Thermal Performance of Cemented Paste Backﬁll Body Considering Its Slurry Sedimentary Characteristics in Underground Backﬁll Stopes

: The combined mine backﬁll–geothermal (CMBG) system can be used to effectively extract geothermal energy by installing a heat exchange tube (HET) in the underground backﬁlled stopes of mines, which can be used as the heat supply for buildings in mines and the surrounding areas. The efﬁcient performance of this system strongly depends on the thermal exchange process between the HET and its surrounding cemented paste backﬁll body (CPB). In this study, a validated simulation model is established to investigate the heat exchange performance of CPB, in which the nonuniformly distributed thermal properties in CPB are fully considered. The results indicate that the increase in the porosity has a negative effect on the heat exchange performance of CPB. With the increase in the porosity, the decreased rate of the conductive heat transfer in CPB could be up to approximately 18%. In conditions with seepage ﬂow, the heat transfer capacity of CPB could be effectively improved. Generally, a higher hydraulic conductivity corresponds to a higher heat transfer performance of CPB. When the seepage velocity rose from 2 × 10 − 6 to 6 × 10 − 6 m/s, the thermal conductivity of CPB achieved a 114% increase from 1.843 to 3.957 W/(m · K). Furthermore, it was found that the thermal energy accumulates along the seepage ﬂow direction, enhancing the thermal inﬂuencing radius of the HET in this direction. Thus, the arrangement of HETs should fully take into account the seepage ﬂow effect. This proposed simulation model could provide a reference for parameter determination and optimization of CMBG systems.


