an integrated metabolic model for the aerobic and denitrifying biological phosphorus removal

An Integrated Metabolic Model for theAerobic and Denitrifying BiologicalPhosphorus Removal

E. Murnleitner, T. Kuba, M. C. M. van Loosdrecht, J. J. Heijnen

Department of Biochemical Engineering, Delft University of Technology,Julianalaan 67, 2628 BC Delft, The Netherlands; telephone:+31-15-2781618; fax: +31-15-2782355; e-mail: [email protected]

Received 12 April 1996; accepted 24 October 1996

Abstract: In this work, an integrated metabolic model forbiological phosphorus removal is presented. Using apreviously proposed mathematical model it was shownto be possible to describe the two known biologicalphosphorus removal processes, under aerobic and deni-trifying conditions, with the same biochemical reactions,where only the difference in electron acceptor (oxygenand nitrate) is taken into account. Though, apart from theATP/NADH ratio, the stoichiometry in those models isidentical, different kinetic parameters were found. There-fore, a new kinetic structure is proposed that adequatelydescribes phosphorus removal under denitrifying andaerobic conditions with the same kinetic equations andparameters. The ATP/NADH ratio (d) is the only modelparameter that is different for aerobic and denitrifyinggrowth. With the new model, simulations of anaerobic/aerobic and anaerobic/denitrifying sequencing batch re-actors (A2 SBR and A/O SBR) were made for verificationof the model. Not only short-term behavior, but alsosteady state, was simulated. The results showed verygood agreement between model predictions and experi-mental results for a wide range of dynamic conditionsand sludge retention times. Sensitivity analysis showsthe influence of the model parameters and the feed sub-strate concentrations on both systems. © 1997 John Wiley& Sons, Inc. Biotechnol Bioeng 54: 434–450, 1997.Keywords: biological phosphorus removal; anaerobic-denitrifying process; anaerobic–aerobic process; denitri-fication, activated sludge; metabolic model

INTRODUCTION

Biological phosphorus (P) removal from wastewater is aprocess that uses the capability of polyphosphate storage ofcertain bacteria. These microorganisms are accumulated byrecirculation of the sludge through a phase without electronacceptor followed by a phase with oxygen or nitrate present.In the anaerobic period, lower fatty acids like acetate aretaken up into the cell and stored as polyhydroxyalcanoates(PHA). Energy (ATP) and reduction equivalents (NADH),which are required for this process, are generated by deg-

radation of the internal storage products polyphosphate andglycogen. In the following electron acceptor phase, where Premoval takes place, the anaerobically produced polyhy-droxyalcanoates are degraded for cell growth, polyphos-phate synthesis, and glycogen production.Acinetobacterisoften identified as the organism responsible for biological Premoval (Deinema et al., 1980; Fuhs and Chen, 1975).However, recent16S-RNA analysis of sludge samplesshowed that this organism plays no significant role (Wagneret al., 1994). At present no pure culture is available of thedominant microorganism. Therefore much work has beendone with highly enriched cultures, all the known physiol-ogy is derived from these cultures (Arun et al., 1988, 1989;Mino et al., 1987, 1995; Smolders et al., 1994, 1995; Went-zel et al., 1988, 1989a). In these cultures acetate is addedunder anaerobic conditions. Only when acetate is fully takenup is an electron acceptor provided. These conditions ensurethat virtually only bacteria using poly P for energy genera-tion for acetate uptake and storage will survive in the sys-tem. Denitrifying as well as aerobic phosphorus removingenrichment cultures can be obtained (Kuba et al., 1993).

Using such enriched cultures, Wentzel et al. (1989b) pro-posed a kinetic model for aerobic P removal, which formedthe basis for the IAWQ activated sludge model (ASM) no.2 (Gujer et al., 1995). Mino et al. (1995) extended this ASMno. 2 model to include glycogen and denitrifying P removal.In all these models only very limited experimental valida-tion was provided and large numbers of stoichiometric andkinetic parameters were needed. Recently, Smolders et al.(1995) proposed a so-called metabolic model for aerobicP-removal, which includes glycogen metabolism.

In a metabolic model (Roels, 1983), the conversions ofcomponents observed on the outside of the organisms arereduced to a number of internal characteristic reactions ofthe metabolism. These are, in the case of biological phos-phorus removal for example, the storage of polyhydroxy-butyrate (PHB), polyphosphate synthesis, or the productionof ATP in the oxidative phosphorylation. In general, thesereactions have been studied extensively by biochemists andhave, for the most, a fixed stoichiometry. With the meta-bolic approach, maximal use is made of both the biochemi-

Correspondence to:M. C. M. van LoosdrechtContract grant sponsor: Dutch Foundation for Water Research

(STOWA)

© 1997 John Wiley & Sons, Inc. CCC 0006-3592/97/050434-17

cal knowledge of the system and the conservation principlesof compounds and elements. A minimal number of inde-pendent reaction rates is obtained leading to a minimal num-ber of necessary kinetic expressions. Consequently, thisleads to a minimal number of model parameters.

