Sergey Kanaun, Daniel Morales
Discrete Model of Hydraulic Fracture Crack Propagation in Media with Filtration
Fracture mechanics, hydraulic fracture, penny shape crack, filtration
An infinite homogeneous isotropic elastic medium with a penny shape crack is considered. The crack is subjected to the pressure of fluid injected in the crack center with a positive injection rate. Description of the crack growth is based on the lubrication equation (balance of the injected fluid and the crack volume), equation for crack opening caused by fluid pressure on the crack surface, Poiseullie equation related local fluid flux with crack opening and pressure gradient, and the criterion of crack propagation of linear fracture mechanics. The crack growth is simulated by a discrete process consisting of three basic stages: increasing the crack volume by a constant crack size, crack jump to a new size defined by the fracture criterion, and filling the new appeared crack volume by the fluid. It is shown that the model results a reasonable dependence of the crack radius on the time as well as the pressure distribution on the crack surface. The model is applied to the case of media with filtration, and numerical examples of hydraulic fracture crack growth with the “leak-off” effect are presented.
Cite this paper
Sergey Kanaun, Daniel Morales. (2017) Discrete Model of Hydraulic Fracture Crack Propagation in Media with Filtration. International Journal of Mechanical Engineering, 2, 28-34