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OUTLINE

Modeling Water Flow andTransport of Particle-Like
Particle Like Substances inSoils and Groundwater
Using the HYDRUS Software Packages

 Introduction – Backgroundg
on HYDRUS
 Historical Development

Jirka Šimůnek
Department of Environmental Sciences, University of California, Riverside, CA

Scott Bradford
US Salinity Laboratory, USDA-ARS, Riverside, CA

Jack Schijfen1 and Liping Pang2
1National Institute of Public Health and the Environment, Bilthoven, The Netherlands
2Institute of Environmental Science & Research Ltd
Ltd., Christchurch
Christchurch, New Zealand

Grazia Gargiulo and Yusong Wang
and

Rien van Genuchten1, Miroslav Šejna2, and Diederik Jacques3((modelsof increasing
g complexity)py) Preferential Flow and Transport
 Spatial Heterogeneity Effects of Chemical Conditions – HP1/2/3
 Colloid-Facilitated Solute Transport Miscellaneous Other Optionsp

1Department of Mechanical Engineering, Federal University of Rio de Janeiro, Brazil
2PC-Progress, Ltd., Prague, Czech Republic
3Belgian Nuclear Research Centre (SCK•CEN), Mol, Belgium

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HYDRUS-1D
Cumulative Fluxes

Profile Information
0

60

-500

40

potToppotRoot
actTop-1000

20actRoot-1500

actBot

0

-2000
-20

-2500

-40

-3000
0.0

0.1

0.2

0.3

0.4

0.5

50

100

150

200

250

300

Time [days]

Water Contents [-]All Fluxes

Observation Nodes

1.0

200

0.5

100

HYDRUS (2D/3D)

0.0

Software for Simulating Water Flowand Solute Transport in Two/ThreeDimensional Variably-Saturatedy
Soils
Using Numerical Solutions

0

-0.5
-100

-1 0
-1.0

-200

-1.5
-2.0

-300

50

100

150

200

250

Time [days]

300

50

100

150

200

250

300

Time [days]

Software for Simulating Water Flow and Solute Transport in OneDimensional Variably-Saturated Soils Using Numerical Solutions

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History of HYDRUS (2D/3D)

History of HYDRUS-1D

Israel: Shlomo P. Neuman [1972] - UNSAT
U. of Arizona: Davis and Neuman [1983]

Princeton University:
Rien van Genuchten [1978]

Agricultural University of Wageningen:
Feddes et al. [1978], SWMII - Vogel [1987]

Massachusetts Institute of Technology:
Celia et al. [1990]

US Salinity Laboratory: SWMS-2D
Šimůnek et al. [1992]
IInternationalttil GroundGd WaterW t ModelingM d li Center:C t
HYDRUS-2D (1.0) - Šimůnek et al. [1996]

SWMS-3D - Šimůnek et al. [1995]
Wetland – Langergraber and Šimůnek [2006]
UNSATCHEM - Šimůnek et al. [1996]
New Modules: Fumigant, DualPerm,
C-Ride, HP2/3, Overland, ??

DOS

US Salinity Laboratory: CHAIN-2D
Šimůnek and van Genuchten [1994]
International Ground Water Modeling Center:
HYDRUS--2D (2.0) - Šimůnek et al. [1999]
HYDRUSHYDRUS (2D/3D)
Version 1 - 2006
HYDRUS ((2D/3D))
Version 2 (Pro) - 2011
Windows

DOS

SWMI [Vogel, 1990]
SUMATRA[van Genuchten
Genuchten, 1978]

WORM [van Genuchten, 1987]
SWMI_ST [Šimůnek, 1993]

HYDRUS[Kool and van Genuchten, 1990]

HYDRUS-1D, version 1.0, 2.0[ŠimůnekŠ
et al., 1998]
UNSATCHEM[Šimůnek et al., 1996]
HYDRUS-1D,HYDRUS
1D version 3.030[Šimůnek et al., 2005]

CHAIN-2D[ŠimůnekŠand van Genuchten, 1994]

Windows
Particle transport in 2002
PHREEQC[Parkhurst[P
kh t andd Appelo,Al 1999]HP1[[Jacquesqand Šimůnek , 2005]]

HYDRUS-1D, version 4.0
HYDRUSŠimůnek et al. [2008]

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Agricultural Applications
Precipitation
Irrigation
 Runoff Evaporation
 Transpiration
 Root Water Uptake
 Capillary Rise
 Deep Drainage

Industrial Applications









Industrial Pollution
Municipal Pollution
 Landfill Covers
 Waste Repositories
 Radioactive Waste
Disposal Sites
 Remediation
 Brine Releases
 Contaminant Plumes
 SeepageS
off W
Wastewaterttfrom Land Treatment
Systems
 Emerging
g g Pollutants(gasoline additives,
industrial additives,
personal hygiene
products,, flamepretardants, explosives,surfactants)

Fertilizers,F
tili
nutrientst i t
Pesticides
 Fumigants
 Emerging Pollutants(steroids and hormones,
pharmaceuticals)

Colloids
Pathogens NanoparticlesTo help protect y our priv acy , PowerPoint prev ented this external picture from being automatically downloaded. To download and display this picture, click Options in the Message Bar, and then click Enable external content.



