activated sludge models

ACTIVATED SLUDGE MODELSASM1, ASM2, ASM2d AND ASM3

Edited by

IWA TASK GROUP ON MATHEMATICAL MODELLING FOR DESIGN AND

OPERATION OF BIOLOGICAL WASTEWATER TREATMENT

Mogens Henze

Willi Gujer

Takashi Mino

Mark van Loosdrecht

Published by IWA Publishing in its Scientific and Technical Report series.

Published by IWA Publishing, Alliance House, 12 Caxton Street, London SW1H 0QS, UK

Telephone: +44 (0) 20 7654 5500; Fax: +44 (0) 20 7654 5555; Email: [email protected]

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First published 2000

Reprinted 2002

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A CIP catalogue record for this book is available from the British Library

ISBN: 1 900222 24 8

ISSN: 1025-0913

odelling of activated sludge processes hasbecome a common part of the design and

operation of wastewater treatment plants.Today models are being used in design, control,teaching and research.

History

In 1982 the International Association on WaterPollution Research and Control (IAWPRC), asit was then called, established a Task Group onMathematical Modelling for Design and Oper-ation of Activated Sludge Processes. At thattime modelling of activated sludge processeshad been a discipline for about 15 years, mostnoticeably and reaching the most advanced levelat the University of Cape Town, South Africa,by the research group headed by ProfessorG.v.R. Marais. The various models developed atthat time had only little use, owing partly tolack of trust in the models, partly to thelimitations in computer power and partly to thecomplicated way in which these models had tobe presented in written form.

The first task

The aim for the Task Group was to create acommon platform that could be used for futuredevelopment of models for nitrogen-removalactivated sludge processes. It was the aim todevelop a model with a minimum of complex-ity. The result was the Activated Sludge ModelNo. 1, todayknownundermanynames: IAWPRCmodel, ASM1, IAWQ model, and so on.The model outline was discussed at an

IAWPRC Specialised Seminar at Kollekolle,Denmark, in 1985, and was published in 1987in its final form in the IAWPRC Scientific andTechnical Report Series as STR No. 1. The fiveyears used for developing the model was spentin discussing with many researchers and prac-titioners in order to get a solid platform for thework and only to include details that couldstand the test of time. What was presented wasnot only a model, but also a guideline forwastewater characterization and developmentof computer codes, plus a set of default valuesthat since then has proved to give realisticmodel results with only minor changes in theparameters.

The ASM1 was well received and has beenwidely used as a basis for further model devel-opment. The direct use of the ASM1 formodelling has been almost nil, but ASM1 hasbeen the core of numerous models with anumber of supplementary details added inalmost every case.It was especially the matrix notation, which

was introduced together with ASM1, that facili-tated the communication of complex modelsand allowed the concentration of discussions onessential aspects of biokinetic modelling.

Biological phosphorus removal

At the time of publication of the ASM1, bio-logical phosphorus removal was already beingused in a (limited number) of full-scaletreatment plants. The theoretical status of theprocesses was such that the Task Group at thattime did not enter into the modelling of it. Butfrom the mid-1980s to the mid-1990s thebiological phosphorus removal processes grewvery popular and at the same time the under-standing of the basic phenomena of the processwas increasing. Thus in 1995 the ActivatedSludge Model no. 2 was published. This modelincluded nitrogen removal and biological phos-phorus removal. In 1994, when the ASM2 wasfinished, the role of denitrification in relation tobiological phosphorus removal was still unclear,so it was decided not to include that element.However, the development in research was fast,and denitrifying PAOs (phosphorus-accumu-lating organisms) were needed for simulation ofmany results from research and practice. Be-cause of this, the ASM2 model was expanded in1999 into the ASM2d model, where denitrify-ing PAOs were included.Although the models might not have been

heavily needed for nitrogen removal processes,the complexity of the combined nitrogen andphosphorus removal processesmakes themodelsimportant for design and control purposes.

New platform

The models have grown more complex over theyears, from ASM1, including nitrogen removalprocesses, to ASM2, including biological phos-phorus removal processes and to ASM2d

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Preface

Preface

M

including denitrifying PAOs. In 1998 the TaskGroup decided to develop a new modellingplatform, the ASM3, in order to create a toolfor use in the next generation of activatedsludge models. The ASM3 is based on recentdevelopments in the understanding of the acti-vated sludge processes, among which are thepossibilities of following internal storage com-pounds, which have an important role in themetabolism of the organisms.

Benefit from the models

The major impact of the ASM model family hasbeen based upon three facts. The first is thecommon language that modellers speak whenusing the concepts, the nomenclature and thematrix notation of the ASMs. This has created astrong model development over the past 15years, which would probably not have been thecase if all the modellers had used their ownconcepts, notation and platforms.

The second is the organizing effect of wor-king with a model. This has helped researchersto achieve more efficient experimental designsand helped treatment plant operators to betterunderstand and organize the information avail-able at their plants – and in many cases to spoterrors in available information. The third is thatthe models have served as guidance forresearch. By demonstrating where research wasneeded, focus has been put on certain details,for example wastewater characterization, out ofwhich much interesting research has grown.

Simulation programs

The ASM1 and ASM2 models, or ASM-based

models, are included in most of today’s com-mercial and non-commercial simulation pro-grams. Thus it is easy to get access to, and usethe models for various purposes.

Future

This report has been produced to give a totaloverview of the ASM model family status at thestart of 2000 and to give to the reader easyaccess to the different models in their originalversions. It is the hope of the present TaskGroup that this may facilitate the use of themodels and their future development.

During the years the members of the TaskGroup have changed. This reflects the devel-opment in research over the years and the wishto develop the models further. The ASM3 isnot the final or ‘general model’ for activatedsludge. Like ASM1, it is a structure and a plat-form for further development. Many modellersare looking for the ‘ultimate general model’ foractivated sludge systems. Experience over thepast 15 years shows that new developmentcomes fast and the ‘general models’ have ashort half-life. Thus for the future developmentof ASMs, suggestions, experience and discus-sion points will be well received if the readersand users wish to share their ups and downs inmodelling with members of the Task Group.

Mogens HenzeWilli Gujer

Mark van LoosdrechtTakashi Mino

iv

Preface

v

Contents

Preface iiiList of Task Group members vi

1. Activated Sludge Model No. 1 1Previously published as: Henze, M., Grady, C.P.L. Jr, Gujer, W., Marais, G.v.R. andMatsuo, T. (1987) Activated Sludge Model No. 1. (IAWPRC Scientific and TechnicalReport No. 1.) London: IAWPRC.

2. Activated Sludge Model No. 2 39Previously published as: Henze, M., Gujer, W., Mino, T., Matsuo, T., Wentzel, M.C. andMarais, G.v.R. (1995) Activated Sludge Model No. 2. (IAWQ Scientific and TechnicalReport No. 3.) London: IAWQ.

3. Activated Sludge Model No. 2d 75Previously published as: Henze, M., Gujer, W., Mino, T., Matsuo, T., Wentzel, M.C.,Marais, G.v.R. and van Loosdrecht, M.C.M. (1999) Activated Sludge Model No. 2d.Wat. Sci. Technol. 39 (1), 165–182.

4. Activated Sludge Model No. 3 99A new version (2000) of the activated sludge model, different from that previouslypublished as Gujer, W., Henze, M., Mino, T. and van Loosdrecht, M.C.M. (1999)Activated Sludge Model No. 3. Wat. Sci. Technol. 39 (1), 183–193.

List of Task Group members

List of Task Group members

IAWPR/IAWPRC Task Group 1982–1990Mogens Henze (Chairman), Technical University of Denmark, DenmarkC.P. Leslie Grady, Clemson University, USAWilli Gujer, Swiss Federal Institute for Aquatic Science and Technology, Zürich, SwitzerlandGerrit v.R. Marais, University of Cape Town, South AfricaTomonori Matsuo, University of Tokyo, Japan

IAWPRC/IAWQ Task Group 1990–1996Mogens Henze (Chairman), Technical University of Denmark, DenmarkWilli Gujer, Swiss Federal Institute for Aquatic Science and Technology, Zürich, SwitzerlandTakashi Mino, University of Tokyo, JapanTomonori Matsuo, University of Tokyo, JapanMark C. Wentzel, University of Cape Town, South AfricaGerrit v.R. Marais, University of Cape Town, South Africa

IAWQ/IWA Task Group since 1996Mogens Henze (Chairman), Department of Environmental Science and Engineering, Technical

University of Denmark, 2800 Lyngby, Denmark ([email protected])Willi Gujer, Swiss Federal Institute for Aquatic Science and Technology, 8600 Dübendorf,

Switzerland ([email protected])Mark van Loosdrecht, Delft University of Technology, Julianalaan 67, 2628 BC Delft,

The Netherlands ([email protected])Takashi Mino, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, Japan

([email protected])

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1

ACTIVATED SLUDGEMODEL NO. 1

by

IAWPRC TASK GROUP ON MATHEMATICAL MODELLING FOR DESIGN AND


M. Henze, DenmarkC.P.L. Grady, Jr, USAW. Gujer, Switzerland

G. v. R. Marais, South AfricaT. Matsuo, Japan

3

Contents

Introduction 5

Method of model presentation 6Format and notation 6Use in mass balances 7Continuity check 7

Model incorporating carbon oxidation, nitrification and denitrification 8Conceptual model 8Components in mathematical models 10Processes in the model 12

Characterization of wastewater and estimation of parameter values 16Characterization of wastewater and estimation of stoichiometric coefficients 16Estimation of kinetic parameters 18

Typical parameter ranges, default values, and effects ofenvironmental factors 23

Typical parameter values 23Default values 24Environmental effects 25

Assumptions, restrictions and constraints 26Assumptions and restrictions associated with the model 26Constraints upon the application of the model 26

Implementation of the activated sludge model 28Modelling of complex flow schemes 28Definition of initial conditions 28Consideration of variable load conditions 29Factors governing step sizes during numerical integration 29A simple integration routine 30Structure of a possible program 30Steady state solution for a single CSTR 31Sample output 34

Conclusion 36

References 37

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Introduction

6

Activated Sludge Model No.1

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Method of model presentation

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Model incorporating carbon oxidation, nitrification and denitrification

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Characterization of wastewater and estimaton of parameter values

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Typical parameter ranges, default values, and effects of environmental factors

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Typical parameter ranges, default values, and effects of environmental factors

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Assumptions, restrictions and constraints

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Implementation of the activated sludge model

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References

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Activated Sludge Model No. 1

39


by

IAWQ TASK GROUP ON MATHEMATICAL MODELLING FOR DESIGN AND


Mogens Henze, Technical University of Denmark, DenmarkWilli Gujer, Swiss Federal Institute of Technology, Switzerland

Takashi Mino, Tokyo University, JapanTomonori Matsuo, Tokyo University, Japan

Mark C. Wentzel, Cape Town University, South AfricaGerrit v. R. Marais, Cape Town University, South Africa

41

Contents

1. Introduction 431.1 Background 431.2 Conceptual approach 431.3 Limitations 431.4 Symbols and definitions 431.5 Final note 43

2. The Activated Sludge Model No. 2 442.1 Components in the model 442.2 Basis for the introduction of ASM2 462.3 Biological processes, stoichiometry and kinetics 472.4 Chemical precipitation of phosphates 52

3. Typical wastewater characteristics, kinetic and stoichiometricconstants for the Activated Sludge Model No. 2 53

4. Wastewater characterization for activated sludge processes 574.1 Variations in wastewater composition 574.2 Characterization of wastewater 574.3 Routine analysis of model components 604.4 Soluble analysis as a tool in characterization 624.5 Model components without standardized analytical procedures 634.6 Present status for measurement/estimation of problematic components 63

5. Calibration of the Activated Sludge Model No. 2 66

5.1 Calibration levels 675.2 Calibration using non-dynamic data (Level 1) 675.3 Calibration using dynamic data (Level 2) 685.4 Calibration of temperature dependency 69

6. Model limitations 706.1 Assumptions regarding phosphate-accumulating organisms (PAOs) 706.2 Restrictions due to model structure 716.3 Constraints for useful simulations 726.4 Important questions for further research 72

7 . Conclusion 73

8. Bibliography 74

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1. Introduction

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2. The Activated Sludge Model No.2

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3. Typical wastewater characteristics, kinetic and stoichiometric constants for ASM2

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3. Typical wastewater characteristics, kinetic and stoichiometric constants for ASM2

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4. Wastewater characterization for activated sludge processes

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5. Calibration of the Activated Sludge Model No.2

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5. Calibration of the Activated Sludge Model No.2

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6. Model limitations

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7. Conclusion

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7. Conclusion

ACTIVATED SLUDGEMODEL NO. 2d

by


OPERATION OF BIOLOGICAL WASTEWATER TREATMENT PROCESSES

Mogens Henze (Chairman), Technical University of Denmark, DenmarkWilli Gujer, Swiss Federal Institute of Technology, Switzerland

Takashi Mino, Tokyo University, JapanTomonori Matsuo, Tokyo University, Japan

Mark C. Wentzel, Capetown University, South AfricaGerrit v. R. Marais, Capetown University, South Africa

Mark C.M. Van Loosdrecht, Delft University of Technology, The Netherlands

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77

7. Conclusion

Contents

1. Introduction 79

2. Conceptual approach 80

3. The Activated Sludge Model No. 2d 813.1 Components in the model 813.2 Basis for the introduction of ASM2 833.3 Biological processes, stoichiometry and kinetics 843.4 Chemical precipitation of phosphates 89

4. Typical wastewater characteristics and kinetic and stoichiometricconstants 91

5. Limitations 96

6. Conclusion 96

7. References and bibliography 97

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his report presents a mathematical modelwhich allows for dynamic simulation of

combined biological processes for chemicaloxygen demand (COD), nitrogen and phospho-rus removal in activated sludge systems. Themodel as presented here is a tool for:

• Research (testing results, selecting andoptimizing experiments)

• Process optimization and troubleshootingat full-scale treatment plants

• Teaching• Design assistance (for optimization of

details, not for full design)

The model presented below is not the finalanswer to biological phosphorus removal mod-els. Rather it is a compromise between com-plexity and simplicity, and between the manyviewpoints on what the correct model wouldbe. It is intended to be a conceptual platformand reference for further model development.ASM2d is an extension of the Activated

Sludge Model No. 2 (Henze et al., 1995) and

the Activated Sludge Model No. 1 (ASM1)(Henze et al., 1987), and uses the conceptsincorporated in these models. ASM1 has sincelong proved to be an excellent tool formodelling nitrification-denitrification processesand has initiated further research in modellingand wastewater characterization. It is hopedthat ASM2d will serve a similar function.ASM2d may be applied as presented, but basedon experience, it will most likely be used as aplatform for future model development. As thisis the basic idea behind presenting the model,this is highly encouraged.In ASM2 an unresolved part was the

denitrification related to PAOs. Since thepublication of ASM2 it has been demonstratedclearly (Mino et al., 1995, Meinhold et al.,1999, Kerrn-Jespersen and Henze, 1993) thatPAOs in a modelling context can be consideredto consist of two fractions, one of which candenitrify. This has created a need for anextension of ASM2, the result being presentedhere as ASM2d.

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1. Introduction

1. Introduction

T

n attempt has been made to limit thenumber of processes used in the model.

The aim has, however, been to produce amodel that can reasonably describe the manydifferent activated sludge system configurationswhich are used for biological phosphorusremoval. This has resulted in the present levelof complexity. In specific cases, it will bepossible to reduce the complexity of the modelby omitting processes that do not play asignificant role, without interfering with thepredictive power of the model.

The kinetics and stoichiometry used to de-scribe the processes have been chosen as sim-

ply as possible, mainly based on Monod kineticsfor all components that can influence the reac-tion rates. Monod kinetics allows for smoothtransitions of the processes, as experience hasshown. Kinetics and stoichiometry are presen-ted using the matrix notation, which has beenintroduced together with ASM1 and appears atthis moment to be the most efficient method tooverview the complex transformations amongthe components. The matrix notation also all-ows control of the conservation of componentsin the stoichiometric coefficients and thusensures that mass balances in the calculationsare correctly maintained.

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Activated Sludge Model No. 2d

2. Conceptual approach

A

he Activated Sludge Model No. 2 (ASM2)is an extension of the Activated Sludge

Model No. 1 (ASM1). ASM2 is more complexand includes many more components which arerequired in order to characterize the waste-water as well as the activated sludge. Additionalbiological processes are included, primarily inorder to deal with biological phosphorus re-moval. The most significant change from ASM1to ASM2 is the fact that the biomass now hascell internal structure, and therefore its con-centration cannot simply be described with thedistributed parameter XBM. This is a prerequi-site in order to include biological phosphorusremoval in the model.The Activated Sludge Model No. 2d is a

minor extension of ASM2. It includes twoadditional processes to account for the fact thatphosphorus accumulating organisms (PAOs)can use cell internal organic storage productsfor denitrification. Whereas ASM2 assumesPAOs to grow only under aerobic conditions,ASM2d includes denitrifying PAOs. This reportis based on the previous report which intro-duced ASM2. All remarks made relative toASM2 are equally valid for ASM2d. If infor-mation is given which relates specifically toASM2d then reference will be made to thisextended model.In addition to the biological processes,

ASM2 includes two ‘chemical processes’, whichmay be used to model chemical precipitation ofphosphorus.Whereas ASM1 was based entirely on COD

for all particulate organic material, as well asthe total concentration of the activated sludge,ASM2 includes poly-phosphates, a fraction ofthe activated sludge which is of prime impor-tance for the performance of the activatedsludge system, but which does not exert anyCOD. For this reason, the possibility of inclu-ding total suspended solids (TSS) in the modelis introduced. TSS also allow for inclusion ofmineral particulate solids in the influent totreatment plants, as well as generation of suchsolids in the context of precipitation of phos-phorus.

