Propagation of planar three-dimensional buoyant hydraulic fractures

Hydraulic fractures are driven by an internal fluid pressure exceeding the minimum compressive stress, propagating in a direction perpendicular to the latter. This class of tensile fractures has gained interest over the last fifty years due to the development of multiple engineering applications. The most-known industrial applications are well-stimulation treatments by hydraulic fracturing used in the petroleum industry to enhance the permeability of tight reservoirs. Other industrial applications include in-situ stress measurement techniques and stimulations of geothermal systems. Natural occurrences include magmatic intrusions and the ascent of geothermal fluids in subduction zones. In sedimentary basins, the minimum compressive stress is usually horizontal and increases with depth, such that hydraulic fractures grow along vertical planes. A buoyant force emerges as the fracturing fluid is subjected to a hydrostatic pressure gradient different from the stress gradient in the solid. This buoyant force elongates the fracture in the direction of gravitational acceleration, and the propagation can become self-sustained without additional fluid released. For fluids lighter than the surrounding material, this favors an upward growth towards possibly environmentally sensitive upper aquifers. When and how such a buoyancy effect impacts three-dimensional hydraulic fracture growth remains quantitatively unexplored. It is notably unclear how the dominant energy dissipation mechanism (viscous flow or fracture creation) will affect the partition between horizontal and vertical growth. This thesis investigates the impact of gravitational effects on the emergence, propagation, and arrest of planar three-dimensional hydraulic fractures using scaling, semi-analytical, and numerical methods. We study the process using linear elastic hydraulic fracture mechanics and consider continuous and finite volume releases from a point source. First, we analyze the behavior of finite-volume axisymmetric hydraulic fractures in the absence of buoyant forces. In impermeable media, we show that the arrested shape is independent of the release history. For a permeable solid, the arrested fracture characteristics are a function of fluid leak-off, fracture toughness, and release history. Second, we investigate buoyant hydraulic fracture propagation under continuous fluid releases in impermeable media. A family of solutions that depends on a single dimensionless number emerges. This dimensionless number combines the properties of the solid (density, elasticity, fracture resistance), the fracturing fluid (density, viscosity), and the fluid release rate. Third, we confirm that the emergence of self-sustained buoyant hydraulic fractures in impermeable media is independent of the release history. The release history governs, however, to the first order how the fracture propagation evolves (the partition between horizontal and vertical growth, ascent rate). We further demonstrate that f