Thermal Performance Insight on a Ground Coupled Heat Pump

Dalya Samara

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)

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 (푅푏). A TRT results in mean values of λ and 푅푏which 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 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. 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

푐 Fluid Specific Heat [퐽/푘푔퐾]

푑 Pipe Diameter [푚]

퐸1 Exponential Integral

푓 Friction Factor [−]

L Borehole Length [푚]

퐻 Head [푚]

∆푃푓 Pressure Drop due to Friction [푃푎]

푄̇푡ℎ푒푟푚푎푙 Thermal Power [푊]

푄̇푐 Cooling Power [W]

푄̇푒푙 Electrical Power [푊]

푄̇ℎ Heating Power [푊]

푄̇푝푢푚푝 Pumping Power [푊]

푄̇ ′ Heat Rate per Unit Length [푊/푚] 푟 Radius [푚]

푟푏 Borehole Radius [푚]

푟푝 Pipe radius [푚]

푚̇ Mass Flow Rate [푘푔/푠]

푅푏 Borehole Thermal Resistance [푚 퐾/ 푊]

푅푐표푛푡푎푐푡 Contact Thermal Resistance [푚 퐾/ 푊]

푅푓푙푢𝑖푑 Fluid to Pipe Thermal Resistance [푚 퐾/푊]

푅푓𝑖푙푙𝑖푛푔 Resistance of Filling Material [푚 퐾/푊]

푅푔푟표푢푡 Grout Resistance [푚 퐾/푊]

푅푝𝑖푝푒 Pipe Thermal Resistance [푚 퐾/푊]

푅푒 Reynolds Number [−]

푡 Time [푠]

푇푏 Borehole Wall Temperature [퐾]

푇푐 Cold Temperature in Heat Pump [퐾]

푇푓 Mean Secondary Fluid Temperature [퐾]

푇푓,𝑖푛 Inlet Fluid Temperature [퐾]

푇푓,표푢푡 Outlet Fluid Temperature [퐾]

푇푔푟,∞ Undisturbed Ground Temperature [퐾]

푇ℎ Hot Temperature in Heat Pump [퐾]

∆푇 Temperature Difference [퐾]

푈푎푣푔 Average Fluid Velocity [푚/푠]

푉̇ Volumetric Flow Rate [푚3/푠]

µ Dynamic viscosity [푘푔/푚푠]

훽0, 훽1 Shape Factor Coefficients (Paul’s Method) [−]

휈 Kinematic Viscosity [푚2/푠] Λ Ground Thermal Conductivity [푊/푚 퐾]

훾 Euler’s Constant [−]

α Ground Thermal Diffusivity [푚2/푠]

휂푝푢푚푝 Pump efficiency

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

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 34 Temperatures of the fluid Tf, avg3, at the borehole wall Tb3, in the borehole water Tw, avg3 and the power Q3 ′in section 3...... 34 Figure 35 Borehole thermal resistance, Rb3 along time for section 3...... 35 Figure 36 Borehole thermal resistance, Rb3 versus borehole water temperature for section 3...... 35 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 38 Borehole thermal resistance, Rb4 along time for section 4...... 37 Figure 39 Borehole thermal resistance, Rb4 versus borehole water temperature for section 4...... 37 Figure 40 Temperatures of the fluid Tf, avg5, at the borehole wall Tb5, in the borehole water Tw, avg5 and the power Q5 ′in section 5...... 38 Figure 41 Borehole thermal resistance, Rb5 along time for section 5...... 39 Figure 42 Borehole thermal resistance, Rb5 versus borehole water temperature for section 5...... 39 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 44 Borehole thermal resistance, Rb6 along time for section 6...... 41 Figure 45 Borehole thermal resistance, Rb6 versus borehole water temperature, Tw, avg6 for section 6...... 41 Figure 46 Temperatures of the fluid Tf, avg7, at the borehole wall Tb7, in the borehole water Tw, avg7 and the power Q7′ in section 7...... 42 Figure 47 Borehole thermal resistance, Rb7 along time for section 7...... 43 Figure 48 Borehole thermal resistance, Rb7 versus borehole water temperature, Tw, avg7 for section 7...... 43 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 51 Borehole thermal resistance, Rb8 versus borehole water temperature, Tw, avg8 for section 8...... 45 Figure 52 Temperatures of the fluid Tf, avg9, at the borehole wall Tb9, in the borehole water Tw, avg9 and the power Q9′ in section 9...... 46 Figure 53 Borehole thermal resistance, Rb9 along time for borehole section 9...... 47 Figure 54 Borehole thermal resistance, Rb9 versus borehole water temperature, Tw, avg9 for section 9...... 47 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 56 Borehole thermal resistance, Rb10 along time for borehole section 10...... 49 Figure 57 Borehole thermal resistance, Rb10 versus borehole water temperature, Tw, avg10 for section 10...... 49 Figure 58 Temperatures of the fluid Tf, avg11, at the borehole wall Tb11, in the borehole water Tw, avg11 and the power Q11′ in section 11...... 50 Figure 59 Borehole thermal resistance, Rb11 along time for borehole section 11...... 51 Figure 60 Borehole thermal resistance, Rb11 versus borehole water temperature, Tw, avg11 for section 11...... 51 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 62 Borehole thermal resistance, Rb12 along time for borehole section 12...... 53 Figure 63 Borehole thermal resistance, Rb12 versus borehole water temperature, Tw, avg12 for section 12...... 53 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 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

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, 푄̇푡ℎ푒푟푚푎푙

(thermal power delivered by the system) to the power input 푄̇푒푙 (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.

1

(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 (푅푏).

A TRT results in mean values of λ and 푅푏which 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 (푇푚) is calculated using the measured temperature of the fluid entering and leaving the 푇 + 푇 ground according to the following; 푇 = 푖푛 표푢푡 . It has been shown that using 푇 will result in 푚 2 푚 an overestimation of 푅푏 (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.

2

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.

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

3

Cooling Mode Heating Mode

Cooling System Heating System

Heat Cold

Heat Pump Heat Pump

Heat

Cold Cold Heat Summer Winter

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.

푄̇푡ℎ푒푟푚푎푙 퐶푂푃 = (1) 푄̇푒푙

Where 푄̇푡ℎ푒푟푚푎푙 is the thermal power output and 푄̇푒푙 is the electric power input. The above equation differs for a heat pump operating in heating mode (퐶푂푃ℎ푒푎푡𝑖푛푔) and cooling mode

(퐶푂푃푐표표푙𝑖푛푔) according to Figure 3 and Equations 2 and 3.

Figure 3 Schematic diagram of a heat pump.

Where 푇푐 is the cold temperature at the cold end of the system, 푇ℎ 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.

