Master of Science Thesis

KTH School of Industrial Engineering and Management

Energy Technology EGI-2017-0107 MSC

Division of applied Thermodynamics and Refrigeration

SE-100 44 STOCKHOLM

Construction and test of a new

compact TRT equipment

Linus Olausson

i

Master of Science Thesis EGI-2017-0107

MSC

Construction and test of a new compact TRT

equipment

Linus Olausson

Approved

Date

Examiner

Björn Palm

Supervisor

Alberto Lazzarotto

Commissioner

Bengt Dahlgren

Contact person

José Acuña

Abstract A relevant contribution to sustainable development can be achieved by providing efficient solutions for

heating buildings. The use of a heat pump taking heat from the bedrock with the help of a borehole heat

exchanger is a common solution in Sweden to accomplish this. In situ measurement of the thermal

conductivity of the ground by means of thermal response test is necessary for medium to large size

installations to ensure proper sizing of the borehole system.

This master thesis was done in cooperation with the department of geo energy at the company Bengt

Dahlgren. The aim was to design a new compact thermal response test equipment, test it on a coaxial

borehole heat exchanger and evaluate the test results and design a simple business model for using the

equipment commercially.

The company already had an equipment for thermal response tests, which formed the basis for the new

equipment. A literature review was done to gain knowledge on thermal response test equipment, its

components and borehole heat exchangers. Also, an evaluation of results from an earlier test of an 800 m

deep borehole with a coaxial borehole heat exchanger was made.

The project resulted in the construction of a new more compact equipment for thermal response tests with

a new, improved heating solution. Two different business models based on renting out the equipment were

designed. The equipment was tested on a 200 m deep borehole with a coaxial borehole heat exchanger. The

test indicated a thermal conductivity of 2.46 𝑊

𝑚∙𝐾 and a borehole resistance of 0.031

m∙K

W.

ii

Sammanfattning En viktig del av en hållbar utveckling är energieffektiva lösningar för uppvärmning av byggnader. En vanlig

lösning i Sverige är att använda en värmepump kopplad till en borrhålsvärmeväxlare och utnyttja

berggrunden som värmekälla. I vissa fall är det motiverat att testa bergets värmeledningsförmåga med hjälp

av ett termiskt responstest för att mer precist kunna dimensionera borrhålen.

Denna mastersuppstas gjordes i samarbete med Bengt Dahlgren geoenergi. Arbetet syftade till att designa

en kompakt utrustning för termiskt responstest, testa den nya utrustningen på en koaxial

borrhållsvärmeväxlare och utvärdera testresultatet samt att designa en enkel affärsmodell för den nya

utrustningen.

Företaget hade sedan tidigare en utrustning för termiskt responstest, som låg till grund för designen av den

nya. En litteraturstudie utfördes för att få mer kunskap om termisk responstestutrustning, dess komponenter

och borrhålsvärmeväxlare. Dessutom gjordes en utvärdering av mätresultat från ett tidigare utfört test på

ett 800m djupt borrhål med en koaxial borrhålsvärmeväxlare.

Arbetet resulterade i en ny kompaktare utrustning för termiskt responstest med en ny smart lösning för

uppvärmningen. Två olika affärsmodeller baserade på uthyrning av den nya utrustningen togs fram.

Utrustningen testades på ett 200 m djupt borrhål med en koaxial borrhålsvärmeväxlare. Borrhålet visade en

termisk värmeledningsförmåga på 2,46 𝑊

𝑚∙𝐾 och ett borrhålsmotstånd på 0,031

m∙K

W.

iii

Acknowledgments This master thesis has been fantastic! Combining practical and theoretical knowledge is something I always

wanted to do, and I could not have done it without some people.

I would like to thank

• José Acuña for giving me the opportunity to do a master thesis like this. Also for your patience

with all my questions and you understanding that it takes time to construct and that it sometimes

fails.

• Milan Stokucha for all the laughs we had during these months and for all help with the software

issues. I will always remember your solutions when life sucks.

• Erik Lindstein for all quick help with software issues.

• Axzel Sequera for help with design ideas.

• Alberto Lazzarotto for being my supervisor, thanks for all the help and good comments about the

report!

• Kenneth Weber for giving me the opportunity to test my new TRT on a coaxial BHE, and for all

the coffee and discussions we had during the test.

• Alice Geber, my colleague during the first months. It would not have been that fun without you.

All the laughs and adventures we had the whole summer, I will visit you in France (Germany) one

day!

• Helena Falk and Lena Falk for helping me with the grammatics in the text, and for being with me

the whole thesis. I could not have done it without you.

• Johan Andrén for teaching me electrics and helping me with construction of the electric box.

• Bengt Dahlgren for letting me do the master thesis, and for all the nice colleagues. Special thanks

to the geo-energy team, electric team and environmental team for taking good care of me.

• The student union Quarnevalen for letting us use your workshop. I could not have built my TRT

equipment without all your tools.

And last, but not least, thanks KTH for all these years!

Thanks, and see you in the future!

Linus Olausson \m/

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Table of contents Abstract ............................................................................................................................................................................ i

Sammanfattning ............................................................................................................................................................. ii

Acknowledgments ........................................................................................................................................................ iii

List of figures ................................................................................................................................................................ vi

List of tables ................................................................................................................................................................. vii

1 Introduction .......................................................................................................................................................... 1

1.1 Aim ................................................................................................................................................................ 2

1.2 Objectives ..................................................................................................................................................... 2

1.3 Limitations ................................................................................................................................................... 2

2 Method ................................................................................................................................................................... 3

3 Theoretical background ....................................................................................................................................... 4

3.1 Boreholes ...................................................................................................................................................... 4

3.1.1 Basics ........................................................................................................................................................ 4

3.1.2 Deep boreholes ....................................................................................................................................... 5

3.2 Borehole Heat exchangers ......................................................................................................................... 5

3.2.1 U-pipe BHE ............................................................................................................................................ 7

3.2.2 Coaxial BHE ........................................................................................................................................... 7

3.2.3 Coaxial BHEs and deep boreholes ...................................................................................................... 9

3.3 TRT .............................................................................................................................................................10

3.3.1 DTRT .....................................................................................................................................................11

3.3.2 Components ..........................................................................................................................................12

3.3.3 Evaluation of TRT data .......................................................................................................................15

3.4 Business model ..........................................................................................................................................16

4 Results ..................................................................................................................................................................19

4.1 Construction of TRT equipment ............................................................................................................19

4.1.1 TRT version 1 .......................................................................................................................................19

4.1.2 TRT version 2 .......................................................................................................................................21

4.2 Business model ..........................................................................................................................................22

4.2.1 Gap .........................................................................................................................................................22

4.2.2 Idea .........................................................................................................................................................22

4.2.3 Canvas ....................................................................................................................................................23

4.2.4 SWOT ....................................................................................................................................................24

4.3 Evaluation of data from Asker ...............................................................................................................25

4.4 Test of new TRT .......................................................................................................................................28

5 Discussion ...........................................................................................................................................................35

5.1 Construction ..............................................................................................................................................35

5.2 Asker ...........................................................................................................................................................37

v

5.3 Test of new TRT .......................................................................................................................................38

6 Conclusion ...........................................................................................................................................................40

7 References ...............................................................................................................................................................41

Appendix 1 ...................................................................................................................................................................43

Appendix 2 ...................................................................................................................................................................44

vi

List of figures Figure 1 Flow chart for existing TRT ........................................................................................................................ 2 Figure 2 Working procedure ........................................................................................................................................ 3 Figure 3 Steel casing ...................................................................................................................................................... 4 Figure 4 Geothermal energy balance (Banks, 2012) ................................................................................................ 5 Figure 5 Borehole resistances ...................................................................................................................................... 6 Figure 6 Single and double U-pipes............................................................................................................................ 7 Figure 7 Coaxial BHE types. ....................................................................................................................................... 8 Figure 8 Borehole resistance in coaxial BHE ........................................................................................................... 9 Figure 9 Temperature distribution in U-pipe ..........................................................................................................10 Figure 10 Basic TRT system ......................................................................................................................................11 Figure 11 Pump curves ...............................................................................................................................................13 Figure 12 Closed expansion vessel ...........................................................................................................................14 Figure 13 Business model Canvas ............................................................................................................................18 Figure 14 Flow chart new TRT .................................................................................................................................19 Figure 15 Dimensions TRT version 1......................................................................................................................20 Figure 16 TRT version1 .............................................................................................................................................20 Figure 17 Dimensions TRT version 2......................................................................................................................21 Figure 18 TRT version 2 ............................................................................................................................................22 Figure 19 Flow and power TRT Asker ....................................................................................................................25 Figure 20 Inlet, outlet and outdoor temperature TRT Asker ..............................................................................26 Figure 21 Borehole resistance TRT Asker with different optimization times ...................................................26 Figure 22 Thermal conductivity TRT Asker with different optimization times ...............................................27 Figure 23 Curve fit start time 30 h and 150 h optimization period.....................................................................27 Figure 24 Curve fit start time 40 h and 150 h optimization period.....................................................................28 Figure 25 Curve fit start time 50 h and 150 h optimization period.....................................................................28 Figure 26 Cutaway view BHE lid ..............................................................................................................................29 Figure 27 Cutaway view suspender solution ...........................................................................................................29 Figure 28 Flow and power TRT Norrtälje ..............................................................................................................30 Figure 29 Inlet, outlet and outdoor temperature TRT Norrtälje .........................................................................31 Figure 30 Thermal conductivity TRT Norrtälje with different optimization times .........................................31 Figure 31 Borehole resistance TRT Norrtälje with different optimization times .............................................32 Figure 32 Curve fit start time 100 h and 50 h optimization period.....................................................................32 Figure 33 Curve fit start time 105 h and 50 h optimization period.....................................................................33 Figure 34 Curve fit start time 110 h and 50 h optimization period.....................................................................33 Figure 35 Borehole resistance TRT Nortälje with higher flow ............................................................................34 Figure 36 Curve fit 50 h optimization period .........................................................................................................34 Figure 37 Inlet and outlet pressure TRT .................................................................................................................35 Figure 38 Pressure difference inlet and outlet ........................................................................................................35 Figure 39 Two TRT in series .....................................................................................................................................37 Figure 40 Filter TRT ...................................................................................................................................................39

vii

List of tables Table 1 Business model canvas description (Osterwalder & Pigneur , 2010) ...................................................17 Table 2 Components TRT version 1 .......................................................................................................................21 Table 3 Components TRT version 2 .......................................................................................................................22 Table 4 Events in the testing .....................................................................................................................................30

1

1 Introduction With the increased effect of human activities on the environment and with the current global warming trend,

sustainable solutions are necessary to provide a viable way to mitigate environmental impact for a more

sustainable future.

