Simplified Mathematical Model for an Anaerobic SequencingBatch Biofilm Reactor Treating Lipid-Rich Wastewater

Subject to Rising Organic Loading Rates

Maıra Ciaramello Fuzzato,1 Maria Angela Tallarico Adorno,2 Samantha Cristina de Pinho,1

Rogers Ribeiro,1 and Giovana Tommaso1,*

1Laboratory of Environmental Biotechnology, Department of Food Engineering, School of Animal Science and Food Engineering;2Laboratory of Biological Processes, Department of Hydraulics and Sanitation, Sao Carlos School of Engineering (EESC);

University of Sao Paulo (USP) Sao Carlos, Sao Paulo, Brazil.

Received: June 16, 2008 Accepted in revised form: May 28, 2009

Abstract

This study proposes a simplified mathematical model to describe the processes occurring in an anaerobicsequencing batch biofilm reactor (ASBBR) treating lipid-rich wastewater. The reactor, subjected to rising organicloading rates, contained biomass immobilized cubic polyurethane foam matrices, and was operated at328C� 28C, using 24-h batch cycles. In the adaptation period, the reactor was fed with synthetic substrate for 46days and was operated without agitation. Whereas agitation was raised to 500 rpm, the organic loading rate(OLR) rose from 0.3 g chemical oxygen demand (COD) �L�1 �day�1 to 1.2 g COD �L�1 �day�1. The ASBBR wasfed fat-rich wastewater (dairy wastewater), in an operation period lasting for 116 days, during which fouroperational conditions (OCs) were tested: 1.1� 0.2 g COD �L�1 �day�1 (OC1), 4.5� 0.4 g COD �L�1 �day�1

(OC2), 8.0� 0.8 g COD �L�1 �day�1 (OC3), and 12.1� 2.4 g COD �L�1 �day�1 (OC4). The bicarbonate alkalinity(BA)=COD supplementation ratio was 1:1 at OC1, 1:2 at OC2, and 1:3 at OC3 and OC4. Total COD removalefficiencies were higher than 90%, with a constant production of bicarbonate alkalinity, in all OCs tested. Afterthe process reached stability, temporal profiles of substrate consumption were obtained. Based on these ex-perimental data a simplified first-order model was fit, making possible the inference of kinetic parameters. Asimplified mathematical model correlating soluble COD with volatile fatty acids (VFA) was also proposed, andthrough it the consumption rates of intermediate products as propionic and acetic acid were inferred. Resultsshowed that the microbial consortium worked properly and high efficiencies were obtained, even with highinitial substrate concentrations, which led to the accumulation of intermediate metabolites and caused lowspecific consumption rates.

Key words: anaerobic process; sequencing batch reactor; ASBBR; lipid-rich wastewater; kinetic model

Introduction

Lipids are noted in literature as problematic to theanaerobic treatment of effluents, where these problems

are always related to biomass wash-out, short circuit forma-tion, and micro-organism inhibition via exposure to long-chain fatty acids (Alves et al., 2000; Vidal et al., 2000; Demirelet al., 2005). However, Hwu et al. (1997) showed that, in

granular reactors, sludge bed wash-out is likely to be en-countered prior to methanogenesis inhibition. In this context,the problem of degrading wastewaters with high levels oflipids seems to be closely related to retention of anaerobicbiomass inside the reactor. Among the industries with highlevels of lipids emissions, the dairy industry stands out as agenerator of wastewaters that are difficult to stabilize viaanaerobic biodegradation. This difficulty stems from the factthat once the lipids in the effluents are in emulsion form, theyhinder physical separation (Leal et al, 2002).

Conventional anaerobic processes are widely employed forthe treatment of dairy wastewaters; although there are fewrecent works regarding the subject, anaerobic filters and up-flow anaerobic sludge blanket (UASB) reactors are the mostcommonly found systems for such treatment (Demirel et al.,

*Corresponding author: Laboratory of Environmental Biotechnol-ogy, Department of Food Engineering, School of Animal Science andFood Engineering, University of Sao Paulo (USP), Av. Duque deCaxias Norte, 225, Jd. Elite, Pirassununga, SP, 13635-900, Brazil.Phone: þ55-19-3565-4304; Fax:þ55-19-3565-4284; E-mail: tommaso@usp.br

ENVIRONMENTAL ENGINEERING SCIENCEVolume 26, Number 7, 2009ª Mary Ann Liebert, Inc.DOI: 10.1089=ees.2008.0175

1197

2005). Typically, dairy industry wastewaters are generatedintermittently, so their flow rates fluctuate significantly.Moreover, due to the variety of products originating from thedairy plant, the wastewater characteristics vary substantially.

Due to these influent characteristics, batch systems havebeen a suitable option to treat this type of wastewater.However, due to their high initial substrate concentrations,which may lead to the accumulation of intermediate metab-olites, the batch reactors operation must be studied carefully.

Among the batch anaerobic configurations, the anaerobicsequencing batch reactor (ASBR) deserves great attention,operating with granular or immobilized biomass. Sung andDague (1995) evaluated the performance of such a reactor intreating a synthetic substrate containing nonfat dry milk(NFDM). They used four bench-scale ASBRs, with granularbiomass, operating with hydraulic detention times of 12, 24,and 48 h, and with different organic loadings (from 2 to 12 gchemical oxygen demand (COD) �L�1 �day�1). With a cycletime of 6 h, the reactors achieved removal efficiencies higherthan 90% under all conditions tested. Dugba and Zhang(1999) employed a two-phase system to treat dairy waste-water, comparing mesophilic and thermophilic operationalconditions with hydraulic retention times (HRTs) of 3 and 6days under increasing organic loadings (2 to 8 g �L�1 �day�1).The authors observed that the mesophilic–thermophilic sys-tem was better than the mesophilic, but remarked the energeticrequirements must be taken into account when consideringthe former option. The treatment of cheese whey was testedby Ratusznei et al. (2003), using an anaerobic sequencing batchbiofilm reactor (ASBBR) with biomass immobilized on poly-urethane foam (PUF) matrices. The reactor was fed with de-hydrated reconstituted cheese whey with increasing CODconcentration, varying from 500 to 4,000 mg COD �L�1. Withan 8-h cycle time and 200 rpm mechanical stirring (at 308C),the global efficiency of the system was always higher than96% (COD removal) and the effluent COD concentrationswere below 160 mg �L�1.

