Pumping Test Analysis Calculator (Cooper–Jacob Straight Line)
Analyse a constant-rate pumping test: transmissivity from the drawdown change per log cycle of time, storativity from the zero-drawdown intercept, hydraulic conductivity from aquifer thickness, plus a Thiem steady-state check from two observation wells.
How it works
T = 2.3 Q ÷ (4π Δs); S = 2.25 T t₀ ÷ r²; K = T ÷ b; Thiem: T = Q ln(r₂/r₁) ÷ [2π (s₁ − s₂)]
A constant-rate pumping test is the standard way to measure an aquifer's hydraulic properties. Plotting drawdown in an observation well against the logarithm of time gives, after early data, a straight line: its slope per log cycle fixes the transmissivity (steeper line, lower T), and the time where the extended line crosses zero drawdown fixes the storativity, because that intercept is where 2.25Tt/(r²S) equals one. Dividing T by the aquifer thickness gives the average hydraulic conductivity. When two observation wells at different distances reach near-steady drawdown, the Thiem equation provides an independent T that needs no storativity at all, and agreement between the two methods is a good sign the confined-aquifer model fits.
Worked example
With Q = 1,500 m³/day, a drawdown slope of 0.95 m per log cycle gives T = 2.3 × 1,500 ÷ (4π × 0.95) = 289 m²/day; a zero-drawdown intercept of 0.0012 days at 25 m gives S = 2.25 × 289 × 0.0012 ÷ 625 = 1.2×10⁻³ (leaky-confined), and K = 16 m/day for an 18 m aquifer. Two observation wells at 25 and 100 m with 3.1 and 2.15 m drawdown give a Thiem T of 348 m²/day, about 20% higher.
Frequently asked questions
How long should a pumping test run?
Long enough for late-time straight-line behaviour at all observation wells and to reveal boundaries: 24 hours is common for small wells, 72 hours or more for municipal wells. Recovery data after shutdown are analysed the same way and are often cleaner.
What if the plot bends?
Flattening indicates recharge (a river or leaky aquitard); steepening indicates an impermeable boundary or dewatering of an unconfined aquifer. Use the straight segment before the bend for T and S.
Related calculators
Textbook hydrogeology equations (Darcy, Theis / Cooper–Jacob, Thiem) with idealised assumptions: homogeneous, isotropic aquifer of infinite extent, fully penetrating well, laminar flow. Field values of K, T and S vary by orders of magnitude; use site pump-test data and a qualified hydrogeologist for well design, dewatering or contaminant-transport decisions.