The Thermodynamic Change Laws of CO₂-Coupled Fractured Rock

Abstract

Under the background of the “dual carbon” target, exploring the pathway of efficient geological storage and high energy utilization of CO₂ is a hot issue in CO₂ emission reduction research. Under the coupling effect of high geopathic stress in deep rock layers and thermal stress generated during the geological sequestration of CO₂, CO₂ infiltration into coal rock changes the ambient temperature around the rock, while thermal diffusion effects cause damage to the rock and influence fracture expansion. In the present study, CO₂-water–rock coupling test system and characterization of fissure surface roughness were conducted to analyze the rock’s mechanical properties, damage, and fracture evolution. Modeling of the equivalent fissure was employed to reveal the heat transfer mechanism between the rock matrix and CO₂. The results obtained illustrate that the rock samples coupled with CO₂ exhibited remarkable changes in mechanical properties. These changes include an increase in the number of pores, enhanced inter-pore connectivity, and a planar type of surface roughness in the fissures, ultimately resulting in an increase in conductivity. Conversely, the remaining rock samples displayed poor mechanical properties and surface fracture connectivity. As pressure decreased, the heat transfer coefficient decreased from 86.9 W/m²·K to 57.5 W/m²·K, accompanied by a temperature drop from 33.6 °C to 30.6 °C, demonstrating a proportional relationship between pressure and the heat transfer coefficient. Furthermore, the flow rate gradually increased with the rise in CO₂ pressure, indicating denser flow lines with faster flow rates. At 15 MPa, CO₂ exhibits enhanced mobility.

1. Introduction

The depletion of resources in shallow coal beds has led to a gradual shift towards deep mines in coal mining. It is characterized by multiple energy sources and low seepage due to high-intensity mining in deep coal beds. High-stress, low-permeability coal rocks seriously restrict safe, efficient production in mines. The transformation of coal rocks has emerged as a fundamental scientific concern in addressing technical challenges encountered in coal mining operations [1]. The excellent mobility and high permeability of supercritical CO₂ play a crucial role in diminishing the mechanical properties of coal rocks, which enables it as a substitute for methane during CO₂ injection into the stratum for geological storage. This holds immense significance in achieving the objective of double carbon [2,3,4,5]. As early as the 1840s, researchers studied the application of CO₂ in mines and discovered its potential to induce alterations in the mechanical properties of coal rocks, which stabilizes reservoirs [6].

There are many studies on the effect of CO₂ on the mechanical properties of rocks. Wen et al. [7] researched CO₂ fracturing and permeability enhancement. Supercritical CO₂, exhibiting acidification and unblocking characteristics as well as excellent permeability, can enhance coal rock permeability and depressurization. CO₂ weakens the compressive strength and elastic modulus of rocks, and the weakening effect of supercritical CO₂ is more obvious compared to CO₂ [8]. Lyu et al. thought that the compressive strength and elasticity modulus of rocks decreased gradually with increased pressure [9]. Tang et al. [10] found that the triaxial compressive and tensile strength of rocks decreases gradually with the increased adsorption time of supercritical CO₂. The elasticity modulus and Poisson’s ratio of rocks increased gradually with increased CO₂ pressure and temperature [11]. Liu et al. [12] believed that supercritical CO₂ has different penetration enhancement effects on coal under different pressures. CO₂ pressure affects the fluidity and modification of the fluid in the coal matrix. Researchers have found that supercritical CO₂ significantly reduces the mechanical properties of coal rocks. Microcracks and fissures develop in rock mass under the interaction of CO₂ and rocks [13,14]. Liang et al. [15] studied the distribution characteristics of cracks in coal after CO₂ fracturing, revealing the extension mechanism of sandstone cracks during the fracturing process. Since water is one of the main factors affecting the mechanical properties of materials [16], the decreased fracture width or increased surface roughness makes the fluid more prone to decreased overpressure [17]. It weakens the discharge capacity of fractures. The mechanical mechanism of hydraulic fracturing for coal structure destruction is investigated, revealing that hydraulic fracturing can enhance the effectiveness of top coal pre-cracking [18]. Li et al. [19,20,21] investigated the mechanism of fracture morphology evolution in fractured coal under water and supercritical CO₂ fracturing conditions. CO₂ significantly affects coal rock wettability and fracture expansion.

