Simple transport models for karst systems

Abstract

Tracer tests are useful field methods with a wide range of applications in karst aquifers. The measured tracer breakthrough curve at a karst spring allows the estimation of the important transport properties of the karst system. The breakthrough curve is typically characterized by a long tailing and a low tracer recovery that is not captured by the classical one-dimensional advection dispersion model. Partitioning models are often used and require a large number of parameters. In the present work, simplified transport models are proposed to simulate the typical karst breakthrough curve. The model setup consists of a karst conduit that is interacting laterally with the surrounding matrix. The solute transport in both the conduit and matrix are governed by the one-dimensional advection-dispersion equation and the resulting mathematical model consists of a coupled system of differential equations. The Laplace transform method is used to derive the transport models for various flow and boundary conditions. The models are in terms of four physically meaningful parameters that represent the advection and dispersion properties of the flow in the conduit and matrix. Algebraic relationships to estimate the model parameters are also derived in terms of the key features of the breakthrough curves. The main advantage of the proposed models are their simple formulation and ability to capture the long tailing of the breakthrough curve in terms of just a few parameters. Application of the models to two real karst aquifers demonstrate their effectiveness in simulating the observed breakthrough curves and estimating the key transport parameters.