Duration of hydraulic fracture containment by tougher bounding layers

The vertical growth of engineered hydraulic fractures above the formation of interest, toward potentially environmentally sensitive layers, is a primary design constraint in hydraulic fracturing well stimulation. In-situ stress jumps have long been recognized as the primary mechanism for containment. Here, we investigate an alternative mechanism related to differences in critical fracture energy between the reservoir and the bounding layers for the containment of a planar 3D hydraulic fracture. We consider a symmetric scenario in which a hydraulic fracture is driven from an injection point located at the center of a layer of given height, bounded by two layers with a higher critical fracture energy than the central layer. We explicitly assume that the other material properties, as well as the in-situ stress, are uniform in order to isolate and properly quantify the importance of fracture toughness variation. By means of numerical simulations and scaling arguments, we quantify how long a hydraulic fracture driven by a constant injection rate can remain confined between the two tougher layers, at least for a finite time. The ratio of fracture toughness between the layers must exceed a minimum critical value for the fracture to remain contained. For toughness ratios above this limit, we prove that the time during which the hydraulic fracture remains contained is always finite, due to the increase in viscous fluid dissipation for fractures with large aspect ratios/contained fractures. In other words, the hydraulic fracture will ultimately break through into the tougher bounding layers. We express the containment duration as a function of both the fracture toughness ratio and the ratio of energy dissipated in fracture creation to that dissipated by viscous fluid flow at the moment when the fracture reaches the interfaces of the tougher layers. We estimate the containment time both analytically and numerically. Our results indicate that containment is likely to be short or very limited for initially viscosity-dominated fractures under realistic toughness contrasts. However, in the toughness-dominated regime, a toughness contrast greater than or equal to 2 is sufficient to significantly increase the containment duration. This is due to the establishment of a toughness-dominated contained fracture growth regime prior to the transition toward the late-time, viscosity-dominated regime, in which breakthrough ultimately occurs.