An effective solution consists of providing efficient heating and cooling to buildings, as the share of energy

for space heating/cooling is significant and energy savings in this area can have a large effect. In this context

heat pumps can play an important role since they can deliver much better performance compared to

traditional heating systems such as gas boilers or electrical heating. Heat pumps enable heat transfer from a

cold source to a warm source at the cost of mechanical work. The performance of a heat pump is measured

using the coefficient of performance (COP), which is the output heat over the input mechanical energy. A

common value for COP is around 3 for a standard heat pump in a villa.

A common choice in Sweden is to couple heat pumps to the ground using borehole heat exchangers (BHEs).

The bedrock can act as a heat sink or as a heat source. For cooling applications, it serves as a heat sink and

the heat is rejected from the building to the ground to maintain the indoor environment at comfort

conditions. Conversely, for heating application the ground is used as heat source and heat is pumped from

the ground to the building.

In order to properly size borehole systems it is crucial to have in situ data regarding the thermal properties

of the ground such as thermal conductivity and vertical temperature profile, and performance of the BHE

such as the borehole thermal resistance.

The state of the art methodology to calculate the thermal conductivity (λ), the temperature profile and the

borehole resistance (Rb) is the thermal response test (TRT). Other testing methodologies such as the

distributed thermal response test (DTRT) can provide additional data regarding the thermal properties along

the vertical axis of a BHE. The equipment for these tests usually consists of one or more portable boxes

mounted on a trailer. The theory behind TRT has been around since 1948 but the first document describing

the equipment and its operation was presented by Mogensen in 1983. However, it took until the 90's before

TRT was developed, and the first mobile device was built in 1995 in both the US and Sweden at the same

time, and this was done independently. The Swedish equipment called "TED" was built at Luleå University

of Technology. Both of these were based on Mogensen's concept with some modifications. Today, the

technology has spread rapidly and exists in about 40 countries (Nordell, 2011).

This master thesis was performed at the company Bengt Dahlgren AB in the Stockholm area. The company

has a TRT unit in house which consists of a flow controlled Grundfos pump of 1.5 Kw, a Nibe electric

heater of 9 kW, a Brunata flowmeter, expansion vessels, valves and electrical apparatus. A simple schematic

of the system can be seen in Figure 1.

The unit has the following shortcomings:

1. The unit is heavy (around 100 kg) and needs to be transported by a trailer.

2. The operators of the equipment have in the past experienced problems with the actuated ball valve.

The valve is no longer in use, and it is kept fully open while running tests. The flow is therefore

controlled only by the pump.

3. The heater is large, and it is not reliable during the whole duration of the test: it can sometimes stop

during the test.

4. There can be difficulties when filling up the system after it is connected to the boreholes if access

to water supply is not available. The expansion vessel has been removed from the system, and it is

now used as an open system with the circulating fluid tank as a storage tank.

2

Figure 1 Flow chart for existing TRT

1.1 Aim The aim of this study was to build a new TRT unit which addresses some of the shortcoming of currently

used rigs. This unit was be designed to be relatively light and compact for better mobility and to be suitable

for performing tests in deep boreholes. The practical knowledge along with the theoretical knowledge will

provide new guidelines on the construction of compact and flexible TRT units.

1.2 Objectives 1. Design and construction of a more compact and lighter TRT unit concept that can be produced in

larger quantities and used for testing deep BHEs.

2. Design a business model for the commercialization of the new TRT unit model.

3. Evaluation of TRT data from an 800 m borehole with coaxial BHE in Asker.

4. Field test with the new TRT in a coaxial BHE in Norrtälje.

1.3 Limitations This report focuses on the design and construction of a TRT unit, and presents choice of components

(pipes, pump, heaters, vessels etc.) and how these components were assembled into the final product. The

electrical part is not included in this study nor is the software that controls the TRT.

3

2 Method The study was carried out in 6 steps:

1. The first step was a literature study providing the required background knowledge on construction

and operation of TRT units. The TRT unit currently used at the Bengt Dahlgren was studied and

the schematic of this unit was used as the base for the design of the new unit. The existing TRT

unit was also tested in the field to get hands on experience on how a TRT rig is operated, and to

find possible improvements that could be applied to the new TRT unit.

2. Step two was a literature study specifically of BHE typologies. This phase provided the foundation

for appropriate choice of the components of TRT units capable to perform properly with different

types of BHEs, different borehole depths and temperature variation.

3. Step three was the design of the new TRT unit, selection of suitable components and construction

of the rig.

4. Step four consisted of performing a set of testing routines to assess that the unit worked properly.

The first test was to run the system without heat load to do a visual inspection to detect leakages.

5. The fifth step was to evaluate data from an already performed TRT in an 800 m deep borehole with

a coaxial BHE. This was done to increase knowledge in data evaluation and to increase knowledge

on TRT in deep boreholes.

6. The sixth step was a test of the equipment in the field on a real borehole. Data was collected and

evaluated.

7. The seventh and last step was the business model of the new TRT, where two business models

were developed.

Figure 2 shows the working procedure of all the steps described above.

Figure 2 Working procedure

Literature study of basic

knowledge about TRT and

a field trip

Litterature study on

Boreholes, BHE and

components

Find suitable components for new TRT

and construct TRT

Check that unit works

Evaluation of deepboreholeCoaxial BHE in

Asker.

Run tests in the field

Develop business

model for the new TRT

4

3 Theoretical background The following section contains the theoretical background which the report is built upon.

3.1 Boreholes

3.1.1 Basics When discussing boreholes and extracting heat from the ground some basic understanding of the ground is

needed. Boreholes are in most cases 100-200 m deep (Gehlin, et al., 2016), and the most common diameters

are 115 mm, 140 mm and 165 mm. The active borehole depth is the distance between the groundwater level

and the bottom of the borehole. Above the groundwater the borehole is air filled and the heat transfer is

low. In the most common cases when drilling a borehole, the first layer consists of a few meters of soil

before reaching the bedrock. To protect the borehole from soil material and to prevent shallow groundwater

from flowing into the borehole a steel casing is used (see Figure 3). The steel casing needs to reach two

meters below the rock surface and then be sealed against the rock. In Sweden the space between collector

and borehole wall is usually allowed to be filled with groundwater. In dry boreholes or if there is any risk of

harming the groundwater (i.e. by transport of contaminants), the borehole needs to be refilled (SGU, 2016).

Figure 3 Steel casing

There are some basic considerations regarding the ground that needs to be taken into account when

designing the borehole. The temperature in the first 15-20 m varies with the season. The average for this

temperature in Sweden is around 9-10 °C in the south and around 2 °C in the north (Erlström, et al., 2016).

Also, if the borehole is in urban areas with buildings around it, the heat flux from the building affects the

ground temperature, and it can go as deep as 100 m (Gehlin, et al., 2016). Below 100 m there will be a stable

temperature gradient along the borehole. A typical temperature gradient for Sweden is about 15-30 °C /km

(1,5-3 °C /100 m) (Erlström, et al., 2016). When extracting heat from the ground, the ground cools down

if the extraction is not in balance with the heat regeneration in the ground. The heat in the ground comes

mainly from two different sources: the insolation from the sun, which is around 100 𝑊

𝑚2 for Scandinavia,

and the geothermal heat flux from the centre of the Earth which is about 20-100 𝑚𝑊

𝑚2 with an average of 50

𝑚𝑊

𝑚2 (see Figure 4) (Banks, 2012). The thermal conductivity of the ground depends on the rock composition.

The most significant mineral for heat transfer in the most common rock is quartz with lambda of ca 7,7 𝑊

𝑚∙𝐾. High quartz content in the rock gives high thermal conductivity (Erlström, et al., 2016).

5

Figure 4 Geothermal energy balance (Banks, 2012)

3.1.2 Deep boreholes How deep the borehole can be is often limited by the drilling equipment. Most common for boreholes

supplying heat pumps is down-the-hole-hammer (DTH) drilling. The air-driven type typically has a

maximum drilling depth of around 300 m. After that the groundwater pressure is too high for the drill to

work. This is not a limiting factor for water-driven drills, which are instead limited by losses caused by rock

fractures. A limited number of water-driven DTH drilling equipment can drill to around 800 m (Gehlin, et

al., 2016).

It is hard to find a definition of what a deep borehole is, however the trend in recent years in Sweden has

been to drill deeper according to statistics (Gehlin, et al., 2015). There can be many reasons for drilling a

deeper hole. One is in situations where the available land is limited, where going deeper gives access to a

greater rock volume using less land area (Räftegård & Gehlin, 2016).

An example from a report shows that one 800 m borehole with coaxial BHE can provide the same heat

load as six conventional boreholes using U-pipes with a depth of 300 m (Holmberg, et al., 2016). Also,

higher temperatures can be reached with a deeper borehole because of the temperature gradient (Gehlin, et

al., 2016), and thereby deeper boreholes are more suitable for heat extraction than for heat injection.

Reaching temperatures high enough for electricity production is very hard in Scandinavia. In Sweden, the

borehole would need to be at least 6-7 km deep to get a temperature that is high enough (Erlström, et al.,

2016).

3.2 Borehole heat exchangers In order to extract or inject heat from/to the ground via for example a heat pump, a closed loop where a

secondary fluid is circulated can be used. The closed system gives the opportunity to use another fluid than

water since the secondary fluid is not in direct contact with the ground (Brekke , 2003). The secondary fluid

is often an antifreeze fluid as the temperatures in the ground can go below zero degrees. The heat transfer

between the fluid and the ground takes place in a collector pipe called borehole heat exhcanger (BHE). The

BHE can be of different types with different characteristics, and is often made of plastic. There are mainly

6

two different collectors on the market; the U-pipe collector, which is the most common, and the coaxial

collector (Björk, et al., 2013)

To understand how the collector behaves, there is a need to understand the heat transfer between the rock

and the secondary fluid, which depends on a thermal resistance. The thermal resistance is the sum of the

resistance in the rock and the resistance in the borehole (see Figure 5). The thermal resistance in the borehole

is the sum of three factors: resistance in the secondary fluid, resistance in the collector wall and resistance

in the filling material between the collector wall and the borehole wall (see Figure 5) (Kamarad, 2012). It is

beneficial to have low resistance in the borehole since lower resistance will lead to smaller temperature

differences between the rock and the secondary fluid. The choice of BHE has an impact on the borehole

resistance. Lowering its resistance leads to more efficient extraction of heat from the ground.

Figure 5 Borehole resistances

The heat transfer in the BHE depends on the flow characteristics, which can both be laminar and turbulent.