푄̇ℎ 퐶푂푃ℎ푒푎푡𝑖푛푔 = (2) 푄̇푒푙

푄̇푐 퐶푂푃푐표표푙𝑖푛푔 = (3) 푄̇푒푙

4

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.

Performance Coefficient Coefficient of

Temperature Difference Condenser- Evaporator

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.

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). 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, 휌 ∙ 푈푎푣푔 ∙ 푑 푅푒 = (4) 휇

3 Where 푈푎푣푔 is the average fluid velocity [m/s], 푑 is the pipe diameter [m], 휌 is the density [kg/m ] 휌 µ is the dynamic viscosity [kg/m s]. Note that = 휈 which is the kinematic viscosity [m2/s]. 휇

6

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.

LAMINAR FLOW

TURBULENT FLOW

Figure 6 Turbulent and laminar flow in pipes. 2.3 Pressure Drop

A pressure drop (∆푃푓) 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, ∆푃. 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.

∆푃 ∙ 푉̇ 푄̇푝푢푚푝,𝑖푛 = (5) 휂푝푢푚푝

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

푈2 퐿 ∆푃 = 푓 ∙ (6) 푓 2푔 퐷

64 푓 = for 푅푒 ≤ 2300 (7) 푅푒

1 푒/퐷 1.11 2.51 = −2.0푙표푔 [( ) + ] for 푅푒 ≥ 2300 (8) √푓 3.7 푅푒√푓

7

Where 푒 is the pipe roughness coefficient 푒 = 3 ∙ 10−6 [푚] for a typical polyethylene pipe 3 (engineeringtoolbox.com), 푉̇ [m /s] is the volume flow rate, 푈 [m/s] is the fluid velocity, 휂푝푢푚푝 is the pump efficiency and 푓 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.

푄̇푝푢푚푝,표푢푡 휂푝푢푚푝 = (9) 푄̇푝푢푚푝,𝑖푛

휌푔푉̇ 퐻 휂푝푢푚푝 = (10) 푄̇푝푢푚푝.𝑖푛

Where 퐻 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).

8

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

푅푏 (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 푅푏 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.

푇푏 푇푓 푇푔푟표푢푛푑

푅 푅 푏 푔푟표푢푛푑 Figure 8 Resistances in borehole.

푅푏 = 푅푓푙푢𝑖푑 + 푅푝𝑖푝푒 + 푅푓𝑖푙푙𝑖푛푔 + 푅푐표푛푡푎푐푡 (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

9 borehole parameters, including shank spacing, borehole diameter (푟푏), U-pipe diameter (푟푝) and grout conductivity (휆푔푟표푢푡).

1 푅푔푟표푢푡 = 훽1 푟푏 (12) 훽0 ( ) 휆푔푟표푢푡 푟푝

Where the coefficients 훽0 and 훽1 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, 푅푏. The value of 푅푏 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 푅푏 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 푅푏 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 푅푏 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 푅푏. Therefore, 푅푏 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 푅푏 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, 푅푏 becomes 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 푅푏 during a heat exctraction test.

10

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 푅푏.

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 (푅푏) which are necessary for the design of the borehole heat exchanger. These are evaluated by analysing the logged temperature response data.

Evaluating 푅푏 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 푅푏 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.

11

A Distributed Thermal Response Test (DTRT) can be carried out to more accurately evaluate

푅푏 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.

Temperature [ºC] 7.5 8 8.5 9 9.5 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 Depth [m] Depth 150 160 170 180 190 200 210 220 230 240 250 260

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 휆 range between 2.60 W/mK and 3.62 W/mK with an average of 3.09 W/mK.

12

λ [W/mK] 2.50 3.00 3.50 1

2

3

4

5

6

Section 7

8

9

10

11

12

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.

13

2.6.1 Infinite Line Source Model

In this study 푅푏 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 (푡) at a distance (푟) from the line source with a constant heat injection/extraction rate per unit length (푄̇ ′).

The heat rate 푄̇ ′ [W/m] per borehole length is calculated using the difference between the inlet fluid temperature (푇푓,𝑖푛) and the outlet fluid (푇푓,표푢푡) temperature as follows:

푚̇ 푐(푇푓,𝑖푛 − 푇푓,표푢푡) 푄̇ ′ = (13) 퐿 Where 푐 [J/kg K] is the fluid’s specific heat, 푚̇ [kg/s] is the measured mass flow rate and 퐿 [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.

14

4.400

4.395

4.390

4.385

4.380

Specific Heat [J/kg K] [J/kg Heat Specific 4.375

4.370

4.365 0 2 4 6 8 10 Temperature [ºC]

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

The temperature, 푇(푡, 푟) is calculated as follows:

푄̇ ′ ∞ 푒−푢 푄̇ ′ 푟2 훼푡 푇(푡, 푟) − 푇 = ∫ 푑푢 = 퐸 ( 푏 ) , 퐹표 = 푔푟,∞ 푟2 1 2 (14) 4휋휆 푏 푢 4휋휆 4휋휆 푟푏 4휋휆

Where 푇푔푟,∞[K] is the undisturbed ground temperature, Fo is the Fourier number, 휆 [W/m K] is the ground thermal conductivity, 푟 [m] the distance from the line source, in this case at the borehole 2 wall 푟= 푟푏 , α is the ground thermal diffusivity [m /s] and 퐸1 is an exponential integral that can be approximated by a series expansion (Abramowitz and Stegun, 1964) as follows:

∞ 푋 퐸 (푋) = − 훾 − 푙푛(푋) − ∑(−1)푛 ≅ 푙푛(푋) − 훾 (15) 1 푛 ∙ 푛! 푛=1

푟2 1 Where 훾 is Euler’s constant ( 훾 ≈ 0.5772) and 푋 = = 4훼푡 4퐹표

The ILS model is recommended to be used for Fourier numbers 퐹표 ≥ 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.

15

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

푄̇ ′ 4훼푡 푇 = (푙푛 ( ) − 휆) + 푇 (16) 푏 4휋휆 푟2 푔푟,∞

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

푇푓 − 푇푏 푅 = (17) 푏 푄̇ ′

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

푄̇ ′ 4훼푡 푇 (푡) = (푙푛 ( ) − 휆) + 푄̇ ′ ∙ 푅 + 푇 (18) 푓 4휋휆 푟2 푏 푔푟,∞

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

푇푓,𝑖푛 + 푇푓,표푢푡 푇 = (19) 푓 2

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

푇푓(푡) = 푘 ∙ 푙푛(푡) + 푚 (20)

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

푄̇ ′ 휆 = (21) 4휋푘

푇푓푚 − 푇푔푟,∞ 1 4훼푡 푅 = − [(푙푛 ( ) − 훾)] (22) 푏 푄̇ ′ 4휋휆 푟2

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

16 calculate the mean temperature at the borehole wall, 푇푏 (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.

