THE MULTI-COMPONENT REACTIVE
TRANSPORT MODULE

CW2DFOR CONSTRUCTED WETLANDSFOR THE HYDRUS SOFTWARE PACKAGE

Manual - Version 1.0
byGünter Langergraber1 and Jirka Šimůnek2
March 2006

1

Institute for Sanitary Engineering and Water Pollution Control
BOKU - University of Natural Resources and Applied Life Sciences, Vienna
Muthgasse 18, A-1190 Vienna, Austria
2

Department of Environmental Sciences
University of California Riverside
Riverside, CA, 92521, USA

Abstract
Langergraber, G. and J. Šimůnek, The Multi-Component Reactive Transport Module
CW2D for Constructed Wetlands for the HYDRUS Software Package, Hydrus Software
Series 2, Department of Environmental Sciences, University of California Riverside,
Riverside, California, USA, p. 72, 2006.
Constructed wetlands are becoming increasingly popular worldwide for removing
nutrients, organics, trace elements, pathogens, or other pollutants from wastewater and/or
runoff water. This manual describes a multi-component reactive transport module CW2D(Constructed Wetlands 2D, Langergraber, 2001, Langergraber and Šimůnek, 2005), thatwas developed as an extension of the HYDRUS-2D variably-saturated water flow andsolute transport program (Šimůnek et al., 1999). CW2D was developed to model thebiochemical transformation and degradation processes in subsurface-flow constructedwetlands. The biochemical degradation and transformation processes for organic matter,
nitrogen and phosphorus are described. The mathematical structure of CW2D is based on
the IWA Activated Sludge Models (Henze et al., 2000). Monod-type expressions are used
to describe the process rates. All process rates and diffusion coefficients are temperaturedependent. The biochemical components defined in CW2D include dissolved oxygen,
three fractions of organic matter (readily- and slowly-biodegradable, and inert), four
nitrogen compounds (ammonium, nitrite, nitrate, and dinitrogen), inorganic phosphorus,
and heterotrophic and autotrophic micro-organisms. Organic nitrogen and organic
phosphorus are modelled as part of the COD. Heterotrophic bacteria are assumed to be
responsible for hydrolysis, mineralization of organic matter (aerobic growth) anddenitrification (anoxic growth). Autotrophic bacteria are assumed to be responsible fornitrification, which is modelled as a two-step process. All micro-organisms are assumed to
be immobile. Lysis is considered to be the sum of all decay and loss processes.
The manual provides a short overview of the constructed wetland technology, describesinternal details of the reactive transport CW2D module, its main principles, its
mathematical formulations, and a set of default parameters based on the literature review.
It also describes how CW2D is implemented into HYDRUS (Šimůnek et al., 2006a,
2006b), what modifications were made in the original code, and how the new module canbe run using the HYDRUS graphical user interface. Finally, it presents several illustrativeand verification examples of the use of CW2D, and description of additional new input andoutput files.

DISCLAIMER
This report documents version 1.0 of the implementation of the CW2D module into the
HYDRUS graphical user interface. The CW2D module was developed as a supplemental
module of the HYDRUS software package, to model the biochemical transformation anddegradation processes in subsurface flow constructed wetlands. The software has beenverified against selected test cases. However, no warranty is given that the program iscompletely error-free. If you do encounter problems with the code, find errors, or havesuggestions for improvement, please contact one of the authors at
Günter LangergraberTel: +43-(0)1-36006-5814
Fax: +43-(0)1-368 99 49
email: guenter.langergraber@boku.ac.at
Jirka Šimůnek
Tel: 1-951-827-7854
Fax: 1-951-787-3993
E-mail: jiri.simunek@ucr.edu

Table of contents
1

Introduction ................................................................................................................ 1

2

Constructed wetland technology............................................................................... 3

3

The CW2D multi-component reactive transport module ...................................... 5
3.1

Background......................................................................................................... 5

3.2

Description of CW2D ......................................................................................... 6

3.3

Parameters of CW2D........................................................................................ 10
3.3.1 Composition parameters ........................................................................ 10
3.3.2 Stoichiometric parameters ..................................................................... 10
3.3.3 Kinetic parameters................................................................................. 12
3.3.4 Temperature dependencies .................................................................... 12
3.3.5 Biofilm parameters ................................................................................ 13

3.4

Parameters of HYDRUS................................................................................... 14
3.4.1 Diffusion coefficients ............................................................................ 14
3.4.2 Adsorption parameters........................................................................... 15
3.4.3 Heat transport ........................................................................................ 16

4

The implementation of CW2D in HYDRUS.......................................................... 17
4.1

General Remarks .............................................................................................. 17

4.2

Modifications of the original HYDRUS-2D program code ............................. 17
4.2.1 Modifications of the main program ....................................................... 17
4.2.2 The ponding boundary condition........................................................... 18
4.2.3 Modifications of Multi-Component Reactive Transport ....................... 19

4.3

The CW2D/HYDRUS user interface ............................................................... 21
4.3.1 Preliminary remarks .............................................................................. 21
4.3.2 Implementation of CW2D into the HYDRUS user interface ................ 22

5

Examples ................................................................................................................... 26
5.1

Pilot-scale subsurface vertical flow constructed wetland for wastewater
treatment ........................................................................................................... 26
5.1.1 System description................................................................................. 26
5.1.2 Measured data........................................................................................ 26
5.1.3 Simulation set up ................................................................................... 27
5.1.4 Simulation results .................................................................................. 28i5.2

Two-stage subsurface flow constructed wetland.............................................. 36
5.2.1 System description................................................................................. 36
5.2.2 Simulation set up ................................................................................... 37
5.2.3 Simulation results .................................................................................. 37

5.3

Constructed wetland for treatment of combined sewer overflow..................... 42
5.3.1 System description................................................................................. 42
5.3.2 Simulation set up ................................................................................... 43
5.3.3 Simulation results .................................................................................. 43

6

7

5.4

Experiences, limitations and research need ...................................................... 47

5.5

Possible future applications .............................................................................. 49

Input data.................................................................................................................. 51
6.1

Extension of the 'selector.in' input file to enter parameters defined in
CW2D ............................................................................................................... 51

6.2

The 'options.in' input file.................................................................... 54

Output data............................................................................................................... 55
7.1

Format of the 'effluent.out' output file............................................... 55

8

List of examples........................................................................................................ 57

9References ................................................................................................................. 59ii

List of Figures
Figure 4.1: Flow chart of the original (left) and modified (right) main program of HYDRUS-2D(gray boxes represent routines that were modified to accommodate CW2D). ............ 18
Figure 4.2: Flow chart of the original (left) and modified (right) 'Solute' subroutine...................... 20
Figure 4.3: Flow chart of subroutines 'CW2D' and 'Coeff'. ............................................................. 20
Figure 4.4: "Geometry Information" window. ................................................................................. 21
Figure 4.5: "Solute Transport" window. .......................................................................................... 22
Figure 4.6: "Solute Transport Parameter" window (length unit: m; time unit: d)............................ 23
Figure 4.7: "Solute Transport – CW2D Model Parameters I" window (time unit: d)...................... 23
Figure 4.8: "Solute Transport – CW2D Model Parameters II" window (time unit: d). ................... 24
Figure 4.9: "Initial Conditions". ....................................................................................................... 24
Figure 4.10: "Results - Graphical Display"...................................................................................... 25
Figure 4.11: "Observation Nodes" window. .................................................................................... 25
Figure 5.1: Schematic of the pilot-scale subsurface constructed wetland (values are in cm). ......... 26
Figure 5.2: Two-dimensional finite element mesh of the PSCW..................................................... 27
Figure 5.3: Measured and simulated cumulated effluent for a single application of 10 litres(4 loadings per day; daily hydraulic load of 40 litres). ................................................ 28
Figure 5.4: Measured and simulated effluent rates for a single application of 10 litres (4 loadings
per day; daily hydraulic load of 40 litres).................................................................... 29
Figure 5.5: Measured and simulated effluent rates (left) and cumulated effluent (right) for a single
feeding of 10 litres (4 loading per day, daily hydraulic load of 40 litres). .................. 29
Figure 5.6: Measured and simulated effluent rates and cumulated effluent for a single feeding of
15 litres (4 loading per day, daily hydraulic load of 60 litres)..................................... 30
Figure 5.7: Simulated pressure heads at the top of the constructed wetland system........................ 30
Figure 5.8: Measured and simulated effluent electrical conductivities for different daily hydraulicloads............................................................................................................................. 31
Figure 5.9: Pressure head (left) and dissolved oxygen (right).......................................................... 33
Figure 5.10: Time series (left) and vertical profile (right) of heterotrophic micro-organims. ......... 33
Figure 5.11: Simulated time series (left) and vertical profile (right) of autotrophic micro-organisms.
..................................................................................................................................... 34
Figure 5.12: Ammonium (left) and nitrate nitrogen (right).............................................................. 34
Figure 5.13: Vertical profiles of ammonium nitrogen at t = 1 minute (end of loading), 6 minutes,
30 minutes, and 2 hours. .............................................................................................. 35
Figure 5.14: Vertical profiles of nitrate nitrogen at t = 1 minute (end of loading), 6 minutes,
30 minutes, and 2 hours. .............................................................................................. 35iii

Figure 5.15: Schematic of a pilot-scale vertical flow constructed wetland (SSP) (distances are incm). .............................................................................................................................. 36
Figure 5.16: Sampling points in the main layer of the SSP (distances are in cm). .......................... 36
Figure 5.17: The unstructured two-dimensional finite element mesh of the SSP. ........................... 37
Figure 5.18: Simulated and measured electrical conductivities for three sampling points and at theoutlet (Langergraber, 2003). ........................................................................................ 38
Figure 5.19: Simulated steady-state distribution of heterotrophic organisms XH. .......................... 39
Figure 5.20: Calculated steady-state distribution of Nitrosomonas XANs. ..................................... 40
Figure 5.21: Simulated time series of dissolved oxygen.................................................................. 41
Figure 5.22: Simulated time series of ammonium nitrogen (left) and nitrate nitrogen (right)......... 41
Figure 5.23: Lab-scale filter column. ............................................................................................... 42
Figure 5.24: Two-dimensional finite element mesh of the lab-scale column. ................................. 43
Figure 5.25: Measured and simulated effluent flow rate of column 6. ............................................ 44
Figure 5.26: Measured and simulated breakthrough curves of column 6. ....................................... 45
Figure 5.27: Comparison of simulations with free drainage BC (time units = minutes) and limited
seepage face flux (time units = hours). ........................................................................ 46
Figure 5.28: Measured and simulated breakthrough curves of column 4 and column 2 (controlled
effluent rate 5 litre/hour and 1 litre/hour, respectively)............................................... 46iv

List of Tables
Table 3.1: CW2D – main principles................................................................................................... 7
Table 3.2: Stoichiometric matrix of reactions in CW2D.................................................................... 8
Table 3.3: Reaction rates in CW2D. .................................................................................................. 9
Table 3.4: The composition parameters (Henze et al., 1995)........................................................... 10
Table 3.5: The stoichiometric parameters for organic matter and micro-organisms (Henze et al.,1995).............................................................................................................................. 10
Table 3.6: Stoichiometric coefficients for ammonium nitrogen. ..................................................... 11
Table 3.7: Stoichiometric coefficients for inorganic phosphorus. ................................................... 11
Table 3.8: Kinetic parameters in CW2D (Henze et al., 1995). ........................................................ 12
Table 3.9: Values of activation energies, Ea, for particular transport and reaction parameters used
in CW2D........................................................................................................................ 13
Table 3.10: Diffusion coefficients in CW2D. .................................................................................. 14
Table 3.11: Coefficient values of linear and Freundlich isotherms for adsorption of ammonium
nitrogen.......................................................................................................................... 15
Table 3.12: Coefficient values of linear and Freundlich isotherms for adsorption of phosphorus. . 15
Table 3.13: Parameters of the volumetric heat capacity. ................................................................. 16
Table 3.14: Parameters of the thermal conductivity function. ......................................................... 16
Table 4.1: Units of concentrations in the liquid and solid phases and of the bulk density .............. 21
Table 5.1. Measured cumulated effluent .......................................................................................... 26
Table 5.2. Median values and confidence intervals (in parenthesis) of the measured influent andeffluent concentrations of NH4+, NO3- and total organic carbon in mg.l-1 (Langergraber,
2003).............................................................................................................................. 27
Table 5.3. Literature and fitted soil hydraulic parameters of the van Genuchten-Mualem model for
the 0.06-4 mm substrate. ............................................................................................... 28
Table 5.4. Parameters of the general equilibrium solute transport model........................................ 31
Table 5.5. Parameters for the physical non-equilibrium transport model ........................................ 31
Table 5.6. Measured and simulated influent and effluent concentrations. ....................................... 32
Table 5.7. van Genuchten-Mualem soil hydraulic parameters for the two-stage constructedwetlands system............................................................................................................. 38
Table 5.8. Parameters for the physical non-equilibrium transport model ........................................ 38
Table 5.9. Influent concentrations for the multi-component reactive transport simulations............ 39
Table 5.10: Drainage regime of the filter columns. ......................................................................... 42
Table 5.11: Values of the van Genuchten model parameters........................................................... 44
Table 6.1: Description of variables of "BLOCK X" in the 'selector.in' input file – Part 1:
kinetic parameters.......................................................................................................... 52v

Table 6.2: Description of variables of "BLOCK X" in the 'selector.in' input file – Part 2:
stoichiometric and composition parameters, and parameters for the model of oxygen reaeration. ......................................................................................................................... 53
Table 6.3: Description of variables used in the 'options.in' input file................................... 54vi

1

Introduction

Constructed wetlands (CWs) are engineering structures designed to improve water quality.
Wetlands involve a complex mixture of water, substrate, plants, litter, and a variety of
micro-organisms to provide optimal conditions for improving water quality. They are
effective in removing organic matter, nitrogen, phosphorus, and also in decreasing theconcentrations of heavy metals, organic chemicals, and pathogens from wastewater and/or
runoff water. Understanding of constructed wetlands function is made difficult by the large
number of physical, chemical, and biological processes, that are all active at the same time
and that mutually influence each other. Numerical simulators can represent invaluable
tools for analysing, studying, and improving understandings of complex systems such as
constructed wetlands.
This manual describes the multi-component reactive transport module CW2D (ConstructedWetlands 2D, Langergraber, 2001, Langergraber and Šimůnek, 2005), which wasdeveloped as an extension of the HYDRUS-2D variably-saturated water flow and solutetransport program (Šimůnek et al., 1999) to model the biochemical transformation anddegradation processes in subsurface flow constructed wetlands. The biochemicaldegradation and transformation processes for organic matter, nitrogen and phosphorus aredescribed. The mathematical structure of CW2D is based on the IWA Activated Sludge
Models (Henze et al., 2000). Monod-type expressions are used to describe the processrates. All process rates and diffusion coefficients are assumed to be temperature dependent.
The biochemical components defined in CW2D include dissolved oxygen, three fractionsof organic matter (readily- and slowly-biodegradable, and inert), four nitrogen compounds(ammonium, nitrite, nitrate, and dinitrogen), inorganic phosphorus, and heterotrophic andautotrophic micro-organisms. Organic nitrogen and organic phosphorus are modelled aspart of the COD. Heterotrophic bacteria are assumed to be responsible for hydrolysis,
mineralization of organic matter (aerobic growth) and denitrification (anoxic growth).
Autotrophic bacteria are considered to be responsible for nitrification, which is modelled
as a two-step process. All micro-organisms are assumed to be immobile. Lysis isconsidered to represent the sum of all decay and sink processes.
Chapter 2 provides a short overview of the constructed wetland technology. Chapter 3
describes internal details of the reactive transport CW2D module, its main principles, its
mathematical formulations, and a set of default parameters based on the literature review.
Chapter 4 describes how CW2D is implemented into HYDRUS, what modifications weremade in the original code, and how the new module can be run using the HYDRUS
graphical user interface (Šimůnek et al., 2006a). Chapter 5 provides several illustrative andverification examples of the use of CW2D. Finally, description of additional new input andoutput files is given in Chapters 6 and 7, respectively.

