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					             New framework for standardized notation in
             wastewater treatment modelling

                          1          1          2           3            1,4                    1            5               6                          7                  8
             Ll. Corominas , L. Rieger , I. Takács , G. Ekama , H. Hauduc , P.A. Vanrolleghem , A. Oehmen , K.V. Gernaey , M.C.M. van Loosdrecht and Y. Comeau


1)
     modelEAU , Université Laval, Pavillon Pouliot, 1065 av. de la Médecine, Quebec (QC) G1V 0A6, Canada.                                                           (E-mail: lluis.corominas@gci.ulaval.ca; leiv.rieger@gci.ulaval.ca; peter.v
2)
     EnviroSim Associates Ltd, 15 Impasse Fauré, Bordeaux 33000 France .                                                                                            (E-mail: imre@envirosim.com)
3)
     Water Research Group, Department of Civil Engineering, University of Cape Town, Rondebosch, 7701, Cape Town, South Africa.                                     (E-mail: george.ekama@uct.ac.za)
4)
   Cemagref, EPURE, Parc de Tourvoie, BP44, F-92163, Antony Cedex, France                                                                                           (E-mail: helene.hauduc@cemagref.fr)
5)
6)
   CQFB / REQUIMTE, Department of Chemistry, FCT, Universidade Nova de Lisboa, P-2829-516 Caparica, Portugal (E-mail: adriano@dq.fct.unl.pt )
   Department of Chemical and Biochemical Engineering. Technical University of Denmark. Building 229. DK-2800 Kgs. Lyngby, Denmark.                                 (E-mail: kvg@kt.dtu.dk)
7)
   Department of Biotechnology, Delft University of Technology, Julianalaan 67, 2628 BC Delft, The Netherlands                                                      (E-mail: M.C.M.vanLoosdrecht@tudelft.nl)
8)
   Department of Civil, Geological and Mining Engineering, Ecole Polytechnique, P.O. box 6079, Station Centre-ville, Montreal (QC) H3C 3A7, Canada                  (E-mail: yves.comeau@polymtl.ca)

Abstract
Many unit process models are available in the field of wastewater treatment. All of these models use their own notation, causing problems for documentation,
implementation and connection of different models (using different sets of state variables). The main goal of this paper is to propose a new notational
framework which allows unique and systematic naming of state variables and parameters of biokinetic models in the wastewater treatment field. The symbols
are based on one main letter that gives a general description of the state variable or parameter and several subscript levels that provide greater specification.
Only those levels that make the name unique within the model context are needed in creating the symbol. The paper describes specific problems encountered
with the currently used notation, presents the proposed framework and provides additional practical examples. The overall result is a framework that can be
used       in       whole       plant       modelling,       which         consists      of       different     fields       such        as      activated
sludg




Keywords Wastewater treatment, modeling, nomenclature, ASM, ADM
i.ulaval.ca; leiv.rieger@gci.ulaval.ca; peter.vanrolleghem@gci.ulaval.ca)
                            Models references: see below                                                                                                              ASM1                    ASM2d                      ASM3                     ASM3 + Bio-P                 New General                   UCTPHO+                           ASM2d + TUD
                            N.B.: see below
                                                                       Description                            Parameter              Units
                                                                                                                            N.
                                                                                                                                                             Symbol   20°C    θpow   Symbol    20°C    θpow   Symbol      20°C   θpow   Symbol         20°C      θpow   Symbol     20°C      θpow   Symbol     20°C    θpow   Symbol    20°C                 θpow
                                                                                                                            B.
                            COD soluble
                            Soluble biodegradable organics                                                      SB                 g COD.m-3                  SS                                                SS                       SS
                            Fermentable organic matter                                                          SF                 g COD.m-3                                          SF                                                                                S BSC                        SF                        SF
                            Fermentation product (Volatil Fatty Acids)                                         S VFA               g COD.m-3                                          SA                                                                                S BSA                        SA                        SA
                                                                                                                SU                 g COD.m-3                  SI                      SI                        SI                        SI                             S US                        SI                         SI
State variables




                            Soluble undegradable organics
                            Dissolved oxygen                                                                    S O2              - g COD.m-3                 SO                      S O2                      SO                       SO                              SO                          S O2                      SO
                            COD particulate and colloidal
                            Particulate biodegradable organics                                                 XC B                g COD.m-3                  XS                      XS                        XS                       XS                             S ENM                       X ENM                      XS
                            Adsorbed slowly biodegradable substrate                                            X Ads               g COD.m-3                                                                                                                                                        X ADS
                            Particulate undegradable organics                                                   XU                 g COD.m-3                                          XI                        XI                        XI                                                                                    XI
                            Particulate undegradable organics from the influent                                X U,Inf             g COD.m-3                  XI                                                                                                         S UP                        XI
State variables




                            Particulate undegradable endogenous products                                       X U,E               g COD.m-3                  XP                                                                                                         ZE                          XE
                            Nitrogen (N)
                                                                                                                                             -3
                            Ammonium and ammonia nitrogen (NH4 + NH3)                                          S NHx                 g N.m                    S NH                   S NH4                     S NH                      S NH                            N H3                       S NH4                      S NH
                            Nitrate and nitrite (NO3 + NO2) (considered to be NO3 only for stoichiometry)      S NOx                 g N.m-3                 S NO                    S NO3                     S NO                      S NO                            N O3                       S NO3                     S NO
                            Dissolved nitrogen gas                                                              S N2                 g N.m-3                                          S N2                     S N2                      S N2                                                                                  S N2
                            Particulate biodegradable organic N                                               XC B,N                 g N.m-3                  X ND                                                                                                       N BP
                                                                                                                                             -3
                                                                                                               S B,N                 g N.m                    S ND                                                                                                       N BS
State variables




                            Soluble biodegradable organic N
                            Soluble inert organic N                                                            S U,N                 g N.m-3                                                                                                                             N US
                            Phosphorus (P)
                            Soluble inorganic phosphorus                                                       S PO4                 g P.m-3                                         S PO4                                              S PO4                            P O4                       S PO4                      S PO
                            Biomass
                            Ordinary heterotrophic organisms                                                   X OHO               g COD.m-3                 X B,H                    XH                        XH                       XH                              ZH                          XH                        XH
                            Autotrophic nitrifying organisms (NH4 to NO3-)                                     X ANO               g COD.m-3                 X B,A                   X AUT                      XA                       XA                              ZA                         X NIT                      XA
State variables




