Development of stochastic models for fracture systems

Hierarchical geometric-mechanical models attempt to capture the relations between the geometry of rock fracture systems and the underlying geologic mechanisms of fracturing. The two-dimensional enhanced hierarchical model can represent complex fracture trace patterns. Since two-dimensional representations of fracture patterns are insufficient for many applications, a three-dimensional hierarchical model is being developed. The model generates hierarchically related sets of fractures using a sequence of three stochastic processes: Poisson plane process, Poisson line process, and a combined translation-rotation process. The modeling that is presented in this paper is still geometric but relations to the underlying mechanisms are discussed as well.