Constant-head and variable-head injection tests for determining the hydraulic parameters of an aquitard

Abstract

Although specific storage (SS) is a crucial parameter for characterizing the dynamic water-release process in an aquitard, the Hvorslev analysis method is only capable of estimating the hydraulic conductivity (K), rather than SS. The Hvorslev method is based on an assumption of steady-state flow and uses the falling-head test. Considering the elastic water-release effect in an aquitard and the actual groundwater flow, two mathematical unsteady-state groundwater flow models (i.e., the constant-head and variable-head models), describing the head distribution are presented for a constant-head injection test (CHIT) and variable-head injection test (VHIT) performed in a multi-layered aquifer-aquitard system. The analytical solutions for the models are derived by Fourier transforms to estimate K and SS. The obtained K and SS values from the CHIT and VHIT were generally consistent, although the VHIT is recommended in practice. For the VHIT, estimating K using the Hvorslev analysis method under steady-state groundwater flow conditions resulted in a small relative error compared to the obtained result from the variable-head model. It was demonstrated that a certain relation existed between the constant-head and variable-head methods when the drawdown rate was lower than 1%, and so the constant-head method was applied to the VHIT data to determine K and SS. The synthetic error in the parameters was smaller than 10%, which indicated that the methods could be used interchangeably under these circumstances, thus simplifying the hydraulic parameter estimation process.