Modelling anaerobic, aerobic and partial nitritation-anammoxgranular sludge reactors - A review
Janis E. Baeten a, *, Damien J. Batstone b, Oliver J. Schraa c, Mark C.M. van Loosdrecht d,Eveline I.P. Volcke a
a Department of Green Chemistry and Technology, Ghent University, Belgiumb Advanced Water Management Centre, The University of Queensland, Australiac inCTRL Solutions Inc., Dundas, Ontario, Canadad Department of Biotechnology, Delft University of Technology, the Netherlands
a r t i c l e i n f o
Article history:Received 10 August 2018Received in revised form18 October 2018Accepted 10 November 2018Available online 13 November 2018
Wastewater treatment processes with granular sludge are compact and are becoming increasinglypopular. Interest has been accompanied by the development of mathematical models. This contributionsimultaneously reviews available models in the scientific literature for anaerobic, aerobic and partialnitritation-anammox granular sludge reactors because they comprise common phenomena (e.g. liquid,gas and granule transport) and thus pose similar challenges. Many of the publications were found to haveno clearly defined goal. The importance of a goal is stressed because it determines the appropriate modelcomplexity and helps other potential users to find a suitable model in the vast amount of literature.Secondly, a wide variety was found in the model features. This review explains the chosen modellingassumptions based on the different reactor types and goals wherever possible, but some assumptionsappeared to be habitual within fields of research, without clear reason. We therefore suggest furtherresearch to more clearly define the range of operational conditions and goals for which certain simpli-fying assumptions can be made, e.g. when intragranule solute transport can be lumped in apparentkinetics and when biofilm models are needed, which explicitly calculate substrate concentration gra-dients inside granules. Furthermore, research is needed to better mechanistically understand detach-ment, removal of influent particulate matter and changes in the mixing behaviour inside anaerobicsystems, before these phenomena can be adequately incorporated in models. Finally, it is suggested toperform full-scale model validation studies for aerobic and anammox reactors. A spreadsheet in thesupplementary information provides an overview of the features in the 167 reviewed models.
Granular sludge technology underpins key emerging andestablished technologies for wastewater treatment across indus-trial and municipal sectors. Pollutant removal in these reactorsrelies on microorganisms that grow in approximately sphericalaggregates (biofilms) that can freely move within the reactor.Compared to flocs, granules have a higher biomass density and amore regular shape, they are mechanically stronger and they canbecome larger (Liu and Tay, 2004). These characteristics can lead tomicroscale substrate concentration gradients inside the aggregates,but even more importantly, they lead to high settling velocities(Winkler et al., 2018). Fast settling is the common benefit of alltypes of granular sludge. It facilitates solid-liquid separation andtherefore allows high reactor biomass concentrations (Nicolellaet al., 2000). In addition, granular sludge reactors provide a highbiofilm specific surface area (Morgenroth, 2008) and the geometryand free movement of granules limits external boundary layer re-sistances, promoting mass transfer of substrate towards the or-ganisms. The combination of the high biomass concentration andfast mass transfer allows high removal rates, ultimately enablingcompact installations (Heijnen et al., 1993).
Anaerobic granular sludge has been applied in upflow sludgeblanket reactors since the 1970s (Lettinga et al., 1980) and later invariations of this technology, to remove organic pollution fromwastewater through biological conversion into biogas. The poten-tial to recover energy in compact installations with a low sludgeproduction made anaerobic granular sludge technologies verypopular (van Lier, 2008), especially for industrial wastewaters.Aerobic treatment processes using small spherical carriers forbiofilm growthwere developed in the 1970s for removal of organicsand ammonium (Jeris et al., 1977), later combined with nitrate andnitrite removal under anoxic conditions, via denitrification (Nuttet al., 1984). Self-sustained granules for aerobic treatment onlybecame feasible much later, with the development of a sequencingbatch reactor technology, which also enables biological phosphorusremoval (de Kreuk and van Loosdrecht, 2004). This has evolved intoa mature technology with distinct benefits compared to conven-tional activated sludge systems. It requires 25e75% less space duehigh biomass concentrations and the absence of settling tanks andit has 20e50% lower energy demands due to the lack of recycle andsludge return pumps and mixers (Pronk et al., 2017). Moreover, thewaste sludge offers potential for recovery of valuable biopolymers(Lin et al., 2015). The discovery of the anammox reaction (Mulderet al., 1995) stimulated the development of a third important typeof granular sludge technology. One-stage partial nitritation-
anammox is now frequently used to treat nitrogen-rich wastewa-ters (Lackner et al., 2014). This also offers potential for the recoveryof phosphorus, because it can accumulate inside the granules(Johansson et al., 2017). Granular sludge is also promising foremerging biological treatment processes, such as phototrophicprocesses (Abouhend et al., 2016) and sulfide-based organicsremoval (Hao et al., 2013) and denitrification (Yang et al., 2016), butthese are not yet available at commercial scale.
Modelling is a widely acknowledged tool for fundamental un-derstanding, design and optimization of wastewater treatmentprocesses (van Loosdrecht et al., 2008). Reviews on wastewatertreatment models have generally focussed on either anaerobic(Batstone et al., 2015; Liotta et al., 2015; Sadino-Riquelme et al.,2018; Tomei et al., 2009) or aerobic processes (Hauduc et al.,2013; Karpinska and Bridgeman, 2016; Liotta et al., 2014),because these require different redox conditions. Except forNicolella et al. (2000), Liu and Tay (2004) and Milferstedt et al.(2017a), reviews focussing on granular sludge have discussedanaerobic (Chong et al., 2012; Saravanan and Sreekrishnan, 2006;Schmidt and Ahring, 1996) and aerobic processes (Bengtsson et al.,2018; Ni and Yu, 2010a; Winkler et al., 2018) separately as well.However, from a physical and chemical point of view, anaerobic,aerobic and partial nitritation-anammox granular sludge reactorsshare much in common, such as hydrolysis of particulate sub-strates, interactions between gas bubbles and the water phase,mass transfer of substrates from the bulk liquid to the granulesurface and acid-base reactions. Also stable granule formationprobably relies on the same interplay between mass transfer ofsolutes, conversion rates and detachment forces (van Loosdrechtet al., 2002). Therefore, modelling these different reactors poseslargely the same challenges.
This review discusses models of anaerobic, aerobic and partialnitritation-anammox granular sludge reactors together to assesscommonalities and discrepancies in approaches. First, the scope ofthe review is defined. Next, the different modelling goals of thestudies are discussed. The twomain sections describe differences inassumptions about transport phenomena and transformations andexplain them based on the different reactor types and modellinggoals wherever possible. As such, suggestions for further modellingstudies are extracted and habitual assumptions and gaps in theknowledge are identified. Afterwards, the trends, advantages anddisadvantages of model complexity are discussed. Next, the avail-ability of calibration and validation studies for different reactorscales is discussed and finally, future research needs aresummarized.
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2. Scope and key phenomena
2.1. Scope of the review
This review focuses on mechanistic models for reactors withmixed microbial granules published in the English scientific liter-ature. The review was limited to anaerobic, aerobic and partialnitritation-anammox (often referred to as simply ‘anammox’further on) granular sludge reactors that are commercially avail-able, as these are commonly applied and numerous modellingstudies exist. Eight different reactor types with or without smallcarriers were identified: upflow sludge blanket, expanded granularsludge bed, internal circulation, baffled, fluidized bed, air-lift,sequencing batch and simple aerated reactors (Fig. 1). Mecha-nistic models are here understood asmodels that are based onmassbalances with transport and reaction terms. Models that onlydescribe batch tests were not considered, because the focus is on
Fig. 1. Several granular sludge reactor types are available commercially for different biologicfor the removal of organics and/or nitrogen and/or phosphorus and partial nitritation-anam
models for operational reactors as a whole, meaning they canpredict the effluent concentration of at least one substrate (i.e.pollutant). In case more than one model for a single reactor typewas described in a publication, only the model that the authorslabelled as the most accurate or reference was analyzed.
With these selection criteria, this review covers 164 publicationsincluding 167 models (Table 1 provides an overview and thespreadsheet in supplementary information shows the model fea-tures). Omitting yearly fluctuations, there has been an increase inpublication rate from the first publication in 1981 until 1997, fol-lowed by a brief decline and then another increase until it stag-nated around 2006 (Fig. 2A). The first publications modellingaerobic systems described fluidized bed and air-lift reactors, butmost models for aerobic systems were developed for sequencingbatch reactors (Fig. 2B) because the focus shifted almost completelysince 2001, preceding the commercialization of this technology (deKreuk et al., 2007a). Anaerobic granular sludge models appeared a
al conversion processes: anaerobic systems for the removal of organics, aerobic systemsmox systems for nitrogen removal.
Table 1Publications selected for analysis by process and reactor type.
Anaerobic - Upflow sludge blanket Anaerobic - Expanded granular sludge bed Aerobic - Sequencing batchBolle et al. (1986) Pontes and Pinto (2006) Beun et al. (2001)Costello et al. (1991a, 1991b) Ersahin et al. (2007) Lübken et al. (2005)Sam-soon et al. (1991) Chou et al. (2008) Su and Yu (2006a, 2006b)Alvarez et al. (1992) Saravanan and Sreekrishnan (2008) de Kreuk et al. (2007b)Hwang et al. (1992) Wang et al. (2010) Xavier et al. (2007)Borja and Banks (1994) Chou et al. (2011a) Ni et al. (2008)Borja et al. (1994) Fuentes et al. (2011) Fang et al. (2009)Lin and Yang (1995) Lopez and Borzacconi (2011) Ni et al. (2009)Cuervo-Lopez et al. (1996) Vafajoo and Beigy (2013) Ni et al. (2010)Kalyuzhnyi and Fedorovich (1997) Ghorbanian et al. (2014a) Ni and Yu (2010b)Wu and Hickey (1997) Ghorbanian et al. (2014b) V�azquez-Padín et al. (2010)Castillo et al. (1999) Yang et al. (2015) Chou et al. (2011b)Kennedy et al. (2001) Odriozola et al. (2016) Huang et al. (2011)Skiadas and Ahring (2002) Anaerobic - Internal circulation Cui and Kim (2013)Batstone and Keller (2003) Sun et al. (2012) Isanta et al. (2013)Elmitwalli et al. (2003) Xu et al. (2013) Su et al. (2013)Fedorovich et al. (2003) Wang et al. (2015) Zhou et al. (2013)Huang et al. (2003) Feldman et al. (2017) Kagawa et al. (2015)Jih et al. (2003) Anaerobic - Fluidized bed Winkler et al. (2015b)Kleerebezem (2003) Furumai et al. (1991) Zhao et al. (2016)Batstone et al. (2004) Costello et al. (1991a, 1991b) Manea et al. (2017)Chowdhury and Mehrotra (2004) Labib et al. (1992) Kim and Cui (2017)Batstone et al. (2005) Ryhiner et al. (1993) Aerobic - Air-liftChou and Huang (2005) Borja et al. (1995) Tang and Fan (1987)Isik and Sponza (2005) Wu and Huang (1995) Tang et al. (1987)Elmitwalli et al. (2006) La Motta and Cascante (1996) Livingston (1991)Huang et al. (2006) Prakash and Kennedy (1996) van Loosdrecht et al. (1995)Kalyuzhnyi et al. (2006) Schwarz et al. (1996) Garrido et al. (1997)Soroa et al. (2006) Suidan et al. (1996) Picioreanu et al. (1997)Pontes and Pinto (2006) Wu and Huang (1996) Mousseau et al. (1998)Angulo et al. (2007) Bonnet et al. (1997) Aerobic - Fluidized bedMu et al. (2007) Schwarz et al. (1997) Tanaka et al. (1981)Vlyssides et al. (2007a) Buffiere et al. (1998) Denac et al. (1983)Vlyssides et al. (2007b) Wu et al. (1998) Stevens et al. (1989)Bhunia and Ghangrekar (2008) Perez et al. (2001) Wisecarver and Fan (1989)Mu et al. (2008a), Tartakovsky et al. (2008) Seok and Komisar (2002) Wang Shi and Zhou (1994)Mu et al. (2008b) Seok and Komisar (2003a, 2003b) Ravindran et al. (1997)Narayanan and Narayan (2008) B�eteau et al. (2005) Hirata et al. (2000)Sponza and Uluk€oy (2008) Fuentes et al. (2005) Tsuneda et al. (2002)Fuentes et al. (2009a) Mussati et al. (2006) Pons et al. (2008)L�opez and Borzacconi (2009) Fuentes et al. (2007) Seifi and Fazaelipoor (2012)Lopez et al. (2009) Fuentes et al. (2008c) Anammox -AeratedDereli et al. (2010) Fuentes et al. (2008b) Volcke et al. (2010)Diamantis and Aivasidis (2010) Fuentes et al. (2008a) Van Hulle et al. (2012)Lopez and Borzacconi (2010) Fuentes et al. (2009b) Vangsgaard et al. (2012)Rodriguez and Moreno (2010a) Fuentes et al. (2009c) Volcke et al. (2012)Rodriguez and Moreno (2010b) Sudibyo et al. (2017) Mozumder et al. (2014)Zhao et al. (2010) Anaerobic e Baffled Hubaux et al. (2015)Turkdogan-Aydinol et al. (2011) Bachmann et al. (1985) Winkler et al. (2015a)Coskun et al. (2012) Setiadi et al. (1996) Castro-Barros et al. (2018)Thamsiriroj et al. (2012) Faisal and Unno (2001) Anammox - Sequencing batchWillquist et al. (2012) Kennedy and Barriault (2007) Jones et al. (2007)Yetilmezsoy (2012) Doaa et al. (2013) Wett et al. (2010)Yu et al. (2012) Antonopoulou et al. (2015) Corbala-Robles et al. (2016)Rodriguez-Gomez et al. (2013) Bustillo-Lecompte and Mehrvar (2016)Rodriguez-Gomez et al. (2014) Li et al. (2016a)Chen et al. (2015) Li et al. (2016b)Haugen et al. (2015) Shi et al. (2016)Lohani et al. (2016)Rodriguez-Gomez and Renman (2016)Sun et al. (2016)Pokorna-Krayzelova et al. (2017)
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few years after the invention of the technology (Lettinga et al.,1980). Models for upflow sludge blanket reactors are by far themost abundant in literature, followed by anaerobic fluidized bedreactors (Fig. 2B), but interest in the latter type has sharply declinedin the last decade, as application of the technology also decreased(van Lier et al., 2016). In 2007, the first model for one-reactor partialnitritation-anammox granular sludge was published, quicklyfollowing the full-scale implementation of the technology (Wett,2007).
2.2. Key phenomena in granular sludge reactors
A number of key phenomena (based on Wanner et al. (2006))that occur in granular sludge reactors can be included in models(Fig. 3).
� Transformations. Both biological conversions (e.g. nitrification)and purely physico-chemical reactions occur, such as precipi-tation and acid-base reactions. These are the main drivers for
Fig. 2. Number of published models for granular sludge reactors over time (A) and perreactor type (B).
J.E. Baeten et al. / Water Research 149 (2019) 322e341326
the removal of pollutants (e.g. ammonia, organics or phosphate)and production of sludge (biomass and precipitates).
� Liquid phase transport. Liquid flows through a reactor with acertain pattern, influencing the transport of solutes and colloidalmatter through advection. The hydraulics determine whetherthe liquid phase is well-mixed or shows spatial gradients.
� Granule transport. Granules move as a result of gravity, dragand contact forces (e.g. collision with a separator). The balance
Fig. 3. The key phenomena that occur inside every granular sludge reactor. The selected modto sections of this review were the model features are discussed.
of these forces regulates the retention of granules inside thesystem and the distribution of biomass along the reactor height.There is a mutual interaction between the movement of gran-ules (solid phase) and liquid.
� Intragranule transport. Solutes move through the granulematrix primarily via diffusion, but also advection can take placevia pores. Together with the biological conversions and physico-chemical reactions, this determines the concentration gradientsinside granules. Also matrix-embedded particles and microor-ganisms move, which influences the microbial population dis-tribution inside granules.
� Liquid-granulemass transfer. Solutes are exchanged across theexternal mass transfer boundary layer surrounding granules andare subsequently potentially adsorbed onto the biofilm matrix.These processes can influence the removal rate of pollutantsfrom the wastewater. Also, exchange of particulate componentsthrough detachment and attachment occurs. This can affect themicrobial population distribution inside granules and thegranule size.
� Granule transformations and size distribution. Granules cangrow, shrink and break up. Together with granule transport (e.g.wash-out of small granules), this determines the size distribu-tion, which ranges from small flocs to millimetre thick granules(Pereboom, 1994; Pronk et al., 2015; Vlaeminck et al., 2010).
