131 8 Diffusion of Substrate and Oxygen in Aerobic Granules Yong Li, Zhi-Wu Wang, and Yu Liu CONTENTS 8.1 Introduction 131 8.2 Size-Dependent Kinetic Behaviors of Aerobic Granules 132 8.3 Description of Diffusion Resistance in Aerobic Granules 133 8.4 Simulation of Mass Transfer in Aerobic Granules 135 8.4.1 Model Development 136 8.4.2 Substrate Prole in Aerobic Granules with Different Radiuses 139 8.4.3 Oxygen Proles in Aerobic Granules with Different Radiuses 139 8.4.4 Diffusion Proles of Substrate in Aerobic Granules at Different Bulk Substrate Concentrations 139 8.4.5 DiffusionProlesofDissolvedOxygeninAerobicGranulesat Different Substrate Concentrations 141 8.4.6 Prediction of Bulk Substrate Concentration in an Aerobic Granules Reactor 143 8.5 Conclusions 144 Symbols 145 References 146 8.1 INTRODUCTION Up-to-date, intensive research has been dedicated to the effect of various operating parameters on aerobic granulation in sequencing batch reactors (SBRs) (chapters 1 to7).However,verylimitedinformationiscurrentlyavailableaboutthediffusion behaviorsofsubstancesinsideaerobicgranules.Tayetal.(2002)foundthatamodel dye was only able to penetrate 800 μm beneath the surface of aerobic granules, while Jangetal.(2003)reportedapenetrationdepthof700μmfordissolvedoxygenfrom the surface of aerobic granules. Meanwhile, oxygen diffusion limitation in nitrifying aerobic granules was detected by microelectrode (Wilen, Gapes, and Keller 2004). Moreover,theunbalancedmicrobialgrowthinsideaerobicgranuleshasbeensup- posedtobeduetothemassdiffusionlimitationinaerobicgranules,whichwould furtherleadtoaheterogeneousinternalstructure(seechapter11).Theseindicate 53671_C008.indd 131 10/29/07 7:19:50 AM © 2008 by Taylor & Francis Group, LLC © 2008 by Taylor & Francis Group, LLC 132 Wastewater Purification that without a proper control of the mass diffusion, the structural stability of aerobic granules might not be sustainable. Inviewoftheimportanceofsubstrateandoxygeninmicrobialculture,this chapterattemptstoofferinsightsintothediffusionbehaviorsofsubstrateandoxy - geninaerobicgranules.Thefactorsthatdeterminetheirrespectivediffusioninaero - bic granules are also discussed, with special focus on the reactor operation as well as aerobic granule characteristics. 8.2 SIZE-DEPENDENT KINETIC BEHAVIORS OF AEROBIC GRANULES Massdiffusionlimitationoftenoccursinattachedmicrobialcommunities,suchas biolms, and it suppresses microorganisms from fully accessing the substrate and oxygeninbulksolution.Asaresult,themicrobialactivityisloweredbydeciency oftheenergysource.Toinspecttheexistenceofmassdiffusionlimitationinaerobic granules,Y.Q.Liu,Liu,andTay(2005)determinedthespecicCODremovalrates andspecicgrowthratesofaerobicgranuleswithdifferentsizes.Itappearsfrom gure8.1thatthespecicCODremovalratedecreasedmarkedlywiththeincrease inthesizeofaerobicgranules,indicatingthatthemicrobialactivityinsideaerobic granulesisinhibitedasthegranulesizeincreases.Moreover,thespecicgrowthrate ofaerobicgranuleswasinverselydependentonthegranulesize(gure8.2).Aplotof the specic growth rate against the specic substrate utilization rate further reveals thattheslowsubstrateutilizationbylarge-sizedaerobicgranulesresultsinalow specicgrowthrate(gure8.3).Sucharelationshipbetweenthespecicgrowthand substrate utilization rates is consistent with the prediction by microbial growth theory (MetcalfandEddy2003).Consequently,thekineticbehaviorsofaerobicgranules depictedbythespecicgrowthandsubstrateutilizationratesaresizedependent.        $&)!#"('% *         FIGURE 8.1 Granule size-dependent specic chemical oxygen demand (COD) removal rate.(DatafromLiu,Y.Q.,Liu,Y.,andTay,J.H.,2005.Lett Appl Microbiol 40: 312–315.) 53671_C008.indd 132 10/29/07 7:19:51 AM © 2008 by Taylor & Francis Group, LLC © 2008 by Taylor & Francis Group, LLC Diffusion of Substrate and Oxygen in Aerobic Granules 133 8.3 DESCRIPTION OF DIFFUSION RESISTANCE IN AEROBIC GRANULES Itappearsfromgures8.1and8.2thattheobservedkineticbehaviorsofaerobic granules with different sizes is ultimately the result of diffusion limitation of sub- strate or oxygen in aerobic granules. In order to look into this, Y. Q. Liu, Liu, and Tay (2005) introduced the concept of an effectiveness factor (I), which can be calculated as follows: H rate with diffusion limitation rate withou tt diffusion limitation (8.1)         #"!! $        FIGURE 8.2 Granule size-dependent specic biomass growth rate of aerobic granules. (Data fromLiu,Y.Q.,Liu,Y.,andTay,J.H.2005.Lett Appl Microbiol 40: 312–315.) Specific COD Removal Rate (h –1 ) 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.30 Specific Biomass Growth Rate (h –1 ) 0.015 0.020 0.025 0.030 0.035 0.040 0.045 FIGURE 8.3 Specic growth rate of aerobic granules versus specic substrate utilization rate;datafromgures8.1and8.2. 53671_C008.indd 133 10/29/07 7:19:54 AM © 2008 by Taylor & Francis Group, LLC © 2008 by Taylor & Francis Group, LLC 134 Wastewater Purification Inacasewherediffusionlimitationisnegligible,I approaches unity, while I is close to zero if the diffusion limitation becomes signicant as compared to the reaction. Figure 8.4 shows that the I tended to drop quickly with the increase of the granuleradius.Thiswouldresultfromthepresenceofmassdiffusionlimitationin large aerobic granules. The Thiele modulus is a measurement of the ratio of granule surface reaction rate tothemassdiffusionrate.IftheMonodkineticsformicrobialreactionisapplied,Y. Q. Liu, Liu, and Tay (2005) proposed the following modied Thiele modulus ( K)by introducing dimensionless concentrations: F M  R X YSD om XS o es () /12 (8.2) TheThielemoduluscombinestheindividualeffectofspecicgrowthrate Mm, granule radius R, initial biomass X 0 , substrate concentrations S 0 , anddiffusivityof substrate D es in granules. Obviously, a high G value means high surface reaction rateandlowdiffusionrate,andviceversa.Aquasi-linearrelationshipoftheThiele modulustothegranulesizesisshowningure8.5.Thisseemstoindicatethatthe massdiffusiondominatesthesurfacereactionandbecomeslimitinginlargeaerobic granules. Under similar cultivation conditions of granules, Tay et al. (2003) also reportedthatsmallgranuleswithradiusofapproximately300μmconsistedentirely oflivebiomass.Ascanbeseeningure8.5,averylowThielemoduluswasfoundin aerobicgranuleswitharadiusof300μm,thatis,themicrobialreactionisdominant over diffusion resistance in granules, and maintained the live cells throughout the entire aerobic granules. In contrast, Tay et al. (2002) detected an anaerobic layer at adepthof800to900μmfromthesurfaceofaerobicgranulesbytheuorescence          $"#!"%     FIGURE 8.4 Effectiveness factor versus (I) the radius of aerobic granule. (Data from Liu,Y.Q.,Liu,Y.,andTay,J.H.2005.Lett Appl Microbiol 40: 312–315.) 