The above studies mainly focus on rock tensile strength. CO₂ plays an important role in weakening rock mechanical properties and microcrack extension. However, the process of injecting CO₂ into the deep earth involves solid mechanics and physical fields as well as temperature and flow field changes triggered by the phase change process of CO₂. Additionally, the analysis of coal–rock structural modification should consider multi-field coupling characteristics such as heat–hydraulic–solid [22,23]. CO₂ exchanges heat with the rock matrix during fissure seepage, which changes the temperature field distribution of the fissured rock and affects the expansion of the fissure.

MTS tests were performed to determine the alteration patterns of rocks’ mechanical properties after the rock samples were treated with CO₂-H₂O coupling in this study. Additionally, the changes in rock pore and fracture structure, as well as surface roughness, were quantified using SEM and 3D electron microscope scanning technology. A coupled heat–fluid–solid model was developed to invert the effect of CO₂ heat convection on the ambient temperature around fissured coal rocks, revealing the heat transfer between the rock matrix and CO₂ in the pores. The results can provide the theoretical basis for the safety evaluation of CO₂‘s deep earth storage and industrialized application in fracturing and permeability enhancement.

2. Materials and Methods

2.1. Experimental Device and Materials

Thermodynamic testing of rock samples was performed using MTS equipment developed by Central South University. This equipment, with a triaxial hydraulic control cabinet and triaxial seepage control cabinet, was used for the triaxial and seepage characterization of rocks under normal and high temperatures. The maximum load was 2600 KN, with a triaxial peripheral pressure of 140 MPa, a penetration pressure of 140 MPa, and a temperature from room temperature to 200 °C (Figure 1).

A CO₂-water–rock coupled experimental device developed by Xi’an University of Science and Technology was employed to prepare the rock samples exhibiting coupled thermodynamic behaviors (Figure 2). The seepage experimental device consists of a pressure chamber, a temperature control system, a coupled fracturing fluid supply device, and a fixed-speed pump. The device can provide a maximum stress of up to 40 MPa and regulate the temperature of the pressure chamber from room temperature to 100 °C. Additionally, the pump can provide constant pressure in the range of 0 to 40 MPa.

2.2. Experimental Methods

The specimens were taken from a low-permeability reservoir in the northern Shaanxi area of the Ordos Basin, which is the most concentrated area of low-permeability, high-stress coal rocks [24]. XRD analysis of the selected rock samples showed that the mass fraction of quartz in the sandstone was 30.15% and the mass fraction of carbonate minerals was 30.16%, including 25.16% of calcite and 5% of dolomite. Sandstone contained minor clay minerals, including 14.7% of illite and 3.4% of kaolinite.

Prior to experiments, standard rock samples were prepared (Φ 50 mm × 100 mm). The samples were classified as follows:

① Group 1 consisted of rock samples in their natural state. The samples were sealed and stored under atmospheric conditions and were labeled as FS-0.

② Group 2 involved water-saturated rock samples. The samples were immersed in water for 24 h and were labeled as water samples.

③ Group 3 comprised saturated CO₂-coupled samples. We placed the rock samples separately in a CO₂-water–rock coupled experimental device with liquid CO₂ concentrations of 0%, 4%, 6%, and 8% for full saturation, which were labeled as CW-0, CW-4, CW-6, and CW-8, as shown in Figure 3a. Then, coupling rock samples containing different concentrations of CO₂ were placed in a high-temperature and high-pressure reactor with temperatures of 25 °C, 35 °C, and 45 °C, which were labeled as B-1, B-2, and B-3; one natural rock sample was numbered F1, as shown in Figure 3b. Finally, we performed MTS seepage experiments under the same pore pressure and action time, as shown in Figure 3c, and the mechanical properties of four types of rock samples were analyzed. The mechanical parameters of the rock samples were obtained through uniaxial testing using the experimental device developed by Xi’an University of Science and Technology, as shown in

Table 1. Mechanical parameters after CO₂-coal sample coupling action.

Sample	Compressive Strength/MPa	Tensile Strength/MPa	Elastic Modulus/GPa
CO2-water–rock coupled rock samples	5.3	0.85	0.21
Clear water rock sample	9.8	1.52	0.38
Natural sample	16.5	2.98	0.57

.

