Q IWA Publishing 2009 Water Science & Technology—WST | 59.9 | 2009

1687

CWM1: a general model to describe biokinetic processes
in subsurface flow constructed wetlands
Guenter Langergraber, Diederik P. L. Rousseau, Joan Garcı́aand Javier Mena

ABSTRACTThis paper presents the Constructed Wetland Model No1 (CWM1), a general model to describe
biochemical transformation and degradation processes for organic matter, nitrogen and sulphurin subsurface flow constructed wetlands. The main objective of CWM1 is to predict effluent
concentrations from constructed wetlands without predicting gaseous emissions. CWM1
describes aerobic, anoxic and anaerobic processes and is therefore applicable to both horizontal
and vertical flow systems. 17 processes and 16 components (8 soluble and 8 particulate) areconsidered. CWM1 is based on the mathematical formulation as introduced by the IWA ActivatedSludge Models (ASMs). It is important to note that besides the biokinetic model a number ofother processes including porous media hydrodynamics, the influence of plants, the transport ofparticles/suspended matter to describe clogging processes, adsorption and desorption processes
and physical re-aeration must be considered for the formulation of a full model for constructedwetlands
Key words | constructed wetlands, CWM1, mechanistic model, numerical simulation,

subsurface flow

Guenter Langergraber (corresponding author)
Institute for Sanitary Engineering and Water
Pollution Control,
University of Natural Resources and Applied Life
Sciences, Vienna (BOKU),
Muthgasse 18, A-1190 Vienna,
AustriaE-mail: guenter.langergraber@boku.ac.at
Diederik P. L. Rousseau
Department of Environmental Resources,
UNESCO-IHE Institute for Water Education,
P.O. Box 3015, 2601 DA,
Delft,The Netherlands
E-mail: d.rousseau@unesco-ihe.org
Joan Garcı́aEnvironmental Engineering Division,
Department of Hydraulics,
Coastal and Environmental Engineering,Technical University of Catalonia,
Jordi Girona 1-3, 08034 Barcelona,Spain
E-mail: joan.garcia@upc.edu
Javier Mena
Department R + D + i,
Research and Development Centre for the
Recuperation of the Environment (CIDRA),
C/Calidad 3, Polı́gono Industrial Sur,13250 Daimiel (Ciudad Real),Spain
E-mail: jmena@alquimiaimasd.com

INTRODUCTION
During the last few years, several models of varying

Rousseau (2005) and Brovelli et al. (2007). Both consider

complexity have been developed to describe the greatbiokinetic models that are based on the IWA Activatedvariety of degradation and removal processes in subsurface

Sludge Models (ASMs) (Henze et al. 2000). For modelling

flow constructed wetlands (CWs) (Langergraber 2008).

vertical flow (VF) CWs with intermittent loading, transient

These models couple hydrodynamic models for either

variably-saturated flow models are required. Due to thevariably saturated or saturated flow in the subsurface withintermittent loading, these systems are highly dynamic,

reaction models. Horizontal flow (HF) systems can be

adding to the complexity of the overall system. Currently,

simulated when only water flow saturated conditions are

the most advanced reaction models are implemented inconsidered. Currently, the most advanced models using

CW2D (Langergraber 2001; Langergraber & Šimůnek 2005),

saturated water flow hydraulics are the one developed byin FITOVERT (Giraldi et al. 2008), both based on thedoi: 10.2166/wst.2009.131

1688

G. Langergraber et al. | CWM1: modelling biokinetic processes in subsurface flow constructed wetlands

Water Science & Technology—WST | 59.9 | 2009

mathematical formulation of the ASMs (Henze et al. 2000);

are referred to as bacteria only. Organic nitrogen is

and in the model developed by Ojeda et al. (2008), thatconsidered as a fraction of organic matter (COD).

considers

In CWM1 16 components (8 soluble and 8 particulate

processes

affectingsolids,organic

matter,nitrogen and sulphur.

components) are considered:Ojeda’s model was developed primarily for HF CWs
but, because of the underlying flow model, it is also capableof simulating VF CWs.

Definition of soluble components, S?

The aim of this paper is to present a general biokinetic
model

to

describe

biochemicaltransformation

anddegradation processes for organic matter and nitrogen in

1.

SO [M(O2) L23]: Dissolved oxygen, O2. Dissolved

subsurface flow CWs. The Constructed Wetland Model No1

oxygen can be directly measured and is subject to gas(CWM1) considers the biokinetic processes in HF and VF

exchange.

