E ﬀ ects of Cyclic Heating and Water Cooling on the Physical Characteristics of Granite

: This paper aims to study the e ﬀ ect of cyclic heating and ﬂowing-water cooling conditions on the physicalproperties ofgranite. Ultrasonictests, gas measuredporosity, permeability, and microscope observations were conducted on granite after thermal treatment. The results showed that the velocity of P- and S-waves decreased as the number of thermal cycles increased. The porosity increased with the number of the thermal cycles attained at 600 ◦ C, while no apparent changes were observed at 200 and 400 ◦ C. The permeability increased with the increasing number of thermal cycles. Furthermore, microscope observations showed that degradation of the granite after thermal treatment was attributed to a large network of microcracks induced by thermal stress. As the number of thermal cycles increased, the number of transgranular microcracks gradually increased, as well as their length and width. The quantiﬁcation of microcracks from cast thin section (CTS) images supported the visual observation.


Introduction
Geothermal energy is an important component of renewable energy, and most of the deep geothermal resource is stored in hot dry rock (HDR) [1]. HDR is defined as a hot and almost waterless geothermal system. Common HDR systems include granite or other crystalline basement rocks. Rock temperature varies from 150 to 500 • C at maximum depths of 5-6 km [2,3]. The use of deep HDR resources will contribute to the mitigation of the environmental pollution caused by traditional fossil energy [4]. Enhanced geothermal system (EGS) is an effective engineering method to exploit HDR resources [5,6]. To enhance the permeability of HDR, typical methods include increasing the heat transfer area and improving the efficiency of the hydraulic fracturing system. During the creation of the fracture network and the subsequent thermal energy exploitation, water is injected into the bedrock [7]. Studying the variation of rock physical properties after cyclic thermal treatment with flowing water cooling can provide a theoretical foundation for the EGS system.
A number of previous studies have conducted experiments to investigate the evolution of the physical and mechanical properties of the bedrock under temperature variations. Typical factors to consider include the heating temperature, heating rate, and cooling condition. With increasing temperature, rock experiences more significant deterioration. Hydraulic properties, such as porosity [8,9] and permeability [10,11], increase with a rise of the temperature, whereas mechanical

Methodology of Heating and Cooling
The granite cylinders were used for the measurement of porosity, permeability, P-and S-wave velocity measurements, whereas the granite disc samples were used for microstructural characterization. The P-wave and S-wave velocity of the cylindrical specimens were measured prior to thermal treatment. Thirty-one cylinders and thirty-one discs with similar P-wave velocities were divided into five groups with six specimens in each group (see Table 1). A SX-G04123 box-type electric furnace was used in heating (power 2.5 kW, maximum temperature 1200 °C). The process of heating a rock specimen to a pre-determined temperature and then cooling it down to room temperature with water was regarded as one thermal cycle. A heating rate of 1.5 °C/min was used to avoid the influence of thermal shock [39]. The pre-determined temperature, once reached, was kept constant for 5 minutes in the furnace to avoid the influence of subsequent heating time at a predetermined temperature. The specimens were then taken out of the furnace and cooled down to room temperature (20 °C) with flowing water (shown in Figure 2). For each group, the pre-determined temperatures were set to 100-600 °C to mimic a high-temperature condition of deep bedrocks in an EGS system. The numbers of thermal cycles for each group was either 0 (i.e., no thermal treatment), 1, 2, 4, 8, and 16. A7, B7 A8, B8 A9, B9 A10, B10 A11, B11 A12, B12 4 A13, B13 A14, B14 A15, B15 A16, B16 A17, B17 A18, B18 8 A19, B19 A20, B20 A21, B21 A22, B22 A23, B23 A24, B24 16 A25, B25 A26, B26 A27, B27 A28, B28 A29, B29 A30, B30

