NOTES

Axial Dispersion Model for Upflow Anaerobic Sludge BlanketReactors

Ashish Singhal,† James Gomes,*,† V. V. Praveen,‡ and K. B. Ramachandran‡

Department of Biochemical Engineering & Biotechnology, Indian Institute of Technology,Delhi, Hauz Khas, New Delhi - 110016, and Department of Chemical Engineering, University of Malaya,50603 Kuala Lumpur, Malaysia

Fluid flow in UASB reactors is usually described by multicompartment modelsconsisting of separate ideally mixed zones, plug flow zones, and stagnant zones linkedwith bypassing flows and back-mixing flows. A closer look at UASB reactor behaviorindicates that this complexity is unnecessary. Our study on the startup and steady-state operation of a UASB reactor shows that its fluid flow can be explained just aswell with a simple axial dispersion model. The physical transitions, which occur indifferent zones of the UASB reactor as the microorganisms acclimate to the wastewater,are adequately described by the model. Further, the number of parameters, which issix in standard UASB reactor models, is reduced to four in the case of the axialdispersion model.

Introduction

The application of upflow anaerobic sludge blanket(UASB) reactors for wastewater treatment began withthe extensive work carried out by Lettinga and co-workers (Lettinga, 1978; Lettinga et al., 1980). Thesuccess of this reactor depends on the formation of highlyflocculated, compact sludge aggregates called granules(Schmidt and Ahring, 1996). The formation of granulesallows the active microbial biomass to be retained in thereactor. The efficiency of the reactor depends mainly onthe active biomass and the influent flow rate. As thereactor reaches steady-state conditions, a dense sludgebed consisting of granules develops at the bottom. Im-mediately above the sludge bed a zone containing finelysuspended particles called the sludge blanket forms. Aclear zone over this sludge blanket constitutes thesettling zone (Schmidt and Ahring, 1996). Because ofthis distinct physical characterization of the UASBreactor, it is well described by models comprising three(sometimes four) compartments (Heertjes and van derMeer, 1978; Heertjes and Kuijvenhoven, 1982; Bolle etal., 1986). These compartments have ideal attributessuch as ideal mixing, plug flow, and undisturbed settlingand are connected with bypassing flows or back-mixingflows.

These multicompartment models are all capable offitting experimental data well. However, each additionalcomponent increases the number of parameters to beevaluated and the complexity of the model. What wehave tried to determine is the usefulness of each com-

ponent in describing the fluid flow. Our investigationshows that the prediction of fluid flow behavior issensitive to the volume of zones and degree of bypassingbetween them and less sensitive to the dead volume. Inthis paper, we show that a simple two-zone axial disper-sion model adequately describes the fluid flow charac-teristics of an UASB reactor.

Materials and Methods

Medium Composition. The medium used (Kosaricet al., 1990a,b) contains 1.8 g/L glucose, 4.8 g/L aceticacid, 1.2 g/L propionic acid, 1.2 g/L n-butyric acid, 1.0g/L NH4Cl, 0.5 g/L yeast extract, 0.4 g/L K2HPO4, 0.15g/L MgCl2‚6H2O, and 0.36 g/L CaCl2‚2H2O. This mediumwas supplemented with a trace metal solution containing2000 mg/L FeCl3‚4H2O, 50 mg/L H3BO3, 50 mg/L ZnCl2,500 mg/L MnCl2‚4H2O, 50 mg/L (NH4)2Mo2O7‚24H2O, 30mg/L AlCl3, 150 mg/L CoCl2‚6H2O, 100 mg/L NiCl2‚6H2O,500 mg/L EDTA, and 1 mL of concentrated HCl. Theresulting medium has a chemical oxygen demand (COD)level of 11 g/L. The pH was adjusted to 6.5 using NaOHsolution. All chemicals used were laboratory-grade re-agents. Details of the medium optimization are pre-sented elsewhere (Praveen, 1995).

Source of Inoculum. The inoculum was procuredfrom a suspended cell anaerobic reactor in the effluenttreatment plant of Vam Organic Chemicals Ltd., Ga-jraula, India. Vam Organic Chemicals produces ethanol,acetic acid, and acetate derivatives from molasses.

