Modelling microbial population dynamics in nitritation processes

Environmental Modelling & Software 26 (2011) 938e949

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Modelling microbial population dynamics in nitritation processes Elisabetta Giusti a, Stefano Marsili-Libelli a, *, Alessandro Spagni b a

University of Florence, Dept. of Systems and Computers, via S. Marta 3, I-50139 Florence, Italy ENEA, Italian National Agency for New Technologies, Energy and the Sustainable Economic Development, Environment Unit, Water Resource Management Section, via M.M. Sole 4, 40129 Bologna, Italy b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 2 July 2010 Received in revised form 23 January 2011 Accepted 1 February 2011 Available online 3 March 2011

In the wastewater treatment industry nitrite is no longer viewed as a toxic and undesirable intermediate in the biological oxidation chain transforming ammonium into nitrate. On the contrary, it is receiving growing attention as the pivotal component in a variety of new processes for biological nutrient removal. These new practises aim at saving energy and resources through the nitritation shortcut as an alternative to full nitrification. In order to understand the biological and engineering implications of nitritation, models have to be adapted to these new process conditions and related changes in microbial community. For this reason a previous modification of the ASM3 model [Iacopozzi, I., Innocenti, V., Marsili-Libelli, S., Giusti, E. 2007. A modified Activated Sludge Model No. 3 (ASM3) with two-step nitrification-denitrification. Environmental Modelling & Software 22: 847e861] was adapted to these particular process conditions, that the conventional models fail to reproduce satisfactorily. As with many new nitrogen removal processes, the nitritating condition does not occur spontaneously on a major scale, but it must be induced and maintained through computer control. The data used to calibrate this modified model were obtained from a long-horizon experiment in which a pilot-scale Sequencing Batch Reactor (SBR) fed with landfill leachate was kept in nitritating conditions. In this paper we set out to investigate the following points: (a) demonstrate that our previous two-step nitrification model could be adapted to describe the nitritating condition; (b) provide a thorough sensitivity/identifiability assessment of this new model, since no general sensitivity study on two-step nitrification models is available as yet; (c) try to relate the observed changes in parameter values to the possible modifications in microbial inventory during the shift from nitrification to nitritation, even if the available data were very scarce. On the first count, the model was modified by fully separating the nitrite and nitrate denitrification routes (a partial decoupling was already attempted in the previous model) and using the mixed substrate assumption. In this way, correct anoxic respiration rates and substrate consumption were obtained even when the oxidation was limited to nitrite alone. The second aspect was investigated by carrying out a complete sensitivity study considering several output combinations and ranking the model parameters according to their identifiability, showing that the most sensitive parameters are those related to the microbial characteristics. For the third aspect, several calibration “windows” were selected, in which nitrite and nitrate measurements were available, and the identifiable parameters were calibrated with each data set. From the examination of the parametric variations in the calibration windows it can be concluded that the nitritating conditions represent a critical process condition forcing drastic changes in the microbial inventory, which may be partly reflected by parametric changes.
2011 Elsevier Ltd. All rights reserved.

Keywords: Microbial kinetics Activated sludge modelling Parameter estimation Population dynamics Nitritation

Software availability Title

ASM3_NO2 (bundle of several modules: a Matlab launch code, a Simulink model and four DLL, in addition to some test input files) Developers Elisabeth Giusti, Stefano Marsili-Libelli, Dept. of Systems and Computers, University of Florence, Via S.

* Corresponding author. Tel./fax: þ39 055 4796264. E-mail addresses: [email protected]fi.it (S. Marsili-Libelli), alessandro.spagni@ enea.it (A. Spagni). 1364-8152/$ e see front matter
2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.envsoft.2011.02.001

Marta, 3 - 50139 Florence, Italy; Tel./fax: þ39 055 47.96.264; e-mail: [email protected]fi.it First year available 2009 Hardware requirements PC with Windows XP or later Programming language Matlab 7.1/Simulink 14 Program size 300 Kb for the whole bundle Program availability Freely available for research purposes, please contact the corresponding author. No installation is needed unzip the folder and include it in the Matlab path and the launch file is Go_SBR_ASM3.m. The

E. Giusti et al. / Environmental Modelling & Software 26 (2011) 938e949

Nomenclature

Model parameters Anoxic endogenous respiration rate of XH (d1) bH;NOX Aerobic endogenous respiration rate of XH (d1) bH;O2 bAOB;NO2 Aerobic endogenous respiration rate of XAOB (d1) bAOB;O2 Aerobic endogenous respiration rate of XAOB (d1) bNOB;O2 Aerobic endogenous respiration rate of XNOB (d1) bNOB;NO3 Aerobic endogenous respiration rate of XNOB (d1) Aerobic respiration rate of XSTO (d1) bSTO;O2 bSTO,NOX Anoxic respiration rate of XSTO (d1) Non settling fraction of COD fAOB Production of SI in hydrolysis ðgCODSI gCOD1 fSI XS Þ Production of XI in endogenous respiration fXI ðgCODXI gCODXBM Þ Nitrogen content in biomass (XH þ XAOB þ XNOB) iN,BM (gN g COD1) Nitrogen content in SI(gN g COD1) iN,SI Nitrogen content in SS ðgN g COD1 Þ iN;SS Nitrogen content in XI ðgN g COD1 Þ iN;XI Nitrogen content in XS ðgN g COD1 Þ iN;XS Saturation constant for alkalinity of XAOB and KA;ALK 3 XNOB ðmol HCO 3 m Þ 3 Saturation constant for alkalinity of XH ðmol HCO KALK 3 m Þ þ 3 KAOB;NH4 Saturation constant for SNH4 of AOB ðg NH4  N m Þ Oxygen mass transfer coefficient ðd1 Þ KL a Saturation constant for SNH4 ðg NH4þ  N m3 Þ KNH4 Inhibition constant for XAOB ðg NH4þ  N m3 Þ KNH4 ;i Saturation constant for SNO2 of AOB KNO2 3 XAOB ðg NO 2 Nm Þ Saturation constant for SNO3 of NOB KNO3 3 XNOB ðg NO 2 Nm Þ Saturation constant for autotrophs KNOX 3 ðXAOB and XNOB Þðg NO 3 Nm Þ Oxygen saturation constant ðg O2 m3 Þ KO2 Oxygen saturation constant for autotrophs ðg O2 m3 Þ KA;O2 Saturation constant for SS ðg CODSs m3 Þ KS Saturation constant for XSTO ðg CODXSTO g COD1 KSTO XH Þ Hydrolysis saturation constant ðg CODXS g COD1 KX XH Þ Hydrolysis rate constant ðg CODXS g CODXH d1 Þ kH Storage rate constant ðg CODSS g CODXH d1 Þ kSTO Anoxic yield of heterotrophic biomass YH;NOX ðg CODXH g COD1 XSTO Þ Aerobic yield of heterotrophic biomass YH;O2 ðg CODXH g COD1 XSTO Þ YAOB;O2 Aerobic yield of XAOB ðg CODXAOB g N1 Þ YNOB;O2 Aerobic yield of XNOB ðg CODXNOB g N 1 Þ Aerobic yield of stored product for YSTO;O2 SS ðg CODXSTO g COD1 SS Þ YSTO;NOX Anoxic yield of stored product for SS ðg CODXSTO g COD1 SS Þ user is prompted to select the desired input files and the simulation ends with the presentation of several graphics with the relevant process variables. 1. Introduction 1.1. Nitrite shortcut vs. full nitrogen removal pathway Nitrification is the biological transformation of ammonium  ðNH4þ Þ into nitrate ðNO 3 Þ with nitrite ðNO2 Þ as an intermediate