� Gas phase transport. The gas phase (air or biogas) mostlymoves upwards due to buoyant forces, but can also flowdownwards, e.g. in the downcomer of air-lift reactors. The gastransport mutually interacts with the liquid phase transport.The different gas-phase constituents, such as oxygen (O2), car-bon dioxide (CO2), methane (CH4), hydrogen sulfide (H2S),nitrous oxide (N2O), nitric oxide (NO) and nitrogen gas (N2), canbe well-mixed or show concentration gradients.
� Liquid-gas mass transfer. Components such as oxygen andmethane experience a resistance when exchanged between thegas and the liquid phase due to stagnant layers on the inside andoutside of a bubble. This resistance determines themass transferrate and therefore affects the distribution of compounds be-tween the liquid and gas-phase.
els were analyzed based on their assumptions for these phenomena. The numbers refer
J.E. Baeten et al. / Water Research 149 (2019) 322e341 327
� Heat transport and production. Heat enters and leaves via theliquid, through work done by mechanical equipment, andthrough heat exchange with the environment, while biologicalconversions and physico-chemical reactions can produce heat.These phenomena determine the temperature (distribution) inthe reactor.
A spreadsheet in the supplementary information provides acomplete overview of the assumptions that were made for thesekey phenomena in all the analyzed models. It also indicates theapplications that were proposed or demonstrated, the scale of thelargest modelled reactor, whether calibration and/or validationwasperformed and which software was used for modelling and simu-lation. This spreadsheet is available as a tool for practitioners andscientists to find an appropriate model to tackle their specificproblem.
3. Modelling goal
Given the vast number of published models and the variationamong them, it becomes ever more important to specifically statethe model purpose in every publication. Still, one third of theanalyzed models had no specific goal e or at least it was not clearlydefined. The publications may state that the model is capable ofcharacterisation, description, understanding, prediction, simula-tion, design, optimization or control of a system, but this is verygeneral. It does not differentiate the model in comparison withother available models. For example, if a model is said to be suitablefor design, it is not clear whether this means that it can determinethe required reactor volume, the optimal height to width ratio orthe required capacity of aerators. Therefore we did not considersuch general applications or goals. This does not mean that themodels are not useful, only that the applications are not clearlycommunicated.
Generally speaking, three different types of applications ofgranular sludge reactor models could be distinguished (Table 2).The first type is to gain fundamental insight in the relationshipbetween micro- and mesoscale phenomena (e.g. intragranuletransport) and macroscale reactor operation (e.g. influent charac-teristics) and performance (e.g. effluent quality). The second type isthe assessment of alternative operational strategies or reactor/plantdesigns to have a better overall reactor performance. For this, mi-cro- or mesoscale phenomena were sometimes included, but onlythe prediction of the macroscale reactor behaviour was of interest.Finally, the third application is to extract more information frommeasurements, e.g. about the microbial activity. Of course, thispragmatic classification of goals is not absolute, e.g. models that areprimarily used for fundamental insight are often used also fordesign and optimization and some models that were purely used
Table 2Different types of applications that can be distinguished for published granular sludge r
Application Description
Insight Understand the relationship between small scale phenomenalarge scale operation or performance
Design/optimization Assess the effect of alternative operational strategies or designon the reactor/plant performance
Monitoring Extract the value of unmeasured variables from measurement
for design/optimization questions in a publication also have po-tential to gain more fundamental insight. Still, it gives a structure tothe vast amount of publications.
4. Transport and mass transfer phenomena
This section discusses how transport of substrates and organ-isms inside the liquid, granule and gas phase or transport of thesephases themselves has been included in models to calculatedifferent kinds of spatial heterogeneity in a reactor. Fig. 4 illustratesthe multi-scale nature of this spatial heterogeneity, which will befurther elaborated in the subsections.
4.1. Liquid phase transport
Liquid phase transport patterns depend on the reactor geometry(Hu et al., 2017), inlet flow (Wang et al., 2009), inlet distribution(Asif et al., 1992) and gas production or injection (Buffiere et al.,1998). For anaerobic granular sludge reactors, the absence ofaeration-induced mixing explains why spatial concentration gra-dients of soluble compounds are often considered (Fig. 5). This wasdone assuming an ideal plug flow (Bonnet et al., 1997; Wang Shiand Zhou, 1994), combinations of tanks (Bolle et al., 1986; Tanakaet al., 1981), the advection-dispersion equation (Kalyuzhnyi et al.,2006; Seifi and Fazaelipoor, 2012) or computational fluid dy-namics (CFD) (Yang et al., 2015). The latter is the only techniquethat can predict the mixing behaviour instead of assuming it. Onlysome authors verified the hydraulic behaviour using tracer tests ormeasurements of concentration profiles in the specific modelledreactor (Huang et al., 2003; Lin and Yang, 1995). No studiesexperimentally verified completemixing in baffled, fluidized bed orinternal circulation reactors, even though it has been assumed. Itseems contradictory that an ideal plug flow or non-ideal flow hasbeen assumed slightly more often for large scale than for lab-scaleanaerobic sludge blanket reactors (zoom on Fig. 5) because exper-iments have shown that mixing improves with the scale (Batstoneet al., 2005). In expanded granular sludge bed reactors, both thor-ough mixing (Chou et al., 2008; Fuentes et al., 2011) and (semi-)plug flow behaviour has been observed (Yang et al., 2015; Zhenget al., 2012) on both large- and small scale.
Because the liquid phase transport can differ even between twoanaerobic reactors of the same type, tracer tests or measurementsof gradients are preferredwhenever possible. If the reactor is still tobe built, e.g. if a model is used for design, tracer tests from reactorswith a similar scale, operation and construction can give anapproximation, but also preliminary CFD calculations (with asimplified conversion model) could help find an appropriateassumption. For baffled reactors in particular, the experimentalevidence and physical compartmentation encourages to always
eactor models.
Specific examples
and - Microbial competition for substrate (Kalyuzhnyi and Fedorovich, 1997)- Role of internal storage compounds (Beun et al., 2001)- Microbial interactions inside granules (Corbala-Robles et al., 2016)- Degree of mixing (Wu and Hickey, 1997)- Intragranule and external mass-transfer resistances (Huang et al., 2011)- Bicarbonate addition (Batstone and Keller, 2003)- On-line temperature control (Angulo et al., 2007)- Selective retention of granules (Wett et al., 2010)- Required aeration capacity and recirculation flow (Tanaka et al., 1981)- Minimal required reactor volume (Lohani et al., 2016)
s - Monitoring microbial populations/activity (L�opez and Borzacconi, 2009)
Fig. 4. Examples of spatial heterogeneity predicted by considering different transport processes. (A) Distribution of degradation rates of substrates in an expanded granular sludgereactor (figure reused with permission from Yang et al. (2015)), simulated through detailed modelling of liquid phase transport (section 4.1). (B) Distribution of biomass along theheight of an upflow sludge blanket reactor (data of phase 1 from Fig. 4 extracted from Tartakovsky et al. (2008)), simulated by considering granule transport (section 4.2.1). (C)Biomass and dissolved oxygen (DO) distributions inside aerobic granules in a sequencing batch reactor (figure reused with permission from Kagawa et al. (2015)), estimated byexplicitly modelling intragranule transport (section 4.2.2). AOB are ammonium oxidizing bacteria, NOB nitrite oxidizing bacteria, Het heterotrophs, PAO phosphate accumulatingorganisms and GAO glycogen accumulating organisms. (D) Evolution of the granule size distribution over time (data of case 4 from Fig. 4 extracted from Su et al. (2013)), estimatedby considering granule transformations and several size classes (section 4.2.4).
Fig. 5. Frequency distribution of assumptions regarding the liquid phase transport.
J.E. Baeten et al. / Water Research 149 (2019) 322e341328
assume a non-ideal flow (Bachmann et al., 1985; Li et al., 2016b).Finally, (semi-)plug flow behaviour is essential for specific appli-cations, e.g. to assess the effect of an internal recirculation flow (Muet al., 2008a) or short-circuiting (Bolle et al., 1986).
For aerobic and partial nitritation-anammox reactors, the choiceof a flow pattern is often more straightforward because active airinjection induces mixing. Only for fluidized bed reactors, tracertests andmeasurements of concentration gradients have confirmedthat complete mixing cannot always be assumed (Seifi andFazaelipoor, 2012; Stevens et al., 1989), which is reflected inFig. 5. For one-stage partial nitritation-anammox reactors, theassumption of a completely mixed liquid phase has not yet receivedexperimental verification, even though it seems a reasonableassumption due to the active aeration. For aerobic sequencing batchreactors, it is known that semi-plug flow behaviour exists duringthe unaerated feeding phase, but this has not been considered inwhole-reactor models yet (Weissbrodt et al., 2017).
4.2. Granules
4.2.1. Granule transportNo heterogeneous vertical distribution of biomass is considered
in aerobic and anammox-based granular sludge reactors (exceptsometimes during a settling phase). This is justified by the air-induced mixing of the sludge bed. In contrast, a vertical biomassconcentration profile is considered in 31% of the anaerobic granular
Fig. 6. Different approaches to model granule retention and intragranule solutetransport: apparent kinetics and loss of granules via the effluent are common foranaerobic systems (right), while a biofilm model with perfectly retained granules ismore popular for aerobic and anammox-based granular sludge reactors (left).
J.E. Baeten et al. / Water Research 149 (2019) 322e341 329
sludge models because it is also often experimentally observed(Lettinga et al., 1980; Wu and Huang, 1996). Sometimes the profileis predefined in the model based on measurements (Feldman et al.,2017) or an educated guess (Sam-soon et al., 1991), but often theprofile is predictedmoremechanistically throughmass transport asa result of upward drag forces and gravity acting upon the sludgebed (Bolle et al., 1986; Bonnet et al., 1997). Only when plug flowcharacteristics are considered, do the simulated effluent concen-trations become sensitive to the assumption of a vertical biomassdistribution. An uneven distribution of biomass has no effect on thereactor performance if the liquid phase is completely mixed.
To avoid that the simulated biomass concentration becomesunrealistically high, models with biomass growth need to includewashout from the reactor as well, apart from decay. Models foranaerobic reactors often (49%) consider imperfect retention ofgranules by imposing a predefined solids retention time (Eq. (1)), assuggested in the ADM1 report (Batstone et al., 2002), or by using afixed solids separation efficiency (Bolle et al., 1986).
dXreactor;i
dt¼ QinXin;i
Vreactor� Xreactor;i
SRTþX
ri (1)
where Xreactor,i represents the concentration of a microbial group i(or other particulate variable) in the reactor, Xin,i its concentrationin the influent (g.m�3), Qin the influent flow (m�3.d�1), Vreactor thereactor volume (m3), SRT the solids retention time (d) and ri theconversion rates of the group, e.g. of decay and growth (g.m�3.d�1).Sometimes the degree of retention is incorporated more mecha-nistically via the settling behaviour of granules and advectiveupflow (Kalyuzhnyi et al., 2006; Saravanan and Sreekrishnan,2008), as described above for granule transport inside the reactor.
Only a few models for aerobic and partial nitritation-anammoxreactors estimate the washout of granules via a fixed separationefficiency (Wett et al., 2010) or mechanistic settling behaviour(Kagawa et al., 2015; Su et al., 2013). In fact, most aerobic (87%) andanammox (80%) models that consider biomass growth, assume thatgranules are perfectly retained (Beun et al., 2001; Stevens et al.,1989; Tang et al., 1987; Volcke et al., 2010). This means that nogranules are lost via the effluent, but loss of biomass throughdetachment followed by wash-out of suspended cells or by inten-tional sludge removal can still be considered. The two approachescan also be combined by defining a perfectly retained granulefraction and imperfectly suspended biomass fraction (Corbala-Robles et al., 2016; Hubaux et al., 2015; Pons et al., 2008).
It is not immediately clear why imperfect granule retention is socommon for anaerobic systems, while perfect retention is oftenused for aerobic and anammox systems (Fig. 6). It could be partlyhabitual within each of these scientific domains. Possibly, authorsinterested in modelling anaerobic systems were inspired by pre-viousmodels of such systems and those about tomodel aerobic andanammox systems based their assumptions on existing models ofthese systems respectively. As such, a habit can arise. A fewmodelsdid not consider any retention of biomass compared to the liquidphase (i.e., HRT ¼ SRT) (Ghorbanian et al., 2014a, b, Setiadi et al.,1996, Shi et al., 2016). This last approach misses one of the keycharacteristics of granular sludge reactors, namely that granulessettle fast and are therefore easily retained, reach high concentra-tions and as such allow high volumetric conversion rates.
4.2.2. Intragranule transportModels of granular sludge reactors can be divided into twomain
categories: those that consider the intragranule transport (biofilmmodels) and those that treat biomass as a suspension in the liquidphase (using apparent kinetics). Biofilm models calculate themacroscale conversion rate by solving the mass-balance of
substrates inside granules. The intragranule substrate concentra-tion profile and related flux are derived considering simultaneousconversion and diffusion (Wanner et al., 2006), e.g. Eq. (2) assumesMonod kinetics and 1D radial transport.
Biofilm model :vCiðz; tÞ
vt Accumulation
¼ Di
v2Ciðz; tÞ
vz2þ 2
zvCiðz; tÞ
vz
!Diffusive transport
þ ri;maxCiðz; tÞXiðz; tÞCiðz; tÞ þ KReaction
(2)
where Ci is the local substrate concentration (g.m�3) at a certaindistance from the granule core z (m) at time t (d), Di the substratediffusivity, ri,max the maximum specific substrate uptake rate(g.m�3.d�1), Xi the local biomass concentration responsible for theconversion (g.m�3) and K the intrinsic half-saturation coefficient(g.m�3). Appropriate boundary conditions are applied, normallyspherical symmetry and a bulk concentration. Biomass concentra-tions inside the granules and granule geometry (size) may belikewise included in biofilm models as state variables (see below).
Mass transport between the bulk liquid and themicroorganismsinside the biofilm decreases macroscale conversion rates comparedto suspended systemswith the same amount of biomass. This effectbecomes more pronounced with a thicker biofilm, faster localconversion rates (through a higher local biomass concentrationand/or specific uptake rate) or lower substrate diffusivity (Wang Shiand Zhou, 1994). This may be considered fundamentally, throughbiofilm modelling, as outlined above. However, when granularsludge is treated as a suspension, intragranule transport is notexplicitly simulated, so this effect on themacroscale rates should berepresented through modified kinetic parameters. ‘Apparent’ ki-netics are thus obtained, for example by increasing half-saturationcoefficients (Eq. (3)) to incorporate the diffusional resistance(Beccari et al., 1992; Manser et al., 2005; P�erez et al., 2005).
where ri,apparent is the macroscale substrate uptake rate (g.m�3.d�1)at time t (d), Ci the bulk substrate concentration (g.m�3), and Kappthe apparent half-saturation coefficient (g.m�3). Changes in thegranule size, microbial population distribution and competitionbetween different microbial groups for the same substrates, e.g.
J.E. Baeten et al. / Water Research 149 (2019) 322e341330
competition for oxygen between nitrifiers and heterotrophs, canalter the apparent kinetics, which may require (re)calibration(Baeten et al., 2018).
Only a minority explicitly modelled intragranule transport ofsubstrates (using a biofilm model) for anaerobic granular sludge(21% of the analyzed models), even though intragranule transporthas been shown to significantly influence macroscale rates for atleast sludge blanket (Wu and Hickey, 1997), expanded granularsludge bed (Chou et al., 2008) and fluidized bed reactors (Seok andKomisar, 2003b). This means that the use of apparent kinetics iswidespread for anaerobic granular sludge (77% of the reviewedmodels). In contrast, more than three quarters of the aerobic andanammox granular sludge models explicitly describe intragranulesolute transport.
It is not immediately clear why biofilm models are more com-mon for aerobic and anammox systems, while apparent kinetics aremostly used for anaerobic ones (Fig. 6). ADM1 might be morecomplex than most aerobic or anammox conversion models, but itis still reasonably technically straightforward to apply it in a biofilmmodel with dedicated software like Aquasim (Reichert, 1994). Thedifference in popularity can also not be solely explained by anincreased availability of tools or computing power, since manymodels for anaerobic systems with apparent kinetics were pub-lished in the same period as biofilm models for aerobic systems(Fig. S1). A possible explanation is that publications on aerobic(Beun et al., 2001; de Kreuk et al., 2007a; Kagawa et al., 2015;Winkler et al., 2015b) and anammox systems (Castro-Barros et al.,2018; Corbala-Robles et al., 2016; Mozumder et al., 2014; Volckeet al., 2010) often looked into intragranule substrate profiles andecological interactions between different microorganisms (insight),while those dealing with anaerobic systems generally focussedmore on overall reactor design and optimization (Batstone andKeller, 2003; Kleerebezem, 2003; Lohani et al., 2016; Mu et al.,2007; Yetilmezsoy, 2012) or were used for monitoring biologicalactivity (Lopez and Borzacconi, 2011; Perez et al., 2001).
