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. 2024 May 24;9(22):23927–23939. doi: 10.1021/acsomega.4c02026

Impact Pressure Characteristics of Carbon Dioxide Phase Transition Fracturing Technique

Bingzhen Yu 1, Shuaishuai Niu 1, Shengtao Zhou 1, Yu Lei 1, Zhijian He 1, Xuedong Luo 1,*
PMCID: PMC11154721  PMID: 38854542

Abstract

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Carbon dioxide phase transition fracturing (CDPTF) is widely regarded as a promising coal seam mining technique because it can effectively improve coal seam permeability and prevent gas outbursts. An impact pressure test system of CDPTF was developed, and the effects of different factors on impact pressure were investigated by combining CO2 release experiments and smoothed particle hydrodynamics numerical simulation. In addition, based on the Peng–Robinson equation and the pipeline pressure drop formula, new mathematical models for the pressure equation in the buffer tank and the velocity of gaseous CO2 at the nozzle were established. The results show that the impact pressure of CDPTF can be divided into rapid boost, fluctuation, and attenuation stages. The impact distance and impact angle have the most significant effects on pressure. The models of the pressure in the buffer tank and the velocity of gaseous CO2 at the nozzle well-simulated the experimentally obtained impact pressure curves. The research results could provide a reference for the loading study of CDPTF.

1. Introduction

China has abundant coal resources, and due to the transfer of coal seam mining from shallow to deep, deep coal seam mining faces the problems of rock bursts,1,2 low permeability, and high mining difficulty. The permeability of coal seams directly affects mine safety, gas extraction, and coalbed methane (CBM) collection efficiency.3,4 To improve the permeability of coal seams, it is necessary to prefracture and modify the coal seams,5 and this process can be realized by hydraulic fracturing technology,6 static fracturing agents,7 and hydraulic slotting,8,9 among other techniques. However, water in fracturing by hydraulic fracturing technique is unfavorable for CBM production, also known as the water lock effect.10 Moreover, this technique requires much water and may even induce earthquakes.11,12 Static fracturing agents have a long reaction time and are sensitive to ambient temperature.13 Hydraulic slotting has the same disadvantages of high water consumption and low efficiency. Compared with other techniques, carbon dioxide phase transition fracturing (CDPTF) is a reliable method of rock fracture,14 which has the advantages of high safety, flame retardancy, and nonpollution of the environment.15 The technique could be well applied in coal seams.

In recent years, scholars have conducted preliminary explorations on CDPTF, including CO2 fractured coal body life cycle,16 crack propagation,17−21 CDPTF vibration,22 energy distribution,23 etc. Among them, the impact pressure of CDPTF on the rock body is essential. Shang et al. used liquid CO2 fracturing to break the coal under triaxial stress conditions.24 They found that the higher release pressure is favorable for coal body fracturing, but the crack formation is hindered by the fracturing zone. To clarify the fracture mechanism of coal rock during CO2 fracturing, Wang et al. established a fracture pressure model and a gas pressure distribution model of CO2 blasting coal rock. They obtained the relationship between crack propagation and pressure distribution.25 On the other hand, Fan et al. used the fracturing test of coal under true triaxial conditions.26 They found that the initial pressure of liquid CO2 fracturing was 83.3% of hydraulic fracturing at the same stress and flow rate, and the pressure increased with the flow rate. Wang et al. carried out several sets of supercritical carbon dioxide (SC–CO2) fracturing experiments, using various parameters as variables to obtain the conclusion that the jet temperature, distance, and pressure are the primary influence factors of fracturing.27 Zhang et al. established the liquid CO2 phase transition jet pressure model based on thermal engineering and elastic mechanics theories, obtained the pressure versus time and cross-section curves, and found that liquid CO2 phase transition fracturing gas pressure and time are exponentially related.28 Considering that the impact pressure signal of CDPTF is disturbed by noise, Zhou et al. proposed a hybrid denoising method based on complete ensemble empirical mode decomposition with adaptive noise, permutation entropy, Hurst exponent, and stationary wavelet transform. After denoising, the impact pressure signal was pure.29 Chen et al. assumed the high-strength steel pipe as a borehole by the self-developed monitoring device, cut monitoring holes in the steel pipe and installed pressure sensors to measure the CO2 impact pressure, and obtained that the impact pressure decayed nonlinearly with the distance from the gas outlet.30 Tian et al. proposed the influence of ambient pressure and impact distance on SC–CO2 jet pressure.31 They discovered that, for short impact distances, the impact pressure significantly decreases as ambient pressure increases, while erosion volume and impact pressure also decrease as impact distance increases.32 Cai et al. used SC–CO2 impact target distance and initial pressure as reference factors to study the relationship between impact pressure and distance through numerical simulation.33 It is concluded that the impact pressure decreases with the increase in distance, and the increase in initial pressure leads to an increase in impact pressure.34 Zhang et al. set SC–CO2 fracturing laminar face angle from 0 to 90° and found that the fracturing pressure showed a decreasing trend with the increase of the laminar face angle.35 Liu et al. believe that the CO2 fracturing process is affected by multiple coupling factors. When the pressure is 1–3 MPa, the Klinkenberg effect dominates the permeability increase. When the pressure is 3–5 MPa, the increase in pressure causes the permeability to increase.36 However, the studies are mostly limited to specific stress states, distances, flow rates, etc. This leads to a lack of systematic knowledge of the impact pressure behavior of CDPTF under different conditions. Extending the range of experimental conditions, especially the initial impact conditions, will help to comprehensively understand the impact pressure characteristics of CDPTF.

