Thermal Performance Insight on a Ground Coupled Heat Pump

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Thermal Performance Insight on a Ground Coupled Heat Pump

Dalya Samara

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Abstract

The use of renewable energy technology is increasing in Europe with a particular market development of ground source heat pumps (GSHP) with more than 500,000 existing GSHP systems. A common method to exchange heat with the ground is through borehole heat exchangers (BHEs) with either open or closed loop systems, the latter being more common in Sweden. The heat is exchanged with the ground by circulating an antifreeze solution with a temperature lower than the surrounding bedrock. Groundwater is commonly used as a filling material in BHEs in North Europe. The natural convection that occurs in groundwater filled boreholes is induced by the temperature gradients around the BHE. An important parameter of the system is the mass flow rate of the secondary fluid circulating in the BHE system. The mass flow rate may affect the pumping power, the efficiency of the pump as well as the COP of the system.

Optimizing BHE systems is an important topic in the GSHP industry. Thermal Response Tests (TRTs) can be carried out to evaluate two important parameters for the BHE design; the ground thermal conductivity (λ) and the borehole thermal resistance (𝑅_𝑏). A TRT results in mean values of λ and 𝑅_𝑏which may affect the accuracy of the BHE design as these parameters may show local variation along the depth of the borehole. A Distributed Thermal Response Test (DTRT), uses fibre optic cables along the depth of the borehole to measure the temperature in order to take these variations into consideration.

The aim of this Master Science thesis is to study and analyse the performance of groundwater-filled boreholes by looking into the change of efficiency in terms of thermal resistance related to working conditions in a U-pipe as well as the effect of the secondary fluid mass flow rate on the Coefficient of Performance of the heat pump system. The objectives are to:

 Observe the effect of convective heat flow on the borehole thermal resistance

 Observe the variation in borehole thermal resistance as the groundwater temperature passes 4 ºC

 Analyse the variation of the borehole thermal resistance along the depth of the borehole

 Analyse the effect of the secondary fluid mass flow rate on the Coefficient of Performance

Master of Science Thesis EGI-2015-023 MSC

Thermal Performance Insight on a Ground Coupled Heat

Pump

Dalya Samara

Approved Examiner Supervisor

Davide Rolando (José Acuna)

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Acknowledgements

It is with immense gratitude that I acknowledge the help and support of my supervisor Davide Rolando whose guidance and patience is what made this thesis possible.

I would also like to thank Dr José Acuna, for introducing me to this exciting field and offering me the opportunity to conduct this experiment.

My sincere thanks goes to my parents who never stopped believing in me and to my husband Nabil, whose encouragement is what got me through the toughest times of my work.

And finally, I dedicate this work to my daughter Maryam, who showed me that

everything is possible, one step at a time.

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Abbreviations

BHE Borehole Heat Exchanger

CFD Computer Fluid Dynamics

COP Coefficient of Performance

ICS Infinite Cylindrical Source Model DTRT Distributed Thermal Response Test DTS Distributed Temperature Sensing

EED Earth Energy Designer

EES Engineering Equation Solver

GSHP Ground Source Heat Pump

ILS Infinite Line Source Model

TRT Thermal Response Test

Nomenclature

𝑐 Fluid Specific Heat [𝐽/𝑘𝑔𝐾]

𝑑 Pipe Diameter [𝑚]

𝐸₁ Exponential Integral

𝑓 Friction Factor [−]

L Borehole Length [𝑚]

𝐻 Head [𝑚]

∆𝑃_𝑓 Pressure Drop due to Friction [𝑃𝑎]

𝑄̇_{𝑡ℎ𝑒𝑟𝑚𝑎𝑙} Thermal Power [𝑊]

𝑄̇_𝑐 Cooling Power [W]

𝑄̇_𝑒𝑙 Electrical Power [𝑊]

𝑄̇_ℎ Heating Power [𝑊]

𝑄̇_{𝑝𝑢𝑚𝑝} Pumping Power [𝑊]

𝑄̇^′ Heat Rate per Unit Length [𝑊/𝑚]

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𝑟 Radius [𝑚]

𝑟_𝑏 Borehole Radius [𝑚]

𝑟_𝑝 Pipe radius [𝑚]

𝑚̇ Mass Flow Rate [𝑘𝑔/𝑠]

𝑅_𝑏 Borehole Thermal Resistance [𝑚 𝐾/ 𝑊]

𝑅_{𝑐𝑜𝑛𝑡𝑎𝑐𝑡} Contact Thermal Resistance [𝑚 𝐾/ 𝑊]

𝑅_{𝑓𝑙𝑢𝑖𝑑} Fluid to Pipe Thermal Resistance [𝑚 𝐾/𝑊]

𝑅_{𝑓𝑖𝑙𝑙𝑖𝑛𝑔} Resistance of Filling Material [𝑚 𝐾/𝑊]

𝑅_{𝑔𝑟𝑜𝑢𝑡} Grout Resistance [𝑚 𝐾/𝑊]

𝑅_{𝑝𝑖𝑝𝑒} Pipe Thermal Resistance [𝑚 𝐾/𝑊]

𝑅𝑒 Reynolds Number [−]

𝑡 Time [𝑠]

𝑇_𝑏 Borehole Wall Temperature [𝐾]

𝑇_𝑐 Cold Temperature in Heat Pump [𝐾]

𝑇_𝑓 Mean Secondary Fluid Temperature [𝐾]

𝑇_{𝑓,𝑖𝑛} Inlet Fluid Temperature [𝐾]

𝑇_{𝑓,𝑜𝑢𝑡} Outlet Fluid Temperature [𝐾]

𝑇_𝑔𝑟,∞ Undisturbed Ground Temperature [𝐾]

𝑇_ℎ Hot Temperature in Heat Pump [𝐾]

∆𝑇 Temperature Difference [𝐾]

𝑈_𝑎𝑣𝑔 Average Fluid Velocity [𝑚/𝑠]

𝑉̇ Volumetric Flow Rate [𝑚³/𝑠]

µ Dynamic viscosity [𝑘𝑔/𝑚𝑠]

𝛽_0, 𝛽₁ Shape Factor Coefficients (Paul’s Method) [−]

𝜈 Kinematic Viscosity [𝑚²/𝑠]

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Λ Ground Thermal Conductivity [𝑊/𝑚 𝐾]

𝛾 Euler’s Constant [−]

α Ground Thermal Diffusivity [𝑚²/𝑠]

𝜂_{𝑝𝑢𝑚𝑝} Pump efficiency

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Table of Contents

1 INTRODUCTION ... 1

2 THEORETICAL BACKGROUND ... 3

2.1 Ground source Heat Pump ... 3

2.1.1 Coefficient of Performance ... 4

2.2 Secondary Fluid Flow Rate and Efficiency ... 5

2.2.1 Flow Regime ... 6

2.3 Pressure Drop ... 7

2.4 Borehole Heat Exchangers ... 8

2.4.1 Borehole Thermal Resistance ... 9

2.4.2 Convective Heat Flow and Freezing in Groundwater-filled Boreholes ...10

2.5 Thermal Response Test ...11

2.6 Thermal Response Test analysis ...13

2.6.1 Infinite Line Source Model ...14

2.6.2 Infinite Cylinder Source Model ...17

3 FIELD EXPERIMENTS ...18

3.1 The Effect of the Secondary Fluid Flow Rate on the Performance of the System ...18

3.2 Experimental Setup...21

3.3 Effect of the Borehole Water Temperature on the Borehole Thermal Resistance ...22

3.4 Experimental Setup...23

4 RESULTS ...23

4.1 The Effect of the Secondary Fluid Mass Flow Rate on the Overall Performance of the System 23 4.2 The Effect of the Borehole Water Temperature on the Borehole Resistance ...25

