453

9Modeling Variably Saturated Water Flowand Multicomponent Reactive Transportin Constructed Wetlands
Günter Langergraber1 and Jirka Šimůnek2
1

Institute of Sanitary Engineering and Water Pollution Control, University of Natural Resources and Life Sciences Vienna(BOKU), A‐1190, Vienna, Austria
2
Department of Environmental Sciences, University of California Riverside, Riverside, CA, 92521, USA

9.1 ­Introduction
Constructed wetlands (CWs) are engineered treatment systems that optimize t­ reatment
processes found in natural environments and are therefore considered to be sustainable,
environmentally friendly solutions to engineering problems. Processes occurring in
CWs are very complex, and include a large number of simultaneously active physical,
chemical, and biological processes that mutually influence each other. CWs are systems
that efficiently treat different types of polluted water (e.g. Kadlec and Wallace, 2009;
García et al., 2010).
For a long time, CWs have been considered ‘black boxes’. Little effort has been madeto understand the main processes leading to contaminant removal. Still today, mostmodels for wetlands are using a ‘black box’ approach – they do not consider processes
in wetlands in detail. For ‘black box’ models, data from experiments are needed toderive model equations. In process‐based models the mathematical equations are basedon processes in wetlands and include balance equations for energy, mass, charge, and soon. Data from experiments are used for calibration and validation of models. Better
predictions should be possible using these models (Langergraber, 2011).
When developing a wetland model, a number of different processes have to be­considered (Langergraber et al., 2009b):
the flow model (describing water flow in the porous media);
the transport model (describing transport of constituents as well as adsorption anddesorption processes);●● the biokinetic model (describing biochemical transformation and degradation­processes of the constituents);●●●●

Reactive Transport Modeling: Applications in Subsurface Energy and Environmental Problems,First Edition. Edited by Yitian Xiao, Fiona Whitaker, Tianfu Xu and Carl Steefel.
© 2018 John Wiley & Sons Ltd. Published 2018 by John Wiley & Sons Ltd.

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Reactive Transport Modeling●●●●the plant model (growth, decay, decomposition, nutrient uptake, root oxygen release, etc);
the clogging model (the transport and deposition of suspended particulate matter,and bacterial and plant growth that may reduce the hydraulic capacity/conductivityof the filter medium).

Different types of CWs require different models to describe water flow. No free waterlevel is visible in subsurface flow (SSF) CWs, and water flows, either horizontally or
vertically, through the porous filter media. Horizontal flow (HF) systems can be simulated when only saturated water flow conditions are considered. For modeling verticalflow (VF) CWs with intermittent loading, transient variably‐saturated flow models are
required. Due to the intermittent loading, these systems are highly dynamic, adding to
the complexity needed to model the overall system. Models applicable to VF CWs use
either the Richards equation or various simplified approaches to describe variably‐saturated flow (Langergraber, 2008).
Wastewaters contain particulate and solute compounds that are transported with theflowing water. Transport equations generally consider convective–dispersive transport
in the liquid phase, diffusion in the gaseous phase, as well as adsorption and desorption
processes between the solid and liquid phases.
Biokinetic models describe the transformation and degradation processes of the pollutants. The complexity of biokinetic models ranges from considering a single process
affecting the concentration of one compound to multiple processes affecting multiple
compounds. The reaction rates are often assumed to be constant, that is, independentof environmental conditions. However, reaction rates are dependent on a number ofenvironmental conditions (e.g. concentrations of oxygen, substrate, nutrients). These
dependencies are often modeled with Monod‐type equations.
Plants are an essential part of wetland treatment systems, and thus plant‐related
processes have to be included in wetland models. Root growth influences the waterflow pattern in the subsurface, and via evapotranspiration the water balance. During
growth and decay, plants take up nutrients and release organic matter and nutrients,
respectively. Additionally, some plants release substances via roots (e.g. oxygen
and/or specific organic substances). Plant models describe uptake and release of­substances either associated with water uptake or as a process dependent on concentration gradients.
Clogging models need to be able to describe (1) the transport and deposition of suspended particulate matter, and (2) the deposition of particulate matter, bacterial andplant growth that may reduce the hydraulic capacity/conductivity of the filter medium.
This is important for simulations of the long‐term CW performance and predictions ofpotential failure due to clogging (Langergraber and Morvannou, 2014).
During the last two decades a couple of mechanistic models have been developed for
simulating CWs (Langergraber, 2008, Langergraber et al., 2009a; Kumar and Zhao,
2011; Meyer et al., 2015; Samsó et al., 2015b). Recent developments, especially towards
implementation of the CWM1 biokinetic model (Langergraber et al., 2009b), include
the works of Langergraber and Šimůnek (2012), Samsó and Garcia (2013), and Mburu
et al. (2012). Table 9.1 compares three tools with respect to the considered submodels
required for a wetland model.
In this chapter, we briefly describe version 2 of the HYDRUS Wetland module(Langergraber and Šimůnek, 2012) and discuss existing experience using wetland

Modeling Multicomponent Reactive Transport in Constructed Wetlands

Table 9.1 Comparison of recent simulation tools for constructed wetlands.
Simulation
tool

HYDRUS Wetland module

BIO_PORE

AQUASIM

Reference

Langergraber and Šimůnek
(2012)

Samsó and Garcia (2013)

Mburu et al. (2012)

Flow
model

Richards equation(variably saturated flow)

Variable water table(saturated flow)

No flow consideredTransport
model

Advection, dispersion,
adsorption

Advection, dispersion,
adsorption

No transport model

Biokinetic
model

CW2D + CWM1

CWM1

CWM1

Influenceof plants

Evapotranspiration, uptake
and release of substances

Evapotranspiration, uptake
and release of substances

Evapotranspiration, uptake
and release of substances

Clogging
model

Not considered

IncludedNot considered­ odels in general and the HYDRUS Wetland module in particular. We further describemremaining challenges in using these tools and summarize needs for further development and research.

9.2 ­The HYDRUS Wetland Module
The HYDRUS software numerically solves the Richards equation for saturated/unsaturated water flow and the convection–dispersion equation for heat and solute transport.
The flow equation incorporates a sink term to account for water uptake by plant roots.
The solute transport equations consider convective–dispersive transport in the liquid
phase, diffusion in the gaseous phase, as well as nonlinear nonequilibrium reactions
between the solid and liquid phases (Šimůnek et al., 2008, 2011).
Version 2 of the HYDRUS wetland module (Langergraber and Šimůnek, 2012)
includes two biokinetic model formulations: (1) the CW2D (Langergraber and Šimůnek,2005), and (2) the CWM1 (Constructed Wetland Model 1) biokinetic models(Langergraber et al., 2009b). In CW2D, aerobic and anoxic transformation and degradation processes for organic matter, nitrogen and phosphorus are taken into account,whereas in CWM1, aerobic, anoxic and anaerobic processes for organic matter, nitrogen and sulfur are considered. CWM1 has been developed with the main goal of providing a widely accepted model formulation for biochemical transformation anddegradation processes in SSF CWs. Table 9.2 summarizes processes and components
described by, and applications of, the biokinetic models CW2D and CWM1, which are
implemented in the HYDRUS Wetland module.
Both CW2D and CWM1 have been developed to describe processes in constructedwetlands treating domestic wastewater. A number of applications of the HYDRUS wetland module shows that a good match between measured data and simulation results
can be achieved (e.g. Langergraber, 2003, 2007; Langergraber et al., 2007). In addition to

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Reactive Transport Modeling

Table 9.2 Processes and components described by (number of components/processes in brackets),
and applications of, the biokinetic models CW2D and CWM1 (adapted from Langergraberand Šimůnek, 2012).
Biokinetic model

CW2D

CWM1

Processes

Aerobic and anoxic (9)Aerobic, anoxic, and anaerobic (17)Components

Oxygen, organic matter, nitrogen,and phosphorus (12)Oxygen, organic matter, nitrogen,and sulfur (16)Type of CW