3. Results

3.1. Experimental Results Thermodynamics of CO₂-Induced Rock Fracturing

The results of the CO₂-water–rock coupling seepage test demonstrate that the compressive strength and elastic modulus of samples subjected to immersion in water and coupled fracturing fluid with a CO₂ mass fraction of 8% exhibit varying degrees of reduction. Figure 4a indicates that the CW-8 sample exhibits a significantly weakened stress–strain diagram in comparison to the rock samples in other states. Figure 4b reveals that the compressive strength and elastic modulus of the rock samples exposed to CO₂-coupled fracturing fluid decreased greatly compared with those of the natural samples and the water-soaked samples; the larger the CO₂ mass fraction, the more obvious the decrease in compressive strength and the elastic modulus. The observed interaction between CO₂, water, and rock weakens the rock’s resistance to mechanical damage. Among the coupled fracturing fluids, CW-8 had the most pronounced weakening effect on the strength of the rock samples. The results of the seepage test and uniaxial test are consistent.

Therefore, this article examines the influence of temperature, stress, and time on the tensile strength of sandstone exposed to CW-8 fracturing fluid.

Table 2. Results of Brazilian splitting tests at different temperatures.

Rock Sample	Temperatures/°C	Pore Pressure/MPa	Active Time/h	Tensile Strength/MPa	Magnitude of Change/%
F1	/	7.0	10.0	4.59	69.85
B-1	25	7.0	10.0	1.96	57.19
B-2	35	7.0	10.0	2.93	36.17
B-3	45	7.0	10.0	3.27	28.68

and Figure 5a,b show that during CO₂-water–rock coupling, the tensile strength of sandstone samples decreases at different temperatures when compared with the tensile strength of the natural rock sample F1. More specifically, the tensile strength was reduced by 2.63 MPa, 1.66 MPa, and 1.32 MPa, exhibiting a decrease of 57.19%, 36.17%, and 28.68% at 25 °C, 35 °C, and 45 °C, respectively. Figure 5a illustrates that CO₂-water–rock coupling results in rock samples reaching their peak load in the shortest duration, which is shorter than that of the natural samples. Moreover, it is observed that as the temperature increases, the time required to reach the peak load becomes longer. This is especially more pronounced at a temperature of 25 °C, with the shortest time to reach the peak being 58.2 s. As shown in Figure 5b, under these conditions, the tensile strength of rock samples experiences the largest decline and as the temperature rises; the reduction in tensile strength diminishes, and it consistently remains lower than the tensile strength of natural rock samples.

Accordingly, it is inferred that temperature affects the tensile strength of rock samples after CO₂-water–rock coupling. The higher the temperature, the lower the viscosity of CO₂-coupled fracturing fluid, and the higher the permeability coefficient. As the temperature rises, the coupled fracturing fluid exhibits greater wetting characteristics on rock samples, which reduces the strength of the rock mass. Additionally, the tensile strength exhibits a positive correlation with the temperature, which may be attributed to the lower solubility of CO₂ in hot water. Consequently, the PH of CO₂-coupled fracturing fluid increases and the acidity of the fluid weakens, thereby reducing the chemical damage to the rock mass.

Based on the distribution of tensile strength shown in Figure 6, the correlation between temperature and tensile strength after CO₂-water–rock coupling can be approximated using the following expression:

$$y=-0.0031x^2+0.286x-3.2212.$$

(1)

Equation (1) indicates that the tensile strength of the rock sample gradually increases with increasing temperature.

3.2. Characteristics of Fracture Evolution of Rock Samples before and after CO₂ Coupling

The coupling conditions were established using a CO₂ mass fraction of 8% in the fracturing fluid, a temperature of 25 °C, a pore pressure of 7 MPa, and a processing time of 10 h. Subsequently, scanning electron microscope (SEM) images of ×500 and ×2000 were captured after conducting the MTS procedure on the sandstone. These images were then compared with SEM images of rock samples in their natural state.

The results show that rock samples in their natural state have less distribution of fractures on the surface, and are primarily dominated by a single fracture. They also exhibit small pore diameters (red circles in the figure), low pore development, poor connectivity, a flatter surface, and mineral filling in both pores and fractures, as shown in Figure 7a,b.