53671_C008.indd 134 10/29/07 7:19:56 AM © 2008 by Taylor & Francis Group, LLC © 2008 by Taylor & Francis Group, LLC Diffusion of Substrate and Oxygen in Aerobic Granules 135 in situ hybridization (FISH) method. This suggests that the oxygen diffusion became the rate limiting factor over microbial reaction, which is evidenced by a large Thiele modulus,asshowningure8.5. Picioreanu, van Loosdrecht, and Heijnen (1998) reported that a porous, mushroom-like,loosebiolmstructurewasobservedatalowmasstransferrate, while the biolm structure was compact and smooth at increased mass transfer rates. In general, the radius of aerobic granules is bigger than the thickness of biolm, thus theeffectofmasstransferresistanceonthestructureofaerobicgranulesisremark - able.Itappearsfromequation8.2thatmasstransferresistanceinaerobicgranules is closely related to the radius of the aerobic granules, the maximum specic growth rate,initialbiomass,andsubstrateconcentrationsanddiffusivityofthesubstrate. So far, it has been reported that selection of slow-growing bacteria and increase of shearratefavorstheformationofcompactandstableaerobicgranules(Tay,Liu,and Liu2001;Y.Liu,Yang,andTay2004).Obviously,slow-growingbacteriahavesmall specic growth rates, leading to small-sized granules. According to equation 8.2, a small value of the Thiele modulus can be expected in this case, that is, the mass transfer resistance in this kind of aerobic granule would be lowered. Similarly, smallaerobicgranulescanbecultivatedatrelativelyhighshearforce,andthisin turnresultsinalowvalueoftheThielemodulus(equation8.2).Infact,theThiele modulus and the effectiveness factor have been widely applied in biolm research for decades. These two parameters also can provide useful information for quantita - tively understating the mass transfer resistance in aerobic granules. 8.4 SIMULATION OF MASS TRANSFER IN AEROBIC GRANULES Mass transfer limitation has been observed in aerobic granules. The modeling ofthesubstratediffusioninbiolmshasbeenwellstudied,forexample,aone- dimensionalmodelforbiolmshasbeenproposedbyWannerandGujer(1986),and Radius of Aerobic Granule 0 200 400 600 800 1000 1200 1400 iele Modulus 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 FIGURE 8.5 Thielemodulusversusradiusofaerobicgranule.(DatafromLiu,Y.Q., Liu, Y., and Tay, J. H. 2005. Lett Appl Microbiol 40: 312–315.) 53671_C008.indd 135 10/29/07 7:19:58 AM © 2008 by Taylor & Francis Group, LLC © 2008 by Taylor & Francis Group, LLC 136 Wastewater Purification a three-dimensional model reecting the heterogeneous structures of biolms was alsoestablishedbyPicioreanu,vanLoosdrecht,andHeijnen(1998).Basedonthe study of biolm, Li and Liu (2005) investigated the description of diffusion process in aerobic granules. 8.4.1 MODEL DEVELOPMENT Matureaerobicgranuleshaveanequilibriumorstablesizewhengrowthanddetachment forcesarebalanced(Y.LiuandTay2002).Inthedevelopmentoftheone-dimensional model for aerobic granules, Li and Liu (2005) made the following assumptions: 1. An aerobic granule is isotropic in physical, chemical, and biological prop - erties,suchasdensityanddiffusioncoefcient 2. An aerobic granule is ideally spherical 3. No nitrication and anaerobic degradation happen in the process 4. Aerobic granules respond to the change of bulk substrate concentration so quickly that the response time can be ignored AccordingtoBaileyandOllis(1986),themassbalanceequationsbetweenthetwo layers whose radiuses are, respectively, r and r + dr canbeexpressedasfollows: D ds dr r ds