Journal of the Indian Institute of Science
A Multidisciplinary Reviews Journal
ISSN: 0970-4140 Coden-JIISAD

Reviews© Indian Institute of Science

Numerical Modeling of Contaminant Transport
Using HYDRUS and its Specialized Modules
Jirka Šimůnek1, Diederik Jacques2, Günter Langergraber3,
Scott A. Bradford4, Miroslav Šejna5 and M. Th. van Genuchten6
Abstract | A broad range of numerical models have been developed during
the past several decades to describe the fate and transport of agricultural,industrial, and other contaminants in soils and groundwater. Such models are now increasingly implemented in both research and engineering
projects addressing subsurface pollution problems. Of particular concern
is especially non-point source pollution stemming from plant and animal
production. In this paper we first briefly review different types of mathematical models that are being used to describe the transport of agricultural chemicals in both the vadose zone and groundwater. We next review
various versions of the HYDRUS computer software packages, including
several specialized modules that were recently developed for simulating
the movement of water, heat, and solutes in the subsurface.
Early versions of the HYDRUS models considered the transport of only
one chemical species and assumed that the behavior of this solute wasindependent of other species present in the soil solution. Physical nonequilibrium transport could be accounted for in later versions of HYDRUS
by assuming a two-region or dual-porosity type formulations that partition
the liquid phase into mobile and immobile regions. Chemical nonequilibrium transport could be accounted for by assuming kinetic interactions
between solutes in the liquid and solid phases. Physical and chemical
nonequilibrium formulations were extended later also to particle transport by including provisions for filtration theory, and time- and/or depthdependent blocking functions.
Subsequent versions of the HYDRUS codes also considered the transport of multiple solutes, which either could be coupled by means of a unidirectional first-order degradation chain, or move independently of eachother. While this approach proved effective for evaluating the subsurface
transport of many chemicals (e.g., nitrogen species, pesticides, radionuclides), many environmental problems require analyses of the transport ofmultiple chemical species that could interact mutually, create complexed
species, precipitate, dissolve, and/or compete with each other for sorption
sites. Several specialized modules have now been developed to simulatetransport processes not accounted for in the earlier standard versions of
HYDRUS. These include a wetlands module, the HP1/2/3 multicomponent transport modules, the facilitated transport C-Ride module, a module

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Department ofEnvironmental Sciences,
University of California
Riverside, Riverside,
CA, USA.

1

jiri.simunek@ucr.edu

Performance
Assessments, Belgian
Nuclear Research Institute
SCK-CEN, Mol, Belgium.

2

djacques@sckcen.be

Institute for SanitaryEngineering and Water
Pollution Control, Universityof Natural Resources andLife Sciences, Vienna(BOKU University), Austria.

3

guenter.langergraber@boku.
ac.at

US Salinity Laboratory,
USDA, ARS, Riverside,
CA, USA.

4

scott.bradford@ars.usda.gov

PC-Progress Ltd.,
Prague 2, Czech Republic.

5

m.sejna@pc-progress.cz

Department of
Mechanical Engineering,Federal Universityof Rio de Janeiro, UFRJ,
Rio de Janeiro, RJ, Brazil.

6

rvangenuchten@hotmail.com

Jirka Šimůnek, et al.

for fumigants, and the major ion Unsatchem module. All of these modules simulate flow and transport processes in two-dimensional transportdomains and are supported by the HYDRUS (2D/3D) graphical user interface. Many processes of these specialized modules are also available aspart of the public domain HYDRUS-1D software. Brief overviews of thesemore recent modules are included in this manuscript.
Keywords: Contaminants, unsaturated flow, numerical models, biogeochemical reactions, physical andchemical nonequilibrium, HYDRUS.

1 Introduction
Modern agriculture produces and uses an unprecedented number of chemicals in plant and animal
production. A broad range of pesticides, fertilizers, and fumigants are now routinely applied toagricultural lands, thus causing agricultural operations to be one of the most important sourcesof especially non-point source pollution.1 Additionally, salts and toxic trace elements are often
unintended consequences of irrigation in arid andsemi-arid regions. While many agricultural chemicals are beneficial in surface soils, their leaching
into the deeper vadose zone and groundwater canpose environmental problems. Thus, management
practices are needed to keep agricultural contaminants in the root zone and prevent their transport into nearby surface water and groundwater.
Animal production now increasingly uses also a
range of pharmaceuticals and hormones, manyof which, along with pathogenic microorganisms,
are being released into the environment throughanimal waste. Animal wastes and wash water are
frequently applied to agricultural lands. Potential
concerns about pharmaceuticals and hormones
appearing in the environment include increased
incidences of cancer, development of antibiotic
resistant bacteria, abnormal physiological processes and reproductive impairment, and increased
toxicity of chemical mixtures. While agriculturecauses mostly non-point source pollution, similar
problems arise with point-source pollution fromindustrial and municipal waste disposal sites,
nuclear waste repositories, leaking undergroundstorage tanks, chemicals spills, mine tailings, andmany other sources.1–3
Once released into the environment, point- or
non-point source contaminants generally are subjected to a large number of simultaneous physical, chemical, and biological processes, including­advective-dispersive transport, sorption-desorption,
volatilization, precipitation-dissolution, complexation, and biodegradation. Most of the predictivemodels currently being used consider the transport266

of only one chemical species and assume that the
behavior of this solute is independent of that ofother species in the soil solution. In reality, the soil
solution is always a mixture of many ions which
mutually may interact in various ways as well as
may compete with each other for available sorption
sites.4,5 Many environmental problems require analyses of the coupled transport and reaction of multiple chemical species. Agricultural examples include
optimization of fertilizer management practices, andmanagement and reclamation of saline and sodic
soils.6 Non-agricultural examples include acid minedrainage, radionuclide transport, the environmental
fate of metal-organic mixed wastes, analyses of redox
zones in organic-contaminated aquifers, disposalof brine/saline waters produced during mining of
coalbed or shale gas, and reactive permeable barriers
for aquifer remediation.2,7,8 In the following sections
we will consider several of such complex problems
that lead to multicomponent transport.
A large number of models of varying levels ofcomplexity and dimensionality are now available todescribe the basic physical and chemical processes
affecting water flow and pollutant transport in thesubsurface. Modeling approaches range from relatively simple analytical and semi-­analytical solutions, to much more complex numerical codes that
permit consideration of a large number of simultaneous nonlinear processes. While analytical andsemi-analytical solutions undoubtedly remain
popular for relatively simple applications,9,10 thedevelopment of more accurate and numericallystable solution techniques and the ever-increasing
power of personal computers are now facilitating
the much wider use of numerical models. The useof numerical models is also significantly enhancedby their availability in both the public and commercial domains, and by the development ofsophisticated graphics-based interfaces that dramatically simplify their use.
The HYDRUS software packages11 are now
widely used to evaluate the fate and transport ofvarious chemicals in especially the vadose zone

