Problem of propagation of a gas fracture in a porous medium

The problem of gas fracture formation in a porous medium is investigated. An inertialess viscous polytropic gas flow along the fracture is considered. The assumption of small fracture width with respect to the height and length makes it possible to adopt the vertical plane cross-section hypothesis on the basis of which the dependence of the gas pressure inside the fracture on its width can be reduced to a linear law. Initially, the soil surrounding the fracture is soaked with oil-bearing fluid. During fracturing the reservoir gas penetrates into the soil mass and displaces the fluid. A closed system of equations, which describes the evolution of the fracture opening, the depth of gas penetration into the reservoir, and the gas velocities inside the fracture, is constructed. The limiting regimes of gas seepage into the surrounding reservoir are considered and a one-parameter family of self-similar solutions of the system is given for each. The asymptotics of the solution in the neighborhood of the fracture nose is investigated and analytic expressions for the fracture length are obtained. The solution of the problem of gas fracture is compared with the hydraulic fracturing problem in an analogous formulation within the framework of the plane cross-section hypothesis.