Problem 59152. Determine aquifer properties: steady pump test in confined or unconfined aquifers

Problem statement
Write a function to determine the hydraulic conductivity K and radius of influence R using data from a steady pump test in either a confined aquifer or an unconfined aquifer. Along with the drawdowns s measured at distances r from the well, the input will include the pumping rate Q0, the piezometric head H in the absence of pumping, and a variable b that is the thickness of the confined aquifer or empty for an unconfined aquifer. Determine K and R from a curve fit to either the drawdown or piezometric head h = H - s.
Background
Conservation of mass for steady flow says that the flow past any cylinder of radius r centered on the well has to be equal to the pumping rate Q0. Then if the flow is defined as positive toward the well (i.e., in the -r direction), Darcy’s law states
Q0 = K(dh/dr)A
where A is the flow area, or surface area of the vertical sides of the cylinder. The key difference between the confined and unconfined cases is that the flow thickness (or height of the cylinder) is the (constant) thickness b for the confined aquifer and the (variable) thickness h for the unconfined aquifer. Along with the condition that no drawdown occurs for distances greater than the radius of influence—that is,
h(R) = H
one can determine an expression for the drawdown for the confined aquifer or piezometric head h for the unconfined aquifer and fit the resulting expression to the measurements to determine the aquifer properties.

Solution Stats

100.0% Correct | 0.0% Incorrect
Last Solution submitted on Nov 10, 2023

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