CWs we consider relevant with the main objective to2.

predict effluent concentrations. In HF CWs, anaerobic

solubleprocesses play a major role. Therefore, the inclusion of

COD.

This

fraction

of

the

COD

is

directly available for biodegradation by heterotrophic

anaerobic processes had to be considered.

and fermenting bacteria and is produced from

Langergraber et al. (2008) reviewed and discussed thehydrolysis.

pros and cons of different model formulations for thedescription of anaerobic processes in CWs (Rousseau

SF [M(COD) L23]: Fermentable, readily biodegradable

3.

SA [M(COD) L23]: Fermentation products as acetate.
For simplicity reasons all fermentation products are

2005; Mena 2008; Ojeda et al. 2008). Rousseau (2005) used
a complex anaerobic reaction model and a simple

assumed to be acetate only. Consumption of SA occurs

hydraulic model consisting of a network of completely

by aerobic and anoxic growth of heterotrophic bacteria

stirred tank reactors. On the contrary, Ojeda et al. (2008)

as well as anaerobic growths of acetotrophic bacteria.

used a simple anaerobic reaction model in a complex
mechanistic hydraulic model. Mena (2008) presented a4.

further degraded in the CW treatment process. It issimplification of Rousseau’s anaerobic reaction model asassumed to be part of the influent organic matter andan extension of CW2D (Langergraber 2001). This discus-

can be produced from hydrolysis.

sion of Langergraber et al. (2008) formed the basis for theformulation of CWM1.

SI [M(COD) L23]: Inert soluble COD. SI can not be

5.

SNH [M(N) L23]: Ammonium and ammonia nitrogen

In terms of notation and structure of the paper, CWM1þ(NHþ
4 -N and NH3-N). SNH is assumed to be all NH4 -is described in a way similar to the presentation of the

N. As organic nitrogen is modelled as fraction of theASMs (Henze et al. 2000). As with Henze’s presentation of

COD, SNH is produced by degradation of organic

the ASMs, the objective of CWM1 is to provide a widely

matter. SNH is transformed by nitrification and can be

accepted model formulation for biochemical transformation

assimilated during biomass growth.

and degradation processes in constructed wetlands that canthen be implemented in various simulation tools.

6.

SNO [M(N) L23]: Nitrate and nitrite nitrogen (No2
3 -N
and NO2
2 -N). SNO is assumed to include all nitrite andnitrate nitrogen since nitrite is not included as separate
model component. For stoichiometric calculations,
SNO is considered to be NO2
3 -N only. SNO is produced

CWM1: DEFINITION OF COMPONENTS IN THE
MODEL

from nitrification and consumed by denitrification andanoxic sulphide oxidation.

As in the ASMs concentrations of soluble components arecharacterized by S? and particulate components by X?. All
microorganisms are considered particulate components and7.

SSO4 [M(S) L23]: Sulphate sulphur. SSO4 is expressed
as sulphur. Sulphate reducing bacteria use SSO4 as an

1689

G. Langergraber et al. | CWM1: modelling biokinetic processes in subsurface flow constructed wetlands

an electron acceptor for oxidation of acetate SA andelectron acceptor for oxidation of SA. SSO4 is produced
from aerobic and anoxic sulphide oxidation.
8.

SH2S [M(S) L23]: Dihydrogensulphide sulphur. SH2S is

Water Science & Technology—WST | 59.9 | 2009

produce SH2S.
16.

XSOB [M(COD) L23]: Sulphide oxidising bacteria.
Sulphur oxidising bacteria are chemoautotrophic

expressed as sulphur and is subject to gas exchange. It isorganisms that use oxygen SO or nitrate SNO to oxidise

produced by reduction of SSO4 as described insulphide SH2S to sulphate SSO4.

component 7 and is converted back to SSO4 by sulphideoxidisers such as Thiobacillus. At higher concentrations SH2S can be toxic for microorganisms.

CWM1: DEFINITION OF PROCESSES IN THE MODEL
Definition of particulate components, X?
9.

23

XS [M(COD) L]: Slowly biodegradable particulate

CWM1 considers the following 17 biochemical transformation and degradation processes:

COD. XS represents organic substances which have toundergo cell external hydrolysis before they are1.

Hydrolysis: Hydrolysis describes the conversion ofavailable for degradation. When bacteria die, theslowly biodegradable organic matter XS into readily

biodegradable parts of their cells are added to thebiodegradable organic matter SF, with a small fraction

amount of XS. XS losses occur through hydrolysis by

being

heterotrophic bacteria.

