Single fractures under normal stress: The relation between fracture specific stiffness and fluid flow

Fracture specific stiffness and fluid flow through a single fracture under normal stress are implicitly related through the geometry of the void space and contact area that comprise the fracture. Data from thirteen different rock samples, each containing a single fracture, show that relationships between fracture specific stiffness and fluid flow through a fracture fall into two general classes of behavior. Fractures either fall on a loosely-defined universal curve relating fluid flow to fracture specific stiffness, or else the flow is weakly dependent on fracture specific stiffness. The second relationship shows that flow decreases slowly with increasing fracture specific stiffness. The first relationship shows that flow decreases rapidly for increases in fracture specific stiffness. To understand this behavior, computer simulations on simulated single fractures were performed to calculate fluid flow, fracture displacement, and fracture specific stiffness as a function of normal stress. Simulated fractures with spatially correlated and uncorrelated aperture distributions were studied. Fractures with spatially uncorrelated aperture distributions tend to exhibit a weak dependence of fluid flow on fracture specific stiffness because these fractures tend to have multiple connected paths across the sample which can support flow with uniformly distributed contact area. Thus an increment in stress will increase the stiffness of the fracture without greatly reducing the amount of fluid flow. On the other hand, fractures with spatially correlated aperture distributions tend to belong to the universal relationship because correlated fractures tend to have only one or two dominant flow paths and the contact area is limited to a few regions resulting in a compliant fracture. Thus an increment in stress on a spatially correlated fracture will result in an increase in stiffness and rapid decrease in fluid flow. These spatial correlations in fracture void geometry can be differentiated in the laboratory based on the observed fracture specific stiffness–fluid flow relationship for a single fracture under normal loading.