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

Solution Stats

100.0% Correct | 0.0% Incorrect
Last Solution submitted on Nov 21, 2023

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers3

Suggested Problems

More from this Author273

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!