A description of the effect of increasing organic loading rate(OLR) and decreasing alkalinity supplementation was pre-sented by Mockaitis et al. (2006), in an ASBBR with granularbiomass fed with reconstituted cheese whey. With a cycle timeof 8 h and OLR varying from 0.6 to 4.8 g COD �L�1 �day�1, theremoval efficiency was higher than 90%; however, biomassflotation occurred with more concentrated substrates.

The treatment of diluted cheese whey by ASBBR wasstudied by Damasceno et al. (2007) under different feedstrategies and OLRs. The applied organic loads were 2, 4, 8,and 12 g COD �L�1 �day�1, obtained by increasing the feedconcentration. PUF cubes were used as supports for biomassimmobilization, and stirring to a speed of 500 rpm was pro-vided by propeller impellers. The reactor treated 2 L ofwastewater in 8-h cycles at 500 rpm and 308C. For each ap-plied organic load, three feed strategies were tested: an 8-hcycle batch operation; a 2-h fed-batch operation followed by a6-h batch; and a 4-h fed-batch followed by a 4-h batch. At allinvestigated OLRs and feeding times, the ASBR containingimmobilized biomass showed high organic matter conver-sions, indicating that this technology can be applied to thetreatment of cheese whey under different operating condi-tions.

Bezerra et al. (2007) evaluated the effects of OLR, shockload, and alkalinity supplementation on the efficiency and

stability of an ASBBR containing biomass immobilized onPUF matrices. Mixing in the reactor, which was kept at30� 18C, was achieved by recirculating the liquid phase. Thereactor treated 2.5 L of cheese whey in 8-h cycles, at con-centrations of 1, 2, and 4 g COD L�1, which corresponded toOLRs of 3, 6, and 12 g COD �L�1 �day�1, respectively. Theremoval efficiencies of total COD were 91� 2, 77� 2, and66� 2% for the applied OLR levels of 3, 6, and 12 g CODL�1 �day�1, respectively. Applying single-cycle shock loads of6, 12, and 24 g COD �L�1 �day�1 did not impair reactor per-formance.

Goblos et al. (2008) studied the performance of anaerobicsequencing batch reactors treating raw acid whey and acidwhey fermented with Kluyveromyces lactis (an ethanol pro-ducer). The OLRs during the experiment ranged from 1.6to 12.8 g COD �L�1 �day�1, with corresponding decreasingHRTs from 40 to 5 days for both reactor systems. At maximumOLR, the COD removal efficiency was 68% for the reactors fedwith raw whey, and 80% for those fed with the prefermentedwhey. In contrast, the methane yield was bigger for reactorsfed with prefermented whey. A relatively large amount ofvolatile fatty acids was produced from the untreated acidwhey, but only acetic acid was detected when prefermentedwhey was used. Without pH control, the reactor fed withprefermented whey remained within a suitable range of pHfor methanogenesis, whereas the reactors treating raw acidwhey pH levels lowered to 5.1.

Process modeling is a useful tool for describing andpredicting the performance of anaerobic digestion systems.Among the models tested, there are Monod-type kineticmodels (Lokshina et al., 2001; Borja et al, 2005; Shimada et al.,2007) and Haldane models (Lokshina et al., 2001); both widelyused to describe the process kinetics of anaerobic digesters.Aguilar et al. (1995) evaluated the kinetic parameters of vol-atile fatty acid (VFA) degradation for two methanogenicpopulations previously enriched in continuous digesters andfed with acetate or glucose as the main carbon source. Thevalues obtained for Ks and Vmax, as calculated for VFA utili-zation, suggested that sludges acclimatized to the presence ofVFA that arose from substrate degradation could use the VFAbetter than not acclimatized sludge. Lokshina and Vavilin(1999) used the integrated Monod and Haldane models toevaluate kinetic coefficients, using the methane accumulationcurves of low-temperature acetoclastic methanogenesis. Forthe wide range of initial acetate concentrations applied to theUASB biomass, a better fit was obtained using the Haldanemodels and their exponential approximations.

Based on the revealed data, simplified models concerningthe VFA dynamic in anaerobic treatment of dairy waste-waters are highly valuable because VFA formation has aninhibitory step [related to long-chain fatty acid (LCFA)presence] that affects its consumption. Thus, to give a con-tribution to the batch treatment of lipid-rich wastewaters,the present study monitored an ASBBR treating real waste-water, which was subject to increasing OLRs, from a dairyindustry. This enabled an evaluation of the importance ofthis parameter (OLR) to the process efficiency. Additionalinformation about intermediate products accumulated in theprocess and overall synthesis yield was obtained by apply-ing a simplified model to the experimental kinetic data,which was also able to predict the higher expected accu-mulated VFA concentration.

1198 FUZZATO ET AL.

Materials and Methods

Operation of the ASBBR

A bench-scale anaerobic sequencing batch biofilm reactor(ASBBR) was employed, with a working volume of 3.9 L. Theinert support used in this study consisted of 1-cm cubic PUFparticles (95% porosity, average pore size of 543� 154mm)arranged in a perforated basket inside the reactor (18-cm di-ameter and 18-cm height), resulting in a bed with porosityaround 40%.

