- Email: [email protected]
Effects of the geothermal load on the ground temperature recovery in a ground heat exchanger
Accepted Manuscript Title: Effects of the geothermal load on the ground temperature recovery in a ground heat exchanger Author: Seung Hyo Baek Myoung Souk Yeo Kwang Woo Kim PII: DOI: Reference:
S0378-7788(16)31704-2 http://dx.doi.org/doi:10.1016/j.enbuild.2016.11.056 ENB 7171
To appear in:
ENB
Received date: Revised date: Accepted date:
9-6-2016 10-10-2016 27-11-2016
Please cite this article as: Seung Hyo Baek, Myoung Souk Yeo, Kwang Woo Kim, Effects of the geothermal load on the ground temperature recovery in a ground heat exchanger, Energy and Buildings http://dx.doi.org/10.1016/j.enbuild.2016.11.056 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Effects of the geothermal load on the ground temperature recovery in a ground heat exchanger Seung Hyo Baeka, Myoung Souk Yeob, Kwang Woo Kimb* a
Department of Architecture and Architectural Engineering, Graduate School of Seoul
National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea b
Department of Architecture and Architectural Engineering, College of Engineering, Seoul
National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea *Corresponding author. Tel.: +82 2 880 7065 Fax: +82 2 885 8057 Email: [email protected].
Highlights
Model of how the geothermal load affects ground temperature recovery
Decreasing the geothermal load and increasing the recovery time can improve recovery
Recovery time is a significantly influence at low soil thermal conductivity
Considering the recovery time can reduce the design length of a borehole
Abstract The effects of the geothermal load on the ground temperature recovery in a ground heat exchanger (GHE) were investigated. A three-dimensional equivalent transient GHE analysis model was developed and validated against measured thermal response test (TRT) data and sandbox reference dataset. The effects of amount of geothermal load, duration of the recovery
time per day, and daily geothermal load pattern on the ground temperature recovery were examined. The results showed that decreasing the amount of geothermal load and increasing the recovery time can improve the ground temperature recovery. However, there is little correlation between the daily geothermal load pattern and ground temperature recovery. The effects of the geothermal load on ground temperature recovery were also analyzed under different soil thermal conductivity conditions. The duration of the recovery time significantly influences the ground temperature recovery at low soil thermal conductivity. These results demonstrate the importance of considering the recovery time in the GHEs design stage to reduce the borehole length. Keywords: Ground coupled heat pump, Ground temperature recovery, Ground heat exchanger, Geothermal load, Recovery time, Soil thermal conductivity, Geothermal load pattern
NOMENCLATURE 𝐿𝑏
Length of the equivalent borehole square side
m
𝐿𝑝𝑖
Length of the equivalent pipe inner square side
m
𝐿𝑝𝑜
Length of the equivalent pipe outer square side
m
𝐷𝑏
Borehole diameter
m
𝐷𝑝𝑖
U-tube pipe inner diameter
m
𝐷𝑝𝑜
U-tube pipe outer diameter
m
Nu
Nusselt number
-
Re
Reynolds number
-
Pr
Prandtl number
-
L
Pipe length
m
𝑅𝑖−1
Thermal resistance between the node and adjacent nodes i − 1, j, k
K/W
𝑅𝑖+1
Thermal resistance between the node and adjacent nodes i + 1, j, k
K/W
𝑅𝑗−1
Thermal resistance between the node and adjacent nodes i, j − 1, k
K/W
𝑅𝑗+1
Thermal resistance between the node and adjacent nodes i, j + 1, k
K/W
𝑅𝑘−1
Thermal resistance between the node and adjacent nodes i, j, k − 1
K/W
𝑅𝑘+1
Thermal resistance between the node and adjacent nodes i, j, k + 1
K/W
ℎ𝑓
Convection coefficient
W/m2K
Greek symbols Δ𝑥
length of the control volume of the ground in the x-direction
m
Δ𝑦
length of the control volume of the ground in the y-direction
m
Δ𝑧
length of the control volume of the ground in the z-direction
m
Δ𝑡
discretization time step
s
ρ
density
kg/m3
i, j, k
Ground discretization steps in the x-, y-, and z-directions
-
f
Fluid material
-
p
Pipe material
-
g
Grout material
-
Subscripts
Superscripts p
Discretization step in time
-
1. Introduction Ground-coupled heat pump (GCHP) systems are widely used in building HVAC applications because it demands significantly less primary energy [1]. The most common type of GCHPs has vertical ground heat exchangers (GHEs). A heat transfer medium is circulated within
vertical GHEs to transfer heat from the fluid to the ground. The temperature distribution is important to enhancing the GCHP performance. Bernier, Chahla, and Pinel [2] examined the thermal interaction among boreholes and showed that the resulting long-term temperature change can have a significant impact on the borefield sizing and annual energy simulation results. A continuous increase or decrease in ground temperature will reduce the GCHP system performance, and some of the buried pipes may fail to work with extreme heat or cold accumulation. Recently, researchers have discovered that ground temperature recovery enhances the thermal performance for discontinuous operation of a GCHP. Cui, Yang, and Fang [3] demonstrated that the discontinuous operation mode and alternative cooling/heating modes can effectively mitigate the heat buildup in the surrounding soil. Gao, Li, and Yu [4] suggested that an effectively controlled intermittent process can optimize the capacity of heat exchange units for better application of the ground energy. Cao et al. [5] analyzed the effect of intermittent operation on the restoration performance of a vertical heat exchanger in a ground source heat pump by changing the intermittent ratio. They proved that maximizing the stopping time improves the restoration performance. Shang, Li, and Li [6] analyzed the geo-temperature distribution during the operation and recovery period of a ground-source heat pump system and concluded that the soil properties have a large effect on the soil recovery, but the environmental factors have little effect. Jalaluddin and Miyara [7] investigated the thermal performances of several types of vertical GHEs with different operation modes. They concluded that discontinuous operation improves the GHEs performance and may allow the borehole depth of the GHEs to be reduced. The ground temperature variation has a significant effect on the GHEs design. According to Cho and Choi [8]’s research, the ground loop heat exchanger length to unit capacity tends to increase with a higher initial underground temperature in cooling mode but decreases in
heating mode. Several design approaches for calculating the borehole or ground temperature to determine the GHEs length are available, including the rule of thumb, PC design tools [9, 10] that rely on the g-function developed by Eskilson [11], and an equation-based method [12]. The ASHRAE procedure and GLHEPro are the most common GHEs design methods [13]. The ASHRAE procedure [12] suggests a temperature penalty to consider the long-term ground temperature change by ground heat transfer imbalances. However, some researchers [14, 15] have pointed out that the ASHRAE procedure overestimates the required ground heat exchanger length. They noted that this error is caused by the load representation and borehole resistance calculation method. GLHEPro [9] is a design tool for predicting the long-term borehole wall temperature based on monthly heating and cooling loads. The heating and cooling loads with the recovery time are approximated as single-step heat pulses within each month. This approximation can make it difficult to consider ground temperature recovery because GLHEPro assumes a continuous constant load throughout a month. The objective of this research was to investigate the effects of the geothermal load on ground temperature recovery. A three-dimensional equivalent transient analysis model was developed and validated against measured thermal response test (TRT) data and sandbox reference dataset. The effects of the geothermal load, recovery time per day, and daily geothermal load pattern on the ground temperature recovery were examined. Based on the simulation results, the effect of geothermal load approximation on GHEs design was discussed. The effects of the geothermal load on the ground temperature recovery under different soil thermal conductivity conditions were also discussed. 2. Development of the three-dimensional equivalent transient GHE analysis model Under the discontinuous operation condition, the GCHP turns on and off frequently during the day. Shirazi and Bernier [16] investigated the thermal capacity effect on a borehole GHE and concluded that the difference in the predicted fluid outlet temperature with and without
borehole thermal capacity increases when the heat pump operates infrequently. In order to investigate the conditions for discontinuous heat extraction, transient analysis is required. Ozudogru, Olgun, and Senol [17] noted that only 3D models can capture the vertical heat transfer inside and outside the GHE. A number of researchers [17-19] used fully discretized analysis models based on the finite element method (FEM) or finite volume method (FVM) to include the transient effect and 3-D heat transfer. However, Bauer, Heidemann, and Diersch [20] noted that the main disadvantage of fully discretized 3D models is their extensive computation time, even with the help of modern and powerful computers and the possibility of parallel computing. To overcome the disadvantage of a fully discretized 3D model, simplified transient numerical analysis models have been suggested. The most commonly used simplified numerical analysis model is the Duct Ground Heat Storage Model (DST) [21]. Other researchers [2225] have suggested thermal resistance capacitance (RC) models that are based on the heat conduction equation under unsteady state conditions to consider the borehole thermal capacitance. Some researchers [26, 27] have suggested an equivalent rectangular numerical model that converts the circular shape of the borehole section to a rectangular shape. This model also considers transient effect of borehole and thermal interference between downward and upward pipes. This approach makes it possible to use the finite difference method and reduce the number of nodes. In this study, we developed a three-dimensional transient GHE analysis model with a rectangular mesh. 2.1. Three-dimensional equivalent transient GHE analysis model The borehole section is changed to a rectangular shape. To maintain the volume and thermal capacity of borehole, the length of the equivalent square side should be 𝜋
𝐿𝑏 = √4 𝐷𝑏 2
(1)
The pipe section is also changed to a rectangular shape. The lengths of the outside and inside
square sides should be 𝜋
𝐿𝑝𝑖 = √ 4 𝐷𝑝𝑖 2
(2)
𝜋
𝐿𝑝𝑜 = √4 𝐷𝑝𝑜 2
(3)
Because a fluid flows inside the pipe, advection heat transfer occurs. Convection heat transfer occurs between the fluid and pipe surface, and conduction heat transfer occurs through the pipe wall. The convective heat transfer coefficient is calculated by considering the Reynolds number. The equations for the convective heat transfer coefficient according to the Reynolds number are described below [28] : 𝑁𝑢 = 1.61 ∙ (𝑅𝑒 ∙ 𝑃𝑟 ∙ 𝑁𝑢 = 0.116 ∙ (𝑅𝑒
2⁄ 3
𝐷𝑝𝑖 𝐿
1⁄ 3
)
(𝑅𝑒 < 2000)
− 125) ∙ 𝑃𝑟
𝑁𝑢 = 0.023 ∙ 𝑅𝑒 0.8 ∙ 𝑃𝑟
1⁄ 3
1⁄ 3 [1
𝐷
(4)
2⁄ 3
+ (𝐿 )
]
(2000 < 𝑅𝑒 < 10000)
(5)
(𝑅𝑒 > 10000)
(6)
The implicit finite difference method (FDM) approach was implemented to develop a 3D equivalent transient GHE analysis model. Based on the energy balance, the governing equations of the downward and upward flows are 𝑝+1
𝜌𝑐𝑝 Δ𝑥Δ𝑦Δ𝑧
𝑝
𝑇𝑖,𝑗,𝑘 −𝑇𝑖,𝑗,𝑘 Δ𝑡
𝑝+1
=
𝑝+1
𝑇𝑖−1,𝑗,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑖−1
𝑝+1
+
𝑝+1
𝑇𝑖+1,𝑗,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑖+1
𝑝+1
+
𝑝+1
𝑇𝑖,𝑗−1,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑗−1
𝑝+1
+
𝑝+1
𝑇𝑖,𝑗+1,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑗+1
+
𝑝+1 𝑝+1 𝑚̇𝑐𝑝 (𝑇𝑖,𝑗,𝑘−1 − 𝑇𝑖,𝑗,𝑘+1 ) 𝑝+1
𝜌𝑐𝑝 Δ𝑥Δ𝑦Δ𝑧
𝑝
𝑇𝑖,𝑗,𝑘 −𝑇𝑖,𝑗,𝑘 Δ𝑡
(7) 𝑝+1
=
𝑝+1
𝑇𝑖−1,𝑗,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑖−1
𝑝+1
+
𝑝+1
𝑇𝑖+1,𝑗,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑖+1
𝑝+1
+
𝑝+1
𝑇𝑖,𝑗−1,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑗−1
𝑝+1
+
𝑝+1
𝑇𝑖,𝑗+1,𝑘 −𝑇𝑖,𝑗,𝑘
𝑝+1 𝑝+1 𝑚̇𝑐𝑝 (𝑇𝑖,𝑗,𝑘+1 − 𝑇𝑖,𝑗,𝑘−1 )
𝑅𝑗+1
+ (8)
