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,E17071 Girona, Catalonia,SpainEmail:
ramon@lequia.udg.cat
;
marilos@lequia.udg.cat
;
J.Colprim@lequia.udg.cat
E. I. P. Volcke
Department of Applied Mathematics,Biometrics and Process Control, Ghent University,Coupure links 653, 9000 Gent,BelgiumEmail:
eveline.volcke@ugent.be
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,E17003 Girona, Catalonia,SpainEmail:
spuig@icra.cat
G. Sin
CAPECDepartment of Chemical and BiochemicalEngineering, Technical University of Denmark,Building 229, DK2800 Kgs Lyngby,DenmarkEmail:
gsi@kt.dtu.dk
This study deals with partial nitriﬁcation in a sequencing batch reactor (PNSBR) 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 shortterm (one cycle) operation of the PNSBR. The evaluation of themodel revealed a good ﬁt to the main physicalchemical 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 modelbased 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) technology for the treatment of nitrogen highloaded 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
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IWA Publishing 2010
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2010
biological processes and the physical phenomena takingplace in a partial nitriﬁcationsequencing batch reactor(PNSBR). Traditional modelling has assumed nitriﬁcationand denitriﬁcation as singlestep 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 buildup, asreviewed by
Sin
et al.
(2008)
. Some of these models focus onthe treatment of nitrogen high loadedstreams (
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 physicalchemical processes and biochemical transformations for agiven application. Besides, the model needs to be calibratedfor inﬂuent and process speciﬁc parameters. This is highlighted 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 theshortterm dynamics (cycle basis). This work also dealswith the usefulness of a systematic calibration guideline andits reﬁnement.
MATERIALS AND METHODS
Reactor setup and operation
The reactor under study concerns a 20L labscale SBR treating raw urban landﬁll leachate. The reactor temperature was controlled at 36
^
1
8
C through a water jacket.Dissolved oxygen was kept at a setpoint value of 2.0mgO
2
L
2
1
by an onoff controller acting on the airﬂow.The SBR was equipped with a monitoring and controlsystem including online probes measuring dissolvedoxygen (DO), pH, oxidationreduction potential (ORP)and temperature (T). A more detailed description of theexperimental setup 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 fedbatch operating strategy was applied,characterised by one long feeding phase. Afterwards, theoperation strategy was switched to a stepfeeding, 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, respectively), each of these operational periods was characterised by ﬁxed cyclic concentration proﬁles. The model calibrationhas been based on the steadystate proﬁles of the fed batch phase, while the data of the stepfeed 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(fedbatch: HRT
¼
1.35 days; stepfeed: 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 PNSBR system, minor modiﬁcations were introduced to this guideline. These changes
AerationFeeding+aerationDrawSettlingTime (min)060120180240300360420480Fedbatch (calibration)Stepfeed (validation)(b)(a)
Figure 1

SBR cycle deﬁnition in both periods. a) fedbatch and b) stepfeed. (Ganigue´
et al.
2008).
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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 ﬁnetuning (
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 experimentally 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 PNSBR 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)
Nondimensional 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.
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Modelling SBR nitriﬁcation of landﬁll leachate
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THE PARTIAL NITRIFICATION MODEL
The partial nitriﬁcation SBR model (implemented inMatlabSimulink
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 stirredtank 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 nonsettlable 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 biodegradable 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 coefﬁcients 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 compounds. 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
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more sensitive parameters could be considered identiﬁable.There is not a clear cutoff value for the
d
j
msqr
(
Ruano
et al.
2007
). Nevertheless, based on experience, a threshold valueof 0.05 was chosen as a cutoff 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 determinant 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 steadystate, 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 stepwise procedure. Theprocess dynamics were ﬁtted by manually ﬁnetuningthe 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 stepfeed operation (Figure 1).Figure 2 presents the results of the calibration (2.a, 2.band 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 buildup, 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 offset of about 0.3–0.4 pH units) between the simulated and experimental values. Taking intoaccount the high sensitivity of pH in nonbuffered 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
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Modelling SBR nitriﬁcation of landﬁll leachate
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2010