MODELLING THE SHARON PROCESS IN VIEW OFCOUPLING WITH ANAMMOX

Eveline I.P. Volcke�

Chris Hellinga���

Sammy Van Den Broeck�

Mark C.M. van Loosdrecht�����

Peter A. Vanrolleghem�

�BIOMATH, GhentUniversity, CoupureLinks653,B-9000Gent,

Belgium���HalotecDelft B.V., Delftechpark26,NL-2628XH Delft, The

Netherlands�����Departmentof BiochemicalEngineering, Delft Universityof

Technology, Julianalaan67,NL-2628BC Delft

Abstract:ThecombinedSHARON-Anammoxprocessfor treatingwastewaterstreamswithhigh ammoniaload,is discussed.Partial nitrification at high temperaturesin a continuouslyaeratedSHARON reactor, shouldyield an optimal ammonium/nitriteratio, that is subse-quentlysentto the Anammoxprocessto form nitrogengas.A mathematicalmodelof theSHARON processis presented.The stoichiometricmatrix is formulatedin termsof yieldcoefficientsand biomasscomposition.Specialattentionis given to the calculationof pH.Preliminarysimulationsof thebehaviour of theSHARON reactorarediscussed.Copyrightc�

2002TiASWiK

Keywords:Environmentalengineering,Equilibrium,Mathematicalmodels,Simulation,SteadyState,WasteTreatment

1. INTRODUCTION

Partial nitrification techniqueshave beendenotedforquiteawhile asverypromisingfor improving sustain-ability of wastewatertreatment(Abeling & Seyfried,1992). The realizationof nitrification/denitrificationwith nitrite asintermediateis beneficialbothin termsof oxygenconsumption,translatedinto reducedaer-ation energy costs,and COD-sourceaddition costs,with savingsof respectively 25%and40%comparedto traditional nitrification/denitrificationvia nitrate.Up till now, the SHARON (Single reactorHigh ac-tivity Ammoniaremoval Over Nitrite) processis theonly reportedprocessin which partial nitrificationof ammoniumto nitrite is successfullymaintainedinpracticeovera long timeperiod(Mulder etal., 2001).TheSHARON processwasdevelopedmorethanfiveyearsagoat the Delft University of Technology. Mi-crobialkinetic andstoichiometricparametersfor am-monia oxidation were determinedunder the actualprocessconditionsby lab-scale(1.5 l) tests(Hellinga

et al., 1999).Making useof both theseexperimentaldataand literature,the developmentof a dynamicalprocessmodel in Matlab/Simulink for the classicalSHARON reactoroperatedwith heterotrophicdeni-trification, wasstartedin view of further processde-signandscale-up(Hellingaet al., 1999).Theinsightsgainedby simulationsallowed the immediatedesignand constructionof a full-scale processwithout theneedfor costlyandtimeconsumingintermediatepilottests.The full-scaleprocessis operationalsinceJan-uary 1999at the RotterdamSluisjesdijksludgetreat-mentplant.Full scaleexperiencewith the SHARONprocesshasrecentlybeendescribedby Mulder et al.(2001)andvanKempenet al. (2001).

Recently, the couplingof the SHARON processwithaso-calledAnammox(anaerobicammoniaoxidation)process,in whichammoniumandnitrite areconvertedto nitrogen gas under anaerobicconditions by au-totrophic bacteria,finds more and more support inthe searchfor sustainablewastewatertreatmenttech-

niques(van Dongenet al., 2001a).Benefitsof thecombinedSHARON-Anammoxprocesscomparedtothe SHARON processwith denitrificationarethe re-ductionby 50%of the aerationcosts,sinceonly halfof theammoniumis convertedto nitrite, theomissionof the needfor additional COD source,the virtualabsenceof sludgeproductionand the possibility toobtain low nitrogen effluent concentrationsthroughthe subsequentautotrophicAnammoxreaction.Thelatter hasbeenan inspiring startingpoint for the de-velopmentof moresustainablemunicipalwastewatertreatmentsystems(Jettenet al., 1997).ProcesseslikeCANON (Hao,2001;Hao et al., 2001)andOLAND(Kuai andVerstraete,1998),that combinepartial ni-trification andAnammoxin onereactor, arecurrentlyalsobeingstudied.