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Numerical Modeling of Contaminant Transport Using HYDRUS and its Specialized Modules

between the soil surface and the groundwater table.
However, the codes are also applicable to flow andtransport in saturated or variably-­saturated systems. The popularity of the HYDRUS models is due
in part to the implementation of a large numberof processes in the codes, their flexibility in allowing application to a broad range of agricultural,industrial and environmental problems, the possibility to consider inverse (parameter estimation)
problems, and their ease of use. In this manuscript
we will briefly review the development of the various HYDRUS versions, including the most recent
versions of HYDRUS-1D and HYDRUS (2D/3D)
for one- and multidimensional transport problems, respectively, and its specialized modules. We
also briefly discuss selected applications.
2 The HYDRUS Computer Software
Packages
The HYDRUS-1D and HYDRUS (2D/3D) codes
are finite element models for simulating the one-,two- and three-dimensional movement of water,
heat, and multiple solutes in variably saturated
media. Tables 1 and 2 provide a historical perspective of the development of the HYDRUS-1D and
HYDRUS (2D/3D) programs, respectively, theirvarious versions, and when different processes andoptions were first developed or added. Both tables
also list the specialized HYDRUS modules, suchas Wetland, HP1/2, and UnsatChem, and when
they were included into the software packages. To
limit the number of references to previous HYDRUS versions, we refer to Šimůnek et al.,11 which
provides a more detailed summary of past development of the HYDRUS codes and their many
earlier versions.
The standard versions of the HYDRUS programs11 numerically solve the Richards equation
for saturated-unsaturated water flow and advection-dispersion type equations for heat and solutetransport. The flow equation incorporates a sinkterm to account for water uptake by plant roots.
The heat transport equation considers movementby conduction as well as advection with flowing
water. The governing advection-dispersion solutetransport equations are written in a very general form by including provisions for nonlinear
nonequilibrium reactions between the solid andliquid phases, and linear equilibrium reactions
between the liquid and gaseous phases. Hence,both adsorbed and volatile solutes, such as certain
pesticides, can be considered. The transport equations also incorporate the effects of zero-orderproduction, first-order degradation independentof other solutes, and first-order decay/production

reactions that provide the required coupling
between solutes involved in a sequential first-order chain. The transport models further accountfor advection and dispersion in the liquid phase,
as well as diffusion in the gas phase, thus permitting the models to simulate solute transport
simultaneously in both the liquid and gaseous
phases. The codes consider up to 15 solutes, which
can either be coupled in a unidirectional chain or
are allowed to move independently of each other.
The HYDRUS codes can consider a range ofphysical and chemical nonequilibrium transport
situations. Physical nonequilibrium solute transport can be accounted for by assuming a two-region, dual-porosity type formulation that partitions
the liquid phase into mobile and immobile regions.
Chemical nonequilibrium solute transport can be
accounted for by dividing the available sorption
sites into two fractions and by assuming instantaneous sorption on one fraction of sorption sites andtime-dependent sorption on the remaining sites.
Physical and/or chemical nonequilibrium models
have been extended recently to particle transport
by including provisions for filtration theory, andtime- and/or depth-dependent blocking functions.
3 Solute Transport
3.1 Transport of single ions
Early versions of both HYDRUS codes could
simulate only the transport of a single ion, which
was assumed to be either nonreactive or could be
linearly sorbed onto the solid phase, and which
could be subject to zero- and first-order degradation/production reactions. The one-dimensionalversion of the transport equation for variably­saturated flow conditions in that case is given by∂(θ c + ρb s) ∂ ∂c = θ D 

∂t
∂z
∂z 


−

∂ ( qc )∂z− θ c µw − ρb s µs + ρbγ s + θγ w − r (1)where t is time [T], z is the spatial coordinate[L], θ is the volumetric water content [L3L−3], q is
the volumetric flux density [LT−1], c [ML−3] ands [MM−1] are concentrations in the liquid and solid
phases, respectively, ρb is the bulk density [ML−3], D
is the hydrodynamic dispersion coefficient [L2T−1],µw and µs are first-order degradation coefficientsfor the liquid and solid phases [T−1], respectively,γw [ML−3T−1] and γs [T−1] are zero-order production
coefficients for the liquid and solid phases, respectively, and r is a sink term for root solute uptake[ML−3T−1].

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Jirka Šimůnek, et al.

Table 1: History of development of the standard HYDRUS-1D code and its specialized modules.
Version (year)

Processes and options

1.0 (1998)• Variably-saturated water flow, and heat and solute transport in one-dimensional porous media• Root water and solute uptake• van Genuchten, modified van Genuchten, and Brooks and Corey models for the soil hydraulicproperties (see HYDRUS manual for references), hysteresis in the hydraulic properties• Nonlinear solute transport, sequential first-order decay chains, volatile solutes• Temperature dependence of soil hydraulic and solute transport parameters• Chemical nonequilibrium—two-site sorption model• Physical nonequilibrium—dual-porosity solute transport with mobile-immobile water• 16 bit GUI• Inverse problems using the Marquardt-Levenberg optimization algorithm• 32 bit GUI• Durner and Kosugi models for the soil hydraulic properties• Dual-porosity water flow
• Snow fall/melting• Compensated root water uptake• Virus, colloid, and bacteria transport (using attachment/detachment concepts and filtration theory)12• UnsatChem module—transport and reactions of major ions and transport of carbon dioxide• Vapor flow
• Coupled water, vapor, and energy transport• Hysteresis model of Lenhard et al.13 and Lenhard and Parker14 to eliminate pumping effects bykeeping track of historical reversal points• Dual-porosity water flow and solute transport, with solute transport subject to two-site sorption
in the mobile zone
• Daily variations in evaporation, transpiration, and precipitation rates• DualPerm module—dual-permeability type water flow and solute transport15• Meteo module—potential evapotranspiration calculated with the Penman-Monteith
combination equation or the Hargreaves equation• HP1 code—obtained by coupling HYDRUS with the PHREEQC biogechemical code16• Option to specify initial conditions in terms of total (instead of liquid only) concentrations• Option to specify nonequilibrium phase concentration to be initially at equilibrium with theequilibrium phase concentration• HP1—support of dual-porosity models• Linking of optimized parameters of different soil layers• Constant mobile water content in multiple layers (in the mobile-immobile water model) when
optimizing immobile water content• Implementation of the tortuosity models of Moldrup et al.17,18 as an alternative to the Millington
and Quirk19 model• Surface energy balance (i.e., the balance of latent, heat, and sensible fluxes) for bare soils• Daily variations in meteorological variables generated with the model using simple meteorologicalmodels• Preliminary (at present relatively simple) support of the HYDRUS package for MODFLOW• Compensated root water and solute uptake (passive and active) based on Šimůnek andHopmans20• Executable programs made about three times faster due to the loop vectorization• New additional output (e.g., solute fluxes at observation nodes and profiles of hydraulicconductivities (thermal and isothermal) and fluxes (liquid, vapor, and total))• Version 2.1.002 of HP1, new GUI supporting HP1 (gas transport, time-variable soil physicalproperties)• Conversions of mass units for the threshold-slope salinity stress model from electric conductivity
to osmotic head
• Input of sublimation constant and initial snow layer• New conversions of constants (EC, osmotic head) for the salinity stress response function• Option to set field capacity as an initial condition21• Triggered irrigation

