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A correction coefficient for pollutant removal in free water surface wetlands using first-order modeling

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A correction coefficient for pollutant removal in free water surface wetlands using first-order modeling
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  EcologicalEngineering 61 (2013) 200–206 ContentslistsavailableatScienceDirect Ecological   Engineering  journalho   me   page:www.elsevier.com/locate/ecoleng A   correction   coefficient   for   pollutant   removal   in   free   water   surfacewetlands   using   first-order   modeling Shang-Shu   Shih a , ∗ ,Pin-Han   Kuo b ,Wei-Ta   Fang c ,Ben   A.   LePage d a HydrotechResearchInstituteof    NationalTaiwanUniversity,Taiwan b DepartmentofHydraulicandOceanEngineeringof    NationalChengKungUniversity,Taiwan c GraduateInstituteof    EnvironmentalEducationofNationalTaiwanNormalUniversity,Taiwan d PacificGasandElectricCompany,USA a   rti   c   le   inf   o  Articlehistory: Received19April2013Receivedinrevisedform9August2013Accepted20September2013 Keywords: HydraulicretentiontimeResidencetimedistributionAspectratioWaterdepthFirst-ordermodelCorrectioncoefficient ab   st   rac   t Pollutantremovalinfree   watersurface   wetlands(FWS)for   practical   purposes   is   calculated   using   the   sim-plified   hydraulic   retention   time   (HRT)ofthe   first-order   model.Although   the   residence   time   distribution(RTD)   represents   thehydraulicconditions   seen   innatural   wetlandsbetter   when   compared   tothe   HRT,theRTD   ismoredifficult   tocalculate.   It   is   crucial   to   determinethe   situationsthat   the   first-order   model   wouldhave   goodperformance   andquantifythe   difference   between   HRTand   RTD.In   thisstudy,thecorrectioncoefficientfor   the   first-order   model   ispresented   andexaminedthrough   28   numerical   experiments.Therelationship   between   the   correctioncoefficient   and   the   related   hydraulicefficiency   isalsoestablishedand   discussed.   The   refining   results   showthat   the   aspect   ratio   has   a   logarithmic   trend   whilethe   waterdepth   has   turnedan   exponential   trend   with   the   variantcorrection   coefficients.   Higheraspect   ratios   orlower   water   depthscan   ensure   betterpollutantremoval   estimation   by   the   first-order   model.Bothwaterdepth   and   aspectratioinfluence   correctioncoefficients;however,   water   depth   isthe   factor   that   has   agreater   impact.It   is   suggested   thatthe   first-order   model   is   employed   for   shallow   water   wetlands   withwater   depthslower   than   0.8m   and   narrowlongwetlandswith   aspect   ratios   higherthan   1.20   withoutmodification.   We   also   concluded   that   the   first-order   modelcould   be   more   widely   and   adequatelyusedforpracticalpurposes   after   modification   by   the   correctioncoefficients.   Furthermore,   increasing   waterdepth   and   decreasing   aspectratioresulted   inlower   hydraulicefficiency.Wetland   designersshould   avoidselectingadysfunctional   plan   whendesigningdeepwaterand   low   aspect   ratio   constructed   wetlands. © 2013 Elsevier B.V. All rights reserved. 