An experimentalstudy on the treatmentof ammo-nium rich wastewater by the combinedSHARON-Anammox processperformed by van Dongen etal. (2001a), showed that the combinedSHARON-Anammoxsystemcanwork stableover long periodsandtheprocessis readyfor full-scaleimplementation.Currently, an Anammoxreactoris being built at theRotterdamSluisjesdijkplant.

In this paper, the SHARON modelis studiedin viewof couplingwith theAnammoxprocess.Specialatten-tion is givento thecalculationof pH, asit is essentialfor future studiesof the pH control, that is a keypoint in obtainingthedesiredammonium/nitriteratio.In this contribution, the behaviour of the SHARONreactor, operatedwithout pH control,is presented.

2. PROCESSCONFIGURATION AND BASICCONVERSIONREACTIONS

Theset-upof theSHARON processbasicallyconsistsof a continuous,completelymixed reactor withoutsludgeretention,operatingathightemperature(35� C)andanaveragepH-valueof about7. Underthesecon-ditions,ammoniumoxidizersgrow fasterthannitriteoxidizers,which can be washedout by sufficientlylowering the hydraulic retention time. The effluentammoniaconcentrationdecreaseswith higher reten-tion time, but is independentof the inlet ammoniaconcentration,atypical featureof achemostatreactor.In this way, the SHARON processis bettersuitedtoachieve substantialammoniaconversionat high reac-tion ratesfor relatively concentratedflows,ratherthanto meetstrict effluent standards.It is very well ap-plicablefor the treatmentof rejectwaterfrom sludgedigestion,wherehigh temperatureand pH are takenadvantageof.

For high-concentratedstreams,the protonsproducedduringnitrificationwouldcauseasignificantpH drop,lowering the microbial conversionrates.In casetheinfluent containsammoniumand bicarbonateon anequimolarbasis,whichcanbereasonablyassumedfor

sludgedigestionrejectionwater, half of theproducedprotonsis removedvia carbondioxidestripping:

������ ��� ������� � ���� �� � � � ��� (1)��� � �� � ���� � � � � ��� (2)

However, asthereactionschemeabove shows, this isnotsufficient for pH controlif nearlyall ammoniahasto be converted.The remaininghalf of the protonsproducedin reaction(1) can be consumedby deni-trification of the producednitrite. For this purpose,thereactoris cyclically aeratedandduringtheanoxicphaseaCOD-sourcesuchasmethanolis added:

� � �� "!#� � �$� � � � � ��%!&�'� � �( ��� � � �)� (3)

Denitrificationfor pH control by addingmethanolischeaperthan alkali addition (Hellinga et al., 1999).Notethatdenitrificationis notanobjectiveon its own,sincetheSHARON-effluent is usuallyrecycledto themainwastewatertreatmentplant,wheretheremainingnitrite is converted.

ThesimplifiedAnammoxreaction,neglectingbiomassgrowth, canbewrittenas��� � � � �� � � �*�� � ��� (4)

The required1/1 ammonium/nitriteratio for Anam-moxcanbeproducedby operatingtheSHARON pro-cesswithout pH control,still assumingtheSHARONinfluent containsequimolaramountsof ammoniumandbicarbonate.Indeed,the momenthalf of the am-moniumis convertedto nitrite, theamountof protonsproducedis balancedby carbondioxidestripping.

��� �� ��� � �� +!&�-,.������/!&�'� ��� � "!#� � � � �� ��� � � � � � � � (5)

Further ammoniaconversion than this 50% wouldleadto a pH drop,preventingfurther nitrification. Inpractice,the ammonium/nitriteratio dependson theactualammonium/bicarbonateratio in theinfluent.

