A fractal analysis of fracture conductivity considering the effects of closure stress

• An acid-rock reaction test installation has a self-owned intellectual property right.
• Fracture conductivity model considering closure stress was developed.
• A combination of the digital calculation method and the fractal theory was performed.
• The effect of fractal dimensions and rock elastic parameters was discussed.

Hydraulic fracturing and acid fracturing are very important in oil and gas reservoir development. The role of fluid flow in artificial fractures is highly complex, and it has been shown that closure stress plays an important role in fracture conductivity. However, it is difficult to predict closure stress accurately due to the randomness of the acid-rock reaction and various influencing factors. In this work, using digital image processing method, novel predictive models for fracture conductivity that consider closure stress are developed based on the fractal theory and the mechanics of materials. Simulation results show that the Young's modulus E, Poisson's ratio ν, crack spacing fractal dimensions and tortuosity fractal dimensions have significant effects on fracture conductivity. The predictions of the fracture conductivity show good agreement with the available experimental data and indicate that the proposed models can accurately characterize the flow in acid-etched fractures under stress.