Not only solutes, but also matrix-embedded particles and mi-croorganisms canmove throughout a granule, which influences themicrobial population distribution along the granule depth. There-fore, this distribution is dependent on the reactor operating con-ditions, even for the same type of reactor (Batstone et al., 2004).Such dynamics can be described mechanistically with an intra-granule mass balance for biomass as state variables, including re-action and transport terms, analogous to Eq. (3). This time, diffusivetransport is often neglected, but advective transport is requiredbecause a net growth of microorganisms causes biofilm geometryto move, i.e., deeper layers push outer layers outwards. Theadvective velocity of particles and microorganisms towards thegranule surface is often calculated in 1D with Eq. (4), as this is usedin Aquasim (Wanner and Reichert, 1996).
Advective velocity uadvectionðt; zÞ ¼1
AðzÞðz0
11� εl
XrXiðt; zÞrXi
AðzÞdz
(4)
were uadvection is the advective velocity of the biofilm incl. mi-croorganisms (m.d�1) at a certain distance from the granule core z(m) at time t (d), A(z) the area of a sphere with radius z (m), εl theporosity of the biofilm (�), rXi the local production rate of partic-ulate component (microbial group) i (g.m�3.d�1) and rXi the den-sity of that component (g.m�3). Individual-based models have alsobeen used to consider these dynamics in granules (Kagawa et al.,2015; Xavier et al., 2007), which considers microorganisms asdiscrete entities instead of a continuum. This approach is especiallyrelevant to study the 2D (or 3D) heterogeneity of granules (Fig. 4C),
but comes at a high computational cost (de Kreuk et al., 2007a).A dynamic microbial population distribution has been predicted
mechanistically in all the biofilmmodels for anammox reactors, butsome of the biofilm models for aerobic and anaerobic systems useda predefined distribution, either heterogeneous (Huang et al., 2006;Saravanan and Sreekrishnan, 2008; Tang et al., 1987; Wu andHickey, 1997) or homogeneous (Chou et al., 2011a; Huang et al.,2011). Huang et al. (2006) claimed that 1D biomass spatial het-erogeneity is necessary to effectively simulate the performance ofan upflow sludge blanket reactor. However, the fact that 28 of theanalyzed publications used a homogeneous distribution(Bachmann et al., 1985; Rodriguez-Gomez et al., 2014) or evenneglected all intragranule transport processes indicates that theseeffects are often lumped in apparent kinetic parameters. Moreover,it has been shown that densemicro-colonies of nitrifiers, which canonly be described in 2D or 3D, can influence themacroscale kinetics(Picioreanu et al., 2016). This shows that even kinetic parametersthat are calibrated for 1D biofilm models might cluster some pro-cesses when dense micro-colonies are present.
4.2.3. Liquid-granule transferAdsorption of solutes on the biofilm matrix is hardly ever
considered (Kennedy et al., 2001; Sam-soon et al., 1991; Tsunedaet al., 2002), even though organic compounds can adsorb ontoanaerobic granules (Ning et al., 1997) and ammonium can adsorbon anammox (Li et al., 2016c) and aerobic granules. The latter isprobably caused by the attraction between the negatively chargedgranule matrix and positively charged ammonium ions (Bassinet al., 2011). These adsorption processes could play a role in theremoval of these pollutants. The compounds are transferred fromthe liquid phase to the solid phase, decreasing their discharge withthe effluent and enabling removal with the waste sludge. At thesame time, adsorption may reduce the availability for biologicalconversions. Desorption can occur when bulk liquid concentrationsdecrease again (Bassin et al., 2011).
Solutes need to pass through an external boundary layer prior toreaching the granule surface. Its negative effect on the overallconversion rates becomes stronger when the local uptake rate in-side the biofilm or boundary layer thickness increases and whenthe limiting substrate concentration or diffusivity decreases(Picioreanu, 2015). Wu and Hickey (1997), Chou et al. (2008) andWu and Huang (1995) estimated that the external resistance wasnot rate-limiting in the upflow sludge blanket, expanded granularsludge bed and anaerobic fluidized bed reactors they respectivelystudied. Stevens et al. (1989) also found that it was not rate-limitingin an aerobic fluidized bed reactor, whereas Tang et al. (1987)judged it to be important for an airlift reactor. Vangsgaard et al.(2012) found that it can sometimes be influential for anammox-based systems. So even though the extra turbulence created byaeration in anammox-based and aerobic systems can decrease theboundary layer thickness, other influencing factors can make itseffect significant, especially a rapid oxygen uptake rate and rela-tively low bulk oxygen concentrations. Understandably, an externalmass transfer resistance is considered most often in aerobic gran-ular sludge models (31%). It is advisable for future modelling tomake a rough estimation of the effect for aerobic and anammox-based reactors under the specific operating conditions, as inStevens et al. (1989), if quantitative predictions are aimed at.Alternatively, the effect can be clustered in apparent kinetic pa-rameters if no significant changes in the turbulence or otherinfluencing factors are expected.
Also solids and microorganisms undergo liquid-granule transferthrough attachment onto the granule surface and detachment fromthe surface. Detachment has a strong impact on biofilm thickness inthe long-term (Wanner et al., 2006). Consequently, steady-state
J.E. Baeten et al. / Water Research 149 (2019) 322e341 331
simulations with biofilm models that included intragranule trans-port of microorganisms always considered detachment to avoidpredicting unrealistically large granule sizes, except for Kagawaet al. (2015), who focussed on the start-up of a reactor. Thedetachment rate is often defined with an equation to obtain aspecific predefined steady-state granule size, for example Eq. (5)was used by Volcke et al. (2010).
Detachment velocity : udetachment
¼
ddsteady�state
!10
uadvectionðdÞ (5)
where udetachment represents the detachment velocity (m.d�1), d thesimulated granule radius, dsteady�state the predefined steady-stateradius which is either measured or based on experience withsimilar systems (m) and uadvection ðdÞ is the advective velocity withwhich the granule expands due to biomass growth (Eq. (4)). Thisapproach allows a dynamic microbial population distributionwhilekeeping the granule size below a realistic limit, but it cannotactually predict the granule size. Also the convergence rate to thesteady-state size relies on the arbitrary exponent 10. A realisticconvergence rate can only be obtained a posteriori, through cali-bration of such empirical parameters (Ni et al., 2010). Finally, only afew publications considered attachment. Batstone et al. (2004)showed that modelling attachment was necessary to explain theobserved acidogenic layer in anaerobic granules treating brewerywastewater.
4.2.4. Granule transformations and size distributionThe majority of granular sludge models (82%) assume a single
granule size with a predefined steady-state value, or implicitly as-sume a constant granule size by using constant apparent kinetics.Sixteen models predict the size dynamically without a predefinedsteady-state value, but this has never been done for partialnitritation-anammox based reactors. Some predicted the granulesize without using detachment, e.g. Rodriguez-Gomez et al. (2014),meaning that the granule size is only limited by decay. The accuracyof the predicted size is doubtful for long-term simulations in thesecases. Since detachment is driven by liquid shear and granule shearstrength, its rate is a function of the operating conditions. Forexample, Odriozola et al. (2016), Su et al. (2013) and Fuentes et al.(2008a) applied an empirical equation linking the detachmentrate to the biogas production rate and liquid upflow velocity oraeration rate. The generalizability of such equations is uncertain, asthey contain an empirical parameter that might require calibrationfor different reactor operating conditions, which again makes itnon-predictive. Detachment rates can in principle be determinedmechanistically from biofilm strength and liquid shear rate (Hornand Lackner, 2014; van Loosdrecht et al., 2002). It might also bepossible to estimate the granule shear strength based on influentwastewater properties (Batstone and Keller, 2001). Yet, integratingthese aspects to fundamentally dynamically predict the granulesize has not yet been done, even though it is technically possible.Note that a dynamic granule size only affects the predicted macro-scale conversion rates directly if intragranule solute transport isincluded. Otherwise, only indirect effects are considered, such asthe better settleability of bigger granules and accompanying higherbiomass concentration, e.g. in Kalyuzhnyi et al. (2006) and Fuenteset al. (2009a).
Some models consider the size distribution of granules inside areactor. The simplest approach is to distinguish two classes, gran-ules and suspended sludge (Fuentes et al., 2008c; Hubaux et al.,2015; Pons et al., 2008), but more size classes have also beenused (Feldman et al., 2017; Huang et al., 2003; Su and Yu, 2006a;
Wu and Huang, 1996). Volcke et al. (2012) showed that the use of asingle, average granule size is sufficient to predict the effluent ni-trogen concentration and speciation from a partial nitritation-anammox reactor. Odriozola et al. (2016) also found that the pre-dicted methane production and effluent soluble substrate con-centrations were similar with and without considering the granulesize distribution in an anaerobic system. This means that a sizedistribution is only necessary for fundamental understanding, e.g.to get insight in the solute exchange between different size classes.
To get insight in the formation of a granular sludge bed, a sizedistribution as well as the dynamics of each size class need to beconsidered. This has been done in three publications (Odriozolaet al., 2016; Seok and Komisar, 2003a; Su et al., 2013). Su et al.(2013) provides the most comprehensive approach, using a popu-lation balance model for an aerobic granular sludge reactor. Apartfrom the mass balances of particulate and soluble compounds, suchmodels use balances on the number of particles in each size class,by estimating wash-out, growth, break-up into smaller pieces etc.As such, the selective retention of larger granules can be simulated,which is seen as one of the factors promoting granulation of sludge(Beun, 1999). Because this approach still relies on calibrated re-lationships for the detachment rate, as discussed above, and acalibrated granule breakage probability, it is difficult to quantita-tively predict the granule size distribution before a reactor isoperational, e.g. for design purposes. This might even be impossiblein a quantitative, deterministic way, given the complex mutualinteraction between the shear stress and granule shear strengthand stochastic processes, like the influent composition, tempera-ture, microbial species (and related kinetics) and breakage events.
4.3. Gas phase transport and liquid-gas transfer
More than half of the selected models (56%) assume an instantequilibrium between the gas and liquid phase concentrations, or donot consider transfer of gases at all. For example, the liquid-gastransfer resistance of methane in anaerobic systems is oftenneglected, probably because it is the final product of the conver-sions and will therefore not directly influence the predicted con-version rates. Nonetheless, if the biogas composition, flow orinducedmixing is of interest, liquid-gas transfer is important (Pausset al., 1990). Gas entrapment onto or inside granules can also causesludge to rise in anaerobic (Bolle et al., 1986) and anammox-basedreactors (Van Hulle et al., 2010). This effect has never been includedexplicitly, but it has been incorporated through calibrated correc-tion parameters to predict the vertical biomass concentration dis-tribution in a reactor as well as wash-out (Bolle et al., 1986;Kalyuzhnyi et al., 2006). When modelling aerobic and anammox-based reactors, the influence of the liquid-phase oxygen concen-tration has often been studied directly, so the gas-phase is actuallynot of interest. Therefore resistances in the liquid-gas boundarylayer for oxygen are neglected by choosing an unrealistically hightransfer rate (Beun et al., 2001; Volcke et al., 2010). Yet, a realisticoxygen transfer resistance would be required to quantify thenecessary airflow rate to obtain a certain liquid-phase oxygenconcentration (Garcia-Ochoa and Gomez, 2009). The mass transferdynamics are also crucial to compare different online controlstrategies for aeration, e.g. under variations in load, a well-knownapplication of activated sludge models (Åmand and Carlsson,2012; Belchior et al., 2012). The delay between an increase in theaeration rate and the resulting increase in the dissolved oxygenconcentration due to the mass transfer resistance can be importantalong with other dynamics, like the sensor response times (Alexet al., 2008).
When a liquid-gas mass transfer resistance is used for gases, anassumption about the transport phenomena within the gas-phase
J.E. Baeten et al. / Water Research 149 (2019) 322e341332
needs to be made. Mostly, a completely mixed gas-phase is used,but some publications consider that vertical concentration gradi-ents can exist within the gas-phase. For now, the only clear benefitof this model feature is that concentration gradients inside the gas-phase can be estimated (Wisecarver and Fan,1989), but theremightbe some indirect effects on the predicted effluent quality, aerationrequirements or biogas quality which have not yet been investi-gated explicitly.
5. Transformations
5.1. Biological conversions
Biological conversions occurring in anaerobic, aerobic and par-tial nitritation-anammox granular sludge reactors show overlapbecause some processes are not specific for certain redox condi-tions (e.g. hydrolysis) and because anaerobic and anoxic conditionscan exist in aerobic and anammox-based reactors due to spatial andtemporal heterogeneity (Fig. 7). Most models include biologicalconversions of substrate as a primary function. These can includedifferent types of organics, ammonium, nitrate and nitrite, phos-phorus and sulfate, under anaerobic, anoxic and aerobic conditions.Models of anaerobic granular sludge reactors all include the con-version of organics to methane because this is the primary goal. Avarying degree of detail has been used regarding the actual path-ways. Conversions of sulfate are generally not included (Fedorovichet al., 2003; Pokorna-Krayzelova et al., 2017; Sun et al., 2016), butare important for sulfate containing wastewaters, since sulfate isreadily reduced to sulfide, causing odour, corrosion and safety is-sues. The sulfide concentration in biogas increases almost linearlywith the influent sulfate to organics ratio, at low sulfate concen-trations (Batstone, 2006; Pokorna-Krayzelova et al., 2017). Highsulfate concentrations (�0.125 g S.g COD�1) also significantlyreduce methane production due to inhibition of conversions bysulfide (Vavilin et al., 1995) and because sulfate reducing bacteriacompete with methanogens for organic substrates.
For aerobic systems, most models consider organics andammonium conversions, sometimes combined with denitrificationof nitrite/nitrate, depending on the wastewater composition andpresence of anoxic conditions. Only four out of 22 models for aer-obic sequencing batch reactors include biological phosphorusremoval, because they were often developed for lab-scale reactorswith short feeding phases. However, in full-scale systems (Ner-eda®), slow anaerobic feeding is applied to promote phosphateaccumulating organisms and achieve more stable granules (deKreuk and van Loosdrecht, 2004; Pronk et al., 2015). This consti-tutes a substantial discrepancy between available models andpractice. Furthermore, the models that did consider phosphorusconversions in a reactor with slow anaerobic feeding requiredsignificant alterations of the kinetic parameters of phosphateaccumulating organisms in order tomatch experimental results (deKreuk et al., 2007b;Winkler et al., 2015b; Xavier et al., 2007), whichmight be due to an inappropriate description of their metabolism(Barnard et al., 2017).
In anammox-based systems, ammonium and nitrate/nitriteconversions via nitritation and anammox are always considered,but conversions of organics are sometimes neglected because theseare generally not the main target. Nevertheless, about300e1400mg COD.L�1 is removed in full-scale reactors (Lackneret al., 2014) and these conversions influence the total nitrogenremoval (Mozumder et al., 2014), so it is always recommended toinclude denitrification and aerobic oxidation of organics.
Particulate organics were considered as separate state vari-able(s) in thirty models for anaerobic granular sludge reactors, butthis was rarely done for aerobic or anammox-based systems. This
lack of particulates conversions in the latter two probably origi-nates from the more complex hydrolysis kinetics that are usuallyassumed for aerobic (Henze et al., 2000) compared to anaerobicsludge (Batstone et al., 2002). Activated sludge models (ASMs,Henze et al. (2000)) use a hydrolysis rate dependent on the con-centration of heterotrophic organisms (Eq. (6)).
ASM : rparticulate
¼ kM1…Mi
Xparticulate.Xheterotrophs
Kþ Xparticulate.Xheterotrophs
Xheterotrophs (6)
where rparticulate is the removal rate of particulates (g.m�3.d�1), k isa rate coefficient (d�1), Mi are Monod expressions (�), K is a half-saturation coefficient (�), Xparticulate the concentration of particu-late organics (g.m�3) and Xheterotrophs the concentration of hetero-trophs (g.m�3). Such kinetics are not easily compatible with biofilmmodels, which are often used for aerobic and anammox granularsludge reactors. The reason is that biofilm models assume that(most of the) heterotrophic organisms reside inside the granules.On the other hand, particulates enter via the bulk liquid and thusthey do not come into contact with heterotrophs. As such, thepredicted rate (Eq. (6)) is zero in the granules because Xparticulate iszero and the rate is small (or zero) in the bulk liquid because Xhe-
terotrophs is small (or zero). Removal would thus only be predicted ifliquid-granule transfer, attachment and/or intragranule transportof particulates are defined to bring this substrate in contact withheterotrophs, but the rates of these transport processes are rarelyanalyzed and the exact mechanisms are poorly understood (Boltzet al., 2010; Pronk et al., 2015). It is unclear how some biofilmmodels predicted removal of influent particulates without definingany transfer of particulates to aerobic granules (Ni et al., 2009, Niet al., 2008, Su and Yu, 2006a, b). Lübken et al. (2005) and Ponset al. (2008) could apply ASM-type kinetics because theyassumed a suspension of biomass (no biofilm modelling), meaningthat both the particulate organics and heterotrophs reside in thebulk liquid. Simpler kinetics could be used in future biofilm modelsfor aerobic and anammox granules (Eq. (7)), as often applied foranaerobic granular sludge systems (Batstone et al. (2004) and Muet al. (2008a)). This more empirical approach predicts conversion,irrespective of the contact between the substrate and heterotrophs.