Colloids,
Colloids
Pathogens
Nanoparticles

Governing Equations

 Carbon Storage and ( h )   h    K ( h) 
 1    S ( h)
t
z 
 z


Fluxes Heat Exchange andFluxesSolute Transport (Convection-Dispersion Equation)

 Nutrient Transport
 Soil Respiration (  s )  ( c )  c   D  qc   
t
t
z 
z


 MicrobiologicalMi bi l i l

Processes
 Effects of Climate
ChangeCh
 Riparian Systems
 Stream-Aquifer
IInteractionsiHillel (2003)

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Heat Movement
C p ( )T  
T 
qqT
   ( ) Cw
 C w ST

t
z 
z 
z

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HYDRUS – Main Processes
Water Flow:
Richards equation for variably-saturated water flow
Various models of soil hydraulicypproperties,p
Hysteresisy Sink term, accounting for water uptake by plant roots(uncompensated and compensated; reduced due to osmotic and pressure stress)
 Preferential flow Isothermal and thermal liquid and vapor flow

HYDRUS – Solute Transport Transport of Single Ions or Particles (colloids, viruses, bacteria)
 Transport of Multiple Ions (sequential first-order decay)

Radionuclides:
Nitrogen: Pesticides:


238Pu -> 234U -> 230Th -> 226Ra

(NH2)2CO -> NH4+ -> NO2- -> NO3-

Solute Transport:
Convective-dispersive transport in water, Diffusion in gas
Linear and nonlinear reactions between the solid and liquid phases
Zero-order production, First-order degradation
Physical and chemical nonequilibrium solute transport
Sink term, accounting for nutrient uptake by plant roots (active and passive)

Heat Transport:
Conduction and convection with flowing water (transport of latent heat)

Inverse Parameter Optimization:Control Planes

Variably-Saturated Water Flow (Richards Equation)

 Ecological Apps

S
SourceZ
Zone

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Environmental Applications







Observation wells

Marquardt-Levenberg method
Optimize soil hydraulic and solute transport parameters

aldicarb (oxime) -> sulfone (sulfone oxime) ->sulfoxide (sulfoxide oxime)



Chlorinated Hydrocarbons: PCE -> TCE -> c-DCE -> VC -> ethylene
Pharmaceuticals Hormones: Estrogen (17bEstradiol ->Pharmaceuticals,> Estrone ->> Estriol),
Estriol)

Explosives:

Testosterone
TNT (-> 4HADNT -> 4ADNT -> TAT), RDX, HMX

 General BioGeoChemical Reactions (the HP1/2/3 module) Colloid-Facilitated Solute Transport (the C-Ride module) Processes in Wetlands (the CW2D and CWM1 modules)
 Transport/Reactions of Major Ions (the UNSATCHEM module)

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HYDRUS-1DHYDRUS (2D/3D)
GUI

Fitting of
BTC and RP

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OUTLINE

One-Site Equilibrium Sorption Model Introduction – Backgroundg
on HYDRUS
 Historical Development((modelsof increasing
g complexity)py) Preferential Flow and Transport
 Spatial Heterogeneity Effects of Chemical Conditions – HP1/2/3
 Colloid-Facilitated Solute Transport Miscellaneous Other Options
p

Solid
Phase

Liquid
Phase


s
c

 c
s  
c  qc    D  tt z z   z
Adsorption Isotherms:

Linear :s  Kd cFreundlich :s  K f cLangmuir :sKlc
1  cF - L Combined : s 

Kd c
1  c 

Retardation Factor:

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Breakthrough Curves with TailingR  1

 Kd
 s
 1
 c


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One-Site Kinetic Sorption Model
Solid
Phase

Liquid
Phase


sk
c

 c
s k
 
c  qc  D  

t
t
z 
 z  z
 Transport of Single Ionss k   K d c - s k  - kt

 – first
first-order
order mass transfer (sorption rate) [T-1] Transport of Particles(colloids, viruses, bacteria)s k ka c  kd  s k - ktka – attachment rate coefficient [T-1]
kd – detachment rate coefficient [T-1]To help protect y our priv acy , PowerPoint prev ented this external picture from being automatically downloaded. To download and display this picture, click Options in the Message Bar, and then click Enable external content.

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One-Site Kinetic Sorption Model
Solid
Phase

LiquidPhasesk

The formulation based on attachmentdetachment coefficients is mathematically
identical to the formulation using firstorder mass transfer coefficients

Filtration Theory
Rajagopalan and Tien [1976], Logan et al. [1995]:

ka 
dc
v



kd  c
ka   K d

 ka
Kd 
 kd

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diameter of the sand grains [L]sticking
ti ki efficiency
ffi i
[-]
[]
pore water velocity [LT-1]
single-collector efficiency [-] ka c  kd  s k    K d c  s k 3(1(  )
 v
2d c

2 / 3
1/ 8
  4 As1/ 3 N Pe
 As N Lo
N R15 / 8  0.00338 As N G1.2 N R0.4

The first, second, and third terms represent removal by diffusion, interception,and gravitational sedimentation
NPe- Peclet number [-]NR- interception number [-]NG- gravitation
it ti numberb [[-]]
NLo- accounts for London-van der Walls attractive forces [-]As- correction factor [-]To help protect y our priv acy , PowerPoint prev ented this external picture from being automatically downloaded. To download and display this picture, click Options in the Message Bar, and then click Enable external content.

