Effects of Contact Area and Contact Shape on Nonlinear Fluid Flow Properties of Fractures by Solving Navier-Stokes Equations

Abstract The influences of contact shape and contact area on nonlinear fluid flow properties through fractures are investigated by solving Navier-Stokes equations. The evolutions of nonlinear relationships between flow rate and hydraulic pressure drop, Forchheimer coefficients, nonlinear factor, critical hydraulic gradient, distributions of flow streamlines, and tracer flow paths at different times are systematically estimated. The results show that the nonlinear relationships between flow rate and hydraulic pressure drop can be well described by Forchheimer’s law, in which the nonlinear term coefficient b is approximately three orders of magnitude larger than the linear term coefficient a. The smaller contact area corresponds to smaller variations in many aspects such as flow rate, critical hydraulic gradient, flow streamlines, and tracer flow paths. The critical hydraulic gradient decreases with the increasing degree of contact shape variations while the contacts have the same mean area. The increase in hydraulic pressure drop can induce significant eddies and decrease the permeability and/or conductivity of fractures. However, the distributions of streamlines and tracer flow paths are not dramatically disturbed under a large hydraulic pressure drop.