Three-Dimensional Numerical Modeling of Submerged Zone of Qanat Hydraulics in Unsteady Conditions

Qanats have been considered as one of the significant and economical methods for groundwater abstraction, thus studying the flow into and along them through numerical modeling is of vital importance. In this study, based on a three-dimensional (3D) analysis of the flow in anisotropic heterogeneous aquifers, the submerged zone of a Qanat has been described using a numerical groundwater model. The 3D finite difference control volume approach has been used to discretize the flow equation in the aquifer. The flow from the aquifer into the Qanat has been described with conductance values, and the hydraulic conditions within the Qanat have been described by the Darcy-Weisbach equation. The boundary condition at the Qanat outlet was set so that both full and partially full channel flow can be considered. Designing a computer code for the proposed model, the 3D hydraulics of a Qanat-aquifer system have been simulated. Model verification has been done by simulating a horizontal well-aquifer system developed in previous studies, and by using the coefficient of variation as verifying criterion. Good agreement between results of the proposed solution and those of previous work has been obtained in the verification process (coefficient of $\mathrm{variation}<0.023$), and the small differences can be attributed to applying different pipe resistance coefficient values and convergence criteria. Furthermore, the model performance was evaluated using observed flow depth and discharge in the Gavgard branch of the Joopar Goharriz Qanat. With this modeling, the behavior of the system, spatially and temporally, can be evaluated for different assumptions and exploitation conditions, and, consequently, the most appropriate exploitation conditions can be defined.