2.0 (1998)
3.0 (2005)

4.0 (2008)

4.04 (2008)

4.05 (2008)

4.06 (2008)
4.07 (2008)

4.08 (2009)4.12 (2009)4.13 (2009)4.15 (2012)
4.16 (2013)• Interception can be considered with the standard HYDRUS input (no need for meteorological input)

268

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Numerical Modeling of Contaminant Transport Using HYDRUS and its Specialized Modules

Table 2: History of development of the standard HYDRUS-2D and HYDRUS (2D/3D) programs and their
specialized modules.
Version (year)

Processes and options

HYDRUS-2D
1.0 (1996)• Variably-saturated water flow and (linear and equilibrium) solute transport in two-dimensional
porous media• Root water and solute uptake• van Genuchten and modified van Genuchten models for the soil hydraulic properties• Linear equilibrium solute transport• 16 bit GUI (including the MeshGen-2D unstructured mesh generator)

2.0 (1999)• Heat transport• Brooks and Corey, Durner, and Kosugi models for the soil hydraulic properties; hysteresis in soil
hydraulic properties• Nonlinear solute transport, sequential first-order decay chains, volatile solutes• Temperature dependence of soil hydraulic and solute transport parameters• Chemical nonequilibrium—two-site sorption model• Inverse problem using the Marquardt-Levenberg optimization algorithm• 32 bit GUI

HYDRUS (2D/3D)
1.0 (2007)• Variably-saturated flow, and heat and solute transport in two- and three-dimensional media• Durner and Kosugi models for the soil hydraulic properties• Hysteresis model of Lenhard et al.13 and Lenhard and Parker14 to eliminate pumping effects bykeeping track of historical reversal points• Physical nonequilibrium—dual-porosity solute transport with mobile-immobile water• New dynamic system-dependent boundary conditions• Compensated root water uptake, spatial root distribution functions of Vrugt et al.22• Virus, colloid, and bacteria transport (using attachment/detachment concepts and filtration
theory)12• Flowing particles in 2D• Wetland module—based on the biokinetic model CW2D (in 2D)23

2.0 (2011)• Option to specify initial conditions in total (instead of liquid) concentrations• Option to specify the nonequilibrium phase concentration initially at equilibrium with theequilibrium phase concentration• Gradient boundary conditions• A subsurface drip boundary condition (with a drip characteristic function reducing irrigation flux
based on the back pressure)24• A surface drip boundary condition with dynamic wetting radius25• A seepage face boundary condition with a specified pressure head
• Triggered irrigation26• Water content dependence of solute reactions parameters using the Walker’s27 formula was
implemented.
• Compensated root water and solute uptake (passive and active) based on Šim nek andHopmans29• Implementation of the tortuosity models of Moldrup et al.17,18 as an alternative to the Millington
and Quirk19 model• An option to use a set of boundary condition records multiple times• Fumigant module—options related to the fumigant transport (e.g., removal of tarp,
temperature dependent tarp properties, additional injection of fumigant)• Wetland module—includes the second biokinetic model CWM1 (in 2D)28• UnsatChem module—transport and reactions of major ions and transport of carbon dioxide (in 2D)• Support for ParSWMS, a parallelized version of SWMS-3D, an early version of the threedimensional computational module of HYDRUS (2D/3D)29• DualPerm module—dual-permeability type water flow and solute transport (in 2D)15• HP2 module—obtained by coupling HYDRUS-2D with the PHREEQC biogechemical code

2.02 (2012)• C-Ride module—colloid transport and colloid-facilitated solute transport (in 2D)30

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Jirka Šimůnek, et al.

3.1.1 Equilibrium solute transport: The mostcommon way to relate the liquid and solid phase
concentrations is to assume instantaneous sorption and to use adsorption isotherms. The simplest form of the adsorption isotherm is a linear
equation, s = Kdc, where Kd is the distribution
coefficient [L3M−1]. Substitution of this equation
into (1) leads to a constant value for the retardation factor R (i.e., R = 1 + ρbKd/θ). While the useof a linear isotherm greatly simplifies the mathematical description of solute transport, sorption and exchange are generally nonlinear andmost often depend also on the presence of competing species in the soil solution. Many models
have been used in the past to describe nonlinear
sorption. The most common nonlinear models
are the Freundlich and Langmuir isotherms,
which in HYDRUS are combined into the general form.

s=

K f cβ1 + ηc β(2)where Kf [M−β L3β], β [-] and η [M−β L3β] are general isotherm coefficients. Eq. (2) reduces to the
traditional Freundlich isotherm when η = 0, andto the Langmuir isotherm when β = 1. The solute
retardation factor for nonlinear adsorption is notconstant, as is the case for linear adsorption, butchanges as a function of concentration. Šimůnek
and van Genuchten1 list in their Table 1 a range of
linear and other sorption models frequently usedin contaminant transport studies.
3.1.2 Chemical
non-equilibrium
solutetransport: An alternative to describing sorption

as an instantaneous process using algebraic equations such as eq. (2), is to assume a kinetic sorption process in which case the time dependencyof the reaction is described using ordinary differential equations. The most popular and simplest
formulation of a chemically controlled kinetic
reaction arises when first-order linear kinetics is
assumed:∂s= α k (K d c − s )∂t(3)where ακ is a first-order kinetic rate coefficient[T−1]. Several other nonequilibrium adsorption
expressions were also used in the past (see Table 1
in ref. 31). Models based on this and other kinetic
expressions are often referred to as one-site sorption models.
270

