Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures

The presence of fracture roughness, isolated contact areas and the occurrence of nonlinear flow complicate the fracture flow process. To experimentally investigate the fluid flow regimes through deformable rock fractures, water flow tests through both mated and non-mated sandstone fractures were conducted in triaxial cell under changing confining stress from 1.0 MPa to 3.5 MPa. For the first time Forchheimer’s nonlinear factor b describing flow in non-mated fractures under variable confining stress has been quantified. The results show that linear Darcy’s law holds for water flow through mated fracture samples due to high flow resistance caused by the small aperture and high tortuosity of the flow pathway, while nonlinear flow occurs for non-mated fracture due to enlarged aperture. Regression analyses of experimental data show that both Forchheimer equation and Izbash’s law provide an excellent description for this nonlinear fracture flow process. Further, the nonlinear flow data indicate that for smaller true transmissivity, the appreciable nonlinear effect occurs at lower volumetric flow rates. The experimental data of both mated and non-mated fracture flow show that the confining stress does not change the linear and nonlinear flow patterns, however, it has a significant effect on flow characteristics. For mated fracture flow, the slope of pressure gradient versus flow rate becomes steeper and the transmissivity decreases hyperbolically with increase of confining stress, while for non-mated fracture flow, the rate of increase of the nonlinear coefficient b used in Forchheimer equation steadily diminishes with the increase of confining stress. Based on Forchheimer equation and taking 10% of the nonlinear effect as the critical state to distinguish between linear and nonlinear flow, the critical Reynolds number was successfully estimated by using a nonlinear effect coefficient E. This method appears effective to determine critical Reynolds numbers for specific flow cases.