Analysis of pumping test data from anisotropic unconfined aquifers considering delayed gravity response

Previously a new analytical model was proposed by the author for the delayed response process characterizing flow to a well in an unconfined aquifer. The new approach differs from that of Boulton (1954, 1963, 1970, 1973) and Boulton and Pontin (1971) in that it is based only on well‐defined physical parameters of the aquifer system. As such, it can be used to develop methods for determining the hydraulic properties of anisotropic unconfined aquifers from field drawdown data. Two methods of analysis are described, one based on the matching of field data with theoretical type curves and the other based on the semilogarithmic relationship between drawdown and time. Owing to the reversible nature of the delayed response process as represented by the analytical model, data from recovery tests can be used to deterrnine aquifer transmissivity. All of these methods are illustrated by applying them to pumping test data collected by the French Bureau de Recherches Géologiques et Minières in Gironde (Bonnet et al., 1970). Similar procedures can be used to analyze data from partially penetrating wells, but this method requires that a special set of theoretical curves be developed for each field situation. Such theoretical curves can easily be developed with the aid of a computer program available from the author. An explicit mathematical relationship is derived between Boulton's (1963) delay index, 1/α, and the physical characteristics of the aquifer. It is shown that contrary to the assumption of Boulton the parameter a is not a characteristic constant of the aquifer but decreases linearly with the logarithm of r , the radial distance from the pumping well. This discovery makes it possible to reinterpret the results of pumping tests that were previously obtained with the aid of Boulton's theory without necessarily reexamining the original drawdown data. Results from pumping tests performed by the Bureau de Recherches Géologiques et Minières in Gironde and by Prickett (1965) in Illinois are used to illustrate this last point.