VF CWsLow‐loaded HF beds

VF and HF CWs

applications involving treatment of municipal wastewater in CWs, the HYDRUS
Wetland module has been also used to model:
CWs treating combined sewer overflow (Dittmer et al., 2005; Henrichs et al. 2007,2009; Meyer, 2011)●● CWs treating effluents of the wastewater treatment plant for irrigation purposes(Toscano et al., 2009; Pálfy et al., 2015a)●● CWs treating artificial wastewater (e.g. Pálfy and Langergraber, 2014; Rizzo et al., 2014)●● CWs treating greywater (Karlsson et al., 2015)●● Runoff from agricultural sites and the effects of streamside management zones(Smethurst et al., 2014).
●●

Besides the Wetland module, the HYDRUS software also includes the HP1/2/3 multicomponent solute transport modules, the colloid‐facilitated solute transport C‐Ride
module, a module for fumigants, and the major ion UnsatChem module. All of thesemodules simulate water flow and solute/heat transport processes in two‐dimensionaltransport domains and are supported by the HYDRUS (2D/3D) graphical user interface.
Many processes of these specialized modules are also available as part of the publicdomain HYDRUS‐1D software (Šimůnek et al., 2013).

9.3 ­The CW2D and CWM1 Biokinetic Models
In this section, the CW2D and CWM1 biokinetic models (i.e., the components andprocesses defined in the two models) are presented in detail. The information is derived
from the original papers of Langergraber and Šimůnek (2005) and Langergraber et al.
(2009b), respectively.
Table 9.3 compares the components defined in the CW2D and CWM1 model formulations. As described above, both biokinetic models consider processes affecting organic
matter and nitrogen. Additionally, CW2D considers processes affecting phosphorus,
whereas CWM1 considers processes affecting sulfur. All components except bacteria
are assumed to be soluble (including the particulate Chemical Oxygen Demand (COD)
fraction) and bacteria are immobile. Organic nitrogen (in CW2D and CWM1) andorganic phosphorus (in CW2D) are modeled as part of the COD. Since wastewater

Modeling Multicomponent Reactive Transport in Constructed Wetlands

Table 9.3 Comparison of CW2D and CWM1 components in the HYDRUS implementation.
CW2D (Langergraber and Šimůnek, 2005)
Organic matter, nitrogen, phosphorus

CWM1 (Langergraber et al., 2009b)
Organic matter, nitrogen, sulfur

CW2D components
1) SO: Dissolved oxygen, O22) CR: Readily biodegradable soluble COD
3) CS: Slowly biodegradable soluble COD
4) CI: Inert soluble COD
5) XH: Heterotrophic bacteria
6) XANs: Autotrophic ammonia oxidizing
bacteria (Nitrosomonas spp.)
7) XANb: Autotrophic nitrite oxidizing
bacteria (Nitrobacter spp.)8) NH4N: Ammonium and ammonia nitrogen9) NO2N: Nitrite nitrogen10) NO3N: Nitrate nitrogen11) N2: Elemental nitrogen
12) PO4P: Phosphate phosphorus
Additional component (in the HYDRUS
implementation)13) Non‐reactive tracer
Nitrification is modeled as a two‐step process

Soluble components
1) SO: Dissolved oxygen, O22) SF: Fermentable, readily biodegradable
soluble COD3) SA: Fermentation products as acetate
4) SI: Inert soluble COD
5) SNH: Ammonium and ammonia nitrogen6) SNO: Nitrate and nitrite nitrogen
7) SSO4: Sulfate sulfur8) SH2S: Dihydrogensulfide sulfur
Particulate components
9) XS: Slowly biodegradable particulate COD
10) XI: Inert particulate COD11) XH: Heterotrophic bacteria
12) XA: Autotrophic nitrifying bacteria
13) XFB: Fermenting bacteria
14) XAMB: Acetotrophic methanogenic
bacteria
15) XASRB: Acetotrophic sulfate reducing
bacteria16) XSOB: Sulfide oxidizing bacteria
Additional component (in the HYDRUS
implementation)17) Non‐reactive tracer

Table 9.4 Definitions of CW2D and CWM1 components in the liquid and solid phases (Langergraberand Šimůnek, 2011).
Component 1 2

3

4

5

6 7 8

9

10

11 12

S S L+S L

L

L

CW2D

L L+S L+S L+S S

CWM1

L L+S L+S L+S L+S L L L

L+S L+S S

13

14 15 16 17

L+S L+S –

–

– –

S

S

S

S

S

L+S

L, defined in the liquid phase only; S, defined in the solid phase only; L + S, defined in both liquid and solid
phases.

constituents considered in the CW2D and CWM1 biokinetic models are different,
there is no direct conversion between two model components.
Table 9.4 summarizes in what phase (i.e. liquid and/or solid) the CW2D and CWM1
components are defined in the HYDRUS Wetland module. For components defined inboth phases (L + S), adsorption and desorption processes can be considered. As mentioned above, suspended particulate organic matter compounds (XS and XI in CWM1)

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Reactive Transport Modelingare considered as solute compounds. Note that the number of components in Table 9.4
is increased by one compared with that given in Table 9.2 for both CW2D and CWM1.
In both models, a non‐reactive tracer that is independent of other components, and thatcan be used to derive the hydraulic retention time, is added in the HYDRUS wetland
module. This non‐reactive tracer is defined in both liquid and solid phases (Langergraberand Šimůnek, 2011).
Table 9.5 compares the processes defined in the CW2D and CWM1 model formulations. Only aerobic and anoxic processes are defined in CW2D. Two main types ofbacteria, heterotrophic and autotrophic bacteria, are considered. One special feature of
CW2D is that nitrification is modeled as a two‐step process, from ammonia via nitrite
to nitrate. Since anaerobic processes are additionally defined in CWM1, six different
types of bacteria need to be considered in this model. In addition to heterotrophic andTable 9.5 Comparison of CW2D and CWM1 processes (Langergraber and Šimůnek, 2011).
CW2D (Langergraber andŠimůnek, 2005)

Heterotrophic bacteria:
1) Hydrolysis: conversion of CS
into CR
2) Aerobic growth of XH on
CR (mineralization oforganic matter)3) Anoxic growth of XH on CR(denitrification on NO2N)
4) Anoxic growth of XH on CR(denitrification on NO3N)
5) Lysis of XH
Autotrophic bacteria:
6) Aerobic growth of XANs on
SNH (ammonium oxidation)7) Lysis of XANs
8) Aerobic growth of XANb on
SNH (nitrite oxidation)9) Lysis of XANb

CWM1 (Langergraber et al., 2009b)

Heterotrophic bacteria:
1) Hydrolysis: conversion of XS into SF2) A erobic growth of XH on SF (mineralization of organic
matter)3) A erobic growth of XH on SA (mineralization of organic
matter)4) Anoxic growth of XH on SF (denitrification)5) Anoxic growth of XH on SA (denitrification)6) Lysis of XH
Autotrophic bacteria:
7) Aerobic growth of XA on SNH (nitrification)8) Lysis of XA
Fermenting bacteria:
9) Growth of XFB (fermentation)10) Lysis of XFBAcetotrophic methanogenic bacteria:11) Growth of XAMB: Anaerobic growth of acetotrophic,
methanogenic bacteria XAMB on acetate SA
12) Lysis of XAMB
Acetotrophic sulfate reducing bacteria:13) Growth of XASRB: Anaerobic growth of acetotrophic,
sulfate reducing bacteria
14) Lysis of XASRB
Sulfide oxidizing bacteria:15) Aerobic growth of XSOB on SH2S: The opposite process to
13, the oxidation of SH2S to SSO4
16) Anoxic growth of XSOB on SH2S: Similar to process 15 butunder anoxic conditions17) Lysis of XSOBModeling Multicomponent Reactive Transport in Constructed Wetlands

autotrophic bacteria, fermenting, acetotrophic methanogenic, acetotrophic sulfate
reducing, and sulfide oxidizing bacteria are also considered, in order to account for themain anaerobic processes.
9.3.1

