Problem 57452. Design a well field in an infinite aquifer

A well field provides water for a community. The design of a well field involves a goal to meet a specified service demand Q_d (i.e., volume of water per time) with the constraint of lowering the water table by no more than s_max, the maximum drawdown. Inputs to the design are properties of the aquifer (the hydraulic conductivity K, the specific yield S_y, and the initial saturated thickness b) and the radius r_w of the well.
The Gupta/Chin method for designing a well field has the following steps:
  1. Compute Q_w, an initial estimate of the pumping rate, such that the drawdown at one well (i.e., at a distance r = r_w) is s_max/2. Compute the transmissivity to be T = K(b-s_{max}/2). Evaluate the drawdown at a time t = 1 year. Realize that for small values of u = S_y r^2/4Tt the unconfined well function* can be approximated and compute the pumping rate from s_max/2 = (Q_w/4 pi T) W(u_w) where W(u) = integral(exp(-x)/x,{x,0,infinity}) and u_w = S_y r_w^2/4Tt.
  2. Compute the number of wells by dividing the demand by the initial estimate of the pumping rate and rounding up to the nearest integer: ceil(Q_d/Q_w)
  3. Set the pumping rate to Q_0 = Q_d/N.
  4. Arrange the wells so that they are equidistant from the central well.
  5. Determine the distance R between the central well and others so that the total drawdown at the central well is s_max. In other words, add the drawdown from the central well to the drawdown from the other wells. If u_R = S_y R^2/4Tt, then
Write a function to design a well field using this method.
*http://www.aqtesolv.com/neuman.htm
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Last Solution submitted on Nov 21, 2023

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