Besides,the optimal ammonium/nitriteinfluent ratiofor theAnammoxreactor, alsorequiresfurtherdiscus-sion, as the above mentioned1/1 ratio hasbeende-rivedfor thesimplifiedcasein which biomassgrowthis notconsidered.VanDongenetal. (2001b)assumeda biomassyield of 0.066, to cometo the followingoverallAnammoxreaction(includinggrowth):

��� �� ��� 01� � � �� +!&� !3232 ��� � �� "!#�4��0 � ��5�3� !�� � � ��6� !30 � � � +!&�'�.2 � � ��

7!&� !3232 �$� �8�:9 ; < � 9); =>< (6)

In thiscaseanammonium/nitriteratioof 1/1.32wouldtheoreticallybe optimal to feed the Anammox pro-cess.The ammonium/nitriteratio neededin practice

dependson the actual growth yield. Note also thatunderthe prevailing anoxicconditionsof the Anam-mox process,a part of the producednitrate can beheterotrophicallydenitrifiedto

� ���� , againinfluenc-ing the ammonium/nitriteratio needed.In any case,processcontrol is recommendedto adjustthe ammo-nium/nitriteratioandin thiswaymaximizetheoverallN-removal.

Experimentsperformedby vanDongenet al. (2001a)showed that the ammonium/nitriteratio producedbytheSHARON processcanbesensitively influencedbychangingthe reactorpH between6.5 and7.5.On theone hand,as pH increases,the equilibrium betweenammoniaandammoniumshiftstowardsmoreammo-nia.Ontheotherhand,theconcentrationof ammonia,ratherthanammoniumbeingthe actualsubstratefornitrification, in a chemostatremainsunchangedwithchangingpH. The combinationof thesetwo effectsresultsin a lower ammoniumeffluent concentrationwith increasingpH. This control law canbe usedforsetting the exact ratio for full nitrogen removal inthe Anammoxprocess.It is further studiedhow theexistingmodelfor theSHARON processwith denitri-ficationshouldbeadaptedfor thispurpose.

3. THE SHARON MODEL

To gaininsightinto thecoupledSHARON-Anammoxprocess,simulations have been performedusing aMatlab-Simulinkmodel.The reactoris of the CSTRtype andconsistsof a liquid phaseanda gasphase,both assumedto be perfectly mixed. Betweenthesephases,transportof oxygen,carbondioxideandnitro-gentakesplace.

3.1 Liquid phasemassbalances

Theliquid phasemassbalancefor a compound? withconcentration

�*@readsas

A�BDC#EGF � EIH @DJA3K LNM @POE F � @POEIH @RQ MTSVU WE F � EIH @$X ERY @RF#Z � �EIH @ Q � ERH @\[]F�C E "^ @RF_C E (7)

The liquid phasevolumeC E

is assumedto be con-stant in comparisonwith liquid phaseconcentrationchanges.Liquid phaseconcentrationsare calculatedby integratingthe correspondingmassbalances.Thecomponentsconsideredaregivenin Table1.

3.2 Biological conversionreactions

Biological conversionreactionstake placein the liq-uid phaseonly. Table1 summarizesthestoichiometryof the processsesconsideredin the form of the sto-ichiometric matrix

B\` @-a_J, expressedin terms of the

correspondingyield coefficients and parametersin-dicatingthebiomasscomposition.All concentrationsandreactionstoichiometriesareexpressedon a molarbasis.Decay(or maintenance)is not includedin themodel,asit is assumedto havelittle impactin systemsthat operateat high microbial specific growth rates(Hellingaet al., 1999).

Theprocessratesb a for eachreactionc (expressedinmol m � �E s� = ) aresummarizedin Table2. Thevaluesof the kinetic parametersare given in the appendix.From thesereactionrates,the volumetricconversionrate ^ @ of a component? is calculatedas

^ @ L<daVe =

`f@'a:F b a (8)

Note that the conversion rate is negative for com-ponentsthat undergo net consumption.In contrastwith the industry-standardActivatedSludgeModels(Henzeet al., 2000),microbial reactionratesareex-pressedhereasfunctionsof theactualsubstrates,i.e.the charged or uncharged appearanceof the com-pounds.This approachis preferredin order to coverthepH influencein amorestraightforwardmanner.