5 Comparison of Results in BHE4 with Previous Work ...57

5.1 FUTURE WORK ...58

6 CONCLUSIONS ...58

7 REFERENCES ...60

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Index of Figures

Figure 1 Ground Source Heat Pump System (Acuna, 2010). ... 3

Figure 2 Heat pump in cooling and heating mode. ... 4

Figure 3 Schematic diagram of a heat pump. ... 4

Figure 4 Temperature difference effect on COP. ... 5

Figure 5 Variation of the overall COP of the system based on the secondary fluid mass flow rate: different colours show different compressor frequencies (Madani et al. 2010). ... 6

Figure 6 Turbulent and laminar flow in pipes. ... 7

Figure 7 Borehole sections studied (Acuna, 2010). ... 9

Figure 8 Resistances in borehole. ... 9

Figure 9 Thermal response test unit (Gehlin, 2002). ...11

Figure 10 Undisturbed ground temperature profile. ...12

Figure 11 Ground thermal conductivity, λ for each section (Acuna,2010). ...13

Figure 12 Specific heat as a function of the fluid temperature. ...15

Figure 13 Temporal Superposition principle of heat transfer rate per unit length. ...17

Figure 14 Fiber loop sketch of BHE4 and BHE5 (Acuna, 2010). ...18

Figure 15 Power during time step 6 with a standard deviation of 2.7 W. ...21

Figure 16 Hameg power meter. ...21

Figure 17 Experimental setup of the heat pump. ...22

Figure 18 Viessmann Vitocal 200-G heat pump (right: www.viessmann.co.uk). ...23

Figure 19 Secondary mass flow rate and Reynolds number effect on the efficiency for a compressor frequency of 50Hz. ...24

Figure 20 Reynolds number development along the mass flow rate at a compressor frequency of 50 Hz. ...24

Figure 21 Mass flow rate and compressor frequency effect on efficiency. ...25

Figure 22 Heat transfer rate for each section in the borehole during the cooling phase. ...26

Figure 23 Borehole water temperature profiles for each borehole section along time. Blue rectangle marks the experiment. ...26

Figure 24 Borehole water temperature profiles for each borehole section during the cooling phase. ...27

Figure 25 Fluid temperature profiles for each borehole section along time. Blue rectangle marks the experiment. ...28

Figure 26 Average fluid temperature in each borehole section during the cooling phase. ...28

Figure 27 Instantaneous secondary fluid temperature profiles along the depth of borehole. ...29

Figure 28 Temperatures of the fluid Tf, avg1, at the borehole wall Tb1, in the borehole water Tw, avg1 and the power Q1 ′in section 1. ...30

Figure 29 Borehole thermal resistance, Rb1 along time for section 1. ...31

Figure 30 Borehole thermal resistance, Rb1 versus borehole water temperature, Tw. avg1 for section 1. ...31

Figure 31 Temperatures of the fluid Tf, avg2, at the borehole wall Tb2, in the borehole water Tw, avg2 and the power Q2 ′in section 2.Figure 32 Borehole thermal resistance, Rb2 along time for section 2. ...32

Figure 33 Borehole thermal resistance, Rb2 versus borehole water temperature, Tw. avg2 for section 2. ...33

Figure 36 Borehole thermal resistance, Rb3 versus borehole water temperature for section 3. ...35

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Figure 37 Temperatures of the fluid Tf, avg4, at the borehole wall Tb4, in the borehole water

Tw, avg4 and the power Q4 ′in section 4. ...36

Figure 43 Temperatures of the fluid Tf, avg6, at the borehole wall Tb6, in the borehole water Tw, avg6 and the power Q6′ in section 6. ...40

Figure 45 Borehole thermal resistance, Rb6 versus borehole water temperature, Tw, avg6 for section 6. ...41

Figure 49 Temperatures of the fluid Tf, avg8, at the borehole wall Tb8, in the borehole water Tw, avg8and the power Q8′ in section 8. ...44

Figure 50 Borehole thermal resistance, Rb8 along time for borehole section 8. ...45

Figure 55 Temperatures of the fluid Tf, avg10, at the borehole wall Tb10, in the borehole water Tw, avg10and the power Q10′ in section 10. ...48

Figure 57 Borehole thermal resistance, Rb10 versus borehole water temperature, Tw, avg10 for section 10. ...49

Figure 61 Temperatures of the fluid Tf, avg12, at the borehole wall Tb12, in the borehole water Tw, avg12and the power Q12′in section 12. ...52

Figure 64 Borehole thermal resistance, Rb versus borehole water temperature for 12 sections. ...54

Figure 65 Borehole thermal resistance for sections 4, 8, 10 and 11. ...55

Figure 66 Borehole thermal resistance for sections 4, 8, 10 and 11 with total average power. ...55

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Figure 67 Borehole thermal resistance for sections 1, 2, 3, 5, 6, 7, 9 and 12. ...56 Figure 68 Borehole thermal resistance for sections 1, 2, 3, 5, 6, 7, 9 and 12 with total average power. ...56 Figure 69 Borehole thermal resistance plotted using inlet and outlet fluid temperatures only as in regular TRT...57 Figure 70 Borehole thermal resistances versus borehole water temperatures for three TRT measurements (Gustafsson et al., 2011). ...57

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1 INTRODUCTION

The ground is a reliable and renewable source of energy with a fairly constant temperature year round. The use of renewable energy technology is increasing in Europe with a particular market development of ground source heat pumps (GSHP). Sweden has been a leading country within this technology since the 1980s and has today the most developed GSHP market in Europe with more than 500,000 existing GSHP systems and around 25,000 new installations per year (Gehlin et al., 2015).

GSHPs are energy efficient systems that use the energy stored in the ground from the sun to supply the heating and cooling demands of a building. A typical GSHP system consists of a ground heat exchanger to extract heat from the ground, a heat pump to transfer the heat to a required temperature for heating or cooling purposes and equipment in the building to transfer the heat or cold into the required space.

The heat pump allows the heat transfer from a lower temperature to a higher one and is driven by external energy (e.g. electricity) to transfer the energy from the heat source to the heat sink. It is desirable to strive for as low electric power input as possible in order to increase the energy efficiency of the system. This efficiency is calculated as the ratio of power output, 𝑄̇_{𝑡ℎ𝑒𝑟𝑚𝑎𝑙} (thermal power delivered by the system) to the power input 𝑄̇_𝑒𝑙 (electric power required to operate the compressor and pump) and is called the Coefficient of Performance (COP), (Granryd, 2009).

