Numerical Simulation Study on the Hydraulic Behavior in Closed Fractures

Abstract:

As the main repositories for groundwater in karst systems, fractures involve the movement and storage of groundwater. Fundamentally, Navier-Stokes (NS) Equations is used to describe flow in fractures. However, due to the complexity of Navier-Stokes Equations, it is rarely applied to solve fracture flow problems. Thus, based on some simplifications, Stokes equations, Reynolds equations and Cubic Law (CL) are derived to describe fracture flow. The validity of the three simplified equations were extensively studies. Among the three simplified equations of NS, CL is the simplest and used to describe flow in open, smooth and paralleled fractures. In the previous work, most researchers focused on the open fractures. But it’s the closed fractures exist widely in the field not the open fractures. The objective of this paper aims to check the validity of CL in closed fractures with different apertures and widths of fracture.

After comparing the experimental results and simulations results from the COMSOL Multiphysics (FEM), this software was applied to solve the 3D or 2D NS equations in the closed fractures. The results obtained from NS simulation results and calculation results from CL were compared to indicate the degree of the validity of CL in application. A critical velocity was proposed to illustrate the validity of CL in closed fractures. Furthermore, the impacts of aperture size, width of fracture size, and velocity magnitude on both the hydraulic conductivity and velocity profile were also analyzed. The results showed the CL was capable of describing flow in closed fractures when the velocity was less than the critical velocity varying from 0.02 to 30.08cm/s. The ratio of NS results and CL results was between 0.9 and 2, with velocity varying from 0 to 40cm/s. The discrepancy between NS equation and CL increased with Reynolds number, increased with aperture size and decreased with width of fracture.