Aerobic growth according to Monod kinetics and lysis according to first order kinetics are ... To the right, in the last column, a process rate equation Pj is defined.
War.
Sci. Tech.
Vol.
23,
Kyoto, pp.
0273-1223/91 $()·()O + ·50 1990 IAWPRC
1011-1023, 1991.
Copyright ©
Printed in Great Britain. All rights reserved.
ACTIVATED SLUDGE MODELLING AND SIMULATION Willi * Swiss
Gujer* and Mogens Henze** Federal Institute for Water Resources and Water Pollution Control
(EAWAG), 8600 Dubendorf, Switzerland * * Department
of
Environmental
Denmark, 2800 Lyngby, Denmark
Engineering,
Technical
University
of
ABSTRACT The matrix format for the presentation of biokinetic models is explained with a simple model and expanded for the 'Activated Sludge Model No. l' of the IAWPRC Task Group for Mathematical Modelling for Design and Operation of Biological Wastewater treatment. With the aid of a simulation program a complex activated sludge model which includes two organic substrates and nitrification is developed stepwise and compared to experimental results. KEYWORDS Activated sludge process, mathematical modelling, simulation, nitrification, hydrolysis, lysis, 'Activated Sludge Model No. 1'. INTRODUCTION Many mathematical models for the activated sludge process have been proposed in the last decades, the most advanced allow for dynamic simulation of complex activated sludge flow schemes and may include degradation of organic material, nitrification, denitrification, even biological phosphorous removal or biomass composition (bulking). None of these models has reached broad acceptance in practical application except simplistic models which are at best suitable to describe the steady state of completely mixed activated sludge processes. The IAWPRC Task Group on Mathematical Modelling for Design and Operation of Biological Wastewater Treatment (1987) proposed an 'Activated Sludge Model No. l' (No. 1 was chosen to indicate that this model shall further be developed) which allows for the dynamic simulation of nitrification/denitrification in a variety of activated sludge flowschemes. Today several public domain and commercial simulation programs are available, which are based on this model and its further developments. Acceptance of these programs for practical application throughout Europe, North America and South Africa is quite good but by no means broad and general. One of the reasons, why the potential of mechanistic models of biological wastewater treatment is not widely accepted, might be the fact, that the literature on mathematical models is not easy to read, is many times not well structured and frequently does not provide the background which led to the development of the model. This paper shall try to identify the elements of an activated sludge model and to demonstrate how a biokinetic model may be improved step by step. Special care is given to the clear distinction between transport and transformation processes. ELEMENTS OF AN ACTIVATED SLUDGE MODEL
Deterministic mathematical models, as they are used here, describe activated sludge systems based on material balance equations. These equations relate changes of the state of the system (concentrations) 1011
1012
w.
GUJER and M. HENZE
to transport and transformation processes. Transport processes are characteristic for the design of a system (reactor configuration, distribution of influent, mixing, excess sludge removal, etc.), they leave the chemical structure of a" materials unchanged. Transformation processes are governed by the local, intensive conditions and involve the change of the chemical structure of the components. A deterministic model of an activated sludge system is therefore composed of at least the following elements (Submodels): - A list of components of interest, expressed as an array of concentrations [Cil. - A characterization of the transformation processes affecting these components: The biokinetic model, consisting of the stoichiometric matrix [Vj .i) and the array of process rate equations [Pj) (see below). - A characterization of the flowscheme of tri e system, including secondary clarifiers, input and output as we" as aeration equipment. - A characterization of internal transport and mixing, possibly separated for dissolved and particulate components (sedimentation, thickening). PRESENTATION OF BIOKINETIC MODELS Many mathematical models of the activated sludge process may be found in the literature, they differ primarily in the way that the biological transformation processes are described (the biokinetic model). In the course of its work, the IAWPRC Task Group realized that many models are presented in the complex form of materials balance equations, which include transport, rather than in the form of identifiable submodels. Frequently it is only with great effort, that the underlying model equations for the transformation processes may be found and isolated. The Task Group therefore proposed to present the model used for the biological transformation processes in the form of a matrix, which is clearly structured, may easily be read, once this structure is understood, and finally it can easily be translated into computer code in the context of simulation programs. The matrix notation is best introduced in the form of a simple example (Table 1): Aerobic growth according to Monod kinetics and lysis according to first order kinetics are the two processes of the model. Therefore: - Three components will be looked at: Dissolved oxygen with concentration A dissolved organic substrate with concentration Heterotrophic biomass with concentration
m-3) gCOD m-3) gcoD m-3)
(902
These have the index i and are introduced in form of an array of concentrations in the first row and with short definitions, combined with an indication of the way they are measured (COD, �) in the lowest row. - Two transformation processes with index j are considered. The aerobic growth of heterotrophic biomass at the expense of the organic substrate. Lysis of heterotrophic biomass, a process which is used to summarize a" processes which lead to a loss of biomass: decay, lysis, endogenous respiration, predation etc. The names of the transformation processes are listed in the first column of Table 1. - The center of Table 1 contains the stoichiometric coefficients Vj,j for the different processes in the form of a stoichiometric matrix. Here the growth process uses aissolved oxygen and substrate as educts, which leads to negative coefficients VII and V12' ' and produces biomass, which leads to a positive coefficient V13' . The exact mathematical form of the coefficients introduced will be discussed below. Lysis consumes biomass, V23 , and liberates biodegradable substrates, which become available for the growth process again. Lysis is assumed not to affect or to be affected by dissolved oxygen.
V22'
- To the right, in the last column, a process rate equation Pj is defined. The Monod equation is used for the growth process, a first order rate equation is used for lysis. - The lower left corner contains a short definition of stoichiometric parameters, the lower right corner contains definitions of kinetic parameters.
1013
Activated sludge modelling and simulation
For each process, one stoichiometric coefficient vji may be chosen freely, preferably as a dimensionless number with the value of +1 or -1. For aerobic growth V1� +1 and for lysis V23 = -1 have been chosen here. Once these coefficients are fixed, the dimensionS/units of the process' rate equations are fixed also. Here the dimensions become [Mt,iomass L-3 T·1]. -
The stoichiometric matrix, as presented in Table1, relates to the conservation of mass, elements etc. in horizontal direction. In the specific example, no COD may disappear in either process. This is clearly indicated for the lysis process, where the sum of all stoichiometric coefficients add up to zero: 1: V2i = O. Since dissolved oxygen is equivalent to negative oxygen demand (-COD), COD continuity for the growth process must be written as: -V11 + V12 + V13 O. The choice of the Yield coefficient YH as the basic stoichiometric parameter for groWth, together with the COD continuity equation, is therefore sufficient to determine all stoichiometric coefficients fot growth. ..
Table 1. Example of a simple biokinetic model as presented in matrix notation. See text for explanation. 1:
Components i List of processe.
1: Aerobic Growth
S
j
o
1 --+1 Y H
2: Lysis Observed transformation rate ri Definition of Stoichio_tric parameters:
Y = Heterotrophic H Yield c oeffic ent - ] [MH MS
i
.
ri = 1: .