Methodology of Heating and Cooling
The granite cylinders were used for the measurement of porosity, permeability, P-and S-wave velocity measurements, whereas the granite disc samples were used for microstructural characterization. The P-wave and S-wave velocity of the cylindrical specimens were measured prior to thermal treatment. Thirty-one cylinders and thirty-one discs with similar P-wave velocities were divided into five groups with six specimens in each group (see Table 1). A SX-G04123 box-type electric furnace was used in heating (power 2.5 kW, maximum temperature 1200 • C). The process of heating a rock specimen to a pre-determined temperature and then cooling it down to room temperature with water was regarded as one thermal cycle. A heating rate of 1.5 • C/min was used to avoid the influence of thermal shock [39]. The pre-determined temperature, once reached, was kept constant for 5 minutes in the furnace to avoid the influence of subsequent heating time at a pre-determined temperature. The specimens were then taken out of the furnace and cooled down to room temperature (20 • C) with flowing water (shown in Figure 2). For each group, the pre-determined temperatures were set to 100-600 • C to mimic a high-temperature condition of deep bedrocks in an EGS system. The numbers of thermal cycles for each group was either 0 (i.e., no thermal treatment), 1, 2, 4, 8, and 16.

Ultrasonic Wave Velocity Measurements
Before measuring the porosity and permeability, P and S-wave velocities of the rock specimens were measured after thermal treatment for different temperatures and numbers of thermal cycles were measured using an ultrasonic apparatus (HS-YS2A Type). Two transducers fixed by a holder applying the same force were positioned at the ends of the specimen. A pressure gauge and hand wheel were used to apply an equal force with transducers during every test (see Figure 3). Each specimen was tested twice to ensure repeatability.

Porosity and Gas Permeability Measurements
We measured the porosity and steady-state permeability of the three temperature groups (200, 400, and 600 °C) using an SCMS-E high-temperature, high-pressure, multi-parameter core measurement system. The test procedure was performed in accordance with the methods suggested by the Practices for Core Analysis (GB/T 29172-2012) in Chinese. The measurement gas was nitrogen, while the test temperature was room temperature (10-15 °C), and the confining pressure was 3.5 MPa (Figure 4).

Ultrasonic Wave Velocity Measurements
Before measuring the porosity and permeability, P and S-wave velocities of the rock specimens were measured after thermal treatment for different temperatures and numbers of thermal cycles were measured using an ultrasonic apparatus (HS-YS2A Type). Two transducers fixed by a holder applying the same force were positioned at the ends of the specimen. A pressure gauge and hand wheel were used to apply an equal force with transducers during every test (see Figure 3). Each specimen was tested twice to ensure repeatability.

Ultrasonic Wave Velocity Measurements
Before measuring the porosity and permeability, P and S-wave velocities of the rock specimens were measured after thermal treatment for different temperatures and numbers of thermal cycles were measured using an ultrasonic apparatus (HS-YS2A Type). Two transducers fixed by a holder applying the same force were positioned at the ends of the specimen. A pressure gauge and hand wheel were used to apply an equal force with transducers during every test (see Figure 3). Each specimen was tested twice to ensure repeatability.

Porosity and Gas Permeability Measurements
We measured the porosity and steady-state permeability of the three temperature groups (200, 400, and 600 °C) using an SCMS-E high-temperature, high-pressure, multi-parameter core measurement system. The test procedure was performed in accordance with the methods suggested by the Practices for Core Analysis (GB/T 29172-2012) in Chinese. The measurement gas was nitrogen, while the test temperature was room temperature (10-15 °C), and the confining pressure was 3.5 MPa (Figure 4).

Porosity and Gas Permeability Measurements
We measured the porosity and steady-state permeability of the three temperature groups (200, 400, and 600 • C) using an SCMS-E high-temperature, high-pressure, multi-parameter core measurement system. The test procedure was performed in accordance with the methods suggested by the Practices for Core Analysis (GB/T 29172-2012) in Chinese. The measurement gas was nitrogen, while the test temperature was room temperature (10-15 • C), and the confining pressure was 3.5 MPa (Figure 4).

Microscopic Observation
Cast thin sections (CTS), i.e., thin sections of rock impregnated with colored epoxy, were used for highlighting the microcracks. The disc rock samples were saturated with blue epoxy to distinguish pores and fracture from rock matrices. The procedure of obtaining CTS is shown in Figure 5. All disc rock specimens were impregnated with colored epoxy after thermal treatment. After leveling, lapping and polishing, a thin section of size 25 × 0.03 mm was obtained. The impregnated sample was bonded to the surface of a piece of glass for further processing. The thin section image was then photographed under plane polarized light and cross polarized light by using a polarizing microscope (Zeiss Scope A1) with an attached digital camera.