Introduction
In recent years, the large consumption of conventional fossil energy has resulted in serious environmental problems [1]. It is urgent to utilize renewable energy to implement a low-carbon strategy. At present, geothermal energy utilization has been one of the most widely used renewable energy technologies [2]. It has been proved that abundant geothermal energy exists in China, approximately equivalent to 9.5 × 10 9 tons of standard coal, and the amount of geothermal energy used in building areas for cooling and heating has reached 5 × 10 8 m 2 [3].
In addition, it has been found that the total energy consumption of buildings accounts for one-third of the total energy consumption [4], while approximately 50% of the building energy consumption is attributed to heating, ventilating, and air conditioning (HVAC) systems [5]. As an environmentally friendly technology extracting geothermal energy, the ground source heat pump (GSHP) system has been widely applied around the world. It extracts geothermal energy to satisfy the heat requirement of buildings and has a positive effect on the replacement of fossil fuel consumption [6][7][8]. There are also many mines in China, which contain considerable geothermal energy. The thermal energy exploitation of the mines could provide an alternative heat source for the heat demand of buildings in mining areas, such as hot water supply or heating in winter, effectively reducing the fossil fuel cost and carbon emission.
As early as the 1980s, the idea of utilizing mine geothermal energy had been put forward [9]. Concerning the relatively high temperature in deep mines, they have been regarded as good geothermal reservoirs [10]. There are many studies that utilize the geothermal energy from abandoned mines around the world [11][12][13][14][15]. Owing to the higher temperature of deep underground mines, the thermal energy contained in the surrounding rocks can be absorbed by HET [16]. In Heerlen, the Netherlands, heating from abandoned mine water provides heat for residential and commercial spaces and community buildings. The heating energy for hot water supply from the geothermal energy of a coal mine could reach 690 kW [17]. In China, Tangkou Coal Mine in Jining uses the recovered mine drainage to heat the mines and surrounding houses [18]. Mine galleries have been adopted for the preheating or precooling of relatively large buildings [12]. The utilization of the geothermal resources in deep mines could offset certain economic costs and supply green heat energy to communities distributed in and around the mine area, including commercial buildings and community buildings nearby, which is a rehabilitative way that effectively reduces the damage to the environment and promotes resource recycling [19].
In order to extract the geothermal energy contained in deep mines in an economic and water-protective way, the concept of the CMBG system was proposed by Liu et al. [20], which is based on the application of backfilling technology in mines [21]. Due to the large mined-out areas, after the ore is exploited, the closed-loop HET could be arranged in the backfill stopes to extract the geothermal energy [22,23]. Before backfilling, the HETs are installed in the mined-out area in advance, and then the backfilling slurry is poured into this area. Finally, the HETs are embedded in the solidified filling slurry (CPB). The thermal energy contained in the mine rock could be indirectly or directly absorbed by the heat medium (typically water) flowing in the HETs and finally supplied to the heat users.
For CMBG systems, one of the priority issues needed to be solved is the heat transfer performance of CPB. Many previous studies have analyzed the effects of different factors on the strength of CPB, such as the porosity [24,25], environment humidity [26], water saturation [27], cement/sand ratio [28,29], mixing grade of cement [30], and quantities of the polymer and fiber [31]. Meanwhile, all these above factors have certain influences on the thermal performance of CPB. For the heat transfer process in the CMBG system, one of the most important influence factors is thermal conductivity, which is also the key parameter in the engineering design of the CMBG system. Kavanaugh [32] found that the thermal conductivity had significant effects on the length deviation of the underground HET. When the deviation of the thermal conductivity of underground rock-soil was around 4.5-5.8%, the length deviation of the underground buried pipe would reach 10%. Abbasy evaluated the effects of design parameters, including the porosity, saturation, sample size, binder content, and pulp density, on the thermal conductivity of CPB [33]. The results indicate that in comparison with the steady-state test, the unsteady testing has a better performance in retaining the moisture content in the sample and outputs more accurate results. Célestin [34] experimentally studied the thermal conductivity of CPB and found that the components of CPB (such as the tailing type and grain diameter) have a very significant influence on its thermal conductivity. The higher content of quartz in the tailings, or the larger diameter of the components, always produces a higher thermal conductivity.
However, the previous studies have not fully considered the sedimentary characteristic of the slurry in backfilling process, which also has an important influence on the thermal Energies 2021, 14, 7400 3 of 18 conductivity of CPB. Due to the gravity effect in the actual situation, particles with different diameters have different movement trajectories when the filling slurry flows in the goaf, which finally leads to a nonuniform component distribution in CPB. Generally, along the horizontal flow direction, the particle size is related to the distance from the slurry inlet. As the distance increases, the percentage of the coarse particles in CPB decreases while that of the fine particles increases. It has been proven that the sedimentation of CPB slurry presents a normal distribution [35]. For an infinite horizontal plane, the cemented filling slurry gradually diffuses along the plane after discharging from the outlet and forms a cone shape. The flow region of CPB slurry can be divided into three zones in terms of particle size. The boundary curves of each zone are all normally distributed [36], as shown in Figure 1. This is mainly attributed to the different sedimentation characteristics of different particles. For a heat exchange material, the thermal conductivity is inevitably affected by the distribution of its components. Lee [37] developed a 3D numerical model to investigate the effect of material components on the heat exchange performance in a GSHP system. The results suggest that with the same complex thermophysical properties, there exists an obvious difference in long-term heat transfer performance between the uniformly distributed soil and the two-layer nonhomogeneous soil. Florides et al. [38] simulated the heat transfer performance of buried pipes installed in a multilayer environment, which consisted of four different soil layers with different thermophysical properties. The results show that under different arrangements of soil layers, the outlet water temperatures are obviously different. The above two studies indicate that the heterogeneity of the ground layer has a significant influence on the heat transfer performance of buried pipes. In the aforementioned studies related to the thermal conductivity of CPB, the filling slurry was filled into a volume cylindrical vessel. In such a limited space, the nonuniform distribution of thermophysical properties of CPB could not be fully exhibited; thus, the corresponding thermal conductivity was significantly different from the actual situation. Therefore, the stratified distribution of CPB components should be fully considered when examining the heat exchange performance of CPB in the CMBG system. However, the previous studies have not fully considered the sedimentary characteristic of the slurry in backfilling process, which also has an important influence on the thermal conductivity of CPB. Due to the gravity effect in the actual situation, particles with different diameters have different movement trajectories when the filling slurry flows in the goaf, which finally leads to a nonuniform component distribution in CPB. Generally, along the horizontal flow direction, the particle size is related to the distance from the slurry inlet. As the distance increases, the percentage of the coarse particles in CPB decreases while that of the fine particles increases. It has been proven that the sedimentation of CPB slurry presents a normal distribution [35]. For an infinite horizontal plane, the cemented filling slurry gradually diffuses along the plane after discharging from the outlet and forms a cone shape. The flow region of CPB slurry can be divided into three zones in terms of particle size. The boundary curves of each zone are all normally distributed [36], as shown in Figure 1. This is mainly attributed to the different sedimentation characteristics of different particles. For a heat exchange material, the thermal conductivity is inevitably affected by the distribution of its components. Lee [37] developed a 3D numerical model to investigate the effect of material components on the heat exchange performance in a GSHP system. The results suggest that with the same complex thermophysical properties, there exists an obvious difference in long-term heat transfer performance between the uniformly distributed soil and the two-layer nonhomogeneous soil. Florides et al. [38] simulated the heat transfer performance of buried pipes installed in a multilayer environment, which consisted of four different soil layers with different thermophysical properties. The results show that under different arrangements of soil layers, the outlet water temperatures are obviously different. The above two studies indicate that the heterogeneity of the ground layer has a significant influence on the heat transfer performance of buried pipes. In the aforementioned studies related to the thermal conductivity of CPB, the filling slurry was filled into a volume cylindrical vessel. In such a limited space, the nonuniform distribution of thermophysical properties of CPB could not be fully exhibited; thus, the corresponding thermal conductivity was significantly different from the actual situation. Therefore, the stratified distribution of CPB components should be fully considered when examining the heat exchange performance of CPB in the CMBG system. In order to test the thermal conductivity of CPB with nonuniformly distributed thermophysical properties, the sample should be large enough. Generally, one of the appropriate approaches is the thermal response test (TRT) [39], which is usually adopted to test the thermophysical properties and heat transfer of rocks and soils, as shown in Figure 2. The principle of this method is that the heated fluid (typically water) circulates in the HET In order to test the thermal conductivity of CPB with nonuniformly distributed thermophysical properties, the sample should be large enough. Generally, one of the appropriate approaches is the thermal response test (TRT) [39], which is usually adopted to test the thermophysical properties and heat transfer of rocks and soils, as shown in Figure 2. The principle of this method is that the heated fluid (typically water) circulates in the HET and transfers heat energy to the surrounding soil, and the linear heat source or the cylindrical heat source theory is used to analyze the response parameters (generally the average fluid Energies 2021, 14, 7400 4 of 18 temperature in the HET). Finally, the soil thermal properties can be calculated in reverse. The theory simplifies the heat transfer inside and outside the tube as a pure heat conduction process, which is a mature technology in GSHP systems. Since it is difficult to accurately examine the values of thermal parameters of CPB via in situ testing, a numerical simulation model that fully takes account of the sedimentary characteristics of CPB slurry is proposed in this study, which is based on the thermal response theory. and transfers heat energy to the surrounding soil, and the linear heat source or the cylindrical heat source theory is used to analyze the response parameters (generally the average fluid temperature in the HET). Finally, the soil thermal properties can be calculated in reverse. The theory simplifies the heat transfer inside and outside the tube as a pure heat conduction process, which is a mature technology in GSHP systems. Since it is difficult to accurately examine the values of thermal parameters of CPB via in situ testing, a numerical simulation model that fully takes account of the sedimentary characteristics of CPB slurry is proposed in this study, which is based on the thermal response theory. In this paper, a validated CFD simulation model is established to evaluate the thermal performance of CPB, in which the sedimentary characteristic of CPB slurry has been fully considered. After this introduction, Section 2 describes the establishment of the numerical model. In Section 3, the validation of the proposed numerical model is discussed. In Section 4, the performance of heat exchange between HET and its surrounding CPB is evaluated under different boundary conditions. Finally, the main conclusions are summarized in Section 5. The results of this study could be useful in the prediction of design parameters of the CMBG system, as well as providing a method of evaluating and optimizing the heat exchange performance of this system.

Heat Transfer Equation
In this study, the heat transfer mechanisms in the CMBG system mainly involve two processes: (1) the heat conduction inside the solid material (CPB) and (2) the heat convection between the circulating fluid and the pipe walls. The governing equations describing these two processes can be expressed by Equations (1) and (2), respectively, as follows: where ρ, T, λ, and c are the density (kg·m −3 ), temperature (K), thermal conductivity (W·m −1 ·K −1 ), and specific thermal capacity (J·kg −1 ·K −1 ), respectively; Q indicates the general heat source (W·m −3 ); the subscripts s and f represent the solid material (CPB) and fluid in In this paper, a validated CFD simulation model is established to evaluate the thermal performance of CPB, in which the sedimentary characteristic of CPB slurry has been fully considered. After this introduction, Section 2 describes the establishment of the numerical model. In Section 3, the validation of the proposed numerical model is discussed. In Section 4, the performance of heat exchange between HET and its surrounding CPB is evaluated under different boundary conditions. Finally, the main conclusions are summarized in Section 5. The results of this study could be useful in the prediction of design parameters of the CMBG system, as well as providing a method of evaluating and optimizing the heat exchange performance of this system.