In most cases the flow is turbulent since the heat transfer increases with higher flow yielding lower thermal

resistance (Gehlin, 2015). With higher flow the temperature difference between the secondary fluid and the

borehole can be decreased. One problem is that the required pumping power increases rapidly with higher

flow since the friction factor in the pipe increases. The length of the collector also has an impact, since a

longer collector implies more friction losses demanding more pumping power (Björk, et al., 2013). The flow

rate needs to be optimized to get turbulent flow without getting too high friction losses in order to keep the

required pumping power down.

Another problem that needs to be taken into consideration is the short-circuiting effect. Thermal short-

circuiting occurs when the inlet pipe and the outlet pipe are affecting each other. The up-going pipe and the

down-going pipe transfer heat between each other, causing the temperature to change in the circuit. This

phenomenon should be avoided, meaning that there should be a high thermal resistance between the up-

going and down-going pipes, and low thermal resistance between the pipe and the borehole wall. The

thermal short circuiting will increase with a deeper borehole but decrease with higher flow rate in the

secondary fluid. When calculating the borehole resistance there are two types, local borehole resistance and

effective borehole resistance. The former is the resistance between the BHE and the borehole wall, while

the latter includes the local resistance as well as the short circuiting effect (Hellström, 2011).

7

3.2.1 U-pipe BHE The U-pipe BHE is the most common as mentioned earlier. They can consist of a single or double U-pipe.

In the single U-pipe BHE there are two pipes going down the borehole, which are connected at the bottom

with a U-shaped bend. The double U-pipe is almost the same but consists of two single U-pipes in the same

borehole (see Figure 6). They are both easy to install and the price is low, but the thermal performance is

low and improvements can be made (Acuña , 2010). The double U-pipe has better performance than the

single U-pipe, since it has lower thermal resistance (Brekke , 2003). Typically, a U-pipe BHE has a borehole

thermal resistance between 0.06 and 0.12 Km/W (Acuña & Palm, 2012).

Figure 6 Single and double U-pipes

The flow in these BHEs is very important as a higher flow leads to lower thermal resistance. Laminar flow

is to be avoided since it leads to high thermal resistance in the BHE. The position of the pipes in the

borehole is also important since you will have a thermal short circuiting which will increase if they are close

to each other. One way to improve this is to use spacers between the down-going and up-going pipes to

increase the space between them (Acuña , 2010).

3.2.2 Coaxial BHE The coaxial BHE consists of two tubes where one is inside the other, so called “tube in tube”. Ideally heat

transfer between the borehole and the BHE occurs only in the annular tube, the inner tube just acting like

a flow tube. The flow direction in the annular tube depends on the purpose i.e. heat injection or heat

extraction (Hellström, 2011).

There are few coaxial BHEs on the market, and few studies have been made. However, these collectors

have the potential to lower the borehole resistance and lower the pressure drop in the pipes. Even though

all this is known the collector type is still in the research phase (Westin, 2012) (Acuña & Palm, 2011). There

are different types and designs of coaxial collectors. A simple type is an open system where the fluid travels

in direct contact with the rock (see Figure 7a). Most common is a closed system with two pipes of different

dimensions. The inner pipe, which can be insulated, goes inside the bigger one (see Figure 7b). Another

type of coaxial collector consists of a central pipe surrounded by several smaller pipes (see Figure 7c). There

is also a type with a flexible pipe in direct contact with the borehole wall, with a central pipe inside. This

utilizes the full borehole diameter (see Figure 7d)(Acuña & Palm, 2011). The local borehole resistance for a

8

coaxial collector ranges between 0,015 – 0,040 Km/W, which is lower than for the U-pipe collector

(ACUÑA, 2013).

Figure 7 Coaxial BHE types.

Short-circuiting occurs in coaxial BHEs just as in U-pipe collectors, but in this case between the annular

and centre pipe. The short-circuiting effect can be decreased by adding insulation to the inner pipe and

thereby increase the thermal resistance in the wall between the pipes (Holmberg, et al., 2016). For a simple

sketch of the resistance in a coaxial BHE see Figure 8.

9

Figure 8 Borehole resistance in coaxial BHE

3.2.3 Coaxial BHEs and deep boreholes Holmberg et al. (2016) suggested that the coaxial BHE is the best solution for deep boreholes. The coaxial

BHE gives a better hydraulic performance than a conventional U-pipe. It uses a larger cross-sectional area

of the borehole to circulate the fluid that leads to lower pressure drop per meter and can thereby handle a

higher mass flow rate which lowers the short-circuiting effect. To lower it further a larger borehole diameter

can be used. Regarding flow direction in the coaxial BHE it is better to use the annular pipe as inlet for heat

extraction, and the centre pipe as inlet for heat injection. A report written by Holmberg et al. (2015),

describes the performance of a deep borehole with a coaxial BHE with a flexible pipe and a centre pipe.

The heat extraction is increasing with the depth following the thermal gradient. In an 800 m borehole about

71 % of the heat is extracted from the lower half of the borehole, and about 10 % from the first 200 m.

There are challenges with deep boreholes. For instance, deeper boreholes put more stress on materials and

equipment. When the BHE gets warmer it expands, and the absolute difference in the length of the BHE

gets bigger the longer it is. For example, a 300 m long PE100 pipe expands 0.6 m when the temperature

goes from 0 to 15 °C. This might cause the BHE to hit the bottom of the borehole, eventually leading to

breakage of the pipe. Another challenge is the fact that a deeper borehole demands a longer BHE leading

to higher pressure loss in the pipe. This makes a collector with a higher dimension more suitable in order

to keep the pump energy consumption down. The density difference between the fluid in the collector pipe

and the surrounding filling material can cause buckling to the pipe. This effect is increasing with the depth.

The larger the density difference, the higher risk of buckling. The density difference is smaller when the

pipe is surrounded by groundwater than if a filling material like grout is used (Gehlin, et al., 2016). The

problem with short-circuiting increase with borehole depth. This can be counteracted by increasing the flow

rate (Gehlin, et al., 2016) (Holmberg, et al., 2015). Due to the geothermal gradient, the temperature is

increasing with depth. At the bottom of the borehole the secondary fluid will have its highest temperature,

but on its way up the surroundings will eventually be colder than the fluid causing it to lose heat to the

surroundings (see Figure 9) (Gehlin, et al., 2016).

10

Figure 9 Temperature distribution in U-pipe

3.3 TRT When designing large installations the properties of the ground are particularly important making an

investigation very beneficial. As an example, the borehole depth that can provide a certain heat load can

vary by 40 % depending on the ground properties (Erlström, et al., 2016). TRT is as mentioned in the

introduction a method for determining the heat transfer properties of the ground. It is basically done by

circulating a heat carrier fluid in the ground, to extract heat from or inject heat to the ground. The borehole

inlet and outlet temperatures are measured while a constant heating or cooling load is exchanged with the

ground loop. The purpose is not to heat or cool the ground, but to measure the behaviour of the ground.

The main parameters from the TRT is the thermal conductivity of the ground, the borehole resistance and

the undisturbed ground temperature. It is important that tests are run with the same parameters as in real

operation. To obtain the undisturbed ground temperatures different methods can be used. Either the

temperature can be measured along the depth and the mean value calculated, or a fluid can be circulated

without heating or cooling and the temperature analysed. In the second case there will be an influence on

the temperature by the pump that is injecting heat to the system. Also for calculating the thermal

conductivity and borehole resistance there are different methods, the most common being the line source

model (Nordell, 2011).

Standards for TRT tests have been published by Svenskt Geoenergicentrum. They are divided into two

parts; one for the test and one for the following data analysis. The simplest equipment consists of a pump,

heater/cooler, flowmeter, valves and sensors for temperature and pressure. See Figure 10 for a sketch of

the basic system. The minimum data to measure is the inlet temperature to the borehole, the outlet

temperature from the borehole, the ambient temperature, the power of the heater/cooler and the flow rate

(Gehlin, 2015).

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Figure 10 Basic TRT system

When the borehole has been drilled about 3 days rest are required for the ground to get back to steady state

after the disturbance. After that the test can begin. No drilling in the surroundings should take place during

the test as this can disturb the ground and change the groundwater flow. The BHE should be of the same

type as in real operation, and the pipes from the apparatus to the borehole should be as short as possible.

When the test starts the liquid is circulated without heat load, to even out temperature differences in the

borehole, until the temperature is stable. It is important to make sure that there is no air in the system during

the test, which could be done with air valves. After these preparations the heater is turned on and the

measurement are made during at least 50 h, recommended is 60-72h. If the load level is changed the test

should continue for 50 more hours (Gehlin, 2015).

The measurement equipment should have a stable heat/cooling load. Most common is using a heat load

which should not vary more than ±2% of the mean value. The heater should have different power steps so

that the power can be adapted to the depth of the borehole. The power used during the test should be the

same as the power that will be used during operation. Most common is 20-80 W/m. The pump should have

an adjustable flow, which should not have fluctuations exceeding ±1% of the mean value, and the error in

the flowmeter should not exceed ±2%. The test should be run with the same flow as will be used during

operation. It is important to keep the flow turbulent. The pressure loss in a BHE depends on the diameter

and length of the collector. A pressure sensor that measures the pressure loss between in- and outlet makes

it possible to monitor. The temperature needs to be measured as close to the borehole as possible for the

in- and outlet, and the error should not exceed ±0.1 K. The ambient temperature is also to be measured.

The equipment is recommended to have a safety functionality turning it off in case of too high pressure or

temperature. Pipes need to be insulated to minimize impact from the surroundings. Possibility to monitor

test data at a distance is recommended so that malfunctions can be detected (Gehlin, 2015).

3.3.1 DTRT Another way to measure and calculate the thermal conductivity and thermal resistance in the borehole is to

do a DTRT. The method is similar to TRT, with the difference that instead of measuring the temperature

difference between inlet and outlet of the borehole the temperature is measured along the depth. Thermal

conductivity and borehole resistance is calculated for different sections and differences along the depth can

12

be seen. To do this an optical cable is used, through which laser pulses are sent and the backscattered light

gives information about the temperature at different depths. The fibre optic cable is placed inside the BHE,

and calibrated before measuring. To analyse the data e.g. a line source model can be used. The thermal

conductivity and borehole resistance for different sections can be averaged to get a mean value (Acuña, et

al., 2009). In a study by Acuña et al. a borehole was evaluated with DTRT and TRT. The result of the two

different methods were compared and the borehole resistance was 28% higher for the TRT test (Acuña, et

al., 2009).