Application to Transport of Colloids
Transport of fluorescent latex colloids in columns with glass beads andOttawa sands
Colloids: dp=0.45, 1, 2, 3.2 mm
Sands: d50=0.7, 0.36, 0.15, 0.24 (mix), 0.26 (GB)Two-Site Sorption Model
 c
s e
s k
 
c  qc  D  

t
t
t
z 
z  z

Liquid
q
Phase

Solid
Phase

se

 Solute Transportse  fe K d c

c

sk



fe - fraction of exchange sites in equilibrium withthe liquid phase [-]k – first-order mass transfer (sorption rate) [T-1]s = se  sk
Bradford, S. A., S. R. Yates, M. Bettehar, and J. Šimůnek, Physical factors affecting the transport and fate ofcolloids in saturated porous media, Water Resources Research, 38(12), 1327, 63.1-63.12, 2002.

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s k  k  (1 - f e ) K d c - s k  - ktSelim et al. [1976], van Genuchten and Wagenet [1989]

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Two Kinetic Sorption Sites Model
Solid
Phase

s1k

s2k

Liquid
q
Phase

s k
s k
 c
 
c  qc
  1   2   D  

t
t
t
z 
z  z

Two Applications with Jack Schijven
Dune Recharge(a field site with a source compartment, and monitoring (W) and production wells)
Groundwater table
Compartment W1 W2 W3 W4cs = s1k  s2k

 Transport of Particles

s k
 1  ka 1 c  kd 1  s1k - k 1
t
s k
 2  ka 2 c  kd 2  s2k - k 2
t
The two kinetic sites model can be used to describe
different processes. While the first kinetic process
could be used for chemical attachment, the second
kinetic process could represent physical straining.

2

W5

W6

Production well
PCQ414

M1

0
M2

-2

M5 M6

M7

M8

-4
M3

-6
-8

M4

10
-10
-12
0

10

20

30

40

50

60

70

Distance [m]MS2 and PRD1 viruses
2D one- and two-site sorption models
Schijven, J., and J. Šimůnek, Kinetic modeling ofvirus transport at field scale, J. of ContaminantHydrology, 55(1-2), 113-135, 2002.

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Retention Functions

Two Applications with Jack Schijven
Deep Well Injection

s k ka ct

A field site with injection (IW), monitoring (WP), and production wells (PW) Time-dependent retention function [Adamczyk et al., 1994]



s 

smax   1 Depth-dependent retention function [Bradford et al., 2003]

MS2
2D one- and two-site sorption models
Homogeneous or heterogeneous profiled  x  c dc 

Schijven, JJ., and JJ. Šimůnek
SchijvenŠimůnek, Kinetic modeling ofvirus transport at field scale, J. of ContaminantHydrology, 55(1-2), 113-135, 2002.

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Retention Functions


Random sequential adsorption model [Johnson and Elimelech,
Elimelech 1995]

  1  4a  3.308a 2  1.4069a 31  bs 

Ripening  max  1, s s

max



for

s  0.8 smax

ffor

8 smaxs  00.8

32d 50 2 b 3
a  0.546

Application to Bacteria Transport

Time- and depth-dependent retention function [Bradford et al., 2005]s   dc  x   1sdc 
max  





s
smax

b

1
smax

s k
 ka  c   kint   s k   c   kd   s k   ka *  c   kd   s k tkkint - the particle interaction rate coefficient [T-1] *    int   s k 
ka[Wang et al., 2012]

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Rh d
Rhodococcus
rhodochrous
h d h
b kth
breakthroughh curves (A) andd retentiont ti profile
fil(B) in 567 µm sand and a water saturation of 80%. Fitted curves wereobtained using the Classical filtration theory (CFT) (red), Langmuirian
blocking (blue)(blue), and straining (black) models
models.

Gargiulo et al. (JCH, 2007)

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Transport of Multiple Species
General structure of the system of solutes considered in HYDRUS

Transport of E. coli [Bradford et al., 2006]
Hypothesis: When a critical value of Scrit is reached, E. coli can bereleased into the aqueous phase as an aggregated species
Species 1: mono-dispersed E. coli

 c1
s k
c  qc1
 
  1   D 1  
t
t
z 
z   zs1k
  ka 1 1c1   kd 1 s1k   k12 Fpt

Fp  max s1k  scrit , 0
After neglecting the gas phase and simplifying: c1  s1  
c  qc1+=   D1 1  - 1  c1   s1 
t
t
z 
z  z  c 2   s2  c  qc2
 1  c1   s1   2  c2   s2 +=   D2 2  ttz z  zSpeciesp
2: aggregated
gg g
E. coli c 2s k
c  qc2
 
  k12 F p
  2   D 2  
t
t
z 
z  z

s2k
  ka 2 2 c2   kd 2 s2k
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OUTLINE

Transport of E. coli [Bradford et al. 2006]
Non-monotonic deposition profiles: Introduction – Backgroundg
on HYDRUS
 Historical Development

Effluent concentration curves (left) and deposition profiles (right) for E. coliin the 240 and 150 mm Ottawa sands.
Attach - attachment and detachment
2 Species - straining and both mono-dispersed and aggregated E. coli

