Mehdi Hassanvand Jamadi,Abolghasem Alighardashi*

Faculty of Civil,Water and Environmental Engineering,Shahid Beheshti University,Tehran 1658953571,Iran

Application of Froude dynamic similitude in anaerobic baffled reactors to prediction of hydrodynamic characteristics of a prototype reactor using a model reactor

Mehdi Hassanvand Jamadi,Abolghasem Alighardashi*

Faculty of Civil,Water and Environmental Engineering,Shahid Beheshti University,Tehran 1658953571,Iran

An anaerobic baffled reactor is a system developed in recent decades and has been used as part of the treatment of high-strength wastewater. Since the function of this system is based on its hydrodynamic features,hydrodynamics and the regime of the flow through the reactor are crucial.In this study,a prototype reactor with eight chambers,which had a total volume of 48 L,and a model reactor,whose dimensions were half of those of the prototype reactor,were used.The Froude dynamic similitude in these reactors was investigated.The results show that the curve dimensionless variances were 0.089 and 0.096 for the prototype and model reactors,respectively,the short-circuiting indices were 0.483 and 0.489 for the prototype and model reactors,respectively,the effective volume and short-circuiting index measurement errors were both 1%, the hydraulic efficiency error was 2%,and the Peclet and dispersion number errors were both 7%.Most of the compared indices were close to one another in value.Therefore,the model reactor can be used based on the Froude dynamic similitude to determine hydrodynamic characteristics of a baffled reactor at a full scale.

Anaerobic baffled reactor;Froude dynamic similitude;Hydrodynamics;Prototype reactor;Dead space

1.Introduction

Hydraulics and hydrodynamics of flow are among the most important factors in design and operation of different wastewater treatment systems.Hydraulic features of the crossing wastewater flow can be important factors in determining the specifications and dimensions of different units of a treatment plant.In biological units of treatment facilities,characteristics of the system depend on its hydraulic features.In a step-feed activated sludge system,for example,the changes in the sludge return ratio have a major effect on the quality of outgoing sewage,and this is completely due to system hydraulics. Moreover,the mixed liquor suspended solids(MLSS)fraction and sludge amount in these systems are generally determined by system hydraulics(Leslie Grady et al.,1999).The basic approach in hydraulic studies is the analysis of mass balance in a reactor(Metcalf and Eddy Inc.staff et al.,2003).The hydraulic retention time(HRT),type,and distribution of materials in a reactor;the reactor's volumetric efficiency;the amount of hydraulic dead space;the existence of shortcircuiting in the reactor;and,ultimately,the type of the flow regime depend on flow hydraulics.Dynamic similitude is used to model hydraulic structures so that the results obtained from the model reactors can be used in the prototype reactors.If the hydraulic structure is an open system(similar to an anaerobic baffled reactor(ABR)),the Froude dynamic similitude is used for the model reactor in addition to geometrical similitude (Streeter et al.,1998).ABRs are defined as upflow anaerobic sludge blanket(UASB)reactors that have been transformed into separate chambers by baffles.In an ABR,the velocity offluid and gas flow is effective in the mixing and contact between biomass(sludge)and incoming wastewater,and therefore affects the extent of mass transfer and reactor performance.The dead space of these reactors(about 8%)is less than that of other anaerobic reactors(about 53%-90%) (Grobicki and Stuckey,1992).Observations indicate that flow in an ABR has an intermediate flow pattern between plug flow and completely mixed flow(Grobicki and Stuckey,1992).This reactor produces a small amount of surplus sludge and does not need any final sedimentation tank(Smith and Scott,2005). Some studies have been conducted on hydrodynamics of ABRs.Sarathai et al.(2010)studied the hydrodynamic characteristics of an ABR with three chambers,which had a total volume of 50.4 L,and a primary sedimentation tank.Li et al. (2015)compared the hydrodynamic characteristics of two 24-L ABRs,a plane-folded plate reactor,and an oppositefolded plate reactor.Li et al.(2016)evaluated the flow hydrodynamics in a modified ABR with four chambers,which had different dimensions and a total volume of 54.8 L.A recent study investigated the hydrodynamics of a paneled anaerobic baffle-cum filter reactor with a net working volume of 100 L(Renuka et al.,2016).These studies indicate that the mixing pattern of ABRs is intermediate between plug flow and completely mixed flow.There is not much dead space in ABRs.However,these studies did not compare their results with a prototype reactor.

Since the retention time plays an important role in design and operation of wastewater treatment reactors,it is necessary to address time similarity between the model and prototype reactors when using model results for the prototype reactor.The dynamic similitude between the two reactors has not been reported in previous studies.In this study,the Froude dynamic similitude was used to compare the results obtained from the model reactor with those from the prototype reactor.

