Analysis of Groundwater Response to Oscillatory Pumping Test in Unconfined Aquifers: Consider the Effects of Initial Condition and Wellbore Storage

Abstract. Oscillatory pumping test (OPT) is an alternative to constant-head and constant-rate pumping tests for determining aquifer hydraulic parameters without water extraction. There is a large number of analytical models presented for the analyses of OPT. The combined effects of wellbore storage and initial condition regarding the hydraulic head prior to OPT are commonly neglected in the existing models. This study aims to develop a new model for describing the hydraulic head fluctuation induced by OPT in an unconfined aquifer. The model contains a typical flow equation with an initial condition of static water table, inner boundary condition specified at the rim of a finite-radius well for incorporating wellbore storage effect, and linearized free surface equation describing water table movement. The analytical solution of the model is derived by the Laplace transform and finite integral transform. Sensitivity analysis is carried out for exploring head response to the change in each of hydraulic parameters. Results suggest that head fluctuation due to OPT starts from the initial condition and gradually tends to simple harmonic motion (SHM) after a certain pumping time. A criterion for estimating the time to have SHM since OPT is graphically presented. The validity of assuming an infinitesimal well radius without wellbore storage effect is investigated. The present solution agrees well to head fluctuation data observed at the Boise hydrogeophysical research site in southwestern Idaho.