1

2

2

Constructed wetland technology

Constructed wetlands (CWs) or wetland treatment systems are wetlands designed to
improve water quality. Such wetlands involve a complex mixture of water, substrate,
plants, litter (fallen plant material), and a variety of micro-organisms (most importantly
bacteria) to provide the treatment conditions for improvement of water quality found innatural wetlands, but have the flexibility of being constructed and thus their various
functions can be optimized as needed. For an optimal support of different treatment
mechanisms, various types of CWs optimised for different applications can be used
(Kadlec and Knight, 1996).
CWs are used worldwide to treat water of different qualities (Kadlec et al., 2000;
Langergraber and Haberl, 2001; Haberl et al., 2003). The experience shows that CWs canbe used successfully with different quality of the influent water and under various climaticconditions. They are effective in removing organic matter, nitrogen, phosphorus, andadditionally for decreasing the concentrations of toxic trace metals, organic chemicals, andpathogens.
In general the use of CWs provides a relatively simple, inexpensive, and robust solution for
the treatment of water. Compared to other treatment options, CWs usually need lower
operational and maintenance expenses. Additional benefits include CWs tolerance tofluctuations in fluxes and pollution loads, their facilitation of water reuse and recycling,creation of habitat for many wetland organisms, and the more aesthetic appearance of
natural systems compared to technical treatment options (Kadlec at al., 2000).
Constructed wetlands include the surface flow (SF) and subsurface flow (SSF) CWs(Kadlec and Knight, 1996). Surface flow constructed wetlands are generally densely
vegetated by a variety of plant species and typically have water depths of less than 0.4 m.
Open water areas can be incorporated into an overall design to optimise hydraulicoperations with wildlife habitat enhancements. Typical hydraulic loading rates are between
0.7 and 5.0 cm.d–1 (between 2 and 14 ha per 1000 m3 per day) in constructed surface flow
treatment wetlands. Subsurface flow wetland technology is based on the work of Seidel(1967). Since then the technology has become increasingly popular in many European
countries and is nowadays applied worldwide (Vymazal et al., 1998; Kadlec at al., 2000).
Surface flow constructed wetlands use a bed of soil or gravel as a substrate for the growthof rooted emergent wetland plants. Mechanically pre-treated wastewater flows by gravity
horizontally or vertically through the bed substrate, where it contacts a mixture offacultative microbes living in association with the substrate and plant roots.
Subsurface vertical flow constructed wetlands (SSVF CWs) with intermittent feeding areused widely today due to their good efficiency regarding the removal of ammonium
nitrogen. Although much experience exists in constructing and operating such systems,
their design is still based mostly on empirical rules, such as requiring a specific area perperson or using simple first-order kinetic rates. However, Kadlec (2000) concluded thatfirst-order models are inadequate for the design of treatment wetlands, especially SSF
CWs.
The main reason for developing a simulation tool that describes complex processes insubsurface flow constructed wetlands was to create a computational tool for analyzing,evaluating, and improving our understanding of various mutually-dependent interactions
within the black box "constructed wetland". Once the simulation tool provides reliable3description of processes in SSF CWs, the existing design criteria can be verified andfinally the design of constructed wetlands can be optimised (Langergraber, 2003).

4

3

The CW2D multi-component reactive transport module

3.1

BackgroundThe need for a numerical model describing biochemical transformation and degradation
processes in subsurface flow constructed wetlands motivated the development of the multicomponent reactive transport module CW2D (Langergraber, 2001) for incorporation into
the HYDRUS-2D variably-saturated water flow and solute transport program. CW2D isable to model the biochemical transformation and degradation processes for organic
matter, nitrogen and phosphorus. The CW2D module considers 12 components and 9
processes. The components include dissolved oxygen, organic matter (three fractions ofdifferent degradability), ammonium, nitrite, nitrate, and dinitrogen nitrogen, inorganic
phosphorus, and heterotrophic and autotrophic micro-organisms. Organic nitrogen andorganic phosphorus are modelled as nutrient contents of the organic matter. The processes
considered are hydrolysis, mineralization of organic matter, nitrification (which ismodelled as a two-step process), denitrification, and a lysis process for the microorganisms.
The mathematical structure of CW2D is based on the mathematical structure of the
Activated Sludge Models introduced by Henze et al. (2000). The Activated Sludge ModelNo. 1 (ASM1) by Henze et al. (1985) was developed to describe organic matter andnitrogen removal in activated sludge plants. ASM1 became very popular and is nowadays
the standard model for simulating activated sludge processes. A lot of extensions and submodels of ASM1 exist that significantly extent its applicability. Further developments led
to the incorporation of phosphorus removal into the Activated Sludge Model (ASM2 byHenze et al., 1995). ASM2 had several limitations that were partly corrected and overcome
in ASM2D (Henze et al., 1999). In the latest version, ASM3 (Gujer et al., 1999), the lysis
process was replaced with a respiration process.
Major assumptions in all Activated Sludge Models are (a) a constant value of pH, (b)constant coefficients in the rate equations, and (c) constant stoichiometric factors. The
various ASM models are valid only for domestic wastewater and are applicable within thetemperature range of 10 to 25°C (Henze et al., 2000). Activated Sludge Models assume
that nitrification occurs in one step, i.e., that ammonium is directly converted (nitrified)
into nitrate. The two-step nitrification model used in CW2D (i.e., sequential nitrification ofammonium into nitrite and nitrate) is based on models presented by Nowak (1996) and
Brouwer et al. (1998).
Activated sludge plants are usually modelled as a number of homogeneous, completely
stirred reactors that are organized in series or parallel. Several papers (e.g., Makina andWells, 2000a, 2000b) addressed the non-ideal hydraulic behaviour of activated sludge
reactors. In their model, solute transport is described using advection-dispersion equationthat is coupled with a reactive model, such as the Activated Sludge Model. The same
principle for coupling the general governing transport equations with the reactive model
was used in CW2D. Due to its implementation in HYDRUS-2D, CW2D additionally also
considers the transient variably-saturated water flow described with the Richards equation.

5

3.2

Description of CW2D

The multi-component reactive transport module CW2D is able to model the biochemicalelimination processes for carbon, nitrogen and phosphorus. The module considers 12
components and 9 processes. The components defined in CW2D include:
•
•
•
•
•
•

dissolved oxygen, O2 [mgO2/l],organic matter [mgCOD/l] (three pools of organic matter (OM) expressed in units ofchemical oxygen demand (COD) are considered: readily and slowly biodegradable,
and inert organic matter; CR, CS, and CI, respectively),
nitrogen [mgN/l] (ammonium nitrogen NH4+, nitrite nitrogen NO2-, nitrate nitrogen
NO3-, and dinitrogen nitrogen N2),
inorganic phosphorus, IP [mgP/l],heterotrophic micro-organisms, XH [mgCOD/l],
autotrophic micro-organisms (Nitrosomonas XANs and Nitrobacter XANb)[mgCOD/l].

Organic nitrogen and organic phosphorus are modelled as nitrogen and phosphorus content
of the COD (chemical oxygen demand). It is assumed that the organic matter is present
only in the aqueous phase and that all reactions occur only in the aqueous phase as well(rsj = 0). Adsorption is considered for ammonium nitrogen (NH4+), and inorganic
phosphorus (IP). Adsorption is assumed to be a kinetic process.
Biofilms in CW2D are assumed to be ideal, composed of a homogeneous matrix of microorganisms with all species uniformly distributed over the biofilms. All micro-organisms
are assumed to be immobile and hence were associated exclusively with the solid phase.
Lysis represents the sum of all decay and loss processes of all micro-organisms involved,
with the rate of lysis being independent of environmental conditions.
In CW2D it is assumed that heterotrophic bacteria include all bacteria that are
responsible for hydrolysis, mineralization of organic matter (aerobic growth) anddenitrification (anoxic growth).
•

•
•

•

Hydrolysis. Hydrolysis describes the conversion of slowly into readily biodegradableorganic matter (COD), with a small fraction being converted into inert COD.
Ammonium (NH4+) and orthophosphate (IP) are released during this transformation
process. It is further assumed that hydrolysis takes place independently of the oxygen
conditions.
Aerobic growth of heterotrophic bacteria. This process consumes oxygen (O2) andreadily biodegradable COD (CR), while ammonium (NH4+) and orthophosphate (IP)are incorporated in the biomass.
Anoxic bacteria growth using nitrate and nitrite. This process produces dinitrogen(due to denitrification) (N2). Both processes consume readily biodegradable COD(CR), ammonium (NH4+), and orthophosphate (IP). The inclusion of both processes isnecessary due to the two-step nitrification model.
Lysis of heterotrophic organisms. Lysis produces organic matter (readily CR, slowly
CS, and inert CI COD), ammonium (NH4+), and orthophosphate (IP).

Autotrophic bacteria are responsible for nitrification, which is modelled as a two-stepprocess. Both steps of the nitrification are strictly aerobic and can therefore only occur
when dissolved oxygen is available.

6

Aerobic growth of Nitrosomonas. This process consumes ammonium (NH4+) andoxygen (O2), and produces nitrite (NO2-). Orthophosphate (IP) and a small portion ofammonium (NH4+) are incorporated in the biomass.
Aerobic growth of Nitrobacter. This process consumes nitrite (NO2-) and produces
nitrate (NO3-). Ammonium (NH4+) and orthophosphate IP) are incorporated in thebiomass.
Similarly to lysis of heterotrophic organisms, lysis of autotrophic bacteria produces
organic matter (readily CR, slowly CS, and inert CI COD), ammonium (NH4+), andorthophosphate (IP).

•••

Table 3.1 shows the main principles of CW2D. A '+' sign means that the process i (i =1, ..., R) is increasing the concentration of the component, a '-' sign signals that the process
is decreasing the concentration of the component. A 'o' sign shows that the concentration of
the component is not affected by the process.
Table 3.1: CW2D – main principles.
N

processes \ components

R

1

2

3

4

5

6

7

8

9

O2

CR

CS

CI

XH

XANs

o

+

–

+

o

o

o

+

o

–

–

o

o

+

o

o

–

o

–

o

o

+

o

o

o

–

o

o

+

o

o

+

+

+

–

10

11

12

N2N

IP

o

o

+

o

o

o

–

–

o

–

+

–

o

–

–

o

+

–

o

o

+

o

o

o

+

XANb NH4N NO2N NO3N

Heterotrophic organisms
1
2
3
4
5

hydrolysis
aerobic growth of heterotrophs onreadily biodegradable COD
NO3-growth of heterotrophs on readily
biodegradable COD
NO2-growth of heterotrophs on readily
biodegradable COD
lysis

Nitrosomonas
6

aerobic growth of N.somonas on NH4

–

o

o

o

o

+

o

–

+

o

o

–

7

lysis of N.somonas

o

+

+

+

o

–

o

+

o

o

o

+

Nitrobacter8

aerobic growth of N.bacter on NO2

–

o

o

o

o

o

+

–

–

+

o

–

9

lysis of N.bacter

o

+

+

+

o

o

–

+

o

o

o

+

+ = process R increases component N; – = process R decreases component N; o = process R has noaffect on component N.

Table 3.2 is obtained by replacing the '+' and '–' symbols in Table 3.1 with stoichiometriccoefficients of reactions. Table 3.2 represents the stoichiometric matrix of CW2D. A
detailed description of the stoichiometric coefficients is given in Table 3.5. The concept ofyield coefficients is used to describe biomass growth. The yield coefficient represents theamount of organic matter that is used for biomass growth. The stoichiometric coefficients(including the yield coefficients) that appear in Table 3.2 are defined, together with theirdefault values, in Table 3.5 (for organic matter and micro-organisms), Table 3.6 (forammonium nitrogen), and Table 3.7 (for inorganic phosphorus).

