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