3.3 Calculationof pH andequilibriumconcentrations

The liquid phaseconcentrationsof someof the com-ponentsarerelatedto eachotherby equilibriumreac-tions. Equilibria areconsideredfor ammonia/ammo-nium, nitrous acid/nitrite, carbonate/bicarbonate/car-bon dioxide andwater. Lumpedcomponentsarede-finedfor which theconcentrationsequalthetotalcon-centrationof thecomponents,activein anequilibrium:

�*gihTj L �khTjml � hTjkno (9)�kgphTq L �kj*hTqRr � hTq�sr (10)�*t�u L �kuvqRr � j*uwq�sl � uvq r sl (11)

At eachtime step,the concentrationsof the compo-nentsthatarenot involvedin a chemicalequilibrium,aredirectly calculatedby integratingthe correspond-ing massbalanceaccumulationterms.Theconcentra-tionsof thelumpedcomponents(9)-(11)areobtainedby integrating the sumof the accumulationtermsofthedifferentformscorrespondingto thatequilibrium.

The necessityto calculatethe concentrationof thelumpedcomponentsfirst insteadof immediatelycal-culating the concentrationsof the individual compo-nentstaking part in a chemicalequilibrium, is in thefirst place due to the fact that every changein theconcentrationof a componentinvolved in a chemicalequilibrium, causeschangesin the concentrationsofall componentstakingpartin thatequilibrium.

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A secondreasonfor calculatingthe concentrationoflumped componentsfirst, lies in the formulation ofthe stoichiometricmatrix. Although ammoniaratherthan ammoniumand nitrous acid ratherthan the ni-trite ion are the actualsubstratesfor the nitrificationprocesses(Anthonisenetal., 1976),thestoichiometryof the reactionssummarizedin Table1 is expressedin termsof ammoniumandnitrite, astypically done.In the sameway, the stoichiometricmatrix doesn’tcontaincoefficientsfor bicarbonateandcarbonate,butonly for carbondioxide. The processratesgiven inTable2 areexpressedin termsof therealsubstrate.Asthe conversionratesare calculatedfrom the processratesof Table 2 and the stoichiometriccoefficientsof Table 1 accordingto equation(8), they will onlybe correct for componentsthat are not involved inchemicalequilibria. The samewill be valid for theaccumulationtermsin themassbalances(7), in whichthe conversionratesappear. For the componentsin-volved in a chemicalequilibrium, only the sum ofthe accumulationtermsof the different forms underwhich they occur, is correspondingto reality. Thisis correctedby consideringlumpedcomponentsfirstandsubsequentlycalculatingtheconcentrationsof theindividual componentsfrom theconcentrationsof thelumpedcomponents,theequilibriumconstantsandthepH, oncethe latter is known andbeforethenext timestepis initiated.

Although stoichiometriccoefficients for protonsaretakenup in Table1 for reasonsof completeness,theyarenot actuallyimplementedin the Matlab/Simulinkmodel. On the contrary, the proton concentrationinthereactoris calculatedfrom thechargebalancein thereactor, in orderto assurethesumof all chargesto bezero.Thechargebalancein thereactorcanbewrittenas

Q � j n � qwj s Q � hTj no � hTq�sr � jkuvq¶sl �� � uwq r sl Q �k· n L¹¸»º½¼ (12)

in which ¸ º½¼ standsfor the ‘gap’ in the charge bal-ance, which should theoretically be close to zero.The ions originatingfrom strongacidsor bases(e.g.Na

�,K

�,Cl � ,F� ), that are not influencedby the es-

tablishmentof an equilibrium pH, areaccountedforbyalumped,artificalcomponent,¾ �

. It representstheamountof netpositivecharges,expressedin mol m � �E .Note that this concentrationis negative if there aremorenegative thanpositive chargespresent.As thesenet positive chargesare not involved in any conver-sionsconsidered,their concentrationin the perfectlymixedreactoris only determinedby theconcentrationenteringthe reactorand their initial concentrationinthe reactor. Theseconcentrationscan be calculatedfrom the charge balancesfor the influent andfor theinitial concentrationsrespectively. Every time step,� · n is calculatedfrom the correspondingmassbal-ance.

