Contents

Groundwater Flow to Wells - I (pp. 156-162)

Terminology

  • Drawdown

  • Cone of Depression

  • Well interference

Have already examined steady flow solutions.

Unsteady Flow Solutions

There are two ways to proceede - just apply the groundwater flow equatrions or use a plasuibility argument to infer what solutions might look like.

Infer Structure

Apply Groundwater Flow Equations

Implementing Solutions

In the olden days, one would look up well function values in tabulations such as TWRI BOOK 3 Chapter B3 TYPE CURVES FOR SELECTED PROBLEMS OF FLOW TO WELLS IN CONFINED AQUIFERS

Many of the special functions were leter embedded in the analysis packages for spreadsheets.

Or one can simply program themselves as shown below:

def W(u): # Theis well function using exponential integral
    import scipy.special as sc
    w = sc.expn(1,u)
    return(w)

def s(radius,time,storage,transmissivity,discharge): # Drawdown function using exponential integral
    import math
    u = ((radius**2)*(storage))/(4*transmissivity*time)
    s = ((discharge)/(4*math.pi*transmissivity))*W(u)
    return(s)

Lets choose an the example from the book on pg. 162 to illustrate the homebrew script. The relevant problem parametrs are:

  • \(K = 14.9 m/d\)

  • \(b = 20.1 m\)

  • \(T = Kb = 299 m^2/d\)

  • \(S = 0.0051\)

  • \(Q_w = 2725 m^3/d\)

  • \(r = 7.0 m \)

  • \(t = 1 d\)

radius=7.0
time=1.0
storage=0.0051
transmissivity=299
discharge=2725

print("Drawdown is ",round(s(radius,time,storage,transmissivity,discharge),2)," meters")

Drawdown is  5.73  meters