Special Section: Reactive
Transport ModelingGünter Langergraber*
Jirka Šimůnek

Two biokinetic models are presented for describing processes inconstructed wetlands for wastewater treatment that are implemented
in the HYDRUS so ware. Simula on
results show the use of both kine cmodels for horizontal flow constructed wetlands. Addi onally, theimportance of considering the eﬀects
of wetland plants is shown.
G. Langergraber, Ins tute of SanitaryEngineering and Water Pollu on Control,
Univ. of Natural Resources and Life SciencesVienna (BOKU), Muthgasse 18, A-1190
Vienna, Austria; and J. Šimůnek, Dep. ofEnvironmental Sciences, Univ. of California,
Riverside, CA 92521. *Corresponding author(guenter.langergraber@boku.ac.at).
Vadose Zone J.
doi:10.2136/vzj2011.0104
Received 3 Aug. 2011.

© Soil Science Society of America
5585 Guilford Rd., Madison, WI 53711 USA.

All rights reserved. No part of this periodical may
be reproduced or transmi ed in any form or by anymeans, electronic or mechanical, including photocopying, recording, or any informa on storage
and retrieval system, without permission in wri ng
from the publisher.

Reac ve Transport Modelingof Subsurface Flow ConstructedWetlands Using the HYDRUS
Wetland Module
Constructed wetlands (CWs) are engineered water treatment systems designed to remove
various types of contaminants. A large number of processes simultaneously contribute towater quality improvement in CWs. During the last decade, there has been a wide interestin the understanding of complex “constructed wetland” systems, including the developmentof numerical process-based models describing these systems. A number of process-based
numerical models for subsurface flow (SSF) CWs have been developed during the last few
years; however, most of them are either in an early stage of development or are available
only in-house. The HYDRUS wetland module is the only implementa on of a CW modelthat is currently publicly available. Version 2 of the HYDRUS wetland module includes twobiokine c model formula ons simula ng reac ve transport in CWs: CW2D and CWM1. In
CW2D, aerobic and anoxic transforma on and degrada on processes for organic ma er,
N, and P are considered, whereas in CWM1, aerobic, anoxic, and anaerobic processes fororganic ma er, N, and S are taken into account. We simulated horizontal flow CWs using
both biokine c models. Compared with the CWM1 implementa on in the RETRASO code,
the HYDRUS implementa on was able to simulate fixed biomass, which is of high importancefor obtaining realis c predic ons for the treatment eﬃciency of CWs. We also compared
simula on results for horizontal flow CWs obtained using both CW2D and CWM1 modules
that showed that CWM1 produces more reasonable results because it also considers
anaerobic degrada on processes. The influence of wetland plants on the simula on results
was also inves gated. Simulated biomass profiles in the filter were completely diﬀerent when
considering O2 release from roots, thus indica ng the importance of considering plant eﬀects.
Abbrevia ons: COD, chemical oxygen demand; CW, constructed wetland; HF, horizontal flow; SSF,
subsurface flow; VF, ver cal flow.

Constructed wetlands are systems that eﬃciently treat different typesof polluted water. Constructed wetlands are engineered treatment systems that optimize treatment 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 (e.g.,
Kadlec and Wallace, 2009). For a long time, CWs have, therefore, been considered “blackboxes,” and little effort has been made to understand the main processes leading to theremoval of contaminants.
During the last decade, models of different complexities have been developed for describing
the processes in SSF CWs. The main objectives for numerical modeling of CWs are toobtain a better understanding of governing biological and chemical transformation anddegradation processes, to provide insights into these “black box” systems, and to evaluate
and improve existing design criteria (Langergraber, 2008, 2011).
No free water level is visible in SSF CWs, and water flows, either horizontally or vertically,
through the porous fi lter media. Horizontal flow (HF) systems are often modeled byconsidering only saturated water flow conditions while the unsaturated zone is neglected.
A series or network of continuously stirred tank reactors are most frequently used todescribe the hydrodynamics of these systems, and reactions are modeled consideringvarious complexities. When modeling vertical flow (VF) CWs with intermittent loading,consideration of transient, variably saturated flow conditions is essential and required. Dueto the intermittent loading, these systems are highly dynamic, adding to the complexity

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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, 2011).
Only a few process-based numerical models have been developedthat are capable of modeling reactive transport in both HF and
VF CWs. According to Langergraber (2011), there are only three
tools that have been designed to describe the transformation anddegradation processes of wastewater pollutants in CWs, i.e., the
HYDRUS wetland module (Langergraber and Šimůnek, 2006,2011), PHWAT (Brovelli et al., 2009a, 2009b), and RETRASO(Ojeda et al., 2008; Llorens et al., 2011a, 2011b). Additionally,
there is a tool for modeling only organic matter removal and O2
transport (Wanko et al., 2006) and a biokinetic model implemented
in MIN3P that describes processes involved in the remediation ofcontaminated groundwater (Maier et al., 2009; De Biase et al., 2011).
Similarly to Wanko et al. (2006), Forquet et al. (2009) and Petitjean
et al. (2011) also modeled diphasic transfer of O2 in VF beds.
In this study, we used Version 2 of the HYDRUS wetland
module. Version 2 includes two biokinetic model formulations:(i) the CW2D module (Langergraber and Šimůnek, 2005), and(ii) the CWM1 (Constructed Wetland Model 1) (Langergraber
et al., 2009b). In CW2D, aerobic and anoxic transformationand degradation processes for organic matter, N, and P are taken
into account, whereas in CWM1, aerobic, anoxic, and anaerobic
processes for organic matter, N, and S are considered. The CWM1
model was developed with the main goal of providing a widely
accepted model formulation for biochemical transformationand degradation processes in SSF CWs. The HYDRUS wetland
module is the only implementation of a CW model that is currently
commercially available to the public.

