Bioresource Technology 101 (2010) 9749–9757

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Bioresource Technology

journal homepage: www.elsevier .com/locate /bior tech

A hydrodynamics–reaction kinetics coupled model for evaluating bioreactorsderived from CFD simulation

Xu Wang, Jie Ding *, Wan-Qian Guo, Nan-Qi Ren **

State Key Laboratory of Urban Water Resource and Environment (HIT), Harbin Institute of Technology, 202 Haihe Road, Nangang District, Harbin, Heilongjiang 150090, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 24 March 2010Received in revised form 22 July 2010Accepted 28 July 2010Available online 2 August 2010

Keywords:Biohydrogen productionExpanded granular sludge bed (EGSB)reactorComputational fluid dynamics (CFD)Hydrodynamics–reactor kinetics coupledmodelReactor design and operation

0960-8524/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.biortech.2010.07.115

* Corresponding author.** Corresponding author. Tel./fax: +86 0 451 862821

E-mail addresses: wangxu_office@163.com (X. W(J. Ding), rnq@hit.edu.cn (N.-Q. Ren).

Investigating how a bioreactor functions is a necessary precursor for successful reactor design and oper-ation. Traditional methods used to investigate flow-field cannot meet this challenge accurately and eco-nomically. Hydrodynamics model can solve this problem, but to understand a bioreactor in sufficientdepth, it is often insufficient. In this paper, a coupled hydrodynamics-reaction kinetics model was formu-lated from computational fluid dynamics (CFD) code to simulate a gas–liquid–solid three-phase biotreat-ment system for the first time. The hydrodynamics model is used to formulate prediction of the flow fieldand the reaction kinetics model then portrays the reaction conversion process. The coupled model is ver-ified and used to simulate the behavior of an expanded granular sludge bed (EGSB) reactor for biohydro-gen production. The flow patterns were visualized and analyzed. The coupled model also demonstrates aqualitative relationship between hydrodynamics and biohydrogen production. The advantages and lim-itations of applying this coupled model are discussed.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Bioreactors used in environmental biotechnology applicationsare usually designed to satisfy the demands of the cell-cultureenvironment by controlling factors such as temperature, pH, andthe availability of oxygen, nutrients, metabolites and biologicallyactive molecules. Additionally, state of the art bioreactors use auto-mated feeding, both to provide effective mass transfer and to allowthe controlled application of external mechanical and physicalstimuli, as well as direct real-time control of the bioreactor func-tions (Hutmacher and Singh, 2008). However, the traditionalsemi-empirical approach to bioreactor design does not produce en-tirely satisfactory results. The application of the experimental tech-niques used to investigate flow fields, heat fluxes, and massconcentration fields are extremely costly, and therefore highly lim-ited in application. Thus, an appropriate mathematical model topredict the performance of a bioreactor is likely to find wide prac-tical application.

Some of the limitations of the semi-empirical approach can beovercome by using a hydrodynamics model, which relies on fluidmechanics to solve continuity, momentum and turbulence quan-tity balance equations (Vrana and Schuurmann, 2002; Li et al.,

ll rights reserved.

93.ang), dingjie123@hit.edu.cn

2003). Bioreactor flow rates and patterns can thus be assessed atthe design stage before committing to manufacture. Further spe-cific factors such as fluid inlet velocities and shear stresses canbe varied to better predict their influence on optimal microorgan-ism growth. Recent work has quantified the influence of hydrody-namic parameters on the performance of bioreactors (Gorczyca,2003; Li et al., 2003). For example, the consideration of the effectof flow regimes and hydrodynamics on characteristics such as sizedistribution, compressibility and settling rate of the sludge in sus-pended growth reactors for waste water treatment (Jin and Lant,2004).

The biological treatment of waste water is a multiphase chem-ical–biological–physical process with numerous internal gas–li-quid–solid interactions. Therefore, bioreactors support intrinsicallycomplex processes, and merely studying physical flow phenomenawith a hydrodynamics model cannot give an adequate representa-tion of the performance of the reactor.

