Design Calculations for Optimising of a Deep Borehole Heat Exchanger

Diplomarbeit

im Studiengang Bergbau

vorgelegt von

Simon Christian Speer

im Juli 2005

Acknowledgement

I thank Prof. Dr. Christoph Clauser to give me the opportunity to do this final thesis at his institute.

I am grateful to my supervisor Lydia Dijkshoorn for her advice.

Special thanks to Roland Wagner for his help and sharing his experience in the field of numerical

simulation and to Margarete Linek for her assistance.

Furthermore, I thank all colleagues of the Institute of Applied Geophysics for the pleasant working

atmosphere.

The measurements were assisted by Frank Höne and Dirk Breuer.

Lithological interpretation of the samples was done by Christoph von Hagke.

Log file interpretation was done with the aid of Dr. Renate Pechnig and Phillip Kuhn.

Last but not least I thank the “Department of Mineral Processing (AMR)” for assisting with special

equipment.

Table of ContentsI Introduction........................................................................................................................................ 4II The RWTH-1 Deep Borehole Heat Exchanger.................................................................................6III Measurements.................................................................................................................................. 9

III.1 Cuttings.................................................................................................................................. 10III.1.1 Density............................................................................................................................11III.1.2 Thermal Conductivity.....................................................................................................12

III.2 Cores...................................................................................................................................... 15III.2.1 Thermal Conductivity.....................................................................................................16III.2.2 Density............................................................................................................................17III.2.3 Porosity...........................................................................................................................19III.2.4 Compressional Wave Velocity....................................................................................... 19

III.3 Thermal conductivity from logging data................................................................................20III.4 Temperature Log ................................................................................................................... 24

IV Model.............................................................................................................................................25IV.1 Model Parameters.................................................................................................................. 28

IV.1.1 Permeability................................................................................................................... 28IV.1.2 Porosity.......................................................................................................................... 28IV.1.3 Thermal Capacity and Density.......................................................................................29IV.1.4 Initial Temperature.........................................................................................................29IV.1.5 Thermal Conductivity.................................................................................................... 29

V Simulations and Results..................................................................................................................32V.1 Temperature Pattern................................................................................................................32V.2 Effect of Time Step size..........................................................................................................35V.3 Effects of the Volume flow rate..............................................................................................40V.4 Effects of the Thermal Conductivity of the Stand Pipe.......................................................... 42V.5 Thermal Capacity of the Standpipe.........................................................................................44V.6 Operating Cycle...................................................................................................................... 45

VI Conclusion.....................................................................................................................................50VII Appendix...................................................................................................................................... 51

VII.1 Principles.............................................................................................................................. 51VII.1.1 Rotary Drilling.............................................................................................................. 51VII.1.2 Mud system...................................................................................................................52VII.1.3 Sampling Procedure......................................................................................................53VII.1.4 Matrix Density.............................................................................................................. 53VII.1.5 Thermal Conductivity from Needle Probe Measurements........................................... 55VII.1.6 Thermal Conductivity from optical scanning............................................................... 58VII.1.7 Multi Sensor Core Logger............................................................................................ 60

VII.1.7.i Density................................................................................................................... 61VII.1.7.ii Compressional Wave Velocity............................................................................. 62

VII.2 Formulae...............................................................................................................................63VII.3 Data.......................................................................................................................................64

VII.3.1 Cuttings.........................................................................................................................64VII.3.2 Cores ............................................................................................................................ 69

VII.4 Bibliography......................................................................................................................... 71

I Introduction

The RWTH Aachen University will build a new student affairs building (picture 1). Because of its

C-shaped form it is called the SuperC, the extraordinary design is supposed to represent the modern

attitude. Since Aachen is famous for its hot mineral springs since Roman times, what would be

more natural than to use (natural) geothermal energy as an energy source and demonstrate the

capability and practical experience of the RWTH on the area of sustainable energies.

The conceptual design of the borehole heat exchanger was done by the "Institute of Mine-

Surveying, Mining Subsidence Engineering and Geophysics in Mining", the drilling operation was

supervised by the "Institute of Surface Mining and Drilling", the examination of the underground

was done by the institutes of the "Geoscience Group". The productivity of the deep borehole heat

exchanger is simulated within the scope of this diploma thesis at the "Institute of Applied

Geophysics", thus assisting the architects at designing the climate control unit of the building.

The concept of the deep borehole heat exchanger of the SuperC does not comprise a heat pump. The

drilling provides insight into the unknown but important geology of the subsurface of Aachen.

While geothermal energy is defined as a resource under the German mining law (Bundesberggesetz)

– heat“mining” is still a unusual thought. Mining is also considered as obsolete and disturbing by

Pic. 1 Artists view of the SuperC.

the German public. The SuperC-project offers a great opportunity to present the modern and

environmentally friendly aspects of “mining”.

The productivity of a deep borehole heat exchanger is strongly affected by the subsurface and its

design is complex as goes beyond simple approximations. The calculation of the energy production

has to be done via numerical simulation and requires information of the thermal rock properties of

the rock in place. The location of the drill site in the centre of the university enabled the collection

of many samples, the base of a detailed data set for the numerical simulation.