6The HYDRUS Wetland Module
Principles

As described by Langergraber et al. (2009b), a number of submodels
are required to simulate a SSF CW. These submodels include:
1. the water flow model, describing water flow in the
porous media is of utmost importance,
2. the transport model, describing transport of constituents, as well as adsorption and desorption processes,
3. the biokinetic model, describing biochemical transformation and degradation processes,
4. the plant model, describing processes such as growth,decay, decomposition, nutrient uptake, and root O2
release, and5. the clogging model, describing clogging processes, i.e.,transport and deposition of suspended particulate matterand bacterial and plant growth that may reduce thehydraulic capacity or conductivity of the filter medium.

Table 1. Principles of the CW2D and CWM1 biokinetic models (numbers in parentheses give the number of processes or components).
Principle

CW2D

CWM1

Processes

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

O2 , organic matter,N, and P (12)O2 , organic matter, N, and S (16)Most of the submodels required for a complete wetland model,
with the exception of the clogging model and some processes of theplant model, are available in HYDRUS. The standard version of
HYDRUS numerically solves the Richards equation for saturated–unsaturated water flow and the convection–dispersion equation
for heat and solute transport. The flow equation incorporates asink term to account for water uptake by plant roots. The solutetransport 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., 2011).
The biochemical transformation and degradation processes aredescribed by the HYDRUS wetland module. In Version 2 of the
HYDRUS wetland module, two biokinetic models simulating thetransformation and degradation processes are implemented. Table
1 compares the principles of CW2D and CWM1.
1. The CW2D model (Langergraber and Šimůnek, 2005)
was mainly developed for modeling VF systems andtherefore includes only aerobic and anoxic transformation and degradation processes. These processes aredescribed for the main constituents of wastewater, i.e.,organic matter, N, and P.
2. The CWM1 model (Langergraber et al., 2009b) was
developed as a general model that describes biochemicaltransformation and degradation processes for organic
matter, N, and S in both HF and VF CWs. The CWM1
model describes all relevant aerobic, anoxic, andanaerobic biokinetic processes occurring in HF and VF
CWs and required to predict effluent concentrations oforganic matter, N, and S.
The influence of plants can be partly simulated using HYDRUS
as well. Langergraber (2005) investigated the plant uptake models
provided by HYDRUS (i.e., passive nutrient uptake coupled withwater uptake) and concluded that it was possible to simulate plant
uptake in high-loaded systems, e.g., systems treating mechanically
pretreated municipal wastewater. For low-strength wastewater,
the simulation results indicate that potential nutrient uptake isoverestimated using these models. Oxygen release via roots canbe modeled in a way similar to nutrient uptake (Toscano et al.,2009). It is not possible, however, to simulate growth, decay, anddecomposition of the wetland plants using HYDRUS. For moredetails on the mathematical formulations used to model uptake

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of water and solutes by plant roots, we refer to Šimůnek andHopmans (2009), who described in detail the considered approach,and to the HYDRUS technical manual (Šimůnek et al., 2011).
It is also not possible to simulate transport and depositionof suspended particulate matter and their influence on thehydraulic conductivity. This would be of importance for long-term
simulations that aim to predict the changes in long-term treatment
performance and, finally, the failure of SSF CWs due to clogging(Langergraber et al., 2009a). In HYDRUS, suspended particulatematter compounds have to be considered as solute compounds.

The Gujer Matrix Representa on of
Biokine c Models
It is common practice to present biokinetic models using the matrix
notation introduced by the International Water Association for
activated sludge models (Henze et al., 2000). The so-called Gujer
matrix consists of three parts, representing (i) stoichiometry, (ii)kinetic rate expressions, and (iii) composition. A simple model
representing aerobic heterotrophic bacteria growth and decay(adapted from Henze et al., 2000) was chosen as an example toillustrate the use of the Gujer matrix. Table 2 describes two processes(growth and decay of heterotrophic bacteria) and three components(biomass, substrate, and dissolved O2). Bacteria need energy tointegrate their C substrate and produce new biomass. Heterotrophs(XOHO) find their energy and their C source in an organic substrate(SB) and use dissolved O2 (SO2) as an electron acceptor under aerobic
conditions. Consequently, only part of the substrate used by bacteria
will directly contribute to biomass growth (1/YOHO), whereas theother part is oxidized to produce energy (1 − 1/YOHO).
In this example, the growth rate depends on the maximum
growth rate of the heterotrophic biomass (μ OHO,max), thebiomass concentration (XOHO), the availability of the substrate

to the bacteria (S B/(KSB,OHO + S B), where KSB,OHO is the halfsaturation coefficient for S B), and the availability of electron
acceptors (SO2/(KSO2,OHO + SO2), where KSO2,OHO is the halfsaturation coefficient for SO2). The ratios S B/(KSB,OHO + S B) andSO2/(KSO2,OHO + SO2) are the Monod-type equations that areused in this model formulation as switching functions for substrate,
nutrients, alkalinity, electron acceptors, and other components.
Similarly, when a process occurs only when a component is absent(e.g., dissolved O2 in anoxic processes), the switching function
takes the following form: KO2,OHO/(KO2,OHO + SO2).
The continuity check for every process is calculated by multiplying
the stoichiometric coefficients by the corresponding term in thecomposition matrix for every component and summing up fordifferent processes (because O2 is negative chemical O2 demand[COD], its coefficient must therefore be multiplied by −1).
Reaction rates for the three components discussed above arecalculated by summing up products of stoichiometric factors andprocess rates for the different processes involved. For example,
reaction rates for heterotrophic biomass (rXOHO), organic substrate(rSB), and O2 (rSO) are calculated as follows:
rX OHO = μ OHO,max

S O2

SB

K S B ,OHO + S B K SO ,OHO + SO2

× X OHO2− bOHO X OHOrS B =−×SB
1
μ OHO,max
YOHO
K S B ,OHO + S B
S O2
K SO ,OHO + SO2

X OHO

[1]

