Models for Optimizing the Activated Sludge Process

11.3.1 Preface

The models discussed in Section 11.2 can only be used for process control via offgas measurements. If we want to find the best process and equipment design with the help of models, we further have to introduce a known formula available for the specific growth rate of bacteria:

in bacterial balances and to couple it with the substrate removal rate: pX

and the oxygen consumption rate: pX


The next step is to find the best equation for Eq. (11.31) (see Chapters 6 and 10).

The construction of such models will be demonstrated in the next Sections 11.3.2 and 11.3.3, starting with a relative simple model consisting of only three balances and ending with the activated sludge model (ASM) 1 with 13 balances. Further models will be mentioned briefly in Section 13.3.5.

Modelling the Influence of Aeration on Carbon Removal

The assumptions for this model are:

• only carbon removal.

• Monod kinetics (considering S and c' as substrates).

• Bacteria concentration is measured as g L-1 COD.

Three balances must be considered, the balance for substrate (as COD; Fig. 6.3):

the balance for heterotrophic bacteria (here as COD; see Fig. 6.3): Qm(Xm-X) S c'

and the overall balance for oxygen (liquid and gas):

The three reaction rates on the right-hand part of the balances differ only in the

YX/S, in the oxygen balance YX/O2;

yield coefficients: in the substrate balance YX/S, in the oxygen balance YX/O2 and the factor 1 in the bacterial balance.

This fact can be written using a simple matrix (Henze et al. 1987a), considering (see Table 11.1):

Table 11.1 Simple model matrix for an activated sludge reactor, only carbon removal, see Eqs. (11.34) to (11.36).


Kinetic formation


Aerobic growth of heterotrophs

Bacteria 1

Substrate 1


Dissolved o2


Growth rate


Equation (11.38) means that the substrate is partly used for catabolism (Yo2/S) and for anabolism (YX/S)

We want to discuss some solutions to Eqs. (11.34) to (11.36). We replace the oxygen consumption rate QG (co2,o—co2)/V by the specific oxygen mass transfer rate using an oxygen balance of the dispersed air:

Qg (co2,o -co2)/V — kla(c*-c') With Eqs. (11.36), (11.37) and (11.39), the balance of oxygen is:


It is possible to define dimensionless numbers which provide several advantages: to minimize the number of parameters and to be free of units. We will use:

The dimensionless concentration of dissolved O2, C' — —

The dimensionless concentration of the substrate, S" — —

• The dimensionless concentration of bacteria, X" = —

Introducing Eqs. (11.41) to (11.43) into Eq. (11.40), we obtain:




: Sm m Semenow number

and — as the dimensionless oxygen saturation concentration.

For high Sm numbers, there is only a very low concentration gradient of dissolved O2 near the bubble surface and the reaction is controlled by growth kinetics of bacteria; for low Sm numbers, c' is very low (c*-c'~ c*) and the reaction is controlled by the mass transfer rate. In a similar manner, the balances of substrate in Eq. (11.34) and bacteria in Eq. (11.35) can be written in dimensionless form (see Section 6.2), with Da = pmaxtR as the Damkohler number, nR = QR/Q0 as the recirculation of sludge, nE=XD/Xa as the thickening ratio and Mo = S0/KS as the Monod number (Mehring, 1979).

Figure 11.1 demonstrates some solutions as:

for Mo = 10 (KS = 50 mg L-1 COD, S0 = 500 mg L-1 COD). The other constant parameters are given in Figure 11.1.

For Da < 0.2 (S*=Mo=10), the mean retention time is low and all bacteria are washed out, even though the substrate concentration is high. Due to the low oxygen consumption rate (low tR), no influence of Sm (or kLa) can be observed for 0.2 < Da < 0.25.

For Da > 2.5, the oxygen consumption rate is again very low because of the very low substrate concentration. Only in the middle region (0.25 < Da < 2.5) can a large influence of Sm (or kLa) be observed. For Sm > 100, carbon removal and bacterial growth are not dependent on aeration intensity.

