On the discharge variation of a qanat in an alluvial fan aquifer

Qanat is a passive (unpumped) horizontal well (or a slant well with a very mild inclined angle) that is capable of extracting water from aquifers by gravity. Many qanats are constructed along the radius of the alluvial fan wedge-shaped aquifers. Analytical modeling of such a qanat-aquifer system provides great benefit for quickly screening different designs of qanats and accessing the performance of qanat discharge in the field. The previous analytical modeling of discharge of qanats, however, did not consider the wedge-shaped aquifers. Thus, the goal of this research is to obtain semi-analytical solutions of discharge variations of qanats in alluvial fan aquifers with nearby pumping wells, subjected to areal recharges due to rainfall. The uniform head boundary is considered inside the qanat (because of its enormous permeability in respect to the background aquifer). The influences of the aquifer lateral boundaries on discharge of qanat and its sensitivity to hydraulic and geometric parameters are explored. The influences of the lateral boundaries on the discharge of qanat due to areal recharge and nearby pumping wells discharge are also explored. The results of this study can be utilized for multiple purposes: 1) to predict the discharge of qanat in an alluvial fan aquifer and explore the influences of the areal recharge and nearby pumping well discharge; 2) to estimate the hydraulic parameters of the alluvial fan aquifer depleted by a qanat; 3) to determine the location of the nearby pumping well to minimize its influences on the discharge of a qanat; 4) to calculate the water budgets of aquifers depleted by qanats and pumping wells and replenished by areal recharge among other applications. This paper is an extension to the work presented by Sedghi and Zhan (2020) (which concerns an infinite unconfined aquifer) for an unconfined alluvial fan aquifer setting.