                                                                                                                                                  -3
                            Phosphorus accumulating organisms                                                  X PAO               g COD.m                                           X PAO                                              X PAO                            ZP                         X PAO                     X PAO
                            Organisms (biomass)                                                                 X Bio              g COD.m-3

                            Internal cells products
                            Storage compound in OHOs                                                         X OHO,Stor            g COD.m-3                                                                  X STO                     X STO
                            Storage compound in PAOs                                                         X PAO,Stor            g COD.m-3                                         X PHA                                              X PHA                           S PHB                       X PHA
                                                                                                                                                  -3
                            Stored poly-β-hydroxyalkanoate in PAOs                                           X PAO,PHA             g COD.m                                                                                                                                                                                    X PHA
                            Stored glycogen in PAOs                                                          X PAO,Gly             g COD.m-3                                                                                                                                                                                  X GLY
State variables




                            Stored polyphosphates in PAOs                                                     X PAO,PP               g P.m-3                                          X PP                                               X PP                                                        X PP                      X PP
                            Releasable stored polyphosphates in PAOs (Low molecular weight)                 X PAO,PP,Lo              g P.m-3                                                                                                                            P PP-LO
                            Non-releasable stored polyphosphates in PAOs (High molecular weight)            X PAO,PP,Hi              g P.m-3                                                                                                                            P PP-HI
                            Inorganics
                            Metal hydroxide compounds                                                         X MeOH               g TSS.m-3                                         X MeOH
                            Metal phosphate compounds                                                          X MeP               g TSS.m-3                                         X MeP
                            Alkalinity (HCO3-)                                                                  S Alk            mol HCO3-.m-3               S ALK                   S ALK                     S ALK                    S HCO                                                                                 S HCO
                            TSS
                                                                                                                                                  -3
                            Total suspended solids                                                             X TSS               g TSS.m                                           X TSS                     X SS                      X SS                                                                                 X TSS
                            Hydrolysis
                                                                                                                                                   -1
                            Fraction of inert COD generated in hydrolysis                                   f SU_XCB,hyd          g SU.g XCB                                           fSI      0               fSI        0              fSI            0                                                                      f SI     0
                                                                                                                                                   -1
                            Hydrolysis efficiency factor (anoxic)                                             Y hyd,Ax            g SF.g XCB                                                                                                                            EANOX       0.9
                                                                                                                                                   -1
                            Hydrolysis efficiency factor (anaerobic)                                          Y hyd,An            g SF.g XCB                                                                                                                             EANA       0.6
                            Biomass
                                                                                                                                                   -1
                            Fraction of XU generated in biomass decay                                        f XU_Bio,lys   1     g XU.g XBio                  fp      0.08            fXI      0.1              fXi      0.2             fXI           0.2
Stoichiometrics




                            Heterotrophic organisms
                                                                                                                                                       -1
                            Yield for XOHO growth                                                              Y OHO             g XOHO.g XCB                  YH      0.67            YH      0.625                                                                                                                           YH       0.63
                                                                                                                                                       -1
                            Yield for XOHO growth (Aerobic)                                                   Y OHO,Ox           g XOHO.g XCB                                                                                                                           YH,AER     0.666             YH1       0.666
                                                                                                                                                       -1
                  Growth




                            Yield for XOHO growth (Anoxic)                                                    Y OHO,Ax           g XOHO.g XCB                                                                                                                           YH,ANOX    0.666             YH2       0.54
                                                                                                                                                       -1
                            Yield for XOHO growth (Anaerobic)                                                 Y OHO,An           g XOHO.g XCB                                                                                                                           YH,ANA      0.1
                                                                                                                                                       -1
                            Yield for XOHO growth per XOHO,Stor (Aerobic )                                  Y Stor_OHO,Ox        g XOHO.g XStor                                                                YH,O2      0.8            YH,O2          0.8
                                                                                                                                                       -1
                            Yield for XOHO growth per XOHO,Stor (Anoxic)                                    Y Stor_OHO,Ax        g XOHO.g XStor                                                               YH,NOX      0.65           YH,NO         0.65
                                                                                                                                                   -1
                  storage




                            Yield for XOHO,Stor formation per SB (Aerobic )                                 Y SB_Stor,Ox          g XStor.g SB                                                                YSTO,O2     0.8           YSTO,O2         0.8
                                                                                                                                                   -1
                            Yield for XOHO,Stor formation per SB (Anoxic)                                   Y SB_Stor,Ax          g XStor.g SB                                                                YSTO,NOX    0.7           YSTO,NO         0.7
                                                                                                                                                   -1
                            Fraction of XU generated in heterotrophic biomass decay                         f XU_OHO,lys         g XU.g XOHO                                                                                                                             fEP,H                       fXE-H                     f XI,H
Stoichiometrics




                                                                                                                            1                                                                                                                                                      0.08                        0.08                     0.1
                                                                                                                                                  -1
                            Yield for fermentation                                                              Y fe              g SAc.g SB                                                                                                                             YAC        0.5
                            Phosphorus accumulating organisms (PAO)
                                                                                                                                                       -1
                            Yield for XPAO growth per XPAO,PHA                                                 Y PAO             g XPAO.g XPHA                                        YPAO     0.625                                                                      YP       0.639
                                                                                                                                                       -1
                            Yield for XPAO growth per XPAO,PHA (Aerobic)                                      Y PAO,Ox           g XPAO.g XPHA                                                                                          YPAO,O2         0.6                                         YPAO1      0.666
                  Growth