7

Table 3.2: Stoichiometric matrix of reactions in CW2D.
R

N
components
processes \ units

1
O2
gO2

2
CR
gCOD

3
CS
gCOD

1-fHyd,CI

-1

4
5
6
7
CI
XH XANs XANb
gCOD gCOD gCOD gCOD

8
NH4N
gN

9
NO2N
gN

10
NO3N
gN

11
N2N
gN

12
IP
gP

f Hyd,CI

ν1,N

ν1,P
ν2,P

Heterotrophic organisms
1 hydrolysis
aerobic growth of
2 heterotrophs on readily
biodegradable COD

-1/YH

1

ν2,N

NO3-growth of
3 heterotrophs on readily
biodegradable COD

-1/YH

1

ν3,N

NO2-growth of
4 heterotrophs on readily
biodegradable COD

-1/YH

1

ν4,N

5 lysisf BM,CR-1

ν5,N

1 - 1/YH

1-f BM,CR-fBM,CI

fBM,CI-(1-YH)/2.86YH (1-YH)/2.86YH

ν3,P(1-YH)/1.71YH

ν4,P-(1-YH)/1.71YH

ν5,P

Nitrosomonas
6

aerobic growth ofN.somonas on NH4-(3.43-YANs)/YANs
f BM,CR

7 lysis of N.somonas

1-f BM,CR-fBM,CI

fBM,CI1

iN,BM-1/YANs

-1

ν7,N

ν6,P

1/YANs

ν7,P

Nitrobacter8

aerobic growth ofN.bacter on NO2-(1.14-YANb)/YANb
f BM,CR

9 lysis of N.bacter

1-f BM,CR-fBM,CI

fBM,CI

1

ν8,N

-1

ν9,N

-1/YANb

ν8,P

1/YANb

ν9,P

See Table 3.5, Table 3.6, and Table 3.7 for definitions of the stoichiometric coefficients.

Equations for the process reaction rates, rcj, are given in Table 3.3. It is assumed thatreactions take place only in the aqueous phase. Therefore the overall reaction term ri forcomponent i can be calculated as follows:R

ri = θ ⋅ ∑ υ j ,i rc j

(3.1)

j =1

where i = 1, ..., N (N is the number of components), j = 1, ..., R (R is the number ofprocesses), and where ri is the reaction term for component i [mgi/(dm³s.h)], θ is thevolumetric water content [m³w/m³s], υj,i is the stoichiometric factor for component i andprocess j [mgi/mgj] (Table 3.2), and rcj is the zero-order reaction rate for process j in the
aqueous phase [mgj/(dm³w.h)] (Table 3.3). Rate coefficients and kinetic parameters thatappear in Table 3.3 are defined, together with their values, in Table 3.8.
The total number of parameters of CW2D is 46 (26 kinetic parameters (Table 3.8), 6
stoichiometric parameters (Table 3.5), 8 composition parameters (Table 3.4), 2 parametersdescribing the oxygen transfer between gaseous and aqueous phase (Table 3.10), and 4
parameters describing the temperature dependency of the kinetic parameters (Table 3.9).
Additionally, the material, diffusion, and adsorption parameters for each component, as
already implemented in HYDRUS-2D, have to be specified as well.

8

Table 3.3: Reaction rates in CW2D.
R Process / Reaction rate rcj
Heterotrophic organisms
1

Hydrolysis

rc1 = K h ⋅2cCS c XH
⋅ c XHK X + cCS c XH

Aerobic growth of heterotrophs on readily biodegradable COD

rc2 = μ H ⋅
3

(3.2)

cO 2
cCR
⋅
⋅ f N , Het ⋅ c XH
K Het ,O 2 + cO 2 K Het ,CR + cCR(3.3)

NO3-growth of heterotrophs on readily biodegradable COD

rc3 = μ DN ⋅K DN ,O 2
K DN ,O 2 + cO 2⋅

K DN , NO 2
c NO3
cCR
⋅
⋅
⋅ f N ,DN ⋅ c XH
K DN , NO3 + c NO3 K DN , NO2 + c NO 2 K DN ,CR + cCR
(3.4)

4

NO2-growth of heterotrophs on readily biodegradable COD

rc4 = μ DN ⋅5

K DN ,O 2
K DN ,O 2 + cO 2⋅

c NO 2cCR⋅⋅ f N , DN ⋅ c XH
K DN , NO 2 + c NO 2 K DN ,CR + cCR(3.5)

Lysis of heterotrophs

rc5 = bH ⋅ c XH

(3.6)

Autotrophic organisms 1 – Nitrosomonas
6

Aerobic growth of Nitrosomonas on NH4

rc6 = μ ANs ⋅7

cO 2
c NH 4c IP⋅⋅⋅ c XANs
K ANs,O 2 + cO 2 K ANs, NH 4 + c NH 4 K ANs, IP + c IP

(3.7)

Lysis of Nitrosomonas

rc7 = bHANs ⋅ c XANs

(3.8)

Autotrophic organisms 2 – Nitrobacter8

Aerobic growth of Nitrobacter on NO2

rc8 = μ ANb ⋅9cO 2
c NO 2⋅⋅ f N , ANb ⋅ c XANb
K ANb,O 2 + cO 2 K ANb, NO 2 + c NO 2

(3.9)

Lysis of Nitrobacter

rc9 = bHANb ⋅ c XANb

(3.10)

Conversion of solid in liquid phase concentrations

c XY =

ρ⋅ s , where Y = H , ANs, ANbθ XY(3.11)

Factor for nutrientsf N ,x =c NH 4c IP⋅, where x = Het , DN , ANb
K x , NH 4 + c NH 4 K x , IP + c IP

(3.12)

See Table 3.8 for definitions of rate coefficients.

9

3.3

Parameters of CW2D

In this chapter we describe parameters of CW2D that are used as default parameters. Usersof the model can, however, specify their own values in the input that may be different fromthose given below.
3.3.1 Composition parameters
Values of composition parameters used in CW2D are taken from Henze et al. (1995) andare given in Table 3.4. The composition parameters provide information about the nitrogenand phosphorus contents of the organic matter and biomass, and therefore are measures ofthe mass of organic nitrogen and organic phosphorus, respectively.
Table 3.4: The composition parameters (Henze et al., 1995).
Composition parameters
iN,CR N content of CR [mgN/mgCOD,CR]
iN,CS N content of CS [mgN/mgCOD,CS]
iN,CI N content of CI [mgN/mgCOD,CI]
iN,BM N content of biomass [mgN/mgCOD,BM]
iP,CR P content of CR [mgP/mgCOD,CR]
iP,CS P content of CS [mgP/mgCOD,CS]
iP,CI
P content of CI [mgP/mgCOD,CI]
iP,BM P content of biomass [mgP/mgCOD,BM]

Value
0.03
0.04
0.01
0.07
0.01
0.01
0.01
0.02

3.3.2 Stoichiometric parameters
Values of the stoichiometric parameters used in CW2D are given in Table 3.5.
Table 3.5: The stoichiometric parameters for organic matter and micro-organisms(Henze et al., 1995).
Stoichiometric parameters
fHyd,CI Production of CI in hydrolysis [mgCOD,CI/mgCOD,CS]
fBM,CR Fraction of CR generated in biomass lysis [mgCOD,CR/mgCOD,BM]
fBM,CI Fraction of CI generated in biomass lysis [mgCOD,CI/mgCOD,BM]YH Yield coefficient for heterotrophs [mgCOD,BM/mgCOD,CR]
YANs Yield coefficient for N.somonas [mgCOD,BM/mgNH4N]
YANb Yield coefficient for N.bacter [mgCOD,BM/mgNO2N]* from Nowak (1996)

Value
0
0.05
0.1
0.63
0.24*
0.24*

Kadlec and Knight (1996) gave for biomass growth related to organic dry matter (ODM) avalue of the stoichiometric parameter of 0.17gODM/gNH4N for the total nitrification process.
Using the ratio of the biomass dry weight (DW) to biomass COD of 0.7gDW,BM/gCOD,BM(Lazarova and Manem, 1995), one gets the same stoichiometric parameter of
0.24gCOD,BM/gNH4N, as used by Nowak (1996).
Other values reported in literature include: For example, Pirsing and Wiesmann (1994)
provided the yield coefficients related to organic dry matter (ODM). For Nitrosomonas andNitrobacter the yield coefficients are 0.147gODM/gNH3N and 0.048gODM/gNO2N, respectively.
10

Using the ratio of Lazarova and Manem (1995) one gets a yield coefficients of
0.21gCOD,BM/gNH4N for Nitrosomonas and 0.07gCOD,BM/gNO2N for Nitrobacter. Jacob et al.
(1997) modelled a biofilter for wastewater treatment as a series of completely mixed tanks.
They used the hydraulic model coupled to a reactive transport model based on the ASM1.
They determined the yield coefficient for the heterotrophic bacteria to be
0.67gCOD,BM/gCOD,CR.
Stoichiometric parameters for ammonium nitrogen, ν1,N to ν9,N, and inorganic phosphorus,
ν1,P to ν9,P, in Table 3.2 can be calculated from the mass balance equations. These massbalance equations can be written for each process j as follows:N∑ν ⋅ i = 0
i =1

j ,i

c ,i

(3.13)

where i = 1, ..., N, with N being the number of components, j = 1, ..., R, with R being thenumber of processes, υj,i is the stoichiometric factor for component i and process j[mgi/mgj], c represents the material to which the mass balance is applied (either N or P),
and ic,i is the conversion factor that converts the unit of component i to the unit of materialc. The resulting equations for the stoichiometric coefficients νj,N, and νj,P are given in
Table 3.6 and Table 3.7, respectively.
Table 3.6: Stoichiometric coefficients for ammonium nitrogen.
ν1,N =
ν2,N =
ν3,N =
ν4,N =
ν5,N =
ν6,N =
ν7,N =
ν8,N =
ν9,N =

iN,CS - (1- fHyd,CI) . iN,CR - fHyd,CI . iN,CI
1/YH . iN,CR - iN,BM
1/YH . iN,CR - iN,BM
1/YH . iN,CR - iN,BM
iN,BM - (1 - fBM,CR - fBM,CI) . iN,CS - fBM,CR . iN,CR - fBM,CI . iN,CI(3.14)- 1/YANs - iN,BM
iN,BM - (1 - fBM,CR - fBM,CI) . iN,CS - fBM,CR . iN,CR - fBM,CI . iN,CI- iN,BM
iN,BM - (1 - fBM,CR - fBM,CI) . iN,CS - fBM,CR . iN,CR - fBM,CI . iN,CI

See Table 3.4 and Table 3.5 for definitions of the composition and stoichiometric parameters, respectively.

Table 3.7: Stoichiometric coefficients for inorganic phosphorus.
ν1,P =
ν2,P =
ν3,P =
ν4,P =
ν5,P =
ν6,P =
ν7,P =
ν8,P =
ν9,P =

iP,CS - (1- fHyd,CI) . iP,CR - fHyd,CI . iP,CI
1/YH . iP,CR - iP,BM
1/YH . iP,CR - iP,BM
1/YH . iP,CR - iP,BM
iP,BM - (1 - fBM,CR - fBM,CI) . iP,CS - fBM,CR . iP,CR - fBM,CI . iP,CI(3.15)- iP,BM
iP,BM - (1 - fBM,CR - fBM,CI) . iP,CS - fBM,CR . iP,CR - fBM,CI . iP,CI- iP,BM
iP,BM - (1 - fBM,CR - fBM,CI) . iP,CS - fBM,CR . iP,CR - fBM,CI . iP,CI

See Table 3.4 and Table 3.5 for definitions of the composition and stoichiometric parameters, respectively.

11

3.3.3 Kinetic parameters
Values of kinetic parameters used in CW2D are given in Table 3.8 at temperatures of 10
and 20°C. For the two-step nitrification model the values of Nowak (1996) are used. The
saturation/inhibition coefficients for hydrolysis and for the first step of nitrification (NH4)
are according to Langergraber (2005b).
Table 3.8: Kinetic parameters in CW2D (Henze et al., 1995).
Kinetic parameterKhhydrolysis rate constant [1/d]KX**
sat./inh. coeff. for hydrolysis [mgCOD,CS/mgCOD,BM]maximum aerobic growth rate on CR [1/d]μHbHrate constant for lysis [1/d]Khet,O2
sat./inh. coeff. for O2 [mgO2/l]
Khet,CR
sat./inh. coeff. for substrate [mgCOD,CR/l]
Khet,NH4N
sat./inh. coeff. for NH4 (nutrient) [mgNH4N/l]
Khet,IPsat./inh. coeff. for P [mgIP/l]maximum denitrification rate [1/d]μDN
KDN,O2
sat./inh. coeff. for O2 [mgO2/l]
KDN,NO3N
sat./inh. coeff. for NO3 [mgNO3N/l]
KDN,NO2N
sat./inh. coeff. for NO2 [mgNO2N/l]
KDN,CR
sat./inh. coeff. for substrate [mgCOD,CR/l]
KDN,NH4N
sat./inh. coeff. for NH4 (nutrient) [mgNH4N/l]
KDN,IP
sat./inh. coeff. for P [mgIP/l]maximum aerobic growth rate on NH4N [1/d]
μANs*
bANs*
rate constant for lysis [1/d]KANs,O2*
sat./inh. coeff. for O2 [mgO2/l]
KANs,NH4N** sat./inh. coeff. for NH4 [mgNH4N/l]
KANs,IPsat./inh. coeff. for P [mgIP/l]maximum aerobic growth rate on NO2N [1/d]
μANb*
bANb*
rate constant for lysis [1/d]KANb,O2*
sat./inh. coeff. for O2 [mgO2/l]
KANb,NO2N* sat./inh. coeff. for NO2 [mgNO2N/l]
KANb,NH4N sat./inh. coeff. for NH4 (nutrient) [mgNH4N/l]
KANb,IPsat./inh. coeff. for P [mgIP/l]* Nowak (1996), ** Langergraber (2005b).

