# Development of a Phase Change Backfill Material with High Heat Capacity and High Thermal Conductivity Used for Ground Source Heat Pumps

Authors: Yixia Chen; Tingting Luo; Peng Pei; Yujin Ran; Long Tang
Journal: International Journal of Energy Research
 (2023)

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## Abstract

To solve the problems of phase change materials (PCM) including low thermal conductivity and easy washout and loss after liquefaction in current studies on borehole backfill materials, capric acid-lauric acid/expanded graphite (CA-LA/EG) PCM admixture with high thermal conductivity and high heat capacity was developed by using expanded graphite as the carrier. The PCM admixture is mixed with original sands (drilling debris) to make phase change backfill materials (PCBM). When the PCM backfilling is applied, the key issue is to dissipate the large amount of heat stored as latent heat in boreholes to the surrounding formation in time; otherwise, serious heat accumulation would be induced. Numerical simulation of application of the PCBM in multiple intermittent operation cycles was conducted when the admixture percentages and thermal conductivities are different. The result shows that compared with conventional low-conductivity PCM admixtures and ordinary backfill sands such as drilling debris, the CA-LA/EG admixture can mitigate the temperature fluctuation in borehole and improve its heat exchange rate. The heat exchange rate was increased by 11.6% when 30% of CA-LA/EG admixture was added. However, the improvement declined as the number of operation cycle increased, so the intermittent operation mode is suggested to match the PCBM application since the heat in borehole should be dissipated in time to reserve storage capacity in the next operation cycle and continuously utilize the high heat capacity of the PCM.


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## Body

## 1. Introduction

Ground source heat pump systems offer an attractive approach for air conditioning using rock and soil at shallow depth as an energy storage body, and the technology is promoted because of its green and energy-saving characteristics [1]. As the heat exchange medium between the buried pipe and the surrounding geological formations, the thermal properties of backfill materials in the borehole directly influence the heat exchange effect of the buried pipe and successful long-term operation of the heat pump system [2]. The thermal resistance of the buried U-pipe (Rp), backfill material (Rb), and rock and soil formation (Rf) is connected in series, so the backfill materials can be considered as the first-level medium for heat pump system to exchange energy with the formations (Figure 1). If the heat capacity of the backfill materials is insufficient, or the received heat cannot be diffused to the surrounding strata in time, heat accumulation will occur in the boreholes.Figure 1
Heat transfer from buried U-pipe to surrounding formation.Phase change materials (PCM) have been successfully applied in such fields as green building [3], thermal control in aerospace [4], and solar thermal utilization [5] due to their large latent heat and small temperature fluctuation during phase change. The PCM can be used as an additive for borehole backfill materials. Their latent heat during phase change can be used to reduce the effect of temperature fluctuation on heat exchange in a short time and thus improve the system operation efficiency.In recent years, many scholars have discussed the feasibility of applying PCM to borehole backfilling of ground source heat pumps. Rabin and Korin [6] theoretically analyzed the feasibility of applying PCM to the geothermal energy storage system, and the results showed that the system thermal storage performance could be significantly improved by adding PCM when the same thermal conductivity is available. Li [7] compared and analyzed the heat transfer characteristics of the buried pipes with PCM backfilling and ordinary material backfilling and concluded that PCM back filling could effectively avoid thermal interference, and the heat exchange rate increased as the flow rate in U-pipe was increased. Bottarell et al. [8, 9] adopted the numerical simulation to study the effect of adding PCM to backfill materials on the heat transfer performance of horizontal buried pipe heat exchanger, and the results showed that PCM could slow down the soil temperature rise and improve the heat pump performance. Lyne et al. [10] discussed the effects of soil, PCM, and graphite PCM backfill materials with high conductivity on the temperature of heat exchange boreholes, and the results showed that PCM could reduce the soil temperature fluctuation. Yang et al. [11–13] tested and simulated the energy storage and heat transfer characteristics of PCM-backfilled buried heat exchangers, and the results showed that in both summer and winter, PCM backfilling could improve the energy storage performance, reduce the variation range of soil temperature outside the boreholes, enhance the recovery rate of soil temperature, and decrease the heat effect radius of borehole. Li et al. [14] compared the heat transfer performance of U-pipe heat exchanger using the shaped PCM and crushed concrete as backfill materials and found that the heat exchange rate per depth of borehole backfilled with the shaped PCM was 1.223 times of crushed concrete, and the heat effect radius was 0.9 times of crushed concrete. Benli and Durmus [15] set up a greenhouse ground source heat pump with a phase change energy storage test device and tested the system, and the results showed that the coefficient of performance (COP) of the ground source heat pump unit and the system was 2.3~3.8 and 2.0~3.5, respectively. These results showed that the utilization of a GSHP-PCM system is a suitable approach for greenhouse heating in the researched district. The studies of Chen et al. [16, 17] showed that PCM backfilling was more suitable for those buildings whose continuous thermal demand is not high. Lei et al. [18–20] conducted theoretical and experimental studies on the PCM-backfilled jacked tube boreholes, and the results showed that PCM backfilling could reduce the spacing between boreholes. If the economic cost of PCM is reduced, PCM backfilling is expected to have a good application prospect. After experimental testing and theoretical analysis, Wu [21] concluded that the ground source heat pumps backfilled with PCM could significantly increase the heat exchange rate of a single borehole.The intermittent operation mode is regarded as an effective approach to mitigate thermal imbalance risk. Zhang et al. [22] conducted experimental and numerical study of thermal performance of a horizontal slinky-coil ground heat exchanger and concluded that the soil temperature operated in intermittent mode can get a recovery, and thus, the heat release rate of the coil can be improved. Wang et al. [23] simulated and studied the heat exchange performance of PCM-backfilled buried pipes under intermittent operation in summer, and the results showed that the PCM with low phase change temperature could significantly improve the heat exchange rate of the buried pipes at the early stage of intermittent operation. As long-term operation continues the improvement of the heat exchange rate of heat exchanger by the PCM with a high phase change temperature is higher than the PCM with a low phase change temperature in the same period.The PCM used in ground source heat pumps and energy piles in current studies are mainly fatty acids (lauric acid (LA), capric acid (CA), palmitic acid [24, 25], etc.), polyols (mannitol [26], erythritol [27], pentaerythritol [28], etc.), paraffin [29], and other organic polymer materials. However, the organic PCM usually has low heat conductivity and might cause potential thermal conductivity deterioration in the borehole. Some researches carbon materials to adsorb the PCM and improve its heat conductivity. Li and Mu [30] described the research progress in utilizing carbon materials to improve thermal properties of PCM and concluded that the 3-dimension carbon material offers a larger contact for the PCM, thanks for its cellular structure, hence improving the heat conductivity and mechanical properties of the PCM. Hu et al. [31] tested the heat conductivity of composite PCM made by paraffin, expanded graphite (EG) and graphite flake, and concluded that when the EG is used as a carrier of the PCM, it can effectively increase the overall heat conductivity of the material, especially in the vertical direction. Li et al. [32] prepared CA/EG composite PCM and proved that the EG can improve the heat conductivity, decrease the phase change temperature and hence improving the heat exchange efficiency of the material.To sum up, preparation and characterization of PCM used in heat exchange borehole backfilling have been reported in recent years, but most studies reported the effect of PCM by simulation of only one operation cycle. There are still some major questions remained unanswered: (1) the PCM in the borehole is able to accommodate a large amount of heat, but on the other hand, its low conductivity would block the heat to be dissipated to surrounding formations in time; (2) if there is no sufficient heat storage capacity for subsequent cycles for long-term operation, how the system performs would be impacted; (3) the operation mode matters, and an appropriate mode should be adopted to match the PCM backfilling; and (4) stability of the PCM against washout by groundwater should be investigated.Focusing on the aforementioned issues, the capric acid-lauric acid/expanded graphite (CA-LA/EG) composite PCM admixture was developed in laboratory in order to simultaneously improve the heat transfer and heat storage capacity of backfill materials, as well as the stability against washout by groundwater. Then, the effects of the PCM admixture of different percentages and different thermal conductivities on borehole temperature and heat exchange rate under multicycle operation were analyzed through numerical simulation. The variation patterns of the temperature in boreholes and the heat exchange power in intermittent multicycle operation mode were obtained. An integrated solution to improve the borehole performance by using the CA-LA/EG PCM admixture collaborated with the intermittent operation mode is finally proposed, which is of theoretical guiding significance for the application of PCM in ground source heat pump borehole backfilling and operation.


## 2. Improved Design of Phase Change Backfill Materials (PCBM)

### 2.1. Design Approach

The categories of the borehole backfill materials depicted in this study are shown in Figure2. The ordinary backfill material, which is often the drilling debris, or called original sands, is used as the reference baseline for comparison in this study. The PCM backfill material is made by adding the PCM admixture to the original sands. The PCM admixture can be made by only the PCM or PCM adsorbed on carriers.Figure 2
Categories of borehole backfill materials.In this paper, the PCM admixture is designed from the perspectives of suitable phase change temperatures, high thermal conductivity, high specific heat capacity, and environmental friendliness. Generally, most of the PCM have defects such as low thermal conductivity and easy loss after liquefaction. Therefore, a carrier with high thermal conductivity is needed to adsorb PCM, preventing it from being washed away by groundwater flow after liquefaction and improving the thermal conductivity of composite PCM.


