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Novel dispersed plug flow model for UASB reactors focusing on sludge dynamics 1
1 Sergey Kalyuzhnyi*, Vyacheslav Fedorovich* and Piet Lens**

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*Departmentof ChemicalEnzymology,ChemistryFaculty, MoscowState University,119899 Moscow,Russia;email:svk@enz.chem..msu.ro **Sub-Department Environmental Technology,Wageningen of University, 6700EV Wageningen, TheNetherlands

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ABSTRACT
A new approac.h model UASB-reactors,referred to as a one-dimensional to dispersedplug flow model, was developed. This model focuses on the sludge dynamics along the reactor height, based on the balance between dispersion, sedimentationand convection using one-dimensional(with regard to reactor height) equations. A univers~l description of ??th the hydrod~amics and sludge dynamics w~s elaboratedby applYIngknown physIcal laws and emplTlcalrelations denved from expenmentalobservations.In addition, the developed model includes (i) multiple-reaction stoichiometry, (ii) microbial growth kinetics, (iii) equil~briumchemis~ in the liquid phase,(iv) major solid-liquid-gasinteractions,and (v) material balances for dIssolved and solid componentsalong the reactor height. The parametersof the integratedmodel have been identified with a set of experimentaldata on the start-up,operationperformance,sludge dynamicsand solute intermediateconcentrationprofiles of a UASB reactor treating cheesewhey. A sensitivity analysisof the model was performed with regard to the key model parameters, which showed that the output of the dispersedplug flow model was most influenced by the sludge settleability characteristicsand the growth properties(especially~) of both protein-degrading bacteriaand acetotrophicmethanogens.

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KEYWORDS Dispersion; mathematical model; partial derivatives; plug flow; sedimentation; UASB reactor

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INTRODUCTION

" The UASB reactor is currently the most popular reactor design for the high rate anaerobic treatment of industrial wastewater (Franklin, 2001). The heterogeneous sludge distribution along the UASB reactor height excludes the application of the majority of the numerous mathematical models developed for completelymixed anaerobic digestion systems, as these models assume a homogeneous biomass distribution andhydrodynamic pattern within the reactor. The objective of the present work was to develop an integrated mathematical model for the UASB reactor concept, combining sludge dynamics, solid-liquid-gas interactions and hydrodynamics with biological conversions (multiple reaction stoichiometry, microbial growth kinetics) and liquid phase equilibrium chemistry. The integrated model was subsequently fitted to experimentaldata on the start-up and operational performance of a UASB reactor treating cheesewhey (Yan etal., 1989; Yan et al., 1993). Finally, a sensitivity analysis of the key model parameters was performed.

BRIEF DESCRIPTION OF MODEL DEVELOPMENT J Inthe present model, all processes(physical, chemical, microbiological) inside the reactor are considered to depend only on the vertical axis of the reactor (distance z from input, z varies from 0 to H) and time t. Thus, j all the process characteristics in a fixed reactor cross-section CSz are assumed to be uniform. In general, the I 1 123


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spacedistribution of the concentration any component (solubleor suspended) of N alongthe reactorheight z canbe written on the basisof the dispersed plug flow conceptby the following equation: ~N(z,

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t)

= -a;:-[D(z, t) . ~N(z,

a

a

t)] - ~[W

a

(z, t) . N(z, t)] + r(z, t) - M (z, t)

(1)

The first term in the right part ofEq. (1) characterises degree mixing by gas-induced the of dispersion. The secondtenDdetermines convectivetransportof component in the vertical direction.The third and fourth a N termsarethe net biotransformation rate andtransferrateto the gasphasefor component respectively. N, In general,the value of W(z,t) for any componentN is determinedby the balancebetweenthe upward velocity Wup(z,t) the apparent and settlingvelocity Ws(z,t): W(z,t) = Wup(z,t) Ws(z,t) (2) I Vertical velocity of sludge aggregates.Under neglecting solid hold-up, the upward velocity can be approximated to: VR Wup= HRT.CS (3) The expression Ws(z,t)for sludgesolids canbe derived from the Stokeslaw underRe < 2 (the region in for which VASE reactorsusuallyoperate): 2 [\fI) .Pag(t) Pl.].g .dag(t) Ws(z,t)= 18.,,(z,t) (4) where \VI represents influence of gas entrapmentand attachmenton the apparentaggregate the density. Thoughthe sludgesuspensions VASE reactorsbehavelike non-Newtonianliquids, they canbe referredto in as pseudo-Newtonian liquids and severalempirical formulasto calculatetheir viscosity ,,(z,t) are available in engineering practice(Darton, 1985).In our model,the following formula was used: ,,(z,t) ="L exp[A1E(Z,tf"5] (5) The solid hold up E(Z,t)given in Eq. 5 canbe calculated from its physicaldefinition: VSSIoI(z, t) ё(z,t ) = (6)

