Abstract
The evaluation of a pump test or a ‘slug’ test in a single well that completely penetrates a leaky aquifer does not yield a unique relation between the hydraulic properties of the aquifer, independent of the testing conditions. If the flow is transient, the drawdown is characterized by a single similarity parameter that does not distinguish between the storativity and the leakage factor. If the flow is quasi stationary, the drawdown is characterized by a single similarity parameter that does not distinguish between the transmissivity and the leakage factor. The general non steady solution, which is derived in closed form, is characterized bythree similarity parameters.
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Abbreviations
- a :
-
e γ≈0.8905 = auxiliary parameter
- b :
-
thickness of the aquifer
- b c :
-
thickness of the semipervious stratum
- B(ξ):
-
auxiliary function
- f(s),g(s):
-
auxiliary functions in the complex plane
- F(t),G(t):
-
auxiliary functions of time
- h ∞ :
-
undisturbed level of the phreatic surface
- K :
-
conductivity of the aquifer
- K c :
-
conductivity of the semipervious stratum
- m 0 :
-
leakage factor
- m :
-
dimensionless leakage factor
- N(s):
-
auxiliary function in the complex plane
- Q′ w (t):
-
discharge flux
- Q ∞ :
-
steady discharge flux
- Q 0 :
-
constant discharge flux during limited time
- Q(t):
-
dimensionless discharge flux
- r 0 :
-
radius of the well
- r′ :
-
radial coordinate
- r :
-
dimensionless radial coordinate
- s :
-
complex variable
- s 0 :
-
pole
- S :
-
storativity of the aquifer
- S n :
-
n'th part of an integration contour
- t′ :
-
time
- t :
-
dimensionless time
- T :
-
transmissivity of the aquifer
- α,β,ε,κ,λ,θ :
-
dimensionless parameters
- γ :
-
Euler's number
- ξ :
-
dummy variable
- ψ 1(ξ),ψ 2(ξ):
-
auxiliary functions
- σ′(r′, t′):
-
drawdown
- σ′0(t′):
-
drawdown in the well
- σ(r, t):
-
dimensionless drawdown
- σ 0(t):
-
dimensionless drawdown in the well
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Rehbinder, G. Theory of single well tests in a leaky aquifer. Analytical solution for non steady flow. Appl. Sci. Res. 55, 211–225 (1995). https://doi.org/10.1007/BF00867512
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DOI: https://doi.org/10.1007/BF00867512