Image Processing
Microcracks appear blue under plane-polarized light because the blue epoxy filled the microcracks. We selected the color of blue epoxy (R: 70, G: 132, B: 171). Usually, it is not consistent in every CTS image. Then, we set the tolerance to 70 to ensure that the blue parts of the image were successfully selected. The results are shown in Figure 6b. Manual interactive thresholding segmentation was used for the segmentation process. The thresholding of 40 was applied to the intermediate image based on the image histogram (see Figure 7). The binarized image result is shown in Figure 6d, which was further used for quantitative analysis (Figure 6c).

Microscopic Observation
Cast thin sections (CTS), i.e., thin sections of rock impregnated with colored epoxy, were used for highlighting the microcracks. The disc rock samples were saturated with blue epoxy to distinguish pores and fracture from rock matrices. The procedure of obtaining CTS is shown in Figure 5. All disc rock specimens were impregnated with colored epoxy after thermal treatment. After leveling, lapping and polishing, a thin section of size 25 × 0.03 mm was obtained. The impregnated sample was bonded to the surface of a piece of glass for further processing. The thin section image was then photographed under plane polarized light and cross polarized light by using a polarizing microscope (Zeiss Scope A1) with an attached digital camera.

Microscopic Observation
Cast thin sections (CTS), i.e., thin sections of rock impregnated with colored epoxy, were used for highlighting the microcracks. The disc rock samples were saturated with blue epoxy to distinguish pores and fracture from rock matrices. The procedure of obtaining CTS is shown in Figure 5. All disc rock specimens were impregnated with colored epoxy after thermal treatment. After leveling, lapping and polishing, a thin section of size 25 × 0.03 mm was obtained. The impregnated sample was bonded to the surface of a piece of glass for further processing. The thin section image was then photographed under plane polarized light and cross polarized light by using a polarizing microscope (Zeiss Scope A1) with an attached digital camera.

Image Processing
Microcracks appear blue under plane-polarized light because the blue epoxy filled the microcracks. We selected the color of blue epoxy (R: 70, G: 132, B: 171). Usually, it is not consistent in every CTS image. Then, we set the tolerance to 70 to ensure that the blue parts of the image were successfully selected. The results are shown in Figure 6b. Manual interactive thresholding segmentation was used for the segmentation process. The thresholding of 40 was applied to the intermediate image based on the image histogram (see Figure 7). The binarized image result is shown in Figure 6d, which was further used for quantitative analysis (Figure 6c).

Image Processing
Microcracks appear blue under plane-polarized light because the blue epoxy filled the microcracks. We selected the color of blue epoxy (R: 70, G: 132, B: 171). Usually, it is not consistent in every CTS image. Then, we set the tolerance to 70 to ensure that the blue parts of the image were successfully selected. The results are shown in Figure 6b. Manual interactive thresholding segmentation was used for the segmentation process. The thresholding of 40 was applied to the intermediate image based on the image histogram (see Figure 7). The binarized image result is shown in Figure 6d, which was further used for quantitative analysis (Figure 6c).  We then measured four different parameters to measure: area, size (width), size (length), dendrites-one pixel thick open branches ( Figure 8). The number of isolated elements was automatically counted (Figure 6d). It should be noted that the size width was not the actual width of the fracture. Finally, the image statistical data were exported to a worksheet for post processing. The image porosity was calculated according to Equation (1).
(1) Figure 6. Schematic view of image processing. (The blue part is the preparation process, while the green part is the measurement process).
Energies 2020, 13, x FOR PEER REVIEW 6 of 20  We then measured four different parameters to measure: area, size (width), size (length), dendrites-one pixel thick open branches ( Figure 8). The number of isolated elements was automatically counted (Figure 6d). It should be noted that the size width was not the actual width of the fracture. Finally, the image statistical data were exported to a worksheet for post processing. The image porosity was calculated according to Equation (1). We then measured four different parameters to measure: area, size (width), size (length), dendrites-one pixel thick open branches ( Figure 8). The number of isolated elements was automatically counted (Figure 6d). It should be noted that the size width was not the actual width of the fracture. Finally, the image statistical data were exported to a worksheet for post processing. The image porosity was calculated according to Equation (1).