CW2D Biokinetic Model

9.3.1.1

Stoichiometric Matrix and Reaction Rates

Table 9.6 and Table 9.7 show stoichiometric coefficients for ammonium nitrogen andinorganic phosphorus, respectively. Table 9.8 shows the stoichiometric matrix of reactions in CW2D, whereas Table 9.9 shows the reaction rates.
9.3.1.2

Model Parameters

Table 9.10 shows the kinetic parameters, and Table 9.11 the temperature dependences, stoichiometric parameters, composition parameters and parameters describing oxygen transfer for the CW2D biokinetic model, as described in Langergraber andŠimůnek (2005).
Table 9.6 Stoichiometric coefficients for ammonium nitrogen(Langergraber and Šimůnek, 2011; see Table 9.11 for definitionsof the composition and stoichiometric parameters).
ν1,N =

iN,CS − (1 − fHyd,CI).iN,CR − fHyd,CI.iN,CI

ν2,N =

1/YH.iN,CR − iN,BM

ν3,N =

1/YH.iN,CR − iN,BM

ν4,N =

1/YH.iN,CR − iN,BM

ν5,N =

iN,BM − (1 − fBM,CR − fBM,CI).iN,CS − fBM,CR.iN,CR − fBM,CI.iN,CI

ν6,N =−1/YANs − iN,BM

ν7,N =

iN,BM − (1 − fBM,CR − fBM,CI).iN,CS − fBM,CR.iN,CR − fBM,CI.iN,CI

ν8,N =−iN,BM

ν9,N =

iN,BM − (1 − fBM,CR − fBM,CI).iN,CS − fBM,CR.iN,CR − fBM,CI.iN,CI

Table 9.7 Stoichiometric coefficients for inorganic phosphorus(Langergraber and Šimůnek, 2011; see Table 9.11 for definitionsof the composition and stoichiometric parameters).
ν1,P = iP,CS − (1 − fHyd,CI).iP,CR − fHyd,CI.iP,CI
ν2,P = 1/YH.iP,CR − iP,BM
ν3,P = 1/YH.iP,CR − iP,BM
ν4,P = 1/YH.iP,CR − iP,BM
ν5,P = iP,BM − (1 − fBM,CR − fBM,CI).iP,CS − fBM,CR.iP,CR − fBM,CI.iP,CI
ν6,P = −iP,BM
ν7,P = iP,BM − (1 − fBM,CR − fBM,CI).iP,CS − fBM,CR.iP,CR − fBM,CI.iP,CI
ν8,P = −iP,BM
ν9,P = iP,BM − (1 − fBM,CR − fBM,CI).iP,CS − fBM,CR.iP,CR − fBM,CI.iP,CI

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Table 9.8 CW2D stoichiometric matrix (Langergraber and Šimůnek, 2005; see Table 9.11 for definitions of the stoichiometric coefficients).
i→j

Process

↓

1

2

3

4

5

6

7

8

9

10

11

12

Component

O2

CR

CS

CI

XH

XANs

XANb NH4N

NO2N

NO3N

N2N

IP

expressed as →

O2

COD

COD

COD

COD

COD

COD

N

N

N

P

1 − fHyd,CR−1

1 − fHyd,CI

N

ν1,N

ν1,P

−1/YH

1

ν2,N

ν2,P

NO3‐growth of heterotrophs onreadily biodegradable COD

−1/YH

1

ν3,N

4

NO2‐growth of heterotrophs onreadily biodegradable COD

−1/YH

1

ν4,N

5

Lysis of heterotrophs

6

Aerobic growth of Nitrosomonason NH4

7

Lysis of Nitrosomonas

8

Aerobic growth of Nitrobacteron NO2

9

Lysis of Nitrobacter1

Hydrolysis

2

Aerobic growth of heterotrophs on 1 1
readily biodegradable COD
YH

3

ν Lysis = 1‐fBM,CR‐fBM,CI

3.43 YA
YA
1.14 YA
YA

fBM,CR

νLysisfBM,CI

fBM,CR

νLysisνLysisfBM,CI

fBM,CI

1 YH
1.71 YH

ν5,N

−1
1

fBM,CR

1 YH
2.86 YH

iN,BM − 1/YANs

1

ν8,N

−1

ν9,N

ν3,P

1 YH
1.71 YH

ν4,P
ν5,P
ν6,P

1/YANs

ν7,N

−1

1 YH
2.86 YH

ν7,P−1/YANb

1/YANb

ν8,P
ν9,P

Modeling Multicomponent Reactive Transport in Constructed Wetlands

Table 9.9 Reaction rates in CW2D (Langergraber and Šimůnek, 2005; see Table 9.10
for definitions of rate coefficients).
R Process/reaction rate rcj

Heterotrophic organisms
1) HydrolysiscCS /cXHKh
cXH
K X cCS /cXH
2) Aerobic growth of heterotrophs on readily biodegradable COD
cO2
cCR
f N , Het cXHH
K Het ,O2 cO2 K Het ,CR cCR3) NO3‐growth of heterotrophs on readily biodegradable COD
K DN ,O2
cNO3
K DN , NO2
cCR
f N , DN cXH
DN
K DN ,O2 cO2 K DN , NO3 cNO3 K DN , NO2 cNO2 K DN ,CR cCR4) NO2‐growth of heterotrophs on readily biodegradable COD
K DN ,O2cNO2cCR
f N , DN cXH
DN
K DN ,O2 cO2 K DN , NO2 cNO2 K DN ,CR cCR
5) Lysis of heterotrophs
bH cXH
Autotrophic organisms 1 – Nitrosomonas
6) Aerobic growth of Nitrosomonas on NH4
cO2
cNH 4
cIP
cXANs
ANs
K ANs ,O2 cO2 K ANs , NH 4 cNH 4 K ANs , IP cIP
7) Lysis of NitrosomonasbHANs cXANs
Autotrophic organisms 2 – Nitrobacter
8) Aerobic growth of Nitrobacter on NO2
cO2
cNO2
f N , ANb cXANb
ANb
K ANb,O2 cO2 K ANb, NO2 cNO29) Lysis of NitrobacterbHANb cXANb
Conversion of solid and liquid phase concentrations
c XY

sXY , whereY

H, ANs, ANb

Factor for nutrients
cNH 4
cIP
fN ,x
, where x Het , DN , ANb
K x , NH 4 cNH 4 K x , IP cIP

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Reactive Transport Modeling

Table 9.10 Kinetic parameters in the CW2D biokinetic model (Langergraber and Šimůnek, 2005).
Parameter

Description [unit]

Hydrolysis

Value

For 20 °C (10 °C)

Kh

Hydrolysis rate constant [1/d]

3 (2)

KX

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

0.1 (0.22)*

Heterotrophic bacteria (aerobic growth)μH

Maximum aerobic growth rate on CR [1/d]bH

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

Khet,O2

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

0.2

Khet,CR

Saturation/inhibition coefficient for substrate [mg CODCR/l]2

Khet,NH4N

Saturation/inhibition coefficient for NH4 (nutrient) [mg N/l]

0.05

Khet,IP

Saturation/inhibition coefficient for P [mg N/l]

0.01

6 (3)

Heterotrophic bacteria (denitrification)
μDN

Maximum aerobic growth rate on CR [1/d]4.8 (2.4)

KDN,O2

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

0.2

KDN,NO3N

Saturation/inhibition coefficient for NO3 [mg N/l]

0.5

KDN,NO2N

Saturation/inhibition coefficient for NO2 [mg N/l]

0.5

KDN,CR

Saturation/inhibition coefficient for substrate [mg CODCR/l]

4

KDN,NH4N

Saturation/inhibition coefficient for NH4 (nutrient) [mg N/l]

0.05

KDN,IP

Saturation/inhibition coefficient for P [mg N/l]

0.01

Ammonia oxidizing bacteria (Nitrosomonas spp.)
μANs

Maximum aerobic growth rate on SNH [1/d]0.9 (0.3)

bANs

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

KANs,O2

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

1

KANs,NH4N

Saturation/inhibition coefficient for NH4 [mg N/l]

0.5 (5.5)*

KANs,IP

Saturation/inhibition coefficient for P [mg N/l]

0.01

Nitrite oxidizing bacteria (Nitrobacter spp.)
μANb

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

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

KANb,O2

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

0.1

KANb,NO2N

Saturation/inhibition coefficient for NO2 [mg N/l]

0.1

KANb,NH4N

Saturation/inhibition coefficient for NH4 (nutrient) [mg N/l]

0.05

KANb,IP

Saturation/inhibition coefficient for P [mg N/l]

0.01

*Langergraber (2007).