After CO₂ coupling, the rock samples were divided into uneven sheet-like structures through pores and cracks. There was a notable increase in the number of pores, and they became larger in size (red circles in the figure). The development degree of the pores significantly improved, with locally visible pores emerging and most of the pores being interconnected with each other. Figure 8a,b reveals that original cracks exhibit irregular changes, and the formation of new cracks resulted in interconnected patterns.

The observed changes in the fracture structure of rock samples before and after the CO₂ coupling effect may be attributed to the thermal and physical properties of CO₂ itself. When the CO₂-coupled fracturing fluid contacts the rock, it reduces the level of free energy in the system and strengthens the wettability of the rock. The presence of CO₂ fracturing fluid enhances the permeability of the rock mass. Furthermore, the convection heat transfer slightly increases the temperature of the rock mass, thereby reducing its density. Secondly, CO₂ transitions into the supercritical state after surpassing the critical temperature. In this supercritical state, CO₂ exhibits low surface tension and weakened intermolecular force. Finally, the combination of CO₂ and water results in the formation of carbonic acid, an acidic fluid that causes the erosion of the coal rocks in the reservoir and its cement. This process is accompanied by the deposition of new minerals and the transportation of debris particles, which changes the pore structure of coal rocks. The enhancement in CO₂ mobility within the fissure facilitates self-pressurization during the fissure expansion. This phenomenon accelerates rock seepage, promoting fissure expansion and effectively increasing the seepage capacity of low-permeability coal rock. It is worth noting that seepage is an affecting parameter during the phase transition of liquid CO₂ to a gaseous state.

3.3. Characterization of Fracture Surface Roughness of Rock Samples before and after CO₂ Coupling

To characterize the features of rock fracture surfaces before and after CO₂ coupling, a three-dimensional electron microscope scanner was employed for scanning, as depicted in Figure 9. The surface roughness of fractures reflects the micro-convex bodies’ fluctuations on the rock fracture surface, which has a size effect and is a key indicator of fracture mechanics characteristics.

Utilizing the Joint Roughness Coefficient method (JRC), the surface of cracks undergoes digitization. In Figure 10a, the rough surface of fractures in the natural state of the rock sample exhibits a stepped shape. Due to significant differences in relief angles, conductivity is poor, resulting in a poor fracturing effect. The rough surface of fractures at the edge of the rock sample is uneven, with a maximum roughness of 0.82 mm. Figure 10b shows that the fracture roughness surface of MTS-coupled rock samples is planar, with the highest roughness reaching 1.13 mm. The fluctuation angle of the rock sample edge is relatively small, indicating good conductivity and a positive fracturing effect. Through comparison, it is evident that stepped rough surfaces exhibit significant size effects compared to planar rough surfaces.

To quantify the roughness of surface cracks in rock samples, the roughness of the crack surface was quantified using an empirical expression that combines characterization statistical parameters with JRC [25].

$$JRC=32.2+32.47\log h_2,$$

(2)

$$h_2={\left[\frac{1}{(n-1){(\Delta x)}^2}{\displaystyle \sum _{i=1}^n{(h_{i+1}-h_i)}^2}\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$

(3)

where x represents the root mean square of the fracture profile wall slope; n is the number of data points; and h denotes the axial distance between points $i$ + 1 and $i$. The height of peak roughness can be obtained from the following expression:

$$\xi =h_{\max }-h_{\min }$$

(4)

where ξ represents the height of peak roughness, mm, and $h_{\max }$ and $h_{\min }$ are the maximum and minimum roughness heights, mm, respectively.

$$R_s=\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n(h_i}-h_a{)}^2}$$

(5)

$$R_n=\frac{1}{n}{\displaystyle \sum _{i=1}^n|h_i-h_a|}$$

(6)

where $R_n$ and $R_s$ represent the average and the root mean square of the roughness height, respectively, and $h_i$ and $h_a$ are the roughness height of point $i$ and the average height of the elevation line, mm, respectively.

The roughness parameters of the fractured sample can be calculated using Equations (2)–(6), as shown in

Table 3. Geometrical parameters and roughness of the fractured samples.

