Free-surface flow toward a well and interface upconing in stratified aquifers of random conductivity

Aquifers are known to display spatial variability of their properties. To account for the seemingly erratic variation and the uncertainty affecting the permeability, the common approach is to regard it as random and to characterize it statistically. The present note studies the steady axisymmetric water table flow toward a well and interface upconing due to freshwater pumping. The hydraulic conductivity is modeled as a stationary random function of the vertical coordinate, and the Dupuit assumption is adopted. It is found that the impact of heterogeneity upon the mean equivalent conductivity and the mean profiles is small. The standard deviation of these variables may be appreciable, depending on the hydraulic conductivity variance, on the ratio between the well head and the conductivity integral scale, and on the drawdown.