Incompletely Coupled Equations of Hydraulic Fracturing

Abstract

We study a three-dimensional coupled problem of the creeping flows of a viscous fluid in a hydraulic (and magmatic) 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 lubricating layer. The external problem is described by the equations of poroelasticity. An ordered sequence of interdependent geomechanical processes occurring under hydraulic (and magma) fracturing is established. In other words, the solution of the coupled problem of hydraulic fracturing is reduced to the sequential solution of three incompletely coupled problems representing the motion in the fracture, as well as the elastic and flow processes in the host rock. The proposed transformation is of practical importance for petroleum geophysics; it allows conducting a more profound in-depth study of the nonisothermal and physicochemical phenomena for occurring in the above-mentioned fractures; and it provides a better insight into the physics of the associated processes.