# Storage coefficient

In hydrogeology, the storage coefficient describes the ability of an aquifer to store or release water. The storage coefficient can be viewed as a measure of the compressibility of the aquifer. The compressibility of air bubbles trapped in the pore space and the deformability of the grain structure are essentially responsible for the storage capacity . Changes in density of the grains and of the water are negligible compared to the volume changes of the grain structure and gas inclusions. The elastic deformation of the fluid and the grain structure when the pore pressure increases enables water to be stored in the grain structure. This process is reversible, so when the pore pressure is relieved (e.g. when pumping a well), the stored water is first released from the grain structure. Only when the water from the change in the storage tank has been released can the pressure change as a result of the lowering of the well spread through the aquifer. This is important when the change in pressure over time is rapid compared to the hydraulic permeability k of the aquifer, for example when draining a construction pit that extends into the groundwater. Due to the delayed reaction due to the storage capacity, large hydraulic gradients can build up, which in the course of a subsequent dissipation process can lead to a reduction in the effective stresses or even to hydraulic ground failure. ${\ displaystyle S}$${\ displaystyle \ textstyle {\ frac {\ Delta P} {\ Delta t}}}$

Formally, a distinction is made between the storage coefficient and the specific storage coefficient, depending on the spatial consideration.

## Specific storage coefficient

The specific storage coefficient describes the volume of water that can be stored in a unit volume of an aquifer (e.g. an imaginary cube with a side length of 1 m) or can be extracted from it when the potential h [L] changes by one unit. ${\ displaystyle S_ {s}}$

According to the definition above, the specific storage coefficient is described by the following formula: ${\ displaystyle S_ {s}}$

${\ displaystyle S_ {s} = - {\ frac {1} {V}} {\ frac {dV_ {w}} {dh}} = - {\ frac {1} {V}} {\ frac {dV_ { w}} {dP}} {\ frac {dP} {dh}} = - {\ frac {1} {V}} {\ frac {dV_ {w}} {dP}} \ gamma _ {w}}$

With

${\ displaystyle S_ {s}}$Specific storage coefficient (m −1 or [L −1 ])
${\ displaystyle V}$ Volume of the considered groundwater body (m 3 or [L 3 ])
${\ displaystyle dV_ {w}}$ Volume of stored or dispensed water (m 3 or [L 3 ])
${\ displaystyle dh}$Change of the hydraulic potential h (m or [L])
${\ displaystyle dP}$Change in pressure (kN / m 2 or [F / L 2 ])
${\ displaystyle \ gamma _ {w}}$specific density of water (kN / m 3 or [F / L 3 ])

With full water saturation of the pore space, the specific storage coefficient has values ​​between 10 −5 m −1 and 10 −6 m −1 . In one m 3 of an aquifer, a water volume dV w of 1 to 10 ml of water can thus be stored when the hydraulic potential is increased by dh = 1 m .

Due to the significantly higher compressibility of gases, however, this value increases significantly as soon as the smallest amount (1 - 2%) of air is trapped in the cavity. Air inclusions occur frequently in nature due to fluctuating groundwater levels. Due to the increase in pressure with depth, there is a depth distribution of the gas volume, which, however, can hardly be measured directly.

## Storage coefficient

In groundwater hydraulics, the groundwater flow is viewed in a simplified manner as being averaged over the entire thickness of an aquifer , whereby, according to Dupuit, the vertical flow components are neglected. In this approach, the storage coefficient S is used, which results from an integration of the specific storage coefficient over the thickness [L] of the aquifer. The storage coefficient S obtained in this way is dimensionless. The storage coefficient is usually determined by means of a pumping test . The orders of magnitude for storage coefficients for confined aquifers are between 10 −5 and 10 −3 . The higher values ​​only occur with air inclusions in the grain structure. In the case of unconstrained pore aquifers , the storage capacity corresponds to the usable porosity and is in the range of 0.10 to 0.25.

## literature

• DIN 4049-3 (hydrology, part 3: terms for quantitative hydrology)
• Bernward Hölting, Wilhelm Georg Coldewey: Hydrogeology. Introduction to general and applied hydrogeology . Elsevier, Munich and Heidelberg 2005, ISBN 3-8274-1526-8 .
• Wolfgang Kinzelbach, Randolf Rausch: Groundwater modeling . Bornträger, Stuttgart and Berlin 1995, ISBN 3-443-01032-6 .
• R. Allan Freeze, John A. Cherry: Groundwater . Prentice Hall, Englewood Cliffs 1979, ISBN 0-13-365312-9 .
• Hanspeter Jordan: Hydrogeology. Basics and methods . Enke, Stuttgart 1995, ISBN 3-432-26882-3 .