Once�T· n is known, the pH is calculatedin the fol-

lowing way. As chemicalequilibrium reactionspro-ceedmuchfasterthanthebiologicalconversionreac-tions, they are assumedto be in steadystate,so thefollowing equationsapply:

¿ÁÀ�hTj o L �*hTjÂl F � j n� hkjTno (13)

¿ÁÀ jkhTq r L� j n F � hTq sr�*jkhTqRr (14)

¿ÁÀ_uvqRr L� j n F � jkuvq¶sl�kuwqRr (15)

¿�À_j*uwqRl L� j n F � uwq r sl� jkuvq¶sl (16)

¿�à L � j n F � qwj s (17)

By substitutingtheconcentrationsof thelumpedcom-ponents (9)-(11) into the steady state expressionsfor equilibria (13)-(17), the concentrationof everychargedcomponentcan be rewritten in termsof theconcentrationof protonsandlumpedcomponents:

� hTj no L �kgihTj�*ÅÄ:Æ>ÇRÈ ou È n

(18)

� hTq¶sr L �kgphTq�* u È nÄ:Æ ÈiÇRÉ r

(19)

� uvq r sl L � t�uu rÈ nÄ:ÆËÊ É r3Ì Ä:Æ È Ê É l u È nÄ:Æ È Ê É l � (20)

� jkuvq�sl L �kt�uu È nÄ:ÆËÊ É r �* Ä:Æ È Ê É lu È n(21)

Theexpressions(18)-(21)aresubstitutedin thechargebalance(12), in which the pH remainsthe only un-known:

¸Íº½¼ B � j n J L Q � j n ¿�Ã� j n Q � gphTj�* Ä:ÆËÇRÈ ou È n �kgphTq

�* u È nÄ:ÆËÈIÇRÉ r �kt�uu È nÄ:ÆËÊ É r �*ÎÄ:ÆËÈ Ê É lu È n$� F �kt�uu r

È nÄ:ÆËÊ É rÏÌ Ä:Æ È Ê É l u È nÄ:Æ È Ê É l �Q �T· n (22)

This equationcanbe solved iteratively for� j n , e.g.

accordingto the Newton-Raphsonmethod,from aninitial guess

� j n H 9 .Once the pH is known besidesthe concentrationsof the lumpedcomponents,the concentrationof theindividual components,involvedin anequilibrium,iscalculatedfromtheexpressions(18)-(21)and(9)-(11).

As stated,the above reasoningassumesthe concen-trationof netpositivechargesnot to varywith varyingpH,assumingthesenetpositivechargesoriginatefrom

Table2. Kinetic rateexpressions

processrateequationÐVÑ [ molem Ò6ÓÔ sÒiÕ ]

Ð ÕwÖØ×�ÙÛÚmÚÚmÙ�ÜÞÝßRàmá lâ ÙÛÚÂÚàmá läã ßRàwá l Ý

ßRå râ ÙÛÚÂÚå ræã ßRå r Ýâ ÙÛÚÂÚç�è áÂàwå râ ÙÛÚÂÚçÛè áÂàmå rvã ßRámàmå r ÝËé ÙÛÚÂÚ