Measurement of Tracer Concentration. The mix-ing and fluid flow behavior in a UASB reactor wasexamined by monitoring the concentration of lithiumtracer injected as a pulse at the reactor inlet. These pulseexperiments were conducted on days 8, 21, 34, 48, 160,and 211 of the operation of the UASB reactor. The data

* Corresponding author. Telephone: 91-11-685 7764. Fax: 91-11-686 8521. E-mail: gomes@dbeb.ernet.iitd.in.

† Indian Institute of Technology.‡ University of Malaya.

645Biotechnol. Prog. 1998, 14, 645−648

S8756-7938(98)00042-3 CCC: $15.00 © 1998 American Chemical Society and American Institute of Chemical EngineersPublished on Web 07/11/1998

collected were used to determine the parameters of theaxial dispersion model.

Tracer samples collected from the effluent were cen-trifuged to remove suspended cells and filtered througha Millipore microfilter assembly. The lithium in thefiltrate was then estimated using an atomic absorptionspectrometer (Perkin Elmer, Plasma 40 Model). Tracersamples collected from the reactor effluent were centri-fuged to remove the suspended cells and filtered througha Millipore microfilter assembly before analysis.

Measurement of Volatile Suspended Solids (VSS).Samples (10 mL) were spun at 12 000 rpm for 15 min ina centrifuge (MSE Ltd., England). The supernatant waspreserved for other analysis. The pellets formed at thebottom of the tube were washed repeatedly with distilledwater and transferred to preweighed aluminum foil cupsfor TSS and VSS measurements by standard procedures.It was observed that the difference between the TSS andVSS of the samples was negligible. This happens becausethe inoculum does not contain any insoluble organic orinorganic particulates. For convenience, the dry weightof the sample is expressed in grams of VSS per liter.

Model DevelopmentWe propose that the UASB reactor can be described

by a model consisting of two compartments. It is as-sumed that the flow patterns of these compartmentsrepresent axially dispersed zones. The extents of mixingin these zones are reflected by their Peclet numbers.When the axial dispersion is minimum (Pe f ∞), thecompartment approaches plug flow behavior. However,when the axial dispersion is maximum (compartment iswell mixed; Pe f 0), the compartment approaches idealwell-mixed behavior. We also assumed that some of theliquid bypasses the first zone and enters directly into thesecond zone (Figure 1). Hence, the equations whichdescribe the UASB reactor are

where all flow rates are normalized with respect to theinfluent flow rate and the volumes are normalized withrespect to the total volume of the reactor. Hence, Q isthe dimensionless volumetric flow rate and S is thedimensionless bypass flow rate. Similarly, V1 and V2 arethe fractional volumes of the first and second zones,respectively. The length of the reactor is L, and u is theaverage linear velocity of liquid in the reactor. Thedimensionless time θ is obtained by dividing the real timet by the mean residence time of the reactor τ. The lengthsof these axially dispersed zones are L1 and L2, respec-tively. Hence the corresponding Peclet numbers for thesezones are respectively Pe1 ) uL1/D1 and Pe2 ) uL2/D2.The dispersion coefficients for each zone are D1 and D2,respectively. It has been observed in UASB reactors that

the volumes of the sludge bed and sludge blanket varyduring the course of operation. Hence the lengths L1 andL2 also vary during the operation. Thus the parametersof the model are Q, V1, Pe1, and Pe2.

The step response of an axially dispersed tubular flowreactor for an inert tracer is described by the followingpartial differential equation:

where C is the dimensionless concentration of the tracer(c/c0), Pe is the Peclet number, η is the dimensionlessdistance (z/L), and θ is the dimensionless time (t/τ). Theinitial condition for solving this problem is given by C )0 for η > 0. The partial differential eq 2 can be solvedanalytically by the procedure outlined by Smith (1981)for the first zone to obtain

The response of the second zone, C2(θ), is obtained bysolving the partial differential equation numericallyusing the Crank-Nicholson method and evaluating thesolution at the end of the second zone. The boundaryconditions in this case are

Finally the impulse response for the system is obtainedby differentiating C2(θ) obtained from the above analysisas

Results and DiscussionThe model parameters were evaluated using the mul-

tidimension downhill simplex method (Nelder and Mead,1965). The variation in the parameters during thereactor operation is presented in Figure 2 and a repre-sentative model prediction in Figure 3.