                                                                                                                                                       -1
                            Yield for XPAO growth per XPAO,PHA (Anoxic)                                       Y PAO,Ax           g XPAO.g XPHA                                                                                          YPAO,NO         0.5                                         YPAO2      0.54
                                                                                                                                                        -1
                            Yield for consumption of XPAO,PHA per XPAO formation (Aerobic)                  Y PHA_PAO,Ox         g XPHA.g XPAO                                                                                                                                                                                YPHAO     1.39         (9,4+3*δ/α)/(2+9*δ)
                                                                                                                                                        -1
                            Yield for consumption of XPAO,PHA per XPAO formation (Anoxic)                   Y PHA_PAO,Ax         g XPHA.g XPAO                                                                                                                                                                                YPHANO    1.72         (19+3*δ/α)/(4+9*δ)
                                                                                                                                                       -1
                            Yield for XPAO,PP storage (SPO4 uptake) per XPAO,Stor utilized                   Y Stor_PP      2    g XPP.g XStor                                       1/YPHA    1/0.2                                    1/YPHA         1/0.2
                                                                                                                                                       -1
                            Yield for XPAO,PP storage (SPO4 uptake) per XPAO,Stor utilized (Aerobic)        Y Stor_PP,Ox         g XPP.g XStor                                                                                                                          fP,UPT1    0.95              YPP1      0.75
                  storage




                                                                                                                                                       -1
                            Yield for XPAO,PP storage (SPO4 uptake) per XPAO,Stor utilized (Anoxic)         Y Stor_PP,Ax         g XPP.g XStor                                                                                                                          fP,UPT2    0.55              YPP2      0.61
cs
Stoichiometrics
                    PP stor
                                                                                                                                                                                   -1
                                  Yield for XPAO,PP formation per XPAO (Anoxic)                                                    Y PAO_PP,Ax                   g XPP.g XPAO                                                                                                                                          YPPNO       3.02       (57+9*δ/α)/(28+4*δ)
                                                                                                                                                                                   -1
                                  Yield for XPAO,PP formation per XPAO (Aerobic)                                                   Y PAO_PP,Ox                   g XPP.g XPAO                                                                                                                                           YPPO       4.42      (57+18*δ/α)/(28+4*δ)
                                                                                                                                                                                    -1
                                  Yield for XPAO,Stor storage per SVFA                                                            Y VFA_Stor,PAO                 g XStor.g SVFA                                                                                                   YPHB     0.889
                                                                                                                                                                                    -1
                                  Yield for XPAO,PHA storage per SVFA (Anoxic)                                                   Y VFA_PHA,PAO,Ax                g XPHA.g SVFA                                                                                                                                         YSANO       0.71     (8,3*YPONO-4,9+8*δ)/(9*δ)
                                                                                                                                                                                    -1
                    PHA storage




                                  Yield for XPAO,PHA storage per SVFA (Anaerobic)                                                Y VFA_PHA,PAO,An                g XPHA.g SVFA                                                                                                                                         YSAAN       1.5
                                                                                                                                                                                              -1
                                  Yield for XPAO,PP requirement (SPO4 release) per XPAO,Stor stored (SVFA utilized)                Y PP_Stor,PAO    3   g XPP.g XStor-1 or g XPO4.g SVFA                           YPO4         0.4                           YPO4       0.35     fP,REL   0.52      YPO4      0.5
                                                                                                                                                                                              -1
                                  Yield for XPAO,PP requirement (SPO4 release) per XPAO,PHA stored (SVFA utilized) (Anoxic)      Y PP_PHA,PAO,Ax    3   g XPP.g XStor-1 or g XPO4.g SVFA                                                                                                                               YPONO       0.23
                                                                                                                                                                                              -1
                                  Yield for XPAO,PP requirement (SPO4 release) per XPAO,PHA stored (SVFA utilized) (Anaerobic)   Y PP_PHA,PAO,An    3   g XPP.g XStor-1 or g XPO4.g SVFA                                                                                                                               YPOAN       0.35          0,184*pH-0,94
                                                                                                                                                                                    -1
                                  Fraction of XPAO,PP that can be released                                                          f PP,Lo_PP                  g XPP,Lo.g XPP                                                                                                     fPP     0.94
                                                                                                                                                                                    -1
                                                                                                                                                                                                                                                                                                                       YGLYNO                 (12.6+2*δ/α)/(9+6*δ)
                  storage




                                  Yield for formation of XPAO,Gly (Anoxic)                                                         Y PAO_Gly,Ax     6            g XGly.g XPAO                                                                                                                                                     1.18
                    Gly




                                                                                                                                                                                    -1
Stoichiometrics




                                  Yield for formation of XPAO,Gly (Aerobic)                                                        Y PAO_Gly,Ox     6            g XGly.g XPAO                                                                                                                                         YGLYO       1.11      (12.6+4*δ/α)/(9+12*δ)
                                                                                                                                                                                -1
                                  Fraction of XU generated in XPAO decay                                                           f XU_PAO,lys                  g XU.g XPAO                                                                                                      fEP,P             fXE-PAO
                  Decay
                  Lysis -




                                                                                                                                                    1                                                                                                                                      0.25               0.25
                                                                                                                                                                                -1
                                  Fraction of SU generated in XPAO decay                                                           f SU_PAO,lys     1            g XU.g XPAO                                                                                   fSI        0       fES,P     0.2     fSI-PAO    0.2
                                                                                                                                                                                         -1
                                  ATP produced per NADH or P/O ratio                                                               Y NADH_ATP                mol ATP.mol NADH                                                                                                                                             δ        1.85
                                                                                                                                                                               -1
                                  Observed biomass ratio TOC over COD                                                               i TOC_COD                     g C.g COD                                                                                                                                               α       0.334
                                  Autotrophic organisms
                                                                                                                                                                                    -1
                                  Yield of XANO growth per SNOx                                                                       Y ANO                     g XAUT.g SNOx                      YA    0.24        YA         0.24       YA      0.24      YAUT        0.24      YA      0.15      YNIT     0.15       YA        0.24
                                                                                                                                                                                 -1
                                  Fraction of XU generated in XANO decay                                                           f XU_ANO,lys                  g XU.g XANO                                                                                                      fEP,A    0.08     fXE-NIT   0.08       fXI,A     0.1
                                  Precipitation
                                  XMeOH requirement per SPO4 utilized                                                             f MeOH_PO4,MW                g XMeOH. g   SPO4-1                                             -3.45
Stoichiometrics




                                  XMeP formation per SPO4 utilized                                                                f MeP_PO4,MW                  g XMeP. g SPO4-1                                                4.86