In this paper, based on the impact pressure test system of CDPTF, several impact pressure tests were carried out with different initial conditions. The variation rules of impact pressure under different liquid CO2 charging masses, heating temperatures, impact distances, and angles were investigated. The pressure model in the buffer tank based on the Peng–Robinson equation and the gaseous CO2 release velocity model based on the pipeline pressure drop formula were established. In addition, the reliability of the test results was verified by the numerical simulation. The research results could provide a reliable experimental reference for the application of CDPTF.

2. Mechanism of CO2 Phase Transition Fracturing Technique

The CDPTF technique uses the energy difference between supercritical and gaseous CO2 to break the rock. There are two phase transition stages from liquid CO2 phase to gaseous CO2. The liquid CO2 in the buffer tank phase transitions to SC–CO2.37 Supercritical carbon dioxide is suddenly released when the rupture disk fails, and SC–CO2 undergoes a phase transition into the gaseous CO2. This phase transition will lead to intense gas volume expansion, resulting in compression waves and explosion effects. The typical rock breakage process of CDPTF is shown in Figure 1. Rock fracture under the CDPTF is essentially the crack propagation behavior of rock mass under the coupling action of stress waves and high-pressure gas. The dynamic impact stress destroys the rock when high-pressure CO2 gas is released, and initial cracks are generated in the rock mass. The crack tip expands forward under high-pressure gas pressure. On the basis of this, CDPTF can be applied to concrete and rock breaking,38,39 coal mining, blasting to remove obstacles, etc.40−42

Figure 1.

Figure 1

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Rock breakage by CO2 phase transition fracturing.

3. Experimental Designs

3.1. Experimental System

A CO2 phase transition impact pressure test system is designed based on the mechanism of CDPTF, as shown in Figure 2. It consists of a pressurization system, buffer tank, impact pressure test system, and temperature–pressure control system.

Figure 2.

Figure 2

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CO2 phase transition impact test system: (a) schematic diagram (unit: mm) and (b) physical diagram.

The pressurization system includes a liquid CO2 storage tank, an air compressor, and a booster pump. Liquid CO2 is pressurized in the booster pump and injected into the buffer tank. The buffer tank has a volume of 1.4 L and can withstand a maximum of 70 MPa. It is equipped with an air intake, a high-speed pneumatic valve to control the gas out, and a temperature–pressure control system to sample the temperature and pressure data in the buffer tank and heat the buffer tank, respectively. When the pressure reaches a predetermined value, the high-speed pneumatic valve is opened, and the SC–CO2 in the buffer tank is released. The length of the release tube is 200 mm, in which SC–CO2 could completely phase transition into gaseous CO2. The gaseous CO2 is rapidly released from the nozzle and impacts the impact plate.