The sludge inoculum was obtained from a full-scale UASBreactor treating slaughterhouse wastewater. To immobilizethe biomass, the granules were macerated and well mixedwith the polyurethane foam particles. The sludge was thenplaced in contact with the foam for 24 h before being placed inthe perforated basket.

During the adaptation period, the reactor was fed with anNFDM-based synthetic substrate for 46 days, with decreasingcycle times of 96, 72, and 48 h, without agitation. After thisperiod, the cycle time was fixed at 24 h. With this proce-dure, the OLR rose from 0.3 g COD �L�1 �day�1 to 1.2 gCOD �L�1 �day�1. After the cycle time was fixed at 24 h, theagitation rate was held at 300 rpm for 13 days and thenat 500 rpm for 14 days. The reactor was maintained in atemperature-controlled chamber at 30� 28C. This bench-scaleinstallation is similar to the one described by Pinho et al.(2005).

After the adaptation period, the substrate was changed towastewater from a dairy plant that processes integral milkand cheese, without serum segregation, with primary CODlevels of 13,303� 2,429 mg �L�1. The reactor was submittedto increasing OLR: 1.1� 0.2 g COD �L�1 �day�1 (OC1, 14days), 4.5� 0.4 g COD �L�1 �day�1 (OC2, 33 days), 8.0�0.8 g COD �L�1 �day�1 (OC3, 42 days), and 12.1� 2.4 gCOD �L�1 �day�1 (OC4, 27 days). The substrate was supple-mented with bicarbonate alkalinity (BA) at BA=COD ratios of1 [operating condition (OC) one (OC1) and OC2), 0.5 (OC3),and 0.3 (OC4). This supplementation also acted as a pH cor-rector, because its original value was always around 4. Thereactor was operated in batch mode with sequential 24-h cy-cles, with feeding and discharge steps lasting for 6 and 2 min,respectively.

COD and solids analyses were performed based on themethods described in Standard Methods for Examination ofWater and Wastewater (American Public health Association,1998), methods 5220 and 5540, respectively. Total volatile acid(TVA) concentration (mgHAc �L�1) and BA (mgCaCO3 �L�1)were performed according to Dillalo and Albertson (1961)modified by Ripley et al. (1986). The pH value was measuredwith a calibrated potentiometer immediately after samplecollection, to avoid variations due to CO2 escape, as re-commended by Speece (1996). The lipid content was mea-sured according to Postma and Stroes (1968) modifiedby Blundi and Gadelha (2001). Suspended (CODSS), filtered(CODF), and colloidal (CODC) COD data were assessed using1.2- and 0.45-mm pore membranes. The filtered fraction wasobtained from samples filtered with 1.2-mm pore membranes,and the colloidal fraction was calculated from the differencebetween the results obtained from the 1.2- and 0.45-mm fil-tered samples. The colloidal fraction was only measured in thetemporal profiles. VFA analyses were performed by gaschromatography according to Moraes et al. (2000).

Temporal COD profiles, obtained throughout the batchcycles under variable OLRs, allowed a broader analysis ofthe influence of this operational condition on the reactor’sperformance. The reactor was left at each OLR until stabilitywas reached, based on COD removal and BA production.

Kinetic treatment

As employed previous authors (Cubas et al., 2004; Pinhoet al., 2004, 2005, 2006; Miqueleto et al., 2005; Mockaitis et al.,2006), a modified first order kinetic model similar to the onedeveloped by Vavilin (2007) was fitted to the data from thetemporal profiles:

CS¼CSRþ (CS0�CSR) exp (�kapp1 t): (1)

In Equation (1), t is the time (min); CS and CS0 are, respec-tively, the substrate concentration (as COD) at t and to (initialtime, assumed as zero); CSR is the residual COD (mg �L�1),and k

app1 is the apparent first-order kinetic constant. From

Equation (1), the value of the initial substrate consumptionvelocity was calculated in accordance with Equation (2).

r0¼ kapp1 (CS0�CSR): (2)

Simplified mathematical model formulation

The model, which does not include the hydrogenotrophicpathway, was applied to the experimental data showing theconversion of soluble organics (excluding the CODF corre-sponding to VFA) into volatile acids (acetic and propionic).Although it certainly occurred, the hydrogenotrophic path-way was not included because it was impossible to measuremethane production. This was because the reactor was notcompletely sealed, which precluded measurement by liquiddisplacement.

In the model described in Fig. 1, r1 and r2 represent ratesof soluble organic matter consumption, whereas r3 and r4

represent rates of propionic acid and acetic acid reactions,respectively.

Through mass balance of a batch reactor, the consumptionand formation rates for each component can be described byEquation (3). That is, the net rate of reaction for each com-ponent j is the sum of reactions in which component j appears.For n reactions taking place:

dCj

dt¼ rj¼

Xn

i¼ 1

rij, (3)

where C is the concentration of j component in COD basis, r isthe reaction rate i, for each component j, as described in Fig. 1.The j components are defined as following: S is soluble or-ganic matter; P is propionic acid; A is acetic acid, and i is the

FIG. 1. Schematic of simplified mathematical model.

KINETIC MODEL APPLIED TO LIPID-RICH EFFLUENT DEGRADATION 1199

mathematic representation of the metabolic pathways presentin Fig. 1.

The simplified model described by Equation (4) was basedon the model proposed by Monod, neglecting biomass decayduring the period of data acquirement.

