Three-dimensional hydraulic fracture propagation in homogeneous and heterogeneous media

Hydraulic fractures are tensile fractures that occur in solid materials due to the natural intrusion or anthropogenic injection of a viscous fluid into a fracture channel. The deliberate creation of hydraulic fractures is part of an industrial technology having various applications. For example, it is used for: the stimulation of hydrocarbon wells, the development of deep geothermal systems, and for measuring the in situ stress in rock formations. Additionally, hydraulic fractures may result from industrial processes such as geological carbon sequestration or wastewater injection. Hydraulic fractures propagate in a plane perpendicular to the minimum in situ compressive stress. In most sedimentary basins, the direction of this stress is horizontal, hence hydraulic fractures propagate in a vertical plane. Their vertical growth, often referred to as height growth, can be detrimental to the effectiveness of their application. For instance, in the stimulation of hydrocarbon wells, excessive height growth above the targeted layer will result in the delivery of fluid and proppant to unproductive zones and possibly the stimulation of water-bearing layers. Concerns have been raised about the migration of fluids into strata containing potable groundwater caused by hydraulic fracturing treatments. Another example is the case of in-situ stress estimation where an excessive height growth can compromise the measurement by connecting the pressurized interval to the rest of the wellbore. It is known that height growth can be hindered or arrested by the presence of different rock layers or in situ stress inhomogeneity. However, a complete understanding of the relative importance of the different types of heterogeneities on hydraulic fracture propagation is still lacking. Significant progress has been made over the last two decades thanks to the understanding of the multi-scale nature of the problem. This progress has led to the development of the Implicit Level Set Algorithm (ILSA). This numerical tool has been verified as capable of efficiently and accurately reproducing the planar propagation of hydraulic fractures, as observed in experiments carried out in both homogeneous and heterogeneous media. In this thesis work, we extend the scope of the ILSA algorithm to cases of large fracture front deformations. These cases are typically encountered when the front is locally pinned by tough and localized heterogeneities. We then further validate the ILSA algorithm by comparing it with new and recent analytical and experimental results. In particular, we highlight the comparison with the co-planar coalescence experiment of two hydraulic fractures. Based on the results obtained during these comparisons, we use the ILSA algorithm to study the effect of heterogeneities on fracture propagation. We determine the conditions under which the fracture front is arrested by a region of material characterized by a higher fracture energy. We determine how long two layers of materi