To produce a useful level of understanding of these complexinteractions requires the hydrodynamics and reaction kineticsmodels to be coupled. The hydrodynamics model is used to formu-late an accurate prediction of the flow field and the reaction kinet-ics model portrays the reaction conversion process. This willrequire a practical and appropriate numerical platform to combinethese two models. A satisfactory combination of the models can beachieved by using computational fluid dynamics (CFD). CFD is amethod of predicting fluid flow, heat and mass transfer, reactionsand other related phenomena by solving a set of appropriate

Notation

J reaction rate constant, h-1 Subscriptfd fermentation degradation

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mathematical equations to describe the processes relating mass,momentum, energy and species balances (Gresch et al., 2009). Ad-vances in CFD have provided an efficient, economical and time-saving tool to investigate the hydrodynamics and reaction conver-sion occurring in a bioreactor. Moreover, the CFD model can be ver-ified by experimental velocimetry techniques, such as laserdoppler anemometry (LDA) and particle image velocimetry (PIV),making the application of CFD simulation both more practicableand creditable (Aeschliman and Oberkampf, 1998).

With the appearance of general purpose codes, such as FLUENT,CFX and others, CFD has become increasingly popular in environ-mental technology (Terashima et al., 2009; Wang et al., 2010; Dinget al., 2010). CFD codes also can be used to visualize detailed flowphenomena, a significant benefit when placing probes within thefluid domains for the direct measurement of parameters such aspressure, velocity and phase volume fraction, can be difficult.

The work mentioned above mainly concentrated on applyingCFD codes to obtain bioreactor hydrodynamics data, thus makingbeneficial suggestions for bioreactor design and optimization. Themodels used were simplified two phase or single phase systems.Related bioreactor simulations based on gas–liquid–solid threephase models are rarely reported, and nor are flow process relatedreaction kinetics models widely studied. For the first time, the fo-cus lies on establishing hydrodynamics–reaction kinetics coupledmodel of a gas–liquid–solid three-phase biotreatment systemusing CFD simulation followed by experimental verification in thispaper.

The expanded granular sludge bed (EGSB) reactor, a three-phasesystem, has been widely used for the treatment of waste water dueto its high operational efficiency even at high organic loading rates(OLR) and heavy biomass accumulation on the support media(Puyol et al., 2009; Colussi et al., 2009). Although EGSB bioreactorshave been used in environmental technology applications for manyyears, little research has been published on bioreactor modeling.The principal objectives of this study are to develop an easy-to-use CFD model of the significant process parameters, based onfundamental science and to validate the model by use of tracerexperiment results. Due to current interest in hydrogen as an energysource (Bhaskar et al., 2008; Guo et al., 2008a, 2009; Chang andLin, 2004), and our parallel research on biohydrogen production(Li et al., 2008; Ren et al., 2009), particularly hydrogen productionprocesses using gas–liquid–solid systems, our coupled model wasapplied and validated on a biohydrogen production process. Oncedeveloped and assessed with the full-scale trial results, the modelcan be employed to analyze the effect of wastewater quality char-acteristics, granule size, and reactor diameter on the performanceof the process. It is expected that this study will prove useful inapplying EGSB technology at other locations with different reactorconfigurations and water quality conditions.

2. Methods

2.1. Methodology for computational fluid dynamics model generation

2.1.1. Eulerian–Eulerian modelThis model solves a set of momentum and continuity equations

for each phase; its detailed description and initial application havebeen conducted successfully in our previous work (Wang et al.,

2009). Coupling is achieved through the pressure and interphaseexchange coefficients. The manner in which this coupling is han-dled depends upon the type of phases involved as granular(fluid–solid) flows are handled differently to non-granular (fluid–fluid) flows. For granular flows, the properties are obtained fromapplication of kinetic theory. Momentum exchange between thephases is also dependent upon the type of mixture being modeled.Applications of the Eulerian multiphase model include bubble col-umns, risers, particle suspension, and fluidized beds (Saurel andAbgrall, 1999; Mathiesen et al., 2000). In this paper, a two-dimen-sional Eulerian–Eulerian three-phase fluid model has been em-ployed to describe the flow behavior of each phase, so the biogas,wastewater and sludge granules are all treated as different con-tinua, with wastewater as the primary phase, and the gas andsludge granules as the secondary phases. This model was chosenbecause of the high proportion of gas bubbles and granular partic-ulates (Bin et al., 2003).

