One-dimensional transient flow in a finite fractured aquifer system

Abstract

A confined finite fractured aquifer bounded by a stream on one side and by an impervious boundary on the other is considered. Unsteady flow in the aquifer resulting from a sudden rise (or drop) of water level in the river stage is analysed. The governing differential equations are based on the double porosity conceptual model with the assumption of pseudo-steady state fracture-to-block flow. By applying finite Fourier sine and Laplace transform techniques to the governing equations, analytical solutions for the piezometric head distribution are obtained. By applying Darcy's law the time-dependent flow rate to (or from) the aquifer per unit length of the stream is evaluated. For negligible storage coefficient or hydraulic conductivity of the blocks, the new solutions reduce to known forms. The proposed analytical solutions may be useful in predicting the variations in the water levels in the aquifer as well as evaluating the time-dependent flow rates especially in the analysis of recession hydrographs in the streams. The solutions may also be used for the identification of the aquifer properties and for numerical model validation.