Tools › Environmental › Groundwater › Well Hydraulics and Pumping Tests › Example
Aquifer test in a confined aquifer: transmissivity and storage coefficient from time-drawdown readings (USGS Professional Paper 708, Table 6)
| Tool | Well Hydraulics and Pumping Tests |
| Source | Lohman, S. W. (1972). Ground-Water Hydraulics. U.S. Geological Survey Professional Paper 708, U.S. Government Printing Office, Washington, DC. Table 6 and the example on p. 19 (equations 46 and 47), with the straight-line equations 56 and 59 on pp. 21-22. |
| Level | Undergraduate |
Problem
A well in a confined aquifer is pumped at a constant 96,000 ft³/day. The drawdown in observation well N-1, 200 ft away, is read 25 times between 1 and 240 minutes (0.66 ft after 1 min, 3.67 ft after 240 min). Find the transmissivity and the storage coefficient. Lohman matches the readings to the Theis type curve by eye; the tool fits the Theis curve by least squares and also fits the Cooper-Jacob straight line to the late readings.
Inputs to Enter
- Pumping rate 96,000 ft³/day; observation well at r = 200 ft
- 25 readings of time (min) and drawdown (ft): 1.0 0.66, 1.5 0.87, 2.0 0.99, 2.5 1.11, 3.0 1.21, 4 1.36, 5 1.49, 6 1.59, 8 1.75, 10 1.86, 12 1.97, 14 2.08, 18 2.20, 24 2.36, 30 2.49, 40 2.65, 50 2.78, 60 2.88, 80 3.04, 100 3.16, 120 3.28, 150 3.42, 180 3.51, 210 3.61, 240 3.67
- Limit on u for the straight line 0.01 (Lohman's rule); late points chosen automatically
Answers
- Book (type-curve match at W(u) = 1.0, u = 0.1, s = 0.56 ft, r²/t = 2.75 × 10⁷ ft²/day): T = 96,000/(4π · 0.56) = 13,700 ft²/day, S = 4 · 13,700 · 0.1/(2.75 × 10⁷) = 2 × 10⁻⁴
- Tool, Theis least squares on all 25 readings: T = 13,372 ft²/day (95 % interval 13,316 to 13,429), S = 2.016 × 10⁻⁴ (1.987 to 2.046 × 10⁻⁴), root-mean-square residual 0.008 ft; u falls from 0.217 to 9.05 × 10⁻⁴
- Tool, Cooper-Jacob line through the 12 readings with u ≤ 0.01 (24 min onward): Δs = 1.318 ft per log cycle, t₀ = 0.391 min, T = 2.303 Q/(4π Δs) = 13,342 ft²/day (13,185 to 13,504), S = 2.25 T t₀/r² = 2.03 × 10⁻⁴
- The least-squares value is 2.4 % below the book's graphical 13,700 ft²/day; wells N-2 (400 ft) and N-3 (800 ft) of the same table give 13,400 and 13,330 ft²/day with S = 2.01 and 2.02 × 10⁻⁴
Notes
The tool's default inputs are this case; press Submit. The difference from the book is the precision of a type-curve match by eye (the book rounds its own result to 14,000 ft²/day). The fits are checked in test_well_hydraulics.php against scipy.optimize.least_squares and against 20 synthetic tests; the well function against the handbook's Table 5.