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The complex high temperature and high stress are commonly encountered in the hot dry rock for geothermal energy development; the thermal effect on the rock properties and corresponding thermal-hydromechanical coupling process has attracted much more attentions in the field of the energy. Taking the sandstones in Chongqing as a case study, the physical and mechanical experiments of the heat-treated sandstones and corresponding permeability tests under triaxial loading conditions have been widely conducted. It can be seen that the quality, porosity, uniaxial compression strength, and elastic modulus of the heated sandstones vary differently with different heat-treated temperature. As for the permeability tests in the process of gradual failure under triaxial loading conditions, the permeability variation divided by four variation stages is the same as that under room temperature condition, and the initial permeability, minimum permeability, and maximum permeability have been characterized with temperature variation, showing that the permeability variation in a certain temperature range from 400°C to 600°C presents more obvious than that in other temperature ranges. Furthermore, the relationship between the permeability and the crack volumetric strain of the heat-treated sandstones is further analyzed to prove the mechanism of the permeability evolution. In addition, a damage model has been proposed to deeply determine the correlation of the permeability and damage variables, indicating that gradual damage variation has caused obvious cracks to form flow paths and abruptly change the permeability variation, revealing that the damage can describe the permeability evolution of the heat-treated sandstones considering different temperature and loading conditions.

Geothermal energy, as a pollution-free and renewable energy resource, existing in rock masses, has attracted much more attentions in the field of energy; however, the traditional geothermal resources are not enough to meet the energy needs. In recent years, many investigations indicate that most geothermal energy with resources distributed at depths of 3-10 km, which is equivalent to 3081 times the total energy consumption in 2018 in mainland China, is found in hot dry rock to be extracted in the future to solve the energy problem in the world. However, the real hot dry rocks including small pores occur in the environment with high temperature and high stress, especially the high temperature will greatly change the physical properties and corresponding permeability while extracting the heat energy, causing the permeability of hot dry rock is different from that at room temperature and atmospheric pressure. Therefore, the permeability parameters obtained at room temperature cannot be directly used to analyze the deep geothermal engineering [

In recent years, many researchers have investigated the temperature influencing on the mechanical properties of the rocks. Dwived et al. [

Furthermore, the thermal effect on the rock damage and corresponding permeability evolution has also been investigated in recent years. Somerton et al. [

Therefore, deep investigations should be done to describe the variation of the physical properties, mechanical properties, and corresponding permeability. And then, the sandstones in Chongqing as a case study, the experiments and theories considering the thermal effect based on temperature variation are further proposed to analyze the damage variation and permeability evolution considering the thermal-hydromechanical coupling effect.

For decreasing the sandstone difference and ensuring the accuracy of corresponding tests, the testing sandstones taken from western Xindianzi anticline in Chongqing city are selected for the experiments. According to the method by the International Society for Rock Mechanics (ISRM), the size of all tested sandstone specimens is cylindrical with 50 mm in diameter and 100 mm in length approximately. And then, the specimen surface of the sandstones shown in Figure

The specimens and corresponding XRD distribution.

Sandstone specimens

XRD distribution of the sandstone specimens

The heated apparatus named high-temperature box resistance furnace (SX2-4-10) was introduced to heat the rocks, including the heating cell with high-resistance Fe Cr Al alloy wire, the thermal insulation materials with lightweight high aluminum insulation brick and aluminum silica fiber composite lining, and the control part with PID intelligent program temperature controller, which has temperature controlling precision of ±1°C.

All tests will be carried out on a rock servo-controlled triaxial equipment named Rock 600-50HT PLUS manufactured by TOP-INDUSTRIE in France plotted in Figure

Triaxial multiphysics coupling testing system.

(1) Divide the specimens into nine groups, and set one group of specimens under room temperature conditions and other eight groups heat-treated by 5°C/min to the setting temperature 100°C, 200°C, 300°C, 400°C, 500°C, 600°C, 700°C, and 800°C, and the specimens are kept in the setting temperature for 2 h and then cooled the specimens to the room temperature. (2) Measure the properties such as the initial quality, volume, and porosity of every group. (3) Conduct the mechanical tests of the heat-treated sandstones with a loading rate of 0.0005 mm/s to obtain corresponding stress and strain.

