Water Extraction Volume Estimator
Estimates the sustainable extraction volume from an aquifer using the Theis equation and aquifer storage/transmissivity parameters.
Rate at which water is transmitted through a unit width of aquifer
Confined: 10⁻⁵ – 10⁻³ | Unconfined: 0.01 – 0.35
Desired or planned extraction rate from the well
Total duration of pumping period
Radius of the pumping well (typically 0.05 – 0.5 m)
Distance from well to point of interest or aquifer boundary
Average annual groundwater recharge (0 = no recharge considered)
Area contributing recharge to the aquifer
Results will appear here.
Formulas Used
Theis (1935) Equation — Drawdown:
s(r, t) = Q / (4πT) × W(u)
where u = r²S / (4Tt)
Well Function W(u): Exponential integral approximated by polynomial series (Abramowitz & Stegun, 1964):
W(u) = −0.5772 − ln(u) + u − u²/4 + u³/18 − ... (for u ≤ 1)
Total Extraction Volume: V = Q × t
Jacob Correction (unconfined, large drawdown): s' = s − s²/(2b)
Annual Recharge Volume: V_r = R × A where R = recharge depth [m/yr], A = catchment area [m²]
Sustainability Ratio: SR = Q_annual / V_r — SR ≤ 1 indicates sustainable extraction
Assumptions & References
- Aquifer is homogeneous, isotropic, and of uniform thickness (Theis, 1935)
- Well fully penetrates the aquifer; pumping rate is constant
- Confined aquifer: water released from elastic storage only; unconfined: gravity drainage (specific yield)
- No boundary effects within the radius of influence during pumping period
- Theis equation is most accurate when u < 0.05 (early-time or large T conditions)
- Jacob (1944) correction applied for unconfined aquifers when drawdown > 50% of saturated thickness
- Recharge is assumed spatially uniform over the catchment area
- References: Theis, C.V. (1935), Trans. AGU; Jacob, C.E. (1944), Trans. AGU; Abramowitz & Stegun (1964), Handbook of Mathematical Functions; Todd & Mays (2005), Groundwater Hydrology