3.3.2 Components

3.3.2.1 Heaters In 2011 a survey on the state-of-the-art within thermal response testing in the world was made. Almost 90

% of the registered TRT equipments use heat injection instead of cooling, and all of them produce heating

or cooling by using electricity. During a TRT the heater needs to deliver constant power to comply with the

requirement of the standard test. A problem that can arise in practise is power stability in the grid as there

are normal fluctuations, with voltage that can vary ± 5%. A solution is to use an electricity stabilization unit

to get constant voltage (Nordell, 2011). There are some different heaters on the market, and some

parameters that needs to be considered. The unit needs to be compact, light and have enough power. A

small review of some large manufacturers of heaters and a check of what the market provides has been

done. There are heaters that have a small storage tank, flow through heaters and heaters that can be put

outside of the pipe. There is also a possibility to buy immersion heaters, and electric cartridges so that you

can construct your own electric heater (Backer, 2017) (IHP, 2017). Immersion heaters or cartridge heaters

are characterized by a property called watt density [𝑊

𝑐𝑚2]. Immersion heaters with high watt density are

compact but can deliver high power.

3.3.2.2 Pump To circulate the fluid in the BHE a pump is required that has to give the right flow rate and also handle

pressure losses in the pipes. The most common pump for fluid circulation is the centrifugal pump. However,

there are different kinds of pumps, some with a fixed and some with a variable speed. Pump performance

is often visualized in a pump chart (see Figure 11 for an example). The pump should be able to handle the

highest flow and the largest pressure drop that will occur in the system. If it is a speed controlled pump it

can be adjusted to the system if flowrate is lower or if the pressure drop is decreased. When choosing a

pump, it is good to choose one with high efficiency. Efficiency changes with the different flow rates, so it

is good to choose a pump that has a high efficiency in the most common operation range. It should be easy

to maintain the pump and it is good to design the system so that it is easy to replace the pump if it breaks.

This can be done e.g. by putting shut off valves before and after the pump (Havtun, et al., 2015).

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Figure 11 Pump curves

One problem that needs to be taken into consideration is cavitation in the pump. Cavitation takes place

when the static pressure at a local point drops below the saturation pressure at the temperature of the fluid.

This creates vapor bubbles and at some point the static pressure will rise again causing the vapor bubbles

to break. This phenomenon generates noise and vibrations and can cause the pump to break. Cavitation

often occurs at the inlet of the pump where the pressure is lower, and can be due to high pressure loss in

the system and that the pump is working outside its optimal point (Homa & Wróblewski, 2014). One way

to prevent cavitation is to make sure that the static pressure before the pump is high enough (Wilo, 2008).

To size the pump the flow and the friction loss in the pipe need to be calculated. The following equations

are from Granryd, et al. (2009). Calculating Reynolds number is the first step in the sizing (see Equation 1).

𝑅𝑒 =𝑣∙𝑑

𝜗 (1)

𝑣: 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 (𝑚

𝑠)

𝑑: 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑖𝑝𝑒 (𝑚)

𝜗: 𝑘𝑖𝑛𝑒𝑚𝑎𝑡𝑖𝑐 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 ( 𝑚2

𝑠)

The next step is to calculate the friction factor in the pipe. There are two equations: one for Re < 2300 and

one Re > 2300 (Equations 2 and 3).

𝑓 =64

𝑅𝑒 𝑓𝑜𝑟 𝑅𝑒 < 2300 (2)

𝑓 =1

(0,79∙ln(𝑅𝑒)−1,64) 𝑅𝑒 > 2300 (3)

The next step is to calculate the total pressure loss in the pipes and (Equation 4).

∆𝑃𝑓 = 𝑓 ∙ 𝜌 ∙𝑣2

2

𝐿

𝑑 (4)

𝐿: 𝑡𝑢𝑏𝑒 𝑙𝑒𝑛𝑔𝑡ℎ (𝑚)

14

𝑣: 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 (𝑚

𝑠)

𝑑: 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑖𝑝𝑒 (𝑚)

𝜌: 𝑑𝑒𝑛𝑠𝑖𝑡𝑦

The final step is to calculate the pump power with Equation 5.

�̇�𝑝𝑢𝑚𝑝 =∆𝑃𝑓∙�̇�

𝑛𝑝 (5)

∆𝑃𝑓: 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑙𝑜𝑠𝑠

�̇�: 𝑣𝑜𝑙𝑦𝑚𝑒𝑡𝑟𝑖𝑐 𝑓𝑙𝑜𝑤

𝑛𝑝: 𝑃𝑢𝑚𝑝 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦

3.3.2.3 Pipes, valves, vessels The studied type of system is a secondary system which often contains brine and works with low

temperatures. It will act like a heating system, and have almost the same requirements for the components

as a heating system. Since change in temperature of the fluid will lead to an expansion, there must be

something that can take up the expansion. There are mainly two types of systems, open and closed. An open

system has an expansion vessel at the highest point that is in direct contact with air, often through a pipe at

the top of the vessel. A closed system is not in direct contact with air and has an expansion vessel with a

rubber membrane. On one side of the membrane there is system fluid and on the other side an air pocket.

When the system fluid expands the air pocket gets compressed (see Figure 12). Since there is no direct

contact with air, if the system pressure increases above the operating pressure the liquid needs evacuate.

This is done through an expansion valve that opens. The system pressure is usually 1-4 bar, depending on

the height of the system (Lundagrosissten A, 2014).

Figure 12 Closed expansion vessel

To circulate the fluid in the system, it needs to be free from air pockets. Since air is lighter than water, it will

travel to the highest points of the system. At every high point of the system there need to be air vents. The

air vents can both be manual with a simple valve or automatic deaerators (Lundagrosissten A, 2014). Airing

of cooling systems needs to be done more frequently than in a heating system, since it is harder to get rid

of air in cold water. A micro bubble separator will make airing easier. Since many systems uses brine, the

airing component needs to be persistent to the system fluid (Lundagrosissten B, 2014).

The pipes that are used in closed systems with low temperatures are like those of a heating system, but since

cold systems often work with lower temperature differences (delta T), the pipes are often larger with higher

flow rates. The material that is used for piping could be copper, steel, stainless steel or plastic. Since low

15

temperatures may result in condense that can lead to corrosion, steel pipes need to be painted with rust

protection paint before they are insulated (Lundagrosissten B, 2014). The choice of material depends on the

size of the system, and on the environment that is surrounding the pipes. For example, in some location it

is not allowed to work with an open flame. For villas with smaller systems, copper is most common up to

a diameter of 54 mm. For bigger systems steel, stainless steel and PE (polyethene) pipes are most common.

Galvanized steel should not be used. Those pipes have small wall thickness and a thin protective layer. Field

experience shows that the pipe may start to corrode on the surface resulting in a leakage (Sundvisson, 2017).

To merge the pipes there are different solutions, and the choice depends on the pipe size and material. The

focus here is on merges that are used with brine pipes according to experience from the field. For copper

pipes, the most common is press fittings, however leakage has been experienced with this type of merge.

Experience has shown that brazing is the best merge method to avoid leakage. For larger dimensions when

using other materials there are other merge methods. For steel pipes, welding is often used. For stainless

steel welding or grooved couplings are used. For plastic PE pipes the most common are butt weld or

electrofusion (Sundvisson, 2017).

To shut off the system there is need for valves. Valves can also be used to control the flow. There are many

different types of valves, e.g. shut off valves, control valves and restriction valves. All those kinds of valves

are used in cooling systems, however the type of the valve depends on its use. Valves that are used for tap

water needs to be dezincification resistant. In a TRT equipment there is a need for shut off valves. The most

common shut off valve is the ball valve, available in many designs (Lundagrosissten A, 2014). Other shut

off valves are e.g. the slide valve, seat valve and butterfly valve. Restriction valves and control valves can

also be used to shut off the system even though it is not their main purpose. In brine systems for the smaller

dimensions, <54 mm, the most common valve is the ball valve, connected via compression fittings. For the

larger systems, it is the butterfly valves, and those are often connected via flanges (Sundvisson, 2017).

The temperature can decrease enough for condensation to occur on the pipes surface. This can cause

corrosion on the pipes, couplings and the surrounding materials. To avoid corrosion the insulation needs

to be diffusion sealed. Also, all suspension points need to be insulated (Lundagrosissten B, 2014).

As mentioned earlier when using DTRT the temperature is measured at different depths in the borehole.

To measure the temperature a fiber optic can be used. The equipment consists of an active monitoring unit

and a passive fiber. The monitor sends a laser signal into the fiber and the signal is back scattered at different

depths. The back scattered light is collected by the monitoring unit and the signals are converted to

temperatures (Samiec, 2017).

3.3.3 Evaluation of TRT data When the test is finished the data from the test needs to be evaluated and a report written. To be able to do

a good result analysis the following information is required (Gehlin, 2015).

- Information about the performer of the measurement and the outsourcer

- Name of the TRT tester

- Company name of the outsourcer

- Information about the borehole and the BHE

- Information about the borehole

- Name of the bore entrepreneur

- Borehole depth and diameter

- Depth to solid rock, groundwater level and casing length

- Observation about type of rock and ground water flow

- Date for the stop of boring

- Location of the borehole

- Bore protocol that should be sent to SGU

- Collector type (U-tube, coaxial)

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- Length of the collector

- Information about the collector pipes (material, type, dimension)

- Secondary fluid, and its composition

- Information about the measurement and the measured values

- Information about the measuring method of undisturbed ground temperature and its value

- Date and time for the start of the test

- Date and time for the stop of the test

- Information about heating/cooling load (mean value, standard deviation) and a graph

showing the load during the test

- Information about the flow (mean value, standard deviation) and a graph showing the flow

during the test

- Values and a graph showing the inlet and outlet temperature during the test

- Values and a graph showing the ambient temperature during the test

The collected data needs to be analyzed. The most common method for evaluation of TRT data and

calculation of thermal conductivity and effective borehole resistance is the line source model (see Equation

6). The standard methodology for the analysis requires the heating/cooling load to be stable. The line source

model only considers heat transfer by conduction in a homogenous ground, so if there is inhomogeneous

heat transfer via e.g. high groundwater flow the model will not be reliable. The result should not differ

depending on the duration of the test. Hence the analysis should be carried out for different time intervals

from the measurement period to ensure that Equation 6 converges towards the same value (Gehlin, 2015).

