Page 88 - Materials Chemistry, Second Edition

Plume Migration in Aquifer and Soil 71

Solution:
(a) We need to determine the hydraulic gradient first:

i = dh/dl
= (560 − 550)/(5,280) = 1.89 × 10 ft/ft = 1.89 × 10 −3
−3

Darcy velocity (v ) = Ki
d

  ft/day  
2
×
-3
=(2,500 gpd/ft ) 0.134 2   (1.89 10 ) = 0.63 ft/day


   gpd/ft   
(b) Seepage velocity (v ) = v /ϕ
d
s
= 0.63/0.35 = 1.81 ft/day
(c) The pollutant is inert, meaning that it will not react with the
aquifer materials. (Sodium chloride is a good example as an inert
substance, and it is one of the common tracers used in aquifer
studies.) Therefore, the velocity of plume migration for this case
is the same as the seepage velocity, 1.81 ft/day.

(d) Time = distance/velocity
= (5,280 ft) ÷ (1.81 ft/day)
= 2,912 days = 8.0 years

Discussion:
1. The conversion factor (1 gpd/ft = 0.134 ft/day), used in part (a), is
2
from Table 3.1.
2. The calculated plume migration velocity is crude at best, and it
should only be considered as a rough estimate. Many factors,
such as hydrodynamic dispersion, are not considered in this
equation. The dispersion can cause parcels of water to spread
transversely to the main direction of groundwater flow and
move longitudinally, downgradient, at a faster rate. The disper-
sion is caused by factors including intermixing of water particles
due to differences in interstitial velocity induced by the hetero-
geneous pore sizes and tortuosity.
3. The migration speeds of most chemicals in a groundwater
plume will be retarded by interactions with aquifer materi-
als, especially with clays, organic matter, and metal oxides
and hydroxides. This phenomenon will be discussed further
in Section 3.5.3.