Analytical Investigation of the Dynamics of a Hydraulic Fracture Using the Principle of Incomplete Coupling

An investigation of a self-similar solution of a coupled problem on the creeping flows of a viscous fluid in a hydraulic fracture and the strain and flow in the external poroelastic medium induced by them. The process is governed by injection fluid into a well. The flow in the fracture is described by the Stokes hydrodynamic equations in the approximation of the lubricant layer. The external problem is described by the equations of poroelasticity. The variant of a uniform pressure in the fracture is considered for three-dimensional and two-dimensional cases. In the second case, a self-similar solution can be obtained in an analytical form.