For the ground region, a fine mesh is generated near the borehole, and a coarse mesh is generated far from the borehole. Conduction heat transfer is dominant, and the underground water flow is negligible. The governing equation of the ground mesh is
𝑝+1
𝜌𝑐𝑝 Δ𝑥Δ𝑦Δ𝑧 𝑝+1
𝑝+1
𝑇𝑖,𝑗,𝑘−1 −𝑇𝑖,𝑗,𝑘 𝑅𝑘−1
𝑝
𝑇𝑖,𝑗,𝑘 −𝑇𝑖,𝑗,𝑘 Δ𝑡 𝑝+1
+
𝑝+1
=
𝑝+1
𝑇𝑖−1,𝑗,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑖−1
𝑝+1
+
𝑝+1
𝑇𝑖+1,𝑗,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑖+1
𝑝+1
+
𝑝+1
𝑇𝑖,𝑗−1,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑗−1
𝑝+1
+
𝑝+1
𝑇𝑖,𝑗+1,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑗+1
+
𝑝+1
𝑇𝑖,𝑗,𝑘+1 −𝑇𝑖,𝑗,𝑘 𝑅𝑘+1
(9)
Eqs. (7)–(9) were solved by the Gauss–Seidel iterative techniques. 2.2. Simulation procedure Fig. 1 shows a flowchart of the simulation program, which consists of main four parts: the design variable inputs, pre-process, calculation, and post-process. The borehole configuration, borehole thermal properties, ground thermal properties, fluid condition, and operation condition are entered as design variable inputs. During the pre-process, the fluid node, grout node, and ground node are generated. The thermal resistance of every node is calculated, and the temperature of every node is initialized. The calculation part of the simulation program determines the flow rate that meets the given geothermal load and calculates the temperature at every node. The geothermal load is recalculated by changing the mass flow rate until the calculated geothermal load matches the given geothermal load. Next, every node temperature is calculated by using the previously calculated mass flow rate with the design inlet fluid temperature and adjacent node temperature. The present node temperature is also recalculated until convergence. During the post-process, the average borehole wall temperature is calculated and printed. 2.3. Mesh sensitivity analysis A fine mesh is known to provide accurate calculation results, but it is more time-consuming. Previous research [20] has suggested that the minimum number of elements for a 100-m-long single U-tube ground heat exchanger is about 10,000 to attain an accuracy of 2% when simulating the transient effects of a TRT, and an FE model of a single U-tube BHE with an accuracy of ∼0.5% uses more than 100,000 elements. To determine the optimum node size and number of nodes, two grids were simulated by
changing the number of nodes in the section of the borehole. The heating operation was simulated for 7 days, and discontinuous heat extraction with a 12 h recovery time was assumed. The average borehole wall temperatures at the end of the simulation of each case were compared. The average borehole wall temperatures of grids 1, 2 were 14.80, 14.80 °C, respectively. While a coarser mesh was generated inside the borehole in grid 1, there was little temperature difference between grids 1 and 2. Grid 1, which had a total number of 134,465 nodes, was employed for the following calculations. 2.4. Validation against measured thermal response test data The developed analysis model was validated against measured TRT data. A TRT is an experimental methodology for estimating the ground thermal conductivity [29]. Fluid is continuously circulated through the borehole with power injected into the fluid. The inlet and outlet fluid temperatures are measured during operation. A TRT was performed at Seoul National University, Seoul, South Korea. Before the TRT, a geological survey was conducted to identify the ground type. The site’s ground layers are mainly composed of gravel, sand, and granite. The gravel and sand make up a thin layer that is less than 4.5 m. Fig. 2 shows ground layers of the site. A vertical borehole was drilled to a depth of 150 m with a diameter of 0.15 m. Water was circulated continuously within a single U-tube. The test was conducted over 48 h, and the inlet and outlet fluid temperatures were measured at 10 min intervals. The dynamic outdoor air temperature and solar irradiation data from the local weather station were used to estimate the heat loss at the ground surface. The initial ground temperature needs to be known. In order to verify the initial ground temperature, the ground temperature at the shallow region up to 5 m from the local weather station was also used. According to previous research, the ground temperature declines with increasing depth. Below 15 m, the ground temperature is stable. The initial temperature at the region below 15 m from the
surface was estimated as water was circulated for 10 min without power injection. Table 2 lists the thermal properties of the ground, and Table 3 lists the simulation input data for the validation. Fig. 3 compares the measured and calculated fluid outlet temperatures and plots the inlet fluid temperature. The average temperature difference between the measured and calculated results was 0.35 °C. After 24 h, the average temperature difference was 0.24 °C, and the maximum temperature difference was 0.36 °C. These results showed good agreement between the TRT measurements and the calculation results. 2.5. Validation against the sandbox reference dataset In the case of using TRT measurement data, the developed analysis model was validated only under the continuous operation condition. In order to validate the model for discontinuous operation condition, it also was validated against the sandbox reference dataset [30]. The test was performed under more controlled conditions than can be obtained in field tests. The sandbox reference dataset included a constant heat input rate test set and interrupted test set. In the interrupted test, the circulating pump was off for 2 h. The interrupted test set was used to validate the developed analysis model under the discontinuous condition with a 2 h recovery time. The laboratory sandbox was constructed with an 18-m-long borehole centered horizontally along the length of the box. The box had sides of 1.8 m consisting of a wooden frame and was filled with saturated sand. The single U-tube was made of HDPE with a nominal diameter of 1 in (0.0254 m). The outer and inner diameters of the pipe were 3.340 and 2.733 cm, respectively. Bentonite grout (20% solids) mixed with water was used to fill the borehole space between the pipe and borehole wall. The thermal conductivity was measured independently. The thermal conductivities of the grout and sand were 0.73 and 2.82 W/mK, respectively. The test was conducted for 50 h, and the circulation pump was off between hours 9 and 11.
Fig. 4 also showed good agreement between measured data and the calculation results. 3. Simulation of the effect of the geothermal load on ground temperature recovery The effect of the geothermal load on ground temperature recovery was investigated from three main perspectives. First, the effect of different amounts of the total geothermal load on the ground temperature recovery was analyzed in discontinuous and continuous heat extraction modes. Under the discontinuous heat extraction condition, the duration of the recovery time was assumed to be the same for all cases. Second, the effect of the duration of the recovery time per day on the ground temperature recovery was analyzed. Third, the effect of the daily geothermal load pattern on the ground temperature recovery was analyzed. The pulse and sinusoidal load patterns were compared in discontinuous and continuous heat extraction modes. 3.1. Description of simulation cases In order to investigate the effect of the geothermal load on the ground temperature recovery of the GHE, 10 simulation cases were set up. Cases 1–6 were analyzed to investigate the effects of different amounts of the total geothermal load on the ground temperature recovery. Discontinuous heat extraction with a 12 h recovery time was assumed for cases 1–3. The total daily geothermal loads were 43.2, 86.4, and 172.8 MJ, respectively. Continuous heat extraction was assumed for cases 4–6. The total daily geothermal loads were 86.4, 172.8, and 345.6 MJ, respectively. Cases 3, 5, 7, and 8 were compared to analyze the effect of the duration of the recovery time per day on the ground temperature recovery. The total daily geothermal loads of the four cases were equal at 172.8 MJ. The recovery times of cases 3, 7, and 8 were 12, 8, and 4 h, respectively. Cases 2, 5, 9, and 10 were analyzed to investigate the effects of the daily geothermal load pattern on the ground temperature recovery. A pulse load pattern (cases 2 and 5) and
sinusoidal load pattern (cases 9 and 10) were compared. Cases 2 and 9 were analyzed in discontinuous heat extraction mode. Cases 5 and 10 were analyzed in continuous heat extraction mode. Table 5 lists the simulation cases. 3.2. Configuration and thermal properties of the ground heat exchanger A single 150 m long borehole with a single U-tube was simulated. Water was circulated within the single U-tube to absorb or release heat to the grout. The inlet water temperature was set to be constant at 1 °C. The flow rate was changed according to the given geothermal load. The borehole gap was filled with a mixture of bentonite and water. The ground was assumed to be homogeneous and isotropic. The ground type was assumed to be granite because this is the most common ground type in Korea. The initial ground temperature was 15 °C. Table 6 presents the configuration and thermal properties of the GHE. The heat loss at the ground surface was neglected because the air temperature, solar radiation, and wind velocity have little effect on soil temperature recovery [6]. The simulation of the heating operation was conducted for 90 days. We calculated the average borehole wall temperature to estimate the degree of ground temperature recovery. 4. Results and discussion The ground temperature recovery of each simulation case was analyzed by using the average borehole wall temperature. When heat is extracted, the average borehole wall temperature is lower than the initial ground temperature. Therefore, if the average borehole wall temperature with heat extraction is close to the initial ground temperature, the ground can be concluded to recover quickly. Conversely, if the average borehole wall temperature is far from the initial ground temperature, the ground can be concluded to recover slowly. 4.1. Effect of the total geothermal load on the ground temperature recovery In order to compare the recovery effect, Figs. 5 and 6 plot the average borehole wall
temperature at the end of each recovery time. The average borehole wall temperature continued to decline over time. At the end of the simulation, the average borehole wall temperatures of cases 1–3 were 14.82, 14.80, and 14.77 °C, respectively. In continuous heat extraction mode, the average borehole wall temperatures of cases 4–6 were 13.80, 13.70, and 13.50 °C, respectively. Increasing the total geothermal load tended to decrease the ground temperature recovery. This tendency was stronger in continuous heat extraction mode. In order to better understand the ground temperature recovery, variations in the average borehole wall temperature during the first 5 days were compared. Fig. 7 shows the results of discontinuous heat extraction mode. Fig. 8 shows the results of continuous heat extraction mode. The results in Fig. 7 show that the average borehole wall temperature decreased during heat extraction time and increased during recovery time. When the heat extraction stopped on the first day, the average borehole wall temperature of case 1 was 0.21 K higher than that of case 3. However, when the recovery ended on the first day, the average borehole wall temperature of case 1 was 0.01 K higher than that of case 3. Although larger amounts of heat were extracted, there was little temperature difference between cases 1 and 3 due to the thermal recovery. 4.2. Effect of the recovery time on the ground temperature recovery GHE with different recovery times were simulated to investigate the effect of the recovery time on the ground temperature recovery. Fig. 9 shows the variation in the average borehole wall temperature for cases 3, 5, 7, and 8. The figure plots the average borehole wall temperature at the end of the recovery time. At the end of the simulation, the average borehole wall temperature in discontinuous heat extraction mode with recovery times of 12, 8, and 4 h were 14.77, 14.70, and 14.61 °C, respectively, and the average temperature in continuous heat extraction mode was 13.70 °C.