2

⎛ 1−YOHO ⎞⎟rSO =−⎜⎜⎜⎟⎟μ OHO,max
⎜⎝ Y
⎠⎟
OHO

×

S O2

SB

K S B ,OHO + S B K SO ,OHO + SO2

× X OHO

2

Table 2. Gujer matrix describing process kinetics and stoichiometry for heterotrophic bacterial growth in an aerobic
environment (adapted from Henze et al. (2000), using the nota-

tions of Corominas et al., 2010). Stoichiometric parameters: YOHO,
heterotrophic yield coefficient; kinetic parameters: μ OHO,max, maximum heterotrophic growth rate; KSB,OHO, half-saturation coefficientfor substrate; KSO2,OHO, half-saturation coefficient for O2; bOHO,
heterotrophic decay rate.

Mass balance ←HeteroDissolved
trophic
Substrate O2
biomass (mg (mg COD (mg COD→ Continuity COD L−1) L−1)
L−1)
Component (i) 123

Process ( j)

XOHO

SB

SO2

1. Growth

1−1/YOHO −(1 −μ OHO,max[S B/
YOHO)/ (KSB,OHO + S B)]
YOHO ×[S /(KO2
SO2,OHO+ SO2)]XOHO

2. Decay−1−1

Process rate ρ j

bOHO XOHO− bOHO X OHOThe CW2D and CWM1 Biokine c Models
Table 3 compares the components defi ned in the CW2D and
CWM1 model formulations. For detailed information about the
CW2D and CWM1 biokinetic models, as well as their parametervalues, see the original studies, i.e., Langergraber and Šimůnek
(2005) and Langergraber et al. (2009b), respectively. As describedabove, both biokinetic models consider processes affecting organic
matter and N. Additionally, CW2D considers processes affecting
P, whereas CWM1 considers processes affecting S. It is assumed
that all components except bacteria are soluble (including theparticulate COD fraction) and that bacteria are immobile. Organic
N (in CW2D and CWM1) and organic P (in CW2D) are modeled
as part of the COD. Note that because wastewater constituentsconsidered in the CW2D and CWM1 biokinetic models are

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Table 3. Comparison of CW2D (Langergraber and Šimůnek, 2005) and CWM1 (Langergraber et al., 2009b) components.
CW2D: organic matter, N, P

CWM1: organic matter, N, S

CW2D components

Soluble components

1. SO: dissolved O2
2. CR: readily biodegradable soluble chemical oxygen demand (COD)
3. CS: slowly biodegradable soluble COD
4. CI: inert soluble COD
5. XH: heterotrophic bacteria
6. XANs: autotrophic NH4 –oxidizing bacteria (Nitrosomonas spp.)
7. XANb: autotrophic NO2–oxidizing bacteria (Nitrobacter spp.)
8. NH4N: NH4 –N and NH3 –N
9. NO2N: NO2–N
10. NO3N: NO3 –N
11. N2: elemental N2
12. PO4P: PO 4 –P

1. SO: dissolved O2
2. SF: fermentable, readily biodegradable soluble COD
3. SA: fermentation products as acetate
4. SI: inert soluble COD
5. SNH: NH4 –N and NH3 –N
6. SNO: NO3 –N and NO2–N
7. SSO4: SO 4 –S
8. SH2S: H2 S-S
Particulate components
9. XS: slowly biodegradable particulate COD
10. XI: inert particulate COD
11. XH: heterotrophic bacteria
12. XA: autotrophic nitrifying bacteria
13. XFB: fermenting bacteria
14. XAMB: acetotrophic methanogenic bacteria
15. XASRB: acetotrophic SO 4–reducing bacteria
16. XSOB: S2−–oxidizing bacteria

Additional component (in the HYDRUS implementation)
13. nonreactive tracer
Nitrification is modeled as a two-step process

Additional component (in the HYDRUS implementation)
17. nonreactive tracer

Table 4. Components of CW2D and CWM1 in the liquid (L) and solid (S) phases. See Table 3 for component definitions.
Component

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

CW2D
CWM1

L
L

L+S
L+S

L+S
L+S

L+S
L+S

S
L+S

S
L

S
L

L+S
L

L
L+S

L
L+S

L
S

L+S
S

L+S
S

–
S

–
S

–
S

–
L+S

different, there is no direct conversion between the two modelcomponents. Component symbols (e.g., SO for dissolved O2), as
defined in Table 3, are used throughout the text and in figures andtables when referring to various chemicals and bacterial groups.
Table 4 summarizes in what phase (i.e., liquid or solid or both) the
CW2D and CWM1 components are defi ned. For components
defined in both phases (L + S), adsorption and desorption
processes can be considered. As mentioned above, suspended
particulate organic matter compounds, i.e., slowly biodegradable(XS) and inert (XI) particulate COD in CWM1, are considered assolute compounds. Note that the number of components in Table
4 is increased by one compared with that given in Table 3 for bothCW2D and CWM1. In both models, a nonreactive tracer that is
independent of other components and that can be used to derive
the hydraulic retention time is added in the HYDRUS wetland
module. This nonreactive tracer is defined in both liquid and solid
phases (Langergraber and Šimůnek, 2011).
Table 5 compares the processes defined in the CW2D and CWM1
model formulations. Only aerobic and anoxic processes are definedin CW2D. Two main types of bacteria, i.e., heterotrophic andautotrophic bacteria, are considered. One special feature of
CW2D is that nitrification is modeled as a two-step process, i.e.,from NH3 via NO2 to NO3 . Because anaerobic processes are

additionally defi ned in CWM1, six different types of bacteria
need to be considered in this model. In addition to heterotrophic
and autotrophic bacteria, fermenting, acetotrophic methanogenic,
acetotrophic SO4 –reducing, and S2−–oxidizing bacteria are also
considered to account for the main anaerobic processes.
For detailed information on additional model equations (e.g., oxygen
re-aeration) and on how to set up models for SSF CWs in HYDRUS,
see the manuals for the HYDRUS wetland module (Langergraberand Šimůnek, 2006, 2011). For more general information aboutthe HYDRUS family of codes, see Šimůnek et al. (2008), andfor detailed information about the soft ware (such as governing
equations for water flow, solute transport, adsorption–desorption
processes, the plant uptake model, and boundary conditions), see
the HYDRUS technical manual (Šimůnek et al., 2011).