푄′̇ [푊/푚]

푄̇′ 2 푄̇ ′1 ̇ 푄 ′3

time

′ 푄̇ [푊/푚]

̇ ′ 푄1

̇ ′ 푄2 time 푄̇ ′ 3 Figure 13 Temporal Superposition principle of heat transfer rate per unit length.

푛 1 푟2 ̇ ′ ̇ ′ 푏 푇푏 = 푇푔푟,∞ + ∑(푄𝑖 − 푄𝑖−1)퐸1 ( ) (23) 4휋휆 4훼(푡 − 푡𝑖−1) 𝑖=1

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.

푄̇ ′ 푄̇ ′ 훼푡 푟 푇(푟, 푡) = ∙ 퐺(퐹표, 푝) = ∙ 퐺 ( 2 , ) (24) 휆 휆 푟 푟0

Where 퐺(퐹표, 푝) is the thermal response factor for ICS model (Ingersoll et al., 1954) and is expressed as:

2 1 ∞ (푒−퐹표훽 − 1) [퐽 (푝훽)푌 (훽) − 퐽 (훽)푌 (푝훽)] 0 1 1 0 (25) 퐺(퐹표, 푝) = 2 ∫ 2 2 ∙ 2 푑훽 휋 0 퐽1 (훽) + 푌1 (훽) 훽

17

Where 퐽0, 퐽1, 푌0 푎푛푑 푌1 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.

18

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:

2퐿 푡 = (26) 푈

Where 퐿 [m] is the depth of the borehole and 푈 [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.

19

Compressor Electric Flow Thermal Re COP Speeds Power Rate Power [rpm] [kW] [kg/s] [kW]

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 푟푝푚 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.

20

1.6 1.598 1.596 1.594 1.592

Power [kW] Power 1.59 1.588 1.586 1.584 4.1 4.2 4.3 4.4 4.5 4.6 4.7 Time [Hr]

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.

21

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 푅푏. 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 푅푏 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 푅푏.

22

- 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, 푇푏. - 푇푏 is then used to calculate 푅푏 according to Equation 17, and 푅푏 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

23 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%.

Reynolds Number 1500 1900 2300 2700 4.3 4.2 4.1 4.0

3.9 COP 3.8 3.7 3.6 3.5 0.18 0.21 0.24 0.27 0.30 Mass Flow Rate [kg/s]

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.

2700

2500

2300

2100 Re

1900

1700

1500 0.18 0.23 0.28 0.33

Mass Flow Rate [kg/s]

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

24

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.

4.40

4.20

4.00

3.80 COP 3.60

3.40

3.20 0.18 0.23 0.28 0.33 0.38 Mass Flow Rate [kg/s] 50 Hz 67 Hz

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 푇푤,푎푣푔 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.

25

-1300 Section 1

-1100 Section 2 Section 3 -900 Section 4 Section 5

-700 Section 6

Section 7 Power [W] Power -500 Section 8

Section 9

-300 Section 10

Section 11 -100 Section 12

186 187 188 189 190 191 192 193 Time [Hr]

Figure 22 Heat transfer rate for each section in the borehole during the cooling phase. Figure 23 shows the borehole water temperature profile for each borehole section during the whole experiment along time. It can be seen how the water temperature decreases sharply as the heat extraction starts around hour 187 and begins to recover as the experiment ends around hour 193.

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

Section 8 Temperature [ºC] Temperature 5 Section 9 Section 10 4 Section 11 3 Section 12 0 50 100 150 200 250 300 350 Time [Hr]

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

26

The borehole water temperature measurements were averaged and plotted in Figure 24 for each borehole section during the cooling phase during the five and a half hours of the experiment. It is during this phase that the borehole thermal resistance is plotted against the water temperature in order to evaluate the effects of the water temperature on 푅푏 as it passes 4ºC.

7.5 Section 1

7 Section 2 6.5 Section 3 6 Section 4 Section 5 5.5 Section 6

5 Section 7

Section 8

Temperature [ºC] Temperature 4.5 Section 9 4 Section 10 3.5 Section 11

3 Section 12 186 187 188 189 190 191 192 193 Time [Hr]

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

27

10 Section 1

9 Section 2

8 Section 3

7 Section 4

6 Section 5

5 Section 6

Section 7

4 Temperature [ºC] Temperature Section 8 3 Section 9 2 Section 10 1 Section 11 0 0 50 100 150 200 250 300 350 Section 12 Time [Hr] Figure 25 Fluid temperature profiles for each borehole section along time. Blue rectangle marks the experiment.

The fluid temperatures for each section of the borehole were measured and averaged a long time and plotted during the cooling phase of the experiment and can be viewed in Figure 26. The borehole thermal resistance is calculated during this phase of the experiment.

4.4 Section 1

3.9 Section 2

3.4 Section 3 Section 4 2.9 Section 5

2.4 Section 6

1.9 Section 7 Temperature [ºC] Temperature Section 8 1.4 Section 9 0.9 Section 10

0.4 Section 11 187 188 189 190 191 192 193 Section 12 Time [Hr]

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

28

Some instantaneous temperature profiles were plotted along the depth of the borehole (Figure 27) for the secondary fluid for each hour of the experiment. It shows the evolution of the secondary fluid temperature along time. It can be seen that all the temperature profiles move towards colder temperatures along time, and the temperatures vary less along time as the experiment progresses. The lowest fluid temperature reached during the experiment is around -1.25 ºC and the maximum temperature is around 3.92 ºC. Figure 27 shows that the true average temperature along the depth cannot be determined as the mean of the inlet and outlet temperatures as is done for a conventional

TRT. These average temperatures for each section are used to evaluate the variations of 푅푏 along the depth.

Temperature [C] -2 -1 0 1 2 3 4 5 0 20 40 60 80 100 120

140 Depth[m] 160 180 200 220 240 260 187 hr 188 hr 189 hr 190 hr 191 hr 192 hr

Figure 27 Instantaneous secondary fluid temperature profiles along the depth of borehole. The density of the water decreases as its temperature increase above 4 ºC, which means the water temperature is higher at the borehole wall and cooler near the pipes where the secondary fluid circulates. This results in convective flow with the water rising close to the borehole wall and sinking close to the pipe wall. Below 4 ºC however, the water is heavier for higher temperatures resulting in the water rising near the pipe wall and sinking near the borehole wall. This is the reason the convective flow changes direction as the water temperature passes 4 ºC (Gustafsson et al., 2011).