Smolders showed, over a wide range of sludge retentiontimes (SRT) in dynamic and steady-state situations, thatgood results were obtained for aerobic P removal. There-fore, Kuba et al. (1996) applied this model to denitrifyingconditions. Denitrifying and aerobic metabolism are identi-cal except that nitrate or oxygen is the final acceptor in theelectron transport phosphorylation process. This means thatthe majority of the metabolic reactions are identical. In ametabolic model one may expect that the kinetic coeffi-cients should therefore be identical and independent of thetype of electron acceptor. The previously derived modelaccurately predicted the stoichiometry of the aerobic anddenitrifying modes. The kinetic parameters, however, werefound to be strongly dependent on the presence of O2 orNO−

3. In the model formulation, a choice has to be made forwhich three reactions kinetic expressions are used. Havingthese three reaction rates, all the other rates follow fromstoichiometry, In the previous model the choice was madeto put the kinetic rate equations on the substrate (PHA)consuming processes (growth, poly-P formation, glycogenproduction), making the total PHA consumption the sum ofthese processes. The strong difference between kinetic co-efficients obtained for aerobic and denitrifying growth in-dicate that a suboptimal choice was made. Here we presenta new model formulation leading to a much more consistentdescription of the P removal processes under aerobic anddenitrifying conditions.

MODEL FORMULATION

All relevant componenets are mentioned in Table I. PHA istreated as poly-b-hydroxybutyrate (PHB), which contrib-utes to approximately 80% of the PHA. For simplification,all components are expressed electroneutrally.

Biomass Fractions

The main part of the metabolism process takes place oninternal storage compounds; therefore, an accurate math-ematical description has to distinguish between active bio-mass and storage products. Accordingly, the polymeric stor-age compounds, PHB, glycogen, and polyphosphate, aretreated separately in the model (Fig. 1). The dry mass of thesludge (suspended solids [SS]) can be separated into volatilesuspended solids (VSS) and ash, whereby approximately95% of the ash consists of polyphosphate, ((KMg)1/3 PO3)n

(Smolders et al., 1995). The VSS are composed of activebiomass, PHB, and glycogen. The concentration of activebiomass remains relatively constant during the cycle,whereas the concentrations of the internal storage compo-nents, PHB, glycogen, and polyphosphate, change substain-tially within one cycle (Smolders et al., 1995).

The fraction,fi , of componenti is defined as the ratio ofthe storage polymer to the active biomass (mol C or P/molC active biomass):

fi =Ci

Cx(1)

Anaerobic Stoichiometry

All the internal processes in the anaerobic phase are as-sumed, based on general microbial physiology, to be com-pletely identical in both the aerobic (A/O) and the denitri-fying (A2) system. The three processes are: (i) acetate up-take and storage as PHB; (ii) polyphosphate degradation forATP production; and (iii) NADH and ATP production fromconversion of glycogen to PHB. According to Smolders etal. (1994a), reactions (i)–(iii) at pH 7 can be summarized as:

(CH3COOH)1/2 + 0.5 (C6H10O5)1/6 + 0.36 HPO3

acetate glycogen polyphosphate

+ 0.023 H2O → 1.33(C4H6O2.)1/4

PHB

+ 0.17 CO2 + 0.36 H3PO4

phosphate (2)

Figure 1. Composition of the biomass and the relation with suspendedsolids (SS) and volatile suspended solids (VSS).

Table I. Relevant components for the description of the biological P-removal process.

Compound Symbol Elemental composition

Acetate ac CH2OPhosphate p H3PO4

Biomass x CH2.09O0.54N0.2P0.015

PHB phb CH1.5O0.5

Poly-P pp HPO3

Glycogen gly CH1.67O0.83

Ammonia nh4 NH3

Nitrate no3 HNO3

Oxygen o2 O2

Carbon dioxide co2 CO2

Nitrogen n2 N2

Water w H2O

MURNLEITNER ET AL.: METABOLIC MODEL FOR AEROBIC AND DENITRIFYING P REMOVAL 435

For anaerobic maintenance, ATP is produced from internalpolyphosphate, which leads to a release of phosphate to thebulk liquid (secondary P release):

HPO3 + H2O → ATP + H3PO4polyphosphate phosphate (3)

Aerobic and Denitrifying Stoichiometry

All the processes in the aerobic/denitrifying phase can bedescribed by six metabolic processes (Kuba et al., 1996).Four processes are completely identical in both the aerobicand the denitrifying system, as no electron acceptor is in-volved:

● Polyphosphate formation:

H3PO4(in) + ATP → HPO3 + H2Ointernal phosphate polyphosphate (4)

● Growth and maintenance:

1.27(C4H6O2)1/4 + 0.2 NH3 + 0.015 HPO3 + H2OPHB ammonia polyphosphate

+ (1.6+ mATP/m) ATP →

CH2.09O0.54N0.2P0.015biomass

+ 0.615 NADH2 + 0.27 CO2 (5)

In Eq. 5, the internal polyphosphate is consumed for bio-mass formation because the P-removing bacteria are ex-pected to be able to grow even without any P present in thebulk liquid (Smolders et al., 1995).