The impact pressure testing device is an impact plate consisting of an angle adjuster, a distance adjuster, and a pressure sensor. The impact plate can withstand pressure up to 80 MPa. It has an angle adjustment range of 60–90° and a controllable distance between the impact plate and the nozzle of 4–30 mm. The pressure data sampling system consists of TP-2004 pressure sensors, a TP-5007 charge amplifier, and a DHDAS-8302 dynamic signal sampling system. The sampling frequency of the DHDAS-8302 dynamic signal sampling system is up to 100 kHz. The TP-2004 pressure sensor belongs to a piezoelectric pressure sensor. The TP-2004 pressure sensor is made of high-strength stainless steel, with a maximum sampling frequency of 200 kHz, a measurement range of 0–50 MPa, and an operating temperature of −30 to 180 °C. During the experiment, the pressure sensor transmits the signal to the signal amplifier, and then, the signal amplifier transmits the signal to the computer through the dynamic signal sampling system. Then, the computer obtained detailed curves of the CO2 phase transition impact process pressure.

3.2. Experiment Program

Table 1 shows the initial parameters of CDPTF pressure tests. The adjustable impact plates could simulate broken objects at different angles and distances from the explosion source. The impact pressure is sampled through the dynamic signal sampling system. During the tests, if the pressure in the buffer tank remains unchanged within 10 min, it is considered that all liquid CO2 has completely phased into SC–CO2.

Table 1. Experimental Arrangement of CO2 Phase Transition Impact Pressure Tests.

no. liquid CO2 mass (g) temperature (°C) impact distance (mm) impact inclination (deg)
A 1000 40 10 90
B-1 400 40 10 90
B-2 600 40 10 90
B-3 800 40 10 90
B-4 1000 40 10 90
B-5 1200 40 10 90
C-1 1000 36 10 90
C-2 1000 38 10 90
C-3 1000 42 10 90
C-4 1000 44 10 90
D-1 1000 40 4 90
D-2 1000 40 8 90
D-3 1000 40 16 90
D-4 1000 40 18 90
D-5 1000 40 20 90
E-1 1000 40 10 60
E-2 1000 40 10 70
E-3 1000 40 10 80
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The procedure of the CO2 phase transition impact test performed as follows:

  • (1)

    Turn on the air compressor and booster pump, charge liquid CO2 into the buffer tank, and weigh the charging mass with the precision electronic scale.

  • (2)

    Start the temperature–pressure control system, control and monitor the temperature in the buffer tank, and record the temperature and pressure data when the temperature and pressure rise to target values and reach stability.

  • (3)

    Open the high-speed pneumatic valve of the buffer tank and release the CO2 from the nozzle. The high-pressure CO2 impacts the impact plates. The pressure sensor installed on the impact plate measures the impact pressure during the release process.

4. Experiment Results

4.1. Effect of Liquid CO2 Charging Mass

Figure 3 shows the impact pressure curves at different liquid CO2 charging masses. It is shown in Figure 3 that a rapid increase occurs within the range of 0–24.8 ms, followed by fluctuations of varying degrees, and then, the pressure decayed sequentially to 0 MPa after 51.5 ms. On the basis of the characteristics of the impact pressure curves, the impact pressure curves could be divided into three stages: (1) rapid boost stage, (2) fluctuation stage, and (3) attenuation stage.

Figure 3.

Figure 3

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Time history of impact pressure at different liquid CO2 charging masses.

In the rapid boost stage, the impact pressure increases exponentially. When the liquid CO2 charging mass values are 400, 600, 800, 1000, and 1200 g, the reaching times of the peak pressure were 24.3, 24.3, 24.5, 24.7, and 24.8 ms, respectively. At this time, the corresponding peak pressures were 5.13, 5.20, 5.31, 5.42, and 5.76 MPa. The time and the peak pressure for the rapid boost stage are less affected by the liquid CO2 charging mass, and then, the pressure curves begin to fluctuate, entering the fluctuation stage.

In the fluctuation stage, the pressure first drops linearly and then rebound when the CO2 charging mass is greater than 400 g. The fluctuation tends to be gentle as the liquid CO2 charging mass decreases. As shown in Figure 3, the rate of pressure decrease in the fluctuation stage gradually decreases as the mass decreases until the pressure rebound phenomenon occurs. The reduction of liquid CO2 charging mass causes the duration of the fluctuation stage to become shorter. When the liquid CO2 charging mass is 400 g, the pressure decays at 51.5 ms. While the liquid CO2 charging mass values are 600, 800, 1000, and 1200 g, the decayed times are 57.6, 60.4, 63.9, and 74.7 ms, respectively.

In the attenuation stage, the pressure decays linearly and decreases sequentially to 0 MPa, starting at 330.2 ms.

