Theoretical evaluation of non-uniform skin effect on aquifer response under constant rate pumping

Under field conditions, well skin may be non-uniformly distributed over the screen section. To investigate such non-uniform skin effect on aquifer response, a model is developed where the non-uniform skin effect is represented by an arbitrary piecewise continuous skin function Sk(z) imposed on the boundary of the pumping well. Wellbore storage is taken into account in the pumping well. Due to Sk(z) the model solutions are in terms of non-orthonormal functions, and the Gram–Schmidt method is employed to determine them. It is found that the wellbore flux distribution of the pumping well Qw(z, t) is inversely related to the variation of Sk(z), creating three dimensional flow in the vicinity of the pumping well. This three dimensional flow exists even when wellbore storage is absent in the pumping well, which is different from the fact that uniform skin effect can influence aquifer drawdown only when wellbore storage exists in the pumping well. However, the three dimensional flow evolves to radial flow at farther distances, where the non-uniform skin effect is transformed into a uniform one that can be represented by a constant skin factor equal to the vertical average of Sk(z) weighted by Qw(z, t). The conventional well hydraulics models of a constant skin factor can thus be used to deal with non-uniform skin problems in the radial flow regime or when vertically average drawdown is concerned.