( 1--

ACag

100

) .( 1--

MCag

100

) 'p ag(t)

Since the aggregate density Pag(t) usually does not vary significantly during an experimentalrun with one type of wastewater(Hulshoff Pol, 1989), the aggregate density is assumedto be constantin the current version of the model. Additionally, aggregates were assumed have a sphericalform and the same(but to variablewith time) diameterdag(t) within the entirereactor(seebelow). Thesesimplifying assumptions were introducedto make the model workable, although it does not reflect completelythe reality. The average granule diameter was found to have a positive relation with the sludge loading rate and the influent concentration (Hulshoff Pol, 1989). Both parametersare often related and determine the substrate penetrationdepth and thus, indirectly the aggregates size. Since it is rather problematicto formalise the observeddependencies betweenthe averageaggregate diameterand the factors mentionedabove,a more simplerelation derivedfrom the net sludgegrowth/decay (ChangandRittman, 1987)was usedin the model: d[d (t)] ag= dt dt \fI .~.ll 23 H{I( J /lj(Z,t)-bj),Xj(Z,t) VSSR (t)

]

.CS.dz

(7)

Dispersion of sludge aggregates.A formulation for D(z,t) in the blanket zone of VASE reactorswas proposed (Narnoli andMehrotra, 1997)on the basisof the so-calleddiffusion concept: [ q(z,t) .(1- exP(-~) ]2 (8) D(z,t) = A2.
,

q(z,t)

This expression beenfound to be valid on the basisof experimental has observations availablein literature about solids concentrations the sludgeblanket zone of VASE reactors.It shouldbe noted that Eq. (8) is in

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similarto several expressions proposed earlierfor the calculation the dispersion of coefficients threein
phasefluidised beds reactors (Darton, 1985). In all these formulations, the value of D(z,t) is highly dependent the surfacegasproduction q(z,t). In our model, Eq. (8) was usedto describethe dispersionof on solidsthroughoutthe reactorheight. D(z,t) of soluteswas shownto be not principally different from the dispersioncoefficientsof the suspended solids(Darton, 1985)due to the physical link betweensolids and liquid dispersion.Therefore,Eq. (8) was usedin the model for the descriptionof solutedispersioncoefficientsthroughoutthe reactorheight. Due to the negligible settling velocity of solutes, the upward velocity Wup (Eq. 3) exclusively determinestheir verticalvelocity. Gaseous components. Although anaerobicreactorshave a gas hold up, it is usually relatively low, e.g., varyingbetween0.01-0.05of the reactor volume dependingon the surfacegasproduction(Buffiere et al., 1998).To avoid an excessiveintricacy, the gas hold up is neglectedin the current version of the model, except its influenceon the apparentdensityof sludgeaggregates for (parameter seeEq. 4). The gaseous 'VI, components (methane,hydrogencarbon dioxide and ammonia) are treated in the model as soluteswith takinginto accounttheir transferto the gasphase, which is considered an ideally mixed medium.Studies as on bubble columns have shown that the masstransfer coefficient kLa mainly dependson the surfacegas productionq(z,t) and various formulations have been proposed(Darton, 1985; Zhukova, 1991) for the description this dependency. following formula was usedin the presentmodel to describethe massof The transfer coefficientsof components from the liquid to gasphase(Zhukova, 1991): kLa(z,t) =

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Soluble components. fluidisedbedsystems, formulafor thecalculation thedispersion For the of coefficients

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Biotransformationkinetics. The present model simulates the anaerobic treatment of soluble organic wastewater,which can be represented by a three-step process: acidogenesis, acetogenesisand methanogenesis. of thesestepsis carriedout by separate Each groupsof bacteria.The kinetic descriptionof biotransformations adapted was from our previousmodel (Kalyuzhnyi andFedorovich,1998)

