hydrodynamics of upflow anaerobic sludge blanket reactors

ENVIRONMENTAL AND ENERGY ENGINEERING

Hydrodynamics of Upflow AnaerobicSludge Blanket ReactorsTing-Ting Ren, Yang Mu, Bing-Jie Ni, and Han-Qing Yu

Dept. of Chemistry, University of Science and Technology of China, Hefei 230026, China

DOI 10.1002/aic.11667Published online December 23, 2008 in Wiley InterScience (www.interscience.wiley.com).

The hydrodynamic characteristics of upflow anaerobic sludge blanket (UASB) reac-tors were investigated in this study. A UASB reactor was visualized as being set-up ofa number of continuously stirred tank reactors (CSTRs) in series. An increasing-sizedCSTRs (ISC) model was developed to describe the hydrodynamics of such a bioreactor.The gradually increasing tank size in the ISC model implies that the dispersion coeffi-cient decreased along the axial of the UASB reactor and that its hydrodynamic behav-ior was basically dispersion-controlled. Experimental results from both laboratory-scale H2-producing and full-scale CH4-producing UASB reactors were used to validatethis model. Simulation results demonstrate that the ISC model was better than theother models in describing the hydrodynamics of the UASB reactors. Moreover, athree-dimensional computational fluid dynamics (CFD) simulation was performed withan Eulerian-Eulerian three-phase-fluid approach to visualize the phase holdup and toexplore the flow patterns in UASB reactors. The results from the CFD simulation werecomparable with those of the ISC model predictions in terms of the flow patterns anddead zone fractions. The simulation results about the flow field further confirm the dis-continuity in the mixing behaviors throughout a UASB reactor. � 2008 American Institute

of Chemical Engineers AIChE J, 55: 516–528, 2009

Keywords: computational fluid dynamics, dispersion, Eulerian-Eulerian, hydrodynam-ics, model, upflow anaerobic sludge blanket

Introduction

The upflow anaerobic sludge blanket (UASB) reactor hasbeen the most widely used high-rate anaerobic reactor forwastewater treatment throughout the world since 1980s. Itstreatment capacity depends on the amount of active biomassretained, as well as the contact between biomass and waste-water. Performance of a UASB reactor, in terms of chemicaloxygen demand (COD) removal and energy yield, is usuallygoverned by two main interrelated factors: microbiologicalprocesses and hydrodynamics. Thus, investigation into the re-actor hydrodynamics is highly desirable.1 Previous studies onthe UASB hydrodynamics have shown that they could be

well described by the multi-CSTR (continuous stirred tankreactor) model,2–5 in which the equal-sized CSTRs (ESC)model is commonly used. Typically, in such a model a num-ber of tanks in series (N) and mean residence time areemployed to describe the deviations from the ideal CSTR orthe plug-flow reactor (PFR). The number of tanks in the ESCmodel, N, can be calculated from the following equation6:

N ¼ 1

r2h(1)

where r2h is the variance of the dimensionless residence timedistribution. The N value calculated from Eq. 1 is an impor-tant criterion to judge the flow patterns in reactor. Generally,N 5 1 represents a completely mixed flow, whereas N 5 1means a plug-flow. Integration of a simple dynamic massbalance around the strand of reactors generates the residence

Correspondence concerning this article should be addressed to H.-Q. Yu [email protected].

� 2008 American Institute of Chemical Engineers

AIChE JournalFebruary 2009 Vol. 55, No. 2516

time distribution (RTD) of the system. The concentration ofa tracer in the Nth reactor is given in Eq. 2, where y isdefined as dimensionless time, i.e., the Erlang distribution.7

E hð Þ ¼ NN

N � 1ð Þ! hN�1e�Nh (2)

Conceptually, this model has a precise definition of the inletand outlet boundary conditions. However, the ESC model isbased on the equal-sized tanks series and is not related withwhether the parameter N is an integer or not. In this case,the dispersion coefficient in a bioreactor is assumed to beuniform. On the other hand, the dispersion coefficientsactually vary at the different heights of a UASB reactor andconsiderably increase near the sludge bed bottom.8–12

Because the superficial liquid velocity is often lower than1 m h21 in a UASB reactor, the distribution of substrate andintermediates along the reactor height is far from uniform.13

Thus, the dispersion should decrease along the axis of aUASB reactor from the bottom to the top, implying that thesize of tanks in the multi-CSTRs model should stepwiseincrease.

Because of its complex nature, the local hydrodynamicbehavior of UASB reactors is not well documented yet.Thus, an in-depth investigation and elucidation of the flowpatterns in a UASB reactor are desirable. A hydrodynamicmodel composed of a hydraulic model for analyzing disper-sion and computational fluid dynamic (CFD) model for flowpatterns and phase holdup visualization should be estab-lished.

