New Features and Developments in HYDRUS Software Packages
Jirka Šimůnek1, Miroslav Šejna2, Diederik Jacques3, Günter Langergraber4, Scott A. Bradford5,
and M. Th. van Genuchten6
1
Department of Environmental Sciences, University of California Riverside, Riverside, CA, USA,
[email protected]
2
PC-Progress, Ltd., Prague 2, Czech Republic, [email protected]
3
Performance Assessments, Belgian Nuclear Research Institute, Mol, Belgium, [email protected]
4
Institute for Sanitary Engineering and Water Pollution Control, University of Natural Resources and Life Sciences,
Vienna (BOKU University), Austria, [email protected]
5
US Salinity Laboratory, USDA, ARS, Riverside, CA, USA, [email protected]
6
Department of Mechanical Engineering, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, RJ, Brazil,
[email protected]
Abstract
The capabilities of the HYDRUS (2D/3D) software package have been substantially expanded
by new modules accounting for processes not available in the standard HYDRUS version. These
new modules include the DualPerm, C-Ride, HP2, Wetland, and UnsatChem. All these
modules simulate flow and transport processes in two-dimensional transport domains and are
fully supported by the HYDRUS graphical user interface. Additionally, the DualPerm module
implements the dual-permeability modeling approach of Gerke and van Genuchten (1993)
simulating preferential flow and transport. The C- Ride module implements colloid transport and
colloid-facilitated solute transport (Šimůnek et al., 2006), the latter often observed for many
contaminants, such as heavy metals, radionuclides, pharmaceuticals, pesticides, and explosives.
HP2 is a two-dimensional alternative of the HP1 module (Jacques and Šimůnek, 2005), currently
available with HYDRUS-1D, that couples HYDRUS flow and transport routines with the
PHREEQC geochemical model of Parkhurst and Appelo (1999). The Wetland module includes
two alternative approaches (CW2D of Langergraber and Šimůnek (2005) and CWM1 of
Langergraber et al. (2009)) for modeling aerobic, anaerobic, and anoxic biogeochemical
processes in natural and constructed wetlands. Finally, the UnsatChem module simulates the
transport and reactions of major ions in a soil profile. A brief description and several
demonstrative applications of each module will be presented. Many processes included into these
specialized modules of HYDRUS (2D/3D) are currently also available as part of HYDRUS-1D.
1. Introduction
We continue to expand the capabilities of the HYDRUS modeling environment (Table 1)
(http://www.pc-progress.com/en/Default.aspx) by developing specialized modules for more
complex applications that cannot be solved using its standard versions. Standard HYDRUS
codes (Šimůnek et al., 2008) simulate one-, two-, and three-dimensional water flow, and solute
and heat transport, in variably-saturated porous media. The following specialized modules have
been developed recently:
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Table 1. HYDRUS and related models and software packages.
Model
UNSATCHEM
Dim
1D
HYDRUS-1D
1D
SWMS_2D
2D
CHAIN_2D
2D
UNSATCHEM-2D
2D
SWMS_3D
3D
HYDRUS (2D/3D)
2D/
3D
Brief Description (processes)
Variably-saturated water flow and transport of major ions and carbon dioxide in
porous media; VGM, 16 bit GUI.
Variably-saturated water flow and solute transport in porous media; root water
and solute uptake; VG, MVG, BC; hysteresis in soil hydraulic properties;
nonlinear solute transport; sequential first-order decay chains; temperature
dependence of soil hydraulic and solute transport parameters; two-site sorption
model; dual-porosity mobile-immobile water solute transport; inverse problem,
32 bit GUI.
Variably-saturated water flow and solute transport in porous media; root water
and solute uptake; MVG; linear solute transport; iterative solvers for the system
of linear equations; predecessor of the 1.0 version of HYDRUS-2D.
