Wellbore cement fracture permeability as a function of confining stress and pore pressure
Cemented annulus fractures are a major leakage path in a wellbore system, and their permeability plays an important role in the behavior of fluid flow through a leaky wellbore. The permeability of these fractures is affected by changing conditions including the external stresses acting on the fracture and the fluid pressure within the fracture. Laboratory gas flow experiments were conducted in a triaxial cell to evaluate the permeability of a wellbore cement fracture under a wide range of confining stress and pore pressure conditions. For the first time, an effective stress law that considers the simultaneous effect of confining stress and pore pressure was defined for the wellbore cement fracture permeability. Here the results showed that the effective stress coefficient (λ) for permeability increased linearly with the Terzaghi effective stress ( -p) with an average of λ = 1 in the range of applied pressures. The relationship between the effective stress and fracture permeability was examined using two physical-based models widely used for rock fractures. The results from the experimental work were incorporated into numerical simulations to estimate the impact of effective stress on the interpreted hydraulic aperture and leakage behavior through a fractured annular cement. Accounting for effective stress-dependent permeability through the wellbore length significantly increased the leakage rate at the wellhead compared with the assumption of a constant cemented annulus permeability.