A composite system with a planar interface

This paper presents a Greenʹs function formulation for flow to a well in a composite system with a planar interface. It is difficult to obtain solutions to the diffusion equation under such circumstances. Usually, for this problem, solutions are obtained in terms of the Laplace transformation followed by a Fourier transformation. But difficulties arise in reducing the solutions to a state that enables efficient numerical calculations. In this work, flow to a well represented by a continuous line-source near a partial hydrologic barrier (a composite system) is solved along the lines proposed by Sommerfeld (1909). His approach to working the problem results in a scheme that is highly efficient from a computational perspective, an essential requirement for processing the inverse problem. Results obtained by the new solution are compared with those of Bixel et al. (1963).