ASM2 is introduced here in a form which ismore complex than a basic version, which couldstill predict many of the phenomena within abiological nutrient removal plant. The complexmodel as presented may easily be simplified byeliminating those components which do nothave a dominant effect upon the kinetics of theprocesses, or the aspects of performance of theplant which are of interest.ASM2 does not distinguish between the

composition (cell internal structure) ofindividual cells but considers only the averagecomposition of the biomass. Since each cell hasa different history, its composition will typicallydeviate from the population average (e.g. itmay not contain storage products whereas theaverage cell still has storage products available).This is of importance because kinetic expres-sions used in ASM2 are non-linear, and there-fore average behaviour may not necessarily bepredicted from average properties. In view ofthe additional problems that population modelswould introduce, the Task Group took the prag-matic decision to accept these problems and topropose ASM2 based on average properties ofthe population.

3.1 Components in the model

All symbols for model components distinguishbetween soluble ‘S?’ and particulate ‘X?’. Withinthe activated sludge systems, particulate com-ponents, X?, are assumed to be associated withthe activated sludge (flocculated onto the acti-vated sludge). They can be concentrated bysedimentation/thickening in clarifiers whereassoluble components, S?, will only be trans-ported with the water.All particulate model components, X?, must

be electrically neutral (no ionic charges),soluble components, S?, may carry ionic charge.Soluble and particulate components may not

necessarily be differentiated by filtrationthrough 0.45 µm membrane filters as isfrequently assumed in the technical literature.Some of these components are defined by theirinteraction with the biomass and requirebioassays for their analysis (see Chapter 4 of

81

3. The Activated Sludge ModelNo. 2d

3. The Activated Sludge Model No. 2d

T

the original report on ASM2 (Henze et al.,1995))All components are assumed to be homo-

geneous and distributed throughout the sys-tems of interest.

3.1.1 Definition of soluble components,‘S?’

SA [M(COD) L−3]: Fermentation products,considered to be acetate. Since fermentationis included in the biological processes, the fer-mentation products must be modelled sep-arately from other soluble organic materials.They are endproducts of fermentation. For allstoichiometric computations, it is assumed thatSA is equal to acetate, in reality a whole rangeof other fermentation products dominated byacetate is possible.

SALK [mol(HCO3−) L−3]: Alkalinity of the

wastewater. Alkalinity is used to approximatethe conservation of electrical charges in bio-logical reactions. Alkalinity is introduced inorder to obtain an early indication of possiblelow pH conditions, which might inhibit somebiological processes. For all stoichiometriccomputations, SALK is assumed to be bicarbon-ate, HCO3

− only.

SF [M(COD) L−3]: Fermentable, readily bio-degradable organic substrates. This fraction ofthe soluble COD is directly available for bio-degradation by heterotrophic organisms. It isassumed that SF may serve as a substrate forfermentation, therefore it does not includefermentation products.

SI [M(COD) L−3]: Inert soluble organicmaterial. The prime characteristic of SI is thatthese organics cannot be further degraded inthe treatment plants dealt with in this report.This material is assumed to be part of theinfluent and it is also assumed to be producedin the context of hydrolysis of particulate sub-strates XS.

SN2[M(N) L−3]: Dinitrogen, N2. SN2

isassumed to be the only nitrogenous product ofdenitrification. SN2

may be subject to gasexchange, parallel with oxygen, SO2

.

SNH4[M(N) L−3]: Ammonium plus ammonia

nitrogen. For the balance of the electricalcharges, SNH4

is assumed to be all NH4+.

SNO3[M(N) L−3]: Nitrate plus nitrite

nitrogen (NO3− + NO2

−-N). SNO3is assumed to

include nitrate as well as nitrite nitrogen, sincenitrite is not included as a separate modelcomponent. For all stoichiometric computa-tions (COD conservation), SNO3

is consideredto be NO3

−-N only.

SO2[M(O2) L−3]: Dissolved oxygen. Dissolved

oxygen may be subject to gas exchange.

SPO4[M(P) L−3]: Inorganic soluble

phosphorus, primarily ortho-phosphates. Forthe balance of electrical charges, it is assumedthat SPO4

consists of 50% H2PO4− and 50%

HPO42−, independent of pH.

SS [M(COD) L−3]: Readily biodegradablesubstrate. This component was introduced inASM1. In ASM2, it is replaced by the sum ofSF + SA.

3.1.2 Definition of particulatecomponents, ‘X?’

XAUT [M(COD) L−3]: Nitrifying organisms.Nitrifying organisms are responsible for nitrifi-cation; they are obligate aerobic, chemo-litho-autotrophic. It is assumed that nitrifiers oxidizeammonium SNH4

directly to nitrate SNO3(nitri-

fiers include both ammonium and nitrite oxi-dizers).

XH [M(COD) L−3]: Heterotrophic organisms.These organisms are assumed to be the ‘all-rounder’ heterotrophic organisms, they maygrow aerobically and anoxically (denitrification)and be active anaerobically (fermentation). Theyare responsible for hydrolysis of particulatesubstrates XS and can use all degradable organ-ic substrates under all relevant environmentalconditions.

XI [M(COD) L−3]: Inert particulate organicmaterial. This material is not degraded withinthe systems of interest. It is flocculated ontothe activated sludge. XI may be a fraction of theinfluent or may be produced in the context ofbiomass decay.

XMeOH [M(TSS) L−3]: Metal-hydroxides. Thiscomponent stands for the phosphorus-bindingcapacity of possible metal-hydroxides, whichmay be in the wastewater or may be added tothe system. For all stoichiometric computa-tions, it is assumed that this component iscomposed of Fe(OH)3. It is possible to ‘replace’this component with other reactants; this wouldrequire adaptation of the stoichiometric andkinetic information.

XMeP [M(TSS) L−3]:Metal-phosphate,MePO4.Thiscomponentresults frombindingphosphorusto the metal-hydroxides. For all stoichiometriccomputations, it is assumed that this compo-nent is composed of FePO4. It is possible to‘replace’ this component with other precipi-tation products; this would require adaptationof the stoichiometric and kinetic information.

XPAO [M(COD) L−3]: Phosphate-accumu-lating organisms: PAO. These organisms are

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assumed to be representative for all types ofpoly-phosphate-accumulating organism. Theconcentration of XPAO does not include the cellinternal storage products XPP and XPHA, butonly the ‘true’ biomass. In ASM2d it isassumed that these organisms may grow in ananoxic as well as an aerobic environmentwhereas in ASM2 only aerobic growth isconsidered.

XPHA [M(COD) L−3]: A cell internal storageproduct of phosphorus-accumulating organ-isms, PAO. It includes primarily poly-hydroxy-alkanoates(PHA). It occurs only associated withXPAO; it is, however, not included in the mass ofXPAO. XPHA cannot be directly compared withanalyticallymeasuredPHAconcentrations;XPHAis only a functional component required formodelling but not directly identifiable chemi-cally. XPHA may, however, be recovered in CODanalysis, where it must satisfy COD conserva-tion. For stoichiometric considerations, PHA isassumed to have the chemical composition ofpoly-β-hydroxy-butyrate (C4H6O2)n.

XPP [M(P) L−3]: Poly-phosphate. Poly-phos-phate is a cell internal inorganic storageproduct of PAO. It occurs only associated withXPAO; it is, however, not included in the mass ofXPAO. It is part of the particulate phosphorusand may be analytically observed. Forstoichiometric considerations, poly-phosphatesare assumed to have the composition of(K0.33Mg0.33PO3)n.

XS [M(COD) L−3]: Slowly biodegradablesubstrates. Slowly biodegradable substrates arehigh molecular weight, colloidal and particulateorganic substrates which must undergo cellexternal hydrolysis before they are available fordegradation. It is assumed that the products ofhydrolysis (SF) may be fermented.

XTSS [M(TSS) L−3]: Total suspended solids,TSS. Total suspended solids are introducedinto the biokinetic models in order to computetheir concentration via stoichiometry. Sincephosphorus removal and precipitation intro-duce mineral fractions into the activatedsludge, prediction of TSS is important.

3.2 Basis for the introduction of ASM2

3.2.1 Matrix notation

The Task Group introduced matrix notation forthe presentation of biokinetic models in itsreport on the ASM1. The same concept will beused for the introduction of ASM2. It isassumed that the reader is familiar with thisway of presenting biokinetics.

As a short summary: the components which

are considered in the model and thetransformation processes are characterized withthe indices i and j respectively. Stoichiometriccoefficients are presented in the form of astoichiometric matrix nj,i. The process rateequations form a vector rj. The rate ofproduction of the component i, ri [Mi L−3 T−1],in all parallel processes may then be computedfrom the sum:

ri = ∑ nj,i . rj j. (3.1)over all processes

Within the stoichiometric matrix one stoi-chiometric coefficient, nj,k, of each process jmay be chosen as dimensionless with the valueof +1 or −1. For all other stoichiometriccoefficients algebraic equations may be given,which introduce conservation principles intothe determination of stoichiometric coeffici-ents. Alternatively nj,i may be given in the formof absolute values with the dimension Mi Mk

−1,where Mk is the unit mass of the component kupon which stoichiometry is based (the compo-nent which has nj,k = +1 or −1).

3.2.2 Conservation equations

Conservation equations are the mathematicalequivalent of the principle that in chemicalreactions, elements, electrons (or COD) andnet electrical charges may neither be formednor destroyed.

The stoichiometry of ASM1 is implicitlybased on three conservation considerations forCOD, electrical charges and nitrogen. ASM2adds phosphorus conservation to these three.Further, an equation is introduced whichconverts the different solid components X?from their unit of measurement, to total sus-pended solids, XTSS.

A conservation equation, which is valid for allprocesses j and all materials c subject to con-servation, may be written as:

∑ nj,i . ic,i = 0 i, (3.2)over all components

wherenj,i = stoichiometric coefficient for compo-

nent i in process j [Mi Mk−1],

ic,i = conversion factor to convert the unitsof component i to the units of thematerial c, to which conservation is tobe applied [Mc Mi

−1].

Each conservation equation contains a prioriinformation and may be applied to eachprocess. Each conservation equation allows theprediction of one stoichiometric coefficientwithout performing an experiment, providedthe other coefficients are known.

In ASM2, these equations are used to

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estimate the stoichiometric coefficients of SO2

(SNO3and SN2

in denitrification) from COD,SNH4

from nitrogen, SPO4from phosphorus,

SALK from charge and XTSS from total solidsconservation. Table 3.1 is a summary of theconversion factors ic,i which must be applied inEquation 3.2. These conversion factors are,wherever possible, obtained from chemicalstoichiometry. ‘COD’ as a conservative propertyis defined as closely as possible to theanalytically obtained COD. Examples are:

iCOD,5 = −64 g O2 /14 g NO3−-N from:

NO3− + H2O + 2 H+ → NH4

+ + 2 O2

Or, one mole of nitrate (14 g N) has a negativeoxygen demand (‘liberates oxygen’) of twomoles of oxygen (64 g O2). Similar argumentslead to:

iCOD,9 = −24 g O2 /14 g N2 from:2 N2 + 6 H2O + 4 H+ → 4 NH4

+ + 3 O2

All conversion factors given with absolutenumbers in Table 3.1 may be obtained fromchemical stoichiometry, based on the definitionof the compounds. All factors identified with asymbol ic,i must be obtained from chemicalanalysis. Since ASM2 does not account forpotassium (K+) and magnesium ions (Mg2+)

XPP must include these counterions. This istaken care of by the conversion factor iCharge,14= −1/31.As an example, the stoichiometric coefficient

for component 2 (i = 2) in the third process( j = 3) may be obtained from the conservationequation for COD based on Equation 3.2according to:

n3,2 = − (n3,1 . iCOD,1 + n3,3 . iCOD,3 + …+ n3,n . iCOD,n) / iCOD,2

or

3,2 = − ⎡⎢⎣∑i

(n3,i . iCOD,i) − n3,2 iCOD,2⎤⎥⎦ / iCOD,2n . .

The introduction of the conservation equa-tions in an abstract form may at first appear tobe complicated. However, the concept isdirected towards its application in computerprograms and helps to simplify the develop-ment of program code.

3.3 Biological processes, stoichiometryand kinetics

The biological processes of ASM2 are intro-duced here. A full stoichiometric matrix usingtypical stoichiometric coefficients is presentedin Table 4.4.

84

Table 3.1. Conversion factors ic,i to be applied in the conservation equation of ASM2. Missing values are equal to 0.The units of ic,i are Mc Mi

−1, e.g. iN,2 = iNSF g N g−1 COD or iCharge,3 = −1/64 moles+ g−1 COD.

Index c: Conservation for COD N P Charge MassFactor iCOD,i iN,i iP,i iCharge,i iTSS,iindex i: Component Units g COD g N g P mole+ g TSS

1 SO2g O2 −1

2 SF g COD 1 iN,SF iP,SF3 SA g COD 1 −1/644 SNH4

g N 1 +1/145 SNO3

g N −64/14 1 −1/146 SPO4

g P 1 −1.5/317 SI g COD 1 iN,SI iP,SI8 SALK mole HC

−3O −1

9 SN2g N −24/14 1

10 XI g COD 1 iN,XIiP,XI

iTSS,XI

11 XS g COD 1 iN,XSiP,XS

iTSS,XS

12 XH g COD 1 iN,BM iP,BM iTSS,BM13 XPAO g COD 1 iN,BM iP,BM iTSS,BM14 XPP g P 1 −1/31a) 3.2315 XPHA g COD 1 0.6016 XAUT g COD 1 iN,BM iP,BM iTSS,BM17 XTSS g TSS −1b)

18 XMeOH g TSS 119 XMeP g TSS 0.205 1

All absolute numbers are obtained based on the chemical composition of the component (see definition ofcomponent). All factors ici are model parameters and must be obtained from experiments (See also Table 9).

a) Since ASM2 does not account for K+ and Mg2+ this factor must compensate for their charge.

b) Since TSS are counted twice, this factor must be negative.


3.3.1 Biological processes, generalremarks

Microorganisms have a complex cell internalstructure and respond to different environmen-tal conditions with adjustment of this structure.A frequently observed phenomenon is unbal-anced growth, a situation where not all frac-tions of the cells are reproduced at an equalrate. Modelling such shifts of cell internalstructure would require modelling of thedifferent fractions of the biomass, a task whichwould be most fruitful if the behaviour ofaxenic cultures were described. Here, onlythree groups of microorganisms represent avast variety of unknown species; each biologicalprocess described in ASM2 represents a largenumber of processes which act upon a varietyof substances, which in the model are summa-rized in terms of COD.Process descriptions in ASM2 are therefore

based on the average behaviour of these differ-ent microorganisms, and are described in theway balanced growth processes would bemodelled.

3.3.2 Hydrolysis processes

Many high molecular weight, colloidal or par-ticulate organic substrates cannot be utilizeddirectly by microorganisms. These substratesmust be made available by cell external enzym-atic reactions which are called hydrolysisprocesses. It is unclear whether the products ofhydrolysis ever exist in true solution or whetherthey are taken up directly by the organismswhich catalyse hydrolysis. Typically hydrolysisprocesses are considered to be surface reac-tions, which occur in close contact between theorganisms which provide the hydrolytic enzymesand the slowly biodegradable substrates them-selves.Parallel with hydrolysis the activity of proto-

zoa contribute to phenomena which are ass-igned to hydrolysis. Whereas it is difficult todistinguish between true hydrolysis and proto-zoan activity it is becoming more and moreevident that the effect of electron acceptorupon the ‘hydrolysis’ process may actually bedue to the inactivity of protozoa under anoxic

and anaerobic conditions. Experimental evi-dence that ‘hydrolysis’ reactions depend on theavailable electron acceptors, leeds to thedifferentiation of three hydrolysis processes inASM2. It is, however, a difficult task to esti-mate hydrolysis rate constants under differentelectron acceptor conditions.

1. Aerobic hydrolysis of slowly biodegradablesubstrate characterizes hydrolysis underaerobic conditions (SO2

> 0).

2. Anoxic hydrolysis of slowly biodegradablesubstrate characterizes hydrolysis underanoxic conditions (SO2

≈ 0, SNO3> 0). This

process is typically slower than aerobichydrolysis.

3. Anaerobic hydrolysis of slowly biodegradablesubstrate characterizes hydrolysis underanaerobic conditions (SO2

≈ 0, SNO3≈ 0).

This process is not well characterized and isprobably slower than aerobic hydrolysis. Itsrate remains to be studied.