6 Simula

on Results

Numerical Verifica on of Biokine cModel Implementa on

Our numerical verification focused on the two biochemical
models. The water f low and solute transport parts of the
HYDRUS model are widely used and generally accepted to beverified (Šimůnek et al., 2008).

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Table 5. Comparison of CW2D (Langergraber and Šimůnek, 2005) and CWM1 (Langergraber et al., 2009b) processes. See Table 3 forcomponent definitions.
CW2D

CWM1

Heterotrophic bacteria:

Heterotrophic bacteria:

1. Hydrolysis: conversion of CS into CR.
2. Aerobic growth of XH on CR(mineralization of organic 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.

1. Hydrolysis: conversion of XS into SF.
2. Aerobic growth of XH on SF (mineralization of organic matter).
3. Aerobic 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 XFB.
Acetotrophic methanogenic bacteria:
11. Growth of XAMB: Anaerobic growth of acetotrophic, methanogenic bacteria XAMB on acetate SA.
12. Lysis of XAMB.
Acetotrophic sulphate reducing bacteria:
13. Growth of XASRB: Anaerobic growth of acetotrophic, sulphate reducing bacteria.
14. Lysis of XASRB.
Sulphide oxidizing bacteria:
15. Aerobic growth of XSOB on SH2S: The opposite process to process 13, the oxidation of SH2S to SSO4.
16. Anoxic growth of XSOB on SH2S: Similar to process 15 but under anoxic conditions.
17. Lysis of XSOB.

To numerically verify the implementation of the two biokinetic
models, the reactions involving organic matter were evaluatedusing a simple example. Due to different components and processes
considered by the CW2D and CWM1 models, no more complex
verification of the model implementation could be made.
In this simple example, it was assumed that only heterotrophic
bacteria (XH) were present, i.e., that only processes of hydrolysis,
mineralization of organic matter, and lysis of XH took place.
Initial concentrations were set, for CW2D, to 1 mg L−1 dissolved
O2 (SO), 1 mg L−1 readily biodegradable soluble COD (CR),
10 mg L−1 slowly biodegradable soluble COD (CS), 10 mg kg−1
XH, and 1 mg L−1 PO4 –P, and for CWM1, 1 mg L−1 SO, 1 mg
L−1 fermentable, readily biodegradable soluble COD (SF), 10
mg L−1 slowly biodegradable particulate COD (XS), and 10 mg
kg−1 XH. Initial PO4 –P concentrations were set to values larger
than zero to prevent inhibition of processes due to the lack ofP, which is required as a nutrient. Initial concentrations for allother components were zero (including initial concentrations
for N components—note that NH3 is released during hydrolysis
and then utilized by bacteria during growth). For the numericalverification, we chose to use low concentrations to verify a greaternumber of processes. For example, having high initial NH 3
concentrations would prevent us from detecting the very low
release of N during hydrolysis.
A vertical domain of 20 by 20 cm was discretized into three columns
and 21 rows. This resulted in a two-dimensional finite element meshconsisting of 63 nodes and 80 triangular finite elements. No flow
was considered into or out of the domain. Default HYDRUS soil
hydraulic parameters (as per the van Genuchten–Mualem modelwith no hysteresis; see Šimůnek et al., 2011) for sand were used. Sand
was chosen in this example because it is commonly used as a filter
material in VF CWs. The water table was set to be 8 cm above thebottom boundary and the simulations were run for 1 d.
Figure 1 shows the simulation results for an observation nodelocated 2 cm above the water table. The location above the watertable was chosen to compare aerobic processes implemented in
CW2D and CWM1 because different processes occur below thewater table after O2 is consumed (note that anaerobic processes
are implemented in CWM1). The volumetric water content at
this observation node was 42%. Figure 1 shows that the same
results could be obtained using both biokinetic models. The

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Comparison of Results Obtained Using
the Implementa on of CWM1 into HYDRUS
and RETRASO
Llorens et al. (2011a, 2011b) implemented CWM1 into the
RETRASO code. The CWM1-RETRASO code is based on thetwo-dimensional finite-element code, RetrasoCodeBright (RCB),
which simulates reactive transport of dissolved and gaseous species
for nonisothermal saturated or unsaturated flow domains. In RCB,
the first module calculates the flow variables and passes them tothe second module, which calculates the reactive transport (Rezaei
et al., 2005; Saaltink et al., 2003).
Llorens et al. (2011b) simulated, as a test case, a HF bed witha length of 10.3 m and a width of 5.3 m. The water level in the
bed was 0.5 m. The first 0.3 m of the bed, the mixing zone, wasfi lled with coarse gravel. Llorens et al. (2011b) simulated only themain layer of the bed (with a length of 10 m fi lled with gravelwith a d60 of 10 mm and porosity of 41%), whereas our HYDRUS
implementation considered the mixing zone as well (the red circle
in Fig. 2B). Figure 2B also shows a typical flow path in a HF bed.