This diploma thesis examines various operating and construction parameters of the deep borehole

heat exchanger of the SuperC, thus enabling the assessment of the thermal productivity of various

designs. As a basis for numerical simulations, samples of cuttings and drill cores were taken and

their relevant physical properties were measured (chapter III.1 and III.2). Borehole logging data

were also used to obtain continuous information of geophysical parameters (chapter III.3). A

detailed model of the deep borehole heat exchanger and its surroundings was designed and

procedures for easy exchange of data or parameters were developed (chapter IV). Simulations to

examine the effects of various operating parameters and designs on the outlet temperature are

described in chapter V.

II The RWTH-1 Deep Borehole Heat Exchanger

This section outlines the principle of borehole heat exchangers and gives a review over the borehole

RWTH-1.

When drilling into the earth crust, temperature rises on average by 30 K/km. This increase is due to

heat transfer from the hot core of the earth and radioactive decay in the rock. In a depth of about 2.5

km a temperature of about 80 °C could therefore be expected. The SuperC deep borehole heat

exchanger is composed of a deep borehole with an inner coaxial pipe (further referred to as

standpipe). A cool fluid is continuously pumped into the annulus and is heated up by the

surrounding rock while travelling to the bottom. The heated fluid rises to the surface through the

well insulated standpipe. In the concept of the SuperC heat is used both to power climate control

units and to heat buildings. Boreholes yielding high temperatures (above 150 °C) can be used to

generate electricity. The thermal power P of a borehole heat exchanger is directly proportional to the

temperature difference

Eq. 1 ΔT = Toutlet – Tinlet

between production (Toutlet) and injection temperature (Tinlet). After heat extraction, the fluid is

returned to the inlet to be heated up again. This way a rock column with a radius depending on the

thermal diffusivity κ of the rock and time, but usually not exceeding 10 m around the borehole, is

affected [Signorelli 2004]:

Eq. 2 =

c

Within years an almost constant heat sink develops resulting in an almost constant production

temperature. As most deep borehole heat exchanger the one planned at Aachen uses water as fluid.

The thermal power P of the medium is calculated from the temperature difference ΔT, volume flow

Q, density of the fluid ρf, and the thermal capacity cf of the fluid [Wagner et al., 2002]:

Eq. 3 P therm=ρ f⋅c f⋅Q⋅ΔT

where ρf ·cf is in [J/(m³,K)] and Q in [m³/s].

The RWTH-1 borehole is located next to the main building in the middle of both the town and the

university, and about 500 m to the North behind the Aachen thrust fault, along which the mineral

springs of Aachen emerge. Its construction copes all the challenges regarding available amount of

space, control of noise emission, safety and acceptance by the public.

A mobile rotary drill rig as shown in picture 2 was used. Picture 3 shows the drill site.

During drilling the rock is broken into small chips (see picture 4) which are flushed to the surface

by the drilling fluid where they are collected by the samplers (for more information see appendix

VII.1.1-3).

The design parameters of the RWTH-1 deep borehole heat exchanger which were defined in

advance of the drilling are as follows:

Parameter value

Total depth > 2500 m

Bottom hole temperature (BHT) > 85 °C

Outlet temperature 70 °C

Minimum required temperature 65°C 1

Inlet temperature 40 °C 1

Thermal power 450 kW

Heat production 625 kWh/y

CO2 savings 300 ton/y

useful life 30-40 years

The cement used in the lower part of the casing should have a high thermal conductivity, the cement

of the upper half should be insulating. The area of the annulus should be 4 times the area of the

standpipe1.

The final depth of 2544.5 m exhausted the mobile drill rig. Drill rigs capable of greater depths were

1 Karat M., supervisor of the drilling, institute of surface mining and drilling, 2005. personal communication.

either not available or would not fit into the available space.

Drilling started at the 19th of July 2004 and was finished at the

22th of November 2004. Except for the complete lack of core

for the entire lower half of the borehole due to technical

difficulties, drilling and coring were a full success.

Pic. 2 The mobile drill rig on its foundations.

Pic. 3 Top view of the drill site: To the left: the housed engines of the mud pumps, the pumps, and the mud pit. The shale shakers are above the pit, in the stilted container above the pumps there is a centrifuge. In the centre: the white noise protection of the drill rig. The drilling is controlled from the housing on the boom right. To the right: the container of the mud engineer.

III Measurements

Simulating the deep borehole heat exchanger

requires certain physical properties of the rock:

Most important is thermal conductivity

[Signorelli, 2004], others are thermal capacity,

porosity, permeability, and density. In this

section the sampling procedure, the

measurements of those parameters and the

results of measurements are discussed.

Figure 1 shows the lithological column,

simplified to units of 25 m, as used in the

model. Basically it is composed of different

kinds of siltstone with thin layers of fine

sandstone2. The locations of the samples (grey)

and the core lengths (black) are also indicated.

Recordings of various borehole measurements

(further referred to as logs) are used to assess

the thermal conductivity of the rock located

between the samples.

2 Oesterreich B., supervisor of Geological Survey, Krefeld, personal communication.

Fig. 1 Simplified and preliminary lithological column of the RWHT-1 borehole; indicated are different kinds of siltstone and the sample locations: grey=cuttings, black=cores.