𝑇𝑓(𝑡) = 𝑇0 +𝑞

4∙𝜋∙𝜆∙ (ln (

4∙𝛼

𝑟𝑏2 𝑡) − 0,5772) + 𝑞 ∙ 𝑅𝑏

∗ (6)

𝑇𝑓: 𝑚𝑒𝑎𝑛 𝑓𝑙𝑢𝑖𝑑 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 (°𝐶)

𝑇0: 𝑢𝑛𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑒𝑑 𝑔𝑟𝑜𝑢𝑛𝑑 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 (°𝐶)

𝑞: 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 ℎ𝑒𝑎𝑡 (𝑊

𝑚)

𝜆: 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 (𝑊

𝑚 ∙ 𝐾)

𝑐: 𝑔𝑟𝑜𝑢𝑛𝑑 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 ℎ𝑒𝑎𝑡 𝐽

𝑘𝑔 ∙ 𝐾

𝛼: 𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑣𝑖𝑡𝑦 (𝜆

𝜌 ∙ 𝑐)

𝑟𝑏: 𝑏𝑜𝑟𝑒ℎ𝑜𝑙𝑒 𝑟𝑎𝑑𝑖𝑢𝑠 (𝑚)

𝑡: 𝑡𝑖𝑚𝑒 𝑓𝑟𝑜𝑚 𝑡𝑒𝑠𝑡 𝑠𝑡𝑎𝑟𝑡 (𝑠)

𝑅𝑏∗ : 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑏𝑜𝑟𝑒ℎ𝑜𝑙𝑒 𝑟𝑒𝑐𝑖𝑠𝑡𝑎𝑛𝑐𝑒 (

𝐾

𝑊 ∙ 𝑚)

For DTRT the fiber optic cable is lowered in one of the pipes and thereby the temperature profile is known

in that leg. There are methods for calculating the temperature profile in the other pipe, e.g. mean temperature

approximation. Since some of these models gives errors a report written by Beier, et al. (2013) suggest a

new model for calculating the temperature profile that gives less errors. The model is different depending

on what type of heat exchanger that is used e.g. U-tube and coaxial.

3.4 Business model The new TRT needs to reach out to the market, have a revenue stream to the company and also give a value

to the customer. There are many different business models and different ways to reach out to the market.

Alexander Osterwalder & Yves Pigneur (2010) describe how to build up a business model and it can be

summarized by nine basic blocks (see Table 1). These nine blocks form a business model canvas (see Figure

13) containing all four main areas in the business: customer, offer, infrastructure and financial variability.

To give two examples on how to reach out on the market with the new TRT equipment two business models

17

have been created using the methodology by Alexander Osterwalder & Yves Pigneur. To evaluate the model

a SWOT (strengths, weaknesses, opportunities and threats) analysis was made.

Table 1 Business model canvas description (Osterwalder & Pigneur , 2010)

Block Description Customer segments “The Customer Segments Building Block defines

the different groups of people or organizations an enterprise aims reach and serve” (p. 20)

Value propositions “The Value Propositions Building block describes the bundle of products and services that create value for a specific customer segment” (p. 22)

Channels “The Channels Building Block describes how a company communicates with and reaches its customer segments to deliver a value proposition” (p. 26)

Customer relationships “The Customer Relationships Building Block describes the types of relationships a company establishes with specific customer segments” (p. 28)

Revenue streams “The Revenue Streams Building Block represents the cash a company generates from each customer segment (costs must be subtracted from revenues create earnings)” (p. 30)

Key resources “The key Resources Building Block describes the most important assets required to make a business model to work” (p. 34)

Key activities “The Key Activities Building Block describes the most important things a company must do to make its business model work (p. 36)

Key partnerships “The Key Partnerships Building block describes the network of suppliers and partners that make the business model work” (p. 38)

Cost structure The Cost Structure Building block describes all costs incurred to operate a business model” (p. 40)

Key partners Key activities Value proportions Customer relationships

Customer segments

18

Key resources Channels

Cost structure

Revenue streams

Figure 13 Business model Canvas

19

4 Results This section contains results regarding the different objectives of this master thesis.

4.1 Construction of TRT equipment In the process of developing the new TRT two prototypes were designed and built.

The first version was designed for optimized compactness but problems with the heaters elements did arise

because the small size resistance element was operating at low voltage and high current making it

incompatible with power supply connections that are usually available in the field. For this reason, it was

decided to substitute the heaters and use larger size elements. This modification required a change in the

design to accommodate larger heaters operating at higher voltage and lower current, however the flowchart

remained the same as used for the first equipment (see Figure 14). The pump, flowmeter and sensors were

the same for both versions. The calculation of the pump was based on a maximum flow of 1.2 l/s and on a

Reynolds number of 5000. The pressure loss for some different collector designs were calculated and can

be seen in Appendix 1. The pump that was selected has a maximum flow of 1.2 l/s and a total system

pressure loss of 3 bar. The flowmeter and sensors were chosen according to the accuracy that is needed.

The heating power was set to be at least 12 kW which is enough for a 600 m borehole with 20 W/m. The

dimension of the pipe in the heaters were set to be one dimension larger than the heater connection (e.g.

with a heater dimension of 1” the pipe would be 1¼”). The flowmeter was mounted according to the

instruction, saying that the flowmeter needs to have a 20 D straight pipe upstream and a 5 D downstream

where D is the pipe dimension. To keep the length as short as possible the pipe dimension was smaller

before and after the flowmeter.

Figure 14 Flow chart new TRT

4.1.1 TRT version 1 The material for the pipes was chosen to be copper, the merging method to be brazing between copper

parts and compression couplings were chosen as connections. The dimensions of the pipes can be seen in

Figure 15 and the 3D model for version 1 can be seen in Figure 16. The components that were chosen are

listed in Table 2. Version 1 contains three heaters with a total power of 13.5 kW.

20

Figure 15 Dimensions TRT version 1

Figure 16 TRT version1

21

Table 2 Components TRT version 1

Component Manufacturer Product reference Pump Grundfos 1,1 kW CME5-3 A-R-A-E-AQQE –

98395019

Heaters Grainger 4,5 kW SG1453-430334

Flowmeter Process center AB LTFM-15-304-P-D-T

Expansion vessel Flamco Flexcon Top 4

Expansion valve Flamco Prescor DN 20

Ball valve A-collection AVI-1326

Filter ball valve Beulco Filterball 51F

Filling pump Flojet 4406-143

Air valve 1 Flamco Flexvent super 1/2

Air valve 2 Flamco Flexvent

Pressure sensor Climacheck 10 Bar, 4-20 mA, 1-5V

Temperature sensor Climacheck PT1000

4.1.2 TRT version 2 The material for the pipes was chosen to be copper, the merging method to be brazing between cooper

parts and compression couplings were chosen as connections. The dimensions of the pipes can be seen

in Figure 17 and the 3D model for version 2 can be seen in Figure 18. The components that were

chosen are listed in Table 3. Version 2 contains four heaters with a total power of 12 kW. These heaters

were larger than those in version 1. Thereby the frame had to be larger and the pump was moved to

another position, meaning that basically the whole TRT was rebuilt.

Figure 17 Dimensions TRT version 2

22

Figure 18 TRT version 2

Table 3 Components TRT version 2

Component Manufacturer Product reference Pump Grundfos 1,1 kW CME5-3 A-R-A-E-AQQE –

98395019

Heaters Escoline 3 kW -

Flowmeter Process center AB LTFM-15-304-P-D-T

Expansion vessel Flamco Flexcon Top 4

Expansion valve Flamco Prescor DN 20

Ball valve A-collection AVI-1326

Filter ball valve Beulco Filterball 51F

Filling pump Flojet 4406-143

Air valve 1 Flamco Flexvent super 1/2

Air valve 2 Flamco Flexvent

Pressure sensor Climacheck 10 Bar, 4-20 mA, 1-5V

Temperature sensor Climacheck PT1000

4.2 Business model In this section, the business model is presented. There are two different scenarios with different suggestions

for the revenue streams, thereby the only difference in the canvas model is the revenue stream section.

4.2.1 Gap When doing a proper design for a heat pump system that uses the rock as heat source a TRT test gives the

thermal conductivity for the specific location, and thereby the borehole depth can be optimized. However,

there are few TRT units on the market, they are expensive to build and the data analysis requires knowledge.

4.2.2 Idea To give a broader access to both TRT equipment and knowledge a new concept is introduced. The

boreholes for the heat source is made by the drillers. They will be given the possibility to rent or borrow a

TRT equipment that is easy to operate. The TRT equipment is connected to the BHE and the data is logged

23

directly to a cloud server accessed by the company providing the TRT equipment. The data can then be

analysed from the office, and the TRT expert and data analyst does not have go to the field. Both the driller

and the TRT company takes profit from this.

4.2.3 Canvas

4.2.3.1 Key partners - Manufactures for the parts used to construct the TRT equipment.

- Resellers for TRT equipment parts.

- Drillers that uses the TRT equipment.

- Researchers developing the technology.

4.2.3.2 Key activities Construct and design the TRT equipment’s. Maintain them to keep them in good shape. Perform data

analysis and deliver reports to the customer. Stay updated on the field of research.

4.2.3.3 Value proposition Offer the possibility to rent an easily operated TRT equipment for a low price. Provide expert knowledge

required to do the data analysis and deliver a written report to the customer. Provide front-edge knowledge

within the field. Guarantee the functionality of the TRT equipment. Give assistance if failure.

4.2.3.4 Key resources Resources can be divided into three types: physical, intellectual and human resources. Physical resources

include the spare parts and the TRT equipment. The intellectual resource is the knowledge in the field. The

human resource is the experienced data analysts that provide the reports.

4.2.3.5 Customer relationships This business idea relies on dedicated personal assistance and hence a very close relationship with the drillers.

The drillers do the physical work with the TRT and the provider analyses the data and writes reports. The

provider also assists physically if there is a failure of the equipment. Both the customer (the driller) and the

provider earn money on the service that they together provide.

4.2.3.6 Channels This is a niche market so personal contact is important to reach the customer, but also to make sure that

the customer is satisfied with the product. A web page is also important, where information can be provided

about the TRT and new customers can be reached.

4.2.3.7 Customer segments The market is niched and the main customers are the drilling companies.

4.2.3.8 Cost structure The costs can be divided into to two parts: fixed costs and variable costs. The fixed costs are the biggest

and include salaries and construction costs for the TRT. The variable costs are related to the maintenance

of the TRT equipments. The costs for the construction of the TRT equipments can be lowered if more is

produced as larger production means lower costs for specific parts.

4.2.3.9 Revenue streams This business model has two alternative types of revenues streams.

1.) The TRT is delivered with a deposit for a fixed time. Only the provider is allowed to do the data

analysis. The customer pays a price X for the TRT equipment for each test. When the test is done

the customer pays a price Y for the data analysis and report writing.

Than the total income is X for each test and Y for each analysis and report.

24

2.) The TRT is delivered with a deposit for a fixed time. Only the provider is allowed to do the data

analysis. The customer pays a monthly leasing cost X for the TRT equipment. When the test is

done the customer pays a price Y for the data analysis and report writing.

Than the total income is X for the monthly rent and Y for each test and report.

4.2.4 SWOT

4.2.4.1 Strengths The business model is built on the fact that there is a demand for TRT tests to do a proper BHE design,

and that there are few providers on the market. This model gives larger access to rent a TRT equipment for

a cheap price, and knowledge for the data analysis is not required since this is handled by the provider. The

providing company has a large knowledge in the field, is in the front edge of the research and has a lot of

experience. The company provides both theoretical and practical knowledge which is one of the biggest

strengths.

