Fracture density reconstruction using direct sampling multiple-point statistics and extreme value theory

The aim of this work is to present a methodology for the reconstruction of missing fracture density within highly fractured intervals, which can represent preferential fluid flow pathways. The lack of record can be very common due to the intense presence of fractures, dissolution processes, or data acquisition issues. The superposition of numerous fractures makes the definition of fracture surfaces impossible, as a consequence, modeling such zones is challenging. In order to address this issue, the usage of direct sampling multiple-point statistics to perform gap filling in well logs is demonstrated as an alternative to other techniques. It reproduces data patterns and provides several models representing uncertainty. The method was tested in intervals from a highly fractured well, by removing previously known fracture density data, and simulating different scenarios with direct sampling. Simulation results are compared to the observed data using cross-validation and continuous rank probability score. The reference scenario training data set consists in one well and two variables: fracture density and fracture occurrence. A sensitivity analysis is carried out considering additional variables, additional wells, different intervals, resampling with extremes, and other gap filling techniques. The auxiliary variable plays an important role in pattern matching, but adding wells and logs increases the complexity of the method without improving pattern retrieval. Best results are obtained applying extreme values theory for stochastic process with the enrichment of the fracture density data at the tail region, followed by resampling of the new values. The enriched data is used for the gap filling resulting in lower continuous rank probability score, and the achievement of extreme fracture density values.