Ð�ê ÖØ×1ë ì4íÚmÙ�ÜkÝßRáÂàwå râ ë�ìîíáÂàmå r ã ßRámàmå r Ý

ßRå râ ë�ìîíå r ã ßRå r ÝËé ë�ìîíÐ Ó¶ÖØ×�ï

àmå rÚmÙ�Ü Ý

ß àwå râ ïàmå ràwå rðã ßRàwå r Ý

ßRñ á l åIáâäòÛó í è Ù ëñ á l åIá ã ß ñ á l åIá Ýâ ç�è å râ ç�è å r ã ßRå r ÝËé

òÛó íÐ ô ÖØ× ï

àmå lÚmÙ�Ü Ý

ßRàwå lâ ïàmå làwå l ã ßRàwå l Ý

ß ñ á l åIáâ òÛó í è Ù ëñ á l åIá ã ß ñ á l åIá Ýâ ç�è å râ ç�è å r ã ßRå r ÝËé

òÛó íÐ�õ ÖØ× Ú ó íÚmÙ�Ü Ý

ßRñ á l åiáâ ò8ó í è ö Üñ á l åIá ã ß ñ á l åIá Ýß å râ òÛó íå r ã ßRå r Ý>é

ò8ó ístrongacids/bases.In reality, weakacidsor basese.g.� � ÷ ,

� �)ø � andvolatilefattyacidscouldcontributeto the concentrationof thesenet positive charges.Also, thesteadystateassumptionmight not beappro-priatefor thebicarbonate/carbondioxideequilibrium,beingratherslow. Theseassumptionscanexplainpos-sible differencesin the pH calculatedby the modelfrom acid-baseequilibriaandthemeasuredpH.

3.4 Gasphase

No reactionsare assumedto take place in the gasphase.Gasphasemassbalancesfor oxygen,carbondioxide andnitrogenareconsidered.In analogywiththeliquid phasemassbalances(7), thegasphasemassbalancefor acompound? readsas

A�B\CpùúF � ù�H @DJA3K LNM @POù F � @POù�H @ Q M SVU�Wù F � ù¶H @Q X ERY @RFpZ � �EIH @ Q � EIH @\[:F C E

(23)

4. SIMULATION RESULTS

Thebehaviourof theSHARONreactor, operatedwith-out denitrification, has beensimulated.Simulationswere performed for an inlet flow of 600m

�Eh � = ,

containing70 molem � �E of ammoniumand an equalamountof bicarbonateat pH 7. The hydraulicreten-tion time, equal to the sludgeretentiontime (SRT),wasvariedby varying the liquid phasevolume.Thereactorwas continuouslyaerated,so no denitrifica-tion took place.Figure1, 2 and3 presentthe steadystateresults(obtainedafter 50 daysof simulation)infunction of the SRT. The concentrationof ammoniaand nitrite oxidizers is given in Figure 1. Ingrowthof ammoniaoxidizersstartsat an SRT of 0.5 days.In order to prevent ingrowth of nitrite oxidizers,theSRT shouldbekeptbelow 1.5 days.This canalsobeconcludedfrom the correspondingnitrate formation,shown in Figure2.

Fig. 1. Influenceof SRT on biomassconcentrations

Fig. 2. Influenceof SRT on nitrogencompoundcon-centrations

Fig. 3. Influenceof SRT on pH andalkalinity

TheoptimaloperatingSRT couldbechosenas1 day,in order to keep a safety margin. At this retentiontime,totalammoniumandnitrite arepresentin a ratioof about 2/1 at pH 7. Figure 3 shows that at thispoint, indeedalmostall alkalinity is consumed.Thisvalue is quite different from the experimentalresultfound by van Dongenet al. (2001a),who observedstableammoniumconversionwithout the formationof nitrate in a SHARON reactor without pH con-trol (pH = 2&�-,kû+!&� 0 ) to anammonium/nitriteratio of1/1.13.This canprobablybe explainedby deviationsin the values of the model affinity constantsfromreality. Furtherstudyof the modelparametersseemsrecommended.

5. CONCLUSION

Looking for sustainableN-removal techniques,thispaper discussesthe SHARON processfor treatingwastewaterstreamswith high ammoniaload, in viewof its coupling with the Anammoxprocess.For thispurpose,a mathematicalmodelof theSHARON pro-cessthat takesinto accountpH effectswasused.Pre-liminary simulationsshow that theammonium/nitriteratio, producedin the SHARON processwithout pHcontrol,candeviatesignificantlyfrom thedesired1/1mixture. In future, pH control will be implementedin the model and its effect on the producedammo-nium/nitriteratiowill bestudied.

ACKNOWLEDGEMENT

A specialword of thank is due to the EU for theirfinancial supportby meansof the IcoN project, no.EVK1-CT2000-054.

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Hao, X., J.J. Heijnen and M.C.M. van Loosdrecht(2001).Model-basedevaluationof the behaviourof theCANON-processwith variabletemperatureandinflow. Water Research, submitted.

