Much study has been conducted on the effect of formation Young’s modulus and
in situ stress on hydraulic fracture height containment in layered formations.
It has been well documented that in situ stress contrast is the dominant
parameter controlling fracture height growth, and that Young’s modulus contrast
is less important. However, a recent study pointed out that modulus contrast
can have significant implications on fracture geometry and proppant placement
(Smith et al. 2001). To expand on this topic, we consider the combined effects
of modulus contrast and in situ stress contrast on fracture geometry. A pseudo
3D (P3D) hydraulic fracture simulator with a rigorous layered modulus
formulation is used in this study. The fracture height calculated based on
uniform modulus versus layered modulus, under the same in situ stress contrast
conditions, is compared.
The results are analyzed and explained, based on fracture mechanics
fundamentals as well as the coupled fluid pressure effect in hydraulic
fracturing. One important finding is that low-modulus layers can also contain
fracture height. The results from this study can be applied to hydraulic
fracturing treatments in formations with moderate to significant modulus
contrast. The mechanisms studied in this work can also partially explain some
recent results from microseismic or tiltmeter mapping that show more fracture
height containment than that predicted by commonly used P3D hydraulic
fracturing simulators based on averaged modulus.
Because fracture height is recognized as one of the critical factors that
can determine the success or failure of a hydraulic fracturing treatment, many
studies have been conducted on the effects of formation Young’s modulus, in
situ stress, fracture toughness, and layer interfaces on hydraulic fracture
height containment in layered formations (Smith et al. 2001; Simonson et al.
1978; Daneshy 1978; van Eekelen 1982; Warpinski et al. 1982, 1998; Teufel and
Clark 1984; Thiercelin et al. 1989; Wang and Clifton 1990). Because of these
studies, it is now well known that in situ stress contrast is the dominant
parameter controlling fracture height growth and that Young’s modulus contrast
is less important. When studying different height-containment mechanisms,
modulus contrast is often considered separately from stress contrast to isolate
the effect of each parameter. In reality, formation layers of different moduli
are likely to have different in situ stresses (Teufel and Clark 1984) and the
contributions of both must be considered together.
With the development of tiltmeter and microseismic mapping services, more
direct measurements or estimates of hydraulic fracture geometry are available.
It has been observed that sometimes the fracture is more contained in height
than predicted by simulators. Some new mechanisms and explanations have been
given, including the “composite layer effect,” “shear dampening,” and fracture
behavior at layer interfaces, for the unexpected height containment (Warpinski
et al. 1998; Barree and Winterfeld 1998; Wolhart et al. 2004).
Alternatively, more advanced numerical models have been developed for
hydraulic fracture simulators (Smith et al. 2001; Siebrits et al. 2001), and
the combined effect of height-containment mechanisms can now be studied with
fewer approximations for hydraulic fracturing conditions. The study of the
layered modulus effect has been investigated using a finite element method that
can rigorously account for different moduli in a hydraulic fracture simulator
(Smith et al. 2001). Two effects of high-modulus layers on fracture height
containment were provided and explained. The shortcomings of using an averaged
modulus were pointed out by comparing simulation results of averaged modulus
with that of layered modulus.
To expand further on the shortcomings of using an averaged modulus, we
consider the combined effect of modulus contrast and in situ stress contrast on
fracture geometry, and show that modulus contrast can have a significant effect
on fracture height. Height growth can be contained by low-modulus layers
because of different mechanisms than those already discussed in the literature
for high-modulus layers (Smith et al. 2001).
In this paper, fracture height-containment mechanisms are briefly reviewed.
A parametric study using a hydraulic fracture simulator that rigorously
accounts for variable modulus is conducted for various combinations of stress
contrast, modulus contrast, and fluid viscosity. The results are analyzed, and
the reasons for limited height growth are explained based on fracture mechanics
fundamentals and the coupled fluid pressure effect in hydraulic fracturing.
© 2008. Society of Petroleum Engineers
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- Original manuscript received:
30 August 2006
- Meeting paper published:
5 December 2006
- Revised manuscript received:
28 December 2007
- Manuscript approved:
8 January 2008
- Version of record:
20 May 2008