A fractal approach for surface roughness analysis of laboratory hydraulic fracture

Abstract

Hydraulic fracturing treatment in rocks creates surfaces that are not smooth but rough in general. Accurate characterization of surface roughness is necessary to relate fracture deformation to fluid flow. In this study, we analyze the surface of an experimentally generated hydraulic fracture using a practical fractal approach which is capable of modeling applications. The hydraulic fracturing test is conducted using a nearly homogeneous siltstone cube in a true triaxial cell, and a fracture is created showing a perfectly radial pattern. To evaluate roughness, each surface profile is decomposed into large-scale fracture waviness and localized surface roughness considering various length scales. Despite the waviness, estimated roughness amplitudes follow a power-law relation up to a length-scale, showing a fractal nature. Unlike ideal brittle materials with an exponent of 0.5, the roughness exponent is found to vary in a narrow range of 0.1 but exceeds 0.5. The fractal dimension (box dimension) of the hydraulic fracture surface is estimated to be 1.4 showing a good match with roughness exponents. An increase in roughness exponent may indicate an increasing difficulty in fracture propagation and fluid and proppant transport along the fracture. As such, the topology of a hydraulic fracture surface is essential to hydraulic fracture growth to assess fracturing performance.