Finite element analysis for a finite conductivity fracture in an infinite poroelastic medium

Abstract

SUMMARYIn the technology of oil recovery, oil production rate can be increased by generation of a vertical conductive fracture adjacent to the well-bore. In this paper the seepage flow and isothermal deformation in both the oil formation and the fracture are studied by modelling the formation as a two-dimensional infinite poroelastic medium and the conductive fracture as a one-dimensional poroelastic material, saturated by a one-phase compressible fluid. The plane strain condition is employed. Solutions for a growing conductive fracture and a stationary conductive fracture in the infinite medium are obtained by means of the finite element method based on a variational principle for the formation which can impose the governing equations of the fracture. Infinite elements are used outside the finite element domain. Numerical results indicate that the injection rate, the applied pressure and the crack mouth opening displacement at the well-bore oscillate during the propagation of the conductive fracture. The production rate of a well with the conductive fracture is compared with that of a well without the conductive fracture. Finally, a new definition of the conductivity coefficient for the conductive fracture is presented.