III.1 Cuttings

After been chipped from the hole bottom by the drilling tool, the cuttings

are flushed to the surface by the drilling mud (mud). Shale shakers were

used to separate them from the mud, which is returned to the borehole. The

cutting samples were collected at a regular depth interval of 1 m resulting

in an amount of 2478 samples. After screening and cleaning they were

stored in numbered boxes.

A total of 57 cutting samples were selected at a regular interval every 50th box, resulting in a depth

interval of about 50 m, and at depths considered to be interesting due to variations in log files. On

these cuttings, mass, density and thermal conductivity were measured. To allow multiple use of

samples, the measurements had to be non-destructive and non-polluting: Only contact with tap

water was allowed. Heating above 60 °C or exposure to vacuum needed consent by all teams which

possibly would perform later examinations and was therefore restricted to the absolute minimum.

The drilling depth matches the real depth quite well: there is an almost constant offset (1 m - 2 m)

between drilling and sampling. Because of mixing effects due to rotation inside the mud column

while raising, samples are diluted with cuttings from other depths.

Pic. 4 Cuttings.

Pic. 5 Sampler cleaning and screening cutting samples.Stored samples are shown in the background.

III.1.1 Density

Matrix density ρm of the cuttings is measured with a helium gas pycnometer (Accupyc by

Micromeritics [Anonymous, 1997]). The device calculates the matrix density from the amount of

helium able to saturate the pores of the dried sample (see appendix VII.1.4 for more details).

The density varies from 2640 kg/m³ - 2840 kg/m³ with a mean of 2780 kg/m³ (figure 2). The usual

accuracy of the device is on the order of 1 kg/m³ - 0.1 kg/m³.

Bulk density was not measured because cuttings can not represent the porosity of the host rock:

While being drilled, the rock breaks where it is weak, i.e. where it is most porous. Therefore, the

cuttings represent the most stable, i.e. massive parts of the host rock.

Fig. 2 Density of the cuttings;the density varies from 2640 - 2840 kg/m³ with a mean of 2780 kg/m³.

III.1.2 Thermal Conductivity

Thermal conductivity of the cuttings could not be measured

directly. The TK04 needle probe (built by TeKa Geophysical

Instruments) was used to measure the thermal conductivity of a

mixture of water and cuttings. The principle is as follows: The

needle probe (see picture 6) is heated by a defined and constant

power. At the same time its temperature is measured at high

accuracy. The analysis software identifies time intervals in which

the measured temperature increase can be explained by thermal

conductivities determined by complex formulae (see appendix

VII.1.5). For each of those thermal conductivities a quality index

(the LET-value) is given. The result is presented in a diagram like

figure 3: The most reasonable thermal conductivity of the sample is the vertical asymptote of the

intervals with high LET. If the thermal conductivity indicated by the majority of the intervals is

differed from the one with the maximum LET, the outlier has to be omitted and the resulting

thermal conductivity is indicated as modified.

Each measurement on a sample consists of 10 – 20 individual measurements. At least half of the

measurements have to meet the following requirements, otherwise the sample was again prepared

and measured:

* a maximum LET above 1000,

* more than 100 intervals with a valid thermal conductivity value

* at least the results of the intervals measured at the beginning of a measurement

had to arrange mainly in a clear vertical asymptote.

The samples were shaken during preparation in order to expel trapped air and to get the sample in

good compact. Additionally, a PVC-pipe with a cap was used to insulate the sample from the

environment. However this had no visible effect on the measurements. In order to prevent free

convection in the water saturated sample the heating power was set to the absolute minimum of 2.0

W – 2.5 W.

The effect of the water can be deducted from the thermal conductivity, the result is a thermal

conductivity value for the cuttings (Eq. 30 30, and Eq. 31).

Pic. 6 Prepared sample with the TK04 needle probe.

Thermal conductivity of the cuttings

varied from 2.2 Wm-1K-1 – 8.9 Wm-1K-1

with a mean of 3.8 Wm-1K-1; the

porosity (water content) of the samples

varied from 40.98 % – 50.14 % with a

mean of 45.16 %. High values of

thermal conductivity could accompany

with average values of porosity, e.g.

sample number SC–1850 and number

SC–2084 (figure 4). At sample number

SC–2050 a thermal conductivity of 8.9

Wm-1K-1 and a porosity of 50.14 % was measured. Because both values were of the extraordinary, I

assumed a mistake in determining the porosity and used the average porosity of 45.10 % to calculate

a thermal conductivity of 6.9 Wm-1K-1. Figure 5 shows the variation with depth: the high values of

the deep samples can be explained by high percentages of quartz which were found in the cuttings

and cores. Figure 6 shows a correlation of thermal conductivity and density (correlation coefficient

σ = 0.8108). The complete list of TK04 results can be found in appendix VII.3.1.

Fig. 4 Thermal conductivity of cuttings vs. porosity of the prepared sample.

Fig. 3 A good result of the TK04 with one outlier. The most reasonable thermal conductivity of the sample is the vertical asymptote.

Fig. 6 Thermal conductivity vs. density (correlation coefficient σ= 0.8108);

Fig. 5 Thermal conductivity vs. depth;higher quartz content was found in cuttings and cores at greater depth, which explains the high thermal conductivity of some of the samples.