### 2.2. Selection of PCM

The design of PCBM should first consider whether its phase change temperature is within the operation temperature range of heat pump and then environmental friendliness, thermal stability, and latent heat capacity. The PCBM developed in this paper were applied in summer cooling condition. Taking the general temperature (18°C or 291 K) of rock formation in the summer and the water inlet temperature of U-pipe (35°C or 308 K) as the reference, the liquefaction temperature of PCM was set slightly higher than the ground temperature. Table1 lists the physical properties of capric acid and lauric acid. It can be seen from Figure 3 that when the molar ratio of capric acid is 60%-70% and lauric acid is 30%-40% in the CA-LA eutectic system, the phase change temperature (292.8 K) of the mixed acid can match the requirement. In this study, the mixed acid was prepared according to the molar ratio (65% : 35%) of CA to LA and used as the PCM.Table 1
Physical parameters of capric acid and lauric acid.
MaterialPurityMelting processSolidification processPhase change temperature, °CEnthalpy of phase change, J/gPhase change temperature, °CEnthalpy of phase change, J/gCapric acid99.3%32.8178.1525173.25Lauric acid99%44.72188.9640.99198.05Figure 3
Phase diagram of capric acid-lauric acid binary system [33].Both capric acid and lauric acid are natural acids, nontoxic, and harmless, and the latent heat of the mixed acid of the two is relatively high. The phase change temperature matching different operation temperature ranges of the heat pump could be obtained by mixing the two in a certain proportion [33]. The mixed acid of the two has a reliable thermal stability and long phase change life [34].


### 2.3. Selection of Adsorption Carrier

The PCM needs to be adsorbed on the carrier in order to prevent it from being washed way and lost by the groundwater after liquefaction. As shown in Table2, the expanded graphite (EG) has the excellent properties of natural graphite such as high thermal conductivity, and corrosion resistance, and its porous reticular structure provides it with a large specific surface area and a strong adsorption capacity [35]. EG can not only adsorb PCM by its pores but also improve the thermal conductivity of the PCM admixture. The EG is nontoxic and harmless and will not affect the environment around the heat exchange borehole group. Based on the aforementioned properties EG was selected as the carrier in this study.Table 2
Specification parameters of expanded graphite.
GranularityPurityDilatabilityVolatile componentMoisture content80 grids99%200~3000.2%≤0.2%As shown in Figure2, the PCM admixture (CA-LA/EG) is formed by the EG and the composite PCM (mixed acid of CA-LA).


### 2.4. Preparation of PCM Admixture

The preparation procedure of CA-LA/EG PCM admixture (Figure4) is as follows:
(1)
Heat capric acid in 80°C water bath until it melts(2)
Weigh the CA liquid and LA powder according to the molar ratio (65% : 35%), mix, and heat mixture in water of 60°C. After the mixture melts, stir it well for 10 min to form the binary composite PCM(3)
Add the mixed acid liquid into EG by several times, stir it for 30 min, and then, let it stand for 30 min. The samples with the mass ratios of 8 : 100 and 10 : 100 of EG (expansion rate: 200~300) to composite PCM were prepared in this studyFigure 4
CA-LA/EG prepared in the laboratory.


### 2.5. Leakage Test of PCM Admixture

The leakage test is performed to investigate the risk whether the composite PCM (CA-LA acid) could be displaced by water when it is used in boreholes penetrating aquifers.First, the composite PCM with different EG ratios were compressed into cylindrical blocks with a diameter of 10 mm and a height of 5 mm by a tablet press. The blocks are placed on the filter paper and then warmed for 6 hours at a constant temperature of 70°C to liquefy the PCM. As shown in Figure5, no large-area PCM leakage marks appeared on the filter paper in the phase change test. In particular, the samples with a mass ratio (10 : 100) of EG to CA-LA had no obvious leakage mark on the filter paper, and its leakage was less than the sample with a mass ratio (8 : 100) of EG to CA-LA.Figure 5
Leakage test of PCM.After the leakage test above, a displacement experiment of the CA-LA/EG was performed. The procedure is as follows:(1)
The EG is compressed to a cylindrical block with a diameter of 50 mm and a height of 10 mm, and its weight is 3.39 g(2)
The EG block was saturated with the CA-LA acid for 72 hours, and the mass of the saturated EG block is 20.02 g, and its height was increased to 11 mm, so the volume after absorbing the mixed acid is 21.59 cm3(3)
Then, the acid-saturated EG block in step 2 was immersed in water for another 72 hours, after which the mass of the EG block was 20.57 g, and the volume of the test block does not changeThe density of the CA-LA acid is 0.88 g/cm3. In step 2, the EG block adsorbed 16.63 g of CA-LA acid. In step 3, its mass increased by 0.55 g, so only 2.91% by volume of the acid is displaced by water. Therefore, it can be considered that the composite PCM is stable in the EG carrier.


### 2.6. Thermal Property Test of PCM Admixture

Differential scanning calorimetry (DSC) and thermal conductivity tests were conducted on the composite PCM admixture with a mass ratio (10 : 100) of expanded graphite to CA-LA. The test results are shown in Figure6. In the figure, there is an obvious concave peak, which indicates that the phase change of the material occurred in this process. The fusion point of CA-LA/EG prepared in this study was Tf=19.41°C, the peak phase change temperature was Tp=22.21°C, and the enthalpy of phase change was 138.8 J/g. The thermal conductivity of PCM admixture was 2.51 W/m·K after being tested by a conductometer.Figure 6
DSC curve of PCM admixture (EG:CA−LA=10:100).


## 2.1. Design Approach

The categories of the borehole backfill materials depicted in this study are shown in Figure2. The ordinary backfill material, which is often the drilling debris, or called original sands, is used as the reference baseline for comparison in this study. The PCM backfill material is made by adding the PCM admixture to the original sands. The PCM admixture can be made by only the PCM or PCM adsorbed on carriers.Figure 2
Categories of borehole backfill materials.In this paper, the PCM admixture is designed from the perspectives of suitable phase change temperatures, high thermal conductivity, high specific heat capacity, and environmental friendliness. Generally, most of the PCM have defects such as low thermal conductivity and easy loss after liquefaction. Therefore, a carrier with high thermal conductivity is needed to adsorb PCM, preventing it from being washed away by groundwater flow after liquefaction and improving the thermal conductivity of composite PCM.


## 2.2. Selection of PCM

The design of PCBM should first consider whether its phase change temperature is within the operation temperature range of heat pump and then environmental friendliness, thermal stability, and latent heat capacity. The PCBM developed in this paper were applied in summer cooling condition. Taking the general temperature (18°C or 291 K) of rock formation in the summer and the water inlet temperature of U-pipe (35°C or 308 K) as the reference, the liquefaction temperature of PCM was set slightly higher than the ground temperature. Table1 lists the physical properties of capric acid and lauric acid. It can be seen from Figure 3 that when the molar ratio of capric acid is 60%-70% and lauric acid is 30%-40% in the CA-LA eutectic system, the phase change temperature (292.8 K) of the mixed acid can match the requirement. In this study, the mixed acid was prepared according to the molar ratio (65% : 35%) of CA to LA and used as the PCM.Table 1
Physical parameters of capric acid and lauric acid.
MaterialPurityMelting processSolidification processPhase change temperature, °CEnthalpy of phase change, J/gPhase change temperature, °CEnthalpy of phase change, J/gCapric acid99.3%32.8178.1525173.25Lauric acid99%44.72188.9640.99198.05Figure 3
Phase diagram of capric acid-lauric acid binary system [33].Both capric acid and lauric acid are natural acids, nontoxic, and harmless, and the latent heat of the mixed acid of the two is relatively high. The phase change temperature matching different operation temperature ranges of the heat pump could be obtained by mixing the two in a certain proportion [33]. The mixed acid of the two has a reliable thermal stability and long phase change life [34].


## 2.3. Selection of Adsorption Carrier

The PCM needs to be adsorbed on the carrier in order to prevent it from being washed way and lost by the groundwater after liquefaction. As shown in Table2, the expanded graphite (EG) has the excellent properties of natural graphite such as high thermal conductivity, and corrosion resistance, and its porous reticular structure provides it with a large specific surface area and a strong adsorption capacity [35]. EG can not only adsorb PCM by its pores but also improve the thermal conductivity of the PCM admixture. The EG is nontoxic and harmless and will not affect the environment around the heat exchange borehole group. Based on the aforementioned properties EG was selected as the carrier in this study.Table 2
Specification parameters of expanded graphite.
GranularityPurityDilatabilityVolatile componentMoisture content80 grids99%200~3000.2%≤0.2%As shown in Figure2, the PCM admixture (CA-LA/EG) is formed by the EG and the composite PCM (mixed acid of CA-LA).