The borehole thermal resistance is evaluated along the depth of the borehole during hours 187 to

193 and is plotted for 12 sections. This is to evaluate the variations of 푅푏 by considering the changes

29 in the ground thermal properties, the secondary fluid properties and the thermal power as well as the changes in temperatures of the borehole wall, the borehole water and the secondary fluid temperature along the depth of the borehole. 푅푏 is plotted using two different power averages, the first is a total average of the power during the entire test. This yielded smoother results as compared to the second average which was every 25 minutes. The 25 minute power average was used for the calculations of 푅푏 whereas the total power average was used for comparison purposes as can be seen in Figure 65, Figure 66, Figure 67 and Figure 68. The temperatures during the cooling phase of the secondary fluid 푇푓,푎푣푔, at the borehole wall 푇푏, in the borehole water 푇푤,푎푣푔 and the power 푄̇′ are plotted for sections all 12 sections of the borehole along time. The fluid and borehole water temperatures decrease along time with the water temperature decreasing at a slower pace. The temperature at the borehole wall also shows a trend of moving toward cooler temperatures along time.

For borehole section 1, Figure 29 shows a peak in the borehole resistance around hour 190.7 with a value of aproximateley 0.116 m K/W. This maximum value is acheived at a borehole water temperature of around 5 ºC (Figure 30) which is above the theoretically expected 4 ºC. The value of Rb1 increases with around 16.8% from the lowest (0.096 m K/W) to the highest value (0.116 m K/W).

The heat extraction rate for section 1 has a total average of around 44.4 W/m during the cooling phase as can be viewed in Figure 28.

8 20

7 10

6 0

5 -10

4 -20

3 -30 [W/m] Power Temperature [ºC] Temperature

2 -40

1 -50

0 -60 186 187 188 189 190 191 192 Time [Hr] Tf,avg Tw,avg Tb Q'

Figure 28 Temperatures of the fluid 푇푓,푎푣푔1, at the borehole wall 푇푏1, in the borehole water 푇푤,푎푣푔1 and the ′̇ power 푄1 in section 1.

30

0.12

0.115

0.11

0.105

RbK/W] [m 0.1

0.095

0.09 187 188 189 190 191 192 193 Time [Hr]

Figure 29 Borehole thermal resistance, 푅푏1 along time for section 1.

0.12

0.115

0.11

0.105

RbK/W] [m 0.1

0.095

0.09 4.5 5 5.5 6 6.5 7 Temperature [ºC]

Figure 30 Borehole thermal resistance, 푅푏1 versus borehole water temperature, 푇푤.푎푣푔1 for section 1.

31

For borehole section 2, Figure 32 shows a peak in the borehole resistance around hour 188.5 with a value of aproximateley 0.089 m K/W. This maximum value is acheived at a borehole water temperature of around 4.54 ºC (Figure 33) slightly above 4 ºC. The value of Rb2 increases with around 22.5 % from the lowest (0.069 m K/W) to the highest value (0.089 m K/W).

The heat extraction rate for section 2 has a total average of around 47.4 W/m during the cooling phase as can be viewed in Figure 31.

7 20

6 10

0 5 -10 4 -20 3

-30 [W/m] Power Temperature [ºC] Temperature 2 -40

1 -50

0 -60 186 187 188 189 190 191 192 Time [Hr] Tf,avg Tw,avg Tb Q'

Figure 31 Temperatures of the fluid 푇푓,푎푣푔2, at the borehole wall 푇푏2, in the borehole water 푇푤,푎푣푔2 and the ′̇ power 푄2 in section 2.

32

0.095

0.09

0.085

0.08

0.075 RbK/W] [m 0.07

0.065

0.06 187 188 189 190 191 192 193 Time [Hr]

Figure 32 Borehole thermal resistance, 푅푏2 along time for section 2. 0.095

0.09

0.085

0.08

RbK/W] [m 0.075

0.07

0.065 3 3.5 4 4.5 5 5.5 6 Temperature [ºC]

Figure 33 Borehole thermal resistance, 푅푏2 versus borehole water temperature, 푇푤.푎푣푔2 for section 2.

33

For borehole section 3, Figure 35 shows a peak in the borehole resistance around hour 191 with a value of aproximateley 0.079 m K/W. This maximum value is acheived at a borehole water temperature of around 3.5 ºC (Figure 36) slightly below 4 ºC. The value of Rb3 increases with around 10.4% from the lowest (0.07 m K/W) to the highest value (0.079 m K/W).

The heat extraction rate for section 3 has a total average of around 52.2 W/m during the cooling phase as can be viewed in Figure 34.

7 20

10 6 0 5 -10

4 -20

3 -30

Temperature [ºC] Temperature -40 2 -50 1 -60

0 -70 186 187 188 189 190 191 192 Time [Hr] Tf,avg Tw,avg Tb Q'

Figure 34 Temperatures of the fluid 푇푓,푎푣푔3, at the borehole wall 푇푏3, in the borehole water 푇푤,푎푣푔3 and the ′̇ power 푄3 in section 3.

34

0.08

0.078

0.076

0.074 RbK/W] [m

0.072

0.07 187 188 189 190 191 192 193 Time [Hr]

Figure 35 Borehole thermal resistance, 푅푏3 along time for section 3.

0.08

0.078

0.076

0.074 RbK/W] [m

0.072

0.07 3 3.5 4 4.5 5 5.5 6 Temperature [ºC]

Figure 36 Borehole thermal resistance, 푅푏3 versus borehole water temperature for section 3.

35

For borehole section 4, Figure 38 shows a peak in the borehole resistance around hour 189.3 with a value of aproximateley 0.316 m K/W. This maximum value is acheived at a borehole water temperature of around 4.47 ºC (Figure 39) slightly above 4 ºC. The results in section 4 are in accordance with the theory regarding the behaviour of 푅푏 around a water temperaure of 4 ºC. The value of Rb4 increases with around 18% from the lowest (0.259 m K/W) to the highest value (0.316 m K/W).

The heat extraction rate for section 4 has a total average of around 20.3 W/m during the cooling phase as can be viewed in Figure 37 which is lower than the heat extraction rate for other sections. As can be seen in Figure 38 and Figure 39, the borehole thermal resistance is considerably higher in section 3 than in other sections of the borehole.

8 20

15 7

10 6 5

5 0

4 -5 Power [W] Power -10 Temperature [ºC] Temperature 3

-15 2 -20

1 -25

0 -30 186 187 188 189 190 191 192 Time [Hr] Tf,avg Tw,avg Tb Q'

Figure 37 Temperatures of the fluid 푇푓,푎푣푔4, at the borehole wall 푇푏4, in the borehole water 푇푤,푎푣푔4 and the ′̇ power 푄4 in section 4.

36

0.32

0.31

0.3

0.29

0.28 RbK/W] [m 0.27

0.26

0.25 187 188 189 190 191 192 193 Time [Hr]

Figure 38 Borehole thermal resistance, 푅푏4 along time for section 4.

0.32

0.31

0.3

0.29

0.28 RbK/W] [m 0.27

0.26

0.25 3.5 4 4.5 5 5.5 6 6.5 Temeperature [ºC]

Figure 39 Borehole thermal resistance, 푅푏4 versus borehole water temperature for section 4.