Value
20°C
10°C
3
2
0.1
0.22
6
3
0.4
0.2
0.2
0.2
2
2
0.05
0.05
0.01
0.01
4.8
2.4
0.2
0.2
0.5
0.5
0.5
0.5
4
4
0.05
0.05
0.01
0.01
0.9
0.3
0.15
0.05
1
1
0.5
5.0
0.01
0.01
1
0.35
0.15
0.05
0.1
0.1
0.1
0.1
0.05
0.05
0.01
0.01

3.3.4 Temperature dependencies
Due to the temperature dependency of biological processes, many parameters used in
CW2D have to be considered as temperature dependent. In this work temperaturedependency is considered for kinetic parameters (growth and decay rates), diffusion
coefficients, and the saturation concentration of dissolved oxygen. Other parameters are
assumed to be independent of temperature.
In HYDRUS-2D (Šimůnek et al., 1999) the Arrhenius equation (Stumm and Morgan,
1996) is used to describe the temperature dependence of various reaction and transportparameters:

12(Ea⋅ T A −T20 A
A

aT = a20°C ⋅ e R⋅T ⋅T20)

A

(3.16)

where TA is the absolute temperature [K], aT is the value of a particular parameter at theabsolute temperature TA, T20A is the absolute reference temperature (20°C = 293.15K), a20°C
is the value of a particular parameter at the reference temperature T20A, R is the universal
gas constant (=8.314 J/mol/K), and Ea is the activation energy [J/mol]. The Arrhenius
equation was also used by Rodrigo et al. (1997) and Wood et al. (1999), who studied thetemperature effects on C-N transformations in soils and on laboratory-scale constructedwetlands, respectively.
Table 3.9 gives values of the activation energies, Ea, for particular transport and reaction
parameters used in CW2D. It is assumed that all diffusion coefficients for the aqueous
phase have the same activation energy and therefore the same temperature dependency.
The temperature dependency of kinetic rates in Table 3.8 is assumed to be the same for allprocesses caused by heterotrophic micro-organisms and for all processes caused by
autotrophic micro-organisms.
Table 3.9: Values of activation energies, Ea, for particular transport and reaction
parameters used in CW2D.
Parameter
0
14.5
6.48
-

5
12.7
-

Temperature [°C]
10
12
15
11.2
10.1
7.20
4.68E-4-Ea
20[J/mol]9.18-15000
(2)
7.69
5700
7.20E-4 29750

Saturation concentration of oxygen
Diffusion coefficients in gas phase
Diffusion coefficients in aqueous
phase
Rates for heterotrophic bacteria(1)12Rates for autotrophic bacteria(1)0.35
2Hydrolysis rate(1)
3
6
(1)
(2)
Source: Luckner and Schestakow (1991); except: = Table 3.8 and = calculated.

47825
69050
27980

3.3.5 Biofilm parameters
Data for biofilm properties are rare, and since different authors often use different
measurement procedures and techniques, their results can not be easily compared. This
chapter summarises biofilm data given in the literature.
Molz et al. (1986) assumed a constant average colony size in their groundwater model.
They reported that the observed colony density was 105colonies/cm³ and the population
density was 6.106 bacteria per g dry matter. Zhang and Bishop (1994) and Lazarova andManem (1995) measured the density of the biofilm to be 37mgBM/cm³BM, and 2530mgBM/cm³BM respectively.
Lazarova and Manem (1995) provided also some additional numbers:• ratio of bacteria dry matter and wet matter content = 0.20mgDM,BM/mgWM,BM;• 50% of the organic carbon content of dry matter is assumed to be biofilm;• organic carbon content of dry weight of biomass = 0.1 – 0.5mg TOC/mg DWBM; and• ratio of biomass dry weight and biomass COD = 0.706mg DWBM/mg CODBM.

13

3.4

Parameters of HYDRUS

3.4.1 Diffusion coefficients
Table 3.10 summarises the diffusion coefficients used in CW2D and compares them withother literature values. It is assumed that all nitrogen fractions have the same diffusion
coefficient. Due to the lack of data the diffusion coefficient for inorganic phosphorus isassumed to be the same as for nitrogen. To describe the relationship of between themolecular diffusion coefficients for oxygen in the gas and water phases as a function of thewater content the relationship defined by Millington and Quirk (1961) using tortuosity
factors for the gas and water phase is used (as in HYDRUS-2D, Šimůnek et al., 1999).
Table 3.10: Diffusion coefficients in CW2D.
Diffusion coefficients [dm²s/h]
Phase
CW2D
L&S
B&C
H&H
M&R
gaseous
7.69
7.69
aqueous 7.20E-04 7.20E-04 7.75E-04 8.75E-04
Organic matteraqueous 4.56E-04 4.56E-04 2.50E-04 2.42E-04 9.54E-05
Ammonium nitrogenaqueous 8.01E-04 8.01E-04 6.54E-04 7.50E-04 2.44E-04
Nitrate nitrogenaqueous 8.01E-04
5.79E-04
5.83E-04
Other nitrogen fractions aqueous 8.01E-04
Inorganic phosphorus
aqueous 8.01E-04
L&S (Luckner and Schestakow, 1991), B&C (Bouwer and Cobb, 1987), H&H (Horn and
Hempel, 1998), M&R (Martin and Reddy, 1997).
CompoundOxygenNote that in Table 3.10, and throughout this report, we often use decimetres (dm) for
length units (despite this unit not being supported by HYDRUS-3D). The reason is that 1
dm3 is equal to 1 litre, which makes relatively easy calculations and conversions of various
variables that include solute concentrations, such as solute fluxes.
The exchange of oxygen from the gas phase into the aqueous phase is described using thestandard modeldcO2= akaer ,O2 ⋅ ( cO2, sat − cO2 )dt(3.17)

where a is the air content [mw3/ms3], kaer,O2 is the oxygen re-aeration rate [1/h] and cO2,sat is
the temperature dependent saturation concentration of dissolved oxygen [mgO2/dmw³]. This
term has to be added to the reaction rate constant for oxygen since this is the only way toincrease the concentration of dissolved oxygen (with the exception of water flow). The
value for the oxygen re-aeration rate, kaer,O2, was chosen to be equal to 10h-1. McBride andTanner (2000) used for surface waters an oxygen re-aeration rate, kaer,O2,of 25h-1.

14

3.4.2 Adsorption parameters
Adsorption is considered for ammonium nitrogen and inorganic phosphorus. It is assumed
that adsorption is a kinetic process. Table 3.11 and Table 3.12 show literature values foradsorption isotherms (linear and Freundlich) of ammonium nitrogen and inorganic
phosphorus, respectively, in the soil-water environment. Values vary widely due todifferent substrates used in various studies.
Table 3.11: Coefficient values of linear and Freundlich isotherms for adsorption ofammonium nitrogen.
Literature coefficient values for adsorption of ammonium nitrogen in the soil-water environment
Linear isotherm
Freundlich isotherm
SourcesNH4N = kLIN . cNH4N
sNH4N = k1,F . cNH4N ^ k2,F
kLIN
k1,F
k2,F
Kadlec and Knight (1996)
14.5
0.86
Martin and Reddy (1997)
1.38
Birkinshaw and Ewen (2000)
60
Antonopoulos and Wyseure (1998)
0.25
Yamaguchi et al.(1996)1
2.79
2.90
0.99
DeSimeone and Howes (1998)
1.20
6.20
0.60
Kaluarachchi and Parker (1988),
0.75
and Padilla et al.(1992)
McBride and Tanner (2000) 2
3.0
0.50
1
only experimental data were given, from which coefficients for isotherms were calculated;2
kinetic adsorption behaviour with ωNH4N = 0.8d-1.
cNH4N and sNH4N – ammonium nitrogen concentrations in the aqueous and sorbed phases,
respectively, [mg/dmw³] and [mg/kgs]
kLIN – the distribution coefficient in the linear sorption isotherm [dmw³/kgs]
k1,F – distribution coefficient in the nonlinear Freundlich sorption isotherm [dmw³/kgs . (dmw³/kgs)b ]k2,F – exponent in the nonlinear Freundlich sorption isotherm [-]Table 3.12: Coefficient values of linear and Freundlich isotherms for adsorption ofphosphorus.
Literature coefficient values for adsorption of inorganic phosphorus in the soil-water environment
Linear isotherm
Freundlich isotherm
SourcesIP = kLIN . cIP
sIP = k1,F . cIP ^ k2,F
kLIN
k1,F
k2,F
Kadlec and Knight (1996)
19
58
0.83
Grosse et al. (1999)
185
Gray et al.(2000) 1
38
0.83
Bolton and Greenway (1999)
0.28
1
only experimental data were given, from which coefficients for isotherms were calculated.
cIP and sIP – inorganic phosphorus concentrations in the aqueous and sorbed phases, respectively[mg/dmw³] and [mg/kgs]
kLIN, k1,F, k2,F – see Table 3.11.

15

3.4.3 Heat transport
Since biological reactions are slower when temperature is low, the consideration of heattransport is important for constructed wetlands. While the governing heat transport
equation, and its initial and boundary conditions are given in Šimůnek et al. (1999), here
we will discuss only the coefficients from the governing heat transport equation.
The volumetric heat capacity of the porous medium C(θ) can be calculated asC(θ) = Cs . θs + Co . θo + Cw . θw + Cg . θg

(3.18)

where θx refers to the volumetric fraction [dmx³/dms³], C refers to the volumetric heat
capacity [kg.dms²/(dmx³.h2.K)], and subscripts x = s, o, w, g represent the solid phase,organic matter, liquid phase (water), and gas phase. Parameters used for the volumetricfractions and for the volumetric heat capacities of solid phase, organic matter, liquid phase,and gas phase are given in Table 3.13.
Table 3.13: Parameters of the volumetric heat capacity.
Substance
Air
Water
Humus
Sand, wet

x
g
w
o
s

Volumetric fraction θx[dmx³/dms³](θS - θ)θ

Volumetric heat capacity C x[J/(cmx³.K)][kg.ms².mx-3.h-2.K-1]
0.0013
1.68E+10
4.19
5.43E+13
2.39
3.10E+13
1.26
2.16E+13

0(1 - θS)
Conversion factor: 1 J = 1 N.m = 1 kg.m².s-2 = 1 kg . m² . 36002 . h-2 = 1.296E+07 kg.m².h-2
1 J/(cm³x.K) = 1.296E+07 kg.m².h-2 . 106 m-3x . K-1 = 1.296E+13 kg.m-1.h-2.K-1

The thermal conductivity function λ0(θ) can be described using the empirical equation
derived by Chung and Horton (1987) as follows

λ0 (θ ) = b1 + b2 ⋅ θ + b3 ⋅ θ 2(3.19)

where λ0(θ) is the thermal conductivity of the porous medium [kg.dms/(h³.K)], and b1, b2,
and b3 are empirical factors. The values for b1, b2, and b3 as given in HYDRUS-2D(Šimůnek et al. 1999) are used (Table 3.14).
Table 3.14: Parameters of the thermal conductivity function.
Parameter[W/(m.K)][kg.ms.h-3.K-1]
b1
0.23
1.07E+10b2-2.41-1.12E+11b3
4.91
2.29E+11
Conversion factor: 1 W = 1 J/s; 1 W/(m.K) = 4.666E+10 kg.m.h-3.K-1

16

4

The implementation of CW2D in HYDRUS

4.1

General Remarks

CW2D has been originally developed as an extension of the HYDRUS-2D software
package. Modifications of the original HYDRUS-2D code (Šimůnek et al., 1999) aredescribed first. Then the implementation of CW2D into the HYDRUS software package(Šimůnek et al., 2006a, 2006b) is described.

4.2

Modifications of the original HYDRUS-2D program code

CW2D has been implemented in the HYDRUS-2D software package (Šimůnek et al.,1999). Version 2.11 of HYDRUS-2D supports the CW2D module. Modifications of theoriginal HYDRUS-2D program that were necessary for the implementation of CW2D aredescribed below. These modifications includea) an additional source code for the CW2D module,b) changes in the structure of the main program,c) an additional input in the input file "Selector.in" and the new input file"Options.in",d) a new output file ("effluent.out"),e) implementation of a new boundary condition, andf) a new iterative procedure for solving solute transport equations.
4.2.1 Modifications of the main program
Figure 4.1 shows the flow chart of the original and modified main program of HYDRUS2D. The principle course of a simulation is as follows: after the start of the executable filethe input files are read and various variables are initialised. The simulation starts at theinitial time with the initial time step. Water flow is calculated first for the one time step,
followed by the heat transport and the solute transport. The time step is then updated andthe same procedure is repeated until the end of the simulation time is reached.
The grey rectangles in Figure 4.1 show the parts of the code where the main modifications
have been made. Additional biochemical parameters needed for CW2D were added to the"Selector.in" input file in the new block (see description in Chapter 6.1). Some
additional parameters that are not supported by the graphical interface of Hydrus-2D areread from the "Options.in" input file (Chapter 6.2). An additional output file providing
information about effluent fluxes ("effluent.out", Chapter 7.1) is generated. A new
boundary condition that enables to simulate flooding of the surface of the constructedwetland during the feeding was implemented (Chapter 4.2.2). Since various components in
CW2D depend on each other (contrary to the original HYDRUS-2D code which
considered dependence between solutes only due to sequential decay), major modifications
had to be made in the iterative procedure to solve the system of coupled solute transport
equations (Chapter 4.2.3).

17

HYDRUS-2DHYDRUS-2D

Reading of input-files
Reading of input-files
Initialisation +Start of the simulation

Initialisation +Start of the simulation

Solution of flow
equation

Solution of flow
equation

Next time step

Solution of heattransport equation

Next time step

Solution of solutetransport equation

Solution of solutetransport equation

NO

Simulation
finished?

Solution of heattransport equation

NO

Simulation
finished?

YES
YES
Write output-files
END

END

Figure 4.1: Flow chart of the original (left) and modified (right) main program of
HYDRUS-2D (gray boxes represent routines that were modified to accommodate CW2D).
4.2.2 The ponding boundary condition
To describe flooding of the surface that usually occurs of during the intermittent loading ofvertical flow constructed wetlands the ponding boundary condition was introduced.
Ponding occurs when the infiltration capacity of the soil is smaller than the rate of loading
and thus when the pressure head at the surface becomes positive and the excess water start
accumulating at the soil surface. Original HYDRUS-2D assumed that no ponding occurs at
the surface and that all excess water is immediately removed by the surface runs off.
The ponding boundary condition was implemented as a modification of the atmosphericboundary condition in CW2D. When 'ponding' occurs, it is assumed that water
accumulates at the soil surface and that at the end of the loading period the remaining
water stored on the surface infiltrates into the soil profile. The water mass balance is used
to calculate the reduction of the surface pressure head until all water infiltrates into thesubstrate and the pressure potential at the surface becomes negative.

