Journal of Engineering

Volume 2018 (2018), Article ID 6793191, 15 pages

https://doi.org/10.1155/2018/6793191

## Thermomechanical Behavior of Late Indo-Chinese Granodiorite under High Temperature and Pressure

^{1}College of Construction Engineering, Jilin University, Changchun 130026, China^{2}Key Laboratory of Groundwater Resource and Environment, Ministry of Education, Jilin University, Changchun 130026, China^{3}College of Applied Technology, Jilin University, Changchun 130026, China^{4}Geological Survey Institute of Liaoning Province, No. 42, Ningshan Middle Road, Huanggu District, Shenyang City, Liaoning Province, China

Correspondence should be addressed to Shuren Hao and Lin Bai

Received 5 September 2017; Revised 25 December 2017; Accepted 1 January 2018; Published 1 February 2018

Academic Editor: Phillips O. Agboola

Copyright © 2018 Yanjun 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

This study investigates the influence of temperature, effective stress, and rock fracture on the bulk modulus and Biot’s coefficient of granodiorite from a hot dry rock geothermal reservoir using the triaxial compression test. Three types of representative granodiorite samples were chosen for comparative experiments. The experiments were conducted with 0–55 MPa effective stress under cyclic loading. Results show that bulk modulus can continuously increase with the increase in effective stress at a constant temperature. The influencing law on Biot’s coefficient is opposite that on bulk modulus. Interestingly, the temperature effects on the drained bulk modulus and Biot’s coefficient depend on the effective stress. With regard to rock fractures, temperature and effective stress exert similar effects on the Biot’s coefficients and bulk moduli of the samples compared with those of intact rock. The data of this experiment have a wide range of applications because most of the reservoir rocks in dry-hot-rock geothermal system have lithology of granite or granodiorite. The change law of rock modulus and Biot’s coefficient with the temperature and pressure in this experiment provide the data basis for the future simulation calculation making the considered factors more comprehensive and the results closer to the real situation.

#### 1. Introduction

The thermomechanical response of saturated porous rock under the influences of temperature, effective stress, and rock fracture offers great significance for field work. In particular, the change law of the parameters under these factors provides a good reference for the disposal of greenhouse gas and exploration of petroleum, natural gas, and hot dry rock resources. For example, when exploiting hot dry rock, the change in a rock mass’s temperature and pore pressure can alter Biot’s coefficient and cause the redistribution of the gravity field [1]. For another, injection of cooling CO_{2} into the deep ground will causes the decrease of vertical effective stress and thus change Biot’s coefficient promoting the reduction of the porosity [2].

By triaxial compression tests, Handin et al. [3] point out the rock’s mechanical deformation characteristics are related to rock porosity. Song and Renner [4] and Fabricius [5] studied Fontainebleau sandstone and showed that rock Biot’s coefficient varies with the change in rock porosity. Furthermore, Ramos da Silva et al. [6] proposed a fitting relationship between Biot’s coefficient and the porosity of saturated limestone. This relationship indicated the increase in Biot’s coefficient with increase in rock porosity. However, altering the temperature not only changes stress but also modifies the physical properties of rock, including the rock bulk modulus and thermal expansion coefficient. Such effects generate nonlinear rock physical properties [7–10]. The nonisothermal triaxial compression experiment of Gallesville sandstone and Feichtinger sandstone has been performed by Blacic et al. [11] and Alireza et al. [12]. Both of the studies show that the thermomechanical parameters of rock mass, such as Biot’s coefficient, bulk modulus, Young’s modulus, and Poisson’s ratio, are affected by temperature and effective stress. The presence of rock fracture is one of the important influences that cause the rock anisotropy. For cracked rock, Goodman et al. [13] proposed an equivalent continuum model of fractured rock mass. And a series of calculation models of fractured rock deformation are established. Equivalent medium parameters are used to describe rock deformation characteristics [14, 15]. Experimental and numerical studies [16–18] also showed that the fractured rock conditions caused a substantial effect on Biot’s coefficient, rock bulk modulus, and other mechanical parameters. However, there is less study on the equivalent deformation parameters of fractured rock under nonisothermal condition.

Numerical simulation is an important technical means for studying and predicting the engineering problem of carbon dioxide geological reservoirs, nuclear waste disposal, dry rock development, and other deep rock mechanics problems [19–23]. Accurately obtaining the rock parameters is the key factor to obtain the accurate simulation results. However, in most of current simulations, the rock parameters are assumed to be constant [19, 20, 22–24]. However, during the exploitation of deep geological resources, parameters of the rock, such as rock bulk modulus and Biot coefficient, will change due to the change of temperature and pressure, thus leading to the numerical simulation results deviate from the true value if we ignore these features [25]. Bai [26] studied the change law of Biot coefficient of reservoir sandstone form a typical CO_{2} geological storage site at Ordos of China, under different temperature and pressure conditions and applied it to the numerical simulation of formation deformation of the site, finding the simulation result more close to the measured data. However, during the development of dry-hot rocks, the change of the strata stress has more obvious influence on the bulk modulus and Biot coefficient of rocks, especially the fractured [23, 24]. The late Indo-granodiorite was selected for the investigation, because it is similar to the geothermal reservoir rock found in China’s first hot dry rock target area, specifically, the Gonghe Basin of Qinghai. More importantly, the lithology of reservoir rock in most dry-hot rock sites in the world is granite or granodiorite [19–23, 27]. Therefore, the rock used in this experiment is very representative.