                                  Nitrogen
                                                                                                                                                                              -1
                                  N content of SB                                                                                     i N_SB                       g N.g SB                                                               iN,SS    0.03       iN,SS      0.03
                                                                                                                                                                              -1
                                  N content of SF                                                                                     i N_SF                       g N.g SF                                         iN,SF       0.03                                                                 iNSF     0.011     iN,SF      0.03
                                                                                                                                                                              -1
                                  N content of SU                                                                                     i N_SU                       g N.g SU                                         iN,SI       0.01      iN,SI    0.01       iN,SI      0.01     fN,SEP   0.07      iNSI     0.035      iN,SI     0.01
                                                                                                                                                                              -1
                                  N content of XU                                                                                     i N_XU                       g N.g XU                                         iN,XI       0.02      iN,XI    0.04       iN,XI      0.03                        iNXI     0.068      iN,XI     0.03
                                                                                                                                                                               -1
                                  N content of XCB                                                                                   i N_XCB                      g N.g XCB                                         iN,XS       0.04      iN,XS    0.03       iN,XS     0.035                       iNENM     0.05      iN,XS      0.03
                                                                                                                                                                               -1
                                  N content of biomass (XOHO, XPAO, XANO)                                                            i N_XBio                     g N.g XBio                       iXB   0.086      iN,BM       0.07      iN,BM    0.07       iN,BM      0.07                        iNBM     0.068     iN,BM      0.07
                                                                                                                                                                               -1
                                  N content of products from biomass                                                                 i N_XUE                      g N.g XUE                        iXE   0.06                                                                                        iNXE     0.068
                                                                                                                                                                               -1
                                  N content of XOHO                                                                                  i N_OHO                      g N.g XOHO                                                                                                      fN,ZH    0.068
Stoichiometrics




                                                                                                                                                                               -1
                                  N content of products from XOHO                                                                  i N_XUE,OHO      1             g N.g XUE                                                                                                       fN,ZEH   0.068
                                                                                                                                                                               -1
                                  N content of XPAO                                                                                  i N_PAO                      g N.g XPAO                                                                                                      fN,ZP    0.07
                                                                                                                                                                               -1
                                  N content of products from XPAO                                                                  i N_XUE,PAO      1             g N.g XUE                                                                                                       fN,ZEP   0.07
                                                                                                                                                                               -1
                                  N content of XANO                                                                                   i N_ANO                     g N.g XANO                                                                                                      fN,ZA    0.068
                                                                                                                                                                               -1
                                  N content of products from XANO                                                                  i N_XUE,ANO      1             g N.g XUE                                                                                                       fN,ZEA   0.068
                                  Phosphorus
                                                                                                                                                                              -1
                                  P content of SB                                                                                     i P_SB                       g P.g SB                                                                                   iP,SS       0
                                                                                                                                                                            -1
                                  P content of SF                                                                                     i P_SF                       g P.g SF                                         iP,SF       0.01                                                                 iPSF       0       iP,SF      0.01
                                                                                                                                                                              -1
                                  P content of SU                                                                                     i P_SU                       g P.g SU                                         iP,SI        0                            iP,SI       0                          iPSI       0        iP,SI      0
                                                                                                                                                                              -1
                                  P content of XU                                                                                     i P_XU
Stoichiometrics




                                                                                                                                                                   g P.g XU                                         iP,XI       0.01                          iP,XI      0.01                        iPXI     0.021      iP,XI     0.01
                                                                                                                                                                              -1
                                  P content of XCB                                                                                   i P_XCB                       g P.g XB                                         iP,XS       0.01                          iP,XS     0.005                       iPENM       0       iP,XS      0.01
                                                                                                                                                                               -1
                                  P content of biomass (XOHO, XPAO, XANO)                                                            i P_XBio                     g P.g XBio                                        iP,BM       0.02                          iP,BM     0.014                        iPBM     0.021     iP,BM      0.02
                                                                                                                                                                              -1
                                  P content of products from biomass                                                                 i P_XUE                      g P.g XUE                                                                                                                          iPXE     0.021
                                                                                                                                                                               -1
                                  P content of XOHO                                                                                  i P_OHO                      g P.g XOHO                                                                                                      fP,ZH    0.021
                                                                                                                                                                              -1
                                  P content of products from XOHO                                                                  i P_XUE,OHO      1             g P.g XUE                                                                                                       fP,ZEH   0.021
                                                                                                                                                                               -1
                                  P content of XPAO                                                                                   i P_PAO                     g P.g XPAO                                                                                                      fP,ZP    0.021
                                                                                                                                                                              -1
                                  P content of products from XPAO                                                                  i P_XUE,PAO      1             g P.g XUE                                                                                                       fP,ZEP   0.021
                                                                                                                                                                               -1
                                  P content of XANO                                                                                   i P_ANO                     g P.g XANO                                                                                                      fP,ZA    0.021
                                                                                                                                                                              -1
                                  P content of products from XANO                                                                  i P_XUE,ANO      1             g P.g XUE                                                                                                       fP,ZEA   0.021
                                                                                                                                                                               -1
                                  Conversion factor for XMeP (FePO4) in P                                                             i P_MeP                     g P.g XMeP                                                  31/150.8
Stoichiometrics