dr s 2 2 2  ¥ § ¦ ´ ¶ µ N (8.3) in which O is the substrate conversion rate, s is the substrate concentration, and D s is thediffusioncoefcient.IntheapproachbyLiandLiu(2005),thesubstrateconver- sionratewasgivenbytheMonod-typeequation: N R M  x xs s Y s Ks / max (8.4) in which S x is the biomass density, Y x/s is the biomass yield, and N and N max are the specic growth rate and the maximum specic growth rate, respectively. Substituting equation8.4intoequation8.3leadstothefollowingexpression: D ds dr r ds dr s KsY s s x xs 2 2 2  ¥ § ¦ ´ ¶ µ   MR max / (8.5) Itwasassumedthatthederivativeatthecenterofthegranuleiszeroandthe substrate concentration at the surface of the granule equals the bulk solution (Li and Liu2005),thatis: ds dr r  0 0(8.6) 53671_C008.indd 136 10/29/07 7:20:01 AM © 2008 by Taylor & Francis Group, LLC © 2008 by Taylor & Francis Group, LLC Diffusion of Substrate and Oxygen in Aerobic Granules 137 sS rR bulk   (8.7) Perez,Picioreanu,andvanLoosdrecht(2005)appliedequation8.5tothestudyof spherical biolms, and analytically solved this equation by assuming that the growth rateiszero-orderorrst-order.AsnotedbyLiandLiu(2005),suchasimplied treatment of equation 8.5 leads to the inaccuracy of the prediction, and also limits theapplicationofthisequationtoaverynarrowrange.Asequation8.5isanon- homogenousequation,anumericalmethodtosolveitcompletelywasdeveloped withoutanyassumptiononit(LiandLiu2005).Thismethodisbasedonthenite differencemethod(FDM)(Hoffman2001).Theradiusisthusdividedinto n grids, that is: D ss s r ss rr s s ii iii     ¥ § ¦ ´ ¶ µ  11 2 11 2 $ $ M max ii si x xs KsY R / (8.8) This numerical scheme is applied to all situations without simplifying assump - tionsandthereforetheaccuracyisincreased.TheprogramwaswritteninMatlab™ languageandrununderMatlab7.0whichallowsaneasyvisualizationofthesimu - lated data (Li and Liu 2005). It should be emphasized that equation 8.8 can also be appliedtooxygenifthesetofparametersforthesubstrateisreplacedwiththesetof parameters for dissolved oxygen. After the substrate concentration is determined, the substrate utilization rate ( O 1 ) ofasingleaerobicgranulecanbecalculatedas: NRM 1 2 0 1 4  ° Y srdr xs x R / (8.9) Summingupthesubstrateutilizationrateofalltheaerobicgranulesgivesthe total substrate utilization rate O all : NRM all xs x R i m Y srdr i   ° ¤  1 4 2 0 1 / (8.10) in which m is the number of aerobic granules in the reactor and R i is the radius of thegranulebeingcalculated(LiandLiu2005).AccordingtoLiandLiu(2005),the average radius R of aerobic granules can be expressed as follows: R m R i i m   ¤ 1 1 (8.11) 53671_C008.indd 137 10/29/07 7:20:06 AM © 2008 by Taylor & Francis Group, LLC © 2008 by Taylor & Francis Group, LLC 138 Wastewater Purification Substituting equation 8.11 into equation 8.10 yields: NRM all xs x R m Y srdr  ° / 4 2 0 (8.12) Afterdeformation,equation8.12becomes: N PR M P all x xs R Rm Y sr R dr  ° 4 3 4 43 2 3 0 / / (8.13) in which 4 3 PRRm x isequaltothetotalbiomassinthereactor.Thus,equation8.13 can be simplied to: N M P all xs R XV Y sr R dr  ° / / 4 43 2 3 0 (8.14) in which V is the reactor volume. At time dt, the change of substrate concentration in the reactor can be described as: dS V dt X Y sr R drdt bulk all xs R   ° N M P / / 4 43 2 3 0 (8.15) Inatimeperiodfrom T 0 to T, the change in the substrate concentration is given by equation 8.16: $S X Y sr R dr bulk xs R T T   ¥ § ¦ ¦ ´ ¶ µ µ °° / / M P 4 43 2 3 0 0 ddt (8.16) At an initial substrate concentration, S bulk 0 , the bulk substrate concentration at any time t can be calculated as: SS S S X Y sr bulk bulk bulk bulk xs    0 0 2 4 43 $ / / M PRR dr dt R T T 3 0 0 °° ¥ § ¦ ¦ ´ ¶ µ µ (8.17) Asdiscussedearlier,equation8.17cannotbesolvedanalytically,andthemethod basedonthenitedifferenceprincipleisthusappliedtosolvethisequation(Liand Liu 2005). At each time step, the state is considered pseudo-static, which means the bulk substrate concentration is constant at each time step. Then change of the bulk substrate concentration is a process of mapping, that is, the substrate concentration is determined by the previous time step. This model is valid for different substrates 53671_C008.indd 138 10/29/07 7:20:12 AM © 2008 by Taylor & Francis Group, LLC © 2008 by Taylor & Francis Group, LLC Diffusion of Substrate and Oxygen in Aerobic Granules 139 so long as the parameters are replaced with the specic substrate parameters. In this study,equation8.8wasappliedtoorganicsubstrateanddissolvedoxygenundervari- ous operation conditions. 8.4.2 SUBSTRATE PROFILE IN AEROBIC GRANULES WITH DIFFERENT RADIUSES LiandLiu(2005)simulatedthesubstrateprolesinbioparticleswithameansize of0.1to1.0mm,andtheinitialacetateconcentrationandgranulebiomassconcen - trationwerekeptat465mgCODL –1 and 6250 mg L –1 volatile solids, respectively, while the initial DO concentration was controlled at 8.3 mg L –1 .Modelpredictions showthattheacetateintermsofCODisabletopenetratetothecenterofallsizesof aerobic granules, and the microbial utilization of COD was able to proceed through - CODprolesingure8.6ctoeshowtheplatformsbeneaththedepthsof0.23,0.11, and 0.07 mm from the surface of aerobic granules with radiuses of 0.5, 0.75, and 1.0mm,respectively.Asassumed,thereshouldbenoautotrophicbacteriainaerobic granule,thustheseCODplatformsingure8.6ctoeseemtoimplythatbacteriaat thoseplatformdepthsoftheaerobicgranuleshouldhaveceasednormalmetabolic activity. Furthermore, the noticeable level of COD present at those granule centers points to another possibility accounting for the lowered microbial activity, that is, dissolvedoxygencouldbealimitingfactoratthosedepths(gure8.6ctoe). 8.4.3 OXYGEN PROFILES IN AEROBIC GRANULES WITH DIFFERENT RADIUSES Oxygenprolesinaerobicgranuleswithradiusesof0.1to1.0mmaresimulated (gure8.7).SimilartotheCODprolesingure8.6,oxygencandiffuseintothe entireaerobicgranuleswithradiusof0.1and0.4mm(gure8.7aandb).Foraerobic granuleswitharadiusbiggerthan0.5mm,prominentoxygendiffusionlimitation turnsout.Oxygenisonlyabletopenetrateto0.27,0.64,and0.1mmfromthesur - faceofaerobicgranuleswithradiusesof0.5,0.75,and1.0mm,andtheremaining depth in the aerobic granule is decient in dissolved oxygen (DO) (gure 8.7c, d, and e). Zero DO depths inside the aerobic granules are in good agreement with those CODplatforms(gure8.6ctoe),andmicrobialactivityatthedepthofthoseCOD platformswasseriouslylimitedbytheavailabilityofDO. The DO-reachable depths shown in gure 8.7 appear to be inversely related to thesizeoftheaerobicgranule.Thissuggeststhatlargeraerobicgranuleswillbe subjectedtoanevenmoreseverediffusionlimitationofDOandfurthercauseadrop inmicrobialactivity.Itcanthusbeconcludedthat,inlargeaerobicgranules,acetate ororganicsubstratewouldnotbealimitingfactor,andthewholemicrobialprocess wouldbedominatedbytheavailabilityofDOinsidetheaerobicgranule. 