Ammonium SNH4 is released during this transformation

10. XI [M(COD) L23]: Inert particulate COD. This part ofconverted

into

inert

organic

matterSI.

process. We further assume that hydrolysis does not

the particulate organic material is not degraded in thetake place under direct dependence of the oxygen

system of interest. XI is assumed to remain in the pore

conditions. Hydrolysis is performed by heterotrophic

space unless higher flow rates exert enough shear

and fermenting bacteria whereby hydrolysis by ferment-

stress to drag along solids.

ing bacteria is assumed to be slower. This considered by

11. XH [M(COD) L23]: Heterotrophic bacteria. These are

the factor hH.

assumed to be the ‘allrounder’ heterotrophic organisms being responsible for hydrolysis, mineralization

2.

Aerobic growth of XH on SF: Heterotrophic growthof organic matter (aerobic growth) and denitrification

rates are dependent on substrate and ammonium(anoxic growth).

availability as well as on electron acceptor concen23

12. XA [M(COD) L

trations (either oxygen or nitrate). Aerobic growth of]: Autotrophic nitrifying bacteria.

Nitrifying organisms are responsible for nitrification.

heterotrophic bacteria XHon readily biodegradable

It is assumed that SNH is directly nitrified to SNO.

organic matter SF (mineralization of organic matter)

Nitrite, as an intermediate product of nitrification, is

consumes oxygen SO, while ammonium SNH4 is

not considered.

incorporated in the biomass.

13. XFB [M(COD) L23]: Fermenting bacteria. Under

3.

Aerobic growth of XH on SA. This process is similar toanaerobic conditions fermenting bacteria consume

the previous one and consumes oxygen SO and acetate

fermentable, readily biodegradable soluble COD sF

SA, while ammonium SNH4 is incorporated in theand produce acetate SA.

biomass.

14. XAMB [M(COD) L23]: Acetotrophic methanogenic
bacteria. Acetotrophic methanogenic bacteria grow in4.

anaerobic conditions, consume acetate SA andand readily biodegradable organic matter SF. Again,

produce methane (which is not considered as a model

ammonium SNH4 is incorporated in the biomass.

component).
15. XASRB [M(COD) L23]: Acetotrophic sulphate reducing bacteria. Sulphate reducing bacteria use SSO4 as

Anoxic growth of XH on SF: Anoxic growth ofheterotrophs (denitrification) consumes nitrate SNO

5.

Anoxic growth of XH on SA: As for aerobic growth,
denitrifiers can also use acetate as substrate. This

1690

6.

G. Langergraber et al. | CWM1: modelling biokinetic processes in subsurface flow constructed wetlands

process consumes nitrate SNO and acetate SA.

This process produces sulphide SH2S and, again,

Ammonium SNH4 is incorporated in the biomass.

ammonia SNH4 is incorporated in the biomass.

Lysis of XH: Lysis is assumed to represent the sum of all
decay and sink processes for bacteria and is describedsimilarly for all types of bacteria. Lysis of heterotrophic
bacteria XH produces organic matter (mainly slowly
biodegradable particulate organic matter XS, and small
fractions of inert particulate organic matter XI andreadilybiodegradableorganic

matterSF)andammonium SNH4.
7.

SNH4 and oxygen SO, and produces nitrate SNO.
Additionally, a small portion of SNH4 is incorporated in
the biomass.

anaerobic

15. Aerobic growth of XSOB on SH2S: The opposite process toprocess 13, the oxidation of SH2S to SSO4, was also
included in the model. This can occur either underaerobic or anoxic conditions. Aerobic growth of sulphideoxidizing bacteria XSOB consumes oxygen SO andammonia SNH4 is incorporated in the biomass.
16. Anoxic growth of XSOB on SH2S: Similar to the previous
process, anoxic growth of sulphide oxidizing bacteria
XSOB consumes sulphide SH2S and nitrate SNO rather thanprocess ammonia SNH4 is incorporated in the biomass.
17. Lysis of XSOB: Lysis of XSOB is described in the same

Growth of XFB: Growth of fermenting bacteria XFB
under

way as process 6.

oxygen SO to produce sulphate SSO4. As with the previous

Lysis of XA: Lysis of XA is described in the same way asprocess 6 (Lysis of XH).

9.

14. Lysis of XASRB: Lysis of XASRB is described in the same

sulphide SH2S and produces sulphate SSO4, whereas

Aerobic growth of XA on SNH: Aerobic growth of
nitrifying bacteria XA (nitrification) consumes ammonia

8.

