Drawdown log-derived analysis for interpreting constant-rate pumping tests in inclined substratum aquifers

Constant-rate pumping tests (CRPT) performed in aquifers having an inclined substratum (IS) cannot be interpreted using Theis-like models, due to an increasing thickness that is beyond conventional hydraulic assumptions. Using an empirical process based on numerical modelling, this study submits original tools for the detection of IS aquifers and the interpretation of their hydrodynamic responses to CRPT, using derivative [ds/dlog(t)] and flow dimension (n) analyses. It is shown that IS aquifers produce a drawdown log-derivative signal composed of two radial regimes and one spherical flow regime (n-sequence = 2-2-3). Comprehensive sensitivity analyses make it possible to constrain relationships between, on one hand, characteristic derivative responses, and on the other hand, hydraulic conditions such as pumping rate, distance from the well to the corner, substratum inclination, and aquifer properties, including anisotropic hydraulic conductivity. This study contributes to widening the array of tools available for the interpretation of pumping tests, by implementing a novel conceptual model for a specific type of nonuniform aquifer that has remained unaddressed; further, it provides another interpretation of the spherical flow regime, which has been interpreted in the petroleum literature to reflect partially penetrating/completing wells. Finally, a field application of the submitted interpretative tools to a CRPT into an IS aquifer is presented.