J
V·
2: S s
3: XH
1 -YH
+1
I1m,H
+1
-1
bH
J,1 Pj •
0> :>. 14 0
OQ 'f'iO c:;u III 0> f.I 0
'tl Q)
'tlQ) Q)+)
c:; N
Q)O
:>
.-i 0 01 01 .f'i Q
Process Rate Equation
•
•
Ss
•
KS + S s
Pj
XH
XH
3 [MiL- T-1]
:> III .-if.! o+) 01 01
.� '§
QfIl'
Definition of kinetic par_ters:
Q 0 U
0 .f'i .t: 0. 0 f.I +JOI o 01 f.! III
11m KS
Q) I1i
bH
+JO
Q).f'i
=111
'H
=maximum specifir growth rate [T- ] =Saturation Coefficient for 3 S ubstrate [McOD L- ] =Rate con� ant for decay [ T ]
I
The stoichiometric matrix relates to materials balance equations in vertical direction. Any materials balance equation is written for one component i. Each process j may affect this component. The observed transformation rate rl, as entered into the materials balance equation, is therefore the sum of the transformation rates of this material in all processes: rl 1: vi.1 Pj' -
•
The way of presenting biokinetic models (or any other array of transformation processes) as indicated in table 1, helps to clearly identify, when we are talking about kinetics, stoichiometry, conservation, materials balances, a process rate, a transformation rate, etc. Experience shows, that once we are familiar with this way of presentin" our transformation models, these models become easy to read and to understand. The task group adVises to accept this form. THE ACTIVATED SLUDGE MODEL NO.1
The goal of the Task Group was to present a state of the art mathematical model for the activated sludge process. The resulting 'Activated Sludge Model No.1' is documented in the final report of the Task Group (1987). The model is introduced here in Table 2 and may be characterized as follows: A total of 7 dissolved and 6 particulate components are used to characterize the wastewater and the activated sludge. In addition to dissolved oxygen and bicarbonate alkalinity these include two forms of biomass, 7 fractions of COD (organic material) and 4 fractions of nitrogen. Nine transformation processes are considered (The original Model No. 1 combines processes NO.6 and 7 into one process). Three relate to growth of heterotrophic and autotrophic (nitrifier) biomass, two
1 YA
5
=
=
I Decay,
.
=
.
'
'
I
O 'M CQ
�
0 ,.Q
Q)
.... �
.S f;l �M ...: 0 ;:;! l:
.... 0
.ii' '"
+1/14
-4.S7+YA -==- iB 7eYA YA �
13 12 11 10 9 SALK So SNO SN SN H Material, Denitrification -iB -l+YH -iB 14 YH iB 1-Y -l+YH H --------iB 40eYH 14 2.86eYH
1 -iB-- YA
7 18 S1 S s Organic -1 YH -1 YH
Lysis Ifpi 1-111-fpliB-fpeiB Hydrolysis of Colloidal, Particulate and Organic Nitrogen Material 6 I Aerobic Hydrolysis of -1 +1 Organic Matter 7 I Anaerobic -1 Hydrolysis of +1 Organic Matter +1 -1 810rg. Nitrogen -1 +1 9 I Ammonification M L r [ i -3 T-1] Observed Conver i � Vj,i e Pj sion Rate ri J ric ;;������;� � z z 8 8 z z 8 8 8 8 8 YH'YA = Y�eld Coefficients for al :J ., � Q) Q) C nS ... Q) ·... Q) M M Heterotrophs an� Q) 0 ., Aut�troph� [MM- ] roo .g � � {l 8' -:;; g � {l iB'�P N�tr�gen !l e � � � c � cQ) e'!l !'i !lM !lM Q) Content of B�o� nS 0 nS nS 0 !Xl III '" Z Z !l t;. 8' mass and paricul' 3 .... 0 iil t;. ., Q) g: Products [�M ] .� � ] 0 � � !l 8 0, � :!J::1 Jl::1 �'" I< M 0 'M 0 M "" fp Fract�onXof c 0 t! Z 'M '" al a cl '" :a :a!l -a e Particula�e nS ::l Q) Q) Q) ., :> '" Prod\1cts �n Decay '" o' ....0 R" �" �" 0 M .... 'M M �'M � I< M [i.1M-1] � '5 � tl t! :;l g .g -;: g t!.g � � il M .... O,.Q I< .... Q) 0 DI Q) ....Q) .... 3" M " 0 C I< .... 'M 0 nS c 'M .... Q.I ::r:: .... O'lO'l CIlO M Ol 2i en CI J
2 I Anoxic Growth +1 Denitrification 1-fpI iB-fpeiB fpl-1 3lDecay, Lysis Autotrophic Organisms, Nitrification 4 I Aerobic Growth +1
6 componentlill 12 13 14 5 � XN I j l procesS �XI Xp XH XA Xs Heterotrophic Organisms, Degradation of 1 I Aerobic Growth +1
I
•
=
h
So X /X -e kh S H .---•KX+XS/XH K oH+SO XH KOH P6eg;e�e�g K NO+SNO (P6+P7) e (XN/XS) kaeSNeXH Kinetic Parameters: 11m i=max.Growth rate,T-l Kii=saturation Coeff. bi �: � !�te Constant [T ] kh =Hydrolysis Rat=l -1 Constant, M�M3 T k a =Ammonificajw� R�re Constant,� M3 IT �g' �h=Correct�on Factor for anoxic Growth and !.iydrolysis [-] 1nd�ces �: H,A for Heterotrophic, Autotrophic Biomass . S,NH,NO,O for Matenals e, 9,10 and 12 X for particul .. Matter
S NH � eXA e KNH+SNH KOA+SO bAeXA e
J.lm.,A
S e s e�eXH IIm,H KS+SS KOH+SO SNO OHe-p1eK--e--- �h So K NO+SNO bHeXH
Proces� rate Law Pj [M L- ;;S T -1]
Table 2. Process kinetics and stoichiometry for the 'Activated Sludge Model NO. l' (IAWPRC Task Group for Mathematical Modelling for Design and Operation of Biological Wastewater Treatment, 1987).