## 2.4. Preparation of PCM Admixture

The preparation procedure of CA-LA/EG PCM admixture (Figure4) is as follows:
(1)
Heat capric acid in 80°C water bath until it melts(2)
Weigh the CA liquid and LA powder according to the molar ratio (65% : 35%), mix, and heat mixture in water of 60°C. After the mixture melts, stir it well for 10 min to form the binary composite PCM(3)
Add the mixed acid liquid into EG by several times, stir it for 30 min, and then, let it stand for 30 min. The samples with the mass ratios of 8 : 100 and 10 : 100 of EG (expansion rate: 200~300) to composite PCM were prepared in this studyFigure 4
CA-LA/EG prepared in the laboratory.


## 2.5. Leakage Test of PCM Admixture

The leakage test is performed to investigate the risk whether the composite PCM (CA-LA acid) could be displaced by water when it is used in boreholes penetrating aquifers.First, the composite PCM with different EG ratios were compressed into cylindrical blocks with a diameter of 10 mm and a height of 5 mm by a tablet press. The blocks are placed on the filter paper and then warmed for 6 hours at a constant temperature of 70°C to liquefy the PCM. As shown in Figure5, no large-area PCM leakage marks appeared on the filter paper in the phase change test. In particular, the samples with a mass ratio (10 : 100) of EG to CA-LA had no obvious leakage mark on the filter paper, and its leakage was less than the sample with a mass ratio (8 : 100) of EG to CA-LA.Figure 5
Leakage test of PCM.After the leakage test above, a displacement experiment of the CA-LA/EG was performed. The procedure is as follows:(1)
The EG is compressed to a cylindrical block with a diameter of 50 mm and a height of 10 mm, and its weight is 3.39 g(2)
The EG block was saturated with the CA-LA acid for 72 hours, and the mass of the saturated EG block is 20.02 g, and its height was increased to 11 mm, so the volume after absorbing the mixed acid is 21.59 cm3(3)
Then, the acid-saturated EG block in step 2 was immersed in water for another 72 hours, after which the mass of the EG block was 20.57 g, and the volume of the test block does not changeThe density of the CA-LA acid is 0.88 g/cm3. In step 2, the EG block adsorbed 16.63 g of CA-LA acid. In step 3, its mass increased by 0.55 g, so only 2.91% by volume of the acid is displaced by water. Therefore, it can be considered that the composite PCM is stable in the EG carrier.


## 2.6. Thermal Property Test of PCM Admixture

Differential scanning calorimetry (DSC) and thermal conductivity tests were conducted on the composite PCM admixture with a mass ratio (10 : 100) of expanded graphite to CA-LA. The test results are shown in Figure6. In the figure, there is an obvious concave peak, which indicates that the phase change of the material occurred in this process. The fusion point of CA-LA/EG prepared in this study was Tf=19.41°C, the peak phase change temperature was Tp=22.21°C, and the enthalpy of phase change was 138.8 J/g. The thermal conductivity of PCM admixture was 2.51 W/m·K after being tested by a conductometer.Figure 6
DSC curve of PCM admixture (EG:CA−LA=10:100).


## 3. Application Simulation of PCBM

### 3.1. Physical Model

The following assumptions were proposed in the simulation:(1)
The working medium (water) in the buried pipe was assumed as incompressible fluid(2)
The formation is assumed as isotropic and homogeneous(3)
Only the thermal conductivity process in rock and soil was studied, and the water migration was ignored(4)
All areas were in close contact, and the effect of contact thermal resistance was ignored(5)
Cooling condition in the summer was simulated(6)
The phase change temperature of PCM was assumed to be 19-20°C(7)
The running-stop ratio of the heat pump unit was assumed to be 0.7 (i.e., operating for 10 h and resting for 14 h), and the simulation duration was 72 h. Each 24 h was a cycle, and there were totally three cyclesBased on the above assumptions, a physical model was established, as shown in Figure7.Figure 7
Schematic diagram of numerical model.


### 3.2. Mathematical Model

#### 3.2.1. Heat Transfer Model of Porous Media

The energy balance equation in the porous matrix is as follows:(1)ρsCp∂T∂t+ρCpu⋅∇T+∇⋅−ks∇T=Q,where ρs (kg/m3) is the density of porous medium; cp (J/kg∙K) is the specific heat capacity at constant pressure; T (K) is the temperature; u (m/s) is the velocity field; and ks (W/m∙k) is the overall thermal conductivity coefficient of the formation, and Q (W/m3) is the heat source.


#### 3.2.2. Heat Transfer Model of Pipe

The energy equation of the pipe is as follows:(2)AρfCp∂T∂t+AρfCpuf⋅∇T=∇⋅AK∇T+fDρfA2dhufuf2+Qwall+Q,where A (m2) is the cross-sectional area of U-pipe; ρf (kg/m3) is the fluid density; uf (m/s) is the fluid velocity in the pipe; k (W/m∙k) is the thermal conductivity coefficient of the fluid; fD (m) is Darcy friction coefficient; dh (m) is the average hydraulic diameter; and Qwall (W/m) is the heat exchange rate outside the pipe wall per length, and Q (W/m) is general heat source per length.The radial heat transferQwall (W/m) between the U-pipe and the surrounding environment is as follows:
(3)Qwall=hZeffTEXT−T,where hZeff (W/(m∙K)) is the effective value of heat transfer coefficient, which is the product of h (W/(m2∙K)) of the pipe multiplied by the circumference Z (m) of the pipe wall, and TEXT (K) is the temperature of the outer wall of the pipe.


#### 3.2.3. Phase Change Heat Transfer Process

The thermophysical properties of PCM keep changing in the process of phase change in which the solid and liquid phases of the materials exist simultaneously. The thermophysical properties of the materials need to be determined according to the volume fraction of solid and liquid. The density (ρ, kg/m3) and thermal conductivity (k, W/(m·K)) of PCM are as follows:
(4)ρ=θTρ1+1−θTρ2,(5)k=θTk1+1−θTk2,where θT is the mass fraction of phase 1 which is a function of temperature T, and phase 1 is solid, and phase 2 is liquid.The equivalent heat capacity method is used to simulate the phase change process of PCM. The heat capacity of PCM is determined as a latent heat item, and its calculation formula is as follows:(6)CP=1ρθTρ1CP1+1−θTρ2CP2+L∂αmT∂T,where αm is a smooth transition function which aims to make the heat capacity value change slowly in order to prevent instability, and its formula is as follows:
(7)αm=121−θTρ2−θTρ1θTρ1+1−θTρ2.PCM admixture is added to ordinary sands (original drilling debris) to make the PCBM. The porous media module is used to simulate the heat transfer process of PCBM. The material properties before and after the phase change can be expressed by the following formulas:(8)R1=1−wt%Rc+wt%Rp,1,(9)R2=1−wt%Rc+wt%Rp,2,where R1 and R1 are thermophysical property parameters of PCBM before and after the phase change, including density ρ (kg/m3), thermal conductivity coefficient k (W/(m·K)), and heat capacity cp (J/(kg·K)); Rc is the thermophysical property parameter of ordinary backfill materials; Rp,1 and Rp,2 are the thermophysical property parameters of PCM before and after the phase change; and wt% is the mass fraction of PCM admixture.


### 3.3. Boundary and Initial Conditions

Initial temperature is as follows:(10)Tlz,τ=Tpr,z,τ=Tsr,z,τ=T0τ=0.Far boundary conditions of rock formation are as follows:(11)Tsr,z,τr=10=T0Upper and bottom boundary conditions are as follows:(12)∂T∂zz=0=0,(13)∂T∂ZZ=120=0,where Tlz,τ (°C) is the fluid temperature in the depth z (m) at the time τ (s); Tpz,τ (°C) is the temperature at the bottom of the heat exchange borehole in the side length r and the depth z at the time τ; Tsz,τ (°C) is the rock and soil temperature in the side length r (m) and the depth z (m) at the time τ; and T0 (°C) is the initial temperature of the formation.Inlet and outlet boundary conditions of U-pipe are as follows:(14)Tin=35°C,(15)vin=0.6ms,where Tin (°C) is the inlet water temperature and vin (m/s) is the inlet water speed.


### 3.4. Meshing and Independence Verification

#### 3.4.1. Meshing

The model is meshed by the free tetrahedral grid. In order to reduce the number of grids, large grid spacing was selected as the temperature gradient was small in the surrounding formation. However, the temperature gradient around the U-pipe was high, so it is necessary to make the mesh in heat exchange borehole dense. The grid division is shown in Figure8.Figure 8
Schematic diagram of grid division.


#### 3.4.2. Independence Verification

In order to verify the reliability of grid division, the independence verification was conducted. Three grid densities (amount of 824,301, 1,357,267, and 1,918,604, respectively) were selected for calculation. When the inlet temperature of the buried pipe was constant, the calculated outlet temperature of the U-pipe was used as a comparison benchmark. The results are shown in Figure9. It can be seen from the analysis that when the number of grids is different, the outlet temperature of buried pipe will show the same trend with time, and the difference is small with the increase of grid numbers. Considering calculation accuracy and calculation time, the grid number in this paper is 1,357,267.Figure 9
Diagram of grid independence verification.