A common method to exchange heat with the ground is through borehole heat exchangers (BHEs).

BHEs can be divided into two main types, open loop and closed loop systems, the latter being more commonly used in Sweden. An antifreeze solution with a temperature lower than the surrounding bedrock is circulated through this closed loop, heated and pumped back to the heat pump which raises the temperature according to the demand of the building. Groundwater is commonly used as a filling material in BHEs in North Europe including Sweden. Natural convection occurs in groundwater filled boreholes and is induced by the temperature gradients around the BHE. Part of this study will investigate the effects of natural convection on the borehole thermal resistance.

An important parameter of the system is the mass flow rate of the secondary fluid circulating in the borehole heat exchange system and is responsible for transferring the heat from the heat source to the heat sink. The mass flow rate may affect the pumping power, the efficiency of the pump as well as the COP of the system.

The type of flow of the secondary fluid in the borehole is related to the amount of heat transferred by the system. The chaotic nature of turbulent flow transfers more heat from its surroundings as compared to laminar flow. For Reynolds numbers > 2300 the flow can be defined as turbulent and the heat pump system can operate with a lower temperature difference as compared to laminar flow (Incropera, 2011).

One of the goals of this thesis is to evaluate the effect of the secondary fluid mass flow rate on the COP of the groundwater filled BHE system using in-situ field measurements. Similar studies have been carried out by He (1996), Granryd (2002), Granryd (2007), Karlsson et al. (2008), Finn et al.

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(2008) and Madani et al. (2010). Simulated results (Madani et al., 2010) concluded that there is an optimum secondary fluid flow rate that yields a maximum overall COP at a given compressor frequency. It was also shown that increasing the mass flow rate may increase the heat pump heating capacity at high compressor speeds.

Optimizing the design of the BHE can further enhance the energy efficiency of GSHP systems and reduce costs. The required length of borehole for a given power output depends on soil characteristics, heat transfer coefficients and geometry of the borehole.

Correct sizing of the BHE continues to be a problem in Sweden. Companies are compromising with the depth of the boreholes to reduce customers’ installation costs.

Thermal Response Tests (TRTs) can be carried out to optimize the design and performance of ground source heat pumps by evaluating two important parameters for the BHE design; the ground thermal conductivity (λ) and the borehole thermal resistance (𝑅_𝑏).

A TRT results in mean values of λ and 𝑅_𝑏which may affect the accuracy of the BHE design as these parameters may show local variation along the depth of the borehole. In a TRT, the mean temperature (𝑇_𝑚) is calculated using the measured temperature of the fluid entering and leaving the ground according to the following; 𝑇_𝑚 = ^𝑇^𝑖𝑛^{+ 𝑇}^𝑜𝑢𝑡

2 . It has been shown that using 𝑇_𝑚 will result in an overestimation of 𝑅_𝑏 (Marcotte and Pasquier, 2008). A Distributed Thermal Response Test (DTRT), like the one performed in this study, uses fibre optic cables along the depth of the borehole to measure the temperature in order to take these variations into consideration.

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2 THEORETICAL BACKGROUND

2.1 Ground source Heat Pump

A ground source heat pump system (GSHP) consists of an evaporator, a compressor a condenser and the borehole heat exchanger (BHE). This system uses the near constant ground temperature for heating or cooling purposes where heat is either extracted or injected to the ground (Figure 1).

The basic concept of a heat pump is the transfer of heat from a heat source with low temperature, in this case the ground, to the heat sink with a higher temperature than the heat source, this type of cycle is referred to as a vapour-compression cycle.

BHEs are one of the common ways to exchange heat with the ground; boreholes are drilled into the ground with collector pipes installed in them, such as U-pipes. In heating mode, an antifreeze solution is circulated through these pipes in order to transfer heat from the surrounding bedrock and transfer it to the heat pump to be turned into usable energy in the form of heating. For cooling purposes, the heat is rejected into the surrounding ground, cooling the antifreeze solution (Figure 2).

The design of a GSHP system depends on several parameters including the length of the boreholes, the type of filling material, the ground thermal properties and the thermal resistance of the borehole.

Figure 1 Ground Source Heat Pump System (Acuna, 2010).

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Figure 2 Heat pump in cooling and heating mode.

2.1.1 Coefficient of Performance

The Coefficient of Performance of a heat pump calculates the efficiency of the heat pump system by taking the ratio of the thermal power produced by the system to the electrical power required to drive the heat pump, Equation 1 shows that the higher the value of COP, the more efficient the system.

𝐶𝑂𝑃 = 𝑄̇_{𝑡ℎ𝑒𝑟𝑚𝑎𝑙}

𝑄̇_𝑒𝑙 (1)

Where 𝑄̇_{𝑡ℎ𝑒𝑟𝑚𝑎𝑙} is the thermal power output and 𝑄̇_𝑒𝑙 is the electric power input. The above equation differs for a heat pump operating in heating mode (𝐶𝑂𝑃_{ℎ𝑒𝑎𝑡𝑖𝑛𝑔}) and cooling mode (𝐶𝑂𝑃_{𝑐𝑜𝑜𝑙𝑖𝑛𝑔}) according to Figure 3 and Equations 2 and 3.

Figure 3 Schematic diagram of a heat pump.

Where 𝑇_𝑐 is the cold temperature at the cold end of the system, 𝑇_ℎ is the hot temperature at the hot end of the system, Q̇_h is the useful heating power produced by the system and Q̇_c the useful cooling power produced by the system.

𝐶𝑂𝑃_{ℎ𝑒𝑎𝑡𝑖𝑛𝑔} = 𝑄̇_ℎ

𝑄̇_𝑒𝑙 (2)

𝐶𝑂𝑃_{𝑐𝑜𝑜𝑙𝑖𝑛𝑔} = 𝑄̇_𝑐

𝑄̇_𝑒𝑙 (3)

Summer Winter

Cooling Mode Heating Mode Cooling System Heating System

Heat Pump ^C Heat Pump

old Heat

Cold Heat Heat

Cold

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The COP of a heat pump is highly dependent on the temperature of the heat source and the output temperature of the heat pump as can be seen in Figure 4. As Figure 4 shows, the smaller the temperature difference between the condenser and evaporator, the higher the efficiency.

Figure 4 Temperature difference effect on COP.

2.2 Secondary Fluid Flow Rate and Efficiency

The effect of the secondary fluid mass flow rate on the BHE system has previously been studied by He (1996), Granryd (2002), Granryd (2007), Karlsson et al. (2008), Finn et al. (2008) and Madani et al. (2010).

Most studies were conducted to analyze the optimal secondary fluid mass flow rate which yields maximum COP and maximum heat capacity, (Granryd, 2007), Finn et al. (2008) and Madani et al.

(2010).

Madani et al. studied the effect of the secondary fluid mass flow rate on the heat distribution along the borehole, the pumping power and efficiency, the heating and cooling capacity and the overall performance of the system. The experimental results concluded that the thermal contact between U-pipe channels increases with decreasing secondary fluid mass flow rate and that increasing the secondary fluid mass flow rate results in more uniform heat distribution extracted along the pipes.

