HydroMechanics of Fractured Rock

Theoretical Analysis

NUMERICAL MODEL
The theoretical model used for this work simulates the deformation of a single, horizontal fracture subjected to a transient change in fluid pressure. The analysis assumes an idealized, circular fracture, located in a porous, linearly elastic matrix under far-field compressive stress with a vertical well intersecting the center of the fracture. Conservation of mass and momentum govern 1-D radial fluid flow within the fracture and 2-D flow in the matrix. The aperture of the fracture is calculated by coupling the elastic displacement from an arbitrary radial pressure distribution with an empirical relationship for asperity deformation.

The fracture is assumed to be initially supported by asperities, but the fracture walls can separate and the fracture can even propagate if the driving pressure becomes high enough. The model uses an analytical solution to the displacements caused by a uniform pressure applied over a narrow ring. The effect of propping by asperities is included by assuming the fracture is partly supported by an effective stress, in addition to the fluid pressure.