� dCS

dt¼ 1

YX=S� lmax � CS

kSþCS� CX, (Monod model)

rij¼lij

YX=j, i� CXij

¼ 1

YX=j, i�lmaxij

� Cj

kSijþCj

� CXij¼

Uij � Cj

kSijþCj

, (4)

where:

rij¼Uij � Cj

kSijþCj

and Uij¼lmaxij

YX=j, i� CXij

,

where lmax ij is the maximum specific growth rate of biomassfrom step reaction i for component j, kS ij is the half-saturationcoefficient from step reaction i for component j, CXij is thebiomass concentration related to step reaction i for componentj, YX=j,i is the yield coefficient conversion of component j fromstep reaction i in biomass CX ij, and Uij is the maximum rate ofsubstrate consumption.

According to the scheme of the simplified mathematicalmodel, the mass balances for each step of the soluble organicmatter consumption, propionic and acetic acid reaction arepresented as follows.

Soluble organic matter fraction:

rS¼ �dCS

dt¼ r1Sþ r2S,

The Monod-like model was used to evaluate soluble or-ganic matter consumption, but this model converged to a firstorder relationship for filtered COD conversion. Consequently,U1S and U2S became first-order kinetic constants (k1S and k2S,respectively). The residual concentration (CSR) was subtractedfrom the organic matter concentration for each OC, becausenot all of it was susceptible to conversion to either acetic orpropionic acid. Thus, the rate of consumption for soluble or-ganic matter can be described by Equation (5).

dCS

dt¼ � k1S(CS�CSR)� k2S(CS�CSR); (5)

where:

k1S¼lmax1S

YX=1S � kS1S

� CX1Sand k2S¼

lmax2S

YX=2S � kS2S

� CX2S:

In Equation (5), t represents time (h); CS is the substrateconcentration (as soluble COD), CSR is the residual solubleCOD, k1S and k2S(h�1) are the first-order kinetic constants.

Propionic acid:

rP¼dCP

dt¼ þ r1P� r3P,

r1P¼YP=S � r1S:

The parameter YP=S was considered a ‘‘mass coefficient’’;that is, it represented the portion of the soluble organic matter

(g COD) that was effectively converted to propionic acid(g COD).

dCP

dt¼YP=SK1S(CS�CSR)� K3PCP

kS3PþCP

: (6)

Acetic acid:

rA¼dCA

dt¼ þ r2Aþ r3A� r4A,

r2A¼YA=S � r2S,

r3A¼YA=P � r3P:

Analogous to the definition of soluble organic matter con-version to propionic acid, YA=S was defined as the portion ofthe soluble organic matter converted effectively to acetic acid(g COD). This is a correction parameter, which is necessarybecause the COD and VFA concentrations are not in the sameunits. The relation between propionic acid consumption andacetic acid formation was based on the stoichiometric ratio(YA=P¼ 0.536 g acetic acid � g�1 propionic acid) proposed byMcCarty (1972).

dCA

dt¼YA=Sk2S(CS�CSR)þYA=P

U3PCP

kS3PþCP

� U4ACA

kS4AþCA

: (7)

The system formed by nonlinear differential Equations (5),(6), and (7) was solved by the fourth-order Runge-Kuttamethod with the aid of the Microsoft Excel� Solver Tool.

Results and Discussion

Operational profiles

The behavior of the system throughout the startup periodwith NFDM clearly indicated that the reactor was fullyadapted to the substrate, produced BA, and had average re-moval efficiencies of 83%; thus, it was ready to receive the realdairy wastewater.

The reactor was then operated for 116 days, and reachedtotal COD removal of 94� 1.5%, 96� 1.2%, 94� 3.5%, and91� 2.7 when the applied OLRs (based on total reactor vol-ume) were 1.1� 0.2 g COD �L�1 �day�1, 4.5� 0.4 g COD �L�1 �day�1, 8.0� 0.8 g COD �L�1 �day�1, and 12.1� 2.4 gCOD �L�1 �day�1, respectively. Figure 2 shows the opera-tional profile of the increasing organic loading rates. Similarefficiencies were obtained by Mockaitis et al. (2006) and Ra-tusznei et al. (2003), but with a synthetic dry whey-basedsubstrate of 4.79 g COD �L�1 �day�1 and a maximum OLRof 5.7 g COD �L�1 �day�1. Bezerra et al. (2007) used a reactortreating diluted cheese whey in 8-h cycles to obtain pri-mary removal efficiencies of total COD of 91� 2%, 77� 2%,and 66� 2% when working with OLRs of 3, 6, and 12 gCOD �L�1 �day�1, respectively. The system exhibited theformation of a viscous problematic polymer-like substance inOC2, OC3, and OC4. This phenomenon had previously beenreported by Miqueleto et al. (2005), who used an ASBBR withbiomass immobilized on 1-cm cubic PUF particles, operatedin 8-h cycles to treat wastewater containing only glucose inconcentrations of 500, 1,000, and 2,000 mg �L�1. The appliedOLRs were 1.5, 3.0, and 6.0 g �L�1 �day�1. The authors ob-served that the reactor showed operating stability whensubmitted to an OLR of 1.5 g �L�1 �day�1, with CODF removal

1200 FUZZATO ET AL.

efficiencies varying from 93 to 97%. The system showed op-erational instability due to polymer formation when submit-ted to OLRs of 3.0 and 6.0 g �L�1 �day�1, which lead to theconclusion that polymer production depends on the organicvolumetric load applied to the reactor.