The CFD method has been demonstrated to be a usefultool for understanding flow behaviors and can be used toreplace the time-consuming and expensive experiments to alarge extent.14 Two main approaches exist, i.e., the Eulerianapproach, which regards the dispersed phases as interpene-trating continua, and the Lagrangian approach, which treatsthe dispersed phases as discrete entities.15–17 With the twoapproaches the same results can be obtained if adequate nu-merical methods are used to solve the resulting equations.18

However, since in the Lagrangian approach tremendous com-putational efforts will be needed to track each single gasbubble and/or solid particle, it is mainly used in dilutesystems.19

Vesvikar and Al-Dahhan20 performed a three-dimensional(3-D) steady-state CFD simulation for mimic anaerobic reac-tors to visualize the flow patterns and estimated the hydrody-namic parameters. Wu and Chen21 introduced the non-New-tonian fluid theory into the CFD model for anaerobic reactorsimulations. However, most relevant studies are focused onsingle- or two-phase flows. Information about the modelingof three-phase (gas–liquid–solid) flows in a UASB reactor isstill very limited.

Therefore, the present work was aimed at developing hy-draulic and CFD models to describe the hydrodynamics ofUASB reactors. An increasing-sized CSTRs (ISC) model wasestablished to describe the dispersion feature of the UASBreactor. Experimental results from both laboratory-scale H2-producing and full-scale CH4-producting UASB reactorswere employed to validate the established mode. Moreover, a3-D unsteady CFD model simulation was performed to visu-alize the phase holdup and flow patterns in the reactors.

Model Development

Hydraulic model

Extended Equal-Sized CSTRs (EESC) Model. The sche-matic diagram of the ESC model is shown in Figure 1a. If thetanks in series model are merely regarded as a residence timedistribution function, whose form depends solely on the Nvalue, it becomes possible to sort out the quantization problemin the analysis of high-dispersion systems. An introduction ofa noninteger number of hypothetical tanks in series will yieldthe desired results. The exit age distribution of the extendedequal-sized CSTRs (EESC) model (shown in Figure 1b) isgiven by a subset of the gamma distribution family6:

E hð Þ ¼ NN

C Nð Þ hN�1e�Nh (3)

When N is an integer, it is identically equal to the Erlangdistribution (Eq. 2). The EESC model sorts out the quantiza-tion problem, as N tends to 1 in the multi-CSTRs model.

Establishment of an Increasing-Sized CSTRs Model. TheUASB reactor is visualized as being set-up of a number ofgradually increasing-sized CSTR tanks (Figure 1c). The ini-tial concentration C0 in the first tank (V1) at t 5 0 isdescribed by Eq. 4:

C0 ¼ M

V1

(4)

The tracer mass (M) balance at the inlet and outlet of eachtank is described as follows:

For the 1st CSTR:

V1

dC1

dtþ QC1 ¼ 0 (5)

Integration of Eq. 5 gives the following equation for thetracer concentration in the first tank:

C1 ¼ C0 exp � t

T1

� �(6)

where T1 is the mean residence time in the first tank and Qis the influent flow rate.

For the 2nd CSTR:

V2

dC2

dtþ QC2 ¼ QC1 ¼ QC0 exp � t

T1

� �(7)

Integration of Eq. 7 results in the following equation for thetracer concentration in the second tank:

C2 ¼ C0T1T2 � T1

exp � t

T2

� �� exp � t

T1

� �� (8)

The following equation can be obtained for the Nth CSTRusing mathematic induction:

CN ¼ C0T1XNi¼1

TN�2iQN

j¼1;j 6¼i

Ti � Tj� � e�

1Tit

26664

37775 (9)

AIChE Journal February 2009 Vol. 55, No. 2 Published on behalf of the AIChE DOI 10.1002/aic 517

The exit age distribution function E(t) is defined asfollows:

E tð Þ ¼ Q

MCN (10)

In Eq. 9, Ti 5 Vi/Q. Substitution of Eqs. 4 and 9 into Eq. 10yields:

E tð Þ ¼XNi¼1

TN�2iQN

j¼1;j 6¼i

Ti � Tj� � e�

1Tit

26664

37775 (11)

Setting V1 5 r1Vtot, V2 5 r2Vtot, . . . , VN 5 rNVtot, where VN

is the volume of the Nth tank, Vtot is the total volume of alltanks, and rN is the fraction coefficient. The resulting dimen-sionless form of Eq. 11 is as follows:

E hð Þ ¼ t 3 E tð Þ ¼ Q

Vtot

XNi¼1

rN�2iQN

j¼1;j 6¼i

ri � rj� � e�

hri

26664

37775 (12)

Then, the governing equations for the ISC model can bewritten as follows:

E hð Þ ¼ Q

Vtot

XNi¼1

rN�2iQN

j¼1;j 6¼i

ri � rj� � e�

hri

26664

37775

r1 þ r2 þ � � � þ rN ¼ 1

rNrN�1

>1

8>>>>>>>>>><>>>>>>>>>>:

(13)

To establish the mass balance equation of tracer in series ofmixed reactor compartments, the water and tracer loadings atthe point proceeding of Nth compartment are described inEq. 14:

Iin;N ¼ QinCN�1 (14)

The UASB reactor could be divided into three compartments:a sludge bed and a sludge blanket, both are mixed withrespect to the liquid phase, and a plug flow region todescribe the internal settler.4 In the present work, a similarapproach is adopted and the settler compartment is assumedas a subsequent plug flow reactor to the ISC model in series.

Parameter Estimation. As most of the model parametersin the ISC models cannot be measured, they have to be esti-mated through minimizing the sum of the squared differencev2 between the measured (Cexp) and calculated (Ccal) valuesof the tracer concentrations at the sampling ports over sam-pling times (Ntime), i.e., the following function is minimized:

v2 ¼XNtime

i¼1

Ccali ðpÞ � Cexp

i

rexpi

� �2

(15)

Software AQUASIM 2.0 is used to estimate the model pa-rameters.22

CFD model

Eulerian-Eulerian Model. A 3-D transient CFD model isused to simulate the hydrodynamics of the three-phase (gas–liquid–solid) UASB reactor. In the CFD simulation, a multi-phase control volume, composed of one continuous (waste-water) and two dispersed phases (gas bubbles and microbialgranules), is analyzed with the Eulerian-Eulerian model. Thismodel is chosen because of the large number of particles.23

Each phase is assumed to be incompressible in this study.

Figure 1. A schematic diagram of the model: (a) ESC model; (b) EESC model; and (c) ISC model.

[Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

518 DOI 10.1002/aic Published on behalf of the AIChE February 2009 Vol. 55, No. 2 AIChE Journal

The wastewater is regarded as pure water at 378C. The sludgetakes up about 50% of the volume in sludge bed region and isconsidered to be spherical solid granules with a density of1070 kg m23, diameter of 2 mm, and dynamic viscosity of 5mPa s. These media values could be appraised as an approxi-mation of the physical properties of the anaerobic granulesobserved in UASB reactors.24 The gas bubbles have a densityof 1.139 kg m23 and a dynamic viscosity of 0.019 mPa s.The gas phase volume fraction is related to the gas productionand the gas bubbles have a diameter of 0.1 mm.

Governing Equations. The mass and momentum conser-vation equations are solved in a computational 3-D mesh.The phase volume fractions comply with the compatibilityconditions:

Xnk¼1

ak ¼ 1 (16)

The conservation equations of mass and momentum for eachphase in the Eulerian-Eulerian formulation are defined asfollows:

r � qkak~ukð Þ ¼ 0 (17)

r � ak qk~uk~ukð Þð Þ ¼ r � ðleff;kakðr~uk þ ðr~ukÞTÞÞ� akrpþ M

!I;k ð18Þ

Where subscript k denotes the physical quantity related tophase k, ak denotes the volume fraction of phase k. leff is theeffective viscosity accounting for turbulence, and P is thepressure. ~MI;k represents the total interfacial momentumbetween the dispersed phase and the continuous phase, and isformed by the sum of the interfacial forces attributed to thedrag, the lift, the virtual mass force, and the turbulent disper-sion force.

Interphase Momentum Transfer. In this study, only dragforces and lift forces between the continuous phase andthe dispersed phase are considered. The drag forcesexerted by the dispersed phase on the continuous phase arecalculated as:

MD;lg ¼ 3

4

CD;lg

dgqlag ug � ul

�� ug � ul� �

(19)

MD;ls ¼ 3

4

CD;ls

dsqlas us � ulj j us � ulð Þ (20)

where CD is the drag coefficient and d is the diameter.As the volume fraction of gas is low, the bubbles are

assumed as spheres and the Schiller and Naumann dragmodel could be used to calculate the drag forces.23 The dragcoefficient exerted by the gas phase on the liquid phase,CD,lg, is obtained as follows:

CD;lg ¼24 1þ 0:15 1� ag

� �Re0:687

� �1� ag� �

Re1� ag� ��2:65

1� ag� �

Re � 1000

0:44 1� ag� �

Re > 1000

8><>: (21)

Where Re is the relative Reynolds number, which is obtainedfrom:

Re ¼ qldg ~ug �~ul�� ll

(22)

The drag coefficient exerted by the solid phase on the liquidphase, CD,ls, is calculated from the Wen and Yu dragmodel23:

CD;ls ¼ 24

asRe1þ 0:15 asReð Þ0:687h i

a�0:265s (23)