939

Model variables 3 SALK Alkalinity ðmol HCO 3 m Þ Soluble inert organics ðg COD m3 Þ SI Dinitrogen released by denitrification ðg N m3 Þ SN2 Ammonium ðg N m3 Þ SNH4 Nitrite-N ðg N m3 Þ SNO2 Nitrate nitrogen ðg N m3 Þ SNO3 Dissolved oxygen ðg O2 m3 Þ SO2 Readily biodegradable substrates ðg COD m3 Þ SS Total biomass ðXH þ XAOB þ XNOB Þðg COD m3 Þ XBM Heterotrophic biomass ðg COD m3 Þ XH Inert particulate organics ðg COD m3 Þ XI Ammonia-oxidizing autotrophs ðg COD m3 Þ XAOB Nitrite-oxidizing autotrophs ðg COD m3 Þ XNOB Slowly biodegradable substrates ðg COD m3 Þ XS Organics stored by heterotrophs ðg COD m3 Þ XSTO Vectors and matrices C parameter covariance matrix C˛
hNOX mH mAOB mNOB xi

Abbreviations AOB Ammonium - oxidizing bacteria XAOB ASM3 Activated Sludge Model n. 3 (Henze et al., 2000) ASM3_2 N Past modification to the ASM3 IWA model (Iacopozzi et al., 2007) ASM3_NO2 Present modification to the ASM3_2 N model to account for nitritation Biochemical Oxygen Demand ðg O2 m3 Þ BOD5 COD Chemical Oxygen Demand ðg O2 m3 Þ FIM Fisher Information Matrix F˛
product. The process consists of two steps, catalyzed sequentially by aerobic autotrophic ammonia-oxidizing bacteria (AOB) and nitriteoxidizing bacteria (NOB). For decades it was believed that the two genera Nitrosomonas spp. (mainly the specie Nitrosomonas europea) and Nitrobacter spp. were responsible for each step of this oxidation, but recent studies have shown that the autotrophic community can be highly diversified and in wastewater treatment plants (WWTPs) other microorganisms may replace Nitrosomonas europea and Nitrobacter spp. and even become dominant in nitrification under special circumstances (Daims et al., 2006a). Moreover, in-depth

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E. Giusti et al. / Environmental Modelling & Software 26 (2011) 938e949

Fig. 1. Nitrification/Denitrification pathways. The shaded area shows the nitrite shortcut whereby molecular Nitrogen is obtained by direct reduction of nitrite. The savings in oxygen (25%) and organic carbon (40%) are indicated under the steps avoided by the shortcut.

studies of microbial communities in WWTPs showed a complex response to changes in operating conditions caused by flow regime (continuous or batch), substrate concentration, feed, etc. (Briones and Raskiny, 2003; Daims et al., 2001; Lydmark et al., 2007; Maixner et al., 2006). Continuous-flow WWTPs normally have a rather diversified AOB community (Layton et al., 2005), but Sequencing Batch Reactors (SBRs) tend to be more selective and when different autotrophs compete for the same substrate typically only one species dominates depending on the operating conditions (Daims et al., 2006b; Volcke et al., 2008). For example, it has been suggested that the relative abundance of Nitrosomonas spp. or Nitrosospira spp. depends on their survival strategies, with the former being a r-strategist (high growth rate) and the latter a Kstrategist (high substrate affinity) (Nogueira and Melo, 2006), which is more likely to dominate in a low substrate condition. Nitritation and denitritation naturally occur in all plants, if only to a limited extent and it takes special process conditions to turn them into the dominant nitrogen pathway. Recently considerable interest has been focussed on the use of nitrite as a shortcut in treating high-nitrogen wastewater, particularly when the COD/N ratio is very low and the COD is recalcitrant. The potential advantages of the nitrogen removal via nitrite are: (a) the decrease (theoretically 25%) of oxygen consumption by limiting the ammonia oxidation to nitrite (nitritation) and (b) the reduction (theoretically 40%) of organic carbon uptake during anoxic respiration (denitritation) (see e.g. Lai et al., 2004). Fig. 1 shows the two nitrogen removal routes and related savings. However, nitritation does not come cheap, because sustained nitrite built-up can only be obtained by creating specific operating conditions (Ossenbruggen et al., 1996; Blackbourne et al., 2008) as in the SHARON - ANAMMOX combination (Hellinga et al., 1999; van Dongen et al., 2001; van Hulle et al., 2007) specifically conceived for treating highammonium effluents. In this context the suitability of discontinuous processes like the SBR (Wilderer et al., 2001; Artan and Orhon, 2005) was demonstrated for wastewater of different origins (Fux et al., 2006; Qing et al., 2007; Spagni and Marsili-Libelli, 2009). In spite of the abundant literature on the nitrite shortcut, the complexity of the processes and conditions leading to nitrite accumulation has not yet been fully understood, as pointed out in a thorough survey of nitrite modelling in wastewater systems (Sin

et al., 2008). In fact the operating conditions favouring the nitrite shortcut induce radical changes in the microbial community, that normally reflect in a change of the kinetic parameters. Though a few examples exist where the specific saturation constants were estimated with ad hoc experiments (Abdul-Talib et al., 2005; Chandran and Smets, 2005) the problem of estimating the coefficients of the nitritation kinetics is still open (Sin et al., 2008) and no general identifiability assessment is available, apart from the partial results by Brockmann et al. (2008). This paper extends a previous two-step conventional nitrification model derived from ASM3 (Iacopozzi et al., 2007) to include the nitrite route. After discussing the conceptual and modelling implications of these changes and assessing the identifiability of the new model, the new kinetics were calibrated using the data from a nitritating SBR treating leachate. The last part of the paper tries to establish a relation between the varying experimental conditions and the parametric changes, discussing the hypothesis that they can be related to changes in the microbial community. 2. Experimental set-up The data source was a bench-scale SBR with a maximum volume of 25 L fed with leachate from a mature landfill whose main characteristics are shown in Table 1. The experiment, carried out in the ENEA Laboratories (Bologna, Italy) lasted 891 consecutive days. During the last 286 days the process was supervised by a control system based on fuzzy logic (Marsili-Libelli, 2006), that kept the process in a sustained nitritating condition. The fuzzy controller (Marsili-Libelli et al., 2008) used three process signals: dissolved oxygen (DO), pH and oxidationreduction potential (ORP) and its logic, composed of a set of fuzzy inference rules, was conceived to favour AOB over NOB. The typical SBR sequence for this experiment is shown Fig. 2: the leachate is fed in short injections at the beginning of each sub-cycle composed of an anoxic/oxic sequence, during which acetate (HAc) is also administered as an additional organic carbon source for denitritation, given the scarce and recalcitrant COD available in the leachate. After four sub-cycles the final extraction of sludge and treated water brings the reactor volume back to its original value. The fuzzy controller adjusts the duration of each phase according to the decision of the inference system whereas the flow remains unchanged. 2.1. Process behaviour in the calibration windows The pilot plant was designed to operate with a Solids Retention Tyne (SRT) of 25 days, so the observation windows are always much shorter than the SRT, being in the range 40e150 h, which means that each group of data refers to a rather stable process condition. The hydraulic retention time (HRT) varied between normal and fuzzy operation, decreasing from 7.85 in the first case to 5.80 days as a consequence of fuzzy control. The detailed analysis of HRT