Modeling Multicomponent Reactive Transport in Constructed Wetlands

Table 9.11 Temperature dependences, stoichiometric parameters, composition parametersand parameters describing oxygen transfer in the CW2D biokinetic model (Langergraberand Šimůnek, 2005).
Parameter

Description [unit]

Value

Temperature dependencies (activation energy [J/mol] for Arrhenius equation)
Tdep_het

Activation energy for processes caused by XH [J/mol]

47,800

Tdep_aut

Activation energy for processes caused by XA [J/mol]

69,000

Tdep_Kh

Activation energy hydrolyses [J/mol]

28,000

Tdep_KX

Activation energy factor KX for hydrolyses [J/mol]−53,000*

Tdep_KNHA

Activation energy for factor KNHA for nitrification [J/mol]−160,000*

Stoichiometric parameters
fHyd,CI

Production of CI in hydrolysis

0.0

fBM,CR

Fraction of CR generated in biomass lysis

0.1

fBM,CI

Fraction of CI generated in biomass lysis

0.02

YHet

Yield coefficient for XH

0.63

YANs

Yield coefficient for XANs

0.24

YANb

Yield coefficient for XANb

0.24

Composition parameters
iN,CR

N content of CR [g N/g CODCR]

0.03

iN,CS

N content of CS [g N/g CODCS]

0.04

iN,CI

N content of CI [g N/g CODCI]

0.01

iN,BM

N content of biomass [g N/g CODBM]

0.07

iP,CR

P content of CR [g P/g CODCR]

0.01

iP,CS

P content of CS [g P/g CODCS]

0.01

iP,CI

P content of CI [g P/g CODCI]

0.01

iP,BM

P content of biomass [g P/g CODBM]

0.02

cO2_sat_20

Saturation concentration of oxygen [g/m3]

9.18

Tdep_cO2_sat

Activation energy for saturation concentration of oxygen [J/mol]−15,000

rate_O2

Re‐aeration rate [1/d]240Oxygen*Langergraber (2007).

9.3.2

CWM1 Biokinetic Model

9.3.2.1

Stoichiometric Matrix and Reaction Rates

Table 9.12 shows the stoichiometric matrix of reactions in CWM1, Table 9.13
the ­stoichiometric coefficients for ammonium nitrogen, and Table 9.14 the reaction rates.

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Table 9.12 CWM1 stoichiometric matrix (Langergraber et al., 2009b; see Table 9.17 for definitions of the stoichiometric coefficients).
i→j

Process

↓

1

2

3

4

5

6

7

8

9

10

11

12

13

14

Component SO

SF

SA

SI

SNH

SNO

SSO4

SH2S

XS

XI

XH

XA

XFB

XAMB XASRB XSOB

expressed
as →

COD

COD

COD

N

N

S

S

COD COD COD COD COD COD

O2

1 Hydrolysis
2 Aerobic growth of XH
on SF

1

1
YH

3 Anoxic growth of XH
on SF
4 Aerobic growth of XH
on SA

1

ν2,5

−1/YH

ν3,5

1
YH

5 Anoxic growth of XH
on SA
6 Lysis of XH
7 Aerobic growthof XA on SNH

4.57 YA
YA

fHyd,SI ν1,5

1 − fHyd,SI
−1/YH

−1/YH

ν4,5

−1/YH

ν5,5
ν6,5

fBM,SFiN ,BM

8 Lysis of XA

fBM,SF

9 Growth of XFB−1/YFB

10 Lysis of XFB

fBM,SF

1 YFB
YFB

ν8,5

−1
1
1 YH
2.86 YH

11

1 YH
2.86 YH
1 1/YA
YA

1
νLysis fBM,XI −1
1
νLysis fBM,XI

ν9,5
ν10,5

−1
1

νLysis fBM,XI

−1

15

COD

16

COD

11 Growth of XAMB

−1/YAMB12 Lysis of XAMB
13 Growth of XASRB
14 Lysis of XASRB
15 Aerobic growthof XSOB on SH2S

−1/YASRB

2 YSOB
YSOB

fBM,SF

16 Anoxic growthof XSOB on SH2S
17 Lysis of XSOBν Lysis = 1 − fBM,SF − fBM,XI

fBM,SF

ν11,5
ν12,5

fBM,SF

ν13,5

1
1 YASRB 1 YASRB
2 YASRB 2 YASRB

ν14,5

νLysis fBM,XI−1
1

νLysis fBM,XI

−1

ν15,5

1/YSOB−1/YSOB

1

ν16,5

1 YSOB 1/YSOB
0.875 YSOB

−1/YSOB1

ν17,5

νLysis fBM,XI

−1

466

Reactive Transport Modeling

Table 9.13 Stoichiometric coefficients for ammonia nitrogen (see Table 9.17 for definitionsof the composition and stoichiometric parameters).
ν1,5 = iN,XS – (1 – fHYD,SI) * iN,SF – fHYD,SI * iN,SI
ν2,5 = ν3,5 = iN,SF/YH – iN,BM
ν4,5 = ν5,5 = ν11,5 = ν13,5 = ν15,5 = ν16,5 = –iN,BM
ν6,5 = ν8,5 = ν10,5 = ν12,5 = ν14,5 = ν17,5 = iN,BM – fBM,SF * iN,SF – (1 – fBM,SF – fBM,XI) * iN,XS – fBM,XI * iN,XI
1
ν7,5 = i
N ,BMYA
ν9,5 = iN,SF/YFB – iN,BM

9.3.2.2

Model Parameters

Table 9.15 shows the kinetic parameters in the CWM1 biokinetic model; Table 9.16
temperature dependences, stoichiometric parameters, composition parameters andparameters describing oxygen transfer as described in Langergraber et al. (2009b).

