Numerical Simulation of Soil Thermal Response Test with Thermal-dissipation Corrected Model

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World Engineers Summit – Applied Energy Symposium & Forum: Low Carbon Cities & Urban Energy Joint Conference, WES-CUE 2017, 19–21 July 2017, Singapore

Numerical Simulation of Soil Thermal Response with ThermalThe 15th International Symposium on District HeatingTest and Cooling dissipation Corrected Model Assessing the feasibility of using the heat demand-outdoor Ling Maa, Zhiyou Gaob, Yongzhen Wanga, Yunchuan Sunb, Jun Zhaoa*,Ning Fengb temperature function for a long-term district heat demand forecast a

Key Laboratory of Efficient Utilization of Low and Medium Grade Energy (Tianjin University), Ministry of Education of China, Tianjin 300072, a,b,c a a China b c c b Shandong Geo-Mineral Engineering Group Co., Ltd., Jinan 250200, China

I. Andrić

*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre

a

IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Abstract Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France

Based on the duct ground heat storage model on TRNSYS software, a thermal-dissipation-corrected transient model which takes the heat dissipation from ground and testing tube surfaces into consideration is established. An experimental platform is built for in-situ thermal response test (in-situ TRT) in Shandong Province, China. The presented model is verified by in-situ TRT with Abstract similar inlet and outlet temperatures of borehole heat exchanger (BHE). Furthermore, the key parameters, such as injected heat power, flowrate,are etc.commonly are analyzed to studyinthe thermal conductivity, thermal Districtcirculation heating networks addressed theinfluences literature on as identified one of thesoil most effective solutions borehole for decreasing the resistance andgas heat flow perfrom unit the length of BHE. It isThese showed that test duration the largestwhich impact identified soil thermal greenhouse emissions building sector. systems require highhas investments areonreturned through the heat conductivity, followed by injected heatconditions power, abandoned initial renovation hours, the circulation flowrate and backfill conductivity; sales. Due to the changed climate and building policies, heat demand in the material future could decrease, injected heat the power has the largest influence on heat flow per unit length of BHE. prolonging investment return period. The main scope of this paper is to assess the feasibility of using the heat demand – outdoor temperature function for heat demand ©forecast. 2017 TheThe Authors. by Elsevier districtPublished of Alvalade, locatedLtd. in Lisbon (Portugal), was used as a case study. The district is consisted of 665 Peer-review under responsibility of the scientific of theThree Worldweather Engineers Summit(low, – Applied Energy buildings that vary in both construction periodcommittee and typology. scenarios medium, high)Symposium and three & district Forum: Low scenarios Carbon Cities Urban Energy Joint Conference. renovation were&developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were compared with results from a dynamic heat demand model, previously developed and validated by the authors. Keywords: Thermal response test; TRNSYS; Thermal-dissipation-correction; Borehole heat Thermal physical property; The results showed that when only weather change is considered, the margin ofexchanger; error could be acceptable for someNumerical applications simulation (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the 1.decrease Introduction in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the Ground-source pumpssuggested (GSHPs)could havebebeen used provideparameters space heating cooling as well as coupled scenarios). heat The values usedwidely to modify thetofunction for theand scenarios considered, and improve the of heat demand estimations. domestic hotaccuracy water (Bandos et al. 2011). Compared with other energy supply forms, they offer high energy efficiency,

reduced noise levels, savings of greenhouse gas emissions and comfort. The design of borehole heat exchanger (BHE) 2017crucial The Authors. Published Elsevier Ltd. is©very to GSHP system.byBHE is responsible for a major part of the initial cost of the whole system and accurate Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Tel.: +86-22-27407320; fax: +86-22-27407320. E-mail address: [email protected]. Keywords: Heat demand; Forecast; Climate change

1876-6102 © 2017 The Authors. Published by Elsevier Ltd.

