Three-dimensional saturated-unsaturated flow to a well in an alluvial fan wedge-shaped aquifer

Alluvial fan aquifers are among the most productive aquifers around the world. At present, in mathematical models of these types of aquifers, the unsaturated flow is usually neglected, and the instantaneous or delayed drainage boundary conditions are considered at the water table. The goal of this work is to present an analytical model of the drawdown due to a partially penetrating well in an unconfined alluvial fan aquifer by considering the unsaturated flow. The linearized version of Richards equation is solved to simulate the unsaturated flow. The solution is obtained via Laplace and Fourier transformations and the principle of superposition. The anisotropy of both saturated and unsaturated zones of the aquifer, the pore size distribution of the unsaturated zone and the compressible storage of the saturated zone are considered. The effect of geometrical parameters of the alluvial fan aquifer and hydraulic parameters of the unsaturated zone on the deviation of the proposed saturated-unsaturated flow solution from its saturated flow counterpart are investigated. The presented model shows that the unsaturated flow should not be neglected, especially in low-angle wedge alluvial fan aquifers and near the alluvial fan apex. The presented solution can be utilized to predict the drawdown due to pumping in alluvial fan aquifers, to determine the hydrogeological conditions under which the unsaturated flow may be neglected; to evaluate the sensitivity of the dimensionless drawdown to hydraulic and geometric parameters of the unsaturated zone; to improve the estimated aquifer parameters by coupling the proposed model to a parameter estimation code.