The critical pressure and temperature for the phase transition from liquid CO2 to SC–CO2 are 7.39 MPa and 31 °C, respectively. When the liquid CO2 charging mass is 400 g, part of the SC–CO2 is first released after the high-speed pneumatic valve is opened. The pressure in the buffer tank is reduced to the critical pressure. Then, the released SC–CO2 phase transitions to gaseous CO2. However, at this time, the expansion caused by the phase transition cannot make the buffer tank pressure rise rapidly but maintain in the vicinity of the critical pressure. Therefore, when the liquid CO2 charging mass is 400 g, the pressure curve fluctuates gently.

4.2. Effect of Heating Temperature

According to existing research, CDPTF has a shorter duration. Based on the limit superheat theory, if the temperature in the buffer tank is higher than the superheat limit temperature under the corresponding pressure, the boiling liquid expanding vapor explosion occurs.43,44 Therefore, the temperature has an effect on CDPTF.45 The impact pressure-time curves at different heating temperatures in the buffer tank are shown in Figure 4. Under different heating temperatures, the rapid boost stages of the curve are 0 to 31.3 ms. After the rapid boost stage, the pressure decreases and enters the fluctuation stage. At this stage, the external environment has an effect on the pressure. The pressure showed a small range of gentle fluctuations at different heating temperatures until the end of the fluctuation stage at 70.8 ms due to decreasing kinetic energy. Subsequently, the curves enter the attenuation stage. When the heating temperatures are 36, 38, 40, 42, and 44 °C, the peak pressure is close. Among them, the peak pressures at different temperatures are 5.15, 5.22, 5.31, 5.37, and 5.39 MPa, respectively. The peak pressure is positively related to the heating temperature. When the release pressure rises to the rated value, the high-speed pneumatic valve opens. At this time, the CO2 charging mass is the same, and the corresponding physical properties of CO2 are the same. The difference in temperature curves is relatively small.

Figure 4.

Figure 4

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Time history of impact pressure at different temperatures.

4.3. Effect of Impact Distance

After CO2 is released, it comes into contact with the external environment and reaches the impact plate. Since the impact pressure will attenuate in the air, the distance may affect the peak pressure.

The pressure curves are significantly different with the varying impact distance. The peak pressure at a distance of 4 mm is the largest, reaching 5.95 MPa. The pressure shows a decreasing trend with the increasing impact distance. The minimum peak pressure of 3.98 MPa occurs at a distance of 20 mm, which is only 66.89% of the peak pressure at an impact distance of 4 mm. The peak pressure at 4 mm occurs at the end of the rapid boost stage, and the corresponding time is 25.5 ms. When the impact distance is 20 mm, the peak pressure appears at 35.1 ms. When the impact distance is 20 mm, it is indicated from the corresponding impact pressure curve that after the rapid boost ends, the pressure begins to decay directly. Therefore, it can be inferred that when the impact distance exceeds 20 mm, there is no fluctuation stage in the postpeak pressure stage.

The impact pressure-time curves at different impact distances are shown in Figure 5. The variation of curves is closely related to the compression wave, and the effect of the compression wave is more obvious the closer the distance. First, the compression wave causes a significant peak in the pressure curve when gaseous CO2 impacts, and then, the pressure decreases in the propagation stage of the stress wave. The second wave peak is caused by SC–CO2 phase transition expansion. Finally, the pressure gradually decreases as the SC–CO2 in the buffer tank decreases.

Figure 5.

Figure 5

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Time history of impact pressure at different impact distances.

4.4. Effect of Impact Angle

In this study, the effect of impact inclination on impact pressure characteristics is also investigated.

The impact pressure-time curves at different impact angles are shown in Figure 6. Except for the impact angle of 90°, other impact angles directly enter the attenuation stage after reaching the peak pressure. The fluctuation stage is not obvious. The peak pressure gradually decreases with the decreasing impact plate inclination angle. The peak pressure 5.04 MPa appears at 77.2 ms when the impact angle is 80°, and the peak pressure 4.14 MPa appears at 102.9 ms when the impact angle is 60°. When the impact angle is 60–80°, the pressure increase rate decreases significantly around 27.2 ms. Then, the curves successively reach the peak pressure after 66.6 ms and enter the attenuation stage. The results show that when there is an inclination angle of the impact, the impact pressure of CO2 does not act entirely on the impact plate, and part of the impact pressure is lost along the direction of the impact plate plane. Therefore, if the impact angle decreases, the impact pressure will decrease at all impact stages.

