The influence of nonuniform transmissivity and storativity on drawdown

Although the existence of spatial variability in hydrogeological parameters is widely recognized, most analyses of pumping test data are performed under the assumption that the aquifer is adequately characterized by a few parameters, for example, constant transmissivity, constant storativity, distance to a barrier, and well skin. Even if the possibility of variability is recognized, pumping tests are often thought to investigate the region between a pumping well and an observation well. Recently, however, investigations of the sensitivity of pumping test data to radially symmetric nonuniform flow properties have shown that the drawdown at an observation well is insensitive to transmissivity and storativity of the region between the pumping well and the observation well. In this paper I use a perturbation approach to derive the Fréchet derivatives and kernels for the effect of two‐dimensional areal variations in transmissivity and storativity on drawdown at an observation well. Fréchet derivatives and kernels are related to sensitivity coefficients, but their definition is independent of zonation. Examination of the Fréchet kernels at large distances from the pumping and observation wells shows that the area of investigation of a pumping test is bounded by an ellipse that encloses both wells. This study also shows that observation well drawdown is relatively sensitive to near‐well transmissivity variation, especially if the nonuniformity is not radially symmetric about the well.