The relative Reynolds number for the liquid phase and thesolid phase is estimated from the following:

Re ¼ qlds ~us �~ulj jll

(24)

The lift force acting perpendicular to the direction of the rel-ative motion of the two phases is given by:

ML;lg ¼ CLqlag ug � ul� �

3 r 3 ulð Þ (25)

ML;ls ¼ CLqlas us � ulð Þ 3 r 3 ulð Þ (26)

where CL is the lift coefficient and has a value of 0.5.The interphase momentum transfer between the two dis-

persed phases, as well as virtual mass force and turbulentdispersion force between the continuous phase and the dis-persed phases are all neglected in this study. If these forceswere taken into account, the complexity of numerical compu-tation would significantly increase, but it is not expected tocontribute to a better understanding of the system. Theeffects of the bubble–bubble and solid–solid interactions are,respectively, considered in the calculation of the drag coeffi-cients between the continuous and dispersed phases.

Turbulence Modeling of the Continuous Phase. The tur-bulence modeling of the continuous phase is based on thetwo-equation (k, e) turbulence model derived in a three-phaseflow, including the interfacial transfer of turbulent kineticenergy and its dissipation rate. The eddy viscosity model isused to calculate the averaged fluctuating quantities. TheReynolds stress tensor for the continuous phase has the fol-lowing form:

s ¼ � 2

3qlkl þ qllt;lr~ul� �

I þ qllt;l r~ul þ r~ulð ÞT�

(27)

The turbulent viscosity lt,l is written in terms of the turbulentkinetic energy of the liquid phase:


lt;l ¼ qlClk2lel

(28)

The kL transport equation in the liquid phase is expressed as:

@

@talqlklð Þ þ r alqlkl~ulð Þ ¼ r � al

lt;lrk

rkl

� �

þ alGk;l � alqlel þ alqlPk;l

(29)

The transport equation of the dissipation rate of eL in the liq-uid phase is expressed as:

@

@talqlelð Þ þ r alqlel~ulð Þ ¼ r � al

lt;lre

rel

8>: 9>;þ al

elkl

C1;eGk;l � C2;eqlel� �þ alqlPe;l

(30)

where Pk,l and Pe,l represent the influence of the dispersedphases on the continuous phase, and Ck,l is the production ofthe turbulent kinetic energy; rk and re are the turbulentPrandtl numbers for k and e, respectively; C1,e and C2,e areconstants.

The term Pk,l can be derived from the instantaneous equa-tion of the continuous phase and has the following form:

Yk;l

¼X2p¼1

kplalql

kpl � 2kl þ~upl �~udr� �

(31)

where kpl is the covariance of the velocities of the continuousphase and the dispersed phase p, ~upl is the relative velocity,and ~udr is the drift velocity.

Thus, the Pe,l is calculated as follows:

Ye;l

¼ C3;eelklPk;l (32)

The values of the model constants are the standard ones: C1,e

5 1.44, C2,e 5 1.92, C3,e 5 1.2, Cl 5 0.09, rk 5 1.0, re 51.3.

Numerical Solution. The finite volume method is used asthe numerical technique. The momentum and continuityequations are discretized using finite volumes. The geometryand the meshes are generated with the preprocessor GAM-BIT 2.2. Commercial code Fluent 6.2 is used to solve thecontinuity and momentum equations. The pressure-velocitycoupling is obtained using the Phase Couple SIMPLE (PC-SIMPLE) algorithm.

Experimental

Laboratory-scale H2-producing UASB reactor

The H2-producing experiments were carried out in a 7.5 lPlexiglas UASB reactor with an internal diameter of 10 cmand a height of 88 cm (Figure 2). The reactor had a workingvolume of 4.0 l and was operated at 37 6 18C.

This UASB reactor was seeded with CH4-producing sludgetaken from a full-scale anaerobic reactor treating citrate-pro-ducing wastewater. It was shifted to an acidogenic reactorfor H2 production by gradually lowering the mixed liquorpH. The pH and volatile suspended solids (VSS) of the seed

sludge were 7.1 and 6.3 g l21, respectively, and the sludgewas seeded into the UASB reactor with a sludge concentra-tion of 20.0 g-VSS l21 after thickening. A synthetic sucrose-rich wastewater with a COD level of 9900 mg l21 was usedas substrate and was supplemented with buffering chemicalsand a sufficient amount of inorganic nutrients as reportedpreviously.24 The detailed information about the start-up andsteady-state performance of this H2-producing UASB reactorcould be found elsewhere.25

Tracer tests

For the tracer test, a pulse injection of tracer Li1 was per-formed at time t 5 0 in the input stream of the reactor, andthe tracer concentrations at time series were measured at theoutlet. A solution containing 594 mg Li2SO4 (75 mg Li1)was applied in each tracer run, producing an average Li1