37

For borehole section 5, Figure 41 shows a peak in the borehole resistance around hour 192.5 with a value of aproximateley 0.128 m K/W. This maximum value is acheived at a borehole water temperature of 3.9 ºC (Figure 42) slightly above 4 ºC. The value of Rb5 increases with around 25.2 % from the lowest (0.096 m K/W) to the highest value (0.128 m K/W).

The heat extraction rate for section 5 has a total average of around 40.1 W/m during the cooling phase as can be viewed in Figure 40.

8 20

7 10

6 0 5 -10 4 -20

3 Temperature [ºC] Temperature -30 2

1 -40

0 -50 186 187 188 189 190 191 192 Time [Hr]

Tf,avg Tw,avg Tb Q'

Figure 40 Temperatures of the fluid 푇푓,푎푣푔5, at the borehole wall 푇푏5, in the borehole water 푇푤,푎푣푔5 and the ′̇ power 푄5 in section 5.

38

0.13

0.125

0.12

0.115

0.11

RbK/W] [m 0.105

0.1

0.095

0.09 187 188 189 190 191 192 193 Time [Hr]

Figure 41 Borehole thermal resistance, 푅푏5 along time for section 5.

0.13

0.125

0.12

0.115

0.11

RbK/W] [m 0.105

0.1

0.095

0.09 3.8 4.3 4.8 5.3 5.8 6.3 Temperature [ºC]

Figure 42 Borehole thermal resistance, 푅푏5 versus borehole water temperature for section 5.

39

For borehole section 6, Figure 44 shows a peak in the borehole resistance around hour 191.4 with a value of aproximateley 0.155 m K/W. This maximum value is acheived at a borehole water temperature of 4.54 ºC (Figure 45) slightly above 4 ºC. The value of Rb6 increases with around 10.4 % from the lowest (0.139 m K/W) to the highest value (0.155 m K/W).

The heat extraction rate for section 6 has a total average of around 32.4 W/m during the cooling phase as can be viewed in Figure 43.

8 20

7 10 6 0 5

4 -10

3 [W/m] Power Temperature [ºC] Temperature -20 2 -30 1

0 -40 186 187 188 189 190 191 192 Time [Hr] Tf,avg Tw,avg Tb Q'

Figure 43 Temperatures of the fluid 푇푓,푎푣푔6, at the borehole wall 푇푏6, in the borehole water 푇푤,푎푣푔6 and the ̇′ power 푄6 in section 6.

40

0.155

0.15

0.145 RbK/W] [m

0.14

0.135 187 188 189 190 191 192 193 Time [Hr]

Figure 44 Borehole thermal resistance, 푅푏6 along time for section 6.

0.16

0.155

0.15

0.145 RbK/W] [m

0.14

0.135 4.3 4.8 5.3 5.8 6.3 Temperature [ºC]

Figure 45 Borehole thermal resistance, 푅푏6 versus borehole water temperature, 푇푤,푎푣푔6 for section 6.

41

For borehole section 7, Figure 47 shows a peak in the borehole resistance around hour 192 with a value of aproximateley 0.069 m K/W. This maximum value is acheived at a borehole water temperature of 4.6 ºC (Figure 48) slightly above 4 ºC. The value of Rb7 increases with around 37.5 % from the lowest (0.04 m K/W) to the highest value (0.069 m K/W).

The heat extraction rate for section 7 has a total average of around 51.4 W/m during the cooling phase as can be viewed in Figure 46.

7 20

6 10

0 5 -10 4 -20 3

-30 [W/m] Power Temperature [ºC] Temperature 2 -40

1 -50

0 -60 186 187 188 189 190 191 192 Time [Hr] Tf,avg Tw,avg Tb Q'

Figure 46 Temperatures of the fluid 푇푓,푎푣푔7, at the borehole wall 푇푏7, in the borehole water 푇푤,푎푣푔7 and the ̇′ power 푄7 in section 7.

42

0.07

0.065

0.06

0.055

RbK/W] [m 0.05

0.045

0.04 187 188 189 190 191 192 193 Time [Hr]

Figure 47 Borehole thermal resistance, 푅푏7 along time for section 7.

0.07

0.065

0.06

0.055

RbK/W] [m 0.05

0.045

0.04 4.5 4.7 4.9 5.1 5.3 5.5 5.7 5.9 6.1 6.3 Temperature [ºC]

Figure 48 Borehole thermal resistance, 푅푏7 versus borehole water temperature, 푇푤,푎푣푔7 for section 7.

43

For borehole section 8, Figure 50 shows a peak in the borehole resistance around hour 192.4 with a value of aproximateley 0.23 m K/W. This maximum value is acheived at a borehole water temperature of around 4.7 ºC (Figure 51) which is above 4 ºC. The value of Rb8 increases with around 21.5 % from the lowest (0.18 m K/W) to the highest value (0.23 m K/W).

The heat extraction rate for section 8 has average of around 25.5 W/m during the cooling phase as can be viewed in Figure 49 which is lower than the heat extraction rate for other sections. As can be seen in Figure 50 and Figure 51, the borehole thermal resistance is considerably higher in section 8 than in other sections of the borehole.

8 20

7 10 6 0 5

4 -10

3 [W/m] Power Temperature [ºC] Temperature -20 2 -30 1

0 -40 186 187 188 189 190 191 192 Time [Hr] Tf,avg Tw,avg Tb Q'

Figure 49 Temperatures of the fluid 푇푓,푎푣푔8, at the borehole wall 푇푏8, in the borehole water 푇푤,푎푣푔8and the ̇′ power 푄8 in section 8.

44

0.23

0.22

0.21

0.2

RbK/W] [m 0.19

0.18

0.17 187 188 189 190 191 192 193 Time [Hr]

Figure 50 Borehole thermal resistance, 푅푏8 along time for borehole section 8.

0.23

0.22

0.21

0.2

RbK/W] [m 0.19

0.18

0.17 4.5 5 5.5 6 6.5 Temperature [ºC]

Figure 51 Borehole thermal resistance, 푅푏8 versus borehole water temperature, 푇푤,푎푣푔8 for section 8.

45

For borehole section 9, Figure 53 shows a peak in the borehole resistance around hour 191 with a value of aproximateley 0.096 m K/W. This maximum value is acheived at a borehole water temperature of 4.9 ºC (Figure 54) well above 4 ºC. The value of Rb9 increases with around 45.7 % from the lowest (0.05 m K/W) to the highest value ( 0.096 m K/W).

The heat extraction rate for section 9 has an average of around 43.3 W/m during the cooling phase as can be viewed in Figure 52.

