Limiting Regimes of a Three-Dimensional Buoyant Hydraulic Fracture Emerging from a Point Source

Buoyant hydraulic fractures occur in nature as magmatic dikes and sills. In industrial applications like well stimulation, the emergence of buoyant fractures is undesirable and often limited by the injected volume and/or variation of in-situ stress. This class of tensile fractures is governed by a buoyancy force resulting from the density contrast between the surrounding solid and the fracturing fluid. We focus here on fluid releases from a point source in an impermeable elastic media with homogeneous rock and fluid properties. The resulting buoyant force is thus constant. We combine scaling arguments and planar 3D hydraulic fracture growth simulations [1] to fully understand the emergence as well as the different propagation regimes of buoyant fractures. For a continuous release, a family of solutions dependent on a dimensionless-viscosity $\mathcal{M}_{\hat{k}}$ exists. In the limit of large toughness ($\mathcal{M}_{\hat{k}} \ll 1$), we retrieve a finger-like shape [2]. The stable breadth of the tail is generally akin to the PKN approximation presented in [2]. The limit of a viscosity-dominated buoyant fracture ($\mathcal{M}_{\hat{k}} \gg 1$) has no stabilized breadth and exhibits a teardrop shape. For the case of a finite fluid volume release, a dimensionless buoyancy $\mathcal{B}_{\bar{k}}$ controls if a buoyant fracture emerges ($\mathcal{B}_{\bar{k}} \geq 1$) or stops and remains at depth ($\mathcal{B}_{\bar{k}}