### 3.5. Simulation Parameters

The parameters used in the model are listed in Tables3 and 4. The low-conductivity PCM admixture is made by mixed acid of CA and LA. The high-conductivity PCM admixture (CA-LA/EG) is made by mixed acid CA and LA adsorbed on the carrier (EG).Table 3
Size of heat exchange model.
ParameterValueParameterValueRadius of calculated area, m10Center distance of U-pipe, mm80Depth of calculated area, m150Inner diameter of U-pipe, mm26Diameter of borehole, m0.18Outside diameter of U-pipe, mm32Depth of borehole, m120Depth of U-pipe, m119.1Table 4
Physical parameters of backfill materials.
MaterialDensity, kg/m3Thermal conductivity coefficient, W/(m·k)Specific heat capacity, kJ/(kg·K)Temperature, °CLatent heat of phase change, kJ/kgRock and soil formation28002.50.8——Original sands25002.30.82——Low-conductivity PCM admixture (CA-LA)8800.1322.420152High-conductivity PCM admixture (CA-LA/EG)6402.512.220139


## 3.1. Physical Model

The following assumptions were proposed in the simulation:(1)
The working medium (water) in the buried pipe was assumed as incompressible fluid(2)
The formation is assumed as isotropic and homogeneous(3)
Only the thermal conductivity process in rock and soil was studied, and the water migration was ignored(4)
All areas were in close contact, and the effect of contact thermal resistance was ignored(5)
Cooling condition in the summer was simulated(6)
The phase change temperature of PCM was assumed to be 19-20°C(7)
The running-stop ratio of the heat pump unit was assumed to be 0.7 (i.e., operating for 10 h and resting for 14 h), and the simulation duration was 72 h. Each 24 h was a cycle, and there were totally three cyclesBased on the above assumptions, a physical model was established, as shown in Figure7.Figure 7
Schematic diagram of numerical model.


## 3.2. Mathematical Model

### 3.2.1. Heat Transfer Model of Porous Media

The energy balance equation in the porous matrix is as follows:(1)ρsCp∂T∂t+ρCpu⋅∇T+∇⋅−ks∇T=Q,where ρs (kg/m3) is the density of porous medium; cp (J/kg∙K) is the specific heat capacity at constant pressure; T (K) is the temperature; u (m/s) is the velocity field; and ks (W/m∙k) is the overall thermal conductivity coefficient of the formation, and Q (W/m3) is the heat source.


### 3.2.2. Heat Transfer Model of Pipe

The energy equation of the pipe is as follows:(2)AρfCp∂T∂t+AρfCpuf⋅∇T=∇⋅AK∇T+fDρfA2dhufuf2+Qwall+Q,where A (m2) is the cross-sectional area of U-pipe; ρf (kg/m3) is the fluid density; uf (m/s) is the fluid velocity in the pipe; k (W/m∙k) is the thermal conductivity coefficient of the fluid; fD (m) is Darcy friction coefficient; dh (m) is the average hydraulic diameter; and Qwall (W/m) is the heat exchange rate outside the pipe wall per length, and Q (W/m) is general heat source per length.The radial heat transferQwall (W/m) between the U-pipe and the surrounding environment is as follows:
(3)Qwall=hZeffTEXT−T,where hZeff (W/(m∙K)) is the effective value of heat transfer coefficient, which is the product of h (W/(m2∙K)) of the pipe multiplied by the circumference Z (m) of the pipe wall, and TEXT (K) is the temperature of the outer wall of the pipe.


### 3.2.3. Phase Change Heat Transfer Process

The thermophysical properties of PCM keep changing in the process of phase change in which the solid and liquid phases of the materials exist simultaneously. The thermophysical properties of the materials need to be determined according to the volume fraction of solid and liquid. The density (ρ, kg/m3) and thermal conductivity (k, W/(m·K)) of PCM are as follows:
(4)ρ=θTρ1+1−θTρ2,(5)k=θTk1+1−θTk2,where θT is the mass fraction of phase 1 which is a function of temperature T, and phase 1 is solid, and phase 2 is liquid.The equivalent heat capacity method is used to simulate the phase change process of PCM. The heat capacity of PCM is determined as a latent heat item, and its calculation formula is as follows:(6)CP=1ρθTρ1CP1+1−θTρ2CP2+L∂αmT∂T,where αm is a smooth transition function which aims to make the heat capacity value change slowly in order to prevent instability, and its formula is as follows:
(7)αm=121−θTρ2−θTρ1θTρ1+1−θTρ2.PCM admixture is added to ordinary sands (original drilling debris) to make the PCBM. The porous media module is used to simulate the heat transfer process of PCBM. The material properties before and after the phase change can be expressed by the following formulas:(8)R1=1−wt%Rc+wt%Rp,1,(9)R2=1−wt%Rc+wt%Rp,2,where R1 and R1 are thermophysical property parameters of PCBM before and after the phase change, including density ρ (kg/m3), thermal conductivity coefficient k (W/(m·K)), and heat capacity cp (J/(kg·K)); Rc is the thermophysical property parameter of ordinary backfill materials; Rp,1 and Rp,2 are the thermophysical property parameters of PCM before and after the phase change; and wt% is the mass fraction of PCM admixture.


## 3.2.1. Heat Transfer Model of Porous Media

The energy balance equation in the porous matrix is as follows:(1)ρsCp∂T∂t+ρCpu⋅∇T+∇⋅−ks∇T=Q,where ρs (kg/m3) is the density of porous medium; cp (J/kg∙K) is the specific heat capacity at constant pressure; T (K) is the temperature; u (m/s) is the velocity field; and ks (W/m∙k) is the overall thermal conductivity coefficient of the formation, and Q (W/m3) is the heat source.


## 3.2.2. Heat Transfer Model of Pipe

The energy equation of the pipe is as follows:(2)AρfCp∂T∂t+AρfCpuf⋅∇T=∇⋅AK∇T+fDρfA2dhufuf2+Qwall+Q,where A (m2) is the cross-sectional area of U-pipe; ρf (kg/m3) is the fluid density; uf (m/s) is the fluid velocity in the pipe; k (W/m∙k) is the thermal conductivity coefficient of the fluid; fD (m) is Darcy friction coefficient; dh (m) is the average hydraulic diameter; and Qwall (W/m) is the heat exchange rate outside the pipe wall per length, and Q (W/m) is general heat source per length.The radial heat transferQwall (W/m) between the U-pipe and the surrounding environment is as follows:
(3)Qwall=hZeffTEXT−T,where hZeff (W/(m∙K)) is the effective value of heat transfer coefficient, which is the product of h (W/(m2∙K)) of the pipe multiplied by the circumference Z (m) of the pipe wall, and TEXT (K) is the temperature of the outer wall of the pipe.


## 3.2.3. Phase Change Heat Transfer Process

The thermophysical properties of PCM keep changing in the process of phase change in which the solid and liquid phases of the materials exist simultaneously. The thermophysical properties of the materials need to be determined according to the volume fraction of solid and liquid. The density (ρ, kg/m3) and thermal conductivity (k, W/(m·K)) of PCM are as follows:
(4)ρ=θTρ1+1−θTρ2,(5)k=θTk1+1−θTk2,where θT is the mass fraction of phase 1 which is a function of temperature T, and phase 1 is solid, and phase 2 is liquid.The equivalent heat capacity method is used to simulate the phase change process of PCM. The heat capacity of PCM is determined as a latent heat item, and its calculation formula is as follows:(6)CP=1ρθTρ1CP1+1−θTρ2CP2+L∂αmT∂T,where αm is a smooth transition function which aims to make the heat capacity value change slowly in order to prevent instability, and its formula is as follows:
(7)αm=121−θTρ2−θTρ1θTρ1+1−θTρ2.PCM admixture is added to ordinary sands (original drilling debris) to make the PCBM. The porous media module is used to simulate the heat transfer process of PCBM. The material properties before and after the phase change can be expressed by the following formulas:(8)R1=1−wt%Rc+wt%Rp,1,(9)R2=1−wt%Rc+wt%Rp,2,where R1 and R1 are thermophysical property parameters of PCBM before and after the phase change, including density ρ (kg/m3), thermal conductivity coefficient k (W/(m·K)), and heat capacity cp (J/(kg·K)); Rc is the thermophysical property parameter of ordinary backfill materials; Rp,1 and Rp,2 are the thermophysical property parameters of PCM before and after the phase change; and wt% is the mass fraction of PCM admixture.


