| Popis: |
This paper describes a KGD-type model of a hydraulic fracture created by injecting fluid in weak, poorly consolidated rocks. The model is based on the key assumption that the hydraulic fracture is propagating within a domain where the hydraulic fields are quasi-stationary. By further assuming a negligible toughness, the fracture is shown to grow as a square root of time. The asymptotic fracture propagation regimes at small and large time are constructed and the transient solution is computed by solving a nonlinear system of algebraic equations formulated in terms of the fracture aperture. At early time the fracture is hydraulically invisible and the injection pressure increases with time $t$ as $\log t$, while at late time leak-off from the borehole is negligible and the injection pressure decreases as $t^{-1/4}$. According to this model, the peak injection pressure observed when injecting fluid in weak, poorly consolidated rocks should not be interpreted as indicating a breakdown of the formation, but rather as marking the transition between two asymptotic flow regimes. The timescale that legislates the transition between the small and large time asymptotic regimes is shown to be a strongly nonlinear function of a dimensionless injection rate. |
