Problem 59147. Determine aquifer properties: steady pump test in a leaky confined aquifer
Write a function to determine the hydraulic conductivity K of a leaky confined aquifer and the hydraulic conductivity of the leaky confining layer given the pumping rate and radius of the well, the drawdowns s measured at distances r from the well, and the thicknesses b and of the leaky confined aquifer and the leaking confining layer, respectively.
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
with the boundary conditions that the drawdown far from the well is zero (i.e., ) and the flow at the well is . Using Darcy’s law and the convention that flow to the well is positive, one finds
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