Heat Transfer Equation
In this study, the heat transfer mechanisms in the CMBG system mainly involve two processes: (1) the heat conduction inside the solid material (CPB) and (2) the heat convection between the circulating fluid and the pipe walls. The governing equations describing these two processes can be expressed by Equations (1) and (2), respectively, as follows: where ρ, T, λ, and c are the density (kg·m −3 ), temperature (K), thermal conductivity (W·m −1 ·K −1 ), and specific thermal capacity (J·kg −1 ·K −1 ), respectively; Q indicates the general heat source (W·m −3 ); the subscripts s and f represent the solid material (CPB) and fluid in the tubes; and Q wall is the equivalent heat source item (W·m −3 ), which results from the heat exchange between the fluid in the HET and its surrounding CPB.

Geometric Model and Mesh
The software ICEM was used for geometric mode establishment and mesh generation in this study. The research of Chen [36] indicated the interface positions of the particle stratification in solidified CPB. Therefore, the boundary conditions of the simulation model in our work were determined in accordance with Chen's experiment, aiming to evaluate the thermal performance of CPB.
By adopting the three dividing curves for stratified CPB from Chen's study, a threedimensional model was established, wherein the stope size is 60 m × 12 m × 30 m, the same as Chen's model [36]. Particularly, according to the sedimentary characteristic, the real height of CPB is 25.6 m after sedimentation. Since the filling slurry on the Y-Z plane is normally distributed, the top of the backfill body presents a curved surface. The HET is a closed circulating system to transfer heat energy with CPB. The dimensions of the HET are shown in Table 1. In addition, the TRT in this study is the heating condition, which means the fluid is firstly heated in a water tank at constant power and then releases heat energy to the surrounding CPB. In order to accelerate the calculation, the heating water tank is represented by a U-bend pipe with 0.6 m length and constant heating power, as shown in Figure 3, which makes the whole HET become a circulating loop.
Energies 2021, 14, 7400 5 of 18 the tubes; and Qwall is the equivalent heat source item (W·m −3 ), which results from the heat exchange between the fluid in the HET and its surrounding CPB.

Geometric Model and Mesh
The software ICEM was used for geometric mode establishment and mesh generation in this study. The research of Chen [36] indicated the interface positions of the particle stratification in solidified CPB. Therefore, the boundary conditions of the simulation model in our work were determined in accordance with Chen's experiment, aiming to evaluate the thermal performance of CPB.
By adopting the three dividing curves for stratified CPB from Chen's study, a threedimensional model was established, wherein the stope size is 60 m × 12 m × 30 m, the same as Chen's model [36]. Particularly, according to the sedimentary characteristic, the real height of CPB is 25.6 m after sedimentation. Since the filling slurry on the Y-Z plane is normally distributed, the top of the backfill body presents a curved surface. The HET is a closed circulating system to transfer heat energy with CPB. The dimensions of the HET are shown in Table 1. In addition, the TRT in this study is the heating condition, which means the fluid is firstly heated in a water tank at constant power and then releases heat energy to the surrounding CPB. In order to accelerate the calculation, the heating water tank is represented by a U-bend pipe with 0.6 m length and constant heating power, as shown in Figure 3, which makes the whole HET become a circulating loop. Since the structured grid can save computer resources and improve the accuracy of numerical simulation results effectively, it was used in this study. During the heat transfer process, the temperature varies greatly along the radial direction; thus, the grid should be intensive around the pipe in this direction. Lastly, the flow field varies sharply to form vortices because the curvature of the bend of the pipe is larger, which means that the Since the structured grid can save computer resources and improve the accuracy of numerical simulation results effectively, it was used in this study. During the heat transfer process, the temperature varies greatly along the radial direction; thus, the grid should be intensive around the pipe in this direction. Lastly, the flow field varies sharply to form vortices because the curvature of the bend of the pipe is larger, which means that the intensive mesh is also required to avoid the inclination angle of the grid. The final mesh results are shown in Figure 4a-c. The total number of elements is more than 3.19 million. intensive mesh is also required to avoid the inclination angle of the grid. The final mesh results are shown in Figure 4a-c. The total number of elements is more than 3.19 million.

Boundary Conditions and Thermophysical Property Settings of the Model
In this model, the fluid inlet surface of the U-bend pipe is defined as Fan, which means that it serves as a water pump for the circulating water system. The wall of the Ubend pipe and the periphery of CPB are defined as the wall. The 0.6 m length of U-bend pipe extends out of CPB (as shown in Figure 3), is heated under constant power, and serves as a heat source for TRT simulation. Therefore, the boundary of it is set as constant heat flux. In addition, the walls are set as insulation. Considering the heat and moisture coupling, each layer of backfill is regarded as an isotropic homogeneous porous medium in this paper, as shown in Figure 5. Finally, the details of the three porous zones with different properties are inputted by UDF. In order to ensure the convergence of the calculation, the under-relaxed iteration method is used for pressure and momentum. The PISO algorithm is used for the pressure-velocity coupling, which has great advantages in dealing with the mesh distortion [40].

Validation of the Simulation Model
To ensure the accuracy of simulation results, the numerical model should be validated at first by experimental data or analytical method. In this study, the analytical TRT method based on linear heat source theory was adopted for the model validation [41], in which the HET is regarded as an infinite linear heat source while CPB outside the pipe is

Boundary Conditions and Thermophysical Property Settings of the Model
In this model, the fluid inlet surface of the U-bend pipe is defined as Fan, which means that it serves as a water pump for the circulating water system. The wall of the U-bend pipe and the periphery of CPB are defined as the wall. The 0.6 m length of U-bend pipe extends out of CPB (as shown in Figure 3), is heated under constant power, and serves as a heat source for TRT simulation. Therefore, the boundary of it is set as constant heat flux. In addition, the walls are set as insulation. Considering the heat and moisture coupling, each layer of backfill is regarded as an isotropic homogeneous porous medium in this paper, as shown in Figure 5. Finally, the details of the three porous zones with different properties are inputted by UDF. In order to ensure the convergence of the calculation, the under-relaxed iteration method is used for pressure and momentum. The PISO algorithm is used for the pressure-velocity coupling, which has great advantages in dealing with the mesh distortion [40]. intensive mesh is also required to avoid the inclination angle of the grid. The final mesh results are shown in Figure 4a-c. The total number of elements is more than 3.19 million.