                                  TSS
                                                                                                                                                                                -1
                                  Conversion factor XU in TSS                                                                        i TSS_XU                    g TSS.g XU                                        iTSS,XI      0.75      iSS,XI   0.75      iTSS,XI     0.75                                           iTSS,XI    0.75
                                                                                                                                                                                   -1
                                  Conversion factor XCB in TSS                                                                      i TSS_XCB                   g TSS.g XCB                                        iTSS,XS      0.75     iSS,XS    0.75      iTSS,XS     0.75                                          iTSS,XS     0.75
                                                                                                                                                                                    -1
                                  Conversion factor XOHO,Stor in TSS                                                              i TSS_XOHO,Stor               g TSS.g XStor                                                            iSS,STO    0.6     iTSS,XSTO    0.6
                                                                                                                                                                                    -1
                                  Conversion factor XPAO,PHA in TSS                                                               i TSS_XPAO,PHA                g TSS.g XPHA                                      iTSS,XPHA     0.6                                                                                    iTSS,PHA    0.6
                                                                                                                                                                                   -1
                                  Conversion factor biomass in TSS                                                                    i TSS_XBio                 g TSS.g XBio                                     iTSS,BM       0.9      iSS,BM     0.9      iTSS,BM     0.9                                           iTSS,BM     0.9
                                                                                                                                                                                   -1
                                  Conversion factor XPAO,PP in TSS                                                                i TSS_XPAO,PP                  g TSS.g XPP                                      iTSS,XPP      3.23                        iTSS,XPP     3.23                                          iTSS,PP     3.23
                                                                                                                                                                                   -1
                                  Conversion factor XPAO,Gly in TSS                                                               i TSS_XPAO,Gly                 g TSS.g XGly                                                                                                                                          iTSS,GLY    0.84
                                                                                                                                                                                    -1
                                  Ratio COD/VSS (OHO)                                                                               i VSS_OHO                   g XOHO.g VSS                                                                                                      fCV,H    1.48
                                                                                                                                                                                    -1
                                  Ratio COD/VSS (ANO)                                                                               i VSS_ANO                   g XANO.g VSS                                                                                                      fCV,A    1.42
                                                                                                                                                                                    -1
                                  Ratio COD/VSS (PAO)                                                                               i VSS_PAO                   g XPAO.g VSS                                                                                                      fCV,P    1.42
                                  COD
                                  Conversion factor for NO3 reduction to N2                                                          i NOx,N2                     g COD.g N-1                            40/14                 40/14               40/14                40/14              40/14              40/14               40/14

                                  Conversion factor for NO3 in COD                                                                  i COD_NOx                     g COD.g N-1                            -64/14                -64/14              -64/14               -64/14             -64/14             -64/14              -64/14

                                  Conversion factor for N2 in COD                                                                    i COD_N2                     g COD.g N-1                            -24/14                -24/14              -24/14               -24/14             -24/14             -24/14              -24/14

                                  Conversion factor for H2 in COD                                                                    i COD_H2                     g COD.g H-1                                                                                                                8
                                  Charge
                                  Conversion factor for SVFA (CH3COO-)in charge                                                    i Charge_VFA                 Charge.g COD-1                                                 -1/64                                                                                              -1/64

                                  Conversion factor for NHx in charge                                                              i Charge_NHx                   Charge.g N-1                           1/14                   1/14               1/14                  1/14                                                      1/14

                                  Conversion factor for NO3 in charge                                                              i Charge_NOx                   Charge.g N-1                           -1/14                 -1/14               -1/14                -1/14                                                     -1/14

                                  Conversion factor for PO4 in charge                                                              i Charge_PO4                   Charge.g P-1                                                -1.5/31                                   -1.5/31                                                   -1.5/31

                                  Conversion factor for XPAO,PP (K0.33Mg0.33PO3)n in charge                                      i Charge_XPAO,PP                 Charge.g P-1                                                 -1/31                                    -1/31                                                     -1/31
                                 Hydrolysis
                                 Maximum specific hydrolysis rate                                               q XCB_SB,hyd      5     g XCB.g XOHO-1.d
                                                                                                                                                                  -1    kh     3     1.116    Kh     3     1.1161     kH        9     1.1161       kH          9     1.1161     KH      2.81    1.05                                     kh       3               1.116
                                                                                                                                                             -1
                                 Half saturation parameter for XCB/XOHO                                          K XCB,hyd               g XCB.g XOHO                  KX     0.03   1.116    Kx    0.1               KX        1                  KX          1                KX      0.15     1                                       KX       0.1            -0.110

                                 Correction factor for hydrolysis under anoxic conditions                         n qhyd,Ax                       -                    ηh     0.4            ηNO3   0.6                                                                       ηS,ANOX    1                                              ηNO       0.8

                                 Correction factor for hydrolysis under anaerobic conditions                      n qhyd,An                       -                                          ηfe    0.4                                                                       ηS,ANA     0.5                                             ηfe      0.2
                                                                                                                                                        -3
                                 Half saturation/inhibition parameter for SO2                                     K O2,hyd                  g SO2.m                                          KO2    0.2                                                                                                                                  KO       0.2
                                                                                                                                                       -3
                                 Half saturation/inhibition parameter for SNOx                                    K NOx,hyd                  g N.m                                           KNO3   0.5                                                                                                                                 KNO       0.5

                                 Biomass
                                                                                                                                                        -3
                                 Half saturation parameter for SPO4 as nutrient                                 K PO4,Bio,gro               g SPO4.m                                                                                                                          KLP,GRO   0.005           KPO4-gro     0.1
                                 Heterotrophic organisms
Kinetics




                                                                                                                                                          -1
                                 Rate constant for XOHO,Stor storage                                              q SB_Stor       5,7   g XCB.g   XOHO-1.d                                                           kSTO      12     1.0718      kSTO        12.5   1.0718
                                                                                                                                                              -1
                                 Rate constant for XAds adsorption                                               q XCB_Ads        5,7   g XAds.g XCB-1.d                                                                                                                                                 KADS        0.17      1.029

                                 Maximum growth rate of XOHO                                                     μ OHO,Max                      d
                                                                                                                                                  -1                   μH      6     1.072    μH     6     1.0718     μH        3     1.0718       μH          3     1.0718     μH       3.2    1.029     μH       3.2 - 4.8   1.029     μH       6               1.072

                                 Reduction factor for anoxic growth of XOHO                                      n μOHO,Ax                        -                    ηg     0.8            ηNO3   0.8              ηNOX      0.5                ηNO,H       0.8              ηgro     0.37              ηH       0 - 0,6              ηNO       0.8

                                                                                                               μ Ads_OHO,Max
           Growth - Storage




                                 Maximum growth rate of XOHO on XAds (hydrolysis + growth)                                                        -1                                                                                                                                                     KMP         1.35      1.08
                                                                                                                                                d
Kinetics




