Influence of roughness of rock fracture on seepage characteristics

In order to study the relationship between surface roughness of rock fracture and seepage mechanism, the rock fracture is divided into several segments along length direction, and the symmetric rough fracture surface is generated by setting random height at the end of each segment. Based on the D2G9 model, which is used for simulating incompressible fluid, the classic Poiseuille flow is verified using the lattice Boltzmann method, the seepage characteristics of rock fracture with different relative roughnesses are calculated, and the influence of surface roughness on the flow state of fluid is discussed. The results show that the fracture wall blocks the flow of fluid, and flow state near wall changes dramatically. At the same time, with the increase of the relative roughness, there are vortices in the local area, where the changes of fracture width are dramatic, which induces the increase of internal friction in the fluid. Under the equal flow discharge of section in unit time and average fracture width, the present numerical solution is compared with the theoretical one of multi-parallel plate. Because the multi-parallel plate theory neglects the partial pressure drop caused by changes of fracture width, the maximum error of the pressure drop in the middle section is 15.2% less than the numerical solution for fracture scheme with relative roughness δ=0.01674. When the relative roughness is small, the pressure in the middle of fracture is similar to that of the smooth plate model, and the trend is almost linear. The pressure deviates from the line direction with the increase of relative roughness, and the changes are larger at the section, where the fracture width changes from narrowness to broadness suddenly.