Boundary Conditions and Thermophysical Property Settings of the Model
In this model, the fluid inlet surface of the U-bend pipe is defined as Fan, which means that it serves as a water pump for the circulating water system. The wall of the Ubend pipe and the periphery of CPB are defined as the wall. The 0.6 m length of U-bend pipe extends out of CPB (as shown in Figure 3), is heated under constant power, and serves as a heat source for TRT simulation. Therefore, the boundary of it is set as constant heat flux. In addition, the walls are set as insulation. Considering the heat and moisture coupling, each layer of backfill is regarded as an isotropic homogeneous porous medium in this paper, as shown in Figure 5. Finally, the details of the three porous zones with different properties are inputted by UDF. In order to ensure the convergence of the calculation, the under-relaxed iteration method is used for pressure and momentum. The PISO algorithm is used for the pressure-velocity coupling, which has great advantages in dealing with the mesh distortion [40].

Validation of the Simulation Model
To ensure the accuracy of simulation results, the numerical model should be validated at first by experimental data or analytical method. In this study, the analytical TRT method based on linear heat source theory was adopted for the model validation [41], in which the HET is regarded as an infinite linear heat source while CPB outside the pipe is

Validation of the Simulation Model
To ensure the accuracy of simulation results, the numerical model should be validated at first by experimental data or analytical method. In this study, the analytical TRT method based on linear heat source theory was adopted for the model validation [41], in which the HET is regarded as an infinite linear heat source while CPB outside the pipe is considered to be an infinite medium. The average fluid temperature in the HET was employed as the evaluation parameter. For the analytical model, the average fluid temperature could be calculated according to the previous studies [42]. Table 2 summarizes the relevant initial Energies 2021, 14, 7400 7 of 18 parameters in the analytical and simulation models. The comparison of average fluid temperature in the HET under these two models is shown in Figure 6. considered to be an infinite medium. The average fluid temperature in the HET was employed as the evaluation parameter. For the analytical model, the average fluid temperature could be calculated according to the previous studies [42]. Table 2 summarizes the relevant initial parameters in the analytical and simulation models. The comparison of average fluid temperature in the HET under these two models is shown in Figure 6.  From Figure 6, it can be found that in the initial phase, the simulated average fluid temperature slightly deviates from the analytical results. However, the values from the two models agreed well with each other over time. The difference attained from the model comparison is in an acceptable range.
Furthermore, a UDF was used in this study to evaluate the nonuniformly distributed thermal properties of CPB; thus, the UDF should also be verified. It was examined through a comparison with results of experiments conducted by Li et al. [43], in which the nonuniform thermal property distribution of the layered subsurface was fully considered. The inlet and outlet fluid temperatures in the HET under simulation and experimental conditions were compared. Figure 7 gives the simulated and measured inlet/outlet water temperatures. It suggests that the numerical results fitted well with the experimental data after 10 h of operation (with a deviation of 0.24 °C). The error in the first 10 h may be attributed to the instability of measuring instruments at the initial experimental stage. In addition, the outside environment may also have an impact on the measurement results because it cannot guarantee complete thermal isolation compared to simulation. In general, the simulation and experiment results showed good agreement. According to the above validation, the proposed numerical model could be adopted to evaluate the thermal performance of CPB. From Figure 6, it can be found that in the initial phase, the simulated average fluid temperature slightly deviates from the analytical results. However, the values from the two models agreed well with each other over time. The difference attained from the model comparison is in an acceptable range.
Furthermore, a UDF was used in this study to evaluate the nonuniformly distributed thermal properties of CPB; thus, the UDF should also be verified. It was examined through a comparison with results of experiments conducted by Li et al. [43], in which the nonuniform thermal property distribution of the layered subsurface was fully considered. The inlet and outlet fluid temperatures in the HET under simulation and experimental conditions were compared. Figure 7 gives the simulated and measured inlet/outlet water temperatures. It suggests that the numerical results fitted well with the experimental data after 10 h of operation (with a deviation of 0.24 • C). The error in the first 10 h may be attributed to the instability of measuring instruments at the initial experimental stage. In addition, the outside environment may also have an impact on the measurement results because it cannot guarantee complete thermal isolation compared to simulation. In general, the simulation and experiment results showed good agreement. According to the above validation, the proposed numerical model could be adopted to evaluate the thermal performance of CPB.

Results and Analyses
This study was carried out under vapor-saturated and liquid-saturated conditions. As aforementioned, the thermal conductivity should be obtained by considering the sedimentary effect of CPB slurry, which results in the nonuniform distributions of particle sizes, porosities, and thermal properties in CPB. Due to the hydration effect at the top region of CPB, the microstructure at this position is more compact and even nonporous compared to the bottom. In order to investigate the effects of different porosities and hydraulic conductivities on thermal conductivity, 3D simulations under different boundary conditions were conducted. The main parameters in each case are shown in Table 3, wherein P1, P2, and P3 represent the bottom, intermediate, and top regions in CPB, respectively (as shown in Figure 5). The seepage flow direction in this paper is defined from the top to the bottom regions of CPB. According to Abbasy's study, the thermal conductivities of CPB under liquid-saturated and vapor-saturated conditions are 1.43 and 0.3 W/m·°C, respectively [22]. The CPB thermal conductivities with different porosities can be obtained by Equation (3):

