Aquifer Storage Calculator: Porosity, Specific Yield and How Long the Water Lasts

How it works

n = 1 − ρ_bulk ÷ ρ_particle · Sr = n − Sy · e = n ÷ (1 − n) · water stored = A × b × n · drainable = A × b × Sy · recharge = A × R · water-table change per year = (pumping − recharge) ÷ (A × Sy) · confined head change = (pumping − recharge) ÷ (A × S) · years of storage = drainable ÷ yearly deficit

Porosity is the fraction of an aquifer’s volume that is empty space. In the lab it comes from the dry bulk density and the density of the mineral grains: n = 1 − ρb/ρs. Only part of that water drains under gravity, the specific yield (Sy); the rest, the specific retention, clings to grain surfaces. That is why a clay with 50% porosity yields almost nothing while a sand with 35% gives up most of it. Multiplying area, saturated thickness and specific yield gives the water a falling water table would release. Comparing yearly pumping with recharge (the share of rainfall that reaches the water table, from a few millimetres a year in dry basins to hundreds in humid ones) shows whether the aquifer is being mined. The deficit divided by A × Sy is the yearly water-table drop, and the drainable volume divided by the deficit gives a rough number of years before the saturated thickness is used up. A confined aquifer is full and under pressure, so pumping first lowers its pressure head instead of draining pores. It releases water only by compressing the grains and expanding the water, measured by the storativity S (typically 0.00001 to 0.001, against 0.1–0.3 for Sy). The same deficit therefore lowers its head hundreds of times faster. Choose Confined to see that decline and the small elastic storage above the aquifer top. All figures treat the aquifer as one uniform block; rivers, leakage, boundaries and uneven pumping make real systems behave differently.

Worked example

With the defaults: sand with a bulk density of 1.65 and a grain density of 2.65 g/cm³ has n = 1 − 1.65 ÷ 2.65 = 37.7% porosity, and with Sy = 0.22 the specific retention is 15.7%. A 4 km² block 15 m thick holds 4,000,000 × 15 × 0.377 = 22.64 million m³ of water, of which 13.20 million m³ (10.7 thousand acre-ft) drains by gravity, equal to 3.30 m of water over the area. Recharge of 80 mm/yr is 0.32 Mm³ (876 m³/day sustainable), so pumping 3,000 m³/day (1.10 Mm³/yr) overdraws by 0.78 Mm³ a year. The water table falls about 0.88 m a year and the drainable storage would last roughly 17 years.

Sources: Heath (1983), Basic Ground-Water Hydrology, USGS Water-Supply Paper 2220 · USGS Water Science School — Aquifers and groundwater · Storativity and specific yield by material (Johnson 1967, USGS WSP 1662-D) — Wikipedia, Specific storage

Frequently asked questions