Storativity from Specific Storage

Storativity, or the storage coefficient, is the volume of water an aquifer releases from storage per unit area per unit drop in head. It is dimensionless, which makes it look simpler than it is. Specific storage $S_s$ is the same idea per unit volume of aquifer, so it carries units of reciprocal length, and the two are related by nothing more complicated than the saturated thickness: $S = S_s b$. Multiply the per-cubic-metre release by the number of metres of aquifer and you have the per-square-metre release.

What makes a confined aquifer release water at all is worth understanding, because it is not what intuition suggests. The aquifer stays completely saturated the whole time. No pores drain. What happens is that lowering the head reduces the pore pressure, which transfers load onto the mineral skeleton and compresses it slightly, while the water itself expands slightly as its pressure falls. Both effects are tiny, which is why confined storativity is tiny: 10⁻⁵ to 10⁻³ across essentially every confined aquifer on earth. A 40 m aquifer with $S_s = 2.5\times10^{-6}$ per metre has $S = 10^{-4}$, meaning a one-metre head drop over a square metre yields one-tenth of a millilitre. It is the enormous area of the cone of depression that turns that into a water supply.

Now the mistake this page exists to prevent. Storativity is not specific yield. Specific yield is the drainable porosity of an unconfined aquifer, where lowering the water table genuinely empties pores, and it runs from about 0.05 to 0.35 — two to four orders of magnitude larger. They are different physics: elastic compression is nearly instantaneous, while gravity drainage is slow and delayed, which is why unconfined pumping tests show a characteristic S-shaped drawdown curve that no confined solution describes. If a "storativity" you have been handed is 0.15, it is a specific yield, the aquifer is unconfined, and Cooper-Jacob is the wrong equation for it.

Getting this wrong is not a small error. $S$ appears directly in the validity parameter $u$ and inside the Cooper-Jacob logarithm, so a storativity out by a factor of a thousand moves your critical time by a factor of a thousand as well. The saving grace is that $S$ sits inside a logarithm in the drawdown equation, so a drawdown prediction is fairly forgiving of a moderate error in it. The validity check is not forgiving at all. Everything on these pages, incidentally, assumes a confined, homogeneous, isotropic aquifer of infinite extent, fully penetrated by the well. Real aquifers are none of those things, which is exactly why a pumping test is interpreted rather than merely computed.