III.2 Cores

Drill core samples (picture 7) enable direct measurements of thermal conductivity.

Core samples were available for 3 sections with a summarised length of 150 m:

Section I 2“ 1391.5 m – 1515.7 m

Section II 2“ 2128.2 m – 2142.8 m

Section III 3.5“ 2536.8 m – 2544.5 m

Samples were selected by their depth of origin and at depths considered to be interesting due to

variations in log files, and their length. Their number indicates the core box, the row of the box and

their relative position in the row, e.g. sample number 44–3–1 is the 1st piece of core in the 3rd row of

the 44th core box. Letters were used to identify the parts of samples which broke after the initial

numbering.

Mass and thermal conductivity were measured on cores by the author. At the institute of Applied

Geophysics additional measurements of density, porosity, magnetic susceptibility, and velocity of

compression waves, and of natural gamma radiation were performed by Dirk Breuer, and Martin

Riess, respectively.

Three “test” samples –from section I and II– were measured in the condition (i) straight from the

storage facility, (ii) after drying at 60 °C, and (iii) after evacuating and saturating. Due to the low

porosity (see III.2.3), the deviations of all these measurements were on the same order as the

accuracy of each measuring device. In conclusion, no drying, evacuating and saturating was

performed for the remaining samples.

Pic. 7 Drill cores in core box.

III.2.1 Thermal Conductivity

Thermal conductivity of the cores was measured using the thermal conductivity scanner (TCS),

build by Lippmann & Rauen GbR (Anonymous, 2002). The thermal conductivity scanner moves a

source of defined thermal radiation along the sample and calculates the thermal conductivity of the

sample from the differences of temperatures measured before and after irradiation (see VII.1.6) for

more details). The manufacturer quotes the error to 3 %. Each sample was measured twice. The

difference of the two measurements was up to 3.6 % with a mean of 1.1 %. The thermal

conductivity of the samples varies between 2.3 Wm-1K-1 – 4.9 Wm-1K-1 with minimum and

maximum values of 2.0 Wm-1K-1 (at sample number 44–3–1ab) and 5.9 Wm-1K-1 (at sample number

61–1–2) respectively. The arithmetic mean calculates to 3.02 Wm-1K-1, the geometric mean to 2.99

Wm-1K-1. Figure 7 shows the results:

Fig. 7 Measurements of the core samples;

III.2.2 Density

Density was measured on cores either using the multi sensor core logger by means of gamma-

adsorption (see appendix VII.1.7.i for further details) and on parts from the cores using the helium

gas pycnometer. The multi sensor core logger uses a source of gamma radiation and measures the

transmitted gamma intensity. Density is calculated from the absorbed gamma radiation. The process

requires careful calibration.

Density by helium gas pycnometer varies between 2391 kg/m³ – 2897 kg/m³ with a mean of 2820

kg/m³.

Gamma density varies between 2576 kg/m³ – 3233 kg/m³ with a mean of 2830 kg/m³ (figure 8).

The few measurements done with both pycnometer and gamma radiation were not comparable

because the samples small enough to fit into the first device were usually too small to be measured

with the multi sensor core logger. Additionally, while the gamma radiation-value is a mean over the

whole core sample, the pycnometer-value of the represents one value for a small part of a core –

even if the multi sensor core logger measures only at one location, this particular location was not

measured by the pycnometer. Core sample number 1–3–5 is the single special case which fitted into

both devices with both measured a density of 2806 kg/m³ (figure 9).

Fig. 8 Gamma-density values of the three core sections.

Fig. 9 Comparison of density measured with helium gas pycnometer and absorbtion of gamma radiation;the measurements with both devices are not comparable because the samples which fit into the pycnometer are too small to be measured with the other device. Additionally, while the gamma-value is a mean over the entire core sample, the pycnometer-value represents one value for a small part of a core. The sample at 1394.1 m is the single special case which fitted into both devices with both measured a density of 2806 kg/m³.

III.2.3 Porosity

The porosity Φ of the three selected core samples were calculated from:

Eq. 4 =msat – mdry

ρH2O⋅ 1

V sample

where msat is the weight of the sample after saturation, mdry the weight after drying, ρH2O the density

of water at room temperature and Vsample the volume of the sample. Vsample is calculated from the

weight of water displaced by the saturated core (accuracy 1 %). As can be seen in table 1, porosity is

almost zero with a mean of 0.012 %.

sample porosity# [%]

1431.6 0.011476.7 0.022134.7 0.01

Tab. 1 Porosity of cores.

The multi sensor core logger calculates porosity from gamma density and a given matrix density. It

is problematic that gamma density is measured at various points of the sample, but only one single

value of matrix density is used for the entire sample. That is why the measurements of porosity with

the multi sensor core logger had to handled with extra care. Nevertheless, the porosity values were

at the lower end of the precision of the multi sensor core logger.

III.2.4 Compressional Wave Velocity

Compressional wave velocity was also measured by the multi sensor core logger (refer to VII.1.7.ii

for further details). It is used in combination with the potassium content to enable the calculation of

thermal conductivities from the log file (Chapter III.3).