While eq. (3) can be used to also describe thetransport of particles, the transport of viruses,
colloids, bacteria, and nanoparticles is more commonly modeled using a modified form of theadvection-dispersion equation in which the kinetic
sorption equation is replaced with an equation
describing the kinetics of particle attachment anddetachment as follows:ρ∂s= θ kaψ c − kd ρ s∂t(4)where c is the (colloid, virus, bacteria) concentration in the aqueous phase [NcL−3], s is thesolid phase (colloid, virus, bacteria) concentration [NcM−1], in which Nc is the number of (colloid) particles, ka is the first-order deposition(attachment) coefficient [T−1], kd is the first-order
entrainment (detachment) coefficient [T−1], andψ is a dimensionless colloid retention function[-] to account for time-dependent blocking and/or depth-dependent retention processes.
Many variants, combinations, and generalizations of (2), (3), and (4) can be formulated. One
option is to further expand the one-site first-­orderkinetic model into a two-site sorption modelthat divides available sorption sites into two
fractions.32,33 In this approach, sorption on one
fraction (type-1 sites) is assumed to be instantaneous and described using isotherms such as (2),while sorption on the remaining (type-2) sites is
considered to be time-dependent and describedusing an ordinary differential equation such as(3). The two-site sorption model has been used
in a great number of studies and will not be discussed here further.
Alternatively, one could assume also that sorption occurs kinetically on two different sets ofsites, with the rates of sorption being different on
both kinetic sites. The two kinetic processes canthen be used to represent different chemical and/or physical processes, such as the removal of particles from the liquid phase. While the first kinetic
process could be used for chemical attachment,
the second kinetic process could represent physical straining.34–36 The two kinetic sorption model
is widely used to simulate the transport of various particle-like substances, such as viruses,37–39
colloids,12,34,40 bacteria,35,36,41 and nanoparticles.42,43
3.1.3 Physicalnon-equilibrium
solute­transport: While chemical nonequilibrium

models of the type discussed above assume thatchemical factors are the cause of nonequilibrium transport, physical nonequilibrium models

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Numerical Modeling of Contaminant Transport Using HYDRUS and its Specialized Modules

assume that nonequilibrium flow or transport iscaused by physical factors.15,44 Physical nonequilibrium models usually divide the pore system
into two regions: one region in which water iseither stagnant (being immobile) or moves only
very slowly, and a second region in which water
can move more quickly (being mobile). For
example, larger soil particles or soil aggregates,
but also the matrix of rocks, may have their own
micro-porosity containing relatively immobile
water, while water will flow mostly only between
the larger particles or soil aggregates, or withinrock fractures. Alternative descriptions arise ifwater flow is assumed to be completely restricted
to, or merely dominant, in the macropores (orinter-aggregate pores and fractures), while waterin the matrix (the intra-aggregate pores or rockmatrix) is assumed to move only very slowly or
not at all. Physical nonequilibrium models havebeen reviewed recently by Jarvis,45 Šimůnek andvan Genuchten,31 and Köhne et al.46,47 The tworeviews by Köhne et al.46,47 in particular provide
a large number of citations in which various
physical nonequilibrium solute transport models(including HYDRUS) have been used.
We note that the HYDRUS codes include also
provisions to simultaneously consider chemicaland physical nonequilibrium transport processes.
This option is especially attractive when simulating the transport of sorbing solutes in preferential
flow pathways, or when particles are transported(roll) over solid surfaces at a different rate than in
the bulk aqueous phase.40,48
3.2

 ransport of multiple ions subject
Tto sequential first-order decay
reactions
Versions 1 of the windows-based HYDRUS
codes (Tables 1 and 2) included an option tosimulate the transport of multiple solutes subject
to sequential first-order decay reactions. Figure 1
shows schematically how these decay reactions are
implemented. In the figure, c, s, and g represent
concentrations in the liquid, solid, and gaseous
phases, respectively, the subscripts s, w, and g refer
to solid, liquid and gaseous phases, respectively,
straight arrows represent the different zero-order(γ ) and first-order (µ, µ') rate reactions, whilecircular arrows indicate equilibrium distribution
coefficients between the liquid and gaseous phases(kg) and liquid and solid phases (kd).
The decay chain option in HYDRUS, in which
solute A degrades to produce solute B, solute B
produces solute C, and so on, has proved to bevery attractive for modeling the fate and transport of different types of solutes. Typical examples of sequential first-order decay chains involve
radionuclides, mineral nitrogen species, certain
pesticides, chlorinated aliphatic hydrocarbons,
hormones, antibiotics, and explosives. Mallants
et al.49 used this structure to simulate the transport of the radionuclides 226Ra, 222Rn, and 210Pb,
with Ra and Pb sorbing to the solid phase and Rnbeing volatile and diffusing also in the gas phase.
Another example with radionuclides is given byPontedeiro et al.50 who evaluated the subsurface
transport of 238U, 234U, 230Th, 226Ra, and 210Pb after
being released from a conventional mining installation processing ore containing naturally occurring radioactive materials.
HYDRUS was used similarly in several studies51–53 to simulate the transport of nitrogen species
involved in a nitrification/denitrification chain.
The reaction pathway in this case involves thehydrolysis of urea ((NH2)2CO) by heterotrophic
bacteria to form ammonium (NH4+), which issequentially nitrified by autotrophic bacteria tonitrite (NO2−) and nitrate (NO3−), with nitrate in

Figure 1: Schematic of the general structure of first-order decay reactions for three solutes (A, B and C)
as implemented in the HYDRUS codes.