Figure 2. A schematic diagram of the laboratory-scaleH2-producing UASB reactor and pulse injection.


concentration of 10 mg l21 in the reactor. Experiments werecarried out at four different hydraulic retention times (HRTs)as shown in Table 1. Samples were taken every 2 h for anHRT of 26.4 h and every 1 h for an HRT of 16.3 h, and ev-ery 0.5 h for an HRT of 8.0 and 4.3 h, respectively. A peri-staltic pump (Longer Co., China) was used to control theflow rate. The effluent samples were taken in each tracer testand analyzed. The lithium concentration was determinedusing flame emission spectroscopy (Vario 6, Analytik JenaAG, Jena, Germany) at a wavelength over 670.8 nm accord-ing to the Standard Methods.26

Results

Laboratory-scale H2-producing UASB reactor

The estimated parameters in the ISC model are shown inTable 2. The effective volumes are 5.9 and 6.7 l at an HRTof 8.0 and 4.3 h, respectively, whereas an actual volume is7.5 l. This indicates that the loss of effective volume isattributed to the granular sludge, bypass flows, and high dis-persion within the UASB reactor. For comparison, the resultsof the EESC model are also displayed in Table 2. The N val-ues in the EESC model calculated from the experimentaldata using Eq. 1 are 1.9, 1.7, 2.1, and 2.1 for an HRT of26.4, 16.3, 8.0, and 4.0 h, respectively. Comparison of thefinal v2 values suggests that the EESC model simulation isnot as accurate as the ISC model.

For the parameter estimation of the ISC model, there is agood agreement between the measured and calculated tracertrajectories (Figure 3). However, the EESC model is noteffective to describe the reactor hydrodynamics. This furtherdemonstrates that the dispersion nonuniformity is the mostimportant factor governing the hydrodynamic characteristicsof the UASB reactor.

If the Monod or first-order kinetics dominate, a plug-flowreactor can be more effective. However, the flow pattern ofthis UASB reactor is not near to plug-flow, because the Nvalue calculated from Eq. 1 is only around 2 at four HRTs(Table 2). This result is different from those of previousstudies.9,27 Generally, mixing in a continuously flow reactorwith three phases (gas–liquid–solid), such as the UASB, willmainly depend on the superficial liquid velocity, superficialgas velocity, phase physical properties, phase hold-up, andreactor geometry.24,28,29 In the present work, both superficialgas and liquid velocities vary simultaneously (Table 1), andtheir effects overlap with each other. Therefore, the flow pat-terns should be different for different reactors and operatingconditions.

Full-scale CH4-producing UASB reactor

The hydrodynamics of a laboratory-scale H2-producingUASB reactor is studied experimentally in this work. How-ever, the hydrodynamics of a full-scale UASB reactor couldbe completely different from those of laboratory-scale UASBreactor in terms of superficial liquid velocity, accumulatingsuperficial gas velocity, and sudden release of enclosed bio-gas bubbles in the sludge bed.

The experimental results reported by Batstone et al.27 areused to validate our model here. This reactor was a full-scaleCH4-producing UASB with a 1400 m3 working volume andwas fed with slaughterhouse wastewater with a COD of 5 gl21 at an HRT of 24 h. Accordingly, the average loading ratewas 2.7 g-COD l21 day21.

The simulated results of this full-scale reactor using ourISC model are shown in Figure 4. The parameter N in theISC model is calculated to be 4, and the volume ratio of thefour tanks is 1:1.5:20:210. The final v2 value in the ISCmodel is estimated to be 2.6. Comparatively, v2 is 4.4 in the1:15 two-tank model and 28.8 in the 1:1 two-tank model,respectively.27 This shows that the ISC model is also applica-ble to describing the hydrodynamics of a full-scale CH4-pro-ducing UASB reactor.

Mixing characteristics of a UASB reactor

It is anticipated that there is a discontinuity in the mixingbehavior throughout a UASB reactor, which could be verifiedby the ISC model. The experimental results reported by Louet al.30 are used to validate this model. Their experimentswere carried out with a 10.4-l UASB reactor. The three sam-pling ports were installed at heights of 2.5, 13.0, and 34.5cm from the bottom, and, respectively, corresponded to thebottom, middle, and top of the anaerobic sludge bed. Asshown in Figure 5, the ISC modeling results match the mea-sured tracer trajectories well.

As the number of CSTR and their volumes in the ISCmodel change with the varying operating conditions and re-actor size, modeling at varied HRTs and reactor sizes is per-formed to explore the reactor mixing characteristics.

