Specific storage

For a confined aquifer or aquitard, storativity is the vertically integrated specific storage value. Specific storage is the volume of water released from one unit volume of the aquifer under one unit decline in head. This is related to both the compressibility of the aquifer and the compressiility of the water itself. Assuming the aquifer or aquitard is homogeneous:

${\displaystyle S=S_{s}b\,}$

For an unconfined aquifer, storativity is approximately equal to the specific yield (${\displaystyle S_{y}}$) since the release from specific storage (${\displaystyle S_{s}}$) is typically orders of magnitude less (${\displaystyle S_{s}b\ll \!\ S_{y}}$).

${\displaystyle S=S_{y}\,}$

The specific storage is the amount of water that a portion of an aquifer releases from storage, per unit mass or volume of aquifer, per unit change in hydraulic head, while remaining fully saturated.

Mass specific storage is the mass of water that an aquifer releases from storage, per mass of aquifer, per unit decline in hydraulic head:

${\displaystyle (S_{s})_{m}={\frac {1}{m_{a}}}{\frac {dm_{w}}{dh}}}$

where

${\displaystyle (S_{s})_{m}}$ is the mass specific storage ([L⁻¹]);

${\displaystyle m_{a}}$ is the mass of that portion of the aquifer from which the water is released ([M]);

${\displaystyle dm_{w}}$ is the mass of water released from storage ([M]); and

${\displaystyle dh}$ is the decline in hydraulic head ([L]).

Volumetric specific storage (or volume specific storage) is the volume of water that an aquifer releases from storage, per volume of aquifer, per unit decline in hydraulic head (Freeze and Cherry, 1979):

${\displaystyle S_{s}={\frac {1}{V_{a}}}{\frac {dV_{w}}{dh}}={\frac {1}{V_{a}}}{\frac {dV_{w}}{dp}}{\frac {dp}{dh}}={\frac {1}{V_{a}}}{\frac {dV_{w}}{dp}}\gamma _{w}}$

where

${\displaystyle S_{s}}$ is the volumetric specific storage ([L⁻¹]);

${\displaystyle V_{a}}$ is the bulk volume of that portion of the aquifer from which the water is released ([L³]);

${\displaystyle dV_{w}}$ is the volume of water released from storage ([L³]);

${\displaystyle dp}$ is the decline in pressure(N•m⁻² or [ML⁻¹T⁻²]) ;

${\displaystyle dh}$ is the decline in hydraulic head ([L]) and

${\displaystyle \gamma _{w}}$ is the specific weight of water (N•m⁻³ or [ML⁻²T⁻²]).

In hydrogeology, volumetric specific storage is much more commonly encountered than mass specific storage. Consequently, the term specific storage generally refers to volumetric specific storage.

In terms of measurable physical properties, specific storage can be expressed as

${\displaystyle S_{s}=\gamma _{w}(\beta _{p}+n\cdot \beta _{w})}$

where

${\displaystyle \gamma _{w}}$ is the specific weight of water (N•m⁻³ or [ML⁻²T⁻²])

${\displaystyle n}$ is the porosity of the material (dimensionless ratio between 0 and 1)

${\displaystyle \beta _{p}}$ is the compressibility of the bulk aquifer material (m²N⁻¹ or [LM⁻¹T²]), and

${\displaystyle \beta _{w}}$ is the compressibility of water (m²N⁻¹ or [LM⁻¹T²])

The compressibility terms relate a given change in stress to a change in volume (a strain). These two terms can be defined as:

${\displaystyle \beta _{p}=-{\frac {dV_{t}}{d\sigma _{e}}}{\frac {1}{V_{t}}}}$

${\displaystyle \beta _{w}=-{\frac {dV_{w}}{dp}}{\frac {1}{V_{w}}}}$

where

${\displaystyle \sigma _{e}}$ is the effective stress (N/m² or [MLT⁻²/L²])

These equations relate a change in total or water volume (${\displaystyle V_{t}}$ or ${\displaystyle V_{w}}$) per change in applied stress (effective stress — ${\displaystyle \sigma _{e}}$ or pore pressure — ${\displaystyle p}$) per unit volume. The compressibilities (and therefore also S_s) can be estimated from laboratory consolidation tests (in an apparatus called a consolidometer), using the consolidation theory of soil mechanics (developed by Karl Terzaghi).