Table 1 Chemical characterization of the leachate sources and experimental features of the calibration windows. Window characteristics

Leachate characteristics

Leachate source

Period of application

Process operation

TSS (g L1)

VSS (g L1)

CODfast (mg L1)

COD (mg L1)

NH4 (mgN L1)

TKN (mgN L1)

1

7 Feb.e30 Mar.

1a - Constant phase length 1b - Fuzzy control begins

0.085

0.043

1716

1769

933

1008

2

31 Mar.e 2 May

2 - Fuzzy control; Constant feed

0.148

0.087

1688

1834

1288

1316

3

3 Maye30 May

3a - Increased aeration 3b - Decreased aeration 3c - Feed flow variation

0.105

0.065

1834

1941

1178

1344

4

31 Maye15 July

4 - Increased leachate feed; Decreased aeration

0.102

0.064

2060

2148

1385

1470

E. Giusti et al. / Environmental Modelling & Software 26 (2011) 938e949 SBR Volume (V)

Acetate feed (HAc)

Aeration (A)

(S) Sludge extraction ext

Leachate feed (L)

(W) Water extraction extra

60 (A)

(A)

25

25 V

(W)

Flowrate (L/h)

(S)

15

21

10

19

5

17 (HAc)

(HAc)

(HAc)

0

SBR Volume (L)

23

20

(HAc)

15 0

5

10 time (h)

15

20 sampling

Fig. 2. Typical operations and volume variations through one SBR sequence. The wastewater to be treated (leachate) is rapidly added at the beginning of each sub-cycle, followed by a slower acetate addition. The aerobic/anoxic sequence is repeated four times before the final water and sludge extraction. The arrow shows the sampling time, between sludge and water extractions.

941

variations and their relation to the increase in efficiency of the controlled operation are described in Table 2 of Spagni et al. (2008). The sampling windows shown in Fig. 3 were chosen to represent widely differing operating conditions, from the initial nitrification to the onset of nitritation to a fully established nitrite shortcut. In window 1a the process was still run in the conventional mode, with fixed-length phases, and its behaviour was recorded for comparison to the subsequent fuzzy operation. Window 1b shows the process behaviour soon after the application of the fuzzy controller, showing wide aeration length variations to adjust to the new requirements. When a new leachate source is introduced (window 2) the controller considerably decreases the aeration length, while acetate addition changes are more limited. The introduction of a third leachate source in window 3a required a substantial aeration increase. Later (window 3b) the controller senses a microbial adaptation to this source and decides that much less aeration is required. The feeding conditions are radically changed in window 3c, whereas window 4 shows a considerable departure from all the previous conditions, with the system being heavily loaded by gradually increasing the feed. However, the controller responds favourably by substantially decreasing the aeration and doubling the acetate feed.

Table 2 Kinetic rate expressions for the ASM3_NO2 model. The grey boxes indicate the terms that have been modified with respect to ASM3_2 N. j

Process

Process rate equation rj

1

Hydrolysis

XS =XH $X kH $ KX þ ðXS =XH Þ H

Heterotrophic organisms, aerobic and denitrifying activity 2

Aerobic storage of SS

3a

Anoxic storage of SS on nitrite

3b

Anoxic storage of SS on nitrate

4

Aerobic growth

5

Anoxic growth on nitrite

6

Anoxic growth on nitrate

7

Aerobic endogenous resp.

8a

Anoxic endogenous resp. on nitrite

8b

Anoxic endogenous resp. on nitrate

9

Aerobic respiration of XSTO

10a

Anoxic resp. of XSTO on nitrite

10b

Anoxic resp. of XSTO on nitrate

SO2 SS kSTO $ $ $X KO2 þ SO2 KS þ SS H KO2 SNO2 SNO2 SS kSTO $hNOX $ $ $ $ $X KO2 þ SO2 KNOX þ SNO2 SNO2 þ SNOX Ks þ SS H KO2 SNO3 SNO3 SS $ $ $ $X kSTO $hNOX $ KO2 þ SO2 KNOX þ SNOX SNO2 þ SNOX KS þ SS H SO2 SNH4 SALK XSTO =XH mH $ $X $ $ $ KO2 þ SO2 KNH4 þ SNH4 KALK þ SALK KSTO þ ðXSTO =XH Þ H SNO2 SNO2 KO2 SNH4 SALK XSTO =XH mH $hNOX $ $ $ $ $ $ $X KNH4 þ SNH4 KNOX þ SNO2 SNO2 þ SNOX KALK þ SALK KO2 þ SO2 KSTO þ XSTO =XH H SNH4 SNO3 SNO3 KO2 SALK XSTO =XH mH $hNOX $ $ $ $ $ $ $X KNH4 þ SNH4 KNOX þ SNOX SNO2 þ SNOX KALK þ SALK KO2 þ SO2 KSTO þ XSTO =XH H SO2 bH;O2 $ $X KO2 þ SO2 H KO2 SNO2 SNO2 bH;NOX $ $ $ $X KO2 þ SO2 KNOX þ SNO2 SNO2 þ SNOX H KO2 SNO3 SNO3 bH;NOX $ $ $ $X KO2 þ SO2 KNOX þ SNOX SNO2 þ SNOX H SO2 bSTO;O2 $ $X KO2 þ SO2 STO KO2 SNO2 SNO2 bSTO;NOX $ $ $ $X KO2 þ SO2 KNOX þ SNO2 SNO2 þ SNOX STO KO2 SNO3 SNO3 bSTO;NOX $ $ $ $X KO2 þ SO2 KNOX þ SNOX SNO2 þ SNOX STO

Autotrophic organisms, nitrifying activity 11

Aerobic growth of XAOB

12

Aerobic growth of XNOB

13

Aerobic endogenous resp. of XAOB

14

Aerobic endogenous resp. of XNOB

15

Anoxic endogenous resp. of XAOB on nitrite

16

Anoxic endogenous resp. of XNOB on nitrate

SO2 SNH4 SALK $ $ $X KA;O2 þ SO2 KAOB;NH4 þ SNH4 KA;ALK þ SALK AOB KI;NH4 SO2 SNO2 SALK mNOB $ $ $ $ $X KA;O2 þ SO2 KI;NH4 þ SNH4 KA;ALK þ SALK KNOB;NO2 þ SNO2 NOB SO2 bAOB;O2 $ $X KA;O2 þ SO2 AOB SO2 bNOB;O2 $ $X KA;O2 þ SO2 NOB KA;O2 SNO2 bAOB;NO2 $ $ $X KA;O2 þ SO2 KNO2 þ SNO2 AOB KA;O2 SNO3 bNOB;NO3 $ $ $X KA;O2 þ SO2 KNO3 þ SNO3 NOB

mAOB $

E. Giusti et al. / Environmental Modelling & Software 26 (2011) 938e949

HAc

1a 1b

2

3a 3b

Leachate

3c

4 20 18 16 14 12 10 8 6 4 2

200 150 100 50

07 July

26 May

30 May

14 May

03 May

18 April

22 April

0 30 March

0

15 March

Aeration – HAc feed (min)

250

14 July

Window

Aeration

Leachate feed (min)

942

time (date)

Fig. 3. Selection of sampling windows during the experiment (shaded areas). The plot shows the injection runtime for the three main process variables: acetate, leachate, and aeration.

