Numerical simulation of hydraulic fracture crack propagation

The plane problem of crack motion in an elastic medium under the pressure of a viscous fluid is considered. Under the condition of a constant fluid flow rate, the fluid is injected at the center of the crack. Contrary to other formulations of the problem, this paper attempts to take into account a possible fluid lag behind the crack tip. The resulting numerical solution is compared with a semianalytic one. It is found that the proposed numerical model can be used to predict the characteristics of a hydraulic fracture crack formed in a medium of a prescribed strength.