Fractal Modeling and Estimation of Karst Conduit Porosity

Abstract

The three-dimensional distribution of karst conduits in a karst aquifer is the main source of its heterogeneity and anisotropy. It also has a strong effect on peak spring discharge, and in the form of the karstic hydrograph, chemograph, and thermograph. The direct access to the conduits is only possible by speleological exploration and cave mapping, which provides a very valuable information for karst modeling. However, this information is biased because the speleologists can only explore a limited part of the conduit network: they can only map conduits of a minimum diameter, the speleological exploration can take many years in order to explore all the leads that appear in a network system and parts of the network are not accessible. In order to estimate conduit porosity we can take advantage of the fractal character of nature. The volume of conduits larger than a given diameter can be estimated in a particular volume of rock. This is done by extrapolating a power law that has been fitted to experimental data. The power law distribution of the volume of conduit voids larger than a particular diameter is related with the fractal behavior of a network of karst conduits. This fact was also used for simulating a three-dimensional network of karst conduits by a stochastic process of diffusion limited aggregation. The procedure is illustrated in the Sierra de las Nieves karst aquifer in the province of Malaga, Southern Spain. Karst conduit porosity can be used for generation of numerical models of karst systems, and for the mathematical modeling of flow in karst aquifers.