Porosity
As shown in Figure 9, high temperatures (600 °C) had a greater effect on porosity than low heating temperatures (200 and 400 °C). Moreover, at 600 °C, porosity increased substantially as the cycle number increased from zero to two. At 200 and 400 °C, the influence of the number of thermal cycles on the porosity and permeability is negligible.

Gas Permeability
The permeability variations with the number of thermal cycles at different heating are plotted in Figure 10. The trends were similar for all three different heating temperatures. A positive correlation was observed between thermal cycling and permeability increase at 400 and 600 °C, while there was an irregular rise against thermal cycles at 200 °C. In addition, the permeability of granite at 600 °C was significantly higher than that at 400 °C and 200 °C. At 600 °C, the permeability of granite increased from 0.0001 to 4.7770 mD after 16 thermal cycles.

Porosity
As shown in Figure 9, high temperatures (600 • C) had a greater effect on porosity than low heating temperatures (200 and 400 • C). Moreover, at 600 • C, porosity increased substantially as the cycle number increased from zero to two. At 200 and 400 • C, the influence of the number of thermal cycles on the porosity and permeability is negligible.

Porosity
As shown in Figure 9, high temperatures (600 °C) had a greater effect on porosity than low heating temperatures (200 and 400 °C). Moreover, at 600 °C, porosity increased substantially as the cycle number increased from zero to two. At 200 and 400 °C, the influence of the number of thermal cycles on the porosity and permeability is negligible.

Gas Permeability
The permeability variations with the number of thermal cycles at different heating are plotted in Figure 10. The trends were similar for all three different heating temperatures. A positive correlation was observed between thermal cycling and permeability increase at 400 and 600 °C, while there was an irregular rise against thermal cycles at 200 °C. In addition, the permeability of granite at 600 °C was significantly higher than that at 400 °C and 200 °C. At 600 °C, the permeability of granite increased from 0.0001 to 4.7770 mD after 16 thermal cycles.

Gas Permeability
The permeability variations with the number of thermal cycles at different heating are plotted in Figure 10. The trends were similar for all three different heating temperatures. A positive correlation was observed between thermal cycling and permeability increase at 400 and 600 • C, while there was an irregular rise against thermal cycles at 200 • C. In addition, the permeability of granite at 600 • C was significantly higher than that at 400 • C and 200 • C. At 600 • C, the permeability of granite increased from 0.0001 to 4.7770 mD after 16 thermal cycles.

P-and S-Wave Velocity
Ultrasonic wave test is commonly used to detect the interior failure in a rock because of its simple and non-destructive characteristics. The typical P-and S-wave forms recorded and used to determine the velocities are presented in Figure 11 and the velocity results are shown in Figure 12. It appears that both P-wave velocity and S-wave velocity exhibited a similar negative correlation with heating temperature and the number of thermal cycles. The gradient of both P-wave and S-wave velocity decreased as the number of cycles increased. At 600 °C and one cycle of the thermal treatment, P-and S-wave velocities decreased by 73.6% and 58.6%, respectively. At 600 °C, after 16 cycles of the thermal treatment, the velocity reduced by 84.3% and 82.4%, respectively.

P-and S-Wave Velocity
Ultrasonic wave test is commonly used to detect the interior failure in a rock because of its simple and non-destructive characteristics. The typical P-and S-wave forms recorded and used to determine the velocities are presented in Figure 11 and the velocity results are shown in Figure 12. It appears that both P-wave velocity and S-wave velocity exhibited a similar negative correlation with heating temperature and the number of thermal cycles. The gradient of both P-wave and S-wave velocity decreased as the number of cycles increased. At 600 • C and one cycle of the thermal treatment, P-and S-wave velocities decreased by 73.6% and 58.6%, respectively. At 600 • C, after 16 cycles of the thermal treatment, the velocity reduced by 84.3% and 82.4%, respectively.