Their modelling results conclude that there is an optimum flow rate that yields a maximum overall COP at a given compressor speed, of a variable capacity heat pump equipped with a variable speed pump on the secondary fluid side. It was also shown that the secondary fluid mass flow rate may increase the heat pump heating capacity at high compressor speeds by increasing the flow rate if the compressor is unable to cover the desired peak load.

The data is simulated as can be viewed in Figure 5 (Madani et al., 2010) using the simulation tool Engineering Equation Solver (EES). The minimum mass flow rate in the simulated data is 0.38 kg/s. According to the simulated data results, the maximum COP yielded for a compressor frequency of 50 Hz was for a mass flow rate of 0.5 kg/s after which the COP begins to decline with increasing mass flow rate. The simulated results give an idea of what would have been expected had the experiment performed for the study in this thesis continued for higher mass flow rates.

Temperature Difference Condenser- Evaporator Coefficient of Performance

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6

Figure 5 Variation of the overall COP of the system based on the secondary fluid mass flow rate: different colours show different compressor frequencies (Madani et al. 2010).

2.2.1 Flow Regime

The amount of heat transferred is dependent on the type of flow regime of the secondary fluid through the pipes. Turbulent flow occurs at higher velocities and is characterized by its chaotic and unpredictable nature as compared to laminar flow which occurs for lower velocities and is characterized by the particles flowing in an orderly fashion in layers parallel to each other with no mixing between the layers (Figure 6). The nature of turbulent flow allows more heat to be transferred than through laminar flow. This is because for laminar flow, the convection in the secondary fluid may give rise to higher thermal resistances between the BHE pipes and the secondary fluid and a higher temperature difference is required to operate as compared to turbulent flow. A non-dimensional parameter called Reynolds number can be used to determine the type of flow regime,

𝑅𝑒 =𝜌 ∙ 𝑈_𝑎𝑣𝑔∙ 𝑑

𝜇 (4)

Where 𝑈_𝑎𝑣𝑔 is the average fluid velocity [m/s], 𝑑 is the pipe diameter [m], 𝜌 is the density [kg/m³] µ is the dynamic viscosity [kg/m s]. Note that ^𝜌_𝜇 = 𝜈 which is the kinematic viscosity [m²/s].

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7

According to the theory of pipe flow (Incropera, 2011), for fully developed flow, the transition period between laminar and turbulent flow occurs around Re > 2300, however for completely turbulent conditions, a higher Reynolds number is required, Re>10000. The COP is expected to increase as the flow transitions from laminar to turbulent.

Figure 6 Turbulent and laminar flow in pipes.

2.3 Pressure Drop

A pressure drop (∆𝑃_𝑓) in the BHE pipes during steady flow can occur due to friction according to Equation 5 also known as the Darcy-Weisbach equation. The exact solution for the Darcy friction factor can be solved using either the Moody-diagram or the Colebrook-White equation (Colebrook, 1939). This pressure drop affects the pumping power and is dependent on the secondary fluid flow rate inside the pipes. The thermal resistances between the fluid flow and the BHE pipes may increase with laminar flow due to the convection in the fluid side and it is therefore desired to keep the flow turbulent. Keeping the flow turbulent means increasing the pumping power and with it increases the pressure drop, ∆𝑃. It is therefore necessary to keep the flow turbulent while, at the same time, using as low pumping power as possible to reduce the pressure drop and increase the efficiency.

𝑄̇_{𝑝𝑢𝑚𝑝,𝑖𝑛} = ∆𝑃 ∙ 𝑉̇

𝜂_{𝑝𝑢𝑚𝑝} (5)

The pressure drop ∆𝑃_𝑓 due to friction is determined according to the following:

∆𝑃_𝑓 = 𝑓𝑈² 2𝑔∙ 𝐿

𝐷 (6)

𝑓 =64

𝑅𝑒 for 𝑅𝑒 ≤ 2300 (7)

1

√𝑓 = −2.0𝑙𝑜𝑔 [(𝑒/𝐷 3.7)

1.11

+ 2.51

𝑅𝑒√𝑓] for 𝑅𝑒 ≥ 2300 (8) LAMINAR FLOW

TURBULENT FLOW

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8

Where 𝑒 is the pipe roughness coefficient 𝑒 = 3 ∙ 10⁻⁶ [𝑚] for a typical polyethylene pipe (engineeringtoolbox.com), 𝑉̇ [m³/s] is the volume flow rate, 𝑈 [m/s] is the fluid velocity, 𝜂_{𝑝𝑢𝑚𝑝} is the pump efficiency and 𝑓 is the friction.

The pump efficiency can be described as the ratio between the input power and the output power of the pump according to Equation 9 and Equation 10.

𝜂_{𝑝𝑢𝑚𝑝} = 𝑄̇_{𝑝𝑢𝑚𝑝,𝑜𝑢𝑡}

𝑄̇_{𝑝𝑢𝑚𝑝,𝑖𝑛} (9)

𝜂_{𝑝𝑢𝑚𝑝} = 𝜌𝑔𝑉̇𝐻

𝑄̇_{𝑝𝑢𝑚𝑝.𝑖𝑛} (10)

Where 𝐻 is the head [m] which is the height of the column of fluid above the suction inlet.

2.4 Borehole Heat Exchangers

Heat is extracted by drilling one or more wells in which collector pipes are installed. A common collector used in Sweden is the U-pipe collector; a plastic, polyethylene, U-shaped tube through which an antifreeze, called secondary fluid, circulates. This secondary fluid (ethanol) transfers the heat from the ground to the heat pump.

In this case, an aqueous solution of 16% ethanol is circulated through a U-pipe installed in a 260 m deep borehole and is heated through heat exchanges with the surrounding bedrock. Fiber optic cables are placed through the U-tube to measure inlet and outlet temperatures as well as the fluid temperatures along the borehole depth and in the borehole water.

The boreholes used for the experiments in this paper are named BHE4 and BHE5. The latter was used to evaluate the effect of the secondary fluid flow rate on the COP of the system while BHE4 was used to study the effects of the borehole water temperature on the borehole thermal resistance.

Figure 7 shows how the borehole was divided into 12 sections of 20 meters each, in order to analyze the BHE system. The first 10 meters and the last 10 meters at a depth of 250 m from the ground surface are neglected in order to eliminate the influences of the ambient air as well as the hemispherical heat transfer around the bottom of the borehole (Acuna, 2010).

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9

𝑇_𝑏

Figure 7 Borehole sections studied (Acuna, 2010).

2.4.1 Borehole Thermal Resistance

The design of the BHE system greatly depends on the borehole thermal resistance denoted 𝑅_𝑏 (Claesson and Hellström, 1988) and (Hellström, 1991). A high thermal resistance will result in a lower efficiency of the GSHP system as opposed to lower resistance. This is because high values of 𝑅_𝑏 result in higher temperature differences between the borehole wall and the secondary fluid.

The borehole resistance depends on the resistances of the BHE pipes, the secondary fluid, the filling material and possible contact resistances as can be seen in Figure 8 and Equation 11.