The temperature change was greater with continuous heat extraction than with discontinuous heat extraction. These results indicate that the duration of the recovery time significantly affects the ground temperature recovery, even if the same amounts of heat are extracted. The temperature difference between the cases with a 12 h recovery time and continuous operation increased over time. The temperature difference was 0.95 K at the end of the first day and 1.07 K at the end of the simulation period. The temperature difference increased rapidly during the first day of the simulation. However, the temperature difference increased gradually after the first day. The duration of the simulation period also affected the ground temperature recovery. In order to better understand the ground temperature recovery, the variations in the average borehole wall temperature during the last five days were compared. Fig. 10 shows the variation in the average borehole wall temperature according to the operation mode. As heat was extracted, the average borehole wall temperature decreased in all simulation cases. Conversely, the average borehole wall temperature increased during recovery. In a typical GHEs design method, the geothermal load with a recovery time is approximated as a continuous load without a recovery time, i.e., a continuous single-step heat pulse. Therefore, cases 3, 7, and 8 are approximated as case 5. Regardless of the duration of the recovery time, the average borehole wall temperature is identical with the typical GHEs design method. However, the above results indicate that the average borehole wall temperature increases with the recovery time. The durations of the recovery and simulation times affect this trend. For cases with a recovery time, a higher average borehole wall temperature can be used in the GHEs design. The borehole length can be reduced with thermal recovery from discontinuous heat extraction. Increasing the recovery duration can further reduce the borehole length. 4.3. Effect of the geothermal load pattern on the ground temperature recovery
Fig. 11 compares the pulse and sinusoidal load patterns with continuous heat extraction and plots the average borehole wall temperature at the end of each recovery time. At the end of the simulation, the average borehole wall temperatures of the pulse and sinusoidal load patterns were 13.70 and 13.81 °C, respectively. Fig. 12 compares the pulse and sinusoidal load patterns with 12 h of heat extraction. At the end of the simulation, the average borehole wall temperatures of the pulse and sinusoidal load patterns were almost the same at 14.80 °C. With discontinuous heat extraction, there was little temperature difference between the pulse and sinusoidal load patterns. With continuous heat extraction, the average borehole wall temperature with the sinusoidal load pattern was 0.11 K lower than that with the pulse load pattern. These results indicate that the daily geothermal load pattern has little effect on the ground temperature recovery. Consequently, the daily geothermal load can be assumed to be a pulse load pattern in GHEs designs that consider the ground temperature recovery. 4.4. Effect of the soil thermal conductivity on the ground temperature recovery in different heat extraction modes According to the previous research [6], soil properties have a great effect on the soil recovery. Therefore, the effect of the soil thermal conductivity on the ground temperature recovery was analyzed by considering the geothermal load and recovery time. Discontinuous heat extraction with 12 h of recovery per day and continuous heat extraction were compared. Four cases were set up. Cases 11 and 12 were used to compare low soil thermal conductivity (𝜆𝑔 = 1.9 W/mK). Cases 13 and 14 were used to compare high thermal conductivity (𝜆𝑔 = 5.2 W/mK). Heat was extracted at a constant 4 kW with the pulse load pattern in cases 11 and 13 and at 2 kW with the pulse load pattern in cases 12 and 14. Table 7 summarizes the simulation cases. Simulations were conducted for 90 days of heating operation. Fig. 13 compares the variations
in the average borehole wall temperature during the simulation time. At the end of the simulation, the average borehole wall temperatures of cases 11–14 were 14.54, 12.66, 14.82, and 14.00 °C, respectively. The average borehole wall temperature with high soil thermal conductivity was higher than the average borehole wall temperature with low soil thermal conductivity. The results showed that the ground temperature recovers more quickly with higher soil thermal conductivity. These findings are similar to those of an earlier study. The results also show that the soil thermal conductivity has a great effect on the ground temperature recovery. Comparing cases 11 and 12, the temperature difference between the discontinuous and continuous heat extraction modes with low thermal conductivity was 1.88 K. Comparing cases 13 and 14, the temperature difference between the discontinuous and continuous heat extraction modes with high thermal conductivity was 0.82 K. The temperature difference between the continuous and discontinuous heat extraction modes increased when the thermal conductivity was low. These results indicate that the temperature difference between a geothermal load with recovery time and a continuous geothermal load increases when the ground temperature recovers slowly. In the GHEs design stage, the geothermal load of case 11 is approximated to that of case 12, and the geothermal load of case 13 is approximated to that of case 14. If the recovery time is considered instead of the geothermal load approximation, a higher average borehole wall temperature can be used in the GHEs design stage. In particular, it is possible to use a higher average borehole wall temperature with low soil thermal conductivity. Using a higher average borehole wall temperature can reduce the borehole length during heating operation. 5. Conclusion A three-dimensional equivalent transient GHE analysis model was developed to analyze the effects of the geothermal load on the ground temperature recovery. The analysis considered
three main perspectives: the effect of the geothermal load on the ground temperature recovery, the effect of the recovery time on the ground temperature recovery, and the effect of the daily geothermal load pattern on the ground temperature recovery. The average borehole wall temperature was determined to estimate the ground temperature recovery. The results showed that decreasing the geothermal load and increasing the recovery time per day can improve the ground temperature recovery. However, the daily geothermal load pattern has little effect on the ground temperature recovery. We also investigated the effect of the soil thermal conductivity on the ground temperature recovery. The ground recovers slowly with low soil thermal conductivity. The duration of the recovery time has a significant influence on ground temperature recovery with low soil thermal conductivity. Considering the recovery time in the GHEs design stage makes it possible to use a higher average borehole wall temperature compared with the geothermal load approximation in the typical GHEs design method. In addition, a lower average borehole wall temperature can be used during a cooling operation. These findings indicate that it is possible to reduce the borehole length by considering the ground temperature recovery. Nevertheless, the results of this study cannot be implemented under real design conditions because it is impossible to enter the average borehole wall temperature in a typical PC design tool. The results were also limited by the conditions of 90 days of operation and a single borehole. Therefore, further study needs to be conducted to develop a design method for a ground heat exchanger that considers heat recovery in order to design a borefield under longterm operation conditions.
ACKNOWLEDGEMENT This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(NRF2015R1D1A1A0906467).
Appendix. Thermal resistances For the fluid region, the thermal resistance between the fluid node and the adjacent grout node is estimated as the sum of the fluid resistance, 𝑅𝑓 , the pipe wall resistance, 𝑅𝑝 , and the grout resistance 𝑅𝑔 : 𝑅𝑖−1 = 𝑅𝑓 + 𝑅𝑝 + 𝑅𝑔
(A.1)
The fluid resistance due to convection is calculated by convective coefficient and length of the equivalent square side of the pipe.
1
𝑅𝑓 = ℎ
(A.2)
𝑓 𝐿𝑝𝑖 Δ𝑦
The pipe wall resistance due to conduction through pipe wall is calculated by Eq. (A.3). ln(
𝐿𝑝𝑜 ) 𝐿𝑝𝑖
𝑅𝑝 = 2πΔ𝑦𝑘
(A.3)
𝑝
The grout resistance due to conduction is calculated by Eq. (A.4). One-half of the length is used because node is located in the center of the control volume. Δ𝑥𝑔
𝑅𝑔 =
2
(A.4)
𝑘𝑔 𝐿𝑝𝑜 Δ𝑦𝑔
For the ground region, conduction heat transfer is dominant. Resistance between adjacent node is calculated by Eq. (A.5).
