Average contaminant concentration and mass flow in aquifers from time-dependent pumping well data:: Analytical framework -: art. no. W08303

Conventional water samples are representative for small subsurface volumes relative to the scale of many natural (geological) heterogeneities. We present an analytical framework for estimation of representative field-scale average concentrations and mass flows on the basis of much larger sampling volumes that are obtained through so-called integral pumping tests. The contaminant concentration is then measured as a function of time in a pumping well and used for estimation of the conditions in the aquifer prior to (and after) pumping, increasing the observation scale to the size of the well capture zone. This method complements (and provides an alternative to) conventional monitoring grids, where mass flow and concentration may be misinterpreted or plumes even missed because of problems related to grid spacing. The (not measured) initial spatial concentration distribution and the time-dependent concentration measured at the well are related through a Volterra integral equation of the first kind. For limiting cases of short and long dimensionless pumping duration, two closed form analytical solutions are given, from which the mass flow and average concentration can be evaluated. Furthermore, a new solution for evaluating integral pumping tests of any duration is provided and used for investigating the applicability of the simple, analytical closed form solutions for interpreting test results from seven large-scale contaminated sites in Europe.