Figure 8 Resistances in borehole.

𝑅_𝑏= 𝑅_{𝑓𝑙𝑢𝑖𝑑}+ 𝑅_{𝑝𝑖𝑝𝑒}+ 𝑅_{𝑓𝑖𝑙𝑙𝑖𝑛𝑔}+ 𝑅_{𝑐𝑜𝑛𝑡𝑎𝑐𝑡} (11) Different methods have been proposed to analyze the borehole thermal resistance as summarized by Lamarche et al. (2010). Most of these models analyze heat transfer in grouted boreholes, with no expressions for calculating the heat transfer in the groundwater of groundwater-filled boreholes.

Studies on grouted boreholes include Paul (1996), Hellström (1991) and Sharqawy et al. (2009).

The Paul method is widely used and is based on experimental results and two dimensional finite element program to express the grout thermal resistance (Equation 12). This method is based on

𝑅_𝑏

𝑇_𝑓 𝑇𝑔𝑟𝑜𝑢𝑛𝑑

𝑅_{𝑔𝑟𝑜𝑢𝑛𝑑}

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10

borehole parameters, including shank spacing, borehole diameter (𝑟_𝑏), U-pipe diameter (𝑟_𝑝) and grout conductivity (𝜆_{𝑔𝑟𝑜𝑢𝑡}).

𝑅_{𝑔𝑟𝑜𝑢𝑡} = 1

𝛽₀(𝑟_𝑏 𝑟_𝑝)

𝛽₁

𝜆_{𝑔𝑟𝑜𝑢𝑡} (12)

Where the coefficients 𝛽₀ and 𝛽₁ depend on the spacing (shank spacing) between the two legs of the U-pipe. Equation 12 is used to calculate the total borehole thermal resistance in Equation 11.

2.4.2 Convective Heat Flow and Freezing in Groundwater-filled Boreholes

Convective flow occurs in groundwater-filled boreholes due to temperature and density gradients around the BHE, and influences the heat transfer in the borehole by affecting the borehole thermal resistance, 𝑅_𝑏. The value of 𝑅_𝑏 is decreased in convective flow as compared to stagnant water. The heat transfer rate as well as the temperature in the water influences the size of this convective flow.

The effect of the convective heat flow on 𝑅_𝑏 has previously been studied using both heat injection and heat extraction tests. In 1999, Kjellsson et al., performed a laboratory heat injection test showing that 𝑅_𝑏 decreased with an increase in heat injection rate. Gustafsson (2008), and Gustafsson et al. (2011) built on previous work, using TRTs and Computer Fluid Dynamic modelling (CFD) to further confirm that the lower the temperature and injection rates, the higher the borehole thermal resistance. It was later shown (Gustafsson, 2006) that if 𝑅_𝑏 increased from 0.07 K m/W to 0.1 K m/W for a fictive BHE system with 15 boreholes, more than 200 m increase was required in borehole length which was calculated using the design program Earth Energy Designer (EED). Heat injection tests involve temperatures higher than 10 °C in the boreholes.

However, water has the largest density around 4 °C and when passing this temperature, the convective flow is stopped and restarted in the opposite direction resulting in an increase in 𝑅_𝑏. Therefore, 𝑅_𝑏 will vary more during heat extraction tests as compared to heat injection tests.

The borehole thermal resistance is lower for the largest convective flow which is reached just before 0 °C as the material parameters change and phase change energy is released affecting the heat transfer rate (Gustafsson et al., 2011). This can be studied with a heat extraction test, which can also be used to evaluate the effect on 𝑅_𝑏 as the groundwater temperature falls below 0 ° and freezing occurs. This does not necessarily always cause problems, but in some cases, the ice causes high pressure in the borehole. This happens when water is trapped between ice formations and eventually freezes causing an overpressure in the water due to the expansion of the ice which may result in the deformation of the U-pipes. This in turn affects the flow of the secondary fluid in the pipes and can hence have an effect on the overall performance of the system.

As ice is formed, material parameters change and latent heat is released during the phase change further affecting the borehole thermal resistance by increasing it above its value at 0 °C. When the entire borehole has frozen, 𝑅_𝑏becomes constant with only conductive heat transfer through the ice. (Gustafsson et al., 2011). These effects are closely studied by Gustafsson et al., (2011) using both measurements and model simulations to evaluate the changes in 𝑅_𝑏 during a heat exctraction test.

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11

Gustafsson et al., (2011) suggested a method that allowed the borehole thermal resistance to change between different time intervals. This method is more time consuming but allows a better understanding of the changes in 𝑅_𝑏.

2.5 Thermal Response Test

Mogensen (1983) was the first to suggest a method to determine the ground thermal conductivity and borehole thermal resistance in a BHE. He developed the thermal response test (TRT), an in- situ experiment that can be used to evaluate the heat transfer performance of a borehole heat exchanger and the ground properties. In his experiment, a constant heat power was extracted from the ground by circulating a fluid into a pilot borehole and the fluid temperature was logged. Based on this method, mobile TRT equipment was later developed in the nineties (Figure 9) by Eklöf and Gehlin (1996) and Austin (1998) for both heat injection and heat extraction experiments.

Figure 9 Thermal response test unit (Gehlin, 2002).

During a TRT, the fluid is first circulated through the BHE without thermal power, thermal power is then extracted (or injected) from (or to) the surrounding ground by circulating a secondary fluid in BHE pipes and the inlet and outlet temperatures are measured and logged over time.

The measured data during a TRT can be analysed using numerical or analytical methods which will be further explained in section 2.6.

One of the main uses of the TRT method today, is to evaluate the effective ground thermal conductivity (λ) and the borehole thermal resistance (𝑅_𝑏) which are necessary for the design of the borehole heat exchanger. These are evaluated by analysing the logged temperature response data.

Evaluating 𝑅_𝑏 through a TRT yields mean values of the borehole thermal resistance and the ground thermal conductivity as only inlet and outlet temperatures are measured. However, these parameters may vary along the depth of the borehole and assuming 𝑅_𝑏 to be constant could overestimate its value. Fuijii et al. (2006) was able to determine the variations of the ground thermal conductivity along the depth of the borehole. However, the variation of the borehole thermal resistance was evaluated a few years later by Acuna et al. (2010) who measured the distributed temperature measurement along the BHE.

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12

A Distributed Thermal Response Test (DTRT) can be carried out to more accurately evaluate 𝑅_𝑏 and hence improve the design of the BHE. A DTRT can measure the borehole thermal resistance’s variation as the secondary fluid is measured and logged at different depths of the borehole using fiber optic cables through which laser light pulses are sent. A detailed explanation of how the Distributed Temperature Sensing (DTS) during a DTRT works can be found in Acuna (2010).

The undisturbed ground temperature is measured by circulating a fluid with no heat power for 43 hours (Figure 10) and has an average value of around 8.328 ºC.

Figure 10 Undisturbed ground temperature profile.

The ground thermal conductivity that is used for the calculations in this paper is determined in a previous DTRT carried out by Acuna (2010). It is evaluated along each borehole section during the recovery phase of the DTRT, neglecting the first 15 hours of the test (Figure 11). The values of 𝜆 range between 2.60 W/mK and 3.62 W/mK with an average of 3.09 W/mK.