Sample	Peak Asperity Height ξ/mm	RS of Asperity Height Rs/mm	Mean Asperity Height Rn/mm	JRC
Natural sample	0.89	0.207	0.172	5.7
Coupled rock Sample	1.17	0.359	0.329	3.6

.

Table 3 indicates that compared to the sample under natural conditions, the CO₂-coupled rock sample has an average roughness 0.15 mm higher, with a difference of 0.16 mm in the root mean square of the roughness height. The JRC is less than that of the natural state samples, and the difference is small. Therefore, the rough surface of the coupled rock sample exhibits a planar shape. This indicates that the heat transfer effect generated by the rock matrix and CO₂ in the cracks is conducive to crack expansion, resulting in good fracture connectivity, strong conductivity, and a significant fracturing effect.

3.4. Simulation of CO₂ Heat Transfer in Pores

3.4.1. Pore Fracture CO₂ Phase Evolution

Based on the observations of high-temperature geothermal development, the surrounding rock is susceptible to cracking and subsidence under external loads, leading to the formation of a “holey” structure within the rock mass. In this structure, major fracture voids may form at intervals [26]. To facilitate the analysis, the complex fracture morphology was simplified using an equivalent fracture structure model where “holes” were used instead of “slits”.

The pore flow CO₂ phase change was plotted based on NIST data [27]. It is found that the volume expansion of CO₂ affects temperature and pressure, while its temperature and pressure affect the phase changes. Furthermore, liquid CO₂ evaporates in the fracture hole [28]. It should be indicated that the triple-point temperature and pressure of CO₂ are 238.98 K (−58.9 °C) and 0.34 MPa, respectively. When CO₂ transforms from the liquid state to the supercritical state, its critical temperature and pressure are 304.2 K (31.14 °C) and 7.38 MPa, respectively. Figure 11 shows that supercritical CO₂ can quickly achieve the goal of energizing phase changes in fracture pores and promoting fissure propagation. However, the process of fracturing rock using liquid CO₂ reduces the temperature surrounding the rock body. Meanwhile, heat transfer takes place between liquid CO₂ and seepage within the rock body. This aligns with the characteristics of heat–fluid–solid coupling.

3.4.2. Fluid–Solid Coupling Model

The heat exchange between liquid CO₂ and the rock in the fractured rock fissure pore affects the temperature surrounding the rock mass [8]. Therefore, the CO₂ fluid and the fissure pore part of the rock mass are studied as the object of heat–fluid–solid coupling.

Based on the similar structural characteristics of the actual rock fracture curvature, the process of fracturing within the rock leads to the creation of a “porous” fracture structure within the rock mass [26]. In order to reveal the heat and mass transfer law between CO₂ in pores and rock mass, internal CO₂ fluid, pore, and external rock mass flow field models were established, as shown in Figure 12. The pore fissure (Φ1 mm) and the rock mass (2 m × 2.4 m × 1.8 m) are used as part of the thermal reservoir formed by CO₂ fracturing, as shown in Figure 13.

3.4.3. Boundary Conditions

The boundary conditions were set as the pressure inlet, the inlet heat temperature was 31.04 °C (TSC-CO₂ ≥ 31.04 °C), and the total reflux temperature was set to 35 °C. The wall boundary conditions were set to thermal convection. To cover various scenarios, three inlet pressures of 15 MPa, 10 MPa, and 5 MPa were considered in the analysis.

3.4.4. Coupled Model Control Equations

The stress field is affected by the temperature and seepage, as well as mechanical and chemical damage during CO₂-coupled fracturing, which can cause rock deformation. The governing equation in the stress field can be expressed as follows [10]:

$$G(u_i+\frac{1}{1-2u})-K(T-T_{tr})-{\alpha }_p{p}_f=0$$

(7)

where $G=E^{*}/2(1+\upsilon )$ is the shear modulus; ${\alpha }_T$ denotes the thermal expansion coefficient of rock; K represents the bulk modulus; $T$ is the rock temperature; $T_{tr}$ denotes the rock temperature in its natural state; ${\alpha }_p=1-\left(K/K_s\right)$ represents the Biot number;$K_s$ is the modulus of rock; and $p_f$ denotes the fluid pressure within the pore.