7 20

6 10

0 5 -10 4 -20 3

-30 [W/m] Power Temperature [ºC] Temperature 2 -40

1 -50

0 -60 186 187 188 189 190 191 192 Time [Hr] Tf,avg Tw,avg Tb Q'

Figure 52 Temperatures of the fluid 푇푓,푎푣푔9, at the borehole wall 푇푏9, in the borehole water ̇′ 푇푤,푎푣푔9 and the power 푄9 in section 9.

46

0.1

0.09

0.08

0.07

RbK/W] [m 0.06

0.05

0.04 187 188 189 190 191 192 193 Time [Hr]

Figure 53 Borehole thermal resistance, 푅푏9 along time for borehole section 9.

0.1

0.09

0.08

0.07

RbK/W] [m 0.06

0.05

0.04 4.6 5.1 5.6 6.1 6.6 Temperature [ºC]

Figure 54 Borehole thermal resistance, 푅푏9 versus borehole water temperature, 푇푤,푎푣푔9 for section 9.

47

For borehole section 10, Figure 56 shows a peak in the borehole resistance around hour 190.7 with a value of aproximateley 0.205 m K/W. This maximum value is acheived at a borehole water temperature of 5.2 ºC (Figure 57) well above 4 ºC. The value of Rb12 increases with around 51.7 % from the lowest (0.099 m K/W) to the highest value (0.205 m K/W).

The heat extraction rate for section 10 has an average of around 28.8 W/m during the cooling phase as can be viewed in Figure 55 which is lower than the heat extraction rate for other sections. As can be seen in Figure 56 and Figure 57, the borehole thermal resistance is considerably higher in section 10 than in other sections of the borehole.

7 20

6 10

5 0

4 -10

3 -20

Power [W/m] Power Temperature [ºC] Temperature 2 -30

1 -40

0 -50 186 187 188 189 190 191 192 Time [Hr] Tf,avg Tw,avg Tb Q'

Figure 55 Temperatures of the fluid 푇푓,푎푣푔10, at the borehole wall 푇푏10, in the borehole water 푇푤,푎푣푔10and ′̇ the power 푄10 in section 10.

48

0.23

0.21

0.19

0.17

0.15

RbK/W] [m 0.13

0.11

0.09

0.07 187 188 189 190 191 192 193 Time [Hr]

Figure 56 Borehole thermal resistance, 푅푏10 along time for borehole section 10.

0.21

0.19

0.17

0.15

0.13 RbK/W] [m 0.11

0.09

0.07 4.9 5.4 5.9 6.4 6.9 Temperature [ºC]

Figure 57 Borehole thermal resistance, 푅푏10 versus borehole water temperature, 푇푤,푎푣푔10 for section 10.

49

For borehole section 11, Figure 59 shows a peak in the borehole resistance around hour 190.2 with a value of aproximateley 0.23 m K/W. This maximum value is acheived at a borehole water temperature of 5.6 ºC (Figure 60) well above 4 ºC. The value of Rb11 increases with around 16.2 % from the lowest (0.187 m K/W) to the highest value (0.23 m K/W).

The heat extraction rate for section 11 has an average of around 29.6 W/m during the cooling phase as can be viewed in Figure 58 which is lower than the heat extraction rate for other sections. As can be seen in Figure 59 and Figure 60, the borehole thermal resistance is considerably higher in section 11 than in other sections of the borehole.

7 20

6 10

5 0 4 -10

3 Power [W/m] Power

Temperature [ºC] Temperature -20 2

1 -30

0 -40 186 187 188 189 190 191 192 Time [Hr] Tf,avg Tw,avg Tb Q'

Figure 58 Temperatures of the fluid 푇푓,푎푣푔11, at the borehole wall 푇푏11, in the borehole water 푇푤,푎푣푔11 and ′̇ the power 푄11 in section 11.

50

0.23

0.22

0.21

0.2 RbK/W] [m

0.19

0.18 187 188 189 190 191 192 193 Time [Hr]

Figure 59 Borehole thermal resistance, 푅푏11 along time for borehole section 11.

0.23

0.22

0.21

0.2 RbK/W] [m

0.19

0.18 5.1 5.3 5.5 5.7 5.9 6.1 6.3 6.5 6.7 Temperature [ºC]

Figure 60 Borehole thermal resistance, 푅푏11 versus borehole water temperature, 푇푤,푎푣푔11 for section 11.

51

For borehole section 12, Figure 62 shows a peak in the borehole resistance around hour 189.6 with a value of aproximateley 0.068 m K/W. This maximum value is acheived at a borehole water temperature of 5.3 ºC (Figure 63) well above 4 ºC. The value of Rb12 increases with around 25.8 % from the lowest (0.05 m K/W) to the highest value (0.068 m K/W).

The heat extraction rate for section 12 has an average of around 59.1 W/m during the cooling phase as can be viewed in Figure 61.

8 20

7 10

0 6 -10 5 -20 4

-30 Power [W/m] Power

Temperature [ºC] Temperature 3 -40 2 -50

1 -60

0 -70 186 187 188 189 190 191 192 Time [Hr] Tf,avg Tw,avg Tb Q'

Figure 61 Temperatures of the fluid 푇푓,푎푣푔12, at the borehole wall 푇푏12, in the borehole water 푇푤,푎푣푔12and ′̇ the power 푄12in section 12.

52

0.07

0.065

0.06

0.055 RbK/W] [m

0.05

0.045 187 188 189 190 191 192 193 Time [Hr]

Figure 62 Borehole thermal resistance, 푅푏12 along time for borehole section 12.

0.07

0.065

0.06 RbK/W] [m

0.055

0.05 4.8 5.3 5.8 6.3 6.8 Temperature [ºC]

Figure 63 Borehole thermal resistance, 푅푏12 versus borehole water temperature, 푇푤,푎푣푔12 for section 12.

53

Figure 64 shows the borehole thermal resistance variations along the borehole water temperature for different sections. A clear decrease in 푅푏 can be observed as the borehole water temperature passes 4-5 º퐶 for each section. Another observation is the variation of the value of 푅푏 along the depth of the borehole which increases with around 86.3 %. The lowest value of 푅푏 is 0.04 m K/W and is reached in section 7 whereas the highest value for 푅푏 is 0.316 m K/W and is reached in section 4, a difference of 0.273 m K/W. These are the variations in 푅푏 that a regular TRT cannot take into account.

0.31 Rb1 0.28 Rb2 Rb3 0.25 Rb4 0.22 Rb5 0.19 Rb6 0.16 Rb7 RbK/W] [m 0.13 Rb8 Rb9 0.1 Rb10 0.07 Rb11 0.04 Rb12 3 3.5 4 4.5 5 5.5 6 6.5 7 Borehole Water Temperature[ºC]

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

The following graphs show Rb studied for sections 4, 8 10 and 11 separately from the rest of the sections of the borehole due to the high values in these two sections. Rb is also plotted for the 12 sections using the total average power.