0 1020 3040 50 6070 8090 100110 120130 140 150160 170180 190200 210220 230 240250 260

7.5 8 8.5 9 9.5

Depth [m]

Temperature [ºC]

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13

Figure 11 Ground thermal conductivity, λ for each section (Acuna,2010).

In this thesis two separate DTRTs are carried out in two different boreholes, BHE4 and BHE5.

BHE5 is used to evaluate the effect of the secondary fluid mass flow rate on the COP of the system.

In BHE4, an experiment is carried out to examine the effect of the borehole water temperature on the borehole thermal resistance.

2.6 Thermal Response Test analysis

Analysis methods for determining the ground thermal conductivity were early developed by Ingersoll and Plass (1948) and Carslaw and Jaeger (1959).These methods mainly focused on evaluating the ground thermal conductivity whereas Mogensen (1983) later suggested that a TRT could also be used to determine the borehole thermal resistance.

To analyse the data results from the TRT measurements, analytical methods such as the Infinite Line Source (Ingersoll and Plass, 1948) and Infinite Cylinder Source (Carlslaw and Jaeger, 1959) models can be used, as well as numerical approaches such as the parameter estimation method.

Ingersoll used Kelvin’s (1882) line source theory to model the radial heat transfer in a borehole heat exchanger.

1 2 3 4 5 6 7 8 9 10 11 12

2.50 3.00 3.50

Section

λ [W/mK]

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14 2.6.1 Infinite Line Source Model

In this study 𝑅_𝑏 is calculated using the Infinite Line Source Model (ILS); an analytical, one- dimensional, heat conduction model which considers the temperature difference between the fluid and the undisturbed ground as a function of time.

The ILS model is based on the following assumptions:

- The BHE is a linear source of infinite length and the thermal properties of the borehole are neglected (thermal mass of the fluid, pipes and groundwater).

- Constant heat transfer rate with pure radial heat conduction where convection is neglected.

- The surrounding ground is infinite and homogenous.

The temperature field is expressed as a function of time (𝑡) at a distance (𝑟) from the line source with a constant heat injection/extraction rate per unit length (𝑄̇^′).

The heat rate 𝑄̇^′ [W/m] per borehole length is calculated using the difference between the inlet fluid temperature (𝑇_{𝑓,𝑖𝑛}) and the outlet fluid (𝑇_{𝑓,𝑜𝑢𝑡}) temperature as follows:

𝑄̇^′= 𝑚̇𝑐(𝑇_{𝑓,𝑖𝑛} − 𝑇_{𝑓,𝑜𝑢𝑡})

𝐿 (13)

Where 𝑐 [J/kg K] is the fluid’s specific heat, 𝑚̇ [kg/s] is the measured mass flow rate and 𝐿 [m] is the borehole length.

The specific heat is determined using Melinder (2007) calculations and Ignatowicz (2014) measured values. The secondary fluid is an aqueous solution of ethanol, 16% in weight, which is the most common secondary fluid used in Sweden in GSHP systems. Figure 12 shows the specific heat plotted as a function of the fluid temperature.

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15

Figure 12 Specific heat as a function of the fluid temperature.

The temperature, 𝑇(𝑡, 𝑟) is calculated as follows:

𝑇(𝑡, 𝑟) − 𝑇_𝑔𝑟,∞ = 𝑄̇^′

4𝜋𝜆∫ 𝑒^−𝑢 𝑢 𝑑𝑢

∞ 𝑟_𝑏² 4𝜋𝜆

= 𝑄̇^′

4𝜋𝜆𝐸₁( 𝑟_𝑏²

4𝜋𝜆) , 𝐹𝑜 = 𝛼𝑡

𝑟_𝑏² (14) Where 𝑇_𝑔𝑟,∞[K] is the undisturbed ground temperature, Fo is the Fourier number, 𝜆 [W/m K] is the ground thermal conductivity, 𝑟 [m] the distance from the line source, in this case at the borehole wall 𝑟= 𝑟_𝑏 , α is the ground thermal diffusivity [m² /s] and 𝐸₁ is an exponential integral that can be approximated by a series expansion (Abramowitz and Stegun, 1964) as follows:

𝐸₁(𝑋) = − 𝛾 − 𝑙𝑛(𝑋) − ∑(−1)^𝑛

∞

𝑛=1

𝑋

𝑛 ∙ 𝑛! ≅ 𝑙𝑛(𝑋) − 𝛾 (15) Where 𝛾 is Euler’s constant ( 𝛾 ≈ 0.5772) and 𝑋 = ^𝑟²

4𝛼𝑡 = ¹

4𝐹𝑜

The ILS model is recommended to be used for Fourier numbers 𝐹𝑜 ≥ 20 (Ingersoll and Plass, 1948). In addition to that, the early hours of the test before the thermal process can reach near steady state are neglected.

4.365 4.370 4.375 4.380 4.385 4.390 4.395 4.400

0 2 4 6 8 10

Specific Heat [J/kg K]

Temperature [ºC]

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16

The temperature at the borehole wall (𝑇_𝑏) is calculated according to the following:

𝑇_𝑏= 𝑄̇^′

4𝜋𝜆(𝑙𝑛 (4𝛼𝑡

𝑟² ) − 𝜆) + 𝑇_𝑔𝑟,∞ (16)

The borehole thermal resistance (𝑅_𝑏) is a defining parameter when designing the borehole, it is determined as the difference between the secondary fluid temperature (𝑇_𝑓) and the borehole wall temperature (𝑇_𝑏) for the specific heat transfer rate,

𝑅_𝑏= 𝑇_𝑓− 𝑇_𝑏

𝑄̇^′ (17)

Hence, the fluid temperature as a function of time 𝑇_𝑓(𝑡) can be calculated according to the following:

𝑇_𝑓(𝑡) = 𝑄̇^′

4𝜋𝜆(𝑙𝑛 (4𝛼𝑡

𝑟² ) − 𝜆) + 𝑄̇^′∙ 𝑅_𝑏+ 𝑇_𝑔𝑟,∞ (18)

Where 𝑇_𝑓is the mean of the inlet and outlet fluid temperatures:

𝑇_𝑓= 𝑇_{𝑓,𝑖𝑛}+ 𝑇_{𝑓,𝑜𝑢𝑡}

2 (19)

Equation (18) can be expressed as a linear equation:

𝑇_𝑓(𝑡) = 𝑘 ∙ 𝑙𝑛(𝑡) + 𝑚 (20)

Where 𝑘 is the slope of the curve and is related to the ground thermal conductivity (λ) and 𝑚 is related to the ground thermal resistance (𝑅_𝑏). Hence the following equations for these parameters can be expressed as:

𝜆 = 𝑄̇^′

4𝜋𝑘 (21)

𝑅_𝑏 =𝑇_𝑓𝑚− 𝑇_𝑔𝑟,∞

𝑄̇^′ − 1

4𝜋𝜆[(𝑙𝑛 (4𝛼𝑡

𝑟² ) − 𝛾)] (22)

Keeping the power supply constant during the experiment was not possible since the heat transfer rate varied. Therefore, in order to take the varying heat fluxes into account and estimate the temperature evolution, the Temporal Superposition Principle (Ingersoll et al., 1954) is used to

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calculate the mean temperature at the borehole wall, 𝑇_𝑏(Equation 24) as described by Eskilson (1987) and Hellström (1991). Eskilson (1987), Yavuzturk and Spitler (1999) and Bernier et al. (2004) also contributed to the work on temporal superposition. Temporal superposition is carried out by superposing the heat transfer rate as a stepwise function of time (Figure 13).