Operating an ASBR containing granular biomass totreat cheese whey, with OLR varying from 0.6 to 4.8 gCOD �L�1 �day�1, Mockaitis et al. (2006) also observed theformation of viscous polymer-like substances. The authorsconcluded that these polymers were probably of microbio-logical origin. The problem occurred mainly with the appliedOLRs of 2.4 and 4.8 g COD �L�1 �day�1, which corroboratedwith the conclusions of Micheleto et al. (2006). In the pres-ent work, this phenomenon occurred when the appliedOLRs were greater than 4.5� 0.4 g COD �L�1 �day�1, which ishigher than those used by Miqueleto et al. (2005) and Mock-aitis et al. (2006). Based on these studies it can be inferred thatthe polymers produced were probably of microbiological or-igin, and were excreted as a function of the applied OLR. The

polymer production necessitated a system cleanup, thus de-creasing the process efficiency. However, the previous re-moval efficiency level was promptly reestablished. For eachset of operational conditions, the same phenomenon occurredwith high stability, which was confirmed by the production ofBA and consumption of TVA as demonstrated by Fig. 3.

The lipid content in the wastewater used herein was 2.4,44.7, 156, and 240 mg �L�1 for OC1, OC2, OC3, and OC4, re-spectively. The temporal profiles showed lipid removal effi-ciencies of 77% in OC1, 97% in OC2, 95% in OC3, and 91% inOC4. A modified first-order kinetic model was fitted to theexperimental data in OC2, OC3, and OC4, with values of k

app1 ,

being 0.29� 0.017 h�1, 0.35� 0.016 h�1, and 0.36� 0.047 h�1,respectively. It is important to highlight that due to themethod utilized to measure lipid concentration, which in-cludes an acid hydrolysis step, the observed concentrationscould include LCFAs. As Vidal et al. (2000) and Pereira et al.(2004) had already verified, despite of the presence of LCFAsoriginating from the lipid metabolism, and even with possi-bility of inhibition caused by these molecules, the anaerobicpopulation was always able to degrade the substrate.

Kinetic analyses

The model expressed in Equation (1) was fitted to the ex-perimental data for CODF from 1.2-mm pore membranes withgood correlation factor (R2) values: 0.99, 0.94, 0.97, and 0.94 forthe fittings presented in Figs. 4a, 5a, 6a, and 7a, respectively.

In Figs. 4b–7b, it can be seen that the organic matter con-sumed at the beginning of the process generated a VFA peak,which was always buffered by the BA supplementation to thesubstrate. This contributed to the maintenance of pH values atacceptable levels for methanogenesis, that is, from 6.8 to 7.7 inall obtained profiles, obviously reaching its lowest values atthe highest VFA concentration. Based on these facts is possibleto infer that, as reported by Ratusznei et al. (2003), reactorperformance is closely related to the BA supplementation. Onthe other hand, the observed BA production, which is prob-ably related to the protein degradation, led to the inferencethat different feed forms could reduce the required amount ofsupplemented alkalinity by maintaining part of the treated

FIG. 2. Operational profile of increasing organic loadingrates. Experimental values: (&) influent CODT; (�) effluentCODT; (&) influent CODF; (�) effluent CODF. Removal effi-ciencies: (~) CODT; (~) CODF. COD, chemical oxygen de-mand.

FIG. 3. Operational profile of bicarbonate alkalinity (BA) and total volatile acid (TVA) along increasing organic loading rate(OLR): (a) (&) influent BA; (&) effluent BA. (b) (�) influent TVA; (�) effluent TVA.

KINETIC MODEL APPLIED TO LIPID-RICH EFFLUENT DEGRADATION 1201

effluent in the reactor. It is important to highlight that thepresence of butyric, isobutyric, caproic, valeric, and isovalericacids were observed only in OC4, but at concentrations muchlower than the propionic and acetic acid concentrations.

These results show that for OC2, OC3, and OC4, the modeldid not fit the filtered CODF data well between the 2nd and11th process hour, a period coincident with the highest VFAconcentrations. These high concentrations are part of the CODfraction (Figs. 5b, 6b, and 7b). This fact necessitated the ap-plication of a more complex model to separate the VFA fromthe organic matter expressed as CODF.

The values estimated for kapp1 and r0 (initial substrate con-

sumption rate) in each OC are presented in Table 1. The initialsubstrate concentration was considered fixed, and representsthe CODF 3 min after the feeding operation. After the k

app1

peak at OC2, its decrease can be related to the high accumu-lated volatile acid concentrations (also measured as COD)observed at OC3 and OC4. The reduction of r0 values did not

occur at OC3 because the increase of the initial substrateconcentration counterbalanced the decrease in k

app1 value. This

compensation did not occur again in the fourth conditionbecause there was a more significant reduction in the k

app1

value. A similar behavior was observed by Mockaitis et al.(2006), in which the authors also noted an increase at the k

app1

values when the OLR was raised from 0.59 to 1.15 gCOD �L�1 �day�1, followed by a decrease.

An important observation of the present work is that, in allkinetic profiles obtained, the colloidal fraction removal effi-ciency reached 96%. According to Petruy and Lettinga (1997),the colloidal fraction is considered recalcitrant in anaerobicprocesses in granular reactors such as UASBs and expandedgranular sludge bed reactors (EGSBs). However, this expectedrecalcitrance was not corroborated observed in the study herepresented with ASBBR, probably due to the more effectivemixing condition provided by the mechanical stirring and tothe biomass immobilization conditions.

FIG. 4. Temporal profiles for samples obtained from the anaerobic sequencing batch biofilm reactor (ASBBR) operated inoperating condition (OC) 1. (a) (&) CODT; (�) COD; (~) CODC. (b) (&) BA (mg CaCO3 �L�1); (�) acetic acid; (~) propionicacid.

FIG. 5. Temporal profiles for samples obtained from the ASBBR in OC2. (a) (&) CODT; (�) CODF; (~) CODC. (b) (&) BA (mgCaCO3 �L�1); (�) acetic acid; (~) propionic acid.