𝑅𝑖−1 =
Δ𝑥𝑖 2
𝑘𝑖 Δ𝑦𝑖 Δ𝑧𝑖
+
Δ𝑥𝑖−1 2
𝑘𝑖−1 Δ𝑦𝑖−1 Δ𝑧𝑖−1
(A.5)
REFERENCES [1] Michopoulos, A., Bozis, D., Kikidis, P., Papakostas, K., & Kyriakis, N. A. (2007). Threeyears operation experience of a ground source heat pump system in Northern Greece. Energy and Buildings, 39(3), 328–334. [2] Bernier, M. A., Chahla, A., & Pinel, P. (2008). Long-Term Ground-Temperature Changes in Geo-Exchange Systems. ASHRAE Transactions, 114(2), 342–350. [3] Cui, P., Yang, H., & Fang, Z. (2008). Numerical analysis and experimental validation of heat transfer in ground heat exchangers in alternative operation modes. Energy and Buildings, 40(6), 1060–1066. [4] Gao, Q., Li, M., & Yu, M. (2010). Experiment and simulation of temperature characteristics of intermittently-controlled ground heat exchanges. Renewable Energy, 35(6), 1169–1174. [5] Cao, X., Yuan, Y., Sun, L., Lei, B., Yu, N., & Yang, X. (2015). Restoration performance of vertical ground heat exchanger with various intermittent ratios. Geothermics, 54, 115–121. [6] Shang, Y., Li, S., & Li, H. (2011). Analysis of geo-temperature recovery under intermittent operation of ground-source heat pump. Energy and Buildings, 43(4), 935–943. [7] Jalaluddin, & Miyara, A. (2012). Thermal performance investigation of several types of vertical ground heat exchangers with different operation mode. Applied Thermal Engineering, 33-34, 167–174. [8] Cho, H., & Choi, J. M. (2014). The quantitative evaluation of design parameter’s effects on a ground source heat pump system. Renewable Energy, 65, 2–6. [9] Spitler, J. D. (2000). GLHEPRO - A Design Tool For Commercial Building Ground Loop
Heat Exchangers. In the Fourth International Heat Pumps in Cold Climates Conference. [10] Hellström, G., Sanner, B., Klugescheid, M., Gonka, T., & Mårtensson, S. (1997). EXPERIENCES WITH THE BOREHOLE HEAT EXCHANGER SOFTWARE EED. In Megastock Conference 1997. Sapporo, Japan. [11] Eskilson P. (1987). Thermal Analysis of Heat Extraction Boreholes, Doctoral thesis, Department of Mathematical Physics, University of Lund. [12] American Society of Heating Refrigerating and Air-Conditioning Engineers. (2011). 2011 ASHRAE Handbook - HVAC Applications. Atlanta: Refrigerating and Air-Conditioning Engineers, American Society of Heating. [13] Staiti, M., & Angelotti, A. (2015). Design of Borehole Heat Exchangers for Ground Source Heat Pumps: A Comparison between Two Methods. Energy Procedia, 78, 1147–1152. [14] Cullin, J. R., Spitler, J. D., Montagud, C., Ruiz-Calvo, F., Rees, S. J., Naicker, S. S., … Southard, L. E. (2015). Validation of vertical ground heat exchanger design methodologies. Science and Technology for the Built Environment, 21(2), 137–149. [15] Cullin, J. R., Ruiz-Calvo, F., & JD Spitler PhD, P. E. (2014). Experimental Validation of Ground Heat Exchanger Design Methodologies Using Real, Monitored Data. ASHRAE Transactions, 120, 357-369. [16] Shirazi, A. S., & Bernier, M. (2013). Thermal capacity effects in borehole ground heat exchangers. Energy and Buildings, 67, 352–364. [17] Ozudogru, T. Y., Olgun, C. G., & Senol,
a. (2014). 3D numerical modeling of vertical
geothermal heat exchangers. Geothermics, 51, 312–324. [18] Marcotte, D., & Pasquier, P. (2008). On the estimation of thermal resistance in borehole thermal conductivity test. Renewable Energy, 33(11), 2407–2415.
[19] Koohi-Fayegh, S., & Rosen, M. a. (2015). Three-Dimensional Analysis of the Thermal Interaction of Multiple Vertical Ground Heat Exchangers. International Journal of Green Energy, 12(11), 1144–1150. [20] Bauer, D., Heidemann, W., & Diersch, H. J. G. (2011). Transient 3D analysis of borehole heat exchanger modeling. Geothermics, 40(4), 250–260. [21] Chapuis, S., & Bernier, M. (2009). Seasonal storage of solar energy in borehole heat exchangers. In Eleventh International IBPSA Conference (pp. 599–606). [22] Zarrella, A., Scarpa, M., & De Carli, M. (2011). Short time step analysis of vertical ground-coupled heat exchangers: The approach of CaRM. Renewable Energy, 36(9), 2357– 2367. [23] Bauer, D., Heidemann, W., Muller-Steinhagen, H., & Diersch, H. J. G. (2007). Thermal resistance and capacity models for borehole heat exchangers. International Journal of Energy Research, 35(4), 312–320. [24] Maestre, I. R., González Gallero, F. J., Álvarez Gómez, P., & Mena Baladés, J. D. (2013). Performance assessment of a simplified hybrid model for a vertical ground heat exchanger. Energy and Buildings, 66, 437–444. [25] Pasquier, P., & Marcotte, D. (2012). Short-term simulation of ground heat exchanger with an improved TRCM. Renewable Energy, 46, 92–99. [26] Li, Y., Mao, J., Geng, S., Han, X., & Zhang, H. (2014). Evaluation of thermal shortcircuiting and influence on thermal response test for borehole heat exchanger. Geothermics, 50, 136–147. [27] Choi, M., Baek, S., Yeo, M., & Kim, K. (2011). MODELING OF HEAT TRANSFER IN GEOTHERMAL HEAT EXCHANGER USING GHX ZONAL MODEL METHOD. In
Proceedings of Building Simulation 2011: 12th Conference of International Building Performance Simulation Association (pp. 1556–1562). Sydney. [28] De Carli, M., Tonon, M., Zarrella, A., & Zecchin, R. (2010). A computational capacity resistance model (CaRM) for vertical ground-coupled heat exchangers. Renewable Energy, 35(7), 1537–1550. [29] Esen, H., & Inalli, M. (2009). In-situ thermal response test for ground source heat pump system in Elazığ, Turkey. Energy and Buildings, 41(4), 395–401. [30] Beier, R. A., Smith, M. D., & Spitler, J. D. (2011). Reference data sets for vertical borehole ground heat exchanger models and thermal response test analysis. Geothermics, 40(1), 79–85.
x 10m
0.15m
10m
z
Soil (Gravel) Soil (Sand)
Soil (Granite)
Top surface Grout
150m
HDPE pipe
Left surface
30m
Bottom surface
Right surface
Table 1. Mesh sensitivity analysis on the numbers of nodes Grid No. Grid1
Number of nodes in the section of borehole
Total number of nodes
12 × 11
134,465
Average borehole wall temperature (°C) 14.80
Grid2
62 × 61
189,215
14.80
Table 2. Thermal properties of the ground Parameters Gravel Depth below the ground surface Thermal conductivity Density Specific heat Sand Depth below the ground surface Thermal conductivity Density Specific heat Granite Depth below the ground surface Thermal conductivity Density Specific heat
Unit
Value
m W/mK kg/m3 J/kgK
1.5 0.52 2000 1840
m W/mK kg/m3 J/kgK
4.5 1.28 1460 880
m
150
W/mK kg/m3 J/kgK
3.8 2600 840
Table 3. Simulation input data for the validation Parameters Site location Measurement period Borehole length Borehole diameter Pipe outside diameter Pipe inside diameter Pipe spacing Fluid Thermal conductivity Density Specific heat Pipe Thermal conductivity Density Specific heat Grout Thermal conductivity Density Specific heat Design fluid flow rate Initial ground surface temperature Initial ground temperature
Unit m m m m m
Value Seoul, South Korea 5th Jan 2010~7th Jan 2010 150 0.15 0.4 0.32 0.8
W/mK kg/m3 J/kgK
0.6 1000 4179
W/mK kg/m3 J/kgK
0.49 550 2250
W/mK kg/m3 J/kgK kg/s °C °C
0.75 1600 800 0.61 0 14.5
Table 4. Parameters for a sandbox test Parameters Borehole diameter (aluminum pipe) Borehole pipe thickness U-tube length U-tube pipe outer radius U-tube pipe inner radius Distance between centers of pipe Pipe wall thermal conductivity Soil thermal conductivity Grout thermal conductivity Average fluid volumetric flow rate Average heat input rate
Description Inner diameter of aluminum pipe Wall thickness of aluminum pipe SDR 11 (1-in.) SDR 11 (1-in.) SDR 11 (1-in.) Centers of U-tube pipes HDPE Wet sand Bentonite grout 20% solids Water Electric heater
Unit m m m m m m W/mK W/mK W/mK L/s W
Value 0.0126 0.0002 18.3 0.0334 0.02733 0.053 0.39 2.82 0.73 0.197 1056
Table 5. Simulation cases Case No. Case1 Case2 Case3 Case4 Case5 Case6 Case7 Case8 Case9 Case10
Heat Extraction Mode Discontinuous Discontinuous Discontinuous Continuous Continuous Continuous Discontinuous Discontinuous Discontinuous Continuous
Recovery Time per day (h) 12 12 12 0 0 0 8 4 12 0
Daily geothermal Load Pattern Pulse Pulse Pulse Pulse Pulse Pulse Pulse Pulse Sinusoidal Sinusoidal
Total daily geothermal load (MJ) 43.2 86.4 172.8 86.4 172.8 345.6 172.8 172.8 86.4 172.8
Table 6. Configuration and thermal properties of the ground heat exchanger (GHE) Parameters Borehole length Borehole diameter Pipe outside diameter Pipe inside diameter Pipe spacing Fluid Thermal conductivity Density Specific heat Pipe Thermal conductivity Density Specific heat Grout Thermal conductivity Density Specific heat Ground Thermal conductivity Density Specific heat Design fluid inlet temperature Initial ground temperature
Unit m m m m m
Values 150 0.15 0.04 0.032 0.08
W/mK kg/m3 J/kgK
0.574 1000 4211
W/mK kg/m3 J/kgK
0.45 940 2250
W/mK kg/m3 J/kgK
0.68 1080 960
W/mK kg/m3 J/kgK °C °C
3.8 2640 880 1 15
Table 7. Soil thermal conductivity and geothermal load conditions Case No. Case11
Soil thermal conductivity (W/mK) 1.9
Heat Extraction Mode Discontinuous
Recovery Time per day (h) 12 hour
Daily geothermal Load Pattern Pulse
Total daily geothermal load (MJ) 172.8
Case12
1.9
Continuous
0 hour
Pulse
172.8
Case13
5.2
Discontinuous
12 hour
Pulse
172.8
Case14
5.2
Continuous
0 hour
Pulse
172.8
S0378-7788(16)31704-2 http://dx.doi.org/doi:10.1016/j.enbuild.2016.11.056 ENB 7171
To appear in:
ENB
Received date: Revised date: Accepted date:
9-6-2016 10-10-2016 27-11-2016
Please cite this article as: Seung Hyo Baek, Myoung Souk Yeo, Kwang Woo Kim, Effects of the geothermal load on the ground temperature recovery in a ground heat exchanger, Energy and Buildings http://dx.doi.org/10.1016/j.enbuild.2016.11.056 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Effects of the geothermal load on the ground temperature recovery in a ground heat exchanger Seung Hyo Baeka, Myoung Souk Yeob, Kwang Woo Kimb* a
Department of Architecture and Architectural Engineering, Graduate School of Seoul
National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea b
Department of Architecture and Architectural Engineering, College of Engineering, Seoul
National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea *Corresponding author. Tel.: +82 2 880 7065 Fax: +82 2 885 8057 Email: [email protected].
