Reply to comment by D.-H. Lim on "Diffusion processes in composite porous media and their numerical integration by random walks: Generalized stochastic differential equations with discontinuous coefficients"

The flow path to a partially penetrating well in a semiconfined aquifer with finite thickness can exhibit nonmonotonic behavior. Water particles entering a semiconfined aquifer far away from a well through the confining layer go downward, and closer to the well they move upward, while under certain circumstances they rise so high that they come down again to finally be captured by the well. An approximative problem is solved analytically under the assumptions that the aquifer is of infinite thickness and that the screen may be represented as a point. It is shown that this phenomenon will occur for particular values of parameters Kc/a > 1.283, where a is the position of the point extraction in the aquifer with respect to the top of the aquifer, K is the hydraulic conductivity of the aquifer, and c is the hydraulic resistance of the covering layer. Such upward bending groundwater path lines have ecological implications in the sense that water from far away will come close to the top of the aquifer in the neighborhood of the well.