P-and S-Wave Velocity
Ultrasonic wave test is commonly used to detect the interior failure in a rock because of its simple and non-destructive characteristics. The typical P-and S-wave forms recorded and used to determine the velocities are presented in Figure 11 and the velocity results are shown in Figure 12. It appears that both P-wave velocity and S-wave velocity exhibited a similar negative correlation with heating temperature and the number of thermal cycles. The gradient of both P-wave and S-wave velocity decreased as the number of cycles increased. At 600 °C and one cycle of the thermal treatment, P-and S-wave velocities decreased by 73.6% and 58.6%, respectively. At 600 °C, after 16 cycles of the thermal treatment, the velocity reduced by 84.3% and 82.4%, respectively.

Rock Microstructure
The microscopic observations of A31 (no thermal treatment) are shown in Figure 13. The granite is mainly composed of feldspar, quartz, and biotite with a small amount of pyroxene and magnetite. Anorthosite is 578 μm in length and 251 μm in width. Quartz is 458 μm in length and 243 μm in width. Clear boundaries were observed between mineral grains (Figure 13b). No blue epoxy was not observed in the plane-polarized image (Figure 13a), indicating that the granite has negligible porosity.

Rock Microstructure
The microscopic observations of A31 (no thermal treatment) are shown in Figure 13. The granite is mainly composed of feldspar, quartz, and biotite with a small amount of pyroxene and magnetite. Anorthosite is 578 µm in length and 251 µm in width. Quartz is 458 µm in length and 243 µm in width. Clear boundaries were observed between mineral grains (Figure 13b). No blue epoxy was not observed in the plane-polarized image (Figure 13a), indicating that the granite has negligible porosity.  Figure 14 presents the CTS observation results for the granite after one thermal cycle at 600 °C. The mineral grains and the associated microcracks are clearly affected by thermal treatment. Two types of microcracks were observed: grain boundary microcracks, transgranular microcracks (including intracrystalline microcracks) [12]. Grain boundary microcracks describe the microcracks developed at the boundary between different minerals, whereas transgranular microcracks are those  Figure 14 presents the CTS observation results for the granite after one thermal cycle at 600 • C. The mineral grains and the associated microcracks are clearly affected by thermal treatment. Two types of microcracks were observed: grain boundary microcracks, transgranular microcracks (including intracrystalline microcracks) [12]. Grain boundary microcracks describe the microcracks developed at the boundary between different minerals, whereas transgranular microcracks are those developed in the interior of the mineral grains. These microcracks were predominantly confined within minerals, with some passing through multiple grains. Occasionally, transgranular microcracks and grain boundary microcracks developed connectivity at an angle of approximately 90 • . Furthermore, the location of the microcracks was related to mineral species. Transgranular microcracks were typically developed in feldspar, and the development direction was almost perpendicular to the optical twin crystal direction of feldspar. Grain boundary microcracks were typically between feldspar and quartz, and between feldspar and feldspar [25,40]. Almost no transgranular microcracks were observed in biotite.  Figure 14 presents the CTS observation results for the granite after one thermal cycle at 600 °C. The mineral grains and the associated microcracks are clearly affected by thermal treatment. Two types of microcracks were observed: grain boundary microcracks, transgranular microcracks (including intracrystalline microcracks) [12]. Grain boundary microcracks describe the microcracks developed at the boundary between different minerals, whereas transgranular microcracks are those developed in the interior of the mineral grains. These microcracks were predominantly confined within minerals, with some passing through multiple grains. Occasionally, transgranular microcracks and grain boundary microcracks developed connectivity at an angle of approximately 90°. Furthermore, the location of the microcracks was related to mineral species. Transgranular microcracks were typically developed in feldspar, and the