Specific storage

From Wikipedia, the free encyclopedia

Specific storage (Ss), storativity (S), specific yield (Sy) and specific capacity are aquifer properties; they are measures of the ability of an aquifer to release groundwater from storage, due to a unit decline in hydraulic head. are often determined in hydrogeology using an aquifer test.

Contents

[edit] Specific storage

The specific storage is the amount of water which a given volume of aquifer will produce, provided a unit change in hydraulic head is applied to it (while it still remains fully saturated); it has units of inverse length, [L-1]. It is the primary mechanism for storage in confined aquifers. It can be expressed as the volume of water released from storage per unit decline in hydraulic head in the aquifer, per unit volume of aquifer. The value of specific storage is typically very small, generally 0.0001 1/ft or less.

S_s = \frac{V_w}{\frac{dH}{V_a}}

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

S_s = \gamma (\beta_p + n \cdot \beta_w)

where

γ 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)
βp is the compressibility of the bulk aquifer material, and
βw 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

σe is the effective stress (N or [MLT-2])

These equations relate a change in total or water volume (Vt or Vw) per change in applied stress (effective stress — σe 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).

[edit] Storativity

Storativity is the volume of water release 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 averaged specific storage value for an aquifer or aquitard. For a 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.

[edit] 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

Vwd is the volume of water drained, and
VT is the total rock or material volume

It is primarily used for unconfined aquifers, since the elastic storage component, Ss, 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 (hysteresis); it clings to the grains of sand and clay in the formation. Also, the value of specific yield may not be fully realized until very large times, due to complications caused by unsaturated flow.


[edit] Specific capacity

Specific capacity is a quantity that which a water well can produce per unit of drawdown. It has units of or , and is expressed as:

S_c=\frac{Q}{h_0 - h}

where

Sc is the specific capacity ([L2T−1]; m²/day or USgal/day/ft)
Q is the pumping rate ([L3T−1]; m³/day or USgal/day), and
h0 − h is the drawdown ([L]; m or ft)

The specific capacity of a well is also a function of the pumping rate it is determined at. Due to non-linear well losses the specific drawdown will be greater at higher pumping rates than it is at low pumping rates. This complication makes the absolute value of specific capacity of little use; though it is useful for comparing the efficiency of the same well through time (e.g., to see if the well requires rehabilitation).

[edit] See also

[edit] Reference

  • 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 Johnson, A.I., 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.
physical aquifer properties used in hydrogeology
hydraulic head | hydraulic conductivity | storativity | porosity | water content
Retrieved from "http://en.wikipedia.org../../../s/p/e/Specific_storage.html"