The company has been working in the field with TRT tests and has thereby established relationships with

the drillers which is an advantage when reaching out to the customers. Both the company and the drillers

earn money from the TRT test.

The new TRT equipment is small and more portable than the older ones, and will result in easier shipping

to the customer. Also, the new TRT is easier to connect to the BHE, and easy to start. The data is sent to

the company via the modem and thereby they can monitor the system directly. The company will provide

the customer with personal assistance if failure with the TRT equipment.

4.2.4.2 Weaknesses The TRT equipment is expensive to manufacture and a large investment is required in the beginning.

If failure in the TRT equipment there could be large distance between the test site and the company, which

will result in a delay before TRT is fixed.

Even though the installation of the TRT equipment is easy there is always a risk when worker lacking specific

training are installing. Failure in the test can be discovered via the data from the modem, but it often requires

staff on site to fix it, e.g. fuse failure.

4.2.4.3 Opportunities In the beginning the company will own just a few TRTs but if the TRT demand grows there is an

opportunity to expand and construct more test units. Also since the TRT is easy to ship the company can

reach out to drillers in a larger area, even across borders to other countries. Especially the Nordic countries

and even other countries in Europe. Since the company has great knowledge in the field they will be

attractive even internationally.

The TRT equipment could be upgraded to do other tests than thermal response test, like flow checks in

BHEs. This gives them a higher value for the driller.

Since the driller is responsible for external damage of the equipment when renting it, there is always a risk

for it to brake. The company can provide the driller with an insurance and thereby it is less risky for the

driller to rent it and the company can earn more money.

4.2.4.4 Threats If the market expands there is always a risk of competitors entering the business and lowering the price

making it less profitable.

Since the business model is new there is always an inertia in the system with a risk of an initially low

willingness to rent. It can take a while to implement the new concept.

25

There is always a risk to lose key persons. If the company loses a key person there can be lack of knowledge.

Since the customer relationship is based on personal contact, if a key person is lost the whole job can be

lost.

4.3 Evaluation of data from Asker This section contains TRT evaluation from an 800 m deep borehole with a coaxial BHE. The test was

started on 27/6-17 18:50 and stopped 6/7-17 08:05, with a total test length of 205 h. The baseline

temperature was 12.4°C measured by fibre, the rock contained limestone and clay slate and in some sections

high quartz content, and the borehole diameter was 0.150 m. The heating power for the test was 19.7 W/m,

which is lower than the recommended 20 W/m, however the heating power was meant to be higher but

problems with power supply made it difficult. Power and flow for the whole test can be seen in Figure 19.

There is a small influence of the outdoor temperature on the inlet and outlet temperature for the test which

can be seen in Figure 20.

Figure 19 Flow and power TRT Asker

1

1,1

1,2

1,3

1,4

1,5

1,6

1,7

1,8

1,9

2

10000

11000

12000

13000

14000

15000

16000

17000

0 50 100 150 200

Flo

w (

l/s)

Po

wer

(W

)

Time (h)

Power Flow

26

Figure 20 Inlet, outlet and outdoor temperature TRT Asker

The time for the optimization was varied between three fixed start times (30h, 40h and 50h). The

optimization time was varied between 10–150 h from each start time. The results can be seen in Figure 21

and Figure 22. The values converge towards a thermal conductivity of 3.01 𝑊

𝑚∙𝐾 and an effective borehole

resistance of 0.101 m∙K

W .

Figure 21 Borehole resistance TRT Asker with different optimization times

0

5

10

15

20

25

30

11

12

13

14

15

16

17

18

19

0 50 100 150 200

Ou

tdo

or

Tem

per

atu

re (°C

)

Tem

per

atu

re b

rin

e (°

C)

Time (h)

T_in T_ut Outdoor

0,04

0,05

0,06

0,07

0,08

0,09

0,1

0,11

0,12

0 20 40 60 80 100 120 140 160

Bo

reh

ole

res

ista

nce

Delta T

Start 30 Start 40 Start 50

27

Figure 22 Thermal conductivity TRT Asker with different optimization times

The response for 150 h optimization for all three cases can be seen in Figure 23-25. All three cases have a

good curve fit.

Figure 23 Curve fit start time 30 h and 150 h optimization period

1,5

2

2,5

3

3,5

4

0 20 40 60 80 100 120 140 160

Ther

mal

co

nd

uct

ivit

y

Delta T

Start 30 Start 40 Start 50

0

1

2

3

4

5

6

0 50 100 150 200Tem

per

atu

re d

iffe

ran

ce b

etw

een

bri

ne

and

gr

ou

nd

(°C

)

Time (h)

DT measured Response

28

Figure 24 Curve fit start time 40 h and 150 h optimization period

Figure 25 Curve fit start time 50 h and 150 h optimization period

4.4 Test of new TRT The new equipment was tested on a 200 m long borehole in Norrtälje. The BHE was a coaxial with a flexible

outer pipe and a diameter of 0.113 m.

First step was to fill the system, and the static pressure was set to 1 bar. This caused the first problem. The

BHE was sealed at the borehole top with a lid (see Figure 26). When the static pressure increased the lid

was pushed out of the borehole. To solve this problem shackles where created and placed between the

casing and the lid to prevent the lid from being pushed out (see Figure 27).

0

1

2

3

4

5

6

0 50 100 150 200

Tem

per

atu

re d

iffe

ran

ce b

etw

een

bri

ne

and

gr

ou

nd

(°C

)

Time (h)

DT measured Response

0

1

2

3

4

5

6

0 50 100 150 200

Tem

per

atu

re d

iffe

ran

ce b

etw

een

bri

ne

and

gr

ou

nd

(°C

)

Time (h)

DT measured Response

29

Figure 26 Cutaway view BHE lid

Figure 27 Cutaway view suspender solution

30

The test was started at 23/10-17 17:13 and was stopped at 1/11-17 10:56. There were some problems with

the software that controls the rig. All these problems were solved during a stop on 25/10-17. For the test

actions see Table 4.

Table 4 Events in the testing

Date Time Action Comment 23/10-17 17:13 Flow starts ~0,66l/s

24/11-17 09:18 Heat starts Two heaters

25/10-17 19:54 Software crashes Emergency stop because of no flow since the pump stopped

27/10-17 09:16 Restart flow 0,66l/s

27/10-17 10:11 Restart heaters Two heaters

30/10-17 09:39 Flow increased ~1 l/s

1/11-17 10:56 End of test

The heat for the test was 28.13 W/m, and there were two different flows of 0.66 l/s and 1 l/s (see Figure

28). The temperature sensors were calibrated with an ice bath (0°C), and an offset was made according to

the corresponding measured error (see Appendix 2). There was some noise in the sensors and the

temperature was fluctuating, which can be seen in Figure 29. Since the heating power is calculated with the

inlet and outlet temperatures this also fluctuates (see Figure 28).

Figure 28 Flow and power TRT Norrtälje

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

2

4000

4500

5000

5500

6000

0 50 100 150 200 250

Flo

w (

l/s)

Po

wer

(W

)

Time (h)

Power Flow

31

Figure 29 Inlet, outlet and outdoor temperature TRT Norrtälje

The time for optimization was varied between three fixed start times (100 h, 105 h and 110 h) for the lower

flow. The optimization period was varied between 10-50 h for each start time. The results for the lower

flow can be seen in Figure 30 and Figure 31. The values converge towards a thermal conductivity of 2.46 𝑊

𝑚∙𝐾 and an effective borehole resistance of 0.031

m∙K

W .

Figure 30 Thermal conductivity TRT Norrtälje with different optimization times

-4

-2

0

2

4

6

8

10

0

2

4

6

8

10

12

14

16

0 50 100 150 200

Ou

tdo

or

tem

per

atu

re (

°C)

Tem

per

atu

re b

rin

e (°

C)

Time (h)

T_in T_out T_outdoor

2

2,1

2,2

2,3

2,4

2,5

2,6

2,7

2,8

2,9

3

0 10 20 30 40 50 60

Ther

mal

co

nd

uct

ivit

y

Delta T

start 100 start 105 start 110

32

Figure 31 Borehole resistance TRT Norrtälje with different optimization times

The response for 50 h optimization for all three cases can be seen in Figure 32-34.

Figure 32 Curve fit start time 100 h and 50 h optimization period

0

0,01

0,02

0,03

0,04

0,05

0 10 20 30 40 50 60

Bo

reh

ole

res

ista

nce

Delta T

start 100 start 105 start 110

0

1

2

3

4

5

6

7

0 50 100 150 200

Tem

per

atu

re d

iffe

ran

ce b

etw

een

bri

ne

and

gr

ou

nd

(°C

)

Time (h)

Dt measured Response

33

Figure 33 Curve fit start time 105 h and 50 h optimization period

Figure 34 Curve fit start time 110 h and 50 h optimization period

Results for the flow of 1 l/s are presented for one fixed start time, and an optimization period varied

between 10 and 40h. The value for thermal conductivity is the same as for the lower flow. The result for

borehole resistance can be seen in Figure 35, and the value is 0,029 m∙K

W. The response for 40 h optimization

can be seen in Figure 36.

0

1

2

3

4

5

6

7

0 50 100 150 200

Tem

per

atu

re d

iffe

ran

ce b

etw

een

bri

ne

and

gr

ou

nd

(°C

)

Time (h)

Dt measured Response

0

1

2

3

4

5

6

7

0 50 100 150 200

Tem

per

atu

re d

iffe

ran

ce b

etw

een

bri

ne

and

gr

ou

nd

(°C

)

Time (h)

Dt measured Response

34

Figure 35 Borehole resistance TRT Nortälje with higher flow

Figure 36 Curve fit 40 h optimization period

The total pressure in the system decreases with time which can be seen in Figure 37. The pressure drop in

the BHE can be seen in Figure 38, and the mean value is 0.69 bar for 0.66 l/s, and 1.61 bar for 1 l/s.

0

0,01

0,02

0,03

0,04

0,05

0 5 10 15 20 25 30 35 40 45

Bo

reh

ole

res

ista

nce

Delta T

Start 165

-1

0

1

2

3

4

5

6

7

0 50 100 150 200 250Tem

per

atu

re d

iffe

ran

ce b

etw

een

bri

ne

and

gr

ou

nd

(°C

)

Time (h)

Dt measured Response

35

Figure 37 Inlet and outlet pressure TRT

Figure 38 Pressure difference inlet and outlet

5 Discussion

5.1 Construction The equipment was built to handle deep boreholes up to around 600 m deep. Since deeper boreholes

demand higher heater power that results in higher demands on the power supply. The power supply is

limited by the fuse: if 12 kW heating is required the fuse has to be 32 A, which is not as common as 16 A.

