Formula & Calculator
Well Drawdown (Thiem Equation, Confined Aquifer)
Calculates steady-state drawdown at a given distance from a pumping well in a confined aquifer, using the Thiem equation.
Interpretation
s = (Q / (2πT)) × ln(R/r). Drawdown in a confined aquifer from pumping. Q is pumping rate, T transmissivity, R radius of influence, r radius from well. Used in well testing.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| s | Drawdown | m |
| Q | Pumping rate | m3/day |
| T | Aquifer transmissivity | m2/day |
| R | Radius of influence | m |
| r | Distance from well | m |
What it means
The Thiem equation (or Thiem solution) gives the steady‑state drawdown (s) in a confined aquifer caused by pumping from a well. It assumes radial, steady flow and a fully penetrating well. The drawdown increases logarithmically with distance from the well and is proportional to the pumping rate. It is used in aquifer testing to determine transmissivity (T) from drawdown data. This equation is a classic in groundwater hydrology and is essential for well design, water supply planning, and environmental assessments. Understanding this helps hydrogeologists evaluate well performance and aquifer properties.
Worked example
Well Drawdown (Thiem Equation) – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| Q (m³/day) | 500 |
| T (m²/day) | 100 |
| R (m) | 300 |
| r (m) | 10 |
| Parameter | Value |
|---|---|
| Q | 1000 |
| T | 200 |
| R | 500 |
| r | 20 |
Common mistakes
- Thiem equation: s = (Q / (2πT)) · ln(R/r) – for steady‑state flow to a well in a confined aquifer.
- Drawdown s: The reduction in hydraulic head at the well – in metres.
- Q: Pumping rate – in m³/s.
- T: Transmissivity – in m²/s.
- R: Radius of influence – often estimated from observation wells.
- r: Well radius (or distance from well).
- Assumes: Fully penetrating well, steady‑state, confined aquifer, homogeneous.
Applications
The Thiem equation for well drawdown in a confined aquifer, s = (Q/(2πT))·ln(R/r), gives the drawdown (s) at a radial distance r from a pumping well, given pumping rate Q, transmissivity T, and radius of influence R. This is used to analyse pumping test data, to determine aquifer properties, and to design well fields. Hydrogeologists use it to estimate T and to predict drawdowns for proposed pumping schemes. By applying the Thiem equation, professionals can assess the feasibility of groundwater development, to avoid excessive drawdown, and to ensure sustainable yields. It is also applied in modelling well interference and in designing dewatering systems.
- Pumping test analysis for aquifer characterisation
- Wellfield design and optimisation of pumping rates
- Prediction of drawdown for environmental impact assessments
- Dewatering system design for excavations and mines
- Groundwater management and sustainable yield analysis
Frequently Asked Questions
s = (Q / (2π·T)) × ln(R/r), where s is drawdown at distance r from the pumping well, Q is pumping rate, T is transmissivity, and R is the radius of influence (distance to the point where drawdown is zero).
- Steady‑state flow (no change with time).
- Confined aquifer (full thickness).
- Homogeneous and isotropic T.
- Fully penetrating well.
- Constant pumping rate.
From two observation wells at distances r₁ and r₂, with drawdowns s₁ and s₂: T = (Q / (2π(s₂−s₁))) × ln(r₂/r₁).
R is the distance beyond which the pumping has negligible effect on the water level. It can be estimated from the slope of the drawdown vs. log(r) plot, or from empirical formulas.
Drawdown increases logarithmically as r decreases. Near the well, drawdown is large; far away, it approaches zero.
The Thiem equation is for steady‑state (equilibrium) conditions. The Theis equation is for transient (unsteady) flow and includes the storage coefficient S.
Not directly, because the saturated thickness changes. The unconfined version is s = (Q / (π·K)) × ln(R/r), but it is less common.
The Thiem equation gives the theoretical drawdown in the aquifer. In reality, the drawdown in the well itself includes additional head losses due to the screen and turbulence (well losses).
By plotting s vs. ln(r) (or log(r)), the slope is Q/(2πT). From the slope, T is calculated.
- It requires steady‑state conditions (often not achieved in short tests).
- It assumes a fully penetrating well.
- It does not account for anisotropy.