1202 FUZZATO ET AL.

It is necessary to highlight that the suspended COD re-moval efficiency was always lower than the removal of otherfractions, varying from 77% (OC4) to 89% (OC3), confirmingthat the filtrating effect was not preponderant to the overallprocess efficiency.

Another important value determined was the biomasspresent in the reactor (32.2 g TVS �L�1), which was found to be1.95 mg total volatile solids (TVS) �mg PUF�1. Values deter-mined by Cubas et al. (2004), and Pinho et al. (2005) were, onaverage, around 1.2 mg TVS �mg PUF�1. The difference be-tween our results and the literature can be explained by theabsence in those studies of polymeric production and bythe possible adsorption of substances present in the substrate(like lipids from the milk) in the present study.

Simplified mathematical model

Fitting the simplified mathematical model described in theMaterials and Methods section [Equations (5), (6), and (7)]resulted in the curves presented in Figure 8.

Figure 8 clearly shows that the proposed simplifiedkinetic model fit the experimental data well, because thecorrelation coefficient found was 0.9829. These results canbe considered expressive, because a very simple mathe-matical model was able to describe a very complex pro-cess: the anaerobic conversion of a real complex substratelike dairy wastewater. The kinetic coefficients valuesobtained via nonlinear regression are summarized inTable 2.

The values of k1 and k2, 2.91 and 2.84 h�1, respectively, werehigher than values of apparent first-order kinetic constants(k

app1 ). This behavior was expected, because kinetic coeffi-

cients k1 and k2 refer specifically to rates of soluble organicmatter consumption, excluding the CODF from acetic andpropionic acids.

It is important to highlight that the estimated half-saturation Monod constant for propionic and acetic acidconsumption were similar, whereas the maximum substrateutilization rate value for acetic acid was 67% higher than thatestimated for propionic acid.

FIG. 6. Temporal profiles for samples obtained from the ASBBR operated in OC3. (a) (&) CODT; (�) CODF; (~) CODC. (b)(&) BA (mg CaCO3 �L�1); (�) acetic acid; (~) propionic acid.

FIG. 7. Temporal profiles for samples obtained from the ASBBR operated in OC4. (a) (&) CODT; (�) CODF; (~) CODC. (b)(&) BA (mg CaCO3 �L�1); (�) acetic acid; (~) propionic acid.

KINETIC MODEL APPLIED TO LIPID-RICH EFFLUENT DEGRADATION 1203

The kinetic values for specific maximum substrate uti-lization rates for propionic (U3P � C� 1

X ) and acetic acid(U4A � C� 1

X ), converted to COD, were 0.51 and 0.60 mg COD.mg�1SVT �day�1, respectively. These were lower than valuesfound in literature, 6.2–7.8 mgCOD �mg�1 volatile suspendedsolids (VSS) �day�1 for propionic acid consumption and 2.6–26 mg COD �mg�1 VSS �day�1 for acetoclastic methanogen-esis (Pavlostathis and Giraldo-Gomez, 1991). Nevertheless,the verified biomass concentration was also higher thanfound in the literature.

The lower values of U4A � C� 1X might also be explained by

the toxic effect of exposure to the LCFA produced via lipidhydrolysis, as previously presented by Alves et al. (2000). Thelow value of U3P � C� 1

X may be explained by the high aceticacid concentrations observed. The conversion of propionicacid to acetic acid is one of the most thermodynamically un-favorable reactions in the suite of biochemical reactions thatcompose the anaerobic digestion (Harper and Pohland, 1986);thus, this reaction cannot happen without a very low con-centration of acetate or H2, both of which are reaction prod-ucts. Along the same lines, Stams et al. (1994) showed that theaddition of acetate inhibited propionate and butyrate oxida-tion, whereas the removal of acetate stimulated the growth ofsyntrophic propionate and butyrate oxidizing bacteria.

Finally, hydrogenotrophic pathways must be considered,because they contribute about 30% of the biogas production ina stable process. Stams et al. (1994) comments that the com-plete mineralization of propionate conversion to methane isdependent on three different micro-organisms: an acetogenicbacterium, a hydrogenotrophic methanogen, and a aceticlasticmethanogen. The author maintains that without a hydro-genotrophic methanogen, the required low H2 pressure

Table 1. Values Predicted by the Modified

First-Order Model to CS0, k1app, and r0

for All Operational Conditions

Operationalcondition

CS0 (CODF)(g � L�1)

CSR (CODF)(g � L�1)

kapp1

(h�1) Errorr0 (g � L�1 �

h�1)

OC1 0.596 0.023 0.30 0.02 0.172OC2 2.435 0.35 0.77 0.11 1.605OC3 5.190 0.474 0.57 0.07 2.688OC4 6.792 0.825 0.28 0.05 1.671

FIG. 8. Fitting of the simplified model to the experimental data (&—COD, �—acetic acid, ~—propionic acid).

1204 FUZZATO ET AL.

necessary to enable the thermodynamically unfavorable pro-pionate conversion to acetate would not occur. In the presentwork, the propionate was removed from the system; thus,even with a low specific utilization rate, it is possible to inferthat methane was being actively produced via the hydro-genotrophic pathway, and that this mechanism played animportant role in maintaining a stable anaerobic process. Onother hand, this must be acknowledged as a limitation of theproposed model that must be considered in its utilization.

Conclusions

The monitoring and kinetic data obtained in the presentwork clearly prove the feasibility of treating dairy wastewaterin an ASBBR. The operational data showed a very stableprocess over time, with very satisfactory BA production andVFA consumption, as well as high levels of COD removalefficiency (all three fractions: total, filtered, and colloidal). Thecolloidal COD removal reached remarkable removal levels,above 95%, in all operational conditions. This result justifiesthe use of a more efficient mixing condition in the batchreactors, a conclusion already shown in several previousstudies.

