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 Mkˆ exists. In the limit of large toughness (Mkˆ≪ 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 (Mkˆ≫ 1) has no stabilized breadth and exhibits a teardrop shape. For the case of a finite fluid volume release, a dimensionless buoyancy Bk¯ controls if a buoyant fracture emerges (Bk¯≥ 1) or stops and remains at depth (Bk¯<1). For a finite release, a single large-time solution corresponding to the solution of [2] exists. Detailed characterization of the fracture evolution requires separation between the cases where the buoyant transition occurs during or after the release (see attached Fig. 1). For natural configurations, the emerging buoyant fractures are typically viscosity-dominated, which may explain the reported discrepancy between field and laboratory measurements of rock fracture toughness. Representative values of industrial single-entry hydraulic fracturing treatments lead to buoyant fractures under homogeneous conditions, which indicate the critical importance of stress and material heterogeneities in the containment of buoyant fractures at depth. [1] Haseeb Zia and Brice Lecampion. Pyfrac: A planar 3d hydraulic fracture simulator. Computer Physics Communications, page 107368, 2020. [2] L.N. Germanovich, D. I. Garagash, Murdoch, L., and Robinowitz M. Gravity-driven hydraulic fractures. In AGU Fall meeting, 2014.

Constraining the moment release of injection-induced earthquakes is of paramount importance to reduce the seismic hazard in the geo-energy industry. Recent studies suggest that a significant part of the moment release during fluid injections can be due to aseismic motion, namely, aseismic moment M0. Current models of injection-induced aseismic moment do not incorporate fault rupture mechanics. Here, we present a theoretical and numerical analysis that highlights a possible scaling relation between the aseismic moment and a key operational parameter, the injected volume of fluid V. The scaling relation emerges from the model of a stable frictional shear crack that propagates in mixed mode (II+III) on a planar fault interface. The interface is characterized by a constant hydraulic transmissivity and a shear strength that is equal to the product of a constant friction coefficient and the local effective normal stress. Fluid is injected right into the fault interface at a constant flow rate. The resulting relation between the aseismic moment and the injected volume is M0=A⋅ V^(3/2). The prefactor A accounts for the dependence of the aseismic moment on the pre-injection stress state, the parameters of the injection (notably, the injection flow rate), and the fault elasto-frictional and hydraulic properties. Unlike previous studies, our model accounts for the possibility that ruptures can propagate beyond the fluid-pressurized fault patch, a condition that is expected to occur in critically stressed and/or highly-pressurized fractures/faults. We test the scaling relation against estimates of moment release due to aseismic motion during fluid injections that vary in size from laboratory experiments to industrial applications. Our predictions are in good agreement with these observations. These results provide a simple means to quantify the size of aseismic ruptures in response to fluid injections related to both natural and human sources.