Deflation dynamics of hydraulic fractures in porous elastic media

Hydraulic fractures occur naturally during ice calving events in glaciers, the sudden draining of glacial lakes, the formation of magma-driven dykes and sills, and the failure of dams. Hydraulic fractures are also engineered by injecting a viscous fluid into rock to increase hydro-carbon recovery, for enhanced geothermal energy production, to remediate and dispose of waste water, and for preconditioning and cave inducement in mining operations. In these engineering applications, once injection is stopped the wellbore is frequently shut-in by closing a valve. Over the last five decades considerable research has been dedicated to building accurate models of propagating hydraulic fractures, but very little research has been done on receding hydraulic fracture - in which the fractures are assumed to close on previously created solid surfaces at the tip.