Table 3.2 summarizes the stoichiometry of thehydrolysis processes. It is assumed that slowlybiodegradable substrateXS is degraded to readilydegradable substrate SFwhereby a small fractionfSI of inert organic material SI is released. Thestoichiometric coefficients for SNH4

, SPO4and

SALK may be computed from ConservationEquation 3.2. These three coefficients are typi-cally positive.The proposed rate equations for the hydro-

lysis processes 1−3 are presented in Table 3.7.They are similar to those of ASM1: hyperbolicswitching functions for SO2

and SNO3consider

the environmental conditions; a surface-limitedreaction (XS/XH)/(KX + XS/XH) is assumed forthe hydrolysis process itself. It is proposed thatonly heterotrophic organisms may catalysehydrolysis. Typically hydrolysis is slower underdenitrifying or anaerobic (fermentation) thanunder aerobic conditions. The rate for anoxicand anaerobic hydrolysis is therefore reducedby the factors hNO3

and hfe respectively.The hydrolysis of particulate, biodegradable

organic nitrogen is included as a separateprocess in ASM1 but not in ASM2. This

85


Table 3.2. Stoichiometry of hydrolysis processes. The stoichiometric parameters are defined in Table 4.2.

Process

1 Aerobic hydrolysis 1 − fSI n1,NH4n1,PO4

fSI n1,ALK −1 n1,TSS

2 Anoxic hydrolysis 1 − fSI n2,NH4n2,PO4


3 Anaerobic hydrolysis 1 − fSI n3,NH4n3,PO4


The stoichiometric coefficients for , , and may be computed from Conservation Equation 3.2SNH4SPO4

SALK XTSS

SF SNH4SPO4

SI SALK XS XTSS

with the aid of Table 3.1. As an example .n1,PO4= − [(1 − fSI) ⋅ iPSF + fSI ⋅ iPSi − 1 ⋅ iPXS

] / 1

process is necessary if the nitrogen content ofXS is variable. In order to simplify ASM2, it isassumed that XS contains a constant fraction ofnitrogen iN,XS

and phosphorus iP,XS. Without

this simplifying assumption, six more hydrolysisprocesses and two more particulate compo-nents would be required.The process of ammonification is included in

ASM1 in order to describe the release ofammonium, SNH4

, from soluble, biodegradableorganic nitrogen. In ASM2 it is assumed thatthe fermentable substrates, SF, contain a con-stant fraction of nitrogen and phosphorus, iN,SFand iP,SF respectively. This allows the process ofammonification to be ignored. Without thissimplifying assumption, two more processes(ammonification as well as phosphatification,the release of phosphate SPO4

from an organicfraction), and two more components (soluble,degradable organic nitrogen and phosphorus)would have to be introduced.

3.3.3 Processes of facultativeheterotrophic organisms

The heterotrophic organisms XH are respon-sible for the hydrolysis of slowly biodegradablesubstrate XS (see above), the aerobic degra-dation of fermentable organic substrates SF andof fermentation products SA (aerobic growth),anoxic oxidation of SF and SA and reduction ofnitrate SNO3

(denitrification), and anaerobicfermentation of SF to SA. In addition theseorganisms are subject to decay and lysis. Thestoichiometry and the kinetics of the processesdescribed below are presented in Tables 3.3and 3.7 respectively.

4 and 5. Aerobic growth of heterotrophic org-anisms on fermentable substrates SF and onfermentation products SA. These processes

are modelled as two parallel processes, whichconsume the two degradable organic sub-strates SF and SA. For both processes iden-tical growth rates mm and yield coefficientsYH are assumed. The rate equations aredesigned such that the maximum specificgrowth rate of the heterotrophic organismsdoes not increase above mm even if both sub-strates, SF and SA, are present in high concen-trations. These processes require oxygen,SO2

, nutrients, SNH4and SPO4

, and possiblyalkalinity, SALK, and they produce suspendedsolids, XTSS.

6 and 7. Anoxic growth of heterotrophic org-anisms on fermentable substrates, SF, and onfermentation products, SA; denitrification.These two processes are similar to theaerobic growth processes, but they requirenitrate, SNO3

, as the electron acceptor ratherthan oxygen. The stoichiometry for nitrate iscomputed based on the assumption that allnitrate, SNO3

, is reduced to dinitrogen, SN2.

Denitrification releases alkalinity, the stoi-chiometry of which is predicted from chargeconservation. Denitrification is assumed tobe inhibited by oxygen SO2

and the maxi-mum growth rate mm is reduced relative toits value under aerobic conditions, by thefactor hNO3

. This accounts for the fact thatnot all heterotrophic organisms XH may becapable of denitrification or that denitrifi-cation may only proceed at a reduced rate.

8. Fermentation. Under anaerobic conditions(SO2

≈ 0, SNO3≈ 0) it is assumed that hetero-

trophic organisms are capable of fermenta-tion,wherebyreadilybiodegradablesubstratesSF are transformed into fermentation pro-ducts SA. Although this process may possiblycause growth of heterotrophic organisms, it

86

Table 3.3. Stoichiometry of the facultative heterotrophic organisms XH. The stoichiometric parameters are definedin Table 4.2. Stoichiometry for , , , SALK and XTSS may be computed from conservation.SO2

SNH4SPO4

Process SO2SF SA SNO3

SN2XI XS XH

4 Aerobic growthon SF

1 −

1

YH−

1

YH1

5 Aerobic growthon SA

1 −

1

YH−

1

YH1

6 Anoxic growthon SA

−

1

YH−

1 − YH2.86⋅YH

1

7 Anoxic growthon SA,

Denitrification−

1

YH−

1 − YH2.86⋅YH

−

1 − YH2.86 ⋅YH

1

8 Fermentation −1 1

9 Lysis f XI1 − f XI

−1

1 − YH2.86 ⋅YH


is introduced here as a simple transformationprocess. A growth process would requiremore complex kinetics, more kinetic andstoichiometric parameters which are difficultto obtain, and possibly different yieldcoefficients for SF and SA in processes 4 to 7.Fermentation releases negatively chargedfermentation products, SA, and therefore hasa requirement for alkalinity, SALK. This ispredicted from charge conservation.

Fermentation is a process which, up to now,has not been well characterized. Little is knownabout the kinetics of this process, which maylead to a large range of kinetic parameters formodelling experimental results. Reliable appli-cation of ASM2 requires that research is direc-ted towards characterizing what is describedhere with the process of fermentation.

9. Lysis of heterotrophic organisms. This pro-cess represents the sum of all decay and lossprocesses of the heterotrophic organisms:endogenous respiration, lysis, predation etc.It is modelled in analogy to ASM1; its rate isindependent of environmental conditions.

3.3.4 Processes of phosphorus-accumulating organisms

Some organisms, XPAO, are known for theirpotential to accumulate phosphorus in the formof poly-phosphate XPP. Currently these organ-isms are not well characterized; historically itwas assumed that they would all be part of theAcinetobacter genus. However, today it is clearthat Acinetobacter may contribute to, but do byfar not dominate, biological phosphorus removal.Initially it was assumed that phosphorus-accu-mulating organisms, PAO, could not denitrify;now evidence has become available that some

of them can denitrify. Phosphate release issometimes slower in the presence of nitrate;this observation is not predicted with ASM2but is included in ASM2d. Glycogen is found tobe an important carbon storage material ofPAO but is not considered in ASM2 in order toreduce model complexity. This restriction leadsto limitations of the applicability of ASM2dwhich will be discussed later.The greater the attempts to characterize PAO,

the more complex this group of organismsbecomes. The Task Group is well aware thatthe time has come when biological phosphorusremoval is being designed and used in actualplants. The introduction of a very detailedmech-anistic model for the processes responsible forbiological phosphorus removal is, however,premature. The Task Group therefore has cho-sen to suggest a simple model, which allows pre-diction of biological phosphorus removal, butdoes not yet include all observed phenomena.The model proposed may be the base forfurther development. With the introduction ofASM2d the most important criticism that PAOcontribute significantly to denitrification whichis not described in ASM2 is taken care of.The following model for the behaviour of

phosphorus-accumulating organisms, XPAO, isvalid for ASM2d only, it assumes that theseorganisms can grow under aerobic (SO2

> 0) aswell as anoxic (SO2

≈ 0, SNO3> 0) conditions.

They can only grow on cell internal storedorganic materials, XPHA. This assumption is asevere restriction of ASM2d and may lead tofurther extensions. The stoichiometry and thekinetics of the processes described below arepresented in Tables 3.4 and 3.7 respectively.

10. Storage of XPHA. It is assumed that PAO may

87


Table 3.4. Stoichiometry of the phosphorus-accumulating organisms, PAO, for ASM2d. The stoichiometricparameters are defined in Table 4.2. Stoichiometry for , , , , , SALK and XTSS may becomputed from conservation. ASM2 does not include processes 12 and 14.

SO2SNH4

SN2SNO3

SPO4

SO2SA SN2

SNO3SPO4

XI XS XPAO XPP XPHA

10 XPHA YPO4−YPO4

11 Aerobic storageof XPP

−YPHA −1 1 −YPHA

12 Anoxic storageof XPP

−n12,NO3n12,NO3

−1 1 −YPHA

13 Aerobic growthof XPAO

n13,O2−iPBM 1 −1/YH

14 Anoxic growthof XPAO

−n14,NO3n14,NO3

−iPBM 1 −1/YH

15 Lysis of XPAO n15,PO4fXI

1 − fXI−1

16 Lysis of XPP 1 −117 Lysis of XPHA 1

Process

Storage of −1

−1

1

release phosphate, SPO4from poly-phosphate,

XPP, and utilize the energy which becomesavailable from the hydrolysis of XPP, in orderto store cell external fermentation productsSA in the form of cell internal organicstorage material XPHA. The process is pri-marily observed under anaerobic conditions.However, since the process has also beenreported to occur under aerobic and anoxicconditions, the kinetic expression does notinclude inhibition terms for SO2

and SNO3.

Experimental observation of this process iseasy if the release of phosphorus is observedrather than the organics which are stored.Experience indicates, however, that the rateof storage of organics is relatively constant,whereas the release of phosphorus varies,indicating a variable stoichiometric relation-ship. The base for the stoichiometry of thisprocess was therefore chosen to be theorganics which are taken up, SA and XPHA.Reliable estimation of the rate constant,qPHA, and the stoichiometric parameter,YPO4

, requires independent measurement ofboth SA removal and SP release. It has beenshown that YPO4

depends on pH.

11 and 12. Aerobic and anoxic storage of poly-phosphate. Storage of ortho-phosphate, SPO4

,in the form of cell internal poly-phosphates,XPP, requires the PAO to obtain energy,which may be gained from the aerobic oranoxic respiration of XPHA. The regenerationof poly-phosphates is a requirement for thegrowth of PAO, because the organic sub-strates, SA, are stored only upon the releaseof poly-phosphate. Storage of XPP isobserved to stop if the phosphorus contentof the PAO becomes too high. This obser-vation leads to an inhibition term of XPPstorage, which becomes active as the ratioXPP/XPAO approaches the maximum allow-able value of KMAX. Under anoxic conditionsthe maximum rate of storage of poly-phos-phate qPP is reduced relative to its valueunder aerobic conditions, by the factor hNO3

.This accounts for the fact that not all PAO(XPAO) may be capable of denitrification orthat denitrification may only proceed at areduced rate. Process 12 is contained inASM2d but not in ASM2.

13 and 14. Aerobic and anoxic growth of phos-phorus-accumulating organisms. These org-anisms are assumed to grow only at theexpense of cell internal organic storage pro-ducts XPHA. As phosphorus is continuouslyreleased by the lysis of XPP, it is possible toassume that the organisms consume ortho-

phosphate, SPO4, as a nutrient for the

production of biomass. It is known that PAOmay grow at the expense of soluble sub-strates (e.g. SA), but it is unlikely that suchsubstrates ever become available under aero-bic or anoxic conditions in a biological nutri-ent removal plant. The Task Group thereforesuggests this possibility to be ignored at thistime. Under anoxic conditions the maximumgrowth rate of PAO mPAO is reduced relativeto its value under aerobic conditions, by thefactor hNO3

. This accounts for the fact thatnot all PAO (XPAO) may be capable ofdenitrification or that denitrification mayonly proceed at a reduced rate. Process 13 iscontained in ASM2d but not in ASM2.

15, 16 and 17. Lysis of phosphorus-accumu-lating organisms and their storage products.Death, endogenous respiration and mainten-ance all result in a loss or decay of allfractions of PAO. Since the storage productsXPP and XPHA are accounted for separatelyfrom the biomass XPAO, all three compo-nents must be subject to separate decay pro-cesses. ASM2 includes three lysis processeswhich are all first-order relative to thecomponent which is lost. If all three rateconstants are equal, the composition of theorganisms does not change due to decay.There is experimental evidence that XPPdecays faster than XPAO and XPHA. Thisadditional loss of poly-phosphates may bemodelled by the choice of an increased rate,bPP, for the lysis of this component. Theproducts of lysis are chosen in analogy to thelysis of heterotrophic organisms; storage pro-ducts are assumed to decay to ortho-phos-phate SPO4

and fermentation products SA.

3.3.5 Nitrification processes

Nitrification is assumed to be a one-step pro-cess, from ammonium SNH4

directly to nitrateSNO3

. The intermediate component, nitrite, isnot included as a model component. In thecontext of nitrification, modelling nitrite pro-duction and consumption would be relativelyeasy. However, nitrite is also produced andconsumed in the context of denitrification wherethe Task Group felt that the required additionto the model complexity does not warrant itsinclusion at the present time. Modelling nitritein nitrification but not in denitrification would,however, not be consistent and could lead toerroneous model predictions.The stoichiometry and the kinetics of the

processes described below, are presented inTables 3.5 and 3.7 respectively.

88


18. Growth of nitrifying organisms. Nitrifyingorganisms are obligate aerobic, they consumeammonium as a substrate and a nutrient, andproduce nitrate. Nitrification reduces alkalin-ity. The process is modelled as proposed inASM1 with the exception of a phosphorusuptake into the biomass.

19. Lysis of nitrifying organisms. The process oflysis of nitrifiers is modelled in analogy toASM1 and to the process of lysis of hetero-trophic organisms. Since the decay productsof lysis (XS and ultimately SF) are availablesubstrates for heterotrophic organisms only,endogenous respiration of nitrifiers becomesmanifest as an increased growth and oxygenconsumption of heterotrophs. This is inanalogy to ASM1.

3.4 Chemical precipitation of phosphates

In biological nutrient removal systems, metals,which are naturally present in the wastewater(e.g. Ca2+), together with the high concentra-tion of released soluble ortho-phosphate, SPO4

,may result in chemical precipitation of phos-phorus (e.g. in the form of apatite or calciumphosphate).Further, simultaneous precipitation of phos-

phorus via the addition of iron or aluminiumsalts is a very common process for phosphorusremoval worldwide. Simultaneous precipitationmay be used in combination with biologicalphosphorus removal if the carbon to phos-phorus ratio is unfavourably small.In order to model the low effluent concen-

trations of ortho-phosphate, SPO4, which are

observed in practice and which are partly due tochemical precipitation, the Task Group suggestsa very simple precipitation model, which maybe calibrated for a variety of situations. For this

purpose, two processes (precipitation and re-dissolution) and two more components (XMeOHand XMeP) are added to ASM2. If chemicalprecipitation is not of any interest, these addi-tions may be deleted from the model.

20 and 21. Precipitation and redissolution ofphosphate SPO4

. The precipitation model isbased on the assumption that precipitationand redissolution are reverse processes, whichat steady state would be in equilibriumaccording to:

XMeOH + SPO4↔ XMeP

Precipitation and redissolution may bemodelled with the following process ratesrespectively:

r20 = kPRE · SPO4· XMeOH

r21 = kRED · XMeP

If both processes are in equilibrium (n20,i · r20= n21,i · r21) then an equilibrium constant maybe derived as:

Keq =n21,i ⋅ kREDn20,i ⋅ kPRE

=SPO4

⋅ XMeOH

XMeP

Processes 20 and 21 are introduced here basedon the assumption thatXMeOHandXMeP are com-posed of ferric-hydroxide, Fe(OH)3, and ferric-phosphate,FePO4, respectively. This leads to thestoichiometry indicated in Table 3.6. The indi-cated rates of the processes result in residualortho-phosphate concentrations, SP, which atsteady state are typical for simultaneous preci-pitation with the addition of FeCl3. In this case,the addition of Fe3+ to the influent of atreatment plant may be modelled by the choiceof XMeOH in the influent recognizing that 1 gFe3+ m−3 leads to 1.91 g Fe(OH)3 m−3 = 1.91 gMeOH m−3 (which also increases influent XTSSand decreases influent alkalinity SALK).

89


Table 3.5. Stoichiometry of the growth and decay processes of nitrifying organisms XAUT. The stoichiometricparameters are defined in Table 4.2. Stoichiometry for , , , SALK and XTSS may be computedfrom conservation.