The superposition principle can be applied both in time and space to any temperature response factor such as the ILS model explained above as well as the Infinite Cylindrical Source model explained in Section 2.6.2. In the experimental analysis, the ILS method is used with the application of the temporal superposition taking into account the varying heat rate.

Figure 13 Temporal Superposition principle of heat transfer rate per unit length.

𝑇_𝑏= 𝑇_𝑔𝑟,∞+ 1

4𝜋𝜆∑(𝑄̇_𝑖^′

𝑛

𝑖=1

− 𝑄̇_𝑖−1^′ )𝐸₁( 𝑟_𝑏²

4𝛼(𝑡 − 𝑡_𝑖−1)) (23)

2.6.2 Infinite Cylinder Source Model

The Infinite Cylinder heat Source model (ICS) introduced by (Carlsaw and Jaeger, 1959) is an analytical method which assumes the heat source to be an infinite cylinder with a constant heat flux surrounded by an infinite homogenous ground. The ICS approach introduces an equivalent diameter to model the two pipes of a U-pipe heat exchanger.

𝑇(𝑟, 𝑡) =^𝑄̇^′

𝜆 ∙ 𝐺(𝐹_𝑜, 𝑝) = ^𝑄̇_𝜆^′∙ 𝐺 (^𝛼𝑡

𝑟², ^𝑟

𝑟₀) (24)

Where 𝐺(𝐹𝑜, 𝑝) is the thermal response factor for ICS model (Ingersoll et al., 1954) and is expressed as:

𝐺(𝐹𝑜, 𝑝) = 1

𝜋²∫ (𝑒^−𝐹^𝑜^𝛽²− 1)

𝐽₁²(𝛽) + 𝑌₁²(𝛽)∙ [𝐽₀(𝑝𝛽)𝑌₁(𝛽) − 𝐽₁(𝛽)𝑌₀(𝑝𝛽)]

𝛽²

∞

0

𝑑𝛽 (25)

𝑄′̇₂ 𝑄̇′1

𝑄′̇₃

time 𝑄′ ̇[𝑊/𝑚]

time 𝑄̇^′[𝑊/𝑚]

𝑄̇₁^′

𝑄̇₂^′

𝑄̇₃^′

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18

Where 𝐽₀, 𝐽₁, 𝑌₀ 𝑎𝑛𝑑 𝑌₁ are the Bessel functions of the first and second kind of order 0 and 1 respectively.

3 FIELD EXPERIMENTS

The experiments were carried out in Hammarbyhöjden in South of Stockholm where a ground source heat pump installation supplies domestic hot water and comfort heating to an apartment building. Six water filled boreholes are installed with borehole diameters of 140mm, separated from each other by at least 4 meters. The groundwater level is around 5.5 m giving an active borehole length of 254.5 m. An aqueous solution of 16% ethanol volume concentration filled the polyethylene U-pipes installed in the boreholes. A diagram of the GSHP installation can be seen in Figure 14 (Acuna, 2010). Two separate experiments were carried out, for each experiment; the system was connected to two different heat pumps.

Figure 14 Fiber loop sketch of BHE4 and BHE5 (Acuna, 2010).

3.1 The Effect of the Secondary Fluid Flow Rate on the Performance of the System The first experiment was carried out in order to evaluate the effect of varying the secondary fluid flow rate on the performance of the heat pump and was conducted in BHE5 (Figure 14). The flow is adjusted by the regulation valve and the measurements are done at 10 different mass flow rates with two compressor speeds (Table 2) in a U-Pipe BHE. The heat pump used in this system was a variable capacity heat pump scroll compressor equipped with vapour injection and permanent magnet motor, more details on the experimental setup can be read in Section 3.2. The test was run for a total of five and a half hours, a longer test would have provided more conclusive results but that was not possible due to a shortage of time.

The mass flow rate has been previously shown (Madani et al., 2010) to have an effect on the thermal resistances inside the borehole, the pressure drop, the heat distribution in the borehole as well as the overall COP of the GSHP system.

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To evaluate the effects of the mass flow rate on the COP of the system, a heat extraction experiment was performed on BHE5 with the goal of studying the effect of the secondary fluid mass flow rate on the performance of the GSHP system. This was done by adjusting the flow rate in time dependent steps and plotting it against the COP. The fluid density, kinematic viscosity and heat capacity are attained using Melinder (2007) calculations.

The installation allowed a maximum flow rate of 0.372 l/s in BHE5 and was systematically decreased to 0.193 l/s in 10 time steps while measuring the temperature for each step. A larger range with higher mass flow rates would have been desired in order to draw a conclusive observation of the optimal mass flow rate to maximize COP. The duration of each time step differed for each flow rate adjustment and was calculated according to the following:

𝑡 =2𝐿

𝑈 (26)

Where 𝐿 [m] is the depth of the borehole and 𝑈 [m/s] is the speed of the flow.

Step Duration(min) 1 21.31

2 22.12 3 22.81 4 23.74 5 25.88 6 27.54 7 29.19 8 30.41 9 34.75 10 41.12

Table 1 Duration of each time step for flow rate adjustment.

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20 Compressor

Speeds [rpm]

Electric Power [kW]

Flow Rate [kg/s]

Thermal Power [kW]

Re COP

4000 2.17 0.372 9.31 3317 4.29

4000 2.16 0.358 8.97 3117 4.08

4000 2.17 0.347 8.85 2933 4.08

4000 2.18 0.334 8.67 2818 3.98

3000 1.59 0.307 6.74 2599 4.25

3000 1.59 0.288 6.57 2437 3.97

3000 1.60 0.271 6.32 2289 3.81

3000 1.60 0.261 6.30 2187 3.87

3000 1.59 0.228 6.02 1899 3.66

3000 1.59 0.193 5.60 1587 3.53

Table 2 Characteristics of DTRT experiment.

The compressor speed was set to 4000 𝑟𝑝𝑚 at a power of around 2.18 kW for the first 90 minutes of the test with an initial flow rate of 0.372 kg/s. It was then lowered to 3000 rpm for the remainder 4 hours of the test with a power of about 1.6 kW and the flow rate was systematically decreased to 0.193 kg/s. This was done in order to allow a wider range of mass flow rates.

The power was measured using a power meter (Figure 16) and then plotted for anomalies and averaged for each time step in order to calculate the COP (Figure 15). The inlet and outlet temperatures were logged and the COP calculated.

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Figure 15 Power during time step 6 with a standard deviation of 2.7 W.

