Well-bore clogging of a pumping well in hydraulic interference with an ambient groundwater flow: the Strack-Kostitsina refraction problem in an annular composite redux

Explicit expressions for the vector fields of specific discharge and scalar fields of stream functions and piezometric heads in a Darcian steady-state essentially two-dimensional (2-D) flow through a three-component composite representing a vertical or horizontal well with a gravel pack and annular skin are obtained and analysed. The refraction conditions along two concentric circles, which represent interfaces between three porous media of contrasting hydraulic conductivities, are exactly satisfied. Flow nets, isotachs, the locus of the stagnation point bounding the capture zone of the well, and functionals quantifying area-averaged hydraulic characteristics are found. The flow topology and drawdowns near the well illustrate that at small pumping rates a common concept of a purely radial 1-D flow can be superficially plausible but misleading.