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((modelsof increasing
g com)) Preferential Flow and Transport
 Spatial Heterogeneity Effects of Chemical Conditions – HP1/2/3
 Colloid-Facilitated Solute Transport Miscellaneous Other Optionsp

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Preferential Flow and Transport
Fractured RockMacroporous Soil

Heterogeneous
S di
Sedimentst

Preferential Flow and Transport Approaches
Approaches commonly used in Soil Physics and Subsurface
Hydrology assume that there are two pore systems:
 Dual-Porosity Models – while water in the macropore
domain is mobile, water in the micropore domain is
immobile; dissolved solutes move into and out of immobile
domain by molecular diffusion (e.g., van Genuchten and
Wierenga, 1976)
 Dual-Permeability Models – while water is mobile in both
domains, it moves slower in the micropores and faster inthe macropores (e.g.,(e g Gerke and van Genuchten,
Genuchten 1992).
1992)

Th DualPerm
The
D lP
M d l
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Alternative Terms:
Matrix – Fracture
Micropores – Macropores
Intra-porosity – Inter-porosity

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Dual-Porosity Model(with Equilibrium Sorption)
 Solute Transport

Immob. Mob.

sime

im mocim

cmo =  mo   imees  smo sim

Dual-Porosity Model(with Equilibrium and Kinetic Sorption)

mocmosc + fmo  mo = mo Dmo mo  tt z 
z 

smoe

q c
 mo mo  ph (cmo  cim ) - mozimcims+ (1  fmo ) im = ph (cmo  cim ) - imttsmo  Kd1cmosim  Kd 2cim
fmo – fraction of exchange sites in contact withthe mobile region [-]ph – mass transfer between mobile andimmobile regions (physical process) [T-1] Solute Transport

Immob. Mob.

[van Genuchten and Wierenga, 1976]

e
sim
i

im mo
cim

cmo

smoe

[Šimůnek et al., 2008]
mocmo
 se
c 

+ fmo  mo = mo Dmo mo  t
t
z 
z 
 qmocmokk- mo  ph (cmo  cim )  ch  smo,e  smo zimcims+ (1  fmo ) im = ph (cmo  cim ) - im
t
t
 sk
k
k
fmo  mo = ch  smo,e  smo  - mo,k
t
e
k
smo
 fem Kd cmosmo,e  (1  fem )Kd cmosmok =  mo   imekes  smo
 smo
 sim

fmo – fraction of exchange sites in contact with the mobile region [-]fem – fraction
f ti off exchange
h
sites
it in
i mobilebil region
i iin equilibrium
ilib iwith
ith theth liliquidid phaseh[-][]ph – mass transfer between mobile and immobile regions (physical process) [T-1]-1ch– first-order mass transfer (sorption rate; chemical process) [T ]

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Dual-Porosity Model

Dual-Porosity Model((with Equilibriumq
and Kinetic Sorption
pand Size Exclusion)) Particle Transport with Size Exclusion

Immob. Mob.

e
sim
i

smoe

im mocimsmok

 =  mo   im
ss

s

k
mo

 qmocmokk- mo  pph (cmo  cim )  ch  smo,e  smo zimcims+ (1  fmo ) im = ph (cmo  cim ) - im
t
t
k
 smo
k
k
fmo 
= ch  smo,e  smo  - mo,k
t
e
k
smo
smo
 fem Kd cmo,e  (1  fem )Kd cmo

im
i

s

 qmocmokk- mo  ch  smo,e  smo 
z
 sk
k
k
fmo  mo = ch  smo,e  smo  - mo,k
t
e
k
smo
 fem Kd cmosmo,e  (1  fem )Kd cmo


cmo

smok

fmo – fraction of exchange sites in contact with the mobile region [-][]fem – fraction of exchange sites in mobile region in equilibrium with the liquid phase [-]ph – mass transfer between mobile and immobile regions (physical process) [T-1]

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Dual-Permeability Model(with Equilibrium Sorption)etSlow Fastsm =  M   F  w f   1  w   m

sfe

cf

 f c f(with Two Kinetic and Two Equil. Sorption Sites)[Gerke and van Genuchten, 1992]

M F
cm

Dual-Permeability Model Solute Transport

Slow Fasts  ws ef   1  w  sme
w – the ratio of the volumes of themacropore/fracture domain and the totalsoil systemdp – mass transfer between fracture andmatrix domains (physical process) [T-1] f c f

s ef

c f  qc f +=  f Df-f  stz 
z   zw

 Solute Transport [Šimůnek et al., 2008]

t

+

t

 =  M   F  w f   1  w   m

sfe

M F
cf

s ef

sfk
=





s  w s ef  s kf   1  w   sme  smk skf

  f  ch, f (1 - f f ) K df c f - s kf  -  f ,k
t
s k
k

 m   m chh,m (1 - f m ) K dm
d c m - sm  -  m , ktc f  qc f -f  s   f
 f Dfz 
 z  zw

 m c ms ec  qcm
 +  m =   m Dm m  - m  s   m
t
t
z 
z   z
1 w

 m c msc  qcm +=   m Dm m  - m  s
t
t
z 
z   z1 w

 s =  dp (1  w ) m (c f  cm )   w c * s =  dp (1  w ) m (c f  cm )   w c *To help protect y our priv acy , PowerPoint prev ented this external picture from being automatically downloaded. To download and display this picture, click Options in the Message Bar, and then click Enable external content.

