Simplified physically based models for free-surface flow in karst systems

Abstract

Most karst aquifers are characterized as a dual-flow system comprised of a highly conductive conduit network embedded in a low porosity matrix. The conduits are hydraulically connected to the matrix and behave either as a drain or a source depending on the recharge conditions. Simplified physically based models are herein employed to simulate the spring outflow for such aquifer systems. The processes consist of a free-surface flow in the conduit that is interacting laterally with a laminar 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 flow system is described by a coupled system of partial differential equations: the conduit flow is approximated by the kinematic wave equation and the groundwater flow by the linearized Boussinesq equation. The governing equations are solved using the Laplace transform method after an appropriate linearization of the nonlinear coefficient. The derived spring discharge models are a function of three dimensionless parameters: the time lag parameter ξ, the lumped conduit parameter λ, and the aquifer parameter η. The simulation results highlight the contrast between pressure-driven and gravity-driven flows and the importance of the conduit-matrix interaction on the response of the karst system. Application of the models on real karst aquifers demonstrates their effectiveness in simulating the observed spring hydrograph using lumped physical parameters of the karst system.