Biogas production might be an important reason for themixed flow at a high hydraulic loading rate, which also cor-responds to a high organic loading rate at a fixed influentsubstrate level. Because of a lower superficial liquid velocity,the biogas production rate has a much more significant effecton the flow patterns of the UASB reactor. In addition to the

Table 1. Operating Conditions for the Laboratory-ScaleH2-Producing UASB Reactor

HRT(h)

FlowRate (l h21)

ug(m h21)

ul(m h21)

COD loading(g l21 day21)

4.3 0.93 0.411 0.118 55.88.0 0.50 0.271 0.064 30.016.3 0.25 0.059 0.031 14.726.4 0.15 0.049 0.019 9.0

Table 2. Parameter Estimation Results of the Two Modelsfor the Laboratory-Scale H2-Producing UASB Reactor

Model Parameter

HRT (h)

4.3 8.0 16.3 26.4

ISCmodel

Veff (l) 6.7 5.9 7.5 7.5N 3 4 3 2

Volume ratioof tanks

1:1.5:4.2 1:2:5:6.75 0.6:1:5.9 1:4

Final v2 25.8 38.0 6.9 9.4EESC

modelVeff (l) 6.7 5.9 7.5 7.5

N 2.1 2.1 1.7 1.9Final v2 45.6 131.4 40.9 26.2


superficial liquid velocity, which is related to HRT, the su-perficial gas velocity is greatly dependent on the gas produc-tion rate and reactor size (i.e., cross section area). In ourwork, the two parameters, i.e., superficial gas and liquid

velocities, are used to evaluate the simulated tracer trajecto-ries for the six data sets (Table 3 and Figure 6a). The volumeratios of the last tank for data sets 1# and 2# are muchgreater than the others (Table 3). This implies that a signifi-

Figure 3. Simulated and measured tracer concentrations for the laboratory-scale H2-producing UASB reactor efflu-ent at various HRTs.


Figure 4. Simulated and measured tracer concentra-tions for the full-scale CH4-producing UASBreactor effluent at an HRT of 24 h.

[Color figure can be viewed in the online issue, which isavailable at www.interscience.wiley.com.]

Figure 5. Simulated and measured tracer concentra-tions along the height of the laboratory-scaleH2-producing UASB reactor.



cant mixing is present in the reactor under the tested condi-tions. However, minor changes are observed for the numberof tanks in the ISC model with the data sets in Table 3. Thissuggests that the steps of dispersion change along the UASBreactor height are of similar levels in most cases. The vol-

ume ratio is dependent heavily on the operating conditions.A higher superficial velocity results in a greater volume ratioof the last tank in the ISC model, and accordingly a morevigorous mixed flow pattern (Table 3).

The simulation results with the ISC model demonstrate thediscontinuity in the mixing behavior throughout the UASBreactor. The tracer concentrations in each tank for the datasets 1# and 6# simulated with the ISC model are shown inFigures 6b,c, respectively, as an example. For the data set 6#with a low superficial velocity (Table 3), the time delaybetween the tracer trajectories at each tank is significant. Onthe other hand, for data set 1# with a higher superficial ve-locity, a minor time delay is observed (except the trajectoryof the last tank), attributed to the near mixing flow patterns.

Flow pattern visualization

A structured numerical grid with a total number of120,000 cells is implemented (Figure 7). The numerical sim-ulation is carried out for transient conditions with a totaltime duration of 22 s. Figure 8 shows the solid phase holdupdistribution in the UASB reactor. The sludge volume fractiondecreases along the reactor height, similar to that reportedpreviously.11 Flow pattern simulation results are shown bythe contours of velocity magnitude. The velocity magnitudeincreases with an increase in inlet flow velocity. However,the overall flow trends keep unchanged. Taking the labora-tory-scale H2-producing reactor as an example, the superficialvelocities of liquid phase at an HRT of 4.3 h are visualized

Table 3. Parameters Values Calculated with the ISC Model Under Different Operating Conditions

Experimental Set # HRT (h) ug (m h21) ul (m h21) N Volume Ratio of Tanks

1 10.3 0.138 0.049 4 1:2.3:3.3:26.72 12.0 0.027 0.042 3 1:1.9:11.43 16.0 0.005 0.032 3 1:2.1:2.84 17.0 0.033 0.030 3 1:1.9:4.35 20.0 0.019 0.025 3 1:1.1:3.86 21.7 0.043 0.024 3 1:1.5:5.2

Figure 6. Modeling results under different operatingconditions: (a) tracer concentrations of thereactor effluent for the six data sets; (b)tracer concentrations of each tank in theISC model for the data set 1#; (c) tracer con-centrations of each tank in the ISC modelfor the data set 6#.


