the reactors, the microbiological and settling parameters of the sludge do not change.
In this analysis, the activated sludge plant is considered to be consisted of two units: activated sludge reactor and settling tank. The design parameter of the reactor is volume and that of the settling tank is the area. Assuming a definite height for the activated sludge reactor, the design parameter of both the units has been reduced to area. Thus the optimization criterion is accepted to be the minimum total area (footprint) of the units. It is assumed that the Monod equation fully describes the growth kinetics of microorganism and the settling characteristics of the sludge follows some power law. It is found that in the designing of the interacting reactorsettler system, three variables such the activated sludge concentration X in the reactor, the sludge recycle ratio α and the sludge waste ratio β determine the total area of the plant. For diminishing the number of variables, the value of β was kept constant at 0.01. Contradicting the popular perception that ‘an increase in α results in an increase in the biodegradation rate and the overall space required for the plant decreases’, it is found that with an increase in α, the total area of the plant monotonously increases. With the sludge waste ratio β kept at constant, the sludge recycle ratio α, however, appears to be the only controllable parameter to maintain the desired level of treatment in the plant when the feed parameters differ from those assumed in the design of the plant. A procedure has been developed for simultaneous design of a reactor and settling tank, ensuring minimum area (footprint) for an activated sludge plant, and also a methodology has been worked out to recalculate the operating sludge recycled ratio in cases when influent parameters differ from those in design.
It should be noted here that the growth kinetic and the settling model used in this work is not the best choice. Analysis would be more precise, if process rate equations are chosen from the Activated Sludge Model series (named as ASM1, ASM2, ASM2d, ASM3), which are the widely accepted models for the design and operation of biological wastewater treatment systems. This is a continuously developing model series, which includes always new elements to entrap new experiences in wastewater treatment (Henze et al. 2002). The ASM1 predicts the performance of singlesludge systems carrying out carbon oxidation, nitrification and denitrification. The ASM2 includes nitrogen and biological phosphorous removal. ASM2d (which is the expanded form of the ASM2) includes the denitrifying activity of the phosphorous accumulating organisms. The ASM3 includes storage of organic substrates as a new process. Iacopozzi et al. (2007) shows that the ASM1, ASM2, ASM2d, and ASM3 are limited to the description of the denitrification on nitrate only, as they present the nitrification dynamics as a singlestep process. The authors propose an enhancement to the basic ASM3 model, introducing a twostep model for the process nitrification and thus consider the denitrification on both nitrite and nitrate.
With the inclusion of newer and newer elements in the rate equations of the processes in the reactor, the complexity of the ASM series models increases along with the increase in the preciseness of the predictions. The main purpose of the present work, however, is to illustrate the principle of a methodology for determining the minimum required area for a plant, and hence in order to avoid complexities, the simple Monod equation (for aerobic growth of heterotrophs in excess oxygen as per ASM1 model) has been chosen as the growth kinetics of the activated sludge in the reactor.
Theoretical
Design equation for the reactor
 (1)
The growth kinetics follows the simple Monod equation,
 (2)
The flow behavior in the reactor is assumed to be completely mixed,
 (3)
The reactor is operating under steady state, and
 (4)
The activated sludge concentration in the influent (kg/m^{3}), X_{ 0 } = 0.
Design equation for the settling tank
Analytical expression for the limiting flux, F_{L}:
 (1)
The settling rate of the floc follows power law of the type v_{s} = aX^{−n}
 (2)
The flow behavior in the settling tank is assumed to be ideally plug flow type; vertical mixing as well any concentrationvariation in the radial direction is ignored,
 (3)
The settling tank is operating under steady state,
 (4)
The growth rate in the settling tank is zero, and
 (5)
The activated sludge concentration in the effluent (kg/m^{3}), X_{e} = 0.
The mathematical expression for the total limiting flux F_{L} from Eq. (11) can be substituted in Eq. (7) to give the equation for determining the settling area A_{s} in terms of X and X_{u}.
