Neuman and Witherspoon (1969) derived a solution for flow to a pumping well in a
confined two-aquifer system that accounts for leakage through a storative confining unit
and drawdown in the unpumped aquifer. The Neuman-Witherspoon solution differs from
the solution by Hantush and Jacob (1955) which assumes the unpumped aquifer acts as a
constant-head boundary and the aquitard releases no water from storage.
Neuman and Witherspoon provided examples to illustrate errors introduced by the
limiting assumptions of Hantush-Jacob solution on the estimation of transmissivity (T) for
the pumped aquifer. Figure 1 shows a new example using a synthetic data set prepared
with the following properties for a confined two-aquifer system:
Pumped Aquifer
Aquitard
Unpumped Aquifer
T=250,000 gal/day/ft
S=0.0003
r/B=0.3
b=0.1
T'=50,000 gal/day/ft
S'=0.1
This synthetic data prepared using the Neuman-Witherspoon solution include the effects
of drawdown in the unpumped aquifer (i.e., a constant-head boundary condition is not
assumed) and storage in the aquitard. The match of the Neuman-Witherspoon (1969)
solution in Figure 1 shows the "true" response of the pumped aquifer at
the observation well.
Figure 1. Drawdown in an observation well in a confined two-aquifer
system matched using Neuman-Witherspoon (1969) solution accounting for storage in the
confining unit and drawdown in the unpumped aquifer.
Figure 2 shows the Hantush-Jacob (1955) solution matched to the synthetic data set for
the confined two-aquifer system. Although the fit of this solution to the data
appears satisfactory, the Hantush-Jacob solution overstates the "true"
transmissivity of the aquifer by 24%. Other examples presented by Neuman and
Witherspoon showed potentially larger errors in the estimates of T when using the
Hantush-Jacob solution.
Figure 2. Drawdown in an observation well in a confined two-aquifer
system matched using Hantush-Jacob (1955) solution assuming no storage in the aquitard and
no drawdown (constant-head boundary condition) in the unpumped aquifer.