9.4 ­Simulation Results for Vertical Flow ConstructedWetlands Treating Domestic WastewaterThis section shows typical simulation results for VF CWs. As described by Langergraber(2008), VF pilot‐scale CWs (Figure 9.1) have been operated in the technical laboratory
hall of the Institute of Sanitary Engineering at BOKU University in Vienna, Austria. The
systems had a surface area of 1 m2 and were loaded four times per day with mechanicallypre‐treated municipal wastewater. The 60 cm main layer consisted of sand with a grain
size of 0.06–4 mm (d10 = 0.2 mm; d60 = 0.8 mm). The intermediate layer (gravel 4–8 mm)
prevents fine particles from being washed out into the drainage layer (gravel 16–32 mm).
For the numerical simulations, only the main layer was considered. The transportdomain (i.e. a vertical cross‐section of the main layer) was discretized into 11 columns
and 40 rows. This resulted in a two‐dimensional finite element mesh consisting of 440
nodes and 780 finite elements. An atmospheric boundary condition is assigned to the
top of the system, a constant pressure head boundary condition with constant head of−2 cm (Langergraber, 2008).
Table 9.17 shows three parameter sets of the van Genuchten‐Mualem model (vanGenuchten, 1980) of the soil hydraulic properties used in simulations of water flow. The“HYDRUS parameter set for ‘Sand’’’ uses default soil hydraulic properties for sand provided by HYDRUS, the ‘Measured Ks and porosity’ parameter set measured values ofporosity and saturated hydraulic conductivity Ks, and the default residual water content
and shape parameters for sand. The third parameter set was obtained by inverse simulation. Measured effluent flow rates were used to estimate the soil hydraulic parameters(i.e. residual water content and shape parameters) using the inverse simulation routine
provided by HYDRUS (Šimůnek et al., 2011). Measured values of porosity and Ks were
kept constant. Figure 9.2 compares the measured and simulated effluent flow rates
using these three parameter sets. The simulated effluent flow rates are rather constantwhen using the default parameter set for sand due to the low Ks value. When usingModeling Multicomponent Reactive Transport in Constructed Wetlands

Table 9.14 Reaction rates in CWM1 part 1 (Langergraber et al., 2009b; see Tables 9.16 and 9.17
for definitions of rate coefficients).
R

Process/reaction rate rcj

Heterotrophic organisms
1) Hydrolysiskh *XS / X HKX

X FB

XS / X H

X FB

* XH

h * X FB

2) Aerobic growth of XH on SF (mineralization)
H*

SF
SO
SNH
K H2SH
SF
*
*
*
*
* XH
K SF SFSF SA
K OH SoK NHH SNHK H2SH SH2S*

3) Aerobic growth of XH on SA (mineralization)
g *

*

H*

SF
SF
K OH
SNO
SNH
*
*
*
*
K NHH SNH
K SF SFSF SA
K OH SoK NOH SNOK H2SH* XH
K H2SH SH2S*

4) Anoxic growth of XH on SF (denitrification)
H*

SA
SA
SO
SNH
K H2SH***** XH
K SA SASF SA
K OH SoK NHH SNHK H2SH SH2S*

5) Anoxic growth of XH on SA (denitrification)
g *

*

H*

SA
SA
K OH
SNO
SNH
*
*
*
*
K NHH SNH
K SA SASF SA
K OH SoK NOH SNOK H2SH* XH
K H2SH SH2S*

6) Lysis of XH
bH * XH
Autotrophic bacteria
7) Aerobic growth of XA on SNH (nitrification)
A*

SNH
SO
K H2SA*** XA
K NHA SNHK OA SoK H2SA SH2S*

8) Lysis of XAbA * XA
Fermenting bacteria
9) Growth of XFB (fermentation)
FB *SF
K H2SFBK OFB
K NOFBSNH***** X FBK SFB SFK H2SFB SH2S*K OFB SO
K NOFB SNO
K NHFB SNH(Continued )

467

468

Reactive Transport Modeling

Table 9.14 (Continued)
R

Process/reaction rate rcj10) Lysis of XFBbFB * XFBAcetotrophic methanogenic bacteria11) Growth of XAMBSAK H2SAMBK OAMBK NOAMB***K NOAMB SNO
K SAMB SAK H2SAMB SH2S*K OAMB SO
SNH** X AMBK NHAMB SNH
AMB *12) Lysis of XAMBbAMB * XAMB
Acetotrophic sulfate reducing bacteria
13) Growth of XASRBSASSO 4K H2SASRBK OASRB
K NOASRB****K NOASRB SNO
K SASRB SA
K SOASRB SSO 4
K H2SSASRB SH2S*K OASRB SO
SNH** X ASRBK NHASRB SNH
ASRB *

14) Lysis of XASRBbASRB * XASRB
Sulfide oxidizing bacteria
15) Aerobic growth of XSOB on SH2S
SOB *

SH2S
SO
SNH
* X SOB**K SSOB SH2SK OSOB SO
K NHSOB SNH

16) Anoxic growth of XSOB on SH2SSOB * SOB *

SH2S
SNO
K OSOBSNH**** X SOBK SSOB SH2SK NOSOB SNO
K OSOB SO
K NHSOB SNH

17) Lysis of XSOBbSOB * XSOB

measured values of porosity and saturated hydraulic conductivity (the ‘Measured
Ks + porosity’ parameter set), measured and simulated effluent flow rates match better;
however, the peak of the effluent flow rate is overpredicted. Using the ‘Fitted parameterset’, a good match between simulated and measured data can be achieved. This indicatesthat it is necessary to measure at least the porosity and the saturated hydraulic conductivity of the filter material to obtain reasonable simulation results for water flow.
Table 9.18 shows measured and simulated concentrations of ammonia and nitrate
nitrogen (NH4‐N and NO3‐N, respectively) for the VF pilot‐scale CWs with twoModeling Multicomponent Reactive Transport in Constructed Wetlands

Table 9.15 Kinetic parameters in the CWM1 biokinetic model (Langergraber et al., 2009b).
Parameter

Description [unit]

Value

Kh

Hydrolysis rate constant [1/d]

3 (2)

KX

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

0.1 (0.22)

H

Correction factor for hydrolysis by fermenting bacteria [‐]0.1

Hydrolysis

For 20 °C (10 °C)

Heterotrophic bacteria (aerobic growth and denitrification)μH

Maximum aerobic growth rate on SF and SA [1/d]

6 (3)

g

Correction factor for denitrification by XH [‐]

0.8

bH

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

KOH

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

0.2

KSF

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

2

KSA

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

4

KNOH

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

0.5

KNHH

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

0.05

KH2SH

Saturation/inhibition coefficient for SH2S [mg S/l]140

Autotrophic bacteria
μA

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

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

KOA

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

1

KNHA

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

0.5 (5)KH2SA

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

140

Fermenting bacteria
μFB

Maximum aerobic growth rate for XFB [1/d]3 (1.5)bFB

Rate constant for lysis [1/d]

0.02

KOFB

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

0.2

KSFB

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

28

KNOFB

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

0.5

KNHFB

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

0.01

KH2SFB

Saturation/inhibition coefficient for SH2S [mg S/l]140

Acetotrophic methanogenic bacteria
μAMB

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

0.085

bAMB

Rate constant for lysis [1/d]

0.008

KOAMB

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

0.0002

KSAMB

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

56

KNOAMB

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

0.0005KNHAMB

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

0.01

KH2SAMB

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

140
(Continued )

469

470

Reactive Transport Modeling

Table 9.15 (Continued)
Parameter

Description [unit]

Value

Acetotrophic sulfate reducing bacteriaμASRB

Maximum aerobic growth rate for XASRB [1/d]bASRB

Rate constant for lysis [1/d]0.012

KOASRB

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

0.0002

KSASRB

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

24

KNOASRB

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

0.0005

0.18

KNHASRB

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

0.01

KSOASRB

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

19

KH2SASRB

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

140

Sulfide oxidizing bacteria
μSOB

Maximum aerobic growth rate for XSOB [1/d]

5.28

SOB*

Correction factor for anoxic growth of XSOB [‐]

0.8

bSOB

Rate constant for lysis [1/d]

0.15

KOSOB

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

0.2

KNOSOB

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

0.5

KNHSOB

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

0.05

KSSOB

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

0.24

*Typing error in the original CWM1 publication.

