**1. Introduction**

Hydraulic fracturing is an important technology of production enhancement of oil and gas wells and intensified injection of wells. The first experimental hydraulic fracturing operation took place in the United States in 1947 in the Hugoton gas field in Grant County, Kansas, and after decades, the hydraulic fracturing technology has being widely used and become the dominant factor that determines the development plan of low permeability oilfield. In practical

© 2013 Men et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

applications, most of the hydraulic fracturing operations in the oil and gas fields are performed through casing, and, the regular or complex bedding structures likely exist in the rock mass formed in the course of rock formation and tectonic movement, so the research of the effect of perforation and bedding angle and modulus contrasts of rock and bedding in heterogeneous rocks under hydraulic fracturing is necessary. It can not only make fracturing decision-making more scientific, but reduce the fracturing cost and improve the fracturing efficiency, and has great theoretical significance and practical value on the perforation parameters optimization design and hydraulic fracturing construction of bedding rockmass.

In this paper, the effect of perforation and bedding angles and bedding materials on initiation pressure, breakdown pressure and hydraulic fractures evolutions of rock specimens under hydraulic fracturing is simulated and analyzed by using RFPA2D(2.0)-Flow which adopts the finite element method and considers the heterogeneous characteristics of rock in meso-scale.

Numerical Simulation of Hydraulic Fracturing in Heterogeneous Rock: The Effect of Perforation Angles…

http://dx.doi.org/10.5772/56012

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RFPA is a numerical experiment tool basing on the realistic failure process analysis method, which can simulate the gradual damage of materials. Its calculation method bases on finite element and statistical damage theory. RFPA considers both heterogeneity of materials and randomness of defect distribution, and puts the statistical distribution hypothesis of these material properties into the numerical calculation method (finite element method) to break the elements which satisfy the strength criterion. The material properties of each element follow Weibull distribution and are different from each other, and the element will fail if its stress reaches the failure strength, moreover, the number of fail elements will increase, which will be connected to each other and form fractures, as the load increases, so that the numerical simulation of heterogeneous material failure process can be realized. RFPA transforms the complex macroscopic nonlinear problem into simple mesoscopic linear problem by consider‐ ing the heterogeneous characteristics of material and the complicated non-continuum me‐ chanics problems into simple continuum mechanics problems by introducing the mathematics continuous and physical discontinuous concept, making the calculation results closer to the

In mining and civil engineering projects, the re-distribution of the stress field during the excavation of tunnels and underground chambers leads to the formation of new fractures. The flow and transport behaviour within developing fractures are dramatically different from those in rocks with existing fractures under the same loading, therefore, the permeability of rocks changes dramatically in the process of damage evolution in fracture rocks. RFPA2D2.0- Flow is the software considering the effects of the extension of existing fractures, the initiation of new fractures, the coupled effects of flow, stress and damage on the extension of existing/new fractures, and the permeability change due to damage evolution of the rocks, and is based on the theories of fluid-saturated porous media and damage mechanics. Flow-stressdamage (FSD) coupling model for heterogeneous rocks that takes into account the growth of existing fractures and the formation of new fractures is established herein. In [10-16],

**2.** Rock is the elastic brittle material with residual strength and the mechanical behaviour of loading and unloading process is in accordance with the elastic damage theory;

**3.** The maximum tensile strength criterion and Mohr Coulomb criterion are used as the

RFPA2D2.0-Flow bases on the following five basic assumptions:

damage threshold to judge whether the elements damage or not;

**1.** The fluid in the rock follows Biot consolidation theory;

**2. Introduction of RFPA2D2.0-Flow**

actual situation.

At present, the perforation parameters are controllable which can be realized easily in practice. Since the hydraulic fracturing technology appeared, many experts have made various researches about the influence of perforation parameters on fracture evolutions under hydraulic fracturing. In [1], Daneshy et al. studied the hydraulic fracturing through perforation in 1973 and found that breakdown pressures of hydraulic fractures would decrease as the number of perforations increased, moreover, the existence of the casing and the perforations had little influence on the direction of the created fracture, which is perpendicular to the minimum principal stress. In [2], Weng et al. studied the hydraulic fracture initiation and propagation from deviated wellbores in 1993, investigated the interaction and link-up of the starter fractures initiated from perforations and the turning of the linked fracture and estab‐ lished a criterion that correlates fracture link-up to stresses and wellbore parameters. In [3], Zhang et al. used two-dimensional model to simulate the initiation and growth of hydraulic fractures in 2011 and developed a dimensionless parameter that is shown to characterise nearwellbore reorientation and curving of hydraulic fractures driven by viscous fluid. In [4], Zhang et al. employed three-dimensional finite element model together with the tensile criterion of rock materials in 2004, investigated that perforation density and perforation angle are the most important parameters controlling the formation fracturing pressure, but the influences of perforation diameter and perforation length are much slighter. In [5], Jiang et al. studied the fracture propagation mechanism of hydraulic fracturing through the experiment in 2009, and the results showed that the turning fracture can be generated by using oriented perforation fracturing technology, and with the increase of azimuth of oriented perforating, the breakdown pressure and turning distance are both growing.

Few studies have been carried on for fracture evolutions on heterogeneous rocks with different bedding angles under hydraulic fracturing at present stage. In [6], Bruno and Nakagawa studied fracture propagation path in non-uniform pore pressure field by test method in 1991, and proved that the fracture is influenced by both pore pressure magni‐ tude on a local scale around the crack tip and the orientation and distribution of pore pressure gradient on a global scale. In [7], Li et al. simulated the experiment of hydraul‐ ic fracturing in non-uniform pore pressure field in 2005, and the results are well agreea‐ ble to that of Bruno and Nakagawa's experiments. In 2010, Abbass et al.'s study on Brazilian tensile text of sandstone in [8-9] showed that the breakdown pressure and fracture pattern are considerably affected by the bedding orientation and larger fracture length correlating with higher strength and applied energy.

In this paper, the effect of perforation and bedding angles and bedding materials on initiation pressure, breakdown pressure and hydraulic fractures evolutions of rock specimens under hydraulic fracturing is simulated and analyzed by using RFPA2D(2.0)-Flow which adopts the finite element method and considers the heterogeneous characteristics of rock in meso-scale.