Figure 7. Mesh partition of the column and the top ofthe UASB reactor.


in Figure 9. The velocity magnitude scale can be referred tothe magnitude bar at the left of each figure. The velocitymagnitude increases along the UASB reactor height whenthe flow pattern is fully developed. Figure 10 shows that thesuperficial velocities of sludge phase are higher in the reactorbottom part and lower in the upper part. The flow field inFigures 9 and 10 further confirms the discontinuity in the

mixing behavior throughout a UASB reactor, i.e., the disper-sion decreases along the reactor axis from the bottom to thetop.

Figure 11 shows the simulation of the gas accumulation inthe sludge bed. With the 3-D unsteady CFD model simula-tion, the transience of the gas flow pattern can be visualized.The simulation results suggest that the mechanisms of the

Figure 8. Transient model predictions of the laboratory-scale H2-producing UASB reactor at an HRT of 4.3 h: (a)sludge volume fraction contours of sludge volume fraction at 0.11, 0.22, and 22 s; (b) average sludge vol-ume fraction along the reactor height at 22 s; and (c) sludge volume fraction contours of sludge volumefraction of the reactor cross section at 22 s.



gas occasional abrupt release should be related to the forcebalance. When the force balance between gas and sludge isbroken up, the gas release from the sludge bed will occur.

Discussion

Dispersion and flow patterns

The dispersion in a UASB reactor is significant. Comparedwith the EESC model, the ISC model is able to simulate thedispersion better. In the ISC model, the dispersion variations

in a UASB reactor are emphasized through gradually increas-ing the size of tanks. This implies that the dispersion coeffi-cient is reduced along the reactor axis and that its hydrody-namic behavior is basically dispersion-controlled.

There are several reasons responsible for the different dis-persion coefficients between the sludge bed region and theblanket one. The size distribution and granule filling gradientare important factors, and they should result in a higherapparent linear superficial velocity and tighter packing in thesludge bed bottom than at the bed top or in the liquid zone

Figure 9. Transient model predictions of the laboratory-scale H2-producing UASB reactor at an HRT of 4.3 h: (a) liq-uid velocity magnitude contours of liquid velocity magnitude at 0.11, 0.22 and 22 s; (b) average liquid rel-ative velocity along the reactor height at 22 s; and (c) liquid velocity magnitude contours of liquid velocitymagnitude of the reactor cross section at 22 s.



(shown in Figures 8–10). Other important axial gradients,such as substrate, volatile fatty acids, and pH, are also signif-icant factors. The dispersion in a UASB reactor cannot beadequately described by the ESC or EESC models because

of the existence of significant gradients in substrate, volatilefatty acids, and pH. Their presence has a number of implica-tions in process monitoring and controlling, especially in thedispersion analysis. As the importance of dispersion model-ing in simulating UASB reactor hydrodynamics is demon-strated in this work, an agreement between the measured andsimulated results is achieved using the ISC model.

Moreover, the number of tanks (N) in the ISC model iscalculated to be no more than four with the experimentalresults in Tables 2 and 3. This is attributed to the fact thatthe dispersion variation along the height of a UASB reactoris of similar levels in most cases. The 3-D CFD simulationresults also show that the overall flow trends are similarunder different hydraulic conditions.

The regions with low velocities are termed as stagnant ordead zones shown in Figures 9 and 10. The volume of thedead zones can be estimated by calculating the total volume ofthe cells with low superficial liquid velocities. The regionswith the superficial liquid velocities less than 5% of the aver-age velocity are considered to be stagnant or inactive regions.For this case, the dead or stagnant volume in the reactor is10% of total reactor volume. This value is comparable withthe results calculated with the ISC model as shown in Table 2.

Validity of the ISC model

The simulation results show that the ISC model is muchbetter than the EESC model for describing the dispersioncharacteristics of UASB reactors (Figures 3 and 4). In theprevious work by Batstone et al.,27 although the ISC modelwas not established and applied, it was observed that thehydrodynamic behaviors of a full-scale CH4-producingUASB reactor could be well simulated by a multi-CSTRsmodel concerning two-tank in series with a volume ratio of1:15, rather than by a model regarding two-tank in serieswith a volume ratio of 1:1 (Figure 4). Results from both lab-oratory-scale H2-producing and full-scale CH4-producting

Figure 10. Contours of sludge velocity magnitude of the reactor cross section at 22 s.


Figure 11. Visualized transience of the gas flow pat-terns in a UASB reactor at 22 s.



UASB reactors demonstrate that the ISC model is appropriatefor describing the hydrodynamics of a UASB reactor, irre-spective of that the reactor is laboratory- or full-scale, andthat it is for H2 or CH4 production. Moreover, the RTD ex-perimental data along the UASB reactor height (Figure 5)further demonstrate the validity of the ISC model. Theresults from the CFD simulation (Figures 8–10) are compara-ble with the ISC model predictions in terms of the similarflow patterns and the dead zone fractions. This suggests thatthese methods can be jointly used to explore the hydrody-namics of the UASB reactors.