● Glycogen formation:

4/3 (C4H6O2)1/4 + 5/6 ATP + 5/6 H2O → (C6H10O5)1/6PHB glycogen

+ 1/3 CO2 + NADH2 (6)

● PHB degradation within the TCA cycle:

(C4H6O2)1/4 + 1.5 H2O → 2.25 NADH2 + 0.5 ATP+ CO2

PHB (7)

The two remaining reactions depend on membrane pro-cesses and, therefore, on the type of electron acceptor.

● ATP production from NADH:with oxygen:

NADH2 + 1/2 O2 → do ATP + H2O (8)

with nitrate:

NADH2 + 2/5 HNO3 → 1/5 N2 + dn ATP + 6/5 H2O

nitrate (9)

wheredo is the amount of ATP that can be produced perNADH with oxygen as electron acceptor anddn is theamount of ATP per NADH that can be produced withnitrate. For the aerobic system, Smolders et al. (1994b)

proposed ado value of 1.8; for the denitrifying system,Kuba et al. (1996) found adn value of 0.9.

The import of phosphate against the membrane poten-tial requires energy. With oxygen as electron acceptor,we obtain:

● Phosphate uptakewith oxygen:

«o H3PO4(out) + NADH2 + 1/2 O2 → «o H3PO4(in) + H2Oexternal phosphate oxygen internal phosphate

(10)with nitrate:

«n H3PO4(out) + NADH2 + 2/5 HNO3

external phosphate nitrate

→ «nH3PO4(in) + 1/5 N2 + 6/5 H2O

internal phosphate (11)

Here,«o and«n is the amount of phosphate, which can betaken up by oxidizing one NADH. Smolders et al.(1994b) proposed, for the aerobic system, an«o value of7, whereas Kuba et al. (1996) obtained:

«n = «o *dn

do

here, the equivalent relation:

« 4 3.8*d (12)

is used, with a value of 1.8 or 0.9 ford for aerobic ordenitrifying conditions, respectively.

Anaerobic Kinetics

The kinetics of anaerobic acetate uptake was described bySmolders et al. (1995) as:

rac = qacmax *

Cac

Cac + Kac* Cx (13)

They used a qacmax of 0.4 mmol C acetate/(mmol C biomass

· h) for the aerobic system, Kuba et al. (1996) used the sameequation, but found qac

max to be 0.2 for the denitrifying sys-tem.

In this work, a mean value of 0.3 mmol C acetate/(mmolC biomass · h) is used for being able to describe both sys-tems with only one set of kinetic parameters. This currentequation for anaerobic acetate uptake does not accuratelydescribe the process, but it has only minor influence on thebehavior of the system in the electron acceptor phase aslong as acetate is taken up completely. For the sequencingbatch reactors (SBRs) investigated, the anaerobic phase waslong enough to ensure complete acetate uptake, but in thefuture a more thorough evaluation of anaerobic acetate up-take kinetics is needed.

For maintenance the following kinetic equation is used:

rpanaerobic4 mp

anaerobic* Cx (14)

436 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 54, NO. 5, JUNE 5, 1997

The specific P release rate for anaerobic maintenance,mp

anaerobic, is 0.0025 mmol P/(mmol C biomass · h) (Kuba etal., 1993, 1994).

Aerobic and Denitrifying Kinetics

In the six processes of the electron acceptor phase, 12 sub-stances (with oxygen) or 13 substances (with nitrate, NO3)are involved.

For solving this system of linear equations, six rates haveto be known (and also the contribution of maintenancematp/m). The three concentrations of ATP, NADH, and internalorthphosphate are considered to be constant (pseudo-steady-state assumption); therefore, their conversion rates can beset to 0. With three additional rates described by kineticequations or obtained by measurements, each of the remain-ing rates can be calculated (Roels, 1983).

In the previous model (Kuba et al., 1996; Smolders et al.,1995), the kinetic equations were chosen for the productformation rates (biomass, poly-P, glycogen), and substrateconversion was the result (Fig. 2a). In the presently pro-posed model, biomass formation is taken as a resultant andkinetic equations are proposed for PHB consumption, poly-P, and glycogen formation (Fig. 2b). Ecologically, the or-ganism has to survive in a dynamic system based on ad-equate levels of internally stored substrate. To outcompeteother organisms it has to resupply its storage pools quickly.Growth rate is of less importance for the competition in thisdynamic process (anaerobic–aerobic/denitrifying condi-tions).

The rate of PHB consumption is assumed to be rate lim-iting and dependent upon the PHB content inside the cells.

It was also observed that the polyphosphate formation rateis (negatively) influenced mainly by the polyphosphate con-tent of the cells and not by the PHB content, as long thePHB content is not limiting. The less polyphosphate insidethe cells, the faster the polyphosphate formation rate be-comes. The remaining PHB flow is then used for both gly-cogen formation and growth. For the third kinetic equationwe assumed that the glycogen formation rate depends on thePHB content (like the PHB consumption rate) and on theglycogen content leading to lower glycogen production athigher glycogen fractions.

Slowing down of a storage rate,ri, at increased storagelevels, fi, could be described, for example, with a Monod-like inhibition term [Eq. (15)], with a maximum fraction[Eq. (16)], or with a simple inverted first-order relation [Eq.(17)].

qi = k1,i *fi

inh

fiinh + fi

(15)

qi = k2,1 *fi

max − fi

fimax (16)

qi = k3,i *1fi

(17)

In the presently derived model, Eq. (17) was used for theinhibitory effect of higher polyphosphate and glycogen lev-els, because these expressions only require one parameterand were capable of adequately describing the process. Thefractions of the storage products are required to always behigher than zero.