18

4.2.3 Modifications of Multi-Component Reactive Transport
The original HYDRUS-2D code considers consecutive first-order decay/degradation
involving the sequential degradation of one into another solute. It was therefore possible tosolve transport equations for individual species of the decay chain sequentially, since thesecond solute depended on the first one (and so on), but not vice versa. However, since in
CW2D various components depend in a relatively complex manner on each other, allsolute transport equations need to be solved simultaneously. Some major modifications
thus had to be made in the iterative procedure to solve the solute transport equations
simultaneously to make multi-component reactive transport possible.
The iterative procedure in the subroutine 'Solute' as implemented in the original HYDRUS2D code is shown in the left part of Figure 4.2. During one iteration step the following
subroutines are called inform the 'solute' subroutine:• 'Disper' calculates nodal values of dispersion coefficients for solute transport,• 'PeCour' computes the maximum local Peclet and Courant numbers and the maximum
permissible time step,• 'Coeff' calculates solute transport coefficients,• 'SolMat' constructs the global matrix equation for solute transport,• 'c_Bound' implements boundary conditions and determines boundary solute fluxes inboundary nodes, and finally• the global matrix equation is solved in either ‘Orthomin” or ‘SolveT’.
Implemented chain reactions in the original version of HYDRUS-2D allowed components
to be evaluated one after the other. A component could thus be influenced only by thecomponent preceding it in the reaction chain. When convergence was reached for aparticular component (needed only for nonlinear problems), the iteration procedure for agiven component was finished and the calculation of the next component could be started.
This scenario changes completely when one wants to consider multi-component reactive
transport where components influence each other. Necessary modifications in the 'Solute'subroutine that were needed to implement these mutual interactions between components
are shown in the right part of Figure 4.2. Modified and new parts are emphasized by grey
rectangles and dotted lines.
Due to the mutual interactions between components, all components have to be evaluatedsimultaneously at each iteration step. The iteration procedure had to be rewritten so that
iteration is not done any more at the level of one single component, but must include allcomponents simultaneously. If convergence is not reached for any component, allcomponents have to be re-calculated during the next iteration. Additionally, evaluation ofsorption processes had to be moved to the end of the iterative procedure. The sorbed
concentrations can be calculated only after all liquid components are known.
The subroutine 'CW2D' (see Figure 4.2) calculates the local zero-order reaction rates rcj(see Šimůnek et al., 1999) and the local reaction terms ri given in Equation (3.1) using theconcentrations from the previous time step. Figure 4.3 (left) shows the flow chart of thesubroutine 'CW2D'. During the iteration process itself the reaction rates are assumed to beconstant.
Calculated reaction terms from the ‘CW2D’ subroutine are then assigned in the 'Coeff'
subroutine (Figure 4.3, right) to zero order coefficients that are then used in a usual mannerto assemble the system of algebraic equations resulting from discretization of governing
advection-dispersion partial differential equation.

19

solutesoluteFirst iteration step
Start calculation with
first component

CW2D

First iteration step

Start calculation with
first component
DisperDisper
PeCour

PeCourNext component

Coeff

Next iteration

Next component

Coeff

Next iteration

SolMatSolMatc_Boundc_Bound
Solution of the global
matrix equation

Solution of the global
matrix equation
Convergence?

NO

YES
Calulate sorbed
concentrationNO

All components?

YES

Convergence?
NONOAll components?

YES
YES

Calulate sorbed
concentration
RETURN

RETURN

Figure 4.2: Flow chart of the original (left) and modified (right) 'Solute' subroutine.
CW2D

Coeff

Calculation offactors of N and P continuity

Calculation oftemperature dependencies

Calculation oftemperature dependencies

Calculation of
zero-order reaction rates

Calculation of
local process rates

Calculation of non-linear andkintic adsorption

Calculation of
local zero-order reaction rates

Calculation of coefficients
Gi(ci) and Fi(ci)

RETURN

RETURN

Figure 4.3: Flow chart of subroutines 'CW2D' and 'Coeff'.

20

4.3

The CW2D/HYDRUS user interface

4.3.1 Preliminary remarks
Concentrations units in the liquid and solid phases, as well as units of the bulk density, arefixed after choosing the length units in the "Geometry Information" window (Figure 4.4)
according to Table 4.1.

Figure 4.4: "Geometry Information" window.
Table 4.1: Units of concentrations in the liquid and solid phases and of the bulk density
Length Unit
m
dm*
cm
mm
Concentrations in liquid phase g.m-3 mg.dm-3 = mg.l-1 µg.cm-3 = µg.ml-1 ng.mm-3 = ng.µl-1
Concentrations in solid phase
g.t-1
mg.kg-1µg.g-1
ng.mg-1-3-3-3
Bulk density
t.m
kg.dm
g.cm
mg.mm-3* not supported by user interface. To use this length unit, user needs to manually rewrite the length
unit at the 6th line in the ‘Selector.in’ file in the temporary working directory created by
HYDRUS (Šimůnek et al., 2006a).

The reactions in CW2D are implemented in the governing solute transport equations aszero-order rate constants. Based on the governing equation for macroscopic transport (e.g.
Equation 3.1 in Šimůnek et al., 1999) the relationship between the units of concentrationsin the liquid and solid phases is therefore defined as:⎡ρ ⎤[c ] = ⎢ s ⎥
⎣θ ⎦

(4.1)

21

where brackets denote units, c is the concentration in the aqueous phase [mg/dmw³], θ isthe volumetric water content [dmw³/dms³], ρ is the soil bulk density [kgs/dms³], and s is theconcentration in the solid phase [mg/kgs], or in units
mg.dmw-3 = kgs .dms-3 . dmw-3.dms3 . mg.kgs-1(4.2)

From Equation (4.2) it becomes clear that the unit of the bulk density has to be kg.dm-3.
The HYDRUS user interface does not provide conversion of mass units, such as kg in
Equation (4.2), and thus the default values of CW2D must be interpreted based on
Table 4.1. Therefore units of concentrations in the liquid and solid phases and of the bulk
density are fixed according to Table 4.1 once the length units are chosen.
In other figures shown in this chapter, "m" and "Days" are used as a length and time units,
respectively.

4.3.2 Implementation of CW2D into the HYDRUS user interface
Pre-processing
To activate the CW2D module in the HYDRUS graphical user interface in the "Solute
Transport" window (Figure 4.5) the "Wetland Module" box has to be ticked. The massunit has to be set according to the chosen length unit (Table 4.1) and the number of solutes
has to be set to 13 (12 CW2D module compounds and one non-reactive tracer compound,that is independent from the other 12 compounds). If the Wetland Module is chosen the"Attachment/Detachment Concept" can not be used.

Figure 4.5: "Solute Transport" window.
Figure 4.6 shows the "Solute Transport Parameter" window where the general transportparameters are set (bulk density, dispersivity, and diffusion coefficients in the liquid andgaseous phases, chemical and physical non-equilibrium transport parameters; fordescription see HYDRUS manual, Simunek et al., 2006a). Figure 4.7 and Figure 4.8 show
22

the two user interface windows for the CW2D model parameters. For definition ofparticular parameters see Chapters 3.3 and 6.1, respectively.

Figure 4.6: "Solute Transport Parameter" window (length unit: m; time unit: d).

Figure 4.7: "Solute Transport – CW2D Model Parameters I" window (time unit: d).

23

Figure 4.8: "Solute Transport – CW2D Model Parameters II" window (time unit: d).
Figure 4.9 shows the definition of the pressure head initial conditions. Names of allcompounds appear under "Initial conditions" in the left sidebar, with the "L" letter
denoting the concentration in the liquid phase and "S" the concentration in the solid phase.

Figure 4.9: "Initial Conditions".

24

Post-processing
Figure 4.10 shows "Results - Graphical Display" where also the names of the compounds
are shown, Figure 4.11 the "Observation Nodes" window. Again names of all variables are
displayed, including all biochemical compounds.

Figure 4.10: "Results - Graphical Display".

Figure 4.11: "Observation Nodes" window.

25

5

Examples5.1

Pilot-scale subsurface vertical flow constructed wetland for
wastewater treatment

5.1.1 System description

Figure 5.1 shows the pilot-scale subsurface constructed wetland (PSCW) that is based on
Austrian standards for vertical flow constructed wetlands for wastewater treatment(ÖNORM B 2505, 1997). One PSCW has a surface area of 1 m², while five PSCW are
operated in parallel (Langergraber et al., 2003). The height of the main layer of the filter
bed is 60 cm. The main layer consists of sand (gravel size 0.06-4 mm or 1-4 mm,
respectively). An intermediate layer of 10 cm thickness with a gravel size of 4-8 mm
prevents fine particles to be washed out into the drainage layer (15 cm thick; gravel 1632 cm) where the effluent is collected by means of tile drains.
The PSCW is loaded intermittently with wastewater. Following Austrian standards, thedaily loading rate is 40 litres at application intervals of 6 hours long (i.e., a single loading
comprised 10 litres). Pressure heads and water contents are measured automatically at
regular time intervals at different depths (every 10 cm in the main layer). Additionally, theeffluent flow rate is measured manually.

60

INLET

15 10

main layerintermediate layer

OUTLETdrainage layer

Figure 5.1: Schematic of the pilot-scale subsurface constructed wetland (values are in cm).
5.1.2 Measured data

The sandy material used for the main layer had a porosity of 0.30 and the saturated
hydraulic conductivity, Ks, of 11.7 dm/h. Table 5.1 shows the measured cumulated effluent
for one loading interval of 6 hours (360 minutes) and a single hydraulic loading of
10 litres.
Table 5.1. Measured cumulated effluent
Time
Cum. effluent
Time
Cum. effluent
Time
Cum. effluent

26

[min]
[litre][min][litre][min][litre]

10
0.16
120
3.11
240
7.31

20
0.31
130
3.54
255
7.70

30
0.48
140
3.95
270
8.08

40
0.64
150
4.37
285
8.45

50
0.80
160
4.75
300
8.78

60
0.99
170
5.12
317
9.16

70
1.20
180
5.47
330
9.43

80
1.49
190
5.80
345
9.70

90
1.87
200
6.14
360
9.99

103
2.39
212
6.53
-

110
2.67
225
6.90
-

Tracer experiments using NaCl were run for daily hydraulic loading rates of 40 and
60 litres. The electrical conductivity of the effluent, which is directly related to the tracer
concentration, was measured automatically. The measured influent conductivity of the
tracer was 30 mS.cm-1, while the background conductivity during the tracer experimentwas 1.5 mS.cm-1. Influent and effluent concentrations of various nitrogen species and totalorganic carbon (TOC) were measured periodically. Table 5.2 shows the median values andconfidence intervals of the measured influent and effluent concentrations for NH4-N,
NO3-N, and TOC.
Table 5.2. Median values and confidence intervals (in parenthesis) of the measured
influent and effluent concentrations of NH4+, NO3- and total organic carbon
in mg.l-1 (Langergraber, 2003).
Component
Influent
Effluent 0.06-4 mm substrate
Effluent 1-4 mm substrate

NH4-N
60.0 (11.2)
0.15 (0.03)
1.20 (0.31)

NO3-N
3.0 (0.8)
38.5 (6.8)
50.0 (8.7)

TOC
82.9 (3.5)
3.9 (0.2)
6.4 (0.3)

5.1.3 Simulation set up

The width of the transport domain was 1 m (only one half of the PSCW width isconsidered), and its depth is 0.6 m (only the main layer is simulated), while the transportdomain itself was discretized into 6 columns and 21 rows. This results in a structured twodimensional finite element mesh consisting of 126 nodes and 200 triangular finite elements(Figure 5.2). An atmospheric BC is assigned to the top and a constant pressure head BC(constant head of -2 cm) to the bottom of the system.

Z

X

Figure 5.2: Two-dimensional finite element mesh of the PSCW.

27

5.1.4 Simulation results

Simulation of water flow
Table 5.3 shows various parameter sets of the van Genuchten-Mualem soil hydraulicproperty model used in flow simulations (Figure 5.3 and Figure 5.4). The "Literature"parameter set 1 is based on default parameters provided by HYDRUS for sand using
pedotransfer functions published by Carsel and Parrish (1988). The shape factors for sandwere also used for parameter set 2 in Table 5.3, but now with the measured values of thesaturated water content θs and the saturated hydraulic conductivity Ks. Parameter set 3 inTable 5.3 was obtained by calibrating the model against cumulative effluent data, whileparameter set 4 represents parameters optimized using the effluent rates. Parameter set 5
are those reported by Langergraber (2003) who, in addition to the effluent rates, also usedwater content measurements at 25 cm depth, while simultaneously optimizing the saturated
hydraulic conductivity Ks.
Table 5.3. Literature and fitted soil hydraulic parameters of the van GenuchtenMualem model for the 0.06-4 mm substrate.
Set Parameter
1
2
3
4
5

Residual water Saturated water
Parameternlcontent θscontent θrαUnit(dmw³.dms-³)(dmw³.dms-³)(dms-1)(-)(-)
Literature
0.045
0.43
1.45
2.68
0.5
0.045
0.30
1.45
2.68
0.5
Measured Ks +θs
Fitted (1)0.08660.30
1.520 2.472 0.696
Fitted (2)0.07240.30
1.596 2.214 0.682
Langergraber (2003)
0.056
0.289
1.26
1.92
0.5

Saturated hydraulicconductivity Ks(dms.h-1)
2.97
11.7
11.7
11.7
8.4

10

Cumulative effluent (liter)

Measured data
Literature parameters
8

Measured ks + porosity
Fitted parameters 1
Fitted parameters 2

6

4

2

0
0

1

2

3

4

5

6

Time (hours)

Figure 5.3: Measured and simulated cumulated effluent for a single application of 10 litres(4 loadings per day; daily hydraulic load of 40 litres).
Figure 5.3 and Figure 5.4 show the measured and simulated cumulated effluents andeffluent flow rates, respectively. Simulation results are presented for parameter sets given
in Table 5.3. The simulation using the fitted parameter set 3 shows a good match with themeasured cumulated effluent (Figure 5.3). However, peak effluent rates are significantly
28

overpredicted (Figure 5.4). The Parameter set 4 describes the effluent rates much better.
However, the best fit was obtained (Figure 5.5) with the parameter set of Langergraber(2003), which indicates that additional water content data and more degrees of freedom in
optimization (i.e., one additional parameter was fitted) can result in a better calibration of
the flow model.
60
Measured data
Literature parameters
Measured ks + porosity
Fitted parameters 1
Fitted parameters 2

Effluent rate (ml/min)

50

40

30

20

10

0
0

1

2

3

4

5

6

Time (hours)

Figure 5.4: Measured and simulated effluent rates for a single application of 10 litres(4 loadings per day; daily hydraulic load of 40 litres).