Results and Analyses
This study was carried out under vapor-saturated and liquid-saturated conditions. As aforementioned, the thermal conductivity should be obtained by considering the sedimentary effect of CPB slurry, which results in the nonuniform distributions of particle sizes, porosities, and thermal properties in CPB. Due to the hydration effect at the top region of CPB, the microstructure at this position is more compact and even nonporous compared to the bottom. In order to investigate the effects of different porosities and hydraulic conductivities on thermal conductivity, 3D simulations under different boundary conditions were conducted. The main parameters in each case are shown in Table 3, wherein P1, P2, and P3 represent the bottom, intermediate, and top regions in CPB, respectively (as shown in Figure 5). The seepage flow direction in this paper is defined from the top to the bottom regions of CPB. According to Abbasy's study, the thermal conductivities of CPB under liquid-saturated and vapor-saturated conditions are 1.43 and 0.3 W/m· • C, respectively [22]. The CPB thermal conductivities with different porosities can be obtained by Equation (3): where n is the porosity and λ f and λ s represent the thermal conductivities of fluid and solid phases in CPB, respectively. The details of material properties in this simulation model are listed in Table 4. In this paper, the initial temperatures of CPB and the fluid in the HET are set to be 290 K while the heating power is set as 2100 W. Figure 8 shows the velocity field in the HET, in which the direction of water flow is clearly denoted. When the fluid flows into the U-shaped part and out of the U-shaped part, the fluid gradually shifts from the center of the tube to the tube wall due to the inertia effect. For TRT duration, the recommended value is not less than 36 h [45]. It is assumed that 1.48 W/(m· • C) is the true value of thermal conductivity to investigate the influence of test duration. The results are shown in Figure 9. It can be seen that the thermal conductivity of CPB first increases with the increase in test time and then stabilizes at 1.43 W/(m· • C). In the actual TRT process, the test time should not be too long. The reason is that the long period will change the moisture content of CPB, which will impact the test results. Thus, with the acceptable test error, the simulation duration of this paper is 48 h.
where n is the porosity and λf and λs represent the thermal conductivities of fluid and solid phases in CPB, respectively. The details of material properties in this simulation mode are listed in Table 4. In this paper, the initial temperatures of CPB and the fluid in the HET are set to be 290 K while the heating power is set as 2100 W. Figure 8 shows the velocity field in the HET, in which the direction of water flow is clearly denoted. When the fluid flows into the U-shaped part and out of the U-shaped part, the fluid gradually shifts from the center of the tube to the tube wall due to the inertia effect. For TRT duration, the recommended value is not less than 36 h [45]. It is assumed that 1.48 W/(m·°C) is the true value of therma conductivity to investigate the influence of test duration. The results are shown in Figure 9. It can be seen that the thermal conductivity of CPB first increases with the increase in test time and then stabilizes at 1.43 W/(m·°C). In the actual TRT process, the test time should not be too long. The reason is that the long period will change the moisture content of CPB, which will impact the test results. Thus, with the acceptable test error, the simulation duration of this paper is 48 h.

Effects of the Porosity on Heat Exchange Performance of CPB
CPB is composed of the solid skeleton and the pores. The porosity and distribution of the pores have an influence on the thermal performance of CPB. In this section, the seepage flow is not considered; thus, CPB could be treated as vapor-saturated. Figure 10a shows the temperature distribution of cross-section Z = 0 after 48 h of operation in Case 1, in which the water in the HET releases heat to its surrounding CPB, improving the CPB temperature from 290 K gradually over time. Owing to the shape of the HET, the thermal influence region approximately tends to be a circular region along the radial direction. The heat transfer performance of CPB could also be indicated. The CPB temperature gradually reduces away from the HET. This is clearly demonstrated in Figure 10b, wherein the CPB temperature drops obviously along the vertical direction (i.e., Y-direction), and the slope is gradually flattened. When the distance from the HET reaches 0.6 m, the CPB temperature approaches its initial value of 290 K, indicating a thermal influencing radius of 0.6 m for the HET. Beyond this range, the effect of the HET on CPB temperature could be ignored.

Effects of the Porosity on Heat Exchange Performance of CPB
CPB is composed of the solid skeleton and the pores. The porosity and distribution of the pores have an influence on the thermal performance of CPB. In this section, the seepage flow is not considered; thus, CPB could be treated as vapor-saturated. Figure 10a shows the temperature distribution of cross-section Z = 0 after 48 h of operation in Case 1, in which the water in the HET releases heat to its surrounding CPB, improving the CPB temperature from 290 K gradually over time. Owing to the shape of the HET, the thermal influence region approximately tends to be a circular region along the radial direction. The heat transfer performance of CPB could also be indicated. The CPB temperature gradually reduces away from the HET. This is clearly demonstrated in Figure 10b, wherein the CPB temperature drops obviously along the vertical direction (i.e., Y-direction), and the slope is gradually flattened. When the distance from the HET reaches 0.6 m, the CPB temperature approaches its initial value of 290 K, indicating a thermal influencing radius of 0.6 m for the HET. Beyond this range, the effect of the HET on CPB temperature could be ignored.

