Problem 49743. Determine aquifer properties: unsteady pump test in a confined aquifer

An important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations.
For example, suppose a confined aquifer initially has no flow. In that case, the piezometric head h, or the level to which water would rise in an observation well, would be a uniform value h0. A well turned on and pumped at a rate Q0 will create a cone of depression; that is, it will draw down the piezometric head to a level h(r), where r is the radial distance from the well. Applying conservation of mass and Darcy’s law to this situation leads to a diffusion equation whose solution for the drawdown s = h0 - h as a function of distance r and time t is
s = (Q0/(4 pi T)) integral(exp(-x)/x, u, infinity)
where T is the transmissivity, S is the storativity, and
u = Sr^2/(4Tt)
Write a function that achieves the objective of a pumping test: to determine the transmissivity and storativity from measurements of drawdown in time.
Solve

Solution Stats

30.0% Correct | 70.0% Incorrect
Last Solution submitted on Nov 14, 2025

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