Range (hydrogeology)

In hydrogeology, the range is the distance from a water extraction point to its lowering area, i.e. the area where the groundwater level no longer changes .

Determination of the range

The range can be estimated using empirically derived equations. The two methods listed below are common. For the meaning of the curly brackets see International System of Units # Related notation of quantities, numerical values ​​and units .

According to Sichardt

According to Sichardt (1928) the range of a well applies ${\displaystyle l_{R}}$

${\displaystyle \{l_{R}\}=3000\cdot \{h_{S}\}\cdot {\sqrt {\{k_{f}\}}}}$.

Here is

• ${\displaystyle l_{R}}$ the range of the well in meters
• ${\displaystyle h_{S}}$the lowering of the water level in the well, i.e. the difference between the water level without extraction and the water level with quasi-stationary flow conditions in meters
• ${\displaystyle k_{f}}$the permeability coefficient of the aquifer in meters per second

After Kussakin

According to Kussakin (1935), also found in the spelling Kusakin, applies to the range of a well ${\displaystyle l_{R}}$

${\displaystyle \{l_{R}\}=575\cdot \{h_{S}\}\cdot {\sqrt {\{k_{f}\}\cdot \{h_{M}\}}}}$.

Here is

• ${\displaystyle l_{R}}$ the range of the well in meters
• ${\displaystyle h_{S}}$the lowering of the water level in the well, i.e. the difference between the water level without extraction and the water level with quasi-stationary flow conditions in meters
• ${\displaystyle k_{f}}$the permeability coefficient of the aquifer in meters per second
• ${\displaystyle h_{M}}$the thickness of the groundwater

Calculation examples and comparison

In an aquifer made of fine-grain sand, the water level was found to have dropped by five meters. Due to the material of the aquifer, the permeability coefficient is estimated at up to meters per second (compare permeability (geosciences) # ranges ). According to Sichardt this results ${\displaystyle 10^{-4}}$ ${\displaystyle 10^{-5}}$

${\displaystyle 3000\cdot \{5m\}{\sqrt {\{10^{-4}m/s\}}}=3000\cdot 5\cdot 10^{-2}=150}$

respectively

${\displaystyle 3000\cdot \{5m\}{\sqrt {\{10^{-5}m/s\}}}=3000\cdot 5\cdot {\sqrt {10^{-5}}}\approx 47{,}4}$

The range is therefore between 47 and 150 meters. If one assumes that the groundwater thickness is 15 meters, then Kussakin follows ${\displaystyle l_{R}}$

${\displaystyle 575\cdot \{5m\}{\sqrt {\{10^{-4}m/s\}\cdot \{15m\}}}=575\cdot 5\cdot {\sqrt {10^{-4}\cdot 15}}\approx 90}$

respectively

${\displaystyle 575\cdot \{5m\}{\sqrt {\{10^{-5}m/s\}\cdot \{15m\}}}=575\cdot 5\cdot {\sqrt {10^{-5}\cdot 15}}\approx 28{,}5}$

The estimated range according to Kussakin is 28.5 to 90 meters and thus lower than that according to Sichardt.

By equating the two approaches, we get that they agree if

${\displaystyle h_{M}=\left({\frac {3000}{575}}\right)^{2}\approx 27{,}2}$

With a groundwater thickness of approx. 27 meters, the range to Kussakin is therefore always lower than that to Sichardt. Above a groundwater thickness of approx. 27 meters, however, the range to Kussakin is always greater than that to Sichardt.

Individual evidence

1. ^ ^{A b c} Bernward Hölting, Wilhelm Georg Coldewey: Hydrogeology . Introduction to General and Applied Hydrogeology. 8th edition. Springer-Verlag, Berlin / Heidelberg 2013, ISBN 978-3-8274-2353-5 , pp. 282-284 , doi : 10.1007 / 978-3-8274-2354-2 .
2. ↑ ^{a b} Dieter D. Genske: Engineering Geology . Basics and application. 2nd, revised and updated edition. Springer-Verlag, Berlin / Heidelberg 2014, ISBN 978-3-642-55386-8 , p. 279 , doi : 10.1007 / 978-3-642-55387-5 .
3. ↑ ^{a b} Helmut Prinz, Roland Strauss: Engineering Geology . 5th, revised and expanded edition. Spektrum Akademischer Verlag, Heidelberg 2011, ISBN 978-3-8274-2472-3 , p. 311 .