Radial flow in heterogeneous aquifers with uncertain hydraulic parameters

We consider flow to a pumping well operating in a heterogeneous aquifer. In recent years this problem has attracted considerable attention due to its importance in many practical applications. A standard approach to dealing with aquifer's heterogeneity and ubiquitous lack of data is to treat hydraulic parameters, such as hydraulic conductivity and transmissivity, as random fields. In this stochastic framework, significant progress has been made in predicting flow and transport toward wells, and in deriving expressions for the corresponding equivalent (upscaled) parameters. The major theoretical difficulty in analyzing radial flows in heterogeneous media is that the equipotential lines (lines of constant hydraulic head) are no longer circular. Yet, most existing studies use this simplifying assumption. To demonstrate this point, we start by reviewing the existing literature. We then present a stochastic variational approach that avoids this oversimplification. This approach is further used to derive bounds for equivalent (upscaled) transmissivity.