Assuming no substrate limitation of ammonia, nitrate,oxygen, etc., the three rates for PHB consumption, glycogenformation, and biomass formation are described as:

rphb = kphb * ~fphb!2/3

* Cx (18)

rpp = kpp *1fpp

* Cx (19)

rgly = kgly *~fphb!

2/3

fgly* Cx (20)

The 2⁄3 exponents in Eqs. (18) and (20) can be explainedwith a surface-related reaction, where 2/3 reflects the spe-cific surface area of a PHB granule of the cell. The fraction,fphb, of millimoles C PHB per millimole C biomass repre-sents a certain volume. Whenfphb doubles, then the surfaceincreases only by 22/3.

From the biochemical equations [Eqs. (4)–(11)], a meta-bolic reaction matrix,RT, for the electron acceptor phase canbe formed (Table II). With the assumption that ATP,NADH, andPin are not accumulated, these rates can be setto 0. Also, all the other rates can be related, by linear rela-tions, torphb, rpp, andrgly. The rates of PHB consumption,polyphosphate formation, and glycogen formation are de-

Figure 2. Kinetic structure of the model as proposed by Smolders et al.(1995) (a), and as proposed in this article (b). Solid lines: rates describedby mathematical equations; dotted line: rate follows from reaction stoichi-ometry.


termined by the mathematical rate equations [Eqs. (18)–(20)]. Now, matrixRT can be simplified and model matrixA is obtained. This matrix, including the anaerobic, aerobic,and denitrifying processess, is given in Table III and showshow the linear relations betweenrphb, rpp, rgly, and rmaint,and all the other rates are influenced bydo dn in the aerobicand denitrifying submatrix.

The rate of the aerobic biomass formation, for example,can be obtained directly from the entry Ac,r (c 4 column,r4 row) of matrix A represented in Table III:

−rx = A4,3 ~do! * rphbaerobic+ A4,4 ~do! * rpp

aerobic

+A 4,5 ~do! * rglyaerobic+A4,6 ~do! * ratp maint

aerobic (21)

All the required kinetic reaction rate equations are shown inTable IV. Apart from the terms describing the kineticmodel, some Monod-like switching functions were used forswitching off the reaction when a cosubstrate is depleted(e.g., ammonia) or when a reaction should not run due to thepresence of nitrate or oxygen. These switching functions aredefined as:

Mi =Ci

Ci + 0.0001(22)

A low half-saturation constant of 0.0001 was used to avoidslowing down the whole reaction rate as long as the cosub-strate is present. For example, a multiplication of the an-aerobic process rates with Eq. (23) ensured that these reac-tions do not run with oxygen or nitrate present:

~1 − Mo2! * ~1 − Mno3! (23)

As the denitrifying reactions should not run when oxygenis present, they were multiplied by:

~1 − Mo2! (24)

EXPERIMENTAL SET-UP

The kinetic parameters have been obtained from batch testson denitrifying metabolism in sludge taken from a denitri-fying SBR in ‘‘steady state.’’ In these tests, the dissolvedcompounds (phosphate, ammonia, nitrate) and the storagecompounds (PHB, glycogen) were measured. The batcheswere performed at different initial phosphate concentra-tions. The obtained kinetic model was subsequently verifiedon the cycle behavior of aerobic and denitrifying SBRs atdifferent SRTs (solid retention times).

MATERIALS AND METHODS

The data set used for model evaluation has already beenused for determination of the ATP/NADH ratio (dn) and wetherefore refer to that article (Kuba et al., 1996).

RESULTS

For the parameter estimation of the proposed model and thesubsequent model verification different parameter sets havebeen used:

1. The kinetic model parameters for the electron acceptorphase were derived from a set of denitrifying P-removing‘‘batch test’’ data as reported earlier (Kuba et al., 1996).

2. For verification of the obtained model, data from cyclemeasurements of the anaerobic/denitrifying enriched P-removing sludge SBR (Kuba et al., 1993) were used,which were obtained 5 months before (SRT of 8 days)and 11 months before (SRT of 14 days). The model wasalso verified with data from the conventional anaerobic/aerobic enriched P-removing sludge SBR, which wereobtained 2 years before for SRTs of 5, 8, and 20 days(Smolders, 1995).

Table II. Metabolic reaction matrix for the electron acceptor phase [mmol/(Lzh)]. The columns represent therates of reactions, the rows represent the conversion rates of the substances.

rPHB degr.,

eq. (7)

ATP from NADHgrowth,Eq. (5)

P uptakePP form.,Eq. (4)

gly form.,Eq. (6)Eq. (8) Eq. (9) Eq. (10) Eq. (11)

phb −1 −1.27 −1.33x 1gly 1pp 1nh4 −0.2p out −3.8*do −3.8*dn

p in −0.015 3.8*do 3.8*dn −1o2 −0.5 −0.5no3 −0.4 −0.4co2 1 0.27 0.33w −1.5 1 1.2 −0.385 1 1.2 1 −0.83n2 0.2 0.2atp 0.5 do dn −1.6-matp/m

a −1 0.83nadh 2.25 −1 −1 0.615 −1 −1 1

am = rx/Cx.


