Geofluids

Volume 2018, Article ID 2053159, 12 pages

https://doi.org/10.1155/2018/2053159

## Fracture Initiation Model of Shale Fracturing Based on Effective Stress Theory of Porous Media

Department of Petroleum Engineering, Northeast Petroleum University, Daqing 163318, China

Correspondence should be addressed to Yuwei Li; nc.ude.upen@iewuyil

Received 19 October 2017; Accepted 3 June 2018; Published 4 July 2018

Academic Editor: Jun Lu

Copyright © 2018 Yuwei Li and Dan Jia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Unconventional oil and gas are important resources of future energy supply, and shale gas is the focus of the development of unconventional resources. Shale is a special kind rock of porous medium, and an orderly structure of beddings aligned in the horizontal direction where causing the strong elastic anisotropy of shale is easy. A new model has been established to calculate the fracture initiation pressure with the consideration of mechanical characteristics of shale and the anisotropic tensile strength when judging rock failure. The fracture initiation model established in this paper accurately reflects the stress anisotropy and matches well with the actual situation in porous media. Through the sensitivity analysis, the results show that , , , , and have a certain impact on the tangential stress when the circumferential angle changes, and there is a positive relationship between the initiation pressure and the above sensitive factors except for . The results can provide a valuable and effective guidance for the prediction of fracture initiation pressure and fracture propagation mechanism under special stratum conditions of shale.

#### 1. Introduction

Unconventional oil and gas are important resources of future energy supply. And shale gas is the focus of the development of unconventional resources. Shale gas can only be profitable by hydraulic fracturing of horizontal wells with the current volume fracturing techniques. Fracture initiation of horizontal well hydraulic fracturing is a technical difficulty related to fracturing technology.

