Hydraulic fractures represent a particular class of tensile fractures that propagate in solid media, under pre-existing compressive stresses, as a result of internal pressurization by an injected viscous fluid. The main application of engineered hydraulic fractures is the stimulation of oil and gas wells to increase production. Several physical processes affect the propagation of these fractures, including flow of viscous fluid, creation of solid surfaces and leak-off of fracturing fluid. The essential complexity of the hydraulic fracturing problem is linked to the existence of a moving boundary and to the multiscale nature of the problem, a consequence of the interplay between competing physical processes affecting fracture propagation.
This course provides an introduction to the mechanics of fluid-driven fractures by focusing on the description of a plane strain model of a hydraulic fracture (known in the literature as a KGD fracture) and on the construction of numerical algorithms to solve the propagation of such fractures. The main topics of the course are:
- Review of the basic equations of linear elastic fracture mechanics and lubrication theory.
- Formulation of a system of nonlinear integro-differential equations in terms of variables defined only along the crack.
- Scaling of the equations to reveal the existence of different regimes of propagation
- Asymptotic solutions in the tip region, a critical component for the development of efficient numerical algorithms.
- Numerical algorithms based on combining the finite volume and the displacement discontinuity methods.
- Outline of contemporary issues in hydraulic fracturing, such as the interaction between closely spaced fractures with application to stimulation of gas shales.