Fig. 1. Simulation results obtained for an observation node located 2
cm above the water table for dissolved O2 (SO), readily biodegradable
soluble chemical O2 demand (COD) (CR), slowly biodegradable
soluble COD (CS), and heterotrophic bacteria (XH) using the
CW2D model (top) and for SO, fermentable, readily biodegradable
soluble COD (SF), slowly biodegradable particulate COD (XS), and
XH using the CWM1 model (bottom).

slowly biodegradable COD (CS in CW2D and XS in CWM1)
is hydrolyzed, while readily biodegradable COD (CR in CW2D
and SF in CWM1) is produced. The readily biodegradable COD
is then mineralized (i.e., converted into CO2 and H2O) due to
aerobic growth of XH. Once the readily biodegradable COD isused up, bacteria start dying at a constant rate. During this lysis
process, bacteria are decomposed into the slowly biodegradableorganic matter and a release of inert organic matter and NH3
takes place (not shown in Fig. 1). At the end of the 1-d simulation,
the NH 3 –N and inert organic matter concentrations at theobservation node were 0.36 and 0.31 mg L−1, respectively.

In the HYDRUS implementation, the vertical domain of 10.3 and0.6 m was discretized into 33 columns and 23 rows, resulting ina two-dimensional finite-element mesh consisting of 805 nodes
and 1496 triangular fi nite elements. An atmospheric boundary
condition with a water flux of 2.1 m d−1 to represent wastewaterloading was applied at the top of the mixing zone, whereas theeffluent boundary was represented using a constant-head boundary
condition (0.5 m) at the bottom of the right end of the bed. Dueto the lack of data about the mixing zone, the same material
parameters as for the main zone were used. Initial concentrationsof 1 mg L−1 were assigned for all solute compounds. Initialconcentrations for bacteria were set to 1 mg kg−1 for all nodes
below the water table and zero above. Various simulations with
HYDRUS were run for 50 d.

This simple example shows that both biokinetic models have been
implemented correctly in the HYDRUS wetland module. Due
to different components and processes considered by the CW2D
and CWM1 models, no more complex comparison of the model
implementations could be made.
Fig. 2. Implementation of the horizontal flow bed in RETRASO(top, Llorens et al., 2011b) and HYDRUS (bottom, dimensions inmeters). The red circle indicates the mixing zone.

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Llorens et al. (2011b) defi ned several influent scenarios to test
their implementation. For our comparison, we used the scenario
in which the HF bed is loaded with 20 mm d−1 of wastewater,
with only dissolved O2 (SO) and slowly biodegradable COD(XS) present in the influent (Scenario 3 of Llorens et al., 2011b).
The influent concentrations were 0.86 and 115 mg O2 L−1 for
SO and XS, respectively. In the HYDRUS simulations, influent
concentrations of bacteria were zero, while in the RETRASO
simulations, constant influent concentrations of bacteria wereconsidered. This was necessary because the RETRASO code
does not consider a fi xed biomass. Bacteria were assumed to betransported through the fi lter similarly to solute components.
Therefore, the initial concentrations of bacteria were assumed by
Llorens et al. (2011b) to be the same as in the influent.
Figure 3 shows the concentration profi les of fermentable, readily
biodegradable soluble COD (SF), fermentation products as acetate(SA), and XS along the flow path simulated using RETRASO(Llorens et al., 2011b). The XS is converted into SF by hydrolysis
and further used for the growth of heterotrophic bacteria (XH). The
maximum concentration of SF was simulated to be around 70 mg
O2 L−1. Due to fermentation and microbial lysis, acetate is built up
along the flow path in the HF bed.
Figure 4 shows the concentration profiles of SF, SA, and XS after
the 50-d simulation time using the CWM1 module of HYDRUS.
The same values for the biokinetic model parameters as reported
by Llorens et al. (2011b) were used for these simulations. The left
side of Fig. 5 presents the corresponding concentration profilesof heterotrophic (XH), autotrophic nitrifying (XA), fermenting(XFB), and acetotrophic methanogenic (XAMB) bacteria. It can

be clearly seen in Fig. 5 that the bacteria concentration profiles arefar from those simulated by Llorens et al. (2011b). Consequently,
the concentration profiles of solute compounds shown in Fig. 4 aredifferent from those presented in Fig. 3. A rapid transformation of XS
into SF by hydrolysis takes place near the inlet, due to high bacteria
concentrations there. Under anaerobic conditions, SF is further
converted into SA by fermenting bacteria (XFB). Contrary to the
RETRASO results (Fig. 3), SA is fully degraded before it reaches theeffluent (Fig. 4). In this specific example with only XS in the influent,
all degradable COD is removed within about half of the flow distancein the HF bed (Fig. 4). Aerobic conditions occur at the end of the HF
bed and therefore all degradable COD produced by lysis processes ismineralized as well.
The concentration of SF is almost constant in the HF bed. In this
scenario, the influent consists of only XS, which is anaerobicallyconverted to SA, with SF being only an intermittent product. The
almost constant value of SF of about 1.5 mg L−1 (Fig. 4) is caused by
the rather high saturation coefficient for SF in the fermentation process.
Concentrations of XH and XFB are highest near the water table(Fig. 5). After the organic matter is degraded, O2 diffuses into deeper
zones of the bed and heterotrophic bacteria can also grow in these
deeper zones (about 7 m away from the inflow in Fig. 5). Although
no free NH3 is introduced in the influent, NH3 is produced insideof the HF bed during degradation of the organic matter and lysis
of bacteria. Nitrifying bacteria (XA) grow in locations where NH3
is available, the organic matter is already removed, and O2 is thus
available for nitrification. Acetotrophic methanogenic bacteria(XAMB) grow on acetate (SA) under anaerobic conditions.

Fig. 3. Concentration profiles (mg L−1) of fermentable, readily biodegradable soluble chemical oxygen demand (COD) (SF) (top), fermentation products
as acetate (SA) (middle), and slowly biodegradable particulate COD (XS) (bottom) for Scenario 3 of Llorens et al. (2011b) simulated using the CWM1
implementation in RETRASO (adapted from Llorens et al., 2011b). Dimensions of the transport domain in RETRASO are 10.0 by 0.7 m.