1.Introduction Freewatersurface(FWS)wetlandsarea   typeof    constructedwetland(CW)combiningopen-waterareasof    varyingwaterdepths,soiltosupportemergentvegetation,andasub-surfacebarriertopreventseepage(USEPA,2000).CWs   aredesignedto   con-trolwaterretentiontimeandhydraulicpathways(Brix,1993).The primaryfunctionofFWS   wetlandsis   totreatwastewaterbyremov-ingpollutants,suchasbiochemicaloxygendemand(BOD)andnitrogen,usingnaturalmicrobial,biological,physical,andchem-icalprocesses.Pollutantremovalis   animportantmetricusedforevaluatingtheeffectivenessof    FWS   wetlandsforwaterqualityimprovement(Reedetal.,1995).Hsuetal.(2011)indicatedthat theHsin-HaiIIandtheDaniaopiConstructedWetlandsachievedmaximumfunctionalperformanceinreducingtheconcentrations ∗ Correspondingauthor.Tel.:+886233662624;fax:+886233662624. E-mailaddresses: uptreeshih@ntu.edu.tw,uptreeshih@gmail.com(S.-S.Shih). of    totalnitrogen,totalphosphorus,loadingsof    biochemicaloxygendemand(BOD),andchemicaloxygendemand(COD)frommunici-palsewage.ThemostcommonmethodtoestimatepollutantremovalinCWs   istousea   first-ordermodelthatincludesthehydraulicreten-tiontime(HRT)ofthewaterflowingthroughthewetland(USEPA,1988;Reedetal.,1995).Thefirst-ordermodelis   deterministicinthatitindicatesthewetlandoutputconcentrationsin   responsetoinputconcentrations,flowdischargeanddetentionvolume(Kadlec,2000).TheHRTis   calculatedbyassuminganaquaticsys-temwithuniformunrestrictedwaterflowwithnomixingand/ordiffusionandanominalretentiontime(Su   etal.,2009).However,suchconditionsarerarelypresentin   FWS   wetlandsbecausewaterflowthroughwetlandsisnotspatiallyandtemporallyuniform(Fisher,1990;Urban,1990;Stairs,1993;Kadlec,1994;KadlecandKnight,1995;WernerandKadlec,1996).Constructedwetlandparameterssuchasaspect,bottomtopog-raphy,waterdepth,vegetation,obstructions,andinlet/outletpositionallinfluencewetlandhydrodynamics,whichultimately 0925-8574/$–seefrontmatter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ecoleng.2013.09.054  S.-S.Shihetal./    EcologicalEngineering  61 (2013) 200–206 201 determinestheretentiontimeandhydraulicandtreatmenteffi-ciency(Thackstonetal.,   1987;Konyhaetal.,1995;ShiltonandPrasad,1996;TaandBrignal,1998;Koskiaho,2003;Su   etal.,2009).Suetal.(2009)andHollandetal.(2004)indicatedthat themostinfluentialparametersareaspectratioandwaterdepth.Theresidencetimedistribution(RTD)quantifiesthedistributionofretentiontimeforagivenwetland(Kadlec,1994).TheRTD approachconsidersthemixing,diffusion,andresidencetimedis-tributionoffluids(Levenspiel,1972;Kadlec,2000),andisthus anadvancedtoolforscienceandengineeringpurposes(Hollandet   al.,2004).As   such,theRTDrepresentsthehydraulicconditionsseeninnaturalwetlandecosystemsbetterwhencomparedtotheHRT.Therefore,tomodelthewaterflowconditionsinreactionves-selssuchasconstructedwetlandsmoreaccuratelyandultimatelyobtainamorerealisticpollutantremovalvalue,theRTD,ratherthanHRTisbeingusedwithscientificrigor(WernerandKadlec,1996;Kadlec,2003;Suetal.,   2009).Despitethelimitationsandinadequacyof    theHRTapproach,the   HRTismorewidelyappliedthantheRTDforpracticalpur-posesbecauseitis   mucheasiertocalculate.However,fewstudiesquantifiedtherelationshipbetweenthese   twoapproaches.Theobjectiveofthisstudyis   toexaminethedifferencebetweenthesetwoapproachesandpresentthecorrectioncoefficientsof    thefirst-ordermodel.ThecorrectioncoefficientisdefinedasthepollutantremovalcalculatedusingtheRTDapproachdividedbythatfoundusingtheHRTapproachundersituationsof    differentaspectratiosandwaterdepths.Thesuitabilityof    usingtheconditionsof    aspectratioandwaterdepthintheHRTmethodwillalsobediscussed. 