60
10

Measured data
Measured ks + porosity

Cumulative effluent (liter)

Effluent rate (ml/min)50

Langergraber (2003)
40

30

20

Measured data
8

Measured ks + porosity
Langergraber (2003)

6

4

2

10

0

0
0

1

2

3

Time (hours)

4

5

6

0

1

2

3

4

5

6

Time (hours)

Figure 5.5: Measured and simulated effluent rates (left) and cumulated effluent (right) for asingle feeding of 10 litres (4 loading per day, daily hydraulic load of 40 litres).

Figure 5.6 shows the measured and simulated effluent rates and cumulative effluents for an
increased daily hydraulic loading rate of 60 litres using fitted parameter set as given byLangergraber (2003, see Table 5.3). Again, it was possible to simulate the measured
hydraulic behaviour.

29

100

25

Effluent rate (simulated)

Effluent rate (ml/min)

80

20

Cumulated effluent (simulated)
Cumulated effluent (measured)

60

15

40

10

20

5

0

Cumulated effluent (litre)Effluent rate (measured)

0
0

1

2

3

4

5

6

Time (hours)

Figure 5.6: Measured and simulated effluent rates and cumulated effluent for a single
feeding of 15 litres (4 loading per day, daily hydraulic load of 60 litres).

Simulation of surface ponding
Figure 5.7 shows the pressure head at the top of the constructed wetland system during aloading when ponding occurred (loading for 1 minute with 0.333 dm/minute). Positive
pressure heads indicate existence of the water layer on the top of the system.

Figure 5.7: Simulated pressure heads at the top of the constructed wetland system.

30

Simulation of single-component solute transport
Table 5.4 shows parameters that were used for the equilibrium general solute transportmodel, and Table 5.5 parameters for the physical non-equilibrium transport model. The
physical equilibrium transport model assumes that all pore water is mobile, whereas thephysical non-equilibrium transport model considers a fraction of the pore water to be
immobile (stagnant). Figure 5.8 compares simulated and measured breakthrough curves(Langergraber, 2003). For both hydraulic loading rates the simulation results matched themeasured data relatively well.
Table 5.4. Parameters of the general equilibrium solute transport modelParameter
Unit
Value

Diffusion coefficient(dms2.h-1)
0.05

Longitudinal dispersivity
(dms)
0.125

Transverse dispersivity
(dms)
0.10

Table 5.5. Parameters for the physical non-equilibrium transport modelParameter
Unit
Value

Fraction of sorption sites incontact with mobile water
(-)
0.95

Immobile
water content(dmw³.dms-³)
0.05

Coefficient for solute exchange
between mobile and immobile water
(h-1)
2

8

Electrical conductivity (mS/cm)

40 litre/day (measured)
7

40 litre/day (simulated)
60 litre/day (measured)

6

60 litre/day (simulated)
5
4
3
2
1
0
0

1

2

3

4

5

Time after start of tracer experiment (days)

Figure 5.8: Measured and simulated effluent electrical conductivities for different daily
hydraulic loads.

Simulation of multi-component reactive transport
Table 5.6 shows measured influent and effluent concentrations of selected components, aswell as the influent concentrations used in the CW2D simulation, and the resulting
simulated effluent concentrations. The simulated and measured effluent concentrations ofammonium nitrogen are lower for the 0.06-4 mm gravel than for the coarser material31

(gravel size of 1-4 mm). The higher flow rates in the main layer with the coarse material
reduce the contact time between water and the bacteria. The effluent concentrations ofammonium nitrogen, NH4N, and the slowly degradable organic matter, CS, aresignificantly higher for the coarser material. Effluent nitrate concentrations are also higher
because of less readily degradable organic matter CR produced by hydrolysis that could be
utilised for denitrification in deeper layers.
Table 5.6. Measured and simulated influent and effluent concentrations.
Component
Unit
Influent
Measured (median)Simulation (input)
Effluent
0.06-4 mm substrate
Measured (median)Simulation (median)
1-4 mm substrate
Measured (median)Simulation (median)

NH4-N(mg.l-1)

NO3-N(mg.l-1)

TOC(mg.l-1)

COD
CR
CS(mgCOD.l-1) (mgCOD.l-1) (mgCOD.l-1)

60.0
60.0

3.0
3.0

82.9
-

300

150

130

0.15
0.01

38.5
41.1

3.9
-

23.8

0.6

0.4

1.20
0.16

50.0
63.0

6.4
-

30.1

0.3

5.7

Results of the reactive transport simulations showed an overall good match with themeasured data. This could be partly explained by the good calibration of the flow model,
which was made possible by having data that provided a good definition of flow processes
in the system.
Below we present several figures showing time series of the simulation results for two
loadings using the "Graphical Display of Results" and the "Observation Nodes" postprocessing windows, respectively. Three observation nodes are defined in 5, 15, and 50 cm
depths of the system (in the 60-cm main layer). Figure 5.9 shows time series for thepressure head and dissolved oxygen. Oxygen depletion at depths of 5 and 15 cm can beobserved to occur immediately after loading due to degradation. However, the oxygen
concentration at 50 cm stays rather constant at a level close to the saturation concentration
during the entire loading interval. After less than 2 hours the oxygen concentration at
depths of 5 and 15 cm reaches saturation again.

32

Figure 5.9: Pressure head (left) and dissolved oxygen (right).
Time series and vertical concentration profiles at the end of the simulation (12 hours) are
shown in Figure 5.10 and Figure 5.11 for heterotrophic and autotrophic organisms,
respectively. During two loading intervals the concentrations of the micro-organisms
remained constant, thus indicating quasi steady-state conditions when growth and lysis
processes are in balance (Figure 5.10 and Figure 5.11, left). Almost all micro-organisms
were present in the top 20 cm of the filter (Figure 5.10 and Figure 5.11, right), where mosttransformations and degradation processes took place.

Figure 5.10: Time series (left) and vertical profile (right) of heterotrophic micro-organims.

33

Figure 5.11: Simulated time series (left) and vertical profile (right) of autotrophic microorganisms.
Figure 5.12 shows time series for ammonium and nitrate nitrogen, respectively. The
effluent concentration for NH4N and NO3N were about 0.01 mg/l and 41 mg/l,
respectively. Vertical concentration profiles at simulation times of 1 minute (end ofloading), 6 minutes, 30 minutes, and 2 hours are shown in Figure 5.13 for ammonium
nitrogen and in Figure 5.14 for nitrate nitrogen, respectively. Notice that the concentration
peaks for NH4N at 5 and 15 cm coincide with minima in the NO3 simulations. By contrast,
concentrations of NH4 and NO3 remained very stable at 50 cm depth.

Figure 5.12: Ammonium (left) and nitrate nitrogen (right).

34

Figure 5.13: Vertical profiles of ammonium nitrogen at t = 1 minute (end of loading),
6 minutes, 30 minutes, and 2 hours.

Figure 5.14: Vertical profiles of nitrate nitrogen at t = 1 minute (end of loading), 6 minutes,
30 minutes, and 2 hours.

35

5.2

Two-stage subsurface flow constructed wetland

5.2.1 System description

The Small-Scale Plot (SSP) system described by Grosse et al. (1999) is a pilot-scale twostage vertical flow constructed wetland for the treatment of heavily polluted surface water.
The total surface area of the SSP is 2 m², being divided into downflow and upflow
chambers (each having a surface area of 1 m²). The inlet is situated on top of the downflow
chamber. The effluent is collected in the upflow chamber by means of perforated pipes. A
separating wall is built between the downflow and upflow chambers.
Figure 5.15 shows a schematic of the SSP (Perfler et al., 1999). Heights of the downflow
and upflow chambers are 85 and 60 cm, respectively. The drainage layer at the bottom ofboth chambers has a height of 15 cm. This layer was connected to the two chambers andcontained two tile drains. The main layers of depths of 55 and 45 cm in the downflow andupflow chambers, respectively, is filled with sand (gravel size 0.06-4 mm, 0-4 mm in
Figure 5.15). The top layer of the downflow chamber has a height of 15 cm (gravel size 48 mm). Algae growth in the top layer was prevented by keeping the water table during
application beneath the soil surface. Figure 5.16 shows sampling points in the main layer
for measurements along the flow path.

Δ10

OUTLETsand - gravel 0/4 mm

drainage layer - gravel 16/32 m m

CHAMBER ADOWNFLOW

45

15

sand - gravel 0/4 mm

15

top layer - gravel 4/8 mm

55

INLET

geotextile

CHAMBER B
UPFLOW

Figure 5.15: Schematic of a pilot-scale vertical flow constructed wetland (SSP) (distances
are in cm).

B-3 x

x A-5

B-2 x

x A-6

B-1 x

50

25

x A-1
x A-2
x A-3
x A-4

20
35

50
35
20

70
65
57.5

25

CHAMBER A
CHAMBER B
DOWNFLOW
UPFLOW
Figure 5.16: Sampling points in the main layer of the SSP (distances are in cm).

36

5.2.2 Simulation set up

The unstructured two-dimensional finite element mesh used for the SSP simulations
consists of 1135 nodes and 2057 elements (Figure 5.17). The inlet distribution pipe at the
top of the downflow chamber is modelled as a time dependent atmospheric boundary
condition. Outlet (effluent) drainage pipes are modelled as circular openings in thetransport domain, and subjected to seepage face boundary condition.

Z

X

Figure 5.17: The unstructured two-dimensional finite element mesh of the SSP.

5.2.3 Simulation results

Simulation of single-component reactive transport
To show the influence of using the physical non-equilibrium transport model incomparison with the physical equilibrium transport model, simulation results are shown
only for the single-component, i.e., the simulation of a tracer experiment (Langergraber,
2003).
During the tracer experiment the background electrical conductivity was 0.75 mS.cm-1.
The loading rate was 50 litres every 2 hours (i.e., 600 litres.day-1). During the first feeding
interval the conductivity of the inflow was 30 mS.cm-1. During the following feedings the
inflow conductivity was 0.75 mS.cm-1.
Table 5.7 shows the soil hydraulic parameters of the van Genuchten-Mualem model used,
Table 5.8 shows the parameters for the physical non-equilibrium transport model. The
same values as shown in Table 5.4 were used for the general solute transport model
parameters.
Figure 5.18 shows breakthrough curves of the simulated and measured electricalconductivities at three different sampling points and at the outlet of the SSP. The figurecompares simulation results with physical equilibrium and non-equilibrium (using conceptof mobile-immobile water) transport models.
Taking into account stagnant (immobile) regions of the pore water results into a better
match of data by the simulation, compared to when only mobile pore water is considered.
Neglecting the immobile regions leads to higher electrical conductivity values than
measured (e.g. upper right graph of Figure 5.18) and to an early rise of the breakthrough37

curves in the upflow chamber (Figure 5.18, lower left graph) and at the outlet (Figure 5.18,
lower right graph). The observed behaviour that the effluent concentration raises earlier
than the concentration in the upper sampling point of the upflow chamber (B-3) could be
simulated for both, physical equilibrium and non-equilibrium transport. However,considering physical non-equilibrium transport the peak values are lower and in the rangeof the observed values.
Table 5.7. van Genuchten-Mualem soil hydraulic parameters for the two-stage
constructed wetlands system
Parameter

Residual water Saturated water Parameterncontent θrcontent θs
α
-1
Unit
(dmw³.dms ³)(dmw³.dms ³)(dms ) (-)
Top layer
0.045
0.41
1.45
5.0
Main layer
0.045
0.30
1.45
2.68
Drainage layer *
0.056
0.15
1.45
1.92
* Drainage layer is always saturated

Saturated hydraulicconductivity Ks(dms.h-1)
6000
11.7
6000

l
(-)
0.5
0.5
0.5

Table 5.8. Parameters for the physical non-equilibrium transport modelParameter
Unit
Value

Fraction of sorption sites incontact with mobile water
(-)
0.95

Immobile
water content(dmw³.dms-³)
0.05

30

Coefficient for solute exchange
between mobile and immobile water
(h-1)
2

16

A - 6 (20cm)
14

25

conductivity [mS/cm]

conductivity [mS/cm]

A - 4 (50cm)
Simulated conductivity(only mobile water)

20

Simulated conductivity(mobile/immobile water)

15

Measured conductivity

10
5

12

Simulated conductivity(only mobile water)

10

Simulated conductivity(mobile/immobile water)

8

Measured conductivity

6
4
2

0

0
0

2

4

6

8

10

0

2

4

6

8

8

5

Simulated conductivity(mobile/immobile water)

4

Measured conductivity

conductivity [mS/cm]

conductivity [mS/cm]

7
Simulated conductivity(only mobile water)

12

14

16

8

B - 3 (50cm)

6

10

18

3
2
1

effluent

7

Simulated conductivity(only mobile water)

6

Simulated conductivity(mobile/immobile water)

5

Measured conductivity

4
3
2
1

0

0
0

2

4

6

8

10

time [h]

12

14

16

18

20

0

2

4

6

8

10

12

14

16

18

time [h]Figure 5.18: Simulated and measured electrical conductivities for three sampling points
and at the outlet (Langergraber, 2003).

