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.
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 [
By triaxial compression tests, Handin et al. [
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 [
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 [
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 [
Under drainage conditions, temperature alters the thermal expansion and pore fluid quality of rock mass as follows:
According to the principle of effective stress,
The concept of effective stress is described by Berryman [
The fluid mass heat
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 follows
Han et al. [
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
Composition of the granodiorite samples from the Jilin Monkey Ridge area and the Gonghe Basin of Qinghai.
Area | The relative contents of minerals (%) | |||||||
---|---|---|---|---|---|---|---|---|
Quartz | Alkali feldspar | Anorthose | Calcite | Amphibole | Andreattite | Kaolinite | Chlorite | |
Gonghe Basin | 39 | 14 | 18 | 1 | 2 | 18 | 4 | 4 |
Monkey Ridge | 27 | 18 | 26 | 0 | 0 | 29 | 0 | 0 |
SEM of the granodiorite. (a) Jilin Monkey Ridge sample and (b) Gonghe Basin of Qinghai sample.
The results show the high similarity between the two samples. Few obvious pores were observed; flaky and granular minerals were both found in the two samples, indicating that rock illite or illite/smectite was present in the two areas. Furthermore, quartz mineral was observed under a higher magnification.
Through density, wave velocity, porosity, and permeability, we compared the degree of compaction of the two samples and specific parameters are shown in Table
Rock parameters of the granodiorite samples from the Jilin Monkey Ridge area and the Gonghe Basin of Qinghai.
Area | Dens |
|
|
Porosity | Permeability |
---|---|---|---|---|---|
(g/cm2) | (km/s) | (km/s) | (%) | (1 |
|
Gonghe Basin | 2.67 | 2.683 | 3.968 | 1.89% | 0.0312 |
Monkey Ridge | 2.56 | 2.229 | 3.379 | 2.67% | 0.0627 |
As shown in Figure
Polarizing micrographs of the granodiorite. (a) Jilin Monkey Ridge sample and (b) Gonghe Basin of Qinghai sample.
The comparison results show the validity of the substitution of the samples from the Gonghe Basin with those extracted from the late Indo-China area. The results obtained from our research can be used in exploiting other hot dry rock reservoirs.
The trial used three sets of samples divided into intact undisturbed granodiorite and artificial vertical and horizontal fractured granodiorite (Figure
Rock samples. I: complete undisturbed granodiorite, II: artificial vertical fractured granodiorite, and III: artificial horizontal fractured granodiorite.
In this paper, the traditional triaxial test was applied to achieve the research goals. In the process, a TAW-2000 computer control servo triaxial rock testing machine was employed as is shown in Figure
TAW-2000 triaxial pressure testing machine.
The machine consisted of test, pressing, and control sections (Figure
The main structural diagram of the experimental device.
The samples were divided into three groups, namely, complete undisturbed granodiorite (I), artificial vertical fractured granodiorite (II), and horizontal artificial cracked granodiorite (III). First, the samples were saturated to ensure a constant initial pore pressure. The three groups of test specimens were then pretreated. During the process, the rock pore pressure system was opened to air. At the same time, the axial and confining pressures were controlled within the range 0–60 MPa under a 5 MPa/min rate, with three-time loading and unloading cycle to prevent negative factors from influencing the experimental system. After the pretreatment, the samples’ confining and axial pressures reached 2 MPa, which was greater than the saturated water pressure at 150°C. These conditions therefore prevented the water-saturated samples from overflowing through gasification. Second, the axial and confining pressures were repeatedly loaded and unloaded at 1 MPa/min within 2–55 MPa. Each cycle consisted of three stages: the uniform loading stage, the equilibrium stage after 15 min, and the uniform unloading stage. Each complete cycle was processed under five different grades of temperature (0, 60, 90, 120, and 150°C), and the temperature error range was ±2°C. The heating rate restriction within 2–5°C/min was adopted to prevent rock damage and changes in microstructure from uneven heating. Additionally, strain, Young’s modulus, and other rock parameters were measured during the test to ascertain the effects of the temperature and pressure coupling on rock mechanical parameters. After the pretreatment of the second group, the third group, which included the artificial vertical and horizontal fractured granodiorite samples (II and III), was tested. During the test, the axial and confining pressures were cyclically loaded and unloaded at a rate of 1 MPa/min within 2–55 MPa. Each complete cycle was processed under three different grades of temperature (60, 90, and 120°C) at an error range of ±2°C and the same heating rate at 2–5°C/min.
The two abovementioned comparison experiments performed under the same pressures and temperatures were designed to obtain the influence of fracture on rock mechanical parameters. Finally, undrained triaxial tests were performed on the three groups of samples to measure the strain. Biot’s coefficient was calculated by the indirect method. The influences of temperature, effective pressure, rock inner fracture, and other factors on Biot’s coefficient were determined from the experiments presented above.
