A pseudo-genetic stochastic model to generate karstic networks

In this paper, we present a methodology for the stochastic simulation of 3D karstic conduits accounting for conceptual knowledge about the speleogenesis processes and accounting for a wide variety of field measurements. The methodology consists of four main steps. First, a 3D geological model of the region is built. The second step consists in the stochastic modeling of the internal heterogeneity of the karst formations (e.g. initial fracturation, bedding planes, inception horizons, etc.). Then a study of the regional hydrology/hydrogeology is conducted to identify the potential inlets and outlets of the system, the base levels and the possibility of having different phases of karstification. The last step consists in generating the conduits in an iterative manner using a fast marching algorithm. In most of these steps, a probabilistic model can be used to represent the degree of knowledge available and the remaining uncertainty depending on the data at hand. The conduits are assumed to follow minimum effort paths in a heterogeneous medium from sinkholes or dolines toward springs. The search of the shortest path is performed using a fast marching algorithm. This process can be iterative, allowing to account for the presence of already simulated conduits and to produce a hierarchical network. The final result is a stochastic ensemble of 3D karst reservoir models that are all constrained by the regional geology, the local heterogeneities and the regional flow conditions. These networks can then be used to simulate flow and transport. Several levels of uncertainty can be considered (large scale geological structures, local heterogeneity, position of possible inlets and outlets, phases of karstification). Compared to other techniques, this method is fast, to account for the main factors controlling the 3D geometry of the network, and to allow conditioning from available field observations