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Jirka Šimůnek, et al.

turn being denitrified to form di-nitrogen (N2 andN2O). In this reaction pathway, ammonium is asorbing and volatile species that can be present in
the liquid phase as well as in the solid and gaseous
phases.
Additional HYDRUS-1D examples for sequential decay chains are given by Wehrhan et al.54 andUnold et al.55 who investigated the fate and transport of the antibiotic sulfadiazine (SDZ) and its
main transformation products in pig manure.
Casey and Šimůnek56 and Schaerlaekens et al.57
considered first-order degradation for the transport of trichloroethylene (TCE). Microbiologicaldegradation of perchloroethylene (PCE) underanaerobic conditions follows a series of chain
reactions in which, sequentially, trichloroethylene(TCE), cis-dichloroethylene (c-DCE), vinylchloride (VC), and ethene are generated.
The transport of hormones was investigatedusing HYDRUS-1D by Casey et al.,58–60 Das et al.,61
and Fan et al.62 Casey et al.58,60 and Das et al.61
studied the transport of estrogenic hormones, i.e.,
17β-estradiol and its primary metabolite estrone,in natural soil. Casey et al. (2004)59 and Das et al.61
evaluated the transport of androgenic hormones(i.e., testosterone and its primary metabolite
androstenedione). Papiernik et al.63 further used
HYDRUS-1D to evaluate the transport of the herbicide isoxaflutole and its diketonitrile and benzoic acid metabolites. Bradford et al.64 similarly
used a variant of the sequential first-order decay
model to simulate the transport and retention
behavior of monodispersed and aggregated species of pathogenic E. coli O157:H7. We further
note the work by Dontsova et al.65,66 who analyzed
the fate and transport of explosives. Additional
examples in which HYDRUS was used to simulate
the transport of first-order degradation chains
can be found in the literature.
3.3 T ransport of mutually dependent
multiple ions
While the above models for solutes subject tosequential first-order degradation reactions has
proved to be very attractive in dealing with different chemicals, they cannot be used to describe
many transport scenarios in which several solute
species are present simultaneously in the soil solution. This is because the soil solution is always amixture of many ions which may mutually interact, create complexed species, precipitate, dissolve, and/or could compete with each other forsorption sites.4,67 For such conditions, one needs
to use multicomponent reactive transport models that consider the various mutual interactions
between the different solutes and integrate those272interactions and reactions with transport modules
for water and solutes.
Following Šimůnek and Valocchi,4 geochemical transport models can be broadly divided into
two major groups: models with specific chemistry and general models. Models with specificchemistry are usually constrained to very specificapplications since they are restricted to certain
prescribed chemical systems. On the other hand,models with generalized chemistry provide users
with much more flexibility in designing particular chemical systems, thus permitting a muchbroader range of applications. Users can theneither select species and reactions from large
geochemical databases, or are able to define theirown species with particular chemical properties
and reactions.
Models simulating the transport of major ions,such as LEACHM68 and UNSATCHEM,6,69 andvarious reclamation models4 are typical examples
of models with specific chemistry. These models
typically consider the transport of major ionsand their mutual reactions such as complexation,
cation exchange, and precipitation/dissolution.
The UNSATCHEM add-on module to HYDRUS(2D/3D), discussed below, is an example of sucha model.
Models are now also increasingly available forsimulating carbon and nitrogen cycles. Examples are CENTURY,70 LEACHN,68 RZWQM,71
and COUP.72 Environmental models of this typetypically distribute organic matter, carbon, andorganic and mineral nitrogen over multiple computational pools, while allowing organic matterto be decomposed by multiple microbial biomass
populations. They can account for most of the
major reaction pathways, such as inter-pool transfer of carbon and nitrogen, nitrification (ammonium to nitrate-N), denitrification (leading to the
production of N2 and N2O), volatilization losses ofammonia (NH3), and microbial biomass growthand death. The Wetland add-on module to HYDRUS (2D/3D), discussed below, is an example ofsuch a model.
Most codes with general geochemistry are
limited to solute transport and biogeochemical
reactions, while water flow paths must be calculated outside of the reactive transport code. Typical examples are PHREEQC,73 CRUNCH,74 and
PHAST.75 Only a few models allow the velocity
field to be calculated internally (e.g., MIN3P).76
Several codes for transient variably-saturated flow
have also been coupled to general biogeochemistrymodels. These include 3DHYDROGEOCHEM,77
TOUGHREACT,78 and the HYDRUS (2D/3D)
add-on module HP1/2/316,79 discussed below.

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Several interesting applications of both the specific and general chemistry models have recently
appeared in a special issue of Vadose Zone Journal entitled “Reactive Transport Modeling”.67
The models with specific chemistry were used instudies by Langergraber and Šimůnek,28 Reading
et al.,80 and Suarez et al.81 Langergraber andŠimůnek28 illustrated the use of reactive transport modeling with the Wetland module within
the HYDRUS software as a tool for evaluatingcomplex physical and chemical processes within
wetland systems constructed for the treatment ofvarious contaminants. Reading et al.80 used the
UNSATCHEM code to evaluate the use of gypsum
to ameliorate a nonsaline sodic clay soil in North
Queensland, Australia, while Suarez et al.81 used
UNSATCHEM to evaluate reactions controllingthe fate and transport of boron in soils, which are
critical for optimal management of B-containing
waste waters in arid systems.
General reactive transport models have beenused in recent studies.82–84 Bea et al.82 used the
MIN3P-D multicomponent reactive transport
code to describe processes occurring within amine tailing impoundment and their impact on
CO2 sequestration. Chang et al.83 used PHREEQC
in combination with laboratory column experiments to evaluate the efficacy of Fe(II)-containing solutions as an in-situ means for reducing
toxic hexavalent chromium (Cr(VI)) to trivalentchromium (Cr(III)), which subsequently coprecipitates with Fe(III). Lichtner and Hammond(2012)84 used PFLOTRAN to evaluate geochemical processes controlling the aqueous phase
distribution and solid phase speciation of ahexavalent uranium [U(VI)] plume below the
Hanford 300 Area bordering the Columbia Riverin Hanford, WA.
4 Specialized HYDRUS Modules
In this section we summarize several newly implemented HYDRUS modules, some of which represent examples of reactive transport with specificchemistry (notably the Wetland and UnsatChem
modules), while others consider general reactive
transport (the HP1 and HP2 models). Also briefly
discussed are several modules not intended for thetransport of multiple solutes but providing additional modeling capabilities, such as to account for
preferential flow (the DualPerm module), colloidfacilitated solute transport (the C-Ride module),or fumigant transport (the Fumigant module).
Except for the older HP1, all modules simulate
flow and transport processes in two-dimensionaltransport domains and are fully supported by
the HYDRUS (2D/3D) graphical user interface.