ADM rparticulate ¼ kXparticulate (7)
Biological conversions of substrates are generally linked tobiomass growth. Biological wastewater treatment is an autocata-lytic process in the sense that biomass is the catalyst for thedegradation of substrates and at the same time more biomass iscreated during these conversions. Most models consider thisexplicitly by using one or more microbial groups, e.g. heterotrophsand nitrifiers, as state variables. The total amount or microbialcomposition of the biomass is then calculated via mass balanceswhich include a growth term. Nevertheless, about one third of themodels for anaerobic and aerobic reactors do not include microbialgrowth. They assume a fixed amount of biomass for everymicrobialgroup, or simply use a fixed maximal conversion rate. When thesemodels are used to design the required reactor volume, the ex-pected biomass concentration or maximal conversion rate must beassumed. For an already operational reactor, these parameters canbe measured directly and used as parameters. Yet, without growth,changes in the biomass or conversion capacity cannot be predicted.Therefore, these models are less suitable to simulate long-termchanges in operating conditions or to design reactors for a signifi-cantly different wastewater composition, concentration or loadingrate.
Fig. 7. Main conversions targeted in anaerobic, aerobic and partial nitritation-anammox granular sludge reactors. Brown, blue and red arrows show reactions that proceed spe-cifically under anaerobic, aerobic and anoxic conditions respectively. (1) Disintegration, (2) Hydrolysis, (3) Acidogenesis (4) Acetogenesis and methanogenesis, (5) Aerobic oxidationof organics, (6) Nitrification, (7) Denitrification, (8) Intracellular storage of organics by phosphorus accumulating organisms, coupled to phosphorus release (anaerobic) and uptakeof phosphorus coupled to oxidation of the storage compounds (aerobic/anoxic) (9) Anammox reaction, (10) Sulfate reduction. The percentage of the analyzed models which includekey substrates as state variables are shown. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
J.E. Baeten et al. / Water Research 149 (2019) 322e341 333
5.2. Physico-chemical reactions
The reactor pH is affected by acid/base consumption and pro-duction during biological conversions and can in turn influencebiological conversion rates. The pH can be calculated by solvingimplicit algebraic acid-base equations (Costello et al., 1991a), bysolving differential equations with reaction rates (Batstone et al.,2004) or through reformulation to an explicit expression for thehydrogen ion concentration (pH¼ -log [Hþ]) in simple cases(Alvarez et al., 1992). The former two can be complicated whenintragranule transfer (Batstone et al., 2004) or a non-ideal liquidphase (Kalyuzhnyi and Fedorovich, 1997) is considered because theequations need to be solved in each grid point. pH prediction isparticularly important in anaerobic systems fed with poorly buff-ered industrial wastewater, which is often the case. These are proneto failure due to acid type overload. Also in other cases, pH can becritical to determine the biogas quality in terms of carbon dioxideand hydrogen sulfide concentrations andwhen ammonia inhibitionis likely to take place. Accordingly, pH calculations are included in afairly high proportion (35%) of the anaerobic granular sludgemodels, despite the technical challenges.
For aerobic and anammox granular sludge reactors, pH calcu-lations are only included in models for one aerobic (Stevens et al.,1989) and two anammox (Jones et al., 2007; Wett et al., 2010)
reactors, which means that a constant pH is assumed in most cases.In aerobic treatment, problems with nitrification are expected forlow alkalinity or nitrogen-rich wastewaters (S€otemann et al., 2005)and about half of the full-scale anammox reactors have been re-ported to have experienced negative effects due to pH fluctuations(Lackner et al., 2014). The large difference in popularity of pH cal-culations between anaerobic and aerobic/anammox reactors mightbe not purely based on commonly encountered issues. It seems thatthe broad application of pH prediction for anaerobic digestion(non-granular sludge) in literature, including ADM1 (Batstone et al.,2002), has been adopted for granular sludge systems. On the otherhand, ASMs do not include extensive pH predictions and this mighthave influenced aerobic and anammox granular sludge reactormodelling. Only alkalinity is used as a state variable to identifywhen pH inhibitions can occur in ASM2 and ASM3 (Henze et al.,2000).
Precipitation reactions occur when the solubility of mineralcomponents in the bulk liquid or granules is exceeded. These arecomplex to model, as acid-base reactions are generally a prereq-uisite to determine supersaturation and the chemistry involved isnot always completely understood (Wilfert et al., 2015). Precipita-tion reactions can occur for all three wastewater treatment pro-cesses. Common precipitants are calcium and magnesiumphosphates and carbonates, including struvite MgNH4PO4.6H2O.
Fig. 8. Average, minimum and maximum complexity index (definition in Table 3) ofthe models used in publications as a function of the year of publication.
J.E. Baeten et al. / Water Research 149 (2019) 322e341334
For example, in anammox (Johansson et al., 2017) and aerobicsystems (Lin et al., 2012), phosphorus precipitates have beenencountered (Huang et al., 2015). This can both contribute tophosphorus removal and open up possibilities for recovery of thisnutrient, but it is also associated with reduced reactor performance(Li et al., 2011). Phosphorus precipitation can also be activelyinduced by addition of metal salts inside aerobic granular sludgereactors to supplement biological phosphorus removal (Pronk et al.,2015). Excessive formation of calcium precipitates in calcium-richindustrial wastewaters can cause cementation of anaerobic gran-ular sludge beds (Batstone and Keller, 2003). Iron sulfide precipi-tation on the other hand, can decrease the sulfide concentrationand thus improve the biogas quality (Wei et al., 2018). Despite thepossible influence of precipitation reactions on the process per-formance, they are only included in eight granular sludge models(Batstone and Keller, 2003; Feldman et al., 2017). Feldman et al.(2017) provided the most rigorous approach with the largestamount of possible precipitation reactions that can occur in thebulk liquid and even inside granules. Their work showed thatintragranule precipitation may reduce conversion rates due tophysical displacement of active biomass from the granules. Similarphenomena might occur when phosphorus precipitates insideaerobic or anammox granular sludge, but this has not been studiedyet.
6. Model complexity
The literature survey (spreadsheet in supplementary informa-tion) shows that there is not one generally accepted way to modelgranular sludge reactors. To get an overall idea of the complexity ofthe models, every model feature was assigned a certain score,qualitatively representing its complexity, and these were summedup to a complexity index of the model as a whole (defined byTable 3). The complexity of models appears to diverge over time(Fig. 8). More complex models become available in literature(Feldman et al., 2017; Fuentes et al., 2009c; Kagawa et al., 2015), butsimple models are still being used. The benefits of simple modelsare the more straightforward interpretation, easier calibration andlower computational demand. However, complex models describemore processes and thus providemore detailed predictions, such asintragranule substrate gradients. It is also sometimes believed that
Table 3Definition of the complexity index. For every phenomenon (column 1), certain model featcomplexity index.
Phenomenon Model feature
Transformations Per acid base reaction considered to pBiomass growth
Liquid phase transport Non-ideal flow using a combination oNon-ideal flow using advection-dispeNon-ideal flow using CFD
Gas phase transport Non-ideal flow or ideal plug flowGranule transport Fixed vertical heterogeneous biomass
Vertical biomass distribution mechanFixed imperfect granule retentionImperfect granule retention mechanis
Liquid-granule transfer External mass-transfer resistance or aAttachmentDetachment
Liquid-gas transfer Per component with a liquid-gas tranIntragranule transport Per dimension considered for solute t
Fixed heterogeneous microbial populMicrobial population distribution mec
Granule transformations and size distribution Two size classes (suspended and granMore than two size classesDynamic granule size without fixed s
Heat transport Temperature mechanistically predicte
more complex models lead to more accurate predictions of theoverall reactor performance over a broader range of operationalconditions. Yet, as Wanner and Gujer (1986) state: “Amodel shouldbe as simple as possible, and only as complex as needed”. Thismeans that the burden of proof for a higher predictive accuracyalways lies with those that develop more complex models. In otherwords, a more complex model should only be used if a simplermodel failed for the intended application, e.g. a completely mixedreactor has failed to predict the effect of an internal recirculation(Mu et al., 2008a) and a biofilm model without attachment hassometimes failed to predict the microbial population distributionqualitatively (Batstone et al., 2004). Moreover, it is difficult tovalidate some sub-models, like intragranule transport, for realisticconditions. For example, micro-sensors (e.g. hydrogen gas, pH oroxygen) can only be used for granules after harvesting them fromthe reactor and positioning them in specialized laboratory equip-ment. The gradients also differ for different sites on a granule andbetween different granules (van Loosdrecht et al., 1995; Winkleret al., 2011). This makes it difficult in practice to know whetherthe quantitative accuracy of these microscale models is highenough to improve the quantitative predictions of the macroscale
ures (column 2) were assigned a complexity score that was added to the value of the
Complexity score
redict the pH, biological conversion or precipitation reaction þ0.1þ0.5
Fig. 9. Two approaches that can be used to find the optimal model complexity fordesign and optimization of the overall reactor performance.
J.E. Baeten et al. / Water Research 149 (2019) 322e341 335
reactor performance.A mechanistic model could be very strictly defined as one that
takes into account every known phenomenon, which would lead toa very high complexity. Our survey found that none of the modelsdo this. Thus, a more pragmatic definition was used, namely amodel based on mass balances with transport and reaction terms.One should acknowledge that every single wastewater treatmentmodel has parameters that cluster several processes, because thesewere not described explicitly. For example, none of the selectedmodels include the many different species within every microbialgroup (Vannecke and Volcke, 2015). As a second, but definitely notconclusive example, the 3D architecture of granules is far morecomplex than ever considered: 3D micro-colonies exist insidegranules (Picioreanu et al., 2016), granules are not perfect spheres(de Kreuk and van Loosdrecht, 2004) and Herrling et al. (2017)stated that even the diffusivity inside granules is spatially hetero-geneous due to variations in the density of thematrix. The inclusionof these aspects could lead to more fundamental understanding,e.g. about 3D substrate gradients and microbial competition, but itis not per se necessary for optimization or design purposes. Inpractice, the estimation of parameters via experiments is alwaysnecessary for quantitative simulations to compensate for neglectedphenomena. Problems arise when simulation results are inter-preted quantitatively when using parameter values for a complexmodel that were calibrated for a simpler model or the other wayaround, or when a simulation scenario differs strongly from theconditions during calibration or validation. To aid further de-velopments, it is thus essential to always clearly state which pro-cesses are neglected. Unfortunately, we were unable to identify theassumptions for at least one of the analyzed model features in 32 ofthe 167 analyzed models.
7. Model calibration and validation
Most publications included calibration of the model (75%), butless included validation with an independent data-set (43%). Thereis especially a lack of published validation results for large-scaleanammox and aerobic granular sludge reactors. Only one studyshows limited validation results for a full-scale anammox-basedreactor (Corbala-Robles et al., 2016) and only one for a pilot-scaleaerobic system (Stevens et al., 1989). Of course, calibration and/orvalidation is not necessary for all modelling goals. For example,most partial nitritation-anammox granular sludge reactor modelsdid not aim at quantitative predictions but at qualitatively under-standing the relationship between micro- and mesoscale phe-nomena. Also the effect of alternative operational strategies on thereactor performance was explored in general, but not for one spe-cific reactor with a specific influent and effluent requirements.Aerobic granular sludge models on the other hand, were mostlyused for simulations of lab-scale systems. This indicates that aer-obic and anammox granular sludge models are not (yet) used in theway that activated sludge models are used for flocculent sludgesystems, e.g. to find a cost-effective approach to improve anexisting full-scale plant through changes in the operation orconfiguration or to design a plant for the treatment of a specificwastewater stream (Brdjanovic et al., 2015). It could also be thatmodels are already used for these purposes, for example usingcommercial simulators, but that the results are simply not pub-lished in scientific literature.
8. Future directions
8.1. Finding the appropriate degree of complexity
It is clear that the appropriate complexity of amodel depends on
the modelling goal. For fundamental insight, the required modelcomplexity follows logically from the research question. Forexample, if the goal is to assess the influence of the oxygen set-point or wastewater type on the microbial population distribu-tion, obviously the dynamics of the microbial population should beincluded by modelling intragranule transport of particulates(Batstone et al., 2004; de Kreuk et al., 2007b). However, if the focusis on optimizing the operation or design for a better overall reactorperformance, the search for optimal complexity to have easy useand interpretation, fast simulations and easy calibration whilemaintaining predictive accuracy is less straightforward. Two ap-proaches have been put forward for this in literature (Fig. 9). Thetop-down approach starts with a simple model and adds moreknown underlying phenomena until the macroscale dynamics ofinterest (e.g. effluent quality) are predicted with the required ac-curacy. This approach was used during the development of ASMs(van Loosdrecht et al., 2008). Model validation is an essential part ofthis approach and it can be used to develop practically applicablemodels on a reasonable time-scale. Other authors have proposed(Arnaldos et al., 2015) or used a bottom-up approach (Baeten et al.,2018; Noguera and Picioreanu, 2004; Volcke et al., 2012), whichuses models with more microscale phenomena to simulate thereactor performance and as such determine under which condi-tions certain phenomena can be neglected. The benefit of thisapproach is that it is clearly understood why certain simplificationscan be made, but it is more time-consuming. Both approaches havetheir value and should be used in parallel to more clearly define therange of operational conditions and modelling goals for whichcertain assumptions can bemade. To find the optimal complexity ofgranular sludge reactor models, the most prominent questionidentified here, is when a biofilm model is necessary and whenapparent kinetics suffice.
8.2. Need for mechanistic understanding
Some phenomena in granular sludge reactors are still poorlyunderstood. For example, the fate of particulate organics from the
J.E. Baeten et al. / Water Research 149 (2019) 322e341336
influent needs to be elucidated. Different particle sizes probablyreact differently. For example, small colloids could enter thegranule matrix, while larger particles probably cannot, but theymight still attach to the surface. Also the exact role of protozoa inthe degradation of particles in aerobic systems is unknown (Pronket al., 2015). Secondly, the liquid phase transport in anaerobicsystems appears to be unpredictable because of the high sensitivitytowards changes in the reactor scale and operation. CFD simula-tions including interactions between the gas and liquid phase ofdifferently sized reactors could help to better understand this de-pendency and develop rules of thumb for suitable assumptions insimpler reactor models. Also the hydraulic behaviours of full-scaleanammox-based reactors and aerobic reactors during the una-erated feeding phase may warrant further characterisation. Finally,the mechanistic dependency of detachment and breakage rates onoperating conditions needs further study to better understand thedevelopment of a granular sludge bed and to simulate changes inthe granule size (distribution).
8.3. Model applications
First of all, more publications with validation results on full-scale aerobic and anammox granular sludge reactors could in-crease confidence in the quantitative simulation results and thusextend the applications beyond general, qualitative optimizationprojects. Secondly, heat balance modelling has further potentialsince it has only been applied once (Haugen et al., 2015). It could beused to find the optimal balance between heat recovery (whichlowers the temperature) or heating (which increases the temper-ature) and biological conversion rates (which increase at highertemperatures). Thirdly, given that only a few aerobic granularsludge models considered phosphorus conversions, there is stillroom to better understand and optimize the phosphorus removalthat occurs in full-scale systems, e.g. to determine the optimalaeration control strategy for phosphorus removal. Furthermore,problems with pH fluctuations in anammox systems could bediagnosed and possibly solved with models. Further research canalso combine available precipitation models (Mbamba et al., 2015;Solon et al., 2017) with granular sludge models, like Feldman et al.(2017) did for an internal circulation reactor. This could help tounderstand precipitation dynamics in these systems, tackle prob-lems caused by excessive precipitation and optimize recovery ofresources like phosphorus. Recent additions of aerobic granularsludge reactor models in commercial simulation software, such asBioWin and SIMBA#,might stimulate awider application of modelsfor granular sludge.
9. Conclusions
This contribution reviewed granular sludge reactor models foranaerobic, aerobic and partial nitritation-anammox processes.
� A clearly defined modelling goal is not always provided, but it isnecessary to find an appropriate model complexity and todifferentiate between the many other available models.
� The immense variation in assumptions about the key phe-nomena in a granular sludge reactor can partly be explained bythe different reactor types and goals.
� To eliminate habitual assumptions, further research shouldmore clearly define the range of operational conditions andgoals for which certain approaches can be used. In particular theapplicability of biofilm models versus the use of apparent ki-netics needs further study.
