Variably Saturated Flow and Transport: Sorbing Solute
Jan 21, 2016
Variably Saturated Flow and Transport: Sorbing Solute
• With variably saturated flow, fluids fill only part of the pore space.
• Flow properties depend on degree of saturation, making Richards’ equation nonlinear
• Often researchers use analytic expressions (e.g., van Genuchten or Brooks & Corey) to describe how material properties vary with the solution.
• This example also shows how to incorporate experimental data directly into the COMSOL Multiphysics model.
• Example based upon Hydrus2d Manual (Simunek and Van Genuchten, 1992)
Variably saturated flow
Fluid in column moves into “disc” where it is distributed over given radius.
Fluid moves from disc into dry soil.
With good control on fluid (and contaminant) coming fromdisc, researchers analyze Subsurface properties and behaviors.
Image fromDepartment of Agriculture and Soil ScienceUniversity of Sidney, Australiahttp://www.usyd.edu.au/su/agric/ACSS/sphysic/infiltration.html
Disc permeameter
Axisymmetry
1.3 m
Ground surface
Inlet “just ponding” at known water height
2-layersoil
column
initially unsaturatedto depth of
about 1.2 m
Extremely low permeability
Upper soil layer
Lower soil layer
Problem set up
0
DHKt
HC
t
HSSe pHp
pHp
pHp
Hp = pressure headSe = effective saturationS = specific storageC = specific moisture capacityK = hydraulic conductivity D = elevation = fluid volume fraction (constitutive relation)
Hp=0
, Se, C, K
- Hp +
Variably saturated flow equation
Hp subscripts to denote dependency on Hp NONLINEAR
We can set up the permeability and retention formulae three ways:
(1) Using analytic formulae predefined from van Genuchten or Brooks & Corey
(2) Defining your own expressions
(3) By interpolating between experimental data
Variably saturated flow equation
00
0)1()()1/( /1/1
p
pmmm
rs
Hif
HifSeSemmC
01
011 2/1
p
p
mmL
rHif
HifSeSekkr Relative permeability
C Specific capacity
Se Effective saturation
Volume liquid fraction
01
01
1
p
pmn
p
Hif
HifHSe
0
0)(
ps
prsr
Hif
HifSe
(1) … van Genuchten (shown in “Sorbing Solute” model from ES Library)
kr Relative permeability
C Specific capacity
Se Effective saturation
Volume liquid fraction
01
0
p
prs
r
Hif
HifSe
01
0
p
p
r Hif
HifvaluesedInterpolatk
0
0
ps
p
Hif
HifvaluesedInterpolat
(3) … Interpolation from experimental data (shown in
“Interpolation” model from ES Library)
00
0
p
pp
Hif
HifHC
Hp = 0
Hp = Hp(x,z,0)
0)( zHpKn
0)( zHpKn
100/)( sKzHpKn
Axisymmetry
No flow
No flow
Leaky
Specified pressure head
Flow: Boundary and Initial Conditions
1 day 5 days
10 days
Day 5:Soil wetting up, stilldry at surface far from disc
Day 10:Almost all porespace filled with water.
Day 1:Mostly unsaturated (Hp<0)Notice wetting front
Flow Snapshots
Flow Movie
c = concentration = liquid volume fractionb = bulk densitykp = linear sorption coefficientC = specific moisture capacityHp = pressure headD = dispersion tensor q = specific discharge = decay rate
ckcccDt
HC
t
ck ppbLij
ppb
u
Variably saturated solute transport
liquid concentrationc
solid concentrationcp = b kp c
c (r,z,0)=0
Transport: Boundary and Initial Conditions
Axisymmetry
Free advection
No flux
Specified concentrationc=1
0)( ccDn ij u
0)( cDn ij
Free advection
0)( cDn ij
Initially pristine
Transport Concentration Snapshots
Surface is liquid concentration; contours are pressure head
1 day 5 days
Transport Retardation Factor
Sorption slows contaminantmovement relative to water
usolute=uwater/RF
Retardation greatest where pore space is emptiest
Transport Concentration Movie