Numerical simulation of crack propagation in layered formations
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ORIGINAL PAPER
Numerical simulation of crack propagation in layered formations Mahmoud Behnia & Kamran Goshtasbi & Mohammad Fatehi Marji & Aliakbar Golshani
Received: 6 May 2012 / Accepted: 4 February 2013 # Saudi Society for Geosciences 2013
Abstract In the present study, a boundary element method based on the higher order displacement discontinuity formulation is presented to solve the general problem of hydraulic fracture propagation in layered formations. Displacement collocation technique is employed to model the higher order displacement variation along the crack and the special crack tip element near its ends. The hydraulic fracture propagation and its interaction with the layer interface in non-homogenous rock materials are studied by the proposed semi-analytical (hybridized boundary element-boundary collocation) method. The maximum tangential stress criterion (or σ-criterion) of fracture mechanics considering different elastic constants (Young modulus and Poisson’s ratio) is used to obtain the fracture path. The fracture propagation from stiff to soft and soft to stiff media for cracks having different inclination angles is modeled, and the effects of elastic constants on the hydraulic fracture propagation is studied. The results show that if the hydraulic fracture originates in the stiffer layer, its capability to cross the layer increases and is vice versa for the softer material. The comparison of the results gained from the numerical method with those in the literature show a good performance of the method in the case of propagation of hydraulic fracture in layered formations. M. Behnia Department of Mining Engineering, Tarbiat Modares University, Tehran, Iran K. Goshtasbi (*) Faculty of Engineering, Tarbiat Modares University, Tehran, Iran e-mail: [email protected] M. F. Marji Faculty of Mining Engineering, Yazd University, Yazd, Iran A. Golshani Department of Civil Engineering, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran
Keywords Hydraulic fracturing . Displacement discontinuity . Layered formations . Fracture propagation
Introduction One of the important features required in hydraulic fracture design is the ability to predict the geometry and characteristics of hydraulically induced fractures. Geological discontinuities such as joints, faults, and flaws, as well as bedding planes, occur in most formations. The intersection of a hydraulic fracture with joints or other discontinuities is inevitable for fractures growing in rock formations and can significantly affect the fracture growth. Hence, a better understanding of how an induced fracture interacts with a discontinuity is fundamental for predicting the ultimate size and shape of the hydraulic fractures formed by a treatment (Warpinski and Teufel 1987; Pollard and Aydin 1988). For instance, Pollard and Aydin (1988) and Cooke and Underwood (2001) have documented cases of fractures arresting at low frictional strength bedding planes because of sliding and opening on bedding planes. In these studies, the material proper
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