## 3.3. Boundary and Initial Conditions

Initial temperature is as follows:(10)Tlz,τ=Tpr,z,τ=Tsr,z,τ=T0τ=0.Far boundary conditions of rock formation are as follows:(11)Tsr,z,τr=10=T0Upper and bottom boundary conditions are as follows:(12)∂T∂zz=0=0,(13)∂T∂ZZ=120=0,where Tlz,τ (°C) is the fluid temperature in the depth z (m) at the time τ (s); Tpz,τ (°C) is the temperature at the bottom of the heat exchange borehole in the side length r and the depth z at the time τ; Tsz,τ (°C) is the rock and soil temperature in the side length r (m) and the depth z (m) at the time τ; and T0 (°C) is the initial temperature of the formation.Inlet and outlet boundary conditions of U-pipe are as follows:(14)Tin=35°C,(15)vin=0.6ms,where Tin (°C) is the inlet water temperature and vin (m/s) is the inlet water speed.


## 3.4. Meshing and Independence Verification

### 3.4.1. Meshing

The model is meshed by the free tetrahedral grid. In order to reduce the number of grids, large grid spacing was selected as the temperature gradient was small in the surrounding formation. However, the temperature gradient around the U-pipe was high, so it is necessary to make the mesh in heat exchange borehole dense. The grid division is shown in Figure8.Figure 8
Schematic diagram of grid division.


### 3.4.2. Independence Verification

In order to verify the reliability of grid division, the independence verification was conducted. Three grid densities (amount of 824,301, 1,357,267, and 1,918,604, respectively) were selected for calculation. When the inlet temperature of the buried pipe was constant, the calculated outlet temperature of the U-pipe was used as a comparison benchmark. The results are shown in Figure9. It can be seen from the analysis that when the number of grids is different, the outlet temperature of buried pipe will show the same trend with time, and the difference is small with the increase of grid numbers. Considering calculation accuracy and calculation time, the grid number in this paper is 1,357,267.Figure 9
Diagram of grid independence verification.


## 3.4.1. Meshing

The model is meshed by the free tetrahedral grid. In order to reduce the number of grids, large grid spacing was selected as the temperature gradient was small in the surrounding formation. However, the temperature gradient around the U-pipe was high, so it is necessary to make the mesh in heat exchange borehole dense. The grid division is shown in Figure8.Figure 8
Schematic diagram of grid division.


## 3.4.2. Independence Verification

In order to verify the reliability of grid division, the independence verification was conducted. Three grid densities (amount of 824,301, 1,357,267, and 1,918,604, respectively) were selected for calculation. When the inlet temperature of the buried pipe was constant, the calculated outlet temperature of the U-pipe was used as a comparison benchmark. The results are shown in Figure9. It can be seen from the analysis that when the number of grids is different, the outlet temperature of buried pipe will show the same trend with time, and the difference is small with the increase of grid numbers. Considering calculation accuracy and calculation time, the grid number in this paper is 1,357,267.Figure 9
Diagram of grid independence verification.


## 3.5. Simulation Parameters

The parameters used in the model are listed in Tables3 and 4. The low-conductivity PCM admixture is made by mixed acid of CA and LA. The high-conductivity PCM admixture (CA-LA/EG) is made by mixed acid CA and LA adsorbed on the carrier (EG).Table 3
Size of heat exchange model.
ParameterValueParameterValueRadius of calculated area, m10Center distance of U-pipe, mm80Depth of calculated area, m150Inner diameter of U-pipe, mm26Diameter of borehole, m0.18Outside diameter of U-pipe, mm32Depth of borehole, m120Depth of U-pipe, m119.1Table 4
Physical parameters of backfill materials.
MaterialDensity, kg/m3Thermal conductivity coefficient, W/(m·k)Specific heat capacity, kJ/(kg·K)Temperature, °CLatent heat of phase change, kJ/kgRock and soil formation28002.50.8——Original sands25002.30.82——Low-conductivity PCM admixture (CA-LA)8800.1322.420152High-conductivity PCM admixture (CA-LA/EG)6402.512.220139


## 4. Simulation Results and Discussion

### 4.1. Thermal Effect of Low-Conductivity PCM Admixture on Boreholes

#### 4.1.1. Temperature Change in Boreholes Filled with Low-Conductivity PCM Admixture

Table5 and Figures 10 and 11 show the temperature changes in heat exchange boreholes when the running-stop ratio is 0.7 (operating for 10 h and resting for 14 h). The results show that in the first half of the operation cycle, as the PCM admixtures were increased, the temperature rose more slowly. The latent heat generated by the PCM during phase change improved the specific heat capacity of the materials in the boreholes.Table 5
Temperature at the end of heat exchange borehole in each cycle with PCM admixtures with low thermal conductivity.
PCM admixtures percentage (θpcm)0%10%20%30%Temperature at the end of the 1st cycle, °C19.5919.772020.23Temperature at the end of the 2nd cycle, °C20.2620.4820.6720.88Temperature at the end of the 3rd cycle, °C20.620.852121.16Figure 10
Diagram of temperature changes of boreholes filled with low-conductivity PCM admixture.Figure 11
Enlarged diagram of temperature changes of borehole filled with low-conductivity PCM admixture.
(a)
Temperature rise stage(b)
Temperature drop stageHowever, it is worth noting that in the second half of the operation, the temperature in the borehole added with a high ratio of PCM admixture was higher. As the admixture was added more, the overall thermal conductivity in the borehole was decreased. The overall thermal conductivity with 30% PCM admixtures was 1.65 W/m·K, which was 28.3% lower than ordinary sand’s borehole (2.3 W/m·K). After all the PCM were liquefied, the latent heat was used up. The heat that was continuously transferred by the U-pipe to the borehole could not be dissipated to the surrounding formations in time, leading to the rapid temperature rise in the second half period of operation.At the end of the rest period, compared with the initial ground temperature (T0=18°C), the temperatures in boreholes filled with different PCM admixtures (0%, 10%, 20%, and 30%) increased by 1.59°C, 1.77°C, 2°C, and 2.23°C, respectively; at the end of the second cycle, the temperatures increased by 2.26°C, 2.48°C, 2.67°C, and 2.88°C, respectively; at the end of the third cycle, the temperatures increased by 2.6°C, 2.85°C, 3°C, and 3.16°C, respectively. At the shutdown stage, the temperature in the borehole gradually decreased, and the PCM in the borehole began to solidify and released the previously absorbed heat. However, the low thermal conductivity of the PCM deteriorated the overall thermal conductivity of the borehole. The heat released by PCM could not diffuse to the surrounding formations, which restrained the temperature recovery and intensified heat accumulation in the borehole.


#### 4.1.2. Heat Exchange Rate per Meter of Borehole Filled with Low-Conductivity PCM Admixture

The heat exchange rate per meter of the buried heat exchanger,q (W/m), can be calculated by the following formula:
(16)q=cp,wρwvπri2ti−to4Hb,where cp,wJ/kg·K and ρw (kg/m3) are specific heat capacity and density of circulating water, respectively; v (m/s) is the inlet flow rate of circulating water; ti (°C) and to (°C) are the inlet and outlet temperatures of circulating water, respectively; ri (m) is the inner diameter of U-pipe; and Hb (m) is the depth of borehole.Table6 and Figure 12 show the heat exchange rates in three cycles. With the heat exchange going on, the water outlet temperature became stable, and the heat exchange rate decreased steadily and slowly. It can be seen from Table 6 that the heat exchange rate of borehole filled with low-conductivity PCM admixture in the first half of the operation cycle was still higher than ordinary boreholes. After the water outlet temperature became stable, the heat exchange rate of low-conductivity PCM boreholes was lower than ordinary boreholes. Taking the heat exchange borehole with 30% admixtures as an example, its average heat exchange rate decreased by 8.2% when compared with the ordinary borehole. The reason is the same as the temperature change in the above borehole.Table 6
Heat exchange rate of boreholes filled with low-conductivity PCM admixture at the end of operation.
PCM admixtures percentage (θpcm)0%10%20%30%10 h75.72 W/m73.39 W/m71.38 W/m68.95 W/m34 h69.54 W/m69.03 W/m66.89 W/m64.22 W/m58 h67.49 W/m66.74 W/m64.72 W/m62.07 W/mFigure 12
Heat exchange rate per meter of boreholes filled with different low-conductivity PCM admixture percentages.
(a)
First cycle(b)
Second cycle(c)
Third cycleTo sum up, low-conductivity PCM admixture may cause thermal deterioration to heat exchange boreholes. That is, after all the PCM are liquefied, the excess heat received in the first half of the operation cycle cannot be transferred to the surrounding formations in time, so the temperature in the borehole rises rapidly, and the heat exchange rate decreases. Therefore, the performance of the buried pipe cannot be effectively improved by adding the low-conductivity PCM admixture.


