Developed Regime of Motion in Hydraulic Fracture in a Double-Porosity Medium

A study is made of a two-dimensional coupled problem on slow motions of a liquid in a hydraulic fracture and on deformations and filtration induced by these motions in a porous medium with double porosity that has two components: the porosity proper and the fracturing. The motions are produced by pumping the liquid into the well. Flow inside the fracture is described by hydrodynamics equations in a hydrostatic approximation. A certain ordered series of interdependent geomechanical processes occurring during the hydraulic fracturing is established. In the main space around the fracture, the liquid moves in the porous component of the two-phase medium. In the boundary layer, there are mixed processes: in addition to the motion of the liquid by the fractures, we have its crossflow between the fractures and the pores. These effects are investigated as a first approximation for a certain small parameter which is represented by the relative time. In contrast to the well-known classical problem with double porosity, in this case the indicated problem is rigorously solved with account of elastic deformations of the skeleton. In actual fact, the present paper is a continuation of the previous work of the author in an analogous formulation in a zero approximation, in which the boundary layer is trivial and is reduced to the boundary layer in a medium with ordinary porosity. Examples of solving concrete problems are given.