Simplified Physically Based Models for Pressurized Flow in Karst Systems

Abstract

Most karst aquifers behave as a dual-flow system composed of a highly conductive karst conduit embedded in a low-permeability rock matrix. Simplified physically based models suitable for such a karst system are presented herein. The physical processes consist of a pressurized flow in a conduit that is interacting laterally with the groundwater flow in the surrounding matrix. The conduit is subject to a concentrated recharge at its upstream end, while the groundwater aquifer is subject to a diffuse recharge over its contributing surface area. The resulting mathematical model is a coupled system of equations that describe one-dimensional flow processes in a two-dimensional domain. The governing differential equations are solved using the Laplace transform method after an appropriate linearization of the nonlinear coefficient. The derived spring discharge expressions are a function of three dimensionless parameters: the lumped conduit parameter γ, the aquifer parameter η, and the recharge parameter μ. The simulation results highlight the importance of the conduit-matrix interaction on the functioning of the karst system, and the application of the flow models to various karst aquifers demonstrates their effectiveness in reproducing the observed spring hydrograph with parameter values within the acceptable range of observed field data. ©2018. American Geophysical Union. All Rights Reserved.