Formula used
The Theis solution describes transient radial flow to a pumping well in a confined aquifer. Drawdown is computed from:
Here Q is discharge, T is transmissivity, S is storage coefficient, r is observation distance, and t is time since pumping began.
How to use this calculator
- Select a calculation mode (drawdown or solve for a parameter).
- Enter the known values and choose matching units for each field.
- Click Calculate to show results above the form.
- Use Download CSV or Download PDF to save outputs.
- If results look unrealistic, re-check units and magnitudes.
Example data table
Sample values for a confined aquifer pumping test scenario.
| Q (m³/day) | T (m²/day) | S (–) | r (m) | t (hr) | Estimated s (m) |
|---|---|---|---|---|---|
| 900 | 1200 | 0.0002 | 30 | 2 | 0.55 |
| 900 | 1200 | 0.0002 | 60 | 2 | 0.36 |
| 900 | 1200 | 0.0002 | 30 | 6 | 0.71 |
Notes and assumptions
- Applies to confined aquifers with radial flow to a fully penetrating well.
- Assumes a constant pumping rate and homogeneous, isotropic conditions.
- Boundary effects and well losses are not included in the ideal solution.
- Very early times (large u) can yield tiny drawdowns.
Practical context for Theis drawdown
Theis drawdown modeling supports pumping‑test interpretation, wellfield planning, and impact screening for nearby users. A constant pumping rate creates a transient cone of depression that expands with time, so drawdown is controlled by both aquifer properties and the observation distance.
Key inputs and typical ranges
Transmissivity T commonly spans 10 to 10,000 m²/day depending on hydraulic conductivity and saturated thickness. Storage coefficient S for confined aquifers often falls between 1×10⁻⁵ and 1×10⁻³, while observation distances may range from tens to hundreds of meters in field tests.
Meaning of the Theis parameter u
The dimensionless parameter u = r²S/(4Tt) captures how “early” or “late” a measurement is. Large u corresponds to early time or far distance, where drawdown may be small and sensitive to noise. Small u indicates late time or closer observations, where drawdown increases and becomes more stable.
Well function behavior and data quality
The well function W(u) decreases as u increases. In practice, reliable parameter estimation benefits from multiple readings across time so the trend is visible. If field data show abrupt steps or recovery artifacts, verify pumping stability and measurement procedures.
Solving for parameters in this tool
This calculator can compute drawdown, or invert the equations to estimate T, S, Q, r, or t. For example, solving for transmissivity uses a numerical search to match observed drawdown in consistent SI units. Keep units aligned with the test dataset to avoid misleading estimates.
Interpreting results for design
For planning, compare drawdown at multiple radii and times to define protective setbacks or operating limits. A higher T usually reduces drawdown for the same pumping rate, while higher S delays drawdown propagation. Use conservative inputs when screening impacts for critical receptors.
Common field corrections to consider
The ideal Theis model does not include well losses, partial penetration, aquifer boundaries, leakage, or anisotropy. If drawdown curves deviate strongly from Theis expectations, consider boundary effects or a leaky aquifer model. Always document site conditions alongside computed outputs.
Reporting and exporting calculation records
Use the CSV export for quick sharing and the PDF export for formal reporting. Include the selected units, the computed u and W(u), and the input set used. Clear recordkeeping helps reproduce results during peer review and future wellfield updates.
FAQs
1) What does the Theis solution assume?
It assumes a confined, homogeneous, isotropic aquifer with a fully penetrating well, radial flow, and a constant pumping rate. It also neglects well losses and boundary effects.
2) What is a reasonable storage coefficient S?
Confined aquifers often range from about 1×10⁻⁵ to 1×10⁻³. Values outside this range can occur, but verify units, data quality, and whether the aquifer is confined or leaky.
3) Why does drawdown sometimes look too small?
Early-time measurements, large observation distances, or very high transmissivity can yield small drawdowns. Also check that discharge units and transmissivity units are consistent with time and distance units.
4) Can I use this for unconfined aquifers?
Use caution. Unconfined systems introduce delayed yield and changing saturated thickness, which can deviate from Theis behavior. Consider unconfined or leaky aquifer methods when field evidence supports them.
5) How many data points are needed to estimate T and S?
More is better. Several readings across time help reveal the drawdown trend and reduce sensitivity to noise. A single observation can produce an estimate, but uncertainty may be high.
6) What does the parameter u tell me?
It summarizes the relative influence of distance and time. Smaller u typically corresponds to later-time behavior with stronger drawdown response, while larger u indicates early time or far distance.
7) Why export u and W(u) in reports?
They document the exact Theis state used to compute results. Including u and W(u) improves transparency, supports peer checks, and helps reproduce calculations if inputs or units are revisited later.