Highlights
Model of how the geothermal load affects ground temperature recovery
Decreasing the geothermal load and increasing the recovery time can improve recovery
Recovery time is a significantly influence at low soil thermal conductivity
Considering the recovery time can reduce the design length of a borehole
Abstract The effects of the geothermal load on the ground temperature recovery in a ground heat exchanger (GHE) were investigated. A three-dimensional equivalent transient GHE analysis model was developed and validated against measured thermal response test (TRT) data and sandbox reference dataset. The effects of amount of geothermal load, duration of the recovery
time per day, and daily geothermal load pattern on the ground temperature recovery were examined. The results showed that decreasing the amount of geothermal load and increasing the recovery time can improve the ground temperature recovery. However, there is little correlation between the daily geothermal load pattern and ground temperature recovery. The effects of the geothermal load on ground temperature recovery were also analyzed under different soil thermal conductivity conditions. The duration of the recovery time significantly influences the ground temperature recovery at low soil thermal conductivity. These results demonstrate the importance of considering the recovery time in the GHEs design stage to reduce the borehole length. Keywords: Ground coupled heat pump, Ground temperature recovery, Ground heat exchanger, Geothermal load, Recovery time, Soil thermal conductivity, Geothermal load pattern
NOMENCLATURE 𝐿𝑏
Length of the equivalent borehole square side
m
𝐿𝑝𝑖
Length of the equivalent pipe inner square side
m
𝐿𝑝𝑜
Length of the equivalent pipe outer square side
m
𝐷𝑏
Borehole diameter
m
𝐷𝑝𝑖
U-tube pipe inner diameter
m
𝐷𝑝𝑜
U-tube pipe outer diameter
m
Nu
Nusselt number
-
Re
Reynolds number
-
Pr
Prandtl number
-
L
Pipe length
m
𝑅𝑖−1
Thermal resistance between the node and adjacent nodes i − 1, j, k
K/W
𝑅𝑖+1
Thermal resistance between the node and adjacent nodes i + 1, j, k
K/W
𝑅𝑗−1
Thermal resistance between the node and adjacent nodes i, j − 1, k
K/W
𝑅𝑗+1
Thermal resistance between the node and adjacent nodes i, j + 1, k
K/W
𝑅𝑘−1
Thermal resistance between the node and adjacent nodes i, j, k − 1
K/W
𝑅𝑘+1
Thermal resistance between the node and adjacent nodes i, j, k + 1
K/W
ℎ𝑓
Convection coefficient
W/m2K
Greek symbols Δ𝑥
length of the control volume of the ground in the x-direction
m
Δ𝑦
length of the control volume of the ground in the y-direction
m
Δ𝑧
length of the control volume of the ground in the z-direction
m
Δ𝑡
discretization time step
s
ρ
density
kg/m3
i, j, k
Ground discretization steps in the x-, y-, and z-directions
-
f
Fluid material
-
p
Pipe material
-
g
Grout material
-
Subscripts
Superscripts p
Discretization step in time
-
1. Introduction Ground-coupled heat pump (GCHP) systems are widely used in building HVAC applications because it demands significantly less primary energy [1]. The most common type of GCHPs has vertical ground heat exchangers (GHEs). A heat transfer medium is circulated within
vertical GHEs to transfer heat from the fluid to the ground. The temperature distribution is important to enhancing the GCHP performance. Bernier, Chahla, and Pinel [2] examined the thermal interaction among boreholes and showed that the resulting long-term temperature change can have a significant impact on the borefield sizing and annual energy simulation results. A continuous increase or decrease in ground temperature will reduce the GCHP system performance, and some of the buried pipes may fail to work with extreme heat or cold accumulation. Recently, researchers have discovered that ground temperature recovery enhances the thermal performance for discontinuous operation of a GCHP. Cui, Yang, and Fang [3] demonstrated that the discontinuous operation mode and alternative cooling/heating modes can effectively mitigate the heat buildup in the surrounding soil. Gao, Li, and Yu [4] suggested that an effectively controlled intermittent process can optimize the capacity of heat exchange units for better application of the ground energy. Cao et al. [5] analyzed the effect of intermittent operation on the restoration performance of a vertical heat exchanger in a ground source heat pump by changing the intermittent ratio. They proved that maximizing the stopping time improves the restoration performance. Shang, Li, and Li [6] analyzed the geo-temperature distribution during the operation and recovery period of a ground-source heat pump system and concluded that the soil properties have a large effect on the soil recovery, but the environmental factors have little effect. Jalaluddin and Miyara [7] investigated the thermal performances of several types of vertical GHEs with different operation modes. They concluded that discontinuous operation improves the GHEs performance and may allow the borehole depth of the GHEs to be reduced. The ground temperature variation has a significant effect on the GHEs design. According to Cho and Choi [8]’s research, the ground loop heat exchanger length to unit capacity tends to increase with a higher initial underground temperature in cooling mode but decreases in
heating mode. Several design approaches for calculating the borehole or ground temperature to determine the GHEs length are available, including the rule of thumb, PC design tools [9, 10] that rely on the g-function developed by Eskilson [11], and an equation-based method [12]. The ASHRAE procedure and GLHEPro are the most common GHEs design methods [13]. The ASHRAE procedure [12] suggests a temperature penalty to consider the long-term ground temperature change by ground heat transfer imbalances. However, some researchers [14, 15] have pointed out that the ASHRAE procedure overestimates the required ground heat exchanger length. They noted that this error is caused by the load representation and borehole resistance calculation method. GLHEPro [9] is a design tool for predicting the long-term borehole wall temperature based on monthly heating and cooling loads. The heating and cooling loads with the recovery time are approximated as single-step heat pulses within each month. This approximation can make it difficult to consider ground temperature recovery because GLHEPro assumes a continuous constant load throughout a month. The objective of this research was to investigate the effects of the geothermal load on ground temperature recovery. A three-dimensional equivalent transient analysis model was developed and validated against measured thermal response test (TRT) data and sandbox reference dataset. The effects of the geothermal load, recovery time per day, and daily geothermal load pattern on the ground temperature recovery were examined. Based on the simulation results, the effect of geothermal load approximation on GHEs design was discussed. The effects of the geothermal load on the ground temperature recovery under different soil thermal conductivity conditions were also discussed. 2. Development of the three-dimensional equivalent transient GHE analysis model Under the discontinuous operation condition, the GCHP turns on and off frequently during the day. Shirazi and Bernier [16] investigated the thermal capacity effect on a borehole GHE and concluded that the difference in the predicted fluid outlet temperature with and without
borehole thermal capacity increases when the heat pump operates infrequently. In order to investigate the conditions for discontinuous heat extraction, transient analysis is required. Ozudogru, Olgun, and Senol [17] noted that only 3D models can capture the vertical heat transfer inside and outside the GHE. A number of researchers [17-19] used fully discretized analysis models based on the finite element method (FEM) or finite volume method (FVM) to include the transient effect and 3-D heat transfer. However, Bauer, Heidemann, and Diersch [20] noted that the main disadvantage of fully discretized 3D models is their extensive computation time, even with the help of modern and powerful computers and the possibility of parallel computing. To overcome the disadvantage of a fully discretized 3D model, simplified transient numerical analysis models have been suggested. The most commonly used simplified numerical analysis model is the Duct Ground Heat Storage Model (DST) [21]. Other researchers [2225] have suggested thermal resistance capacitance (RC) models that are based on the heat conduction equation under unsteady state conditions to consider the borehole thermal capacitance. Some researchers [26, 27] have suggested an equivalent rectangular numerical model that converts the circular shape of the borehole section to a rectangular shape. This model also considers transient effect of borehole and thermal interference between downward and upward pipes. This approach makes it possible to use the finite difference method and reduce the number of nodes. In this study, we developed a three-dimensional transient GHE analysis model with a rectangular mesh. 2.1. Three-dimensional equivalent transient GHE analysis model The borehole section is changed to a rectangular shape. To maintain the volume and thermal capacity of borehole, the length of the equivalent square side should be 𝜋
𝐿𝑏 = √4 𝐷𝑏 2
(1)
The pipe section is also changed to a rectangular shape. The lengths of the outside and inside
square sides should be 𝜋
𝐿𝑝𝑖 = √ 4 𝐷𝑝𝑖 2
(2)
𝜋
𝐿𝑝𝑜 = √4 𝐷𝑝𝑜 2
(3)
Because a fluid flows inside the pipe, advection heat transfer occurs. Convection heat transfer occurs between the fluid and pipe surface, and conduction heat transfer occurs through the pipe wall. The convective heat transfer coefficient is calculated by considering the Reynolds number. The equations for the convective heat transfer coefficient according to the Reynolds number are described below [28] : 𝑁𝑢 = 1.61 ∙ (𝑅𝑒 ∙ 𝑃𝑟 ∙ 𝑁𝑢 = 0.116 ∙ (𝑅𝑒
2⁄ 3
𝐷𝑝𝑖 𝐿
1⁄ 3
)
(𝑅𝑒 < 2000)
− 125) ∙ 𝑃𝑟
𝑁𝑢 = 0.023 ∙ 𝑅𝑒 0.8 ∙ 𝑃𝑟
1⁄ 3
1⁄ 3 [1
𝐷
(4)
2⁄ 3
+ (𝐿 )
]
(2000 < 𝑅𝑒 < 10000)
(5)
(𝑅𝑒 > 10000)
(6)
The implicit finite difference method (FDM) approach was implemented to develop a 3D equivalent transient GHE analysis model. Based on the energy balance, the governing equations of the downward and upward flows are 𝑝+1
𝜌𝑐𝑝 Δ𝑥Δ𝑦Δ𝑧
𝑝
𝑇𝑖,𝑗,𝑘 −𝑇𝑖,𝑗,𝑘 Δ𝑡
𝑝+1
=
𝑝+1
𝑇𝑖−1,𝑗,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑖−1
𝑝+1
+
𝑝+1
𝑇𝑖+1,𝑗,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑖+1
𝑝+1
+
𝑝+1
𝑇𝑖,𝑗−1,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑗−1
𝑝+1
+
𝑝+1
𝑇𝑖,𝑗+1,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑗+1
+
𝑝+1 𝑝+1 𝑚̇𝑐𝑝 (𝑇𝑖,𝑗,𝑘−1 − 𝑇𝑖,𝑗,𝑘+1 ) 𝑝+1
𝜌𝑐𝑝 Δ𝑥Δ𝑦Δ𝑧
𝑝
𝑇𝑖,𝑗,𝑘 −𝑇𝑖,𝑗,𝑘 Δ𝑡
(7) 𝑝+1
=
𝑝+1
𝑇𝑖−1,𝑗,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑖−1
𝑝+1
+
𝑝+1
𝑇𝑖+1,𝑗,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑖+1
𝑝+1
+
𝑝+1
𝑇𝑖,𝑗−1,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑗−1
𝑝+1
+
𝑝+1
𝑇𝑖,𝑗+1,𝑘 −𝑇𝑖,𝑗,𝑘
𝑝+1 𝑝+1 𝑚̇𝑐𝑝 (𝑇𝑖,𝑗,𝑘+1 − 𝑇𝑖,𝑗,𝑘−1 )
𝑅𝑗+1
+ (8)
For the ground region, a fine mesh is generated near the borehole, and a coarse mesh is generated far from the borehole. Conduction heat transfer is dominant, and the underground water flow is negligible. The governing equation of the ground mesh is
𝑝+1
𝜌𝑐𝑝 Δ𝑥Δ𝑦Δ𝑧 𝑝+1
𝑝+1
𝑇𝑖,𝑗,𝑘−1 −𝑇𝑖,𝑗,𝑘 𝑅𝑘−1
𝑝
𝑇𝑖,𝑗,𝑘 −𝑇𝑖,𝑗,𝑘 Δ𝑡 𝑝+1
+
𝑝+1
=
𝑝+1
𝑇𝑖−1,𝑗,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑖−1
𝑝+1
+
𝑝+1
𝑇𝑖+1,𝑗,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑖+1
𝑝+1
+
𝑝+1
𝑇𝑖,𝑗−1,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑗−1
𝑝+1
+
𝑝+1
𝑇𝑖,𝑗+1,𝑘 −𝑇𝑖,𝑗,𝑘 𝑅𝑗+1
+
𝑝+1
𝑇𝑖,𝑗,𝑘+1 −𝑇𝑖,𝑗,𝑘 𝑅𝑘+1
(9)