During seepage of the liquid CO₂, heat transfer affects the temperature distribution within the rock mass. The total specific heat capacity of the rock mass is linearly correlated to its mass and the specific heat capacity of liquid CO₂. This can be mathematically expressed as follows [11]:

$${(\rho C)}_t=\left(1-{\varphi }_m-{\varphi }_f\right){\rho }_s{C}_s+s_w{\varphi }_f{\rho }_w{C}_w$$

(8)

where C_s and C_w are the specific heat capacity of the rock mass and CO₂, respectively.

During rock fracturing, deformation is related to the physical properties of the rock mass and its volumetric strain, which can be expressed in the form below [11]:

$$W_T=T{\alpha }_s{K}_v\frac{𝜕{\epsilon }_v}{𝜕t}$$

(9)

where α_s is the thermal expansion coefficient of rock; K_v is the bulk modulus; ε_v denotes the volumetric strain; and T is the rock temperature.

The convective heat exchanged between liquid CO₂ and the rock mass is

$$Q_{tr}=\nabla \cdot \left[-(\frac{K_f{k}_w}{{\mu }_w}\nabla p_w\cdot {\rho }_w{C}_w)\Delta T\right]$$

(10)

where ${\mu }_w$ and $p_w$ are the viscosity and pressure of the liquid CO₂, respectively.

Finally, the energy conservation law in the CO₂-coupled fracturing fluid can be summarized as follows:

$$\frac{𝜕\left[{\left(\rho C\right)}_t\Delta T\right]}{𝜕t}+T{\alpha }_{s}K\frac{𝜕{\epsilon }_v}{𝜕t}+Q_{te}+\nabla ·\left(K_t\nabla T\right)+\Delta Q_m=Q_T.$$

(11)

The coupling between temperature and stress fields is initially manifested through heat exchange. Subsequently, it is obtained using fluid seepage and changes in the thermophysical properties of CO₂.

The mass conservation equation can be expressed as follows [11]:

$$\frac{𝜕(\rho \mu )}{𝜕t}+𝛻\cdot \left(\rho \mathrm{v}\right)=-\mathsf{\Delta }$$

(12)

where ρ is the density of supercritical CO₂; μ is the rock porosity; t denotes time; Δ represents the seepage process source; and ν is the fluid flow rate.

The temperature gradient between the liquid CO₂ and the rock induces convective heat transfer. According to Fourier’s law, the heat transfer in the rock mass is proportional to the temperature difference between liquid CO₂ and the rock [11]:

$$q_c=-\lambda \mathsf{\Delta }t$$

(13)

where λ and t are the thermal conductivity and temperature of liquid CO₂, respectively.

By coupling the stress and temperature field equations, the governing equations for heat transfer in CO₂-coupled fractured rocks can be expressed in the form below:

$$u_{ij}=\left(1-\Delta Q_m\right){\alpha }_p{p}_f+Q_{\mathrm{te}}.$$

(14)

The geometric model involving flow and rock mass was constructed and meshed, and the initial boundary conditions were set. The k-epsilon model was employed to approximate turbulent stresses.

3.5. Mass Transfer Analysis

When fracturing rock formations to create rock fracture voids through CO₂ fracturing fluids injected into the pipeline, the fracturing process results in increased seepage through the rock. This seepage affects conductive and convective heat transfer, causing spatial changes in CO₂ density. Figure 14a indicates that when the temperature is 320 K, the density of CO₂ is 200 kg/m³, but when the temperature increases to 420 K, the corresponding density of CO₂ reduces to 105 kg/m³. On the other hand, when the stress is 11.5 MPa, the CO₂ density is 105 kg/m³, but when the stress increases to 18 MPa, the corresponding density increases to 205 kg/m³. When the temperature and pressure of CO₂ exceed the critical values of 304 K and 8 MPa, its density exhibits a positive correlation with pressure, while Figure 14b indicates that the temperature exhibits a negligible impact on the density.

The thermophysical properties of CO₂ change significantly near its critical point, which leads to rapid pressurization of CO₂ at the bottom of the wellbore. This accelerates the fracturing of the reservoir, intensifying the effects of rock seepage. Additionally, the thermal convective temperature gradient generated by liquid CO₂ contributes to the heat–fluid–solid-coupled heat-transfer effect within coal–rock fissures during seepage.

