Models of plane fractures expansion

Approximate models of crack opening in the reservoir under the action of the filtered fluid are derived. The cross-sections of the fracture are assumed to be plane-parallel and have a small thickness. The models are based on exact solutions of the equations for viscous fluid motion including invariant solutions. Filtration of a fluid through a moving boundary, the absence of a tangential motion at the boundary, and elastic forces compressing the crack are taken into account.