Bidirectional and unidirectional fracture growth during hydrofracturing: Role of driving stress gradients

摘要

An unexpected observation from induced seismicity during stimulation experiments was the identification of asymmetric bidirectional and unidirectional growth of the seismic front and back front, indicating asymmetric growth of the hydrofracture itself. We develop and analyze a new analytical hydrofracture model that considers for the first time the effect of stress and pore pressure gradients on growth. It is based on plane strain linear elastic fracture mechanics and further considers 1-D laminar flow, the opening shape of the fracture, and a Griffith fracture criterion. The model explains asymmetric bidirectional growth during the injection and bidirectional and unidirectional growth during the postinjection phase. Analytical relations are derived for both cases to estimate the front and back front of the seismicity as a function of injection pressure, volume rate, stress gradients, viscosity, and elastic modules of the rock. Interestingly, the postinjection phase can be described by self-similar solutions, which depend only on the stress gradient and the injection pressure and which predict a parameter-independent length increase of the fracture after the injection stops. We use the theoretical opening shape of the fracture to calculate time- and space-dependent Coulomb stress changes in the rock in order to predict the patterns of induced seismicity in the neighborhood of the fracture. The model explains in detail the patterns of earthquakes induced during hydrofracturing stimulation experiments in a low-permeable gas field sandstone in west Texas, and we estimate a lateral stress or pore pressure gradient of more than 0.8 MPa km-I. If the downhole net pressure during the experiments was 1 MPa, the gradient is constrained at about 10 MPa km I.