Fluid Flow Modeling in Fractures

In this paper we study fluid flow in fractures using numerical simulation and address the challenging issue of hydraulic property characterization in fractures. The methodology is based on Computational Fluid Dynamics, using a finite-volume based discretization scheme. Steady-state, viscous, laminar flow simulations for a Newtonian fluid are carried out in both 2D and 3D fracture models. In 2D, flow is analyzed in single fractures, series and parallel combination of fractures, inclined fractures, intersecting fractures, mixed networks, and in real (rough-surface) fractures. In 3D, flow is simulated in both uniform and variable aperture fracture models. To characterize each fracture model with an equivalent hydraulic aperture, equations are derived for all possible scenarios followed by comparison and validation with results derived from flow simulation. Based on the fracture models analyzed, the following are some of the important findings: 1) For fractures connected in series, the equivalent hydraulic aperture is a weighted harmonic mean of cubed apertures of all fractures. 2) For fractures connected in parallel, the equivalent flow is simply the sum of all flows through individual fractures. 3) If a fracture is inclined with respect to the axis of pressure gradient, then the amount of flow will be reduced by a factor of cosine of the inclination angle. 4) Any network of randomly intersecting fractures can be replaced by a single fracture to give flow equivalence; the aperture of that equivalent fracture will roughly be close to the aperture of the fracture in the network that cuts across the boundaries (inlet and outlet) in the most continuous fashion and have the smallest inclination (with respect to the pressure gradient axis). 5) For hydraulic characterization purposes, fluid flow in fractures can be sufficiently modeled using both Stokes and Navier-Stokes equations for flow Reynolds number upto approximately 100.