China has abundant reserves of fossil and hot dry rock (HDR) geothermal energy in deep formations. Efficient development and utilization of such deep resources are of great significance for consolidating the foundation of China's energy self-supply^[1,2]. However, the existing drilling technology cannot meet the needs of efficient exploration and development of the deep resources. Deep formations are generally characterized by high rock strength and hardness, high abrasiveness, low drillability, high temperature and fracture development. Compared with the shallow formations, issues such as low drilling rate, long drilling period and corresponding high cost become more pronounced^[3]. It is urgent to explore a more efficient rock-breaking method suitable for deep hard formations, so as to greatly improve the drilling rate and reduce the cost of development.

In the 1970s, scholars first put forward the concept of low-temperature drilling technology and this technology and its equipment have developed and evolved to better suit for different well types and formations^[4,5]. In this concept, the drilling fluid was cryogenic gas, which has very weak thermal shock effect due to the poor thermal conductivity. Thermal shock occurs when the temperature changes suddenly, and thermal stresses can be induced to damage the rock. To improve the thermal shock effect and its ability to fail the rock, some scholars proposed to use liquid nitrogen (LN₂) to crack rocks in deep formations^[6,7]. This method was successfully applied in the stimulation of unconventional reservoirs in the 1990s. Recently, sponsored by the United State Department of Energy, researchers investigated the cracking mechanism of rocks subjected to LN₂-cooling treatment comprehensively^[8,9]. LN₂ is a cryogenic fluid with the boiling temperature of -196 °C at atmosphere pressure. High temperature difference between LN₂ and deep rocks can induce very strong thermal shock effect, initiating and propagating micro-cracks. These cracks play an important role in deteriorating mechanical properties and reducing the threshold breakage pressure of rock.

Based on previous studies, we proposed a novel drilling method that uses high-pressure LN₂ jets to assist rock-breaking in deep formations. This technique has three merits: (1) The impinging jet is an efficient heat transfer enhancement method which can substantially improve the heat transfer rate and the corresponding thermal stress^[10,11]. (2) Thermal shock induce by LN₂-cooling can weaken mechanical properties of hard rocks in deep formations and thereby greatly facilitate rock-breaking^[12,13]. (3) The impact of high-pressure jet contributes to extending the thermal cracks and aggravating rock failure. Combining thermal shock and jet impact, this technique is expected to greatly reduce the threshold of rock-breaking pressure and significantly enhance the drilling rate in deep formations.

To determine the feasibility of the LN₂ jet in breaking hard high-temperature rocks, we conducted a series of experiments on various rocks. Physical and mechanical property responses of rocks to LN₂ thermal shock were obtained. The scanning electron microscope (SEM) analysis and heat transfer analysis were performed to reveal the rock-breaking mechanisms under the impact of high-pressure LN₂ jet.

Three different rocks (i.e. sandstone, shale and granite) were used in our work. We cored cylinder samples with the dimension of 25 mm in diameter and 50 mm in length, and dry these samples to constant mass in an air dry oven. Then the P-wave velocity (V_p) of all the samples were tested to select 12 samples with similar V_p values for each rock. As a nondestructive test technique, the acoustic wave test is usually used to detect internal flaws in rock. Samples with similar V_p values generally have similar initial damage. Sample selection based on similar V_p values contributes to reducing the effect of heterogeneity between the samples and thereby enhances comparability of the samples.

We divided the 12 samples of each rock into LN₂-cooling group L and air-cooling group A. Group L and group A were subdivided into three subgroups, i.e. L-1^#—L-3^# and A-1^#— A-3^#, respectively. Each subgroup contained two rock samples. In the group L, we heated the samples in L-1^#, L-2^#, L-3^# to 25, 150, 260 °C, respectively, then keep them at the target temperatures for 10 hours, followed by rapid cooling in a LN₂ Dewar. After fully cooled, these samples were took out and restored to room temperature. The thermal loading process in group A was similar to that in the group L. The only difference was that the samples in group A were cooled in air after keeping them at target temperatures for 10 hours. After thermal treatment, we tested the physical and mechanical properties of these samples respectively.

