# Specific storage

In the field of hydrogeology, storage properties are physical properties that characterize the capacity of an aquifer to release groundwater. These properties are storativity (S), specific storage (Ss) and specific yield (Sy).

They are often determined using some combination of field tests (e.g., aquifer tests) and laboratory tests on aquifer material samples. Recently, these properties have been also determined using remote sensing data derived from Interferometric synthetic-aperture radar.

## Storativity

Storativity or the storage coefficient is the volume of water released from storage per unit decline in hydraulic head in the aquifer, per unit area of the aquifer. Storativity is a dimensionless quantity, and is always greater than 0.

$S={\frac {dV_{w}}{dh}}{\frac {1}{A}}=S_{s}b+S_{y}\,$
• $V_{w}$  is the volume of water released from storage ([L3]);
• $h$  is the hydraulic head ([L])
• $S_{s}$  is the specific storage
• $S_{y}$  is the specific yield
• $b$  is the thickness of aquifer
• $A$  is the area ([L2])

### Confined

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:

$S=S_{s}b\,$

### Unconfined

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

$S=S_{y}\,$

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:

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

where

$(S_{s})_{m}$  is the mass specific storage ([L−1]);
$m_{a}$  is the mass of that portion of the aquifer from which the water is released ([M]);
$dm_{w}$  is the mass of water released from storage ([M]); and
$dh$  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):

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

where

$S_{s}$  is the volumetric specific storage ([L−1]);
$V_{a}$  is the bulk volume of that portion of the aquifer from which the water is released ([L3]);
$dV_{w}$  is the volume of water released from storage ([L3]);
$dp$  is the decline in pressure(N•m−2 or [ML−1T−2]) ;
$dh$  is the decline in hydraulic head ([L]) and
$\gamma _{w}$  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

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

where

$\gamma _{w}$  is the specific weight of water (N•m−3 or [ML−2T−2])
$n$  is the porosity of the material (dimensionless ratio between 0 and 1)
$\beta _{p}$  is the compressibility of the bulk aquifer material (m2N−1 or [LM−1T2]), and
$\beta _{w}$  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:

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

where

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

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

## Specific yield

Values of specific yield, from Johnson (1967)
Material Specific Yield (%)
min avg max
Unconsolidated deposits
Clay 0 2 5
Sandy clay (mud) 3 7 12
Silt 3 18 19
Fine sand 10 21 28
Medium sand 15 26 32
Coarse sand 20 27 35
Gravelly sand 20 25 35
Fine gravel 21 25 35
Medium gravel 13 23 26
Coarse gravel 12 22 26
Consolidated deposits
Fine-grained sandstone   21
Medium-grained sandstone   27
Limestone   14
Schist   26
Siltstone   12
Tuff   21
Other deposits
Dune sand   38
Loess   18
Peat   44
Till, predominantly silt   6
Till, predominantly sand   16
Till, predominantly gravel   16

Specific yield, also known as the drainable porosity, is a ratio, less than or equal to the effective porosity, indicating the volumetric fraction of the bulk aquifer volume that a given aquifer will yield when all the water is allowed to drain out of it under the forces of gravity:

$S_{y}={\frac {V_{wd}}{V_{T}}}$

where

$V_{wd}$  is the volume of water drained, and
$V_{T}$  is the total rock or material volume

It is primarily used for unconfined aquifers, since the elastic storage component, $S_{s}$ , is relatively small and usually has an insignificant contribution. Specific yield can be close to effective porosity, but there are several subtle things which make this value more complicated than it seems. Some water always remains in the formation, even after drainage; it clings to the grains of sand and clay in the formation. Also, the value of specific yield may not be fully realized for a very long time, due to complications caused by unsaturated flow. Problems related to unsaturated flow are simulated using the numerical solution of Richards Equation, which requires estimation of the specific yield, or the numerical solution of the Soil Moisture Velocity Equation, which does not require estimation of the specific yield.