It is found that the effective radial permeability decreases rapidly with increasing radial distance, and the planar macroscopic porosity and fractal dimension of fractures on the well-rock interface show a significant effect on the effective permeability.
The appearance of the dimensions of fracture toughness implies that classical failure scaling is at work.
We show that the amount of ejecta mass is proportional to the impact velocity squared times the square root of the projectile diameter, a quantity which has the dimensions of fracture toughness.
A new method is proposed to calculate the fractal dimension of the fracture surface, and based on this method, it is found that the fractal characteristics of the main fracture surface of the red sandstone specimen show that the fractal dimension along the shear direction increases first and then decrease, and appears maximum value in the middle.
Near wellbore complexity often resulted in low lateral dimension of induced fracture hence the fracking effect of the treatment.
Both fracture surfaces were generated using the same parameters, in particular the Hurst exponent (a parameter linked to the fractal dimension of the fracture surfaces) equal to 0.7, and had the same in-plane dimensions of 32 cm × 32 cm.
Previous studies have shown that both single fractures and complex fracture networks exhibit fractal properties, and recent studies have established analytical and/or empirical expressions between the permeability and fractal dimension of the fracture networks.
In this study, the fractal dimension of the fracture surface was estimated to describe the surface roughness of four types of track boards in terms of utilizing the improved projective covering method.
The critical pillar diameter ∼1.2μm associated with lithiation-induced fracture of ⟨111⟩ Ge pillars, determined through our statistical investigation, is much greater than the critical dimension for fracture of ⟨111⟩ silicon pillars (∼300 nm).
The exact displacement at which the flow stops is expected to depend on the initial aperture, the fracture roughness distribution, and the in-plane dimensions of the fracture.