different sandy filter materials used for the main layer. Besides the sand with a grain sizeof 0.06–4 mm, sand with a grain size of 1–4 mm was also tested. The different levels of
the NO3‐N effluent concentrations for the two filter materials could be simulated. The
effluent concentrations of NO3‐N for the 1‐4 mm substrate have been higher, because
less readily degradable organic matter is produced by hydrolysis that could be utilized
for denitrification in deeper layers (Langergraber, 2003).
For the VF pilot‐scale CWs with main layer of 0.06–4 mm sand, the distribution of
microbial and bacterial biomass in different depths of the filter was also measured(Tietz et al., 2007). Converting the measured data into biomass COD results in meanvalues of 3400 to 5100 µg COD/g DW (dry weight of the substrate, i.e. sand) for the firstcentimetre of the main layer, 1100 to 2600 µg COD/g DW from 1–5 cm, and 640 to
1400 µg COD/g DW from 5–10 cm, respectively. Most of the biomass could be found in
the upper 10 cm of the VF bed (Langergraber et al., 2007).
Simulated microbial biomass COD in the first centimetre of the main layer isbetween 5600 and 3400 µg COD/g DW (the range of the measured values) whenusing heterotrophic lysis rates of between 0.25 and 0.35 d−1. Figure 9.3 compares­calculated (from substrate‐induced respiration) and simulated microbial biomass
COD in different depths of the main layer for a heterotrophic lysis rate of 0.30 d−1.
When comparing measured and simulated biomass COD in different depths of themain layer, simulations seem to overpredict biomass COD in 1–5 cm depth andunderpredict biomass COD in 5–10 cm depth. This could be an indication that theModeling Multicomponent Reactive Transport in Constructed Wetlands

Table 9.16 Temperature dependences, stoichiometric parameters, composition parametersand parameters describing oxygen transfer in the CW2D biokinetic model (Langergraber et al., 2009b).
Parameter

Description [unit]

Value

Temperature dependences (activation energy [J/mol] for Arrhenius equation)
Tdep_HyKh

Activation energy hydrolyses [J/mol]

28,000

Tdep_HyKX

Activation energy factor KX for hydrolyses [J/mol]−54,400

Tdep_H

Activation energy for processes caused by XH [J/mol]

47,800

Tdep_A

Activation energy for processes caused by XA [J/mol]

75,800

Tdep_KNHA

Activation energy for factor KNHA for nitrification [J/mol]−160,000

Tdep_mueFB

Activation energy for XFB growth [J/mol]

47,800

Tdep_bFB

Activation energy for XFB lysis [J/mol]0

Tdep_AMB

Activation energy for processes caused by XAMB [J/mol]0

Tdep_ASRB

Activation energy for processes caused by XASRB [J/mol]0

Tdep_SOB

Activation energy for processes caused by XSOB [J/mol]0

Stoichiometric parameters
fHyd,SI

Production of SI in hydrolysis

fBM,SF

Fraction of SF generated in biomass lysis

0.05

fBM,XI

Fraction of XI generated in biomass lysis

0.1

YH

Yield coefficient for XH

0.63

YA

Yield coefficient for XA

0.24

YFB

Yield coefficient for XFB

0.053

YAMB

Yield coefficient for XAMB

0.032

YASRB

Yield coefficient for XASRB

0.05

YSOB

Yield coefficient for XSOB

0.12

0.0

Composition parameters
iN,SF

N content of SF [g N/g CODSF]

iN,SI

N content of SI [g N/g CODSI]

0.01

iN,XS

N content of XS [g N/g CODXS]

0.04

iN,XI

N content of XI [g N/g CODXI]

0.03

iN,BM

N content of biomass [g N/g CODBM]

0.07

cO2_sat_20

Saturation concentration of oxygen [g/m3]

9.18

Tdep_cO2_sat

Activation energy for saturation concentration of oxygen [J/mol]−15,000

rate_O2

Re‐aeration rate [1/d]

240

0.03

Oxygeninfluence of biomass growth on the hydraulic properties has to be considered in themodel (Langergraber et al., 2007).
Additionally, outdoor experiments were carried out at experimental CWs located at
the wastewater treatment plant at Ernsthofen (Lower Austria). The experimental plant­consisted of three parallel operating VF beds with a surface area of about 20 m2 each.

471

Reactive Transport Modeling

Figure 9.1 Schematic representation of theindoor pilot‐scale CW (values are in cm).

60

Main layer

15 10

INLET

Intermediate layer

OUTLET

Drainage layer

Table 9.17 Soil hydraulic parameters of the van Genuchten‐Mualem model for the 0.06–4 mm main
layer (shape parameters α, N and L: van Genuchten, 1980).
Residual
watercontent r(–)

Saturated
water
content s(–)α(cm−1)

N
(–)

L
(–)

Saturatedhydraulicconductivity Ks(cm/h)HYDRUS parameterset for ‘Sand’

0.045

0.43

0.145

2.68

0.5

29.7

Measured Ks andporosity

0.045

0.30

0.145

2.68

0.5

117

Fitted parameter set

0.013

0.30

0.147

2.42

0.636

117

Parameter

Shape parameters

4
Measured data

3.5

HYDRUS parameter set for ′Sand′
Measured Ks and porosity

Efflunet flow rate (L/h)

472

3

Fitted parameter set

2.5
2
1.5
1
0.5
0

0

1

2

3
4
Time after loading (h)56Figure 9.2 Measured and simulated effluent flow rates for a single feeding of 10 litres (‘HYDRUS
parameter set or Sand’, ‘Measured Ks and porosity’ and ‘Fitted parameter set’ represent the parameter
sets from Table 9.17).

Modeling Multicomponent Reactive Transport in Constructed Wetlands

Table 9.18 Median values of measured and simulated influent and effluent concentrations for NH4‐N
and NO3‐N in mg/l (adapted from Langergraber, 2003).
Influent

Effluent (0.06–4 mm sand)Effluent (1–4 mm sand)Parameter

Measured

Measured

NH4‐N

60.0

0.15

0.01

1.20

0.16

NO3‐N

3.0

38.5

41.1

50.0

63.0

Simulated

Measured

Simulated

Microbial biomass COD (μg/gDW)

7′000
Calculated from biomass C (SIR)

6′000

Simulated
5′000
4′000
3′000
2′000
1′000
0

0

5

10

15
Filter depth (cm)

20

25

30

Figure 9.3 Calculated and simulated microbial biomass COD in different depths of the main layer(Source: adapted from Langergraber et al., 2007; Langergraber, 2015).

The organic loads for bed 1 to 3 were 20, 27 and 40 g COD/m2/d, which correspond to
hydraulic loading rates of 32.2, 43.0, and 64.7 mm/d. The main layer of the filter consisted of 50 cm sandy substrate (gravel size 0.06–4 mm, d10 = 0.2 mm; d60 = 0.8 mm). The
beds are planted with common reed (Phragmites australis). The data gained from thisexperiment have been used to verify the temperature model incorporated into CW2D
(Langergraber, 2007).
The width of the transport domain in the numerical simulations was 4 m, and its
depth 0.8 m, while the transport domain itself was discretized into 31 columns and 33
rows. This resulted in a two‐dimensional finite element mesh consisting of 1023 nodes
and 1920 triangular finite elements. An atmospheric boundary condition was assigned
to the top of the system representing the influent distribution system, and a constantpressure head boundary condition (constant head of −4 cm) was assigned to one side ofthe drainage layer (Langergraber, 2007).
Results for water flow comparing measured and simulated effluent flow rates and thecumulative effluent of the experimental CW are shown in Langergraber (2007).
Simulated effluent flow rate and cumulative effluent flow match the measured data well.

473

Reactive Transport Modeling70
NH4-N simulated

60
COD, NH4-N (mg/l)

474

COD simulated
NH4-N measured
COD measured

50
40
30
20
10
0

0

2

4

6

8

10

12

14

16

18

20

Temperature (°C)

Figure 9.4 Measured and simulated COD and NH4‐N effluent concentrations using the modified
parameter set (adapted from Langergraber, 2007).

Using the calibrated flow model, the effluent concentrations during summer could be
simulated using the standard CW2D parameter set (Langergraber and Šimůnek, 2005).
However, measured COD and NH4‐N effluent concentrations at low temperatures
could not be simulated because hydrolysis and nitrification at low temperatures were
overpredicted. The standard CW2D parameter set considers temperature dependencies only for maximum growth, decay and hydrolysis rates. Figure 9.4 shows measured
and simulated COD and NH4‐N effluent concentrations using a modified parameter
set that includes temperature dependencies for the half‐saturation constants of hydrolysis and nitrification. Using this modified parameter set, it was possible to simulate the
COD and NH4‐N effluent concentrations at low temperatures (Langergraber, 2007).