Water Science & Technology—WST | 59.9 | 2009

conditions

consumes

way as process 6.

readilybiodegradable organic matter SF and results in the
production of acetate SA. Again, ammonium SNH4 is

CWM1: STOICHIOMETRY AND KINETICS

incorporated in the biomass.
The CWM1 stoichiometric matrix is presented in Table 1
10. Lysis of XFB: Lysis of XFB is described in the same way
as process 6.

and the CWM1 process rates are defined in Table 2. The
kinetic parameters used in Tables 1 and 2 are defined in

11. Growth of XAMB: Anaerobically growing acetotrophic,
methanogenic bacteria XAMB consume acetate SA andincorporate SNH4 in the biomass.
12. Lysis of XAMB: Lysis of XAMB is described in the same
way as process 6.

Table 3, whereas the stoichiometric and composition
parameters are defined in Table 4.
The presentation of the CWM1 stoichiometric matrix
Table 1 is based on the IWA ASM mathematical formulation (Henze et al. 2000). Blank fields in the stoichiometricmatrix indicate that a process does not influence the13. Growth of XASRB: Anaerobic growth of acetotrophic,

concentration of a respective component. The stoichio-sulphate reducing bacteria XASRB uses sulphate SSO4 as

metric factors v5,j for ammonia SNH4 calculated from mass

an electron acceptor for oxidation of acetate SA.

balances over each process are as follows:

v5;1 ¼ iN;XS 2 ð1 2 fHYD;SI Þ £ iN;SF 2 fHYD;SI £ iN;SI
v5;2 ¼ v5;3 ¼ iN;SF =YH 2 iN;BM
v5;4 ¼ v5;5 ¼ v5;11 ¼ v5;13 ¼ v5;15 ¼ v5;16 ¼ 2iN;BM
v5;6 ¼ v5;8 ¼ v5;10 ¼ v5;12 ¼ v5;14 ¼ v5;17 ¼ iN;BM 2 fBM;SF £ iN;SF 2 ð1 2 fBM;SF 2 fBM;XI Þ £ iN;XS 2 fBM;XI £ iN;XI
v5;7 ¼ 2iN;BM 2 Y1A
v5;9 ¼ iN;SF =Y FB 2 iN;BM

ð1Þ

1691

i!

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

SO
O2

SF

SA

SI

SNH

SNO

SSO4

SH2S

XS

XI

XH

XA

XFB

XAMB

XASRB

XSOB

COD

COD

COD

N

N

S

S

COD

COD

COD

COD

COD

COD

COD

COD

Process componentjexpressed as !

