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. Ecoulement transitoire unidimensionnel dans un aquifère fracturé en communication avec une rivièreRésumé On considère une nappe captive finie au sein d'un aquifère fracturé, limitée d'un côté par une rivière et de l'autre par une formation imperméable. Nous avons étudié l'écoulement transitoire dans la nappe résultant d'une modification brusque du niveau de l'eau dans la rivière. Les équations aux dérivées partielles de l'écoulement sont basées sur le modèle conceptuel de double porosité sous l'hypothèse d'un écoulement quasi-tationaire entre les blocs et les fractures. En utilisant les transformations de Laplace et de Fourier, on a obtenu les solutions analytiques donnant la variation de la cote piézométrique dans la nappe. A l'aide de la loi de Darcy, nous avons évalué le débit entrant dans la nappe par unité de longueur de la rivière. Pour des valeurs très faibles du coefficient d'emmagasinement et de la conductivité hydraulique des blocs, les nouvelles solutions proposées se ramènent aux formes connues. Les solutions analytiques peuvent être utilisées pour la prédiction de la variation des cotes piézométriques dans la nappe, ainsi que pour la détermination du débit d'échange entre la rivière et la nappe, en particulier dans l'analyse des hydrogrammes de la rivière au cours des étiages (pendant les périodes de récession). Les solutions proposées peuvent également être utiles pour identifier les paramètres hydrauliques de la nappe et pour valider des modèles numériques.
Non-Darcian flow in a finite fractured confined aquifer is studied. A stream bounds the aquifer at one side and an impervious stratum at the other. The aquifer consists of fractures capable of transmitting water rapidly, and porous blocks which mainly store water. Unsteady flow in the aquifer due to a sudden rise in the stream level is analysed by the double-porosity conceptual model. Governing equations for the flow in fractures and blocks are developed using the continuity equation. The fluid velocity in fractures is often too high for the linear Darcian flow so that the governing equation for fracture flow is modified by Forcheimer's equation, which incorporates a nonlinear term. Governing equations are coupled by an interaction term that controls the quasi-steady-state fracture-block interflow. Governing equations are solved numerically by the Crank-Nicolson implicit scheme. The numerical results are compared to the analytical results for the same problem which assumes Darcian flow in both fractures and blocks. Numerical and analytical solutions give the same results when the Reynolds number is less than 0.1. The effect of nonlinearity on the flow appears when the Reynolds number is greater than 0.1. The higher the rate of flow from the stream to the aquifer, the higher the degree of nonlinearity. The effect of aquifer parameters on the flow is also investigated. The proposed model and its numerical solution provide a useful application of nonlinear flow models to fractured aquifers. It is possible to extend the model to different types of aquifer, as well as boundary conditions at the stream side. Time-dependent flow rates in the analysis of recession hydrographs could also be evaluated by this model. Mots clefs double porosité; aquifère fracturé; équation de Forcheimer; écoulement non-Darcien
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