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Fig. 4. Concentration profiles (mg L−1) of fermentable, readily biodegradable soluble chemical oxygen demand (COD) (SF) (top), fermentation
products as acetate (SA) (middle), and slowly biodegradable particulate COD (XS) (bottom) simulated with HYDRUS using the CWM1 biokinetic
model. Dimensions of the transport domain in HYDRUS are 10.3 by 0.6 m.

Fig. 5. Bacteria concentration profiles (mg kg−1) simulated with HYDRUS using the CWM1 (left) and CW2D (right) biokinetic models. Left (fromtop to bottom): heterotrophic bacteria (XH), autotrophic nitrifying bacteria (XA), fermenting bacteria (XFB), and acetotrophic methanogenic
bacteria (XAMB); right (from top to bottom): heterotrophic bacteria (XH), autotrophic NH4–oxidizing bacteria (XANs), and autotrophic NO2–
oxidizing bacteria (XANb).

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Simulated XAMB concentrations are lower after 50 d because theygrow more slowly than the other bacteria types.

Comparison of the CWM1 and CW2D Models
for Simula ng Horizontal Flow Beds
The aim of this example is to compare simulation results for thesame CW system obtained with the two biokinetic models, i.e.,
CWM1 and CW2D. The same setup as described above was also
used for simulations with the CW2D biokinetic model. Again, theinfluent concentrations were 0.86 and 115 mg O2 L−1 for SO andslowly biodegradable COD (CS in CW2D), respectively. Because
no anaerobic processes are considered in CW2D, hydrolysis of CS
produces the readily biodegradable COD (CR), which is consumed
by heterotrophic bacteria (XH). Contrary to CWM1 (Fig. 4), abuildup of readily biodegradable COD is simulated by CW2D
(Fig. 6). Concentration profiles of heterotrophic bacteria (XH) andautotrophic bacteria (XANs and XANb), as shown in Fig. 5 (right),
were similar to those for XH and XA predicted using CWM1 (Fig.
5, left). As shown in Fig. 5, both biokinetic models predict aerobic
bacteria growth also in deeper depths of the HF bed, at about 75%of the flow distance. This can be explained by the fact that all organic
matter is consumed by this point and O2 can diff use into deeper
zones of the HF bed, facilitating aerobic processes.
The concentration profiles for slowly biodegradable COD (XS) in
Fig. 4 and (CS) in Fig. 6 look almost the same, although CWM1
considers acetotrophic methanogenic bacteria (XAMB), from which
one would expect an additional removal of the organic matter. Thiscan be explained by the fact that XAMB grows very slowly anda longer simulation time (e.g., 1 yr) would be needed to establish
significant XAMB concentrations in the HF bed; however, we did
not do calculations for time periods of 1 yr or longer in this example.

Figure 7 shows the concentration profiles of NH 3 and NO3
simulated using CWM1 and CW2D. The concentrations of all Ncompounds are low because no N was in the influent and all N was
released only during hydrolysis. The amounts of built-up NH3 aswell as the final NO3 concentrations in the effluent of the HF bed
are similar for both biokinetic models. The NO3 profi les differ alittle in the zones where nitrification occurs. This can be explainedby different nitrification models in CW2D and CWM1, which
are modeled as a two-step and a one-step process, respectively. In
CW2D, where nitrification is modeled as a two-step process, only
low concentrations of NO2 occur (Fig. 8), indicating that there isenough O2 available for the second nitrification step.

Considering the Influence of Plants
in Wetlands
With the aim of evaluating the influence of wetland plants on
the removal of contaminants in HF beds, the HF bed of Llorens
et al. (2011b) that we described above was used. In these new
simulations, the HF bed was loaded with wastewater with ahydraulic loading rate of 36 mm d−1. The influent concentrations
used for the CWM1 and CW2D simulations were (see Table 3 fordefinitions): CWM1 components (in mg L−1): SO, 0.86; SF, 170;
SA, 27; SI, 13; SNH, 57; SNO, 0; SSO4, 33; SH2S, 0; XS, 33;
and XI, 13; CW2D components (in mg L−1): SO, 0.86; CR, 197;
CS, 33; CI, 26; NH4N, 57; NO2N, 0; NO3N, 0; N2N, 0; andPO4P, 10. The CWM1 influent concentrations were the same as
those used in Scenario 5 of Llorens et al. (2011b), while the CW2D
influent concentrations were calculated from the CWM1 influent
concentrations (CR = SF + SA, CS = XS, and CI = SI + XI).
In the CW2D simulations, PO4 –P was considered in the inflow,whereas S was not considered.
Figure 9 shows the spatial distribution of root water uptake inthe vertical domain. As reported by Headley et al. (2005), root

Fig. 6. Concentration profiles (mg L−1) of readily biodegradable soluble chemical oxygen demand (COD) (CR) (top) and slowly biodegradable soluble
COD (CS) (bottom) simulated with HYDRUS using the CW2D biokinetic model.

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Fig. 7. Concentration profiles (mg L−1) of NH4– and NH3–N (SNH4) (top left) and (NH4N) (top right), and NO3– and NO2–N (SNO) (bottom
left) and NO3–N (NO3N) (bottom right) simulated with HYDRUS using the CWM1 (left) and CW2D (right) biokinetic models.

Fig. 8. Concentration profile (mg L−1) of NO2–N (NO2N) simulated with HYDRUS using the CW2D biokinetic model.