2.1.2. Governing equationsThe mass and momentum conservation equations are solved in

a desired mesh. The pressure field was assumed to be shared by thethree phases, in proportion to their respective volume fractions.The motion of each phase is governed by the respective massand momentum conservation equations.

2.1.3. Turbulence closureA standard k–e model for single phase flows (with extra terms

that include interphase turbulent momentum transfer (Elghobashiand Abouarab, 1983)) can take into account the effects of turbu-lence. The modeling of multiphase turbulent flows is much morecomplex and computationally expensive for three phase flows,mainly because of the influence of the secondary phases on the tur-bulence of the primary phase (Murthy et al., 2007). Therefore, wehave assumed for our three-phase CFD turbulence model, that tur-bulence in a multiphase fluidized bed is restricted to the primaryphase.

2.1.4. Species transport & reaction modelCFD codes can model the mixing and transport of chemical spe-

cies by solving conservation equations describing convection, dif-fusion, and reaction sources for each component species(Sivertsen and Djilali, 2005). Multiple simultaneous chemical reac-tions can be modeled, with reactions occurring in the bulk phase(volumetric reactions) and/or on wall or particle surfaces, and inthe porous region.

2.2. Application to biohydrogen production process

Hydrogen has been an unrealized potential ‘‘fuel of the future”for over 30 years, but there are now finally signs that hydrogenmay become an important component of the energy balance of aglobal economy (Logan et al., 2002; Cao et al., 2010). Our teamfound that high hydrogen producing potential and better opera-tional stability could be achieved with the EGSB system from eth-anol-type fermentation of organic wastewater (Guo et al., 2008b).Therefore, we chose a laboratory-scale biohydrogen productionprocess to demonstrate the application of the method.

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2.2.1. Description of the laboratory-scale H2-producing EGSBbioreactor

A sequence of H2-production experiments were carried out in aPlexiglas EGSB reactor with an internal diameter of 6 cm and aheight of 120 cm.

2.2.2. Biochemical reaction and kineticsIn this work, we assumed that the fermentation process took

place in the sludge bed zone, and that as soon as the water phasecame into contact with the sludge phase, fermentation occurred.The species reaction model was implemented to determine themass fractions of glucose, ethanol, acetic acid, carbon dioxide andhydrogen resulting from ethanol-type fermentation:

C6H12O6 þH2O! CH3COOHþ CH3CH2OHþ 2H2 þ 2CO2 ð1Þ

Our research indicates that the reaction is nominally a first orderhomogeneous reaction. The rate equation for the reaction is writtenas:

Rfd ¼ �jCC6H12O6ð2Þ

The reaction rate constant (j) is obtained by our work, which equalto 2.06 h�1 at 35 �C.

2.2.3. Numerical solutionIn this paper, we have analyzed the complete geometry of our

EGSB reactor with a computational two-dimensional mesh(Fig. 1). For efficient use of computational time, our simulation of

Fig. 1. Two-dimensional computational domain: A. simplified diagram of

the EGSB reactor exploits the symmetric geometry of the reactorand simulates half the geometry in a two-dimensional surface.The meshes were created in the ANSYS Fluent GAMBIT preproces-sor program and exported into the ANSYS Fluent 6.3 CFD flowmodeling software package to solve the continuity and momentumequations.

In the Eulerian–Eulerian model, we presume for the purposes ofthis study, that each phase is incompressible. The wastewater wasregarded as mixed liquid, initially containing pure water and glu-cose, and the density was determined using a volume weightedmixing law. The sludge granules took up about 35% of the volumein the bed region and were considered to be 1 mm-diameter spher-ical solid granules with a density of 1460 kg/m3. The biogas was as-sumed to have a density defined by the incompressible–ideal-gaslaw (FLUENT 6.0 User’s Guide, 2001). The gas phase volume fractionwas related to gas production in reaction and the gas bubbles wereassumed to have a diameter of 0.1 mm.

