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, the shut-in time t_s/t_{om}, and the propagation time t/t_s. mathcal {K}_m characterizes the energy dissipation ratio between fracture surface creation and viscous fluid flow under constant rate injection. t_s and 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). 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 and 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.