Many of the processes are also available as part of
HYDRUS-1D.
4.1 The HP1/HP2 modules
The one-dimensional program HP1, which couples the PHREEQC geochemical code73 with
HYDRUS-1D, was first released in 2005,16 and usedsuccessfully in many applications. HP1, which
is an acronym for HYDRUS-PHREEQC-1D, isa relatively comprehensive simulation modulethat can be used to simulate (1) transient water
flow, (2) the transport of multiple components,(3) mixed equilibrium/kinetic biogeochemical
reactions, and (4) heat transport in one-dimensional variably-saturated porous media. HP279
is the two-dimensional equivalent of HP1. The
HP1 and HP2 modules both can simulate a broad
range of low-temperature biogeochemical reactions in water, the vadose zone and/or groundwater systems, including interactions with minerals, gases, exchangers and sorption surfaces basedon thermodynamic equilibrium, kinetic, or mixed
equilibrium-kinetic reactions.
The versatility of HP1 was demonstrated by
Jacques and Šimůnek16 and Jacques et al.5,7 on
several examples, including (a) the transport ofheavy metals (Zn2+, Pb2+, and Cd2+) subject tomultiple cation exchange reactions, (b) transportwith mineral dissolution of amorphous SiO2 andgibbsite (Al(OH)3), (c) heavy metal transport in a
medium having a pH-dependent cation exchange
complex, (d) infiltration of a hyperalkaline solution in a clay sample (this example consideredkinetic precipitation-dissolution of kaolinite,
illite, quartz, calcite, dolomite, gypsum, hydrotalcite, and sepiolite), (e) long-term transient flow
and transport of major cations (Na+, K+, Ca2+, andMg2+) and heavy metals (Cd2+, Zn2+, and Pb2+) ina soil profile, (f) cadmium leaching in acid sandy
soils, (g) radionuclide transport, and (h) longterm uranium migration in agricultural field soils
following mineral P-fertilization.
More recent applications of HP1 include
Bessinger and Marks,85 who used HP1 to evaluate laboratory and field experiments involving thetreatment of mercury-contaminated soils withactivated carbon, and Jacques et al.86,87 who used
HP1 to model chemical degradation of concreteduring leaching with rain and different types ofwater. Jacques et al.87 also considered the effects
of chemically degrading concrete on its hydraulic properties such as porosity, tortuosity, and thehydraulic conductivity. Jacques et al.88 additionally combined HP1 with the general optimization UCODE program89 to inversely optimize
hydraulic, solute transport, and cation exchange

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Jirka Šimůnek, et al.

parameters pertaining to column experiments
subject to transient water flow and solute transport with cation exchange.
The versatility of HP2 was demonstrated
recently by Šimůnek et al.79 on several examples:(a) a sodic soil reclamation problem using furrow irrigation, which demonstrated the cationexchange features of HP2, and (b) the release andmigration of uranium from a simplified uranium
mill tailings pile towards a river. These examples
included the processes of water flow, solute transport, precipitation/dissolution of the solid phase,cation exchange, complexation, and many otherreactions. As an example of possible modelingoutput, Figures 2 and 3 show uranium concentration profiles at two different times, and final
pH, calcite, and gypsum profiles, respectively, for
the uranium tailings example adapted from Yeh
and Tripathi.90 Detailed information about thisproject, as well as instructions on how to implement the project using HP2, can be found inŠimůnek et al.79

4.2 The C-Ride module
The C-Ride module91 considers the transport ofparticle-like substances (e.g., colloids, microorganisms, and nanoparticles) as well as colloidfacilitated transport,30 the latter often observed formany strongly sorbing contaminants such as heavy
metals, radionuclides, pharmaceuticals, pesticides,and explosives. These contaminants are associated predominantly with the solid phase, whichis commonly assumed to be stationary. However,the contaminants may also sorb/attach to mobileand deposited colloidal particles (e.g., microbes,
humic substances, suspended clay particles, andmetal oxides), which then can act as pollutant carriers and thus provide a rapid transport pathway
for the pollutants.
The C-Ride module fully accounts for the
dynamics of colloid transfer (attachment/straining)and solute transfer (kinetic/equilibrium sorption
onto soil and mobile/deposited colloids) between the
different phases. A schematic of the colloid transportand colloid-facilitated transport module is shown

Figure 2: Uranium concentration profiles at times 0 (left), and 500 (right) d for the Uranium Tailing Pile
Leaching example.

Figure 3: Plots of pH (top), calcite (mol/L) (middle), and gypsum (mol/L) (bottom) after 1000 d for the
Uranium Tailing Pile Leaching example.
274

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Numerical Modeling of Contaminant Transport Using HYDRUS and its Specialized Modules

in Figure 4. The module assumes that the porous
medium consists of three phases (i.e., solid, air andwater). Following van der Weerd and Leijnse,92 theC-Ride module assumes that (a) only one type of
colloid exists in the system, and that the colloids
can be described by their mean behavior, (b) colloids are stable and that their mutual interactionsin the liquid phase may be neglected, (c) immobile
colloids do not affect the flow and transport properties of the porous medium because of possible
clogging of small pores, and (d) the transport ofcolloids is not affected by sorption of contaminantson colloids. Colloids are assumed to exist in threestates (Fig. 4, top): mobile (suspended in water), Cc[NcL−3], attached to the solid phase, Scatt [NcM−1],
and strained by the solid phase, Scstr [NcM−1]. Colloid
phase changes are described in terms of nonlinear
first-order processes of attachment, kac [T−1], detachment, kdc [T−1], and straining, kstr [T−1].

C-Ride further assumes that contaminants canbe dissolved in the liquid phase, C [ML−3], as wellas can be sorbed instantaneously (Se [MM−1]) andkinetically (Sk [MM−1]) to the solid phase, and to
colloids in all of their states (Smc, Sic [MNc−1]). Six
different states of contaminants (Fig. 4, bottom)
are thus distinguished: dissolved, instantaneously or kinetically sorbed to the solid phase, andsorbed to mobile or immobile colloids (the latter
either strained or attached to the solid phase). The
coefficients kamc, kaic, kdmc, kdic [T−1] in Figure 4 represent various first-order attachment/detachment
rates to/from mobile and immobile colloids. The
coefficients Kd and ω represent instantaneous andkinetic solute sorption to the solid phase, respectively, while the factors ψ account for nonlinearityof the various processes.30,91
Figure 5 shows a conceptual model for
cadmium (and virus) transport facilitated by

Figure 4: Schematic of the C-Ride module for colloid transport (top) and colloid-facilitated solute transport(bottom).

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Jirka Šimůnek, et al.

Figure 5: Schematic of a conceptual model for bacteria-facilitated transport of heavy metal ions andviruses.