Fig. 9. Root water uptake distribution simulated with HYDRUS.

biomass was only found in the upper half of the HF bed. The same
assumption—that the roots are dense in the upper 20 cm and thendecrease rapidly with depth—was made here. In HYDRUS, solute
uptake and release from roots is coupled to water flux. Because
water uptake is assumed to be constant, O2 release is constant as
well. The root water and solute uptake parameters used are given
in Table 6. The negative value of the cRoot variable for dissolved
O2 was used to model the O2 release from the plant roots. The
parameters in Table 6 resulted in a transpiration rate of 7.4 mm
d−1 and a specific O2 release of 5 g m−2 d−1. The selected valueof the specific O2 release is a typical value reported for common
reed [Phragmites australis (Cav.) Trin. ex Steud.], a plant species
commonly used in CWs (Kadlec and Wallace, 2009).
Figure 10 shows how the O2 concentration profi les are affectedby the O2 release. There is no dissolved O2 available in the bed
when the wetland plants are not considered (Fig. 10, top). Oxygen
concentrations in the root zone when the O2 release from plantroots is considered (Fig. 10, bottom) are also very low (0.01–0.02

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Table 6. Root water and solute uptake parameters used in the example
considering the influence of wetland plants.
Parameter

Value

Potential transpiration rate, cm d−1
cRoot (NH4), mg L−1
cRoot (NO3), mg L−1
cRoot (dissolved O2), mg L−1w

0.74
50
50
−675

mg.L−1). There is a constant supply of O2 from the plant roots,
however, that is readily consumed by aerobic microorganisms.
Figure 11 shows the bacteria concentration profiles of XH,
XFB, and XA when the O2 release from plant roots is either notconsidered (left) or considered (right). The bacteria concentration
profi les of acetotrophic methanogenic (XAMB), acetotrophic
SO 4 –reducing (XASRB), and S2−–oxidizing (XSOB) bacteria
for conditions both with and without the O2 release from plantroots are shown in Fig. 12.
Few aerobic bacteria are growing near the top of the water table
when no O2 is released from plant roots and is therefore available(XH and XA in the left part of Fig. 11 and XSOB in the left part of
Fig. 12). The XFB bacteria are also growing only in regions where
XH produces SF from hydrolysis. Other anaerobic bacteria, i.e.,
XAMB and XASRB, are growing in the rest of the fi lter bed, but
their concentrations are rather low.

Fig. 10. Concentration profiles (mg L−1) of dissolved O2 (SO) simulated with HYDRUS using the CWM1 biokinetic model while not considering(top) and considering (bottom) the O2 release by plant roots.

Fig. 11. Bacteria concentration profiles (mg kg−1) of heterotrophic bacteria (XH) (top), fermenting bacteria (XFB) (middle), and autotrophic nitrifying
bacteria (XA) (bottom) simulated with HYDRUS using the CWM1 biokinetic model while not considering (left) and considering (right) the O2
release from plant roots.

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Fig. 12. Bacteria concentration profiles (mg kg−1) of acetotrophic methanogenic bacteria (XAMB) (top), acetotrophic SO4–reducing bacteria (XASRB)(middle), and S2−–oxidizing bacteria (XSOB) (bottom) simulated with HYDRUS using the CWM1 biokinetic model while not considering (left)
and considering (right) the O2 release from plant roots.

When O2 is released from plant roots (Fig. 11 and 12, right),
the bacteria concentration profiles are completely different.
The XH and XSOB bacteria are growing in the root zone. Dueto the availability of SF, XFB can also grow in the root zone.
Because the O2 concentrations in the root zone are too low
for autotrophic bacteria (XA), however, they can only grow at
the end of the bed, where the organic matter has already been
consumed (Fig. 11, right). Anaerobic processes occur only outsideof the root zone, as indicated by the higher concentrations of
XAMB and XASRB there (Fig. 12, right).

NH3 concentrations are higher than in the influent, indicatingthat organic N was released as NH3 during degradation of theorganic matter and no nitrification occurred.
Table 8 compares the effluent concentrations simulated using
CW2D for conditions with and without plants. There is a big
difference in COD effluent concentrations whether the O2
release from plant roots is considered or not. Without plants, theCOD effluent concentrations are high, while with plants, they
are comparable to the effluent concentration simulated using
CWM1 (Table 7). Because CW2D does not consider anaerobic
processes, degradation of the organic matter can only occur
when O2 from plant roots is provided. Llorens et al. (2011b)
calculated that about 75% of the COD removal for this scenario
was caused by anaerobic processes, thus clearly indicating theneed to model anaerobic processes in HF CWs. Similarly to the
CWM1 simulations, the effluent NH3 concentrations are higher
than in the influent, indicating the release of organic N and alack of nitrification.

Table 7 compares the effluent concentrations simulated using
CWM1 for conditions both with and without the O2 releasefrom plant roots. When using CWM1, the simulated COD
effluent concentrations are similar for both conditions; however,the composition of the COD is quite different. When thewetland plants are not considered, the main part of COD is
still biodegradable (XS), while when the wetland plants are
considered, the main part of COD is inert (SI and XI). Effluent

Table 7. Effluent concentrations simulated with HYDRUS using CWM1 for the example considering the influence of wetland plants. Chemical O2
demand (COD) is shown in bold type. See Table 3 for parameter definitions.
Condition

SO2

SF

SA

SI

XS

XI

COD

L−1 ———————————

Without O2 release
With O2 release——————————— mg O2
<0.01
0.5
0.3
<0.01
3.5
7.9

13.0
16.2

SNH4

SNO

——— mg N L−1 ————
29.8
2.8

46.6
42.1

3.0
11.7

61.9
64.6

0.09
0.02

Table 8. Effluent concentrations simulated with HYDRUS using CW2D for the example considering the influence of wetland plants. Chemical O2
demand (COD) is shown in bold type. See Table 3 for parameter definitions.
Condition
Without O2 release
With O2 release

