Gas Phase Transport

Principal Sources:

VLEACH, A One-Dimensional Finite Difference Vadose Zone Leaching Model, Version 2.2 – 1997. United States Environmental Protection Agency, Office of Research and Development, National Risk Management Research Laboratory, Subsurface Protection and Remediation Division, Ada, Oklahoma.

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 variably-saturated media. Version 2.0, IGWMC - TPS - 70, International Ground Water Modeling Center, Colorado School of Mines, Golden, Colorado, 202pp., 1998.

Effective Diffusion

• Tortuosity (T = Lpath/L) and percolation (2D)

3/4

2

0a

a

D

D

dx

dCDJ

C

xJD

0

0.1

0.2

0.3

0.4

0.5

0 0.1 0.2 0.3 0.4 0.5Volumetric Air Content

D/D

o

Maxwell (1873)

Buckingham (1904)

Penman (1940)

Marshall (1959)

Millington (1959)

Wesseling (1962)

Currie (1965)

WLR(Marshall):Moldrup et al (2000)

Total Mass

• At Equilibrium:

Henry’s Law

• Dimensionless:

• Common:

wHg CKC

atm m3 mol-1

VLEACH

• VLEACH simulates vertical transport by advection in the 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– adsorbed compound in

the solid phase • Equilibration between

phases based on distribution coefficients

• Processes are conceptualized as occurring in a number of distinct, user-defined polygons that are vertically divided into a series of user-defined 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 adjacent cells is calculated

DEPTH

TCE CONCENTRATION

(ft) (µg/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

Mass loading to ground water

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

0

20

40

60

80

100

0 5 10 15 20Time (years)

C (

mg

/l)

VLEACH 0.1 m cells

VLEACH 1 m cells

VLEACH 10 m cell

CDE Flux-averagedconcentrations (Dispersivity asshown)

Initial and Boundary Conditions:

C(x,0) = 100 mg/lC(0,t) = 0 mg/l

General Conditions:

q = 1 m/year = 0.5

VLEACH time step:

0.01 years

= 0.05 m

= 0.5 m

= 5 m

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

1,1,1, and ,, kskgkw Provide linkage with preceding members of the chain

Hydrus Input Files