Mathematical Modelling of Wastewater Treatment Plants

Part III: Dynamic Modelling of theActivated Sludge Process

Gilles G. PatryUniversity of Ottawa

Outline

• Introduction• Notation used by the Task Group (applies to all ASM models)

• ASM1 Model Development– ASM1 Model Structure– Processes

• Aerobic growth of heterotrophs• Anoxic growth of heterotrophs• Aerobic growth of autotrophs• Decay of heterotrophs• Decay of autotrophs• Ammonification of soluble organic nitrogen• Hydrolysis of entrapped organics• Hydrolysis of entrapped organic nitrogen

– Petersen matrix formulation of ASM1• Formulating the differential equations

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Activated Sludge Modelling Timeline(adapted from Bruce Johnson, CH2M Hill)

Empirical Design, Piloting & Guesswork

Kinetics-Based Design

Whole Plant Simulators

1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

Arden & Lockett (1914) ActivatedSludge« invented »

Monod (1942) Pure Culture Kinetics

McKinney(1962) Complete Mix ActivatedSludgeKinetics

Dold et al. (1980) General Model

Henze et al. (1995) ASM2

Penfold and Norris (1912) BacteriaGenerationTime

Garrett and Sawyer (1952) Mixed Culture Kinetics

Busby and Andrews (1975). First Computer Model (CSMP)

Henze et al. (1986)ASM1

Henze et al. (1999) ASM2d

Gujer et al. (1999) ASM3

Activated Sludge Model No. 1 (ASM1)

• Introduced in 1987 as IAWQ Model no. 1 (ASM1) -IAWQ Task Group on Activated Sludge Modeling

• ASM1 is a simple model consisting of:– 8 processes– 13 state variables or components– 19 parameters

• Model enhanced several times to address specific shortcomings of ASM1– ASM No. 2– ASM No. 2d– ASM No. 3– others

Henze, M., Grady Jr., C.P.L., Gujer, W., Marais, G.v.R., Matsuo, T. (1987). “Activated Sludge Model No.1” IAWQ Scientific and Technical Report No.1,IAWQ, London, Great Britain.

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Carbonaceous Components

Total COD

BiodegrableCOD

Soluble

SS

Particulate

XS

Nonbiodeg. COD

Soluble

SI

Particulate

XI & XP

Biomass

Heterotrophs

XB,H

Autotrophs

XB,A

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Nitrogenous Components

Total Kjeldahl N

TKN

Free and saline ammonia

SNH

Organically bound N

Soluble organic N

Nonbiodeg N

SNI

Biodegrable N

SND

Particulate organic N

Biodegrable N

XND

Nonbiodeg. N

XNI & XNP

Active mass N

XNB

Nitrate and nitrite N, SNO

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Processes in ASM1

• Aerobic growth of heterotrophs• Anoxic growth of heterotrophs• Aerobic growth of autotrophs• Decay of heterotrophs• Decay of autotrophs• Ammonification of soluble organic nitrogen• Hydrolysis of entrapped organics• Hydrolysis of entrapped organic nitrogen

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Decay

Aerobic G

Hydrolysis

Anoxic G

HydrolysisAmmonification

Decay

Growth

Heterotrophs (aerobic and anoxic)

Autotrophs (nitrifiers)

State variable

Process

XBHHeterotrophicbiomass

SODissolvedoxygen

SSReadilybiodegrablesubstrate

SNO

Nitrate -nitritenitrogen

SNHAmmonianitrogen

Soluble inertorganicsSI

XIParticulateinert organics

XPInert particulateProducts frombiomass decay

XS

Slowlybiodegrablesubstrate

XND

Particulatebiodegrableorganicnitrogen

SND

Solublebiodegrableorganicnitrogen

SNH

Ammonianitrogen

SODissolvedoxygen

XBAAutotrophicbiomass SNO

Nitrate -nitritenitrogen

ASM1 Model Structure

Aerobic Growth of Heterotrophs

• A fraction of the readily biodegradable substrate is used for growth of heterotrophic biomass and the balance is oxidized for energy.