2.Materials and methods

2.1.Anaerobic baffled reactors

In this study,two ABRs were used to examine the Froude dynamic similitude.The prototype reactor had eight chambers. Each chamber was 10 cm long(ain Fig.1),15 cm wide,and 40 cm high(bin Fig.1).The length-to-height ratio(1:4)was based on Renuka et al.(2016).The volume of each chamber was 6 L and the total volume of the prototype reactor was 48 L.Each chamber was divided into upflow and downflow sections.The length and volume of the upflow section were three times those of the downflow section(Dama et al.,2000). The end of the internal baffle that divides the chambers was bent 45°to direct the flow into middle sections(Bachmann et al.,1982,1985).The dimensions of the model reactor were half of those of the prototype reactor.

Since the reactors were not under pressure and were considered open hydraulic structures,the Froude dynamic similitude was used in terms of Eq.(1)to describe the dynamic similitude between the reactors(Streeter et al.,1998):

Fig.1.Schematic plot of used reactor(ais 10 cm for prototype reactor and 5 cm for model reactor,andbis 40 cm for prototype reactor and 20 cm for model reactor).

whereuis the flow velocity,lis the characteristic length,gis the gravitational acceleration,and the subscripts P and M represent the prototype and model reactors,respectively.Since the gravitational acceleration is constant,the geometrical similarity ratioScan be obtained as follows:

Time similarity for the two reactors is as follows:

wheretis time.

In other words,the results obtained from hydrodynamic studies on the model reactor with retention timetshould be reliable for a prototype reactor with retention timeTo examine this,studies on hydrodynamic characteristics of model and prototype reactors were conducted with retention times of 180 min and 255 min,respectively.

2.2.Hydrodynamic characteristics

The residence time distribution(RTD)curve is used for hydrodynamic studies on different reactors in process engineering(Fogler,2006).The normalized distribution curve is used for better comparison of two reactors.The normalized curve parameters are defined in the following equations (Metcalf and Eddy Inc.staff et al.,2003):

whereHRTis the theoretical retention time and is equal to the reactor volume divided by the input flow rate,θ is the normalized time,C(t)is the concentration at timet,C0is thenominal concentration equal to the mass of tracer injected into the reactor divided by the reactor volume,andC(θ)is the normalized concentration at normalized time θ.

Hydraulic and hydrodynamic features existing in the reactor are accessible through examination of the information obtained from the RTD curve.The mean and variance of normalized curves are as follows:

The percentage of hydraulic dead space is defined as follows(Sarathai et al.,2010):

whereVdis the volume of dead space in the reactor andVis the total volume of the reactor.

Short-circuiting is a non-ideal flow caused by inadequate mixing,dense currents due to temperature differences,circulated flow,poor design,and axial dispersion(in plug-flow reactors).The short-circuiting index(SCI)is defined in Eq.(9)(Metcalf and Eddy Inc.staff et al.,2003):

wheretiis the first observation time of tracer at the outlet.

Based on the type of hydraulic flow regime,reactors are divided into completely mixed and plug-flow types.A completely mixed reactor is a reactor in which inflow contents are mixed totally.A plug-flow or piston reactor is a reactor in which no mixing occurs(Smith and Scott,2005).To detect the hydraulic flow regime in the reactor,tanks-in-series and axial dispersion models are used.In the tanks-in-series model,it is assumed that the reactor consists of a series of tanks with complete mixing in each tank(Levenspiel,1999).The number of tanks in series(N)is as follows:

IfNapproaches 1,the flow in the reactor tends toward completely mixed flow,and it will be near plug flow ifNreaches∞.

In the axial dispersion model,radial mixing is neglected and only axial mixing is considered(Yang et al.,2008).The dispersion number(d)and the Peclet number(Pe)are two dimensionless factors that show the extent of dispersion:

whereDis the axial dispersion coefficient.

The dispersion and Peclet numbers are opposite to one another.With the increase of the dispersion number and decrease of the Peclet number,the reactor becomes a completely mixed vessel.In the same way,the decrease of the dispersion number and increase of the Peclet number makes it a plug-flow vessel.The hydraulic efficiency,another hydraulic parameter of the reactor,was examined.It is obtained as follows(Persson,1999):

where λ is the hydraulic efficiency,andeis the useful volume percent of a reactor.