The ultrasonic pulse tester was used to measure the p-wave velocity of the rock samples before and after thermal loading. Each core sample was measured 3 times. Vaseline was smeared at both ends of the core samples during the test to ensure effective contact between the rock and the test sensor. The TAW1000 deep water pore pressure servo machine was used to conduct uniaxial compression mechanical tests. The maximum axial load capacity of this machine is 1000 kN. The tests were conducted in displacement controlled mode at the constant displacement rate of 0.05 mm/min.

Changes in P-wave velocity reflect the damage of rocks subjected to thermal loading. As shown in Fig. 1, the V_p test results of the three different rocks (shale, sandstone and granite) before and after LN₂-cooling indicate that: (1) At 25 °C, the V_p of shale, sandstone and granite decreases by -5.5,110.3 and 189.2 m/s after LN₂-cooling, respectively. (2) At 260 °C, the V_p of these three rocks decreases by 35.8, 421.8 and 823.7 m/s respectively. Compared with the V_p drop at 25 °C, the V_p drop of shale, sandstone and granite at 260 °C increased by 35.8, 421.8 and 823.7 m/s, respectively. Obviously, V_p of the rock samples decrease significantly after heating and subsequent LN₂-cooling treatment, reflecting that the pore space of rock grows after thermal treatment. Such phenomenon may be attributed to the generation of new micro-cracks and/or extension of pre-existed micro-cracks. According to the comparison among the three rocks, the change of shale in V_p is substantially lower than that of sandstone and granite. The V_p reduction of rocks subjected to LN₂-cooling increases with rising initial rock temperature.

In fact, rocks underwent two thermal loading processes in the present experiment, namely the heating treatment and the cooling treatment. Thereby there are two potential causes for the V_p reduction: (1) The evaporation of pore water and the corresponding porosity growth in the heating process. (2) The cracking of the rock in the rapid cooling process. Due to the low heat transfer rate of gas, natural air-cooling cannot induce strong thermal shock. Hence, the V_p reduction of the rock samples in the air-cooling group is mainly attributed to the loss of pore water in the heating process. In contrast, LN₂ boils and gasifies intensely when contacting with rock. The boiling heat transfer of LN₂, as an efficient heat transfer enhancement method, can cause a large temperature drop in a short time and thereby bring about much stronger thermal shock to the rock. As the rock samples in LN₂-cooling group and air-cooling group both underwent the same heating process, the influence of water loss and other factors in the heating process can be eliminated by comparing the V_p results in the two cooling groups. The difference in V_p drop between LN₂-cooled rocks and air-cooled rocks reflects the effect of thermal shock on rock damage. According to the comparison of V_p of the rock samples cooled in the two ways, the V_p reduction induced by LN₂-cooling is more significant than that induced by air-cooling. For rocks with temperatures of 25-260 °C, shale, sandstone and granite samples reduce by -0.12%-0.81%, 3.2%-3.3% and 4.1%-18.4% in V_p respectively after LN₂-cooling, which is -0.12%-1.1%, 3.2%-4.8% and 4.1%-7.7% higher than the V_p drop of corresponding types of rock samples after air-cooling respectively. It is evident that the LN₂ thermal shock results in remarkable rock damage. As the initial temperature rocks rises, the thermal shock effect and the corresponding rock damage becomes more significant.

Fig. 2 shows the uniaxial compression stress-strain curves of the rock samples subjected to air-cooling and LN₂-cooling. The peak of the curve represents the uniaxial compressive strength (UCS) of the rock sample. Under air-cooling condition (Fig. 2a), the UCS increases with the heating temperature of the rock. This phenomenon indicates that the heating and subsequent air-cooling treatment strengthens mechanical properties of the rock to some extent. Previous literature^[14] also reported such phenomenon. This was attributed to the irreversible plastic deformation of minerals in the heating process and the corresponding growth of frictions between particles. In the air-cooling process, the thermal shock effect is too weak to damage the rock significantly. Thus, mechanical properties of rocks are strengthened after heating and subsequent air-cooling treatment. In contrast, the strength of the rock samples subjected to LN₂-cooling is weakened (Fig. 2b), although these rock samples underwent the same heating process with air-cooled samples. This is because the thermal shock effect of LN₂-cooling is more significant, and the damage caused by cooling is more pronounced than the strengthening induced by heating. Therefore, the rock samples after heating and LN₂-cooling deteriorated considerably in mechanical properties. The slope of the linear part of the stress- strain curve represents the elastic modulus of the rock. The variation trend of the elastic modulus shows a similar trend with the UCS. Under the air-cooling condition, the elastic modulus of rock rises with the increase of rock temperature; while under the LN₂-cooling condition, the elastic modulus declines with the increase of rock temperature.

