Fracture orientation characterization: Minimizing statistical modelling errors

Abstract

Natural fractures are by nature extremely heterogeneous. Among the principal properties, fracture orientation is arguably the most diversified yet understudied. Fracture orientation contributes significantly to directional permeability and network connectivity. This paper proposes a multimodal circular statistical model to characterize fracture orientation data. First, the linear statistics is upgraded to circular statistics on modified orientation data to account for truncation and observational biases. Second, multimodal density functions are applied, in relations to the multiple stress directions and complex geological history. Third, while previous works represent dip and azimuth as separate properties, correlations between the two parameters exist and in some cases, are very strong. The introduction of circular representations, multimodal distributions and statistical correlations to characterization of fracture orientation is both significant and innovative. As shown in the case study, several disadvantages of previous studies, including observational and truncation biases, are omitted. The proposed characterization approach is also more versatile, data-driven, accurate and conclusive.