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 identities which generalizes a corresponding Weber identity. The two transforms are, therefore, named the Weber–Goldstein transforms. Their properties are presented. For the first, second, and third type boundary conditions, the new transforms remove the radial portion of a Laplacian in the cylindrical coordinates. They are used to straightforwardly rederive known solutions to the problems of a fully penetrating flowing well and a fully penetrating pumped well. A novel solution for a fully penetrating flowing well with infinitesimal skin situated in a leaky aquifer is also found by means of one of the new transforms. This solution is validated by comparison to a numerical solution obtained via the finite-difference method and to a quasi-analytic solution obtained 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 test in estimating the well skin factor and aquifer parameters depends on the availability of data on the sufficiently early well response.     

Sensitivity of Intrinsic Permeability to Electrokinetic Coupling in Shaly and Clayey Porous Media

Classical Darcy’s law assumes that the intrinsic permeability of porous media is only dependent on the micro-geometrical and structural properties of the inner geometry of the medium. There are, however, numerous experimental evidences that intrinsic permeability of shaly and clayey porous material is a function of the fluid phase used in the experiments. Several pore-scale processes have been proposed to explain the observed behavior. In this study, we conduct a detailed investigation of one such mechanism, namely the electrokinetic coupling. We have developed a numerical model to simulate this process at the pore-scale, incorporating a refined model of the electrical double layer. The model is used to conduct a detailed sensitivity analysis to elucidate the relative importance of several chemical–physical parameters on the intensity of the electrokinetic coupling. We found that permeability reduction due to this mechanism is likely to occur only if the effective pore-radius is smaller than 10⁻⁶ m. We also observed that electrokinetic coupling is strongly sensitive to electrophoretic mobility, which is normally reduced in clays compared to free-water conditions. Based on these findings, we set up a suite of stochastic pore-network simulations to quantify the extent of permeability reduction. We found that only if the effective pore-radius is ranging from 5 × 10⁻⁷ m to 5 × 10⁻⁸, electrokinetic coupling can be responsible for a 5–20% reduction of the intrinsic permeability, and, therefore, this mechanism has a minor impact on situations of practical environmental or mining interest.