                                                                                                                                                             -1
                                 Maximum adsorption on XOHO (XAds/XOHO ratio)                                   f Ads_OHO,Max            g XAds.g XOHO                                                                                                                                                    fMA         1
                                                                                                                                                              -1
                                 Rate constant for fermentation / Maximum specific fermentation growth rate     q SF_VFA,Max      4,7    g SF.g XOHO-1.d                                     qfe     3     1.0718                                                               KC       4      1.029     KFE        0.04                qfe      3               1.072
                                                                                                                                                       -3
                                 Half saturation parameter for SB                                                K SB,OHO         5          g SB.m                    Ks     20                                      KS       10                 KSS,H       10
                                                                                                                                                       -3
                                 Half saturation parameter for SF                                                K SF,OHO         5          g SF.m                                           KF     4                                                                         KS,H      5       1        KF          5         1        KF       4
                                                                                                                                                        -3
                                 Half saturation parameter for SVFA                                              K VFA,OHO        5                                                          KA      4                                                                         KS,H      5       1        KA          5         1       KAc       4
Kinetics




                                                                                                                                            g SVFA.m
                                                                                                                                                             -1
                                 Half saturation parameter XOHO,Stor/XOHO                                        K Stor_OHO              g XStor.g XOHO                                                              KSTO      0.1               KSTO,H       0.1
                                                                                                                                                             -1
                                 Half saturation parameter for hydrolysis/growth on XAds                         K Ads_OHO               g XAds.g XOHO                                                                                                                                                    KSP       0.027      0.91

                                 Decay rate for XOHO                                                                                              -1
                                                                                                                   b OHO                        d                      bH     0.62   1.12     bH    0.4    1.0718                                                               bH      0.62    1.029     bH         0.62      1.02      bH       0.4
                                                                                                                                                  -1
                                 Endogenous respiration rate of XOHO                                               m OHO                        d                                                                                                  bH         0.3    1.0718                                                                                       1.072

                                 Reduction factor for Anoxic endogenous respiration of OHO                       n mOHO,Ax                        -                                                                                             ηNO,end,H     0.33
Kinetics
           Decay-Lysis




                                                                                                                                                  -1
                                 Endogenous respiration rate of XOHO (Aerobic)                                   m OHO,Ox                       d                                                                    bH,O2     0.3    1.0718
                                                                                                                                                  -1
                                 Endogenous respiration rate of XOHO (Anoxic)                                     m OHO,Ax                      d                                                                    bH,NOX    0.1    1.0718
                                                                                                                                                  -1
                                 Endogenous respiration rate of XOHO,Stor                                          m Stor                       d                                                                                                 bStor       0.3    1.0718
                                                                                                                                                  -1
                                 Endogenous respiration rate of XOHO,Stor (Aerobic)                               m Stor,Ox                     d                                                                   bSTO,O2    0.3    1.0718

                                                                                                                                                  -1
                                 Endogenous respiration rate of XOHO,Stor (Anoxic)                                m Stor,Ax                                                                                         bSTO,NOX   0.15   1.072
Kinetics




                                                                                                                                                d
                                                                                                                                                       -3
                                 Half saturation parameter for fermentation of SF                                  K SF,fe                   g SF.m                                          Kfe     4                                                                        KS,ANA     2       1                                      Kfe       20
           Switching functions




                                                                                                                                                        -3
                                 Half saturation parameter for SO2                                                K O2,OHO                  g SO2.m                    KO,H   0.2            KO2    0.2               KO2      0.2                KO,H        0.2             KO,HET    0.002            KOH        0.002                KO       0.2
                                                                                                                                                        -3
                                 Half saturation parameter for SNOx                                              K NOx,OHO        5         g SNOx.m                   KNO    0.5            KNO3   0.5              KNOX      0.5               KNO,H        0.5              KNO       0.1             KNO3        0.2                KNO       0.5
                                                                                                                                                        -3
                                 Half saturation parameter for SNHx                                              K NHx,OHO                  g SNHx.m                                         KNH4   0.05             KNH4      0.01              KNH,H        0.01             KNA      0.005            KNH4        0.01                KN      0.05
                                                                                                                                                        -3
                                                                                                                 K PO4,OHO
Kinetics




                                 Half saturation parameter for SPO4                                                                         g SPO4.m                                         KP     0.01                                         KPO4,H       0.01                                                                       KP      0.01
                                                                                                                                                             -3
                                 Half saturation parameter for SAlk                                               K Alk,OHO              mol HCO3-.m                                         KALK   0.1              KALK      0.1               KHCO,H       0.1                                                                      KHCO       0.1
                                 Phosphorus accumulating organisms (PAO)
           PHA Storage




                                                                                                                                                                  -1
                                 Rate constant for SVFA uptake rate (XPAO,Stor storage)                        q PAO,VFA_Stor     5     g XStor.g XPAO-1.d                                   qPHA    3     1.1161                                 qPHA         6     1.041      KP       2       1       qPHA         6
                                                                                                                                                                  -1
                                 Rate constant for SVFA uptake rate (XPAO,PHA storage) (anaerobic)            q PAO,VFA_PHA,An    5     g XPHA.g XPAO-1.d                                                                                                                                                                               qAc       8               1.091
                                                                                                                                                                  -1
                                 Rate constant for SVFA uptake rate (XPAO,PHA storage) (anoxic)               q PAO,VFA_PHA,Ax    5     g XPHA.g XPAO-1.d                                                                                                                                                                              qAcNO      1.2    1.5*qAc*exp(0.09*(T-20))
Kinetics




                                                                                                                                                              -1
                                 Rate constant for storage of XPAO,PP                                          q PAO,PO4_PP       5     g XPP.g XPAO-1.d                                     qPP    1.5    1.1161                                  qPP        1.5    1.041                                                              kPP       0.1             1.031

                                 Reduction factor for KO2 for XPAO,PP formation                                     n KO2                         -                                                                                                                                                                                     gPP      0.22
           PP storage




                                 Reduction factor for KNOx for XPAO,PP formation                                   n KNOx                         -                                                                                                                                                                                     gPP      0.22
                                                                                                                                                             -1
                                 Maximum ratio of XPAO,PP/XPAO                                                  f PP_PAO,Max              g XPP.g XPAO                                       KMAX   0.34                                        Kmax,PAO      0.2                                                                      fPPmax    0.35
                                                                                                                                                             -1
                                 Half saturation parameter for XPAO,PP/XPAO                                     K S,fPP_PAO               g XPP.g XPAO                                       KPP    0.01                                        KPP,PAO       0.05
Kinetics




