1 Environmental, Water and Agricultural Engineering, Faculty of Civil & Environmental Engineering, Technion - Israel Institute of Technology, Technion City, Haifa 32000, Haifa, Israel

2 Department of Fluid Mechanics and Heat Transfer, Faculty of Engineering, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel

Abstract Transmissivity of aquifers is spatially variable in the plane. Hoeksema & Kitanidis (1985) have analysed field data of tens of aquifers and found that the log-transmissivity, regarded as a normal stationary random function, is characterized by integral scales of the order of kilometres to tens of kilometres. We examine the impact of transmissivity heterogeneity upon steady flow toward a pumping well, for realistic values of the ratio between the integral scale and the well radius of 2000 or larger. Our main finding is that in the zone of influence of the well, of radius up to 2000 well radii, the aquifer practically behaves like a homogeneous one, with the constant transmissivity pertaining to the location of the well. Flow can be modelled, therefore, as one-dimensional (in the radial coordinate) and randomness is parametric. Thus uncertainty can be practically eliminated by conditioning the head on transmissivity measured at the well. We conclude that flow and transport in the zone adjacent to the well are impacted by the three-dimensional local variability of the hydraulic conductivity, but not by the large-scale transmissivity heterogeneity.

Keywords groundwater flow; groundwater hydrology; random media; scaling; steady-state; stochastic processes; transmissivity; wells