One Dimensional Transient Flow in a Finite Fractured Aquifer under Constant Discharge Condition

One-dimensional unsteady flow in a finite confined fractured aquifer resulting from a constant discharge, pumped from a stream, is considered. The stream is assumed to penetrate the full thickness of the aquifer. The governing differential equations are based on the double porosity conceptual model with the assumption of pseudo-steady state fracture-to-block flow. A new transient solution is developed by solving the governing differential equations analytically in Laplace domain and then inverting Laplace space solution to real physical domain by using the Stehfest numerical algorithm. The resulting solutions relate the drawdowns in the aquifer to aquifer parameters and the discharge out of the stream. The validity of the proposed method is checked by comparing the results with the available exact analytical solutions for the case of homogeneous aquifers. A non-dimensional drain function D (u,η,δ) is defined based on the solution. Selected type curves for the drain function are plotted. These proposed solutions may be used to predict the drawdowns in the aquifer in the prediction problems. They may also be useful for the validation of numerical models. It is also stated that, based on these solution, techniques may be developed for the determination of the aquifer properties in the identification problems.