                                                                                                                                                             -1
                                 Half Inhibition parameter for XPAO,PP/XPAO                                      K I,fPP_PAO              g XPP.g XPAO                                       KiPP   0.02                                        KiPP,PAO      0.05                                                                      KfPP     0.01
                                                                                                                                                              -1
                                 Rate constant for formation of XPAO,Gly                                            q Gly
           Gly storage




                                                                                                                                        g XGly.g XPAO-1.d                                                                                                                                                                               kGLY     0.93             1.128
                                                                                                                                                              -1
                                 Maximum ratio of XPAO,Gly/XPAO                                                 f Gly_PAO,Max           g XGly.g XPAO-1.d                                                                                                                                                                              fGLYmax    0.5
                                                                                                                                                             -1
                                 Saturation constant for XPAO,Gly/XPAO                                           K fGly_PAO               g XGly.g XPAO                                                                                                                                                                                KfGLY     0.01

                                                                                                                 μ PAO,Max
Kinetics




                                 Maximum growth rate of XPAO                                                                                      -1                                         μPAO    1     1.1161                                 μPAO         1     1.072     µP1      0.95     1       µPAO1       1.2
                                                                                                                                                d

                                 Maximum growth rate of XPAO (when P is limiting)                              μ PAO,Max,Plim                   d
                                                                                                                                                  -1                                                                                                                           µP2      0.42     1       µPAO2       0.42

                                 Reduction factor for anoxic growth of XPAO                                        n μPAO                         -                                          ηNO3   0.6                                         ηNO,PAO       0.6               ηp       0.4             ηPAO      0 - 0.7
           Gowth




                                                                                                                                                             -1
                                 Saturation constant for XPAO,PHA/XPAO                                          K fPHA_PAO               g XPHA.g XPAO                                                                                                                                                                                 KfPHA      0.2
                                                                                                                                                             -1
                                 Saturation constant for XPAO,Stor/XPAO                                          K fStor_PAO             g XStor.g XPAO                                      KPHA   0.01                                          KPHA        0.1              KSP1      0.1     1      KPHA1        0.18
Kinetics




                                                                                                                                                             -1
                                 Saturation constant for XPAOStor/XPAO (P limit)                               K fStor_PAO,Plim          g XStor.g XPAO                                                                                                                        KSP2     0.05     1      KPHA2        0.18
                                                                                                                                                                  -1
                                 Rate for XPAO,PHA consumption (XPAO growth)                                     q PHA_PAO        6     g XPHA.g XPAO-1.d                                                                                                                                                                               kPHA     5.51             1.128

                                 Reduction factor for denitrifying processes                                       n qPAO                         -                                                                                                                                                                                     ηNO       0.8
                                                                                                                                                              -1
                                 Observed oxygen consumption for maintenance                                     m PAO,O2               g SO2.g XPAO-1.d                                                                                                                                                                                mOC      0.096
                                                                                                                                                  -1
                                 Endogenous respiration rate of XPAO                                               m PAO                        d                                            bPAO   0.2    1.072                                  bPAO        0.2    1.072      bP      0.04     1       bPAO        0.04
Kinetics




                                 Reduction factor for anoxic endogenous respiration of XPAO                        n mPAO                         -                                                                                            ηNO,end,PAO    0.33
                                                                                                                                                  -1
                                 Maintenance rate for XPAO (Aerobic)                                              m PAO,Ox                      d                                                                                                                                                                                       mO       0.06    (3*δ*m OC)/(3.2+δ/α)
                                                                                                                                                  -1
                                                                                                                                                                                                                                                                                                                                                         (6*δ*m OC)/(6.3+δ/α)
           Decay-Lysis




                                 Maintenance rate for XPAO (Anoxic)                                               m PAO,Ax                      d                                                                                                                                                                                       mNO      0.09
                                                                                                                                                             -1
                                 Maintenance rate for XPAO (Anaerobic)                                            m PAO,An               g P.g XPAO-1.d                                                                                                                                                                                 mAN      0.05             1.072
                                                                                                                                                  -1
                                 Rate constant for Lysis of XPAO,PP                                               b PP_PO4                                                                   bPP    0.2    1.072                                   bPP        0.2    1.072     bPP      0.03     1        bPP        0.03
Kinetics




                                                                                                                                                d

                                 Reduction factor for anoxic lysis of XPAO,PP                                    n bPP_PO4                        -                                                                                             ηNO,lys,PP    0.33
                                                                                                                                                  -1
                                 Rate constant for respiration of XPAO,Stor                                      b Stor_VFA                     d                                            bPHA   0.2    1.072                                  bPHA        0.2    1.072

                                 Reduction factor for anoxic respiration of XPAO,Stor                            n bStor_VFA                      -                                                                                            ηNO,resp,PHA   0.33
                                                                                                                                                       -3
                                 Half saturation parameter for SB                                                 K SB,PAO                   g SB.m                                                                                             KSS,PAO       10
etics




                                                                                                                                                        -3
                                 Half saturation parameter for SVFA                                              K VFA,PAO                  g SVFA.m                                         KA      4                                                                        KSSEQ      2.5              KAC         1                 KAc       4
Kineti                             Half saturation parameter for SO2                                           K O2,PAO                    g SO2.m
                                                                                                                                                     -3                               KO2    0.2                                      KO,PAO       0.2                                            KOH       0.002              KO     0.2
                                                                                                                                                      -3
             Switching functions   Half saturation parameter for SNOx                                         K NOx,PAO                    g SNOx.m                                   KNO3   0.5                                     KNO,PAO       0.5                                            KNO3       0.2               KNO    0.5
                                                                                                                                                      -3
                                   Half saturation parameter for SNHx                                          K NHx,PAO                   g SNHx.m                                   KNH4   0.05                                    KNH,PAO       0.05                                           KNH4       0.01              KN     0.05
                                                                                                                                                      -3
                                   Half saturation parameter for SPO4 uptake (XPAO,PP storage)               K PO4,PAO,stor                g SPO4.m                                   KPS    0.2                                     KPO4,PP       0.2               KLP,UPT    0.25             KPO4-up     0.25              KPO     1
Kinetics