Peer-review under responsibility of the scientific committee of the World Engineers Summit – Applied Energy Symposium & Forum: Low Carbon Cities & Urban Energy Joint Conference. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the World Engineers Summit – Applied Energy Symposium & Forum: Low Carbon Cities & Urban Energy Joint Conference. 10.1016/j.egypro.2017.12.719



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design procedures are needed to ensure the higher efficiency and better economy (Cai et al. 2016). The performance of the BHE mostly depends on TRT used to estimate the ground thermal parameters, borehole thermal resistance and heat flow per unit length of BHE. According to Zhang (2009), if there is 10% error on soil thermal conductivity, the relative difference of designed length of BHE will be about 4.5-5.8% and the largest and smallest temperature differences of U-pipes are about 1.1°C-1.2°C and 0.3°C-0.4°C respectively. This will result in 1% change in heating or cooling capacity and increase on initial cost. Besides, the economic advantages of GSHP will be lost once the deviation between required and designed length of BHE reaches 10%-33% (Zhao 2013). Therefore, the accurate and effective ground thermal properties play a key role in the long-term stable operation of the GSHP system. Several methods can be used to estimate ground thermal properties, including soil and rock identification, steady heat flow experimental testing of drill cuttings, in-situ probes and inverse heat conduction methods (Zhang et al. 2014). The parameter determination methods of TRT include slope method or double parameters optimization method which base on the Infinite Line Source Model (ILSM) introduced by Ingersoll (1948) and Mogensen (1983). In addition to analytical calculation, there are numerical simulation models in recent years. The most typical models are Eskilson heat-transfer model (Eskilson 1988) and Hellström duct storage system (DST) model (Thornton et al. 1997). The former has been applied to business software GLHEPRO and GLD while the latter has been applied to TRNSYS. In this paper, in-situ TRT has been conducted in Zhaotong Village of Binzhou area, Shandong Province in China. Then combining the experimental data and TRNSYS software, a thermal-dissipation-corrected model has been proposed. Furthermore, with the indoor soil test results and experimental data, the new model is verified and key parameter (i.e. injected heat power, circulation flowrate, etc.) influence studies on the identified soil thermal conductivity, borehole thermal resistance and heat flow per unit length of BHE are simulated. The results of the study provide feasible suggestion for the application and promotion of GSHP system. 2. System description 2.1 General situation for testing region and experimental set up The in-situ TRT is located in Zhaotong Village on the downstream of The Yellow River in Binzhou Area of Shandong Province in China. Geographic coordinate of Zhaotong Village is 117.94°E, 37.32°N in the southeast of Binzhou. Testing area is covered by Quaternary with the depth of 250-400 m and on the top of Minghuazhen formation. The main structures of the geology are sandy conglomerate, mudstone and sand-shale stone. Cohesive soil is the major component with the thermal conductivity of 1.67-1.97 W/(m·K). G * Tout

Qt

Tin* Qa

D

Tin

Tout

H

Fig.1 The physics appearance of TRT apparatu

Fig.2 Schematic diagram of in-situ TRT apparatus

The testing device is a vehicle-mounted shallow geothermal energy TRT tester. The main components of the TRT apparatus are as follows: data acquisition system, thermal storage water tank, electric auxiliary heater, temperature sensor (Pt100), variable speed pump, electromagnetic flowmeter, flow control valve, pressure sensor, etc. The maximum test error of TRT system is ±0.20%. Fig.1 and Fig.2 show the physical appearance and schematic diagram of in-situ TRT apparatus respectively. 2.2 Experimental results

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Table1. shows the basic parameters of in-situ TRT. The backfill materials are medium-coarse. The TRT was conducted 72 h after drilling completion, at which time soil temperature recovered to initial state. The ILSM and slope method were adopted to estimate the soil thermal conductivity. The experimental steps are as follows: 1) The soil was taken underground every 5 meters in depth and tested in geotechnical laboratory to estimate soil conductivity, capacity and thermal diffusivity. 2) The ground initial temperature was determined by wattles circulation method. 3) The insitu TRT lasted 48 h from 9:00 April 17th, 2016 under heating condition. The data of initial 12 hours was abandoned since steady state hadn’t been reached in the testing borehole at that time. According to the data analysis, the ground initial temperature is 17.32 °C. Besides, the identified soil conductivity is 1.828 W/(m·K) and the heat flow per unit length of BHE is 46.94 W/m. Table.1 Basic parameter of in-situ TRT Parameters Buried pipe type Borehole diameter/mm Borehole depth/m Outer diameter of pipe/mm Inner diameter of pipe/mm Center-to-center half distance/mm Buried pipe material

