Estimates of fracture density and uncertainties from well data

This paper aims at building a method to estimate the probability law governing the 3D fracture density of a fractured rock conditioned to the number of traces observed on a borehole image when the spatial distribution of fracture centers is assumed to follow a Poisson process. A closed-form expression of this law, allowing to calculate its mean value as well as a confidence interval, is derived in both cases of a lineic well (scanline) and a cylindrical well. The latter is better adapted to the situation of fracture size of the same order of magnitude as the well radius, which enables the presence of partial traces. In particular, the method takes into account the bias in the density estimate due to the fact that a fracture may cut the well along two distinct traces according to the considered fracture size. Monte Carlo simulations finally show a good agreement with the theoretical results of mean density and confidence interval.