Transient free surface flow to a well: An analysis of theoretical solutions

Abstract

Several simplifying assumptions are in general required to solve analytically the set of differential equations controlling transient free surface flow to a fully penetrating gravity well. Results based on the linearization technique as well as on the delayed yield concept provide the most advanced theoretical developments to date. A review of available solutions is presented together with some complementary interpretations of their physical behavior and an analysis of the interrelations between the corresponding basic theories. If the elastic storage coefficient S8 is markedly less than the specific yield Sy, the vertical fluid transport is predominant in a cylindrical zone of the water table aquifer included between two regions where flow is essentially radial and is controlled by two different Theis equations. Its boundary surfaces move in time far from the well. If S8 is of the same order of or greater than Sy, the vertical components always tend to become subordinate throughout the aquifer, which at any instant basically behaves as an artesian formation. The physical meaning of Boulton's (1955) delay index 1/α is extensively discussed. It is shown that, contrary to Neuman's (1975) conclusions, the true physical α does not vary linearly with the logarithm of the radial distance r from the pumping well, but it is almost linearly related to 1/r and becomes practically constant at some distance from the well (equal to twice the aquifer thickness if the medium is isotropic). An empirical delay index is also found by equating Boulton's (1963) solution and the linearized average drawdown. Its expression enables us to use the classical delayed yield solution to compute the average piezometric decline with an accuracy equal to that of the linearization approach whose final outcome is, however, more complex and needs more computational time for its numerical evaluation. The two major assumptions underlying the present solutions, which are generally more accurate than the Dupuit‐Boussinesq equation, essentially require small water table drawdowns and an aquifer of infinite areal extent.