Type curves in patchy aquifers

Abstract

A simple analytical derivation of type curve equations for pumping test analysis in a patchy aquifer has been presented. A patchy aquifer has different hydraulic parameters in the vicinity of the well. Any aquifer with a certain domain around the well with different hydraulic properties than the remaining parts can be considered as a patchy aquifer. In this sense, any skin effect around the well can be treated as a patchy aquifer. The basis of the methodology developed herein is to combine mathematically the continuity and the Darcy laws in the forms of simultaneous partial differential equations. The solution is obtained through the use of Boltzmann transformation which renders the partial differential equations into the ordinary counterparts that can be solved without recourse to the Laplace transformations. The region of the aquifer, in which the pumping well exists, has very special type curves and the applications of neither the Theis nor the Jacob straight line methods are possible except in few restrictive cases. However, in the second region the Theis method is applicable for a number of special combinations of parameters and the Jacob method is applicable always for large times only.