Value Double-U tubes 150 117 32 28 64 PE

Parameters Storage volume/m3 Pipe thermal conductivity/W·(m·K)-1 Fill thermal conductivity (λg)/ W·(m·K)-1 Circulation flowrate (G)/m3·h-1 Injected heat power (P)/kW Abandoned initial hours (ta)/h Testing duration (td)/h

Value 1580.2 1.5122 2.00 1.5 6 12 48

3. Corrected model in TRNSYS 3.1 Thermal-dissipation-corrected method A non-dimensional parameter η is introduced to estimate heat dissipation. It is defined in Eq. (1) and its physical meaning can be inferred from physical parameters (Bandos, Montero, Córdoba and Urchueguía 2011). Then, the actual inlet and outlet temperatures of BHE can be determined by Eq. (2) and Eq. (3). =

D Ra C p G

(1)

Tin =Tin* e- +Ta (1  e- ) *  out

(2)



Tout =T e +Ta (1  e ) (3) where D is length along the piping between the temperature probe location and the borehole inlet or outlet (m) (see Fig. 2), Ra is thermal resistance between fluid and ambient air (KmW−1), Cp is specific volumetric heat capacity of circulating fluid at constant pressure (kJm-3K-1), G is volume flowrate (m3h−1), Ta is ambient air temperature (°C), Tin is inlet temperature of BHE (°C), Tout is outlet temperature of BHE (°C), T*in is measured inlet temperature of BHE (°C), T*out is measured outlet temperature of BHE (°C). Based on the energy conversation equation, the heat transfer rate from soil and heat dissipation rate to the ambient air can be calculated by Eq. (4) and Eq. (5) respectively. ql  , t  H  C pG Tin  Tout  Qt (4) Rb  Qt  Qair  t   (5)  Tf  , t   Ta  t  H

where ql is heat flow per unit length of BHE (W/m) which is the function of η and time t, H is depth of BHE (m), Qt is total heat transfer rate from soil (W) which consists of effective heat absorption and heat dissipation rate to the ambient air (W), Qair(t) is heat dissipation rate to the ambient air (W), Tf is average temperature of heat carrier fluid (°C), Rb is borehole thermal resistance (KmW −1). It should be noted that two corrections have been taken into account: the heat-conduction dissipation from pipe surface and heat-convection dissipation from ground surface by ambient air. 3.2 Simulation model and validation The transient model of TRT is simulated by TRNSYS shown in Fig.3. TRNSYS adopts modular dynamic simulation program and every model with specific function can be linked to others. When models are called and linked, the program runs based on given input condition. Type557a (vertical BHE) is the most important component and its numerical calculation is derived from Hellström (1989). The superposition principle is adopted to estimate temperature difference and process of the ground heat transfer can be divided into three parts: 1) the steady state heat transfer



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among BHE; 2) local transient heat transfer in the BHE area; 3) the heat transfer between whole buried pipe area with other area. The input parameters are in line with experiment’s. Soil is sliced into ten layers and thermal physical properties of every layer are set by the results of previous indoor soil tests. What’s more, η is approximated as 0.004 by comparison with in-situ TRT. The surplus temperature at a simple time t and a radius r is defined by Diao (2006). Tf  T0 =

 1   r2  ln  t   ql  Ei  b   Rb    4s 4 4 t   s   ql

(6)

where λs is identified soil thermal conductivity (W/m·K), α is soil thermal diffusivity (m2/s), Ei( ) is Euler function and rb is borehole radius (m). When the αt/r2b ＞5, Eq.(5) can be approximated to liner formula as Eq.(7) (7)

 Tf k ln t  m k=

ql

(8)

4s

 1  4   m=T0 +ql  Rb +  ln 2 -   rb   4  s  

(9)