� More mechanistic understanding is needed on the dependencyof the detachment rate on the operational conditions, the fate of
particulate organics and the transition between plug flow andmixed conditions with increasing anaerobic reactor scale.
� More full-scale calibration and validation studies would help inextending the applications of aerobic and anammox granularsludge models beyond qualitative studies and quantitativepredictions on lab-scale, e.g. to diagnose and prevent pH prob-lems and optimize biological phosphorus removal.
Acknowledgements
The doctoral research work of Janis Baeten has been financiallysupported by the Research Foundation Flanders (FWO) through aPhD fellowship.
Appendix A. Supplementary data
Supplementary data to this article can be found online athttps://doi.org/10.1016/j.watres.2018.11.026.
References
Abouhend, A.S., Butler, C., El-Moselhy, K.M., Park, C., 2016. The oxygenic photo-granule (OPG) for aeration-free and energy-recovery wastewater treatmentprocess. In: Water Environment Federation Technical Exhibition and Confer-ence, pp. 1e8. New Orleans, USA. https://doi.org/10.2175/193864716819712926.
Alvarez, J., Monroy, O., Ruiz, V., 1992. Model and control strategies of a two stageanaerobic digestor. In: Karim, M.N., Stephanopoulos, G. (Eds.), Modeling andControl of Biotechnical Processes, pp. 191e194. Keystone, Colorado. https://doi.org/10.1016/S1474-6670(17)50349-3.
Åmand, L., Carlsson, B., 2012. Optimal aeration control in a nitrifying activatedsludge process. Water Res. 46 (7), 2101e2110. https://doi.org/10.1016/j.watres.2012.01.023.
Angulo, F., Munoz, R., Olivar, G., 2007. Control of a bioreactor using feedback line-arization. In: Mediterranean Conference on Control & Automation,pp. 1368e1373. Athens, Greece. https://doi.org/10.1109/MED.2007.4433763.
Antonopoulou, G., Alexandropoulou, M., Lytras, C., Lyberatos, G., 2015. Modeling ofanaerobic digestion of food industry wastes in different bioreactor types. WasteBiomass Valorization 6 (3), 335e341. https://doi.org/10.1007/s12649-015-9362-7.
Arnaldos, M., Amerlinck, Y., Rehman, U., Maere, T., Van Hoey, S., Naessens, W.,Nopens, I., 2015. From the affinity constant to the half-saturation index: un-derstanding conventional modeling concepts in novel wastewater treatmentprocesses. Water Res. 70, 458e470. https://doi.org/10.1016/j.watres.2014.11.046.
Asif, M., Kalogerakis, N., Behie, L.A., 1992. Hydrodynamics of liquid fluidized bedsincluding the distributor region. Chem. Eng. Sci. 47 (15), 4155e4166. https://doi.org/10.1016/0009-2509(92)85165-8.
Bachmann, A., Beard, V.L., McCarty, P.L., 1985. Performance characteristics of theanaerobic baffled reactor. Water Res. 19 (1), 99e106. https://doi.org/10.1016/0043-1354(85)90330-6.
Baeten, J.E., van Loosdrecht, M.C.M., Volcke, E.I.P., 2018. Modelling aerobic granularsludge reactors through apparent half-saturation coefficients. Water Res. 146,134e145. https://doi.org/10.1016/j.watres.2018.09.025.
Barnard, J.L., Dunlap, P., Steichen, M., 2017. Rethinking the mechanisms of biologicalphosphorus removal. Water Environ. Res. 89 (11), 2043e2054. https://doi.org/10.2175/106143017X15051465919010.
Bassin, J.P., Pronk, M., Kraan, R., Kleerebezem, R., van Loosdrecht, M.C.M., 2011.Ammonium adsorption in aerobic granular sludge, activated sludge andanammox granules. Water Res. 45 (16), 5257e5265. https://doi.org/10.1016/j.watres.2011.07.034.
Batstone, D.J., 2006. Mathematical modelling of anaerobic reactors treating do-mestic wastewater: rational criteria for model use. Rev. Environ. Sci. Biotechnol.5 (1), 57e71. https://doi.org/10.1007/s11157-005-7191-z.
J.E. Baeten et al. / Water Research 149 (2019) 322e341 337
microbial community structure in granular anaerobic biomass. Water Res. 38(6), 1390e1404. https://doi.org/10.1016/j.watres.2003.12.003.
Batstone, D.J., Puyol, D., Flores-Alsina, X., Rodríguez, J., 2015. Mathematicalmodelling of anaerobic digestion processes: applications and future needs. Rev.Environ. Sci. Biotechnol. 14 (4), 595e613. https://doi.org/10.1007/s11157-015-9376-4.
Beccari, M., Pinto, A.C.D., Ramadori, R., Tomei, M.C., 1992. Effects of dissolved oxy-gen and diffusion resistances on nitrification kinetics. Water Res. 26 (8),1099e1104. https://doi.org/10.1016/0043-1354(92)90146-U.
Belchior, C.A.C., Araújo, R.A.M., Landeck, J.A.C., 2012. Dissolved oxygen control of theactivated sludge wastewater treatment process using stable adaptive fuzzycontrol. Comput. Chem. Eng. 37, 152e162. https://doi.org/10.1016/j.compchemeng.2011.09.011.
Bengtsson, S., de Blois, M., Wilen, B.M., Gustavsson, D., 2018. Treatment of munic-ipal wastewater with aerobic granular sludge. Crit. Rev. Environ. Sci. Technol. 48(2), 119e166. https://doi.org/10.1080/10643389.2018.1439653.
B�eteau, J.F., Otton, V., Hihn, J.Y., Delpech, F., Ch�eruy, A., 2005. Modelling of anaerobicdigestion in a fluidised bed with a view to control. Biochem. Eng. J. 24 (3),255e267. https://doi.org/10.1016/j.bej.2004.06.010.
Beun, J., 1999. Aerobic granulation in a sequencing batch reactor. Water Res. 33 (10),2283e2290. https://doi.org/10.1016/S0043-1354(98)00463-1.
Beun, J.J., Heijnen, J.J., van Loosdrecht, M.C.M., 2001. N-removal in a granular sludgesequencing batch airlift reactor. Biotechnol. Bioeng. 75 (1), 82e92. https://doi.org/10.1002/bit.1167.
Bhunia, P., Ghangrekar, M.M., 2008. Analysis, evaluation, and optimization of kineticparameters for performance appraisal and design of UASB reactors. Bioresour.Technol. 99 (7), 2132e2140. https://doi.org/10.1016/j.biortech.2007.05.053.
Bolle, W.L., Vanbreugel, J., Vaneybergen, G.C., Kossen, N.W.F., Vangils, W., 1986. Anintegral dynamic model for the UASB reactor. Biotechnol. Bioeng. 28 (11),1621e1636. https://doi.org/10.1002/bit.260281106.
Boltz, J.P., Morgenroth, E., Sen, D., 2010. Mathematical modelling of biofilms andbiofilm reactors for engineering design. Water Sci. Technol. 62 (8), 1821e1836.https://doi.org/10.2166/wst.2010.076.
Bonnet, B., Dochain, D., Steyer, J.P., 1997. Dynamical modelling of an anaerobicdigestion fluidized bed reactor. Water Sci. Technol. 36 (5), 285e292. https://doi.org/10.1016/s0273-1223(97)00485-x.
Borja, R., Banks, C.J., 1994. Kinetics of an upflow anaerobic sludge blanket reactortreating ice-cream waste-water. Environ. Technol. 15 (3), 219e232. https://doi.org/10.1080/09593339409385423.
Borja, R., Banks, C.J., Wang, Z., 1994. Performance and kinetics of an upflowanaerobic sludge blanket reactor treating slaughterhouse waste-water.J Environ Sci Health Part a-Environ Sci Eng Toxic Hazardous Substance Control29 (10), 2063e2085. https://doi.org/10.1080/10934529409376165.
Borja, R., Banks, C.J., Wang, Z.J., 1995. Kinetic evaluation of an anaerobic fluidized-bed reactor treating slaughterhouse waste-water. Bioresour. Technol. 52 (2),163e167. https://doi.org/10.1016/0960-8524(95)00019-b.
Buffiere, P., Fonade, C., Moletta, R., 1998. Mixing and phase hold-ups variations dueto gas production in anaerobic fluidized-bed digesters: influence on reactorperformance. Biotechnol. Bioeng. 60 (1), 36e43. https://doi.org/10.1002/(SICI)1097-0290(19981005)60:1%3C36::AID-BIT4%3E3.0.CO;2-1.
Bustillo-Lecompte, C.F., Mehrvar, M., 2016. Treatment of an actual slaughterhousewastewater by integration of biological and advanced oxidation processes:modeling, optimization, and cost-effectiveness analysis. J. Environ. Manag. 182,651e666. https://doi.org/10.1016/j.jenvman.2016.07.044.
Castillo, A., Llabres, P., Mata-Alvarez, J., 1999. A kinetic study of a combinedanaerobic-aerobic system for treatment of domestic sewage. Water Res. 33 (7),1742e1747. https://doi.org/10.1016/s0043-1354(98)00405-9.
Chong, S., Sen, T.K., Kayaalp, A., Ang, H.M., 2012. The performance enhancements ofupflow anaerobic sludge blanket (UASB) reactors for domestic sludge treatmente a State-of-the-art review. Water Res. 46 (11), 3434e3470. https://doi.org/10.1016/j.watres.2012.03.066.
Chou, H.-H., Huang, J.-S., 2005. Role of mass transfer resistance in overall substrateremoval rate in upflow anaerobic sludge bed reactors. J. Environ. Eng. 131 (4),548e556. https://doi.org/10.1061/(ASCE)0733-9372(2005)131:4(548).
Chou, H.-H., Huang, J.-S., Chen, S.-K., Lee, M.-C., 2011a. Process kinetics of anexpanded granular sludge bed reactor treating sulfate-containing wastewater.Chem. Eng. J. 170 (1), 233e240. https://doi.org/10.1016/j.cej.2011.03.061.
Chou, H.-H., Huang, J.-S., Jheng, J.-H., Ohara, R., 2008. Influencing effect of intra-granule mass transfer in expanded granular sludge-bed reactors treating aninhibitory substrate. Bioresour. Technol. 99 (9), 3403e3410. https://doi.org/10.1016/j.biortech.2007.08.011.
Chou, H.-H., Huang, J.-S., Tsao, C.-W., Lu, Y.-C., 2011b. Comparative influential effectsof mass transfer resistance in acetate-fed and glucose-fed sequential aerobicsludge blanket reactors. Chem. Eng. J. 174 (1), 182e189. https://doi.org/10.1016/j.cej.2011.08.072.
Chowdhury, R., Mehrotra, I., 2004. Minimization of short-circuiting flow throughupflow anaerobic sludge blanket reactor. J. Environ. Eng. 130 (9), 951e959.https://doi.org/10.1061/(ASCE)0733-9372(2004)130:9(951).
Corbala-Robles, L., Picioreanu, C., van Loosdrecht, M.C.M., P�erez, J., 2016. Analysingthe effects of the aeration pattern and residual ammonium concentration in apartial nitritation-anammox process. Environ. Technol. 37 (6), 694e702. https://doi.org/10.1080/09593330.2015.1077895.
Coskun, T., Kabuk, H.A., Varinca, K.B., Debik, E., Durak, I., Kavurt, C., 2012. AntibioticFermentation Broth Treatment by a pilot upflow anaerobic sludge bed reactorand kinetic modeling. Bioresour. Technol. 121, 31e35. https://doi.org/10.1016/j.biortech.2012.06.102.
Costello, D.J., Greenfield, P.F., Lee, P.L., 1991a. Dynamic modelling of a single-stagehigh-rate anaerobic reactor - I. Model derivation. Water Res. 25 (7), 847e858.https://doi.org/10.1016/0043-1354(91)90166-N.
Costello, D.J., Greenfield, P.F., Lee, P.L., 1991b. Dynamic modelling of a single-stagehigh-rate anaerobic reactor - II. Model verification. Water Res. 25 (7),859e871. https://doi.org/10.1016/0043-1354(91)90167-O.
Cuervo-Lopez, F.D., Monroy, H.O., Gonzalez, O., 1996. Anaerobic digestion modellingand UASB reactor performance. In: MooYoung, M., Anderson, W.A.,Chakrabarty, A.M. (Eds.), International Symposium on Environmental Biotech-nology, pp. 557e568. Waterloo, Canada. https://doi.org/10.1007/978-94-017-1435-8.
Cui, F.H., Kim, M., 2013. Use of steady-state biofilm model to characterize aerobicgranular sludge. Environ. Sci. Technol. 47 (21), 12291e12296. https://doi.org/10.1021/es4025639.
de Kreuk, M.K., Kishida, N., van Loosdrecht, M.C.M., 2007a. Aerobic granular sludge- state of the art. Water Sci. Technol. 55 (8e9), 75e81. https://doi.org/10.2166/wst.2007.244.
de Kreuk, M.K., Picioreanu, C., Hosseini, M., Xavier, J.B., van Loosdrecht, M.C.M.,2007b. Kinetic model of a granular sludge SBR: influences on nutrient removal.Biotechnol. Bioeng. 97 (4), 801e815. https://doi.org/10.1002/bit.21196.
de Kreuk, M.K., van Loosdrecht, M., 2004. Selection of slow growing organisms as ameans for improving aerobic granular sludge stability. Water Sci. Technol. 49(11), 9e17. https://doi.org/10.2166/wst.2004.0792.
Denac, M., Uzman, S., Tanaka, H., Dunn, I.J., 1983. Modeling of experiments onbiofilm penetration effects in a fluidized-bed nitrification reactor. Biotechnol.Bioeng. 25 (7), 1841e1861. https://doi.org/10.1002/bit.260250713.
Dereli, R.K., Ersahin, M.E., Ozgun, H., Ozturk, I., Aydin, A.F., 2010. Applicability ofAnaerobic Digestion Model No 1 (ADM1) for a specific industrial wastewaterOpium alkaloid effluents. Chem. Eng. J. 165 (1), 89e94. https://doi.org/10.1016/j.cej.2010.08.069.
Diamantis, V., Aivasidis, A., 2010. Kinetic analysis and simulation of UASB anaerobictreatment of a synthetic fruit wastewater. Global Nest J 12 (2), 175e180. https://doi.org/10.30955/gnj.000562.
Doaa, M., Amr, A.K., Walid, E., Medhat, M., 2013. Treatment of food industrialwastewater by using anaerobic baffled reactors (ABR). In: Lekkas, T.D. (Ed.),International Conference on Environmental Science and Technology (Athens,Greece).
Elmitwalli, T., Al-Sarawey, A., El-Sherbiny, M., Zeeman, G., Lettinga, G., 2003.Anaerobic biodegradability and treatment of Egyptian domestic sewage.J. Environ. Sci. Health - Part A Toxic/Hazard. Subst. Environ. Eng. 38 (10),2043e2055. https://doi.org/10.1081/ESE-120023331.
Elmitwalli, T., Feng, Y.C., Behrendt, J., Otterpohl, R., 2006. Anaerobic digestion po-tential for ecological and decentralised sanitation in urban areas. Water Sci.Technol. 53 (9), 45e54. https://doi.org/10.2166/wst.2006.276.
Ersahin, M.E., Insel, G., Dereli, R.K., Ozturk, I., Kinaci, C., 2007. Model based evalu-ation for the anaerobic treatment of corn processing wastewaters. Clean. - Soil,Air, Water 35 (6), 576e581. https://doi.org/10.1002/clen.200700105.
Faisal, M., Unno, H., 2001. Kinetic analysis of palm oil mill wastewater treatment bya modified anaerobic baffled reactor. Biochem. Eng. J. 9 (1), 25e31. https://doi.org/10.1016/S1369-703X(01)00122-X.
Fang, F., Ni, B.-J., Li, X.-Y., Sheng, G.-P., Yu, H.-Q., 2009. Kinetic analysis on the two-step processes of AOB and NOB in aerobic nitrifying granules. Appl. Microbiol.Biotechnol. 83 (6), 1159e1169. https://doi.org/10.1007/s00253-009-2011-y.
Fedorovich, V., Lens, P., Kalyuzhnyi, S., 2003. Extension of anaerobic digestion modelNo. 1 with processes of sulfate reduction. Appl. Biochem. Biotechnol. 109 (1e3),33e45. https://doi.org/10.1385/ABAB:109:1-3:33.
Feldman, H., Flores-Alsina, X., Ramin, P., Kjellberg, K., Jeppsson, U., Batstone, D.J.,Gernaey, K.V., 2017. Modelling an industrial anaerobic granular reactor using amulti-scale approach. Water Res. 126, 488e500. https://doi.org/10.1016/j.watres.2017.09.033.
