Early-Time Shut-In for Plane-Strain Hydraulic Fractures

Abstract

One investigates the post-shut-in growth of a plane-strain hydraulic fracture in an impermeable medium while accounting for the possible presence of a fluid lag. After the stop of fluid injection, the fracture may present three distinct propagation patterns: an immediate arrest, a temporary arrest with delayed propagation, and a continuous fracture growth. These three patterns are all followed by a final fracture arrest yet the fracture behaviour prior to that results from the interplay between the dimensionless toughness $$\mathcal {K}_m$$ K m , the shut-in time $$t_s/t_{om}$$ t s / t om , and the propagation time $$t/t_s$$ t / t s . $$\mathcal {K}_m$$ K m characterizes the energy dissipation ratio between fracture surface creation and viscous fluid flow under constant rate injection. $$t_s$$ t s and $$t_{om}$$ t om represent respectively the timescale of shut-in and the coalescence of the fluid and fracture fronts. The immediate arrest occurs when the fracture toughness dominates the fracture growth at the stop of injection ($$\mathcal {K}_m \gtrapprox 4.3$$ K m ⪆ 4.3 ). It may also occur upon an early shut-in at low dimensionless toughness associated with an overshoot of fracture extension and a significant fluid lag. For intermediate values of $$\mathcal {K}_m$$ K m and $$t_s/t_{om}$$ t s / t om , the fracture may experience a temporary arrest followed by a restart of fracture propagation. The period of the temporary arrest becomes shorter with higher dimensionless toughness and later shut-in until it drops to zero. The fracture behaviour after shut-in then transitions from temporary arrest to continuous propagation. These propagation patterns result in different evolution of fracture dimensions which possibly explains the various emplacement scaling relations reported in magmatic dikes.