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Home/Biophysics, Fluids & Geoscience/Groundwater Well Drawdown (Theis)

Groundwater Well Drawdown (Theis)

Confined-aquifer Theis solution: cone of depression s(r,t) = (Q/(4πT)) W(u), u = r²S/(4Tt); transmissivity, storativity, observation well.

Theis well drawdown

0.02 m³/s
-2.5
-4
1 day
50 m

Confined aquifer, Theis (1935): s = (Q/(4πT)) W(u) with u = r²S/(4Tt). Idealized infinite homogeneous aquifer, constant Q, no wellbore storage.

Shortcuts

  • •Space — play / pause time · R — reset t → early time

Measured values

T3.16e-3m²/s
S1.00e-4
u2.29e-4
W(u)7.806
s(r,t)3.929m

About this model

The Theis (1935) solution gives transient drawdown around a vertical well that pumps at constant rate Q from a confined, infinite, homogeneous aquifer. With transmissivity T and storativity S, the dimensionless argument u = r²S/(4Tt) enters the well function W(u) = −Ei(−u), and s(r,t) = (Q/(4πT)) W(u). The simulator plots the cone of depression s(r) and an observation-well readout so students can see how T, S, Q and time reshape the cone.

Who it's for: Hydrogeology, groundwater engineering, environmental engineering, and water-resources courses.

Key terms

  • Theis equation
  • Drawdown
  • Transmissivity
  • Storativity
  • Well function W(u)
  • Cone of depression

How it works

Theis solution for drawdown around a pumping well in a confined aquifer. Tune transmissivity T, storativity S, pumping rate Q and time to grow the cone of depression and read s at an observation well.

Key equations

u = r² S / (4 T t)
s(r,t) = (Q / (4π T)) · W(u) , W(u) = −Ei(−u)
Cooper–Jacob approx. for small u: W(u) ≈ −γ − ln u

Frequently asked questions

What does small u mean?
Late time or small radius: the Cooper–Jacob approximation W(u) ≈ −γ − ln u becomes useful, and drawdown grows roughly as log(t).
What is idealized away?
Wellbore storage, skin, boundaries, leaky aquitards, and unconfined delayed yield are omitted — this page is the classic confined Theis type curve.