Through rock uniaxial and triaxial compression testing, as well as rock hydrostatic testing, we obtained the mechanical parameter of the rock granodiorite samples. Moreover, with the steps elaborated in Section
The rock Poisson’s ratio and Young’s modulus E were measured under half of the peak strength by the rock uniaxial test. The results of the test are shown in Table
Elastic parameters of the granodiorite specimens.
Poisson’s ratio |
Young’s modulus |
Peak strength (MPa) | Yield strength (MPa) |
---|---|---|---|
0.28 | 56.8 | 137.5 | 98 |
The indirect method for the determination of rock Biot’s coefficient requires the knowledge of rock framework’s bulk modulus. Unjacketed
Framework’s bulk modulus of the three groups of granodiorite.
Groups | I | II | III |
---|---|---|---|
Rock framework’s bulk modulus (GPa) | 19.35 | 19.85 | 19.68 |
Under the influence of temperature and stress, rock shows nonlinearity. Even in the stage of elastic loading-unloading, irreversible inelastic loading-unloading deformation is induced [
Inelastic deformation during the cyclic loading process.
As shown in Figure
Inelastic deformation under different temperatures.
Temperature (°C) | 30 | 60 | 90 | 120 | 150 |
---|---|---|---|---|---|
Inelastic deformation ( |
3.7 | 5.7 | 10.3 | 13.7 | 15.6 |
The experiment was performed in accordance with the procedure presented in Section
Relationship between drained bulk modulus and effective stress and temperature.
Effective stress significantly influences the drained bulk modulus but the comparative effect of temperature is meager. As displayed in Figure
Relationship between bulk modulus and temperature within different stress region.
Low stress region
High stress region
Results revealed that the temperature effects on granodiorite can be described by interrelations between the bulk modulus and the thermal expansion coefficient. The thermal expansion coefficient influenced by stress, as well as the heat-transfer processes influenced by path, affects the rock thermomechanical behavior. Different heat-transfer modes (constant pressure and constant volume) resulted in different trends of temperature effects on the bulk modulus of rocks and minerals. As observed previously by Carmichael [
The temperature effects on bulk modulus under constant pressure can be viewed as the summation extrinsic and intrinsic changes. At the low stress regime, the heating process was dominated by a constant-pressure heat-transfer mode, and the rock particles expanded to the external space. In this case, the volumetric effects were dominant and softened the rock. By contrast, at the high stress regime, the path of the external expansion was constrained by high confining stress, and the rock particles shifted to internal expansion. In this condition, the pressure effects prevailed and stiffened the rock. Therefore, the competition between volume and pressure with respect to temperature contributes to the three stages of variation characteristics of the late Indo-granodiorite. A transition region existed with a very wide variation range (12–23 MPa for the intact sample), and this can be explained by the anisotropic rock components.
The experiment was repeated on the cracked specimens (vertical [II] and horizontal [III]), which were preprocessed to eliminate the effects of inelastic deformation as a consequence of incomplete crack closure. The results were also modified depending on the amount of creep deformation from long-time loading listed in Table
Relationships of drained bulk modulus with effective stress and temperature in cracked specimens: (a) specimens within vertical fractures and (b) specimens within horizontal fractures.
By comparing the results of the cracked rock specimens with the former test findings, we obtained a similar conclusion. In particular, the intact rock specimens subjected to the same temperature yielded an increase in bulk modulus with increased effective pressure. Furthermore, under the same pressure, the variation trend of bulk modulus with temperature differs because of the varying stress; the drained bulk modulus decreases with increasing temperature in the low stress region and increases with increasing temperature in the high stress region. Notably, the low stress region is 0–20 MPa and 0–17 MPa for the rock samples within horizontal fractures, whereas the high stress region is 33–55 MPa for the rock within vertical fractures and 27–55 MPa for rock within horizontal fractures during this series of experiments.
The change laws for the intact and cracked rocks under different effective stresses and temperatures remained the same. The equivalent rock tangent bulk modulus decreased with temperature in the low pressure regime and increased with temperature in the high pressure regime. However, compared with intact rock, the cracked rock required additional pressure to alter the negative effect of temperature on the equivalent bulk modulus.
The cracked rocks mass consists of joints and isotropic block matrices separated by the joints. We assume that the thermodynamic parameters of the rock blocks belong to specimens II (containing vertical cracks) and III (containing horizontal cracks) remain the same with the intact specimens I. Because the prefabricated cracks of specimens II and III in this research extend to vertical and horizontal direction and the rocks are compressed by equal axial pressure and confining pressure, there is no displacement along the tangential direction of the fracture. Therefore, the existence of joints in the rock mass can be viewed as altering the mechanical boundary conditions of the blocks. On the microlevel a large number of discrete points exist within the scope of interface. Contact parts of rock particles can be considered as the constraint boundary with fixed pressure; while the discrete parts can be viewed as free boundary in a limited range, the rock particles could freely expand when heated. In the presence of equivalent low stress regime, for the rock blocks, the volumetric effects were more distinct than that of the intact specimens I. As a result, more pressure is needed to change the negative effects of temperature on the bulk modulus. As fractures developed further, greater pressure was needed for corresponding changes. In other words, the more area of the block is exposed to the fracture, the more boundary is changed, and more additional stress is needed. And the discrepancy between specimens II and III in the critical pressure that change the influence type of temperature on the bulk modulus is also consistent with this phenomenon.