Optimal design
Optimum value of the activated sludge concentration, X_{opt}
Equation (18) shows that ∂A_{r}/∂X is negative, but ∂A_{s}/∂X is positive for any value of X. Thus, for some given value of α andβ, the reactor area (correspondingly reactor volume) decreases as the activated sludge concentration increases. The settling area, however, increases with the increase in the activated sludge concentration. Naturally, it is expected that the total area A_{T} will pass through minimum for some optimal value of X = X_{opt}.
Equation (19) gives an optimal value of X for assigned value to α ≥ 0 and β ∈ (0, 1). All values of X_{opt}, however, cannot be used effectively. The effective values are those, which satisfy Equation/Inequality (6).
Optimum value of the sludge recycle ratio, α_{opt}
It appears that ∂A_{r}/∂α is always positive and the reactor area (correspondingly volume) increases as the sludge recycle ratio α increases. ∂A_{s}/∂α, on the other hand, may assume positive, negative or zerovalue depending on the sign of the parameter ξ. In the range of low values of α, ∂A_{r}/∂α may become negative and the settling area decreases as the sludge recycled ratio increases. For high values of α, the value of ξ, becomes positive and the settling area increases as the sludge recycled ratio increases.
Condition of absolute minimum for A_{T}
The first term on the left hand side of Eq. (21) is always positive. The second term on the left hand side may be positive, negative or zero depending on the sign of the parameter ξ. Thus, if Eq. (21) has got some solution for α = α_{opt}, then putting that value of α in Eq. (19), the value of X_{opt} can also be calculated, and finally, the minimum total area (A_{T}/Q_{0})_{min} can be calculated from Eq. (16). Attempts have been made to solve Eq. (21) by trial and error method, but it was found that it had no solution and for any value of α under study, ∂A_{T}/∂α is greater than zero (illustrated later in Fig. 5), which will mean that the total area increases monotonously as α increases.
Illustration of the model
Data for the illustration of the model and plant design
Water parameter  
Influent flow rate (Q_{0})  20,000 m^{3}/day 
Inlet substrate concentration (S_{0})  0.25 kg/m^{3} 
Outlet substrate concentration (S)  6.0 × 10^{−3} kg/m^{3} 
Microbial parameters  
Endogenous decay coefficient (k_{d})  0.06 d^{−1} 
Maximum yield coefficient (Y)  0.5 kg/kg 
Sludge settling characteristics  
Empirical coefficients  
a  350 m/day 
n  2.5 
Operational parameters  
Sludge recycled ratio (α)  Variable 
Sludge waste ratio (β)  0.01 
Activated sludge concentration (X)  Variable 
Additional data  
Assigned value to reactor height/depth (H_{r})  4 m 
As seen from Fig. 4 the reactor area (consequently volume) decreases as the activated sludge concentration X increases. The settling area, however, increases as the activated sludge concentration increases. Reasonably, the total area for the facilities passes through minimum. For the given data set in Table 1 and for α = 0.7, the minimum total area is obtained at X = 3.23 kg/m^{3}, which is the same as the optimum sludge concentration X_{opt} predicted by Eq. (19) (and also as that illustrated in Fig. 3).
Design procedure
 (1)
Choose a height, H_{r}, for the reactor
 (2)
Choose waste sludge ratio, β
 (3)
Define the range of F/M ratio
 (4)
Determine the value of α_{min} and α_{max} analytically (Eqs. 22, 23) or graphically from the plots analogous to those in Fig. 3.
 (5)
Choose a suitable sludge recycled ratio α_{min} < α < α_{max}
 (6)
Determine the permissible Xrange for which the F/M ratio is maintained (Use Equation/inequality (6) for the purpose)
 (7)
Calculate the optimum value of X by Eq. (19)
 (8)
Calculate the area of the settling tank by Eq. (14)
 (9)
The total area calculated by the above procedure will give the minimum area for the facilities for the chosen α, β and H_{r}. There remains, however, a very confusing element in the design as to why the designer should choose higher α with complete awareness that it leads to higher area, while the lower α with lower total area could ensure the same performance. To find the answer of the question, the role of α should be analyzed in maintaining the stable performance of the plant in the event the feed parameters deviate from those assumed in the design. In the next sections, how and to what extent, a plant built with the proposed design method could be adjusted to the influent parameters will be discussed.
