Page 111 - Materials Chemistry, Second Edition

94 Practical Design Calculations for Groundwater and Soil Remediation

3.5.1 Advection–Dispersion Equation
Design and selection of optimal remediation schemes, such as the number
and locations of extraction wells, often require prediction of the COC distri-
bution in the subsurface over time. These predictions are then used to evalu-
ate different remediation scenarios. To make such predictions, we need to
couple the equation describing the flow with the equation of mass balance.
More discussions on the mass balance concept can be found in Chapter 4.
To describe the fate and transport of a COC, the one-dimensional form of
the advection–dispersion equation can be expressed as:

∂ C = D ∂ 2 C − v ∂ C ± RXNs (3.22)
t ∂ ∂ x 2 ∂ x

where C is the COC concentration, D is the dispersion coefficient, v is the
velocity of the fluid flow, t is the time, and RXNs represents the reactions.
Equation (3.22) is a general equation, and it is applicable to describe the fate
and transport of COCs in the vadose zone or in the groundwater. The first
term of Equation (3.22) describes the change in COC concentration in fluid,
contained within a specific volume of an aquifer or a vadose zone, with time.
The first term on the right-hand side describes the net dispersive flux of the
COC in and out of the fluid in this volume, and the second term describes
the net advective flux. The last term represents the amount of COC that may
be added or lost to the fluid in this volume due to physical, chemical, and/or
biological reactions. For plume migration in groundwater, v is the ground-
water velocity that can be determined from Darcy’s law and the porosity of
the aquifer (i.e., Equation 3.3).

3.5.2 Diffusivity and Dispersion Coefficient
The dispersion term in Equation (3.22) accounts for both the molecular dif-
fusion and hydraulic dispersion. The molecular diffusion, strictly speaking,
is due to concentration gradient (i.e., the concentration difference). The COC
tends to diffuse away from the higher concentration zone, and this can occur
even when the fluid is not moving. The hydraulic dispersion here is mainly
caused by flow in porous media. It results from (1) velocity variation within
a pore, (2) different pore geometrics, (3) divergence of flow lines around the
soil grains in the porous media, and (4) the aquifer heterogeneity [7].
The unit of the dispersion coefficient is (length) /(time). Field studies of
2
the dispersion coefficient revealed that it varies with groundwater veloc-
ity. They show that the dispersion coefficient is relatively constant at low
velocities (where the molecular dispersion dominates), but increases linearly
with velocity as the groundwater velocity increases (when the hydraulic