Pumping in an Infinite Confined Aquifer - The Theis Solution
Theis (1935) presented an exact analytical solution for the transient drawdown in an infinite uniform confined aquifer (See Fig 1).
Analytical Solution
The analytical solution of the drawdown as a function of time and distance is expressed by equation (1):
Problem A: Use the theis solution to show: the influence radius for a confined aquifer increases with time at a rate that is an order(s) of magnitude faster than that for an unconfined aquifer
Problem B: for the following set of parameters, calculate influence radius R(t) corresponding to a drawdown of 0.1 m
- Q = 1000 m3/day
- Aquifer thickness = 20 m, Hydraulic conductivity = 50 m/day
- S = 0.0001, Sy = 0.1
Problem C - Develop a MAGNET model that can reproduce the Theis solution for the above specific situation
Suggested numerical parameters (also see Figure below):
- 10m =∆ x
- 10m =∆ y
- ∆t =1.036 sec
Problem D: Sensitivity analysis
Explore using MAGNET how each of them and their combination influence drawdown. Be quantitative in your work. Use plots, maps and other means of communicating information to make your description clear. Be concise, but complete.
Write a 1 page memo summarizing your results / findings from your numerical experimentation on aquifer drawdown dynamics, particularly the difference in drawdown dynamics between confined and unconfined aquifers.
MAGNET/Modeling Hints:
- Use 'Synthetic Mode' to set up your flow model ( 'Other Tools' > 'Utilities' > 'Go to Synthetic Case Area'). The default model domain for synthetic mode is identical to the domain depicted in the figure above.
- Conceptualize the model as 1-layer, confined aquifer.
- Use the given inputs in Problem B to parameterize your flow model.