For flexibility the equipment was designed to switch between 16 A and 32 A fuse, only the highest power

setting requiring 32 A. To contain both the 16 A and 32 A fuse the electrical box had to fit more components

than first estimated, making it larger. The larger box also makes it possible to add more heaters in the future.

0

0,5

1

1,5

2

2,5

0 50 100 150 200 250

Bar

Time (h)

P_out P_in

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

0 50 100 150 200 250

Bar

Time (h)

36

Installation of one more 3 kW heater is easy and would enable the use of the equipment on even deeper

boreholes.

The choice of heater was a critical step. There are different types available and they are usually not designed

for this purpose. If the equipment had been constructed to handle a depth of around 100-200 m the demand

on heater power would have been smaller. Then only one small Grainger 4,5 kW heater would have been

used with a 16 A fuse and the equipment had been much smaller. A rough estimation is that the equipment

would then have been half the size and about 10 kg lighter.

The pipes and equipment need to be supported by a frame. An iron frame and angle brackets were chosen.

The frame became larger than first expected making it heavier than necessary. If aluminium had been used

instead the weight of the support would have been far lower. This is a possible improvement for future

designs.

An important learning outcome is that the delivery time for material can be long. As an example, the pump

arrived 6 weeks after the order date. This became a restricting factor for the material choice, as the time for

the master thesis was limited. For the same reason the time for comparison of options was also limited and

quick decisions required. As a consequence, the choice of material and components could be further

optimized with respect to economy and weight.

The system was designed as a closed system with a pressure vessel, but without a fixed volume and delta T

as opposed to common closed systems. This makes it hard to use the standard model to calculate the vessel

volume. The vessel volume choice was based on discussions and system experience. The closed vessel

prevents cavitation in the pump and acts as a water buffer when air is removed from the system. However,

it is important to monitor the pressure in the vessel when airing the system. When air is removed pressure

falls and water needs to be filled. There is a possibility to use an open vessel instead, but then it is important

that no shut-off valve is connected between the vessel and the system.

When the equipment was tested it was discovered that the level of the system is important when removing

the air. If the equipment is not on the right level there is risk for air pockets in the pipes which will cause

problems and noise. A solution would be to use level indicators on the sides of the equipment, and make

sure that the operator is aware of this problem.

Components of the equipment are sensitive to dirt, especially the flowmeter. This problem is solved by a

filter ball valve. However, this filter ball valve has a fine strainer which needs to be cleaned often, especially

when the equipment is coupled to recently drilled boreholes. During the first test in the workshop dirt in

the filter from the construction caused an extra pressure drop of 0.1 bar. Cleaning the filter is easy and can

be done without draining the system, but a circlip plier is required.

The new equipment is lighter than the old one, and the transportability is increased as the volume is smaller.

A box with wheels would increase transportability further. Such a box would also protect the equipment

from external damage which would be useful as the equipment will be exposed to outdoor conditions.

When testing boreholes deeper than 600 m there is a possibility to couple two TRT units in series to increase

the total heating and pumping power. Then the inlet temperature of the first unit would need to be

compared to the outlet temperature of the second unit or vice versa. This could be done by adding an extra

temperature sensor to the first TRT and place it at the in- or outlet of the second TRT (see Figure 39).

37

Figure 39 Two TRT in series

5.2 Asker It can be seen in Figure 21 and 22 that there is a big variation of lambda and borehole resistance when

choosing an optimization period shorter than 50 hours. This indicates that a longer optimization time is

required to find the correct values. The reason that it takes time before the curves converge could be that

the power was lower than recommended in combination with the borehole depth. It is worth noting that

there are fluctuations in the power (see Figure 19) which are close to the recommended maximum

fluctuation of ±2% and at some points even bigger.

The effective borehole resistance was higher than expected. This could be due to the fact that thermal short-

circuiting increases with the depth. To investigate this the DTRT data could be studied with respect to

influence between the inner and outer tube. What could also affect the test results is influence from the

outdoor temperature, since the inlet and outlet temperatures tend to follow the outdoor temperature (see

Figure 20). This is probably caused by poor insulation of the pipes.

This test shows how high the demands are on the TRT equipment when testing deeper boreholes. High

power is needed which puts a demand on the power connection in the test location. In this case the heating

power had to be lowered to run the test because of problems with fuses. The equipment needs to be built

with cables and fuses that can handle high current. As long as these requirements are met an external

38

generator is a good alternative for the power supply if no connection is available. Also, this test shows the

importance of proper insulation of the pipes.

5.3 Test of new TRT The pressure in the system decreases with time, and this is probably caused by a leakage in the BHE. The

lid of the BHE was a problem in the beginning, it is very likely that there is still a small leakage around the

lid. The leakage rate decreases with decreasing static pressure, so it is preferable to run the system with a

low static pressure until the problem is solved.

The lid/sealing solution can be improved in the future. The solution that was implemented on site is just

temporary, but something similar needs to be built to protect the lid from being pressed out from the casing.

One solution that can be an alternative for the future is to use a grooved coupling between the lid and

casing, this will both prevent leakage and stop it from being pushed up.

The temperature sensors provide noisy data that makes the measured temperature fluctuate. It was hard to

estimate a temperature offset since there was no stable temperature from the sensors in the ice bath. The

error due to the temperature sensors also affects the power output increasing the overall uncertainty in the

test. Sensor error should therefore be reduced in the future to improve robustness in the test. One solution

for the problem could be to use a filter in the signal from the sensors.

The power output is lower than the set power for the heaters. Since there is an error in the temperature

sensors it is hard to estimate the exact number. The power loss increases with higher flow and this is

probably because higher flow leads to higher heat transfer. All the pipes are insulated except for the heater

connections. Improvement could be to insulate them, and less heat will be lost to the ambient.

There were some problems with the software in the beginning of the test. These problems have been solved

after the first failure. The location for the field test of the new TRT equipment was 100 km away and there

was no remote connection with the equipment. The only option to fix it was to go to the location. This

showed how important it is to be able to have workers close to the TRT equipment in case of failure.

The results from the test shows a low thermal conductivity in the ground. The borehole resistance in the

BHE is low and it shows that Coaxial BHE have the potential to lower the borehole resistance. When

increasing the flow, the borehole resistance decreases, and this is because heat transfer rate increases. The

pressure loss in the BHE increases with higher flow so the pump power increases. There is a tradeoff

between gaining lower borehole resistance and increasing pump power.

What can be seen in Figure 38 is that delta P increases with time for the higher flow. This was because

higher flow led to more dirt in the filter from the BHE (see Figure 40).

39

Figure 40 Filter TRT

40

6 Conclusion - The new equipment is compact and has a lower weight than the existing one, it is easy to use and

robust. The new TRT can be used in every country that has 400V and 50 Hz. There is a possibility

to choose between 16 and 32 A connection. The unit is standardised and easy to build with the new

concept. It can be coupled in series with another TRT to handle deep boreholes.

- A new business model has been developed for the TRT with the tool business model canvas. The

business model is built up on a leasing concept where both the company and the driller earn money.

- Data from an earlier TRT in Asker was evaluated. The result was evaluated with different

optimization periods and the result shows that it converges towards the same value. The result

shows a thermal conductivity of 3.01 𝑊

𝑚∙𝐾 and borehole resistance of 0.10

m∙K

W.

- The new TRT was tested in a coaxial BHE with flexible outer pipe in Norrtälje. The new TRT

works well, only some small problems with the software were discovered in the beginning of the

test. It is easy to fill and remove the air from the new TRT when it is connected to a borehole. The

new closed system makes it possible to put a static pressure up to 2,4 bars in the in the TRT and

thereby prevent cavitation in the pump. The test result shows a thermal conductivity of 2.46 𝑊

𝑚∙𝐾

and a borehole resistance of 0.031 m∙K

W and with increased flow the borehole resistance is 0,029

m∙K

W.

41

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43

Appendix 1

44

Appendix 2

Time Power Tmeas Tin Tout Tamb Flow Pabs Pdiff h W degC degC degC degC l/s bar bar

