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Systematic model development for partial nitrification of landfill leachate in a SBR

Systematic model development for partial nitrification of landfill leachate in a SBR
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  Systematic model development for partial nitrificationof landfill leachate in a SBR R. Ganigue´ , E. I. P. Volcke, S. Puig, M. D. Balaguer, J. Colprim and G. Sin ABSTRACT R. Ganigue´   (corresponding author) M. D. Balaguer  J. Colprim Laboratory of Chemical and EnvironmentalEngineering (LEQUIA),Institute of the Environment, University of Girona,Campus Montilivi s/n, Facultat de Cie `ncies,E-17071 Girona, Catalonia,SpainE-mail:  ;  ;  E. I. P. Volcke Department of Applied Mathematics,Biometrics and Process Control, Ghent University,Coupure links 653, 9000 Gent,BelgiumE-mail: S. Puig Catalan Institute for Water research (ICRA).Parc Cientı´fic i Tecnolo `gic de la Universitat deGirona, C/Emili Grahit, 101. Edifici H 2 O,E-17003 Girona, Catalonia,SpainE-mail:  G. Sin CAPEC-Department of Chemical and BiochemicalEngineering, Technical University of Denmark,Building 229, DK-2800 Kgs Lyngby,DenmarkE-mail:  This study deals with partial nitrification in a sequencing batch reactor (PN-SBR) treating rawurban landfill leachate. In order to enhance process insight (e.g. quantify interactions betweenaeration, CO 2  stripping, alkalinity, pH, nitrification kinetics), a mathematical model has been setup. Following a systematic procedure, the model was successfully constructed, calibrated andvalidated using data from short-term (one cycle) operation of the PN-SBR. The evaluation of themodel revealed a good fit to the main physical-chemical measurements (ammonium, nitrite,nitrate and inorganic carbon), confirmed by statistical tests. Good model fits were also obtainedfor pH, despite a slight bias in pH prediction, probably caused by the high salinity of the leachate.Future work will be addressed to the model-based evaluation of the interaction of differentfactors (aeration, stripping, pH, inhibitions, among others) and their impact on the processperformance. Key words  |  anammox, calibration, identifiability, modelling, partial nitrification, SBR INTRODUCTION During partial nitrification, ammonium is oxidised tonitrite while further nitrification to nitrate is suppressed.This reaction plays an important role during biologicalnitrogen removal from streams with high ammoniumconcentrations (e.g. sludge digester supernatant, landfillleachate), when aiming at lower oxygen and organicmatter consumption, in comparison with conventionalnitrification/denitrification treatments. For instance, partialnitrification reactors can be coupled with an anammoxprocess, ending up in a fully autotrophic system capableof removing high nitrogen loads in a more sustainableway ( Van Dongen  et al.  2001 ).Previous studies ( Lai  et al.  2004 ;  Ganigue ´   et al.  2007 )demonstrated the feasibility of achieving a successfulnitritation using the Sequencing Batch Reactor (SBR) tech-nology for the treatment of nitrogen high-loaded streams.However, despite the experience acquired, the reactor’sresponse to changes in the operational conditions andinfluent characteristics is not always easy to understand orpredict, given the complexity of the system, e.g. interactions between oxygen supply, CO 2  stripping, alkalinity, pH,inhibition effects, nitrification kinetics, among others.Mathematical models can be a useful tool to increasethe process knowledge and help to better understand doi: 10.2166/wst.2010.979 2199  Q  IWA Publishing 2010  Water Science & Technology—WST  |  61.9  |  2010   biological processes and the physical phenomena takingplace in a partial nitrification-sequencing batch reactor(PN-SBR). Traditional modelling has assumed nitrificationand denitrification as single-step processes ( Henze  et al. 2000 ). Nevertheless, when modelling a partial nitrificationsystem it is necessary to consider nitrite as an intermediarystep of nitrification and denitrification. Nowadays there areseveral biological models describing nitrite build-up, asreviewed by  Sin  et al.  (2008) . Some of these models focus onthe treatment of nitrogen high loaded-streams ( Hellinga et al.  1999 ;  Volcke  et al.  2002 ;  Wett & Rauch 2003 ; amongothers) and can be used as a basis when modelling specificprocesses. It is clear that existing models may need to bemodified or extended to include all relevant physical-chemical processes and biochemical transformations for agiven application. Besides, the model needs to be calibratedfor influent and process specific parameters. This is high-lighted in this study for partial nitrification of landfillleachate in a SBR, aiming at increased process knowledge(e.g. quantify interactions between aeration, CO 2  stripping,alkalinity, pH, nitrification kinetics) and focusing on theshort-term dynamics (cycle basis). This work also dealswith the usefulness of a systematic calibration guideline andits refinement. MATERIALS AND METHODS Reactor set-up and operation The reactor under study concerns a 20L lab-scale SBR treating raw urban landfill leachate. The reactor tempera-ture was controlled at 36 ^ 1 8 C through a water jacket.Dissolved oxygen was kept at a set-point value of 2.0mgO 2 L 2 1  by an on-off controller acting on the airflow.The SBR was equipped with a monitoring and controlsystem including on-line probes measuring dissolvedoxygen (DO), pH, oxidation-reduction potential (ORP)and temperature (T). A more detailed description of theexperimental set-up can be found in  Ganigue ´   et al.  (2007) .The SBR was operated for more than 400 days with aconstant cycle length of 8 h. During a first period (day 0to 245), a fed-batch operating strategy was applied,characterised by one long feeding phase. Afterwards, theoperation strategy was switched to a step-feeding, withmultiple feeding events (days 245 to 410). Figure 1 presents both strategies in a schematic way.After a transition period (of 58 and 27 days, respect-ively), each of these operational periods was characterised by fixed cyclic concentration profiles. The model calibrationhas been based on the steady-state profiles of the fed- batch phase, while the data of the step-feed phase have been used for model validation. During both phases, thenitrogen loading rate (NLR) was 1.3kgNm 2 3 d 2 1 . Despitethe variations in influent ammonium, the NLR waskept constant by adjusting the inflow, ending up indifferent hydraulic retention times (HRT) for each phase(fed-batch: HRT  ¼  1.35 days; step-feed: HRT  ¼  1.53days). In both phases the sludge retention time (SRT) wasaround 3–5 days. Calibration guideline In order to perform the modelling procedure in a systematicand organised way, the guideline presented in  Corominas(2006)  for the SBR systems was followed. Nevertheless, dueto specific features of the PN-SBR system, minor modifi-cations were introduced to this guideline. These changes AerationFeeding+aerationDrawSettlingTime (min)060120180240300360420480Fed-batch (calibration)Step-feed (validation)(b)(a)  Figure 1  |  SBR cycle definition in both periods. a) fed-batch and b) step-feed. (Ganigue´   et al.  2008). 2200  R. Ganigue´   et al.  |  Modelling SBR nitrification of landfill leachate  Water Science & Technology—WST  |  61.9  |  2010  included: (i) the adaptation of the influent wastewatercharacterisation to the available historical data, (ii) theinclusion of an identifiability analysis to find an identifiableparameter subset for model fine-tuning ( Ruano  et al.  2007 )and (iii) the use of additional statistical tests for theevaluation of the model fits to data. Wastewater characterisation Four state variables involving nitrogen fractionationwere considered in  Corominas (2006) :  S NH  (linked toammonium),  S NO  (equivalent to the sum of nitrites andnitrates), and  S ND  and  X  ND  (which accounted for thesoluble and particulate nitrogen fractions of soluble andparticulate organic matter, respectively). In our partialnitrification model, nitrite and nitrate are consideredseparately. On the other hand,  S ND  and  X  ND  are nottaken up, since organic nitrogen is considered as a fractionof the organic matter ( S S ,  S I ,  X  S  and  X  I ).Regarding the organic matter, the available historicaldata sets did not contain soluble chemical oxygen demand(COD S ) measurements, essential for the organic matterfractionation. Nevertheless, dissolved organic carbon(DOC) measurements were available. In this way, COD S at the influent and effluent were calculated from the DOCvalues, applying empirical ratios. These ratios were exper-imentally found to be 1.86mg COD S  per mg DOC at theinfluent, and 2.3mg COD S  per mg DOC at the effluent. Identifiability analysis The methodology defined in  Brun  et al.  (2002) , based on alocal sensitivity analysis, was used to find an identifiablesubset of parameters to calibrate the PN-SBR model. To beidentifiable, a parameter subset has to fulfil two conditions.First, a model output,  y , has to be sufficiently sensitive toindividual changes of each parameter,  j . This is addressed bythe sensitivity measure  d   yj msqr . Secondly, variations in themodel output due to changes in single parameters maynot be approximately cancelled by appropriate changesin other parameters. This analysis of the parameterinterdependences is addressed by the collinearity index, g  K  . The determinant value,  r  K  , takes into account bothidentifiability conditions simultaneously and is, therefore,particularly suited for the assessment of identifiability of parameter subsets. The identifiability analysis has beencarried out following the different steps gathered in Table 1. Statistical tests for model evaluation To support the visual evaluation, the quality of the fits wasassessed also by statistical tests (Table 2, see  Power 1993 ).MAE and RMSE are statistical tests directly related toeach output, accounting for the same units. On the otherhand, ARD is a test that informs about relative deviations.Finally, the Janus coefficient measures the predictiveaccuracy of the model, and its value should be close to 1. Table 1  |  Different steps of the identifiability methodology of  Brun  et al.  (2002) Non-dimensional sensitivity ( S  ij  ) Sensitivity measure ( d   yj  msqr  ) Collinearity index ( g  K  ) Determinant value ( r  K  ) S ij  ¼  ›  y i › u   j · u   j  y i d  msqr  yj  ¼  ffiffiffiffiffiffiffiffiffiffiffiffi 1 n P ni ¼ 1  S 2 ij q   g  K   ¼  1  ffiffiffiffiffiffi min ~ l k p   r  K   ¼  det  S T K  S K    1  =  2 k where  d   y  i  / du   j   is defined as the absolute sensitivity of the model output  y  i   to the parameter  u   j  ;  n  the number of measurements (at different time instants); min  l ˜ k   is the smallest eigenvalue of the normalised subset matrix  ~  S T K  ~  S K  , and det S TK  S k    1  =  2k is the determinant function of the  n  £  K   subset matrix of   S . Table 2  |  Statistical tests Mean absolute error (MAE) Root mean squared error (RMSE) Average relative deviation (ARD) Janus coefficient (  J  2 ) MAE  ¼  1 n P ni ¼ 1  y meas ; i 2  y ð t i Þ   RMSE  ¼  ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 n P ni ¼ 1  ð  y meas ; i 2  y ð t i ÞÞ 2 q   ARD  ¼  ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 n P ni ¼ 1  y meas ; i 2  y ð t i Þ j j  y meas ; i  s   J  2 ¼ 1 n  _val P n  _  vali ¼ 1  ð  y meas ; i 2  y ð t i ÞÞ 21 n  _cal P n  _  cali ¼ 1  ð  y meas ; i 2  y ð t i ÞÞ 2 n  is the total number of observations of the variable  y  ;  y  meas, i   is the  i  th measurement of the variable  y  , and  y(t  i  ) is the corresponding model output at time  i  ;  n _cal and  n _val are the totalnumber of measurements in calibration and validation period, respectively. 2201  R. Ganigue´   et al.  |  Modelling SBR nitrification of landfill leachate  Water Science & Technology—WST  |  61.9  |  2010  THE PARTIAL NITRIFICATION MODEL The partial nitrification SBR model (implemented inMatlab-Simulink w ) was based on the SHARON modeldeveloped by  Volcke  et al.  (2002) . This model was adaptedfrom state variables expressed on a molar basis to the sameunits as the Activated Sludge Models (ASM,  Henze  et al. 2000 ). Firstly, the hydraulic model was changed from acontinuous stirred-tank reactor (CSTR) to a SBR, byimplementing a cycle that was repeated over time.Biological reactions took place during feeding and reactionphases. Settling and draw phases were ideally modelled,assuming that no biological reactions were taking place.Furthermore, settling was modelled considering the SBR asa point settler. The total suspended solids in the effluentwere assumed to be the non-settlable fraction (  f  ns ).Regarding the biokinetic model (given as appendix inmatrix format), reversible inhibition kinetics were includedfor free ammonia and free nitrous acid for both ammoniumand nitrite oxidation processes (the original model onlycontained nitrous acid inhibition of ammonium oxidation).In addition, bicarbonate limitation was taken up. Focusingon the heterotrophic conversions, a general readily bio-degradable organic matter component ( S S ) was consideredas a substrate for heterotrophic biomass, instead of methanol. Besides, the following biokinetic conversionswere added: hydrolysis of the slowly biodegradable organicmatter and the endogenous respiration processes (nine intotal) of each biomass type (  X  AOB ,  X  NOB ,  X  H ) on eachpossible electron acceptor (O 2 , NO 2 2 and NO 3 2 ). As a result,this model considers 15 different microbial transformationprocesses, all taking place in the liquid phase. Thestoichiometry and kinetics for the biological conversionreactions can be found in the appendix (Table A.1), as wellas the kinetic and stoichiometric parameters (Tables A.2and A.3). Temperature dependency was also taken intoaccount on the kinetic parameters by an Arrhenius typeexpression, despite the reactor being operated at a constanttemperature. In this way, temperature correction coeffi-cients are also included in the appendix (Table A.4).Besides the reactor liquid phase, in which the biologicalreactions take place, the model also considers a gas phase(i.e. the bubbles in the liquid phase). Between these phases,which are both assumed to be perfectly mixed, transportof oxygen, carbon dioxide, nitrogen and ammonia occurs. Volcke  et al.  (2002)  did not take up interphase transport(stripping) of ammonia, but it is considered in this studydue to the very high influent concentration of ammonium(about 2gNL 2 1 ).Nitrification of wastewater streams with highammonium concentrations combined with CO 2  strippingcauses high pH variations. In its turn, pH affects thechemical equilibrium of substrates and inhibitory com-pounds. It is therefore essential to take up pH as a modelvariable. Nevertheless pH is not a state variable. Itsconcentration is not calculated from a mass balance(which would result in a differential equation) but from acharge balance over the reactor, expressing that the sum of all charges must be zero (Equation (1)). D ch  ¼ ½ H þ  2 ½ OH 2  þ ½ NH þ 4   2 ½ NO 2 2   2 ½ NO 2 3   2 ½ HCO 2 3   2 2· ½ CO 2 2 3   2 ½ H 2 PO 2 4   2 2· ½ HPO 2 2 4  þ ½ Z þ  ð 1 Þ In this equation, Z þ represents the concentration of netpositive charges which are not involved in chemicalequilibrium reactions, and do not take part in biologicalconversions. Note that the concentration of Z þ can benegative if there are more negative than positive charges.A detailed description of pH calculation by means of acharge balance can be found in  Volcke  et al.  (2002) . MODEL CALIBRATION AND VALIDATION Identifiability analysis An identifiability analysis was performed to determine anidentifiable subset of parameters to calibrate the model.For this purpose, 30 parameters (all kinetic parametersplus the temperature correction coefficients) have beenconsidered, as well as five different outputs (NH 4 þ , NO 2 2 ,NO 3 2 , IC and pH).First, the total sensitivity of each parameter,  d   j msqr , wascalculated, taking into account the sensitivity measures forall the outputs. High  d   j msqr values imply high parametersignificance. In this way, all parameters were rankedaccording to their importance. From this ranking, only the 2202  R. Ganigue´   et al.  |  Modelling SBR nitrification of landfill leachate  Water Science & Technology—WST  |  61.9  |  2010  more sensitive parameters could be considered identifiable.There is not a clear cut-off value for the  d   j msqr ( Ruano  et al. 2007 ). Nevertheless, based on experience, a threshold valueof 0.05 was chosen as a cut-off value to select the moresignificant parameters, and reduce the computational timefor further collinearity index and determinant measurescalculation. As a result, a subset containing the 12parameters presenting the higher  d   j msqr was selected.Subsequently, the collinearity index ( g  ) and the deter-minant measures ( r  ) for each output variable werecalculated for all possible subsets containing two to 12 of the 12 most significant parameters. From these results, thelarger parameter subsets satisfying the identifiabilitythreshold (taken as  g   ¼  5 in this study, based on previouslyreported experiences) were selected (see Table 3). Note thatno subset is presented for NO 3 2 , since no parameter subsetyielded a collinearity index lower than the threshold value( g  , 5) for this output. Calibration and validation The calibration step was conducted in two stages, asproposed in  Corominas (2006) . First, the model wassimulated with a constant influent to reach quasi steady-state, and the volatile suspended solids (VSS) concentrationinside the reactor was adjusted by tuning the  f  ns . Onceachieved proper conditions, the cycle evolution calibrationwas performed following a step-wise procedure. Theprocess dynamics were fitted by manually fine-tuningthe identifiable parameter subsets previously found in theidentifiability analysis (see Table 3). A maximum of 10%variation on the parameter, in respect to its defaultvalue, was considered acceptable. The model fitting to therespective output was visually assessed. In this sense,only  m maxAOB ,  m maxNOB and pH opt  (accounting for the higher d   j msqr values) gave a significant response. The initialand final values of the tuned parameters are presentedin Table 4.After finishing the calibration step, the model wasvalidated using an independent data set, in this case cyclicprofiles corresponding to step-feed operation (Figure 1).Figure 2 presents the results of the calibration (2.a, 2.c) and the validation (2.d, 2.e and 2.f) for the nitrogencompounds, inorganic carbon and pH.Figure 2 shows a good model fit to the data in bothcalibration and validation steps. The model accuratelyfollows the dynamic trends in the nitrogen compounds(nitrite build-up, without nitrate production) and inorganiccarbon. On the other hand, Figure 2(c,f) present theexperimental and simulated pH profiles. As it can be seen,the model is capable of forecasting the pH dynamics,despite a slight bias (an off-set of about 0.3–0.4 pH units) between the simulated and experimental values. Taking intoaccount the high sensitivity of pH in non-buffered systems,this deviation is deemed acceptable. One of the mainhypotheses for this deviation may be the effect of salinity.Raw leachate used in this study presented a conductivityabove 35,000 m Scm 2 1 . In this sense, elevated ionicstrengths may affect pH calculation. Under such a highvalue, it is recommended to use activities instead of concentrations ( Smith & Chen 2006 ). Statistical tests for model evaluation Besides the visual judgement described above, the modelfit for the calibration and validation data sets was alsoquantified on the basis of statistical tests. Results aresummarised in Table 5.As can be seen in Table 5, ammonium and nitritepresent MAE and RMSE values higher than 40. This is dueto the elevated concentration of these compounds, and maynot imply poor fittings. In this way, ARD could be useful to Table 3  |  Parameter subsets selected on the identifiability analysis Output Parameter subset  g r  NH 4 þ m maxAOB ,  m maxNOB ,  m maxH ,  b H ,  K  NOBI ; HNO 2 4.77 3.5NO 2 2 b AOB ,  b H ,  K  SSH 4.23 8.57IC  m maxH ,  h  ,  b AOB ,  b H ,  K  NOBI ; HNO 2 , pH opt  4.28 120.50pH  m maxNOB ,  m maxHET ,  h  ,  b AOB ,  b H ,  K  IC ,  K  SSH ,  K  I,O 2  4.7 1.29 Table 4  |  Initial and calibrated values Parameter Initial Calibrated m maxAOB 2.1 2.31 m maxNOB 1.05 0.945pH opt  7.23 7.63 2203  R. Ganigue´   et al.  |  Modelling SBR nitrification of landfill leachate  Water Science & Technology—WST  |  61.9  |  2010
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