Eqs. (7)–(9) were solved by the Gauss–Seidel iterative techniques. 2.2. Simulation procedure Fig. 1 shows a flowchart of the simulation program, which consists of main four parts: the design variable inputs, pre-process, calculation, and post-process. The borehole configuration, borehole thermal properties, ground thermal properties, fluid condition, and operation condition are entered as design variable inputs. During the pre-process, the fluid node, grout node, and ground node are generated. The thermal resistance of every node is calculated, and the temperature of every node is initialized. The calculation part of the simulation program determines the flow rate that meets the given geothermal load and calculates the temperature at every node. The geothermal load is recalculated by changing the mass flow rate until the calculated geothermal load matches the given geothermal load. Next, every node temperature is calculated by using the previously calculated mass flow rate with the design inlet fluid temperature and adjacent node temperature. The present node temperature is also recalculated until convergence. During the post-process, the average borehole wall temperature is calculated and printed. 2.3. Mesh sensitivity analysis A fine mesh is known to provide accurate calculation results, but it is more time-consuming. Previous research [20] has suggested that the minimum number of elements for a 100-m-long single U-tube ground heat exchanger is about 10,000 to attain an accuracy of 2% when simulating the transient effects of a TRT, and an FE model of a single U-tube BHE with an accuracy of ∼0.5% uses more than 100,000 elements. To determine the optimum node size and number of nodes, two grids were simulated by
changing the number of nodes in the section of the borehole. The heating operation was simulated for 7 days, and discontinuous heat extraction with a 12 h recovery time was assumed. The average borehole wall temperatures at the end of the simulation of each case were compared. The average borehole wall temperatures of grids 1, 2 were 14.80, 14.80 °C, respectively. While a coarser mesh was generated inside the borehole in grid 1, there was little temperature difference between grids 1 and 2. Grid 1, which had a total number of 134,465 nodes, was employed for the following calculations. 2.4. Validation against measured thermal response test data The developed analysis model was validated against measured TRT data. A TRT is an experimental methodology for estimating the ground thermal conductivity [29]. Fluid is continuously circulated through the borehole with power injected into the fluid. The inlet and outlet fluid temperatures are measured during operation. A TRT was performed at Seoul National University, Seoul, South Korea. Before the TRT, a geological survey was conducted to identify the ground type. The site’s ground layers are mainly composed of gravel, sand, and granite. The gravel and sand make up a thin layer that is less than 4.5 m. Fig. 2 shows ground layers of the site. A vertical borehole was drilled to a depth of 150 m with a diameter of 0.15 m. Water was circulated continuously within a single U-tube. The test was conducted over 48 h, and the inlet and outlet fluid temperatures were measured at 10 min intervals. The dynamic outdoor air temperature and solar irradiation data from the local weather station were used to estimate the heat loss at the ground surface. The initial ground temperature needs to be known. In order to verify the initial ground temperature, the ground temperature at the shallow region up to 5 m from the local weather station was also used. According to previous research, the ground temperature declines with increasing depth. Below 15 m, the ground temperature is stable. The initial temperature at the region below 15 m from the
surface was estimated as water was circulated for 10 min without power injection. Table 2 lists the thermal properties of the ground, and Table 3 lists the simulation input data for the validation. Fig. 3 compares the measured and calculated fluid outlet temperatures and plots the inlet fluid temperature. The average temperature difference between the measured and calculated results was 0.35 °C. After 24 h, the average temperature difference was 0.24 °C, and the maximum temperature difference was 0.36 °C. These results showed good agreement between the TRT measurements and the calculation results. 2.5. Validation against the sandbox reference dataset In the case of using TRT measurement data, the developed analysis model was validated only under the continuous operation condition. In order to validate the model for discontinuous operation condition, it also was validated against the sandbox reference dataset [30]. The test was performed under more controlled conditions than can be obtained in field tests. The sandbox reference dataset included a constant heat input rate test set and interrupted test set. In the interrupted test, the circulating pump was off for 2 h. The interrupted test set was used to validate the developed analysis model under the discontinuous condition with a 2 h recovery time. The laboratory sandbox was constructed with an 18-m-long borehole centered horizontally along the length of the box. The box had sides of 1.8 m consisting of a wooden frame and was filled with saturated sand. The single U-tube was made of HDPE with a nominal diameter of 1 in (0.0254 m). The outer and inner diameters of the pipe were 3.340 and 2.733 cm, respectively. Bentonite grout (20% solids) mixed with water was used to fill the borehole space between the pipe and borehole wall. The thermal conductivity was measured independently. The thermal conductivities of the grout and sand were 0.73 and 2.82 W/mK, respectively. The test was conducted for 50 h, and the circulation pump was off between hours 9 and 11.
Fig. 4 also showed good agreement between measured data and the calculation results. 3. Simulation of the effect of the geothermal load on ground temperature recovery The effect of the geothermal load on ground temperature recovery was investigated from three main perspectives. First, the effect of different amounts of the total geothermal load on the ground temperature recovery was analyzed in discontinuous and continuous heat extraction modes. Under the discontinuous heat extraction condition, the duration of the recovery time was assumed to be the same for all cases. Second, the effect of the duration of the recovery time per day on the ground temperature recovery was analyzed. Third, the effect of the daily geothermal load pattern on the ground temperature recovery was analyzed. The pulse and sinusoidal load patterns were compared in discontinuous and continuous heat extraction modes. 3.1. Description of simulation cases In order to investigate the effect of the geothermal load on the ground temperature recovery of the GHE, 10 simulation cases were set up. Cases 1–6 were analyzed to investigate the effects of different amounts of the total geothermal load on the ground temperature recovery. Discontinuous heat extraction with a 12 h recovery time was assumed for cases 1–3. The total daily geothermal loads were 43.2, 86.4, and 172.8 MJ, respectively. Continuous heat extraction was assumed for cases 4–6. The total daily geothermal loads were 86.4, 172.8, and 345.6 MJ, respectively. Cases 3, 5, 7, and 8 were compared to analyze the effect of the duration of the recovery time per day on the ground temperature recovery. The total daily geothermal loads of the four cases were equal at 172.8 MJ. The recovery times of cases 3, 7, and 8 were 12, 8, and 4 h, respectively. Cases 2, 5, 9, and 10 were analyzed to investigate the effects of the daily geothermal load pattern on the ground temperature recovery. A pulse load pattern (cases 2 and 5) and
sinusoidal load pattern (cases 9 and 10) were compared. Cases 2 and 9 were analyzed in discontinuous heat extraction mode. Cases 5 and 10 were analyzed in continuous heat extraction mode. Table 5 lists the simulation cases. 3.2. Configuration and thermal properties of the ground heat exchanger A single 150 m long borehole with a single U-tube was simulated. Water was circulated within the single U-tube to absorb or release heat to the grout. The inlet water temperature was set to be constant at 1 °C. The flow rate was changed according to the given geothermal load. The borehole gap was filled with a mixture of bentonite and water. The ground was assumed to be homogeneous and isotropic. The ground type was assumed to be granite because this is the most common ground type in Korea. The initial ground temperature was 15 °C. Table 6 presents the configuration and thermal properties of the GHE. The heat loss at the ground surface was neglected because the air temperature, solar radiation, and wind velocity have little effect on soil temperature recovery [6]. The simulation of the heating operation was conducted for 90 days. We calculated the average borehole wall temperature to estimate the degree of ground temperature recovery. 4. Results and discussion The ground temperature recovery of each simulation case was analyzed by using the average borehole wall temperature. When heat is extracted, the average borehole wall temperature is lower than the initial ground temperature. Therefore, if the average borehole wall temperature with heat extraction is close to the initial ground temperature, the ground can be concluded to recover quickly. Conversely, if the average borehole wall temperature is far from the initial ground temperature, the ground can be concluded to recover slowly. 4.1. Effect of the total geothermal load on the ground temperature recovery In order to compare the recovery effect, Figs. 5 and 6 plot the average borehole wall
temperature at the end of each recovery time. The average borehole wall temperature continued to decline over time. At the end of the simulation, the average borehole wall temperatures of cases 1–3 were 14.82, 14.80, and 14.77 °C, respectively. In continuous heat extraction mode, the average borehole wall temperatures of cases 4–6 were 13.80, 13.70, and 13.50 °C, respectively. Increasing the total geothermal load tended to decrease the ground temperature recovery. This tendency was stronger in continuous heat extraction mode. In order to better understand the ground temperature recovery, variations in the average borehole wall temperature during the first 5 days were compared. Fig. 7 shows the results of discontinuous heat extraction mode. Fig. 8 shows the results of continuous heat extraction mode. The results in Fig. 7 show that the average borehole wall temperature decreased during heat extraction time and increased during recovery time. When the heat extraction stopped on the first day, the average borehole wall temperature of case 1 was 0.21 K higher than that of case 3. However, when the recovery ended on the first day, the average borehole wall temperature of case 1 was 0.01 K higher than that of case 3. Although larger amounts of heat were extracted, there was little temperature difference between cases 1 and 3 due to the thermal recovery. 4.2. Effect of the recovery time on the ground temperature recovery GHE with different recovery times were simulated to investigate the effect of the recovery time on the ground temperature recovery. Fig. 9 shows the variation in the average borehole wall temperature for cases 3, 5, 7, and 8. The figure plots the average borehole wall temperature at the end of the recovery time. At the end of the simulation, the average borehole wall temperature in discontinuous heat extraction mode with recovery times of 12, 8, and 4 h were 14.77, 14.70, and 14.61 °C, respectively, and the average temperature in continuous heat extraction mode was 13.70 °C.