Fig. 3 shows the comparison in UCS between LN₂-cooling and air-cooling. Among the three rocks, shale has the highest UCS, followed by granite and sandstone. The effect of LN₂ thermal shock on the sandstone is the weakest. The uniaxial compressive strength of sandstone before and after LN₂- cooling does not change noticeably. However, the effect on shale and granite is much more remarkable. For these two rocks, UCS after LN₂-cooling is obviously lower than that after air-cooling, and the difference in UCS between these two cooling ways grows with rising rock temperature. The results above show that the thermal shock effect of LN₂-cooling and the mechanical property deterioration of rocks become more pronounced with the rise of rock temperature.

To determine the rock-breaking characteristics under the joint actions of jet impact and thermal shock effect, we con- ducted rock-breaking experiments using high-pressure LN₂ jets. The influence of initial temperature of rocks on the rock-breaking performance of LN₂ jet was analyzed in this section. SEM was also used to reveal the microscopic damage mechanisms of rock under the impact of the LN₂ jet.

Fig. 4 shows the experimental setup for the high-pressure LN₂ jet. This system consists of a LN₂ tank, a cryogenic fluid pump, jet nozzles, a core chamber, temperature and pressure data acquisition devices and pipe manifolds. The cryogenic liquid pump is the central unit of the experiment system, with a maximum displacement of 4 000 L/h and maximum pressure bearing capacity of 35 MPa. The control station can control the jet pressure by adjusting the motor speed. Pipe manifolds are made of stainless steel with high resistance to the LN₂-cooling. Thermal insulation materials are wrapped on the pipelines to avoid the boiling of LN₂ during flowing in the pipe. Before the jet experiment, LN₂ should be circulated in the system to fully cool the devices in advance.

Cubic granites with the dimension of 13 cm in side length were used in the present experiment. We divided the granite samples into 5 groups, with 2 granite samples in each group (i.e. 1^# and 2^#). The granite samples in different groups were first slowly heated to different target temperatures (25, 150, 260, 370, 480 °C), and then moved to the rock chambers quickly after keeping them at the target temperatures for 4 hours. A cone-straight nozzle with an exit diameter of 1.5 mm was used in the experiments. Distance between the nozzle exit and the impact surface was set at 2 times the nozzle exit diameter. The jet pressure was kept at a constant 25 MPa. Fluid ambient pressure was the atmosphere pressure, and the confining stress for rocks were not considered in this experiment.

The rock-breaking results with LN₂ jet under different temperatures are shown in Fig. 5. As a brittle material, the granite shows obvious tensile failure under the impact of LN₂ jet. Granite is high in strength, and LN₂ jet can’t break the granite at the temperature of less than 150 °C at the jet pressure of 25 MPa. In contrast, for the granite with the initial temperature of 260 °C, massive breakage was observed after the high-pressure LN₂ jet impinged on the granite, and several radially propagating cracks were generated around the impact pit. It seems there is a threshold temperature for the massive volume breakage of granite subjected to LN₂ jet impact. According to the present results, the threshold temperature for the massive failure of granite falls in the range of 150-260 °C at the jet pressure of 25 MPa. At 370 °C, the granite blasted drastically under LN₂ jet impact, and a larger breakage was created. As the initial temperature increased to 480 °C, the damage of granite further aggravated. The granite block was blasted in half in a short time after contact with the LN₂ jet.