SO2SNH4

SPO4

Process SO2SNH4

SNO3SPO4

XI XS XAUT

18 Aerobic growth of −4.57 − YA

YAn18,NH4

1

Ya1

19 Lysis n19,NH4fXI

1 − fXI−1

XAUT

n19,PO4

−iP,BM

Table 3.6. Stoichiometry of the processes describing simultaneous precipitation of phosphorus. The absolute valuesof stoichiometry (and kinetics in Table 4.3) are based on the assumption that Fe(OH)3 is used toprecipitate in the form of FePO4 + Fe(OH)3. Stoichiometry for SALK and XTSS may be computedfrom conservation.

SPO4

Process SPO4SALK XMeOH XMeP XTSS

20 Precipitation −1 n20, ALK −3.45 4.87 1.4221 Redissolution 1 n21, ALK 3.45 −4.87 −1.42

90

Table 3.7. Process rate equations for ASM2d. The kinetic parameters are defined in Table 4.3.

j Process Process rate equation [MI L−3 T−1]rj, rj ≥ 0

Hydrolysis processes:

1 Aerobic

hydrolysisKh ⋅

SO2

KO2+ SO2

⋅XS /XH

KX + XS /XH

⋅ XH

2 Anoxichydrolysis

Kh ⋅ hNO3⋅

KO2

KO2+ SO2

⋅SNO3

KNO3+ SNO3

⋅XS /XH

KX + XS /XH

⋅ XH

3 Anaerobic

hydrolysisKh ⋅ hfe ⋅

KO2

KO2+ SO2

⋅KNO3

KNO3+ SNO3

⋅XS /XH

KX + XS/XH

⋅ XH

Heterotrophic organisms: XH

4 Growth on

fermentableSFsubstrates,

mH ⋅SO2

KO2+ SO2

⋅SF

KF + SF⋅

SF

SF + SA⋅

SNH4

KNH4+ SNH4

⋅SPO4

KP + SPO4

⋅SALK

KALK + SALK⋅ XH

5 Growth onfermentation

SAproducts,

mH ⋅SO2

KO2+ SO2

⋅SA

KA + SA⋅

SASF + SA

⋅SNH4

KNH4+ SNH4

⋅SPO4

KP + SPO4

⋅SALK

KALK + SALK⋅ XH

6 Denitrification

with fermentableSFsubstrates,

mH ⋅ hNO3⋅

KO2

KO2+ SO2

⋅KNO3

KNO3+ SNO3

⋅SF

KF + SF⋅

SF

SF + SA⋅

SNH4

KNH4+ SNH4

⋅SPO4

KP + SPO4

⋅SALK

KALK + SALK⋅ XH

7 Denitrificationwith fermentation

SAproducts,

mH ⋅ hNO3⋅

KO2

KO2+ SO2

⋅KNO3

KNO3+ SNO3

⋅SA

KA + SA⋅

SASF + SA

⋅SNH4

KNH4+ SNH4

⋅SPO4

KP + SPO4

⋅SALK

KALK + SALK⋅ XH

8 Fermentation qfe ⋅KO2

KO2+ SO2

⋅KNO3

KNO3+ SNO3

⋅SF

KF + SF⋅

SALKKALK + SALK

⋅XH

9 Lysis bH ⋅ XH

Phosphorus-accumulating organisms (PAO): XPAO

10 Storage ofXPHA

qPHA ⋅SA

KA + SA⋅

SALK

KALK + SALK⋅

XPP/XPAO

KPP + XPP/XPAO

⋅ XPAO

11 Aerobic

storageXPPof

qPP ⋅SO2

KO2+ SO2

⋅SPO4

KPS + SPO4

⋅SALK

KALK + SALK⋅

XPHA/XPAO

KPHA + XPHA /XPAO⋅

KMAX − XPP /XPAO

KPP + KMAX − XPP/XPAO⋅ XPAO

12 Anoxic

storageXPPof

r12 = r11 ⋅ hNO3⋅KO2

SO2

⋅SNO3

KNO3+ SNO3

13 Aerobic

growthXPHAon

mPAO ⋅SO2

KO2+ SO2

⋅SNH4

KNH4+ SNH4

⋅SPO4

KP + SPO4

⋅SALK

KALK + SALK⋅

XPHA/XPAO

KPHA + XPHA/XPAO⋅ XPAO

14 Anoxicgrowth

XPPonr14 = r13 ⋅ hNO3

⋅KO2

SO2

⋅SNO3

KNO3+ SNO3

15 Lysis of XPAO bPAO ⋅ XPAO ⋅ SALK/ (KALK + SALK)

16 Lysis of XPP bPP ⋅ XPP ⋅ SALK/ (KALK + SALK)

17 Lysis of XPHA bPHA ⋅ XPHA ⋅ SALK /(KALK + SALK)

Nitrifying organisms (autotrophic organisms): XAUT

18 Aerobicgrowth

XAUTofmAUT ⋅

SO2

KO2+ SO2

⋅SNH4

KNH4+ SNH4

⋅SPO4

KP + SPO4

⋅SALK

KALK + SALK⋅ XAUT

19 Lysis of XAUT bAUT ⋅XAUT

Simultaneous precipitation of phosphorus with ferric hydroxide Fe(OH)3

20 Precipitation kPRE ⋅ SPO4⋅ XMeOH

21 Redissolution kRED ⋅ XMeP ⋅ SALK/ (KALK + SALK)


t is the responsibility of the user of theActivated Sludge Model No. 2 (ASM2 and

ASM2d) to determine the concentrations ofrelevant components in the wastewater, as wellas the stoichiometric and kinetic parameterswhich apply to the specific case to be dealtwith. Absolute numbers of these parametersare neither part of ASM2 nor of ASM2d, butare necessary for the application of the modelto a specific case.In this section, the Task Group suggests a list

of typical concentrations of model componentsin a primary effluent as well as a set of modelparameters. This neither indicates that ASM2or ASM2d is meant to be reliable with these

parameters in any case, nor that these para-meters are the state of the art. They are merelypresented as a reference for testing computercode and a first estimate for the design ofpossible experiments which are proposed todetermine these parameters more accurately.Table 4.1 contains a list of all model compo-

nents and typical concentrations in a primaryeffluent. This wastewater contains a total CODof 260 g COD m−3, a total nitrogen content of25 g N m−3 and approximately 140 g TSS m−3.The analytically measured TSS are lower thanthe value of XTSS = 180 g TSS m−3, since a frac-tion of XS in the influent would pass throughmembrane filters but must be included in the

91

4. Typical wastewater characteristicsand kinetic and stoichiometricconstants

4. Typical wastewater characteristics and kinetic and stoichiometric constants

I

Table 4.1 Short definition of model components and typical wastewater composition (primary effluent),considering the composition of the different model components as indicated in Table 4.2.

CODtot = 260 g COD m−3, TKN = 25 g N m−3, TP = 6 g P m−3

Dissolved components:SO2

Dissolved oxygen 0 g O2 m−3

SF Readily biodegradable substrate 30 g COD m−3

SA Fermentation products (acetate) 20 g COD m−3

SNH4Ammonium 16 g N m−3

SNO3Nitrate (plus nitrite) 0 g N m−3

SPO4Phosphate 3.6 g P m−3

SI Inert, bon-biodegradable organics 30 g COD m−3

SALK Bicarbonate alkalinity 5 mole HC

Particulate components:XI Inert, non-biodegradable organics 25 g COD m−3

XS Slowly biodegradable substrate 125 g COD m−3

XH Heterotrophic biomass 30 g COD m−3

XPAO Phosphorus-accumulating organisms, PAO 0 g COD m−3

XPP Stored poly-phosphate of PAO 0 g P m−3

XPHA Organic storage products of PAO 0 g COD m−3

XAUT Autotrophic, nitrifying biomass 0 g COD m−3

XMeOH ‘Ferric-hydroxide’, Fe(OH)3 0 g Fe(OH)3 m−3

XMeP ‘Ferric-phosphate’, FePO4 0 g FePO4 m−3

XTSS Particulate material as model componenta) 180a) g TSS m−3

a) This value is larger than TSS which may be measured analytically, since it includes the fraction of XS, whichwould pass the filter in the TSS analysis. XTSS may also include some inert mineral material, which is contained inthe influent but not accounted for by other components. If this is the case, then XTSS in the influent will be largerthan predicted from the conservation equation, which for the above values and based on the conversion factorsgiven in Table 4.2 would result in 140 g TSS m−3. Analytically measured TSS (0.45 µm) would be approximately120 g TSS m−3.

m−3−

3O

model component XTSS since it will later adsorbonto the activated sludge. The total nitrogen(and phosphorus) in the influent may be com-puted with the aid of all influent concentrationsmultiplied with the relevant conversion factorsfrom Tables 3.1 and 4.2.Table 4.2 is a list of typical stoichiometric

coefficients of ASM2 and ASM2d and includesthe factors which are required for the use ofthe conservation equations (see also Table 3.1).Many of the conversion factors have been esti-mated without performing specific experimentsfor their determination. These values indicatean order of magnitude. The stoichiometriccoefficients are either based on previous exper-ience with ASM1 or they are derived from

verification trials of ASM2 relative to full-scaleexperience. Experience with the three yieldcoefficients, YPAO, YPO4

and YPHA of the PAOare still scarce.Table 4.3 is a summary of the definitions and

typical values of all kinetic parameters of themodels ASM2 and ASM2d. Again, some kineticparameters were estimated based on theexperience with ASM1, those relating tobiological phosphorus removal are estimatedbased on laboratory experience and full-scaleverification trials of ASM2. Note that saturationcoefficients Ki for any specific compound maybe different for different organisms (e.g. KO2

may have four different values, depending onthe process and organism to which it relates).

92

Table 4.2. Definition and typical values for the stoichiometric coefficients of ASM2.

Typical conversion factors for conservation equation

Nitrogen:Soluble material:iN,SI N content of inert soluble COD SI 0.01 g N (g COD)−1

iN,SF N content of fermentable substrates SF 0.03 g N (g COD)−1

Particulate material:iN,XI

N content of inert particulate COD XI 0.02 g N (g COD)−1

iN,XSN content of slowly biodegradable substrate XS 0.04 g N (g COD)−1

iN,BM N content of biomass, XH, XPAO, XAUT 0.07 g N (g COD)−1

Phosphorus:Soluble material:iP,SI P content of inert soluble COD SI 0.00 g P (g COD)−1

iP,SF P content of fermentable substrates SF 0.01 g P (g COD)−1

Particulate material:iP,XI

P content of inert particulate COD XI 0.01 g P (g COD)−1

iP,XFP content of slowly biodegradable substrate XS 0.01 g P (g COD)−1

iP,BM P content of biomass, XH, XPAO, XAUT 0.02 g P (g COD)−1

Total suspended solids: TSSiTSS,XI

TSS to COD ratio for XI 0.75 g TSS (g COD)−1

iTSS,XSTSS to COD ratio for XS 0.75 g TSS (g COD)−1

iTSS,BM TSS to COD ratio for biomass, XH, XPAO, XA 0.90 g TSS (g COD)−1

Typical stoichiometric parameters

Hydrolysis:fSI Production of SI in hydrolysis 0 g COD (g COD)−1

Heterotrophic biomass: XH

YH Yield coefficient 0.625 g COD (g COD)−1

fXIFraction of inert COD generated in biomass lysis 0.10 g COD (g COD)−1

Phosphorus-accumulating organisms: XPAO

YPAO Yield coefficient (biomass/PHA) 0.625 g COD (g COD)−1

YPO4PP requirement (PO4 release) per PHA stored 0.40 g P (g COD)−1

YPHA PHA requirement for PP storage 0.20 g COD (g P)−1


Nitrifying organisms: XAUT

YA Yield of autotrophic biomass per N -N−

3O 0.24 g COD (g N)−1



93


Table 4.3. Definition and typical values for the kinetic parameters of ASM2d.

Temperature: 20 ºC 10 °C Units

Hydrolysis of particulate substrate: XS

Kh = Hydrolysis rate constant 3.00 2.00 d−1

hNO3= Anoxic hydrolysis reduction factor 0.60 0.60 –

hf e = Anaerobic hydrolysis reduction factor 0.40 0.40 –KO2

= Saturation/inhibition coefficient for oxygen 0.20 0.20 g O2 m−3

KNO3= Saturation/inhibition coefficient for nitrate 0.50 0.50 g N m−3

KX = Saturation coefficient for particulate COD 0.10 0.10 g XS (g XH)−1


mH = Maximum growth rate on substrate 6.00 3.00 g XS (g XH)−1 d−1

qfe = Maximum rate for fermentation 3.00 1.50 g SF (g XH)−1 d−1

hNO3= Reduction factor for denitrification 0.80 0.80 –

bH = Rate constant for lysis and decay 0.40 0.20 d−1

KO2= Saturation/inhibition coefficient for oxygen 0.20 0.20 g O2 m−3

KF = Saturation coefficient for growth on SF 4.00 4.00 g COD m−3

Kfe = Saturation coefficient for fermentation of SF 4.00 4.00 g COD m−3

KA = Saturation coefficient for growth on acetate SA 4.00 4.00 g COD m−3

KNO3= Saturation/inhibition coefficient for nitrate 0.50 0.50

KNH4= Saturation coefficient for ammonium (nutrient) 0.05 0.05

KP = Saturation coefficient for phosphate (nutrient) 0.01 0.01 g P m−3

KALK = Saturation coefficient for alkalinity (HC )−

3O 0.10 0.10 mole HC m−3−

3O

Phosphorus-accumulating organisms: XPAO

qPHA = Rate constant for storage of XPHA (base XPP) 3.00 2.00 g XPHA (g XPAO)−1 d−1

qPP = Rate constant for storage of XPP 1.50 1.00 g XPP (g XPAO)−1 d−1

mPAO = Maximum growth rate of PAO 1.00 0.67 d−1

hNO3= Reduction factor for anoxic activity 0.60 0.60 –

bPAO = Rate for lysis of XPAO 0.20 0.10 d−1

bPP = Rate for lysis of XPP 0.20 0.10 d−1

bPHA = Rate for lysis of XPHA 0.20 0.10 d−1

KO2= Saturation/inhibition coefficient for oxygen 0.20 0.20 g O2 m−3

KNO3= Saturation coefficient for nitrate, SNO3

0.50 0.50 g N m−3

KA = Saturation coefficient for acetate, SA 4.00 4.00 g COD m−3

KNH4= Saturation coefficient for ammonium (nutrient) 0.05 0.05 g N m−3

KPS = Saturation coefficient for phosphorus in storage of PP 0.20 0.20 g P m−3

KP = Saturation coefficient for phosphate (nutrient) 0.01 0.01 g P m−3


3O 0.10 0.10 mole HC m−3−

3OKPP = Saturation coefficient for poly-phosphate 0.01 0.01 g XPP (g XPAO)−1

KMAX = Maximum ratio of XPP/XPAO 0.34 0.34 g XPP (g XPAO)−1

KIPP = Inhibition coefficient for PP storage 0.02 0.02 g XPP (g XPAO)−1

KPHA = Saturation coefficient for PHA 0.01 0.01 g XPHA (g XPAO)−1


mAUT = Maximum growth rate of XAUT 1.00 0.35 d−1

bAUT = Decay rate of XAUT 0.15 0.05 d−1

KO2= Saturation coefficient for oxygen 0.50 0.50 g O2 m−3

KNH4= Saturation coefficient for ammonium (substrate) 1.00 1.00 g N m−3


3O 0.50 0.50 mole HC m−3−

3OKP = Saturation coefficient for phosphorus (nutrient) 0.01 0.01 g P m−3

Precipitation:kPRE = Rate constant for P precipitaion 1.00 1.00 m3 (g Fe(OH)3)−1 d−1

kRED = Rate constant for redissolution 0.60 0.60 d−1

KALK = Saturation coefficient for alkalinity 0.50 0.50 mole HC m−3−

3O

g N m−3

g N m−3

94

Table 4.4. An example of a stoichiometric matrix for ASM2d for soluble and particulate components and forprecipitation processes. The absolute values of the stoichiometric coefficients are based on the typicalstoichiometric parameters introduced in Table 4.2. These values are not the ASM2d but rather a typicalapplication of the model.

