Problem 59516. Determine aquifer properties: slug test

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. This approach is demonstrated in Cody Problems 59152, 49473, and 59147, which involve steady pump tests in confined or unconfined aquifers, an unsteady pump test in a confined aquifer, and a steady pump test in a leaky confined aquifer. In these cases, a well is pumped at a constant rate, and properties such as the hydraulic conductivity K of the aquifer are determined.
Instead of pumping a well, one can displace the water in the well—by pouring water into the well, bailing it out of the well, or inserting a “slug” and removing it quickly—and observing how the water level recovers. In the Bouwer-Rice model of a slug test, the displacement H of water in the well is given as a function of time t by
H = H0 exp(-2KLet/(rc^2 ln(Re/R)))
where H0 is the initial displacement, rc is the radius of the well casing, R is the radius of the well screen, Le is the length of the well screen, and Re is the effective distance over which the water table returns to its undisturbed level. If the distance Lw from the undisturbed water table to the bottom of the well is smaller than the initial saturated thickness h, then
ln(Re/R) = [1.1/ln(Lw/R) + [A+Bln((h-Lw)/R)]/(Le/R)]^{-1}
If Lw = h,
ln(Re/R) = [1.1/ln(Lw/R) + C/(Le/R)]^{-1}
Bouwer and Rice provided the coefficients A, B, and C in a figure, and Yang and Yeh (2004) fit the curves as functions of x = log10(Le/R):
A(x) = 1.353+2.157x-4.027x^2+2.777x^3-0.460x^4
B(x) = -0.401+2.619x-3.267x^2+1.548x^3-0.210x^4
C(x) = -1.605+9.496x-12.317x^2+6.528x^3-0.986x^4
Write a function that computes the distance Re and determines the hydraulic conductivity K by fitting the Bouwer-Rice formula to measurements of displacement as a function of time.
Schematic of the Bouwer-Rice slug test
Solve

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Last Solution submitted on Jan 05, 2024

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