RESULTSAND DISCUSSION Theparameters the integratedmodel havebeenidentified with a set of experimental of dataon the start-up, operation performance,sludgedynamicsand solute intermediateconcentration profiles of a UASB reactor. treatingcheesewhey (Yan et al., 1989; 1993).The resultsof superimposing experimentaldata and model predictions presented Figs. 1-4. In general,the predictionsagreewith the experimen~all,>: are in recorde~ data duringthe start-upperiod (Fig. 1) as well as with the reportedsteady-state performance Indicators(FIg. 2) andsludgecharacteristics (Fig. 3) underthe variousOLR applied.The model overestimates effluent VSS the duringthe start-upperiod (Fig. 1b) and a cumulativeVSS washoutduring the first 4 OLR applied(Fig. 3b). However, satisfactoryagreement a betweenthe simulationsand the experimental observations obtained was for thetotal quantity ofVSS in the reactor(Fig. 3~).On ~he other hand,the model under~stimates steadythe stateeffluent COD during the last 3 OLR applIed (FIg. 2a) and as a result overestImates methane the productionin the sameperiods (Fig. 2b). These discrepancies can be mainly attributed to a simplified description the VSS dynamicsand, consequently, quite accuratedescriptionof sludgetransportalong of not thereactorheight in the dispersed plug flow model. Satisfactory agreement betweenmodel and experimenthas also beenobtainedfor the COD- and pH profile alongthe reactorheight (Fig. 4). The major discrepancies were found at the OLR of 7.62 g COD/dm3/day for both pH- and COD-profiles (Figs. 4b and d), namely, a prolonged plug-flow region was experimentally observed the bottom of the sludgebed whereas model predictsthis region asmore n~ow. The reason in the might be related.to the i~adequatedescription of .dispersionat the reactor bottom, I.e., the model

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Fig. 3. Model versus experiment: (a) total VSS in reactor at the end of each the OLR applied; (b) integral VSS wash-out during each period. Considering the big number of variable model parameters (in total 33) and the rather arbitrary fixation of the seed sludge characteristics (in total 5), one can expect significant difficulties in the parameter identification. So, it was of primary importance to investigate the model sensitivity to these parameters. A sensitivity analysis of the model was performed with regard to the seed sludge characteristics and the key model parameters. The sensitivity analysis showed that the output of the dispersed plug flow model was most influenced by the sludge settleability characteristics and the growth properties (especially ~m) of both protein-degrading bacteria and acetotrophic methanogens(data not shown). The developed model allows to derive additional information about the UASB reactor investigated. As an example, Fig. 5 presents the calculated concentration profiles of the total VSS and the aceticlastic methanogens (the most important bacteria in the system) along the reactor height at the end of each the OLR applied. Fig. 5a clearly shows that the height of the high-density sludge zone (sludge bed) varies significantly under the various operational regimes applied. Namely, this height significantly decreased during the first two periods of operation due to increased sludge wash out during this period (Fig. 3b). However, continuous improvement of the settling characteristics of the remaining sludge led to a gradual increase of the sludge bed height followed by a substantial elevation of VSS concentration in this zone (Fig. 5a). Interestingly, at a 10w'OLR of 1.91 g COD/dm3/day, there is a sharp distinction between the sludge bed (high and constant solid concentration) and the sludge blanket (lower and gradually decreasing solid concentration). This sharp distinction disappearsduring the subsequentincreasesof the OLR (Fig. 5a). Thus, 126 !


due to the continuous description of sludge dynamics along the reactor height, the dispersedplug-flow model is able to predict the position as well as the granularsludgeconcentrationgradient at the boundary betweenthe sludge bed and blanket zonesin a VASE reactor. According to our knowledge,none of the previouslyreported models of VASE reactorspossess this ability without any arbitrarily division of the reactor volume into different zones with postulated mixing regimes. It should also be noted that that subsequent increases the OLR led to a significant enrichmentof the sludgeby aceticlasticmethanogens of (Fig. 5b), which agreeswith many other experimentalobservations. However,the model also predictsthat evena sludge substantiallyenrichedby aceticlasticmethanogens (e.g., at the end of experiment)can not copewith a heavy overloadingof the reactor,as indicatedby a simulation where the OLR was doubledin comparison with the OLR applied during the last period (data not shown). In the latter case,the reactor failedbecause VFA productionexceeded assimilativemethanogenic the the capacityof the sludge.

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Fig. 4. Model versusexperimentfor the pH (a-b) and COD (c-d) profiles along the reactorheight after an operating period of3 HRTs at an OLR (g COD/dm3/day) (a,c) 5.76 and (b,d) 7.82 (points - experimental of data; lines - model).