Fig. 6 shows the variation of the rock-breaking depth at the impact center under the impact of the high-pressure LN₂ jet. Under the same jet pressure, the rock-breaking depth increases exponentially with the rise of the initial rock temperature, suggesting that the higher the rock temperature, the better the rock-breaking performance of the LN₂ jet will be. Fig. 7 shows the fragments of granite with the initial temperature of 480 °C after the impact of LN₂ jet at the jet pressure of 25 MPa and standoff distance of 3 mm. It is found that the rock failure under the impact of LN₂ jet is characterized by large massive breakage, with fragments at sizes of a few centimeters. According to previous study, the larger the fragments during the jet impact, the lower the specific energy required for breaking the rock^[15]. Therefore, in addition to the advantage of high rock-breaking efficiency, the LN₂ jet also has the merit of low rock-breaking energy consumption.

In addition to granite, we also conducted rock-breaking experiments on shale and sandstone. The experimental setup for these two kinds of rock is the same as that for granite. Under the jet pressure of 25 MPa, no significant damage will occur in the rock if the initial temperature of rock is no higher than 150 °C. As the shale temperature increases to 260 °C, macro cracks as shown in Fig. 8a appear on the impact surface. Nevertheless, large-volume breakage still didn’t appear. For the sandstone with the initial temperature of 260 °C, no cracking occurred on the surface. The macroscopic netted cracks didn’t appear until the initial temperature of the sandstone increased to 480 °C, as shown in Fig. 8b. According to the comparison in rock-breaking features, the volume-breakage threshold temperature for granite is the lowest among the three rocks.

Hence, compared to the sandstone and shale, the LN₂ jet has more superior capacity to break granite.

To reveal the micro damage mechanism of rock subjected to the impact of LN₂ jet, we observed the microstructure of the impact zone using SEM. As shown in Fig. 9, many micro-cracks were generated after LN₂ jet impact. According to the cracking mode, these cracks can be classified into two modes: intercrystalline cracks and intracrystalline cracks. Rock is a mixture composed of many different mineral particles. Due to the differences in thermal expansion coefficient of the particles, neighboring mineral particles mismatch in deformation during LN₂ cooling, creating strong thermal stress at the boundaries of minerals. Such thermal stress grows continuously with cooling. Once this stress exceeds the cementation strength between the particles, the intercrystalline cracks as shown in Fig. 9a would be generated. Moreover, even for the same kind of mineral particles, the thermal expansion coefficients in different crystallization axis directions may differ greatly. Quartz, for example, the thermal expansion coefficient parallel to c-axis is 7.7×10^-6·K^-1; while the thermal expansion coefficient vertical to the c-axis is 14.0×10^-6·K^-1, roughly 2 times higher than that parallel to the c-axis^[16]. Thus, the differential deformation also occurs in mineral particles. Such deformation mismatch can cause intracrystalline cracks as shown in Fig. 9b. Compared with intercrystalline cracks, intracrystalline cracks are smaller in size and number. Therefore, the intercrystalline cracking is the primary microscopic failure mode under the impact of LN₂ jet.

In order to study the transient evolution of thermal and stress fields in rocks during LN₂ cooling, we measured the temperature inside rocks while being cooled by LN₂, using the experimental facility sketched in Fig. 10. The apparatus consists of a double-walled stainless steel dewar, an auxiliary inflow device, a rock sample, T-type thermocouples and a vacuum pump, etc. The vacuum pump was used to vacuummize the dewar for minimizing heat loss. Three rock types, i.e. sandstone, shale and granite were selected, and the samples were cut into circular plates 8 cm in diameter and 3 cm in thickness. A small hole was drilled vertically inside the rock samples to accommodate the thermocouple. The T-type thermocouple was used to measure the temperature variation 2 mm below the top surface of the rock samples.

In the drilling process, the downhole rock was confined by surrounding rock, and the corresponding thermal stress caused by temperature gradients can be calculated as ^[17]:

The mechanical properties of studied rocks are listed in Table 1. Based on the experimentally measured temperatures and Eq. (1), the transient thermal stress on the surface of the rock samples were computed and shown in Fig. 11. It can be seen that the temperature dropped suddenly at t=200 s. Before this the temperature decreased only mildly and the curve slope became steep at t=200 s. After t=400 s the temperature curve turned flat again, indicating the rock surface temperature was close to the liquid nitrogen temperature. In accordance with the temperature change, the thermal stress also changed abruptly at t=200 s, with a dramatic increase in magnitude.