The Morrill dispersion index(MDI)is calculated with Eq.(14).For an ideal plug-flow reactor,MDIis 1,and for a completely mixed reactor,it is about 22.Avalue ofMDIequal to or less than 2 is considered to be a value for an effective plug-flow reactor(Metcalf and Eddy Inc.staff et al.,2003).

whereP10andP90are,respectively,the 10th and 90th percentile values obtained from a log-probability plot of time versus the cumulative percentage of the total injected tracer. The Morrill volumetric efficiencyEis defined by Eq.(15) (Metcalf and Eddy Inc.staff et al.,2003):

For an effective plug-flow reactor(MDI≤2),the volumetric efficiency will be greater than 50%.

3.Results and discussion

RTD curves for the two reactors at dynamically similar times are drawn in Fig.2.To verify the compliance of hydraulic indices obtained from two diagrams,we compared theindices for the curves of the two reactors.The modeling error σ for an indexIis calculated as follows:

Fig.2.RTD curves for model and prototype reactors.

whereIPandIMare the indices of the prototype and model reactors,respectively.

Fig.2 shows to a large extent the conformity of dispersion curves for the two reactors at a dynamically similar retention time.The hydrodynamic indices and Froude dynamic similitude errors between the model and prototype reactors are shown in Tables 1 and 2,respectively.According to this table, curve dimensionless variances,which show data dispersions, are 0.089 and 0.096 for the model and prototype reactors, respectively.The similarity error is 7%.In other words,the two curves overlap with a 7%error with respect to the amount of data dispersion.In addition to curve variance,the normalized mean retention time,normalized peak time,and normalized peak concentration obtained from RTD curves have also been evaluated.Their values are 0.99,0.89,and 1.59 for the prototype reactor and 0.98,0.90,and 1.61 for the model reactor,respectively,showing that different indices for RTD curves are almost consistent for the two reactors.This shows that dispersion curves for the two different reactors with geometrical and dynamic similarities will be the same.The mean retention time error is 1%and the peak time error and peak concentration error are both 1%,which are low levels. The closer the mean retention time gets to 1,the closer the reactor will be to its optimum retention time.In other words, hydraulic and biologic retention times coincide and this optimizes the reactor's performance.The results of this study show that ABR acts almost at its optimum retention time.

The useful volume of a reactor is a part of the reactor space in which chemical and biological reactions occur.No signif icant process occurs outside of this section due to insignificant mixing with inflow(Parsamehr,2012).The hydraulic dead space is one of the important parameters evaluated in hydrodynamic studies of reactors.The effect of dead space is to reduce the effective volume of the reactor in which chemical reactions occur(Parsamehr,2012).The hydraulic dead space of a reactor is not mixed with the inflow(Metcalf and Eddy Inc.staff et al.,2003).In fact,the dead space or stagnant area has negligible mixing degrees(Parsamehr,2012). Therefore,the extent of hydraulic dead space plays an important role in reactor performance.Grobicki and Stuckey (1992)considered that the hydraulic dead space of an ABR has a very low value(below 8%).The useful and dead space volumes of the model reactor are 99%and 1%of the reactor volume,respectively.These values show a high useful volume and insignificant dead space.The useful volume and dead space of the prototype reactor are 98%and 2%,respectively, showing a high conformity with the results of the model reactor.The measurement error of the useful volume is 1%.

Short-circuiting is a complicated phenomenon with significant effects on a reactor's performance(Tsai et al.,2012).It is also one of the largest impediments to successful design of reactors(Persson et al.,1999),leading to dead spaces(Metcalf and Eddy Inc.staff et al.,2003)and decreasing reactor eff iciency(Dierberg et al.,2005).Moreover,it is an important factor in low hydraulic efficiency(Singh et al.,2009;Xanthos et al.,2011).Short-circuiting indices for the model and prototype reactors are 0.483 and 0.489,respectively.The shortcircuiting index indicates the ratio of the time of the first tracer exit to the reactor's retention time.As this value approaches 1,less short-circuiting occurs.When it approaches zero,short-circuiting will increase such that a value smaller than 0.3 demonstrates significant short-circuiting(Sarathai et al.,2010).If 0.3 indicates short-circuiting in the reactor,it should be said that no significant short-circuiting occurred in the prototype and model reactors.Like the useful volume error, the measurement error for the short-circuiting index is 1%.