esmk cmem

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Pore--Scale Flow Field
Poremocmo
 se
c 

+ fmo  mo = mo Dmo mo  t
t
z 
z 

e
k
s  smo smo

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

smoe

mo

 =  mo   ime
im

fmo – fraction of exchange sites in contact with the mobile region [-]fem – fraction
f ti off exchange
h
sites
it in
i mobilebil region
i iin equilibrium
ilib iwith
ith theth liliquidid phaseh[-][]ph – mass transfer between mobile and immobile regions (physical process) [T-1]-1ch– first-order mass transfer (sorption rate; chemical process) [T ]sm

 Particle Transport with Size Exclusion

Immob. Mob.

mocmo
 se
c 

+ fmo  mo = mo Dmo mo  t
t
z 
z 


cmo

e
mo

((with Equilibriumq
and Kinetic Sorption
pand Size Exclusion))

Navier Stokes and continuity equations
Incompressible fluid and negligible inertial terms

Colloid Transport in Dual-Permeability Media
Bradford et al. [2009] Colloids colliding
g with solid surfaces in fast

s1
k s
 ka 11c1  kd 1  s1 - 12 1
t
1 w
 s2
k s

 ka 2 2 c2  kd 2  s2  12 1w
t
 s = dp (1  w )1 (c2  c1 )Rolling of particles into stagnant regions

Hypothesis:
regions of the pore space experience
different hydrodynamic forces than colloids
in slow regions.
 The higher hydrodynamic forces in the fast
region act to remove colloids from the solid
surface, thus causing the fast region to be
associated with lower rates of colloid
retention.
 Colloid exchange occurs between the tworegions in the aqueous phase.
 Colloid exchange may also occur on the solid
phase from fast to slow regions due to either
rolling or sliding of colloids on the solid
surface.

k12 – transfer of colloids from solid phase region 1 to 2 [T-1]dp – colloid exchange between liquids in regions 1 to 2 [T-1]To help protect y our priv acy , PowerPoint prev ented this external picture from being automatically downloaded. To download and display this picture, click Options in the Message Bar, and then click Enable external content.

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Colloid Transport in Dual-Permeability Media
Sensitivity to dp

Sensitivity to k12

Application to column data

Colloid Transport in Dual-Permeability Media
Hypothesis:

Bradford et al. [2011] Colloids are transported through the bulk

1c1  c  q c  1 D1 1   1 1   s
t
z 
z 
z
 2 c 2 c  q c
s  
 D 2  2 2 stt z  2 2 z z
3 m colloids
colloids, q=0.1
q=0 1 cm/min,
cm/min IS=6 mM,
mM
pH=10, and d50=360, 240, and 150 mm.

dp – colloid exchange between liquid regions 1 to 2 [T-1]

k12 – transfer of colloids from solid phase region 1 to 2 [T-1]

Bradford et al. [2009]

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 s = 1 k12 c1   2  1    k21c2s  2 s k2 s c2   kd  s  f c si taqueous
q
phase
p
by
y advection and dispersionpin Region 1.
 Region 2 is associated with the zone ofcolloid interaction with the SWI. The
thickness of this region is very small
small.
Colloids may be transported by advection
and dispersion, but with much lower velocity
than in Region 1.
 Mass transfer of colloids to and from regions
1 to 2 is quantified using first-order kinetic
expressions (k12; (1-)k21).
 Colloids in Region 2 interacts with SWI(kinetic retention and release, k2s and kd).
Immobilized colloids on the solid phase may
fill up retention locations over time
(blocking, ).
Bradford et al. [2011] provide initial estimatesof various model parameters.

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Physical Nonequilibriump
Models in HYDRUS
Solute Transport

Application to the Transport of E. coli
Non-monotonic deposition profiles [Bradford et al. 2006, 2011]:
a)

b)
Water

SoluteEffluent concentration curves (left) and deposition profiles (right) for E. coliin the Ottawa sand (qT=0.1=0 1 cm/min; d50=150 mm; rc=250 nm).
nm)

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Chemical Nonequilibrium
SoluteSo
ute Transport
a spo t Models
ode s in HYDRUS
USŠimůnek and van Genuchten (2008):

a)

b)

c)

se

s1 k

d)

Slow Fast







sk
c

sk

c

s2 k

c

sime

im

mo

cim

cmo

smoe

sm e

smok

sm k

m

f

cm

cf

a) One-Site Kinetic Modelb)) Two-Site Model ((kinetic and instantaneous sorption)p)c) Two Kinetic Sites Model(particle transport, e.g., colloids, viruses, bacteria)d) Dual-Porosity
Dual Porosity with One Kinetic Site Modele) Dual-permeability with Two-Site Model

Water
Immob. Mobile

SoluteSoluteMobileImmob. Mobile = im   mo

 = im   mo

Immob.

Water
Slow

Fast

SoluteSlowFast = M  F

Nonequilibrium Models in
the HYDRUS GUI

Variably-Saturated Water Flowe)Immob. Mob.