As for the seepage tests of the heat-treated sandstones, steady method has been used to measure the rock permeability [

Where ^{2}), ^{3}) from the pump in time ^{2}),

Before the permeability testing of the heat-treated sandstones, all the specimens should be saturated, vacuumized for 4 h, and dehumidified for 4 h, then immersed into distilled water for 16 h to fill the rock pores. And then, the saturated specimens are taken into the apparatus and set the confining pressure to the presetting value. Design the testing conditions as follows: (1) confining pressure and permeable pressure are, respectively, set to a certain value, and the axial loading rate is set to 0.0001 mm/s until the rocks have been failed. (2) Suppose the confining pressure as 12 MPa and 16 MPa combining the permeable pressure of 2 MPa, 3 MPa, 4 MPa, 5 MPa, 6 MPa, and 7 MPa to conduct the seepage tests. Furthermore, the testing data are recorded and saved, and the permeability of the heat-treated rocks under different stages can be measured to describe the permeability variation under the designed loading conditions.

Some free water and bound water in the natural rocks may evaporate in the process of the heat treatment and greatly change corresponding physical and mechanical properties. The mass variation of sandstones treated by different temperature has been obtained and plotted in Figure

Mass variation rate of the heat-treated sandstone.

The porosity variation of the heat-treated sandstones considering different heated temperature [

Porosity variation of the heat-treated sandstone.

Where

The uniaxial compressive strength of the heat-treated sandstone [

Uniaxial compressive strength of heat-treated sandstone.

The elastic modulus of the heated sandstone considering different heated temperature is plotted in Figure

Elastic modulus of the heat-treated sandstone.

Where

For describing the permeability of the heat-treated sandstones, the load combination of the axial pressure, different confining pressure, and different water pressure is considered to apply for the permeability tests, and corresponding testing data are plotted in Figures

Permeability of the sandstones considering axial pressure 10 MPa and confining pressure 12 MPa considering different heated temperature.

Permeability of the sandstones considering axial pressure 10 MPa and confining pressure 16 MPa considering different heated temperature.

Therefore, the permeability of the heat-treated sandstones by different heated temperature even under same loading conditions is different; the main reason is that the heat treatment causes inhomogeneous thermal stress in the sandstones to form new cracks and changes the flow paths, explaining the obvious thermal effect on permeability variation considering different heated temperature.

The comparison plotted in Figures

Permeability evolution of the heat-treated sandstone considering different temperatures.

Temperature 25°C~200°C

Temperature 300°C~500°C

Temperature 600°C~800°C

Also, the permeability evolution curves of the heat-treated sandstones under loads combination indicate that the variation patterns of mechanical response and permeability under different confining pressures are similar. However, it can also be observed from the Table

Different permeability of the heat-treated sandstones considering different temperature.

Temperature/(°C) | 25 | 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 |
---|---|---|---|---|---|---|---|---|---|

Initial permeability | 3.8 | 1.74 | 1.09 | 1.74 | 3.34 | 6.10 | 5.81 | 3.89 | 4.10 |

Minimum permeability | 1.68 | 0.85 | 0.11 | 0.32 | 1.93 | 5.14 | 2.92 | 0.69 | 0.87 |

Maximum permeability | 38.22 | 37.22 | 14.05 | 23.49 | 34.20 | 40.58 | 33.25 | 32.08 | 32.50 |

Permeability and crack volumetric strain variation vs. axial strain of the heat-treated sandstones.

25°C~200°C

300°C~500°C

600°C~800°C

The above figures describe the permeability variation of the heat-treated sandstones by different heated temperature. For better presenting the permeability variation in the process of gradual damage under triaxial loading conditions, the crack volumetric strain proposed by Martin and Chandler [

Where

The relationship of the permeability and the crack volumetric strain under triaxial loading conditions has been calculated and plotted in Figure

Curves of the crack volumetric strain and permeability considering different heated temperature.