B. subtilis spores or E. coli in saturated coarse alluvial gravels.96 This application of the C-Ride module
successfully simulated Cd transport involving advection, dispersion, kinetic adsorption-desorption of
Cd to/from the aquifer and to/from mobile/immobile bacteria, and kinetic attachment/detachment of
the bacteria to/from the aquifer.
4.3 The DualPerm module
The DualPerm module94 simulates preferential and/or nonequilibrium water flow andsolute transport in dual-permeability mediausing the approach suggested by Gerke andvan Genuchten.15 The module assumes thatthe porous medium consists of two interacting
regions: one associated with the inter-aggregate,
macropore, or fracture system, and one comprising micropores (or intra-aggregate pores) insidesoil aggregates or the rock matrix. Water flow canoccur in both regions, albeit at different rates.
Modeling details are provided by Šimůnek andvan Genuchten.31 The dual-permeability formulation has seen many applications, especially in
1D.95–97 Several of these examples are discussed by
Köhne et al.46,47
An example of pressure head profiles calculated for a tension disc infiltration experiment isshown in Figure 6. The transport domain for thematrix and fracture was taken to be 50 cm wide and150 cm deep, while the disc radium was assumed
to be 10 cm. Different ratios of the anisotropy ofthe hydraulic conductivity were employed in thesimulations (KxA/KzA = 1, 10, and 0.1 from left toright in the figure). Various parameters used for
276

these calculations using the DualPerm module are
given by Šimůnek et al.94
4.4 The UnsatChem module
The UnsatChem geochemical module98 has
been implemented into both the one- and two­dimensional computational versions of HYDRUS. This module simulates the transport ofmajor ions (i.e., Ca2+, Mg2+, Na+, K2+, SO42−, CO32−,
and Cl−) and their equilibrium and kinetic geochemical interactions, such as complexation,
cation exchange and precipitation-dissolution(e.g., of calcite, gypsum and/or dolomite).
Possible applications include studies of thesalinization/reclamation of agricultural soils,
sustainability of various irrigation systems, andthe disposal of brine waters from mining operations. Since the computational driver for thismodule was developed already some 20 years
ago,69 the UnsatChem module (especially its
one-dimensional version) has been used inmany applications.99–105
Gonçalves et al.106 and Ramos et al.107 recently
demonstrated the applicability of Unsatchem tosimulating multicomponent major ion transport
in soil lysimeters irrigated with waters of different
quality. The UnsatChem module of HYDRUS-1D
was used in their work to describe field measurements of the water content, overall salinity, theconcentration of individual soluble cations, as wellas the Sodium Adsorption Ratio (SAR), Electric
Conductivity (EC), and the Exchangeable Sodium
Percentage (ESP). Figure 7 summarizes results forthis application.

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Numerical Modeling of Contaminant Transport Using HYDRUS and its Specialized Modules

Figure 6: Pressure head profiles for the matrix (left), an isotropic fracture, a fracture with KAx /KAz = 10, anda fracture with KAx /KAz = 0.1 (right).

Figure 7: Measured and simulated volumetric water contents (top), soluble sodium concentrations (middle), and sodium adsorption ratios (SAR) for lysimeters irrigated with waters of different quality (A, B, and
C). I and R correspond to the irrigation and rainfall periods, respectively. Adapted from Gonçalves et al.106
Source: This material is reproduced with permission of John Wiley & Sons, Inc.

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Jirka Šimůnek, et al.

Figure 8: Measured and simulated COD and NH4-N effluent concentrations of a vertical flow constructedwetland. Adapted from Langergraber.110

Figure 9: Tarped broadcast (top left), tarped bed drip (top right) and volatilization fluxes (bottom) for different fumigants application scenarios (adopted from Spurlock et al.).119

4.5 The Wetland module
The Wetland module simulates aerobic, anoxic,
and anaerobic transformation and degradation
processes for organic matter, nitrogen, phosphorus, and sulphur during treatment of polluted
278

wastewater in subsurface constructed wetlands.28
Constructed wetlands are engineered water treatment systems that optimize treatment processes
found in natural environments. Constructedwetlands have become popular since they can be

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Numerical Modeling of Contaminant Transport Using HYDRUS and its Specialized Modules

relatively efficient in treating different types ofpolluted water and provide sustainable, environmentally friendly solutions. A large number ofphysical, chemical and biological processes are
simultaneously active and may mutually influenceand stimulate each other.
The Wetland module uses two biokinetic
model formulations (CW2D of Langergraber andŠimůnek23 and CWM1 of Langergraber et al.)108
to account for complex conditions that may occur
in various types of wetlands. Both biokinetic
model formulations have been developed forconstructed wetlands treating municipal wastewater. A good match with measured effluent concentration data could be achieved, especially forvertical flow constructed wetlands with intermittent loadings.109–111 As an example, Figure 8 shows
a comparison of simulated and measured effluent
concentrations of a vertical flow constructed wetland treating municipal wastewater. In addition toapplications involving municipal wastewater, theWetland model has been also used for constructedwetlands treating combined sewer overflow,112–115
treating effluent of a wastewater treatment plantfor irrigation purposes,116 and treating run-off
from agricultural sites including predictions of
the effects of streamside management zones.117,118
4.6 The Fumigants module
The Fumigants module implements multiple
additional options required to simulate processes
related to fumigant applications and transport.
This module allows users to specify an additional
injection of fumigants into the transport domain
at a specified location and time, consider the presence or absence of a surface tarp, allow the tarp
properties to depend on temperature, and permit
tarp removal at a specified time. The Fumigants
module was recently used to investigate the effectof different application scenarios, such as tarped
broadcasting, tarped bedded shank injection,
tarped drip line-source application, and otheroptions (e.g., having different initial water contents and tarp permeability) on fumigant volatilization.119 Figure 9 illustrated an application.
5 Conclusions
In this paper we provided an overview of the
HYDRUS codes and various specialized modules
that were recently added to the computer software
packages. We believe the that HYDRUS models
have provided, and will continue to provide, an
important service to the soil environmental andhydrological communities, especially but not limited to vadose zone processes. This is reflected bytheir frequent use in a wide range of applications

in both basic and applied research and engineering. For example, the HYDRUS website (http://
www.pc-progress.com/en/Default.aspx) lists over
one thousand publication in which the HYDRUS
codes have been used. The codes cover a large
number of processes, from relatively simple onedimensional solute transport problems to multidimensional flow and transport applications at thefield scale, including relatively complex problems
involving a range of biogeochemical reactions.
Examples of the latter are the HP1/HP2 modules
that couple the HYDRUS software packages with
the PHREEQC geochemical code, and the Wetland module that includes two biokinetic model
formulations (CW2D and CWM1). The need forcodes such as HYDRUS is reflected further by thefrequency of downloading from the HYDRUS
web site. For example, HYDRUS-1D was downloaded more than 10,000 times in 2012 by users
from some 50 different countries. The HYDRUS
web site receives on average about 700 individual
visitors each day.
The wide use of the HYDRUS models is inlarge part due also to their ease of use becauseof the implementation of relatively sophisticated interactive graphical user interfaces, which
are continuously being updated in attempts tomake the codes as attractive as possible for nonexpert users. Feedback from users is continuously being used also to improve the codes, toidentify particular strengths and weaknesses ofthe models, and to define additional processes orfeatures that should be included in the models.
We believe that the codes and associated manuals hence are serving an important role in thetransfer of vadose zone research and development technologies to both the scientific community and practitioners.
Received 2 April 2013.