Stoichiometric matrix for soluble components

Process component SO2SF SA SI SNH4

SN2SNO3

SPO4SALK

expressed as→ O2 COD COD COD N N N P mole

1 Aerobic hydrolysis 1.00 0.01 0.0012 Anoxic hydrolysis 1.00 0.01 0.0013 Anaerobic hydrolysis 1.00 0.01 0.001


4 Growth on SF −0.60 −1.60 −0.022 −0.004 −0.0015 Growth on SA −0.60 −1.60 −0.07 −0.02 0.0216 Denitrification with SF −1.60 −0.022 0.21 −0.21 −0.004 0.0147 Denitrification with SA −1.60 −0.07 0.21 −0.21 −0.02 0.0368 Fermentation of SF −1. 1 . 0.03 0.01 −0.0149 Lysis 0.031 0.01 0.002


10 Storage of PHA −1. 0.4011 Aerobic storage of PP −0.20 −1.12 Anoxic storage of PP 0.07 −0.07 −1. 0.02113 Aerobic growth −0.60 −0.07 −0.02 −0.00414 Anoxic growth −0.07 0.21 −0.21 −0.02 0.01115 Lysis of PAO 0.031 0.01 0.00216 Lysis of PP 1. −0.01617 Lysis of PHA 1. −0.016


18 Aerobic growth −18.0 −4.24 4.17 −0.02 −0.6019 Lysis 0.031 0.01 0.002

Simultaneous precipitation of phosphorus with ferric hydroxide (Fe(OH3)):20 Precipitation −1. 0.048

21 Redissolution 1. −0.048

Stoichiometric matrix for particulate components

Process component XI XS XH XPAO XPP XPHA XA XTSS XMeOH XMeP

expressed as→ COD COD COD COD P COD COD TSS TSS TSS

1 Aerobic hydrolysis −1. −0.752 Anoxic hydrolysis −1. −0.753 Anaerobic hydrolysis −1. −0.75


4 Growth on SS 1 0.905 Growth on SA 1 0.906 Denitrification with SS 1 0.907 Denitrification with SA 1 0.908 Fermentation9 Lysis 0.10 0.9 −1 −0.15


10 Storage of PHA −0.40 1. −0.6911 Aerobic storage of PP 1. −0.20 3.1112 Anoxic storage of PP 1. −0.20 3.1113 Aerobic growth 1 −1.60 −0.0614 Anoxic growth 1 −1.60 −0.0615 Lysis of PAO 0.10 0.90 −1 −0.1516 Lysis of PP −1. −3.2317 Lysis of PHA −1. −0.60


18 Aerobic growth 1 0.9019 Lysis 0.10 0.90 −1 −0.15

Simultaneous precipitation of phosphorus with ferric hydroxide (Fe(OH3)):20 Precipitation 1.42 −3.45 4.8721 Redissolution −1.42 3.45 −4.87

0.0090.016


Future experience may well lead to different‘good estimates’ of the parameters of themodel. Since experimental results of many pilotstudies have been performed without consider-ing the requirements of model calibration, we donot currently have a sufficient basis to calibrateASM2 or ASM2d to a ‘typical wastewater’.

Finally a full stoichiometric matrix forASM2d, based on the proposed stoichiometric

parameters in Table 4.2 is presented in Table4.4. Table 4.4 is not meant to be a part ofASM2d but rather it should indicate approxi-mate values of stoichiometric coefficients nj,i.Table 4.4 may be used to test computer code,which might be developed to predict stoi-chiometric coefficients nj,i based on conversionfactors and stoichiometric constants as intro-duced in Table 4.2.

95


ll models have limitations. For ASM2damong the more important ones are:

• the model is valid for municipal waste-water only

• processes with overflow of SA to the aera-tion tank cannot be modelled

• the wastewater must contain sufficientMg2+ and K+

• pH should be near neutral• temperature is expected to be in the range

of 10−25 °C

Use of the model outside of these limitationsis not recommended.

SM2d should be used as a basis formodelling of simultaneous biological phos-

phorus uptake and nitrification–denitrification.As compared with ASM2 it will improve theaccuracy when modelling nitrate and phos-phate dynamics. ASM2d is considered to be aplatform and a reference for further researchand development of kinetic models forbiological nutrient removal in activated sludgesystems.

96

5. Limitations

A

6. Conclusion

A


Henze, M., Gujer, W., Mino, T., Matsuo, T., Wentzel, M.C.and Marais, G.v.R. (1995) Activated Sludge Model No. 2.(IAWQ Scientific and Technical Report No. 3). London:IAWQ.

Henze, M., Grady, C.P.L. Jr, Gujer, W., Marais, G.v.R. andMatsuo, T. (1987) Activated Sludge Model No. 1.(IAWPRC Scientific and Technical Report No. 1).London: IAWPRC.

Kerrn-Jespersen, J.P. and Henze, M. (1993) Biologicalphosphorus uptake under anoxic and aerobic conditions.Wat. Res. 27, 617–624.

Meinhold, J., Filipe, C.D.M., Daigger, G.D. and Isaacs, S.(1999) Characterization of the denitrifying fraction ofphosphate accumulating organisms in biologicalphosphate removal.Wat. Sci. Technol. 39 (1), 31–42.

Mino, T., Liu, W-T., Kurisu, F. and Matsuo, T. (1995)Modelling glycogen storage and denitrification capability

of microorganisms in enhanced biological phosphateremoval processes.Wat. Sci. Technol. 31 (2), 25–34.

Bibliography

The following literature is not explicitly cited inthis text but it has significantly contributed tothe process of model building in the TaskGroup.Brdjanovic, D (1998) Modeling biological phosphorus removal

in activated sludge systems. Ph.D thesis, IHEE and DelftUniversity of Technology.

Wanner, J., Cˇ ech, J.S. and Kos, M. (1992) New process designfor biological nutrient removal. Wat. Sci. Technol. 25,(4–5), 445–448.

97

7. References and bibliography

7. References and bibliography

98


99


by



Willi Gujer, Swiss Federal Institute of Technology, SwitzerlandMogens Henze, Technical University of Denmark, Denmark

Takashi Mino, Tokyo University, JapanMark C.M. Van Loosdrecht, Delft University of Technology, The Netherlands

100


101

Contents

1. Introduction 103

2. Comparison of ASM1 and ASM3 105

3. ASM3: definition of compounds in the model 1063.1 Definition of soluble compounds, S? 1063.2 Definition of particulate compounds, X? 107

4. ASM3: definition of processes in the model 108

5. ASM3: stoichiometry 109

6. ASM3: kinetics 1116.1 Estimation of readily biodegradable substrate SS 111

7 . Limitations of ASM3 113

8. Aspects of application of ASM3 114

9. ASM3C: a carbon-based model 1169.1 Definition and measurement of fractions of organic carbon 1169.2 Transition from ASM3 to ASM3C 1169.3 Adjusting kinetic and stoichiometric parameters for ASM3C 1169.4 Typical kinetic and stoichiometric parameters for ASM3C 1179.5 Modelling pH with ASM3C 1179.6 Limitations of ASM3C 119

10. Conclusion 120

11. References 121

102


ith the introduction of the ActivatedSludgeModel No. 1 (ASM1) the IAWPRC

(later IAWQ and now IWA) Task Group onMathematical Modelling for Design and Oper-ation of Biological Wastewater TreatmentProcesses introduced a new paradigm for themathematical modelling of activated sludgesystems. ASM1 as it was introduced in 1987(Henze et al., 1987) has become a majorreference for many scientific an practicalprojects. Today, mathematical models related toASM1 are implemented in various computercodes for the simulation of the behaviour ofactivated sludge systems treating municipalwastewater of mainly domestic origin.With over ten years of experience with the

application of ASM1, some defects of thismodel have become apparent, including:

• ASM1 does not include kinetic expressionsthat can deal with nitrogen and alkalinitylimitations of heterotrophic organisms. Theresult is that computer code cannot bebased on the original form of ASM1,where under some circumstances negativeconcentrations of, for example, ammoniummay occur. This led to the development ofcomputer codes based on different ver-sions of ASM1, which can hardly be differ-entiated any more.

• ASM1 includes biodegradable soluble andparticulate organic nitrogen as model com-pounds. These cannot easily be measuredand made the use of ASM1 unnecessarilycomplicated. Therefore this distinction ofnitrogen compounds has in the meantimebeen eliminated in many models based onASM1.

• The kinetics of ammonification in ASM1cannot easily be quantified, moreover theprocess is fast and therefore hardly affectsmodel predictions. Again in many versionsof ASM1 assuming a constant compositionof all organic compounds (constant N toCOD ratio) has eliminated this process.

• ASM1 differentiates inert particulate org-anic material depending on its origin, influ-ent or biomass decay, but it is impossibleto differentiate these two fractions in reality.

• In the structure of ASM1, the process ofhydrolysis has a dominating effect uponthe predictions of oxygen consumption anddenitrification by heterotrophic organisms.In reality this process stands for somecoupled processes such as hydrolysis, lysisof organisms and storage of substrates.Therefore the identification of the kineticparameters for this combined process isdifficult.

• Lysis combined with hydrolysis and growthis used to describe the lumped effects ofendogenous respiration of, for example,storage compounds, death, predation andlysis of the biomass. This leads to furtherdifficulties in the evaluation of kineticparameters.

• With elevated concentrations of readilybiodegradable organic substrates, storageof poly-hydroxy-alkanoates and sometimeslipids or glycogen is observed under aero-bic and anoxic conditions in activatedsludge plants. This process is not includedin ASM1.

• ASM1 does not include the possibility todifferentiate decay rates of nitrifiers underaerobic and anoxic conditions. At highsolids retention times (SRT) and high frac-tions of anoxic reactor volumes this leadsto problems with the prediction of maxi-mum nitrification rates.

• ASM1 does not directly predict the fre-quently measured mixed liquor suspendedsolids concentration.

• In respiration tests frequently high bio-mass yield coefficients are obtained. Evenif only soluble, readily biodegradable sub-strates such as acetate are added, itappears from respiration tests that thissubstrate includes a slowly biodegradablefraction.

Considering all these defects and the ad-vance in experimental evidence on storage oforganic compounds, the Task Group hasproposed the Activated Sludge Model No. 3(ASM3) (Gujer et al., 1999) which should cor-rect for these defects and which could becomea new standard for future modelling. ASM3

103

1. Introduction

1. Introduction

W

relates to the same dominating phenomena asdoes ASM1: oxygen consumption, sludge pro-duction, nitrification and denitrification inactivated sludge systems treating wastewater ofprimarily domestic origin.

ASM3 is designed to be the core of manydifferent models. Modules for biological pho-sphorus removal (as contained in the ActivatedSludge Model No. 2 (ASM2 and ASM2d)(Henze et al., 1995, 1999), chemical precipi-tation, growth of filamentous organisms or pHcalculations are not part of ASM3 but can easilybe connected as add on modules. With increa-sing experience with ASM3 the Task Group maywell suggest such modules which would servemany purposes in practical simulation work.

Introduction of ASM1 has spurred andfocused research internationally. Based on acommon platform it became possible to discussrather complex results of careful research.Today interest is with topics such as modellingpopulation dynamics, biological phosphorus

removal and structured biomass (storageproducts). ASM3 may provide the backbone,which describes the processes of minor interestin research, such that we can concentrate onnew frontiers again. In this we should realizethat scientific research and model applicationin engineering practice have different goals.Whereas the detailed structure of the models isused to convey the message on new mecha-nisms which have been identified in our ad-vanced research projects, model application inengineering must rely on manageable modelswith a moderate number of parameters but ahigh potential to predict system behaviour.ASM3 is designed to satisfy primarily therequirements of model application. Neverthe-less, the Task Group has tried to fulfil thedidactic requirement to keep as many details asare necessary to obtain some insight into theinterconnected processes. ASM3 may wellbecome a basis for teaching advanced biologicalwastewater treatment courses.

104


n ASM1 a single decay process (lysis) wasintroduced to describe the sum of all decay

processes under all environmental conditions(aerobic, anoxic). The reason was that in 1985,when ASM1 was first published, computingpower was still scarce. The simplest descriptionpossible saved computation time. Today, as com-putation is not limiting simulation to the sameextent, a more realistic description of decay pro-cesses is introduced in ASM3: endogenous res-piration is close to the phenomena observed (wetypically measure a respiration rate) and therelevant rate constants can be obtained directlyand independent of stoichiometric parameters(from the slope of ln(rO2,endog) versus time).The flow of COD in ASM1 is rather

complex. The death (decay) regeneration cycleof the heterotrophs and the decay process ofnitrifiers are strongly interrelated (Figure 2.1).The two decay processes differ significantly intheir details. This results in differing andconfusing meanings of the two decay rates inASM1. In ASM3 all the conversion processes ofthe two groups of organisms are clearly separ-ated and decay processes are described withidentical models (Figure 2.1).

The complexity of ASM3 is comparable toASM1. There is a shift of emphasis fromhydrolysis to storage of organic substrates, aprocess, which has been postulated andobserved by many researchers. Characteri-zation of wastewater must consider this change.Readily available organic substrates (SS) mustnow be estimated based on the storage ratherthan the growth process. Differentiation ofsoluble and particulate substrates (SS and XS)remains somewhat arbitrary as in ASM1 and ismainly based on time constants for degrada-tion. Correct characterization of wastewater forthe use of ASM3 might still rely on bioassays,which relate to respiration.Similarly to ASM2 (Henze et al. 1995) ASM3

includes cell internal storage compounds. Thisrequires the biomass to be modelled with cellinternal structure. Decay processes (whichinclude predation) must include both fractionsof the biomass, hence four decay processes arerequired (aerobic and anoxic loss of XH as wellas XSTO) and the kinetics of the growthprocesses (aerobic and anoxic) must relate tothe ratio of XSTO/XH.

105

2. Comparison of ASM1 and ASM3

2. Comparison of ASM1 and ASM3

SNO

XI

Nitrifiers

Heterotrophs

Nitrifiers

Heterotrophs

Decay

Growth

Hydrolysis

Decay

Growth

Hydrolysis Storage Growth Endogenousrespiration

Growth Endogenousrespiration

XA

SS

XS

XH

SO

ASM1 ASM3SO SNH SO SO

XISNH XA

SO SO SO

XSTO XIXS SS XH

Figure 2.1. Flow of COD in ASM1 and ASM3. In ASM1 (left) heterotrophic organisms use COD in a cyclicreaction scheme: Decay feeds into hydrolysis and triggers additional growth. Nitrifiers decay andthereby enhance heterotrophic growth. Autotrophic and heterotrophic organisms cannot be entirelyseparated. Only two entry points for oxygen exist. In ASM3 (right) nitrifiers and heterotrophs areclearly separated, no COD flows from one group to the other. Many entry points for oxygen exist. Fordefinitions of state variables see later.

I

he following compounds are used in ASM3.Concentrations of soluble compounds are

characterized by S and particulate compoundsby X. Within the activated sludge systems theparticulate compounds are assumed to be asso-ciated with the activated sludge (flocculatedonto the activated sludge or contained withinthe active biomass). Particulate compounds canbe concentrated by sedimentation/thickening inclarifiers whereas soluble compounds can onlybe transported with the water. Only soluble com-pounds may carry ionic charge. As in ASM1and ASM2 filtration over 0.45 µm membranefilters cannot be used to differentiate modelsoluble from model particulate compounds inthe influent (typically primary effluent): parti-culate, slowly biodegradable substrates (XS, seelater) will partially not be retained on the filtermembrane. In the activated sludge reactors,where large amounts of surfaces exist, thesesubstrates will rapidly adsorb to the suspendedsolids, resulting in a better differentiation ofsoluble and particulate compounds.Conservation of Theoretical Oxygen De-

mand (ThOD) will be used extensively in thedevelopment of process stoichiometry. For org-anic materials COD may analytically approxi-mate this ThOD. For some inorganic materialsThOD must be calculated based on redoxequations relative to the redox reference ofH2O, CO2, NH4

+, PO43−, SO4

2−. NH4 rather thanNO3

− is chosen as reference for nitrogen be-cause the standard COD analysis with chro-mate does not oxidize the reduced nitrogencompounds present in wastewater. An exampleof calculation of ThOD is given in Table 3.1.

3.1. Definition of soluble compounds, S?SO2

[M(O2) L−3]: Dissolved oxygen, O2. Dis-solved oxygen can directly be measured and issubject to gas exchange. In stoichiometric com-putations SO2

is introduced as negative ThOD.

SI [M(COD) L−3]: Inert soluble organicmaterial. The prime characteristic of SI is thatthese organics cannot be further degraded inthe treatment plants dealt with in this report.This material is assumed to be part of theinfluent and may be produced in the context ofhydrolysis of particulate substrates XS. It can

readily be estimated from the residual solubleCOD in the effluent of a low loaded activatedsludge plant.

SS [M(COD) L−3]: Readily biodegradableorganic substrates (COD). This fraction ofthe soluble COD is directly available for con-sumption by heterotrophic organisms. InASM3, for simplification, it is assumed that allthese substrates are first taken up by heterotro-phic organisms and stored in the form of XSTO.SS is preferentially determined with the aid of abioassay (respiration test). Measuring the sumof SI + SS in the form of the total soluble CODin wastewater as determined with 0.45 µmmembrane filtration may lead to gross errors.This is due to the fact that some XS (see later)in wastewater (e.g. starch) cannot adsorb to thesmall amount of biomass present in the influentand therefore contributes to the analyticallydetermined soluble material.

SNH4[M(N) L−3]: Ammonium plus ammo-

nia nitrogen (NH4+-N + NH3-N). For the

balance of the ionic charges, SNH4is assumed to

be all NH4+. Because ASM3 assumes that org-

anic compounds contain a fixed fraction of org-anic nitrogen (iN,i, see Table 8.2), the influentSNH4,0 cannot be observed directly (measuredanalytically) but should be computed fromwastewater composition: Kjeldahl nitrogen -organic nitrogen (SNH4,0 = CTKN,0 − ßiN,i @ Ci,0+ SN2,0 + SNOX,0). In the activated sludge reac-tors and in the effluent SNH4

is equivalent toobserved concentrations. With the redox refer-ence level chosen, SNH4

does not have a ThOD.

