Assessing the Transient Flow Behavior in Falling-head Permeameter Tests

Abstract

The proportionality constant in Darcy's Law is called hydraulic conductivity (K), and it is the most fundamental parameter to groundwater studies. There are a number of in situ and laboratory techniques employed to determine K, one of which is falling head permeameter (FHP). In FHP, determining K involves two steps: measuring hydraulic head change over time and calculating the K value. In the past, calculating K was done using Darcy's Law, which states linear correlation between the flux and the hydraulic gradient, but this is only true when the inertial forces are negligible at small velocities. At higher velocities, flow becomes unsteady because of the change over time in flow magnitude and hydraulic gradient, which requires mass conservation law to be combined with Darcy’s Law and eventually leads to Laplace’s equation for an incompressible matrix. If the media is compressible, specific storativity should be taken into account, as well. In this study, we investigated the transiency of flow in FHP tests by analyzing the effect of specific storativity on K calculations. We have developed a new semi- analytical solution for transient flow in FHP in Laplace domain and used the de Hoog algorithm to attain the inverse Laplace transform of this solution to yield solutions in time domain. We have also provided some analysis and a comparison of steady-state solution along with using experimental data and the data from the literature to analyze the solution. Upon these, we concluded that the transient flow in falling-head tests has minimal effect in general, although using the transient solution provided may improve the accuracy without a major effect.