In the Eq.(6)-Eq.(9), λs and Rb can be estimated by slope k and intercept m. Fig.4 shows the comparison of measured and simulated temperatures. The results show that without correction (η=0) the relative difference of average temperature of BHE is 6.76% and maximum value is 7.83% based on experiment. The relative difference of identified soil thermal conductivity and heat flow per unit length of BHE is 7.06% and 11.24%. However, the above parameters decrease to 2.81%, 3.49%, 5.38%, 6.71% in the same order with heatdissipation correction (η=0.004). It is showed that heat-dissipation correction is effective to estimate the soil thermal properties. 34

Weather Data

32

Online Plotter

Temperature (°C)

30

Pump

Calculation Center

28 26

Experimental Tin

24

Corrected Tin

22

Experimental Tout

Uncorrected Tin Corrected Tout

20

GHE

Heater

Fig.3 Model structure of TRT

4. Simulation results analysis

Flowrate Fluctuation Correction

18

Uncorrected Tout 0

5

10

15

20

25

Time (h)

30

35

40

45

50

Fig.4 Comparison of simulated temperature and experimental temperature under the same input condition

4.1 Influence of circulation flowrate on simulation results of TRT The Technical Code for Ground-source Heat Pump System of the PRC (“the Code”) requires that fluid velocity not be lower than 0.2 m/s to ensure turbulence in the pipes. Seven flowrates from 1.00 to 2.50 m3/h are set to study its influence on λs, Rb and ql. Simulation results are shown in Fig.5. With other operation parameters constant, λs changes slightly with the circulation flowrate and the variation is less than 0.02 W/(m·K), while Rb and ql vary quickly in the initial stage but slowly later. As G increases, the Re number grows linearly, which results in the enhancement of turbulent intensity in pipes and decrease of convective thermal resistance. Because of a tiny share of convective thermal resistance in Rb, circulation flowrate induces only a modest increase in heat transfer performance. The reasonable value of G is 1.0 to1.5 m3/h according to simulated results. 4.2 Influence of injected heat power on simulation results of TRT The Code requires that constant heat power be adopted in in-situ TRT but has no regulation on value. The American Society of Heating, Refrigerating, and Air Conditioning Engineers (ASHRAE) requires that the heat power should be

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50-80 W/m which is roughly equal to peak load of BHE, so 7 injected heat powers from 4-10 kW are simulated and shown in Fig.6. From Fig.6, λs decreases sharply with heating power but is close to experimental result (1.828 W/(m·K)) in the end while ql increases linearly and Rb increases with the rising rate slower. Concrete analysis is based on the theory of layer heat transfer (Wang 2006). It points that there are three regions of soil in depth, namely full heat transfer layer, heat transfer layer and none heat transfer layer. Within the first layer close to ground surface, large temperature difference causes intense heat transfer between borehole and ambient soil, which makes temperature difference become smaller and smaller and close to zero finally. Effective heat transfer occurs at second layer because the temperature difference approximates to constant and steady. The third layer is the deepest region of soil and BHE, where fluid temperature is close to soil temperature and the performance of heat transfer degrades. The area of heat transfer layer decreases with increasing heating power, which results in the increase of Rb. The reasonable heating power is about 6-7 kW. It is also concluded that ql is improper to be used in the design of GSHP because it is strongly correlated to heat load and soil properties. 4.3 Influence of duration on simulation results of TRT The Code requires that 48 h be the least time for TRT while the recommended time of ASHERA is 36-48 h. Seven durations from 24-96 h are simulated and shown in Fig.7. When td is less than 42 h, large deviation is identified on λs and Rb. When td is more than 50 h, the results vary slightly. Specially, if td is 96 h, λs is very close to experimental results with relative difference of 0.97%, but the relative difference of ql is 6.37%, which confirms that ql is changeable and relates to soil structure and heat load. So 50 h is enough to ensure the accuracy, which is consistent with the recommended value.