As the effect of dispersion variation along the reactor axisis taken into account in the ISC model, the application of thismodel to systems with similar dispersion behaviors isexpected. It is convenient to modify this model to adapt anew anaerobic wastewater treatment system. This hydrody-namic model might be also useful in simulating other bioreac-tors, such as fluidized bed reactor,31 sequencing batch biofilmreactor28 and packed-bed reactor.32 Furthermore, through acombination of the hydrodynamics model with the biochemi-cal kinetics and mass transfer models, a comprehensive modelcould be established to simulate the overall behaviors of an-aerobic reactors, including reactor performance, sludge bedexpansion and contraction, biogas accumulation and entrap-ment, biogas abrupt occasional release, granulation and de-granulation process, granular sludge flotation, etc.

Conclusions

An ISC model was developed and successfully used todescribe the hydrodynamics of UASB reactors. In such amodel, a UASB reactor was visualized as being made-up of anumber of CSTRs in series, and the dispersion coefficientdecreases along the axis of the UASB reactor. As a result, itshydrodynamic behavior is basically dispersion-controlled. Ex-perimental results from both laboratory-scale H2-producing andfull-scale CH4-producing UASB reactors demonstrate that theISC model established in this work was able to better describethe hydrodynamics of the UASB reactors than the other mod-els. Moreover, a 3-D unsteady CFD model simulation was per-formed to visualize the phase holdup and obtain their flow pat-terns in a UASB reactor. The simulation results further confirmthe discontinuity in the mixing behavior throughout the UASBreactor, i.e., the dispersion decreased along the reactor axisfrom bottom to top. These methods could be jointly used toelucidate the hydrodynamics of UASB reactors. The approachcan be further used to design operate and optimize the UASBreactors. Furthermore, through a combination of a hydrodynam-ics model with biochemical kinetics and mass transfer models,a comprehensive model could be established for simulating theoverall behaviors of anaerobic reactors.

Acknowledgments

The authors wish to thank the Natural Science Foundation of China(20577048, 50625825 and 50738006), the NSFC-JST Joint Project(20610002), and the National Basic Research Program of China(2004CB719602) for the partial support of this study.

Notation

C5 tracer concentration, mg l21

C(p)5 calculated value of the model variable, mg l21

C05 initialize concentration in the 1st tank at t 5 0 for the increas-ing-sized CSTRs model, mg l21

C1,e5 constant, dimensionlessC2,e5 constant, dimensionlessC3,e5 constant, dimensionlessCD5drag coefficient, dimensionlessCk5 turbulent production, kg m21 s23

CL5 lift coefficient, dimensionlessCl5 constant, dimensionlessd5diameter, m

E(t)5 exit age distribution function, h21

E(y)5dimensionless exit age distribution function, dimensionlessH5 relative height, dimensionlessIin5 tracer loadings into the compartment, mg h21

k5 turbulent kinetic energy, m2 s22

kpl5 covariance of the velocities of the continuous phase and the dis-persed phase, dimensionless

M5 tracer mass, mgMD5drag force, N m23

MI5 interphase momentum transfer force, N m23

ML5 lift force, N m23

N5number of tanks in equal-sized CSTRs modelNtime5 all sampling times

p5model evaluated parameters or pressure, dimensionless or PaQ5 influent flow rate, m3 h21

Qin5discharge of water into the compartment, m3 h21

r5 volume fraction of a tank to the total volume of series tanks forthe increasing-sized CSTRs model, dimensionless

Re5Reynolds number, dimensionlesst5 time, ht5 average residence time, hT5 temperature, KTi5 mean residence time in the single tank for the increasing-sized

CSTRs model, hu5 superficial velocity, m h21

~upl 5 relative velocity, m s21

~udr 5drift velocity, m s21

Vtot5 total volume of all tanks for the increasing-sized CSTRsmodel, L

Greek letters

a5volume fraction, dimensionlesse5dissipation rate, m s23

y5dimensionless time, dimensionlessl5viscosity accounting for turbulence, Pa slt5 turbulent viscosity, Pa sq5density, kg m23

r5 standard deviation, mg l21

rk5 turbulent Prandtl numbers for k, dimensionlessre5 turbulent Prandtl numbers for e, dimensionlessry

25 variance of the dimensionless residence time distribution, dimen-sionless

s5 stress tensor, Pa

v25 squared difference between measured and calculated values oftracer concentrations at the sampling ports over all samplingtimes, dimensionless

Subscripts

eff5 effective valueg5gasi5 i-th element of functionj5 j-th element of functionk5physical quantity related to phasel5 liquidN5quantities in the Nth compartment for the increasing-sized CSTRs

models5 solid

Superscripts

cal5 calculated valueexp5measured value


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hydrodynamics of upflow anaerobic sludge blanket reactors

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