Experimental study of non-linear fluid flow though rough fracture based on fractal theory and 3D printing technique

Abstract

In this note, the non-linear fluid flow through rough fracture is investigated experimentally. The rough surface of fracture is generated synthetically based on the fractal dimension (D) and standard deviation (σ). 3D printing technique is used to produce the fracture specimen, in which, different components of the specimen are printed and assembled so that the fracture roughness and aperture can be easily controlled. After that, the self-designed apparatus is used to conduct the fluid flow test on the fractured specimens under various pressure gradients. It is found that, the surface roughness imposes an important impact on the nonlinear characteristics of fluid flow through fracture; and the root-mean-square of the first derivative of profile, Z2, is found effective in characterizing the fracture roughness. Based on the test results and the derived parameters in Forchheimer equation, an empirical equation is proposed to relate the hydraulic aperture (eh) to Z2 and mechanical aperture (em). Furthermore, the correlation among the nonlinear coefficient β, em and Z2 is established.