• Growth model used Monod kinetics• Ammonia is used as nitrogen source and is

incorporated in cell mass• Both the substrate (SS) and oxygen (SO) may be rate

limiting for the growth process and removal of COD• Dissolved oxygen switching function is introduced• Alkalinity change

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ASM1

Aerobic G

XBHHeterotrophicbiomass

SODissolvedoxygen

SSReadilybiodegrablesubstrate

SNHAmmonianitrogen

Aerobic Growth – Heterotrophs

• Process Rate:

ˆ µ HSS

KS + SS

SO

KO, H + SO

XB, H

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where ˆ µ H = heterotrophic maximum specific growth rate, d-1

KS = half saturation coefficient for heterotrophs, g COD m-3

KO,H = oxygen half saturation coefficient for heterotrophs, g O2 m-3

SwitchingFunction

ASM1

Aerobic G

XBHHeterotrophicbiomass

SODissolvedoxygen

SSReadilybiodegrablesubstrate

SNHAmmonianitrogen

Anoxic Growth of Heterotrophs• In the absence of oxygen,

the heterotrophic organismsare capable of using nitrateas the terminal electronacceptor with SS as thesubstrate

• Leads to production of heterotrophic biomass andnitrogen gas (as a result of thereduction of nitrate with associated alkalinity change)

• Growth modeled using same Monod kinetics as aerobic growth except that kinetic rate is multiplied by ηg ( < 1 )– Why ηg < 1 ?

• Lower maximum growth rate under anoxic conditions OR• Only a fraction of the heterotrophic biomass is able to function with

nitrate as electron acceptor• Ammonia serves as nitrogen source for cell

synthesis, which affects alkalinity

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Anoxic G

XBHHeterotrophicbiomass

SODissolvedoxygen

SSReadilybiodegrablesubstrate

SNO

Nitrate -nitritenitrogen

SNHAmmonianitrogen

Anoxic Growth of Heterotrophs

• Process rate:

ˆ µ HSS

KS + SS

KO,H

KO,H + SO

SNO

KNO + SNO

ηgXB,H

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where ηg = correction factor for anoxic growth of heterotrophs

KNO = nitrate half saturation coefficient for denitrifying heterotrophs, g NO3 - N m-3

ASM1

Anoxic G

XBHHeterotrophicbiomass

SODissolvedoxygen

SSReadilybiodegrablesubstrate

SNO

Nitrate -nitritenitrogen

SNHAmmonianitrogen

Decay of Heterotrophs

• Organisms die at a certainrate and – a portion of the material is

considered to be non-biodegradableand adds to the particulate fraction XP

– the remainder adds to the pool ofslowly biodegradable substrate

• Organic nitrogen in particulate substrate (XS) becomes available as particulate organic nitrogen

• Process is assumed to take place at same rate under aerobic, anoxic or anaerobic conditions

8/17/2009 13ASM1

Decay

XBHHeterotrophicbiomass

XPInert particulateProducts frombiomass decay

XS

Slowlybiodegrablesubstrate

Decay of Heterotrophs

• Process rate:

bHXB,H

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where bH = heterotrophic decay rate, d-1

ASM1

Decay

XBHHeterotrophicbiomass

XPInert particulateProducts frombiomass decay

XS

Slowlybiodegrablesubstrate

Aerobic Growth of Autotrophs

• Ammonia is oxidized to nitrate (single step process) resulting in production of autotrophic biomass and associated oxygendemand

• Ammonia is also used as nitrogensource for synthesis and incorporated in cell mass

• Process has an effect on alkalinity and total oxygen demand

• Amount of biomass formed is generally small because of the low yield autotrophic nitrifiers

• Growth rate modeledusing Monod kinetics

8/17/2009 15ASM1

Growth

SNH

Ammonianitrogen

SODissolvedoxygen

XBAAutotrophicbiomass SNO

Nitrate -nitritenitrogen

Aerobic Growth of Autotrophs

• Process rate:

ˆ µ ASNH

KNH + SNH

SO

KO,A + SO

XB,A

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3-2OA

3-NH

-1A

m O g ,autotrophsfor t coefficien saturation halfoxygen

m COD g ,autotrophsfor t coefficien saturation half ammonia

d rate,growth specific maximum cautotrophi ˆ where

=

=

=

KK

µ

ASM1

Growth

SNH

Ammonianitrogen

SODissolvedoxygen

XBAAutotrophicbiomass SNO

Nitrate -nitritenitrogen

Decay of Autotrophs

• Modeled in same way as decay of heterotrophs

• Process rate:

bAXB,A

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where bA = autotrophic decay rate, d-1

ASM1

Decay

XPInert particulateProducts frombiomass decay

XSSlowlybiodegrablesubstrate

XBAAutotrophicbiomass

Hydrolysis of Entrapped Organics

• Slowly biodegradable substrateenmeshed in sludge mass is broken down extracellularly, producing readily biodegradable substrate available to organisms for growth