#1

Hydrolysis

1 2 fHyd;SI
1 2 Y1H

2

Aerobic growthof XH on SF

3

Anoxic growthof XH on SF

4

Aerobic growthof XH on SA

5

Anoxic growthof XH on SA

6

Lysis of XH

7

Aerobic growthof XA on SNH

8

Lysis of XA

fBM,SF9

Growth of XFB21/YFB

21/YH

v5,2

21/YH

v5,3

1 2 Y1H

21/YH

v5,5

1
12YH
2 2:86·Y
H

1
1

12YH
2 2:86·YH

1
v9,Lysis fBM,XI 21

2iN;BM 2 Y1A 1/YA

16 Anoxic growthof XSOB on SH2S
fBM,SF

v9,Lysis fBM,XI

21
1

v5,11
v9,Lysis fBM,XI

21

ASRB
2 12Y
2·YASRB

12YASRB
2·YASRB

v5,15

1/YSOB

21/YSOB

1

v5,16

12YSOB
2 0:875·Y
1/YSOBSOB

21/YSOB

1v5,13v9,Lysis fBM,XI

v5,14

v5,17

1

v9,Lysis fBM,XI

21

21

Water Science & Technology—WST | 59.9 | 2009

fBM,SF

21
1

v5,12
21/YASRB

SOB
2 22Y
YSOB

v9,Lysis fBM,XI

v5,9
v5,10

fBM,SF

13 Growth of XASRB

1v5,8
12Y FBY FB

21/YAMB

14 Lysis of XASRB

21

v5,6

fBM,SF

12 Lysis of XAMB

v9,Lysis¼1 2 fBM,SF2fBM,XI

v5,4

fBM,SF

11 Growth of XAMB

17 Lysis of XSOB

21/YH

A
2 4:572Y
YA

10 Lysis of XFB

15 Aerobic growthof XSOB on SH2S

fHyd,SI v5,1

G. Langergraber et al. | CWM1: modelling biokinetic processes in subsurface flow constructed wetlands

Table 1 | CWM1 stoichiometric matrix

G. Langergraber et al. | CWM1: modelling biokinetic processes in subsurface flow constructed wetlands

1692

Water Science & Technology—WST | 59.9 | 2009

Table 2 | CWM1 process ratesjProcess

Process rate rj

1

Hydrolysis

2

Aerobic growth of XH on SF

3

Anoxic growth of XH on SF

4

Aerobic growth of XH on SA

5

Anoxic growth of XH on SA

6

Lysis of XH

7

Aerobic growth of XA on SNH

8

Lysis of XA

9Growth of XFB

10

Lysis of XFB

11Growth of XAMB

12

Lysis of XAMB

13

Growth of XASRB

14

Lysis of XASRB

15

Aerobic growth of XSOB on SH2S

16

Anoxic growth of XSOB on SH2SbASRB £ XASRB

 
 

SH2S
SO
SNH
mSOB £ KSSOB
þSH2S £ KOSOB þSO £ KNHSOB þSNH £ XSOB

 
 
 

SH2S
SNO
KOSOB
SNH
mSOB £ hSOB £ KSSOB
þSH2S £ KNOSOB þSNO £ KOSOB þSO £ KNHSOB þSNH £ XSOB

17

Lysis of XSOBbSOB £ XSOBhi
Xs =ðXH þXFB Þ
kh £ KX þðX£ ðXH þ hh £ XFB Þ
S =ðXH þXFB ÞÞ

 
 
 
 

KH2SH
SNH
SF
SF
mH £ KSF þSF £ SF þSA £ KOHSOþSo £ KNHH
þSNH £ KH2SH þSH2Sp £ XH

 
 
 
 
 

KOH
SNO
KH2SH
SNH
F
F
£ SFSþS
£ KOH
ng £ mH £ KSFSþSþSo £ KNOH þSNO £ KNHH þSNH £ KH2SH þSH2Sp XH
F
A

 
 
 
 

SA
SO
KH2SH
SNH
A
£
£
£
£
£ XH
mH £ KSASþS
S
þS
K
þS
K
þS
K
þS
o
F
NHH
NH
OH
H2SH
H2Sp
A
A

 
 
 
 
 

SA
SA
KOH
SNO
SNH
KH2SH
ng £ mH £ KSA þSA £ SF þSA £ KOH þSo £ KNOH þSNO £ KNHH þSNH £ KH2SH
þSH2Sp £ XH
bH £ XH

 
 

KH2SA
SO
SNH
mA £ KNHA
þSNH £ KOA þSo £ KH2SA þSH2Sp £ XA
bA £ XA

 
 
 
 

KH2SFB
KOFB
KNOFB
SNH
mFB £ KSFBSFþSF £ KH2SFB
þSH2Sp £ KOFB þSO £ KNOFB þSNO £ KNHFB þSNH £ XFB
bFB £ XFB

 
 
 
 

KH2SAMBKOAMB
KNOAMBSA
SNH
mAMB £ KSAMBþSA £ KH2SAMB þSH2Sp £ KOAMB þSO £ KNOAMB þSNO £ KNHAMB þSNH £ XAMBbAMB £ XAMB

 

 
 
 

SSO4
KH2SASRB
KOASRBKNOASRBSA
SNH
mASRB £ KSASRBþSA £ KSOASRB þSSO4 KH2SASRB þSH2Sp £ KOASRB þSO £ KNOASRB þSNO £ KNHASRB þSNH £XASRBSuch as in the IWA ASMs, the kinetic expressions of
CWM1 are based on switching functions (hyperbolic ofsaturation terms and Monod equations, Henze et al. 2000).

CWM1: TYPICAL WASTEWATER CHARACTERISTICS,KINETIC AND STOICHIOMETRIC PARAMETERS

In Table 2, the CWM1 kinetic expressions for the 17

It is the responsibility of the user of CWM1 to determine theprocesses considered are presented. Lysis processes areconcentrations of the relevant components in the influent

modelled using first-order decay rates.