development direction was almost perpendicular to the optical twin crystal direction of feldspar. Grain boundary microcracks were typically between feldspar and quartz, and between feldspar and feldspar [25,40]. Almost no transgranular microcracks were observed in biotite. Plane-polarized and cross-polarized CTS images of the granite specimens with different heating temperatures (100-600 °C, one cycle) are presented in Figures 15 and 16, respectively. Heating temperature affected the microcracks development behaviors. In the range of 100-300 °C, minimal blue epoxy was observed in the images. Grain boundary microcracks were sparsely distributed in a specimen heated to 400 °C (see Figure 15d), however, as the temperature exceeded 400 °C, more grain Plane-polarized and cross-polarized CTS images of the granite specimens with different heating temperatures (100-600 • C, one cycle) are presented in Figures 15 and 16, respectively. Heating temperature affected the microcracks development behaviors. In the range of 100-300 • C, minimal blue epoxy was observed in the images. Grain boundary microcracks were sparsely distributed in a specimen heated to 400 • C (see Figure 15d), however, as the temperature exceeded 400 • C, more grain microcracks could be observed in the granite. For the specimen treated at 500 • C heating temperature (see Figures 15e and 16e), transgranular microcracks were observed in feldspar. Grain boundary microcracks also existed but in a smaller proportion than those transgranular microcracks in the granite subjected to 600 • C. According to the plane-polarized microscope observation, as shown in Figure 15f (600 • C), abundant grain boundary microcracks were found along feldspar and quartz grains. Moreover, the transgranular microcracks and grain boundary microcracks occasionally coalesced.
Thermal cycles also had a significant influence on microcrack evolution, especially that of transgranular. The plane-polarized and cross-polarized photographs of CTS for granite specimens treated at 600 • C with different numbers of thermal cycles are presented in Figures 17 and 18. With the increase of thermal cycles, both the length and width of transgranular microcracks increased, as well as the number of grain boundary microcracks and transgranular microcracks. Figures 17f and 18f present sample A30, which was subject to 600 • C heating and 16 thermal cycles. The maximal width of transgranular reached approximately 20 µm. Microcracks were well developed and most mineral boundaries had grain boundary microcracks. The width of the transgranular microcracks was larger than that of grain boundary microcracks.
(see Figures 15e and 16e), transgranular microcracks were observed in feldspar. Grain boundary microcracks also existed but in a smaller proportion than those transgranular microcracks in the granite subjected to 600 °C. According to the plane-polarized microscope observation, as shown in Figure 15f (600 °C), abundant grain boundary microcracks were found along feldspar and quartz grains. Moreover, the transgranular microcracks and grain boundary microcracks occasionally coalesced.   microcracks also existed but in a smaller proportion than those transgranular microcracks in the granite subjected to 600 °C. According to the plane-polarized microscope observation, as shown in Figure 15f (600 °C), abundant grain boundary microcracks were found along feldspar and quartz grains. Moreover, the transgranular microcracks and grain boundary microcracks occasionally coalesced.   the increase of thermal cycles, both the length and width of transgranular microcracks increased, as well as the number of grain boundary microcracks and transgranular microcracks. Figures 17f and  18f present sample A30, which was subject to 600 °C heating and 16 thermal cycles. The maximal width of transgranular reached approximately 20 μm. Microcracks were well developed and most mineral boundaries had grain boundary microcracks. The width of the transgranular microcracks was larger than that of grain boundary microcracks.   18f present sample A30, which was subject to 600 °C heating and 16 thermal cycles. The maximal width of transgranular reached approximately 20 μm. Microcracks were well developed and most mineral boundaries had grain boundary microcracks. The width of the transgranular microcracks was larger than that of grain boundary microcracks.