2.Materialsandmethods  2.1.Hydraulicretentiontime(HRT)approach The   followingequationis   a   simplifiedHRTapproachforcalcu-latingpollutantremoval. R HRT  = 1 − C  e C  i = 1 − e − K  t  t  HRT (1)where, e istheexponentialnotation ≈   2.718282; C  e  istheeffluentconcentration,mg/L; C  i  istheinfluentconcentration,mg/L; k t   isthefirst-orderrateconstant=0.3/day(TaiwanEPA,2008); t  HRT  istheretentiontimecalculatedbytheHRTapproachestimatedfromthevolumeofwaterdividedbythedailydischarge,days;and R HRT  isthecalculatedpollutantremovalusingtheHRTapproach.Eq.(1)impliesthatthemicrobialandbiochemicalprocessesare synchronous.Therefore,pollutantremovalisdependentonthe k t  and t  HRT .Anumberof    studieshaveindicateddifferentvaluesof  k t   forlocalpurposes(USEPA,1988;Hammer,1989;Cooperetal.,1996)andthe k t   inthisstudywasdeterminedto   be0.3/dayforbothoftheHRTandRTDapproaches(TaiwanEPA,2008).  2.2.Residencetimedistribution(RTD)approach TheRTDapproachconsidersthemixing,diffusion,andresidencetimedistributionofafluidinareactorvessel(Fig.1)andmodelsthe flowconditionsof    fluidsin   a   reactorbetterthantheHRTmethod(Levenspiel,1999).ThesimplestwaytoobtaintheRTDofa   reactorisbyusinga   pulseexperimentthatevaluatesRTDusinga   tracertestornumericalsimulation(Suetal.,   2009).UsingtheRTDmodelthepollutantremoval( R RTD )is   computedusingthefollowingequation: R RTD  = 1 − e − K  t  t  RTD (2)where, e istheexponentialnotation ≈ 2.718282; k t  isthefirst-orderrateconstant=   0.3/day(TaiwanEPA,2008);   t  RTD  istheresidence Fig.1. Illustrationof    apulseexperimentinaconstructedfreewatersurfacewetlandwherethewetlandis   alargereactorvessel.The   RTDwasusedtocalculatetherealpollutantremovalperformance. timecalculatedbytheRTDapproachwiththenumericalmodel,TABS-2,days;and R RTD  isthecalculatedpollutantremovalusingtheRTDapproach.  2.3.Correctioncoefficientforthefirst-ordermodel Thecorrectioncoefficient( C  r  )isdefinedasthepollutantremovalcalculatedusingtheRTDapproachdividedbythatfoundusingtheHRTapproach.The C  r   forthefirst-ordermodeliscal-culatedusingEq.   (3)andthevalueofthe C  r   rangesfrom0to1. C  r   = R RTD R HRT = 1   − e − K  t  t  RTD 1 − e − K  t  t  HRT (3)where, e istheexponentialnotation ≈   2.718282; R HRT  isthecal-culatedpollutantremovalusingtheHRTapproach; R RTD  isthecalculatedpollutantremovalusingtheRTDapproach;and C  r   isthecorrectioncoefficientforthefirst-ordermodel.  2.4.Hydraulicefficiency Theperformanceof    wastewatertreatmentfacilitiessuchasconstructedFWS   wetlandsiscloselyrelatedtotheirhydrauliceffi-ciency(Kadlec,2000;KadlecandKnight,1995;DalandPersson,2000;Dierbergetal.,   2005).Thehydraulicefficiencyiscalculatedasshowninthefollowingequation(Perssonetal.,1999):  = t   p t  n (4)where, t   p  isthetimeof    pickoutflowconcentration,day; t  n  isthenominaldetentiontime,day;and    isthehydraulicefficiency.  2.5.Numericalexperiments To   determinetheimpactof    differentphysicalaspectsonres-idencetimedistributionandhydraulicefficiencyweperformeda   seriesofnumericalexperiments.TABS-2is   ahorizontaltwo-dimensionalhydrodynamicandwaterqualitytransportmodelthatcanbe   usedtosimulatea   tracerpulseexperimentto   obtaintheRTDofa   FWS   wetland.Itincludesthreemodules:RMA2,RMA4,andSED-2D.Thehydrodynamicmodel(RMA2)andwaterqual-itytransportmodel(RMA4)wereimplementedinour   numericalexperiment.TheRMA2isthetwo-dimensionaldepthaveragedfiniteelementhydrodynamicmodelforcomputingwatersurfaceelevationsandhorizontalvelocitycomponentsofthesubcriticalfree-surfaceflowfieldwhichFroudenumberislowerthan1.0(Donnell,1997).TheRMA4is   thefiniteelementwaterqualitytransportmodelin   whichthedepthconcentrationdistributionisassumeduniform(King,2003).Theboundaryconditionsofthe RMA2modelaretheflowdischargein   theinletandthewaterlevelintheoutlet;whiletheboundaryconditionoftheRMA4ispollut-antconcentrationintheinlet.ThewaterdepthandwatervelocitysimulatedfromtheRMA2modelwereinputtotheRMA4modelfromtimetotimeasafundamentalflowfieldateachtimestep.  