Adjustability of the designed activated sludge plant
Design parameters for three activated sludge plants I, II and III
Water parameters  
Influent flow rate (Q_{0})  20,000 m^{3}/day  
Inlet substrate concentration (S_{0})  0.25 kg/m^{3}  
Outlet substrate concentration (S)  6.0 × 10^{−3} kg/m^{3}  
Assumed parameters  Plant PI  Plant PII  Plant PIII 
Sludge recycled ratio (α)  0.35  0.50  0.90 
Sludge waste ratio (β)  0.01  0.01  0.01 
Activated sludge concentration (X), kg/m^{3}  2.85  3.07  3.32 
Height of the reactor (H_{r}), m  4  4  4 
Calculated parameters  
Volume of the Reactor (V_{r}), m^{3}  1,776  3,444  5,364 
Area of the reactor (A_{r}), m^{2}  444  861  1,341 
Area of the settling tank (A_{s}), m^{2}  1,428  1,328  1,205 
Total area of the Plant (A_{T}), m^{2}  1,872  2,189  2,546 
Let the three plants be working in complete mix regime. If the influent parameters (flow rate and influent substrate concentration) do not vary from those assumed in designing and also the microbiological and settling parameters of the sludge do not change, then the operator simply has to maintain the designed sludge recycled ratio α = 0.35, 0.50 and 0.90, respectively, for the three plants and the desired performance (S = 6.0 × 10^{−3} kg/m^{3}) will be achieved. The steady state activated sludge concentration X in all the three reactors will be maintained as that assumed in design spontaneously (without direct intervention from the operator). The question is how the performance of the plant be maintained at the desired level if the flow rate and/or the influent substrate concentration differ within certain range from that assumed in designing. The operator has got only one operating parameter to control and that is the sludge recycled ratio α. How can the new operating sludge recycled ratio α be chosen (maintaining the F/M ratio) such that the treatment level of the plant remains the same as that assumed in designing?
Recalculation of α for new influent flow rate and substrate concentration
It should be noted here that for the maintenance of desired F/M level in the reactor during design, the Xrange was bounded by complicated inequalities defined by the restriction Equation/inequality (6). During operation, the restriction Equation/inequality (23) has got much simpler form. This is so, as during the design, V_{r} is unknown and varies with α, but in operation V_{r} is known and independent of α.
Solution of the system of Eqs. (25–27)
Recalculation procedure for α_{re}:
 Step1

calculate the Xrange in compliance with f_{min} ≤ F/M ≤ f_{min} using Equation/Inequality (28);
 Step2

solve Eq. (30) for α_{re} > 0 by trial and error method;
 Step3

calculate X_{re} using Eq. (29) and check whether it satisfies the Xrange calculated in the Step 1. If yes, then accept the α_{re} as the operating parameter.
In the events, Monod equation describes the biodegradation process and the settling rate follows the power law, whatever might be the values of microbiological and settling parameter, Eqs. (25–27) can be solved for determining the operation parameter α. Even if no concrete method is strictly followed in the design of the reactor and the settling tank, Eqs. (25–27) would again give the correct α (if found such satisfying Eqs. 25–27) for operation.
Illustration of the new operating conditions
Let’s determine the operating sludge recycled ratio for the three plants described in Table 2 for two cases: (1) The influent flow rate is different from that used in design Q_{0} (λ_{q} ≠ 1), but the influent substrate concentration remains the same as S_{0} (λ_{s} = 1) and (2) The influent flow rate is the same as that used in design Q_{0} (λ_{q} = 1), but the influent substrate concentration is different from that used in design S_{0} (λ_{s} ≠ 1). For λ_{q} = λ_{s} = 1, the plants carries the organic load as designed (which is equal to Q_{0}S_{0}). For λ_{q} and/or λ_{s} > 1, the plants carry the organic load higher than that designed for, and for λ_{q} and/or λ_{s} < 1, the plants carry lower organic load than that designed for.