Water

d)

a) Uniform Flowb) Mobile-Immobile Waterc) Dual-Porosity (Šimůnek et al.,al 2003)d) Dual-Permeability (Gerke and van Genuchten, 1993)

Fitted values of , smax, k2s, and k21.
Nonmonotonic profile that slowly move with time reflect a
decrease in the rates of release (k21) and immobilization (k2s)

•
•

c)

sf e

sfk

Solute Transport

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OUTLINE

Spatial Heterogeneity

 Introduction – Backgroundg
on HYDRUS

Deterministic

Stochastic

 Historical Development(models of increasing complexity)
 Preferential Flow and Transport
 Spatial
S ti l Heterogeneity
H tit Effects of Chemical Conditions – HP1/2/3
 Colloid-Facilitated Solute Transport Miscellaneous Other Options

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Conductivities
Explicit definition of material
layersWater Contents

Randomly generated fields ofvarious parameters, such as scaling
factors (for the pressure heads,
water contents and hydraulicconductivities)

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Stochastic Spatial Heterogeneity

Transport in Heterogeneous Soils

HYDRUS: The spatial variability of hydraulic properties canbe approximated by means of a set of linear scalingtransformations, which relate the individual soil hydrauliccharacteristics [(h) and K(h)] to reference characteristics[*((h*) and K*((h*)])]:

Miller-Miller Similitude: generate scaling factors for pressure heads (ah) andcalculate scaling factors for hydraulic conductivities (aK=ah-2)
St d d Deviation
Standard
D i ti off log10(al 10( h)= 0.5
05
Correlation length in the horizontal direction= 50 (left) and 10 (right) cm
Correlation length in the vertical direction= 10 (left) and 50 (right) cm

K ( h)   K K * ( h* )

 ( h)   r   [ * ( h* ) -  *r ]h   h h*
HYDRUS GUI can generate random fields for K, h, and .
- Normally or log-normally distributed- Correlation lengthsgin x and z direction- Miller-Miller geometrical similitude (aK=ah-2)

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Horizontal Layering

Vertical Preferential Pathways

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Transport in Heterogeneous Soils

Column Studies with Artificial Macropore
and Different Solution Chemistryy Conditions

Miller-Miller Similitude: generate scaling factors for pressure heads (ah)and calculate scaling factors for hydraulic conductivities (aK=ah-2)
Standard Deviation of log10(ah)= 0.505Correlation length in the horizontal direction= 20 cm
Correlation length in the vertical direction= 50 cm

Yusong Wang (PhD student) (submitted to WRR):
 Homogeneous columns (fine/coarse sand, 120/710 m; L=13 cm, r=4.8 cm)
 Columns (L=20 cm,
cm r=13.2
r=13 2 cm) with an artificial macropore (r= 1.14
1 14 cm)
 Saturated flow
 Bromide, microorganisms E.coli D21g (1.84 m) and coliphage X174 (27 nm)
 Ionic Strength IS
IS=0,0, 1, 5, 20, and 100 mM

0.330.340.350.360.370.380.390.400.410.420.43

Stochastic
Conductivity Field

I

Water Content
Field

II

0.0

0.5

1.0

1.5

2.0

Velocity Field

2.5

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

Concentration
Field

III

Photo of a heterogeneous soil column with a lens in the middle
and simulated flow field.

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Column Studies with Artificial Macropore andDifferent Solution Chemistryy Conditions

Column Studies with Artificial Macropore andDifferent Solution Chemistryy Conditions

Homogeneous Columns:

Heterogeneous Columns:

Measured and predicted
Br breakthrough curves

Measured and fitted Br
breakthrough curves

Yusong Wang et al. (submitted to WRR)

Measured and fitted breakthrough curves
and retention profiles of E.coli

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Yusong Wang et al. (submitted to WRR)

Measured and predicted breakthrough curves
and retention profiles of E.coli and X174

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OUTLINE

Transients in Solution IS

 Introduction – Backgroundg
on HYDRUS
 Historical Development(models of increasing complexity)
 Preferential Flow
 Spatial
S ti l Heterogeneity
H tit Effects of Chemical Conditions – HP1/2/3
 Colloid-Facilitated Solute Transport Miscellaneous Other Options

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HP1/2/3 (HYDRUS+PHREEQC)
Simulating water flow, transport and biogeochemical reactions in environmental
soil quality problems

A Coupledp
Numerical Code for
Variably Saturated Water Flow,
Solute Transport and
BioGeoChemistryin Soil Systems

HP1/2/3 (HYDRUS+PHREEQC)
HYDRUS--1D or HYDRUS (2D/3D):HYDRUSyVariably-Saturated
Water Flow
Solute Transport
 Heat transport
 Root water uptake


PHREEQC [Parkhurst and Appelo,
Appelo, 1999]:
Available chemical reactions:Aqueous complexation
 Redox reactions
 Ion exchange (Gains-Thomas)
 Surface complexation – diffuse double-layer model and nonelectrostatic surface complexation model Precipitation/dissolution
 Chemical kinetics
 Biological reactions


Flow and transport model
HYDRUS-1D 4.0
HYDRUS (2D/3D) 2.x

Biogeochemical model
PHREEQC 2 4
PHREEQC-2.4

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HYDRUS GUI for HP1/2/3

HYDRUS GUI for HP1/2/3
Four text editors
to define thegeochemical model

Jacques, D.,
Jacques
D and JJ. Šimůnek
Šimůnek, Notes on the HP1 software – a coupled code for variably
variably-saturated
saturated water
flow, heat transport, solute transport and biogeochemistry in porous media, HP1 Version 2.2,
SCK•CEN-BLG-1068, Waste and Disposal, SCK•CEN, Mol, Belgium, 114 pp., 2010.