ttl
�
::c
�
[
ttl �
S
�
a
8 ...
Activated sludge modelling and simulation
1015
represent decay of biomass and four describe 'hydrolysis' processes, in which complex organic material is made available for biodegradation in the form of simpler molecules. The process rate equations rely on hyperbolic, ' Monod type' switchin� functions, to determine which processes are active under what environmental conditions. P.e. Aerobic growth is switched on in the presence of readily biodegradable substrate (Ss/ +Ss» and dissolved oxygen (So/(Ko H+So)) whereas denitrification is activated by nitrate (SOO/( 0+800» and deactivated by dissolved oxygen ([Sd(KOH+SQ)]o[KQflSo1=Kofl(Ko +So», The growt of nitrlflers is switched on under aerobic conditions (Sd(KoA+SoJ) in the presence 0rammonium (St.W(KNH+SNH». The switching functions are important in order to avoid negative concentrations of limiting components in the course of simulation. Further details, such as the saturation kinetics for hydrolysis, or correction factors 1lg and 1lh for anoxic conditions, may be taken from the original documentation of the model.
�
The stoichiometry for the nine transformation processes considers conservation principles for COD, nitrogen and electric charges. Observe however that not all nitrogen can be accounted for, since nitrogen gas is not included in the components considered. The 'Activated Sludge Model No. l' is useful in the prediction of: - DeQradation of organic material and denitrification - Nitnfication - The distribution of oxygen consumption along a 'plug flow' type reactor and in the course of diurnal variations. - Sludge production - Variation of effluent quality under dynamic loading conditions. In the application of the model the following problems are encountered: - The hydrolysis process is not well documented because of the difficulty to design experiments, which are specific for the investigation of this process. - The use of multiple Monod type switching function in the process rate equations leads to a general lowering of the calculated rate, which must be compensated by the use of a hi�her specific maximum growth rate. This is not a problem from the point of view of the model, b ut it might confuse the user if the growth rate is looked on without considering its form of application. - A pH influence on the process rates is not included. This would have required to include organic and CO2 forms of c arbon in the model and would have made the model even more complex. As a simpler altemative bicarbonate alkalinity has been included as a model component, this allows to estimate a pH value, which is primarily important if low alkalinity wastewater is to be nitrified. - The correction factors for d�nltrlflcatlon (1'19 and 1'Ih) are a considerable simplification of the model. They may depend on the composition of the wastewater and the process flow scheme used for denitrification. It is unclear yet how these values may be predicted accurately. - The characterization of the wastewater in the form of the model components is complex. No direct chemical analysis is known for readily biodegradable organic material Sa, it is necessary to rely on expensive and complex biological tests. Experience with the model indicates, that wastewater composition varies from location to location, therefore wastewater characterization is important. - The model relies on many kinetic parameters. Good estimates for these parameters are available and appear to be quite uniform for different locations, as long as the water is of domestic origin. For other waste the necessary determination of these parameters is costly and complex. Despite of all these problems, the model has developed into a valuable analytical tool for a�ivated sludge processes for domestic wastewater, primarily for non steady state conditions. SIMULATION PROGRAMS
The application of a biokinetic model as complex as the 'Activated Sludge Model No. l' for the prediction of the behavior of a multi reactor flowscheme under time dependent external loading conditions and possibly with the considerations of process control strategies is only possible with the aid of simulation programs. Today such programs are readily available for personal computers and may be used for a variety of applications such as teaching, research, design and operation.
