Insights on pumping well interpretation from flow dimension analysis: The learnings of a multi-context field database

The flow dimension parameter n, derived from the Generalized Radial Flow model, is a valuable tool to investigate the actual flow regimes that really occur during a pumping test rather than suppose them to be radial, as postulated by the Theis-derived models. A numerical approach has shown that, when the flow dimension is not radial, using the derivative analysis rather than the conventional Theis and Cooper-Jacob methods helps to estimate much more accurately the hydraulic conductivity of the aquifer. Although n has been analysed in numerous studies including field-based studies, there is a striking lack of knowledge about its occurrence in nature and how it may be related to the hydrogeological setting. This study provides an overview of the occurrence of n in natural aquifers located in various geological contexts including crystalline rock, carbonate rock and granular aquifers. A comprehensive database is compiled from governmental and industrial sources, based on 69 constant-rate pumping tests. By means of a sequential analysis approach, we systematically performed a flow dimension analysis in which straight segments on drawdown-log derivative time series are interpreted as successive, specific and independent flow regimes. To reduce the uncertainties inherent in the identification of n sequences, we used the proprietary SIREN code to execute a dual simultaneous fit on both the drawdown and the drawdown-log derivative signals. Using the stated database, we investigate the frequency with which the radial and non-radial flow regimes occur in fractured rock and granular aquifers, and also provide outcomes that indicate the lack of applicability of Theis-derived models in representing nature. The results also emphasize the complexity of hydraulic signatures observed in nature by pointing out n sequential signals and non-integer n values that are frequently observed in the database.