202  S.-S.Shihetal./EcologicalEngineering  61 (2013) 200–206  Table1 Calculatedresultsofthepollutantremovalperformanceof    theHRTandRTDapproachesandtherelatedcorrectioncoefficientswithwaterdepth0.7m   anddifferentaspectratios.ExampleAspectratio t  HRT  (day) R HRT  (%)   t  RTD  (day) R RTD  (%) C  r    First-ordermodelperformance1A0.210.6116.70.5013.90.840.04Poor1B   0.300.6116.70.5114.30.860.06Poor1C   0.53 0.61 16.70.5214.50.870.11Poor1D   0.830.6116.70.5314.80.890.26Poor1E   1.200.6116.70.5415.00.900.33Satisfactory1F   1.880.6116.70.5615.40.920.43Satisfactory1G   2.130.6116.70.5615.50.930.45Satisfactory1H   3.330.6116.70.5715.80.950.56Satisfactory1I   4.80 0.61 16.7 0.58 15.9 0.95 0.64Satisfactory1J   7.50 0.61 16.7 0.5916.20.970.73Satisfactory1K   11.720.6116.70.5916.30.980.81Good1L    13.330.6116.70.6016.40.980.83Good1M   20.830.6116.70.6016.50.990.88Good1N   30.000.6116.70.6016.50.990.92Good Theparametersof    TABS-2weresetfollowingthoseof Kuoetal.(2008)andSuetal.(2009),   andinclude:0.03   forManning’srough-nessvalue;25 ◦ Cfortemperature;50(Pas)   foreddyviscosity;and0.05(m 2 /s)forthediffusioncoefficient.Variationsin   aspectratioandwaterdepthweredevelopedandinvestigatedasfollows:(1)Aspectratio Fig.2. Fig.2aillustratesthefourteenreactionvesselswithdifferentaspectratios.Fig.2b   illustratesa   reactionvesselandthe   fourteenscenariosbasedondifferentwaterdepths.  S.-S.Shihetal./    EcologicalEngineering  61 (2013) 200–206 203 (a) (b) 0.00 0.05 0.10 0.15 0.20 100 90 80 70 60 50 40 30 20 10 0      C    o    n    c    e    n     t    r    a     t     i    o    n Time (hr) α = 0.21α = 0.30α = 0.53α = 0.83α = 1.20α = 1.88α = 2.13α = 3.33α = 4.80α = 7.50α =11.72α =13.33α =20.83α =30.00 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 100 90 80 70 60 50 40 30 20 10 0      C    o    n    c    e    n     t    r    a     t     i    o    n Time (hr) D = 0.1D = 0.3D = 0.5D = 0.6D = 0.7D = 0.8D = 0.9D = 1.0D = 1.1D = 1.2D = 1.3D = 1.4D = 1.5D = 2.0 Fig.3. Fig.3aillustratestheRTDsofthefourteenmodeledscenariosthatwerebasedondifferentaspectratios.Fig.3billustratestheRTDsofthefourteenmodeledscenarios that   werebasedon   differentwaterdepths. Fourteenscenarioswithdifferentaspectratiosweremodeled.Theaspectratiowascalculatedbythewetlandlengthdividedbywetlandwidth.Thewetlandlengthandwetlandwidthare   definedasthelengthsthatare   parallelandperpendiculartoflowdirection.Detailsofthedimensionsandcorrespondingaspectratiosarepro-videdinTable1andillustratedinFig.   2a.Theinletsandoutletsarelocatedatthemidpoint–midpointandthedesignparametersof eachexamplewereconsistent:area3000m 2 ;waterdepth0.7   m;inflowof0.04m 3 /s;andanHRTof0.61days.We   adoptedexam-ple1Ffromourpreviousstudyasthereferenceexample(Su   etal.,2009).(2)WaterdepthFourteenscenarioswithdifferentwaterdepthsweremodeledandtheresultsare   providedin   Table2andillustratedin   Fig.2b.Waterdepthsvariedfrom0.1mto2.0mandtheaspectratiowas   setas1.88(referenceexample),whichcorrespondsto   a   reactionvesseldimensionof75mlongand40mwide.Example2Eis   usedasthereferenceexampleforthismodelbecauseexamples1Fand2Ehavethesamedimensionswithanaspectratioof    1.88andtherefore,wecancomparetheinfluenceandeffectivenessof    aspectratioversuswaterdepthon   pollutantremovaldirectly. 3.Resultsanddiscussion Theresultsof    themodeledscenariosareprovidedinTables1and2.   