Tab

leIII

.M

odel

mat

rix:

colu

mns

repr

esen

tth

eco

nver

sion

rate

sof

the

rele

vant

subs

tanc

es,

the

row

sre

pres

ent

the

reac

tion

rate

s[m

mol

/(L

·h)

].R

ows

1to

2:an

aero

bic

phas

e;ro

ws

3to

6:ae

robi

cph

ase;

row

s7

to10

:de

nitr

ifica

tion

phas

e.

1.r p

2.r g

ly3.

r ph

b4.

r x5.

r no

36.

r o2

7.r n

h4

8.r p

p9.

r ac

Ana

erob

icph

ase

1.r a

ca

na

ero

bic

0.36

−0.

51.

33−

0.36

−1

2.r p

ma

int

an

ae

rob

ic1

−1

Aer

obic

phas

e

3.r p

hb

ae

rob

ic−

19*

do

+2

8.97

*do

+9.

17−

1

1.15

*do

+1.

141

0.2*

9*d

o`

2

8.97

*do

+9.

17−0

.015

*9*

do

+2

8.97

*do

+9.

17

4.r p

pa

ero

bic

−1

−1

0.46

7*d

o+

0.47

7−

1

0.41

7*d

o+

0.42

60.

2*

1

0.46

7*d

o+

0.47

71

+0.

015

*1

0.46

7*d

o+

0.47

7

5.r g

lya

ero

bic

1−

4*d

o+

3

4.49

*do

+4.

47

1

3.68

*do

+3.

760.

2*

4*d

o+

3

4.49

*do

+4.

470.

015

*4*

do

+3

4.49

*do

+4.

47

6.ra

ero

bic

atp

ma

int

−8*

do

+8

9*d

o+

2−

0.5

do

+1

0.2

*8*

do

+8

9*d

o+

20.

015

*8*d

o+

8

9*d

o+

2D

enitr

ifica

tion

phas

e

7.r p

hb

de

nitri

−1

9*d

n+

2

8.97

*dn

+9.

17−

1

1.44

*dn

+1.

43−0

.2*

9*d

n+

2

8.97

*dn

+9.

17−0

.015

*9*

dn

+2

8.97

*dn

+9.

17

8.r p

pd

en

itri

−1

−1

0.46

7*d

n+

0.47

7−

1

0.52

1*d

n+

0.53

20.

2*

1

0.46

7*d

n+

0.47

71

+0.

015

*1

0.46

7*d

n+

0.47

7

9.r g

lyd

en

itri

1−

4*d

n+

3

4.49

*dn

+4.

47

1

4.6*

dn

+4.

70.

2*

4*d

n+

3

4.49

*dn

+4.

470.

015

*4*

dn

+3

4.49

*dn

+4.

47

10.

rde

nitri

atp

ma

int

−10

*dn

+10

9*d

n+

2−

0.4

dn

+1

0.2

*10

*dn

+10

9*d

n+

20.

015

*10*d

n+

10

9*d

n+

2


Model Evaluation

Estimation of the Kinetic Parameters

The data sets derived in the denitrifying ‘‘batch tests’’ wereused to fit the kinetic parameters of Eqs. (18)–(20).kpp, kphb,and kgly were fitted independently by the least-squaresmethod.kpp was fitted against the phosphate concentrations,

kphb against the PHB concentrations, andkgly against theglycogen concentrations. Reaction orders of 2, 1, 2/3, and1/2 were examined. The best results were achieved with afirst-order inhibition for glycogen and polyphosphate andwith a 2/3 order for the PHB content [Eqs. (18)–(20)].

The obtained kinetic constants,kphb, kgly, and kpp, to-gether with the other model parameters, are given in TableV. The validity of the obtained parameters is shown in

Table IV. Kinetic rate equations (units are millimoles, liters, and hours) for the model.

Model equation Switch functionsa

Anaerobic conditions

racanaerobic= qac

max,anaerobic*Cac

Kacanaerobic+ Cac *Mgly*Mpp *(1 − Mo2) * (1 − Mno3) *Cx

rp maintanaerobic= mp

anaerobic *Mpp * (1 − Mo2) * (1 − Mno3) *Cx

Aerobic conditions

rphbaerobic= kphb * fphb

2/3 *Mo2 * Mnh4 * Mpp *Cx

rppaerobic= kpp *

1

fpp*

Cp

Kp + Cp *Mo2 *Cx

rglyaerobic= kgly *

fphb2/3

fgly *Mo2 *Mnh4 * Mpp *Cx

ratp maintaerobic = matp *Mo2 *Cx

Denitrifying conditions

rphbdenitri = kphb * fphb

2/3 *Cno3

Kno3phb,gly + Cno3 *Mnh4 * Mpp *(1 − Mo2) *Cx

rppdenitri = kpp *

1

fpp*

Cno3

Kno3pp + Cno3

*Cp

Kp + Cp *(1 − Mo2) *Cx

rglydenitri = kgly *

fphb2/3

fgly*

Cno3

Kno3phb,gly + Cno3 *Mnh4*Mpp *(1 − Mo2) *Cx

ratp maintdenitri = matp *Mno3 * (1 − Mo2) *Cx

aSwitching functions are defined as:Mi = Ci / Ci + 0.0001.