wastewater. In Tables 3 and 4, the kinetic and stoichio-

Using Tables 1 and 2, the reaction rate ri for component
i can be calculated as:

metric parameters, respectively, are listed and literature
values for these parameters are given.
Kinetic parameters in Table 3 are given for 208C and if

ri ¼

R
X

relevant for 108C. It is assumed that only rate constantsvi;j £ rj

ð2Þ

j¼1

express temperature dependencies with the exception being
KX, the saturation coefficient for hydrolysis, and KNHA, thesaturation/inhibition coefficient for SNH for nitrification

where i ¼ 1, … , N, N

¼ number of components (16),j ¼ 1, … , R, R ¼ number of processes (17), vi,j is the(Langergraber 2007). Temperature dependencies should bemodelled as described by Henze et al. (2000).

stoichiometric factor for component i and process j

The experience with CW2D (Langergraber & Šimůnek(Table 1), and rj is the reaction rate for process j as defined2005) showed that a good match to measured quality data

in Table 2.

can be obtained if the hydraulic behaviour of the CW is1693

Parameter

Description [unit]

Value

Reference

Kh

Hydrolysis rate constant [1/d]3 (2)Henze et al. (2000)

KX

Saturation/inhibition coefficient for hydrolysis [g CODSF/g CODBM]

0.1 (0.22)

Langergraber (2007)

hH

Correction factor for hydrolysis by fermenting bacteria [-]0.1

Henze et al. (2000)

Hydrolysis

Heterotrophic bacteria (aerobic growth and denitrification)mH

Maximum aerobic growth rate on SF and SA [1/d]6 (3)Langergraber & Šimůnek (2005)hg

Correction factor for denitrification by heterotrophs [-]0.8

Henze et al. (2000)

bH

Rate constant for lysis [1/d]0.4 (0.2)

Langergraber & Šimůnek (2005)

KOH

Saturation/inhibition coefficient for SO [mg O2/L]

0.2

Langergraber & Šimůnek (2005)

KSF

Saturation/inhibition coefficient for SF [mg CODSF/L]

2

Langergraber & Šimůnek (2005)

KSA

Saturation/inhibition coefficient for SA [mg CODSA/L]

4

Henze et al. (2000)

KNOH

Saturation/inhibition coefficient for SNO [mg N/L]

0.5

Henze et al. (2000)

KNHH

Saturation/inhibition coefficient for SNH (nutrient) [mg N/L]

0.05

Langergraber & Šimůnek (2005)

KH2SH

Saturation/inhibition coefficient for SH2S [mg S/L]

140

Rousseau (2005)

Autotrophic bacteria
mA

Maximum aerobic growth rate on SNH [1/d]1 (0.35)

Henze et al. (2000)

bA

Rate constant for lysis [1/d]0.15 (0.05)

Henze et al. (2000)

KOA

Saturation/inhibition coefficient for SO [mg O2/L]

1

Langergraber & Šimůnek (2005)

KNHA

Saturation/inhibition coefficient for SNH [mg N/L]

0.5 (5)Langergraber (2007)

KH2SA

Saturation/inhibition coefficient for SH2S [mg S/L]

140

Rousseau (2005)

mAMB

Maximum aerobic growth rate for XFB [1/d]3 (1.5)Henze et al. (2000)

bAMB

Rate constant for lysis [1/d]0.02

Kalyuzhnyi & Fedorovich (1998)

KOFB

Saturation/inhibition coefficient for SO [mg O2/L]

0.2

Henze et al. (2000)

KSFB

Saturation/inhibition coefficient for SF [mg CODSF/L]

28

Kalyuzhnyi & Fedorovich (1998)

KNOFB

Saturation/inhibition coefficient for SNO [mg N/L]

0.5

Henze et al. (2000)

KNHFB

Saturation/inhibition coefficient for SNH (nutrient) [mg N/L]

0.01

Rousseau (2005)

KH2SFB

Saturation/inhibition coefficient for SH2S [mg S/L]

140

Kalyuzhnyi & Fedorovich (1998)

Water Science & Technology—WST | 59.9 | 2009

Fermenting bacteria

G. Langergraber et al. | CWM1: modelling biokinetic processes in subsurface flow constructed wetlands

Table 3 | Kinetic parameters (at 208C, values in brackets at 108C)

1694

Description [unit]

Value

Reference

Acetotrophic methanogenic bacteria
mAMB

Maximum aerobic growth rate on for XAMB [1/d]0.085

Kalyuzhnyi & Fedorovich (1998)

bAMB

Rate constant for lysis [1/d]0.008

Kalyuzhnyi & Fedorovich (1998)

KOAMB

Saturation/inhibition coefficient for SO [mg O2/L]

0.0002

Rousseau (2005)

KSAMB

Saturation/inhibition coefficient for SF [mg CODSA/L]

56

Kalyuzhnyi & Fedorovich (1998)