For Sm = 25 and a substrate removal of 90% (S* = 1 for S* = Mo = 10), a Da = 0.5 is needed if an aeration system is to be used effectively (Fig. 11.1). The reaction is limited by dissolved oxygen. Using pure oxygen (c*/K' = 475), the mean retention time tR can be reduced by about a factor of 2 and oxygen limitation is avoided nearly completely (Fig. 11.2).


M \


IOO \ VSO \25


- 10






Fig. 11.1 Influence of dimensionless mean retention time Da = |maxtR and dimensionless specific mass transfer rate Sm = kLa/|max on dimensionless effluent substrate concentration S/K S. Constant parameters: Mo = S0/K2 = 10, nR = 0.45, nE = 3, c*/K' = 95 (aeration).

Fig. 11.1 Influence of dimensionless mean retention time Da = |maxtR and dimensionless specific mass transfer rate Sm = kLa/|max on dimensionless effluent substrate concentration S/K S. Constant parameters: Mo = S0/K2 = 10, nR = 0.45, nE = 3, c*/K' = 95 (aeration).


I v

c*/K = 95{air)

\ \ X x

/ \ V c*/K'= 475 (O2 j**

Fig. 11.2 Influence of dimensionless mean retention time Da = |maxtR and dimensionless saturation concentration c*/K' = 95 (air) and 475 (pure oxygen) on dimensionless effluent substrate concentration S/KS. Constant parameters: Mo = S0/KS = 10, nR = 0.45, nE = 3, Sm = 25.

Activated Sludge Model 1 (ASM 1)

This model describes the relatively complex process of aerobic and anoxic C and N removal from municipal wastewater. It is based on the post-doctoral work of Gujer (1985) and the work of Henze et al. (1987a, b). In order to present the model in its fundamental form, it is shown as a matrix which contains only reaction terms as sources (positive) or sinks (negative). This matrix is normally published without further explanations or is explained only briefly (Grady et al. 1999; Henze et al. 2000). In this section, we try to give an introduction to provide a better understanding.

The model can be fit to:

• Primary models describing different kinds of reactor configurations (anoxic/aerobic; aerobic/anoxic).

• Models describing different kinds of reactors (CSTR in one stage or as a cascade, plug flow or flow with axial dispersion, see Chapter 6).

The very simple matrix in Table 11.1 consists of only three different substances (bacteria, substrate and oxygen) and only one process (aerobic growth of hetero-trophs and removal of organic substrates). ASM 1 consists of 13 different substances and eight different processes. At the beginning, we will give an overview of these 13 substances (Table 11.2).

Table 11.2 The 13 substance concentrations of ASM 1. Units for symbols 1-7: mol L-1 COD; units for symbol 8: -mol L-1 COD; units for symbols 9-12: mol L-1 N; units for symbol 13: mol L-1.






Soluble inert organic matter



Readily biodegradable substrate



Particulate inert organic matter



Slowly biodegradable substrate



Active heterotrophic biomass



Active autotrophic biomass



Particulate products from biomass decay



Dissolved oxygen



Nitrate and nitrite nitrogen



Ammonium and amonia nitrogen



Soluble degradable organic nitrogen



Particulate degradable organic nitrogen




It should be emphasized that, besides the readily biodegradable substances SS, slowly biodegradable substances XS are considered as solid particles, which must first be hydrolyzed by exoenzymes. Xj is the corresponding inert organic matter which cannot be disregarded, as we will see below. Particulate products XP result from the lysis of bacteria or remain as insoluble solids.

The eight processes are summarized in Table 11.3.

The matrix of the ASM 1 model consists, therefore, of a 13 x 8 matrix for the 13 substances in the columns and eight processes in the rows.

For a CSTR in non-steady condition, 13 balances must be taken into account, each of which is written in the same way as Eq. (11.47):

dS Qm

dt V

eight for different dissolved components (7 S + c') and five for different undissolved components X. Only the reaction terms rSi are arranged in the matrix.

The reaction terms should be discussed in some detail before the matrix is constructed (see Table 11.4). We will begin with the reaction terms for soluble inert organic matter.