Table V. Model parameters used in the simulations.

Parameter Value Unit Description Source

Kinetic parameters for the anaerobic phaseqac

max’anerobic 0.3 mmol C ac./(mmol C biomass · h) Max. specific anaerobic acetate uptake rate Param. estim.mp

anaerobic 0.0025 mmol P/(mmol C biomass · h) Secondary P release due to anaerobicmaintenance

Kuba et al., 1993

Kacanaerobic 1 mmol C acetate/L Half sat. const. for acetate Smolders et al., 1995

Stoichiometric parameters for the electron acceptor phasedo 1.8 mmol ATP/mmol NADH ATP/NADH with oxygen (=P/O ratio) Smolders et al., 1995dn 0.9 mmol ATP/mmol NADH ATP/NADH with nitrate Kuba et al., 1993

Kinetic parameters for the electron acceptor phasekphb 0.30 mmol C PHB(mmol C-biomass · h) Rate constant for PHB consumption Param. estim.kpp 0.0050 mmol P-poly-P/(mmol C biomass · h) Rate constant for polyphosphate formation Param. estim.kgly 0.02 mmol C-gly/(mmol C biomass · h) Rate constant for glycogen formation Param. estim.matp 0.010 mmol ATP/(mmol C biomass · h) ATP for maintenance Kuba et al., 1993Kp 0.1 mmol P/L Half-saturation constant for P

uptake/polyphosphate formationSmolders et al., 1995

Kno3phb,gly 0.1 mmol nitrate/L Half-saturation constant for nitrate

consumption for growth and glycogenformation

Param. estim.

Kppno3 0.01 mmol nitrate/L Half-saturation constant for nitrate

consumption for polyphosphateformation

Param. estim.


Figure 3. Model evaluation—fitting results(denitrifying batch tests). Lines: simulation results. Measured concentrations: nitrate (l); phosphate (■);ammonia (+); PHB (●); and glycogen (n). (a) Experiment without phosphate; (b) experiment with low initial phosphate concentration; (c) experiment withnormal initial phosphate conc., (d) experiment with high initial phosphate concentration. (1) Soluble components; (2) storage components.

Figure 3. Although nitrate and ammonia concentrationswere not used in the fitting procedure of the parameters, themodel describes these concentrations as well, showing thatthe stoichiometry used (dN 4 0.9) is adequate.

The nitrate concentration was not limiting in the batchtest; therefore, the half-saturation constant of nitrate forPHB consumption and glycogen formationKno 3

phb,glywas fit-ted from one cycle of the anaerobic-denitrifying (A2) SBR.Experimental results indicate that P uptake is not influencedstrongly by the nitrate concentrations. The uptake rate wasidentical for the ‘‘batch tests’’ and the A2 SBR. In the latter,nitrate was in the magnitude of the affinity constant fornitrate uptake. Therefore, we definedKno3

pp 4 0.1 * Kno3phb,gly.

Model Verification: Simulations, Results, andSensitivity Analysis

For validation of the derived model, simulations were madefor reactor configurations and operations as they were set upin our laboratory previously. The anaerobic/aerobic P-removing SBR was simulated with SRTs of 5, 8, and 20days; the anaerobic/denitrifying SBR was simulated withSRTs of 8 and 14 days. All flows, as they occurred in theSBRs, together with the new integrated model, were put intoa computer program (AQUASIM, version 1.0e for MS Win-dows) (Reichert, 1994).

Simulations of a cycle were initialized with measured (attime 0) concentrations of biomass, PHB, polyphosphate,and glycogen. Independently from the start values, the sys-tem should always reach the same steady state. Therefore,simulations were made, until the concentrations did notchange any further from cycle to cycle. Figure 4 shows thesimulation results of the concentrations of soluble com-pounds of the anaerobic/aerobicP-removing SBR at differ-ent sludge retention times after start of the simulation (a1,b1, c1) and the cycle behavior in steady state (a2, b2, c2).Figure 5 shows the behavior of the polymeric storage com-pounds in those experiments. Simulation results of thesoluble compounds and polymeric storage compounds ofthe anaerobic/denitrifyingP-removing SBR at differentsludge retention times are given in Figures 6 and 7. Bothfigures show also measured values, which were obtainedfrom measurements in steady-state SBRs.

Sensitivity

The sensitivity of the concentrations of storage polymerswith respect to the model parameters and to the feed sub-strate concentrations in the anaerobic/aerobic SBR and inthe anaerobic/denitrifying SBR are shown in Figures 8 and9, respectively. The figures show the absolute change of theconcentrations of the storage compounds (in millimoles perliter) per 100% change of the parameter. Each of the 10columns represents four cycles of 6 h (sum 240 h). Forcalculation of the sensitivity, the parameters were changed

one by one in reasonable ranges (Table VI) and the absolutedeviations were normalized to 100%.