The pattern of temperature evolution on rock surface is closely related to the boiling mode of liquid nitrogen. At the initial stage of contact, the rock temperature was around 20 °C, which was well above the boiling point of liquid nitrogen (-196 °C). As a consequence, liquid nitrogen boiled off intensely and a vapor film was created on the rock surface, blocking the heat exchange between liquid nitrogen and the rock. This regime is termed as film boiling associated with a relatively low heat flux. At some point, the vapor film started to collapse due to local cold spots. The collapse of vapor film resulted in solid-liquid contact and an enhancement in heat transfer rate. The temperature at which the vapor film starts to break up is Leidenfrost temperature (LFP). When the rock surface temperature is below LFP, the boiling regime of liquid nitrogen would transit from film boiling to transition and nucleate boiling consecutively. The result shown in Fig. 11 is consistent with the quenching curves in Ref. [18] where hot metallic spheres/cylinders were quenched in water.

Shown in Fig. 12 are temperature and stress curves for all the three rock types as listed in Table 1. Several observations can be made here: (1) The duration of film boiling for sandstone and granite was shorter than for shale. In addition, the LFP temperature was also higher for sandstone and granite, the latter being slightly higher than the former. (2) The thermal stress increases with time for all the three rock types and the increasing rate goes down, then up, and finally down again. (3) Although similar in variation trend of thermal stress, the 3 kinds of rocks differ widely in thermal stress value; in film boiling period, the granite and shale are similar in thermal stress, but as the granite has shorter film boiling duration than shale, its thermal stress curve turns steep earlier, and the granite has much higher thermal stress than shale in the following boiling periods. (4) The sandstone has lower thermal stress than the other two kinds of rocks.

The difference in thermal stress among rock types may be attributed to two factors: (1) Difference in microscopic structure of the rocks; (2) Difference in macroscopic mechanical properties of the rocks. Sandstone, with more micro pores in matrix, can better accommodate the thermal strain caused by liquid nitrogen cooling. As a result, the mineral grains can deform more freely and the corresponding thermal stress would be lower. Moreover, the sandstone has the smallest Young’s modulus among the three kinds, as seen in Table 1. Since the thermal stress is proportional to the modulus, the thermal stress in sandstone is naturally lower than the other two rock types.

The LN₂ jet combines the impact effect of high-velocity jet and the thermal shock effect of cryogenic fluid. Under the thermal shock effect of cryogenic LN₂, thermal stress is created to destroy the cementation between rock particles and generate micro-cracks. Generation of these cracks weakens mechanical properties of the rock and thereby reduces the threshold rock-breaking pressure for jet. The stress wave induced by high speed jet and the water wedge effect promote extension of the micro-cracks jointly, and these cracks intersect with each other to cause macroscopic failure at last. Moreover, the liquid nitrogen gasifies and expands in the confined fractures, producing lateral force to promote the propagation of these cracks, which further aggravates the damage to rock.

According to the rock-breaking experiment results, the LN₂ jet works best in breaking granite, followed by shale and sandstone. For the three rocks, the distinguished differences in the breaking performance are mainly attributed to the discrepancies in mechanical deterioration of the different rock samples under the effect of LN₂ thermal shock. To evaluate the mechanical deterioration quantitatively, we define a deterioration factor as:

Based on the test results of mechanical properties, we calculated the UCS deterioration factor and the elastic modulus deterioration factor using Eq. (2). The results are listed in Table 2. It is seen that the granite has the highest UCS deterioration factor and elastic modulus deterioration factor, followed by shale and sandstone. Among the three rocks, the granite is the most sensitive to the LN₂ thermal shock, and its mechanical properties deteriorate most significantly. In contrast, the sensitivity of sandstone to thermal shock is the weakest. Both the UCS and the elastic modulus of sandstone do not change greatly after LN₂-cooling treatment. The weak sensitivity of the sandstone to LN₂ thermal shock is responsible for its poor breaking performance under the impact of LN₂ jet.

