Geofluids

Volume 2019, Article ID 2624716, 13 pages

https://doi.org/10.1155/2019/2624716

## Numerical Simulations of Fracture Propagation in Jointed Shale Reservoirs under CO_{2} Fracturing

^{1}School of Resources and Safety Engineering, Central South University, Changsha, 410083 Hunan, China^{2}State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, 221116 Jiangsu, China^{3}Department of Energy and Mineral Engineering, EMS Energy Institute and G3 Center, Pennsylvania State University, University Park, PA 16802, USA

Correspondence should be addressed to Dan Ma; nc.ude.usc@am.nad

Received 8 November 2018; Revised 5 February 2019; Accepted 5 March 2019; Published 7 April 2019

Guest Editor: Qianbing Zhang

Copyright © 2019 Qi Zhang et al. 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

Water-based hydraulic fracturing for the exploitation of shale gas reservoirs may be limited by two main factors: (1) water pollution and chemical pollution after the injection process and (2) permeability decrease due to clay mineral swelling upon contact with the injection water. Besides, shale rock nearly always contains fractures and fissures due to geological processes such as deposition and folding. Based on the above, a damage-based coupled model of rock deformation and gas flow is used to simulate the fracturing process in jointed shale wells with CO_{2} fracturing. We validate our model by comparing the simulation results with theoretical solutions. The research results show that the continuous main fractures are formed along the direction of the maximum principal stress, whilst hydraulic fractures tend to propagate along the preexisting joints due to the lower strength of the joints. The main failure type is tensile damage destruction among these specimens. The preexisting joints can aggravate the damage of the numerical specimens; the seepage areas of the layered jointed sample, vertical jointed sample, and orthogonal jointed sample are increased by 32.5%, 29.16%, and 35.05%, respectively, at time s compared with the intact sample. The preexisting horizontal joints or vertical joints promote the propagation of hydraulic fractures in the horizontal direction or vertical direction but restrain the expansion of hydraulic fractures in the vertical or horizontal direction.

#### 1. Introduction

In recent years, the application of hydraulic fracturing has significantly increased the production of oil and natural gas. It is estimated that hydraulic fracturing has improved recoverable reserves of oil by at least 30% and of natural gas by 90% [1]. In addition, more than 60% of oil and gas wells need to be fractured first, especially for unconventional gas resource deposited in deep underground shale layers with extremely small permeability (usually less than 1 mD) [2, 3]. Hydraulic fracturing may increase permeability of shale by three to five orders of magnitude [4]. Thus, the production of the fractured gas wells increases dramatically. In all, hydraulic fracturing introduced in oil and gas fields has revolutionized gas production around the world [5, 6].

However, the water-based fracturing technology has some limitations and environmental concerns. First, hydraulic fracturing consumes large amounts of water. According to a report [7], the water use for hydraulic fracturing accounts for 9% of total freshwater consumption in Texas. The large consumption of water will restrict the oil and gas reservoir developments in a water-deficient area [8, 9]. Second, due to the large amount of water and chemical reagents used in the hydraulic fracturing, it may cause potential water pollution and chemical pollution if the treatment of flowback fluids with chemical reagents is insufficient [10–12]. Third, for the reservoirs containing clay minerals, the permeability may decrease after water injection, thereby decreasing the production of gas reservoirs [13–15]. The main reason is that, when the hydration minerals meet injection water, clay minerals can swell and result in blockage of seepage channels [16]. All of these disadvantages of hydraulic fracturing promote the study and development of waterless fracturing [17].

Several waterless fracturing technologies have been introduced in oil and gas industries over the past few decades, including oil-based fracturing, N_{2} fracturing, and CO_{2} fracturing [18]. Oil-based fracturing was first used in Colorado, Texas, and Kansas in late 1940s [19]. Compared with hydraulic fracturing, it could be conducted in frozen areas. However, oil-based fracturing is expensive and may impair the effective permeability of wells [20]. N_{2} fracturing and CO_{2} fracturing are the two most popular fracturing methods because they are more economical and efficient compared with hydraulic fracturing [21]. According to engineering production data [22], the production of the reservoirs stimulated by CO_{2} is 1.9 times as much as the production of those stimulated by N_{2}. The laboratory experiment results indicate that the gas with lower viscosity, higher diffusivity, and lower surface tension can penetrate into smaller pore space to create more complex fracture networks compared with hydraulic fracturing [23, 24]. In addition, the fracture surface created by gas fracturing has a larger roughness and complexity, resulting in a greater increase in permeability [4].