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Transport and Cation Exchange
Heavyy Metals

HP1/2/3 for Colloid Transport
Additions to Thermodynamic Database

Major ions (Ca, Na, Al, Cl) and Heavy Metals (Zn, Pb, Cd)
8E 0048E-004Cl

Conce ntration ((m ol/l)Conceentration (m ol/l)

0 01
0.01
0.008
Na

0.006

Ca

0.004
0.002
Al
0
0

3

6

9

12

Definition of Solution Compositions

15

Zn

6E-0044E-004Pb

2E-004Cd

Geochemical Model

0E 000
0E+000Time (days)

0

3

6

9

12

15

Time (days)

8-cm column is initially contaminated with heavy metals (in equilibrium with the cationexchanger). The column is then flushed with a solution (CaCl2) without heavy metals.

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HP1/2/3 for Colloid Transport

Uranium Transport from Mill Tailing Pile

HP1 Example with Cation Exchange

Identical results by HYDRUS-1Dand HP1 with ka=kd=0.1 h-1
HP1: it is possible to express colloid/pathogentransport and reaction properties to depend on
any variables/parameters of the chemicalsystem, e.g., pH, pe, IS, alkalinity, aqueous or
exchange concentrations, etc.

HP1 with kd *= kd *(NaX/CEC)

105*25 m
1560 FE
Aqueous Complexation for Uranium Species
Calcite and Gypsum Precipitation/Dissolution
Cation ExchangeTo help protect y our priv acy , PowerPoint prev ented this external picture from being automatically downloaded. To download and display this picture, click Options in the Message Bar, and then click Enable external content.

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OUTLINE

HP1 Examples
 Transport of Heavy Metals (Zn2+, Pb2+, and Cd2+) subject to a

multiple pH
pH-dependent
dependent Cation Exchange Transport and mineral dissolution of Amorphous SiO2 andGibbsite Infiltration of a Hyperalkaline Solution in a clay sample(kinetic precipitation-dissolution of kaolinite, illite, quartz, calcite,
dolomite, gypsum, hydrotalcite, and sepiolite)
 Kinetic biodegradation of NTA (biomass, cobalt)

 Long-term Uranium transport following mineral phosphorus

f tili ti (pH-dependent surface complexation and cation exchange)
fertilization
 Transport of Explosives, such as TNT and RDX
 Property Changes (porosity/conductivity) due toprecipitation/ dissolution reactions

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 Introduction – Background on HYDRUS
 Historical Development(models of increasing complexity)
 Preferential Flow
 Spatial Heterogeneity Effects of Chemical Conditions – HP1/2/3
 Colloid-Facilitated Solute Transport (C-Ride) Miscellaneous Other Options

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Colloid-Facilitated Solute Transport

HYDRUS + add-on Module C-Ride Many contaminants should be relatively

 HYDRUS and HYDRUS (2D/3D)- variably saturated water flow
- heat transport- root water uptake- solute transport

immobile in the subsurface since under normal
conditions they are strongly sorbed to soil.
 They can also sorb to colloids, which often moveat rates similar or faster as non-sorbing tracers.
 Experimental evidence exists that many
contaminantst it are transportedtt d nott onlyl in
i a
dissolved state by water, but also sorbed tomovingg colloids.
 Examples: heavy metals, radionuclides,
pesticides, viruses, pharmaceuticals, hormones,andd otherth contaminants.
t it

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 C-Ride (Šimůnek et al.,al 2006,
2006 2012)- Particle Transport- colloids, bacteria, viruses, nanoparticlesp- attachment/detachment, straining, blocking- Colloid-Facilitated Solute Transport- transporttt off solutes
l t attached
tt h d tto particles
ti l

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Colloid, Virus, and Bacteria Transport
Air

Colloid-Facilitated Solute Transport
Air

Air-Water Interface Colloids, cContaminant sorbed to colloids at air-water interface, Sac

g

aca

kdca

kaca

kdca

kaca
Contaminant sorbed tomobilebil colloids,ll id Smc

kaac

kamc

Mobile Colloids, Cc

Water
kstr

sstr
Strained Colloids, Scstr

Solid

m

kdac

kac

kdc

Water

kstr

Kd

s
Attached Colloids, Scatt

Solid

kdmc

Dissolved
Di
l dContaminant, C

Instantaneously Sorbed
Contaminant, Se

kac

kdc

kdic



kaic

i
Kinetically Sorbed
Contaminant, Sk

Contaminant sorbed to immobile colloids, Sic

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Colloid-Facilitated Solute Transport
Pang et al. [2005]: Bacteria act as carriers for heavy
metals in gravel aquifers

Since bacteria may be excluded from small
pores, they move through interconnectedlarger pores and cracks where water moves
quicker.
Provide a vehicle for rapid transport of lessmobile contaminants.