### 4.2. Thermal Effect of CA-LA/EG PCM Admixture on Boreholes

#### 4.2.1. Temperature Change in Boreholes Filled with CA-LA/EG PCM Admixture

In 2.2-2.5, the CA-LA/EG composite PCM admixture with high heat capacity and high thermal conductivity was made by using the expanded graphite as the adsorption carrier and thermal conductivity improvement material. In this section, the performance of heat exchange boreholes after adding this material to the backfill sands was simulated.Figures13 and 14 show the temperature changes in boreholes. It can be seen from Figure 14(a) that the temperature curves with high-conductivity PCM do not show the intersection of the curves in Figure 10, and the temperature of high-conductivity PCM boreholes was always lower than the ordinary borehole at the rising stage of each operation cycle.Figure 13
Temperature curves at the center of the boreholes filled with CA-LA/EG PCM admixture.Figure 14
Partially enlarged diagram of temperature curves in boreholes filled with CA-LA/EG PCM admixture.
(a)
Temperature rise stage(b)
Temperature drop stageIn the first operation cycle, the average temperatures of boreholes with the admixtures were reduced by 0.18°C, 0.44°C, and 0.67°C, respectively, when compared with the ordinary backfill materials. Compared with low-conductivity PCM admixture, the boreholes filled with high-conductivity PCM admixture could exchange heat with the surrounding formations more efficiently. The more PCM were added, the more obvious the effect was. With the intermittent heat exchange, the temperature difference of boreholes with different PCM admixtures percentages was not significant when it was operated in the third cycle. Compared with ordinary materials, the average temperature in the borehole with 30% PCM admixtures was only 0.01°C lower than the ordinary borehole.It can be seen from Figure14(b) that at the end of the third operation cycle, the temperature of boreholes filled with high-conductivity PCM admixtures was 2.78°C, 3.00°C, and 3.17°C higher than the initial temperature, respectively. With the increase of operation cycles, the initial temperature in each subsequent cycle would increase. The PCM gradually returned to the solid state and released the previously adsorbed latent heat during the shutdown of the unit. Although the thermal conductivity of the backfill materials had been improved, the heat released in a large amount still could not completely diffuse to the surrounding formations in a short time. This restrained the temperature recovery in the boreholes. Such a phenomenon gradually accumulated in each cycle. By the end of the second and third resting periods, the center temperature near the borehole was close to or higher than the phase change (solidification) temperature of PCM (Tf=20oC or 293.15 K), which made the PCM in this area unable to return to the solid state completely and resulted in the reduction of available latent heat in the next cycle and the decrease of the heat capacity of the backfill materials.Therefore, operation of the ground source heat pump system with phase change backfilling would require a longer rest time. The PCM in the borehole should be restored to the solid state so that the heat exchange capability of borehole can be improved effectively.


#### 4.2.2. Heat Exchange Rate of Boreholes Filled with CA-LA/EG PCM Admixture

Figure15 shows the heat exchange rates per meter of boreholes filled with different percentages of CA-LA/EG admixtures. With the increase of the PCM admixtures, the heat exchange rate was improved. Taking the first cycle as an example, the heat exchange rates with 10%, 20%, and 30% PCM admixtures were increased by 5.0%, 8.4%, and 11.6% on average when compared with ordinary heat exchange boreholes.Figure 15
Heat exchange rate of boreholes filled by o CA-LA/EG PCM admixture.
(a)
First cycle(b)
Second cycle(c)
Third cycleIn the third cycle, there was little difference in the heat exchange rate of different admixture percentages. Compared with ordinary heat exchange boreholes, boreholes with 10%, 20%, and 30% of CA-LA/EG PCM admixtures only increased by 2.7%, 3.2%, and 3.8%. Although the heat exchange rate of PCM backfilled borehole was increased, the improvement compared to ordinary backfilled borehole weakened as the operation cycles increased. The latent heat released during PCM solidification restrained the temperature recovery in the borehole, so the initial temperature and initial liquid phase fraction of the PCM rose in each cycle, and the available latent heat in subsequent cycles was insufficient. This proves once again that a longer resting period will be required for the system using PCM.


#### 4.2.3. Comparison of Thermal Effect Range between the CA-LA/EG PCM Materials and Ordinary Sands

The thermal effect radius of buried heat exchanger is one of the important indicators to evaluate the thermal interference. Temperatures within the radius of heat effect are described by [36]
(17)ΔTr=Tr−Te≥Tin−Te×1%,where ΔTr (K) is the temperature difference within the radius of thermal interference; Tr (K) is represents the average temperature of a point within the thermal interference radius; Te (K) is the initial temperature of rock and soil mass; and Tin (K) is the water inlet temperature of U-pipe.Figure16 shows the ranges of thermal effect of ordinary sands and CA-LA/EG PCM at the depth of 60 m after operation for 72 h. It can be seen from the figure that the thermal effect radius of borehole of 30% CA-LA/EG PCM admixtures was about 1.2 m, and ordinary sands filled borehole was about 0.8 m. Due to the addition of high-conductivity EG, the heat exchange effect between the borehole and surrounding formations is improved, which is conducive to the heat diffusion in the boreholes and avoids heat accumulation. According to Figure 11, the center temperature in the borehole was still higher than the solidification temperature of PCM, and the PCM in the borehole were not completely solidified. Since the thermal release process still continued, the temperature in the PCM filled borehole was higher than that in the ordinary borehole.Figure 16
Temperature distribution at the depth of 60 m in boreholes (t=72h, by the end of the third rest period).
(a)
Ordinary backfilled borehole(b)
CA-LA/EG admixture filled borehole


## 4.1. Thermal Effect of Low-Conductivity PCM Admixture on Boreholes

### 4.1.1. Temperature Change in Boreholes Filled with Low-Conductivity PCM Admixture

Table5 and Figures 10 and 11 show the temperature changes in heat exchange boreholes when the running-stop ratio is 0.7 (operating for 10 h and resting for 14 h). The results show that in the first half of the operation cycle, as the PCM admixtures were increased, the temperature rose more slowly. The latent heat generated by the PCM during phase change improved the specific heat capacity of the materials in the boreholes.Table 5
Temperature at the end of heat exchange borehole in each cycle with PCM admixtures with low thermal conductivity.
PCM admixtures percentage (θpcm)0%10%20%30%Temperature at the end of the 1st cycle, °C19.5919.772020.23Temperature at the end of the 2nd cycle, °C20.2620.4820.6720.88Temperature at the end of the 3rd cycle, °C20.620.852121.16Figure 10
Diagram of temperature changes of boreholes filled with low-conductivity PCM admixture.Figure 11
Enlarged diagram of temperature changes of borehole filled with low-conductivity PCM admixture.
(a)
Temperature rise stage(b)
Temperature drop stageHowever, it is worth noting that in the second half of the operation, the temperature in the borehole added with a high ratio of PCM admixture was higher. As the admixture was added more, the overall thermal conductivity in the borehole was decreased. The overall thermal conductivity with 30% PCM admixtures was 1.65 W/m·K, which was 28.3% lower than ordinary sand’s borehole (2.3 W/m·K). After all the PCM were liquefied, the latent heat was used up. The heat that was continuously transferred by the U-pipe to the borehole could not be dissipated to the surrounding formations in time, leading to the rapid temperature rise in the second half period of operation.At the end of the rest period, compared with the initial ground temperature (T0=18°C), the temperatures in boreholes filled with different PCM admixtures (0%, 10%, 20%, and 30%) increased by 1.59°C, 1.77°C, 2°C, and 2.23°C, respectively; at the end of the second cycle, the temperatures increased by 2.26°C, 2.48°C, 2.67°C, and 2.88°C, respectively; at the end of the third cycle, the temperatures increased by 2.6°C, 2.85°C, 3°C, and 3.16°C, respectively. At the shutdown stage, the temperature in the borehole gradually decreased, and the PCM in the borehole began to solidify and released the previously absorbed heat. However, the low thermal conductivity of the PCM deteriorated the overall thermal conductivity of the borehole. The heat released by PCM could not diffuse to the surrounding formations, which restrained the temperature recovery and intensified heat accumulation in the borehole.


### 4.1.2. Heat Exchange Rate per Meter of Borehole Filled with Low-Conductivity PCM Admixture

The heat exchange rate per meter of the buried heat exchanger,q (W/m), can be calculated by the following formula:
(16)q=cp,wρwvπri2ti−to4Hb,where cp,wJ/kg·K and ρw (kg/m3) are specific heat capacity and density of circulating water, respectively; v (m/s) is the inlet flow rate of circulating water; ti (°C) and to (°C) are the inlet and outlet temperatures of circulating water, respectively; ri (m) is the inner diameter of U-pipe; and Hb (m) is the depth of borehole.Table6 and Figure 12 show the heat exchange rates in three cycles. With the heat exchange going on, the water outlet temperature became stable, and the heat exchange rate decreased steadily and slowly. It can be seen from Table 6 that the heat exchange rate of borehole filled with low-conductivity PCM admixture in the first half of the operation cycle was still higher than ordinary boreholes. After the water outlet temperature became stable, the heat exchange rate of low-conductivity PCM boreholes was lower than ordinary boreholes. Taking the heat exchange borehole with 30% admixtures as an example, its average heat exchange rate decreased by 8.2% when compared with the ordinary borehole. The reason is the same as the temperature change in the above borehole.Table 6
Heat exchange rate of boreholes filled with low-conductivity PCM admixture at the end of operation.
PCM admixtures percentage (θpcm)0%10%20%30%10 h75.72 W/m73.39 W/m71.38 W/m68.95 W/m34 h69.54 W/m69.03 W/m66.89 W/m64.22 W/m58 h67.49 W/m66.74 W/m64.72 W/m62.07 W/mFigure 12
Heat exchange rate per meter of boreholes filled with different low-conductivity PCM admixture percentages.
(a)
First cycle(b)
Second cycle(c)
Third cycleTo sum up, low-conductivity PCM admixture may cause thermal deterioration to heat exchange boreholes. That is, after all the PCM are liquefied, the excess heat received in the first half of the operation cycle cannot be transferred to the surrounding formations in time, so the temperature in the borehole rises rapidly, and the heat exchange rate decreases. Therefore, the performance of the buried pipe cannot be effectively improved by adding the low-conductivity PCM admixture.