                                                                                                                                                      -3
                                   Half saturation parameter for SPO4 as nutrient (XPAO growth)              K PO4,PAO,gro                 g SPO4.m                                   KP     0.01                                    KPO4,PAO      0.01                                                                        KP     0.02
                                                                                                                                                     -3
                                   Half saturation parameter for XPAO,PP                                       K PP,PAO                    g XPP.m                                                                                                                    KXP       0.01              KPP         1                KPP    0.01
                                                                                                                                                      -3
                                   Half saturation parameter for XPAO,PHA                                     K PHA,PAO                    g XPHA.m                                                                                                                                                                            KPHA   0.01
                                                                                                                                                     -3
                                   Half saturation parameter for XPAO,Gly                                      K Gly,PAO                   g XGly.m                                                                                                                                                                            KGLY   0.01
                                                                                                                                                           -3
                                   Half saturation parameter for SAlk                                          K Alk,PAO               mol HCO3-.m                                    KALK   0.1                                     KHCO,PAO      0.1                                                                         KHCO   0.01
Kinetics




                                   Autotrophic organisms
                                   Maximum growth rate of XANO                                                 μ ANO,Max                       d
                                                                                                                                                -1              μA     0.8    1.103   μAUT    1     1.111    μA        1.3   1.111      μA       0.9 - 1.8   1.111     μA      0.2 - 1.0 1.123    μNIT     0.2 - 1.2    1.1     μA     1     1.111
                                                                                                                                                -1
                                   Decay rate for XANO                                                          b ANO                          d                bA     0.15   1.072   bAUT   0.15   1.116                               bA         0.2       1.111     bA       0.04    1.029     bNIT       0.04      1.029    bA    0.15   1.116
                                                                                                                                                -1
                                   Endogenous respiration rate for XANO                                         m ANO                                                                                                                   bA
             Decay-Lysis




                                                                                                                                               d                                                                                                   0.2       1.111

                                   Reduction factor for anoxic endogenous respiration of XANO                   n mANO                          -                                                                                    ηNO,end,A     0.5
Kinetics




                                                                                                                                                -1
                                   Endogenous respiration rate for XANO (Aerobic)                              m ANO,Ox                        d                                                            bA,O2      0.2   1.116

                                                                                                                                                -1
                                   Endogenous respiration rate for XANO (Anoxic)                               m ANO,Ax                        d                                                            bA,NOX     0.1   1.096
                                                                                                                                                           -1
                                   Rate constant for ammonification                                              q am                  m3.g XCB,N-1.d            ka    0.08   1.072                                                                                    KR       0.08    1.029
                                                                                                                                                     -3
                                   Half saturation parameter for SO2                                           K O2,ANO                    g SO2.m              KO,A   0.4            KO2    0.5            KA,O2      0.5             KO,A        0.5               KO,AUT      0.5              KON       0.002              KA,O   0.5
           functions
           switching




                                                                                                                                                      -3
                                   Half saturation parameter for SNHx                                          K NHx,ANO                   g SNHx.m             KNH     1             KNH4    1             KA,NH4     1.4            KNH,A        1-2                KNH         1     1.123     KNH4        1        1.123   KNH     1
                                                                                                                                                      -3
                                   Half saturation parameter for SPO4                                         K PO4,ANO                    g SPO4.m                                   KP     0.01                                     KPO4,A       0.01                                                                        KP     0.01
                                                                                                                                                           -3
                                   Half saturation parameter for SAlk                                          K Alk,ANO               mol HCO3-.m                                    KALK   0.5            KA,ALK     0.5            KHCO,A       0.5                                                                         KHCO   0.5

                                   Precipitation
                                                                                                                                       3                -1
                                   Rate constant for P precipitation                                            q P,pre               m .g   Fe(OH)3-1.d                              kPRE    1
                                                                                                                                                -1
                                   Rate constant for redissolution                                              q P,red                        d                                      kRED   0.6
                                                                                                                                                           -3
                                   Half saturation parameter for alkalinity                                    K Alk,pre               mol HCO3-.m                                    KALK   0.5


N.B.
    1. The organism type can be skipped in models where no differences is made between those parameters (ASM1, ASM2d, ASM3 and ASM3+Bio-P)
    2. To have consistent units between models for the same parameter and to keep the notation simple, it was chosen to use the inverse of the parameter Y PHA for ASM2d and ASM3+Bio-P
    3. The units g XPP/g XPHA or g XPO4/g SA (in ASM2d+TUD) are equivalent since there is no yield between XPP and XPO4, and between XPHA and SA in other models than ASM2d+TUD
    4. zero or first order kinetics / first order kinetic for UCTPHO+ (no S_F/(K_fe + S_F) term)
    5. If a parameter name is used for different organisms, the name of the organism should appear. Otherwise, it can be ommitted.
    6. If the organism name appear twice (as organism name and as reactant_product) it is possible to simplify and just keep the reactant_product part
    7. If the reactant_product subscript is self explaining, the specification of the process can be ommitted.

           References
           Barker P.S. and Dold, P.L. (1997). General model for biological nutrient removal activated-sludge systems: model presentation, Wat. Env. Res., 69 (5), 969-984.
           Henze M., Grady C. P. L. Jr, Gujer W., Marais G. v. R. and Matsuo T. (2000) Activated Sludge Model No. 1, IWA Publishing, Scientific and Technical Report No. 9, London IWA.
           Henze M., Gujer W., Mino T., Matsuo T., Wentzel M. C., Marais G.v.R., and van Loosdrecht M.C.M. (2000). Activated Sludge Model No. 2d, IWA Publishing, Scientific and Technical Report No. 9, London IWA.
           Hu Z.R., Wentzel M.C. and Ekama G.A. (2007). A general kinetic model for biological nutrient removal activated sludge systems: Model development. Biotechnology and Bioengineering, 98(6), 1242-1258.
           Koch G., M. Kuhni, W. Gujer and H. Siegrist (2000). Calibration and validation of activated sludge model no. 3 for Swiss municipal wastewater.Water research 34(14), 3580-3590
           Meijer, S. C. F. (2004). Theoretical and practical aspects of modelling activated sludge processes. Department of Biotechnological Engineering. Delft University of Technology, The Netherlands: 218
           Rieger L., Koch G., Kühni M., Gujer W. and Siegrist H. (2001) The EAWAG bio-P module for activated sludge model No.3. Wat. Res., 35 (16), 3887-3903.

				
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