Figure 6.

Figure 6

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Time history of impact pressure at different impact angles.

4.5. Peak Pressure Characteristics

Figure 7 shows the peak impact pressure at different liquid CO2 charging masses and temperatures. It is observed in Figure 7 that the peak impact pressure increases linearly with the increasing charging mass and temperature. For every 2 °C increase in temperature starting from 36 °C, the peak pressure increases by an average of 1.26%. Moreover, starting from 0.4 kg, the peak pressure increased by an average of 3.07% for every 0.2 kg increase in liquid CO2 charging mass. The increase of the liquid CO2 charging mass generates more SC–CO2 in the buffer tank, resulting in a higher impact pressure on the impact plate. The maximum difference between the fitting curves and the measured value is only 0.08 MPa.

Figure 7.

Figure 7

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Peak pressure at different initial states.

Figure 8 presents the variation of peak pressure with impact distance and angle, which decreases with the increase of impact distance and increases with the increase of impact angle. For every 2 mm increase in impact distance, the peak pressure decreases by an average of 7.52%. Since the CO2 is released into the external environment, the degree of gas diffusion is more obvious with the increasing impact distance. The kinetic energy of the CO2 impact flow is reduced, and the corresponding peak pressure will also be reduced. During this process, gaseous CO2 diffuses into the air. Carbon dioxide reaches the impact plate with a significant loss of kinetic energy.

Figure 8.

Figure 8

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Peak pressure under different impact conditions.

The peak impact pressure drops with decreasing inclination angles. From 60°, with each 5° increase in angle, the average increase in peak impact pressure is 5.85%. Compared with the liquid CO2 charging mass increase of 3.07% for every 0.2 kg, the heating temperature increases by 1.26% for every 2°, and the percentage in impact distance and angle variation is greater. The impact distance and angle have a more significant effect on the peak pressure.

5. Mathematical Model

5.1. Pressure Equation in the Buffer Tank

After reaching the critical temperature and pressure, the liquid CO2 in the buffer tank has completely phased into SC–CO2. Supercritical carbon dioxide is not an ideal gas and has both gaseous and liquid properties. Therefore, the ideal gas equation of state cannot be used to determine the pressure in the buffer tank. In 1976, Peng and Robinson proposed the Peng–Robinson equation for calculating the state of carbon dioxide. This is an equation of state that describes the properties of carbon dioxide. It is considered the optimal third-order equation of state suitable for calculating gas–liquid flatness and thermodynamic properties of pure substances.46,47 Therefore, the Peng–Robinson equation was introduced to describe the state of SC–CO2 in the buffer tank

5.1. 1
5.1. 2

where P1 is the pressure of carbon dioxide, MPa; R is the gas constant, is 8.314 J·mol–1·K–1; V is the gas molar volume, L·mol–1; Pc refers to the critical pressure, MPa; ω denotes the eccentricity factor; T is the absolute temperature in the buffer tank, K; Tc is the critical temperature, K; and Tr = T/Tc.

For SC–CO2, ω = 0.225; Pc = 7.39 MPa; Tc = 304.19 K; and when substituting eq 1 into eq 2, the following equation could be obtained

5.1. 3

The following conversion could be further carried out by the definition of density

5.1. 4
5.1. 5

where ρ represents the density, kg·m–3; M is the molar mass, g·mol–1; the molar mass of CO2 is 44 g·mol–1; m stands for the liquid CO2 charging mass in the buffer tank, kg; and V0 = 1.4 L is the volume of the buffer tank.

Based on eqs 3–5, the pressure P equation in the buffer tank can be obtained

5.1. 6

Comparing the pressure equation in the buffer tank and the measured data, the curves of eq 6 and the measured data show the same trend. The average error of pressure in Figure 9a is 8.35%, and the average error of pressure in Figure 9b is 6.94%. It shows that eq 6 can accurately represent the pressure in the buffer tank.

Figure 9.

Figure 9

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Buffer tank measured pressure and eq 6 calculation results: (a) different liquid CO2 charging masses and (b) different heating temperatures in the buffer tank.