Effects of the Porosity on Heat Exchange Performance of CPB
CPB is composed of the solid skeleton and the pores. The porosity and distribution of the pores have an influence on the thermal performance of CPB. In this section, the seepage flow is not considered; thus, CPB could be treated as vapor-saturated. Figure 10a shows the temperature distribution of cross-section Z = 0 after 48 h of operation in Case 1, in which the water in the HET releases heat to its surrounding CPB, improving the CPB temperature from 290 K gradually over time. Owing to the shape of the HET, the thermal influence region approximately tends to be a circular region along the radial direction. The heat transfer performance of CPB could also be indicated. The CPB temperature gradually reduces away from the HET. This is clearly demonstrated in Figure 10b, wherein the CPB temperature drops obviously along the vertical direction (i.e., Y-direction), and the slope is gradually flattened. When the distance from the HET reaches 0.6 m, the CPB temperature approaches its initial value of 290 K, indicating a thermal influencing radius of 0.6 m for the HET. Beyond this range, the effect of the HET on CPB temperature could be ignored.  After 48 h of operation, the variation of average water temperatures in the HET in Case 1, Case 2, and Case 3 is shown in Figure 11a. The water temperatures in different cases increased from 290 K to 328.48, 331.65, and 334.93 K, respectively. In different simulation cases, the water in the HET is heated under a constant heat flux and then releases thermal energy to the surrounding CPB; thus, the higher water temperature in the tube means an inefficient heat transfer between the tube and surrounding CPB, as well as a low CPB thermal conductivity. In view of different porosities in Cases 1 to 3, it is manifested that the heat transfer performance between HET and CPB varies with the CPB porosity. As shown in Figure 11a, the higher porosity corresponds to a weaker heat conductive performance of CPB (Case 3). This is mainly because a higher porosity has a higher air content, the heat conductivity of which is much less than that of the solid phase, reducing the comprehensive heat conduction of CPB. Furthermore, under the TRT method [46], the average fluid temperature in the HET (T f ) keeps a linear relation with lnt, where t is system operation duration, as shown in the following equations: where k and b are fitted values according to the data of T f and lnt; λ c denotes the thermal conductivity of CPB; and q l represents the heating power, which is a known value under TRT method. When the values of T f and lnt are obtained, λ c can be calculated by Equations (4) and (5). The relations between T f and lnt in Cases 1 to 3 are shown in Figure 11b, and the corresponding complex thermal conductivities of CPB in these three cases are calculated to be 0.324, 0.298, and 0.273 W/(m·K), respectively. Comparing the results of each case with the thermal conductivity values in Table 4, it can be found that in each case, the value of complex thermal conductivity of CPB falls between the lower and upper limit values that correspond to the maximum porosity and minimum porosity, respectively. For example, for CPB in Case 1, the thermal conductivity of CPB ranges from 0.316 W·m −1 ·K −1 (corresponding to a minimum porosity of 0.3) to 0.364 W·m −1 ·K −1 (corresponding to a maximum porosity of 0.4). The complex thermal conductivity of CPB obtained by simulation is 0.324 W/(m·K), which is not equal to the average of the upper and lower limit values. This indicates that it is not feasible to acquire the comprehensive thermal conductivity of CPB by the arithmetic average method. After 48 h of operation, the variation of average water temperatures in the HET in Case 1, Case 2, and Case 3 is shown in Figure 11a. The water temperatures in different cases increased from 290 K to 328.48, 331.65, and 334.93 K, respectively. In different simulation cases, the water in the HET is heated under a constant heat flux and then releases thermal energy to the surrounding CPB; thus, the higher water temperature in the tube means an inefficient heat transfer between the tube and surrounding CPB, as well as a low CPB thermal conductivity. In view of different porosities in Cases 1 to 3, it is manifested that the heat transfer performance between HET and CPB varies with the CPB porosity. As shown in Figure 11a, the higher porosity corresponds to a weaker heat conductive performance of CPB (Case 3). This is mainly because a higher porosity has a higher air content, the heat conductivity of which is much less than that of the solid phase, reducing the comprehensive heat conduction of CPB. Furthermore, under the TRT method [46], the average fluid temperature in the HET (Tf) keeps a linear relation with lnt, where t is system operation duration, as shown in the following equations: where k and b are fitted values according to the data of Tf and lnt; λc denotes the thermal conductivity of CPB; and ql represents the heating power, which is a known value under TRT method. When the values of Tf and lnt are obtained, λc can be calculated by Equations (4) and (5). The relations between Tf and lnt in Cases 1 to 3 are shown in Figure 11b, and the corresponding complex thermal conductivities of CPB in these three cases are calculated to be 0.324, 0.298, and 0.273 W/(m·K), respectively. Comparing the results of each case with the thermal conductivity values in Table 4, it can be found that in each case, the value of complex thermal conductivity of CPB falls between the lower and upper limit values that correspond to the maximum porosity and minimum porosity, respectively. For example, for CPB in Case 1, the thermal conductivity of CPB ranges from 0.316 W·m −1 ·K −1 (corresponding to a minimum porosity of 0.3) to 0.364 W·m −1 ·K −1 (corresponding to a maximum porosity of 0.4). The complex thermal conductivity of CPB obtained by simulation is 0.324 W/(m·K), which is not equal to the average of the upper and lower limit values. This indicates that it is not feasible to acquire the comprehensive thermal conductivity of CPB by the arithmetic average method.

Effects of the Hydraulic Conductivity on Heat Exchange Performance of CPB
The effect of seepage has a significant influence on the heat transfer between CPB and HET, which will have a certain impact on the heat exchange performance. Due to the bleeding behavior of CPB, there often exists bleeding water on the top surface of CPB after solidification. In addition, the underground environment usually induces seepage flow. Therefore, the effect of seepage flow was evaluated. The seepage direction was set from the top region to the bottom of CPB. Relative parameter settings are shown in Tables 3 and 4. Figure 12 indicates the temperature distribution of cross-section Z = 0 under seepage condition, with a hydraulic conductivity of 2 × 10 −6 (Case 8). By comparing Figure 12a-d, it can be seen that as time increases, the thermal influencing region of the HET gradually extends. The temperature field of the cross-section is no longer symmetrically distributed along the vertical direction. Instead, the thermal energy is gradually accumulated to the bottom region of CPB, forming a higher temperature than the upper region. This is clearly illustrated in Figure 13, wherein a higher temperature and larger influencing region are exhibited in the negative Y-direction compared to the positive Y-direction. Generally, with the increase in the hydraulic conductivity, the temperature field of the surrounding CPB near the HET deviates along the seepage flow direction. The higher the hydraulic conductivity is, the more uneven the temperature distribution is. Furthermore, the thermal influencing region shown in Figure 12d is larger than that in Figure 10a, indicating that the seepage flow could enlarge the thermal influencing radius of the HET in comparison with conditions without the seepage effect.