Table 11.3 The eight processes of ASM 1.

No. Process

1 Aerobic growth of heterotrophs

2 Anoxic growth of heterotrophs

3 Aerobic growth of autotrophs

4 Decay of heterotrophs

5 Decay of autotrophs

6 Ammonification of soluble organic nitrogen

7 Hydrolysis of particulate organics

8 Hydrolysis of particulate organic nitrogen

Table 11.4 Process kinetics and stoichiometric parameters of the activated sludge model ASM 1 plotted in a matrix form (13 parameters, 8 processes; Henze et al. 2000)

Component fi)-

Process rate rf [ML~3T_1]

1 Aerobic growth ofheterotrophs

2 Anoxic growth ofheterotrophs


3 Aerobic growth of autotrophs

4 Decay of heterotrophs

5 Decay of autotrophs

6 Ammonification of soluble organic nitrogen

7 Hydrolysis of particulate organics

IXB fpixi


Ki0 SNOj

8 Hydrolysis of particulate organic nitrogen

This assumption is a simplification made by ASM 1. In reality, such dissolved inert substances (non-biodegradable) can be formed by the hydrolysis or lysis of solid particles or other dissolved substances or they can be adsorbed on solid surfaces.

i = 2, SS - Readily Biodegradable Substrate

rSS = - Y- Pm»,H—— I——' + ' K +s ) XH (11.48)

rSS is the rate of COD removal by aerobic and anoxic bacteria.

The measured COD is:

and SS can only be determined if Si is known. n is the ratio of pmax,H values for anoxic and aerobic bacteria (Henze 1986).

i = 3, Xi - Particulate Inert Organic Matter rXi = 0

Nearly the same remarks are valid as those above (see i = 1, Sj). Nevertheless, Xj is needed for the definition of fi (see Eq. 11.52) and for the formation of the balance describing non-steady state transport:

dXi Qm

dt V

i = 4, XS - Slowly Biodegradable Substrate rXs= (1-f) kdHXH + (1-f) kdAXA

formation from formation from decay of heterotrophs decay of autotrophs

Kx + Xs/Xh \Kh + c Ki0 + c Kno + Sno3/ ^_v_q hydrolysis of entrapped organics by aerobic and anoxic bacteria Xi fi =--(11.52)

rH,Ax hydrolysis by anoxic bacteria rH,Ae hydrolysis by aerobic bacteria

11.3 Models for Optimizing the Activated Sludge Process | 279 i = 5, XH - Active Heterotrophic Biomass ss / c n Ki0 sNO3 , X

.._v_q growth of aerobic and anoxic bacteria

decay of heterotrophs i = 6, XA - Active Autotrophic Biomass rxA = Fmax,^—^^- ^ , XA - ^XA (11.56)

growth of autotrophs decay of autotrophs i = 7, XP — Particulate Products from Biomass Decay rXP = fP kdH Xh+ fpkdAXA (11-57) ^_v_q production rate by decay

reflects oxygen consumption (or COD removal) by aerobic heterotrophs and auto-trophs. Therefore, the units of rO2 are g m-3 h-1 COD.

YO2/XH follows from:

anabolism catabolism

Yxh/ss Yxh/ss


280 | 11 Modelling of the Activated Sludge Process For autotrophic nitrifiers one can write: Yo

o yxa/nh4


catabolism anabolism as well as:

rO2 64 g O2


Finally, Eqs. (11.61) and (11.65) are introduced into the matrix of Table 11.4 (space i = 8 for j = 1, j = 3).

i = 9, SNO3 - Nitrate Nitrogen

As already assumed for nitrifier growth (i = 6), where nearly no NO2 is produced, denitrification goes directly to nitrogen and the denitrification of NO2 is not considered (Chapter 10).

