Fracture growth in layered formations where the stresses and rock mechanical properties change frequently with depth is of great interest to researchers, especially when estimating the vertical growth of fractures in hydraulic fracturing treatments. The influence of formation stresses on fracture growth has been well documented and supported by numerous case histories, but the height-growth limitations resulting from intersection and crossing of various interfaces by the fracture continues to be investigated. This paper describes a model and a method to predict potential locations where a horizontal fracture can develop and limit the vertical growth of the fracture.

Most height growth predictions using traditional pseudo-3D (P3D) models result in planar fractures of widths that vary depending on the stresses and mechanical property of the layers that the fracture crosses. As evinced from the literature and laboratory experiments, the propagating cracks may have a three-dimensional (3D) characteristic given the observed combination of deviation (kinking) and out-of-plane displacements that can hinder the vertical growth. Multiple flaws leading to a 3D crack can be approximated as a two-dimensional (2D) model by considering it as a mixed boundary value triple pressurized-crack problem. In this paper, such representations are first used to obtain discrete stress intensity factors (SIF) at specific locations, and then, are superimposed on routine SIFs to include the influence of real-world 3D cracks on vertical growth estimation.

Fracture width profiles across several layers were generated using a modified equilibrium height growth model and were key to identifying the regions where complex growth in layered formations could potentially exist. These predictions resemble the analog for 3D fractures and given the fact that a portion of the treatment was injected at pressures that exceeded the overburden, alludes to the presence of a horizontal fracture component. Micro-seismic survey from the treatment shows vertical growth containment at the location where minimal width is projected. Three cases histories where these observations were made are also presented in the paper along with pertinent theory and explanations.

The model developed in the study is helpful in predicting potential locations where a horizontal fracture can develop and limit the vertical growth or even curtail the extension of the main fracture. The method developed in the study requires discrete layered formation and fluid properties such as stresses, rock moduli, SIFs, leakoff, and fracturing fluid rheology, as the only inputs, and hence can be applied to a variety of examples worldwide.

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