As for fracture initiation, a lot of studies have been conducted on this topic in recent years [1–8]. There are several studies that demonstrated the initiation of transverse fractures by laboratory observations [9, 10] and field observations [11]. Fairhurst [12] revealed the possibility of a fracture initiating as transverse and in the longitudinal direction. However, it is shown [13] that the axial stress is not a good predictor of transverse fracture initiation, because it remains constant during hydraulic pressurization. Based on the minimum strain energy density criterion, Ayatollahi and Sedighiani [14] took the effect of T-stress into account, and they studied and analyzed the effect of T-stress on the critical mode stress intensity factor of brittle and quasi-brittle materials. However, for all cases in their experiments, the material was assumed to be homogeneous and isotropic with linear elastic behavior. By true triaxial hydraulic fracturing experiments, Peng et al. [15] observed the diversion and the following propagation of hydraulic fractures both horizontally and vertically after initiation from a directional wellbore with a skew angle. They mentioned that due to strong heterogeneity of coal rocks, primary and secondary cracks were developed, which would lead to discontinuity and anisotropy of mechanical characteristics in coal. However, they did not make a further study of this problem in view of this limitation. Fallahzadeh et al. [16] modeled various scenarios of vertical and horizontal wells and in situ stress regimes; in addition to experimental studies, analytical solutions were developed to simulate the mechanism of fracture initiation in perforated boreholes in tight formations. Furthermore, it was found that stress anisotropy influences the fracturing mechanism in a perforated borehole and affects the geometry of the initiated near-wellbore fracture. Considering the existence of bedding planes, cracks and other structural planes are the preconditions of the simulated reservoir volume of shale formations. In order to analyze the effect of bedding planes on the propagation of hydraulic fractures in shale formation, Heng et al. [17] carried out three-point bending tests of notched cylindrical specimens with different bedding orientations, based on the distribution of stress field around a crack tip of anisotropic materials. In addition to the experimental methods, theoretical research and numerical simulation methods have also been applied to analyze the fracture initiation mechanism. Lecampion [18] proposed an approximation of the mixed criteria which accounts for solving a single nonlinear equation. He held that a higher mean compressive far-field stress tends to make the failure more strength-driven, while a higher differential far-field compressive stress promotes an energy-driven tensile failure. But they are solely interested in tensile fracture initiation and did not investigate shear failures which may occur in the beginning depending on the stress condition. Tunsakul et al. [19] investigated the failure behavior of underground gas storage caverns under high pressure. The observation and analysis results revealed that the lateral earth pressure coefficient at rest has a strong influence on the position of this initiation point, while the depth of the cavern has an insignificant effect. However, the findings in this research are based on limited testing conditions with specific rock, and therefore a broader set of studies is needed to enhance the reliability. Xie and Min [20] realized that there are several distinctive features of enhanced geothermal system stimulation compared with common hydraulic treatments in the hydrocarbon reservoirs. Based on the hydroshearing concept, they established generic models to estimate the location of the shearing onset, the required injection pressure, and the overall shearing growth direction during enhanced geothermal system hydraulic stimulation. They adopt the Coulomb failure criterion to define the shear strength of a single rock joint but neglected the cohesion of fracture. Mohr-Coulomb and Hoek-Brown [21] applied the shear failure strength criteria to the borehole stability analysis associated with a homogeneous linear poroelastic model, which ignored the influence of the intermediate principal stress on rock failure. Based on borehole stress solutions, Zhang et al. [22] analyzed the influencing factors, such as Poisson’s ratio and shear stress, but the solutions were all derived from the homogeneous linear poroelastic theory. Sun et al. [23] thought that shear failure, plastic deformation, and the coupling effect near the fracture tip play an important role in the fracture initiation and propagation, and a new coupled model is presented. But they assumed that the rock density and the fluid viscosity and density are uniformly distributed in the formation without the consideration of rock anisotropy. An orderly structure of shale beddings aligned in the horizontal direction caused the strong elastic anisotropy of shale. Based on the rock transverse isotropic constitutive relation and seepage and deformation coupling numerical method, Li et al. [24] established a three-dimensional finite element numerical model for a horizontal well with perforating completion. Considering the elastic mechanics anisotropy difference of shale, the sensitivity analysis of perforation parameters on the fracture initiation pressure and location of the horizontal well was proposed. With both the numerical simulations and experiments, Huang et al. [25] discussed the initiation mechanisms of natural fractures during hydraulic fracturing. They concluded that the lateral stress coefficient plays a critical role in determining the stress magnitude and orientation around the fracture tip and predicted that there is a high probability for developing inclined fractures in the coals with strong heterogeneity. But no detailed reasons were given. Gong et al. [26] analyzed variation rules of fracture in initiation pressure and fracture starting point of hydraulic fractures in a radial well; based on fluid-solid coupling effect and the maximum tensile-stress criterion, they simulate and study local stress accumulation situation caused by the vertical and radial section in the drilling process and the fracturing section in the hydraulic fracturing process through the finite element method. By using Abaqus finite element calculation software, Guo et al. [27] established the fracture initiation models for a 3D single-stage three-cluster perforation and a single-cluster perforation (containing natural fracture). The results show that the initiation pressure of the open-hole perforation is far below that of the casing perforation. However, the calculation model assumes that the shale reservoir is homogeneously linear and is different from the accrual situation.

To calculate the stress distribution around the borehole and judge the failure of the wellbore rock, the previous research work about fracture initiation of horizontal well fracturing basically assumed that shale is an isotropic homogeneous rock. In fact, the shale rock has obvious anisotropic mechanical properties. The influence of the anisotropy should be considered when calculating the effective stress distribution around the borehole and confirming the tensile strength of the rock.

#### 2. Borehole Stress Distribution of Transverse Isotropic Shale

Because shale gas is mainly developed by horizontal wells or extended reach wells and there is a certain angle between the direction of the borehole axis and the geographic coordinate system or the stress coordinate system, therefore, the coordinate system transformation should be performed before calculating the borehole stress distribution, and the process is transforming the far-field in situ stresses from a geographic coordinate system to a borehole coordinate system.

Firstly, the far-field in situ stress distribution is transformed from the principal stress coordinate system to the geographic coordinate system as shown in Figure 1(a). The stress transformation relationship can be listed as follows: where is the far-field stress tensor under the principal stress coordinate system, is the far-field stress distribution tensor under the geographic coordinate system, is the azimuth of the maximum horizontal principal stress, and is the angle between the direction of and -axis.