Ditto + nonlinear solute transport; sequential first-order decay chains; gas
diffusion; two-site sorption model; temperature dependence of soil hydraulic and
solute transport parameters; predecessor of the 2.0 version of HYDRUS-2D.
Variably-saturated water flow and transport of major ions and carbon dioxide in
porous media; VGM.
Variably-saturated water flow and solute transport in porous media; root water
and solute uptake; MVG; linear solute transport; iterative solvers for the system
of linear equations; predecessor of the 1.0 version of HYDRUS (2D/3D).
HYDRUS-2D (2.0) + SWMS_3D + 32 bit GUI; two- and three-dimensional
variably-saturated water flow and solute transport in porous media; VG, MVG,
Durner (1994), and Kosugi (1996) soil hydraulic property models; hysteresis in
the soil hydraulic properties; nonlinear solute transport; sequential first-order
decay chains; gas diffusion; temperature dependence of soil hydraulic and solute
transport parameters; two-site sorption model; dual-porosity mobile-immobile
water flow; virus, colloid and bacteria transport; constructed wetland module.
HP1/HP2: Modules to simulate a broad range of low-temperature biogeochemical reactions in
water, the vadose zone and/or ground water systems, including interactions with minerals, gases,
exchangers and sorption surfaces based on thermodynamic equilibrium, kinetic, or mixed
equilibrium-kinetic reactions. The HP modules (Jacques et al., 2008) couple HYDRUS with the
PHREEQC geochemical code (Parkhurst and Appelo, 1999).
C-Ride: Module to simulate the transport of particle-like substances (e.g., colloids, viruses,
bacteria, and nanoparticles) as well as colloid-facilitated solute transport (Šimůnek et al., 2006),
which often occurs for strongly sorbing contaminants (e.g., heavy metals, radionuclides,
pharmaceuticals, pesticides, and explosives). Such contaminants may sorb/attach to mobile
colloidal particles (e.g., microbes, humic substances, suspended clay particles, and metal oxides),
which then can act as pollutant carriers and thus provide a rapid transport pathway for the
pollutants.
DualPerm: Module to simulate preferential and/or non-equilibrium water flow and solute
transport in dual-permeability media using the approach suggested by Gerke and van Genuchten
(1993). Modeling details are provided by Šimůnek and van Genuchten (2008).
2
UnsatChem: Module to simulate the transport of major ions (i.e., Ca, Mg, Na, K, SO4, CO3,
and Cl) and their equilibrium and kinetic geochemical interactions. Possible applications are
studies of the salinization/reclamation of agricultural soils, and the disposal of brine waters in
mining operations.
Wetland: Module to simulate aerobic, anoxic, and anaerobic transformation and degradation
processes for organic matter, nitrogen, phosphorus, and sulphur during treatment of polluted
wastewater in constructed wetlands, using two biokinetic model formulations (Langergraber and
Šimůnek, 2012).
2. Applications of HYDRUS to Particle Transport
Several solute transport models within Hydrus can be adapted for the transport of particles
(colloids, microorganisms, nanoparticles). However, additional complexities frequently must be
considered for particle transport and retention because of differences in the underlying physics.
Consequently, transport models that only consider the average pore-water velocity and a single
attachment rate coefficient are not always applicable to particle retention processes in porous
media. The additional options that are currently available in HYDRUS codes are described
below.
2.1. Two-Site Kinetic Model
Similar as for solute transport, this model allows for reversible or irreversible particle retention
on two kinetic sites (sa and sstr, eq. (1)):

sa
  ka 1c  kd  s
t
s
 str   kstr 2 c
t
(1)
where ka is the first-order deposition (attachment) coefficient [T-1], kd is the first-order
entrainment (detachment) coefficient [T-1], kstr is the first-order straining coefficient [T-1] and 
are dimensionless colloid retention functions [-].