25°C~200°C

300°C~500°C

600°C~800°C

As we all know, rock cracks will initiate and generate under thermal conditions, resulting in the variation of the mechanical properties of the heat-treated rocks; thus, the thermal damage should be considered and corresponding damage variable [

Where

Thermal damage variables of the heat-treated sandstone by different heated temperature.

Furthermore, the relationship between the permeability and the thermal damage has been investigated for the sandstones treated by different heated temperature; thus, the curves of the permeability and thermal damage considering the axial pressure 10 MPa and confine pressure with 12 MPa and 16 MPa have been compared. It can be seen from the Figure

Comparison of the permeability and the thermal damage variable.

Confining pressure 12 MPa

Confining pressure 16 MPa

As evidenced by the experimental results mentioned above, microcracks tend to propagate causing obvious damage inside the sandstones under loading conditions, which induces significant variation in permeability [

Where

In which, the Weibull parameters are supposed to be the functions of temperature

And the Drucker–Prager criterion is introduced to be the failure criterion written by

Where

Furthermore, the damage occurs under a critical stress conditions; thus, the damage variable should be written by

Where

Based on Lemaitre’s theory [

Where

And suppose the stress-strain of the sandstones obeying the generalized Hook’s Law, the effective strain tensor can be written by

Therefore, as for the stress before reaching the critical damage, it can be expressed by quadratic function through the origin points (0,0), and as for the stress once exceeding the critical damage, the Eq. (

Where

In addition, considering the principle stress-stain

Therefore, the relationship of the stress and strain of the heat-treated sandstone under hydromechanical coupling conditions can be expressed by

In addition, the measured axial deviatoric stress can be written by

Therefore, a simplified constitutive model based on real experiments is written by

In which,

In which,

And then, the statistical parameters can be described by

Where

Finally, parameters A and B have been determined considering the continuity of the first-order derivative as follows [

In which,

Based on the mentioned theory and corresponding experiments, the curves about the damage vs. axial strain and damage vs. permeability of the heat-treated sandstones are plotted in Figure

Curves of the permeability and damage variable vs. axial strain of the heat-treated sandstones.

25°C~200°C

300°C~500°C

600°C~800°C

In addition, increasing axial strain representing the cracks propagation can describe the permeability variation; however, the damage and corresponding permeability of the sandstones with different heated temperature are different, indicating that the temperature has important thermal influence on the rock damage and further permeability evolution.

And for better describing the permeability of the heat-treated sandstones [

Where ^{2});

The permeability evolution the damage variables of the heat-treated sandstone.

25°C

100°C

200°C

300°C

400°C

500°C

600°C

700°C

800°C

The heat-treated sandstones as a case study, the physical properties and mechanical properties are researched for the heat-treated sandstones, and also, the permeability evolution under triaxial loading conditions is investigated based on the experiments and theoretical analysis; thus, the corresponding permeability characteristics have been deeply obtained to reveal the evolution mechanism of the heat-treated sandstones considering the thermal effect by different heated temperature. The main conclusions obtained as follows:

The physical properties and the mechanical properties related to the heated temperature such as the mass, porosity, elastic modulus, and uniaxial compression strength have been obtained and the variations satisfy with the Boltzmann equation, indicating that the heat treatment causes obvious thermal effect on the sandstones properties

The permeability of the heat-treated sandstones varies including the descending, smooth changing, stable increasing and abrupt ascending stage, and the characterized permeability have been obtained in range of different temperature, indicating that the heat treatment causes more effective flow paths

The permeability and the crack volumetric strain has been deeply researched, indicating that loads causing different crack propagation resulting in different permeability evolution, and also the relationship between the permeability and crack volumetric strain reveals the important thermal effect on the permeability

A constitutive model considering the thermal-hydromechanical coupling effect has been proposed to reveal the relationship of the damage and the permeability, indicating that the damage can represent the evolution process of the permeability under the loading conditions considering the thermal effect by different heated temperature

The data in this manuscript is based on the lab experiments, and the analysis is based on the experimental data.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The research is financially supported by the National Natural Science Foundation of China No. 51779021 and the Fundamental Research Funds for the Central Universities No. 2020CDCGJ021. The authors declare that there is no conflict of interest regarding the publication of this paper.