When CO₂ is used as the fracturing medium to fracture the rock body, it intensifies the role of rock seepage, and the CO₂ medium exchanges heat with the rock mass. When the temperature and pressure of CO₂ exceed their critical values of 304 K and 7.38 MPa, the CO₂ transits into the supercritical state and exhibits low surface tension, weak intermolecular forces, and strong mobility. Consequently, CO₂ rapidly diffuses in the pores, and seepage contributes to heat transfer.

Figure 14c shows that as the CO₂ temperature reaches 260 K, its viscosity is 0.10 μ/Pa·s. When the temperature increases to 320 K, the CO₂ viscosity reduces to 0.06 μ/Pa·s. On the other hand, the CO₂ viscosity is 0.08 μ/Pa·s at the pressure of 18 MPa. As the pressure reduces to 11.5 MPa, the corresponding viscosity increases to 0.12 μ/Pa·s. Figure 14d indicates that the viscosity exhibits a negative correlation with temperature, and the temperature is closely related to the flow rate. As a result, adjusting the flow rate can effectively increase the heat transfer coefficient while reducing the viscosity of the CO₂ flow.

The viscosity and pressure contours reveal that the change in pressure and temperature significantly affects the viscosity. As the fracture length expands during fracturing, the temperature of liquid CO₂ in the fracture of the rock gradually increases through convective and conductive heat transfer. Consequently, CO₂ gradually transforms into a low-viscosity supercritical state within the coupled fractured rock fractures, thereby increasing the resistance to seepage of supercritical CO₂ in the rock fractures. However, seepage is an effective parameter in heat–fluid–solid coupling. Therefore, it is of significant importance to analyze the flow rate variations to study heat–fluid–solid coupling.

3.6. Simulation Results

The temperature and heat transfer coefficient of supercritical fluids are affected by the heat exchange, thermophysical properties, pressure, and flow rate. According to the analysis, liquid CO₂ is very sensitive to the flow rate and pressure, and different flow rates and pressures result in significantly different heat transfer coefficients and temperatures.

Figure 15a shows that when liquid CO₂ is injected at a pressure of 15 MPa, heat transfer occurs to different degrees between the fluid and the rock mass. The heat transfer coefficient reaches a maximum value of 86.9 W/m²·K at the edge of the middle part of the fluid, and the heat transfer coefficient reaches its maximum value when the temperature of the fluid approaches the critical temperature of 31.04 °C. Furthermore, it is found that the heat transfer coefficient decreases gradually at the outlet boundary. The maximum temperature at the fluid–rock interface is 33.6 °C, wherein CO₂ is in the critical state. Figure 15b indicates that the temperature of the fluid–solid interface gradually decreases from inlet to outlet and drops to 30.9 °C at the outlet of the lower right part.

Figure 16a shows the contours of temperature and the heat transfer coefficient when liquid CO₂ is injected at a pressure of 10 MPa. Compared with Figure 15, the heat transfer coefficient between the fluid and the rock mass decreases, with the maximum heat transfer coefficient at the middle edge of the fluid being 74.6 W/m²·K, indicating a reduction of 48.8 W/m²·K at the outlet boundary. It is observed that as the pressure changes, the maximum temperature at the fluid–rock interface reaches 31.5 °C and the temperature decreases to 27.9 °C from inlet to outlet boundaries, as shown in Figure 16b.

Figure 17 illustrates the heat transfer and temperature contours for injection pressures of 5 MPa and 10 MPa. It is observed that the heat transfer coefficient between the fluid and the rock mass is significantly reduced compared with Figure 16. Figure 17a shows that the maximum heat transfer coefficient reaches 57.5 W/m²·K and 28.1 W/m²·K at the middle edge and outlet boundary, respectively. Furthermore, Figure 17b indicates that the temperature at the fluid–rock interface decreases from 32.1 °C at the inlet boundary to 24.7 °C at the outlet boundary.