KNOAMB

Saturation/inhibition coefficient for SNO [mg N/L]

0.0005

Rousseau (2005)

KNHAMB

Saturation/inhibition coefficient for SNH (nutrient) [mg N/L]

0.01

Rousseau (2005)

KH2SAMB

Saturation/inhibition coefficient for SH2S [mg S/L]

140

Kalyuzhnyi & Fedorovich (1998)
Kalyuzhnyi & Fedorovich (1998)

Acetotrophic sulphate reducing bacteriamASRB

Maximum aerobic growth rate for XASRB [1/d]

0.18

bASRB

Rate constant for lysis [1/d]0.012

Kalyuzhnyi & Fedorovich (1998)

KOASRB

Saturation/inhibition coefficient for SO [mg O2/L]

0.0002

Rousseau (2005)

KSASRB

Saturation/inhibition coefficient for SF [mg CODSA/L]

24

Kalyuzhnyi & Fedorovich (1998)

KNOASRB

Saturation/inhibition coefficient for SNO [mg N/L]

0.0005

Rousseau (2005)

Saturation/inhibition coefficient for SNH (nutrient) [mg N/L]

0.01

Rousseau (2005)

Saturation/inhibition coefficient for SSO4 [mg S/L]

19

Kalyuzhnyi & Fedorovich (1998)

KH2SASRB

Saturation/inhibition coefficient for SH2S [mg S/L]

140

Kalyuzhnyi & Fedorovich (1998)

Sulphide oxidising bacteriamSOB

Maximum aerobic growth rate for XSOB [1/d]5.28

de Wit et al. (1995)

bSOB

Rate constant for lysis [1/d]0.15

Rousseau (2005)

KOSOB

Saturation/inhibition coefficient for SO [mg O2/L]

0.2

Rousseau (2005)

KNOSOB

Saturation/inhibition coefficient for SNO [mg N/L]

0.5

Rousseau (2005)

KNHSOB

Saturation/inhibition coefficient for SNH (nutrient) [mg N/L]

0.05

Rousseau (2005)

KSSOB

Saturation/inhibition coefficient for SHsS [mg S/L]

0.24

de Wit et al. (1995)

Water Science & Technology—WST | 59.9 | 2009

KNHASRB
KSOASRB

G. Langergraber et al. | CWM1: modelling biokinetic processes in subsurface flow constructed wetlands

Table 3 | (continued)
Parameter

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Water Science & Technology—WST | 59.9 | 2009

Table 4 | Stoichiometric parameters for organic matter and bacteria and composition parameters

Stoichiometric parameters
fHyd,SI Production of SI in hydrolysis [g CODSI/g CODXS]

0.0

Langergraber & Šimůnek (2005)

fBM,SF

Fraction of SF generated in biomass lysis [g CODSF/g CODBM]

0.05

Langergraber & Šimůnek (2005)

fBM,XI

Fraction of XI generated in biomass lysis [g CODXI/g CODBM]

0.1

Langergraber & Šimůnek (2005)

YH

Yield coefficient for heterotrophic bacteria [g CODBM/g CODSF]

0.63

Henze et al. (2000)

YA

Yield coefficient for autotrophic bacteria [g CODBM/g N]

0.24

Henze et al. (2000)

YFB

Yield coefficient for fermenting bacteria[g CODBM/g CODSF]

0.053 Kalyuzhnyi & Fedorovich (1998)

YAMB

Yield coefficient for acetotrophic methanogenic bacteria [g CODBM/g CODSA]

0.032 Kalyuzhnyi & Fedorovich (1998)

YASRB Yield coefficient for acetotrophic sulphur reducing bacteria [g CODBM/g CODSA] 0.05

Kalyuzhnyi & Fedorovich (1998)

YSOB

0.12

de Wit et al. (1995)

Yield coefficient for sulphide oxidizing bacteria [g CODBM/g S]

Composition parameters
iN,SF

N content of SF [g N/g CODSF]

0.03

Langergraber & Šimůnek (2005)

iN,SI

N content of SI [g N/g CODSI]

0.01

Langergraber & Šimůnek (2005)

iN,XS

N content of XS [g N/g CODXS]

0.04

Langergraber & Šimůnek (2005)

iN,XI

N content of XI [g N/g CODXI]

0.03

Henze et al. (2000)

iN,BM

N content of biomass [g N/g CODBM]

0.07

Langergraber & Šimůnek (2005)

correctly described. Then literature parameters for the

Aerobic and anoxic microbial processes affecting

biokinetic model can be used. It is assumed that this isorganic matter and nitrogenalso true for CWM1 and therefore the model parameterspresented have been chosen from applications shown in theliterature. No ranges of the parameters are given. Whileranges can be easily found for model parameters describing
aerobic and anoxic reactions (e.g. Reichert & Vanrolleghem
2001; Hulsbeek et al. 2002), there is a lack of information formodel parameters describing anaerobic processes.

