Flow in a falaj (qanat) in an unconfined aquifer system considering the head loss inside the falaj, arbitrary trajectory of falaj, and areal recharge

A falaj (plural aflaj) (also known as qanat) is a type of horizontal or nearly horizontal well that extracts water from an aquifer by gravity. Despite their importance, aflaj with arbitrary trajectories has not yet been mathematically modeled. Moreover, the available analytical models do not include the effects of several head losses, including head loss inside the falaj due to friction with the inner falaj wall, change of flow direction from the aquifer to the falaj, acceleration due to a change in velocity and minor loss caused by change of the falaj direction. Driven by these knowledge gaps, this study aims to develop a semi-analytical solution for the discharge variations of a falaj with an arbitrary trajectory subjected to arbitrary areal recharge. To obtain the solution, the point sink/source solution of groundwater drawdown in an unconfined aquifer is modified to simulate the drawdown due to the specified flux line sink/source of arbitrary trajectory that is known as a snake well. Then, the specified-flux line sink/source solution is converted into an equivalent specified-head line sink/source via well-screen segmentation. Finally, the Darcy–Weisbach equation, along with equations associated with the minor head loss due to the change of flow direction, is employed to simulate the head variation inside the falaj. This study finds that the hydraulic diffusivity of the aquifer and the length of the falaj significantly affect discharge; the trajectory of the falaj affects its late-time discharge, and head loss in falaj tends to mask the influences of its geometric parameters. Furthermore, the presented model can be employed to determine if it is possible to reduce the discharge of a falaj during the wet season when the groundwater is not needed without affecting the dry season discharge.