The accumulation and posterior washing of polymeric se-cretions did not influence on the overall reactor performance orthe final mg TVS=mg PUF ratio, which are both in an acceptablerange when compared to other similar studies. Nevertheless,for further studies concerning this subject, the potential accu-mulation of polymer-like substances must be concerned, as thebiogas and methane must be measured, to close the COD bal-ance and confirm the high removal efficiencies.

The modified first-order kinetic analyses resulted in coef-ficients of the same numerical order of similar studies, whichhelps corroborate the model validity. It is also notable that the24-h cycle time was long enough to appropriately treat thewastewater, even when higher OLRs were applied to thesystem.

The integrated simplified model presented in this studyshould be used to evaluate kinetic coefficients of anaerobicdegradation from dairy wastewater in ASBBRs. The kineticvalues calculated for specific maximum substrate utilizationrates for propionic and acetic acid were lower than in theliterature; nevertheless, the verified TVS concentration washigher than is typical, and partial inhibition of the biomasscould be happening due to the presence of LCFA. Despite itsintrinsic limitations, due to the inability of the experiments tomeasure methane and the absence of hydrogenotrophicpathway, the model may form a basis for future work on thetopic. Thus, these limitations must be considered in its utili-zation.

Based on these conclusions, the results strongly encouragethe scale-up of this reactor to treat dairy wastewater. How-ever, because agitation rate is among the most important as-pects related to scaling up from bench to industrial scale, afocused study should further investigate this operational pa-rameter. Techniques of scale-up mixing conditions are widelydescribed in the literature, and can certainly be applied to thecase of ASBBR.

Acknowledgments

The authors are grateful to FAPESP—Fundacao de Am-paro a Pesquisa do Estado de Sao Paulo for the financialsupport (2005=04353-9, 2006=02323-8), to E. Monterrey-Quintero for the ever-present encouragement and technicalsupport, to P.J. Sobral for the motivation, and to A.L. Gabas,for the space given for the experimental setup.

Author Disclosure Statement

The authors declare that no competing financial interestsexist.

References

Aguilar, A., Casas, C., and Lema, J.M. (1995). Degradation ofvolatile fatty acids by differently enriched methanogenic cul-tures: Kinetics and inhibition. Water Res. 29, 505.

Alves, M.M., Mota Vieira, J.A., Alvares Pereira, R.M., Pereira,M.A., and Mota, M. (2000). Efects on lipids and oleic acid onbiomass development in anaerobic fixed-bed reactors. Part II:Oleic acid toxicity and biodegradability. Water Res. 35, 264.

American Public Health Association=American Water WorksAssociation=Water Environment Federation. (1998). StandardsMethods for the Examination of Water and Wastewater, 20th ed.Washington, DC: APHA.

Bezerra, R.A., Jr., Rodrigues, J.A.D., Ratuszney, S.M., Zaiat, M.,and Foresti, E. (2007). Whey treatment by AnSBBR with cir-culation: Effects of organic loading, shock loads, and alkalinitysupplementation. Appl. Biochem. Biotechnol. 143, 257.

Blundi, C.E., and Gadelha, R.F. (2001). Methodology for specificdetermination of organic material in wastewaters. In: C.A.L.Chernicharo, Ed. Post-treatment of Effluent of anaerobic Reactors:Methodological Aspects. PROSAB: Belo Horizonte, 2001, p. 9 (inPortuguese).

Borja, R., Martın, A., Sanchez, E., Rincon, B., and Raposo, F.(2005). Kinetic modelling of the hydrolysis, acidogenic andmethanogenic steps in the anaerobic digestion of two-phaseolive pomace (TPOP). Proc. Biochem. 40, 1841.

Cubas, S.A., Foresti, E., Rodrigues, J.A.D., Ratusznei, S.M., andZaiat, M. (2004). Influence of liquid-phase mass transfer on the

Table 2. Values Predicted by the Simplified

Model for All Operational Conditions

Parameter Value

k1S (h�1) 2.91k2S (h�1) 2.82U3P (g COD from propionic acid expressed

as COD �L�1 �h�1)0.62

U4A (g COD from acetic acid expressedas COD �L�1 �h�1)

0.75

kS3P (g COD from propionic acid expressedas COD �L�1)

0.58

kS4A (g COD from acetic acid expressedas COD �L�1)

0.46

YA=S (g COD from acetic acid expressedas COD � g�1 CODF)

0.334

YP=S (g COD from propionic acid expressedas COD � g�1 CODF)

0.271

YA=P (g COD from acetic acid expressedas COD � g�1 COD from propionic acidexpressed as COD)

0.536

CSR-OC2 (g CODF �L�1) 0.134CSR-OC3 (g CODF �L�1) 0.090CSR-OC4 (g CODF �L�1) 0.254

KINETIC MODEL APPLIED TO LIPID-RICH EFFLUENT DEGRADATION 1205

performance of a stirred anaerobic sequencing batch reactorcontaining immobilized biomass. Biochem. Eng. J. 17, 99.

Damasceno, H.S., Rodrigues, J.A.D., Ratuszney, S.M., Zaiat, M.,and Foresti, E. (2007). Effects of feeding time and organicloading in an anaerobic sequencing batch biofilm reac-tor (ASBBR) treating diluted whey. J. Environ. Manage. 85, 927.

Demirel, B., Yenigun, O., and Onay, T.T. (2005). Anaerobictreatment of dairy wastewaters: A review. Proc. Biochem. 40,2583.

Dillalo, R., and Albertson, O.E. (1961). Volatile acids by directtitration. J. WPCF 33, 356.

