Whether used to enhance the hydrocarbon production from low permeability rocks or to measure the minimum in-situ principal stress in rock formations, height growth of a hydraulic fracture above the formation of interest is a key metric for the design of successful hydraulic fracture applications. If the confining stress variation between rock layers represents one of the main reasons for fracture containment at depth, a contrast of fracture toughness can also lead to fracture containment. Fracture toughness contrasts are presents at different scales. They are due to lithological changes at the scale of layers, but they also appear at smaller scales, down to the size of bedding planes. The interaction of a hydraulic fracture with a repetitive sequence of multiple layers of different fracture toughness can ultimately lead to the emergence of an elongated fracture or, alternatively, to the propagation of an elliptical-like fracture with a fixed aspect ratio. Combining theory and simulations, we study the possible emergence of an elongated hydraulic fracture from layers of alternating fracture toughness considering typical hydraulic fracturing treatments as well as micro-hydraulic fracturing test cases.
Hydraulic fracturing is an industrial technology in which a viscous fluid is deliberately injected into a solid to initiate and propagate one or more tensile fractures. This technology is successfully applied to measure the in-situ minimum stress in rock formations (Desroches and Thiercelin, 1993), but also to enhance the hydrocarbon production from low permeability rocks (Economides and Nolte, 2000). These rocks, usually referred as unconventional hydrocarbon reservoirs, are primarily located in sedimentary basins at depths ranging from one to few kilometers. In these basins the in-situ minimum stress is usually directed horizontally causing the hydraulic fracture to propagate on vertical plane and to interact with layer-like heterogeneities. To varying degrees, these heterogeneities comprise differences in the in-situ minimum stress, fracture energy, elastic properties, and leak-off-related quantities. Understanding their effect on the vertical hydraulic fracture growth, above the formation of interest, is of primary importance for the design of a successful hydraulic fracturing application (Bunger and Lecampion, 2017).
