A Similarity Solution for Coupled Deformation and Fluid Flow in Discrete Fractures

Abstract

A semi-analytical similarity solution was developed for coupled deformation and one-dimensional transient fluid flow in a uniform plane fracture located normal to the free surface in a semi-infinite impermeable rock formation. For cubic-law fracture conductivity and constant normal fracture stiffness constitutive laws, dimensionless solutions were computed for the fluid pressure, flow rate, and aperture distributions. Large amplitude transient pressure test type curves are presented for fluid injection and production at constant pressure at the free surface. This solution provides a reliable test case for verifying complex computer codes, a means of performing scoping and experimental design calculations, and a method for interpreting large amplitude transient pressure test data for stress-dependent fracture properties.