Factors Controlling the Vertical Growth of Hydraulic Fractures
Authors: Daneshy A. Ali 
Published: January 2009

Abstract
There is compelling evidence that majority of industrial hydraulic fractures have limited vertical growth (height). Theoretical and experimental work on fracture extension show that limiting the fracture height will result in continuously increasing fluid pressure during the treatment. Yet, field data does not support this point. This paper resolves the contradiction between theoretical and experimental data and field evidence.
In the past, three mechanisms have been offered for fracture containment. These are stress contrast, modulus contrast, and fracture slippage. This paper shows that stress and modulus contrast do not stop the fracture height growth by themselves. They mainly change the fracture width and conductivity. Shear failure (slippage), on the other hand, results in blunting of the fracture tip and completely stops its local growth. This has important implications for the length and width of the fracture; the former becoming shorter and latter wider.
A new mechanism offered for fracture containment is fracture re-orientation near an interface. Although the mechanism for such behavior is not well-defined, its presence has been observed directly in coal mines, and anecdotally by microseismic and tiltmeter surveys.
The long length of the tip area means that different mechanisms may account for containment of the same fracture at different points and times. Contrast between the Young's moduli and stresses of the bounding layers may sometimes be enough to hald local fracture growth.
Due to formation inhomogeneity the fracture may be contained at a given point and time, but cross the interface at a later time.

General Background
Estimation or determination of fracture height has been the most difficult technical question in hydraulic fracturing. The significance of the subject spans issues related to containment of reservoir fluid, production of unwanted water or gas, as well as optimizing the reservoir production. There is strong evidence suggesting that the vertical extent of many industrial hydraulic fractures is much less than their lateral growth. Such evidence consists of production mixture (absence or smaller than expected flow of water or gas), temperature and tracer logs, and seismic and tiltmeter fracture mapping.
The early attempts to address fracture containment were focused on formation elastic properties. Using stress intensity computations for a fracture approaching an interface, Simonson et al1 argued that a formation with a higher Young's modulus can act as a barrier for a fracture propagating in a lower modulus rock. However, laboratory experiments conducted by Daneshy2 and field experiments by Sandia National Laboratory at Nevada Test Site3 showed that contrast in elastic moduli is not sufficient to stop the growth of a hydraulic fracture across an interface. Daneshy also introduced the concept of shear sliding of the fracture at interfaces and argued that blunting of the fracture tip due to sliding is a more plausible mechanism for fracture containment. The significance of shear sliding at the interface was later confirmed by the experimental work of Anderson4.