III.3 Thermal conductivity from logging data

The logging data are used to assess the thermal conductivity of the rock located between the

samples. The resulting thermal conductivity plot was averaged over the cell sizes of the model (see

also chapter IV.1.5).

It is not possible to measure thermal conductivity directly in the borehole, so an approach to

determine thermal conductivity from the existing logs had to be found: It is a standard procedure in

commercial log interpretation to calculate the volume content of clay (VCLGR) from the

contribution of potassium to the entire gamma radiation. Identifying a thermal conductivity λ1 on the

scale of clay with the clay-content and a thermal conductivity λ2 on the scale of quartz with the rest

of of the rock yields a thermal conductivity λlog for the logging point.

An internal procedure of the “Interactive Petrophysics” software from Schlumberger [Anonymous,

2006] was used to calculate the volume content of clay-values. Compressional wave velocity and

potassium contribution to natural gamma radiation were used to identify 7 zones of individual

definitions of 100 % clay (figure 10)3: Assuming clay as the only source of relevant potassium

radiation, 0 % clay was allocated to the lowest overall value. Individual 0 % clay definitions would

ad a greater error to this two component system, because in each zone there is a different sort of clay

with a different intensity of radiation. Each zone has also an individual background radiation. This

way, a third component is added to the formula, because no clay does not automatically mean 100 %

quartz.

The log has a vertical resolution of 0.076 m and the values were smoothed over an interval of 2 m.

To calculate thermal conductivity the arithmetic (ari) and the geometric (geo) means were used.

Eq. 5 λari=λ1⋅V clayλ2⋅1−V clay

Eq. 6 λgeo=λ1V clay⋅λ2

1−V clay

3 Courtesy of Dr. R. Pechnig, Geophysikalische Beratungsgesellschaft, Stollberg

For each previously identified zone individual thermal conductivities were assigned to the contents

in clay and the remaining rock. For each value measured on a sample the corresponding log value

was identified. The calculated λlog were matched to the measured ones by varying λ1 and λ2.

The matching was done either by minimising the standard deviation of the population of the values

(resulting in a thermal conductivity pattern named AM85, see figure 11):

Eq. 7 variance [Davis, 2002] VAR=n⋅∑ i

2−∑ i ²n2

where λi are the thermal conductivities of all corresponding sample- and log-values,

or by minimising the sum of the deviations of the corresponding values (resulting in a thermal

Fig. 10 7 zones of different clay were identified and shown. Potassium content is plotted against compressional wave slowness DTC (courtesy of 3).

conductivity pattern named GM87, see figure 11):

Eq. 8 (minimised) average deviation MAD=1n⋅∑∣λlog – λsample∣ and

Eq. 9 (minimised) square deviation MSD= 1n⋅∑ λlog – λsample

2.

where n is the number of values and λsample is the measured thermal conductivity of the sample.

Minimising equation 7 led to higher values than minimising equation 8 or equation 9. Minimised

square deviation (Eq. 9) was preferred, because it led to to the lowest thermal conductivities. The

differences in thermal conductivity due to the method of matching were greater than the difference

due to the use of arithmetic or geometric mean.

This yields an approximation of thermal conductivity which is more detailed and accurate than

simple averages of the sample values.

The thermal conductivity derived from the log λlog were averaged over the length of the cell size of

the model after [Beardsmore and Cull, 2001]:

Eq. 10 arithmetic mean: λcell horizontal=∑ θ i⋅λi

which is important for the calculation of the deep borehole heat exchanger and

Eq. 11 harmonic mean: 1λcell vertical

=∑ θ i

λi

which is important for the steady state temperature profile and heat flux, where λi is the ith λlog and θi

is the ratio of the thickness zi of the ith layer to the thickness Z of the whole layer. Because the

resolution of λlog is constant 0,076 m:

Eq. 12 θ i=z i

Z=

z i

z i⋅n=1

n

where n is the number of values averaged by the cell.

Therefore:

Eq. 13 λcell horizontal=1n⋅∑ λi and

Eq. 141

λcell vertical=1

n∑1λi

The factors of anisotropy acell (required by the simulation software) can now be calculated:

Eq. 15 λcell horizontal=λcell vertical⋅acell acell=λcell horizontal

λcell vertical

Zone 4 is special, because in the lower third of the section the clay free part is dominated by

dolomite and marl instead of quartz, so the zone was divided into zone 4–1 and zone 4–2 and

thermal conductivity for clay λ1 and not-clay λ2 was assigned individually. Recalculation of the

volume content of clay (VCLGR) would not have resulted in different values.

Future work may tune the thermal conductivities to reproduce recently and future measured

temperature logs.

Fig. 11 Comparison of the used thermal conductivity patterns: “Samples90” is based on samples values and their arithmetic means,“AM85” is based on the arithmetic mean over λlogs calculated with arithmetic mean, calibrated by minimising the variance of the values and corrected manually.“GM87” based on the harmonic mean over λlogs calculated with geometric mean, calibrated by minimising the minimum square deviation of sample- and corresponding log-values and corrected manually (the number indicates the required heat flow density [mW/m²] to achieve a BHT of about 80°C).