Effects of the Hydraulic Conductivity on Heat Exchange Performance of CPB
The effect of seepage has a significant influence on the heat transfer between CPB and HET, which will have a certain impact on the heat exchange performance. Due to the bleeding behavior of CPB, there often exists bleeding water on the top surface of CPB after solidification. In addition, the underground environment usually induces seepage flow. Therefore, the effect of seepage flow was evaluated. The seepage direction was set from the top region to the bottom of CPB. Relative parameter settings are shown in Tables 3  and 4. Figure 12 indicates the temperature distribution of cross-section Z = 0 under seepage condition, with a hydraulic conductivity of 2 × 10 −6 (Case 8). By comparing Figure 12a-d, it can be seen that as time increases, the thermal influencing region of the HET gradually extends. The temperature field of the cross-section is no longer symmetrically distributed along the vertical direction. Instead, the thermal energy is gradually accumulated to the bottom region of CPB, forming a higher temperature than the upper region. This is clearly illustrated in Figure 13, wherein a higher temperature and larger influencing region are exhibited in the negative Y-direction compared to the positive Y-direction. Generally, with the increase in the hydraulic conductivity, the temperature field of the surrounding CPB near the HET deviates along the seepage flow direction. The higher the hydraulic conductivity is, the more uneven the temperature distribution is. Furthermore, the thermal influencing region shown in Figure 12d is larger than that in Figure 10a, indicating that the seepage flow could enlarge the thermal influencing radius of the HET in comparison with conditions without the seepage effect.   Figure 14a. It can be seen tha water temperatures in the HET vary with the hydraulic conductivity. A higher hydrauli conductivity corresponds to a lower water temperature, indicating a better heat exchange performance between the tube and its surrounding CPB. With relatively similar hydrauli conductivities, which are 0, 1 × 10 −7 , and 4 × 10 −7 m/s, respectively, the variations of average water temperature exhibited in Cases 4 to 6 are almost the same. This result manifests tha the seepage flow can enhance the heat exchange capacity of CPB.  Figure 14b denotes the relationship between average water temperature in the HET and operation time. By Equations (4) and (5), the complex thermal conductivity of CPB under different hydraulic conductivities could be acquired, as shown in Figure 15. Com paring Cases 2 and 4 in Figure 15, it is found that the complex thermal conductivity o CPB in Case 4 is 1.497 W/(m·K), much higher than that of 0.298 W/(m·K) in Case 2. The porosities in these two cases are set with the same values while the seepage behavior i not considered (as shown in Table 3). This suggests that under the same porosities and seepage conditions, the heat exchange performance of CPB under liquid-saturated condi tion is higher than that under vapor-saturated condition. The reason is that the therma conductivity of water is much higher than that of air. The pore-water of liquid-saturated CPB could effectively improve its heat exchange capacity. Compared to the results shown in Section 4.1, it is indicated that the effect of the saturation condition of CPB on its therma  Figure 14a. It can be seen that water temperatures in the HET vary with the hydraulic conductivity. A higher hydraulic conductivity corresponds to a lower water temperature, indicating a better heat exchange performance between the tube and its surrounding CPB. With relatively similar hydraulic conductivities, which are 0, 1 × 10 −7 , and 4 × 10 −7 m/s, respectively, the variations of average water temperature exhibited in Cases 4 to 6 are almost the same. This result manifests that the seepage flow can enhance the heat exchange capacity of CPB.  Figure 14a. It can be seen that water temperatures in the HET vary with the hydraulic conductivity. A higher hydraulic conductivity corresponds to a lower water temperature, indicating a better heat exchange performance between the tube and its surrounding CPB. With relatively similar hydraulic conductivities, which are 0, 1 × 10 −7 , and 4 × 10 −7 m/s, respectively, the variations of average water temperature exhibited in Cases 4 to 6 are almost the same. This result manifests that the seepage flow can enhance the heat exchange capacity of CPB.  Figure 14b denotes the relationship between average water temperature in the HET and operation time. By Equations (4) and (5), the complex thermal conductivity of CPB under different hydraulic conductivities could be acquired, as shown in Figure 15. Comparing Cases 2 and 4 in Figure 15, it is found that the complex thermal conductivity of CPB in Case 4 is 1.497 W/(m·K), much higher than that of 0.298 W/(m·K) in Case 2. The porosities in these two cases are set with the same values while the seepage behavior is not considered (as shown in Table 3). This suggests that under the same porosities and seepage conditions, the heat exchange performance of CPB under liquid-saturated condition is higher than that under vapor-saturated condition. The reason is that the thermal conductivity of water is much higher than that of air. The pore-water of liquid-saturated CPB could effectively improve its heat exchange capacity. Compared to the results shown in Section 4.1, it is indicated that the effect of the saturation condition of CPB on its thermal conductivity is stronger than the effect of the porosity.  Figure 14b denotes the relationship between average water temperature in the HET and operation time. By Equations (4) and (5), the complex thermal conductivity of CPB under different hydraulic conductivities could be acquired, as shown in Figure 15. Comparing Cases 2 and 4 in Figure 15, it is found that the complex thermal conductivity of CPB in Case 4 is 1.497 W/(m·K), much higher than that of 0.298 W/(m·K) in Case 2. The porosities in these two cases are set with the same values while the seepage behavior is not considered (as shown in Table 3). This suggests that under the same porosities and seepage conditions, the heat exchange performance of CPB under liquid-saturated condition is higher than that under vapor-saturated condition. The reason is that the thermal conductivity of water is much higher than that of air. The pore-water of liquid-saturated CPB could effectively improve its heat exchange capacity. Compared to the results shown in Section 4.1, it is From Figure 15, it is also suggested that the complex thermal conductivities of CPB are increased with the increase in hydraulic conductivity, especially when the seepage velocity is above 10 −7 m/s. In Cases 8 to 10, seepage velocities are 2 × 10 −6 , 4 × 10 −6 , and 6 × 10 −6 m/s, while the corresponding complex thermal conductivities of CPB are 1.843, 2.649, and 3.957 W/(m·K), respectively, showing an obvious increasing trend. This is because with the velocity enhancement of the seepage flow, the effect of convective heat transfer becomes dominant. Figure 16a shows the temperature field of cross-section Z = 0 under 28 days of operation in Case 5. In comparison with Figures 10a and 12d, a larger thermal influencing region of the HET can be found in Figure 16a, indicating a more thorough heat exchange between CPB and tubes. However, in view of the economical property of the system, a long operation duration does not mean a better exchange performance. In Figure 16b, the variation of average water temperature for 28 days in Case 5 is demonstrated. According to the fitting curve of Tf-lnt expressed in Figure 16b, the complex thermal conductivity of CPB after 28 days of operation is calculated to be 1.488 W/(m·K), with little difference from 1.498 W/(m·K) obtained in Case 5, wherein the operation duration is 48 h (as shown in Figure 15). This denotes that the operation duration has no significant effect on the complex thermal conductivity of CPB once the TRT simulation achieves stable operation, manifesting the feasibility of operation duration setting (i.e., 48 h) in this simulation for the evaluation of the complex thermal conductivity of CPB. From Figure 15, it is also suggested that the complex thermal conductivities of CPB are increased with the increase in hydraulic conductivity, especially when the seepage velocity is above 10 −7 m/s. In Cases 8 to 10, seepage velocities are 2 × 10 −6 , 4 × 10 −6 , and 6 × 10 −6 m/s, while the corresponding complex thermal conductivities of CPB are 1.843, 2.649, and 3.957 W/(m·K), respectively, showing an obvious increasing trend. This is because with the velocity enhancement of the seepage flow, the effect of convective heat transfer becomes dominant. Figure 16a shows the temperature field of cross-section Z = 0 under 28 days of operation in Case 5. In comparison with Figures 10a and 12d, a larger thermal influencing region of the HET can be found in Figure 16a, indicating a more thorough heat exchange between CPB and tubes. However, in view of the economical property of the system, a long operation duration does not mean a better exchange performance. In Figure 16b, the variation of average water temperature for 28 days in Case 5 is demonstrated. According to the fitting curve of T f -lnt expressed in Figure 16b, the complex thermal conductivity of CPB after 28 days of operation is calculated to be 1.488 W/(m·K), with little difference from 1.498 W/(m·K) obtained in Case 5, wherein the operation duration is 48 h (as shown in Figure 15). This denotes that the operation duration has no significant effect on the complex thermal conductivity of CPB once the TRT simulation achieves stable operation, manifesting the feasibility of operation duration setting (i.e., 48 h) in this simulation for the evaluation of the complex thermal conductivity of CPB.