3. Modification to the ASM3_2 N model A common limitation of the Activated Sludge Models (ASM) (Henze et al., 2000; Gernaey et al., 2004) is that nitrification is modelled as a single-step process and that denitrification occurs only on nitrate. In a previous paper (Iacopozzi et al., 2007) this limitation was removed by modelling both steps of the nitrification process and, consequently, considering anoxic respiration (denitrification) on both nitrite and nitrate. That model, referred to as ASM3_2 N, was tested and validated in the benchmark context (Copp, 2002) and was found to model the biological nitrogen cycle with sufficient accuracy provided that the operating conditions are those normally encountered in continuousflow wastewater treatment processes, where full nitrification is pursued with very low nitrite concentration. However, when the nitrogen cycle is steered towards nitritation the ASM3_2 N model fails to reproduce this extreme condition. The purpose of this section is to describe the changes to the ASM3_2 N model and extend its applicability to include the case of nitrite shortcut. 3.1. Adapting the ASM3_2 N model to the nitritation conditions The main problem with the ASM3_2 N model, which in this respect is similar to the original ASM3, is that the anoxic growth is controlled by the sum of the oxidized nitrogen species SNOX ¼ SNO2 þ SNO3 as a whole through the limiting term ðSNOX Þ=ðKNOX þ SNOX Þ, irrespective of the relative abundance of either species. In particular, the rates of anoxic storage on SS and those of endogenous and anoxic respiration on XSTO were defined in terms of the global concentration SNOx : This could lead to the unreasonable condition in which the soluble substrate SS was still consumed even when nitrate was not available. Conversely, in this new model the single limiting term is replaced by two separate partial rates, one for each species of oxidized nitrogen, using two separate rates with a partition coefficient accounting for the relative abundance of either form of oxidized nitrogen, i.e.

SNO2 SNO2 SNO3 SNO3 $ and $ : KNOX þ SNO2 SNO2 þ SNO3 KNOX þ SNO3 SNO2 þ SNO3

(1)

The first term in both expressions reflects the mixed substrate assumption (i.e. equal preference) to describe the electron acceptor alternative when nitrite and nitrate are available regardless of their concentration, as suggested by Sin et al. (2008). Therefore, in Eq. (1)

the saturation constant of the denitrifying biomass KNOx is assumed to have the same value for both electron acceptors. As a result of the mixed substrate assumption, when the nitrate concentration approaches zero, the nitrate-based processes are inactivated whereas the nitrite kinetics is still active. Conversely, in the previous ASM3_2 N model the anoxic respiration on soluble organic carbon continued with the same rate even after nitrate was depleted. As a consequence, as already pointed out by Sin et al. (2008), without the “mixed substrate assumption” the combined denitrification rate could be higher than the aerobic respiration rate when both nitrite and nitrate are available at high concentration. With these assumptions the anoxic respiration terms are fully decoupled and the amount of consumed organic carbon depends separately on the availability of nitrite and nitrate. The kinetics of the new model ASM3_NO2 are shown in Table 2, whereas Table 3 reports the stoichiometric matrix. In both tables the modified terms are shaded in grey. 3.2. Comparison with the previous ASM3_2 N model In order to compare this new model with the parent ASM3_2 N model, the latter was adapted to the SBR conditions, still retaining the same parameter values as in Iacopozzi et al. (2007). The same loading sequence of Fig. 2 was used in both models. Fig. 4 compares the nitrite ðSNO2 Þ and nitrate ðSNO3 Þ experimental data from widow 2 with outputs of the ASM3_2 N and ASM3_NO2 models, whereas Fig. 5 does the same for the COD data. The comparison clearly shows that the nitrification dynamics of the previous ASM3_2 N model is unable to reproduce the nitritating conditions with nitrite SNO2 quickly vanishing, whereas the nitrate concentration SNO3 remains high. On the contrary the new ASM3_NO2 model is in good agreement with the data, denoting its capability to describe the nitritating process conditions. 4. Model calibration The previous ASM3_2 N model was calibrated with respect to the standard benchmark settings (Copp, 2002; Iacopozzi et al., 2007), but the structural changes introduced in this new model require a new identifiability assessment for which the data sampled in the seven windows of Table 1 and Fig. 3 were selected, as they are considered representative of the changing situations during the experiment and therefore may yield information about the adaptation of the microbial community.

E. Giusti et al. / Environmental Modelling & Software 26 (2011) 938e949

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Table 3 Stoichiometric matrix of the ASM3_NO2 model. The coefficients in the shaded cells were changed with the respect to the AMS3_2 N model. j

