Several methods are proposed for simulation of hydraulic fracturing process in rock material. In most of this models it is assumed that the rock mass is a linear elastic solid and the criterion of fracture propagation is mostly expressed by the conventional stress intensity factor calculation approach of linear elastic fracture mechanics (LEFM). In the analysis of fracturing processes, LEFM theory is valid until the non-linear behavior of the material, in particular at the crack tip, does not affect the propagation of the crack. In this paper, considering the effect of the plastic behavior of rock on the hydraulic fracturing process, the non-linear fracture mechanics concepts (J-integral) were applied to the analysis of hydraulic fracture propagation. The J-integral was related to the energy released associated with crack growth and was used as a measure of intensity of deformation at the crack tip for both linear and non-linear materials. The finite element code, ABAQUS, was used to simulate the hydraulic fracturing process. A typical 2-D section of a cylindrical oil reservoir was considered in the analysis. Assuming a plane strain condition, the energy release rate was calculated based on J-integral in an arbitrary path around the crack tip and the propagation of crack was analyzed. The results obtained from numerical modeling were compared against theoretical solution successfully. In the next phase, considering a Mohr-Coulomb material model for the rock, the effects of plastic deformation at crack tip on the fracturing process was investigated. Using this plastic material model, the obtained results were compared against the results obtained from conventional elastic analysis used in common and the effects of crack tip plastic deformations on the fracturing were demonstrated.
Hydraulic fracturing is a process in which cracks are initiated and propagated by pumping fluid at relatively high flow rates and pressure. This technique is commonly used in oil and gas reservoirs to enhance the production capacity of the oil and gas reservoirs [1,2]. The hydraulic fracturing process is a fairly complex problem involving the following processes: a) mechanical deformation occurred at crack surface as a result of fluid pressure b) fluid flow within crack c) propagation of crack as a function of applied loading Various numerical techniques have been used by many researchers to evaluate and predict the location, direction and extent of these hydraulic fractures [3,4,5]. Depending of the reservoir and fracture geometries and the required accuracy of prediction conducted, simulation ranges from simple 2D to complex 3D analyzes [6,7]. Analytical solutions proposed by Bowie (1956), Newman (1969,1971), Ingraffea (1977), Rummel and Winter (1982–1983) provided the bases for the analysis of crack propagation in hydraulic fracturing process [8,9]. Rummel and Winter (1982–1983) proposed the general analytical solution for crack propagation in hydraulic fracturing process. They used the traditional stress intensity factor concept, employed in linear elastic fracture mechanics (LEFM), to express their fracturing criterion . LEFM approach is valid where the non-linear plastic behavior is limited to a small area at the crack tip [10,11].