Page 104 - Materials Chemistry, Second Edition

Plume Migration in Aquifer and Soil 87

groundwater extracted during a pump test will give engineers a more
realistic estimation of the COC concentrations for treatment system
design than those just based on the data from sampling of monitoring
wells. The main disadvantage of a pumping test is the expenses associ-
ated with conductance of the test, data analysis, and treatment and dis-
posal of the extracted water.
A cheaper alternative to a pumping test is a slug test in which a slug of
known volume is inserted into the water inside a well. The rate at which
water level falls is collected and analyzed. The disadvantages of a slug test
are (1) it provides the hydrological information related only to the vicinity
of the well, and (2) it provides no information for estimates of the extracted
COC concentrations once the full-scale remediation program starts. No fur-
ther discussion on slug tests will be given here.
The flow in the aquifer during a pumping test is considered to be under
unsteady-state conditions. Three common methods are used to analyze the
unsteady-state data: (1) Theis curve matching, (2) the Cooper–Jacob straight-
line method, and (3) the distance–drawdown method.

3.4.1 Theis Method
The drawdown for confined aquifers under unsteady-state pumping was
first solved by C. V. Theis as:

114.6 Q  u 2 u 3 u 4 
s =  − 0.5772 ln()− u + − + − +   (AmericanPractical
u
T  22!⋅ 3 3!⋅ 44!⋅  Units)
Q  u 2 u 3 u 4 
u + −
−
=  − 0.5772 ln() u + − +   (SIUnits) (3.15)
4π T  22! 3 3! 44! 
⋅
⋅
⋅
where the argument u is dimensionless and given as
2
1.87 rS
u = (AmericanPracticalUnits)
Tt
2
rS
= (SIUnits) (3.16)
4 Tt
where
s = drawdown at time t (in ft or m)
Q = constant pumping rate (in gpm or m /day)
3
r = radial distance from the pumping well to the observation well (in ft or m)
S = aquifer storativity (dimensionless)