SO2

SS

SN2

SNH4

SNO2

SNO3

SI

SALK

XI

XS

XH

XSTO

XAOB

XNOB

1

e

1  fSI

e

iN;SS ð1  fSI Þ fSI ,iN;SI þ iN;XS

e

e

fSI

e

1

e

e

e

e

2

YSTO;O2  1

1

e

iN;SS

e

e

e

iN;XS  iN;SS ð1  fSI Þ  fSI ,iN;SI 14 iN;SS 14

e

e

e

YSTO;O2

e

e

e

iN;SS þ 14 1YSTO;NOX iN;SS þ 1:72 14

e

e

e

YSTO;NOX

e

e

e

e

e

YSTO;NOX

e

e

iN;BM  14

e

e

1



1 YH;O2

e

e

e

e

1



1 YH;NOX

e

e

e

e

1



1 YH;NOX

e

e

iN;BM  fXI ,iN;XI 14

fXI

e

1

e

e

e

1fXI 2:86

fXI

e

1

e

e

e

fXI

e

1

e

e

e

e

e

e

1

e

e

e

e

e

1

e

e

e

e

e

1

e

e

e

e

e

e

3a

e

1

3b

e

1

4

1


1  YH;O2

e

1  YSTO;NOX 2:86 1  YSTO;NOX 1:72

iN;SS

e

YSTO;NOX 1 2:86

iN;SS

YSTO;NOX 1 1:72

e

e

e

iN;BM

e

e

e

e

e

1

e

5

e

1 YH;NOX

1  YH;NOX

iN;BM

1

1:72

1:72 e

6

e

1 YH;NOX

iN;BM

1

1 1  YH;NOX

e

2:86

e

1YSTO;NOX 2:86

1Y

iNBM  14 1

iN;BM  14

1 H;NOx

1:72

1 YH;NOX 2:86

2:86

7

f XI  1

e

e

iN;BM  fXI ,iN;XI

e

8a

e

e

1  f XI 2:86

iN;BM  fXI ,iN;XI

e

8b

e

e

1  f XI 1:72

iN;BM  fXI ,iN;XI

e

f XI  1 1:72

e

þ iN;BM  fXI ,iN;XI 14 1  fXI þ iN;BM  fXI ,iN;XI 1:72 14

e 1 2:86

e

9

1

e

10a

e

e

10b

e

e

1 1:72

e

e

11

1


3:43  YNOB;O2
1:14 

e f XI  1 2:86

e e

e

e

e

e

e

e

1 2:86

e

e

e

1 1:72

e

1  iN;BM  YNOB;O2

1 YAOB;O2

e

e

1 2:86,14 1 1:72,14 1 7,YAOB;O  iN;BM

1

e

2

14 e

e

iN;BM

1  YNOB;O2

1 YNOB;O2

e

iN;BM  14

e

e

e

e

e

f XI  1

e

e

iN;BM  fXI ,iN;XI

e

e

e

iN;BM  fXI ,iN;XI 14

fXI

e

e

e

1

e

14

f XI  1

e

e

iN;BM  fXI ,iN;XI

e

e

e

iN;BM  fXI ,iN;XI 14

fXI

e

e

e

e

1

15

e

e

1fXI 1:72

iN;BM  fXI ,iN;XI

fXI  1 1:72

e

e

1fXI 1:72

þ iN;BM  fXI ,iN;XI 14

fXI

e

e

e

1

e

16

e

e

1fXI 2:86

iN;BM  fXI ,iN;XI

e

f XI  1 2:86

e

1fXI 2:86

þ iN;BM  fXI ,iN;XI 14

fXI

e

e

e

e

1

old model (ASM3_2N )

data

12

1

13

YNOB;O2

new model (ASM3_NO2 )

old model (ASM3_2N )

data

new model (ASM3_NO2 ) 1400

40 1380

30 20

1360

10 0

0

5

10

15

20 time (h)

25

30

35

40

COD (mg L-1 )

2

-1 S NO (mgN L )

50

1340

1320

30 20

1300

3

-1 SNO (mgN L )

1

10 0

0

5

10

15

20 time (h)

25

30

35

Fig. 4. Oxidized nitrogen data e model agreement in window 2 comparing the performance of the new model ASM3_NO2 and that of the old model ASM3_2 N in nitritation conditions. The old model is clearly unable to match the observations.

0

5

10

15

20 time (h)

25

30

35

Fig. 5. COD data e model agreement in window 2 comparing the performance of the new model ASM3_NO2 and that of the old model ASM3_2 N in nitritation conditions. The old model is clearly unable to match the observations.

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E. Giusti et al. / Environmental Modelling & Software 26 (2011) 938e949

Table 4 Parametric sensitivity ranking with respect to model output choices. Rank

Model output

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

KNH4 bH;O2 bSTO;O2 bH;NOX

SNO2

SO2 227908.95 55137.58 24896.45 14506.52 12442.65 5970.16 4993.02 4236.75 3334.85 1780.68 1076.66 1040.74 957.33 404.98 280.93 245.88 99.89 92.83 68.64 54.19 43.80 34.63 22.04 9.95 9.67 6.09 4.20 1.36 0.01

mAOB bAOB;O2 bAOB;NO2

mNOB bSTO;NOX

mH bNOB;O2 KO2 bNOB;NO3 KA;O2 fAOB KL a

hNOX kSTO kH KAOB;NH4 KSTO KNOX KALK KNO2 KX KA;ALK KNO3 KS KNH4 ;i

SNO2

KNH4 bH;NOX bSTO;NOX

mNOB bH;O2 bSTO;O2

mH mAOB bAOB;O2 bAOB;NO2 bNOB;O2 bNOB;NO3 KO2 KA;O2

hNOX KL a KNOX KSTO kSTO fAOB KAOB;NH4 kH KALK KNO2 KA;ALK KX KNO3 KS KNH4 ;i

165923.49 62315.91 32060.67 28187.75 21278.35 15251.84 14356.72 13274.42 6771.33 3269.12 3236.24 2474.39 2183.62 721.83 590.18 459.03 368.07 323.19 274.16 231.29 54.03 31.01 18.39 16.18 4.90 3.91 3.24 2.30 0.01

KNH4

mNOB bH;NOX bH;O2 bSTO;O2 bSTO;NOX

mH bNOB;O2 bAOB;NO2

mAOB bAOB;O2 bNOB;NO3 KO2

hNOX KNOX fAOB KL a KA;O2 KSTO kSTO KNO2 kH KAOB;NH4 KALK KNO3 KX KA;ALK KS KNH4 ;i

SNO2 SNO2 85392.34 34619.99 28082.32 25465.56 13483.43 12134.36 5031.32 4027.59 3230.02 2842.66 1251.61 726.79 323.46 158.17 156.24 147.93 139.15 117.04 105.68 52.91 32.77 24.45 16.93 8.26 4.62 2.96 1.82 0.55 0.02

KNH4 bH;NOX

mNOB bH;O2 bSTO;NOX bSTO;O2

mH mAOB bAOB;O2 bNOB;O2 bNOB;NO3 bAOB;NO2 KO2 KA;O2

hNOX KL a KNOX KSTO fAOB kSTO KAOB;NH4 kH KNO2 KALK KNO3 KX KA;ALK KS KNH4 ;i

4.1. Sensitivity analysis and identifiable parameters

20

10

A

Set of identifiable parameters

10

E

SNH4 SNO2 SNO2

SO2 SNH4 SNO2 SNO2

ALL

KNH4 bH;NOX bH;O2

KNH4 bH;O2 bH;NOX

KNH4 bH;O2 bH;NOX

mNOB bSTO;NOX bSTO;O2

mH mAOB bAOB;O2 bNOB;O2 bAOB;NO2 bNOB;NO3 KO 2 KA;O2

hNOX KL a kSTO KNOX fAOB KSTO kH KAOB;NH4 KNO2 KALK KX KA;ALK KNO3 KS KNH4 ;i

modE

2

ynom  ypert y j j Spji y nom pj $dpi

mNOB bSTO;O2 bSTO;NOX

mAOB mH bAOB;O2 bAOB;NO2 bNOB;O2 bNOB;NO3 KO 2 KA;O2 KL a

hNOX fAOB kSTO KNOX KSTO kH KAOB;NH4 KALK KNO2 KX KA;ALK KNO3 KS KNH4 ;i

688415.05 126780.47 124895.34 72079.31 65587.99 56469.66 34327.28 24659.40 17114.36 11656.03 9693.85 7570.42 4156.02 1511.16 1034.58 1024.44 791.11 773.83 675.57 550.11 178.38 150.05 67.91 65.10 22.56 18.56 16.24 7.65 0.05

mH bSTO;O2

mAOB bSTO;NOX bAOB;O2

mNOB bAOB;NO2 bNOB;NO3 bNOB;O2 KO2 KL a KSTO KA;O2

hNOX kH fAOB kSTO KNOX KAOB;NH4 KALK KX KNO2 KA;ALK KNO3 KS KNH4 ;i

46704702.22 5896059.30 4905226.58 3593687.91 2266509.95 1404543.71 782189.14 681640.78 665428.75 515237.909 185921.631 164362.368 158215.448 129703.858 78336.517 60988.787 46251.813 15180.268 10670.956 9642.351 8371.559 7987.526 3871.200 1827.191 1422.563 858.547 648.347 181.760 1.404

y

Sp11

6 y2 6 S ¼ 6 Sp1 4. y Spq1

Sp12

y

.