Due to a lower power in sections 4, 8, 10 and 11, Rb values for these four sections are higher compared to the rest of the borehole sections. The values of Rb range from 0.316 m K/W to 0.099 m K/W in these sections as can be seen in Figure 65 which are not very realistic values of

Rb compared to the other sections as well as previous work (Gustafsson et al., 2011).

54

0.33 0.3 0.27 0.24 0.21

0.18 RbK/W] [m 0.15 0.12 0.09 3.2 3.7 4.2 4.7 5.2 5.7 6.2 6.7 Borehole Water Temperature[ºC] Rb4 Rb8 Rb10 Rb11

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

It can be seen in Figure 66 that using the total average power to calculate Rb results in smoother curves as compared to using the 25 minute power average as can be seen in Figure 65. 0.31

0.28

0.25

0.22

0.19 RbK/W] [m 0.16

0.13

0.1 3.6 4.1 4.6 5.1 5.6 6.1 6.6 Borehole Water Temperature [ºC] Rb4 Rb8 Rb10 Rb11

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

Sections 1, 2, 3, 5, 6, 7, 9 and 12 have more realistic values of Rb and range from around 0.155 m K/W to 0.04 m K/W as can be seen in Figure 67.

55

0.16

0.13

0.1 RbK/W] [m 0.07

0.04 3.2 3.7 4.2 4.7 5.2 5.7 6.2 6.7 Borehole Water Temperature[ºC] Rb1 Rb2 Rb3 Rb5 Rb6 Rb7 Rb9 Rb12

Figure 67 Borehole thermal resistance for sections 1, 2, 3, 5, 6, 7, 9 and 12.

As mentioned above, calculating Rb in sections 1, 2, 3, 5, 6, 7, 9 and 12 using the total power average results in smoother plots as can be seen in Figure 68 as compared to the 25-minute power average seen in Figure 67.

0.15 Rb1

0.13 Rb2 Rb3 0.11 Rb5

0.09 Rb6 RbK/W] [m 0.07 Rb7 Rb9 0.05 Rb12 0.03 3.4 3.9 4.4 4.9 5.4 5.9 6.4 6.9 Borehole Water Temperature [ºC]

Figure 68 Borehole thermal resistance for sections 1, 2, 3, 5, 6, 7, 9 and 12 with total average power.

56

5 Comparison of Results in BHE4 with Previous Work In order to compare the results from the experiment carried out in BHE4 with previous results by Gustafsson et al. (2011) during an over 300 hour TRT experiment, 푅푏 was calculated using inlet and outlet fluid temperatures only as in a regular TRT (Figure 69). 푅푏 was then plotted and compared to Gustafsson’s plots (Figure 70) as well as the values of 푅푏 from the DTRT calculations in this report. Figure 69 and Figure 70 both show peak values of 푅푏 around 4 ºC with a smoother and wider peak in Figure 70 which could indicate that a longer test yields better results.

0.13

0.125

0.12

0.115 Rbm/W] [K

0.11

0.105 3.8 4.3 4.8 5.3 5.8 Temperature in the Borehole Water [ºC]

Figure 69 Borehole thermal resistance plotted using inlet and outlet fluid temperatures only as in regular TRT.

Figure 70 Borehole thermal resistances versus borehole water temperatures for three TRT measurements (Gustafsson et al., 2011).

57

5.1 FUTURE WORK While studying the effect of the secondary fluid flow rate on the performance of the system in BHE5, it would have been desired to repeat all the mass flow rates with different compressor speeds in order to describe the performance of the heat pump more accurately. A wider and higher range of mass flow rates could be used in order to get a more complete conclusion of the performance as the mass flow rate increases.

The heat extraction experiment performed in BHE4 studying the effect of the borehole water temperature on 푅푏 would have been more thorough had it continued for a longer time in order to evaluate 푅푏 under more stable conditions. Another interesting effect to study would have been allowing the borehole water temperature to fall below 0 ºC until ice is formed and study the effect of freezing on 푅푏 and the BHE system as a whole.

6 CONCLUSIONS The design of a GSHP system is affected by parameters such as the secondary fluid mass flow rate and the borehole thermal resistance. It was shown with an in-situ Distributed Thermal Response Test (DTRT) that increasing the secondary fluid mass flow rate up to 3.72 kg/s and keeping the flow regime turbulent increases the Coefficient of Performance (COP) of the system. Increasing the flow rate from 0.193 to 0.307 with a compressor frequency of 50 Hz yields a COP increase of approximately 16.9%.

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 around 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 achieves the same efficiency as a higher mass flow rate and compressor frequency would achieve making the former more energy and cost efficient. These results indicate that there is an optimal secondary fluid mass flow rate and compressor frequency that maximizes the efficiency of the GSHP system, sbe performed in order to define the optimum working conditions for maximizing the COP.

The borehole thermal resistance (푅푏) varies during a heat extraction/injection test and a regular Thermal Response Test (TRT) is unable to account for these variations. Therefore, a heat extraction DTRT was performed in order to investigate the effects on 푅푏 as the borehole water temperature passes 4 ºC. Water has the highest density at 4ºC and hence has the highest density at that point causing the convective flow in the borehole to slow down and restart in the opposite direction. This has been shown to increase the borehole thermal resistance as the heat transfer rate decreases during the change in the direction of the convective flow.

The change in 푅푏 is studied for 12 sections of the borehole, in order to analyse the variations along the depth of the borehole. The plots show that the value of 푅푏 varies with around 86.3 % from the lowest value of 0.04 m K/W reached in section 7 at a borehole water temperature of around 6.15 ºC to the highest value of 0.315 m K/W reached in section 4 at a borehole water temperature of around 4.5 ºC. The reason the variation is so high could be due to the fact that the heat extraction rate was not constant along the depth. In section 7 the heat extraction rate has an average of around 51.4 W/m compared to around 20.3 W/m in section 4. Another reason could be due to the temperature difference 푇푓 − 푇푏 which also varied for different sections of the borehole.

58

The reason the highest value of 푅푏 is reached at a temperature above 4ºC could be due the fact that the power of the heat pump (12 kW) used was too high for the length of the borehole (260 푚). However, lowering the power would have meant a longer wait to get results. A more suitable set up would have been lowering the power and having a shorter borehole length resulting in a lower power per unit length.

Based on these results, it is recommended to take into account the variations of 푅푏 when designing the GSHP system as it affects the design of the borehole such as borehole length as well as the working temperatures of the system.