III.4 Temperature Log

Due to problems during logging only the upper part of the temperature log was known. About four

months after the completion of the borehole, a detailed and precise temperature log was recorded4

(figure 12). The log was used to assess the quality of the thermal conductivity patterns of the model

(see chapter V.1).

The temperature log can also be used to calibrate the thermal conductivity pattern.

4 Courtesy of S. Lundershausen, supervisor of drilling, institute of surface mining and drilling, 2005.

Fig. 12 Temperature log and gradient, measured about 5 months after completion of the borehole (20.04.2005). BHT is 78.6 °C, the mean temperature gradient is 26.3 K/km.

IV Model

In the previous section the obtaining of the data set was described. This section is about the model

and the values of its parameters. The model will be used to simulate the cross current heat

exchanger of the RWTH-1 borehole with a length of 2550 m which is supposed to generate 450 kW

of thermal power with a minimum production temperature of 65 °C. It consists of two concentric

pipes: cool water is continuously pumped through the annulus to the bottom of the drillhole and is

heated up by the surrounding rock. The heated water rises to the surface through the well insulated

inner pipe.

The Finite Difference (FD) numeric simulation tool SHEMAT –Simulator for HEat and MAss

Transport– [Clauser, 2003] was used to examine the effects of various operating and design

parameters on the outlet temperature.

Numerical models based on the FD method calculate values for the prognostic quantities at discrete

points in space (nodes). Nodes are identified by their grid indices i, j, k, and are separated by grid

lines. Constant material properties are specified for each block. All kinds of flows (fluid, heat,

mass) are calculated across the interfaces separating the blocks (staggered grid approach). The

governing equations are solved at the grid's discrete nodal points by approximating differentials in

the prognostic partial differential equations by finite differences. The result of this discretisation is a

system of linear finite difference equations which is solved numerically.

The equations for coupled flow and heat transport on a FD grid in a cylindrical coordinate system

are

Eq. 16 K 1r

ddrr dh

drKd²hdz²=S s

dhdt−W

Eq. 17 κr

ddrrdT

dr−T vrκ d

dzdTdzTv z=dT

dt

where h is the hydraulic head, Ss is the specific storage coefficient of the tubes and W is the fluid

source/sink at the tube inlet/outlet. The hydraulic conductivity K and the rock thermal diffusivity κ

are constant scalars [Wagner R. & Clauser C., 2005].

The user interface (Processing SHEMAT) communicates via ASCII input files. An input file

comprises amongst others the following sections:

1. Scalar parameters to describe the model (name, dimension, type of simulation, etc.) and heat

transport;

2. Time- and period-dependent parameters, like total simulation time and time steps for simulation

periods;

3. Arrays associated with flow and heat transport, like grid properties and physical material

parameters. Each array stores its values in a single line.

The size of the model (7 parameters and about 18300 cells) designed in this study could not be

handled with the existing user interface, therefore the following procedure was developed to set up

the model:

1) Grid design and assignment of values using a spread sheet

2) Writing a program which generates the grid

3) Exporting of the charts to individual files in ASCII-format

4) Transforming these charts into lines using self-programmed DOS-commands

5) Copying the lines into the SHEMAT input file

For a start, there were charts with depth related data from the measurements, the preliminary

lithology-cell structure, and the casing scheme. After designing the grid, a coordinate system

plotting the cell sizes on x- and y-axis was set up in a chart. The cells were coloured according to

the material or the lithology they should represent, e.g. cells which should represent casing became

black. The result of these procedure is shown in figure 13. This chart was duplicated for each

parameter. The colours of the parameter charts were used to set pointers to the appropriate cells of

an additional material property chart which stores the material or depth-related values of the

parameters in columns. This way, data exchange was very easy: changes in one cell of the material

property chart immediately take place in the whole parameter chart. The contents of these charts are

copied into text files which are transformed into the SHEMAT format by a self programmed DOS

command. The results of this command are pasted into the input file at the appropriate locations.

Due to the fact, that the permeabilities are very low and no natural groundwater flow was detected, a

cylindrically symmetric model could be used. Because of the symmetry, only a 2D-grid is required.

It consists of horizontal layers both due to the low inclination of the layers relative to the borehole

(about 10°) and due to the limitations of a model of this type. It simulates a cylinder with a radius of

99.5 m and a depth of 2973.5 m. The cooling effect of a single borehole heat exchanger affects only

an area of about 10 m around the borehole [Signorelli, 2004], therefore the radial extension is more

than sufficient. A minimum cell size of 5 mm was used in every zone of special interest, i.e. inlet,

reversal, outlet, and the whole casing, due to the required high accuracy at this locations. Transition

zones with an increasing size by a factor of 1.5 were used to to lead over to maximum cell size of 25

m for the remaining cells. The number of cells accounts to 91 x 201 = 18291 cells. Each calculation

step took about 0.8 seconds on a workstation5.

Figure 13 shows the model in comparison to the reality. The lithological column was simplified to

units of 25 m (maximum cell size) and warped until it fitted into the grid. The radii and depths of

the casing as well as the changes of lithology are well represented. In contrast to the concept the

reversal is at the very bottom of the model. This was done both to achieve maximum bottom hole

temperature and to limit the number of cells: For the purpose of accuracy of the simulation, the

whole reversal has to have minimum cell size. The reversal of the model is located about 15 m

deeper (about half of maximum cell size) than in reality due to dimensions of the grid.