SN2[M(N) L−3]: Dinitrogen (N2). SN2

isassumed to be the only product of denitrifica-tion. SN2

may be subject to gas exchange, paral-lel with oxygen, SO2

. It can then be used topredict problems due to supersaturation withN2 in secondary clarifiers. Alternatively the N2contained in the influent and gas exchange canbe neglected. SN2

may then be used to calculatethe amount of nitrogen lost due to denitrifi-cation. SN2

has a negative ThOD.

SNOX [M(N) L−3]: Nitrate plus nitrite nitro-gen (NO3

−-N + NO2−-N). SNOX is assumed to

include nitrate as well as nitrite nitrogen, sincenitrite is not included as a separate model

106


3. ASM3: definition of compounds inthe model

T

compound. For all stoichiometric computations(ThOD conservation), SNOX is considered to beNO3

−-N only. SNOX has a negative ThOD.

SALK [mole(HCO3) L−3]: Alkalinity of thewastewater.Alkalinity isusedtoapproximatetheconservation of ionic charge in biological reac-tions. Alkalinity is introduced in order to obtainan early indication of possible low pH condi-tions,whichmight inhibit somebiologicalproces-ses. For all stoichiometric computations, SALKis assumed to be bicarbonate, HCO3, only.

3.2. Definition of particulate compounds,X?

XI [M(COD) L−3]: Inert particulate organicmaterial (COD). This material is notdegraded in the activated sludge systems forwhich ASM3 has been developed. It isflocculated onto the activated sludge. XI maybe a fraction of the influent and is produced inthe context of biomass decay.

XS [M(COD) L−3]: Slowly biodegradablesubstrates (COD). Slowly biodegradable sub-strates are high molecular weight, soluble, coll-oidal and particulate organic substrates whichmust undergo cell external hydrolysis beforethey are available for degradation. It is assumedthat the products of hydrolysis of XS are eitherreadily biodegradable (SS) or inert (SI) solubleorganics. As compared to ASM1 this fractionhas a different origin. In ASM3 all XS is con-tained in the influent and none is generated indecay processes. In ASM1 a large fraction of XSis assumed to originate from decay processes.

XH [M(COD) L−3]: Heterotrophic organ-isms (COD). These organisms are assumed tobe the ‘allrounder’ heterotrophic organisms,they can grow aerobically and many of themalso anoxically (denitrification). These organ-isms are responsible for hydrolysis of particulatesubstrates XS and can metabolize all degradableorganic substrates. They can form organic stor-age products in the form of poly-hydroxy-alkanoates or glycogen. XH are assumed to haveno anaerobic activity except cell external hyd-

rolysis, which is the only anaerobic process inASM3.

XSTO [M(COD) L−3]: A cell internal storageproduct of heterotrophic organisms(COD). It includes poly-hydroxy-alkanoates(PHA), glycogen, etc. It occurs only associatedwith XH; it is, however, not included in the massof XH. XSTO cannot be directly compared withanalytically measured PHA or glycogen concen-trations; XSTO is only a functional compoundrequired for modelling but not directly identifi-ablechemically.XSTOmay,however,berecoveredin COD analysis and must satisfy ThOD con-servation. For stoichiometric considerations,XSTO is assumed to have the chemical com-position of poly-hydroxy-butyrate (C4H6O2)n.

XA [M(COD) L−3]: Nitrifying organisms(COD). Nitrifying organisms are responsiblefor nitrification; they are obligate aerobic,chemo-litho-autotrophic. It is assumed thatnitrifiers oxidize ammonium, SNH4

, directly tonitrate, SNOX. Nitrite as an intermediate com-pound of nitrification is not considered inASM3.

XSS [M(SS) L−3]: Suspended solids (SS).Suspended solids are introduced into the bio-kinetic models in order to compute their con-centration via stoichiometry. Treatment plantoperators typically follow SS in day to dayanalysis. In the influent, SS (XSS,0) include aninorganic fraction of SS and the ‘soluble’ frac-tion of XS,0, which passes membrane filters. SSmeasured in the influent are therefore smallerthan XSS,0 used to describe the influent in theterms of the model compounds. Describinginfluent SS correctly should allow predictingMLSS as observed in the activated sludge reac-tors. If chemicals are added in order to precipi-tate phosphorus, the precipitates formed mustin ASM3 be added to the concentration of SScomputed in the influent (XSS,0). AlternativelyXSS may be used to model volatile suspendedSolids (VSS). This requires the relevant choiceof absolute numbers for the compositionparameters for SS (iSS,? in Table 8.2).

107

3. ASM3: definition of compounds in the model

Table 3.1. Computation of Theoretical Oxygen Demand ThOD. Each reactive electron is equivalent to a ThOD of 8g mole−1. Therefore each element can be associated with a ThOD which relates to the redox reference ofThOD (H2O, CO2, N , S , P ). ThOD may then be computed by adding the individualcontributions to each molecule.

H+

4 O2 -4 O3 -

4

Element Equivalent ThOD Examples

Carbon C + 32 g ThOD (mol C)−1 What is the ThOD of 1 mole of N ?O-

3

Nitrogen N − 24 g ThOD (mol N)−1 N: − 24 g mole−1

Hydrogen H + 8 g ThOD (mol H)−1 3 O: − 48Oxygen O − 16 g ThOD (mol O)−1 −: + 8 g mole−1 Total: −64 g ThOD (mole N )−1O−

3

Sulphur S + 48 g ThOD (mol S)−1 What is the ThOD of 1 mole of S ?O2 -4

Phosphorus P + 40 g ThOD (mol P)−1 S: + 48 g mole−1

Negative charge − + 8 g ThOD (mol (−))−1 4 O: − 64 g mole−1

Positive charge + − 8 g ThOD (mol (+))−1 2−: + 16 g mole−1 Total: 0 g ThOD (mole S )−1O2 −4

SM3 includes only the microbiological trans-formation processes. Chemical precipita-

tion processes are not included, but may easilybe added based on the information providedfor ASM2 (Henze et al., 1995). ASM3 considersthe following transformation processes:

1. Hydrolysis. This process makes available allslowly biodegradable substrates XS containedin the influent to an activated sludge system.Hydrolysis is assumed to be active indepen-dently of the electron donor. This process isdifferent from the hydrolysis process inASM1; it is of less dominating importancefor the rates of oxygen consumption anddenitrification.

2. Aerobic storage of readily biodegradablesubstrate. This process describes the storageof readily biodegradable substrate SS in theform of cell internal storage products XSTO.This process requires energy, which isobtained from aerobic respiration. It isassumed that all substrates first become storedmaterial and later are assimilated to biomass.This is definitely not observed in reality,however at this moment no reliable model isavailable which can predict the substrate fluxinto storage, assimilation and dissimilationrespectively. Therefore the Task Group sug-gests for the time being this simplest assum-ption. However using a low yield coefficientfor storage (YSTO) and a higher one for sub-sequent growth (YH) allows to approximatethe consequences of direct growth ratherthan storage followed by growth.

3. Anoxic storage of readily biodegradable sub-strate. This process is identical to aerobicstorage, but denitrification rather than aero-bic respiration provides the energy required.Only a fraction of the heterotrophic organ-isms XH in activated sludge is capable ofdenitrification. ASM3 considers this byreducing the anoxic heterotrophic storagerate as compared to the aerobic rate.

4. Aerobic growth of heterotrophs. The sub-strate for the growth of heterotrophic organ-isms is assumed to consist entirely of storedorganics XSTO. This assumption simplifiesASM3 considerably.

5. Anoxic growth of heterotrophs. This processis similar to aerobic growth but respiration isbased on denitrification. Only a fraction ofthe heterotrophic organisms XH in activatedsludge is capable of denitrification. ASM3considers this by reducing the anoxic hetero-trophic storage rate as compared to theaerobic rate.

6. Aerobic endogenous respiration. This pro-cess describes all forms of biomass loss andenergy requirements not associated withgrowth by considering related respirationunder aerobic conditions: decay, (mainten-ance), endogenous respiration, lysis, preda-tion, motility, death, and so on. The model ofthis process is significantly different from thedecay (lysis) process introduced in ASM1.

7. Anoxic endogenous respiration. This processis similar to aerobic endogenous respirationbut typically slower. Especially protozoa (pre-dation) are considerably less active underdenitrifying than under aerobic conditions.

8. Aerobic respiration of storage products. Thisprocess is analogous to endogenous respir-ation. It assures that storage products, XSTO,decay together with biomass.

9. Anoxic respiration of storage products. Thisprocess is analogous to the aerobic processbut under denitrifying conditions.

As compared with ASM1, ASM3 includes amore detailed description of cell internal pro-cesses (storage) and allows for better adjust-ment of decay processes to environmentalconditions. The importance of hydrolysis hasbeen reduced and degradation of soluble andparticulate organic nitrogen have been integ-rated into the hydrolysis, decay and growthprocess.

108

4. ASM3: definition of processes inthe model


A

able 5.1 introduces the stoichiometricmatrix nj,i of ASM3 together with the com-

position matrix ik,i as proposed by Gujer andLarsen (1995). Whereas the stoichiometricmatrix nj,i is well known since the introductionof ASM1, the composition matrix is less wellknown. Relating to Table 5.1 the compositionmatrix may be read as follows: i2,3 is filled withthe symbol iN,SS and indicates that any g CODin the form of SS contains iN,SS g of N. Theindex k = 2 relates to the second conservativewhich is nitrogen, the index i = 3 relates to thethird compound which is SS. SS is measured interms of g COD (as indicated below the symbolSS) and the conservative ‘nitrogen’ is expressedin g N (as indicated to the right of nitrogen inthe composition matrix). iN,SS therefore indi-cates the composition of SS relative to nitrogen,hence ik,i is called the composition matrix.All empty elements of nj,i or ik,i indicate

values of 0. All values of xj, yj and zj can beobtained from the conservation Equation 5.1for the three conservatives k: ThOD, nitrogenand ionic charge:

∑i

nj,i ⋅ ik,i = 0 i = 1 12 (5.1)for to

As introduced earlier, ThOD stands forTheoretical Oxygen Demand and is the conser-vative form of COD. In most cases ThOD oforganic compounds may analytically be approxi-mated by standard dichromate COD analysis.ThOD is a conservative quantity since it effec-tively accounts for the electrons involved in thebiological redox processes.The stoichiometric coefficient for SN2

in anydenitrification process is the negative of the co-efficient for SNOX. The composition coefficientsfor ThOD for SN2

(−1.71 g ThOD (g N2)−1) andSNOX (−4.57 g ThOD (g NO3

−-N)−1) as well asSO2

(−1 g ThOD (g O2)−1) are negative for elec-tron donors relative to the redox reference forThOD.The stoichiometric coefficients for the obser-

vable XSS can be obtained from the Compo-sition Equation 5.2:

nj,13 = ∑i

nj,i ⋅ i4,i i = 8 (5.2)for to 12

It is known that the biochemical energy(ATP) yield of anoxic respiration is smaller thanin aerobic respiration. This leads to the factthat aerobic yield coefficients (YSTO,O2

andYH,O2

) exceed the anoxic yield coefficients(YSTO,NOX and YH,NOX). Assuming the anoxicenergy yield to be hanoxic = 0.70 of the aerobicenergy yield the following energy relationship(Equation 5.3) applies:

1 − YSTO,O2

YSTO,O2

=hanoxic ⋅ (1 − YSTO,NOX)

YSTO,NOX

and

(5.3)1 − YO2

YO2

=hanoxic ⋅ (1 − YNOX)

YNOX

It is suggested that Equation 5.3 is used torelate anoxic and aerobic yields in ASM3.The net (true) yield of heterotrophic biomass

XH produced per unit of substrate SS removedin ASM3 is obtained from:

Ynet,O2= YSTO,O2

⋅ YH,O2and

Ynet,NOX = YSTO,NOX ⋅ YH,NOX (5.4)

All stoichiometric parameters are definedtogether with their units and a typical value inTable 8.2. A numeric example of allstoichiometric coefficients is given in Table 8.4.In the composition matrix ik,i of Table 5.1 the

composition of all organic fractions relative toThOD is assumed to be unity. These valueshave units however (iThOD,SI = 1 g ThOD(g COD)−1, ...) and it should be realized thatthese values are actually model parameterswhich here have been assumed to be unitywhereas in reality COD analysis recovers only afraction of ThOD, typically 95% in domesticwastewater.

109

5. ASM3: stoichiometry

5. ASM3: stoichiometry

T

110


Table 5.1. Stoichiometric matrix and composition matrix ik,i of ASM3. The values of xj, yj, zj and tj can beobtained in this sequence from mass and charge conservation (Equation 5.1) and composition(Equation 5.2).

nj,i

1 2 3 4 5 6 7 8 9 10 11 12 13

j SO2SI SS SNH4

SN2SNOX SALK XI XS XH XSTO XA XSS

↓ O2 COD COD N N N Mole COD COD COD COD COD SS

1 Hydrolysis x1 y1 z1 −1 −iXS

Heterotrophic organisms, aerobic and denitrifying activity2 Aerobic storage of SS x2 −1 y2 z2 YSTO,O2

t23 Anoxic storage of SS −1 y3 −x3 x3 z3 YSTO,NOX t34 Aerobic growth of x4 y4 z4 1 −1 / YH,O2

t45 Anoxic growth (denitrific.) y4 −x5 x5 z5 1 −1 / YH,NOX t56 Aerobic endog. respiration x6 y6 z6 fI −1 t67 Anoxic endog. respiration y7 −x7 x7 z7 fI −1 t78 Aerobic respiration of x8 −1 t89 Anoxic respiration of XSTO −x9 x9 z9 −1 t9

Autotrophic organisms, nitrifying activity10 Aerobic growth of XA x10 y10 1/YA z10 1 t1011 Aerobic endog. respiration x11 y11 z11 fI −1 t1112 Anoxic endog. respiration y12 −x12 x12 z12 fI −1 t12

Composition matrix ik,I

k Conservatives1 ThOD g ThOD −1 1 1 −1.71 −4.57 1 1 1 1 1

2 Nitrogen g N iN,SI iN,SS 1 1 1 iN,XIiN,XS

iN,BM iN,BM3 Ionic charge Mole + 1/14 −1/14 −1

Observables4 SS g SS iSS,XI

iSS,XSiSS,BM 0.60 iSS,BM

Compound i→

Process

Expressed as→

fSI

XSTO

XH

he kinetic expressions of ASM3 are basedon switching functions (hyperbolic or satur-

ation terms, Monod equations, S/(K+S)) for allsoluble compounds consumed. This form ofkinetic expression is chosen not because ofexperimental evidence but rather for mathem-atical convenience: these switching functionsstop all biological activity as educts of a processapproach zero concentrations, an importantdifference between ASM1 and ASM3. Similarlyfor particulate educts the switching functionsrelate to the ratio of XSTO/XH resp. XS/XH.Inhibition is modelled with 1 − S/(K + S) =K/(K + S).Table 6.1 is a summary of all kinetic expres-

sions of ASM3. The kinetic parameters aredefined in Table 8.1 together with their unitsand a typical value at 10 °C and 20 °C. It isrecommended to interpolate kinetic paramet-

ers k to different temperatures T (in °C) withthe following temperature equation:

k(T) = k(20 ) ⋅ exp (qT ⋅ (T − 20 (6.1)°C °C))

where qT (in °C) may be obtained from

qT =ln (k (T1) / k (T2))

t1 − T2

(6.2)

6.1 Estimation of readily biodegradablesubstrate SS

As indicated earlier, readily biodegradable sub-strate SS in wastewater is best determined froma bioassay. Kinetics of the storage and growthprocesses are such that the storage process inASM3 will be related to the additional rapiduptake of oxygen after addition of wastewaterto biomass. Therefore the yield of the storage

111

Table 6.1. Kinetic rate expressions rj for ASM3. All rj ≥ 0.

j Process Process rate equation , all .rj rj ≥ 0

1 Hydrolysis

Heterotrophic organisms, aerobic and denitrifying activity

2 Aerobic storage of SS

3 Anoxic storage of SS kSTO ⋅ hNOX ⋅KO2

KO2+ SO2

⋅SNOX

KNOX + SNOX⋅

SS

KS + SS⋅ XH

4 Aerobic growth mH ⋅SO2

KO2+ SO2

⋅SNH4

KNH4+ SNH4

⋅SALK

KALK + SALK

⋅XSTO / XH

KSTO + XSTO / XH

⋅ XH

5 Anoxic growth(denitrification)

mH ⋅ hNOX ⋅KO2

KO2+ SO2

⋅SNOX

KNOX + SNOX⋅

SNH4

KNH4+ SNH4

⋅SALK

KALK + SALK⋅

XSTO /XH

KSTO + XSTO / XH⋅ XH

6 Aerobic endogen-ous respiration

bH,O2⋅

SO2

KO2+ SO2

⋅ XH

7 Anoxic endogen-ous respiration

bH,NOX ⋅KO2

KO2+ SO2

⋅SNOX

KNOX + SNOX⋅ XH

8 Aerobic respirationXSTOof

bSTO,O2⋅

SO2

KO2+ SO2

⋅ XSTO

9 Anoxic respirationXSTOof

bSTO,NOX ⋅KO2

KO2+ SO2

⋅SNOX

KNOX + SNOX⋅ XSTO

Autotrophic organisms, nitrifying activity

10 Aerobic growth ofXA, nitrification

mA ⋅SO2

KA,O2 + SO2

⋅SNH4

KA,NH4 + SNH4

⋅SALK

KA,ALK + SALK

⋅ XA

11 Aerobic endogen-ous respiration

bA,O2⋅

SO2

KA,O2+ SO2

⋅ XA

12 Anoxic endogen-ous respiration

bA,NOX ⋅KA,O2

KA,O2 + SO2

⋅SNOX

KA,NOX + SNOX

⋅ XA

kSTO ⋅SO2

KO2+ SO2

⋅SS

KS + SS

⋅ XH

kH ⋅XS / XH

KX + XS / XH⋅ XH

6. ASM3: kinetics

T

6. ASM3: kinetics

process must be used in order to relate oxygenuptake to substrate consumption:

SS ( ) = ∫ ∆rSS ⋅ t =nSS

nSO2∫ ∆rSO2

⋅ tbatch d d

=∫ ∆rSO2

⋅ t

1 − YO2,STO(6.3)

d

It is recommended to simulate the batchexperiment, which is used to identify SS withthe aid of ASM3. This allows the identificationof possible errors that could be introduced bythis simple procedure.