9.5 ­Experiences and Challenges using Wetland Models
9.5.1

Description of Water Flow

It is generally agreed that the hydraulics have a high impact on the treatment performance of CWs. When simulating SSF CWs, the first step thus should be a good calibration of the water flow model. Experience shows that simulated effluent concentrations
can match the measured data only when the hydraulic behaviour of the system is welldescribed.
For VF CWs, the influence of the parameters describing the hydraulic properties ofthe filter material (such as for the van Genuchten‐Mualem function in HYDRUS;Šimůnek et al., 2011) is much higher than the influence of the parameters of the biokinetic model. To achieve a good calibration of the water flow model, it is advised tomeasure at least the porosity and the saturated hydraulic conductivity of the filter material and, if possible, the volumetric effluent flow rate between two intermittent loadings(Langergraber, 2011). With these measurements, it is possible to estimate the remainingModeling Multicomponent Reactive Transport in Constructed Wetlands

parameters describing the hydraulic properties of the filter material using the inverse
simulation implemented in HYDRUS (Šimůnek et al., 2011).
Morvannou et al. (2012) showed that macropores/cracks in some layers of a VF CW
might serve as preferential flow paths through which water can bypass most of the soil
porous matrix in a largely unpredictable way. This is especially true for the sludge layer
in French‐type VF CWs (Molle et al., 2005; Troesch and Esser, 2012). Water flow in such
systems cannot be modeled with uniform flow models (such as using the Richards
equation combined with the van Genuchten‐Mualem function in HYDRUS; Šimůnek
et al., 2011). The comparison between measured and simulated tracer breakthroughcurves indicates that the nonequilibrium approach (i.e. using a model that separately
describes flow and transport in preferred flow paths and slow or stagnant pore regions)seems to be more appropriate for simulating preferential flow. Such a dual‐porosity
model therefore also needs to be incorporated into the software tools to describe waterflow and solute transport accurately in French VF CWs.
For HF CWs, in which the filter material is usually gravel and the saturated hydraulicconductivity is much larger than the actual water flow in the filter, tracer experiments
are usually used to calibrate the water flow and single solute transport models.
9.5.2 Values of the Biokinetic Model Parametersand Influent Fractionation
Bacteria in CWs behave similarly to those in activated sludge systems. Based on thisassumption, Langergraber (2001), when developing the first biokinetic model for CWs,
proposed that parameters of the biokinetic models developed for activated sludge systems should be applicable to describe processes in CWs as well. This assumption was
confirmed when it was shown that a good match between measured and simulated
concentrations can be achieved when the hydraulic behaviour of the system is welldescribed (see above). Additionally, Morvannou et al. (2011) found good agreement
between measured and calculated volumetric nitrification rates (Table 9.19).
When using the biokinetic models such as CW2D or CWM1, it is therefore advised
not to change the default parameters of the biokinetic model, except for good reasons.
However, parameters characterizing the wastewater are related to the chosen biokinetic
model. Influent fractionation has a high impact on the simulation results and needs tobe adapted for each simulation study. These parameters include (1) fractionation of
influent COD (i.e. estimation of different COD model fractions from measured total
COD) and (2) organic N content of different COD fractions.
Table 9.19 Comparison of measured and calculated volumetric nitrification rates (adaptedfrom Morvannou et al., 2011).

MethodMeasured with solid respirometry

Results [mg O2/lsample/h]

32–50(mean = 41, SD = 9; 2 values)

Calculated fromsimulation results*

30.5*From simulations using parameters for the biokinetic model from activated sludge systems.

475

Reactive Transport Modeling150

NH4 inflow
Half NH4 inflow
No NH4 inflow

100
NH4out [mg/I]

476

50

0

0

20

40

60

80

100

120

t [d]

Figure 9.5 Influence of inflow NH4‐N concentrations on effluent NH4‐N concentrations (adapted from
Langergraber and Morvannou, 2014).

Rizzo et al. (2014) described the setup of a model to simulate experimental data froma HF CW fed with artificial wastewater. During the experiments, the only nitrogenparameter measured in influent was TKN (Total Kjehldal Nitrogen). As the model
requires influent concentrations of ammonia nitrogen, the organic N content of different COD fractions had to be adapted from standard values for the type of used artificial
wastewater. This results in different ratios of ammonia nitrogen to TKN. Figure 9.5
shows the impact of different influent concentrations of ammonia nitrogen on simulated effluent concentrations. When all influent TKN is assumed to be ammonia (i.e. noorganic nitrogen is present), simulated effluent concentrations of ammonia nitrogen are
higher than measured effluent concentrations. In contrast, when all influent TKN isassumed to be organic nitrogen (i.e. no ammonia is present), simulated effluent concentrations are too low.
Pucher and Langergraber (2015) simulated vertical flow filters treating domestic
wastewater using experimental data from Dal Santo et al. (2010). The main layer of thefilters consisted of sand with a grain size of 1–4 mm or zeolite with a grain size of
2–5 mm. Both filters had an impounded drainage layer. After calibrating the flow modelfor the sand and zeolite filters (Table 9.20), the procedure for calibrating the biokinetic
model was as follows: the standard parameter set of the CW2D biokinetic model(Langergraber and Šimůnek, 2012) was used in the first simulation of the sand filter(‘simulated sand 1’ in Table 9.21). This resulted in overprediction of nitrification, that is,simulated ammonia nitrogen concentrations were much lower than measured data.
After reducing the maximum nitrification rate from 0.9 to 0.175 d−1, the simulated
effluent concentrations of ammonia nitrogen matched measured data well (‘simulated
sand 2’ in Table 9.21). After adding the measured adsorption isotherms according to
Dal Santo et al. (2010) and a first‐order rate coefficient for nonequilibrium adsorptionModeling Multicomponent Reactive Transport in Constructed Wetlands

Table 9.20 Estimated soil hydraulic parameters of the van Genuchten‐Mualem model (shapeparameters α, N and L: van Genuchten, 1980).
Shape parameters

Parameter

Residual watercontent θr(–)

Saturated watercontent θs(–)α(cm−1)

N
(–)

L
(–)

Saturated hydraulicconductivity Ks(cm/min)

Sand (1–4 mm)

0.063

0.37

0.124

3.2

0.49

55

Zeolite (2–5 mm)

0.045

0.42

0.096

4.6

1.27

154

Table 9.21 Measured and simulated influent and effluent concentrations (in mg/l, measured data:
average values and standard deviations in brackets, simulated data: average values over 1 day).
Parameter

Influent
Effluent(sand)

Effluent(zeolite)

CR

CS

CI

COD

NH4‐N

NO2‐N

NO3‐N

Measured–

Simulated

274

–

–

294

93

0.008

0.59

100

20

–

93

0.008

0.59

Measured–––35 (5)

14.5 (4.6)

0.026 (0.040) 70.8 (8.4)

Simulated sand 1
Simulated sand 2

0.17 0.08

31.2

31.5

0.42

<0.00385.7

0.14 0.01

29.4

30.0

15.3

0.016

76.2

Measured––29 (9)

0.06 (0.05) 0.52 (1.10)

51.8 (4.6)

