Page 117 - Materials Chemistry, Second Edition

100 Practical Design Calculations for Groundwater and Soil Remediation

Discussion:
In the second case, the groundwater movement is very slow at 3.0 × 10
-5
cm/s (or 31 ft/yr), but the hydraulic dispersion is still the dominant
mechanism (for dispersivity = 2 m). The diffusion coefficient will
become more important only if the flow rate and/or the dispersivity
is smaller. Nonetheless, the molecular diffusion accounts for a com-
mon phenomenon that the plume usually extends slightly upstream
of the entry point into the aquifer.

3.5.3 Retardation Factor for Migration in Groundwater
Physical, chemical, and biological processes in subsurface that can affect the
fate and transport of COCs include biotic degradation, abiotic degradation,
dissolution, ionization, volatilization, and adsorption. Adsorption of COCs
is probably the most important and most studied mechanism for removal
of COCs from the dissolved plume in groundwater. If adsorption is the pri-
mary removal mechanism in the subsurface, the reaction term in Equation
(3.22) can then be written as (ρ /ϕ)∂S/∂t, where ρ is the dry bulk density of
b
b
soil (or the aquifer matrix), ϕ is the porosity, t is time, and S is the COC con-
centration adsorbed onto the aquifer solids.
When the COC concentration is low, a linear adsorption isotherm is usu-
ally valid. (See Section 2.4.3 for further discussion on the adsorption iso-
therms.) Assume a linear adsorption isotherm (e.g., S = K C), thus
p
∂ S =
∂ C K p (3.29)

The following relationship can then be derived:

∂ S =  ∂ S  ∂  = ∂ C
C
 
∂ C   ∂ C   t ∂   K p t ∂ (3.30)

Substitute Equation (3.30) into Equation (3.22) and rearrange the equation

∂ C  b ρ  ∂ C =  1+ b ρ K p  ∂ C = D ∂ 2 C − v ∂ C
+
t ∂   φ   K p t ∂   φ   t ∂ ∂ x 2 ∂ x (3.31)

By dividing both sides by (1 + ρ K /ϕ), Equation (3.31) can be simplified into
p
b
the following form:
∂ C = D ∂ 2 C − v C
∂
t ∂ R x∂ 2 R x∂ (3.32)