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CONCLUSIONS This paper presenteda newly developed dispersedplug flow model of VASE reactors based on the combination sludge dynamics and bacterial metabolism.According to our knowledge,this is the first of successful attemptin the creationof modelsof a new generation which are able to simulatecomplex space heterogeneous dynamics,not only of solutesbut also of the granularsludge(e.g., immanentformation and 127

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development sludgebed and blanketzones,sludgewash-out)inside VASE reactors. of The second princil difference of the presentedmodel with the models of VASE reactorsproposedbefore is that it gives universal descriptionof both hydrodynamics and solids dynamicsby continuousequationsthroughoutt

reactorvolume.The third prominent feature the dispersed of plug flow modelis that it reliessolely4
internal mechanisms the bioprocesses predict sludgewashoutfrom the reactor.This featureis a distin of to advantage over the world-wide used approachto model anaerobicreactorswith a fixed sludgeretenti< time. The latter was routinely transferredfrom the activated sludge reactor models but can no longer 1 valid, at least,for the descriptionof high-rateanaerobic reactorsbecause the principal differences of betwe( thesetreatmentsystems.The above-mentioned abilities of the describeddispersedplug flow model mal this type of mathematical modelsa powerful tool for the designandcontrol ofUASB reactors. Despite its conceptualadvantages over the modelsproposedthus far, the describedmodel also usedsom assumptions empirical equations, and which have to be further fine-tuned.It should, nevertheless, note be that so far no alternativemathematicalexpressions available for the empirical relations adoptedin th are presentpaperto describethe time dependency the average of aggregate diameterand sludgedensity.Furthe research derive theserelationsis requiredto fine-tunethe developed to mathematical model. The paramete sensitivity analysis showed that the growth properties of protein-degradingbacteria and acetotrophil methanogens (especially ~m) as well as the sludge settleability characteristics the parameters, are whicl influencean VASE reactormost. The kinetic propertiesof the bacteriainvolved in anaerobic digestionhavc receivedextensiveattention in the literature.In contrast,internal sludgedynamicsin VASE reactorshav( beenstudiedscarcely, which hampers further comprehensive validation,justification and development ofth( dispersedplug flow model. Therefore, further elucidation of internal mechanismsof the functioning oj VASE reactors, which allow to upgradethe present model, requires new comprehensive experimental studiesincluding both traditionally measured "black box" characteristics (overall reactorperformance, gas production etc.), supplemented with detailed documentationof the profiles of COD, VFA, VSS, specific metabolicactivity, aggregate diameteranddensityalongthe reactorheight. REFERENCES

Buffiere P., Fonade C. and Moletta R. (1998). Mixing and phasehold-ups variations due to gas production in anaerobicfluidized-beddigesters:influence on reactorperformance. Biotechnol.Bioeng.,60, 36-43. ChangH.T. and Rittman B.E. Mathematicalmodelingofbiofilm on activatedcarbon.(1987).Environ. Sci. Technol.,21, 273-280. Darton R.C. (1985). The physical behaviour of three-phasefluidized beds. In: Fluidization, J.F. Davidson,R. Clift, and D. Harrison(eds.),2nd edn,AcademicPress, London,New York, pp. 495-525. Franklin R.J. (2001). Full scale experiences with anaerobictreatmentof industrial wastewater. In: Anaerobic digestion sustainabledevelopment. for Papersof thefarewell seminarof prof GatzeLettinga, J. van Lier andM. Lexmond(eds.),Wageningen, Netherlands, the pp.2-8. Hulshoff Pol L.W. (1989). The phenomenonof granulation of anaerobic sludge. Ph.D. thesis, Wageningen Agricultural University, The Netherlands. Kalyuzhnyi S.V .and Fedorovich V. V. (1998). Mathematical modelling of competition between sulphate reductionandmethanogenesis anaerobic in reactors. Biores. Technol.65,227-242. Narnoli S.K. and Mehrotra I. (1997). Sludgeblanketof VASE reactor:mathematical simulation.Wat. Res.,31,715-726. Yan J.Q.; Lo K.V. and Liao P.H. (1989).Anaerobicdigestionof cheese whey using up-flow anaerobic sludgeblanketreactor.Bioi. Wastes, 289-305. 27, Yan J.Q., Lo K.V. and Pinder K.L. (1993). Instability causedby high strengthof cheese whey in a VASE reactor.Biotechnol.Bioeng.,41,700-706. Zhukova, T.B. (1991). Investigationand modeling of bubble column reactors.ftogi Nauki i Tekhniki, Ser.Processes Apparatuses ChemicalTechnology, 18,VINITI Press:Moscow. and of v.

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