Physical interpretations of these two kinetic sites are left to the user. Hydrus includes an option
to estimate the attachment rate coefficient on one site using filtration theory. The retention
coefficients are multiplied by dimensionless functions to account for time- and/or depthdependent retention processes (Bradford et al., 2003). Attractive (ripening) or repulsive
(liberation) particle-particle interactions on the solid phase can be accounted for by using a
second order interaction term (kci) as shown in Figure 1.
3
Figure 1. Breakthrough curves showing the effect of the second-order interaction term kci.
2.2. Multispecies Model
Particle population heterogeneity can be simulated explicitly using multispecies transport models
in Hydrus. This option increases the flexibility of the simulation output, but requires knowledge
of the population heterogeneity, exchange rates between the subpopulations, and retention
coefficients for each subpopulation. Independent determination of all of these parameters is a
daunting task. Consequently, multispecies modeling of particle transport has only received
limited attention thus far in the literature (Bradford et al., 2006).
2.3. Dual-Permeability Model
Particles may be transported at different rates in the bulk aqueous phase, and when rolling over
the solid phase. The dual-permeability model has been used to account for these different rates of
transport, for exchange between the two flow domains, as well as for time-dependent retention
on the solid phase. Parameter values can be constrained by output from filtration theory and
pore-scale water flow simulations in sphere packs. Dual-permeability simulations (Bradford et
al., 2011) provide valuable insight on causes of exponential, hyper-exponential, uniform, and
non-monotonic retention profiles. Figure 2 illustrates the various retention profiles that can be
considered.
Figure 2. Various retention profiles produced by the dual-permeability model.
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2.4. Coupled Geochemical Model
Particle transport, retention, and release are known to be sensitive to transient solution and solid
phase chemistry conditions. The HP1/HP2 codes provide powerful tools to investigate the
coupling of particle transport with chemistry. This is achieved by sequentially solving transport
equations for geochemistry and particles, and making relevant particle transport parameters
functions of the solute concentrations (e.g., ionic strength and adsorbed divalent cations).
Bradford et al. (2012) outlined such an approach for transient ionic strength conditions.
3. Applications of HP1 to Transport of Reactive Solutes
A particularly interesting feature of coupled reactive transport modeling is the link between
geochemical changes and transport properties of the porous medium. Considerable flexibility
now exists in HP1/HP2 by allowing user-defined relations between geochemical state variables
and porous media properties related to water flow (porosity and hydraulic parameters),
advective-dispersive transport (porosity, tortuosity and dispersivity) and heat transport (heat
capacity, heat conductivity and heat dispersivity). Leaching and decalcification of concrete
illustrate these strongly coupled interactions (Jacques et al., 2011). Concrete is a typical example
of a multi-scale porous medium consisting of:
Calcium-Silicate Hydrates Phase (CSH): Calcium-silicate hydrates minerals with an internal
gel pore network.
Hardened Cement Paste (HCP): Impermeable cement phases (e.g., Portlandite), CSH, and a
capillary pore network.
Concrete Matrix: Impermeable aggregates, interfacial transition zone ITZ (between aggregates
and HCP), HCP and micro-cracks.
The tortuosity in concrete depends on the amount of CSH (gel pores), cement phases (capillary
porosity) and aggregates (ITZ). Closed-form equations exist to relate geochemical state variables
to tortuosity (e.g., Oh and Jang, 2004) based on homogenization schemes for composite theories,
such as a general effective media model and a composite sphere assemblage model. Model
simulations of concrete leaching during diffusive transport conditions show that the tortuosity
may increase several orders of magnitude. Figure 3 illustrates the effect of water composition:
soil water (with a higher pCO2) causes pore clogging due to calcite precipitation.