Case 1: (λ_{q} ≠ 1, λ_{s} = 1)
Figure 7 shows that choosing appropriate operating sludge recycle ratio α, for λ_{q} > 1 the recycled ratio of the plants PII and PIII can be readjusted to the new influent flow rate and ensure the same performance as designed. This is, however, not possible for the plant PI, which has been designed with α = 0.35 (almost equal to α_{min} = 0.349). It appears that the plant PI can not carry influent load higher than Q_{0} (with substrate concentration S_{0}). The plants PII and PIII have got some capacity in reserve. The plant PIII being designed with α = 0.9 has got higher reserve (up to λ_{q} = 2.0) than the plant PII designed with α = 0.5 (up to λ_{q} = 1.8).
For λ_{q} < 1, the sludge recycle ratio of all the three plants can again be readjusted. But the recalculated α for the plants PII and PIII appears to be unexpectedly high to be applied for influent flow less than that foreseen in design and some alternative/additional solution is to be sought for such cases.
Case 2: λ_{q} = 1, λ_{s} ≠ 1
Figure 8 shows that the effect of λ_{s} is similar to that of λ_{q}. Although not completely proportional both the variation factors have unidirectional effect on the recalculated operating parameters. Both Figs. 7 and 8 clearly indicate that the ‘optimal design’ is not enough for optimal operation of a plant in cases, when the load deviates from that assumed in the design.
For λ_{q}, λ_{s} < 1, the recalculated recycled ratio is not appealing to be applied for practical purposes. It should be remembered that the design equation was derived in terms of area per unit flow rate. Therefore if the design area/volume is partitioned and is used partially in necessity, the area per unit flow rate can be kept nearly equal to that assumed in design and the recalculated α will be similar to that in the design. Thus, the distribution of the reactor and the settling tank into several parallel units might be helpful to handle to organic load rate lower than that in the design. More study is required on series and parallel arrangement of the units to make a conclusion in this respect.
Conclusions
A design procedure has been developed, which would ensure the minimum area (footprint) for an activated sludge plant consisting of a reactor and settling tank. It is found that the reactor volume increases as the sludge recycled ratio α increases. The total area of the plant also increases with an increase in α. A methodology has also been worked out to recalculate the operating sludge recycled ratio in cases when influent parameters differ from those assumed in the design.
In fact, this work describes the principle of the development of a methodology and it is illustrated with the assumption that the growth kinetics and the settling characteristics of the activated sludge are described by simple Monod equation and a power law, respectively. More precise result is expected, if the methodology is applied to more precise rate equations as recommended by the ASM models for a given case. Also, the assumption of ideal flow behavior in the reactor as well as in the settling tank will bring some error in the estimation. A correction factor could be introduced to account for the deviation the flow pattern from ideality. The procedure and mathematical formulations developed in this work for design and operation can be used in the development of software for the purpose.
Notes
Acknowledgments
Part of the work was done in The Hochschule Karlsruhe (HsK). The financial support from Alexander von Humboldt Foundation for renewed research stay of Prof. Islam in HsK is highly appreciated.
References
 Bürger R, Diehl S, Nopens I (2011) A consistent modelling methodology for secondary settling tanks in wastewater treatment. Water Res 45:2247–2260CrossRefGoogle Scholar
 Cho SH, Chang HN, Prost C (1996) Steady state analysis of the coupling aerator and secondary settling tank in activated sludge process. Water Res 30(11):2601–2608CrossRefGoogle Scholar
 Coe HS, Clevenger GH (1916) Methods for determining the capacities of slimeset tling tanks. Trans AIME 55:356–384Google Scholar
 David R, Vasel JL, Wouwer AV (2009) Settler dynamic modeling and MATLAB simulation of the activated sludge process. Chem Eng J 146:174–183CrossRefGoogle Scholar