Fuentes, M., Aguirre, P.A., Scenna, N.J., 2009a. Heterogeneous anaerobic biofilmreactor models application to UASB, EGSB and AFB reactors. In: de BritoAlves, R.M., do Nascimento, C.A.O., Biscaia, E.C. (Eds.), International Symposiumon Process Systems Engineering, pp. 297e302. https://doi.org/10.1016/S1570-7946(09)70270-6.
Fuentes, M., Mussati, M.C., Aguirre, P.A., Scenna, N.J., 2005. A three-phase fluidizedbed anaerobic biofilm reactor model for treating complex substrates. In:Puigjaner, L., Espuna, A. (Eds.), European Symposium on Computer-aided Pro-cess Engineering, pp. 553e558. Barcelona, Spain. https://doi.org/10.1016/S1570-7946(05)80214-7.
Fuentes, M., Mussati, M.C., Aguirre, P.A., Scenna, N.J., 2009b. Experimental andtheoretical investigation of anaerobic fluidized bed biofilm reactors. Braz. J.Chem. Eng. 26 (3), 457e468. https://doi.org/10.1590/S0104-66322009000300002.
J.E. Baeten et al. / Water Research 149 (2019) 322e341338
Fuentes, M., Mussati, M.C., Scenna, N.J., Aguirre, P.A., 2009c. Global modeling andsimulation of a three-phase fluidized bed bioreactor. Comput. Chem. Eng. 33(1), 359e370. https://doi.org/10.1016/j.compchemeng.2008.10.001.
Fuentes, M., Scenna, N.J., Aguirre, P.A., 2011. A coupling model for EGSB bioreactors:hydrodynamics and anaerobic digestion processes. Chem. Eng. Process: ProcessIntensification 50 (3), 316e324. https://doi.org/10.1016/j.cep.2011.01.005.
Fuentes, M., Scenna, N.J., Aguirre, P.A., Mussati, M.C., 2007. Anaerobic digestion ofcarbohydrate and protein-based wastewaters in fluidized bed bioreactors. Lat.Am. Appl. Res. 37 (4), 235e242. http://ref.scielo.org/msk54m.
Furumai, H., Kuba, T., Imai, T., Kusuda, T., 1991. Transient responses of waste-watertreatment and biomass development in a methanogenic fluidized-bed. WaterSci. Technol. 23 (7e9), 1327e1336. https://doi.org/10.2166/wst.1991.0585.
Garcia-Ochoa, F., Gomez, E., 2009. Bioreactor scale-up and oxygen transfer rate inmicrobial processes: an overview. Biotechnol. Adv. 27 (2), 153e176. https://doi.org/10.1016/j.biotechadv.2008.10.006.
Garrido, J.M., vanBenthum, W.A.J., vanLoosdrecht, M.C.M., Heijnen, J.J., 1997. Influ-ence of dissolved oxygen concentration on nitrite accumulation in a biofilmairlift suspension reactor. Biotechnol. Bioeng. 53 (2), 168e178. https://doi.org/10.1002/(SICI)1097-0290(19970120)53:2%3C168::AID-BIT6%3E3.0.CO;2-M.
Ghorbanian, M., Lupitskyy, R.M., Satyavolu, J.V., Berson, R.E., 2014a. Impact of hy-draulic retention time at constant organic loading rate in a two- stage expandedgranular sludge bed reactor. Environ. Eng. Sci. 31 (6), 317e323. https://doi.org/10.1089/ees.2013.0501.
Ghorbanian, M., Lupitskyy, R.M., Satyavolu, J.V., Berson, R.E., 2014b. Impact ofsupplemental hydrogen on biogas enhancement and substrate removal effi-ciency in a two-stage expanded granular sludge bed reactor. Environ. Eng. Sci.31 (5), 253e260. https://doi.org/10.1089/ees.2013.0496.
Hao, T., Lu, H., Chui, H.K., van Loosdrecht, M.C.M., Chen, G.H., 2013. Granulation ofanaerobic sludge in the sulfate-reducing up-flow sludge bed (SRUSB) of SANI(R) process. Water Sci. Technol. 68 (3), 560e566. https://doi.org/10.2166/wst.2013.182.
Hauduc, H., Rieger, L., Oehmen, A., van Loosdrecht, M.C.M., Comeau, Y., H�eduit, A.,Vanrolleghem, P.A., Gillot, S., 2013. Critical review of activated sludge modeling:state of process knowledge, modeling concepts, and limitations. Biotechnol.Bioeng. 110 (1), 24e46. https://doi.org/10.1002/bit.24624.
Haugen, F., Bakke, R., Lie, B., Hovland, J., Vasdal, K., 2015. Optimal design andoperation of a UASB reactor for dairy cattle manure. Comput. Electron. Agric.111, 203e213. https://doi.org/10.1016/j.compag.2015.01.001.
Heijnen, J.J., Vanloosdrecht, M.C.M., Mulder, R., Weltevrede, R., Mulder, A., 1993.Development and scale-up of an aerobic biofilm airlift suspension reactor.Water Sci. Technol. 27 (5e6), 253e261. https://doi.org/10.2166/wst.1993.0505.
Henze, M., Gujer, W., Mino, T., van Loosdrecht, M.C.M., 2000. Activated SludgeModels ASM1, ASM2, ASM2d and ASM3. IWA Publishing, London, UK. https://doi.org/10.2166/9781780402369.
Hirata, A., Takemoto, T., Ogawa, K., Auresenia, J., Tsuneda, S., 2000. Evaluation ofkinetic parameters of biochemical reaction in three-phase fluidized bed biofilmreactor for wastewater treatment. Biochem. Eng. J. 5 (2), 165e171. https://doi.org/10.1016/S1369-703X(00)00051-6.
Horn, H., Lackner, S., 2014. In: Muffler, K., Ulber, R. (Eds.), Productive Biofilms.Springer, Cham, Switzerland, pp. 53e76. https://doi.org/10.1007/10_2014_275.
Hu, Y.F., Dan, J.F., Pua, W.H., Yang, C.Z., Yang, J.K., 2017. CFD optimization of the baffleangle of an expanded granular sludge bed reactor. J. Environ. Chem. Eng. 5 (5),4531e4538. https://doi.org/10.1016/j.jece.2017.07.050.
Huang, J.-S., Chou, H.-H., Ohara, R., Wu, C.-S., 2006. Consecutive reaction kineticsinvolving a layered structure of the granule in UASB reactors. Water Res. 40(15), 2947e2957. https://doi.org/10.1016/j.watres.2006.05.024.
Huang, J.-S., Tsao, C.-W., Lu, Y.-C., Chou, H.-H., 2011. Role of mass transfer in overallsubstrate removal rate in a sequential aerobic sludge blanket reactor treating anon-inhibitory substrate. Water Res. 45 (15), 4562e4570. https://doi.org/10.1016/j.watres.2011.06.003.
Huang, J.S., Jih, C.G., Lin, S.D., Ting, W.H., 2003. Process kinetics of UASB reactorstreating non-inhibitory substrate. J. Chem. Technol. Biotechnol. 78 (7), 762e772.https://doi.org/10.1002/jctb.858.
Huang, W., Huang, W., Li, H., Lei, Z., Zhang, Z., Tay, J.H., Lee, D.-J., 2015. Species anddistribution of inorganic and organic phosphorus in enhanced phosphorusremoval aerobic granular sludge. Bioresour. Technol. 193, 549e552. https://doi.org/10.1016/j.biortech.2015.06.120.
Hubaux, N., Wells, G., Morgenroth, E., 2015. Impact of coexistence of flocs andbiofilm on performance of combined nitritation-anammox granular sludge re-actors. Water Res. 68, 127e139. https://doi.org/10.1016/j.watres.2014.09.036.
223e230. https://doi.org/10.1016/0960-8524(92)90006-j.Isanta, E., Figueroa, M., Mosquera-Corral, A., Campos, L., Carrera, J., P�erez, J., 2013.
A novel control strategy for enhancing biological N-removal in a granularsequencing batch reactor: a model-based study. Chem. Eng. J. 232, 468e477.https://doi.org/10.1016/j.cej.2013.07.118.
Isik, M., Sponza, D.T., 2005. Substrate removal kinetics in an upflow anaerobicsludge blanket reactor decolorising simulated textile wastewater. Process Bio-chem. 40 (3), 1189e1198. In: https://doi.org/10.1016/j.procbio.2004.04.014.
Jeris, J.S., Owens, R.W., Hickey, R., Flood, F., 1977. Biological fluidized-bed treatmentfor BOD and nitrogen removal. Journal (Water Pollution Control Federation) 49(5), 816e831. http://www.jstor.org/stable/25039354.
Jih, C.G., Huang, J.S., Huang, S.Y., 2003. Process kinetics of upflow anaerobic sludgebed reactors treating inhibitory substrate. Water Environ. Res. 75 (1), 5e14.https://doi.org/10.2175/106143003x140773.
Johansson, S., Ruscalleda, M., Colprim, J., 2017. Phosphorus recovery through bio-logically induced precipitation by partial nitritation-anammox granularbiomass. Chem. Eng. J. 327, 881e888. https://doi.org/10.1016/j.cej.2017.06.129.
Jones, R.M., Dold, P.L., Tak�acs, I., Chapman, K., Wett, B., Murthy, S.,Shaughnessy, M.O., 2007. Simulation for operation and control of reject watertreatment processes. In: Proceedings of the Water Environment Federation,pp. 4357e4372. San Diego, USA. https://doi.org/10.2175/193864707787974599.
Kagawa, Y., Tahata, J., Kishida, N., Matsumoto, S., Picioreanu, C., vanLoosdrecht, M.C.M., Tsuneda, S., 2015. Modeling the nutrient removal process inaerobic granular sludge system by coupling the reactor- and granule-scalemodels. Biotechnol. Bioeng. 112 (1), 53e64. https://doi.org/10.1002/bit.25331.
Kalyuzhnyi, S., Fedorovich, V., 1997. Integrated mathematical model of UASB reactorfor competition between sulphate reduction and methanogenesis. Water Sci.Technol. 36 (6e7), 201e208. https://doi.org/10.1016/s0273-1223(97)00524-6.
Kalyuzhnyi, S., Fedorovich, V., Lens, P., 2006. Dispersed plug flow model for upflowanaerobic sludge bed reactors with focus on granular sludge dynamics. J. Ind.Microbiol. Biotechnol. 33 (3), 221e237. https://doi.org/10.1007/s10295-005-0217-2.
Karpinska, A.M., Bridgeman, J., 2016. CFD-aided modelling of activated sludgesystems e a critical review. Water Res. 88, 861e879. https://doi.org/10.1016/j.watres.2015.11.008.
Kennedy, K., Barriault, M., 2007. Treatment kinetics of aircraft deicing fluid in ananaerobic baffled reactor. J. Environ. Eng. Sci. 6 (1), 11e17. https://doi.org/10.1139/s06-024.
Kennedy, K.J., Ning, Z., Fernandes, L., 2001. Modeling simultaneous removal ofprimary substrates and chlorinated phenols in upflow anaerobic sludge blanketreactors. Can. J. Civ. Eng. 28 (6), 910e921. https://doi.org/10.1139/cjce-28-6-910.
Kim, M., Cui, F., 2017. Use of Nonsteady-state Biofilm Model to characterize het-erotrophic and autotrophic biomass within aerobic granules. Ksce Journal ofCivil Engineering 21 (7), 2584e2589. https://doi.org/10.1007/s12205-017-1245-y.
Kleerebezem, R., 2003. Combining mixing regimes for optimized anaerobicwastewater treatment. Appl. Biochem. Biotechnol. 109 (1e3), 3e13. https://doi.org/10.1385/abab:109:1-3:3.
La Motta, E.J., Cascante, P., 1996. Substrate consumption kinetics in anaerobic bio-film fluidized bed reactor. J. Environ. Eng. 122 (3), 198e204. https://doi.org/10.1061/(ASCE)0733-9372(1996)122:3(198).
Labib, F., Ferguson, J.F., Benjamin, M.M., Merigh, M., Ricker, N.L., 1992. Anaerobicbutyrate degradation in a fluidized-bed reactor: effects of increased concen-trations of hydrogen and acetate. Environmental Science & Technology 26 (2),369e376. https://doi.org/10.1021/es00026a019.
Lackner, S., Gilbert, E.M., Vlaeminck, S.E., Joss, A., Horn, H., van Loosdrecht, M.C.M.,2014. Full-scale partial nitritation/anammox experiences e an application sur-vey. Water Res. 55, 292e303. https://doi.org/10.1016/j.watres.2014.02.032.
Lettinga, G., Vanvelsen, A.F.M., Hobma, S.W., Dezeeuw, W., Klapwijk, A., 1980. Use ofthe upflow sludge blanket (USB) reactor concept for biological waste-watertreatment, especially for anaerobic treatment. Biotechnol. Bioeng. 22 (4),699e734. https://doi.org/10.1002/bit.260220402.
Li, J., Shi, E., Antwi, P., Leu, S.-Y., 2016a. Modeling the performance of an anaerobicbaffled reactor with the variation of hydraulic retention time. Bioresour.Technol. 214, 477e486. https://doi.org/10.1016/j.biortech.2016.04.128.
Li, X., Xiao, Y., Liao, D., Zheng, W., Yi, T., Yang, Q., Zeng, G., 2011. Granulation ofsimultaneous partial nitrification and anammox biomass in one single SBRsystem. Appl. Biochem. Biotechnol. 163 (8), 1053e1065. https://doi.org/10.1007/s12010-010-9108-8.
Li, Y., Li, J., Zhang, Y.Z., Wang, X.J., Zheng, Z.M., 2016c. Capability of ammoniumadsorption by anaerobic ammonia oxidation granular sludge. Water Air SoilPollut. 227 (8). https://doi.org/10.1007/s11270-016-2965-1.
Lin, K.C., Yang, J.Z., 1995. A steady-state mathematical model for an upflow anaer-obic sludge blanket (UASB) process. In: Wrobel, L.C., Latinopoulos, P. (Eds.),International Conference on Water Pollution - Modelling, Measuring and Pre-diction, pp. 355e362. Porto Carras, Greece. https://doi.org/10.2495/WP950411.
Lin, Y.M., Bassin, J.P., van Loosdrecht, M.C.M., 2012. The contribution of exopoly-saccharides induced struvites accumulation to ammonium adsorption in aer-obic granular sludge. Water Res. 46 (4), 986e992. https://doi.org/10.1016/j.watres.2011.11.072.
Lin, Y.M., Nierop, K.G.J., Girbal-Neuhauser, E., Adriaanse, M., van Loosdrecht, M.C.M.,2015. Sustainable polysaccharide-based biomaterial recovered from waste
J.E. Baeten et al. / Water Research 149 (2019) 322e341 339
aerobic granular sludge as a surface coating material. Sustainable Materials andTechnologies 4, 24e29. https://doi.org/10.1016/j.susmat.2015.06.002.
Liotta, F., Chatellier, P., Esposito, G., Fabbricino, M., Van Hullebusch, E.D., Lens, P.N.L.,2014. Hydrodynamic mathematical modelling of aerobic plug flow andnonideal flow reactors: a critical and historical review. Crit. Rev. Environ. Sci.Technol. 44 (23), 2642e2673. https://doi.org/10.1080/10643389.2013.829768.
Liotta, F., Chatellier, P., Esposito, G., Fabbricino, M., Van Hullebusch, E.D., Lens, P.N.L.,Pirozzi, F., 2015. Current views on hydrodynamic models of nonideal flowanaerobic reactors. Crit. Rev. Environ. Sci. Technol. 45 (20), 2175e2207. https://doi.org/10.1080/10643389.2015.1010426.
Liu, Y., Tay, J.-H., 2004. State of the art of biogranulation technology for wastewatertreatment. Biotechnol. Adv. 22 (7), 533e563. https://doi.org/10.1016/j.biotechadv.2004.05.001.
Livingston, A.G., 1991. Biodegradation of 3,4-dichloroaniline in a fluidized-bedbioreactor and a steady-state biofilm kinetic model. Biotechnol. Bioeng. 38(3), 260e272. https://doi.org/10.1002/bit.260380308.
Lohani, S.P., Wang, S., Lackner, S., Horn, H., Khanal, S.N., Bakke, R., 2016. ADM1modeling of UASB treating domestic wastewater in Nepal. Renew. Energy 95,263e268. https://doi.org/10.1016/j.renene.2016.04.014.
Lopez, I., Borzacconi, L., 2010. UASB reactor hydrodynamics: residence time distri-bution and proposed modelling tools. Environ. Technol. 31 (6), 591e600.https://doi.org/10.1080/09593331003646638.
Lopez, I., Borzacconi, L., 2011. Modelling of an EGSB treating sugarcane vinasse usingfirst-order variable kinetics. Water Sci. Technol. 64 (10), 2080e2088. https://doi.org/10.2166/wst.2011.697.
L�opez, I., Borzacconi, L., 2009. Modelling a full scale UASB reactor using a COD globalbalance approach and state observers. Chem. Eng. J. 146 (1), 1e5. https://doi.org/10.1016/j.cej.2008.05.007.
