A Leaky-Conduit Model of Transient Flow in Karstic Aquifers

Abstract

Karst Flow Model (KFM) simulates transient flow in an unconfined karstic aquifer having a well-developed conduit system. KFM treats the springshed as a two-dimensional porous matrix containing a triangulated irregular network of leaky conduits. The number and location of conduits can be specified arbitrarily, perhaps using field information as a guide, or generated automatically. Conduit networks can be tree-like or braided. Rainwater that has infiltrated down from the surface leaks into the conduits from the adjacent porous matrix at a rate dictated by Darcy’s law, then flows turbulently to the spring via the conduits. KFM is calibrated using the known steady state; geometry and recharge determine the steady fluxes in the conduits, and the head distribution determines conduit gradients and sizes. Spring flow can vary with time due to spatially and temporally variable recharge and due to prescribed variations in the elevation of the spring. KFM is illustrated by four examples run on a test aquifer consisting of 27 nodes, 42 elements, and 26 conduits. Three examples (drought, uniform rainstorm, storm-water input to one element) are simulations, while the fourth uses data from a spring-basin flooding event. The qualitative fit between the predicted and observed spring discharge in the fourth example provides support of the hypothesis that the dynamic behavior of a karst conduit system is an emergent property of a self-organized system, largely independent of the locations and properties of individual conduits.