Question

Radius of influence may be approximatly calculated by

Answer 1

Since an homogenous aquifer was modelled, there is an interest in comparing the results with an analytical solution. Some formulas give the drawdown value into the well for a steady flow in confined and unconfined aquifers that are homogeneous, isotropic and infinite in the horizontal extent with a single full penetrating well.

Those formulas are [Braun, Färber, 2004]:

Confined Case:



Unconfined Case: 



Where:

sw :       drawdown at the outer perimeter of the well filter

Qo :       pumping rate

ho :       undisturbed saturated aquifer thickness          

m  :       height of the confined aquifer

rw :       well radius

K   :       hydraulic conductivity

R  :       radius of influence

All of the parameters listed above were defined in the model conceptualization except the values for the well radius and the radius of influence. The well radius can be estimated from a standard well casing, but the radius of influence has to be determined with the help of some formulas.

The “Radius of Influence” is defined as the maximum distance at which the drawdowns can be detected with the usual measure devices in the field [Dragoni, 1998].  Due to the use of numerical tools, the concept of “Radius of Influence” is nowadays of limited use [Dragoni, 1998].

The most common way to find the “Radius of Influence” is the use of empirical formulas. Those formulas are listed below.



With:

N   =      groundwater recharge          

ho =      saturated aquifer thickness  

K   =      hydraulic conductivity          

ne =      effective porosity                

sw =      drawdown at the well outer perimeter

t    =      time                                      

Some formulas require some other parameters (recharge, effective porosity and pumping time). It is worth mentioning that none of this formulas use the pumping rate as a parameter for calculation.

It is also possible to estimate the radius of influence, or in particular, the area of influence of a cone of depression as the area where the drawdown exceeds 1 foot (30,48 cm.)[Myette, Olimpio, Johnson, 1987].

The most common formula to determine the radius of influence is the Sichardt formula, although the radius value for this formula is the smallest one and represents 40 % of the maximum drawdown. Thus, the Sichardt radius value can’t match the radius of influence definition. Similar situations occur for both Kusakin formulas.

Dispersion of the radius of influence values reveal the empirical nature of the formulas that depend only on the parameters considered.

References

Dragoni W.: Some consideration regarding the radius of influence of a pumping well. Perugia Italy, 1998. Web:http://www.unipq.it/~denz/Dragoni.pdf