W. GUJER
1016
and \1.
HENZE
START BLOCKS OF A SIMPLE ACTIVATED SLUDGE SYSTEM SIMULATION PROGRAM
OUTPUT Text/Graphic
INT EGRATION OF MATER IALS BALANCE EQUATIONS FIGURE 1. Flowdiagram for a simple activated sludge system simulation program Mod u l es of a Simulation program
A simulation program must be distinguished from the mathematical model on which it is based. For any model it is possible to design severar different simulation programs, and a program may be deSigned for the application of different biokinetic models. Figure 1 presents a general flowscheme of an activated sludge system sim ulation program. After the program is initialized, several blocks of information m ust be entered: - A definition of stOichiometry, which is usually independent of temperature, b ut specific for the underlying biokinetic model. - A definition of kinetic expressions and parameters. These usually are temperature dependent. - A definition of influent concentrations. These are specific for the biokinetic model which is used. - A definition of the flowscheme with the relevant transport processes ( Influent, connection of reactor compartments, recirculations, excess sludge removal, solids separation, etc.). Based on the above entered information it is possible to set up the materials balance equations, usually these are non linear, coupled, ordinary differential equations, written for each component in each reactor compartment, frequently resulting in a large number of equations. The next step is the determination of initial conditions as required to integrate the differential materials balance equations forward in time. Many times steady state solutions are used as starting values. These may be found with different algebraic or relaxation techniques. Finally integration routines must be available, which allow for consideration of time dependent external forcing functions (flow rate, influent concentrations) and possibly process control algorithms. A convenient user interface should allow for graphic presentation of predicted time dependent results and interactive application of the program.
IOl7
Activated sludge modelling and simulation
The Program ASIM
For all simulations in this paper the program ASIM (Activated Sludge SIMulation Program, Gujer 1989) has been used. It allows for free definition of the biokinetic model used for the simulation, whereas the routines to define the flowscheme, initial conditions, steady state solutions, dynamic simulations, graphic presentations of results etc. are made available independent of the biokinetics used. The program has been developed as a didactic tool, it is not meant for professional application but rather for education purposes. STEPWISE DEVELOPMENT OF
A
BIOKINETIC MODEL
In this chapter a biokinetic model for the activated sludge process shall be developed, which comes close to the 'Activated Sludge Model No. 1'. The development starts with a simple view of the activated sludge process and is improved stepwise in order to better describe some experimentally observed phenomena. As the biokinetic model will be improved, the following components and concentrations will play a role: So
SI Ss SNH SNO XH Xs XI XA
Dissolved Oxygen Concentration [g02 m -3j Inert dissolved COD (non biodegradable) [9cOD m-Sj Readily biodegradable COD (dissolved) [geoD m-Sj Ammonium Concentration (NHt ) [gN m-Sj Nitrate Concentration (NOa) [gN m-3j Heterotrophic Biomass Concentration [geoD m-Sj Slowly biodegradable COD (adsorbed) [geoD m-Sj Inert particulate COD (non biodegradable) [geoD m-Sj Autotrophic Biomass Concentration (Nitrifiers) [9cOD m-Sj
Experimental data
Ekama and Marais (1978) published the results of an experiment with a laboratory scale, completely mixed activated sludge system. The pilot was fed with domestic waste (primary effluent), the influent was active for 12 hours per day and was stopped during the other 12 hours every day. The data collected include frequent measurements of oxygen uptake (Fig. 2) and nitrate concentrations (Fig.6). Mean operating conditions (24 hour averages) are summarized in Table 3. The pilot was nitrifying and was kept at room temperature. Table 3.