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Colloid-Facilitated Solute Transport
Mass Balance of Total Contaminant:Contaminant

SS C SS S
 C  e   k  w c mc   c ic 
t
t
t
t
t
C c  qc Cc Smc 
C  qqC  
mc
D
 S D
R




x 
x  x x  w mc c x 
xLeft-hand side sums the Mass of Contaminant:- in the liquid phase- sorbed instantaneously and kinetically to the solid phase- sorbed to mobile and immobile colloids
Right-hand side considers various Mass Fluxes- dispersive and advective transport of the dissolved contaminant- dispersive and advective transport of contaminant sorbed tomobilebil colloids
ll id
and Transformation/Reaction (e.g., degradation).

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Colloid-Facilitated Solute Transport
C-Ride Module

Bacteria-Facilitated Cadmium Transport
Column Experiments [Pang et al., 2005; Pang and Šimůnek, 2006]
 Column: 18 cm long and 10 cm

internal diameter.

 Bulk density = 1.9 g/cm3
 Effective porosity = 0.27
 Pore-water velocity = 22 m/d
 5 PV of a solution containing Cdof about 4 mg/L and bromide(Br) of about 2 mg/L before
injection of bacteria
 The Bacillus subtilis spores werethen introduced to the column
with Cd and Br for next 3.4 PV
 Column was then flushed withtap water (no bacteria, Cd, or Br)

The Retardation Factor for colloids is equal to 1 and for solute to 4
Unit input concentrations.

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B subtilis C 0 = 5B.
5.6
6 x 107 cfu/ml,
cfu/ml pH = 7.0
70

1.2
1.0

0.4

Br
0.3

B. subtilis
0.8

Total Cd
Filtered Cd

0.6

0.2

Cd C/C0

C/C0

Breakthrough curves forf colloidsi (black(line),i ) solute sorbed to colloidsi (blue(line), and dissolved solute (red line):
Left: solute and colloids are applied independently
Right: solute is attached initially to colloids

0.4
0.1
0.2
0.0

0.0
0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Hours

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OUTLINE Introduction – Background on HYDRUS
 Historical Development(models of increasing complexity)
 Preferential Flow
 Spatial Heterogeneity Effects of Chemical Conditions – HP1/2/3
 Colloid-Facilitated Solute Transportp Miscellaneous Other Options((e.g.,
g , parallelp
computing,pg, other HYDRUS
modules, HYDRUS web)ParSWMS – Parallelized Version of HYDRUS
 ParSWMS (Hardelauf et al., 2007) - Parallelized version of

SWMS_3D, an earlier and simpler version of HYDRUS-3D.

 Developed by Forschungszentrum Jülich, Germany.
 MPI (Message-Passing Interface). LINUX or UNIX OSs.
 Test - Supercomputer with 41 SMP nodes with 32

processors each (total 1312 processors)
2D Water flow and solute transport (Hardelauf et al., 2007)
492 264 fi
492,264
finiteit elementlt nodesd

3D Water flow problem
275,706 finite element nodes(Herbst et al., 2008)

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HYDRUS and its Modules
 HYDRUS + PHREEQC = HP1/2/3(hydrological + biogeochemical processes)

 HYDRUS + C-Ride(colloid-facilitated solute transport)

 HYDRUS + DualPerm

Overland Flow Module
Kinematic Wave Equation (with Manning hydraulic resistance law):
law):
h Q

 q ( x, t )t x
S 1/ 2
  1.49
andn(preferential water flow and solute transport)m  5/3h- unit storage of water (or mean depth) [L]Q- discharge per unit width [L2T-1],
q(x,t) - rate of local input, or lateral inflows(precipitation - infiltration) [LT-1]n- Manning’s roughness coefficient foroverland flowS- slope2.52Depth [cm ] HYDRUS + Wetland
W tl d (CW2D/CWM1)

Analytical solution
1 minutes
2 minutes
4 minutes
10 minutes
i t
15 minutes

1.5(processes in constructed wetlands)

 HYDRUS + UNSATCHEM

10 m

1

4m
2m

0.5

(hydrological + CO2 + geochemical processes)

1m
0
10000

 HYDRUS + MODFLOW

8000

15 m
6000

4000

2000

0

Length [cm]High intensity rainfall of 0.00666 cm/s (i.e., 24 cm/hour) of 10 minutes duration.
Loamy soils with Ks= 25 cm/d, and Ks= 25 m/d in the middle of the transect.
Soil transect is 100 m long, with a slope of 0.01. Roughness coefficient n = 0.01.

(hydrological processes at the large scale)

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Q   hm

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Over 3 thousand downloads in 2008, over 5 thousand in 2009, and over 10 thousand
downloads annually in 2010 and after; over 13 thousand registered members.
http://www.pc-progress.com/en/Default.aspx

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HYDRUS Tutorials

Public Library of HYDRUS-1D Projects

Examples demonstrating the use of HYDRUS-1D to simulate:
B t iBacteriattransportt off bbacteriat i iin soils
il (from(fGargiulo
G i l ett al.,l 2007,2007 2008)
CFTr
colloid-facilitated solute transport (Šimůnek et al., 2006)
Centrifuge
flow and transport in centrifuge (Šimůnek and Nimmo, 2005)

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HYDRUS Discussion Forums

Public Library of HYDRUS (2D/3D) Projects

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HYDRUS Web Site: References

Questions and Suggestions?

Thank
Th
k you ffor
your attention
Over one thousand applications of HYDRUSHYDRUS-1D and HYDRUS (2D/3D) published inpeer--reviewed journal articles, and many more unpublished.
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