The reactor operation was started with an initialloading rate of approximately 4 kg of COD/(m3 d). Theloading was then increased according to the schedule inTable 1. During the startup phase, the sludge inside thereactor is a thick slurry consisting of loose cells. Sincethe microorganism population at the early stages of theoperation is low, the gas production rate and the turbu-lence created by gas evolution are also small. Conse-quently, the influent stream fluidizes and mixes theportion of the sludge bed closest to the bottom. The VSSin the sample taken from port 2 is about 80 g/L and theCOD uptake rate about 0.2 (g of COD)/(g of VSS d) duringthis stage. The VSS remains about 80 g/L even on day34 of the reactor operation (Table 1), whereas the VSSin the sample taken from port 4 gradually decreases from75 to 60 g/L during this period. It is also observed thatthe COD uptake rate increases to 0.55 (g of COD)/(g ofVSS d) on day 34. This indicates that the active biomasswas gradually settling to the bottom while the inactiveloosely suspended particles and inactive biomass were

Figure 1. Schematic of the two-compartment axial dispersionmodel.

Q ) 1 - S

V2 ) 1 - V1

τ ) L/u

θ ) t/τ (1)

1Pe

∂2C

∂η2- ∂C

∂η) ∂C

∂θ(2)

C1(θ) ) 12{1 - erf((Pe1)

1/2

2(1 - θ/V1)

(θ/V1)1/2 )} (3)

- 1Pe(∂C

∂η)η>0+ (C)η>0 )

S + QC1(θ)

(S + Q)η ) 0, θ g 0

∂C∂η

) 0 η ) 1 , θ g 0(4)

E(θ) )dC2(θ)

dθ(5)

646 Biotechnol. Prog., 1998, Vol. 14, No. 4

gradually being washed out of the reactor with increasingloading rates.

In terms of our two-compartment model, most of themixing activity is restricted to the first zone during thestartup period. The remaining section of the reactorremains relatively undisturbed since the turbulencecreated by the influent stream is not sufficient to mixthe upper region (second zone) of the reactor. Hence,during the initial stages of the reactor operation, weexpect that the Peclet number of the first zone (Pe1) willbe low, whereas the Peclet number in the second zone(Pe2) will be high. Figure 2 shows that the Peclet number

values Pe1 ) 0.1 and Pe2 ) 3.8 predicted by the modelare in agreement with the physical situation in thereactor.

As the reactor operation progressed the volume of thefirst zone increased initially to accommodate the increas-ing biomass. However, when granulation set in, thesludge particles became heavy and less fluidized, arrest-ing further the increase in volume. Granulation alsoresulted in a decrease in the mixed flow nature of thefirst zone. At the same time, due to the activity of thecells, gas production increased as indicated by theincrease in the COD uptake rate to 0.68 (g of COD)/(g ofVSS d). This increased the extent of mixing in the secondzone. The axial dispersion accounts correctly for thischange in flow behavior in the two zones in terms of thePeclet number. For the first zone, Pe1 increases to about1.4, while for the second zone, Pe2 drops to about 0.8. Itwas also visually observed that the extent of channelingof the influent through the UASB reactor increased asthe granulation process progressed. We find that themodel also predicts an increase of the bypass S from6.55% to 36.24%. Finally, toward the end of the reactoroperation, the cells started to settle and compact, reduc-ing the volume of the first zone. These changes causedinsufficient mixing in the first zone and are reflected bythe increase in the Peclet number to 4.6 for the first zoneand a corresponding reduction in the Peclet number to0.5 for the second zone.

Conclusions

Our work on modeling started with an attempt todetermine which parameters were important for describ-ing the fluid flow in UASB reactors. This excursion ledus to investigate many different models proposed fordescribing the fluid flow or simple variations of them.We observed that the relative volumes of zones in whichthe active and nonactive biomass resided as well as thedispersion coefficients in these zones were the sensitiveparameters. Adding compartments in the model didimprove the prediction behavior but the gains were notsignificant. A simple two-compartment axial dispersionmodel was adequate to explain the fluid flow character-istics without sacrificing on the accuracy of the predic-tions and interpretations. This treatment is simplersince two zones are used in comparison to three or fourzones traditionally used for modeling the UASB reactors.Consequently, the number of parameters required to beestimated is reduced by at least two. The axial dispersionmodel is also able to describe the effects of granulationon the hydrodynamics in terms of the increase in chan-neling or bypass flow. It also gives a realistic picture ofthe changes in flow patterns by accounting for the extentof mixing in different zones of the reactor in terms of thePeclet numbers. The axial dispersion model will besuitable for most situations unless incorporating moredetail is necessary.