112


SM3 (and ASM1) was developed for thesimulation of the aerobic and anoxic treat-

ment of domestic wastewater in activatedsludge systems. It is not advised to apply it tosituations where industrial contributions domi-nate the characteristics of the wastewater.ASM3 (and ASM1) has been developed based

on experience in the temperature range of8–23 °C. Outside of this range model applica-tion may lead to very significant errors and evenmodel structure may become unsatisfactory.ASM3 (and ASM1) does not include any pro-

cesses that describe biomass behaviour in ananaerobic environment. Simulation of systemswith large fractions of anaerobic reactor volumemay therefore lead to gross errors.Development of ASM3 is based on experi-

ence in the range of pH values from 6.5 to 7.5.The concentration of bicarbonate alkalinity(SALK) is supplied to give early warnings whenpH values below this range are to be expected.

Alkalinity must be dominated by bicarbonate.ASM3 cannot deal with elevated concentra-

tions of nitrite.ASM3 (and ASM1) is not designed to deal

with activated sludge systems with very highload or small SRT (<1 day) where flocculation/adsorption of XS and storage may becomelimiting.ASM3 provides the structure of a model but

not absolute values of model parameters. It isthe responsibility of the user of this model toidentify the applicable parameters and the rel-evant characterization of the wastewater.Neither the Task Group nor IWA can under

any circumstances accept any liability for dama-ges of any sort that may result from the applica-tion of this model. It is provided here as a servicefor the scientific and practical engineeringcommunity and it is hoped to serve as areference for future scientific work.

113

7. Limitations of ASM3

7. Limitations of ASM3

A

t is the responsibility of the user of ASM3 todetermine the concentrations of relevant

compounds in the wastewater, as well as the stoi-chiometric and kinetic parameters, which applyto the specific case to be dealt with. Absolutevalues of these parameters are not part ofASM3. They are necessary, however, if ASM3is to be applied to any specific case.In Tables 8.1–8.4 a set of typical model para-

meters and concentrations of model com-pounds in a primary effluent is provided forconvenience. This neither indicates that ASM3is meant to be reliable with these parameters in

any case, nor that these parameters are thestate of the art. They are merely presented hereas a reference for testing computer code and asa first estimate for the design of possibleexperiments that may be used to identify theseparameters more accurately.Table 8.1 contains a list of typical kinetic

parameters; Table 8.2 suggests some typicalstoichiometric parameters. Table 8.3 indicatesthe composition of a typical primary effluentand finally Table 8.4 is a stoichiometric matrix,based on Table 5.1 and the specific valuesintroduced in Table 8.2.

114


8. Aspects of application of ASM3

Table 8.1. Typical values of kinetic parameters for ASM3. These values are provided as examples and are notpart of ASM3.

Temperature

Symbol Characterization 10 °C 20 °C Units

kH Hydrolysis rate constant 2. 3. g (g )−1 d−1XSCOD XH

CODKX Hydrolysis saturation constant 1. 1. g (g )−1XS

COD XHCOD

Heterotrophic organisms XH, aerobic and denitrifying activitykSTO Storage rate constant 2.5 5. g (g )−1 d−1SSCOD XH

COD

hNOX Anoxic reduction factor 0.6 0.6 —KO2

Saturation constant for SNO20.2 0.2 g O2 m−3

KNOX Saturation constant for SNOX 0.5 0.5 g N -N m−3O−

3

KS Saturation constant for substrate SS 2. 2. g m−3SSCOD

KSTO Saturation constant for XSTO 1. 1. g (g )−1XSTOCOD XH

COD

mH Heterotrophic max. growth rate of 1. 2. d−1

KNH4Saturation constant for ammonium, SNH4

0.01 0.01 g N m−3

KALK Saturation constant for alkalinity for XH 0.1 0.1 mole HC m−3O−

3

bH,O2Aerobic endogenous respiration rate of XH 0.1 0.2 d−1

bH,NOX Anoxic endogenous respiration rate of XH 0.05 0.1 d−1

bSTO,O2Aerobic respiration rate for XSTO 0.1 0.2 d−1

bSTO,NOX Anoxic respiration rate for XSTO 0.05 0.1 d−1

Autotrophic organisms XA, nitrifying activitymA Autotrophic max. growth rate of XA 0.35 1.0 d−1

KA,NH4Ammonium substrate saturation for XA 1 . 1. g N m−3

KA,O2Oxygen saturation for nitrifiers 0.5 0.5 g O2 m−3

KA,ALK Bicarbonate saturation for nitrifiers 0.5 0.5 mole HC m−3O−

3

bA,O2Aerobic endogenous respiration rate of XA 0.05 0.15 d−1

bA,NOX Anoxic endogenous respiration rate of XA 0.02 0.05 d−1

XH

I

115

8. Aspects of application of ASM3

Table 8.2. Typical stoichiometric and composition parameters for ASM3. These values are given as examples andare not part of ASM3.

Symbol Characterization Value Units

fSI Production of SI in hydrolysis 0 g (g )−1SICOD XSCOD

YSTO,O2Aerobic yield of stored product per SS 0.85 g (g )−1XSTO

COD SSCODYSTO,NOX Anoxic yield of stored product per SS 0.80 g (g )−1XSTO

COD SSCODYH,O2

Aerobic yield of heterotrophic biomass 0.63 g (g )−1XHCOD XSTO

CODYH,NOX Anoxic yield of heterotrophic biomass 0.54 g (g )−1XH

COD XSTOCOD

YA Yield of autotrophic biomass per N -NO-

3 0.24 g (g )−1XACOD SNOXN

fXIProduction of XI in endog. respiration 0.20 g (g )−1XI

COD XBMCOD

iN,SI N content of SI 0.01 g N (g )−1SICODiN,SS N content of SS 0.03 g N (g )−1SSCODiN,XI

N content of XI 0.02 g N (g )−1XICOD

iN,XSN content of XS 0.04 g N (g )−1XS

COD suggested if XSS is used toiN,BM N content of biomass, XH, XA 0.07 g N (g )−1XBM

COD model VSS rather than SS:iSS,XI

SS to COD ratio for XI 0.75 g SS (g )−1XICOD 0.75 g VSS (g )−1XI

CODiSS,XS

SS to COD ratio for XS 0.75 g SS (g )−1XSCOD 0.75 g VSS (g )−1XS

CODiSS,BM SS to COD ratio for biomass, XH, XA 0.90 g SS (g )−1XBM

COD 0.75 g VSS (g )−1XH or XACOD

Equation 5.3

Equation 5.3

The values below are

Table 8.3. Short definition of model compounds and typical wastewater composition (primary effluent) for ASM3.The value of TKN considers the composition of the different model compounds as indicated in Table 8.2:TKN = ßCi ⋅ i2,i over all compounds i − − . CODtot = 260 g COD m−3, TKN = 25 g N m−3.SNOX SN2

CompoundsConcen-tration Units

Dissolved compoundsSO2

Dissolved oxygen 0 g O2 m−3

SI Soluble inert organics 30 g COD m−3

SS Readily biodegradable substrates 60 g COD m−3

SNH4Ammonium 16 g N m−3

SN2Dinitrogen, released by denitrification 0 g N m−3

SNOX Nitrite plus nitrate 0 g N m−3

SALK Alkalinity, bicarbonate 5 mole HC m−3O−3

Particulate compoundsXI Inert particulate organics 25 g COD m−3

XS Slowly biodegradable substrates 115 g COD m−3

XH Heterotrophic biomass 30 g COD m−3

XSTO Organics stored by heterotrophs 0 g COD m−3

XA Autotrophic, nitrifying biomass >0 g COD m−3

XSS Total suspended solids 125 g SS m−3

The value below issuggested if XSS is used tomodel VSS rather than SS:

100 g VSS m−3

Table 8.4. Stoichiometric matrix of ASM3 based on the stoichiometric parameters in Table 8.2. This matrix is atypical application of ASM3 but it is not suggested as a reliable form of ASM3.

1 2 3 4 5 6 7 8 9 10 11 12 13

j SO2SI SS SNH2


↓ O2 COD COD N N N Mole COD COD COD COD COD SS

1 Hydrolysis 0 −1 −0.01 −0.001 −1 −0.75

Heterotrophic organisms, aerobic and denitrifying activity

2 Aerobic storage of SS −0.15 −1 −0.03 −0.002 −0.85 −0.513 Anoxic storage of SS −1 −0.03 0.07 −0.07 −0.007 −0.80 −0.484 −0.60 −0.07 −0.005 −1 −1.60 −0.065 Anoxic growth (denitrific.) −0.07 0.30 −0.30 −0.016 −1 −1.85 −0.216 Aerobic endog. respiration −0.80 −0.066 −0.005 0.20 −1 −0.757 Anoxic endog. respiration −0.066 0.28 −0.28 −0.025 0.20 −1 −0.758 Aerobic respiration of XSTO −1 −1 −0.60

9 Anoxic respiration of XSTO 0.35 −0.35 −0.025 −1 −0.60

Autotrophic organisms, nitrifying activity

10 Aerobic growth of XA −18.04 −4.24 −4.17 −0.600 −1 −0.9011 Aerobic endog. respiration −0.80 −0.066 −0.005 0.20 −1 −0.7512 Anoxic endog. respiration −0.066 0.28 −0.28 0−.025 0.20 −1 −0.75

Compound i→

Process

Expressed as →

Aerobic growth of XH

n some countries the chemical determina-tion of COD-Cr in routine analysis is not

possible because of the heavy metals (Hg, Crand Ag) involved in the analytical procedures.The alternative COD-Mn is not very valuablein the context of ASM3 since it greatly under-estimates ThOD. This is a severe limitation forthe application of models such as ASM3. Inorder to facilitate the application of ASM3, theTask Group proposes ASM3C as an adaptedversion of ASM3, where organic state variablesare expressed in terms of organic carbon ratherthan COD. This allows the use of TOC insteadof COD-Cr measurements in order to charac-terize wastewater and activated sludge. Sinceexperience with TOC is rather limited at thistime, ASM3C should be used with great care.

9.1 Definition and measurement offractions of organic carbon

TOC [M(C) L−3] stands for Total Organic Car-bon and is analytically available in wastewater.For samples with suspended solids, carefulhomogenization of the samples is important.Care has to be taken that sedimentation ofcoagulating solids does not lead to erroneousresults. This is especially relevant if auto-samplers are usedwhere the sample is not stirredbefore it is injected into the TOC analyser.Depending on the pretreatment of the sam-

ple, the TOC analysis can be used to character-ize different fractions of wastewater. In relationto TOC the terms DOC (Dissolved OrganicCarbon) and POC (Particulate Organic carbon)are sometimes used. By definition TOC =DOC + POC. DOC is measured after filtrationof the samples. All soluble organic model com-pounds (SI, SS) may be expressed in terms ofDOC.POC is available from the difference TOC −

DOC. POC may be used to characterize someof the particulate organic model compounds inthe influent (XI, XH, XSTO, XA) but not forothers (not XS, since a fraction of XS passesthrough the membrane filters).For the characterization of activated sludge

as a whole, standard estimation of TOC mayeasily lead to gross analytical errors. Hereelementary analysis of a dry washed sample or

the use of specialized TOC equipment may bethe methods of choice.Since the fractionation of TOC in DOC and

POC is not entirely compatible with the defin-ition of the model compounds (XS being theproblem), this report will use TOC only, inorder to express that a compound is measuredin terms of organic carbon.

9.2 Transition from ASM3 to ASM3C

Deriving ASM3C from ASM3 is an easy task ifthe composition of the organic compounds isredefined (COD is replaced by TOC). Introdu-cing new units (g ThOD (g TOC)−1 rather thang ThOD (g COD)−1) and accordingly new ab-solute values for the composition parametersiThOD,i for all organic compounds in the com-position matrix yields the basis for estimatingthe unknown stoichiometric coefficients xj, yj, zjand tj with the aid of Equations 5.1 and 5.2.Realizing that the values of iThOD,?? =

1 g ThOD (g COD)−1 are actually model para-meters chosen to be unity in ASM3 (which isbased on the assumption that ThOD is identi-cal to the measured COD), the transition ofASM3 to ASM3C is a rather minor one.Table 9.1 includes the stoichiometric matrix

for ASM3C, revised from Table 5.1. Changesinclude transition from COD to TOC for ex-pressing the organic state variables, introduc-tion of the iThOD,?? values in the first row of thecomposition matrix and adjusting the fixedvalues for storage compounds (XSTO) in thecomposition matrix.

9.3 Adjusting kinetic and stoichiometricparameters for ASM3C

With the introduction of TOC basedcompounds in ASM3C the absolute values andthe units of some kinetic and stoichiometricparameters must be adjusted. As an examplethe aerobic yield of autotrophic biomass YA inASM3C may be obtained from:

YA(ASM3) has the units[g CODXA

(g NO3−-N)−1]

YA(ASM3C) has the units[g TOCXA

(g NO3−-N)−1]

iThOD,BM(ASM3) has the units[g ThODBM (g CODBM

−1)]116


9. ASM3C: a carbon-based model

I

iThOD,BM(ASM3C) has the units[g ThODBM (g TOCBM

−1)]From this we obtain (with absolute values

from Tables 8.2 and 9.3):

= YA ⋅iThOD,BM

iThOD,BM

(ASM3C) (ASM3)(ASM3)

(ASM3C)

= 0.24 O−3 ⋅

1

2.8g CODBM (g N -N)−1

= 0.09 )−1O−3g TOCBM (g N -N

Adjustments are best based on careful ana-lysis of the units of the parameter to be adjusted.Even the magnitude of seemingly dimension-less coefficients such as YH must be adjusted.

9.4 Typical kinetic and stoichiometricparameters for ASM3C

Again the following remarks apply to ASM3Cas well.It is the responsibility of the user of ASM3C

to determine the concentrations of relevantcompounds in the wastewater, as well as thestoichiometric and kinetic parameters, whichapply to the specific case to be dealt with.Absolute values of these parameters arenot part of ASM3C. They are necessary, how-ever, if ASM3C is to be applied to any specificcase.In Tables 9.2–9.5 a set of typical kinetic and

stoichiometric parameters and concentrations

of model compounds in a primary effluent isprovided for convenience. This indicatesneither that ASM3C is meant to be reliablewith these parameters in any case, nor thatthese parameters are the state of the art. Theyare merely presented here as a reference fortesting computer code and as a first estimatefor the design of possible experiments that maybe used to identify these parameters moreaccurately. In comparison to the values given inTables 8.1–8.4 these values have been adjustedto TOC units based on typical compositionparameters in Table 9.4. There may be somerounding errors resulting in slight deviations inmodel predictions between ASM3 and ASM3C.The extra decimal is not provided because it isthought to be accurate but rather in order toresult in better comparison of predictions rela-tive to ASM3.Table 9.2 provides a list of typical kinetic

parameters, Table 9.3 suggests some typicalstoichiometric parameters, Table 9.4 indicatesthe composition of a typical primary effluentand finally Table 9.5 is a stoichiometric matrix,based on Table 9.1 and the specific valuesintroduced in Table 9.3.