Microcrack Morphology
The granite morphology was analyzed through the CTS images (Figure 19), which were sorted according to the microcrack area and arranged vertically. The length of microcracks and the number of inflexion points increased with the number of thermal cycles (see Figure 19). This implies that the development and cross-cutting of grain-boundary microcracks and transgranular microcracks developed and crossed together. Hence, thermal cycles had a substantial influence on high-temperature granite subjected to water cooling.
The granite morphology was analyzed through the CTS images (Figure 19), which were sorted according to the microcrack area and arranged vertically. The length of microcracks and the number of inflexion points increased with the number of thermal cycles (see Figure 19). This implies that the development and cross-cutting of grain-boundary microcracks and transgranular microcracks developed and crossed together. Hence, thermal cycles had a substantial influence on hightemperature granite subjected to water cooling. We conducted a statistical analysis of the microcracks area to explore the distribution of pores size. As shown in Figure 20, relative frequency of microcracks descended rapidly from 0.35 to 0.05. 80% of pores contained less than 21 pixels or 17.01 μm 2 (1 pixel ≈ 0.81 μm 2 ). Tiny pores were the most numerous among all microcrack sizes. We conducted a statistical analysis of the microcracks area to explore the distribution of pores size. As shown in Figure 20, relative frequency of microcracks descended rapidly from 0.35 to 0.05. 80% of pores contained less than 21 pixels or 17.01 µm 2 (1 pixel ≈ 0.81 µm 2 ). Tiny pores were the most numerous among all microcrack sizes. The results of the CTS image processing are presented in Figure 21. Generally, differences were observed between the porosity measured via gas permeability measurement and microscope observations. The latter increased by 3.5 times from one cycle to 16 cycles, which rose from 1.61% to 5.67%. Conversely, the former only increased from 1.73% to 3.42% (Figure 21a). Measurements of maximum porosity, maximum length, and maximum width tended to increase with a greater number of thermal cycles (see Figure 21b-d). The line charts revealed that the development of microcracks The results of the CTS image processing are presented in Figure 21. Generally, differences were observed between the porosity measured via gas permeability measurement and microscope observations. The latter increased by 3.5 times from one cycle to 16 cycles, which rose from 1.61% to 5.67%. Conversely, the former only increased from 1.73% to 3.42% (Figure 21a). Measurements of maximum porosity, maximum length, and maximum width tended to increase with a greater number of thermal cycles (see Figure 21b-d). The line charts revealed that the development of microcracks induced by thermal stress increased with the rise of thermal cycles. The number of measured dendrites is shown in Figure 22, which also increased with the number of thermal cycles, by almost 13 times to 63. This clearly illustrates the expansion of microcracks with the number of thermal cycles at high heating temperatures.

Discussion
Porosity and crack density are the most important properties, playing a major role in the structural integrity of a rock [30]. They are related to the type and arrangement of mineral grains, internal pores, and microcracks. High temperature thermal treatment could increase the porosity of

Discussion
Porosity and crack density are the most important properties, playing a major role in the structural integrity of a rock [30]. They are related to the type and arrangement of mineral grains, internal pores, and microcracks. High temperature thermal treatment could increase the porosity of granite. Some researchers reported that 400 • C is a threshold temperature for granite to change its structure [9,30,41]. Below the threshold temperature, no significant relationship was found between the porosity of granite and the number of thermal cycles, suggesting that the increasing number of thermal cycles does not contribute to the propagation of microcracks. However, beyond a temperature of 600 • C, the increase of cyclic thermal treatment is associated with the increase of rock porosity.
Permeability is in relation to pores and especially fractures. Generally, fractures play an important role in the percolation capacity. Obviously, the thermal treatments can enhance the permeability of granite. The permeability is significantly improved as heating temperature rises [11,17,42]. Interestingly, the porosity at 400 • C was lower than that at 200 • C except after two thermal cycles, whereas the permeability exhibited the exact opposite trend. This reflected that the enhanced connectivity between granite microcracks was enhanced. Pore and crack networks facilitated fluid flow through the specimens, leading to the increased permeability. As a result, it demonstrated reversely that propagation of microcracks increased with the number of thermal cycles. The number of thermal cycles also had significant effects on the permeability of granite.
The CTS image processing employed in this study exhibits some limitations. First of all, the images cannot reveal all microcracks in the sample because of their finite resolution and size. Secondly, the images are 2D images rather than 3D images; thus, some microcracks cannot be observed for technical reasons. These two limitations would result in an underestimation of the porosity. Third, due to the inconsistent blue color of epoxy, some noise pollution is inevitable in the CTS image, which would lead to an overestimated porosity. Nevertheless, these images still provide useful and quantitative descriptions of microcracks in the granite.
During the process of heating and cooling, a series of physical and chemical reactions have occurred in granite (see Figure 23). When the heating temperature exceeded 100 • C, water inclusions that originally existed in the granite pores due to wettability and capillary force-escaped rock in the form of gas [8]. As a result, the P-wave velocity decreased. The chemical formula for biotite is K (Mg <0.67 , Fe >0.33 ) 3 [AlSi 3 O 13 ](OH) 2 . In the temperature range of 300-500 • C, due to the escape of crystal water and dissociation of the H + and OH − (the existing form of constitution water in the mineral crystal lattice structure), the mineral framework was destroyed and microcracks developed in rock [17,42]. When the heating temperature reaches 573 • C, low-temperature α quartz turns into high-temperature β quartz, which is accompanied by a sudden volume expansion [7,[43][44][45]. This transition results in severe derogation of the granite. During the heating process, due to differences in the thermal expansion coefficients of different minerals, thermal stresses accumulate at granular interfaces, even if the temperature field outside is uniform. This expansion mismatch primarily contributes to the development of grain boundary microcracks [24,46]. During the cooling process, granite specimens are placed in the flowing water, which induces the sudden variation of temperature and results in the gradual formation of grain boundary microcracks and transgranular microcracks among rock minerals. Water then invades the connected microcracks, resulting in new chemical reactions in the minerals. Because the transition of quartz to β quartz is a reciprocal reaction, the granite specimens experience repeated damage with an increasing number of thermal cycles.

