Page 85 - Materials Chemistry, Second Edition

68 Practical Design Calculations for Groundwater and Soil Remediation

This chapter covers the basic calculations needed to answer most of these
questions. The first section presents calculations for groundwater movement
and clarifies some common misconceptions about groundwater velocity
and hydraulic conductivity. The procedures to determine the groundwater
flow gradient and flow direction are also given. The second section dis-
cusses groundwater extraction from confined and unconfined aquifers.
Since hydraulic conductivity plays a pivotal role in groundwater movement,
several common methodologies of estimating this parameter are covered,
including the aquifer tests. The discussion then moves to the migration of
the plume in the aquifer and in the vadose zone.

3.2 Groundwater Movement
3.2.1 Darcy’s Law

Darcy’s law is commonly used to describe laminar flow in porous media. For
a given medium, the flow rate is proportional to the head loss and inversely
proportional to the length of the flow path. Flow in typical groundwater
aquifers is laminar, and therefore Darcy’s law is valid. Darcy’s law can be
expressed as
Q dh
v d = = − K (3.1)
A dl

where v is the Darcy velocity, Q is the volumetric flow rate, A is the cross-sec-
d
tional area of the porous medium perpendicular to the flow, dh/dl is the hydrau-
lic gradient (a dimensionless quantity), and K is the hydraulic conductivity.
The hydraulic conductivity tells how permeable the porous medium is to
the flowing fluid. The larger the K of a formation, the easier it is for the fluid
to flow through it.
Commonly used units for hydraulic conductivity are either in velocity
units such as ft/day, cm/s, or m/day, or in volumetric flow rate per unit
area such as gpd/ft or m /day/m . You may find the unit conversions in
2
2
3
Table 3.1 helpful.
TABLE 3.1
Common Conversion Factors for Hydraulic Conductivity
m/day cm/s ft/day gpd/ft 2
1 1.16 × 10 −3 3.28 2.45 × 10 1
8.64 × 10 2 1 2.83 × 10 3 2.12 × 10 4
3.05 × 10 −1 3.53 × 10 −4 1 7.48
4.1 × 10 −2 4.73 × 10 −5 1.34 × 10 −1 1