  In impermeable media, a hydraulic fracture can continue to expand even
without additional fluid injection if its volume exceeds the limiting volume of
a hydrostatically loaded radial fracture. This limit depends on the mechanical
properties of the surrounding solid and the density contrast between the fluid
and the solid. Self-sustained fracture growth is characterized by two
dimensionless numbers. The first parameter is a buoyancy factor that compares
the total released volume to the limiting volume to determine whether buoyant
growth occurs. The second parameter is the dimensionless viscosity of a radial
fracture at the time when buoyant effects become of order 1. This dimensionless
viscosity notably depends on the rate at which the fluid volume is released,
indicating that both the total volume and release history impact self-sustained
buoyant growth. Six well-defined propagation histories can be identified based
on these two dimensionless numbers. Their growth evolves between distinct
limiting regimes of radial and buoyant propagation, resulting in different
fracture shapes. We can identify two growth rates depending on the dominant
energy dissipation mechanism (viscous flow vs fracture creation) in the
fracture head. For finite values of material toughness, the toughness-dominated
limit represents a late-time solution for all fractures in growth rate and head
shape (possibly reached only at a very late time). The viscosity-dominated
limit can appear at intermediate times. Our three-dimensional simulations
confirm the predicted scalings and highlight the importance of considering the
entire propagation and release history for accurate analysis of buoyant
hydraulic fractures.