Discussion
Considerable heat energy is consumed in buildings in mining areas for both production and daily life. The abundant geothermal energy contained in mining areas could be adopted as a supplementary heat source for the heat demand of users in mining [9][10][11]. The CMBG system is an efficient solution for achieving the collaborative exploitation of mines and geothermal energy [20]. For this system, the thermal conductivity and heat exchange performance of CPB are crucial factors for thermal exploitation performance [24,[32][33][34]. Furthermore, due to the sedimentary characteristic of slurry in the backfilling process, the thermal conductivities in solidified CPB are nonuniformly distributed along both the vertical and horizontal directions. In view of the above factors, the heat exchange performance of CPB under different boundary conditions was evaluated, while the nonuniformly distributed thermal properties in CPB were fully considered.
According to the results, the porosity had significant effects on the heat exchange performance of CPB. For Cases 1 to 3 shown in Figure 11, as the porosities increased, the corresponding complex thermal conductivities were calculated to be 0.324, 0.298, and 0.273 W/(m·K), respectively, with a maximal reduction rate of 18%. This indicated that the increase in porosity exerted negative effects on the heat exchange performance of CPB. Since CPB is composed of different ingredients, the proportion of each component is highly relevant to the porosity distribution in CPB. Thus, in the practical design process, component proportions in CPB should be well designed for the thermal performance optimization of the CMBG system. Besides, the seepage flow also showed an obvious influence on the heat transfer performance of CPB. Results in this study illustrated that the heat transfer performance of CPB improved with the increase in seepage velocity, especially when the seepage velocity exceeded 2 × 10 −6 m/s (as shown in Figure 15). When the seepage velocity rose from 2 × 10 −6 to 6 × 10 −6 m/s in Cases 8 to 10, the thermal conductivity of CPB achieved a 114% increase from 1.843 to 3.957 W/(m·K). Furthermore, due to the seepage flow, the thermal influencing radius of the HET was no longer symmetrically distributed along the seepage flow direction, causing a larger thermal influencing region under the HET in comparison with that above the HET (as shown in Figure 12). For the above reasons, in the practical engineering design of the CMBG system, the determination of layout parameters of the HET (such as tube pitch) should fully take into account the effect of seepage flow, avoiding the thermal interference among multiple HETs.

Discussion
Considerable heat energy is consumed in buildings in mining areas for both production and daily life. The abundant geothermal energy contained in mining areas could be adopted as a supplementary heat source for the heat demand of users in mining [9][10][11]. The CMBG system is an efficient solution for achieving the collaborative exploitation of mines and geothermal energy [20]. For this system, the thermal conductivity and heat exchange performance of CPB are crucial factors for thermal exploitation performance [24,[32][33][34]. Furthermore, due to the sedimentary characteristic of slurry in the backfilling process, the thermal conductivities in solidified CPB are nonuniformly distributed along both the vertical and horizontal directions. In view of the above factors, the heat exchange performance of CPB under different boundary conditions was evaluated, while the nonuniformly distributed thermal properties in CPB were fully considered.
According to the results, the porosity had significant effects on the heat exchange performance of CPB. For Cases 1 to 3 shown in Figure 11, as the porosities increased, the corresponding complex thermal conductivities were calculated to be 0.324, 0.298, and 0.273 W/(m·K), respectively, with a maximal reduction rate of 18%. This indicated that the increase in porosity exerted negative effects on the heat exchange performance of CPB. Since CPB is composed of different ingredients, the proportion of each component is highly relevant to the porosity distribution in CPB. Thus, in the practical design process, component proportions in CPB should be well designed for the thermal performance optimization of the CMBG system. Besides, the seepage flow also showed an obvious influence on the heat transfer performance of CPB. Results in this study illustrated that the heat transfer performance of CPB improved with the increase in seepage velocity, especially when the seepage velocity exceeded 2 × 10 −6 m/s (as shown in Figure 15). When the seepage velocity rose from 2 × 10 −6 to 6 × 10 −6 m/s in Cases 8 to 10, the thermal conductivity of CPB achieved a 114% increase from 1.843 to 3.957 W/(m·K). Furthermore, due to the seepage flow, the thermal influencing radius of the HET was no longer symmetrically distributed along the seepage flow direction, causing a larger thermal influencing region under the HET in comparison with that above the HET (as shown in Figure 12). For the above reasons, in the practical engineering design of the CMBG system, the determination of layout parameters of the HET (such as tube pitch) should fully take into account the effect of seepage flow, avoiding the thermal interference among multiple HETs.

Conclusions
In this study, a validated numerical model was established to evaluate the heat exchange performance of CPB under stratified distribution conditions. Based on this model, the thermal influencing region of the HET and heat transfer performance of CPB were investigated under different porosities and hydraulic conductivities.
The heat exchange performance of CPB with different porosities was evaluated, and it was found that CPB with a higher porosity exhibits a weaker heat conductive performance. In actual conditions, porosities in CPB are nonuniformly distributed; the complex thermal conductivity of CPB obtained by the arithmetic average method could not represent its actual value. The proposed model provides an effective method for the prediction of the complex thermal conductivity of CPB. Seepage flow has an enhancement effect on the heat exchange between the HET and its surrounding CPB. The heat transfer performance of CPB strengthens with the increase in hydraulic conductivity. In addition, in conditions with seepage flow, the CPB temperature field of the vertical cross-section is no longer evenly distributed along the plumb direction. Thus, the seepage flow effect should be fully considered in the determination of HET arrangement, avoiding the thermal interference caused by the overlap of the thermal influencing radius of the HET.
The complex thermal conductivity of CPB cannot be accurately calculated by an arithmetic average method. The values obtained by the proposed simulation model and the arithmetic average method should be comparatively analyzed and discussed in the following work. In addition, the existing fractures in CPB could also affect the heat exchange performance of CPB; the influence of the fractures on the heat transfer performance of the CMBG system also needs to be evaluated in the future.

Data Availability Statement:
The data that support the findings of this study are available from the corresponding author upon reasonable request.