The simulation results vary little with grid density so truncationerrors in the numerical simulation can be neglected. An analysisindependent of the grid was performed to eliminate errors in sim-ulation accuracy, numerical stability, convergence and computa-tional steps related to grid coarseness (Ait-Ali-Yahia et al., 2002;Lu et al., 2009). The grid independent analysis was done. Whenthe optimum cell number was used, the difference in pressure dropwas below 5%. Therefore, a two-dimensional computational do-main of the complete geometry of the EGSB reactor was devisedwith 14,440 cells, 29,780 faces, and 15,341 nodes (Fig. 1). The

the EGSB reactor; B. three-phase separation zone; C. reaction zone.

Table 1EGSB reactor simulation and operating conditions.

Working condition HRT (h) Inlet chemical oxygen demand (mg/L)

C1 4 2000C2 4 4000C3 4 6000C4 4 8000C5 2 8000C6 1 8000

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initial sludge bed was packed with granular solids with a volumefraction of 0.5. The reactor wastewater inlet was modeled with avelocity-inlet boundary condition, and the outlet was set as a pres-sure outlet boundary condition. All other solid surfaces were de-fined by wall boundary conditions with free slippage for thebiogas and no slip for the sludge or wastewater. In this study,the simulation was operated in unsteady state conditions (timestep sides equal to 0.001 s, maximum iterations per time stepequal to 50 steps). The convergent solution was defined as thesolution for which the normalized residual for all variables was lessthan 1 � 10�3 and the calculated outflow rate had reached a con-stant value. Convergence was typically reached after 33,500 itera-tions. All the simulations were carried on a computer with a 32 bitprocessor (Intel� Core™ 2 Duo CPU T9300) with 2 GB of randomaccess memory, run at a clock speed of 2.50 GHz.

2.3. Tracer experiment

Velocity patterns were obtained from tracer experiments usingparticle image velocity (PIV) measurements. For the test, a pulse ofglass micro-beads was injected as a tracer into the reactor inputstream. A planar cross-section of the flow was illuminated with asheet light source, and an image of the tracer particles was formed.The measurement of velocity was based on the displacement of thetracer particles during a given time interval.

Fig. 2. Experimental and simulated values of the water velocity at C5 reactor operating crate with varying MFR and HRT: (C) constant inlet chemical oxygen (8000 mg/L) and va

3. Results and discussion

3.1. Model verification and error evaluation

As far as the CFD model verification is concerned, Fig. 2A and Bpresent a comparison between the experimentally measured andthe simulated data of the water velocity in the reaction zone show-ing a good level of agreement between the measured and predictedvalues. The relative error between measured and simulated datawas within 10% indicating that the model provides a good overalldescription of reactor behavior.

The errors incurred in calculation derived from several sources,such as geometry meshing, numerical treatment of initial andboundary conditions, and incomplete iteration (Ferziger and Peric,

onditions: (A) reaction zone; (B) three-phase separation zone; Hydrogen productionrying HRT; (D) constant HRT (4 h) and varying inlet chemical oxygen demand.

Fig. 3. (A) Water velocity contours of water (m/s) in the EGSB at C5 reactor operating conditions; magnified views taken from area marked by a square in the Figure: (B) liquidvelocity; (C) gas velocity.

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1996). With regard to geometry meshing, the grid selected wasconsidered to be grid independent, thus related influences (suchas truncation errors) can be ignored.

Adopting an iterative approach, discrete equations cannot sat-isfy absolute convergence, and the iterative process will only stopwhen a certain condition occurs, for example, the normalizedresidual for all variables. This is why we see incomplete iterations.However, it should be noted that in the study, the inaccuracy dueto incomplete iteration was less than 1 � 10�3. The definition ofinitial values and boundary treatments are the most significant(and complex) steps in the setup of the numerical calculation. To

obtain a high accuracy simulation, in addition to selecting the rightparameters, the virtual conditions should be suitably simplified.Errors incurred at this stage are difficult to analyze and quantify,and require further examination (to be described elsewhere).