The model formulations for aerobic degradation of organic
matter as well as for nitrification and denitrification are
derived from ASM2 (Henze et al. 2000). A Monod term for
SH2S is included for aerobic and anoxic processes to
describe the toxicity effects at high SH2S concentrations(Kalyuzhnyi et al. 1998).

Anaerobic microbial processes

DISCUSSION

Kinetics of anaerobic microbial processes (fermentation,

The CWM1 model formulation aims at using a minimum

methanogenesis and sulphate reduction) is based on thenumber of processes to predict the effluent concentrations

model presented by Kalyuzhnyi & Fedorovich (1998), whichbased on the aerobic, anoxic and anaerobic processes

takes into account the competition between sulphate

occurring in subsurface flow systems. As it is not the aim

reducing and methanogenic bacteria. In order to reduceto predict gaseous emissions methane and other gases (e.g.

the number of overall processes, the following anaerobic

N2) are not considered as a model components. Phos-

processes are neglected:

phorus is also not considered as microbial processes play a

1.

Processes with iron as electron acceptor: Burgoon

minor role for phosphorus transformation and removal in(1993) demonstrated that in subsurface flow CWs ironsubsurface flow CWs. However, CWM1 assumes that there

reduction contributes only a maximum of 0.1% andis no limitation of the processes due to a lack of

0.2% of the total removed acetate in nitrate rich andphosphorus.

sulphate rich environment, respectively. Therefore, it is1696

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Water Science & Technology—WST | 59.9 | 2009

assumed that these processes play a minor role whendesorption processes, as well as physical re-aeration, havetreating domestic wastewater. However, they can be

to be considered.

easily added if necessary e.g. for modeling the treatment
of industrial and mining wastewaters.
2.

Processes with hydrogen as electron donor: It is
assumed that hydrogen occurs only as intermediate
product and is rapidly consumed. Therefore, it is further
assumed that processes with hydrogen as electron
donor (SO4 reduction with H2, etc.) and H2 volatilisation is not considered (Mena 2008).

SUMMARY
This paper introduces the Constructed Wetland Model No1(CWM1) that describs the most relevant aerobic, anoxic
and anaerobic biokinetic processes, occurring in HF and VF
CWs, required to predict effluent concentrations of organic
matter, nitrogen and sulphur. 17 processes and 16 components (8 soluble and 8 particulate) are considered. It is
assumed that by using the CWM1 model formulation, it will

Biological sulphide oxidation

be possible to model the effluent concentration of both HF

Biological sulphide oxidation (that occurs under aerobic

and VF CWs. The authors hope that CWM1, such as theand anoxic conditions) has been reported to play a role in

IWA ASMs, will become a widely accepted model formu-

some CW systems (e.g. Gonzalias 2008) and is therefore

lation for biochemical transformation and degradation

included in the CWM1 model formulation. The model used

processes in subsurface flow constructed wetlands andis based on the formulation presented by de Wit et al. (1995)

will be implemented in many simulation platforms.

that was used by Rousseau (2005).

ACKNOWLEDGEMENTS
Hydrolysis and lysis of bacteria
The processes hydrolysis and lysis of bacteria are derived
from the ASM2 formulations (Henze et al. 2000).

Other processes to be considered for a full model
for CWsAs CWM1 describes only the biochemical transformation
processes caused by microorganisms the authors want topoint out that there are a number of other processes thathave to be considered for the formulation of a full model for
CWs. Previous experience has shown that the flow model
describing water flow in the porous media is of utmost
importance (see e.g. Langergraber 2008). Therefore it issuggested that finite element or finite difference models
shall be used for describing water flow instead of tanks-inseries models. The influence of plants on the treatment
processes has to be modelled by taking into consideration
plant growth, decay, decomposition, nutrient uptake, root
oxygen release, etc. To model the transport of particles andsuspended matter is a precondition to be able to describeand predict clogging processes. Further on, adsorption and

The authors thank Dr. Damien Batstone, University of
Queensland, Australia, for his comments on the formulationof the anaerobic processes in CWM1.

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