5.2. CO2 Release Velocity Equation

Based on the experimental results from Section 4, the impact pressure is directly correlated with the initial parameters. The pressure in the buffer tank affects the velocity of gaseous CO2 at the nozzle. During the impact experiment, the SC–CO2 phase transitions into gaseous CO2 in the release tube. As the internal pressure of the buffer tank decreases and the gaseous CO2 velocity increases, there is a pressure drop in the release tube. The CO2 impact velocity at the nozzle is selected as the key variable to quantitatively describe the impact pressure. Therefore, the pipeline pressure drop formula could be introduced to calculate the velocity of gaseous CO2 at the nozzle48

5.2. 7

where, Δp is the fluid pressure drop, kPa; λ is the friction factor; d is the inner diameter of the release tube, which is 0.01 m in this study; L refers to the length of the release tube, which is 0.2 m; g is the gravitational acceleration, m·s–2; H stands for the height difference between the head and end of the tube, m; and V1 is the velocity of gaseous CO2 at the nozzle, m·s–1. The friction factor λ is considered as a function of the Reynolds coefficient Re by the Panhandle (B) equation49

5.2. 8
5.2. 9

where μ is the hydrodynamic viscosity, Pa·s; the unit of Re is kg·s·m–2. The velocity of gaseous CO2 at the nozzle equation can be obtained by eqs 7–9

5.2. 10

According to eqs 6 and 10, substituting the experimental data, the initial velocity of gaseous CO2 at the nozzle is 278.27 m/s when the liquid CO2 charging mass is 1 kg.

6. Numerical Simulations Based on the Smoothed Particle Hydrodynamics Method

6.1. SPH Method

The SC–CO2 phase transitions into gaseous CO2, showing intense volume expansion. The SPH can effectively implement fluid computations, so it is suitable for CO2 phase transition impact simulation.50,51 The SPH method is a Lagrangian-type particle method for simulating fluid flow, which has great advantages in calculating gaseous deformation. Unlike mesh methods such as finite element and finite difference methods, it does not require the mesh to partition the computational domain. It could discretize the computational domain into a series of interacting particles.52Figure 10 shows the particle partitioning and the neighborhood search in the SPH method.53 These particles carry various physical quantities, including mass, density, velocity, acceleration, energy, etc. When SPH simulates a particle flow, the particles are regarded as substances with continuity and fluid properties, and the interactions between neighboring particles are represented through a smooth kernel function,54,55 which could calculate the interaction strength between the particles based on the distance between them.

Figure 10.

Figure 10

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Particle partitioning and neighborhood search.

For the SPH method, based on interpolation theory, any set of functions may be represented on the disordered points. The particle positions are represented by the smooth kernel function.33 The function values of particles in the scope can be derived by smooth kernel functions W(x – x’, h)

6.1. 11

where ⟨ ⟩ represents the approximate value of eq 11; f(x) is the 3D coordinate function; W is the smooth kernel function; x stands for the location vector of the particle; x’ refers to a neighboring particle in the domain; x – x′ is the two-particle spacing; h is the smooth length; and Ω is the field of action.

The use of particle approximation to the kernel function to achieve interpolated discretization, i.e., the continuous integral form of the kernel function approximation is converted to a discrete form of the summation of all particles in the neighborhood. The volume of the particles Vj is used to approximate the infinitesimal dx’ at the particle j in the integral, and the particle mass can be expressed as eq 12

6.1. 12

where mj and ρj are the mass and density of the particle (j = 1,2,···, N), respectively. eq 13 can be obtained by eqs 11 and 12

6.1. 13

Moreover, any interactive particles obey the conservation rules of mass, momentum, and energy.

Eq 14 is the rule of mass conservation

6.1. 14

Eq 15 represents the rule of momentum conservation

6.1. 15

Eq 16 stands for the rule of energy conservation

6.1. 16

where α and β represent space vectors; ρi is the density of the particle; xiβ denotes the coordinate component of x along β; Wij is the smooth function between particles i and j; vijβ refers to the velocity of the particle i relative to j; viα and vjα are the velocity components of particles i and j along α; and σjαβ and σiαβ are the total stress tensors of particles i and j.

6.2. Numerical Model

Using ABAQUS software to simplify the external environmental conditions, a three-dimensional numerical model of CO2 phase transition impact can be established. The finite element model geometric dimensions are 15 cm × 15 cm × 2 cm. Models of SC–CO2 and gaseous CO2 were established using the SPH method. In the established model, the buffer tank and release tube are rigid bodies. The volume of the buffer tank is 1.4 L, and the inner diameter is 60 mm. The four sides of the impact plates were constrained. The impact distance and angle settings follow the test arrangement. Figure 11 presents the numerical model of CO2 phase transition impact.