59

7 REFERENCES

Abramowitz M., I. A. Stegun (1964) Handbook of Mathematical Functions. Dover Publications. ISBN: 0-486-61272-4 Acuña J. (2010) Improvements of U-pipe Borehole Heat Exchanger. Licentiate Thesis in Energy Technology. Stockholm: KTH

Acuña J. (2013) Distributed thermal response tests – New insights on U-pipe and Coaxial heat exchangers in groundwater-filled boreholes. [Doctoral Thesis]. Stockholm: KTH

Austin W.A (1998) Development of an in-situ system for measuring ground thermal properties. Oklahoma State University.

Awan U. (2012) Experimental Analysis of Variable Capacity Heat Pump System Equipped with Vapour Injection and Permanent Magnet Motor. Stockholm: KTH

Bernier M., P., Pinel, R. Labib R. Paillot (2004) A Multiple Load Aggregation Algorithm for Annual Hourly Simulations of GCHP Systems. Int. J. Heating, Ventilating, Air-Conditioning and Refrigeration Research 10 (471-488)

Carslaw H.S, J.C Jaeger (1959) Conduction of Heat in Solids. Great Britain: Oxford Science Publications.

Claesson J., G. Hellström (1988) Theoretical and Experimental study of the local heat transfer in a borehole with heat exchanger pipes. Fourth International Conference on Energy Storage for Building Heating and Cooling. pp. 139-143. Versailles: JIGASTOCK.

Colebrook, C. (1939) Turbulent Flow in Pipes, with Particular Reference to the Transition Region between the Smooth and Rough Pipe Laws. London: Journal of the Institution of Civil Engineers, pp. 133–156

Eklöf C., S. Gehlin (1996) TED- A Mobile Equipment for Thermal Response Test. Master Thesis. Luleå: Luleå University of Technology

Eskilson P. (1987) Thermal Analyses of Heat Extraction Boreholes. Lund: Lund Institute of Technology

Finn D., F. Murphy et al. (2008) Control algorithms for system integration of heat pumps: steady state and seasonal analysis. Proceedings of 9th IEA heat pump conference. Zurich, Switzerland

Fuijii et al. (2006) Thermal Response Test Using Optical Fiber Thermometers. GRC Transactions, 2006. – Vol. 30., Fukuoka: Kyushu University

Gehlin S. (2002) Thermal Response Test – Method, Development and Evaluation. [Doctoral Thesis]. Luleå: Luleå University of Technology

Gehlin S., O. Andersson, L. Bjelm, PG. Alm, JE. Rosberg (2015) Country Update for Sweden. Proceedings, World Geothermal Congress. Melbourn, Australia

60

Granryd E. (2002) Optimum circulation rates in indirect systems. Proceeding of the IIR International Conference on Minimum Charge Refrigerating systems. Stockholm, Sweden

Granryd E. (2007) Optimum flow rates in indirect systems. Proceedings of the International Congress of Refrigeration. Beijing, China

Granryd E. (2009) Refrigeration Engineering. Stockholm: KTH. ISBN: 978-91-7415-3

Gustafsson A-M., S. Gehlin (2006) Thermal Response Test – Power Injection Dependance. Ecostock, 2006, 10th International Conference on Thermal Energy Storage. USA: The Richard Stockton College of New Jersey

Gustafsson A-M., S. Gehlin (2008) Influence of Natural Convection in Water-filled Boreholes for GCHP. ASHARE Transactions, New York

Gustafsson A-M., I. Westerlund, G. Hellström (2010) CFD-modelling of Natural Convection in Groundwater-filled Borehole Heat Exchanger. Applied Thermal Engineering 30 Pp. 683-691

Gustafsson A-M., L. Westerlund (2011) Heat Extraction Thermal Response Test in Groundwater-filled Borehole Heat Exchanger – Investigation of the Borehole Thermal Resistance. Department of Civil, Mining and Environmental Engineering. Luleå: Luleå University of Technology

He X.D., (1996) Dynamic modelling and multivariable control of vapour compression cycles in air conditioning systems. Department of Mechanical Engineering. Doctoral Thesis. MIT.

Hellström G. (1994) Fluid to Ground Thermal Resistance in Duct Ground Heat Storage. Finland: Prodeecings of Calorstock’94, 6th International Conference on Thermal Energy Storage.

Hellström G. (1991) Ground Heat Storage, Thermal Analyses of Duct Storage Systems. [Doctoral Thesis]. Lund: KTH.

Ignatowicz M. (2014) Evaluation Of Thermophysical Properties Of Ethyl Alcohol Based Secondary Fluids. Stockholm: KTH

Incropera F. P., D.P. Dewitt (2011) Fundamentals of Heat Mass Transfer Seventh Edition. USA. ISBN: 978- 0470-50197-9

Ingersoll L.R., H. Plass (1948) Theory of the Ground Pipe Heat Source for the Heat Pump. ASHVAE Transactions, Vol. 54. Pp. 339-348

Ingersoll L.R., O.J. Zobel, A.C Ingersoll (1954) Heat Conduction: with Engineering, Geological and other Applications. University of Wisconsin Press.

Karlsson F., P. Fahlen (2008) Capacity control and optimized operation of domestic heat pump heating system. Proceeding of 9th IEA heat pump conference. Zurich, Switzerland

Kjellsson E., G. Hellström (1999) Laboratory Study of the Heat Transfer in Water-filled borehole with a c- pipe – preliminiary report. Lund, Sweden: Lund University

61

Kundu P.K., I.M Cohen, (2004) Fluid Mechanics. London: Elseiver Academic Press. ISBN: 9780- 080-555-836

Lamarche L., Kajl S., Beauchamp B. (2010) A Review of Methods to Evaluate Borehole Thermal Resistances in Geothermal Heat Pump Systems. Geothermics 39, 187-200

Madani H., J. Acuna, J. Claesson, P. Lundqvist, B. Palm (2010) The Ground Source Heat Pump: A System Analysis with a Particular Focus on the U-Pipe Borehole Heat Exchanger. 14th ASME IHTC International Heat Transfer Conference, Washington D.C

Marcotte D., P. Pasquier, (2008) On the estimation of thermal resistance in borehole thermal conductivity test. Renewable Energy 33, 2407-2415

Melinder Å. (2007) Thermophysical Properties of Aqueous Solutions Used as Secondary Working Fluids. [Doctoral Thesis]. Stockholm: KTH

Mogensen P. (1983) Fluid to Duct Wall Heat Transfer in Duct System Heat Storages. The International Conference on Subsurface Heat Storage Theory and Practice, Stockholm. pp. 652-657

Paul, N.D (1996) The effect of grout thermal conductivity on vertical geothermal heat exchanger design and performance. South Dakota: State University.

Sharqawy M., E. Mokheimer, H. Badr (2009) Effective Pipe-to-Borehole Thermal Resistance for Vertical Ground Heat Exchangers. Geothermics 38, 271-277

Yavuzturk, C., J.D. Spitler. (1999) A Short Time Step Response Factor Model for Vertical Ground Loop Heat Exchangers. ASHRAE.

62