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3D Numerical Modeling of the Propagation of Hydraulic Fracture at Its Intersection with Natural (Pre-existing) Fracture

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Abstract

A variety of 3D numerical models were developed based on hydraulic fracture experiments to simulate the propagation of hydraulic fracture at its intersection with natural (pre-existing) fracture. Since the interaction between hydraulic and pre-existing fractures is a key condition that causes complex fracture patterns, the extended finite element method was employed in ABAQUS software to simulate the problem. The propagation of hydraulic fracture in a fractured medium was modeled in two horizontal differential stresses (\(\Delta \sigma\)) of 5e6 and 10e6 Pa considering different strike and dip angles of pre-existing fracture. The rate of energy release was calculated in the directions of hydraulic and pre-existing fractures (\(G_{\text{frac}} /G_{\text{rock}}\)) at their intersection point to determine the fracture behavior. Opening and crossing were two dominant fracture behaviors during the hydraulic and pre-existing fracture interaction at low and high differential stress conditions, respectively. The results of numerical studies were compared with those of experimental models, showing a good agreement between the two to validate the accuracy of the models. Besides the horizontal differential stress, strike and dip angles of the natural (pre-existing) fracture, the key finding of this research was the significant effect of the energy release rate on the propagation behavior of the hydraulic fracture. This effect was more prominent under the influence of strike and dip angles, as well as differential stress. The obtained results can be used to predict and interpret the generation of complex hydraulic fracture patterns in field conditions.

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Abbreviations

\(a_{J}^{\tau }\) :

Unknowns associated with node \(J\) for enrichment function \(\tau\)

C :

Cohesive strength of natural fracture plane

E :

Young’s modulus of elasticity

E′:

Plane-strain modulus of elasticity

e :

Void ratio

G :

Energy release rate

G c :

Critical energy release rate

G rock :

Rock fracture energy

G frac :

Energy required to overcome the cement strength in the natural fracture

k :

Permeability

K :

Stress intensity factor

K c :

Fracture toughness

K I :

Mode I stress intensity factor

K II :

Mode II stress intensity factor

K III :

Mode III stress intensity factor

K f :

Coefficient of friction (internal friction coefficient of natural fracture plane)

N I :

Shape function at node I

\(\tilde{N}_{\text{J}}\) :

Shape function for enrichment at node J

\(n_{\text{enr}}\) :

Number of enrichment types

S :

Set of all nodes in the domain

\(S^{\tau }\) :

Set of nodes enriched by \(\varPsi^{\tau }\)

U :

Displacements

u C :

Continuous displacement field

u E :

Discontinuous displacement field

u I :

Nodal unknowns

T o :

Tensile strength of the specimen containing the pre-existing fracture

\(\alpha\) :

Angle between the direction of hydraulic fracture propagation and the pre-existing fracture dip

\(\beta\) :

Angle between the direction of hydraulic fracture propagation and the pre-existing fracture strike

\(\gamma\) :

Unit weight of the cement specimen

\(\Delta \sigma\) :

Horizontal differential stress

\(\nu\) :

Poisson’s ratio

\(\sigma_{\text{h}}\) :

Minimum principal stress in horizontal direction

\(\sigma_{\text{H}}\) :

Maximum principal stress in horizontal direction

\(\sigma_{\text{V}}\) :

Principal stress in vertical direction

\(\sigma_{\text{c}}\) :

Unconfined compressive strength

\(\phi\) :

Porosity

\(\varPsi^{\tau }\) :

Enrichment functions

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Acknowledgments

The authors would like to particularly thank Prof. Giovanni Barla for his valuable and helpful comments on this paper. This work was supported by the National Natural Science Foundation of China (grant no. 51174217).

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Authors and Affiliations

  1. Department of Mining Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Ali Naghi Dehghan & Kaveh Ahangari

  2. Department of Mining Engineering, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran

    Kamran Goshtasbi

  3. College of Petroleum Engineering, China University of Petroleum, Beijing, 102249, China

    Yan Jin

  4. Department of Mechanical and Mechatronics Engineering, University of Waterloo, University Avenue 200, Waterloo, ON, N2L3G1, Canada

    Aram Bahmani

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  1. Ali Naghi Dehghan
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Correspondence to Ali Naghi Dehghan.

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Dehghan, A.N., Goshtasbi, K., Ahangari, K. et al. 3D Numerical Modeling of the Propagation of Hydraulic Fracture at Its Intersection with Natural (Pre-existing) Fracture. Rock Mech Rock Eng 50, 367–386 (2017). https://doi.org/10.1007/s00603-016-1097-7

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