Characterization methods for natural fractures distribution in shale and tight reservoirs

Aperture distribution and spatial arrangement are fundamental characteristics of natural fractures. Since it is impossible to directly measure the aperture of all existing fractures, a power law (fractal model) has been commonly used to describe fracture apertures, which has also been extended to estimate fracture spacing and macrofractures density. Although a power law (fractal model) has commonly been used to describe fracture apertures, data points in small and large fracture size ranges tend to deviate from this distribution. In this study, a Variable Shape Distribution (VSD) method was derived from a fractal theory to model fracture size distribution. The VSD method was compared with seven other commonly used models. Eleven fracture datasets collected from five countries on four continents were regressed using these methods. The scale-free methods of the VSD and power law models showed more advantages than the scale-dependent methods. The VSD method was found to best fit all variable aperture size distribution patterns, with an average coefficient of determination of 0.99. The average fractal dimension for all samples calculated by the VSD method (1.36) was slightly higher than that of the power law (1.06). This study is unique in showing that the VSD method can solve a boundary character-ization problem that has been widely neglected in previous studies. With the assumption of an even fracture distribution, the VSD method was further applied to estimate average fracture spacing, predict a threshold fracture length that controls the linkage of fractures, and predict fractures outside of the measurement range. This study not only proposes an advanced fractal method to model aperture size distributions in shale and tight rocks but also helps to better understand the importance of fractal dimensions and boundary characterizations.