Lopez, I., Passeggi, M., Pedezert, A., Borzacconi, L., 2009. Assessment on the per-formance of a series of two UASB reactors compared against one of the sametotal volume using Anaerobic Digestion Model No 1 (ADM1). Water Sci. Technol.59 (4), 647e652. https://doi.org/10.2166/wst.2009.011.
Lübken, M., Wichern, M., Schwarzenbeck, N., Wilderer, P.A., 2005. Modellingnutrient removal of an aerobic granular sludge lab-scale SBR using ASM3. In:Bathe, S., De Kreuk, M., Mcswain, B., Schwarzenbeck, N. (Eds.), Aerobic GranularSludge, pp. 103e110 (München, Germany).
Manser, R., Gujer, W., Siegrist, H., 2005. Consequences of mass transfer effects onthe kinetics of nitrifiers. Water Res. 39 (19), 4633e4642. https://doi.org/10.1016/j.watres.2005.09.020.
Mbamba, C.K., Tait, S., Flores-Alsina, X., Batstone, D.J., 2015. A systematic study ofmultiple minerals precipitation modelling in wastewater treatment. Water Res.85, 359e370. https://doi.org/10.1016/j.watres.2015.08.041.
Milferstedt, K., Hamelin, J., Park, C., Jung, J., Hwang, Y., Cho, S.-K., Jung, K.-W.,Kim, D.-H., 2017a. Biogranules applied in environmental engineering. Int. J.Hydrogen Energy. https://doi.org/10.1016/j.ijhydene.2017.07.176.
Morgenroth, E., 2008. Biofilm reactors (chapter 18). In: Henze, M., vanLoosdrecht, M.C.M., Ekama, G.A., Brdjanovic, D. (Eds.), Biological WastewaterTreatment: Principles, Modelling and Design. IWA Publishing, London, UK,pp. 493e511. https://doi.org/10.2166/9781780401867.
Mousseau, F., Liu, S.X., Hermanowicz, S.W., Lazarova, V., Manem, J., 1998. Modelingof turboflo - a novel biofilm reactor for wastewater treatment. Water Sci.Technol. 37 (4e5), 177e181. https://doi.org/10.2166/wst.1998.0613.
Mozumder, M.S.I., Picioreanu, C., van Loosdrecht, M.C.M., Volcke, E.I.P., 2014. Effectof heterotrophic growth on autotrophic nitrogen removal in a granular sludgereactor. Environ. Technol. 35 (8), 1027e1037. https://doi.org/10.1080/09593330.2013.859711.
Mu, S.J., Zeng, Y., Tartakovsky, B., Wu, P., 2007. Simulation and control of an upflowanaerobic sludge blanket (UASB) reactor using an ADM1-based distributedparameter model. Ind. Eng. Chem. Res. 46 (5), 1519e1526. https://doi.org/10.1021/ie060853l.
Mu, S.J., Zeng, Y., Wu, P., Lou, S.J., Tartakovsky, B., 2008a. Anaerobic digestion modelno. 1-based distributed parameter model of an anaerobic reactor: I. Modeldevelopment. Bioresour. Technol. 99 (9), 3665e3675. https://doi.org/10.1016/j.biortech.2007.07.060.
Mu, S.J., Zeng, Y.Z., Wu, P., 2008b. Multivariable control of anaerobic reactor byusing external recirculation and bypass ratio. J. Chem. Technol. Biotechnol. 83(6), 892e903. https://doi.org/10.1002/jctb.1888.
Mulder, A., Vandegraaf, A.A., Robertson, L.A., Kuenen, J.G., 1995. Anaerobic ammo-nium oxidation discovered in a denitrifying fluidized-bed reactor. FEMS (Fed.Eur. Microbiol. Soc.) Microbiol. Ecol. 16 (3), 177e183. https://doi.org/10.1111/j.1574-6941.1995.tb00281.x.
Mussati, M.C., Aguirre, P., Fuentes, M., Scenna, N., 2006. Aspects on methanogenicbiofilm reactor modeling. Lat. Am. Appl. Res. 36 (3), 173e180. http://ref.scielo.org/c2kqdb.
Narayanan, C.M., Narayan, V., 2008. Multiparameter models for performanceanalysis of UASB reactors. J. Chem. Technol. Biotechnol. 83 (8), 1170e1176.https://doi.org/10.1002/jctb.1959.
Ni, B.-J., Sheng, G.-P., Li, X.-Y., Yu, H.-Q., 2010. Quantitative simulation of the gran-ulation process of activated sludge for wastewater treatment. Ind. Eng. Chem.Res. 49 (6), 2864e2873. https://doi.org/10.1021/ie901252k.
Ni, B.-J., Xie, W.-M., Liu, S.-G., Yu, H.-Q., Wang, Y.-Z., Wang, G., Dai, X.-L., 2009.Granulation of activated sludge in a pilot-scale sequencing batch reactor for thetreatment of low-strength municipal wastewater. Water Res. 43 (3), 751e761.
technol. Adv. 28, 895e909. https://doi.org/10.1016/j.biotechadv.2010.08.004.Ni, B.-J., Yu, H.-Q., 2010b. Modeling and simulation of the formation and utilization
of microbial products in aerobic granular sludge. American Institute of Chem-ical Engineers Journal 56 (2), 546e559. https://doi.org/10.1002/aic.11888.
Ni, B.-J., Yu, H.-Q., Sun, Y.-J., 2008. Modeling simultaneous autotrophic and het-erotrophic growth in aerobic granules. Water Res. 42 (6e7), 1583e1594. https://doi.org/10.1016/j.watres.2007.11.010.
Nicolella, C., van Loosdrecht, M.C.M., Heijnen, J.J., 2000. Wastewater treatment withparticulate biofilm reactors. J. Biotechnol. 80 (1), 1e33. https://doi.org/10.1016/S0168-1656(00)00229-7.
Ning, Z., Kennedy, K.J., Fernandes, L., 1997. Anaerobic degradation kinetics of 2,4-dichlorophenol (2,4-DCP) with linear sorption. Water Sci. Technol. 35 (2e3),67e75. https://doi.org/10.1016/s0273-1223(96)00916-x.
Noguera, D.R., Picioreanu, C., 2004. Results from the multi-species BenchmarkProblem 3 (BM3) using two-dimensional models. Water Sci. Technol. 49(11e12), 169e176.
Nutt, S.G., Melcer, H., Pries, J.H., 1984. 2-stage biological fluidized-bed treatment ofcoke plant wastewater for nitrogen control. J. Water Pollut. Control Fed. 56 (7),851e857. www.jstor.org/stable/25042362.
Odriozola, M., L�opez, I., Borzacconi, L., 2016. Modeling granule development andreactor performance on anaerobic granular sludge reactors. J. Environ. Chem.Eng. 4 (2), 1615e1628. https://doi.org/10.1016/j.jece.2016.01.040.
Pauss, A., Andre, G., Perrier, M., Guiot, S.R., 1990. Liquid-to-gas mass-transfer inanaerobic processes - inevitable transfer limitations of methane and hydrogenin the biomethanation process. Appl. Environ. Microbiol. 56 (6), 1636e1644.
Pereboom, J.H.F., 1994. Size distribution model for methanogenic granules from full-scale UASB and IC reactors. Water Sci. Technol. 30 (12), 211e221. https://doi.org/10.2166/wst.1994.0613.
P�erez, J., Picioreanu, C., van Loosdrecht, M.C.M., 2005. Modeling biofilm and flocdiffusion processes based on analytical solution of reaction-diffusion equations.Water Res. 39 (7), 1311e1323. https://doi.org/10.1016/j.watres.2004.12.020.
Perez, M., Romero, L.I., Sales, D., 2001. Organic matter degradation kinetics in ananaerobic thermophilic fluidised bed bioreactor. Anaerobe 7 (1), 25e35. https://doi.org/10.1006/anae.2000.0362.
Picioreanu, C., 2015. Advanced Course on Environmental Biotechnology. Chapter 9:Biofilms and Flocs: Diffusive Transport - Modelling of the Structures. TU Delftand Leiden University, Delft, Netherlands.
Picioreanu, C., P�erez, J., van Loosdrecht, M.C.M., 2016. Impact of cell cluster size onapparent half-saturation coefficients for oxygen in nitrifying sludge and bio-films. Water Res. 106, 371e382. https://doi.org/10.1016/j.watres.2016.10.017.
Picioreanu, C., vanLoosdrecht, M.C.M., Heijnen, J.J., 1997. Modelling the effect ofoxygen concentration on nitrite accumulation in a biofilm airlift suspensionreactor. Water Sci. Technol. 36 (1), 147e156. https://doi.org/10.2166/wst.1997.0034.
Pokorna-Krayzelova, L., Mampaey, K.E., Vannecke, T.P.W., Bartacek, J., Jenicek, P.,Volcke, E.I.P., 2017. Model-based optimization of microaeration for biogasdesulfurization in UASB reactors. Biochem. Eng. J. 125, 171e179. https://doi.org/10.1016/j.bej.2017.06.009.
Pons, M.N., da Silva, M.D.L., Potier, O., Arnos, E., Battaglia, P., 2008. Modelling of anhybrid wastewater treatment plant. In: Braunschweig, B., Joulia, X. (Eds.), Eu-ropean Symposium on Computer Aided Process Engineering, pp. 907e912.Lyon, France. https://doi.org/10.1016/S1570-7946(08)80157-5.
Pontes, R.F.F., Pinto, J.M., 2006. Analysis of integrated kinetic and flow models foranaerobic digesters. Chem. Eng. J. 122 (1), 65e80. https://doi.org/10.1016/j.cej.2006.02.018.
Prakash, R., Kennedy, K.J., 1996. Kinetic of an anaerobic fluidized bed reactor usingbiolite Carrier. Can. J. Civ. Eng. 23 (6), 1305e1315. https://doi.org/10.1139/l96-939.
Pronk, M., de Kreuk, M.K., de Bruin, B., Kamminga, P., Kleerebezem, R., vanLoosdrecht, M.C.M., 2015. Full scale performance of the aerobic granular sludgeprocess for sewage treatment. Water Res. 84, 207e217. https://doi.org/10.1016/j.watres.2015.07.011.
Pronk, M., Giesen, A., Thompson, A., Robertson, S., van Loosdrecht, M., 2017. Aerobicgranular biomass technology: advancements in design, applications and furtherdevelopments. Water Pract. Technol. 12 (4), 987e996. https://doi.org/10.2166/wpt.2017.101.
Ravindran, V., Kim, S.H., Badriyha, B.N., Pirbazari, M., 1997. Predictive modeling forbioactive fluidized bed and stationary bed reactors: application to dairywastewater. Environ. Technol. 18 (9), 861e881. https://doi.org/10.1080/09593331808616606.
Reichert, P., 1994. AQUASIM e a tool for simulation and data analysis of aquaticsystems. Water Sci. Technol. 30 (2), 21e30. https://doi.org/10.2166/wst.1994.0025.
Rodriguez-Gomez, R., Moreno, L., Liu, L., 2013. A model to predict the behavior ofUASB reactors. Int. J. Environ. Res. 7 (3), 705e714. https://doi.org/10.22059/ijer.2013.640.
Rodriguez-Gomez, R., Renman, G., 2016. Sequential UASB and dual media packed-bed reactors for domestic wastewater treatment - experiment and simula-tion. Water Sci. Technol. 73 (12), 2959e2970. https://doi.org/10.2166/wst.2016.162.
Rodriguez-Gomez, R., Renman, G., Moreno, L., Liu, L.C., 2014. A model to describethe performance of the UASB reactor. Biodegradation 25 (2), 239e251. https://doi.org/10.1007/s10532-013-9656-z.
J.E. Baeten et al. / Water Research 149 (2019) 322e341340
Rodriguez, R., Moreno, L., 2010a. Modeling of substrate degradation and microor-ganisms growth in an UASB reactor. In: Kai, L. (Ed.), International Conference onChemical, Biological and Environmental Engineering, pp. 76e80. Singapore,Singapore. https://doi.org/10.1142/9789814295048_0016.
Rodriguez, R., Moreno, L., 2010b. In: Marinov, A.M., Brebbia, C.A. (Eds.), WaterPollution X. WIT Press, Southampton, UK, pp. 301e310. https://doi.org/10.2495/WP100261.
Ryhiner, G.B., Heinzle, E., Dunn, I.J., 1993. Modeling and simulation of anaerobicwaste-water treatment and its application to control design - case whey. Bio-technol. Prog. 9 (3), 332e343. https://doi.org/10.1021/bp00021a013.
Sadino-Riquelme, C., Hayes, R.E., Jeison, D., Donoso-Bravo, A., 2018. Computationalfluid dynamic (CFD) modelling in anaerobic digestion: general application andrecent advances. Crit. Rev. Environ. Sci. Technol. 48 (1), 39e76. https://doi.org/10.1080/10643389.2018.1440853.
Sam-soon, P., Wentzel, M.C., Dold, P.L., Loewenthal, R.E., Marais, G.R., 1991. Math-ematical-modeling of upflow anaerobic sludge bed (UASB) systems treatingcarbohydrate waste-waters. WaterSA 17 (2), 91e106.
Saravanan, V., Sreekrishnan, T.R., 2008. A mathematical model for a hybrid anaer-obic reactor. J. Environ. Manag. 88 (1), 136e146. https://doi.org/10.1016/j.jenvman.2007.01.036.
Schwarz, A., Mosche, M., Wittenberg, A., Jordening, H.J., Buchholz, K., Reuss, M.,1997. Mathematical modelling and simulation of an industrial scale fluidizedbed reactor for anaerobic wastewater treatment - scale-up effect on pH-gra-dients. Water Sci. Technol. 36 (6e7), 219e227. https://doi.org/10.1016/s0273-1223(97)00526-x.
Schwarz, A., Yahyavi, B., Mosche, M., Burkhardt, C., Jordening, H.J., Buchholz, K.,Reuss, M., 1996. Mathematical modelling for supporting scale-up of an anaer-obic wastewater treatment in a fluidized bed reactor. Water Sci. Technol. 34(5e6), 501e508. https://doi.org/10.1016/0273-1223(96)00685-3.
Seifi, M., Fazaelipoor, M.H., 2012. Modeling simultaneous nitrification and denitri-fication (SND) in a fluidized bed biofilm reactor. Appl. Math. Model. 36 (11),5603e5613. https://doi.org/10.1016/j.apm.2012.01.004.
Seok, J., Komisar, S.J., 2002. Sequential kinetic parameter estimation of anaerobicfluidized bed bioreactor using an optimization technique. Biotechnol. Lett. 24(19), 1579e1586. https://doi.org/10.1023/a:1020331505988.
Seok, J., Komisar, S.J., 2003a. Integrated modeling of anaerobic fluidized bedbioreactor for deicing waste treatment. I: model derivation. J. Environ. Eng. 129(2), 100e109. https://doi.org/10.1061/(asce)0733-9372(2003)129:2(100).
Seok, J., Komisar, S.J., 2003b. Integrated modeling of anaerobic fluidized bedbioreactor for deicing waste treatment. II: simulation and experimental studies.J. Environ. Eng. 129 (2), 110e122. https://doi.org/10.1061/(asce)0733-9372(2003)129:2(110).
Setiadi, T., Husaini, Djajadiningrat, A., 1996. Palm oil mill effluent treatment byanaerobic baffled reactors: recycle effects and biokinetic parameters. Water Sci.Technol. 34 (11), 59e66. https://doi.org/10.1016/s0273-1223(96)00821-9.
Shi, E., Li, J., Leu, S.-Y., Antwi, P., 2016. Modeling the dynamic volatile fatty acidsprofiles with pH and hydraulic retention time in an anaerobic baffled reactorduring the startup period. Bioresour. Technol. 222, 49e58. https://doi.org/10.1016/j.biortech.2016.09.085.
Skiadas, I.V., Ahring, B.K., 2002. A new model for anaerobic processes of up-flowanaerobic sludge blanket reactors based on cellular automata. Water Sci.Technol. 45 (10), 87e92. https://doi.org/10.2166/wst.2002.0297.
Solon, K., Flores-Alsina, X., Mbamba, C.K., Ikumi, D., Volcke, E.I.P., Vaneeckhaute, C.,Ekama, G., Vanrolleghem, P.A., Batstone, D.J., Gernaey, K.V., Jeppsson, U., 2017.Plant-wide modelling of phosphorus transformations in wastewater treatmentsystems: impacts of control and operational strategies. Water Res. 113, 97e110.https://doi.org/10.1016/j.watres.2017.02.007.
S€otemann, S., Musvoto, E., Wentzel, M., Ekama, G., 2005. Integrated biological,chemical and physical processes kinetic modelling Part 1eAnoxic-aerobic C andN removal in the activated sludge system. WaterSA 31 (4), 529e544. https://doi.org/10.4314/wsa.v31i4.5144.