8.4.4 DIFFUSION PROFILES OF SUBSTRATE IN AEROBIC GRANULES AT D IFFERENT BULK SUBSTRATE CONCENTRATIONS The results presented in gures 8.6 and 8.7 were obtained at a xed bulk COD con- centration of 465 mg L –1 , the effect of bulk COD concentration on the mass diffusion in aerobic granule is not taken into account. In order to clarify this point, the COD 53671_C008.indd 139 10/29/07 7:20:13 AM © 2008 by Taylor & Francis Group, LLC © 2008 by Taylor & Francis Group, LLC outaerobicgranuleswiththeradiusof0.1to0.4(gure8.6aandb).Incontrast,the 140 Wastewater Purification prolesinanaerobicgranulewithradiusof0.5mmweresimulatedatdifferentbulk COD concentrations of 100, 200, and 300 mg L –1 ,respectively(LiandLiu2005). Figure8.8showssolubleCODcanpenetratethroughtheentireaerobicgranuleat abulkCODconcentrationof300mgL –1 or above, while COD becomes a limiting factor and sharply drops to nil at depths of 0.25 and 0.1 mm at the bulk COD con - centrationsof100and200mgL –1 , respectively. This suggests that COD availability mayalsobealimitingfactorformicrobialgrowthatlowconcentrations,andthisis stronglydependentonthelevelofexternalsubstrateconcentrationinbulksolution. Radius (mm) 0.00 0.02 0.04 0.06 0.08 0.10 COD (mg L –1 ) 0 200 400 600 800 1000 COD (mg L –1 ) 0 200 400 600 800 1000 COD (mg L –1 ) 0 200 400 600 800 1000 COD (mg L –1 ) 0 200 400 600 800 1000 COD (mg L –1 ) 0 200 400 600 800 1000 Radius (mm) 0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 0.5 0.00 0.25 0.50 0.75 (a) (b) Radius (mm) (c) Radius (mm) (d) 0.0 0.2 0.4 0.6 0.8 1.0 Radius (mm) (e) FIGURE 8.6 Substrateprolesinaerobicgranuleswithradiusesof0.10(a),0.40(b), 0.50 (c), 0.75 (d), and 1.00 mm (e). (Data from Li, Y. and Liu, Y. 2005. Biochem Eng J 27: 45–52.) 53671_C008.indd 140 10/29/07 7:20:15 AM © 2008 by Taylor & Francis Group, LLC © 2008 by Taylor & Francis Group, LLC [...]... of aerobic granules in a sequencing batch reactor J Biotechnol 105: 71 82 Laspidou, C S 2003 Modeling heterogeneous biofilms including active biomass, inert biomass and extracellular polymeric substances Ph.D thesis, Northwestern University, Evanston, IL Li, Y and Liu, Y 2005 Diffusion of substrate and oxygen in aerobic granule Biochem Eng J 27: 45–52 Liu, Q S 2003 Aerobic granulation in a sequencing. .. Biotechnol Bioeng 28: 314–3 28 Wilen, B M., Gapes, D., and Keller, J 2004 Determination of external and internal mass transfer limitation in nitrifying microbial aggregates Biotechnol Bioeng 86 : 445–457 Yang, S F., Liu, Q S., Tay, J H., and Liu, Y 2004 Growth kinetics of aerobic granules developed in sequencing batch reactors Lett Appl Microbiol 38: 106–112 © 20 08 by Taylor & Francis Group, LLC © 20 08 by Taylor... removal kinetics by aerobic granules is size dependent (figures 8. 1 and 8. 4) In order to investigate the interaction of diffusion and reaction in aerobic granules, the effectiveness factor ( ) was calculated and further compared with the determined from experiments with different-sized aerobic granules (figure 8. 11) It can be seen in figure 8. 11 that both theoretical and experimental values are in good... and Heijnen 19 98; Laspidou 2003) As shown in figures 8. 8 and 8. 9, diffusion of substances in aerobic granules is a dynamic process, and is interrelated with one another The approach presented here may offer a more reasonable tool for the study of diffusion phenomena in aerobic granules 8. 