Modeling three‐dimensional hydraulic fracture propagation using virtual multidimensional internal bonds

Kai Huang1, Z. Zhang1, Ahmad Ghassemi1
1Department of Petroleum Engineering Texas A&M University College Station TX 77843 U.S.A.

Tóm tắt

SUMMARYPropagation of fractures, especially those emanating from wellbores and closed natural fractures, often involves Mode I and Mode II, and at times Mode III, posing significant challenges to its numerical simulation. When an embedded inclined fracture is subjected to compression, the fracture edge is constrained by the surrounding materials so that its true propagation pattern cannot be simulated by 2D models. In this article, a virtual multidimensional internal bond (VMIB) model is presented to simulate three‐dimensional (3D) fracture propagation. The VMIB model bridges the processes of macro fracture and micro bond rupture. The macro 3D constitutive relation in VMIB is derived from the 1D bond in the micro scale and is implemented in a 3D finite element method. To represent the contact and friction between fracture surfaces, a 3D element partition method is employed. The model is applied to simulate fracture propagation and coalescence in typical laboratory experiments and is used to analyze the propagation of an embedded fracture. Simulation results for single and multiple fractures illustrate 3D features of the tensile and compressive fracture propagation, especially the propagation of a Mode III fracture. The results match well with the experimental observation, suggesting that the presented method can capture the main features of 3D fracture propagation and coalescence. Moreover, by developing an algorithm for applying pressure on the fracture surfaces, propagation of a natural fracture is also simulated. The result illustrates an interesting and important phenomenon of Mode III fracture propagation, namely the fracture front segmentation. Copyright © 2012 John Wiley & Sons, Ltd.

Từ khóa


Tài liệu tham khảo

10.1007/s10704-005-4042-4

10.1002/nme.1620280413

10.1016/j.geothermics.2010.12.001

10.1016/j.ijrmms.2011.02.002

Ghassemi A, 2005, Poro‐thermoelastic response of a stationary crack using the displacement discontinuity method, ASCE Journal of Engineering Mechanics, 132, 26, 10.1061/(ASCE)0733-9399(2006)132:1(26)

Koshelev V, 2004, Complex variable BEM for stationary thermoelasticity & poroelasticity, Journal Engineering Analysis with Boundary Elements, 28, 825, 10.1016/j.enganabound.2003.08.006

CurranJH CarvalhoJL.A displacement discontinuity model for fluid‐saturated porous media.Proceedings 6th Congress of the ISRM Montreal Ca vol. 1 1987;73–78.

10.1002/nag.1610140103

10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S

10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J

10.1016/S0022-5096(97)00047-1

10.1016/S0013-7944(98)00048-4

10.1016/j.tafmec.2005.03.005

Zhang ZN, 2005, A new quasi‐continuum constitutive model for crack growth in an isotropic solid, European Journal of Mechanics ‐ A/Solids, 24, 243, 10.1016/j.euromechsol.2004.11.007

Zhang ZN, 2006, Micromechanical modelling of elastic continuum with virtual multi‐dimensional internal bonds, International Journal for Numerical Methods in Engineering, 65, 135, 10.1002/nme.1500

MinKS ZhangZN GhassemiA.Numerical Analysis of Multiple Fracture Propagation in Heterogeneous Rock induced by Hydraulic Fracturing. Proc.44th US Rock Mechanics Symposium Salt Lake City 2010.

10.1002/nag.905

Huang K, 2010, Three dimensional element partition method and numerical simulation for fracture subjected to compressive and shear stress, Engineering Mechanics, 27, 51

10.1016/j.ijrmms.2009.01.003

10.1016/S0148-9062(98)00005-9

Knauss WG, 1970, An observation of crack propagation in anti‐plane shear, International Journal of Fracture Mechanics, 6, 183, 10.1007/BF00189825

Adams M, 1978, Crack extension from flaws in a brittle material subjected to compression, Tectonophysics, 79, 97, 10.1016/0040-1951(78)90099-9

10.1016/S0013-7944(02)00240-0