Average operating conditions of the laboratory scale activated sludge process (Ekama and Marais, 1978)
Influent flow rate Aeration tank volume Solids retention time Temperature
Model
A:
18.0 6.73 2.5 20.4
lid
1
d °c
Influent total COD Influent total Kj eldahl N Average MLVSS or
570 4 6.8 1375 2090
Heterotrophic Growth and Lysis
Model A has already been introduced in Table 1. It includes only three components and a growth and a decay (Lysis) process. The lysis process is favored here versus endogenous respiration, because it is similar to the decay process used in the 'Activated Sludge Model No. 1'. It has the advantage, that it can describe decay processes (maintenance, lysis, predation etc.) independent of the electron acceptor (aerobic, anoxic, anaerobic) available. The process rate equation for the growth process is expanded with a hyperbolic (Monod) term for dissolved oxygen, this is necessary in order to stop growth if oxygen is absent. Simulation programs might predict negative oxygen concentrations if this term were not introduced. Table 4 summarizes all influent concentrations as well as kinetic and stoichiometric parameters used for the simulation. Table 5 summarizes the biokinetic model with absolute numbers for stoichiometry. In Fig. 2 the prediction of the oxygen uptake rate is compared with experimental observations. The feed of substrate between 0200 and 1400 hours causes a rapid increase of oxygen uptake after 0200 hours, and theoretically an equally rapid decrease after 1400 hours. Experimental observations deviate strongly from theoretical predictions. It appears that a fraction of material is stored in the system and degraded only slowly between 1400 and about 2200 hours.
JWST 23':4/6-E£
1018
W. GUJER and M. HENZE
Table 4. Summary of influent concentrations, stoichiometric and kinetic parameters for all four models used. The waste water composition in terms of total COD and TKN remains unchanged. Model
A
B
C
0
570 30 540
570 30 110 430
570 30 110 330 100
570 30 110 330 100 47 10 0.08
Symbol
Units
Influent Concentrations Total COD Dissolved inert COD Readily biodegradable COD Slowly biodegradable COD Particulate inert COD Total Kjeldahl Nitrogen NH4+ - N Nitrogen in particulate COD
gcoom-3 gcoom-3 9ooom-3 gcoom-3 gcoom-3 gNm-3 gNm-3 9N9ooo-1
SI
Ss Xs
XI
SNH
Heterotrophic Growth Maximum growth rate Saturation constant for 02
Dissolved COD NH +- N Biomass ield Coefficient
�
4.0
4.0
4.0
4.0
�.H
d-1
0.1 5.0
0.1 5.0
0.1 5.0
0.67
0.67
0.67
0.1 5.0 0.1 0.67
Ko H Ks �H.H YH
g02m 3 gcoom-3 gNm -3 9co09ooo-1
0.6
0.6
0.6 0.08
0.6 0.08
fl
�
d-1 gcoogcoo-1
2.0 0.04
2.0 0.04
2.0 0.04
�x
gco09ooo-1d-1 gco09ooo-1
1.0 0.5 1.0 0.24
�� K NH A
d-1 g02m-3 gNm -3 9co09N-1
0.1
bA
d- 1
-
,
Heterotrophic Lysis Decay Rate Constant Fraction of inert Products Hydrolysis Rate Constant Saturation Constant Autotrophic (Nitrifier) Growth Maximum growth rate Saturation Constant for
0
N �4 Yield Coefficient: Biomass per NOa-N produced
YA
'
Autotrophic (Nitrifier) Lysis Decay rate constant
It was this deviation between theory and experiment, which can only be observed in dynamic, time
dependent experiments, which led Dold, Ekama and Marais (1980) to sug�est, that the biodegradable
organics in domestic waste might be modelled by two fractions: (i) A fraction of readily biodegradable organic material Ss, which causes the rapid decrease of the oxygen consumption after 1400 hours. This fraction has properties similar to those assumed tor the substrate Ss in Model No. A. (ii) A fraction of high molecular weight to colloidal and even particulate material, which must first be hydrolyzed in order to become available for degradation. This fraction was called slowly biodegradable material Xs and is assumed to be associated (adsorbed, entrapped) with the solid phase of the activated sludge. Table 5.