Hao, X. (2001).Model-basedoptimisationof sustai-nablebiological nutrient removal processes.PhDThesis,TU Delft, TheNetherlands.

Kuai, L. and W. Verstraete(1998). Ammonium re-moval by the oxygenlimited autotrophicnirifica-tion anddenitrification(OLAND) system.Appliedenvironmentalmicrobiology, 64, 4500-4506

Hellinga,C.,M.C.M. vanLoosdrechtandJ.J.Heijnen(1999).Model baseddesignof a novel processfornitrogenremoval from concentratedflows.Mathe-maticalandcomputermodellingof dynamicalsys-tems, 5, 351-371.

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APPENDIX: GLOSSARY

symbol characterization dimension`�@-astoichiometriccoefficientof component? in reactionc mole� ù�H @gasphase(bulk) concentrationof component? molem � �ù� @POù�H @inlet concentrationof component? molem � �ù� EIH @liquid phase(bulk) concentrationof component? molem � �E� @POEIH @inlet concentrationof component? molem � �E�ü�EIH @saturationconcentrationof component? at gas/liquidinterphase molem � �EX E Y @ volumetricmasstransfercoefficient for component? s� =ýmolarmass g mole� =^ a volumetricconversionrateof reactionc molem � �E s� =þ7@volumetricproductionrateof component? molem � �E s� =Cpùgasphasevolume m

�ùCpEliquid phasevolume m

�Eÿ&ayield coefficient for reactionc moleX (molesubstrate)� =M @POùinlet volumetricgasflow rate m

�ùs� =M SVU Wù

outletvolumetricgasflow rate m�ù

s� =M EIH @POinlet volumetricflow rate m

�Es� =M EIH SVU�W outletvolumetricflow rate m

�Es� =

symbol characterization dimension valuemaximumspecificgrowthrates

������������ ammoniaoxidizers s� = 2.43E-5

� =�O.@ W����� nitrite oxidizers s� = 1.22E-5

� =���

hTq r����� nitrite denitrifiers s� = 1.74E-5

� =���

hTqRl����� nitratedenitrifiers s� = 3.01E-5

� ��� � Æ W����� methanoloxidizers s� = 8.33E-5

� ��affinity constants¿ � ���hTjÂlammonia(for ammoniaoxdizers) molem � �E 0.0334

� =¿ � ���qRroxygen(for ammoniaoxidizers) molem � �E 0.045

� =�¿ O3@ WjkhTqRrnitrousacid(for nitrite oxidizers) molem � �E 0.019

� ��¿ O3@ WqRroxygen(for nitrite oxidizers) molem � �E 0.034

� ��¿ �hTqRrhTqRr nitrite (for nitrite denitrifiers) molem � �E 0.0085

� ��¿ ¼ Æ W H � OuwjmlVqvj methanol(duringanoxicgrowth) molem � �E 0.521� ��¿ �

hTq lhTqRl nitrate(for nitratedenitrifiers) molem � �E 0.01� ��¿ ¼ Æ W H S �uwj l qvj methanol(duringoxic growth) molem � �E 2.083� ��¿ ¼ Æ WqRr

oxygen(for methanoloxidizers) molem � �E 0.0025� ��

inhibition constants¿ � ���t H jkhkqRrnitrousacid(for ammoniaoxidizers) molem � �E 0.0145

� =¿ t H q r‘mathematicalswitch’ molem � �E 0.0001equilibriumconstants¿�À_hTj o ammoniumequilibriumconstant molem � �E 1.13E-6

� =¿�À_jkhTqRrnitrousacidequilibriumconstant molem � �E 5.71E-1

� =¿�À uwq rcarbondioxideequilibriumconstant molem � �E 4.91E-4

� =¿�À_jkuvqRlbicarbonateequilibriumconstant molem � �E 1.24E-6

� =¿ Ãwaterdissociationconstant mole

�m ���E 1.89E-8

� =� =

Valueat35� C, Lochtman(1995)� ��Valueat35� C, Wiesmann(1994)