## 4.1.1. Temperature Change in Boreholes Filled with Low-Conductivity PCM Admixture

Table5 and Figures 10 and 11 show the temperature changes in heat exchange boreholes when the running-stop ratio is 0.7 (operating for 10 h and resting for 14 h). The results show that in the first half of the operation cycle, as the PCM admixtures were increased, the temperature rose more slowly. The latent heat generated by the PCM during phase change improved the specific heat capacity of the materials in the boreholes.Table 5
Temperature at the end of heat exchange borehole in each cycle with PCM admixtures with low thermal conductivity.
PCM admixtures percentage (θpcm)0%10%20%30%Temperature at the end of the 1st cycle, °C19.5919.772020.23Temperature at the end of the 2nd cycle, °C20.2620.4820.6720.88Temperature at the end of the 3rd cycle, °C20.620.852121.16Figure 10
Diagram of temperature changes of boreholes filled with low-conductivity PCM admixture.Figure 11
Enlarged diagram of temperature changes of borehole filled with low-conductivity PCM admixture.
(a)
Temperature rise stage(b)
Temperature drop stageHowever, it is worth noting that in the second half of the operation, the temperature in the borehole added with a high ratio of PCM admixture was higher. As the admixture was added more, the overall thermal conductivity in the borehole was decreased. The overall thermal conductivity with 30% PCM admixtures was 1.65 W/m·K, which was 28.3% lower than ordinary sand’s borehole (2.3 W/m·K). After all the PCM were liquefied, the latent heat was used up. The heat that was continuously transferred by the U-pipe to the borehole could not be dissipated to the surrounding formations in time, leading to the rapid temperature rise in the second half period of operation.At the end of the rest period, compared with the initial ground temperature (T0=18°C), the temperatures in boreholes filled with different PCM admixtures (0%, 10%, 20%, and 30%) increased by 1.59°C, 1.77°C, 2°C, and 2.23°C, respectively; at the end of the second cycle, the temperatures increased by 2.26°C, 2.48°C, 2.67°C, and 2.88°C, respectively; at the end of the third cycle, the temperatures increased by 2.6°C, 2.85°C, 3°C, and 3.16°C, respectively. At the shutdown stage, the temperature in the borehole gradually decreased, and the PCM in the borehole began to solidify and released the previously absorbed heat. However, the low thermal conductivity of the PCM deteriorated the overall thermal conductivity of the borehole. The heat released by PCM could not diffuse to the surrounding formations, which restrained the temperature recovery and intensified heat accumulation in the borehole.


## 4.1.2. Heat Exchange Rate per Meter of Borehole Filled with Low-Conductivity PCM Admixture

The heat exchange rate per meter of the buried heat exchanger,q (W/m), can be calculated by the following formula:
(16)q=cp,wρwvπri2ti−to4Hb,where cp,wJ/kg·K and ρw (kg/m3) are specific heat capacity and density of circulating water, respectively; v (m/s) is the inlet flow rate of circulating water; ti (°C) and to (°C) are the inlet and outlet temperatures of circulating water, respectively; ri (m) is the inner diameter of U-pipe; and Hb (m) is the depth of borehole.Table6 and Figure 12 show the heat exchange rates in three cycles. With the heat exchange going on, the water outlet temperature became stable, and the heat exchange rate decreased steadily and slowly. It can be seen from Table 6 that the heat exchange rate of borehole filled with low-conductivity PCM admixture in the first half of the operation cycle was still higher than ordinary boreholes. After the water outlet temperature became stable, the heat exchange rate of low-conductivity PCM boreholes was lower than ordinary boreholes. Taking the heat exchange borehole with 30% admixtures as an example, its average heat exchange rate decreased by 8.2% when compared with the ordinary borehole. The reason is the same as the temperature change in the above borehole.Table 6
Heat exchange rate of boreholes filled with low-conductivity PCM admixture at the end of operation.
PCM admixtures percentage (θpcm)0%10%20%30%10 h75.72 W/m73.39 W/m71.38 W/m68.95 W/m34 h69.54 W/m69.03 W/m66.89 W/m64.22 W/m58 h67.49 W/m66.74 W/m64.72 W/m62.07 W/mFigure 12
Heat exchange rate per meter of boreholes filled with different low-conductivity PCM admixture percentages.
(a)
First cycle(b)
Second cycle(c)
Third cycleTo sum up, low-conductivity PCM admixture may cause thermal deterioration to heat exchange boreholes. That is, after all the PCM are liquefied, the excess heat received in the first half of the operation cycle cannot be transferred to the surrounding formations in time, so the temperature in the borehole rises rapidly, and the heat exchange rate decreases. Therefore, the performance of the buried pipe cannot be effectively improved by adding the low-conductivity PCM admixture.


## 4.2. Thermal Effect of CA-LA/EG PCM Admixture on Boreholes

### 4.2.1. Temperature Change in Boreholes Filled with CA-LA/EG PCM Admixture

In 2.2-2.5, the CA-LA/EG composite PCM admixture with high heat capacity and high thermal conductivity was made by using the expanded graphite as the adsorption carrier and thermal conductivity improvement material. In this section, the performance of heat exchange boreholes after adding this material to the backfill sands was simulated.Figures13 and 14 show the temperature changes in boreholes. It can be seen from Figure 14(a) that the temperature curves with high-conductivity PCM do not show the intersection of the curves in Figure 10, and the temperature of high-conductivity PCM boreholes was always lower than the ordinary borehole at the rising stage of each operation cycle.Figure 13
Temperature curves at the center of the boreholes filled with CA-LA/EG PCM admixture.Figure 14
Partially enlarged diagram of temperature curves in boreholes filled with CA-LA/EG PCM admixture.
(a)
Temperature rise stage(b)
Temperature drop stageIn the first operation cycle, the average temperatures of boreholes with the admixtures were reduced by 0.18°C, 0.44°C, and 0.67°C, respectively, when compared with the ordinary backfill materials. Compared with low-conductivity PCM admixture, the boreholes filled with high-conductivity PCM admixture could exchange heat with the surrounding formations more efficiently. The more PCM were added, the more obvious the effect was. With the intermittent heat exchange, the temperature difference of boreholes with different PCM admixtures percentages was not significant when it was operated in the third cycle. Compared with ordinary materials, the average temperature in the borehole with 30% PCM admixtures was only 0.01°C lower than the ordinary borehole.It can be seen from Figure14(b) that at the end of the third operation cycle, the temperature of boreholes filled with high-conductivity PCM admixtures was 2.78°C, 3.00°C, and 3.17°C higher than the initial temperature, respectively. With the increase of operation cycles, the initial temperature in each subsequent cycle would increase. The PCM gradually returned to the solid state and released the previously adsorbed latent heat during the shutdown of the unit. Although the thermal conductivity of the backfill materials had been improved, the heat released in a large amount still could not completely diffuse to the surrounding formations in a short time. This restrained the temperature recovery in the boreholes. Such a phenomenon gradually accumulated in each cycle. By the end of the second and third resting periods, the center temperature near the borehole was close to or higher than the phase change (solidification) temperature of PCM (Tf=20oC or 293.15 K), which made the PCM in this area unable to return to the solid state completely and resulted in the reduction of available latent heat in the next cycle and the decrease of the heat capacity of the backfill materials.Therefore, operation of the ground source heat pump system with phase change backfilling would require a longer rest time. The PCM in the borehole should be restored to the solid state so that the heat exchange capability of borehole can be improved effectively.


### 4.2.2. Heat Exchange Rate of Boreholes Filled with CA-LA/EG PCM Admixture

Figure15 shows the heat exchange rates per meter of boreholes filled with different percentages of CA-LA/EG admixtures. With the increase of the PCM admixtures, the heat exchange rate was improved. Taking the first cycle as an example, the heat exchange rates with 10%, 20%, and 30% PCM admixtures were increased by 5.0%, 8.4%, and 11.6% on average when compared with ordinary heat exchange boreholes.Figure 15
Heat exchange rate of boreholes filled by o CA-LA/EG PCM admixture.
(a)
First cycle(b)
Second cycle(c)
Third cycleIn the third cycle, there was little difference in the heat exchange rate of different admixture percentages. Compared with ordinary heat exchange boreholes, boreholes with 10%, 20%, and 30% of CA-LA/EG PCM admixtures only increased by 2.7%, 3.2%, and 3.8%. Although the heat exchange rate of PCM backfilled borehole was increased, the improvement compared to ordinary backfilled borehole weakened as the operation cycles increased. The latent heat released during PCM solidification restrained the temperature recovery in the borehole, so the initial temperature and initial liquid phase fraction of the PCM rose in each cycle, and the available latent heat in subsequent cycles was insufficient. This proves once again that a longer resting period will be required for the system using PCM.