3.2. Visualization of flow patterns

In a bioreactor set up for wastewater treatment, flow pattern,sludge activity, and mass balance analysis are interdependent. Agood flow regime is required for efficient contact between mi-crobes and wastewater, which in turn supplies a good growing

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environment for the culture (Su and Yu, 2006). To obtain hydrody-namic information from the EGSB reactor, six unsteady state sim-ulations (Table 1), at different HRTs (assuming uniform recycleratio, and HRT matched to inlet up-flow velocity) and inlet chem-ical oxygen demands were conducted.

Fig. 3A portrays the water velocity in the complete geometry ofthe EGSB reactor under C5 operating conditions (see Table 1). Ascan been seen, after a few seconds (from 0.2 to 0.5 s), there is a

Fig. 4. (A) Contours of gas volume fraction (C5 operating conditions); Magnified views ta(B) liquid velocity vectors, m/s.

large velocity gradient distribution within the sludge bed region,which may be beneficial for solid–liquid mixing. However, in thereaction zone above the bed region, which is far away from thewater inlet, there are little velocity fluctuations and consequentlyfew contributions from this source to mass transfer. When biogasis produced and the gas is released from the bed region (after0.5 s), there is a high velocity distribution over the medial area ofthe reaction zone, which can be attributed to the biogas production

ken from area marked by a square in the Figure: A. contours of gas volume fraction;

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and the work done when the gas expands. In this special area, gasbubbles produced by fermentation, such as carbon dioxide andhydrogen, will flow upwards with the stream swirl. This move-ment will make the bulk up-flow velocity greater than the up-flowvelocity of liquid alone, and the cross-sectional velocity will benon-homogeneous. Moreover, the core-annulus structure (seeFig. 3B–C) will form in the reaction zone because the velocities inthe core region are much lower than those in the annulus region,whereas because velocities near the wall are increasing and down-ward in direction, this may lead to back-mixing and internal circu-lation behavior.

Another significant reactor hydrodynamic characteristic, influ-encing the process of waste water treatment is the relative volumefraction of the sludge and the gas phases is sludge bed expansionand the existence of sludge flocs. This greatly changes the natureof the interaction between the liquid and gas phases. This interac-tion plays a significant role in the expanded sludge bed reactor(Dou et al., 2008). In this paper the expansion process of sludgebed is not analyzed, instead the study concentrates on the bed re-gion, and conducting a simulation at the stabilization period of thebed region after expansion. Fig. 4A presents the biogas volumefraction predicted by the CFD simulation. Biogas initial productionin the bed region to release can be readily seen from this result. Thedistribution of gas volume fraction is heterogeneous and mainlydistributed about the middle. This non-homogeneity is caused by

Fig. 5. Contours of species of mass fraction (C5 o

the circular liquid flow under the liquid–gas interaction. Thus fora three-phase separator, it should be installed near the middle ofthe cylindrical body, letting the biogas be released from this posi-tion, to improve the efficiency of phase disengagement. In thiswork, we also find (see Fig. 4B–C) that some biogas escaped, fol-lowing the reactor wall near the separator baffle, which is not goodfor biogas collection. This loss may be caused by the angle of incli-nation of the three-phase separator baffles. In our EGSB reactor,there may be some sub-optimal design concerning the angle ofthe separator baffle, which leads to the strong velocity fluctuationsnear the baffle with the consequence that some biogas is carriedout by the up-flow water and far away from separator.

3.3. Glucose conversion and biohydrogen production

To predict the degree of glucose conversion and biohydrogenproduction, ethanol-type fermentation reactions were included inthe species transport and reaction models via the CFD codes.Fig. 5, as an example of glucose conversion shows the mass transferprocess from glucose to ethanol. At the beginning of the reaction,mass transfer mainly occurred in the sludge bed region becauseof liquid–solid mixing. Then with increasing production and re-lease of biogas, the mass transfer was upward, caused by high tur-bulence and intensive mixing, and thus the efficiency of mass

perating conditions) (A) glucose; (B) ethanol.

