K-means clustering

Specific storage (S_s), storativity (S), specific yield (S_y) and specific capacity are physical properties that characterize the capacity of an aquifer to release groundwater. They are sometimes referred to as "storage properties". In the field of hydrogeology, these properties are often determined using some combination of field tests (e.g., aquifer tests) and laboratory tests on aquifer material samples.

Specific storage

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 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).

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, or:

$S={\frac {dV_{w}}{dh}}{\frac {1}{A}}$

Storativity is the vertically integrated specific storage value for a confined aquifer or aquitard. For a confined homogeneous aquifer or aquitard they are simply related by:

$S=S_{s}b\,$

where $b$ is the thickness of aquifer. Storativity is a dimensionless quantity, and ranges between 0 and the effective porosity of the aquifer; although for confined aquifers, this number is usually much less than 0.01.

The storativity or storage coefficient of an unconfined aquifer is approximately equal to the specific yield, $S_{y}$, since the release from specific storage, $S_{s}$ is typically orders of magnitude less.

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.

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See also

• Aquifer test
• Soil mechanics
• Groundwater flow equation describes how these terms are used in the context of solving groundwater flow problems

References

• Freeze, R.A. and J.A. Cherry. 1979. Groundwater. Prentice-Hall, Inc. Englewood Cliffs, NJ. 604 p.
• Johnson, A.I. 1967. Specific yield — compilation of specific yields for various materials. U.S. Geological Survey Water Supply Paper 1662-D. 74 p.
• Morris, D.A. and A.I. Johnson. 1967. Summary of hydrologic and physical properties of rock and soil materials as analyzed by the Hydrologic Laboratory of the U.S. Geological Survey 1948-1960. U.S. Geological Survey Water Supply Paper 1839-D. 42 p.

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