Syp22 .: y Spq2

. . .

y

Sp1np

3

7 Syp2np 7; 7 . 5 yq Spnp

(2)

where ynom is the nominal j-th output corresponding to the j and ypert is the perturbed j-th nominal i-th parameter value pnom i j output obtained by altering the i-th parameter by a small quantity dpi , i.e. pnom /ðpnom þ dpi Þ. De Pauw (2005) provided an in-depth i i study on the selection of the optimal value for dpi. Considering k ¼ 1, ., N sampling instants along the sensitivity trajectory and summing the sensitivities of parameter pi to all the selected outputs yout ˛
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N
2 X u1 X y t xi ¼ Spji ðkÞ : N j˛n out

Value of OED criteria

460506.10 110388.82 71642.88 67842.56 53134.81 40691.54 22878.72 21884.62 11144.20 8617.19 6663.01 6613.08 3115.27 1106.18 924.54 788.70 680.99 640.93 510.18 506.31 109.73 95.86 55.15 45.86 12.88 12.47 12.04 6.28 0.04

Almost all these studies were based on incremental approximations of the sensitivity trajectory functions

Though most of the model parameters were borrowed from the literature (Henze et al., 2000; Gernaey et al., 2004; Iacopozzi et al., 2007; Sin et al., 2008) this section assesses the influence on the whole model of the new parameters introduced by the modified kinetics. For this reason a global sensitivity study was performed considering the whole set of 29 model parameters, excluding the stoichiometric and composition coefficients, for which exact values have already been derived from stoichiometric equations (Henze et al., 2000). In the context of microbiological system identification, sensitivity analysis plays a fundamental role (Petersen, 2000; Dochain and Vanrolleghem, 2001; Brun et al., 2002; De Pauw, 2005; Kim et al., 2006; Benedetti et al., 2010; Ferrai et al., 2010).

15

251315.84 90398.23 62807.74 46743.92 44195.03 28735.28 19388.04 16117.09 8022.94 7263.83 5704.41 3995.91 2507.09 838.88 748.36 598.19 524.31 428.88 379.23 327.07 70.96 55.47 48.96 26.65 7.86 6.87 6.72 2.86 0.03

(3)

k¼1

10

10

5

10

0

10

-5

10

-10

10

2

5

10

15

20

25

29

Ranked parameters Fig. 6. Selection of the set of identifiable parameters based upon the FIM and the OED criteria assuming SNO2 and SNO3 as observations.

From this index, similar to Brun et al. (2002), an identifiability ranking criterion can be derived to produce the scores of Table 4, but does not give any clue as to how many parameters can be efficiently estimated with a given output set yout . There are several approaches to identifiability ranking; for example Brockmann et al. (2008) use a collinearity index derived from eq. (3) to rank the identifiability of groups of parameters for a biofilm two-step nitrification model. In this paper a method based on the Fisher Information Matrix (FIM) is used (Marsili-Libelli and Giusti, 2008; Machado et al., 2009) to determine the practically identifiable parameter subset. The sensitivities given by eq. (2) together with the measurement accuracy matrix Q ¼ ð1=s21 ; 1=s22 ; .; 1=s2nout Þ, which is assumed constant for all the sampling instants, yield the FIM

E. Giusti et al. / Environmental Modelling & Software 26 (2011) 938e949

945

Fig. 7. Variations of sensitivity ranking depending of the choice of model outputs.

Table 5 Estimated parameters and 95% confidence intervals using SNO2 and SNO3 as model outputs. For the parameter units please refer to the Nomenclature. Window

1a

1b

2

3a

3b

3c

4

VAF

98.55

88.06

99.99

99.82

99.98

94.62

98.97

FEE

0.624909

1.6

0.13832

0.242258

0.085

0.9

0.3103

Parameters KNH4 bH;NOX

b  95% confidence intervals Estimated values p 0.0102  0.0014 0.0095  0.0005 0.0721  0.0114 0.0288  0.0048 0.0552  0.0072 0.3192  0.0336 0.2664  0.0336 1.0176  0.1512 0.0312  0.0048 0.0504  0.0072 0.0744  0.0120 0.2448  0.1032 0.0672  0.0096 0.0408  0.0072 0.0528  0.0120 0.1632  0.0216 0.0192  0.0024 0.5832  0.2112 0.8976  0.1248 2.8968  0.4272 3.3528  0.9840 0.4296  0.0576 0.6096  0.0888 0.3552  0.0072

0.0096  0.0006 0.0312  0.0048 0.0648  0.0096 0.0096  0.0024 0.0960  0.0120 0.0312  0.0048 0.6144  0.0312 0.3696  0.0552

0.0087  0.0009 0.0432  0.0072 0.1248  0.0168 0.0240  0.0048 0.0384  0.0048 0.0864  0.0120 0.5088  0.048 0.4080  0.0648

0.0634  0.0094 0.2088  0.0264 0.1848  0.0288 0.0240  0.0024 0.0360  0.0048 0.0696  0.0096 0.5016  0.0672 0.4896  0.072

0.0614  0.0081 0.3336  0.0144 0.1488  0.0072 9  103  0.4  103 3.8  103  1.8  103 0.1776  0.0072 1.4515  0.072 1.0824  0.1056

mNOB bH;O2 bSTO;NOX bSTO;O2

mH mAOB

The VAF and FEE goodness-of-fit indicators are defined in Eqs. (6) and (7).

This matrix has a fundamental role in computing an approximation to the parameter covariance matrix C because CyF1 (Dochain and Vanrolleghem, 2001; Marsili-Libelli et al., 2003; De Pauw, 2005). However, in this context it is also used to compute some identifiability criteria (De Pauw, 2005; Lindner and Hitzmann, 2006; Checchi et al., 2007; Franceschini and Macchietto, 2008; Romero and Navarro, 2008) that depend on F. These criteria were originally aimed at maximizing the estimation accuracy by optimal experiment design (De Pauw, 2005; Checchi and Marsili-Libelli, 2005) but in this study they are used to select the maximum identifiable parameter subset, as described in Marsili-Libelli and Giusti (2008). They are usually referred to as the A criterion, minðtrðF1 ÞÞ, minimizing of the arithmetic mean of parameter errors; the E criterion, maxðlmin ðFÞÞ, maximizing the smallest eigenvalue lmin of F, and the mod E criterion, minðlmax =lmin Þ, which minimizes the condition number of F by minimizing the ratio between the largest lmax and the smallest eigenvalue lmin . Following this procedure, Table 4 ranks the parameters according to their sensitivity index x for several choices of the output variables. It can be seen that as the number of the observed outputs increases, so does the number of identifiable parameters, shaded in grey. To determine the identifiable parameter subset the following algorithm is used (Marsili-Libelli and Giusti, 2008): a collection of matrices Fi is formed by expanding the principal minors of order

S NO2

data model

data model

S NO3

12

12

1a 10

10

8

8

6

6

4

4

2

2

3

(4)

k¼1

S NO (mgN L-1)

vp

ranging from 2 to np, starting with the two most sensitive parameters and adding parameters according to their descending sensitivity rank. Thus the generic matrix Fi of the sequence is defined as

2

k¼1

  N X vyðkÞ $Q $ ST ðkÞ$Q $SðkÞ: ¼ vp

-1 SNO (mgN L )

F ¼

 N  X vyðkÞ T

0

0

50

100

0 150

time (h) Fig. 8. Model calibration with the SNO2 and SNO3 data in window 1a. The process operation is with fixed phase length.