4.6 PREDICTION OF BULK SUBSTRATE CONCENTRATION IN AN AEROBIC GRANULES REACTOR According to equation 8. 16, the substrate... in is observed However, the effectiveness factor decreases quickly with the further increase of radius of the aerobic granules, which indicates that the mass transfer limitation begins to play an important role in the overall reaction of aerobic granules This is in good agreement with the results presented in figures 8. 5 and 8. 6 8. 5 CONCLUSIONS Mass diffusion limitation in aerobic granules result in. .. oxygen penetration depth in a sequential batch airlift reactor was smaller than the acetate penetration depth However, this point would be valid only when the substrate concentration is high, whereas it is invalid in the case where substrate is the limiting factor, as shown in figure 8. 8 In addition, in modeling biofilm, substrate was regarded as the limiting substance without taking account of the oxygen... activity has been ignored © 20 08 by Taylor & Francis Group, LLC © 20 08 by Taylor 142 53671_C0 08. indd & Francis Group, LLC 10/29/07 7:20:19 AM Diffusion of Substrate and Oxygen in Aerobic Granules 143 (figures 8. 8 and 8. 9) In another study on activated sludge by Beun, Heijnen, and van Loosdrecht (2001), the oxygen profile in activated sludge floc was considered dynamic, but the interrelation between oxygen... of aerobic granules in a reactor REFERENCES Bailey, J E and Ollis, D F 1 986 Biochemical engineering and fundamentals, 2nd ed New York: McGraw-Hill Beun, J J., Heijnen, J J., and van Loosdrecht, M C M 2001 N removal in a granular sludge sequencing batch airlift reactor Biotechnol Bioeng 75: 82 –92 Beun, J J., Hendriks, A., van Loosdrecht, M C M., Morgenroth, E., Wilderer, P A., and Heijnen, J J 1999 Aerobic. .. granules; and (2) the size of the aerobic granules needs to be properly controlled in order to maximize their metabolic activity According to Li and Liu (2005), the inflection points in figure 8. 10a to d indeed represent a turning point from oxygen limitation to substrate limitation Under the condition of oxygen limitation, the substrate removal rate is determined mainly by the availability of dissolved... Substrate and Oxygen in Aerobic Granules 8 DO (mg L–1) 10 8 DO (mg L–1) 10 6 4 2 6 4 2 0 0.00 0 0.02 0.04 0.06 0. 08 0.10 0.0 0.1 0.2 0.3 Radius (mm) (a) (b) 10 8 8 DO (mg L–1) 10 DO (mg L–1) 0.4 Radius (mm) 6 4 2 6 4 2 0 0 0.0 0.1 0.2 0.3 0.4 0.5 0.00 Radius (mm) (c) 0.25 0.50 0.75 Radius (mm) (d) 10 DO (mg L–1) 8 6 4 2 0 0.0 0.2 0.4 0.6 0 .8 1.0 Radius (mm) (f) FIGURE 8. 7 Oxygen profiles in aerobic granules . 145 References 146 8. 1 INTRODUCTION Up-to-date, intensive research has been dedicated to the effect of various operating parameters on aerobic granulation in sequencing batch reactors (SBRs) (chapters 1 to7).However,verylimitedinformationiscurrentlyavailableaboutthediffusion behaviorsofsubstancesinsideaerobicgranules.Tayetal.(2002)foundthatamodel dye. aggregates. Biotechnol Bioeng 86 : 445–457. Yang,S.F.,Liu,Q.S.,Tay,J.H.,andLiu,Y.2004.Growthkineticsofaerobicgranulesdevel - oped in sequencing batch reactors. Lett Appl Microbiol 38: 106–112. 53671_C0 08. indd 147. In addition,inmodelingbiolm,substratewasregardedasthelimitingsubstancewith - outtakingaccountoftheoxygen(Picioreanu,vanLoosdrecht,andHeijnen19 98; Laspidou2003).Asshowningures8.8and8.9,diffusionofsubstancesinaerobic granulesisadynamicprocess,andisinterrelatedwithoneanother.Theapproach presented