Controlling factors of wormhole growth in karst aquifers

Abstract

Flow and water discharge in karst aquifers are controlled by the conduit network. Therefore, understanding karst conduit formation is important to conjecture the aquifer topology, i.e., conduit density and size, and to predict the aquifer dynamics. Conduits are generated by preferential pathways to flow known as wormholes that grow competing with each other. The success of a wormhole is determined by its ability to drive water away from its neighbors. Once a wormhole forms, water tends to flow along this preferential path thus reducing the availability of water for the enlargement of less developed wormholes. Wormhole growth is then controlled by the flow rate, the dissolution mechanisms and the heterogeneity of the hydraulic conductivity field. In this work, we propose two conceptual models to describe the geometry of the wormhole capture zone and its effect on the surrounding wormholes. First, we consider a cross-section intersecting the wormhole longitudinally. Second, we consider a radial model centered in the wormhole. These models are representative of field (fracture) and laboratory (tube), respectively. We perform a series of steady state simulations to obtain the dependence of the capture zone on the wormhole’s geometry. This naturally leads to a relation between the wormhole’s geometry and the density of wormholes because only one wormhole grows within a capture zone.