Comparison of the fully penetrating well drawdown in leaky aquifers between fiite and infiite radius of inflence under steady-state pumping conditions

Abstract

In the paper theoretical derivation of steady state groundwater well pumping from leaky aquifers with infinite and finite radius of influence are presented. Based on the extensive literature review following mainly Jacob and Hantush work equations were derived from the cylindrical Bessel partial differential equation and results expressed in the combination of modified Bessel functions of zero order of the first and the second kind (I0, K0). We have shown that equation for steady state well pumping in the infinite aquifer is infinite limit of Hantush integral. Mathematical characteristics of solutions for infinite and finite radius of well influence were combined in the way that they can be represented as relative and absolute differences of drawdowns of each model. In the case when available data do not allow us to make a decision on the type of the radius of influence of the pumping well, they can help us in the interpretation of various errors due to application of different analytical models of pumping test.