In the high-pressure LN₂ jet assisted drilling, the cryogenic liquid nitrogen is taken as the drilling fluid. The high-pressure LN₂ jets are generated through a downhole pressurization device to break the hard rock. The schematic diagram for the implementation of this technique is shown in Fig. 13. In this method, the double layer insulated drilling string should be used to deliver LN₂ to the well bottom. After flowing into the pressurization device, LN₂ is pressurized and ejected from the nozzles to break the rock. In order to enhance the insulation capacity of drilling string and prevent LN₂ from gasification intensely during injection, air is injected into the annular between the inner pipe and the outer pipe of the double layer string. The air flows out from the lateral outlet at the string bottom to keep the wellbore rock warm and prevent the wellbore from collapsing due to overcooling. Similar to the gas drilling method, LN₂ gasifies intensely into nitrogen gas after contact with the high-temperature rock at the well bottom. The nitrogen gas flows at extremely high velocity in the annulus, bringing the downhole cuttings to the ground.

The high-pressure LN₂ jet technique, combining the LN₂ low temperature shock and the high-velocity jet impact, can facilitate the breakage of hard rock and improve the rock-breaking efficiency significantly. This technique has a wide application prospect in improving the drilling rate of hard formations in deep wells. Especially for the hot dry rock (HDR) geothermal, the thermal shock effect of LN₂ can be enhanced dramatically due to the high rock temperature in such reservoirs. The temperature of HDR geothermal reservoir rock is generally in the range of 150-500 °C, while the boiling temperature of LN₂ is -196 °C at atmosphere pressure. Temperature difference between LN₂ and HDR amounts to about 350-700 °C. Under such a high temperature difference, the thermal shock effect would be very strong and mechanical properties of the hard rock can be weakened dramatically. Hence, the LN₂ jet can greatly increase the drilling rate and reduce the drilling period and cost for HDR development. Moreover, the LN₂ jet method can be combined with the cavitation jet and the underbalance drilling techniques to eliminate the chip hold effect and avoid the repeated crushing of cuttings, which helps to further improve well drilling rate^[19]. In the drilling method assisted by the LN₂ jet, the liquid nitrogen gasifies to bring cuttings to the ground. Like the gas drilling approach, the current drilling method also shows a great application to address the severe leakage and the circulation lost issues. Therefore, it will be helpful for the well drilling in the fracture developed formations. Additionally, the drilling method assisted by the LN₂ jet is also suitable for the water sensitive formations. Nitrogen is a nonpolluted and inert medium with extremely stable chemical properties. Swelling of clay minerals existing in the conventional water-based drilling can be well resolved.

Thermal shock induced by LN₂-cooling can deteriorate mechanical properties of rocks, such as uniaxial compressive strength and elastic modulus. The deterioration becomes more pronounced as the initial temperature of rock increases. Among the three rocks, granite and shale are more sensitive to the LN₂ thermal shock. Mechanical property deteriorations for these two rocks are more remarkable than sandstone.

Among the three rocks, the LN₂ jet has the highest breaking efficiency on granite. The rock-breaking performance of the LN₂ jet improves with increasing initial temperature of rock. For granite, the threshold temperature for large-volume breakage falls in the range of 150-260 °C under the jet pressure of 25 MPa.

Thermal stress can be induced by LN₂-cooling, and the thermal stress in granite is significantly higher than that in sandstone and shale. The thermal stress grows with cooling continuously, but its growth rate declines first and increases at the LFP point then declines again as the film boiling transits to nuclear boiling during LN₂-cooling.

Characterized by large-volume breakage, the LN₂ jet has merits of high rock-breaking efficiency and low threshold rock-breaking pressure. It shows a great potential in the drilling rate improvement of high-temperature granite formations such as HDR geothermal.

D_I—deterioration factor of rock mechanical properties, %;

E—elastic modulus, GPa;

I_air, I_LN2—mechanical properties after air-cooling and after LN₂-cooling;

V_p—P-wave velocity of rock, m/s;

α—thermal expansion coefficient, K^-1;

ΔT—temperature drop, K;

ΔV_p—change in P-wave velocity, m/s;

${{\sigma }_{\text{T}}}$—thermal stress, MPa.