Pumping-induced leakage in a bounded aquifer: An example of a scale-invariant phenomenon

A new approach is presented for calculation of the volume of pumping-induced leakage entering an aquifer as a function of time. This approach simplifies the total leakage calculation by extending analytical-based methods developed for infinite systems to bounded aquifers of any size. The simplification is possible because of the relationship between drawdown and leakage in aquifers laterally bounded by impermeable formations. This relationship produces a scale-invariant total leakage; i.e., the volume of leakage as a function of time does not change with the size of the aquifer or with the location of the pumping well. Two examples and image well theory are used to demonstrate and prove, respectively, the generality of this interesting phenomenon.