Acknowledgment

The authors thank Dr. T. R. Sreekrishnan for his manycritical comments and valuable suggestions which helpedshape this paper.

References and Notes

Bolle, W. L.; van Breugel, J.; van Eybergen, G. C.; Kossen, N.W. F.; Zoetemeyer, R. J. Modeling the Liquid Flow in Up-Flow Anaerobic Sludge Blanket Reactors. Biotechnol. Bioeng.1986, 28, 1615-1620.

Figure 2. Variation of Pe1 (Peclet number in the first zone),Pe2 (Peclet number in the second zone), V1 (volume of the firstzone), and S (bypass flow) during the course of the UASB reactoroperation.

Figure 3. Axial dispersion model fit for the response of theUASB reactor to impulse input of the lithium tracer on day 21of its operation.

Table 1. Operation and Performance of the UASBReactor

VSS (g L-1)daya

loading rate(kg of COD/(m3 d)) port 2b port 4c

CODd uptake rate(g of COD/(g of VSS d))

8 9.8 80 75 0.2021 15.5 82 65 0.2834 21.2 80 60 0.5548 28.8 87 42 0.68

160e 23.2211e 23.2

a Days since the start of the operation when the residence timedistribution (RTD) experiment was conducted. b Sample taken at20% volume from the bottom of the reactor. c Sample taken at 40%volume from the bottom of the reactor. d Based on total reactorvolume. e Steady-state operation.

Biotechnol. Prog., 1998, Vol. 14, No. 4 647

Heertjes, P. M.; Kuijvenhoven, L. J. Fluid Flow Pattern inUpflow Reactors for Anaerobic Treatment of Beet SugarFactory Wastewater. Biotechnol. Bioeng. 1982, 24, 443-459.

Heertjes, P. M.; van der Meer, R. R. Dynamics of Liquid Flowin an Upflow Reactor Used for Anaerobic Treatment ofWastewater. Biotechnol. Bioeng. 1978, 20, 1577-1594.

Kosaric, N.; Blaszczyk, R.; Orphan, L. Factors Influencing theFormation and Maintenance of Granules in Anaerobic SludgeBlanket Reactors. Water Sci. Technol. 1990a, 22, 272-292.

Kosaric, N.; Blaszczyk, R.; Orphan, L.; Valladares, J. TheCharacteristics of Granules From Upflow Anaerobic SludgeBlanket Reactors. Water Res. 1990b, 24, 1473-1477.

Lettinga, A. W. Feasibility of Anaerobic Digestion for Purifica-tion of Industrial Wastewater. In Proceedings of the 4thEuropean Sewage and Refuge Symposium, EAS Munich,1978.

Lettinga, G.; Van Velson, A. F. M.; Hobma, S. W.; de Zeeuw,W.; Klapwijk, A. Use of the Upflow Sludge Blanket (USB)

Reactor Concept for Biological Wastewater Treatment, Es-pecially for Anaerobic Treatment. Biotechnol. Bioeng. 1980,22, 699-734.

Nelder, J. A.; Mead, R. A. A simplex Method for FunctionMinimization. Comput. J. 1965, 7 (4), 308-313.

Praveen V. V. Operational Characteristics of Upflow AnaerobicSludge Blanket Reactor During and After Startup. Ph.DThesis, IIT Delhi, India, 1995.

Schmidt, J. E.; Ahring, B. K. Granular Sludge Formation inUpflow Anaerobic Sludge Blanket (UASB) Reactors. Biotech-nol. Bioeng. 1996, 49, 229-246.

Smith, J. M. Chemical Engineering Kinetics, 3rd ed.; McGrawHill Inc.: New York, 1981.

Accepted May 8, 1998.

BP980042F

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