A recovery test measures the residual drawdown after an aquifer pumping test has ended and analyzes the recovery data to determine hydrogeological parameters such as transmissivity and storage coefficient. To our knowledge, the solution for the distribution of residual drawdown following a constant-head test has never been presented. In this paper, we first develop a mathematical model that describes the residual drawdown taking into consideration the wellbore-storage effect and the drawdown distribution occurring at the end of a previous constant-head test. Then, the Laplace-domain solution of the model is developed using the Laplace transforms and its time-domain solution is obtained using the Stehfest algorithm. Numerical results show that the distribution of residual drawdown depends on the boundary condition related to the well drawdown and the initial condition related to the aquifer drawdown. The well residual drawdown (i.e., the residual drawdown at wellbore) during the early recovery period will be over-estimated by the approximate residual drawdown solution based on the Theis-type solution and superposition principle due to the neglect of wellbore storage. For a large recovery time, the effect of wellbore storage is negligible and the approximate residual drawdown solution is therefore applicable.
- Analytical solution
- Recovery test