The temperature change was greater with continuous heat extraction than with discontinuous heat extraction. These results indicate that the duration of the recovery time significantly affects the ground temperature recovery, even if the same amounts of heat are extracted. The temperature difference between the cases with a 12 h recovery time and continuous operation increased over time. The temperature difference was 0.95 K at the end of the first day and 1.07 K at the end of the simulation period. The temperature difference increased rapidly during the first day of the simulation. However, the temperature difference increased gradually after the first day. The duration of the simulation period also affected the ground temperature recovery. In order to better understand the ground temperature recovery, the variations in the average borehole wall temperature during the last five days were compared. Fig. 10 shows the variation in the average borehole wall temperature according to the operation mode. As heat was extracted, the average borehole wall temperature decreased in all simulation cases. Conversely, the average borehole wall temperature increased during recovery. In a typical GHEs design method, the geothermal load with a recovery time is approximated as a continuous load without a recovery time, i.e., a continuous single-step heat pulse. Therefore, cases 3, 7, and 8 are approximated as case 5. Regardless of the duration of the recovery time, the average borehole wall temperature is identical with the typical GHEs design method. However, the above results indicate that the average borehole wall temperature increases with the recovery time. The durations of the recovery and simulation times affect this trend. For cases with a recovery time, a higher average borehole wall temperature can be used in the GHEs design. The borehole length can be reduced with thermal recovery from discontinuous heat extraction. Increasing the recovery duration can further reduce the borehole length. 4.3. Effect of the geothermal load pattern on the ground temperature recovery
Fig. 11 compares the pulse and sinusoidal load patterns with continuous heat extraction and plots the average borehole wall temperature at the end of each recovery time. At the end of the simulation, the average borehole wall temperatures of the pulse and sinusoidal load patterns were 13.70 and 13.81 °C, respectively. Fig. 12 compares the pulse and sinusoidal load patterns with 12 h of heat extraction. At the end of the simulation, the average borehole wall temperatures of the pulse and sinusoidal load patterns were almost the same at 14.80 °C. With discontinuous heat extraction, there was little temperature difference between the pulse and sinusoidal load patterns. With continuous heat extraction, the average borehole wall temperature with the sinusoidal load pattern was 0.11 K lower than that with the pulse load pattern. These results indicate that the daily geothermal load pattern has little effect on the ground temperature recovery. Consequently, the daily geothermal load can be assumed to be a pulse load pattern in GHEs designs that consider the ground temperature recovery. 4.4. Effect of the soil thermal conductivity on the ground temperature recovery in different heat extraction modes According to the previous research [6], soil properties have a great effect on the soil recovery. Therefore, the effect of the soil thermal conductivity on the ground temperature recovery was analyzed by considering the geothermal load and recovery time. Discontinuous heat extraction with 12 h of recovery per day and continuous heat extraction were compared. Four cases were set up. Cases 11 and 12 were used to compare low soil thermal conductivity (𝜆𝑔 = 1.9 W/mK). Cases 13 and 14 were used to compare high thermal conductivity (𝜆𝑔 = 5.2 W/mK). Heat was extracted at a constant 4 kW with the pulse load pattern in cases 11 and 13 and at 2 kW with the pulse load pattern in cases 12 and 14. Table 7 summarizes the simulation cases. Simulations were conducted for 90 days of heating operation. Fig. 13 compares the variations
in the average borehole wall temperature during the simulation time. At the end of the simulation, the average borehole wall temperatures of cases 11–14 were 14.54, 12.66, 14.82, and 14.00 °C, respectively. The average borehole wall temperature with high soil thermal conductivity was higher than the average borehole wall temperature with low soil thermal conductivity. The results showed that the ground temperature recovers more quickly with higher soil thermal conductivity. These findings are similar to those of an earlier study. The results also show that the soil thermal conductivity has a great effect on the ground temperature recovery. Comparing cases 11 and 12, the temperature difference between the discontinuous and continuous heat extraction modes with low thermal conductivity was 1.88 K. Comparing cases 13 and 14, the temperature difference between the discontinuous and continuous heat extraction modes with high thermal conductivity was 0.82 K. The temperature difference between the continuous and discontinuous heat extraction modes increased when the thermal conductivity was low. These results indicate that the temperature difference between a geothermal load with recovery time and a continuous geothermal load increases when the ground temperature recovers slowly. In the GHEs design stage, the geothermal load of case 11 is approximated to that of case 12, and the geothermal load of case 13 is approximated to that of case 14. If the recovery time is considered instead of the geothermal load approximation, a higher average borehole wall temperature can be used in the GHEs design stage. In particular, it is possible to use a higher average borehole wall temperature with low soil thermal conductivity. Using a higher average borehole wall temperature can reduce the borehole length during heating operation. 5. Conclusion A three-dimensional equivalent transient GHE analysis model was developed to analyze the effects of the geothermal load on the ground temperature recovery. The analysis considered
three main perspectives: the effect of the geothermal load on the ground temperature recovery, the effect of the recovery time on the ground temperature recovery, and the effect of the daily geothermal load pattern on the ground temperature recovery. The average borehole wall temperature was determined to estimate the ground temperature recovery. The results showed that decreasing the geothermal load and increasing the recovery time per day can improve the ground temperature recovery. However, the daily geothermal load pattern has little effect on the ground temperature recovery. We also investigated the effect of the soil thermal conductivity on the ground temperature recovery. The ground recovers slowly with low soil thermal conductivity. The duration of the recovery time has a significant influence on ground temperature recovery with low soil thermal conductivity. Considering the recovery time in the GHEs design stage makes it possible to use a higher average borehole wall temperature compared with the geothermal load approximation in the typical GHEs design method. In addition, a lower average borehole wall temperature can be used during a cooling operation. These findings indicate that it is possible to reduce the borehole length by considering the ground temperature recovery. Nevertheless, the results of this study cannot be implemented under real design conditions because it is impossible to enter the average borehole wall temperature in a typical PC design tool. The results were also limited by the conditions of 90 days of operation and a single borehole. Therefore, further study needs to be conducted to develop a design method for a ground heat exchanger that considers heat recovery in order to design a borefield under longterm operation conditions.
ACKNOWLEDGEMENT This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(NRF2015R1D1A1A0906467).
Appendix. Thermal resistances For the fluid region, the thermal resistance between the fluid node and the adjacent grout node is estimated as the sum of the fluid resistance, 𝑅𝑓 , the pipe wall resistance, 𝑅𝑝 , and the grout resistance 𝑅𝑔 : 𝑅𝑖−1 = 𝑅𝑓 + 𝑅𝑝 + 𝑅𝑔
(A.1)
The fluid resistance due to convection is calculated by convective coefficient and length of the equivalent square side of the pipe.
1
𝑅𝑓 = ℎ
(A.2)
𝑓 𝐿𝑝𝑖 Δ𝑦
The pipe wall resistance due to conduction through pipe wall is calculated by Eq. (A.3). ln(
𝐿𝑝𝑜 ) 𝐿𝑝𝑖
𝑅𝑝 = 2πΔ𝑦𝑘
(A.3)
𝑝
The grout resistance due to conduction is calculated by Eq. (A.4). One-half of the length is used because node is located in the center of the control volume. Δ𝑥𝑔
𝑅𝑔 =
2
(A.4)
𝑘𝑔 𝐿𝑝𝑜 Δ𝑦𝑔
For the ground region, conduction heat transfer is dominant. Resistance between adjacent node is calculated by Eq. (A.5).
