Problem 59147. Determine aquifer properties: steady pump test in a leaky confined aquifer

Problem statement
Write a function to determine the hydraulic conductivity K of a leaky confined aquifer and the hydraulic conductivity K' of the leaky confining layer given the pumping rate Q0 and radius rw of the well, the drawdowns s measured at distances r from the well, and the thicknesses b and b' of the leaky confined aquifer and the leaking confining layer, respectively.
Background
Cody Problem 59002 dealt with one-dimensional flow in a leaky confined aquifer. This problem involves flow to a well in a leaky confined aquifer. As in other pumping tests, the idea is to determine the properties of the aquifer by disturbing it, observing the response, and comparing to an analytical solution. Here the two unknown hydraulic conductivities are determined from two observations of drawdown.
An analytical solution for the drawdown can be determined by solving the equation
d2s/dr2 + (1/r)ds/dr - K's/Kbb' = 0
with the boundary conditions that the drawdown far from the well is zero (i.e., s(inf) = 0) and the flow at the well is Q0. Using Darcy’s law and the convention that flow to the well is positive, one finds
Q0 = -2pi rw b K (ds/dr)|_{r=rw}
The governing equation is related to the one in Cody Problem 51783, and it is the polar coordinates version of the equation in Cody Problem 59002.
Steady pump test in a leaky confined aquifer

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100.0% Correct | 0.0% Incorrect
Last Solution submitted on Nov 07, 2023

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