 Diehl S (2007) Estimation of the batchsettling flux function for an ideal suspension from only two experiments. Chem Eng Sci 62:4589–4601CrossRefGoogle Scholar
 Diehl S, Jeppsson U (1998) A model of the settler coupled to the biological reactor. Water Res 32(2):331–342CrossRefGoogle Scholar
 Ekama GA, Marais P (2004) Assessing the applicability of the 1D flux theory to fullscale secondary settling tank design with a 2D hydrodynamic model. Water Res 38:495–506CrossRefGoogle Scholar
 Flamant O, Cockx A, Guimet V, Doquang Z (2004) Experimental analysis and simulation of settling process. Trans IChemE Part B Process Saf Environ Prot 82((B4)):312–318CrossRefGoogle Scholar
 Flores X, Bonmatí A, Poch M, BañaresAlcántara R, RodríguezRoda I (2005) Selection of the activated sludge configuration during the conceptual design of activated sludge plants. Ind Eng Chem Res 44:3556–3566CrossRefGoogle Scholar
 Gernaey KV, van Loosdrecht MCM, Henze M, Lind M, Jørgensen SB (2004) Activated sludge wastewater treatment plant modelling and simulation: state of the art. Environ Modell Softw 19(9):763–783CrossRefGoogle Scholar
 Gujer W, Henze M, Mino T, van Loosdrecht M (1999) Activated sludge model No. 3. Water Sci Technol 29(1):183–193Google Scholar
 Henze M, Gujer W, Mino T, van Loosdrecht M (2002) Activated sludge models ASM1, ASM2, ASM2d and ASM3. IWA publishing, CornwallGoogle Scholar
 Hu ZR, Wentzel MC, Ekama GA (2003) Modelling biological nutrient removal activated sludge systems—a review. Water Res 37:3430–3444CrossRefGoogle Scholar
 Iacopozzi I, Innocenti V, MarsiliLibelli S, Giusti E (2007) A modified activated sludge model no. 3 (ASM3) with twostep nitrification–denitrification. Environ Modell Softw 22(6):847–861CrossRefGoogle Scholar
 Islam MA, Karamisheva RD (1998) Initial settling rate/concentration relationship in zonesettling. J Environ Engg 124(1):39–42CrossRefGoogle Scholar
 Metcalf and Eddy (1998) Wastewater engineering, 3rd edn. Tata McGrawHill, New DelhiGoogle Scholar
 Moulleca YL, Potiera O, Gentrica C, Leclerc JP (2011) Activated sludge pilot plant: comparison between experimental and predicted concentration profiles using three different modelling approaches. Water Res 45(10):3085–3097CrossRefGoogle Scholar
 Patziger M, Kainz H, Hunze M, Józsa J (2012) Influence of secondary settling tank performance on suspended solids mass balance in activated sludge systems. Water Res 46(7):2415–2424CrossRefGoogle Scholar
 Pholchan MK, de C, Baptista J, Davenport RJ, Curtis TP et al (2010) Systematic study of the effect of operating variables on reactor performance and microbial diversity in laboratoryscale activated sludge reactors. Water Res 44(5):1341–1352CrossRefGoogle Scholar
 Riddell MDR, Lee JS, Wilson TE (1983) Method for estimating the capacity of an activated sludge plant. J WPCF 55(4):360–368Google Scholar
 Rigopoulos S, Linke P (2002) Systematic development of activated sludge process designs. Comput Chem Eng 26:585–597CrossRefGoogle Scholar
 Scuras SE, Jobbagy A, CPLG Jr (2001) Optimization of activated sludge reactor configuration: kinetic considerations. Water Res 35(18):4277–4284CrossRefGoogle Scholar
 Sheintuch M (1987) Steady state modeling of reactorsettler interaction. Water Res 21(12):1463–1472CrossRefGoogle Scholar
 Sherrard JH, Kincannon DF (1974) Operational control concepts for the activated sludge processes. Wat Sewage Works, March, pp 44–66Google Scholar
 Smollen M, Ekama G (1984) Comparison of empirical settling velocity equations in flux theory for secondary settling tanks. War SA 10(4):175–184Google Scholar
 Tench HB (1994) A theory of operation of full scale activated sludge plants. Water Res 28(5):1019–1024CrossRefGoogle Scholar
 Vanderhasselt A, Vanrolleghem PA (2000) Estimation of sludge sedimentation parameters from single batch settling curves. Water Res 34(2):395–406CrossRefGoogle Scholar
 Vesilind PA (1968) Design of prototype thickeners from batch settling tests. Water Sewage Works 115(7):302–307Google Scholar
 Zhang D, Li Z, Lu P, Zhang T, Xu D (2006) A method for characterizing the complete settling process of activated sludge. Water Res 40:2637–2644CrossRefGoogle Scholar
Copyright information
This article is published under license to BioMed Central Ltd. Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.