𝑅𝑖−1 =
Δ𝑥𝑖 2
𝑘𝑖 Δ𝑦𝑖 Δ𝑧𝑖
+
Δ𝑥𝑖−1 2
𝑘𝑖−1 Δ𝑦𝑖−1 Δ𝑧𝑖−1
(A.5)
REFERENCES [1] Michopoulos, A., Bozis, D., Kikidis, P., Papakostas, K., & Kyriakis, N. A. (2007). Threeyears operation experience of a ground source heat pump system in Northern Greece. Energy and Buildings, 39(3), 328–334. [2] Bernier, M. A., Chahla, A., & Pinel, P. (2008). Long-Term Ground-Temperature Changes in Geo-Exchange Systems. ASHRAE Transactions, 114(2), 342–350. [3] Cui, P., Yang, H., & Fang, Z. (2008). Numerical analysis and experimental validation of heat transfer in ground heat exchangers in alternative operation modes. Energy and Buildings, 40(6), 1060–1066. [4] Gao, Q., Li, M., & Yu, M. (2010). Experiment and simulation of temperature characteristics of intermittently-controlled ground heat exchanges. Renewable Energy, 35(6), 1169–1174. [5] Cao, X., Yuan, Y., Sun, L., Lei, B., Yu, N., & Yang, X. (2015). Restoration performance of vertical ground heat exchanger with various intermittent ratios. Geothermics, 54, 115–121. [6] Shang, Y., Li, S., & Li, H. (2011). Analysis of geo-temperature recovery under intermittent operation of ground-source heat pump. Energy and Buildings, 43(4), 935–943. [7] Jalaluddin, & Miyara, A. (2012). Thermal performance investigation of several types of vertical ground heat exchangers with different operation mode. Applied Thermal Engineering, 33-34, 167–174. [8] Cho, H., & Choi, J. M. (2014). The quantitative evaluation of design parameter’s effects on a ground source heat pump system. Renewable Energy, 65, 2–6. [9] Spitler, J. D. (2000). GLHEPRO - A Design Tool For Commercial Building Ground Loop
Heat Exchangers. In the Fourth International Heat Pumps in Cold Climates Conference. [10] Hellström, G., Sanner, B., Klugescheid, M., Gonka, T., & Mårtensson, S. (1997). EXPERIENCES WITH THE BOREHOLE HEAT EXCHANGER SOFTWARE EED. In Megastock Conference 1997. Sapporo, Japan. [11] Eskilson P. (1987). Thermal Analysis of Heat Extraction Boreholes, Doctoral thesis, Department of Mathematical Physics, University of Lund. [12] American Society of Heating Refrigerating and Air-Conditioning Engineers. (2011). 2011 ASHRAE Handbook - HVAC Applications. Atlanta: Refrigerating and Air-Conditioning Engineers, American Society of Heating. [13] Staiti, M., & Angelotti, A. (2015). Design of Borehole Heat Exchangers for Ground Source Heat Pumps: A Comparison between Two Methods. Energy Procedia, 78, 1147–1152. [14] Cullin, J. R., Spitler, J. D., Montagud, C., Ruiz-Calvo, F., Rees, S. J., Naicker, S. S., … Southard, L. E. (2015). Validation of vertical ground heat exchanger design methodologies. Science and Technology for the Built Environment, 21(2), 137–149. [15] Cullin, J. R., Ruiz-Calvo, F., & JD Spitler PhD, P. E. (2014). Experimental Validation of Ground Heat Exchanger Design Methodologies Using Real, Monitored Data. ASHRAE Transactions, 120, 357-369. [16] Shirazi, A. S., & Bernier, M. (2013). Thermal capacity effects in borehole ground heat exchangers. Energy and Buildings, 67, 352–364. [17] Ozudogru, T. Y., Olgun, C. G., & Senol,
a. (2014). 3D numerical modeling of vertical
geothermal heat exchangers. Geothermics, 51, 312–324. [18] Marcotte, D., & Pasquier, P. (2008). On the estimation of thermal resistance in borehole thermal conductivity test. Renewable Energy, 33(11), 2407–2415.
[19] Koohi-Fayegh, S., & Rosen, M. a. (2015). Three-Dimensional Analysis of the Thermal Interaction of Multiple Vertical Ground Heat Exchangers. International Journal of Green Energy, 12(11), 1144–1150. [20] Bauer, D., Heidemann, W., & Diersch, H. J. G. (2011). Transient 3D analysis of borehole heat exchanger modeling. Geothermics, 40(4), 250–260. [21] Chapuis, S., & Bernier, M. (2009). Seasonal storage of solar energy in borehole heat exchangers. In Eleventh International IBPSA Conference (pp. 599–606). [22] Zarrella, A., Scarpa, M., & De Carli, M. (2011). Short time step analysis of vertical ground-coupled heat exchangers: The approach of CaRM. Renewable Energy, 36(9), 2357– 2367. [23] Bauer, D., Heidemann, W., Muller-Steinhagen, H., & Diersch, H. J. G. (2007). Thermal resistance and capacity models for borehole heat exchangers. International Journal of Energy Research, 35(4), 312–320. [24] Maestre, I. R., González Gallero, F. J., Álvarez Gómez, P., & Mena Baladés, J. D. (2013). Performance assessment of a simplified hybrid model for a vertical ground heat exchanger. Energy and Buildings, 66, 437–444. [25] Pasquier, P., & Marcotte, D. (2012). Short-term simulation of ground heat exchanger with an improved TRCM. Renewable Energy, 46, 92–99. [26] Li, Y., Mao, J., Geng, S., Han, X., & Zhang, H. (2014). Evaluation of thermal shortcircuiting and influence on thermal response test for borehole heat exchanger. Geothermics, 50, 136–147. [27] Choi, M., Baek, S., Yeo, M., & Kim, K. (2011). MODELING OF HEAT TRANSFER IN GEOTHERMAL HEAT EXCHANGER USING GHX ZONAL MODEL METHOD. In
Proceedings of Building Simulation 2011: 12th Conference of International Building Performance Simulation Association (pp. 1556–1562). Sydney. [28] De Carli, M., Tonon, M., Zarrella, A., & Zecchin, R. (2010). A computational capacity resistance model (CaRM) for vertical ground-coupled heat exchangers. Renewable Energy, 35(7), 1537–1550. [29] Esen, H., & Inalli, M. (2009). In-situ thermal response test for ground source heat pump system in Elazığ, Turkey. Energy and Buildings, 41(4), 395–401. [30] Beier, R. A., Smith, M. D., & Spitler, J. D. (2011). Reference data sets for vertical borehole ground heat exchanger models and thermal response test analysis. Geothermics, 40(1), 79–85.
x 10m
0.15m
10m
z
Soil (Gravel) Soil (Sand)
Soil (Granite)
Top surface Grout
150m
HDPE pipe
Left surface
30m
Bottom surface
Right surface
Table 1. Mesh sensitivity analysis on the numbers of nodes Grid No. Grid1
Number of nodes in the section of borehole
Total number of nodes
12 × 11
134,465
Average borehole wall temperature (°C) 14.80
Grid2
62 × 61
189,215
14.80
Table 2. Thermal properties of the ground Parameters Gravel Depth below the ground surface Thermal conductivity Density Specific heat Sand Depth below the ground surface Thermal conductivity Density Specific heat Granite Depth below the ground surface Thermal conductivity Density Specific heat
Unit
Value
m W/mK kg/m3 J/kgK
1.5 0.52 2000 1840
m W/mK kg/m3 J/kgK
4.5 1.28 1460 880
m
150
W/mK kg/m3 J/kgK
3.8 2600 840
Table 3. Simulation input data for the validation Parameters Site location Measurement period Borehole length Borehole diameter Pipe outside diameter Pipe inside diameter Pipe spacing Fluid Thermal conductivity Density Specific heat Pipe Thermal conductivity Density Specific heat Grout Thermal conductivity Density Specific heat Design fluid flow rate Initial ground surface temperature Initial ground temperature
Unit m m m m m
Value Seoul, South Korea 5th Jan 2010~7th Jan 2010 150 0.15 0.4 0.32 0.8
W/mK kg/m3 J/kgK
0.6 1000 4179
W/mK kg/m3 J/kgK
0.49 550 2250
W/mK kg/m3 J/kgK kg/s °C °C
0.75 1600 800 0.61 0 14.5
Table 4. Parameters for a sandbox test Parameters Borehole diameter (aluminum pipe) Borehole pipe thickness U-tube length U-tube pipe outer radius U-tube pipe inner radius Distance between centers of pipe Pipe wall thermal conductivity Soil thermal conductivity Grout thermal conductivity Average fluid volumetric flow rate Average heat input rate
Description Inner diameter of aluminum pipe Wall thickness of aluminum pipe SDR 11 (1-in.) SDR 11 (1-in.) SDR 11 (1-in.) Centers of U-tube pipes HDPE Wet sand Bentonite grout 20% solids Water Electric heater
Unit m m m m m m W/mK W/mK W/mK L/s W
Value 0.0126 0.0002 18.3 0.0334 0.02733 0.053 0.39 2.82 0.73 0.197 1056
Table 5. Simulation cases Case No. Case1 Case2 Case3 Case4 Case5 Case6 Case7 Case8 Case9 Case10
Heat Extraction Mode Discontinuous Discontinuous Discontinuous Continuous Continuous Continuous Discontinuous Discontinuous Discontinuous Continuous
Recovery Time per day (h) 12 12 12 0 0 0 8 4 12 0
Daily geothermal Load Pattern Pulse Pulse Pulse Pulse Pulse Pulse Pulse Pulse Sinusoidal Sinusoidal
Total daily geothermal load (MJ) 43.2 86.4 172.8 86.4 172.8 345.6 172.8 172.8 86.4 172.8
Table 6. Configuration and thermal properties of the ground heat exchanger (GHE) Parameters Borehole length Borehole diameter Pipe outside diameter Pipe inside diameter Pipe spacing Fluid Thermal conductivity Density Specific heat Pipe Thermal conductivity Density Specific heat Grout Thermal conductivity Density Specific heat Ground Thermal conductivity Density Specific heat Design fluid inlet temperature Initial ground temperature
Unit m m m m m
Values 150 0.15 0.04 0.032 0.08
W/mK kg/m3 J/kgK
0.574 1000 4211
W/mK kg/m3 J/kgK
0.45 940 2250
W/mK kg/m3 J/kgK
0.68 1080 960
W/mK kg/m3 J/kgK °C °C
3.8 2640 880 1 15
Table 7. Soil thermal conductivity and geothermal load conditions Case No. Case11
Soil thermal conductivity (W/mK) 1.9
Heat Extraction Mode Discontinuous
Recovery Time per day (h) 12 hour
Daily geothermal Load Pattern Pulse
Total daily geothermal load (MJ) 172.8
Case12
1.9
Continuous
0 hour
Pulse
172.8
Case13
5.2
Discontinuous
12 hour
Pulse
172.8
Case14
5.2
Continuous
0 hour
Pulse
172.8