WELL HYDRAULICS WITH THE WEBER-GOLDSTEIN TRANSFORMS

Two new integral transforms, ideally suited for solving boundary value problems in well hydraulics, are derived from one of the Goldstein id entities which generalizes a corresponding Weber identity. The two tra nsforms are, therefore, named the Weber-Goldstein transforms. Their pr operties are presented. For the first, second, and third type boundary conditions, the new transforms remove the radial portion of a Laplaci an in the cylindrical coordinates. They are used to straightforwardly rederive known solutions to the problems of a fully penetrating flowin g well and a fully penetrating pumped well. A novel solution for a ful ly penetrating flowing well with infinitesimal skin situated in a leak y aquifer is also found by means of one of the new transforms. This so lution is validated by comparison to a numerical solution obtained via the finite-difference method and to a quasi-analytic solution obtaine d by numerical inversion of the corresponding solution in the Laplace domain. Based on the new solution, a flowing well test is proposed for estimating the hydraulic conductivity and specific storativity of the aquifer and the skin factor of the well. The test can also be used in a constant-head injection mode. A type-curve estimation procedure is developed and illustrated with an example. The effectiveness of the te st in estimating the well skin factor and aquifer parameters depends o n the availability of data on the sufficiently early well response.