Fracture Surfaces, Fractal, Variogram Analysis, Power Spectral Density, Brazilian Indirect Tension Experiments

Abstract

The hydraulic behavior of geothermal reservoirs is influenced by many different fracture properties. Roughness of the fracture surface is one of them that needs to be considered in modeling studies. This requires a quantification of fracture surface roughness. This study uses fractal geometry to describe the fracture surfaces quantitatively. First, the outcrop samples of natural fractures that represent common geothermal reservoir rocks (metamorphized limestone, crystallized limestone, marble etc.), are selected and the fractal dimension of these samples are computed after data acquisition. An automatically controlled device is used to map the fracture roughness. A 32x32 data set is acquired, 1 mm, apart using the device. Then, the fractal dimensions of single fracture profiles and the fracture surfaces are measured using different fractal methods (variogram analysis and power spectral density, respectively) that are applicable to self-affine fractal data sets. Similar analysis is applied to synthetically-developed fracture surfaces. For this purpose, synthetic fractures are created by indirect tensional stress experiments on a wide variety of rock samples that represent very common geothermal reservoir rock types. Eventually, the fractal characteristics are related to the rock type and initial-boundary stress conditions. Preliminary results of an extensive experimental study are provided in this paper. The results show that the fracture surfaces present fractal characteristics. However, power spectral density and variogram analysis yield inconsistent results for natural samples while they exhibit accordance for synthetic fracture surfaces. Also, the relationship between fracture development parameters and fractal dimension is analyzed for synthetic fractures.