38

20

time [h]time [h]20Simulation of multi-component reactive transport
Table 5.9 shows the influent concentrations for the multi-component reactive transport
simulations. Since this system was used to treat polluted surface water, the concentrations
are much lower compared to wastewater.
Table 5.9. Influent concentrations for the multi-component reactive transport simulations.
Parameter O2
Value
1

CR
15

CS
1

CI
1

NH4N
6.5

NO2N
0.1

NO3N
2

N2N
10

IP
0.4

Figure 5.19 shows the distribution of heterotrophic organisms XH. The maximum XH
concentration is in the upper part of the main layer of the downflow chamber. Bacteria
concentrations decrease with depth. In the upflow chamber the bacteria concentration is
low because of a lack of substrate.
Figure 5.20 shows the distribution of Nitrosomonas XANs. The distribution of the second
autotrophic organism, Nitrobacter XANb, was found to be very similar (not further shownhere). Again, most autotrophic bacteria were located in the upper part of the downflow
chamber. The maximum concentration of autotrophic bacteria was lower than the
maximum concentration of the heterotrophic bacteria. The concentration decreased fasterwith the depth for the autotrophic bacteria than for the heterotrophic bacteria. This is adirect consequence of nitrification being a strictly aerobic process, with oxygen being only
available in the upper parts of the downflow chamber (see also Figure 5.21).

Z

X

0.933

22.45643.97965.50387.026 108.549 130.072 151.596 173.119 194.642 216.165 237.689

Heterotr. Micro. - S5[-], Min=0.933, Max=237.689

Figure 5.19: Simulated steady-state distribution of heterotrophic organisms XH.

39

Z

X

0.895

6.438 11.981 17.525 23.068 28.611 34.155 39.698 45.241 50.785 56.328 61.871

Autotr. Micro - NS - S6[-], Min=0.895, Max=61.871

Figure 5.20: Calculated steady-state distribution of Nitrosomonas XANs.
Figure 5.21 shows time series of dissolved oxygen for two consecutive applications to themain layer in the downflow chamber (0 cm) and at two different depths (5 cm and 15 cm,
located in the unsaturated and saturated zones, respectively). After loading, the DOconcentration decreases at the surface and at the 5 cm depth. At 15 cm depth, however, theDO concentration increases due to advective DO transport with the infiltrating water. Still,
oxygen decreased quickly (within 15 minutes after loading) due to the consumption ofoxygen. No oxygen was found at 15 cm depth (i.e., in the saturated zone) during theremainder of the simulation. In the unsaturated zone (5 cm depth) the DO concentration
increases again due to re-aeration, and reaching oxygen saturation after about 1 hour after
loading.
Figure 5.22 shows time series of ammonium and nitrate nitrogen at the surface of the main
layer (0 cm) and at three different depths (5 cm, located in the unsaturated zone, and 15 cm
and 30 cm, located in the saturated zone). After loading, NH4N increases whereas NO3N
decreases. Further on NH4N is nitrified resulting in an increasing NO3N concentration. At
15 cm depth changes in concentration occur mainly due to convection since oxygen isalready a limiting factor (Figure 5.21). Notice, again, that only small changes inconcentrations occur at 30 cm depth.

40

Figure 5.21: Simulated time series of dissolved oxygen.

Figure 5.22: Simulated time series of ammonium nitrogen (left) and nitrate nitrogen (right).

41

5.3

Constructed wetland for treatment of combined sewer overflow

5.3.1 System description

CW2D was tested to model a subsurface flow constructed wetland for the treatment of
combined sewer overflow (CSO). CWs for the treatment of CSO are generally designed asvertical flow soil filters with a detention basin on top of the filter layer. Main treatment
objectives are (1) detention and reduction of peak flows, (2) reduction of suspended solids
by filtration and (3) reduction of soluble and particulate pollutants by adsorption andsubsequent biological degradation (Dittmer et al., 2005). To reach the first objective
throttle valves are applied to limit the maximum effluent flow rate and therefore the flow
velocity in the filter itself. For simulation purposes the maximum allowed effluent flowrate had to be implemented.
Fundamental differences between wetlands for wastewater and CSO treatments are theloading regime and the quality parameters of the inflow. In the CSO treatment thesuccession of loading events and dry periods is characterized by the stochastic nature of
rainfall and the runoff behaviour of the catchment area. Extreme cases involve a permanentloading for weeks on the one hand, and several months without any loading event on theother. Loading rates (inflow/filter area) show a high variability ranging from mean valuesof 0.02 mm/s for less intensive rain events, up to peak flows of 1 mm/s during intensive
storm events.
Quality parameters of CSO show generally lower pollution than wastewater. Organic
matter predominantly occurs in particulate form, which can mainly be attributed toremobilisation of sewer sediments. As thiseffect is strongly related to the flow rate, totalsuspended solid concentrations, as well as
solute/particulate ratio of pollutants, are highly
supernatantΔH
variable within the course of a rain event.
water
deaeration
pipe

sand,
0/2 mm100 cmSimulations were performed for a lab-scalecolumn (diameter 19 cm, Figure 5.23). The
laboratory layout corresponds to the layering ofa full scale CW. The main layer consists of sand(grain size 0/2 mm, effective size 0.1 mm,
coefficient of uniformity 2.8). The upper gravel
layer serves to prevent erosion, while the gravel
layer below the filter represents the drainage
system.

gravel,2/8 mm
25 cm

The test site consists of 6 columns, which are all
fed identically. The filtration rate of columns 1
to 4 is manually controlled by a throttle in theoutlet; Columns 5 and 6 have a free drainage(Table 5.10).

gravel,2/8 mm,5 cm

throttle

Figure 5.23: Lab-scale filter column.

42

Table 5.10: Drainage regime of the filter
columns.
ColumnDrainage
Filtration rate (m/h)
Effluent flow (litre/h)

C 1/2
throttled
0.036
1

C 3/4
throttled
0.180
5

C 5/6
free
-

The columns are loaded regularly once a week with 15.7 litres of synthetic sewer, whichcorresponds to a loading rate of 0.5 m/event. The entire volume is applied within about
3 minutes. During infiltration the level of the supernatant water, the water level in the
deaeration pipe and the effluent flow rate are measured (variable time steps 30 sec to
30 min). The synthetic sewer is based on the OECD guideline 303A (OECD, 1981), but isdiluted to obtain concentrations within therange of CSO quality parameters.
Tracer experiments using potassium
bromide (KBr) were carried out. The
loading procedure was divided into threesteps. The columns were first loaded with
9.5 litres of bromide-free water, and after
this volume has infiltrated, another 2.5 litres
were applied containing 10 mg/l Br-. Finallyafter the tracer has infiltrated, the last
3.5 litres of bromide-free were loaded. Brconcentrations in the effluent were
measured with an ion-selective electrode.
5.3.2 Simulation set up

For the simulation a structured twodimensional finite element mesh with
105 rows and 3 columns resulting in
315 nodes and 416 elements was used
(Figure 5.24). An atmospheric boundary
condition was applied on top of the upper
layer, while a free drainage or seepage facewith maximum allowed flux was used at thebottom.
Z

X

Figure 5.24: Two-dimensional finite
element mesh of the lab-scale column.

The supernatant water level decreases fromabout 40 to 45 cm immediately after theloading with a rate of 2.5 cm/minute. To
simulate this behaviour a "virtual" layer
with 100 % pore volume was used at the top(Dittmer et al., 2005).

5.3.3 Simulation results

Calibration of Flow and Transport Models
CW2D has successfully been applied to model wetlands with free drainage. CWs for CSO
treatment are generally operated with a controlled effluent flow rate. As loading rates andintervals are determined by rainfall, operation of the effluent throttle is the only way to
influence the performance of the plant. It is therefore essential that the model gives correct
results for a wide span of possible effluent flow rates. Hence, the flow model wascalibrated on the basis of data obtained from operation with free drainage. The calibrated
model was than applied to the columns with controlled effluent rates (Dittmer et al., 2004).
The retention and hydraulic conductivity functions for unsaturated conditions weremodelled using the van Genuchten-Mualem equations (van Genuchten, 1980) implemented
in HYDRUS-2D. Values for the sand (gravel) layer are given in Table 5.11 (Dittmer et al.,43

2005). The virtual layer for supernatant water was simulated with θr = 0 and θs = 1 andKs = 106 cm/h. With these values, head loss and retardation within this layer are negligible.
The longitudinal dispersivity used was 2 cm in the top layer and 3 cms in the other layers,
the transverse dispersivity used was 10 cms for all layers.
Table 5.11: Values of the van Genuchten model parameters.
Parameter

Depth

Unit
1) Top layer2) Gravel3) Main layer4) Gravel

(cm)
100
5
100
25

Residual watercontent θr(cmw³ / cms³)
0
0.05
0.055
0.05

Saturated watercontent θs(cmw³ / cms³)
1
0.37
0.30
0.37

Parametersn(cms-1)
(-)
0.35
3
0.05
2. 8
0.02
3
0.05
2.8

α

Saturated hydraulicconductivity Ks(cm/h)
1000000
36000
1000
36000

14
12
Measured data 1

Effluent (ml/s)

10Measured data 2
Simulation

8
6
4
2
0
0

10

20

30

40

50

60

Time after loading (min)Figure 5.25: Measured and simulated effluent flow rate of column 6.
Figure 5.25 and Figure 5.26 show the measured and simulated effluent flow rates andtracer breakthrough curves for column 6, respectively. Several measured curves of effluent
rates in Figure 5.25 show significant variations that occurred despite virtually identicalconditions of all loading events. This confirms that the infiltration process under the given
combination of basic conditions (free drainage, extremely high loading rate and pressure
head of supernatant water) is extremely sensitive. Considering these uncertainties
simulated and measured data show a good match.

44

10

Tracer concentration (mg/l)

987Measured6

Simulated
5
4
3
2
1
0
0

5

10

15

20

25

30

Cumulated effluent volume (litre)

Figure 5.26: Measured and simulated breakthrough curves of column 6.

Simulation with controlled flow rate
As described above the operation of a constructed wetland for CSO treatment is generallywith a controlled flow rate. This was implemented by setting a maximum for a seepage
face flux. This option, i.e., the maximum allowed flux at the seepage face, is initiated by
setting the logical variable lSeepLimit to true in the "options.in" input file (seedescription in Chapter 6.2).
Parameters obtained above were used for simulation runs with the controlled flow rate. The
throttle has no influence on the infiltration rate (gradient of supernatant water level) at the
beginning. When the soil becomes largely saturated after about 11 minutes, the simulated
infiltration rate abruptly drops to the level of the effluent rate. In the laboratory experiment
this decrease took about another 10 minutes. The final level of saturation is not reachedinstantaneously. This difference can be explained by the influence of air flow within thecolumns, which is not considered in the model.
Figure 5.27 shows results of simulations for the lab-scale columns with free drainage andcontrolled effluent flow rates, respectively. The settings for the controlled effluent ratecase: qSLimit = 3.6 cm/h (the maximum allowed flow rate, corresponding to 68.4 cm²/h or
1 litre/hour) and hSeep = -100 cm (the maximum allowed pressure head). Note that while
the left graph in Figure 5.27 uses minutes as time units, the right graph uses hours. Whilein the flow unrestricted case the bulk of water passed through the CW system in only about
1 hour, in the flow restricted case this happened in about 17 hours. Obviously, in the flow
restricted case, the water and dissolved pollutants had much longer contact with the gravelmaterial.

45

Figure 5.27: Comparison of simulations with free drainage BC (time units = minutes) andlimited seepage face flux (time units = hours).
Figure 5.28 shows measured and simulated breakthrough curves of column 4 and column 2
with controlled effluent rates 5 litres/hour and 1 litre/hour, respectively. Using the transportparameters obtained from the free drainage simulations (column 6) the tracer experimentswith controlled effluent rate could be simulated.

Tracer concentration (mg/l)

12

10

8

6
Column 4 (5 litre/h) - measured
4

Column 4 (5 litre/h) - simulated
Column 2 (1 litre/h) - measured

2

Column 2 (1 litre/h) - simulated

0
0

1

2

3

4

5

6

7

Time after start of the tracer experiment (h)Figure 5.28: Measured and simulated breakthrough curves of column 4 and column 2(controlled effluent rate 5 litre/hour and 1 litre/hour, respectively).

46

5.4

Experiences, limitations and research need

Our simulation results showed a good match with the measured data for both single- andmulti-component reactive transport when the hydraulic behaviour of the system was
accurately described. The importance of the water flow model was evident from asensitivity analysis that showed that results of the reactive transport simulations were very
sensitive to model parameters describing the unsaturated properties of the substrate. The
good match of the experimental data with the reactive transport simulations could beobtained using literature values for the CW2D model parameters (Langergraber, 2001).
The CW2D module at present considers the main constituents of domestic wastewater.
Therefore, CW2D is only applicable to constructed wetlands that treat domestic
wastewater or waters with properties that can be described with parameters currently
incorporated into CW2D. If other components and/or waters are to be modelled, extensions
to the present model will be needed.
Further limitations of CW2D result from assumptions of the basic model, the ActivatedSludge Model (ASM). These include consideration of: a) a constant value of pH, b)
constant coefficients in the rate equations, c) constant stoichiometric factors, and d) alimited temperature range from 10°C to 25°C (Henze et al., 2000).
Although simulations showed a good match with the measured data, much researchremains so as to produce a reliable tool for constructed wetland design. The main researchneeds regarding modelling of constructed wetland processes as listed by Langergraber(2003) are:
1. Detailed hydraulic investigations of full-scale constructed wetlands: A good match
between simulation results and measured data can be obtained when sufficient data are
available to describe the hydraulic behaviour of the system and thus when the flow
model can be successfully calibrated. For full-scale systems, the match between themodel and data was relatively poor thus far, most probably due to a lack of data toaccurately describe the hydraulic behaviour of the system (Langergraber, 2001) anddue to the inherent heterogeneity of large-scale systems. The heterogeneity of thesubstrate and uneven distribution of influent water on the surface are the main reasonsfor needing detailed hydraulic investigations of full-scale systems.

