Handbook of Solvents - George Wypych - ChemTech - Ventech!

23.1 Natural attenuation of chlorinated solvents 1577
23.1.2.4 One-dimensional advection-dispersion equation with retardation
In one dimension, the advection-dispersion equation is given by:
R C
t D
C
v
x
C
2
∂ ∂ ∂
= x −
2 x
∂ ∂ ∂x
[23.1.9]
where:
vx average linear ground-water velocity [L/T]
R coefficient of retardation [dimensionless]
C contaminant concentration [M/L 3 ]
Dx hydrodynamic dispersion [L 2 /T]
T time [T]
x distance along flow path [L]
23.1.2.5 Dilution (recharge)
Ground water recharge can be defined as the entry into the saturated zone of water made
available at the water-table surface. 20 Recharge may therefore include precipitation that infiltrates
through the vadose zone and water entering the ground-water system due to discharge
from surface water bodies (i.e., streams and lakes). Recharge of a water table aquifer
has two effects on the natural attenuation of a dissolved contaminant plume. Additional water
entering the system due to infiltration of precipitation or from surface water will contribute
to dilution of the plume, and the influx of relatively fresh, electron acceptor-charged
water will alter geochemical processes and in some cases facilitate additional
biodegradation.
Wiedemeier et al. 1 present the following relationship for estimating the amount of dilution
caused by recharge:
RW
C C
L ⎡ ⎛ ⎞⎤
⎢ ⎜ ⎟
⎜V⎟⎥
D
L = o exp −
⎢ ⎝ ⎠⎥
[23.1.10]
⎢ WThV ⎥
D
⎢ ⎥
⎣⎢
⎦⎥
eliminating the width and rearranging, gives:
where:
⎛ RL
CL= Coexp⎜−
⎜
⎝ Th VD
( )
2
⎞
⎟
⎟
⎠
[23.1.11]
CL concentration at distance L from origin assuming complete mixing of recharge with
groundwater (mg/L)
Co concentration at origin or at distance L=0(mg/L)
R recharge mixing with groundwater (ft/yr)
W width of area where recharge is mixing with groundwater (ft)
L length of area where recharge is mixing with groundwater (ft)
Th thickness of aquifer where groundwater flow is assumed to completely mix with recharge
(ft)
Darcy velocity of groundwater (ft/yr)
V D