The obtained results can be interpreted as follows: the temperature difference between liquid CO₂ and the rock mass is significant, resulting in a substantial heat exchange between the two. As the temperature decreases, the viscosity of CO₂ increases while its permeability decreases. During the phase transition of CO₂ from liquid to gas, the heat transfer between the fluid and the rock wall gradually decreases until it reaches an equilibrium state. This analysis aligns with the thermal dynamic relationship between rock tensile strength and temperature presented in Section 3.1.

The performed analysis is intended to establish a relationship between the heat transfer coefficient and temperature. As shown in Figure 18, the heat transfer coefficient of liquid CO₂ rapidly increases with the increase in fluid temperature. When the flow reaches its equilibrium state, the heat exchange gradually decreases as the temperature increases. This suggests that the heat transfer coefficient is directly related to the temperature in the early stage near the critical temperature of 31.04 ℃. Meanwhile, the critical temperature significantly influences the heat transfer coefficient. This simulation demonstrates the heterogeneous characteristics of the thermal fluid–solid coupling process.

Based on the performed heat transfer analysis, the fluid reaches high temperatures due to the extension of the crack length and exhibits high viscosity, which increases the resistance of liquid CO₂ in the crack. However, the variations in temperature and pressure are sensitive to the flow rate, and the appropriate flow rate can significantly enhance the heat exchange coefficient and reduce the flow resistance, which is enhanced for the less-viscous CO₂ fluid.

Figure 19 reveals that when liquid CO₂ is discharged from 5 MPa to 15 MPa, the faster the flow rate, the denser the flow line. Meanwhile, the flow volume increases gradually with increasing pressure. The initial pressure of the fluid decreases due to the influence of the permeability of the gas–water–rock coupling. The reason for this is that, with the continuous heat exchange between the fluid and the rock, the thermal expansion of the liquid CO₂ phase change is faster as the temperature and pressure increase. Ultimately, as gaseous CO₂ is discharged, there is an exponential increase in pressure and flow rate. Indicating that the sensitivity of flow velocity is directly proportional to the overall heat exchange coefficient, and the flow resistance gradually decreases with the increase in CO₂ temperature and pressure.

4. Discussion

This work investigated the impact of CO₂ coupling on the evolution of fractures and the roughness of rock samples, with a focus on the alteration process in the rocks’ pore structure induced by acidic fluids generated from CO₂ and water. CO₂-induced rock fracturing involved obtaining the crack propagation law of fractured rocks and inverting the effect of CO₂ heat convection on the ambient temperature around fissured coal rocks, revealing the heat transfer between the rock matrix and CO₂ in the pores.

The results obtained illustrate that the interaction between CO₂, water, and rock weakens the rock’s resistance to mechanical damage. It is inferred that temperature affects the tensile strength of rock samples after CO₂-water–rock coupling. The CO₂ exchanges heat with the rock matrix during fissure seepage, which changes the temperature field distribution of the fissured rock and affects the expansion of the fissure. The results can provide a theoretical basis for the safety evaluation of CO₂’s deep earth storage and industrialized application in fracturing and permeability enhancement.

5. Conclusions

Based on the MTS tests and computational fluid dynamics analysis method, the mechanical evolution mechanism of CO₂-water–rock coupling in the fissure seepage process and the flow characteristics and the heat transfer mechanism of the CO₂ heat exchanges with the rock matrix are studied. Based on the obtained results and performed analyses, the main achievements can be summarized as follows:

As the temperature increased, the reduction in the tensile strength of rock samples became less pronounced, ranging from 2.61 to 1.30 MPa. The effect was attributed to the decreased viscosity of CO₂-coupled fracturing fluid. Additionally, wettability was enhanced and the strength of the rock samples was weakened.

The distribution of surface cracks on natural rock samples was relatively small, primarily composed of single cracks. The CO₂-coupled rock sample was divided into uneven sheet-like structures by pores and fractures. The nodal roughness coefficient of CO₂-coupled rock samples was smaller than that of the natural state sample, and the roughness surface was planar, indicating good fracture connectivity and significant permeability. The temperature, heat transfer coefficient, and flow rate changes between the rock wall and CO₂ were directly proportional to the CO₂ inlet pressure. The fluid flow line became denser, and the CO₂ volume flow rate gradually increased with increased pressure. The resistance to flow decreased gradually with increased CO₂ temperature and pressure.