We can also infer from Figure
Experimental results of the specimens with different failure modes: relationship of drained bulk modulus with effective stress at (a) 60°C, (b) 90°C, and (c) 120°C.
With the results of the rock framework’s bulk modulus (Table
Biot’s coefficient as a function of Terzaghi effective pressure for intact rock samples.
Biot’s coefficient as a function of Terzaghi effective pressure for cracked rock samples: (a) specimens within vertical fractures and (b) specimens within horizontal fractures.
As shown in Figure
At lower stress, the changing trend of Biot coefficient with effective stress presents the nonlinear characteristics whereas in higher stress it shows linear behavior. This is mainly determined by the structure characteristics of the granodiorite. Granodiorite is characteristic with compact structure and low porosity. The microfractures close quickly when compressed, and the increasing stress makes the deformation from microfracture and porosity transfer to rock matrix. Because the fissures containing in fractured rocks in this paper is perpendicular to the axial and confining pressures, the deformation process of the specimens is shown as the summation of cracks closure and porosity and rock particles’ compression when subjected to the same axial and confining pressure. The presence of fractures has not changed the fact that the deformation is elastic. And the cracked specimens can be treated as equivalent continuum media. Therefore the calculation of equivalent Biot coefficient is still within the scope of quasi-static theory of poroelasticity. The Biot coefficient and equivalent Biot coefficient for intact and cracked rock samples were compared under the same temperature and pressure condition as is shown in Figure
Biot’s coefficient as a function of Terzaghi effective pressure for different types of granodiorite specimens at (a) 60°C, (b) 90°C, and (c) 120°C.
A series of experiments were performed to study the effects of temperature and Terzaghi effective stress on the bulk modulus and Biot’s coefficient of Indo-granodiorite rocks. The bulk modulus and Biot’s coefficient of the intact as well as the cracked specimens were determined through the triaxial compression experiment. However, it should be noted that, according to the research of Goodman et al., we regard the cracked samples as equivalent continuum model and discuss the equivalent rock deformation parameters of them. The main conclusions drawn from this study can be summarized as follows: By means of experiments we compared the composition, structure, and degree of density of the granodiorite samples taken from Jilin Monkey Ridge and Gonghe Basin of Qinghai, and we found that the two samples are very similar in all respects. Given that sampling from Gonghe Basin is too difficult, the Jilin Monkey Ridge samples are good alternatives to Republican Basin samples to investigate the thermomechanical behavior of the granodiorite. The drained bulk modulus was strongly affected by effective pressure. As the effective stress increases from 3 MPa to 55 MPa, the drained bulk modulus increases from 3.1 GPa to 7.9 GPa and from 2.5 GPa to 8.2 GPa, respectively, at temperatures 30 and 150°C. Along with the change in temperature and pressure, the trend of Biot’s coefficient countered the trend of the drained bulk modulus. When effective stress increased from 0 to 60 MPa and temperature increased from 30°C to 150°C, Biot’s coefficient of granodiorite varied between 0.55 and 1. The effect of temperature on thermomechanical parameters was more complicated than the pressure and can be divided into three stages: a low stress regime, where the temperature derivative of the drained bulk modulus was negative; a high stress regime, where the temperature derivative of the drained bulk modulus was positive; and a transitional regime. When the temperature regularly changed from 30 to 150°C, the bulk modulus decreased as much as 15% in the low effective stress regime while increased as much as 12% in the high effective stress regime. Such reaction of the granodiorite to pressure and temperature can be explained by a potential competition between volume and pressure with respect to temperature. According to equivalent elastic theory, the joints are treated as elastic medium. And when subjected to heat and stress, they were not sensitive to hardening effects caused by stress but to the softening effects by temperature. In the fractured rock, the temperature and effective stress exerted effects on the samples’ equivalent Biot coefficient and equivalent bulk modulus similar to those in the intact rock. However, the ranges of the low and high stress regimes differed. The cracked rock required more pressure to change the negative effect of temperature on the bulk modulus.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This study was supported by the National High Technology Research and Development Program of China (863 Program) (no. 2012AA052801), the Natural Science Foundation of China (no. 41372238 and no. 41602243), Specialized Research Fund for the Doctoral Program of Higher Education of China (no. 20110061110055), and Cooperative Project of Government and Jilin University: New Energy Technology Project (SXGJSF2017-5).