9.5 Modelling pH with ASM3C

Including organic carbon in ASM3C allowsmodelling the pH value in the different reactorcompartments. If bicarbonate is assumed to be

117


Table 9.1. Stoichiometric matrix nj,i and composition matrix ik,i of ASM3C. The values of xj, yj, zj and tj can beobtained in this sequence from mass and charge conservation (Equation 5.1) and composition(Equation 5.2). The stoichiometric coefficients ( , fI, YSTO and YH) must be based on organic carbon(Table 9.3).

fSI

1 2 3 4 5 6 7 8 9 10 11 12 13

j SO2SI SS SNH4


↓ O2 TOC TOC N N N Mole TOC TOC TOC TOC TOC SS

1 Hydrolysis x1 y1 z1 −1 −iXS

Heterotrophic organisms, aerobic and denitrifying activity2 Aerobic storage of SS x2 −1 y2 z2 YSTO,O2

t23 Anoxic storage of SS −1 y3 −x3 x3 z3 YSTO,NOX t34 Aerobic growth of XH x4 y4 z4 1 −1 / YH,O2

t45 Anoxic growth (denitrific.) y4 −x5 x5 z5 1 −1 / YH,NOX t56 Aerobic endog. respiration x6 y6 z6 fI −1 t67 Anoxic endog. respiration y7 −x7 x7 z7 fI −1 t78 Aerobic respiration of XSTO x8 −1 t89 Anoxic respiration of XSTO −x9 x9 z9 −1 t9

Autotrophic organisms, nitrifying activity10 Aerobic growth of XA x10 y10 1/YA z10 1 t1011 Aerobic endog. respiration x11 y11 z11 fI −1 t1112 Anoxic endog. respiration y12 −x12 x12 z12 fI −1 t12

Composition matrix ik,I

k Conservatives1 ThOD g ThOD −1 iThOD,SS −1.71 −4.57 iThOD,XI

iThOD,XSiThOD,BM 3.00 iThOD,BM

2 Nitrogen g N iN,SI iN,SS 1 1 1 iN,XIiN,XS

iN,BM iN,BM

3 Ionic charge Mole + 1/14 −1/14 −1

Observables4 SS g SS iSS,XI

iSS,XSiSS,BM 1.80 iSS,BM

Compound i →

Process

Expressed as →

fSI

iThOD,SI

118


Table 9.2. Typical values of kinetic parameters for ASM3C. These values are provided as examples and are notpart of ASM3. In comparison to the values given in Table 8.1 these values have been adjusted to TOCunits based on typical composition parameters in Tables 8.2 and 9.3. There may be some roundingerrors resulting in slight deviations in model predictions between ASM3 and ASM3C. The extra decimalis provided not because it is thought to be accurate but rather in order to result in better comparison ofpredictions relative to ASM3.

Temperature

Symbol Characterization 10 °C 20 °C Units

kH Hydrolysis rate constant 2.3 3.4 g (g )−1 d−1XSTOC XH

TOCKX Hydrolysis saturation constant 1. 1. g (g )−1XS

TOC XHTOC

Heterotrophic organisms XH, aerobic and denitrifying activitykSTO Storage rate constant 2.9 5.7 g (g )−1 d−1SSTOC XH

TOC

hNOX Anoxic reduction factor 0.6 0.6 –KO2

Saturation constant for SNO20.2 0.2 g O2 m−3

KNOX Saturation constant for SNOX 0.5 0.5 g N -N m−3O−

3

KS Saturation constant for substrate SS 0.6 0.6 g m−3SSTOC

KSTO Saturation constant for XSTO 1.1 1.1 g (g )−1XSTOTOC XH

TOC

mH Heterotrophic max. growth rate 1. 2. d−1

KNH4Saturation constant for ammonium, SNH4

0.01 0.01 g N m−3

KALK Saturation constant for alkalinity for XH 0.1 0.1 mole HC m−3O−

3

bH,O2Aerobic endogenous respiration rate of XH 0.1 0.2 d−1

bH,NOX Anoxic endogenous respiration rate of XH 0.05 0.1 d−1

bSTO,O2Aerobic respiration rate for XSTO 0.1 0.2 d−1

bSTO,NOX Anoxic respiration rate for XSTO 0.05 0.1 d−1

Autotrophic organisms XA, nitrifying activitymA Autotrophic max. growth rate of XA 0.35 1.0 d−1

KA,NH4Ammonium substrate saturation for XA 1 . 1. g N m−3

KA,O2Oxygen saturation for nitrifiers 0.5 0.5 g O2 m−3

KA,ALK Bicarbonate saturation for nitrifiers 0.5 0.5 mole HC m−3O−

3

bA,O2Aerobic endogenous respiration rate of XA 0.05 0.15 d−1

bA,NOX Anoxic endogenous respiration rate of XA 0.02 0.05 d−1

Table 9.3. Typical stoichiometric and composition parameters for ASM3C. These values are given as examples andare not part of ASM3.

Symbol Characterization Value Units

fSI Production of SI in hydrolysis 0 g (g )−1SITOC XSTOC

YSTO,O2Aerobic yield of stored product per SS 0.91 g (g )−1XSTO

TOC SSTOCYSTO,NOX Anoxic yield of stored product per SS 0.85 g (g )−1XSTO

TOC SSTOCYH,O2

Aerobic yield of heterotrophic biomass 0.67 g (g )−1XHTOC XSTO

TOCYH,NOX Anoxic yield of heterotrophic biomass 0.58 g (g )−1XH

TOC XSTOTOC

YA Yield of autotrophic biomass per N -NO-

3 0.09 g (g )−1XATOC SNOX

NfXI

Production of XI in endog. respiration 0.20 g (g )−1XITOC XBM

TOCiThOD,SI ThOD content of SI 2.8 g ThOD (g )−1SITOCiThOD,SS ThOD content of SS 3.2 g ThOD (g )−1SSTOCiThOD,XI

ThOD content of XI 2.8 g ThOD (g )−1XITOC

iThOD,XSThOD content of XS 3.2 g ThOD (g )−1XS

TOCiThOD,BM ThOD content of biomass, XH, XA 2.8 g ThOD (g )−1XBM

TOCiN,SI N content of SI 0.03 g N (g )−1SITOCiN,SS N content of SS 0.10 g N (g )−1SSTOCiN,XI

N content of XI 0.06 g N (g )−1XITOC

iN,XSN content of XS 0.13 g N (g )−1XS

TOC suggested if XSS is used toiN,BM N content of biomass, XH, XA 0.20 g N (g )−1XBM

TOCiSS,XI

SS to TOC ratio for XI 2.1 g SS (g )−1XITOC 2.1 g VSS (g )−1XI

iSS,XSSS to TOC ratio for XS 2.4 g SS (g )−1XS

TOC 2.4 g VSS (g )−1XS

iSS,BM SS to TOC ratio for biomass, XH, XA 2.5 g SS (g )−1XBMTOC

Equation 5.3

Equation 5.3

The values below are

model VSS rather than SS:

2.4 g VSS (g XH or )−1AX

the dominating buffer system, pH can be mod-elled by adding dissolved carbon dioxide (CO2,SCO2

) and the proton (H, SH+) as additionalstate variables and two processes describing theequilibrium (forward and backward reaction) ofbicarbonate dissociation, with fast reactionrates (the ratio of these reaction rates is givenby the equilibrium constant). Further the addi-tional stoichiometric coefficients for SCO2

canbe obtained from conservation of carbon (afourth conservative). Stripping of SCO2

must berelated to aeration, considering the correctHenry coefficients and possible saturation ofrising air bubbles with CO2.It is recommended to derive stoichiometric

coefficients zj from a charge balance over bicar-bonate rather than the proton. This typically all-ows for faster numeric integration because theturnover of large amount of charge is modelledvia the large pool of SALK rather than the verysmall pool of H.Accurate modelling of pHmay require expan-

sion of the model to include carbonate, nitrite,ammonium and phosphate buffers as well.

9.6 Limitations of ASM3C

The limitations introduced above for ASM3apply equally to ASM3C. Since experience withTOC is still rather scarce, extra care should betaken in analytical procedures.

119


Table 9.4. Short definition of model compounds and typical wastewater composition (primary effluent) forASM3C. The value of TKN considers the composition of the different model compounds as indicated inTable 9.3: TKN = ßSi ⋅ i2,i over all compounds i − − . CODtot = 260 g COD m−3, TKN = 25 g Nm−3.

SNOX SN2

CompoundsConcen-tration Units

Dissolved compoundsSO2

Dissolved oxygen 0.0 g O2 m−3

SI Soluble inert organics 11.0 g TOC m−3

SS Readily biodegradable substrates 19.0 g TOC m−3

SNH4Ammonium 15.4 g N m−3

SN2Dinitrogen, released by denitrification 0.0 g N m−3

SNOX Nitrite plus nitrate 0.0 g N m−3

SALK Alkalinity, bicarbonate 5.0 mole HC m−3O−

3

Particulate compoundsXI Inert particulate organics 9.0 g TOC m−3

XS Slowly biodegradable substrates 36.0 g TOC m−3

XH Heterotrophic biomass 11.0 g TOC m−3

XSTO Organics stored by heterotrophs .0 g TOC m−3

XA Autotrophic, nitrifying biomass .0 g TOC m−3

XSS Total suspended solids 125.0 g SS m−3

The value below issuggested if XSS is used tomodel VSS rather than SS:

100 g VSS m−3

0>0

Table 9.5. Stoichiometric matrix of ASM3C based on the stoichiometric parameters in Tables 9.1 and 9.3. Thismatrix is a typical application of ASM3C but it is not suggested as a reliable form of ASM3C.

Compound i→ 1 2 3 4 5 6 7 8 9 10 11 12 13

j Process SO2SI SS SNH4


↓ Expressed as→ O2 TOC TOC N N N Mole TOC TOC TOC TOC TOC SS

1 Hydrolysis 0 1 0.03 0.002 −1 −2.40

Heterotrophic organisms, aerobic and denitrifying activity2 Aerobic storage of SS −0.47 −1 0.10 0.007 0.91 1.643 Anoxic storage of SS −1 0.10 0.23 −0.23 0.023 0.85 1.534 Aerobic growth of XH −1.61 −0.20 −0.014 1 −1.47 −0.155 Anoxic growth (denitrific.) −0.20 0.83 −0.83 0.045 1 −1.72 −0.606 Aerobic endog. respiration −2.24 0.19 0.013 0.20 −1 −2.087 Anoxic endog. respiration 0.19 0.78 −0.78 0.069 0.20 −1 −2.088 Aerobic respiration of XSTO −3.00 −1 −1.809 Anoxic respiration of XSTO 1.05 −1.05 0.075 −1 −1.80

Autotrophic organisms, nitrifying activity10 Aerobic growth of XA −48.0 −11.3 11.1 −1.60 1 2.5011 Aerobic endog. respiration −2.24 0.19 0.013 0.20 −1 −2.0812 Anoxic endog. respiration 0.19 0.78 −0.78 0.069 0.20 −1 −2.08

SM3 and ASM3C correct for most of thedefects identified in ASM1. The ASM3

models provide a common base for the simu-lation of nitrogen removing activated sludgesystems for chemical oxygen demand as well asorganic carbon based characterization of waste-water and biomass. These two characterizationpossibilities can analytically be approximated byCOD and TOC analysis. The structure of theASM3 models provides sufficient details suchthat they may be used in an advanced course onbiological wastewater treatment as a didactictool. These models are designed as the core forfurther development and inclusion of addi-tional processes and states as may becomenecessary when biological phosphorus removal,chemical phosphorus precipitation, growth offilaments etc. ought to be included.

The systematic notation, based on an array ofstate variables, a stoichiometric matrix, a com-position matrix, an array of process rates andconservation equations made it especially easyto introduce these models and indicate how a

COD based model may be transformed intoanother base (here organic carbon, TOC).

Neither ASM3 nor ASM3C has yet beentested against a large variety of experimentaldata. It is expected that future improvements ofmodel structure may still be required, espec-ially for the description of the storage pheno-mena. It is obvious that in the beginningexperience with ASM3 might be inferior toexperience with ASM1. But as our experiencewill improve the two models might well proveto be equivalent. ASM3 has the advantage thatits structure does not have to be adjusted inorder to be applicable even if ammonium orbicarbonate limits microbial activity. Thereforeif we report in a publication that a simulationwas performed with ASM3 or ASM3C, it maybe assumed that themodel structures introducedin this report have been applied unchanged.It is good practice to indicate if model

structure has been changed: This wouldthen be a dialect of ASM3 but not ASM3itself.

120


10. Conclusion

A

The following limited citations relate to thetopic discussed in this report and may be usefulto understand the background and the presen-tation of ASM3. The Task Group would like toapologize for not following the standard rulesof citation of scientific work and acknowledgesthat a vast literature (and communication withpeers) has stimulated its work. It appears im-possible to explicitly identify the specific sourceof the elements of ASM3 and ASM3C.

Gujer, W. and Larsen, T.A. (1995) The implementation ofbiokinetics and conservation principles in ASIM. Wat.Sci. Technol. 31 (2), 257–266.

Gujer, W., Henze, M., Mino, T. and van Loosdrecht, M.C.M.(1999) Activated Sludge Model No. 3. Wat. Sci. Technol.39 (1), 183–193. [During publication of this paper some

typographical errors were introduced. These werecorrected in an erratum: Gujer, W., Henze, M., Mino, T.and van Loosdrecht, M. (1999) Errata: Activated SludgeModel No. 3. Wat. Sci. Technol. 39 (12), page I.Additionally, the original of this paper was published inthe preprints of the 4th IAWQ Seminar on Modelling andMicrobiology of Activated Sludge Processes, Kollekolle,Denmark, 16–18 March 1998.]

Henze, M., Grady, C.P.L. Jr, Gujer, W., Marais, G.v.R. andMatsuo, T. (1987) Activated Sludge Model No. 1.(IAWPRC Scientific and Technical Report No. 1.)London: IAWPRC.

Henze, M., Gujer, W., Mino, T., Matsuo, T., Wentzel, M.C.and Marais, G.v.R. (1995) Activated Sludge Model No. 2.(IAWQ Scientific and Technical Report No. 3.) London:IAWQ.

Henze, M., Gujer, W., Mino, T., Matsuo, T., Wentzel, M.C.,Marais, G.v.R. and van Loosdrecht, M.C.M. (1999)Activated Sludge Model No. 2d, ASM2d. Wat. Sci.Technol. 39 (1), 165–182.

121

11. References

11. References

IWA Scientific and Technical Report Series

Titles available to order

Scientific and Technical Report No. 14

Solids in Sewers

IWA Task Group on Sewer Sediments

May 2002; c.300 pages; 1 900222 91 4


Anaerobic Digestion Model No. 1 (ADM1)

IWA Task Group for Mathematical Modelling of

Anaerobic Wastewater

April 2002, c.88 pages; 1 900222 78 7

Scientific and Technical Report No.12

River Water Quality Model No.1

IWA Task Group on River Water Quality Modelling:

Peter Reichert, Dietrich Borchardt, Mogens Henze,

Wolfgang Rauch, Peter Shanahan, László Somlyódy

and Peter A. Vanrolleghem

September 2001; 144 pages; ISBN: 1 900222 82 5


Respirometry in Control of the Activated Sludge

Process: Benchmarking Control Strategies

J.B. Copp, P.A. Vanrolleghem, H. Spanjers

March 2002; c.176 pages; ISBN: 1 900222 51 5


Sequencing Batch Reactor Technology

Peter A. Wilderer, Robert L. Irvine and Mervyn C.

Goronszy with Nazik Artan, Gunnar Demoulin, Jürg

Keller, Eberhard Morgenroth, Geert Nyhuis,

Kazuhiro Tanaka and Michel Torrijos

March 2001; 96 pages; ISBN: 1 900222 21 3


Activated Sludge Models ASM1, ASM2, ASM2d

and ASM3

IWA Task Group on Mathematical Modelling for

Design and Operation of Biological Wastewater

Treatment: Task Group (3): Mogens Henze, Willi

Gujer, Mark van Loosdrecht, Takahashi Mino; Task

Group (2d): Mogens Henze, Willi Gujer, Takahashi

Mino, Tomonori Matsui, Mark C. Wentzel, Gerrit v. R.

Marais, Mark van Loosdrecht; Task Group (2): Mogens

Henze, Willi Gujer, Takahashi Mino, Tomonori Matsui,

Mark C. Wentzel, Gerrit v. R. Marais; Task Group (1):

Mogens Henze, C.P.L. Grady Jnr, Willi Gujer, Gerrit v.

R. Marais, T. Matsuo.

June 2000; 130 pages; ISBN: 1 900222 24 8


Constructed Wetlands for Pollution Control:

Processes, Performance, Design and Operation

IWA Specialist Group on Use of Macrophytes in

Water Pollution Control

Robert H. Kadlec, Robert L. Knight, Jan Vymazal,

Hans Brix, Paul Cooper, Raimund Haberl

April 2000; 164 pages; ISBN: 1 900222 05 1


Respirometry in Control of the Activated Sludge

Process: Principles

Edited by H. Spanjers, P.A. Vanrolleghem, G. Olsson

and P.L. Dold

1998; 48 pages; ISBN: 1 900222 04 3


Secondary Settling Tanks: Theory, Modelling,

Design and Operation

Edited by G.A. Ekama, J.L. Barnard, Reid Crowther,

F W Günthert, P Krebs, J A McCorquodale, D S Parker

and E J Wahlberg

1997; 232 pages; ISBN: 1 900222 03 5


Microbial Community Analysis: The Key to the

Design of Biological Wastewater Treatment Systems

Edited by T.E. Cloete and N.Y.O. Muyima

1997; 98 pages; ISBN: 1 900222 02 7


Real Time Control of Urban Drainage Systems:

The State-of-the-Art

IAWPRC Task Group on Real-time Control of

Urban Drainage Systems

Edited by W Schilling

1989; 84 pages; ISBN: 0 08 040145 7

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