5
Rain W - 300 y
Rain W - 600 y
Rain B - 300 y
Rain B - 600 y
Soil - 300 y
Soil - 600 y
1.2
0.8
Calcite (mol/dm3)
Portlandite (mol/dm3)
5
1.6
0.4
3
2
1
0
0
0
0.5
1
1.5
2
0
 (mm/y0.5)
0.5
0.3
0.2
0.1
1
1.5
2
1.5
2
 (mm/y0.5)
100
Tortuosity factor
0.4
Porosity
4
10-1
10-2
10
-3
10-4
0
0
0.5
1
1.5
2
 (mm/y0.5)
0
0.5
1
 (mm/y0.5)
Figure 3. Profiles of geochemical state variables (top) and transport properties (bottom) during diffusive
leaching with three different water types, expressed as a function of the Boltzmann variable λ
(=distance/time0.5).
References
Bradford, S. A., J. Šimůnek, M. Bettahar, M. Th. van Genuchten, and S. R. Yates, Modeling colloid
attachment, straining, and exclusion in saturated porous media, Environmental Science & Technology,
37, 2242-2250, 2003.
Bradford, S. A., J. Šimůnek, and S. L. Walker, Transport and straining of E. coli O157:H7 in saturated
porous media, Water Resources Research, 42, W12S12, doi:10.1029/2005WR004805, 12 pp., 2006.
Bradford, S. A., S. Torkzaban, and J. Šimůnek, Modeling colloid transport and retention in saturated
porous media under unfavorable attachment conditions, Water Resources Research, 47, W10503,
doi:10.1029/2011WR010812, 2011.
Bradford, S. A., S. Torkzaban, H. Kim, and J. Šimůnek, Modeling colloid and microorganism transport
and release with transients in solution ionic strength, Water Resources Research, 48, W09509, 2012.
Gerke, H. H., M. Th. van Genuchten, A dual-porosity model for simulating the preferential movement of
water and solutes in structured porous media, Water Resources Research, 29, 305-319, 1993.
Jacques, D., J. Šimůnek, D. Mallants, and M. Th. van Genuchten, Modelling coupled hydrogeological and
chemical processes in the vadose zone: a case study of long-term uranium transport following mineral
P-fertilization, Vadose Zone Journal, 7(2), 698-711, 2008.
Jacques, D., J. Šimůnek, D. Mallants, M. Th. van Genuchten, and L. Yu, A coupled reactive transport
model for contaminant leaching from cementitious waste matrices accounting for solid phase
alterations, Proceedings of Thirteenth International Waste Management and Landfill Symposium,
October 3-7 2011, S. Margherita di Pula (Cagliari), Sardinia, Italy, 8 pp., 2011.
Langergraber, G., and J. Šimůnek, Reactive transport modeling of subsurface flow constructed wetlands,
Vadose Zone Journal, 11(2), doi:10.2136/vzj2011.0104, 14 pp., 2012.
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Oh, B., and S. Jang, Prediction of diffusivity of concrete based on simple analytic equations, Cement and
Concrete Res., 34, 463-480, 2004.
Parkhurst D. L., and C. A. J. Appelo, User’s guide to PHREEQ C (Version 2) – A computer program for
speciation, batch-reaction, one-dimensional transport and inverse geochemical calculations, WaterResources Investigations, Report 99–4259, Denver, Co, USA, 312 pp., 1999.
Radcliffe, D., and J. Šimůnek, Soil Physics with HYDRUS: Modeling and Applications, CRC Press, Taylor &
Francis Group, Boca Raton, FL, ISBN: 978-1-4200-7380-5, pp. 373, 2010.
Šimůnek, J., Changming He, J. L. Pang, and S. A. Bradford, Colloid-facilitated transport in variablysaturated porous media: Numerical model and experimental verification, Vadose Zone Journal, 5(3),
1035-1047, 2006.
Šimůnek, J., and M. Th. van Genuchten, Modeling nonequilibrium flow and transport processes using
HYDRUS, Vadose Zone Journal, 7(2), 782-797, 2008.
Šimůnek, J., M. Th. van Genuchten, and M. Šejna, Development and applications of the HYDRUS and
STANMOD software packages, and related codes, Vadose Zone Journal, 7(2), 587-600, 2008.
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