Page 87 - Materials Chemistry, Second Edition

70 Practical Design Calculations for Groundwater and Soil Remediation

3. Using the maximum cross-sectional area is a legitimate approach
that represents the “contact face” between the fresh groundwa-
ter and the impacted zone. The maximum cross-sectional areas
could be found as the multiplication product of the maximum
plume thickness and the maximum plume width.

3.2.2 Darcy Velocity versus Seepage Velocity
The velocity term in Equation (3.1) is often called the Darcy velocity (or the
discharge velocity). Does the Darcy velocity represent the actual ground-
water flow velocity? The straight answer to this question is “no.” The Darcy
velocity in Equation (3.1) assumes the flow occurs through the entire cross-
section of the porous medium. In other words, it is the velocity with which
water moves through an aquifer as if the aquifer were an open conduit.
Actually, the flow is limited only to the available pore space (i.e., the effective
cross-sectional area available for flow is smaller). Consequently, the actual
fluid velocity through a porous medium would be larger than the corre-
sponding Darcy velocity. This flow velocity is often called the seepage veloc-
ity or the interstitial velocity. The relationship between the seepage velocity,
v , and the Darcy velocity, v , is
d
s
Q
v s = = v d (3.3)
φ A φ

where ϕ is the effective porosity. For example, for an aquifer with an effective
porosity of 33%, the seepage velocity will be three times that of the Darcy
velocity (i.e., v = 3 v ).
d
s

Example 3.2: Darcy Velocity versus Seepage Velocity
There was a spill of an inert substance into subsurface. The spill infiltrated
the unsaturated zone and quickly reached the underlying water-table aqui-
fer. The aquifer consists mainly of sand and gravel, with a hydraulic conduc-
tivity of 2,500 gpd/ft and an effective porosity of 0.35. The static water level
2
in a well neighboring the spill is 560 ft and that in another well, one mile
directly downgradient, is 550 ft. Determine:
• The Darcy velocity of the groundwater
• The seepage velocity of the groundwater
• The velocity of the plume migration
• How long it will take for the plume to reach the downgradient well