In the anaerobic/aerobicP-removing SBR, concentrationsof active biomass and glycogen are most sensitive, mainlyfor the value of the ATP/NADH ratio (do), the amount ofadded acetate, and also for the kinetic constantskphbandkgly

(Fig. 8).In the anaerobic/denitrifyingP-removing SBR, the con-

centrations of active biomass, polyphosphate, and particu-larly PHB are very sensitive (Fig. 9). Here, the ATP/NADHratio (dn) and the amounts of added substrates (acetate andnitrate) have the most influence on the long-term behavior.

The different sensitivities of both systems can also beseen in Figure 10, where the influence of 5% difference inacetate load on the simulation of the steady state is shownfor an aerobic and denitrifying system. A 5% lower acetateload leads to a dramatic decrease of PHB concentration inthe anaerobic/denitrifyingSBR, whereby the PHB con-sumption rate becomes slower in the beginning of eachdenitrifying phase. As a result, the nitrate profile is alsochanged (and now fits the measurements). The concentra-tion profiles of all the relevant compounds of the anaerobic/aerobicSBR are not much influenced by the difference ofacetate feed. Similar effects for the denitrifying SBR can beobtained by increasing the nitrate flow by 5%.

DISCUSSION

Dissolved Compounds

Simulation results of the concentrations of the dissolvedcompounds in the aerobic phase of the anaerobic/aerobicP-removing SBR seem to be very adequate compared withmeasurements. Not only the initial cycle (Fig. 4a1, b1, c1)but also the steady-state cycle (Fig. 4a2, b2, c2) can be veryaccurately simulated with the new model. The simulationresults of the dissolved compounds in the denitrifying phaseof the anaerobic/denitrifyingP-removing SBR (Fig. 6a1, b1[initial cycle] and a2, b2 [steady state]) could be satisfac-torily predicted except for the initial cycle of the 8-day SRT(Fig. 6a1). Here a probably overestimated fraction of poly-phosphate leads to a loss of phosphate in the first cycles.However, after several cycles, the phosphate profile is inaccordance with the measurements (Fig. 6a2).

Storage Compounds

Except for the glycogen concentration for the steady statecycle at the high SRT (20 days), where glycogen is pre-dicted as two times higher (Fig. 5c2), all concentrations ofthe storage compounds of the anaerobic/aerobicSBR weresimulated adequately (initial cycles: Fig. 5a1, b1,c1; steady-state cycles: Fig. 5a2, b2, c2). Possible reasons for thewrong prediction of glycogen could be the large deviations


Figure 4. Model verification—simulation of the aerobic SBR: soluble compounds. Simulation of systems with (a) SRT 5, (b) SRT 8, and (c) SRT 20.(1) Simulation of first cycle; (2) simulation of steady-state cycle. Lines: simulation results. Measured concentrations: phosphate (■); acetate (V); andammonia (+).

Figure 5. Model verification—simulation of the aerobic SBR: polymeric storage compounds. Simulation of systems with (a) SRT 5, (b) SRT 8, and (c)SRT 20. (1) Simulation of first cycle; (2) simulation of steady-state cycle. Lines: simulation results. Measured concentrations: PHB (d); glycogen (n); andpolyphosphate (h).

observed in glycogen measurements or the high sensitivityto kphb, kgl, andCac (see Sensitivity Analysis subsection).

The concentrations of the storage compounds of the ini-tial cycle of the anaerobic/denitrifyingP-removing SBRcould be very well predicted (Fig. 7a1, b1). However, due tothe accumulation of small errors due to the repetitive cycliccalculation, there are deviations of up to approximately 30%in steady state (Fig. 7a2, b2).

Sensitivity Analysis

Sensitivity analysis was made for a solids residence time of8 days in both aerobic and denitrifying systems; for longer

residence times, the sensitivity is expected to becomehigher. A different sensitivity for the anaerobic/aerobic(Fig. 8) and the anaerobic/denitrifying system (Fig. 9) wasobserved. The much higher sensitivity of the latter system iscaused by a shortage of electron acceptor (nitrate) and canbe explained as follows:fphb is a result of PHB productionand consumption. These are two large numbers. Small er-rors in this balance are accumulated by a factor equal to thenumber of cycles per sludge age (i.e., 32 or 56 times for 8or 14 days SRT, respectively). In the aerobic case, a surplusof PHB formation is greatly balanced out by extra PHBconsumption due to unlimited oxygen supply. In the deni-

Figure 6. Model verification—simulation of the denitrifying SBR: soluble compounds. Simulation of systems with (a) SRT 8, (b) SRT 14. (1) Simulationof first cycle; (2) simulation of steady-state cycle. Lines: simulation results. Measured concentrations: nitrate (l); phosphate from two cycles (■ h); acetate(s); ammonia (+).


trifying case the amount of nitrate converted is fixed (due toa fixed rate of nitrate addition) leading to a higher sensitiv-ity of PHB fraction for the estimation of acetate or nitrateadded or the value ofdn. The shortage of nitrate leads alsoto a slight release of phosphate from cycle to cycle whichaffects the polyphosphate concentrations and thus also thephosphate uptake profile as it is kinetically connected to thefraction of polyphosphate.