• Process modeled on basis of surfacereaction kinetics

• Process occurs under aerobic and anoxic conditions• Rate of hydrolysis is reduced under anoxic conditions

by a factor ηh ( < 1 )• Rate is first-order wrt heterotrophic biomass and

saturates as the amount of entrapped organics becomes large

8/17/2009 18ASM1

Hydrolysis

SSReadilybiodegrablesubstrate

XS

Slowlybiodegrablesubstrate

Hydrolysis of Entrapped Organics

• Process rate:

kh

XS

XB,H

KX +XS

XB,H

SO

KO,H + SO

+ ηh

KO,H

KO,H + SO

SNO

KNO + SNO

XB,H

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where kh = maximum specific hydrolysis rate, g slowly biodeg. COD (g cell COD day)-1

KX = half saturation coefficient for hydrolysis of slowly biodeg. substrate, g slowly biodeg. COD (g cell COD day)-1

ηh = correction factor for anoxic hydrolysis

ASM1

Hydrolysis

SSReadilybiodegrablesubstrate

XS

Slowlybiodegrablesubstrate

Hydrolysis of Entrapped Organic Nitrogen

• Biodegradable particulate organic nitrogen is broken down into soluble organic nitrogen at a rate defined by the hydrolysis reaction for entrapped organics

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Hydrolysis XND

Particulatebiodegrableorganicnitrogen

SND

Solublebiodegrableorganicnitrogen

Hydrolysis of Entrapped Organic Nitrogen

• Process rate:

where ρ7 is given by:

ρ7

XND

XS

kh

XS

XB,H

KX +XS

XB,H

SO

KO,H + SO

+ ηh

KO,H

KO,H + SO

SNO

KNO + SNO

XB,H

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Hydrolysis XND

Particulatebiodegrableorganicnitrogen

SND

Solublebiodegrableorganicnitrogen

Ammonification of Soluble Organic Nitrogen

• Biodegradable soluble organic nitrogen is converted to free and saline ammonia using first-order process mediated by active heterotrophs

• Hydrogen ions consumed in the process resulting in an alkalinity change

8/17/2009 22ASM1

Ammonification SND

Solublebiodegrableorganicnitrogen

SNH

Ammonianitrogen

Ammonification of Soluble Organic Nitrogen

• Process rate:

kaSNDXB,H

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where ka = ammonification rate, m3 (g COD day)-1

ASM1

Ammonification SND

Solublebiodegrableorganicnitrogen

SNH

Ammonianitrogen

ASM1 State VariablesSi Soluble inert organics g COD/m3Ss Readily biodegradable (soluble) substrate g COD/m3Xi Particulate inert organics g COD/m3Xs Slowly biodegradable (particulate) substrate g COD/m3Xbh Active heterotrophic biomass g COD/m3Xba Active autotrophic biomass g COD/m3Xp Unbiodegrad. particulates from cell decay g COD/m3So Dissolved oxygen g O2/m3Sno Nitrate and nitrite g N/m3Snh Free and ionized ammonia g N/m3Snd Soluble biodegradable organic nitrogen (in ss) g N/m3Xnd Particulate biodegradable organic N (in xs) gN/m3Xii Inert inorganic suspended solids g/m3

S - Soluble Components X - Particulate Components

Adapted from Hydromantis, Inc.

Mapping of State Variables toComposite Variables

sBODu

xBODu

BODu

fbod

BOD5

sCOD

xCOD

COD

VSS

icv

TSSExample: ASM1

Si

Ss

Xs

XBH

XBA

XP

Xi

Xii

Adapted from Hydromantis, Inc.

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Model

• For a completely mixed reactor ASM1 results in 13 nonlinear ordinary differential equations (NODE)

• Given a set of initial conditions, solve these using numerical methods techniques, i.e.,– General solvers such as Matlab, Simulink, ACSL, etc.– Specialized simulators such as GPS-X, BioWin, etc. as we

will see later.

• A plug flow reactor consisting for example of 10 CSTR would result in 130 NODEs – if you have 8 such reactors in parallel, this translates to more than 1000 NODEs.

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ASM1, ASM2, ASM2d, ASM3, etc.

Decay

Aerobic G

Hydrolysis

Anoxic G

HydrolysisAmmonification

Decay

Growth

Heterotrophs (aerobic and anoxic)

Autotrophs (nitrifiers)

State variable

Process

XBHHeterotrophicbiomass

SODissolvedoxygen

SSReadilybiodegrablesubstrate

SNO

Nitrate -nitritenitrogen

SNHAmmonianitrogen

XPInert particulateProducts frombiomass decay

XS

Slowlybiodegrablesubstrate

XND

Particulatebiodegrableorganicnitrogen

SND

Solublebiodegrableorganicnitrogen

SNH

Ammonianitrogen

SODissolvedoxygen

XBAAutotrophicbiomass SNO

Nitrate -nitritenitrogen

ASM1 Model Structure

Return

Soluble inertorganicsSI

XIParticulateinert organics