Discharge variation of multiple springs associated with a fractured aquifer

Abstract

Springs are important source of fresh water for many regions of the world. Most mathematical models simulating spring discharge are linear and non-linear reservoir-based models that are simple and easy to use. They, however, suffer from oversimplification and a lack of physical processes that limit their applicability. The goal of this work is to present process-based analytical model of discharge variation of multiple springs associated with a rectangular fractured aquifer subjected to arbitrary recharge. The solution is obtained via Laplace and Fourier transformations along with the superposition principle and image well method for a constant flux point sink. Then the constant head point sink solution representing a single spring is obtained from the constant flux point sink solution. Finally, the constant head point sink solution is extended to simulate the multiple constant head sinks (or springs) utilizing the principle of superposition and matrix solution. The solution considers the vertical anisotropy of fractures, the inter-porosity flow between fractures and matrix blocks and the instantaneous gravity drainage of the water table. The results of this study are presented in the form of dimensionless discharge-time curve and dimensionless spring depletion volume-time curves. The influences of aquifer geometric and hydraulic parameters on spring discharge variation are explored. The presented model can be utilized to simulate the discharge variation of multiple springs depleting a fractured aquifer, to estimate the hydraulic parameters of the aquifer utilizing the discharge data of springs, and to evaluate the dynamic storage volume of multiple springs depleting a fractured aquifer, among other applications.