Non-linear regimes of fluid flow in rock fractures

• DOI: 10.1016/j.ijrmms.2004.03.036
• Publication Date: 2004-07-08T02:42:27Z
• Authors: Robert W Zimmerman; Azzan Al-Yaarubi; Chris C Pain; Carlos A Grattoni
• Keywords: 0205 materials engineering; 0208 environmental biotechnology; 02 engineering and technology

We have conducted high-resolution Navier-Stokes simulations and laboratory measurements of fluid flow in a natural sandstone fracture. First, epoxy casts were made of the two opposing fracture surfaces. The surface profiles of the two surfaces were then measured at a vertical resolution of ±2 μm, every 20 μm in the x and y-directions, over 2 cm × 2 cm regions of the fracture. These data were then used to create a finite-element mesh for the fracture void space, and the Navier-Stokes equations were solved within this domain. Flow experiments were also conducted within the same fracture casts, over a range of flowrates. The simulations confirm the existence of a weak inertia regime for Reynolds numbers in the range of 1-10, in which the non-Darcy pressure drop varies with the cube of the flowrate. Although of theoretical interest, this effect is, however, probably too small to be of engineering interest. At Reynolds numbers above about 20, both the simulations and experiments exhibit a Forchheimer-type regime, in which the non-Darcy pressure drop is quadratic in the flowrate.