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transfer is higher than in other regions, meaning that more glucosewill be degraded.

The strategy of operation for the hydrogen production experi-ment using the laboratory-scale H2-producing EGSB reactor isshown in Table 1. Fig. 2C–D shows the relationship between theexperimental biohydrogen production rate and the outlet hydro-gen mass flow rate (MFR) in simulation. From our experimentaldata (see C of Fig. 2) we see that HRT, being related to water up-flow velocity, affects biohydrogen production. When the HRT ex-ceeds 2 h the hydrodynamic behavior occurring is suitable for bio-hydrogen production. This is because (see also section on‘‘visualization flow patterns”), this behavior gives an appropriatevelocity distribution to maximize interphase interaction. By inte-grating this information with the previous simulation results, aqualitative relationship between hydrodynamics and biohydrogenproduction can be obtained. Additionally, using the reaction model,the response of biohydrogen production with varied inlet chemicaloxygen demands in simulation has predictive and directive func-tions for experimental control and operation (see D of Fig. 2).

3.4. Advantages and limitations

The application of the method proposed here relies on experi-mental data obtained from tracer experiments and reactor opera-tion. Thus, this method can be credibly used for bioreactordesign, optimization and even operation prediction. In addition,the application of the model to biohydrogen production may pro-vide some beneficial information for researchers who are lookingfor suggestions on how to analyze flow patterns in reactors andoptimize the process to improve biohydrogen yield, or studyingthe complicated multiphase systems of waste water treatment toincrease the phase separation efficiency and improve quality oftreatment.

In spite of the advantages mentioned above, there are some lim-itations in the current model. For example, some hydrodynamicsparameters involved in our model were chosen from default val-ues, for example, the interphase drag coefficient and the sludge vis-cosity coefficient. Thus some sources of error between model andactuality were not minimized. If this method is to be applied inother reactor systems and the accuracy of results is to be improved,such parameters should be obtained through process measure-ment. Another limitation is the relationship between simulatedvalues and actual operational data, such as HPR and MFR(Fig. 2C–D). As this is an initial study of a hydrodynamics–reactionkinetics coupled model, a simple reaction kinetics model was used.To get a better correlation between simulation and operation, andto employ the simulation as predictor or guide for operation, estab-lishing a complex but logical reaction kinetics model will lead to asignificant improvement.

This method is suitable for continuous flow systems, such as theEGSB reactor mentioned above, because of the model’s continuityand steady behavior. This method cannot be applied to batch sys-tems or to systems with strongly unsteady hydrodynamic behaviorwithout significant model modifications.

4. Conclusion

In this paper, a coupled hydrodynamics–reaction kinetics modelwas generated from CFD code to simulate a gas–liquid–solid three-phase biotreatment system for the first time. According to the out-come of analysis, the flow patterns were visualized, and significantparameters were evaluated. The coupled model also demonstratesa qualitative relationship between hydrodynamics and biohydro-gen production, pointing out that controlling hydraulic retentiontime (HRT) is a key factor in biohydrogen-production. This method

is suitable for continuous flow systems, but it cannot be applied tobatch systems or to systems with strongly unsteady hydrodynamicbehavior without significant model modifications.

Acknowledgements

The authors would like to thank the National Natural ScienceFund of China (No. 30870037), the National Natural Science KeyFund of China (No. 50638020), the Project 50821002 (National Cre-ative Research Groups) supported by National Nature ScienceFoundation of China, the State Key Laboratory of Urban Water Re-source and Environment, the Harbin Institute of Technology(2008QN02), the Fundamental Research Funds for the Central Uni-versities (Grant No. HIT. NSRIF. 2009115), and the DevelopmentProgram for Outstanding Young Teachers in Harbin Institute ofTechnology (HITQNJS.2009.046) for their support of this study.

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