Figure 11.

Figure 11

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Numerical model of CO2 phase transition impact.

The basic properties of SC–CO2 and high-pressure gaseous CO2 were defined by the MAT_NULL material and the expandable Mie–Gruneisen equation of state in ABAQUS.56 The Mie–Gruneisen equation of state takes the attractive and repulsive forces between molecules into account and defines the impact pressure in expansion

6.2. 17

The material expansion pressure could be defined as follows

6.2. 18

where C is the μs–μp curve intercept; S1, S2, and S3 are the slope coefficients of the μs–μp curve; γ0 is the Gruneisen coefficient; a is the first-order volumetric correction for γ0 and μ = ρ1/ρ0 – 1; ρ1 and ρ0 denote the density and the initial density, respectively; P2 is the equation of state defining the pressure of the compressed state; and E is the internal energy per unit volume. Table 2 shows the material parameter of CO2. Table 3 presents the impact plate adopts properties assigned to the pressure sensor material 316L stainless.

Table 2. Material Parameters of the Carbon Dioxide.

density (kg/m3) C (m/s) γ0 S1 S2 S3
0.879 1480 0.4934 2.56 –1.986 0.2286
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Table 3. Material Model Parameters of 316L Stainless.

density (kg/m3) Young’s modulus (MPa) Poisson’s ratio yield strength (MPa)
7900 2 × 105 0.3 300
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6.3. Numerical Results

6.3.1. Liquid CO2 Charging Mass

Figure 12 presents the pressure evolution of the impact plate at 1000 g of liquid CO2 charging mass, 40 °C, 10 mm of impact distance, and 90° of impact angle. As the duration of CO2 impact increases, the impact plate is continuously impacted by gaseous CO2, and the repeated reflection and superposition of the stress wave leads to an increase in pressure. The rapid boost stage reaches a peak of 4.82 MPa at 46.2 ms. The pressure showed attenuation characteristics and decreased to 3.55 MPa at 96 ms. The more liquid CO2 charging mass causes the pressure in the buffer tank to increase. At this time, the increase in CO2 impact velocity causes a greater dynamic load on the impact plate surface. Therefore, in the process of impacting the coal seam, the more liquid CO2 is charged, the better the fracturing effect is increasing permeability. However, charging liquid CO2 reasonably according to the strength of the coal seam to avoid lower energy utilization efficiency. The numerical simulation results are slightly smaller due to the more complex actual phase transition process, as shown in Figure 13.

Figure 12.

Figure 12

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Process of impact pressure evolution.

Figure 13.

Figure 13

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Peak impact pressure at different liquid CO2 charging masses.

6.3.2. Heating Temperature

As shown in Figure 14, the pressure of the CO2 impact on the impact plate increases as the heating temperature rises, which increases the range of peak pressure and impact pressure effects. The rise in temperature increases the average kinetic energy of SC–CO2 in the buffer tank, which promotes the ability of molecules to collide with each other and increases pressure. At 36, 38, 40, 42, and 44 °C, the peak pressures of the impact plate were 4.67, 4.67, 4.79, and 4.96 MPa, respectively. According to the superheat limit theory of boiling liquid expanding vapor explosion, the severity of phase transition is related to the temperature difference. The rise in heating temperature results in an increase in impact pressure. However, the heat absorbed by the liquid CO2 phase transition in the buffer tank is the same, and the corresponding SC–CO2 physical properties are also the same. Therefore, temperature has less influence on peak pressure.

Figure 14.

Figure 14

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Impact pressure and peak pressure at different temperatures: (a) 36, (b) 38, (c) 42, and (d) 44 °C.

6.3.3. Impact Distance

Figure 15 shows the impact pressure and peak pressure at different impact distances. When the impact distance is 4–8 mm, the distance is less disturbed by the environment and other factors. However, much kinetic energy is lost when CO2 reaches the impact plate at an impact distance exceeding 16 mm. The impact distance affects the kinetic energy transfer and dissipation of the impact. When the impact distance increases, the CO2 is affected by environmental, and its volume expands rapidly, resulting in a decrease in kinetic energy and a significant decrease in the pressure at the impact plate.

