Analysis of a deformable fracture in permeable material

Abstract

The response of deformable fractures to changes in fluid pressure controls phenomena ranging from the flow of fluids near wells to the propagation of hydraulic fractures. We developed an analysis designed to simulate fluid flows in the vicinity of asperity-supported fractures at rest, or fully open fractures that might be propagating. Transitions between at-rest and propagating fractures can also be simulated. This is accomplished by defining contact aperture as the aperture when asperities on a closing fracture first make contact. Locations on a fracture where the aperture is less than the contact aperture are loaded by both fluid pressure and effective stress, whereas locations where the aperture exceeds the contact aperture are loaded only by fluid pressure. Fluid pressure and effective stress on the fracture are determined as functions of time by solving equations of continuity in the fracture and matrix, and by matching the global displacements of the fracture walls to the local deformation of asperities. The resulting analysis is implemented in a numerical code that can simulate well tests or hydraulic fracturing operations. Aperture changes during hydraulic well tests can be measured in the field, and the results predicted using this analysis are similar to field observations. The hydraulic fracturing process can be simulated from the inflation of a pre-existing crack, to the propagation of a fracture, and the closure of the fracture to rest on asperities or proppant. Two-dimensional, multi-phase fluid flow in the matrix i