1.93

0.42

1.92

λs

1.91 1.0

1.2

1.4

Rb 1.6

1.8

0.41

ql 2.0

2.2

2.4

2.6

0.40

46 44

0.448

1.90

0.446

1.88

42 40

1.84

Fig.5 The influence of circulation flowrate on identified results P=6 kW, td=48 h, ta=12 h, λg=2 W·(m·K)-1

60

2.1

0.444 λs 4

5

Rb 6

7 P/kW

ql 8

50

0.46

0.44

2.0

40

1.9

30

1.8

20

1.7

0.43 0.42

10

0.440

Fig.6 The influence of injected heat power on identified results G=1.5 m3·h-1, td=48 h, ta=12 h, λg=2 W·(m·K)-1

Rb

λs

0.442 9

52

0.45

20

30

40

50

60

Td/h

50

48

0.41

ql 70

ql/W·m-1

0.450

1.92

1.86

G/m3·h-1

0.452

54

0.47

Rb/(mK)·W-1

48

2.2

λs/W·(mK)-1

50

2.3

70

ql/W·m-1

0.43

1.94

0.454

1.94

Rb/(mK)·W-1

0.44

1.95

52

0.456

1.96

54 Rb/(mK)·W-1

λs/W·(mK)-1

1.96

0.8

56

0.45

1.97

80

0.458

1.98

λs/W·(mK)-1

1.98

1.90

58

0.46

0.460

2.00

60

0.47

1.99

ql/W·m-1

2.00

80

90

0.40

100

46

Fig.7 The influence of duration on identified results G=1.5 m3/h, P=6 kW, ta=12 h, λg=2 W·(m·K)-1

4.4 Influence of abandoned initial hours on simulation results of TRT According to assumptions of ILS model – αt/r2b ＞5 and steady heat transfer in borehole, in several initial hours the data cannot be used for calculation. There is no regulation on abandoned initial hours so far. Seven abandoned initial hours from 12 to 48 h are simulated and td in this part is 96 h. There is an apparent turning point at 30 h shown in Fig.8, which indicates that full heat transfer layer occurs at this time. This layer reduces the effective area for heat transfer and increases Rb. With the increase of ta, the area of full heat transfer layers becomes larger, further increasing Rb, so that λs and ql more and more deviated from experimental results. It indicates that the full heat transfer layer should be avoided both for in-situ TRT and actual operation of GSHP to ensure effective heat transfer intensity. The initial hours should be 12~30 h according to the simulation. 4.5 Influence of backfill materials on simulation results of TRT Fig.9 shows simulated results with 8 backfill materials whose conductivity ranges from 1.60 to 2.30 W/(m·K). The results indicate that Rb decreases with the conductivity of backfill materials while λs and ql vary slightly because thermal resistance of backfill materials is a major proportion in Rb, but it cannot enhance heat transfer outside borehole



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effectively. In other words, the influence of the thermal conductivity of backfill materials on the ground thermal parameters is limited. Nevertheless, increasing backfill material conductivity will raise the cost of investment. 4.6 The simulated accuracy analysis of key parameters The simulation accuracy analysis of 5 key parameters is shown in Fig.10. For λs, Rb and ql, the key parameters are sorted by the sensitivity on simulated results, from highest to lowest respectively. For λs, the order is td > ta >P > G > λg. For Rb, the order is td > ta > G > P > λg. For ql, the order is P > G > td > ta > λg We also conclude that ql is more sensitive than λs and Rb, so it is improper to use ql to design GSHP system. Compared with experiment, injected heat power has the largest impact on ql with the deviation ranging from -27.52% to 75.01%; duration has the largest impact both on λs and Rb with the maximum deviation 24.88% and -7.78% respectively. Compared comprehensively, testing duration has the largest influence while backfill material has the least. It is concluded that user load directly effects the performance of BHE, so refined design must be taken on GSHP to ensure the efficiency and economic advantages.

1.71

0.460

1.68 λs

1.65 10

15

20

Rb 25

30

0.455

ql 35

49.0 48.8

Rb/(mK)·W-1

0.465

1.74

49.2

λs/W·(mK)-1

1.77

0.456

49.4

ql/W·m-1

0.470

λs/W·(mK)-1

1.80

Rb/(mK)·W-1

1.83

1.98

49.6

1.95

0.453

1.92

0.450

48.6 48.4

40

45

50

0.450

48.0

Fig.8 The influence of abandoned initial hours on identified results G=1.5 m3/h, P=6 kW, td=98 h, λg=2·W(m·K)-1