Glycogen was predicted too high in the aerobic systemand too low in the anaerobic system. The deviations have to

be considered relative to the inaccuracy of the measure-ments, where deviations of up to 50% may occur. The ki-netic for glycogen formation may not be well establishedwith the limited set of experimental data.

Model Structure

For keeping the model structure as simple as possible, frac-tions of internal storage compounds are not limited in the

Figure 7. Model verification—simulation of the denitrifying SBR: polymeric storage compounds. Simulation of systems with (a) SRT 8 and (b) SRT 14.(1) Simulation of first cycle; (2) simulation of steady-state cycle. Lines: simulation results. Measured concentrations: PHB (d); glycogen (n); andpolyphosphate (h).


current model. Under certain extreme circumstances, forexample, the PHB could become very high or zero, which isnot realistic. This is not accounted for in the current modelstructure, and the model should only be applied in the rangeof polymer contents used in our study. More research atextreme polymer contents is needed to establish the kineticbehavior at these extremes.

The kinetic equations for anaerobic acetate uptake couldnot always accurately describe the experimentally observed

behavior (Figure 4b1, 6b2). It was not possible to find, withthe data available, a better kinetic description for the processby, for instance, using a correlation to the PHB or glycogencontent. In our set-up, the kinetic equation used had noinfluence on the overall simulation results. Under practicalconditions, where production of fatty acids from fermenta-tion is rate limiting, the form of the equation also has nosignificant effect on the simulation. However, it is useful toestablish the exact kinetic relation, especially for systems in

Figure 8. Model verification—absolute/relative sensitivity of the polymeric compounds in the aerobic SBR (SRT 8). Change of the concentrations ofstorage compounds (mmol/L) at the end of four cycles (total of 40 cycles) per 100% change of parameter.


which acetate is added to the sludge or where fatty acidsform a main component of the influent.

CONCLUSIONS

Results of this work show clearly that biological phosphorusremoval systems, both aerobic and denitrifying, can be de-scribed with the same metabolic model. With a minimum ofthree stoichiometric constants (the anaerobic P-uptake/

acetate-release ratio and the ATP/NADH ratios:do, dn) and10 kinetic constants (including four Michaelis–Menten half-saturation constants) the anaerobic, aerobic, and denitrify-ing phases could be simulated properly.

Short-term behavior of the aerobic and the denitrifyingphases can be well simulated with the new model. Evenlong-term behavior, which is influenced by many param-eters, can be simulated satisfactorily. However, in long-termsimulations, the sensitivity of the system to the feed sub-

Figure 9. Model verification—absolute/relative sensitivity of the polymeric compounds in the denitrifying SBR (SRT 8). Change of the concentrationsof storage compounds (mmol/L) at the end of four cycles (total of 40 cycles) per 100% change of parameter (divisorKno3 4 Kno3

phb,gly/Kno3pp ).


strate concentrations has to be taken into account. Smallerrors sum up from cycle to cycle and lead to considerabledeviations in steady state. As substrate concentrations havea large influence on long-term behavior, these concentra-tions should be considered as model parameters.

NOMENCLATURE

d, dn, do ATP/NADH ratio (mmol/mmol)« P imported into the cell per ATP (mmol/mmol)m growth rate [mmol/(mmol·h)]A model matrixCi concentration of compoundi (mmol/L)

Table VI. Variation of the parameters for sensitivity analysis.

Parameter Value Variation Unit

kphb 0.3 0.03 mmol/(mmol · h)kgly 0.02 0.01 mmol/(mmol · h)kpp 0.005 0.0005 mmol/(mmol · h)qac

max, anerobic 0.3 0.1 mmol/(mmol · h)dn 0.9 0.1 mmol/mmoldo 1.8 0.2 mmol/mmolCac in 12.5 0.5 mmol/LCp in 0.475 0.025 mmol/LCno3 in 117 5 mmol/LKno3

phb,gly 0.1 0.1 mmol/LKno3

phb.gly/Kppno3 10 10 —

Kp 0.1 0.1 mmol/L

Figure 10. Influence of 5% less acetate load on the simulated steady-state behavior of (a) the aerobic SBR (SRT 8) and (b) the denitrifying SBR (SRT8). Solid lines: steady-state simulation results with 12.5 mmol acetate/L (4100%); broken lines: steady-state simulation results with 11.9 mmol acetate/L(495%). Measured concentrations: nitrate (l); phosphate (j h); acetate (s); ammonia (+); PHB (d); glycogen (n); polyphosphate (h). Active biomassin the aerobic SBR (measured/100%/95%): 61/64/61 mmol/L active biomass in the denitrifying SBR (measured/100%/95%): 30/36/35 mmol/L.


fi fraction of polymer per active biomass (mmol/mmol)ki kinetic coefficient [mmol/(mmol·h)]Ki half-saturation concentration (mmol/L)M Monod-like switching functionmi specific rate for maintenance [mmol/(mmol·h)]qi specific conversion rate [mmol/(mmol·h)]RT transposed metabolic reaction matrixri conversion rate (mmol/h)t time (h)

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an integrated metabolic model for the aerobic and denitrifying biological phosphorus removal

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