On the emergence of reciprocity gaps during interference pumping tests in unconfined aquifers

We present a theoretical analysis of the conditions under which reciprocity gaps between vertically-averaged (square) drawdowns can be observed during typical interference pumping tests performed in unconfined heterogeneous aquifers. This work expands on the analysis of Delay et al. [2011] and indicates that reciprocity gaps between vertically-averaged heads monitored during two consecutive tests can be due to vertical trends in aquifer properties (i.e., hydraulic conductivity and specific storage). These are then reflected in the vertical averaging procedure which is performed within a screened borehole and give rise to different observed dynamics of the averaged system responses. Spatially distributed recharge reflecting drainage from the unsaturated region during pumping can also significantly contribute to non-reciprocal behavior, especially for large test durations. Our theoretical findings are then illustrated through a suite of numerical simulations under a variety of vertical distributions of hydraulic parameters and in the presence of saturated/unsaturated flow conditions. We conclude that proper identification of the causes underlying reciprocity gaps can significantly enhance our conceptual understanding of the system response to a sequence of pumping stresses.