Page 123 - Materials Chemistry, Second Edition

106 Practical Design Calculations for Groundwater and Soil Remediation

3.6 COC Transport in the Vadose Zone
The travel of COCs in the vadose zone can occur in three ways: (1) volatil-
izing into the air void and traveling as vapor, (2) becoming dissolved into the
soil moisture and/or into the infiltrating water and then traveling with the
liquid, and (3) moving downward by gravity as the immiscible phase. This
section describes these transport pathways.

3.6.1 Liquid Movement in the Vadose Zone

Liquid flow through the vadose zone can be described by a differential equa-
tion, and its one-dimensional form is

∂  ∂Ψ  + ∂ K = ∂θ ∂Ψ
w
∂ z  K ∂ z  z ∂ ∂Ψ t ∂ (3.35)
 

where K is the hydraulic conductivity, θ is the volumetric water content,
w
ψ is the soil water pressure head (the sum of the gravity potential and the
moisture potential), z is the distance, and t is the time. The major differences
between this equation and the equation for one-dimensional groundwater
flow (i.e., Darcy’s law) are: (1) the hydraulic conductivity in the vadose zone
is a function of ψ, and hence of θ , and (2) the pressure head is a function
w
of time. These make Equation (3.35) nonlinear, time-dependent, and more
difficult to solve than the simple Darcy’s equation. (If K is a constant and
pressure head is independent of time, then Equation (3.35) can be simplified
to the Darcy’s equation.)
The hydraulic conductivity of a vadose zone is the largest at water satura-
tion and decreases as the water content decreases. As the moisture content
decreases, air occupies most of the pore void and leaves a smaller cross-
sectional area for water transport. Consequently, the hydraulic conductivity
decreases. At a very low moisture content, the water film covering the soil
particles becomes very thin. The attractive forces between the water mol-
ecules and the soil grains become so strong that no water will move. At this
point, the hydraulic conductivity is approaching zero. The hydraulic con-
ductivity at a given moisture can be found from the relative permeability for
that moisture, k (a dimensionless term), and the hydraulic conductivity at
r
saturation, K , as
s
K = k K s (3.36)
r
The relative hydraulic conductivity varies from 1.0 at 100% saturation to 0.0
at 0% saturation.