Figure 15.

Figure 15

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Impact pressure and peak pressure at different impact distances: (a) 4, (b) 8, (c) 16, (d) 18, and (e) 20 mm.

The impact peak pressure zone shows that when the impact distance is 4 to 8 mm, the center of the impact plate forms a high-pressure zone due to the superposition of compression wave reflections. The pressure of the impact plate gradually decreases outward from the high-pressure zone until about 10% of the maximum value. In addition, with the increase of the impact distance, the pressure distribution of the impact plate tends to be irregular. At the impact distance of 16 to 20 mm, the peak pressure was located in the upper part of the impact plate, and the diffusion of CO2 and the compression wave transmission led to complex variations in the pressure. Therefore, the impact distance largely influences the rock breakage of CDPTF. A shorter impact distance results in a smaller CO2 expansion zone and more significant peak pressure. On the contrary, a longer impact distance results in the diffusion of gaseous CO2, resulting in a lower peak pressure.

6.3.4. Impact Angle

The impact pressure of CDPTF with different angles are shown in Figure 16. The variation of angle will affect the pressure during the rapid boost stage. The smaller the angle, the slower the pressure increase rate, ultimately affecting the peak pressure. When the impact angle is less than 70°, the pressure begins to decrease significantly, and the impact kinetic energy cannot be completely applied to the surface of the impact plate. Therefore, the smaller the impact angle, the worse the effect on coal seam fracturing.57

Figure 16.

Figure 16

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Impact pressure and peak pressure at different impact angles: (a) 60, (b) 70, and (c) 80°.

The high-pressure zone shows that as the impact angle decreases, the CO2 is reflected to the inclined surface, resulting in compression zones in the middle and upper part of the impact plate. The angle between the CO2 impact direction and the target object influences the CDPTF final impact effect, and the pressure on the plate surface is significantly reduced under the inclined condition. Specifically, different impact inclinations lead to different directions of CO2 diffusion and expansion, resulting in different pressure distributions. As a result, the fracturing effect and the peak impact pressure of CDPTF are affected. Vertical impact on the target surface generally produces the maximum peak impact pressure.

7. Conclusions

To investigate the impact pressure characteristics of CO2 phase transition fracturing. An impact pressure test system was established, and the impact pressure of CO2 phase transition fracturing with varying initial conditions was tested. Based on the tests that were conducted, a mathematical model of the pressure in the buffer tank and the velocity of gaseous CO2 at the nozzle was established. Finally, the reliability of the mathematical models was verified through numerical simulation. The main findings are as follows:

  • (1)

    The impact pressure curve of CO2 phase transition fracturing could be divided into three stages: rapid boost, fluctuation, and attenuation. In the rapid boost stage, pressure increases rapidly. In the fluctuation stage, the pressure is constantly fluctuating, and the pressure in this stage may be greater than in the rapid boost stage. During the attenuation stage, the pressure decreases with time and eventually decays to 0.

  • (2)

    The impact pressure increases with the increase of liquid CO2 charging mass, heating temperature, and impact angle. On the contrary, the impact pressure decreases with the increase in impact distance. The impact distance and angle have a more significant effect on the peak pressure. The peak pressure decreases by 7.52% for every 2 mm increase in the impact distance, and the peak pressure increases by 5.85% for every 5° increase in the impact angle.

  • (3)

    The variation in impact pressure caused by increasing liquid CO2 charging mass and heating temperature is small. When performing this technique in rock breaking, the liquid CO2 charging mass and heating temperature should be reasonably determined based on the strength of the coal seam or rock mass to avoid energy waste.

  • (4)

    The mathematical models for the pressure equation in the buffer tank and the equation of CO2 initial velocity at the nozzle can well describe the pressure in the buffer tank and the impact of the CO2 phase transition impact. The formula and numerical method better simulate the impact pressure variation of CO2 phase transition.

Acknowledgments

This research was jointly funded by the National Natural Science Foundation of China (grant nos. 42072309), the Fundamental Research Funds for National University, China University of Geosciences (Wuhan) (grant no. CUGDCJJ202217), the Knowledge Innovation Program of Wuhan-Basic Research (grant no. 2022020801010199), and the Hubei Key Laboratory of Blasting Engineering Foundation (grant no. HKLBEF202002).

The authors declare no competing financial interest.

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