A karst networks generation model based on the anisotropic Fast Marching algorithm

Abstract

Karst aquifers are difficult to model due to their complex conduit networks that are heterogeneous and anisotropic. Here, we present a heuristic algorithm for modeling karst networks by calculating minimum-effort paths based on our knowledge of karst evolution that is constrained by field observations.The methodology consists of a) using discrete fracture network models along with fracture-parameter estimates (e.g., frequency, extent, spacing, and apertures) to equivalent porous media properties (e.g., size of the representative elementary volume, hydraulic conductivity tensor), b) rendering the velocity field using the tensor field coupled with the 3D regional hydrogeology that includes likely recharge and discharge locations, and c) generating karst conduits using the Anisotropic Fast Marching Algorithm (AFMA). This approach a) avoids the need to model discrete fractures by replacing them with a tensor that incorporates small-scale, dense and interconnected fractures, b) assumes that conduits follow the minimum-effort path from sinkholes toward springs, and c) efficiently accounts for regional hydrogeology, anisotropy, and regional flow conditions within 3D conduit networks. The application of the proposed approach in Wulongdong Basin in Hubei Province, China is taken as the demonstrate example. Compared to other techniques, this methodology substantially improves computational efficiency and reduces computer memory, thus providing a useful tool for generating ensembles of possible karstic conduit networks to analyze flow and transport prediction uncertainty associated with a lack of knowledge about network geometry.