Abstract
Hydraulic fracture height containment is a critical issue in the development of unconventional reservoirs. The extent of fracture height growth depends on a variety of factors, particularly stress and stiffness contrasts between adjacent layers. Accurate simulation of fracture growth and containment requires a reliable fracturing criterion. The virtual crack closure technique (VCCT) is a widely used method for computing energy release rate. However, it is based on the assumption that a small crack extension does not significantly alter the state of the crack tip, which is generally not the case when a fracture crosses strong stress and/or stiffness contrasts. In this work, we assess the applicability and accuracy of a modified virtual crack closure technique (MVCCT) for a fluid-driven fracture in breaking through interfaces with significant stress and/or stiffness contrasts, through comparisons with analytical and reference numerical solutions. The results show that significant error could occur when the fracture tip is very near or at stress/stiffness interfaces. However, this error is localized to the interface and proves to be inconsequential to the predicted penetration depth into the rock layer beyond the interface. This study validates the applicability of MVCCT in 3D hydraulic fracturing simulation in strongly heterogeneous rock formations.
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Abbreviations
- E :
-
Young’s modulus
- G :
-
Energy release rate
- G c :
-
Critical energy release rate
- G I :
-
Energy release rate for Mode I
- K Ic :
-
Critical stress intensity factor for Mode I (known as “fracture toughness”)
- U :
-
Elastic strain energy
- W :
-
Potential energy of the applied loading
- \(\Pi\) :
-
Total potential energy
- ε :
-
Strain tensor
- C :
-
Stiffness matrix
- \(\varvec{b}\) :
-
Body force
- f :
-
Nodal force
- h :
-
Half fracture height
- h 0 :
-
Half thickness of middle-layer or the layer that the fracture is propagating from
- p :
-
Fracture pressure
- \(\hat {{\varvec{t}}}\) :
-
Boundary force
- v :
-
Poisson’s ratio
- w :
-
Fracture width
- σ :
-
In situ stress magnitude
- Δσ :
-
Stress contrast magnitude
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This manuscript has been authored by Lawrence Livermore National Security, LLC under Contract no. DE-AC52-07NA27344 with the US. Department of Energy. The United States Government retains, and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. This document is LLNL report LLNL-JRNL-751676.
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Huang, J., Fu, P., Settgast, R.R. et al. Evaluating a Simple Fracturing Criterion for a Hydraulic Fracture Crossing Stress and Stiffness Contrasts. Rock Mech Rock Eng 52, 1657–1670 (2019). https://doi.org/10.1007/s00603-018-1679-7
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DOI: https://doi.org/10.1007/s00603-018-1679-7