Dugba, P.N., and Zhang, R. (1999). Treatment of dairy waste-water with two-stage anaerobic sequencing batch reactorsystems—Thermophilic versus mesophilic operations. Bior-esource Technol. 68, 225.

Goblos, S.Z., Portor}oo, P., Bordas, D., Kalman, M., and Kiss, I.(2008). Comparison of the effectivities of two-phase andsingle-phase anaerobic sequencing batch reactors during dairywastewater treatment. Renew. Energy 33, 960.

Harper, S.R., and Pohland, F.G. (1986). Recent developments inhydrogen management during anaerobic biological waste-water treatment. Biotechnol. Bioeng. 28, 585.

Hwu, C.-S., and Lettinga, G. (1997). Acute toxicity of oleate toacetate-utilizing methanogens in mesophilic and thermophilicanaerobic sludges. Enzyme Microbial Technol. 21, 297.

Leal, M.C.M., Camarota, M.C., Freire, D.M.G., Sant’Anna, G.L.,Jr. (2002). Hydrolytic enzymes as coadjuvants in the anaerobictreatment of dairy wastewaters. Braz. J. Chem. Eng. 19, 175.

Lokshina, L.Y., and Vavilin, V.A. (1999). Kinetic analysis of thekey stages of low temperature methanogenesis. Ecol. Model.117, 285.

Lokshina, L.Y., Vavilin, V.A., Kettunen, R.H., Rintala, J.A.,Holliger, C., and Nozhevnikova, A.N. (2001). Evaluation ofkinetic coefficients using integrated Monod and Haldanemodels of low-temperature acetoclastic methanogenesis. Wa-ter Res. 35, 2913.

McCarty, P.L. (1972). Energetics of organic matter degradation.Water pollution. In: R. Mitchell, Ed. Microbiology. New York:Wiley Interscience.

Miqueleto, A.P., Rodrigues, J.A.D., Ratusznei, S.M., Foresti, E.,and Zaiat, M. (2005). Treatment of easily degradable waste-water in a stirred anaerobic sequencing batch biofilm reactor.Water Res. 39, 2376.

Mockaitis, G., Ratusznei, S.M., Rodrigues, J.A.D., Zaiat, M., andForesti, E. (2006). Anaerobic whey treatment by a stirred se-quencing batch reactor (ASBR): Effects of organic loading andsupplemented alkalinity. J. Environ. Manage. 8, 1.

Moraes, E.M., Adorno, M.A.T., Zaiat, M., and Foresti, E. (2000).Determination of volatile fatty acids by gas chromatographyin effluents from anaerobic reactors treating solid and liquidwastes. In: Proceedings of Workshop and Symposium on AnaerobicProcesses. Recife, 2 p. 231 (in Portuguese).

Pavlostathis, S.G., and Giraldo-Gomez, E. (1991). Kinetics ofanaerobic treatment. Water Sci. Technol. 24, 35.

Pereira, M.A, Sousa, D.Z., Mota, M., and Alves, M.M. (2004).Mineralization of LCFA associated to anaerobic sludge: Ki-netics, transport limitations, enhancement of methanogenicactivity and effect of VFA. Biotechnol. Bioeng. 88, 502.

Petruy, R., and Lettinga, G. (1997). Digestion of a milk–fatemulsion. Bioresource Technol. 61, 141.

Pinho, S.C., Foresti, E., and Zaiat, M. (2006). Treatment of partiallysoluble wastewater in an anaerobic sequencing batch biofilmreactor: The role of impeller type. Environ. Eng. Sci. 23, 384.

Pinho, S.C., Ratusznei, S.M., Rodrigues, J.A.D., Foresti, E., andZaiat, M. (2004). Influence of the agitation rate on the treat-ment of partially soluble wastewater in anaerobic sequencingbatch biofilm reactor (ASBBR). Water Res. 38, 4117.

Pinho, S.C., Ratusznei, S.M., Rodrigues, J.A.D., Foresti, E., andZaiat, M. (2005). Influence of bioparticle size on the degrada-tion of partially soluble wastewater in an anaerobic sequenc-ing batch biofilm reactor (ASBBR). Proc. Biochem. 40, 3206.

Postma, T., and Stroes, J.A.P. (1968). Lipid screening in clinicalchemistry. Clin. Chim. Acta 22, 569.

Ratusznei, S.M., Rodrigues, J.A.D., Camargo, E.F.M., and Zaiat,M. (2003). Operating feasibility of anaerobic sequencing batchreactor containing immobilized biomass. Water Sci. Technol.48, 179.

Ripley, L.E., Boyle, W.C., and Converse, J.C. (1986). Improvedalkalimetric monitoring for anaerobic digestion of high-strength wastes. J. WPCF 58, 406. Shimada, T., Zilles, J., Ra-skin, L., and Morgenroth, E. (2007). Carbohydrate storage inanaerobic sequencing batch reactors. Water Res. 41, 4721.

Speece, R.E. (1996). Anaerobic Biotechnology for Industrial Waste-water. Nashville, TN: Archae Press.

Stams, A.J.M. (1994). Metabolic interactions between anaerobicbacteria in methanogenic environments. Antonie van Leeu-wenhoek 66, 271.

Sung, S., and Dague, R.R. (1995). Laboratory studies on theanaerobic sequencing batch reactor. Water Environ. Res. 67, 03.

Vavilin, V.A. (2007). Corrected first-order model of DEHP deg-radation. Chemosphere 68, 1992.

Vidal, G., Carvalho, A., Mendez, R., Lema, J.M. (2000). Influenceof the content in fats and proteins on the anaerobic biode-gradability of dairy wastewaters. Bioresource Technol. 74, 231.

1206 FUZZATO ET AL.