### 4.2.3. Comparison of Thermal Effect Range between the CA-LA/EG PCM Materials and Ordinary Sands

The thermal effect radius of buried heat exchanger is one of the important indicators to evaluate the thermal interference. Temperatures within the radius of heat effect are described by [36]
(17)ΔTr=Tr−Te≥Tin−Te×1%,where ΔTr (K) is the temperature difference within the radius of thermal interference; Tr (K) is represents the average temperature of a point within the thermal interference radius; Te (K) is the initial temperature of rock and soil mass; and Tin (K) is the water inlet temperature of U-pipe.Figure16 shows the ranges of thermal effect of ordinary sands and CA-LA/EG PCM at the depth of 60 m after operation for 72 h. It can be seen from the figure that the thermal effect radius of borehole of 30% CA-LA/EG PCM admixtures was about 1.2 m, and ordinary sands filled borehole was about 0.8 m. Due to the addition of high-conductivity EG, the heat exchange effect between the borehole and surrounding formations is improved, which is conducive to the heat diffusion in the boreholes and avoids heat accumulation. According to Figure 11, the center temperature in the borehole was still higher than the solidification temperature of PCM, and the PCM in the borehole were not completely solidified. Since the thermal release process still continued, the temperature in the PCM filled borehole was higher than that in the ordinary borehole.Figure 16
Temperature distribution at the depth of 60 m in boreholes (t=72h, by the end of the third rest period).
(a)
Ordinary backfilled borehole(b)
CA-LA/EG admixture filled borehole


## 4.2.1. Temperature Change in Boreholes Filled with CA-LA/EG PCM Admixture

In 2.2-2.5, the CA-LA/EG composite PCM admixture with high heat capacity and high thermal conductivity was made by using the expanded graphite as the adsorption carrier and thermal conductivity improvement material. In this section, the performance of heat exchange boreholes after adding this material to the backfill sands was simulated.Figures13 and 14 show the temperature changes in boreholes. It can be seen from Figure 14(a) that the temperature curves with high-conductivity PCM do not show the intersection of the curves in Figure 10, and the temperature of high-conductivity PCM boreholes was always lower than the ordinary borehole at the rising stage of each operation cycle.Figure 13
Temperature curves at the center of the boreholes filled with CA-LA/EG PCM admixture.Figure 14
Partially enlarged diagram of temperature curves in boreholes filled with CA-LA/EG PCM admixture.
(a)
Temperature rise stage(b)
Temperature drop stageIn the first operation cycle, the average temperatures of boreholes with the admixtures were reduced by 0.18°C, 0.44°C, and 0.67°C, respectively, when compared with the ordinary backfill materials. Compared with low-conductivity PCM admixture, the boreholes filled with high-conductivity PCM admixture could exchange heat with the surrounding formations more efficiently. The more PCM were added, the more obvious the effect was. With the intermittent heat exchange, the temperature difference of boreholes with different PCM admixtures percentages was not significant when it was operated in the third cycle. Compared with ordinary materials, the average temperature in the borehole with 30% PCM admixtures was only 0.01°C lower than the ordinary borehole.It can be seen from Figure14(b) that at the end of the third operation cycle, the temperature of boreholes filled with high-conductivity PCM admixtures was 2.78°C, 3.00°C, and 3.17°C higher than the initial temperature, respectively. With the increase of operation cycles, the initial temperature in each subsequent cycle would increase. The PCM gradually returned to the solid state and released the previously adsorbed latent heat during the shutdown of the unit. Although the thermal conductivity of the backfill materials had been improved, the heat released in a large amount still could not completely diffuse to the surrounding formations in a short time. This restrained the temperature recovery in the boreholes. Such a phenomenon gradually accumulated in each cycle. By the end of the second and third resting periods, the center temperature near the borehole was close to or higher than the phase change (solidification) temperature of PCM (Tf=20oC or 293.15 K), which made the PCM in this area unable to return to the solid state completely and resulted in the reduction of available latent heat in the next cycle and the decrease of the heat capacity of the backfill materials.Therefore, operation of the ground source heat pump system with phase change backfilling would require a longer rest time. The PCM in the borehole should be restored to the solid state so that the heat exchange capability of borehole can be improved effectively.


## 4.2.2. Heat Exchange Rate of Boreholes Filled with CA-LA/EG PCM Admixture

Figure15 shows the heat exchange rates per meter of boreholes filled with different percentages of CA-LA/EG admixtures. With the increase of the PCM admixtures, the heat exchange rate was improved. Taking the first cycle as an example, the heat exchange rates with 10%, 20%, and 30% PCM admixtures were increased by 5.0%, 8.4%, and 11.6% on average when compared with ordinary heat exchange boreholes.Figure 15
Heat exchange rate of boreholes filled by o CA-LA/EG PCM admixture.
(a)
First cycle(b)
Second cycle(c)
Third cycleIn the third cycle, there was little difference in the heat exchange rate of different admixture percentages. Compared with ordinary heat exchange boreholes, boreholes with 10%, 20%, and 30% of CA-LA/EG PCM admixtures only increased by 2.7%, 3.2%, and 3.8%. Although the heat exchange rate of PCM backfilled borehole was increased, the improvement compared to ordinary backfilled borehole weakened as the operation cycles increased. The latent heat released during PCM solidification restrained the temperature recovery in the borehole, so the initial temperature and initial liquid phase fraction of the PCM rose in each cycle, and the available latent heat in subsequent cycles was insufficient. This proves once again that a longer resting period will be required for the system using PCM.


## 4.2.3. Comparison of Thermal Effect Range between the CA-LA/EG PCM Materials and Ordinary Sands

The thermal effect radius of buried heat exchanger is one of the important indicators to evaluate the thermal interference. Temperatures within the radius of heat effect are described by [36]
(17)ΔTr=Tr−Te≥Tin−Te×1%,where ΔTr (K) is the temperature difference within the radius of thermal interference; Tr (K) is represents the average temperature of a point within the thermal interference radius; Te (K) is the initial temperature of rock and soil mass; and Tin (K) is the water inlet temperature of U-pipe.Figure16 shows the ranges of thermal effect of ordinary sands and CA-LA/EG PCM at the depth of 60 m after operation for 72 h. It can be seen from the figure that the thermal effect radius of borehole of 30% CA-LA/EG PCM admixtures was about 1.2 m, and ordinary sands filled borehole was about 0.8 m. Due to the addition of high-conductivity EG, the heat exchange effect between the borehole and surrounding formations is improved, which is conducive to the heat diffusion in the boreholes and avoids heat accumulation. According to Figure 11, the center temperature in the borehole was still higher than the solidification temperature of PCM, and the PCM in the borehole were not completely solidified. Since the thermal release process still continued, the temperature in the PCM filled borehole was higher than that in the ordinary borehole.Figure 16
Temperature distribution at the depth of 60 m in boreholes (t=72h, by the end of the third rest period).
(a)
Ordinary backfilled borehole(b)
CA-LA/EG admixture filled borehole


## 5. Conclusions

(1)
Although the low-conductivity PCM admixture provides a high heat capacity, the simulation results show that it cannot effectively slow down the temperature rise in the borehole after multiple operation cycles. The heat exchange rate of borehole filled with low-conductivity PCM admixtures is lower than ordinary sand filled borehole. Low-conductivity PCM admixture will aggravate the heat accumulation in long-term multicycle operation(2)
The CA-LA/EG composite PCM has a high thermal conductivity, so the heat exchange between the boreholes and the surrounding strata is reinforced, and the temperature in boreholes is lower than ordinary sand filled boreholes during the operation. With the increase of the PCM admixtures, the heat exchange rate per meter will increase correspondingly(3)
Due to the latent heat released during the solidification of the PCM, the boreholes filled with PCM admixtures require a longer recovery period. Therefore, ground source heat pumps that use PCBM should be operated under the short-operation and long-rest mode(4)
The ground source heat pump system uses the rock and soil mass to store energy and should make full use of the heat storage capacity of the boreholes and formations around and far away. However, the thermal resistance among these energy storage bodies is connected in series. If the heat storage capacity in the borehole is increased but the thermal conductivity is not correspondingly increased or even decreased, the heat cannot be transferred layer by layer. When the heat storage capacity in the borehole is depleted, it will lead to more serious heat accumulation in the boreholeIt should be recognized that the borehole is essentially a “transfer station” for receiving heat. While its heat capacity is improved, the received heat should be transferred out in time, or sufficient resting period should be given for the heat to be transferred out. Therefore, the PCM with high heat capacity should be used together with the carrier or additive with high thermal conductivity, and the heat in the borehole should be dissipated in time through intermittent operation to reserve room for heat storage in the next operation cycle and continuously utilize the high heat capacity of PCM.



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*Source: 9180217-2023-02-06.xml*