Simulated zeolite

0.16 0.01

29.1

29.3

0.27

43

–

<0.003of 0.01 d−1, a good match between simulated and measured data could be obtained forthe zeolite filter (‘simulated zeolite’ in Table 9.21).
Pálfy and Langergraber (2014) simulated experimental results from batch‐fed column experiments using the CWM1 biokinetic model. They described the need toadjust some parameters of the biokinetic model to be able to simulate anaerobic,
anoxic, and aerobic processes to occur in parallel. These phenomena occurred inpractice and can be explained by the local effect of root zone re‐aeration. Figure 9.6
shows measured and simulated sulfate concentrations before and after the adjustment of parameters of the biokinetic model. Batch experiments can be used to calibrate the biokinetic model parameters as there is no impact of water flow on thetreatment performance.
9.5.3

Clogging Model

Modeling of clogging processes is not possible using the HYDRUS Wetland module.
Langergraber and Šimůnek (2009) coupled the colloids attachment/detachment modelaccording to Bradford et al. (2003) (implemented in the standard HYDRUS module)with the CW2D biokinetic model. It was assumed that CS, the slowly biodegradableorganic matter (as defined by Langergraber and Šimůnek, 2005), consists of a particulate matter XS that can be divided into five different classes according to different

477

Reactive Transport Modeling
SO4-S

20

Measured concentrations
Model results
Concentration[mg L–1]

15

10

5

0

0

5

10
time [days]

15

20

SO4-S

20

Measured concentrations
Model results
15
Concentration[mg L–1]

478

10

5

0

0

5

10
time [days]

15

20

Figure 9.6 Measured and simulated sulfate concentrations for a batch‐fed column at 24 °C plantedwith Carex (left: with the standard parameter set of the biokinetic model; right: after adjusting
inhibition and half‐saturation coefficients to allow anaerobic, anoxic, and aerobic processes to occur
in parallel). Adapted from Pálfy (2013).

particle sizes (<1, 1–3, 3–10, 10–30, and 30–100 µm, respectively). It was further
assumed that particles are transported in the liquid phase until they are attached. Once
attached the particles undergo hydrolysis and cCR (readily biodegradable organic
matter; Langergraber and Šimůnek, 2005) in the liquid phase is produced. An additional assumption was that particles with different sizes have the same density anddegradability.
The model was tested using measurements of particle concentrations in different
depths within the 50‐cm main layer of the VF pilot‐scale CW, as described earlier.
Particle measurements at the inlet were used to calculate fractionation of COD influent.
Measured and simulated soluble particulate COD concentrations for the 10–30 µm particle class before and after loading of the VF filter along the filter depth are shown in
Figure 9.7. ‘Measured’ COD was derived from particle measurements. In general, theModeling Multicomponent Reactive Transport in Constructed Wetlands
70
10–30 μm

Particulate COD (mg/l)

60
50
40
30

Measured
Simulated - before loading

20

Simulated - after loading

10
0

0

10

20
30
Filter depth (cm)40

50

Figure 9.7 Comparison of measured and simulated particulate COD for the 10–30 µm particle class(adapted from Langergraber and Šimůnek, 2009).

first test showed a good agreement between measured and simulated particulate COD.
However, there is still a great need for further testing of the particle transport modeland for finding an optimal parameter set for various conditions present in constructedwetlands.
Several clogging models have been developed for BIO_PORE (Samsó and García,
2013). Samsó and García (2014) described the relationship between bacterial communities and accumulated solids, leading to clogging in a HF CW. The so‐called ‘Cartridge
Theory’ describes how the active bacterial zone moves in the filter. In this model, theeffect of the inert organic matter accumulated in pores upon the hydraulic conductivity
is not considered. Description of limited growth of bacteria was implemented by adding
two parameters. The first parameter provides a negative feedback term to the growthof all bacteria groups to prevent their unlimited growth in areas where substrateconcentrations are high (which is especially relevant for the influent zones of HF
CWs). The second parameter provides a negative feedback term to the growth equations, but in this case, it decreases the growth rate of bacteria due to progressive accumulation of inert solids in the pore space of the granular media. Samsó et al. (2015a)
described in their simulation study the effect of bacteria density and accumulated inert
solids on effluent pollutant concentrations, but again only without considering theeffect of organic matter accumulation on water flow. Samsó et al. (2016) additionallydescribed the effects of a pore size reduction on the hydraulic conductivity using thebiological clogging model proposed by Mostafa and Van Geel (2007). Using thisapproach, Samsó et al. (2016) were able to simulate realistic behaviour of HF CWs,
including overland flow and re‐infiltration of water in the unused filter material.
9.5.4

Models as CW Design Tools

Langergraber (2011) concluded that further developments of existing models areneeded to make them a useful and applicable tool for a CW design. A simplified

479

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Reactive Transport Modelingcomputer‐based CW design tool, based on process‐based numerical models, should be
developed that:
could be used with knowledge about a CW design, but without requiring special
knowledge about numerical modeling;●● allows designing CWs for different boundary conditions (such as different climaticconditions, wastewater characterization, filter material, etc.); and●● makes the description of the dynamic behaviour of the designed CW possible, thus
allowing demonstration of the greater robustness of CW treatment systems, forexample, for fluctuating inflows and peak loads.
●●

Several advances have been made to develop such a simplified design tool. Meyer andDittmer (2015) developed RSF_Sim, which supports the design of CWs for a combined
sewer overflow treatment: retention soil filters (RSFs). This simplified, yet robust andreliable, model was developed for design purposes based on experiences with the
HYDRUS Wetland module. RSF_Sim has only a few parameters and is therefore simple
to use. RSF_Sim was developed specifically for RSFs for German conditions. Pálfy et al.
(2015b) adapted RSF_Sim for CWs for a combined sewer overflow treatment for French
conditions (e.g. for different design rules and effluent requirements).
A similar approach was taken by Morvannou et al. (2015). The aim of their work was
to develop a simple model to support the design of French‐type VF CWs. Numericalsimulation using the HYDRUS Wetland module were first performed, varying a number of design parameters. The design parameters included the depth of the main layerof the first‐stage filter, the hydraulic loading rate, and the inlet COD concentration andtemperature. Effluent concentration of the first‐stage filter was then verified using
measured data and a surrogate model was developed to estimate COD and NH4‐N
removal in relation to the design parameters. Although the first results were promising,Morvannou et al. (2015) concluded that more work needs to be done to develop a robust
design model.

9.6 ­Summary and Conclusions
Interest in modeling processes in CWs has increased over the last 15 years. Several
mechanistic models to describe processes in subsurface flow CWs have been developed. However, the HYDRUS Wetland module is the only one that is commerciallyavailable and thus available for wider use.
Experiences with applying the HYDRUS Wetland module and other existing simulation tools can be summarised as follows:●●

Simulation studies often suffer from a lack of data. When the use of dynamic models
is anticipated, experiments have to be planned in a way that data for model calibration and validation are available. Data requirements are different for different models,
but always include careful planning of sampling frequency and analysed parameters(Meyer et al., 2015). The amount and nature of data needed for calibration depends
on the objectives of the simulation study. In general, for calibration of the water flow
model, more data are required for vertical flow CWs compared with horizontal flow
CWs. The amount of data required for calibrating reactive transport simulations

Modeling Multicomponent Reactive Transport in Constructed Wetlands

depends on biokinetic model parameters (e.g. influent fractionations), as well as the
dynamics of influent in the system.
●● Good calibration of the water flow model is a prerequisite for achieving a good match
between measured and simulated pollutant concentrations. If the water flow model iscalibrated, good results can be obtained in most applications when using the standard
parameter sets of the biokinetic CW2D and CWM1 models (Langergraber andŠimůnek, 2012). Influent fractionation (i.e. fractionation of influent COD and the N
and P contents of different COD fractions) has a high impact on simulation results
and thus is an essential part of calibrating reactive transport models. This is especiallytrue when simulating CWs treating other than domestic wastewater.
●● One of the main obstacles for the wider use of available simulation tools is that they
are rather complicated and difficult to run. Simplified, yet robust and reliable, models
for the design of CWs need to be developed (such as RSF_Sim, developed to support
the design of CWs treating combined sewer overflow; Meyer and Dittmer, 2015).

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