Analytical study of falling-head test in confined aquifer with consideration of non-instantaneous injection

Abstract

A falling-head test is a common method to estimate aquifer properties in which the water level in a well is increased suddenly, which is a key assumption for the data to be analyzed by traditional methods such as Cooper et al. and Hvorslev methods. However, there are situations where the water level increases in the well occurs for a relatively long period before it falls. In this case theoretically, there is no existing method to analyze the data. Hydrogeologists or geotechnical engineers still use the traditional methods to analyze the data even the water level increase is not instantaneous. This study derives a semi-analytical solution to describe water level change in this case. The mathematical model consists of the injection stage and water level fall stage. It is found that the water level mound induced by non-instantaneous injection leads to slower decrease of water level in the well comparing to the instantaneous injection. This study further analyses the errors of the estimated hydraulic properties if the data are analyzed by traditional methods. If calculated by Cooper et al. method, the storativity is underestimated but there is no impact on estimated hydraulic conductivity. The hydraulic conductivity calculated by Hvorslev method is underestimated and the error of underestimation increases with injection time and aquifer parameters. The actual hydraulic conductivity can be a few times of the estimated value for typical aquifer parameters in Hong Kong. Furthermore, a field experiment is conducted to compare the instantaneous method, non-instantaneous method and field data. The present solution fits the data well, and the errors of estimated parameters by instantaneous injection method are consistent with the conclusions in the error analysis.