0,006623 0 -1,042 -0,946 -1,138 -0,169 0 -0,03 -0,03

0,009996 0 -0,9775 -0,855 -1,1 -0,171 0 -0,03 -0,03

0,013576 0 -0,98 -0,81 -1,15 -0,144 0 -0,03 -0,03

0,017207 0 -0,936 -0,86 -1,012 -0,326 0 -0,03 -0,03

0,020821 0 -0,9215 -0,825 -1,018 -0,268 0 -0,03 -0,03

0,024416 0 -0,93 -0,86 -1 -0,182 0 -0,03 -0,03

0,028031 0 -1 -0,86 -1,14 -0,241 0 -0,03 -0,03

0,031651 0 -0,9545 -0,887 -1,022 -0,08 0 -0,03 -0,03

0,035232 0 -0,9855 -0,91 -1,061 -0,137 0 -0,03 -0,03

0,038888 0 -0,9845 -0,919 -1,05 -0,24 0 -0,03 -0,03

0,042497 0 -0,9815 -0,86 -1,103 -0,338 0 -0,03 -0,03

0,046104 0 -0,7175 -0,825 -1,103 -0,338 0 -0,04 -0,03

0,049718 0 -0,9375 -0,875 -1 -0,242 0 -0,03 -0,03

0,053341 0 -1,0035 -0,907 -1,1 -0,344 0 -0,03 -0,03

0,056909 0 -0,9195 -0,837 -1,002 -0,192 0 -0,03 -0,03

0,060558 0 -0,9615 -0,815 -1,108 -0,23 0 -0,03 -0,03

0,064167 0 -0,9965 -0,96 -1,033 -0,207 0 -0,03 -0,03

0,067771 0 -0,917 -0,87 -0,964 -0,324 0 -0,03 -0,03

0,071344 0 -0,98 -0,86 -1,1 -0,13 0 -0,03 -0,03

0,075001 0 -0,8785 -0,81 -0,947 -0,148 0 -0,03 -0,03

0,078604 0 -0,964 -0,738 -1,19 -0,18 0 -0,03 -0,03

0,082211 0 -1 -0,762 -1,238 -0,128 0 -0,03 -0,03

0,085788 0 -1,0185 -0,921 -1,116 -0,31 0 -0,03 -0,03

0,089441 0 -1,048 -0,94 -1,156 -0,18 0 -0,03 -0,03

0,093011 0 -1,0265 -0,908 -1,145 -0,18 0 -0,03 -0,03

0,096621 0 -1,0485 -0,837 -1,26 -0,156 0 -0,03 -0,03

0,100232 0 -0,9505 -0,854 -1,047 -0,239 0 -0,03 -0,03

0,103855 0 -1,005 -0,86 -1,15 -0,096 0 -0,03 -0,03

0,10748 0 -0,9615 -0,839 -1,084 -0,156 0 -0,03 -0,03

0,111079 0 -1,039 -0,86 -1,218 -0,141 0 -0,03 -0,03

0,114718 0 -0,978 -0,738 -1,218 -0,22 0 -0,03 -0,03

0,11832 0 -1 -0,85 -1,15 -0,265 0 -0,03 -0,03

0,121904 0 -1,013 -0,926 -1,1 -0,23 0 -0,03 -0,03

0,125284 0 -0,994 -0,81 -1,178 -0,209 0 -0,03 -0,03

0,12889 0 -0,9945 -0,905 -1,084 -0,231 0 -0,03 -0,03

0,132492 0 -0,9595 -0,845 -1,074 -0,13 0 -0,03 -0,03

0,1361 0 -0,9815 -0,851 -1,112 -0,135 0 -0,03 -0,03

0,13971 0 -0,955 -0,91 -1 -0,203 0 -0,03 -0,03

0,143332 0 -0,958 -0,812 -1,104 -0,08 0 -0,03 -0,03

0,146922 0 -0,9715 -0,784 -1,159 -0,332 0 -0,03 -0,03

0,150539 0 -1,012 -0,81 -1,214 -0,279 0 -0,03 -0,03

0,154137 0 -1,0035 -0,899 -1,108 -0,095 0 -0,03 -0,03

0,15776 0 -1,0365 -0,923 -1,15 -0,121 0 -0,03 -0,03

45

0,16136 0 -0,9995 -0,777 -1,222 -0,122 0 -0,03 -0,03

0,164969 0 -0,88 -0,76 -1 -0,08 0 -0,03 -0,03

0,168585 0 -0,9345 -0,838 -1,031 -0,354 0 -0,03 -0,03

0,1722 0 -1,1065 -0,916 -1,297 -0,21 0 -0,03 -0,03

0,175822 0 -0,97 -0,81 -1,13 -0,017 0 -0,03 -0,03

0,17942 0 -0,988 -0,817 -1,159 -0,23 0 -0,03 -0,03 0,183045 0 -1,107 -0,904 -1,31 -0,084 0 -0,03 -0,03

0,186649 0 -0,9635 -0,91 -1,017 -0,178 0 -0,03 -0,03

0,190264 0 -0,975 -0,957 -0,993 -0,082 0 -0,03 -0,03

0,193865 0 -0,955 -0,86 -1,05 -0,118 0 -0,03 -0,03

0,19746 0 -0,9705 -0,916 -1,025 -0,362 0 -0,03 -0,03

0,201077 0 -1,0025 -0,871 -1,134 -0,33 0 -0,03 -0,03

0,204709 0 -0,8825 -0,76 -1,005 -0,242 0 -0,03 -0,03

0,208322 0 -0,9905 -0,897 -1,084 -0,221 0 -0,03 -0,03

0,21195 0 -0,955 -0,81 -1,1 -0,26 0 -0,03 -0,03

0,215821 0 -0,865 -0,86 -0,87 -0,13 0 -0,03 -0,03

0,219446 0 -0,9705 -0,864 -1,077 -0,23 0 -0,03 -0,03

0,223013 0 -0,922 -0,86 -0,984 -0,18 0 -0,03 -0,03

0,226638 0 -1,003 -0,892 -1,114 -0,253 0 -0,03 -0,03

0,230264 0 -1,048 -0,988 -1,108 -0,114 0 -0,03 -0,03

0,233863 0 -1 -0,85 -1,15 -0,213 0 -0,03 -0,03

0,237488 0 -1,021 -0,942 -1,1 -0,253 0 -0,03 -0,03

0,241068 0 -0,9885 -0,874 -1,103 -0,26 0 -0,03 -0,03

0,244683 0 -1,005 -0,86 -1,15 -0,228 0 -0,03 -0,03

0,248292 0 -0,8885 -0,836 -0,941 -0,112 0 -0,03 -0,03

0,251636 0 -1,065 -0,91 -1,22 -0,119 0 -0,03 -0,03

0,255259 0 -1,012 -0,874 -1,15 -0,14 0 -0,03 -0,03

0,258897 0 -1,0985 -0,941 -1,256 -0,212 0 -0,03 -0,03

0,262471 0 -1,007 -0,914 -1,1 -0,18 0 -0,03 -0,03

0,266081 0 -1,0065 -0,908 -1,105 -0,182 0 -0,03 -0,03

0,269715 0 -1,005 -0,86 -1,15 -0,135 0 -0,03 -0,03

0,273293 0 -0,988 -0,91 -1,066 -0,221 0 -0,03 -0,03

0,276915 0 -0,98 -0,86 -1,1 -0,28 0 -0,03 -0,03

0,280555 0 -0,9955 -0,91 -1,081 -0,254 0 -0,03 -0,03

0,284164 0 -0,9915 -0,815 -1,168 -0,131 0 -0,03 -0,03

0,287747 0 -1,078 -0,965 -1,191 -0,18 0 -0,03 -0,03

0,291382 0 -1,045 -0,952 -1,138 -0,268 0 -0,03 -0,03

0,294994 0 -1,075 -1,032 -1,118 -0,205 0 -0,03 -0,03

0,298578 0 -0,9825 -0,832 -1,133 -0,28 0 -0,03 -0,03

0,301945 0 -1,018 -0,91 -1,126 -0,03 0 -0,03 -0,03

0,305815 0 -0,984 -0,822 -1,146 -0,215 0 -0,03 -0,03

0,3094 0 -1,1095 -0,949 -1,27 -0,08 0 -0,03 -0,03

0,312759 0 -1,098 -0,882 -1,314 -0,086 0 -0,03 -0,03

0,316392 0 -1,07 -0,873 -1,267 -0,189 0 -0,03 -0,03

0,319975 0 -0,9885 -0,91 -1,067 -0,198 0 -0,03 -0,03

0,323617 0 -0,999 -0,932 -1,066 -0,208 0 -0,03 -0,03

0,327182 0 -1,0075 -0,936 -1,079 -0,217 0 -0,03 -0,03

46

0,33084 0 -0,905 -0,904 -0,906 -0,133 0 -0,03 -0,03

0,334407 0 -1,0215 -0,893 -1,15 -0,318 0 -0,03 -0,03

0,338062 0 -1,059 -0,96 -1,158 -0,175 0 -0,03 -0,03

0,341671 0 -0,994 -0,888 -1,1 -0,18 0 -0,03 -0,03

0,345239 0 -0,9745 -0,875 -1,074 -0,192 0 -0,03 -0,03

0,348847 0 -0,984 -0,868 -1,1 -0,18 0 -0,03 -0,03

0,352733 0 -0,984 -0,86 -1,108 -0,195 0 -0,03 -0,03

0,35607 0 -0,9325 -0,797 -1,068 -0,3 0 -0,03 -0,03

0,359731 0 -0,94 -0,846 -1,034 -0,162 0 -0,03 -0,03 0,36329 0 -1,0245 -0,949 -1,1 -0,196 0 -0,03 -0,03

0,366918 0 -0,904 -0,81 -0,998 -0,271 0 -0,03 -0,03

0,370517 0 -1,0055 -0,91 -1,101 -0,214 0 -0,03 -0,03

0,374154 0 -0,9315 -0,764 -1,099 -0,036 0 -0,03 -0,03

0,377743 0 -0,971 -0,892 -1,05 -0,2 0 -0,03 -0,03

0,381351 0 -0,972 -0,81 -1,134 -0,3 0 -0,03 -0,03

0,384996 0 -0,9865 -0,81 -1,163 -0,192 0 -0,03 -0,03

0,388587 0 -0,8995 -0,849 -0,95 -0,28 0 -0,03 -0,03

0,392199 0 -0,973 -0,826 -1,12 -0,117 0 -0,03 -0,03

0,395829 0 -1,023 -0,876 -1,17 -0,243 0 -0,03 -0,03

0,399441 0 -1,0065 -0,874 -1,139 -0,212 0 -0,03 -0,03

0,403059 0 -1,009 -0,813 -1,205 -0,08 0 -0,03 -0,03

0,4069 0 -0,9525 -0,912 -0,993 -0,23 0 -0,03 -0,03

0,41028 0 -1,1235 -1,054 -1,193 -0,08 0 -0,03 -0,03

0,414142 0 -1,0265 -0,952 -1,101 -0,194 0 -0,03 -0,03

0,417766 0 -0,961 -0,904 -1,018 -0,13 0 -0,03 -0,03

0,421377 0 -0,9895 -0,883 -1,096 -0,15 0 -0,03 -0,03

0,424995 0 -0,993 -0,86 -1,126 -0,15 0 -0,03 -0,03

0,428618 0 -1,1245 -0,908 -1,341 -0,18 0 -0,03 -0,03

0,432226 0 -0,936 -0,784 -1,088 -0,309 0 -0,03 -0,03

0,43581 0 -1,003 -0,931 -1,075 -0,38 0 -0,03 -0,03

0,439428 0 -0,999 -0,876 -1,122 -0,24 0 -0,03 -0,03

0,443051 0 -1,0535 -0,91 -1,197 -0,252 0 -0,03 -0,03

0,446641 0 -1,007 -0,882 -1,132 -0,23 0 -0,03 -0,03

0,450278 0 -0,984 -0,968 -1 -0,13 0 -0,03 -0,03

0,453863 0 -1,0515 -0,992 -1,111 -0,19 0 -0,03 -0,03

0,457497 0 -1,0015 -0,83 -1,173 -0,196 0 -0,03 -0,03

0,461079 0 -0,957 -0,833 -1,081 -0,192 0 -0,03 -0,03

0,464711 0 -0,991 -0,782 -1,2 -0,145 0 -0,03 -0,03

0,468306 0 -0,6635 -0,731 -1,2 -0,145 0 -0,03 -0,03

0,471918 0 -0,8625 -0,769 -0,956 -0,263 0 -0,03 -0,03

0,475557 0 -0,92 -0,814 -1,026 -0,181 0 -0,03 -0,03

0,479131 0 -1,044 -0,87 -1,218 -0,281 0 -0,03 -0,03

0,482772 0 -1,08 -0,91 -1,25 -0,18 0 -0,03 -0,03

0,486381 0 -0,9575 -0,782 -1,133 -0,306 0 -0,03 -0,03

0,489956 0 -0,86 -0,81 -0,91 -0,355 0 -0,03 -0,03

0,493318 0 -0,961 -0,81 -1,112 -0,23 0 -0,03 -0,03

0,4969 0 -0,9635 -0,97 -0,957 -0,194 0 -0,03 -0,03

47

0,500546 0 -0,98 -0,86 -1,1 -0,159 0 -0,03 -0,03

0,504133 0 -0,883 -0,81 -0,956 -0,215 0 -0,03 -0,03

Offset -0,87 -1,10549 -0,19916