Surface roughness is a crucial characteristic of fracture surfaces in the rock mass; however, its influence on hydraulic fracture propagation is not fully explored yet. For a brittle or quasi-brittle rock, roughness is found to be a scale-dependent parameter, and it is necessary to identify a suitable length-scale for relating fracture growth and fluid flow behaviors to the surface roughness. From this perspective, the fracture trajectory at a larger length-scale can be re-considered due to its connection to the small length-scale roughness characteristics, because the fluid flow near the fracture tip can affect the hydraulic fracturing process.

This study simulates hydraulic fracture propagation by including fracture surface attributes in two different length scales. To do so, we decompose an experimental hydraulic fracture trajectory into its large-scale and small-scale components, namely, waviness and roughness profiles. The fracture profile is then analyzed using our recent fractal method for simulation purposes. Subsequently, a numerical model is constructed using a robust hydraulic fracturing simulator to explore the effect of surface roughness on fracturing by the finite element method. Two different scenarios, including rough and smooth fracture models, are considered for numerical analysis. The numerical results are then discussed on the effect of surface roughness on fracture energy required to propagate a penny-shaped hydraulic fracture. We observe that the roughness inclusion may notably decrease the hydraulic fracture length by 10%, whereas its aperture increases.

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