Model
A is similar to the growth-lysis model introduced in Table 1.
Heterotrophic Growth Heterotrophic Lysis
Ss
xH
-1.5
+1.0
Ilm.,H
1 0
-1.0
bH
So
Component -
0 5 .
+
.
Process Rate Equation
•
.
�
XH
K +S S S
.
So
K O,H+ So
•
XH
1019
Activated sludge modelling and simulation
1400 IE 1200 �1000 .,.q!UI fl 1Q 800 I" 600 400 .. 200 'c
MODEL A
(W)
N
I'"
(1)
.....
Iii--
.
0::
o
o
--. III
....... •••
4
12
8
�
20
16
Time hrs
-..
24
Figure 2. Comparison of experimentally observed values (data points) with theoretically predicted ( continuous line) oxygen uptake rate of the activated sludge from Model A. The influent to the pilot plant is active between 0200 and 1400 hours. Data from Ekama and Marais (1978). Model B: Two Substrate Model with Growth, Lysis and Hydrolysis Model B is based on model A, but in addition a slowly biodegradable organic fraction with concentration
Xs is introduced (Table 6). Further, a process is introduced which hydroly zes slowly biodegradable
material Xs to readily biodegradable material $s. Dold, Ekama and Marais (1980) proposed to use an adsorption kinetic expression as rate eq':lation for this process - hydrolysable material Xs is assumed to adsorb onto the heterotrophic biomass �, where Kx is a measure of the saturation of this process. The stOichiometry of lysis is changed, lysis products are assumed to be slowly biodegradable and are added to the pool of Xs. They are made available for growth again through the process of hydrolysis. Table 6. Model B is similar to model A but includes slowly biodegradable material Xs and a process for hydrolysis of this material in order to make it available for growth. Component Heterotrophic Growth
S
o
-0.5
S
x
H
s
-1.0 +1. 0
Process Rate Equation S
s
�,H--K +S - K
+1.0
-1.5
Heterotrophic Lysis Hydrolysis
Xs
S
+1.0
bH-XH
-1.0
kh-
S
S
o X S - H O,H+ o
XS / XH XH K +XS / X H X
With the influent composition and the stoichiometric and kinetic parameters summarized in Table 4, theoretical predictions match experimentally observed oxygen consumptions perfectly (Fig. 3). Obviously the two substrate model, together with adsorption kinetics for hydrolysis is able to describe observed phenomena much better. Model B predicts the activated sludge concentration to be 1640 9coom-3, whereas the experimental observation is 2090 gcoQ,m-3 (Table 3), indicating, that the model underestimates sludge production by approx. 22%. One poSSibility to increase slud e production is to include a further fraction of organic material X I' which Is non biodegradable (inert and particulate. This traction may be present in the influent and might be produced in the context of cell lysis, as observed by McCarty and Brodersen (1962).
s
1020
W. GUJER and M. HENZE
'T
1400 E 1200 �1000 $ 800 600 400 200 0 0 "0
«
MODEL B
N
CO 0:
.".
-- . ,...,.. ....IL.
k
.
1
...
••�1Ii..
�
4
8
12
...
16
��
�.
20
Time hrs
24
Figure 3. Comparison of experimentally observed values (data points) with theoretically predicted (continuous line) oxygen uptake rate of the activated sludge from Model B. The influent to the pilot plant is active between 0200 and 1400 hours. Data from Ekama and Marais (1978). Model
C:
Inert Particulate Solids and Sludge Production
Model C is identical to model B except that it allows for particulate inert organic material in the influent and its production in the context of lysis. This requires introduction of one more component, >