In addition, shale reservoirs always contain kinds of joints caused by the geological deposition and folding [25–27]. The existing joints have a significant influence on the initiation and propagation of the induced hydraulic fractures [28–30]. The fracture networks of jointed reservoirs may be very complex due to the reopening of the existing joints, the expansion of hydraulic fractures, and the intersection between joints and hydraulic fractures [31]. Nitrogen fracturing experiments were conducted on shale samples vertical and parallel to the bedding plane; the results indicated that a relative complex fracture surface is formed in the shale sample vertical to the bedding plane [32]. He et al. [33] performed hydraulic fracturing on shale with bedding planes; the results showed that the bedding planes in shale formation have a significant influence on the propagation of hydraulic fractures. However, the mechanism of the fracture initiation and propagation in kinds of jointed reservoirs is not well investigated. It is important to learn the distribution of fracture networks for the successful design of stimulation in jointed reservoirs.

To this end, the numerical tools COMSOL and MATLAB are used to simulate the hydraulic fracture propagation driven by injection fluids in several jointed reservoirs. The distribution of fracture networks and the development of horizontal and vertical fracture radii are studied in this work.

#### 2. Governing Equations

In the numerical simulation, CO_{2} is injected into the borehole. Then, the rock mass begins to fracture with the increasing injection pressure. The process of CO_{2} fracturing involves solid deformation and fluid seepage. In this part, a series of governing equations are set up for solid mechanic field and flow field. Besides, damage equations are introduced to describe the destruction of the calculation elements.

##### 2.1. Rock Deformation and Damage Evolution Equations

In this work, shale rock is assumed as an elastic continuum material, whose constitutive relation satisfies with the physical equation of elasticity. It should be noted that the influence of pore pressure on stress distribution is also considered in the equation. Thus, the modified physical equation can be induced as where is the total stress tensor, is the total strain tensor, is the shear modulus of rock, is the elastic modulus of the rock, is Poisson’s ratio of the rock, is the volumetric strain, is the Kronecker delta, is the Biot coefficient, and is the pore pressure.

The relationship between strain and displacement is expressed by a geometric equation as follows: where and are the components of displacement in and directions, respectively.

Substituting the modified physical equation (1) and the geometric equation (2) into the equilibrium equation, then the modified Navier-type equation is induced as where is the component of the net body force.

Since the initiation and propagation of hydraulic fractures are studied in this work, a damage model is introduced to characterize the damage condition during the injection process. The damage model is used to determine whether shale damage occurs after every calculation step. For the calculation element, when the stress state meets the maximum tensile stress criterion or the Mohr-Coulomb criterion, the tensile crack or shear crack occurs. It should be noted that the tensile crack is first generated, because the compressive strength is ten times greater than the tensile strength. Equations (4) and (5) are the maximum tensile stress criterion and the Mohr-Coulomb criterion, respectively: where and are the first and third principle stresses; and are the tensile strength and compressive strength of rock, respectively; and is the internal friction angle.

When elements start to be damaged, the elastic modulus reduces correspondingly according to damage theory [34]. The evolution of elastic modulus is defined as where is the initial elastic modulus of rock and is the damage variable and is calculated as [35–37] where and are the first and third principal strains and and are the tensile strain and compressive strain, respectively.

##### 2.2. Gas Flow Equation

Gas flow equations are defined to describe the injection gas flow in this part. The gas continuity equation during gas transportation is defined as where is the gas mass per volume of rock, is the density of the injection gas, is the seepage velocity of the gas, is the source origin, and is the time variable.

On the basis of Darcy’s law, the seepage velocity of gas is shown as where is the permeability of the rock and is the dynamic viscosity coefficient.

Assuming that shale rock is saturated by CO_{2} after the injection, the gas content per volume of rock can be defined as , and is the porosity of the rock. Injected CO_{2} gas enters the supercritical state when the pressure exceeds 7.56 MPa at the temperature 76.8 degrees Celsius [38]. When the injection CO_{2} is transformed from the gaseous state to the supercritical state, density and viscosity change dramatically under the different pressure. The evolution of density and viscosity of CO_{2} varying with pressure is shown in Figure 1. The relationship between density, viscosity, and pressure can be described by interpolating function in the model calculation. Thus, the first item in equation 7 is induced to equation (10) [39] as