Sponza, D.T., Uluk€oy, A., 2008. Kinetic of carbonaceous substrate in an upflowanaerobic sludge sludge blanket (UASB) reactor treating 2,4 dichlorophenol (2,4DCP). J. Environ. Manag. 86 (1), 121e131. https://doi.org/10.1016/j.jenvman.2006.11.030.
Stevens, D.K., Macberthouex, P., Chapman, T.W., 1989. Dynamic model of nitrifica-tion in fluidized-bed. J. Environ. Eng. 115 (5), 910e929. https://doi.org/10.1061/(ASCE)0733-9372(1989)115:5(910).
Su, K.-Z., Ni, B.-J., Yu, H.-Q., 2013. Modeling and optimization of granulation processof activated sludge in sequencing batch reactors. Biotechnol. Bioeng. 110 (5),1312e1322. https://doi.org/10.1002/bit.24812.
Su, K.-Z., Yu, H.-Q., 2006a. A generalized model for aerobic granule-basedsequencing batch reactor. 1. Model development. Environ. Sci. Technol. 40(15), 4703e4708. https://doi.org/10.1021/es060141m.
Su, K.-Z., Yu, H.-Q., 2006b. A generalized model for aerobic granule-basedsequencing batch reactor. 2. Parametric sensitivity and model verification.
Sudibyo, H., Guntama, D., Budhijanto, W., 2017. Assessment of start-up mechanismsfor anaerobic fluidized bed reactor in series based on mathematical simulation.In: Taufany, F., Widiyastuti, W., Nurkhamidah, S. (Eds.), International Seminaron Fundamental and Application of Chemical Engineering. Surabaya, Indonesia.https://doi.org/10.1063/1.4982337.
Suidan, M.T., Flora, J.R.V., Boyer, T.K., Wuellner, A.M., Narayanan, B., 1996. Anaerobicdechlorination using a fluidized-bed GAC reactor. Water Res. 30 (1), 160e170.https://doi.org/10.1016/0043-1354(95)00098-6.
Sun, L., Wan, S., Yu, Z., Wang, Y., Wang, S., 2012. Anaerobic biological treatment ofhigh strength cassava starch wastewater in a new type up-flow multistageanaerobic reactor. Bioresour. Technol. 104, 280e288. https://doi.org/10.1016/j.biortech.2011.11.070.
Tanaka, H., Uzman, S., Dunn, I.J., 1981. Kinetics of nitrification using a fluidized sandbed reactor with attached growth. Biotechnol. Bioeng. 23 (8), 1683e1702.https://doi.org/10.1002/bit.260230803.
Tang, W.T., Fan, L.S., 1987. Steady-state phenol degradation in a draft-tube, gas-liquid-solid fluidized-bed bioreactor. AIChE J. 33 (2), 239e249. https://doi.org/10.1002/aic.690330210.
Tang, W.T., Wisecarver, K., Fan, L.S., 1987. Dynamics of a draft tube gas-liquid-solidfluidized-bed bioreactor for phenol degradation. Chem. Eng. Sci. 42 (9),2123e2134. https://doi.org/10.1016/0009-2509(87)85033-9.
Tartakovsky, B., Mu, S.J., Zeng, Y., Lou, S.J., Guiot, S.R., Wu, P., 2008. Anaerobicdigestion model No. 1-based distributed parameter model of an anaerobicreactor: II. Model validation. Bioresour. Technol. 99 (9), 3676e3684. https://doi.org/10.1016/j.biortech.2007.07.061.
Thamsiriroj, T., Nizami, A.S., Murphy, J.D., 2012. Use of modeling to aid design of atwo-phase grass digestion system. Bioresour. Technol. 110, 379e389. https://doi.org/10.1016/j.biortech.2012.01.113.
Tsuneda, S., Auresenia, J., Inoue, Y., Hashimoto, Y., Hirata, A., 2002. Kinetic model fordynamic response of three-phase fluidized bed biofilm reactor for wastewatertreatment. Biochem. Eng. J. 10 (1), 31e37. https://doi.org/10.1016/S1369-703X(01)00152-8.
Turkdogan-Aydinol, F.I., Yetilmezsoy, K., Comez, S., Bayhan, H., 2011. Performanceevaluation and kinetic modeling of the start-up of a UASB reactor treatingmunicipal wastewater at low temperature. Bioproc. Biosyst. Eng. 34 (2),153e162. https://doi.org/10.1007/s00449-010-0456-0.
Vafajoo, L., Beigy, B., 2013. A dynamic model for glucose fermentation in a three-phase bioreactor. In: Dan, Y. (Ed.), International Conference on EnvironmentalScience and Development, pp. 328e332. Dubai, United Arab Emirates. https://doi.org/10.1016/j.apcbee.2013.05.056.
Van Hulle, S.W.H., Callens, J., Mampaey, K.E., van Loosdrecht, M.C.M., Volcke, E.I.P.,2012. N2O and NO emissions during autotrophic nitrogen removal in a granularsludge reactor - a simulation study. Environ. Technol. 33 (20), 2281e2290.https://doi.org/10.1080/09593330.2012.665492.
Van Hulle, S.W.H., Vandeweyer, H.J.P., Meesschaert, B.D., Vanrolleghem, P.A.,Dejans, P., Dumoulin, A., 2010. Engineering aspects and practical application ofautotrophic nitrogen removal from nitrogen rich streams. Chem. Eng. J. 162 (1),1e20.
van Lier, J.B., van der Zee, F.P., Frijters, C., Ersahin, M.E., 2016. In: HattiKaul, R.,Mamo, G., Mattiasson, B. (Eds.), Anaerobes in Biotechnology, pp. 363e395.https://doi.org/10.1007/10_2015_5012.
van Loosdrecht, M.C.M., Ekama, G.A., Wentzel, M.C., Brdjanovic, D., Hooijmans, C.M.,2008. Modelling activated sludge processes (Chapter 14). In: Henze, M., vanLoosdrecht, M.C.M., Ekama, G.A., Brdjanovic, D. (Eds.), Biological WastewaterTreatment: Principles, Modelling and Design. IWA Publishing, London, UK,pp. 361e392. https://doi.org/10.2166/9781780401867.
van Loosdrecht, M.C.M., Heijnen, J.J., Eberl, H., Kreft, J., Picioreanu, C., 2002. Math-ematical modelling of biofilm structures. Antonie Van Leeuwenhoek Interna-tional Journal of General and Molecular Microbiology 81 (1e4), 245e256.https://doi.org/10.1023/a:1020527020464.
van Loosdrecht, M.C.M., Tijhuis, L., Wijdieks, A.M.S., Heijnen, J.J., 1995. Population-distribution in aerobic biofilms on small suspended particles. Water Sci. Tech-nol. 31 (1), 163e171. https://doi.org/10.2166/wst.1995.0037.
Vangsgaard, A.K., Mauricio-Iglesias, M., Gernaey, K.V., Smets, B.F., Sin, G., 2012.Sensitivity analysis of autotrophic N removal by a granule based bioreactor:influence of mass transfer versus microbial kinetics. Bioresour. Technol. 123,230e241. https://doi.org/10.1016/j.biortech.2012.07.087.
J.E. Baeten et al. / Water Research 149 (2019) 322e341 341
P�erez, J., 2010. Modelling aerobic granular SBR at variable COD/N ratiosincluding accurate description of total solids concentration. Biochem. Eng. J. 49(2), 173e184. https://doi.org/10.1016/j.bej.2009.12.009.
Vlaeminck, S.E., Terada, A., Smets, B.F., De Clippeleir, H., Schaubroeck, T., Bolca, S.,Demeestere, L., Mast, J., Boon, N., Carballa, M., Verstraete, W., 2010. Aggregatesize and architecture determine microbial activity balance for one-stage partialnitritation and anammox. Appl. Environ. Microbiol. 76 (3), 900e909. https://doi.org/10.1128/AEM.02337-09.
Vlyssides, A., Barampouti, E.M., Mai, S., 2007a. An alternative approach of UASBdynamic modeling. AIChE J. 53 (12), 3269e3276. https://doi.org/10.1002/aic.11342.
Vlyssides, A., Barampouti, E.M., Mai, S., 2007b. Effect of ferrous ion on the biologicalactivity in a UASB reactor: mathematical modeling and verification. Biotechnol.Bioeng. 96 (5), 853e861. https://doi.org/10.1002/bit.21154.
Volcke, E.I.P., Picioreanu, C., De Baets, B., van Loosdrecht, M.C.M., 2010. Effect ofgranule size on autotrophic nitrogen removal in a granular sludge reactor.Environ. Technol. 31 (11), 1271e1280. https://doi.org/10.1080/09593331003702746.
Volcke, E.I.P., Picioreanu, C., De Baets, B., van Loosdrecht, M.C.M., 2012. The granulesize distribution in an anammox-based granular sludge reactor affects theconversiondimplications for modeling. Biotechnol. Bioeng. 109 (7), 1629e1636.https://doi.org/10.1002/bit.24443.
Wang, J., Yan, J., Xu, W., 2015. Treatment of dyeing wastewater by MIC anaerobicreactor. Biochem. Eng. J. 101, 179e184. https://doi.org/10.1016/j.bej.2015.06.001.
Wang Shi, H., Zhou, P., 1994. Organic matter degradation kinetics in a fluidized bedbioreactor. Water Res. 28 (9), 2021e2028. https://doi.org/10.1016/0043-1354(94)90177-5.
Wang, X., Ding, J., Guo, W.Q., Ren, N.Q., 2010. A hydrodynamics-reaction kineticscoupled model for evaluating bioreactors derived from CFD simulation. Bio-resour. Technol. 101 (24), 9749e9757. https://doi.org/10.1016/j.biortech.2010.07.115.
Wang, X., Ding, J., Ren, N.Q., Liu, B.F., Guo, W.Q., 2009. CFD simulation of anexpanded granular sludge bed (EGSB) reactor for biohydrogen production. Int. J.Hydrogen Energy 34 (24), 9686e9695. https://doi.org/10.1016/j.ijhydene.2009.10.027.
Wanner, O., Eberl, H., Morgenroth, E., Noguera, D., Picioreanu, C., Rittmann, B.E., vanLoosdrecht, M.C.M., 2006. Mathematical Modeling of Biofilms. IWA publishing,London, UK.
Wanner, O., Gujer, W., 1986. A multispecies biofilm model. Biotechnol. Bioeng. 28(3), 314e328. https://doi.org/10.1002/bit.260280304.
Wei, J., Hao, X., van Loosdrecht, M.C.M., Li, J., 2018. Feasibility analysis of anaerobicdigestion of excess sludge enhanced by iron: a review. Renew. Sustain. EnergyRev. 89, 16e26. https://doi.org/10.1016/j.rser.2018.02.042.
Weissbrodt, D.G., Holliger, C., Morgenroth, E., 2017. Modeling hydraulic transportand anaerobic uptake by PAOs and GAOs during wastewater feeding in EBPRgranular sludge reactors. Biotechnol. Bioeng. 114 (8), 1688e1702. https://doi.org/10.1002/bit.26295.
Wett, B., 2007. Development and implementation of a robust deammonificationprocess. Water Sci. Technol. 56 (7), 81e88. https://doi.org/10.2166/wst.2007.611.
Wett, B., Nyhuis, G., Tak�acs, I., Murthy, S., 2010. Development of enhanced deam-monification selector. In: Water Environment Federation Technical Exhibitionand Conference. New Orleans, Louisiana. https://doi.org/10.2175/193864710798194139.
Wilfert, P., Kumar, P.S., Korving, L., Witkamp, G.-J., van Loosdrecht, M.C.M., 2015. Therelevance of phosphorus and iron chemistry to the recovery of phosphorusfrom wastewater: a review. Environmental Science & Technology 49 (16),9400e9414. https://doi.org/10.1021/acs.est.5b00150.
Willquist, K., Nkemka, V.N., Svensson, H., Pawar, S., Ljunggren, M., Karlsson, H.,Murto, M., Hulteberg, C., van Niel, E.W.I., Liden, G., 2012. Design of a novelbiohythane process with high H2 and CH4 production rates. Int. J. HydrogenEnergy 37 (23), 17749e17762. https://doi.org/10.1016/j.ijhydene.2012.08.092.
Winkler, M.-K.H., Meunier, C., Henriet, O., Mahillon, J., Su�arez-Ojeda, M.E., DelMoro, G., De Sanctis, M., Di Iaconi, C., Weissbrodt, D.G., 2018. An integrativereview of granular sludge for the biological removal of nutrients and
recalcitrant organic matter from wastewater. Chem. Eng. J. 336, 489e502.https://doi.org/10.1016/j.cej.2017.12.026.
Winkler, M.K.H., Ettwig, K.F., Vannecke, T.P.W., Stultiens, K., Bogdan, A., Kartal, B.,Volcke, E.I.P., 2015a. Modelling simultaneous anaerobic methane and ammo-nium removal in a granular sludge reactor. Water Res. 73, 323e331. https://doi.org/10.1016/j.watres.2015.01.039.
Winkler, M.K.H., Hong, Q.L., Volcke, E.I.P., 2015b. Influence of partial denitrificationand mixotrophic growth of NOB on microbial distribution in aerobic granularsludge. Environ. Sci. Technol. 49 (18), 11003e11010. https://doi.org/10.1021/acs.est.5b01952.
Winkler, M.K.H., Kleerebezem, R., Kuenen, J.G., Yang, J.J., van Loosdrecht, M.C.M.,2011. Segregation of biomass in cyclic anaerobic/aerobic granular sludge allowsthe enrichment of anaerobic ammonium oxidizing bacteria at low tempera-tures. Environmental Science & Technology 45 (17), 7330e7337. https://doi.org/10.1021/es201388t.
Wisecarver, K.D., Fan, L.-S., 1989. Biological phenol degradation in a gas-liquid-solidfluidized bed reactor. Biotechnol. Bioeng. 33 (8), 1029e1038. https://doi.org/10.1002/bit.260330812.
Wu, C.S., Huang, J.S., 1995. Performance enhancement with tapered anaerobicfluidized-bed bioreactors. J. Chem. Technol. Biotechnol. 63 (4), 353e360.https://doi.org/10.1002/jctb.280630408.
Wu, C.S., Huang, J.S., 1996. Bioparticle characteristics of tapered anaerobic fluidized-bed bioreactors. Water Res. 30 (1), 233e241. https://doi.org/10.1016/0043-1354(95)00112-x.
Wu, M.M., Hickey, R.F., 1997. Dynamic model for UASB reactor including reactorhydraulics, reaction, and diffusion. J. Environ. Eng. 123 (3), 244e252. https://doi.org/10.1061/(ASCE)0733-9372(1997)123:3(244).
Xavier, J.B., de Kreuk, M.K., Picioreanu, C., van Loosdrecht, M.C.M., 2007. Multi-scaleindividual-based model of microbial and bioconversion dynamics in aerobicgranular sludge. Environ. Sci. Technol. 41 (18), 6410e6417. https://doi.org/10.1021/es070264m.
Xu, F., Huang, Z.X., Miao, H.F., Ren, H.Y., Zhao, M.X., Ruan, W.Q., 2013. Identical full-scale biogas-lift reactors (BLRs) with anaerobic granular sludge and residualactivated sludge for brewery wastewater treatment and kinetic modeling.J. Environ. Sci. 25 (10), 2031e2040. https://doi.org/10.1016/s1001-0742(12)60268-x.
Yang, J.X., Yang, Y.Q., Ji, X., Chen, Y.P., Guo, J.S., Fang, F., 2015. Three-Dimensionalmodeling of hydrodynamics and biokinetics in EGSB reactor. J. Chem. 1e7, 2015.https://doi.org/10.1155/2015/635281.
Yang, W., Lu, H., Khanal, S.K., Zhao, Q., Meng, L., Chen, G.-H., 2016. Granulation ofsulfur-oxidizing bacteria for autotrophic denitrification. Water Res. 104,507e519. https://doi.org/10.1016/j.watres.2016.08.049.
Yetilmezsoy, K., 2012. Integration of kinetic modeling and desirability functionapproach for multi-objective optimization of UASB reactor treating poultrymanure wastewater. Bioresour. Technol. 118, 89e101. https://doi.org/10.1016/j.biortech.2012.05.088.
Yu, L., Zhao, Q.B., Ma, J.W., Frear, C., Chen, S.L., 2012. Experimental and modelingstudy of a two-stage pilot scale high solid anaerobic digester system. Bioresour.Technol. 124, 8e17. https://doi.org/10.1016/j.biortech.2012.08.088.
Zhou, M., Gong, J., Yang, C., Pu, W., 2013. Simulation of the performance of aerobicgranular sludge SBR using modified ASM3 model. Bioresour. Technol. 127,473e481. https://doi.org/10.1016/j.biortech.2012.09.076.