SO2

CR

CS

———————————— mg O2
<0.01
84.7
0.01
0.2

CI

COD

NH4 –N

NO2–N

NO3–N
−1
———————— mg N L —————————

142.6
45.6

60.5
71.7

< 0.010.01

L−1 ————————————
27.8
2.5

30.2
42.9

www.VadoseZoneJournal.org< 0.01
1.95

6 Discussion
The CWM1 model (Langergraber et al., 2009b) has been proposedwith the main goal of providing a widely accepted model formulationthat would consider various biochemical transformation anddegradation processes in CWs and that could be implemented
in various simulation tools. Although CWM1 has been recently
implemented into the RETRASO code by Llorens et al. (2011a,
2011b), Version 2 of the HYDRUS wetland model provides the first
implementation of CWM1 that is commercially available.
The main difference between CWM1 implementations in
RETRASO and HYDRUS is that RETRASO, contrary to
HYDRUS, cannot consider a fixed biomass. Within a very simple
example in Fig. 5, it was shown that bacteria concentration profiles
that develop in HF beds are far more complicated than the constantprofi les assumed by Llorens et al. (2011b). To maintain constantbacteria concentrations in the bed, Llorens et al. (2011b) had to add
unrealistically high concentrations of bacteria to the influent water.
The bacteria concentration profiles simulated using HYDRUS appear
to be much more realistic than those simulated using RETRASO.
Version 2 of the HYDRUS wetland module (Langergraber andŠimůnek, 2011) includes two biokinetic models that have beendeveloped to describe transformation and degradation processes in
CWs treating wastewater. In addition to CWM1, the HYDRUS
wetland module also includes CW2D (Langergraber andŠimůnek, 2005). The CW2D code was already implemented in
the first version of the HYDRUS wetland module (Langergraberand Šimůnek, 2006). In contrast to CWM1, CW2D does notconsider any anaerobic processes. The CW2D biokinetic model
was originally developed to model VF CWs and only later was
also applied to model HF beds. Reasonably good results wereobtained with CW2D for low-loaded HF beds (e.g., Toscano etal., 2009). Table 9 provides guidance on which biokinetic model touse for different types of CWs and for what type of CW processes.
As mentioned above, CW2D models nitrification as a two-stepprocess and considers P, whereas CWM1 also includes anaerobic
processes and considers processes affecting S.
Both biokinetic models included in the HYDRUS wetland module
have been developed to model CWs treating municipal wastewater.
Table 9. Different applications of the biokinetic models CW2D
(Langergraber and Šimůnek, 2005) and CWM1 (Langergraber etal., 2009b).
Biokinetic model

CW2D

CWM1

Type of constructed vertical flow
wetlandlow loaded horizontal
flow beds

vertical and horizontal flow

Processes

modeling anaerobic
processes
modeling transportand fate of S

modeling retention of P
modeling nitrification asa two-step process

A number of studies have been published that show that good
simulation results can be achieved especially for VF CWs (e.g.,Langergraber, 2003, 2007; Langergraber et al., 2007). In addition
to applications involving CWs treating municipal wastewater, the
HYDRUS wetland model has been also used to model• CWs treating combined sewer overflow (Dittmer et al.,2005; Henrichs et al., 2007, 2009; Meyer et al., 2008);• CWs treating effluents of a wastewater treatment plant for
irrigation purposes (Toscano et al., 2009);• runoff from agricultural sites and the effects of streamside
management zones (Smethurst et al., 2011).
In addition to the HYDRUS wetland module that considers
various biochemical transformation and degradation processes, the
HYDRUS software provides most of the other important submodels
needed to model a SSF CW, as defined by Langergraber et al.
(2009b). By solving the Richards equation for water flow in porous
media under variably saturated conditions, HYDRUS provides asuitable model for water flow. As discussed by Langergraber (2008),
the calibration of the water flow module is of great importance and anecessary tool for subsequently achieving good results with reactive
transport modeling. The HYDRUS code solves the convection–
dispersion equations for both heat and solute transport. Transport
equations for single components are linked by reaction terms thatare calculated using the biokinetic models.
We have shown above that considering wetland plants, i.e., O2
release from wetland plant roots, significantly influences thesimulation results. With HYDRUS, it is also possible to simulate
the plant nutrient uptake, which is coupled with the plant water
uptake. Using this option, it is possible to model O2 release fromroots; however, HYDRUS is not able to model growth, decay, or
decomposition of the wetland plants.
The only submodel that was mentioned by Langergraber et al.
(2009b) and that is not available in HYDRUS is an option tosimulate the transport and deposition of suspended particulatematter and its influence on the hydraulic conductivity. As clogging
of SSF CWs is still one of the main, often-occurring, operational
problems; the inclusion of such a model would allow prediction of
the failure of SSF CWs due to clogging.

6 Summary and Conclusions
We have presented Version 2 of the HYDRUS wetland
module, which includes two biokinetic models for simulating
biochemical transformation and degradation processes in CWs.
The CW2D and CWM1 biokinetic models describe different
processes affecting different water constituents. As such, the twobiokinetic models may be used for different types of CWs. We
have shown that the implementation of CWM1 into HYDRUS
is mathematically correct. Additionally, the HYDRUS wetland

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module allows simulation of a fi xed biomass in the filter bed, whichis essential for simulating SSF CWs. Considering the influenceof wetland plants resulted in different profi les of various bacteriagroups in the bed of HF CWs.
The following conclusions can be drawn:• Version 2 of the HYDRUS wetland module is the only
publicly available implementation of the CWM1.
• It is essential for modeling SSF CWs that fi xed bacteria
can be simulated.
• Because CWM1 is able to describe anaerobic processes, it
is more suitable for modeling HF CWs, whereas CW2D ismore suitable for VF CWs.
• The influence of wetland plants on various biochemical transformation and degradation processes due to therelease of O2 by plant roots in a HF bed is significant andtherefore has to be considered.
• More experience needs to be gained in the use of theCWM1 biokinetic model.

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