Given the problems mentioned above, the influences of temperature, effective stress, and rock fracture on bulk modulus and Biot’s coefficient were investigated in this study aiming at experimentally quantifying the influence. To simulate the actual effective stress and pore stress of underground rock, which is usually caused by the injection of water into and out of reservoirs, the temperature was set to increase gradually, and circular loading and unloading axial pressures and confining pressure were applied under constant temperature [28].

To simulate the actual effective stress and pore stress of underground rock, which is usually caused by the injection of water into and out of reservoirs, the temperature was set to increase gradually, and circular loading and unloading axial pressures and confining pressure were applied under constant temperature [28].

#### 2. Theoretical Background

##### 2.1. Theory of Rock Elasticity under the Influence of Pressure and Temperature

Under drainage conditions, temperature alters the thermal expansion and pore fluid quality of rock mass as follows: where is the volume strain, is the initial temperature, is the change in temperature, is the volume thermal expansion coefficient of solid skeleton, is the effective pressure, and is the bulk modulus of drainage.

According to the principle of effective stress, and the effective stress can be obtained using the following equation:where is the effective stress; is the total stress; is the pore water pressure; is the Kronecker constant, which takes the value of either 0 or 1; and is Biot’s coefficient, which can be defined as the efficiency of the pore fluid in rock in counteracting the external total stress.

The concept of effective stress is described by Berryman [29] and Gueguen [30], in different fields. The study of Zimmerman [31] provided a theoretical basis on analyzing the influence of Terzaghi effective stress on the effective rock bulk modulus. Bouteca [32] and Hart (1998) yielded similar conclusions after experimentation. Therefore, the expression of pressure and effective stress herein is based on Terzaghi’s law. The Terzaghi law is derived from energetics; therefore, the effects of effective stress and temperature on Biot’s coefficient can be analyzed from the perspective of energy.

The fluid mass heat was calculated using the coefficients of thermal expansion of pore fluid and as follows:where is the fluid density, is the porosity, is the pore water pressure, and is the ratio of fluid mass content to the total rock mass with the same density. Normally, is smaller than , implying that is negative, which indicates that the fluid mass decreases with an increase in temperature. The change in pore fluid quality is affected not only by temperature but also by the changes in pore pressure and rock deformation. where is the density in the initial state, is the Skempton pore pressure parameter, and is the nondrainage volume modulus. The pore pressure change rate and confining pressure are related to the changes in confining pressure in the nondrainage experiment. Equations (4) and (5) describe the change law of the heating expansion of the rock pore fluid, and the heating expansion of rock is related to the rock solid particles and the rule of thermal expansion of the skeleton. The rock is composed of a variety of minerals; hence, the solid thermal expansion coefficient of rock can be calculated using the coefficient of thermal expansion of the composition [33–35]. For example, in a solid phase composed of two kinds of minerals, the coefficient of thermal expansion () can be estimated by the following equation:where and are the bulk modulus and the coefficient of thermal expansion of components, respectively. Campanella and Mitchell [36] believed that the coefficient of thermal expansion of rock matrix is equivalent to the coefficient of the thermal expansion of solid particles . Palciauskas and Domenico [37] argued that the coefficient of thermal expansion of rock matrix is related to the coefficient of the thermal expansion of solid particles and the coefficient of thermal expansion of pore fluid .

The volume change of rock pore fluid and solid particles differs with varying effective pressure and temperature. Consequently, rock parameters, such as bulk modulus and Biot’s coefficient, change correspondingly.

Biot’s coefficient is calculated as followswhere is Biot’s coefficient, is the rock drainage volume modulus, and is the drainage volume modulus of the rock solid particle skeleton. The calculation formula of bulk modulus is as follows:where is the rock Young’s modulus and is the rock Poisson’s ratio. The stress-strain curve can be generated to obtain the bulk modulus. Through the drainage and nondrainage tests, the rock drainage volume modulus and the drainage volume modulus of rock solid particle skeleton can be measured. These variables can be entered into (8) to calculate for Biot’s coefficient.

Han et al. [15] derived the equivalent elastic modulus and equivalent Poisson’s ratio based on the assumption that the rock block is isotropic elastic body and the stress and displacement of the fracture meet the linear relationship. The equivalent elastic modulus and equivalent Poisson’s ratio are expressed aswhere and are equivalent modulus and equivalent Poisson’s ratio of the fractured rock. and are the normal stiffness and the tangential stiffness of the fracture. is the fracture spacing, and is the angle of the fracture.

#### 3. Test Sample, Test Instruments, and Test Steps

##### 3.1. Test Sample

###### 3.1.1. Selection of Test Sample

The cost of sampling in the Gonghe Basin of Qinghai is high because of the area’s deep reservoir. Therefore, all samples (granodiorite) used in our experiment were extracted from the late Indo-China samples in the Jilin Monkey Ridge area, the properties of which are highly similar to those in the Gonghe Basin. We compared the two samples in terms of four different properties to verify whether the substitution was valid or not. The results of the composition analysis by X-ray diffraction and scanning electron microcopy (SEM) are shown in Table 1 and Figure 1.