3.2 Experimental Setup

A variable capacity heat pump scroll compressor equipped with vapour injection and permanent magnet motor (Figure 17) is used to analyse the performance of the heat pump. The heat pump extracts heat from BHE5 (Figure 16) by circulating the secondary fluid along the BHE, the temperature of the fluid is then lifted by the compressor to reach the heating demand of the building. More details about this heat pump are available in Awan (2012). The temperatures are measured with eight thermocouples and are logged for analysis using a software called ClimaCheck with the compressor power being measured with a Hameg power meter (Figure 17).

The fluid mass flow rate was measured and adjusted using a Brunata HGS-R6 flow meter along with an STA-D regulation valve connected to the borehole.

Figure 16 Hameg power meter.

1.584 1.586 1.588 1.59 1.592 1.594 1.596 1.598 1.6

4.1 4.2 4.3 4.4 4.5 4.6 4.7

Power [kW]

Time [Hr]

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22

Figure 17 Experimental setup of the heat pump.

The measurements were processed using Excel for plotting and analysis. The results from this experiment are meant to help optimize the design of the GSHP system and suggest improved efficiency by evaluating the COP of the system.

3.3 Effect of the Borehole Water Temperature on the Borehole Thermal Resistance The aim of the second experiment was to investigate the effect of the borehole water temperature on the borehole thermal resistance by a heat extraction DTRT that lasted for five and a half hours.

A longer test would have been desired but that was not possible. The aim was to study the effect of the borehole water temperature on the borehole resistance as it passes 4 ºC and investigate the changes in the convective flow and their effect on 𝑅_𝑏. It was also expected to extract enough heat from the ground to allow the borehole water to reach freezing point in order to investigate its effect on 𝑅𝑏 as well as the probable damages on the BHE system, however this was not possible.

This experiment was conducted on BHE4 and the system connected to a Viessmann Vitocal 200- G heat pump with a power of 12 kW (Figure 18).

The geometry of the BHE as well as the properties of the heat carrier fluid were needed in order to carry out the calculations for the borehole thermal resistance. During the test, the temperatures were measured using fiber optic cables and logged along the depth of the borehole including the inlet and outlet temperatures and the borehole water temperature. Data for the temperatures were saved every 5 minutes and the logged measurements were exported to Excel for processing. Code was then written in Excel for the Infinite Line Source Model and Temporal Superposition calculations in order to calculate and plot the variation of the borehole thermal resistance as the borehole water temperature dropped. Below is the detailed step-by-step method for the evaluation of 𝑅_𝑏.

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- The measured values for the fluid temperature, water temperature, undisturbed ground temperature and power were averaged for each evaluated section.

- The specific heat was plotted against the fluid temperature and an average value for each evaluated section was calculated using Melinder (2007)

- The ground thermal conductivity was determined for each section using predetermined values (Figure 11) by Acuna (2010).

- The specific heat and ground thermal conductivity were used to determine the ground thermal diffusivity, α which is used to calculate the Fourier number as can be seen in Equation 14.

- The Infinite Line Source model along with the superposition principle is then applied according to Equation 23 to calculate the borehole wall temperature, 𝑇_𝑏.

- 𝑇_𝑏 is then used to calculate 𝑅_𝑏 according to Equation 17, and 𝑅_𝑏 is plotted against time and the water temperature for each evaluated section which can be viewed in section 4 below.

3.4 Experimental Setup

To investigate the effect of the borehole water temperature on the borehole resistance, a Viessmann Vitocal 200-G heat pump was used (Figure 18) with a power of 12kW. This heat pump was connected to BHE4 through which heat was extracted from the ground and the borehole water temperature reached below 4 ºC.

Figure 18 Viessmann Vitocal 200-G heat pump (right: www.viessmann.co.uk).

4 RESULTS

4.1 The Effect of the Secondary Fluid Mass Flow Rate on the Overall Performance of the System

The results of the in-situ measurements can be viewed in Figure 19 and Figure 21. The compressor was run for two different compressor frequencies, 50 Hz (3000 rpm) and around 67 Hz (4000 rpm).

The effect of the mass flow rate on the COP can be seen in Figure 19 and Figure 21 which shows that for mass flow rates up to 3.72 kg/s COP increases with increasing secondary fluid mass flow rate for a compressor frequency of 50 Hz. The minimum mass flow rate was chosen to be 0.193

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24

kg/s in order to capture the transition of turbulent flow to laminar flow which can clearly be observed as the slight drop in Figure 19 and Figure 21 around 0.271 kg/s for a Reynolds number of around 2300 which is in accordance to theory. From that point, a sharper increase in COP can be observed which is due to the more favourable turbulent conditions. The COP increased with 0.72 from the lowest mass flow rate to the highest during the experiment, a total increase of efficiency of 16.9%.

Figure 19 Secondary mass flow rate and Reynolds number effect on the efficiency for a compressor frequency of 50Hz.

Figure 20 shows that Reynolds number increases with increasing mass flow rate and that turbulent flow which is achieved around Re ≥ 2300 is reached for a mass flow rate of 0.271 kg/s.

Figure 20 Reynolds number development along the mass flow rate at a compressor frequency of 50 Hz.

1500 1900 2300 2700

3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3

0.18 0.21 0.24 0.27 0.30

Reynolds Number

COP

Mass Flow Rate [kg/s]

1500 1700 1900 2100 2300 2500 2700

0.18 0.23 0.28 0.33

Re

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25

The experiment was first run for a compressor frequency of around 67 Hz and then lowered to 50 Hz. It can be observed in Figure 21 that the same COP can be achieved for both compressor frequencies of 50 Hz with a flow rate of 0.288 kg/s and compressor frequency of 67 Hz with a flow rate of 0.334 kg/s. This may indicate that a lower mass flow rate in combination with a lower compressor speed is able to achieve the same efficiency as a higher mass flow rate and compressor frequency would achieve making the former more energy and cost efficient. The maximum COP yielded with a compressor frequency of 50 Hz (3000 rpm) is COP = 4.25 with a mass flow rate of 0.307 kg/s. The maximum COP yielded for a compressor frequency of 67 Hz (4000 rpm is COP

= 4.29 with a mass flow rate of 0.372 kg/s.

Figure 21 Mass flow rate and compressor frequency effect on efficiency.

4.2 The Effect of the Borehole Water Temperature on the Borehole Resistance

The results of the heat extraction DTRT were plotted for 12 different sections of the borehole. As can be viewed in Figure 23 the water temperature in the borehole 𝑇_{𝑤,𝑎𝑣𝑔} reaches just below 4 ºC where, as mentioned above, the water reaches its largest density and hence the borehole thermal resistance is expected to be the highest, (Gustafsson et al., 2011).

The fluid temperature in each borehole section is averaged and plotted as can be seen in Figure 25 below for the entire experiment. The temperature difference between the sections decreases along the depth of the borehole.

Figure 22 shows the power extracted during the heat extraction phase from hour 187 to hour 193.

The power varies along the borehole depth and is not constant for each section.

3.20 3.40 3.60 3.80 4.00 4.20 4.40

0.18 0.23 0.28 0.33 0.38

COP

50 Hz 67 Hz