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52. Ravikumar, V., G. Vijayakumar, J. Šim nek, S. Chellamuthu,
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53. Ramos, T. B., J. Šim nek, M. C. Gonçalves, J. C. Martins,
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54. Wehrhan, A., R. Kasteel, J. Šim nek, J. Groeneweg,
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56. Casey, F. X. M., and J. Šim nek, Inverse analyses of thetransport of chlorinated hydrocarbons subject to sequential transformation reactions, Journal of Environmental
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58. Casey, F. X. M., G. L. Larsen, H. Hakk, and J Šim nek, Fateand transport of 17β-Estradiol in soil-water systems, Environmental Science & Technology, 37(11), 2400–2409, 2003.
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64. Bradford, S. A., J. Šim nek, and S. L. Walker, Transport and straining of E. coli O157:H7 in saturated
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Numerical Modeling of Contaminant Transport Using HYDRUS and its Specialized Modules

nonlabile uranium(VI) on Hanford 300 area plume longevity, Vadose Zone J., 11(2), doi:10.2136/vzj2011.0097,
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85. Bessinger, B. A., and C. D. Marks, Treatment of MercuryContaminated Soils With Activated Carbon: A Laboratory,
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transport model, NUWCEM 2011, Proceedings of the 1st
International Symposium on Cement-based Materials for
Nuclear Wastes, 11 pp., Avignon, France, October 11–14,
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88. Jacques, D., C. Smith, J. Šim nek, and D. Smiles, Inverse
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95. Pot, V., J. Šim nek, P. Benoit, Y. Coquet, A. Yra, and
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96. Köhne, J. M., S. Köhne, and J. Šim nek, Multi-process
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97. Dousset, S., M. Thevenot, V. Pot, J. Šim nek, and F.
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98. Šim nek, J., M. Šejna, and M. Th. van Genuchten, The
UNSATCHEM Module for HYDRUS (2D/3D) Simulating
Two-Dimensional Movement of and Reactions Between
Major Ions in Soils, Version 1.0, PC Progress, Prague,
Czech Republic, 54 p., 2012a.
99. Kaledhonkar, M. J., and A. K. Keshari, Modelling theeffects of saline water use in agriculture, Irrig. and Drain.,55(2), 177–190, 2006.
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101. Kaledhonkar, M. J., D. R. Sharma, N. K. Tyagi, A. Kumar,and S.E.A.T.M. Van Der Zee, Modeling for conjunctive use
irrigation planning in sodic groundwater areas, Agricultural Water Management, 107, 14–22, 2012.
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105. Rasouli, F., A. J. Pouya, and J. Šim nek, Modeling theeffects of saline water use in wheat-cultivated lands using
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106. Gonçalves, M. C., J. Šim nek, T. B. Ramos, J. C. Martins, M. J. Neves, and F. P. Pires, Multicomponent solutetransport in soil lysimeters irrigated with waters of different quality, Water Resources Research, 42, W08401,
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107. Ramos, T. B., J. Šim nek, M. C. Gonçalves, J. C. Martins,
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CWM1—A general model to describe biokinetic processes in subsurface flow constructed wetlands, Water Sci.
Technol., 59(9), 1687–1697, 2009.

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109. Langergraber, G., Simulation of subsurface flow constructed wetlands—Results and further research needs.
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117. Smethurst, P.J., Petrone, K.C., Baillie, C.C., Worledge, D.,
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119. Spurlock, F., J. Šim nek, B. Johnson, and, A. Tuli,
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vzj2012.0130, 12 p, 2013.

Jirka Šimůnek is a Professor at the Universityof California Riverside. His research interests
are in numerical modeling of various equilibrium and nonequilibrium water flow, heat andsolute transport processes in variably-saturated
porous media (soils). He is also interested in modeling reactive solute transport and in inverse procedures for estimating soil hydraulic and solute transport parameters. He is oneof the leading authors of the widely used HYDRUS models.

Dr. Scott Bradford serves as a research scientist with the USDA, ARS, Salinity Laboratory
in Riverside, California. He has a PhD in Soil
Science, specializing in Soil Physics, from the
University of California, Riverside. His current
research focuses on understanding and simulating the transport and fate of microorganisms, colloids, colloid-associatedcontaminants, and nanoparticles in soil and groundwater
environments.

Dr. Diederik Jacques is a head if the Performance Assessment Unit, Institute of Environment, Health and Safety of the Belgian Nuclear
Research Centre (SCK•CEN) in Mol, Belgium.
His expertise is in modeling water flow andsolute transport in unsaturated porous media and characterizing its spatial variability. He is working on different
aspects of coupling unsaturated water flow, solute transport,
and geochemical reaction into the HP1/HP2 modules andtheir application to solute transport in soils and interactions between different components in waste disposal systems (e.g., clay-concrete or soil-concrete).
Dr. Günter Langergraber is a Senior Scientist at
the Institute of Sanitary Engineering and Water
Pollution Control at the University of Natural
Resources and Life Sciences, Vienna (BOKU).
His main research fields are in wastewater
treatment with constructed wetlands, numerical modelingof constructed wetlands and activated sludge systems, andresources-oriented sanitation systems. He is the main developer of the HYDRUS wetland module.

284

Dr. Miroslav Šejna is a director and development lead of PC Progress, a Software company
located in Prague, Czech Republic. Dr. Šejna
has a MSc in Applied Mathematics and PhD in
Fluid Mechanics from the Czech Academy of
Sciences. His expertise is in numerical modeling of transonicflow with homogeneous and heterogeneous condensationand chemicals in steam through turbine cascades. Over thelast two decades he has been specialized in the developmentof graphical user interfaces for FEM/CFD software packages
for Windows.
Dr. Rien van Genuchten is a soil physicist,currently with the Federal University of Riode Janeiro in Brazil and Utrecht ­University
in the Netherlands. His interests are invariably-saturated flow and contaminant transport, analytical and numerical modeling, nonequilibriumtransport, characterization of the unsaturated soil hydraulic functions, and root-water uptake. He is probably best
known for the equations he developed for the constitutive
relationships between capillary pressure, water content, andthe hydraulic conductivity of unsaturated porous media.

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