The numbers of equivalent tanks in series are 11.27 and 10.44 for model and prototype reactors,respectively,and are accompanied by a 7%error.The Peclet and dispersion numbers are 21.48 and 0.047 for the model reactor and 19.83 and 0.050 for the prototype reactor,respectively,and,like the tanks-inseries model error,they are accompanied by a 7%error.The obtained error was the same for both tanks-in-series and axial dispersion models,i.e.,from the viewpoint of modeling error, use of either of the two models(tanks-in-series or axial dispersion)in the model reactor to predict the flow regime in a prototype reactor does not differ from the other model.In the tanks-in-series model,if the number of tanks is lower than orequal to 3,dispersion is considered high.Moreover,in the case of using the axial dispersion model,a Peclet number equal to 5 is the criterion and any value less than 5 indicates significant dispersion(Ji et al.,2012).Considering the mentioned criteria and using both models for determination of the flow regime type,the studied model and prototype reactors have low dispersion amounts and tend to be plug-flow reactors.

Table 1 Comparison of indices obtained from model and prototype reactors.

Table 2 Froude dynamic similitude errors between indices obtained from model and prototype reactors.

Fig.3.Time versus tracer cumulative percentage plots for model and prototype reactors.

Hydraulic efficiencies for the model and prototype reactors are 90%and 88%,respectively,showing a 2%error.Hydraulic efficiency can be divided into three groups(Ji et al.,2012): high hydraulic efficiency(λ＞75%),good hydraulic efficiency (50%＜λ≤75%),and poor hydraulic efficiency(λ≤50%). Both the model and prototype reactors in this study had high hydraulic efficiencies and this indicates a desirable performance of ABR and a high capability for wastewater treatment. The Morrill dispersion index for the model and prototype reactors was obtained through time-cumulative percentage plots of an outgoing tracer in a log-probability coordinate system (Fig.3).Using these charts,Morrill dispersion indices of 2.075 and 2.084 were obtained for the model and prototype reactors, respectively,with a 0.4%error.Moreover,the Morrill volumetric efficiencies were 48.18%for the model reactor and 47.99%for the prototype reactor,showing an error similar to that of the Morrill dispersion index.

4.Conclusions

(1)Hydrodynamic and hydraulic results obtained from pilot studies on an ABR can be generalized with a close approximation to a reactor with larger scales,provided that there are geometrical and dynamic similarities between the two reactors. This is especially important for the design offull-scale reactors. Through pilot studies,appropriate estimation of hydrodynamic features of a reactor can be obtained before the reactor is built.

(2)Because of the importance of hydraulic retention time in wastewater treatment reactors,it is required that a time similarity obtained from the Froude dynamic similitude be established between the model and prototype reactors.The retention time of the prototype reactor should be considered equal to the retention time of the model reactor multiplied by the square root of the geometrical similarity ratio(the ratio of prototype dimensions to model dimensions).

(3)The errors of the results related to data distribution(the variance,number of tanks in series,Peclet number,and dispersion number)are the same(7%).

(4)As for the indices related to the ratio of two series of data obtained from the distribution curve(the useful volume,shortcircuiting index,Morrill dispersion index,and Morrill volumetric efficiency),the errors of results are not more than 1%.

(5)As for the indices that are a combination of distributional and proportional indices(hydraulic efficiency),the error is 2%.This error falls between the error of indices related to data distribution and that of indices related to data ratio, though it is closer to the ratio data error.

Bachmann,A.,Beard,V.L.,McCarty,P.L.,1982.Comparison of fixed-film reactors with a modified sludge blanket reactor.In:Wu,Y.C., Smith,E.D.,eds.,Proceedings of the First International Conference on Fixed-Film Biological Processes.Defense Technical Information Center, Ohio,pp.1192-1211.

Bachmann,A.,Beard,V.L.,McCarty,P.L.,1985.Performance characteristics of the anaerobic baffled reactor.Water Res.19(1),99-106.http:// dx.doi.org/10.1016/0043-1354(85)90330-6.

Dama,P.,Bell,J.,Brouckaert,C.J.,Buckley,C.A.,Stuckey,D.C.,2000. Computational fluid dynamics:Application to the design of the anaerobic baffled reactor.In:Proceeding of WISA Biennial Conference.Water institute of South Africa,Sun City.

Dierberg,F.E.,Juston,J.J.,DeBusk,T.A.,2005.Relationship between hydraulic efficiency and phosphorus removal in a submerged aquatic vegetation-dominated treatment wetland.Ecol.Eng.25(1),9-23.http:// dx.doi.org/10.1016/j.ecoleng.2004.12.018.

Fogler,H.S.,2006.Elements of Chemical Reaction Engineering,fourth ed. Pearson Education,Inc.,Massachusetts.

Grobicki,A.,Stuckey,D.C.,1992.Hydrodynamic characteristics of the anaerobic baffled reactor.Water Res.26(3),371-378.http://dx.doi.org/ 10.1016/0043-1354(92)90034-2.