20

50.0

15

49.6 49.2 48.8

1.89

0.447 λs

48.2

ta/h

25

50.4

1.86

1.5

1.6

1.7

Rb 1.8

1.9

ql 2.0

2.1

2.2

2.3

0.444

2.4

Relative error/%

0.475

50.8

ql/W·m-1

0.459

49.8

1.86

1.62

2.01

50.0

0.480

1.89

75.01

λs Rb ql

10 5 0

48.4 48.0

λg/W·(mK)-1

Fig.9 The influence of backfill materials on identified results G=1.5 m3·h-1, P=6 kW, td=48 h, ta=12 h

-5 -10

-27.52 G G

PP

ttdd

ttaa

λλgg

--

Fig.10 The simulated accuracy analysis of key parameters G=1.5 m3/h, P=6 kW, ta=12 h, td=48 h, λg=2 W·(m·K)-1

5. Conclusions In this paper, in-situ TRT was carried out in Shandong Province, China. The thermal-dissipation model is developed based on the DST model. With TRNSYS as software platform, the accuracy of model is verified by the comparison between experimental and simulation results. In addition, analysis of 5 key parameters is conducted. The conclusions can be summarized as follows: 1) non-dimensional parameter η is basically applicable to estimate the heat dissipation from surface of pipes and ground. Besides, it is effective to increase the accuracy of identified parameters; 2) parameters should be listed as duration, abandoned initial hours, injected heat power, circulation flowrate and backfill materials, sorted by the sensitivity on simulated results, from highest to lowest; 3) the circulation flowrate has little impact on λs and 5% increase on ql. The duration of TRT should be at least 50 h and the injected heating power must be determined and controlled to ensure steady heat transfer in borehole and avoid the full heat transfer layer. Abandoned initial hours should be at least 12h but no more than 30h. The effect of backfill conductivity on soil thermal conductivity is limited, less than 1% deviation on λs and ql. Besides, higher thermal conductivity of backfill material causes increasing on initial investment and serious thermal interference between two adjacent legs of U-tubes. 4) the full heat transfer layer affects effective heat transfer between BHE and soil, resulting in 5.5% deviation of soil conductivity. Careful design must be conducted to ensure flowrate and load balance among pipes to avoid full heat transfer layer. References [1] T.V. Bandos, Á. Montero, P.F.D. Córdoba and J.F. Urchueguía. (2011)"Improving parameter estimates obtained from thermal response tests: Effect of ambient air temperature variations." Geothermics 40.2 (2011): 136-143. [2] Y. Cai, H. Xu and S. Chen. (2016)"Testing and analysis of the influence factors for the ground thermal parameters." Applied Thermal Engineering 107. (2016): 662-671.

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[3] J. Zhang. (2009) Studying of Determination of the Thermal Properties of Geotechnical Parameters Based on Genetic Algorithm Wuhan: Huazhong University of Science and Technology [4] F. Zhao. (2013) In-situ Soil Thermal Response Test and its Data Processing Methods Studies. Xi'an: Xi`an University of Architecture and Technology [5] C. Zhang, Z. Guo, Y. Liu, X. Cong and D. Peng. (2014)"A review on thermal response test of ground-coupled heat pump systems." Renewable & Sustainable Energy Reviews 40.C (2014): 851-867. [6] L.R. Ingersoll and H.J. Plass. (1948)"Theory of the ground pipe heat source for the heat pump." Heating Piping & Air Conditioning 54.7 (1948): 339-348. [7] P. Mogensen. (1983)"Fluid to duct wall heat transfer in duct system heat storage." (1983). [8] C. Eskilson. (1988)"PC design model for heat extraction boreholes." Geothermal Energy (1988): 135-137. [9] J.W. Thornton, T.P. Mcdowell, J.A. Shonder, P. Hughes, D. Pahud and G. Hellstrom. (1997)"Residential Vertical Geothermal Heat Pump System Models: Calibration to Data." American Society of Heating, Refrigerating and Air-Conditioning Engineers 103. (1997): 660-674. [10] G. Hellström. (1989)"Duct Ground Heat Storage Model." (1989). [11] Z.F. Nairen Diao, Ground–Coupled Heat Pump Technology, Higher Education Press, Beijing, 2006. [12] Y. Wang. (2006) A Study on Performance of GSHP under Dynamic Load. Chongqing: Chongqing University

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