Fractures are the main channels of production in naturally fractured reservoirs, therefore the fracture permeability is a key parameter to production optimization and reservoir management. The perturbation of effective stress acting on a fracture can change the fracture aperture, thereby changing the fracture permeability. Pressure depletion in a naturally fractured reservoir can result in effective stress change that, in turn, can change fracture permeability. The displacement discontinuity method is a boundary element method with the ability to handle the rock discontinuities and fractures. The coupled poroelastic displacement discontinuity method also involves into the interaction of fluid flow and the discontinuity. A nonlinear mechanical model is applied to represent the fracture deformation including normal and shear deformation. In this work we apply displacement discontinuity method combining with the fracture deformation model to model the variation of stress and fracture aperture and resulting permeability variation during production in naturally fractured reservoirs.
The effect of stress on reservoir permeability as a change in reservoir porosity has been well investigated [1,2,3,4,5]. The effective stress increases with the decrease in pore pressure due to production from wells. The increase of effective stress compacts the reservoir rock and reduces the reservoir porosity, thereby reducing the reservoir permeability. But the effect of stress on the fracture aperture and fracture permeability in naturally fractured reservoirs has not been studied in sufficient detail. The fracture aperture and permeability are often treated as constant during production. However, A few investigations have shown that stress had an important effect on the fracture aperture and permeability.
Min et al  investigated the fracture aperture change of a complicated fracture network in an impermeable material using a two-dimensional distinct element method program UDEC (universe distinct element code). Their numerical modeling shows that hydrostatic stress tends to reduce the fracture aperture, and thereby fracture permeability, and that the deviatoric stress tends to increase the aperture of those fractures oriented parallel or close to the maximum principal stress direction (compression is positive), and reduce the aperture of those fractures oriented perpendicular to the maximum principal stress direction. The interface flow between the fracture and matrix can affect the pore pressure inside fracture, and therefore the fracture aperture. However, UDEC does not model permeable porous media, and so cannot account for the effect of production from matrix to the fracture.
Asgian [7,8] applied the displacement discontinuity method to model fracture aperture changes while injecting fluid into a fracture network in a naturally fractured reservoir. The matrix was assumed impermeable and an elastic displacement discontinuity solution was applied. Still the affect of flow from matrix to natural fractures was not addressed.
We apply a poroelastic displacement discontinuity method fully coupling the fracture change with stress and pore pressure in both matrix and fractures to investigate stress dependent fracture aperture and permeability under two-dimensional single phase flow conditions. The fluid is compressible and the fluid density is pressure dependent. Fractures are deformable and a nonlinear mechanical model is applied to represent the fracture deformation due to stress change.