Ji,J.Y.,Zheng,K.,Xing,Y.J.,Zheng,P.,2012.Hydraulic characteristics and their effects on working performance of compartmentalized anaerobic reactor.Bioresour.Technol.116,47-52.http://dx.doi.org/10.1016/ j.biortech.2012.04.026.

Leslie Grady Jr.,C.P.,Daigger,G.T.,Lim,H.C.,1999.Biological Wastewater Treatment,second ed.Marcel Dekker,Inc.,New York.

Levenspiel,O.,1999.Chemical Reaction Engineering,third ed.John Wiley& Sons,Inc.,New York.

Li,S.N.,Nan,J.,Li,H.Y.,Yao,M.,2015.Comparative analyses of hydraulic characteristics between the different structures of two anaerobic baffled reactors(ABRs).Ecol.Eng.82,138-144.http://dx.doi.org/10.1016/ j.ecoleng.2015.04.095.

Li,S.N.,Nan,J.,Gao,F.,2016.Hydraulic characteristics and performance modeling of a modi fied anaerobic baf fled reactor(MABR).Chem.Eng.J. 284(15),85-92.http://dx.doi.org/10.1016/j.cej.2015.08.129.

Metcalf and Eddy Inc.staff,Burton,F.L.,Stensel,H.D.,Tchobanoglous,G., 2003.Wastewater Engineering:Treatment and Reuse,fourth ed.McGraw-Hill,New York.

Parsamehr,M.,2012.Modeling and Analysis of a UASB Reactor.M.E. Dissertation.Lule? University of Technology,Lule?.

Persson,J.,1999.Hydraulic Ef ficiency in Pond Design.Ph.D.Dissertation. Chalmers University of Technology,Gothenburg.

Persson,J.,Somes,N.L.G.,Wong,T.H.F.,1999.Hydraulics ef ficiency of constructed wetlands and ponds.Water Sci.Technol.40(3),291-300. http://dx.doi.org/10.1016/S0273-1223(99)00448-5.

Renuka,R.,Mohan,S.M.,Raj,S.A.,2016.Hydrodynamic behaviour and its effects on the treatment performance of panelled anaerobic baf fle-cum filter reactor.Int.J.Environ.Sci.Technol.13(1),307-318.http:// dx.doi.org/10.1007/s13762-015-0824-z.

Sarathai,Y.,Koottatep,T.,Morel,A.,2010.Hydraulic characteristics of an anaerobic baf fled reactor as onsite wastewater treatment system.J.Environ. Sci.22(9),1319-1326.http://dx.doi.org/10.1016/S1001-0742(09)60257-6.

Singh,S.,Haberl,R.,Moog,O.,Raj Shrestha,R.,Shrestha,P.,Shrestha,R., 2009.Performance of anaerobic baffled reactor and hybrid constructed wetland treating high-strength wastewater in Nepal:A model for DEWATS.Ecol.Eng.35(5),654-660.http://dx.doi.org/10.1016/ j.ecoleng.2008.10.019.

Smith,P.G.,Scott,J.S.,2005.Dictionary of Water and Waste Management, second ed.IWA Publishing,London.

Streeter,V.L.,Wylie,E.B.,Bedford,K.W.,1998.Fluid Mechanics,ninth ed. McGraw-Hill,Boston.

Tsai,D.D.W.,Rmaraj,R.,Chen,P.H.,2012.A method of short-circuiting comparison.Water Resour.Manag.26(9),2689-2702.http://dx.doi.org/ 10.1007/s11269-012-0040-2.

Xanthos,S.,Gong,M.,Ramalingam,K.,Fillos,J.,Deur,A.,Beckmann,K., McCorquodale,J.A.,2011.Performance assessment of secondary settling tanks using CFD modeling.Water Resour.Manag.25(4),1169-1182. http://dx.doi.org/10.1007/s11269-010-9620-1.

Yang,Y.J.,Goodrich,J.A.,Clark,R.M.,Li,S.Y.,2008.Modeling and testing of reactive contaminant transport in drinking water pipes:Chlorine response and implications for online contaminant detection.Water Res. 42(6-7),1397-1412.http://dx.doi.org/10.1016/j.watres.2007.10.009.

Received 6 March 2016;accepted 28 July 2016

Available online 11 March 2017

*Corresponding author.

E-mail address:a_ghardashi@sbu.ac.ir(Abolghasem Alighardashi).

Peer review under responsibility of Hohai University.

http://dx.doi.org/10.1016/j.wse.2017.03.002

1674-2370/?2017 Hohai University.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license(http:// creativecommons.org/licenses/by-nc-nd/4.0/).

?2017 Hohai University.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license(http:// creativecommons.org/licenses/by-nc-nd/4.0/).