5 with a "SPECfp®_rate2000 for (Linux) 4P Systems" of 65, see www.spec.org/cpu2000/ for further details

Fig. 13 The casing scheme of the RWTH-1 (left) - a view of the model (centre) - the lithological column (right);The left side of the model represents the casing with water, liners, and concrete backfilling; the right side represents the lithology. The distorted view results from displaying all grid cells as equal sized.

IV.1 Model Parameters

This section gives short descriptions of parameters selected for the simulation. To be mentioned

again, all values can easily be changed to examine other criteria than output temperature.

IV.1.1 Permeability

Rock permeability in the model was set to zero because of the following aspects:

* the very low porosity measured at the cores (0.2 0/00);

* during the drilling no fluid loss or inflow was observed;

* one of 81 attempts to sample fluid at selected promising locations was successful, but with too

little fluid to be analysed properly 6.

The flow field is completely defined by a fixed injection rate. Therefore, the value of permeability

of the water-bearing parts of the deep borehole heat exchanger does not affect the simulation results

and was arbitrary set to 10-8 m².

IV.1.2 Porosity

Porosity was set to values of 0.95 for the pipe-system and close to zero for the remaining; SHEMAT

does not allow using porosities of 1.0 and 0.0 in order to prevent “division by zero” errors.

6 Personal communication, Trautwein U.

IV.1.3 Thermal Capacity and Density

SHEMAT uses density ρ and specific heat capacity cp only as a product ρcp, the thermal capacity;

density is only used to assist the interpretation of the result.

Fortunately, thermal capacity is almost constant for most rocks with an average value of

2.2x106 Jm-3K-1 ± 20 % [Mottaghy et al., 2005; Beck, 1988; Vosteen & Schellschmidt, 2003]. This

mean value was used in the simulations.

IV.1.4 Initial Temperature

In order to determine the initial temperature distribution of the model several steady-state

simulations were run for each of the three thermal conductivity patterns and a fixed surface

temperature of 10.35 °C. Heat flow density was varied until the expected, and later measured

bottom hole temperature of about 80 °C were reached (see chapter V.1)

The temperature of the injected water was set to 40 °C, according to the design parameters of the

deep borehole heat exchanger.

IV.1.5 Thermal Conductivity

Basically three thermal conductivity patterns were examined, they are shown in figure 14:

The first one (Samples90) based only on sample values. Missing values for thermal conductivity

were generated by arithmetic mean of adjacent cells or taking the first or last measured value

Eq. 18 λmissing=λ1λ2

2,

where λmissing is the missing thermal conductivity and λ1 and λ2 are the thermal conductivity of the

adjacent cells.

It was done to understand the behaviour of the model and its reactions to parameter variations. In

this approach a heat flow density as high as 90 mW/m² was required to achieve a bottom hole

temperature of about 80 °C.

The second one (AM85) is based on the arithmetic mean (Eq.10) over values of thermal

conductivity derived from logging data (λlog, see chapter III.3) calculated with an arithmetic mean

(Eq.6). It was calibrated by minimising the variance of corresponding sample- and log-values (VAR,

Eq. 7). When necessary, λcell was corrected by hand, e.g. if high values of λlog could not be explained

by high contents of quartz in the correspondent cutting samples. In this approach a heat flow density

as high as 85 mW/m² was required to achieve a bottom hole temperature of about

80 °C.

The last one (GM87) is based on the harmonic mean (Eq. 8) over values of λlog calculated using a

geometric mean (Eq. 6). It was calibrated by minimising the minimum square deviation of

corresponding sample- and log-values (MSD Eq. 9). It was corrected in the same way as AM85. In

this approach a heat flow density as high as 87 mW/m² was required to achieve a bottom hole

temperature of about 80 °C. It was used to examine the cycled operations.

Using Eq. 7 to calibrate λlog led to a temperature pattern which fits much better to the measured one

(see figure 15, AM85). Unfortunately, these results only in the very last days of this study, when a

temperature log of good quality became available. Although, this is important for the initial

temperature distribution, it is less important for the calculation of the thermal productivity: the mean

difference of thermal conductivity of GM87 and of AM85 is less than 4.4 %, and generally, the

thermal conductivities of GM87 are higher than those of AM85, therefore the calculations of thermal

productivity are maximum estimates.

For the steel liners, 50 Wm-1K-1 was used. The values of the backfill were given by M. Karat:

0.52 Wm-1K-1 for the insulating cementation, 2.02 Wm-1K-1 for the heat conducting one and 1.21

Wm-1K-1 for the normal one. Based on the logging data of the cementation, a perfect backfilling

could be assumed.

For the standpipe, values between 0.1 Wm-1K-1 and 0.0001 Wm-1K-1 had been tested.

Fig. 14 Comparison of the used thermal conductivity patterns: “Samples90” is based on samples values and their arithmetic means;“AM85” is based on the arithmetic mean over λlogs calculated with arithmetic mean, calibrated by minimising the variance of the values and corrected manually;“GM87” based on the harmonic mean over λlogs calculated with geometric mean, calibrated by minimising the minimum square deviation of sample- and corresponding log-values and corrected manually (the number indicates the required heat flow density [mW/m²] to achieve a BHT of about 80°C).

