soil-water flow and solute transport during redistribution
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Morteza Sadeghi and Scott B. Jones
Dept. Plants, Soils and Climate, Utah State University
Scaling Solute Transport during the Soil-Water Redistribution Process
Large amounts of chemicals are applied in agriculture, industry, and transportation for use in the topsoil.
Chemicals are transported to greater depths, leading to contamination of soils and groundwater.
*Fertilizer and Pesticide
Application
Fertilizers & Pesticides
*Accidental Chemical Spills
Accidental chemical spills
Leakage from corroded tanks
Hanford Site
Road Deicing
Nitrate risk in shallow groundwater
Fertilizers are a main source of Nitrate contamination
Arsenic concentration in groundwater
USGS: high arsenic concentration in groundwater associated with landfills and
arsenical pesticides is common.
To Manage,
Quantifying Solute Transport in soil is of
paramount importance for a wide range of
environmental and agricultural issues.
Solute Transport is one of the most complex phenomena in vadose zone!!!
cj D qc
z
mnrs
r h ])(1[
)(
2/
21
])(1[
}])(1[)(1{mn
mnn
s h
hhKK
L w w
qD D D
7/3
2ws
1R
c: solute concentration (mass-per-solvent volume)
hq K K
z
q
t z
cR j
t z
Solute flux
Ret
arda
tion
Wat
er fl
ow
VG models
Diffusivity
Tort
ousi
ty
The System is highly highly nonlinear
There are analytical solutions only for simplified
cases (simple hydraulic models, neglecting the
dispersion/diffusion process or solute reaction).
Tedious numerical calculations have to be
repeated for any soils and any initial/boundary
conditions separately.
TO overcome this complexity,
We introduce a method for scaling different
soils into a unique non-dimensional
medium so that one numerical solution of any soil
can be used for many other soils.
One scenario of interest concentration
dept
h
Solution to this case is important to manage solutes movement to avoid moving beyond the root zone for use only by plant roots.
Solutes are incorporated in irrigation water
an initial wetted zone is created Irrigation water is redistributed
carrying solutes to deeper depths.
θfiθi θ
q=0
zfi
θ = θi
z
qfi
cfici c
j=0
zfi
c = ci
z
Initial and Boundary Conditions:
Water Flow Solute Transport
* i
fi i
fiz
zz *
*
fi
q
* fi
fi i fi
qt t
z
/fi
i
h
fi fi fihq Kdh z K
* i
fi i
c cc
c c
*
fi fi
J JJ
J q
We propose scaling variables as follows:
where:
Scaled water content: Scaled concentration:
Scaled depth: Scaled time:
Scaled water flux: Scaled solute flux:
* * *
* *
c J
t z
* *
* *
q
t z
* *(0, ) 0q t
* *( , ) 0t *
* **
1, 0< < 1( ,0)
0, > 1z
zz
* *( , ) 0c t
* *(0, ) 0J t
** *
*
1, 0< < 1( ,0)
0, > 1z
c zz
A scale-invariant system is obtained:
The only remaining soil-dependent variable is φ (normalized retardation/exclusion) :
i
fi i
ε: Solute reaction coefficient
θi: Initial water content at dry zone
θfi: Initial water content at wet zone
0.0 0.1 0.2 0.3 0.4 0.50
10
20
30
40
50
60
70
80
90
100
loam
clay
clay loam
sandy clay
θz
(cm
)
Water content profile(t = 5 day)
HYDRUS-1D results:
Concentration profile(t = 5 day)
0.0 2.0 4.0 6.0 8.0 10.00.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
c (mmol)
z (c
m)
0.0 0.2 0.4 0.6 0.8 1.00.0
0.5
1.0
1.5
2.0
2.5
3.0
c*
z*
Scaled results ( φ is the same for all cases)
0.0 0.2 0.4 0.6 0.8 1.00.0
0.5
1.0
1.5
2.0
2.5
3.0
*θ
z*
Scaled water content profile(t *= 5) Scaled concentration profile(t* = 5)
0.0 0.2 0.4 0.6 0.8 1.00.0
0.5
1.0
1.5
2.0
2.5
3.0
c*z*
0.0 0.2 0.4 0.6 0.8 1.00.0
0.5
1.0
1.5
2.0
2.5
3.0
c*
smallest φ
(t* = 5) (t* = 10)
Effect of φ (normalized retardation/exclusion) on scaled data: i
fi i
largest φ
smallest φ
largest φ
0.0 0.2 0.4 0.6 0.8 1.00
5
10
15
20
25
30
35
40
* or c*θ
t = 65.95 d
t = 6.59 d
0.0 0.2 0.4 0.6 0.8 1.00
5
10
15
20
25
30
35
40
* or c*θ
t = 22.56 d
t = 2.25 d
0.0 0.2 0.4 0.6 0.8 1.00
5
10
15
20
25
30
35
40
* or c*θ
z (c
m)
t = 48.59 d
t = 4.85 d
(φ = 0.54)
(φ = 0.13)
(φ = 2.34)
Effect of φ:when φ > 0.5, Solute movement is slower than wetting front when φ < 0.5, Solute movement is faster than wetting front
dotted lines: water content profilessolid lines: solute concentration profiles
0.0 0.2 0.4 0.6 0.8 1.010
20
30
40
c*
z (c
m)
1370 (loam)t = 2.16 day
0.0 0.2 0.4 0.6 0.8 1.00
5
10
15
20
25
30
35
40
c*
Pima clay loamt = 7.57 day
0.0 0.2 0.4 0.6 0.8 1.00
10
20
30
40
50
60
70
80
c*
Beit Netofa clayt = 504.92 day
Approximate solutions using the proposed scaling method:
dashed lines: HYDRUS simulations solid lines: approximate solutions
0.0 20.0 40.0 60.0 80.0 100.0 120.01.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
t*
zf*
Solute front (φ = 0.1)a = 0.542b = 0.255
Wetting fronta = 0.413b = 0.299
Solute front (φ = 10)a = 0.013b = 0.407
Scaled wetting and solute front depths vs scaled time.
* *1b
fz at
An Empirical Solution for solute penetration depth:By fitting a curve to the scaled results of one case
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.00.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
wetting front
solute front ( = 0.1)φ
solute front ( = 10)φ
zf by Hydrus (cm)
zf b
y em
piri
cal e
quat
ion
/
1
fi
i
bh
fi fih
f fi
fi i fi
Kdh z Kz z a t
z
* *1b
fz at De-scaling
A new method is proposed for scaling coupled water flow and solute transport during soil water redistribution.
The scaled solutions are invariant for a wide range of soils and initial conditions when the scaled exclusion/retardation term, φ, is identical for all the cases.
The invariance of the scaled solutions provides an insight to the factors influencing solute transport.
The new method provides opportunities to easily obtain approximate solutions of the highly non-linear governing equations.
Summary & Conclusions
Future Studies
The new scaling method considers a single irrigation
event. It is worthwhile to apply such a method to
frequent applications of irrigation water to track the
solute front in long run.
So far, we have not been able to do so.
For more Details read:
Sadeghi, M., and S.B. Jones. 2012. Scaled
Solutions to Coupled Soil-Water Flow and
Solute Transport during the Redistribution
Process. Vadose Zone Journal, 11(4): -.
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