Thiem Equilibrium Aquifer Pumping Test: Transmissivity (T) & K

Choose the model before entering measurements

These are idealized steady radial-flow calculations for a constant extraction rate, a homogeneous isotropic aquifer and a fully penetrating well. Check that the field setting and stabilized measurements support those assumptions. A numerical result does not establish equilibrium.

The confined calculation uses drawdowns from a common initially horizontal head surface, so s1−s2 equals h2−h1. With a regional gradient, that substitution needs additional interpretation. This worksheet takes extraction Q as a positive magnitude.

Confined transmissivity and conductivity

B2 is Q in m³/day; B3 and B4 are inner and outer distances in metres. B5 and B6 are their respective drawdowns in metres. B13 computes T=Q ln(r2/r1)/(2π(s1−s2)). B14 divides the unrounded result by the constant confined thickness B7.

The initial inputs give T≈285.1674 m²/day and K≈14.2584 m/day. This does not identify the material as clean sand. Changing B5 from 3.2 to 5 doubles the drawdown difference and halves both estimates when all other inputs stay fixed.

=IF(B9<>"OK",B9,IF(B10<>"OK",B10,B2*LN(B4/B3)/(2*PI()*(B5-B6))))

Separate unconfined calculation

E2 and E3 are saturated heights above the same horizontal aquifer base, not drawdowns, ground elevations or depth-to-water readings. They represent a separate illustrative unconfined case using the same pumping rate and radii.

Under the Dupuit horizontal-flow approximation, E7 computes K=Q ln(r2/r1)/(π(h2²−h1²)). The denominator is written as (h2−h1)(h2+h1). With h1=18 m and h2=19 m, the output is approximately 27.7460 m/day.

Do not reuse confined thickness b as either height or assume a single constant transmissivity across the unconfined cone. The saturated thickness varies with position. Check the applicability of the unconfined approximation for the drawdown involved.

=IF(B9<>"OK",B9,IF(E5<>"OK",E5,B2*LN(B4/B3)/(PI()*(E3-E2)*(E3+E2))))

Input checks and experiments

B9 requires numeric Q>0 and r2>r1>0. B10 requires numeric s1>s2≥0. B11 requires positive numeric confined thickness. E5 requires numeric h2>h1>0. Invalid inputs produce messages before logarithms or division are evaluated.

A missing confined thickness blocks confined K but does not block T or the separate unconfined K. Invalid drawdowns do not block the unconfined calculation. The worksheet retains full precision; shorten the displayed decimals with formatting.

Try doubling Q: all three estimates double. Double both radii: their ratio stays unchanged, so the estimates stay unchanged. Very small measured head differences make the estimates sensitive to measurement error; input validation cannot fix that uncertainty.

Further reading

• The Groundwater Project — Steady-state confined system, equation 17
• The Groundwater Project — Steady-state unconfined aquifer, equation 19