Semi-analytical solutions of discharge variation of a qanat in an unconfined aquifer subjected to general areal recharge and nearby pumping well discharge

Qanat is a type of drain that extract water from aquifers by gravity. Significant amount of fresh water used in Middle East and other parts of the world are supplied by qanats. Despite their importance, discharge variation of these type of wells received almost no attention. The aim of this research is to obtain a Laplace domain solution of discharge variation of a qanat installed in an anisotropic unconfined aquifer subjected to arbitrary areal recharge and nearby pumping well(s) discharge. A new semi-analytical solution of drawdown is obtained first to implement the effects of arbitrary areal recharge and nearby pumping well(s) using the principle of super-position. Then, the discharge variation solution of the qanat is obtained from the drawdown solution. To establish a constant-head boundary condition at the qanat periphery, the qanat is discretized into several segments. The results of this study are presented in dimensionless discharge-dimensionless time curves. The effects of hydraulic as well as geometric parameters on the discharge variation of the qanat due to arbitrary areal recharge, falling of water table from its initial position and discharge of nearby wells are explored. We also investigate the influences of distance and screen depth and location of the nearby well on the discharge variation of the qanat. The results of this study can be utilized for multiple purposes: 1) to predict discharge of qanat in response to rainfall and nearby pumping well(s); 2) to estimate the aquifer parameters using hydrograph of the qanat; 3) to determine optimal location and pumping pattern of the nearby wells to minimize their influences on the discharge of the qanat; 4) to calculate water budget of aquifers drained by a qanat. The equation presented in this work can also be used to estimate discharge of a horizontal drain installed in cropland subjected to arbitrary irrigation pattern.