# 2 MB PPT - FIU Faculty Websites

```Gas Phase Transport
Principal Sources:
VLEACH, A One-Dimensional Finite
Model, Version 2.2 – 1997. United States
Environmental Protection Agency, Office
of Research and Development, National
Risk Management Research Laboratory,
Subsurface Protection and Remediation
Šimůnek, J., M. Šejna, and M.T. van
Genuchten. 1998. The HYDRUS-1D
software package for simulating the
one-dimensional movement of water,
heat, and multiple solutes in variablysaturated media. Version 2.0,
IGWMC - TPS - 70, International
Ground Water Modeling Center,
Effective Diffusion
• Tortuosity (T = Lpath/L) and percolation (2D)
x
D  J
C
dC
J  D
dx
2
D  a  4/3
    a
D0   
0.5
Maxwell (1873)
Buckingham (1904)
0.4
Penman (1940)
Marshall (1959)
0.3
D/Do
Millington (1959)
Wesseling (1962)
0.2
Currie (1965)
WLR(Marshall):
Moldrup et al (2000)
0.1
0
0
0.1
0.2
0.3
Volumetric Air Content
0.4
0.5
Total Mass
• At Equilibrium:
Henry’s Law
Cg  KH Cw
• Dimensionless:
• Common:
atm m3 mol-1
VLEACH
• VLEACH simulates
vertical transport by
liquid phase and by
gaseous diffusion in
the vapor phase
VLEACH
• VLEACH describes the
movement of solutes
within and between
three different phases:
– solute dissolved in
water
– gas in the vapor phase
the solid phase
• Equilibration between
phases based on
distribution coefficients
• Processes are
conceptualized as
occurring in a
number of
distinct, userdefined polygons
that are vertically
divided into a
series of userdefined cells
Voronoi
Polygons/
Diagram
• Voronoi_polygons
– close('all')
– clear('all')
– axis equal
– x = rand(1,100); y
= rand(1,100);
– voronoi(x,y)
• The polygons may differ in soil properties,
recharge rate, and depth to water
• However, within each polygon homogeneous
conditions are assumed except for contaminant
concentration, which can vary between layered
cells
• Hence, VLEACH can account for
heterogeneities laterally but does not simulate
vertical heterogeneity
• During each time step the migration of the
contaminant within and between vertically
DEPTH
(ft)
TCE
CONCENTRATION
(&micro;g/kg of soil)
1 – 20
100
20 – 30
50
30 - 40
10
40 - 50
0
Chemical Parameters
• Organic Carbon Partition Coefficient (Koc)
= 100 ml/g
• Henry’s Law Constant (KH) = 0.4
(Dimensionless)
• Free Air Diffusion Coefficient (Dair) = 0.7
m2/day
• Aqueous Solubility Limit (Csol) = 1100
mg/l
Soil Parameters
•
•
•
•
Bulk Density (rb) = 1.6 g/ml
Porosity (f) = 0.4
Volumetric Water Content (q) = 0.3
Fraction Organic Carbon Content (foc) =
0.005
Environmental Parameters
• Recharge Rate (q) = 1 ft/yr
• Concentration of TCE in Recharge Water
= 0 mg/l
• Concentration of TCE in Atmospheric Air =
0 mg/l
• Concentration of TCE at the Water Table =
0 mg/l
Computational Parameters
• Length of Simulation Period (STIME) = 500
years
• Time Step (DELT) = 10 years
• Time Interval for Writing to .OUT file (PTIME) =
100 yrs
• Time Interval for Writing to .PRF file (PRTIME) =
250 yrs
• Size of a Cell (DELZ) = 1.0 ft
• Number of Cells (NCELL) = 50
• Number of Polygons (NPOLY) = 1
Output
Something missing?
Dispersion!
• Dispersivity is implicit in the cell size (l)
and equal to l/2 (Bear 1972)
• Numerical dispersion but can be used
appropriately
Dispersion
100
VLEACH 0.1 m cells
Initial and Boundary
Conditions:
VLEACH 1 m cells
C(x,0) = 100 mg/l
C(0,t) = 0 mg/l
 = 0.05 m
 = 0.5 m
C (mg/l)
80
General Conditions:
 =5m
60
VLEACH 10 m cell
q = 1 m/year
 = 0.5
CDE Flux-averaged
concentrations
(Dispersivity as
shown)
40
VLEACH time step:
0.01 years
20
0
0
5
10
Time (years)
15
20
M.C. Sukop. 2001. Dispersion in VLEACH and similar models. Ground Water 39, No. 6, 953-954.
Hydrus
Hydrus
• Solves
– Richards’ Equation
– Fickian solute transport
– Sequential first order decay reactions
Governing Equation
w ,k 1, g ,k 1, and s,k 1