| A number of variational principles and the corresponding finite element methods are established for simulation of deformation, temperature and flow fields in poroelastic media, associated with the water flood technique in both primary recovery and secondary recovery projects for oil exploration. The study is based on the assumption of small, quasi-static and plane strain deformation of the media, which are homogeneous, isotropic or transversely isotropic. In the primary recovery problem, a production well with or without a conductivity fracture is located in an infinite medium subjected to non-zero confining stress and initial pore pressure. In the study of the secondary recovery problems with stationary cracks in finite media, the layout of injection wells and production wells is considered to have a regular pattern where symmetry conditions exist. The injected fluid diffuses into the formation through initially generated vertical cracks. In the study of the secondary recovery with growing cracks in the porous media, the stress intensity factor at the crack tip is maintained at a constant value of the fracture toughness of the medium during the crack propagation. The study starts with a simple problem, in which an impermeable crack in an infinite elastic medium is driven by an internal hydraulic pressure. Both problems of inviscid flow and viscous flow in the fracture are considered. In the case of inviscid flow, a self-similar solution associated with power functions of time and a general solution are obtained. In the case of viscous flow, the physical picture changes. A rapid pressure drop and a fluid front in the fracture are found in the vicinity of the crack tip. These exists a small cavity between the fluid front and the crack tip. In the study of growing cracks in porous media, a technique of moving and relaying finite element is used for simulation of crack propagation. The effect of viscous flow of fluid in the fracture is included in the study. The injection wells and the production wells are regularly arranged in the growing crack problem. Useful information is provided for improvement of water flooding technique in petroleum engineering. |