= n SS Ki0 SNO3 x rNO3 = _ 7NO3/XH pmax,H n —-— —-' —-"- XH

KS + SS Ki0 + c KNO + SNO3 ^_^_q reduction of NO3 by denitrification o SNH4 c

formation of NO3 by nitrification



AYO2/nO3 is the oxygen savings by denitrification after nitrification and can be calculated using:

YO2/NH4_N,x = 4.57 g O2 (g NH4_N)_1 follows from Eq. (11.64).

For the calculation of Yo2/No3 we have to use the catabolic production of No— by nitrification:

and the consumption of No— by denitrification using methanol as an energy source:

6No— + 5 CH3oH ^ 3N2 + 5 Co2 + 7 H2o + 6oH— (11.69b)

in comparision with the aerobic oxydation of methanol:

For nitrification of 6 NH+ (using 5CH3oH for denitrification), 24 moles o are needed; for aerobic oxydation of the same amount of 5 CH3oH, 15 moles o must be used. Therefore, the difference of both follows to:

Considering Eq. (11.68), one obtains:

AYo2/no3 = Yo2/nh4 — Yo2/no3 = 4.57 — 1.71 = 2.86 g o2 (g No3 — N)—1

From Eqs. (11.67) and (11.61), it follows (i = 9, j = 2):

i = 10, SNH4 - Ammonium Nitrogen

Ks + Ss Kh + C NH4 uptake by aerobic heterotrophs

SS Ki0 SNo3 v

NH4 uptake by anoxic heterotrophs

NH4 uptake and NH4 oxidation by autotrophs

+ ka SNDXH

NH4 formation by anoxic hydrolysis of heterotrophs i = 11, SND - Soluble Degradable Organic Nitrogen

NH4 + NH3 formation of uptake by organic nitrogen heterotrophs by hydrolysis i = 12, XND - Particulate Degradable Organic Nitrogen rND = (iXB — fPiXP) kdHXH + (iXB — fPiXP) kdAXA — kenXND

formation from formation from hydrolysis decay of heterotrophs decay of autotrophs

XN nitrogen in bacteria

XH +XA+XS mass of bacteria + slowly biodegradable substrate

XN nitrogen in bacteria

Xj particulate inert organic matter in bacteria

biodegradable organic nitrogen ixB fpixp =-—r--:----(11-77)

particulate organic matter fP see Eq. (11.58).

SAlk is the concentration of anions (alkalinity). The balance: dSAlk Qm

dt V

describes the change of pH. For SAlkP SAlk0 the pH increases and vice versa. The pH influences some equilibria (NH+/NH3, NO-/HNO3) and the activity of bacteria. In wastewater with a low SAlk0 and nitrification, rAlk cannot be neglected. The balance of anions is written in moles.

use of NO3 for growth of aerobic heterotrophs jxb 1 YXh/ss \ n SS Ki0 SNO3 X T"!--- Pmax,H ' n ~-- ~-T ---- XH

use of NO3 for growth of heterotrophs and production of HCO- by denitrification

14 + 7 YXA/NH4/ FmaX,A Ksa + Snh4 KA + c' Xa+ 14 en Xs (')

use of NO- for growth of autotrophs production of NO-

and use of HCO- for H+ uptake by hydrolysis of par-

during nitrification ticular orgaic nitrogen

The production of HCO- during denitrification is described by the stoichiometry for catabolism and anabolism using CH3OH as an energy source (see Eqs. 10.43 and 10.44)'

As follows from the catabolism of nitrification without NO- enrichment:

and with the use of HCO3- as an electron acceptor:

12 HCO- are needed for 6NH+, these are 6 more moles anions than those recovered by denitrification (see Eq. (11.69) and consider OH- + CO2 = HCO-).

Because: YHCO-/NHj = 2, we write for the rate of HCO- consumption by nitrification (Table 11.4, space i = 13, j = 3 in the matrix):

The ASM 1 model makes it possible to simulate different loadings of municipal activated sludge plants in steady and non-steady state without biological phosphorous removal. It can be used as the basis for a training program for the staff of wastewater treatment plants and for design calculation of the plant and optimization of the processes.

After intensive study of the model, the reader of the matrix (see Table 11.4) will see the advantage in using the matrix in combination with a computer program.

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