TheRTDvaluesareillustratedinFig.3anddemon- stratethatwaterflowconditionsandRTDvalueswerestronglyinfluencedbychangesintheaspectratioandwaterdepth.Ourresultsconfirmthoseof    Kuoetal.(2008)thatindicatethatpol-lutantremovalisover-estimatedwhencomputedusingtheHRT  Table2 Calculatedresultsof    pollutantremovalperformanceof    theHRTandRTDapproachesandtherelatedcorrectioncoefficientswithaspectratio1.88anddifferentwaterdepths.ExampleWaterdepth(m)   t  HRT  (day) R HRT  (%) t  RTD  (day) R RTD  (%) C  r      First-ordermodelperformance2A0.10.092.6   0.092.61.000.86Good2B   0.30.267.5   0.267.51.000.62Good2C   0.50.4312.20.4211.90.970.50Satisfactory2D   0.6 0.5214.50.4913.70.950.46Satisfactory2E   0.70.6116.70.5615.40.920.42Satisfactory2F   0.80.6918.80.6217.00.900.39Satisfactory2G   0.90.7820.90.6718.20.870.36Poor2H   1.00.8722.90.7219.50.850.34Poor2I   1.10.9624.90.7620.50.820.32Poor2J   1.21.0426.80.8121.50.800.30Poor2K   1.31.1328.70.8522.40.780.28Poor2L    1.41.2230.60.8823.30.760.27Poor2M   1.51.3032.30.9124.00.740.25Poor2N   2.01.7440.61.0527.00.670.20Poor  204  S.-S.Shihetal./EcologicalEngineering  61 (2013) 200–206 (a) (b) 0 5 10 15 20 30 25 20 15 10 5 0    P  o   l   l  u   t  a  n   t   R  e  m  o  v  a   l   (   %   ) Aspect Ratio HRT approach (simplifed method)RTD approach Cr = 0.0326ln(α) + 0.8952R² = 0.980.00 0.20 0.40 0.60 0.80 1.00 1.20 302520151050    C  r Aspect Ratio Fig.4. Fig.4aillustratesthepollutantremovalperformanceof    thefourteenmodeledscenariosthatwerebasedondifferentaspectratios.Fig.4billustratestherelation- ship   betweenthecorrectioncoefficient( C  r  )   andaspectratio( ˛ ).The C  r   increasesfrom   0.84to0.99whentheaspectratiorisesfrom0.21to30.00. approach,especiallywhentheaspectratiowaslessthan5andthewaterdepthwasgreaterthan0.5m(Figs.4aand5a).Astheaspectratioincreases,thedifferencebetweenthe R HRT and R RTD  valuesdecreasesandthe C  r   increasesapproaching1.0indicatingoptimalpollutantremoval(Fig.4b).Alternatively,asthe (a) (b) 0 10 20 30 40 50 2.0 1.5 1.0 0.5 0.0    P  o   l   l  u   t  a  n   t   R  e  m  o  v  a   l   (   %   ) Water Depth (m) HRT approach (simplifed method)RTD approach Cr= 1.0745e-0.24DR² = 0.99 0.0 0.2 0.4 0.6 0.8 1.0 1.2 2.01.51.00.50.0    C  r Water Depth (m) Fig.5. Fig.5aillustratesthepollutantremovalperformanceofthefourteenmodeledscenariosbasedondifferentwaterdepths.Fig.5billustratestherelationship betweencorrectioncoefficient( C  r  )   andwaterdepth( D ).Thedifferencebetween R HRT  and   R RTD  increasesaswaterdepthincreases,whilethe C  r   decreasesfrom1.00to   0.67asthewaterdepthincreasedfrom0.1mto2.0m. waterdepthincreasesthedifferencebetweenthe R HRT  and R RTD valuesincreasesandthe C  r   decreasesindicatingthatoptimalpol-lutantremovalshouldoccurwhenthewetlandis   shallow(Fig.5b). Thechangesof    the C  r   aremorenoticeablewithdifferentwaterdepthsthanwithchangingaspectratios. Cr = 0.2682 λ   + 0.7731R² = 0.60 0.5 0.7 0.9 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0    C  r λ  Aspect rao casesWater depth casesRegression line Poor   performanceSatisfactory   performanceGood   performance Cr =0.98 Cr =0.90         λ      =        0  .        7        5         λ      =        0  .        5        0 Fig.6. Therelationshipbetweencorrectioncoefficient( C  r  )andhydraulicefficiency(  )indicatesthathigher    leadstohigher C  r  .   Thehydraulicefficiencyis   satisfactorywhenthe   aspectratioisgreaterthan1.20orthewaterdepthis   lessthan0.8   m.   Furthermore,the C  r   isgreaterthan0.98inthegoodhydraulicefficiencyzoneandgreaterthan0.90in   thesatisfactoryhydraulicefficiencyzone.
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