2. Numerical simulations of outdoor constructed wetland systems: Simulations of outdoor(full-scale) constructed wetland systems are also needed to validate the temperaturedependencies of various processes considered in CW2D. It has been shown that byintroducing temperature dependencies for the half-saturation constants of hydrolysis
and nitrification it is possible to simulate the effluent concentrations at low
temperatures (Langergraber, 2005b). Temperature dependency for these kinetic
parameters (KX and KANs,NH4) has been considered also by other authors (e.g.
Bornemann et al., 1998).
3. Investigation of plant uptake models: Models describing nutrient (nitrogen andphosphorus) uptake by plants have to be considered in order to describe thecontribution of plants to the overall treatment process. Langergraber (2005a) showed
the important influence of plant uptake on effluent concentrations and removal
efficiency using plant uptake models that are currently available in HYDRUS-2D(Šimůnek et al., 1999). These models describe nutrient uptake associated with water
uptake (i.e., active uptake). For wastewater the simulated plant uptake matched thepotential uptake that was calculated using literature values. In the less loaded systems

47

(lower nutrient concentrations in the influent water) the concentrations of nitrogen andphosphorus in the liquid phase are too low to reach the potential uptake rates.
It can be said that it is possible to simulate plant uptake in subsurface flow constructedwetlands using a model that describes nutrient uptake coupled to water uptake. For
high loaded systems the model gives good results, whereas for waters with lower
nutrient contents the simulation results indicate that potential nutrient uptake will be
substantially overestimated when using literature values to calculate the potential
uptake, compared to simulations using models that couples nutrient uptake to water
uptake.
4. Need for a module describing substrate clogging: One limitation of CW2D is that up to
now only dissolved solutes are being considered. Wastewater often contains suspended
solids that may cause pore clogging. Clogging is considered to be the biggest
operational problem affecting vertical flow in constructed wetlands. It causes a
reduction in the infiltration capacity of the substrate surface, and therefore often a rapid
decline in the treatment performance of the system (e.g., Platzer and Mauch, 1997,
Winter and Goetz, 2003, Langergraber et al., 2003). The clogging module should be
able to describe pore size reductions due to the settling of suspended solids and due tobacteria growth. Both particle transport and bacteria growth models are currently
available (e.g., Mackie & Bai, 1993; Vandeviere et al., 1995; Kildsgaard &Engesgaard, 2001) and could be incorporated into CW2D/HYDRUS. The effects ofpore size reduction on the hydraulic properties of the substrate may also need to betaken into account (e.g., Taylor & Jaffé, 1990; Magnico, 2000).
5. Improved experimental methods for estimating CW2D model parameters: There is alsoa need for improved technologies to measure CW2D model parameters of the reactive
transport part of the model. This is important before the model can be used as a design
tool. A number of measurement techniques have been developed to characterise theparameters of Activated Sludge Models as applied to activated sludge wastewater
treatment plants (Henze et al., 2000; Vanrolleghem et al., 1999). However, no
experimental techniques are currently available to measure CW2D model parameters.
Detailed investigations on microbial biocoenosis in particular must be carried out, witha need to adapt existing measurement methods to soil and/or wastewater environments.
The Austrian research project "Characterisation of microbial biocoenosis to optimise
removal efficiency and design of subsurface flow constructed wetlands for wastewater
treatment", funded by the Austrian Science Fund (FWF, project No. P16212-B06,
duration 05/2003-04/2006), targets this problem (Tietz et al., 2005).

48

5.5

Possible future applications

CW2D was developed to model subsurface flow constructed wetlands for wastewater
treatment. However, it was already successful applied also to model constructed wetlands
for the treatment of combined sewer overflows (see Chapter 5.3). Possible futureapplications could include:•

Constructed wetlands for other types of wastewater, such as industrial andagricultural wastewaters with a composition similar to municipal wastewater.

•

Infiltration of treated (waste)water into soil for e.g. groundwater recharge•

Carbon and nitrogen cycling in soils•

Processes in natural wetlands•

Processes in riparian areas

49

6

Input data

6.1

Extension of the 'selector.in' input file to enter parameters
defined in CW2D

At its end the file 'selector.in' includes the additional block containing parameters
defined in CW2D (BLOCK_X see below). These parameters include kinetic parameters
and their temperature dependencies, stoichiometric parameters, and parameters for themodel of oxygen re-aeration. The kinetic parameters are described in Table 6.1 (see also
Table 3.8), the stoichiometric and composition parameters, and parameters for the modelof oxygen re-aeration in Table 6.2 (see also Table 3.5 and Table 3.4).
*** BLOCK_X:_parameters_for_biokinetic_model ***********************
Hydrolysis
Kh_20_[1/d]
KX_20
3.0
0.1
Heterotrophic organisms: Mineralisation
mueHet_20
bHet_20
KHet_O2_20 KHet_CR_20 KHet_NH4_20 KHet_IP_20 [g/m3]
6.0
0.4
0.2
2
0.05
0.01
Heterotrophic organisms: Denitrification
mueDN_20 KDN_O2_20
KDN_NO3_20 KDN_NO2_20
KDN_CR_20 KDN_NH4_20 KDN_IP_20
4.8
0.2
0.5
0.5
2
0.05
0.01
Autotrophic bacteria: Nitrosomonas
mueANs_20
bANs_20
KANs_O2_20 KANs_NH4_20 KANs_IP_20
0.9
0.15
1
0.5
0.01
Autotrophic bacteria: Nitrobacter
mueANb_20
bANb_20
KANb_O2_20 KANb_NO2_20 KANb_NH4_20 KANb_IP_20
1.0
0.15
0.1
0.1
0.05
0.01
Temperature dependency (activation_energy [J/mol] for Arrhenius equation)
Tdep_het
Tdep_aut
Tdep_Kh
Tdep_KX
47800
69000
28000
-53000
Stoichiometric_parameters
f_Hyd_CI f_BM_CR f_BM_CI [gCOD/gCOD]
0.
0.1
0.02
Y_Het_[gCOD(BM)/gCOD(CR)] Y_ANs_[gCOD(BM)/gNH4N]
0.65
0.24
iN_CR iN_CS iN_CI iN_BM [gN/gCOD]
0.03 0.04 0.01 0.07
iP_CR iP_CS iP_CI iP_BM [gP/gCOD]
0.01 0.01 0.01 0.02

Y_ANb_[gCOD(BM)/gNO2N]
0.24

OxygencO2_sat_20_[mg/l] Tdep_cO2_sat_[J/mol] rate_O2_[1/d]9.18-15000240.0*********************************************************************

51

Table 6.1: Description of variables of "BLOCK X" in the 'selector.in' input file –Part 1: kinetic parameters.
Variable name
Type Unit
Default
Hydrolysis
Kh_20
float
[1/d]
3.00
KX_20
float
[g/m³]
0.10
Heterotrophic organisms 1: Mineralisation
mueHet_20
float
[1/d]
6.00
bHet_20
float
[1/d]
0.40
KHet_O2_20
float[g/m³]
0.20
KHet_CR_20
float[g/m³]
2.00
KHet_NH4_20
float[g/m³]
0.05
KHet_IP_20
float[g/m³]
0.01
Heterotrophic organisms 2: Denitrification
mueDN_20
float
[1/d]
4.80
KDN_O2_20
float[g/m³]
0.20
KDN_NO3_20
float[g/m³]
0.50
KDN_NO2_20
float[g/m³]
0.50
KDN_CR_20
float[g/m³]
2.00
KDN_NH4_20
float[g/m³]
0.05
KDN_IP_20
float[g/m³]
Autotrophic bacteria 1: Nitrosomonas
mueANs_20
float
[1/d]
bANs_20
float[1/d]
KANs_O2_20
float[g/m³]
KANs_NH4_20 float[g/m³]
KANs_IP_20
float[g/m³]
Autotrophic bacteria 2: Nitrobacter
mueANb_20
float
[1/d]
bANb_20
float[1/d]
KANb_O2_20
float[g/m³]
KANb_NO2_20 float[g/m³]
KANb_NH4_20 float[g/m³]

Descriptionhydrolysis rate constantsat./inh. coeff. for hydrolysis
maximum aerobic growth rate on CR
rate constant for lysis
saturation/inhibition coefficient for O2
saturation/inhibition coeff. for substratesaturation/inhibition coeff. for NH4(nutrient)saturation/inhibition coeff. for P

0.01

maximum denitrification rate
saturation/inhibition coeff. for O2
saturation/inhibition coeff. for NO3
saturation/inhibition coeff. for NO2
saturation/inhibition coeff. for substratesaturation/inhibition coeff. for NH4(nutrient)saturation/inhibition coeff. for P

0.90
0.15
1.00
0.05
0.01

maximum aerobic growth rate on NH4N
rate constant for lysis
saturation/inhibition coeff. for O2
saturation/inhibition coeff. for NH4
saturation/inhibition coeff. for P

maximum aerobic growth rate on NO2N
rate constant for lysis
saturation/inhibition coeff. for O2
saturation/inhibition coeff. for NO2
saturation/inhibition coeff. for NH4(nutrient)
KANb_IP_20
float[g/m³]
0.01
saturation/inhibition coeff. for P
Temperature dependency (activation energy for Arrhenius equation)
Tdep_hetfloat[J/mol]47'800activation energy for heterotrophic bacteria
Tdep_aut
float[J/mol]69'000activation energy for autotrophic bacteria
Tdep_Khfloat[J/mol]28'000activation energy for hydrolysis rate
Tdep_KX
float[J/mol]-53'000
activation energy for KX

52

1.00
0.15
0.10
0.10
0.05

Table 6.2: Description of variables of "BLOCK X" in the 'selector.in' input file –Part 2: stoichiometric and composition parameters, and parameters for the modelof oxygen re-aeration.
Variable name Type
Unit
Stoichiometric and composition parameters[gCOD/gCOD]
f_Hyd_CI
float[gCOD/gCOD]
f_BM_CR
float

Default

Description

0.00
0.10

production of CI in hydrolysis
fraction of CR generated inbiomass lysis
fraction of CI generated inbiomass lysis
yield coefficient for heterotrophs
yield coefficient for N.somonas
yield coefficient for N.bacter
N content of CR
N content of CS
N content of CI
N content of biomass
P content of CR
P content of CS
P content of CI
P content of biomass

f_BM_CI

float[gCOD/gCOD]

0.02

Y_Het
Y_ANs
Y_ANb
iN_CR
iN_CS
iN_CI
iN_BM
iP_CR
iP_CS
iP_CI
iP_BM
OxygencO2_sat_20

float
float
float
float
float
float
float
float
float
float
float

[gCOD(BM)/gCOD(CR)][gCOD(BM)/gNH4N][gCOD(BM)/gNO2N][gN/gCOD][gN/gCOD][gN/gCOD][gN/gCOD][gP/gCOD][gP/gCOD][gP/gCOD][gP/gCOD]

0.65
0.24
0.24
0.03
0.04
0.01
0.07
0.01
0.01
0.01
0.02

float

[g/m³]

9.18

Tdep_cO2_sat

float[J/mol]-15000

rate_O2

float

[1/d]

240

saturation concentration ofoxygenactivation energy for saturation
concentration of oxygen
re-aeration rate

53

6.2

The 'options.in' input file

Two additional options, namely limited effluent flow rates and assignment of temperaturedependency for the saturation/inhibition coefficient for NH4 in the first step of nitrification
as described by Langergraber (2005b), can be specified in the additional input file
'options.in'. The third additional option, personalized print intervals for thesimulation results, is only needed for the HYDRUS-2D software package whereas thisfeature is already supported by the HYDRUS graphical user interface.
The 'options.in' input file is not supported by the graphical user interface of the
HYDRUS software. It needs to be created manually and placed in the temporary working
directory created by HYDRUS (Šimůnek et al., 2006a). If this input file does not exist,
CW2D/HYDRUS considers its default values.
The definition of variables used in 'options.in' is given in Table 6.3, and an exampleof the file is given below:

Input file "Options.in"hSeep [L] lSeepLimitqSLimit (positive)0.
f0.
Tdep_KANs_NH4 [J/mol]
0.
lPrintD
tPrintInt [T]nPrintInt [time steps]
t
0.05
20

Table 6.3: Description of variables used in the 'options.in' input file.
Variable name
hSeep

Type
float

Unit
[L]

lSeepLimit

logical-qSLimitfloat
Tdep_KANs_NH4 float[L/T][J/mol]lPrintD

logical-tPrintInt
nPrintInt

float
integer[T][time steps]

54

Description
Maximum allowed seepage face pressure head
If the pressure head exceeds the hSeep value, theseepage face flux is limited to qSLimit= true: use the maximum effluent flow rate for a
seepage face BC;= false: normal seepage face BC
Maximum allowed seepage face flux (positive)= activation energy for saturation/inhibition coeff.
for NH4 in the first step of nitrification(Tdep_KANs_NH4 = -160'000 J/mol; Langergraber,
2005b)= true: print results at the specified time interval= false: normal print
Print results after every tPrintInt time interval
Print results after every nPrintInt time steps

7

Output data

7.1

Format of the 'effluent.out' output file

An additional output-file 'effluent.out' is created that contains information about
effluent concentrations along the outflow boundary. If multiple outflow boundaries exist, only
the concentration value for the first boundary from this list (free drainage boundary, seepage
face boundary, variable flux boundary, and constant flux boundary) is printed. This file isprinted during the simulation run.

All solute fluxes and cumulative solute fluxes are positive out of the regionTimecEff(1)cEff(2)...

cEff(12)cEff(13).0000010.0009541.0033000::.870194E+01.870195E+01.870198E+01.227306E+00.227296E+00.227269E+00

...
...
...

.162806E+01.162805E+01.162804E+01.138496E+01.138496E+01.138496E+01

TempEff
20.0000
20.0000
20.0000

The 'effluent.out' output file can be found in the temporary working directory createdby HYDRUS (Šimůnek et al., 2006a).

55

8

List of examplesa) Wetland1

Pilot-scale vertical flow constructed wetland (PSCW, chapter 5.1) for flow and reactive
transport simulations.
b) Wetland2

Two-stage vertical flow constructed wetland (SSP, chapter 5.2) for reactive transport
simulation.
c) Wetland3

Lab-scale vertical flow constructed wetland for treatment of combined sewer overflow(CSOCW, chapter 5.3) as an example for controlled effluent rate.

57

9
[1]

[2]
[3]
[4]

[5]
[6]

[7]
[8]

[9]
[10]
[11]

[12]
[13]

[14]
[15]
[16]

[17]

[18]

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