Conclusions
We conducted a set of physical experiments to investigate the effect of cyclic thermal treatment and water cooling on the physical characteristics of granite. The results show that the thermal cycling has a significant influence on the physical characteristics (i.e., porosity, permeability, the seismic velocity). The results contribute to the fundamental understanding of the evolution of porosity and permeability in HDR geothermal systems. Qualitative and quantitative analyses of CTS images led to the following conclusions: (1) Physical characteristics changed significantly after flowing water cooling at high heating temperatures versus the number of thermal cycles. P-and S-waves reduced with the increase of thermal cycles. Porosity did not change substantially at heating temperatures of less than 400 °C. The permeability increased by four orders of magnitude compared to the samples without thermal treatment, which is susceptible than porosity. (2) Both grain boundary microcracks and transgranular microcracks were found. The primary effect of heating was grain boundary cracking during the first thermal cycle. Increasing the number of thermal cycles, transgranular microcracks also developed in the rock. Both types of grain boundary microcracks and transgranular microcracks coalesced to form a fracture network. (3) Quantification of the crack morphology from CTS images indicated that the large number of microcracks that developed in the granite during high-temperature treatment changed the rocks physical properties. The length of microcracks increased by one order of magnitude.

Conclusions
We conducted a set of physical experiments to investigate the effect of cyclic thermal treatment and water cooling on the physical characteristics of granite. The results show that the thermal cycling has a significant influence on the physical characteristics (i.e., porosity, permeability, the seismic velocity). The results contribute to the fundamental understanding of the evolution of porosity and permeability in HDR geothermal systems. Qualitative and quantitative analyses of CTS images led to the following conclusions: (1) Physical characteristics changed significantly after flowing water cooling at high heating temperatures versus the number of thermal cycles. P-and S-waves reduced with the increase of thermal cycles. Porosity did not change substantially at heating temperatures of less than 400 • C. The permeability increased by four orders of magnitude compared to the samples without thermal treatment, which is susceptible than porosity. (2) Both grain boundary microcracks and transgranular microcracks were found. The primary effect of heating was grain boundary cracking during the first thermal cycle. Increasing the number of thermal cycles, transgranular microcracks also developed in the rock. Both types of grain boundary microcracks and transgranular microcracks coalesced to form a fracture network. (3) Quantification of the crack morphology from CTS images indicated that the large number of microcracks that developed in the granite during high-temperature treatment changed the rocks physical properties. The length of microcracks increased by one order of magnitude.
Author Contributions: Conceptualization, X.S. and C.Z.; data curation, J.W. and L.G.; formal analysis, L.G. and S.C.; supervision, C.Z. and L.G.; validation, X.Z. and X.S.; writing-original draft, L.G., X.Z. and X.S. All authors have read and agreed to the published version of the manuscript.