GeoMiner Free earth-science tools

Built by a geologist

Theis Equation Well Drawdown Calculator

Calculate idealized transient drawdown at one observation point around a constant-rate pumping well using the classical Theis solution. The dimensionless argument is u = r squared times S divided by 4Tt, where r is radial distance from the pumping well, S is storativity, T is transmissivity, and t is elapsed pumping time. The well function W u is the exponential integral E1 u , evaluated from u to infinity. Drawdown is s = QW u divided by 4 pi T, where pumping rate Q and transmissivity T must use compatible length and time units. GeoMiner evaluates the full well function numerically rather than silently substituting a late-time approximation. It also reports hydraulic diffusivity T/S and shows a Cooper-Jacob approximation only when u is no greater than 0.01. Metric inputs use cubic metres per day, square metres per day, metres, and either days or hours. U.S. customary inputs use U.S. gallons per minute, square feet per day, feet, and either days or hours; pumping rate and elapsed time are converted internally before evaluation. Output drawdown is metres or feet according to the selected system. Sensitivity snapshots compare quarter and four-times elapsed time plus half and twice the radial distance. These are mathematical comparisons, not uncertainty bounds or predictions of an actual cone edge. Transmissivity is conductivity integrated through saturated aquifer thickness and has area-per-time units. Do not substitute hydraulic conductivity without representative thickness and direction. Storativity is dimensionless water released from storage per unit aquifer area per unit head decline under the model definition; it is not automatically specific yield. Drawdown is modelled pumping-induced head decline at the evaluated point, not total depth to water, available drawdown, well loss, or pumping-water level. The classical solution assumes an infinite, horizontal, confined, homogeneous, isotropic aquifer of uniform thickness; a constant-rate, fully penetrating well of negligible diameter; horizontal laminar flow; an initially horizontal potentiometric surface; and water released instantaneously from aquifer storage. Real aquifers and tests can be affected by recharge and discharge boundaries, leakage, unconfined delayed yield, changing saturated thickness, anisotropy, heterogeneity, fractures, partial penetration, skin, well loss, wellbore storage, variable pump

Verification resources

Cross-check terminology, classification, methods, and safety with these authoritative external resources.

  • undefined. States the confined-aquifer Theis assumptions, u = r2S/(4Tt), the well-function series, and s = QW(u)/(4 pi T).
  • undefined. Explains transient cones of depression, transmissivity, storage, time dependence, recharge, discharge, and the limits of an ideal aquifer.
  • undefined. Provides a government Theis implementation and states infinite, confined, homogeneous, isotropic, horizontal-flow, and negligible-well-diameter assumptions.
  • undefined. Documents Theis inputs and common U.S. customary units for transmissivity, storativity, time, pumping rate, distance, and drawdown.

Read GeoMiner's editorial methodology.

Common questions

What does the Theis equation calculate?
The Theis solution calculates idealized transient drawdown at a radial distance from a constant-rate pumping well in a confined, infinite, homogeneous, isotropic aquifer.
What is the Theis well function W(u)?
W(u) is the exponential integral E1(u). Its dimensionless argument u combines squared distance, storativity, transmissivity, and elapsed pumping time.
What is the difference between transmissivity and hydraulic conductivity?
Transmissivity has units of area per time and represents conductivity integrated across saturated aquifer thickness. For a uniform horizontal aquifer, T = Kb, but thickness and directional conductivity must be supported.
When is the Cooper-Jacob approximation shown?
GeoMiner reports it only when u is no greater than 0.01, a commonly stated late-time or small-u criterion. The full Theis well function remains the primary result.
Can this calculator determine a safe pumping rate or well yield?
No. Boundaries, recharge, leakage, unconfined response, partial penetration, well losses, wellbore storage, pumping history, interference, water quality, ecological effects, and legal requirements need site-specific evaluation.

JavaScript is loading the interactive GeoMiner experience. The identification tools provide educational candidates, not laboratory confirmation.