946

E. Giusti et al. / Environmental Modelling & Software 26 (2011) 938e949

data model

S NO2

data model

S NO3

1b

18

14

data model

S NO3

1.4

35

20

16

data model

S NO2

3a

30

1.2

25

1

20

0.8

15

0.6

10

0.4

5

0.2

2

8

6

6 4

4

2

2 0

10

20

30

40

50

0

0 60

0

5

10

15

Fig. 9. Model calibration with the SNO2 and SNO3 data in window 1b, at the beginning of the fuzzy operation. The nitrite build up has just started. The estimation is made difficult by the quickly changing conditions.

. . .

3 F1;i .5 Fi;i

i ¼ 2; .; np :

(5)

The three previous OED criteria (A, E, modE) are computed for each Fi ði ¼ 2; .; np Þ. The maximum identifiable subset is then the one after which the criteria exhibits the first plateau. The variability of the three criteria is depicted in Fig. 6 showing that, if SNO2 and SNO3 are the observed outputs, the first eight parameters in the shaded area can be reliably estimated. In fact it can be seen that between the seventh and the eighth parameter the sensitivity index x has the first plateau, then they continue to degrade. From Table 4 it can be seen that increasing the number of observed outputs produces only a moderate increase in the number of identifiable parameters, from seven in the case of dissolved oxygen alone to ten in the extreme case in which all the model outputs are available (shaded areas in Table 4). Since SNO2 and SNO3 data were available, the eight most sensitive parameters indicated in the pertinent column of Table 4 were estimated. A final identifiability assessment as a function of model outputs considers the variations in relative identifiability of

data model

S NO2

2

0.6

25

0.5

20

0.4

15

0.3

10

0.2

5

0.1 5

10

15

20

25

30

35

1.6

0 40

time (h) Fig. 10. Model calibration with the SNO2 and SNO3 data in window 2. The process operation is now in fuzzy mode, which progressively decreased the aeration length, and the leachate was switched from source 1 to source 2.

35

1.4

30

1.2

25

1

20

0.8

15

0.6

10

0.4

5

0.2

2

30

-1 SNO (mgN L )

0.7

data model

S NO3

3b

3

35

0

data model

40

S NO (mgN L-1)

0.8

0

After assessing the parametric sensitivity and considering the practical availability of experimental data, it was concluded that the

0.9

40

0 45

4.2. Parameter calibration

S NO2

2

-1 SNO (mgN L )

45

40

the parameters indicated by the OED criteria: Fig. 7 shows that the most sensitive parameters are almost always the same, largely independent of the available outputs, though the relative ranking may change. Reminding that the smaller the rank the higher the identifiability, KNH4 is always the most identifiable parameter, whereas bH;NOX ranks between second and fourth place. Regarding the growth rates, the identifiability of the ammonium-oxidizing bacteria mAOB is lowest when SNO3 is observed and obviously improves as more outputs are available, especially those proceeding SNO3 in the oxidation chain. It is important to observe that the most sensitive parameters are those related to the microbial characteristics. For example the ammonium saturation constant is related to the affinity of the substrates. In fact the decreased substrate concentration favours the selection of K-strategists like the AOB, in agreement with a well-known ecological concept.

1.0

50

35

Fig. 11. Model calibration with the SNO2 and SNO3 data in window 3a. The leachate source was switched from 2 to 3 and the fuzzy controller significantly increased the aeration length.

data model

S NO3

30

3

F1;1 Fi ¼ 4 . Fi;1

25

time (h)

time (h)

2

20

S NO (mgN L-1)

0

3

10

S NO (mgN L-1)

12

8

3

10

2

14

S NO (mgN L-1)

-1 SNO (mgN L )

12

-1 SNO (mgN L )

16

0

0

10

20

30

40

50

60

70

80

0

time (h) Fig. 12. Model calibration with the SNO2 and SNO3 data in window 3b. The aeration is substantially decreased with respect to the previous window 3a. The nitritating regime is now well established.

E. Giusti et al. / Environmental Modelling & Software 26 (2011) 938e949

data model

S NO2

was dropped. The estimation results are summarized in Table 5, listing the parameter values and their 95% confidence intervals computed with the Hessian approximation of the covariance matrix, as described in Checchi et al. (2007). For each experimental window of Fig. 3, Table 5 shows also two goodness-of-fit indicators, b both computed for the optimal value of the parameter vector p. These indicators are the Variance-Accounted-For (VAF)

data model

S NO3

0.7

60

4 0.6

50

2 PNw
exp mod ðkÞ B S ðkÞ  S NO2 NO2 k¼1 B VAF ¼ 100  B1   þ1 PNs
exp @ avg 2 S ðkÞ  S NO NO k¼1 2 2

0.2

10

0

0

3

0.3 20

S NO (mgN L-1)

0.4 30

2

-1 SNO (mgN L )

0.5 40

PNw


0.1

0

10

20

30

40

50

60

70



0 80

exp SNO3 ðkÞ k¼1

PNs

Fig. 13. Model calibration with the SNO2 and SNO3 data in window 4. The leachate feed was manually increased to a considerable extent and the fuzzy controller decreased the aeration length, with only a slight increase in acetate addition. As a result the NO3 output decreases, whereas NO2 remains constant.

best compromise was to use the nitrite and nitrate measurements sampled in the windows of Fig. 3 to estimate the corresponding identifiable parameters listed in Table 4, i.e. [KNH4 , bH;NOX , mNOB , bH;O2 , bSTO;NOX , bSTO;O2 , mH , mAOB ]. The error functional to be minimized is therefore

1

Nw
X

Nw
2 1 X exp exp SNO2 ðkÞ  Smod SNO3 ðkÞ þ 2 NO2 ðkÞ

 Smod NO3 ðkÞ

2

1

C C 2 C A

avg Sexp NO3 ðkÞ  SNO3

(7)

FEE ¼

Nw
X

þ

Sexp NO2 ðkÞ

Nw
X

i¼1



Smod NO2 ðkÞ

 2   b p

mod Sexp NO3 ðkÞ  SNO3 ðkÞ

 2   b : p

ð8Þ

The samples were always taken between sludge and water extractions, at the time indicated by the arrow in Fig. 2. 4.3. Discussion of the calibration results

sNO3 i ¼ 1

;



2

Smod NO3 ðkÞ

and the Final Estimation Error (FEE)

k¼1

s2NO2 k ¼ 1




k¼1

time (h)

EðpÞ ¼

947

(6)

where for each window Nw is the number of experimental data, exp Sexp NO2 and SNO3 are the experimental nitrite and nitrate values, and mod are the corresponding parameter-dependent model and S Smod NO2 NO3 outputs. The terms 1=s2NO2 and 1=s2NO3 represent the constant measurement accuracy of the observed outputs, hence the index k

Since it has been demonstrated that in environmental biotechnological systems the changes in operating conditions may induce radical changes in the microbial community (Daims et al., 2006b; Lydmark et al., 2007; Maixner et al., 2006; Nogueira and Melo, 2006), it is expected that the calibrated parameters reflect these changes. It should be reminded, though, that the primary aim of the experiment was to demonstrate the ability of a controller based on fuzzy logic to maintain stable nitritating conditions and not to

Fig. 14. Variation of the estimated parameters over the seven calibration windows. The error bars represent the 95% confidence intervals of the estimated parameters (see Table 5).

948

E. Giusti et al. / Environmental Modelling & Software 26 (2011) 938e949

conduct an in-depth microbiological study. Therefore an ad-hoc indepth sampling campaign including microbiological assays was not carried out, as would normally be required for microbial modelling studies, having being considered out of scope, time-consuming and expensive (Hauduc et al., 2009) when planning the experiment. Nevertheless it is the opinion of the authors that the available experimental data still contain enough information to consider the hypothesis that there may exist some correlation between the trend of the kinetic constants and the evolution of the microbial community during the experiment. Fig. 8 refers to the pre-fuzzy operation (window 1a), when the process is managed on a fixed time-basis. The concentration of nitrite and nitrate are almost equal and the transitions between aerobic and anaerobic phases occur at equal intervals. As showed by the experimental data (remembering that they were always sampled in the effluent of the SBR, at the time shown in Fig. 2), nitrate was the main nitrogen component in the effluent, whereas nitrite was only observed as an intermediate. Fig. 9 shows the process adaptation to the new fuzzy control (window 1b), that results in a steady increase of nitrite whereas nitrate progressively decreases. The model, following the experimental data, shows that nitrite is the main nitrogen form in the effluent. The fast change in operating conditions makes the estimation more difficult as shown by the highest value of FEE in Table 5. Fig. 10 shows the estimation in window 2, when the fuzzy controller decreases the aeration substantially in order to favour nitritation, also given the higher ammonium-N content of the new leachate source (Table 1). Fig. 11 shows the process behaviour in window 3a: in this interval the aeration is substantially increased in response to the third leachate source. Fig. 12 shows the estimation in the subsequent window 3b, when the controller maintains the aeration at a lower level. Finally, Fig. 13 shows the model response in window 4, when the fuzzy controller is severely tested by a staircase increases of leachate, that is accommodated with only a moderate acetate increase to insure nitritation and a progressive aeration decrease. This confirms that the biomass has adapted well to the new process conditions. As a final remark on data scarcity, normally the data set is chosen to be plentiful enough to describe the process evolution over its entire frequency spectrum. In this case it is not so and it may be argued that fitting the model to few sparse data detracts from the estimation validity. On the other hand, given the frequent oscillations of the SBR cycles, the fact that they are still well approximated by the model in spite of their long time gaps demonstrates that the calibrated model can withstand under-sampling, which adds to its robustness. The calibration results confirm that the developed model was able to simulate the behaviour of nitrogen removal via nitrite in SBR under the experimental conditions applied. It should be noticed that the model was also able to predict the rapid change from (classical) nitrification/denitrification to nitritation/denitritation, and therefore it can also be applied for predicting the operational condition that should be applied for the nitrite route. 4.4. Correlation between experimental phases and parametric variations The calibrated parameters of Fig. 14 seem to correlate to some extent with the varying operating conditions. Windows 1a and 1b refer to the transition from the pre-fuzzy condition, with fixedlength phases, to the fuzzy operation, with variable-length phases. In this initial situation the growth rates of the microorganisms fall in the conventional range with mH > mNOB > mAOB because the C/N ratio is still favourable to the heterotrophic growth and nitrate is the end-product of nitrification. These values are typical of the conventionally operated WWTPs. In window 2 the nitritating condition has already been established and the decreased aeration

(see Fig. 3) favours the ammonium-oxidizers over the nitriteoxidizers, thus mNOB become smaller than mAOB . Likewise, the ammonium saturation constant KNH4 increases in window 2 and decreases in widows 3a and 3b, denoting a prevalence of r-strategists (low substrate affinity), whereas the increase in windows 3c and 4 can be related to a further community adaptation in favour of K-strategists. In window 4 the feed is progressively increased in steps and the controller responds by decreasing the aeration. This may indicate that efficient nitritating bacteria are now firmly established, requiring less oxygen for their conversion. The application of the control system confirmed that the SBR increased the loading rate as a result of the reduced hydraulic retention time (Spagni et al., 2008). The calibration results showed that the initial loading rate resulted in the increase of the maximum growth rates and of the saturation constants as a result of the rstrategy population selection, whereas the parameter values in the final part of the experiment support the established ecological theory that low substrate concentration leads to the selection of Kstrategy species, with higher substrate affinity. The storage constants also increase as a result of the increased available soluble COD and the selection of microorganisms with higher storage capacity. The calibration results with their variations during the experiment seem to indicate that different operating conditions lead to a microbial community (Daims et al., 2006b; Lydmark et al., 2007; Maixner et al., 2006; Nogueira and Melo, 2006) characterized by different kinetic parameters.

5. Conclusion This paper has presented an extension of the ASM3_2 N twostep nitrification model (Iacopozzi et al., 2007) derived from the ASM n. 3 model (Henze et al., 2000) to describe previously intractable process conditions, like nitritation. This condition, normally avoided in conventional wastewater treatment plants, is now emerging as a smart way of biologically removing nitrogen from wastewater using specialized processes where particular process conditions are applied. This new model (ASM3_NO2) was calibrated using the data from a nitritating SBR operated by an automatic controller with the aim of maintaining consistent nitritation for nearly one year. The modelling exercise had a twofold purpose: broadening the applicability of the previous ASM3_2 N model to include the nitritating conditions and try to establish a relation between the varying microbial population and the model parametric variations. Some inconsistencies of the ASM3_2 N model were removed, such as the possibility of having substrate consumption for denitrification not directly related to the relative abundance of either electron acceptor. This decoupling was obtained through the mixed substrate assumption and produced a complete separation of the nitrite and nitrate denitrification routes. The second aspect was investigated by carrying out a complete sensitivity study considering several output combinations and ranking the model parameters according to their identifiability. The most sensitive parameter for all output combinations was the ammonium saturation constant KNH4 , followed by the parameters directly related to microbial growth and heterotrophic decay. The NOB maximum growth rate mNOB was generally better identifiable than that of AOB mAOB , but the situation is reversed in the limit case when all the process variable are observed (see Table 4 and Fig. 7). Once the parameters were ranked according to their sensitivity, a criterion based on the FIM was used to determine the identifiable parameters subset, indicated by the first plateau in the OED criteria. As shown in Fig. 6, all the indicators show a gradual loss of identifiability as the number of parameters increase. To stay on the safe side, given

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the data scarcity, the criterion was strictly applied and the parameters after the first plateau were not considered identifiable. Regarding the agreement of the calibrated model with the data in the observation windows (Figs. 8e13), it might be argued that the data are very few and wide apart in time, hence the agreement has little value. On the contrary, given the frequent oscillations of the SBR cycles compared to the large time gap between the measurements, the agreement demonstrates that the estimation is robust enough to withstand under-sampling and the model can simulate long time-horizons. Some considerations can be drawn on the possible relation between parameter values and variations in the microbial metabolism: though lacking specific microbial assays, the parameter changes reflect the evolution of the process condition, though there is still not enough evidence to claim that this is caused by a change in the microbial inventory rather than a metabolic modification. This research may develop in two directions: on the microbiological side, this model could assist in the design of specific experiments for a better understanding of the modification in the microbial community induced by sustained nitritation, as suggested by the observed parametric changes. From the engineering viewpoint, the model could be used to design more efficient controllers to optimize the nitrogen removal via nitritation.

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