Fig. 15 Comparison of the reduced temperatures calculated with the different thermal conductivity patterns:to visualise the temperature differences, a constant temperature of 12 °C and a gradient of 0.0263 K/m were subtracted from the temperatures. The thermal conductivity model AM85 yields a good match to the measured values.

V Simulations and Results

The technical layout of the deep borehole heat exchanger of the RWTH-1 specifies a thermal power

of 450 kW at a production temperature of at least 65 °C for 30 – 40 years. The previous sections

described how values of the physical parameters were assessed, and the numerical model was

designed. The following section describes and discusses the simulations of the production

temperature Tout and the time interval of production temperatures greater 65 °C t(T>65°C).

If not stated otherwise, the simulations were performed with the first available thermal conductivity

pattern samples90 and the corresponding temperature pattern. As can be seen in figure 14, this

thermal conductivity pattern is generally (not always) above the other two (the mean difference to

GM87 is 14 %), results may be interpret as upper bands. Nevertheless, samples90 was used only to

examine parameter variations and to give relative values, not absolute ones. It was not used to

predict the thermal power of the deep borehole heat exchanger.

V.1 Temperature Pattern

Prior to the operation of a deep borehole heat exchanger the subsurface is supposed to be in thermal

equilibrium. Therefore, the first subject to be simulated is the undisturbed temperature distribution.

It was simulated using models with undisturbed subsurface, i.e. without the deep borehole heat

exchanger: The models were assigned an overall temperature of 10 °C, which is close to the annual

mean air temperature of Aachen of 10.35 °C [Clauser, 1984]. The surface temperature was fixed

and the model was heated with a constant heat flux from below until a temperature equilibrium was

reached. By comparison of calculated and measured temperatures, the thermal conductivities of the

lithology could have been optimised.

Subject to thermal conductivity pattern, heat flow densities of 85 mW/m² to 90 mW/m² were

required to reproduce the measured bottom hole temperature of 79 °C. This is far more than the

German average of 69 mW/m² [Schellschmidt et al, 2002] and still exceeds the 72 mW/m²

measured at the nearby borehole Konzen [Karg, 1995]. On the other hand, flows of 110 mW/m² in a

depth of 1312 m and above 90 mW/m² between 1791 m to 2291 m were measured at the boreholes

Peer and Soumange [Verkeyn, 1995]. While the borehole RWTH-1 is located about 500 m to the N

of the Aachen thrust fault; Konzen lies 15 km to the S-E and to the S of the Aachen thrust fault;

Peer is 52 km to the N-W and to the N of the Aachen thrust fault, and Soumange is 20 km to the S-

W and penetrates the fault.

The heat flow density used in the model includes the yet unknown heat production due to

radioactive decay and possible lateral heat transfer from the hot mineral fluids travelling alongside

the Aachen thrust fault. It is used only to reproduce the measured bottom hole temperature. Since

temperatures are not yet in in equilibrium this heat flow density may still differ from the real one.

Figure 16 shows the gradient of the measured temperatures in comparison to the gradients of the

calculated ones:

The variations between zone 1 to 4–2 at 500 m, 900 m, 1016 m, 1207 m, 1375 m, and 1440 m can

be identified. At 240 m and between 1160 m – 1260 m there is a change in the casing layout (see

figure 13, page 27). It may be of interest, that the measured gradient has a mean of 0.026 K/m and is

lower than 0.025 K/m at the end.

To visualise the temperature differences in figure 16, the measured surface temperature of 12 °C

and a constant gradient of 0.0263 K/m was subtracted in figure 17. The borders of zone 2, 3, and 4

can clearly be seen, and to some extend also the division of zone 4 and the borders of zone 6. The

thermal conductivity model AM85 yields a good match to the measured values, while the thermal

conductivities in the lower part of GM87 and the heat flow density were overestimated. Using just

sample values yields an unsatisfactory result.

The temperature distribution achieved with the thermal conductivities of AM85 fitted best the

measured ones. With references to chapter III.3, a match of sample values and log values by

minimising the deviation of all values (VAR, Eq. 7) resulted in a better approximation of the reality

than minimising the deviations between corresponding values (MSD, Eq. 9).

The approximation of the thermal conductivities could be further improved by using equilibrated

temperature log for calibration.

Fig. 16 Comparison of calculated gradients with the measured one:Shown are the gradients of the temperature distributions calculated with the indicated thermal conductivity patterns. The borders of zone 1:2, 2:3, 3:4, and 4:5 are clearly reflected by the measured gradient.

Fig. 17 Comparison of the reduced temperatures: to visualise the temperature differences, a constant temperature of 12 °C and a gradient of 0.0263 K/m were subtracted from the temperatures The borders of zone 2, 3, and 4 can clearly be seen.AM85 matches the measured values quite well, the thermal conductivities in the lower part of GM87 are probably overestimated. Using just sample values yields an unsatisfactory result.

V.2 Effect of Time Step size

The time step size has a great effect on the duration of a simulation and its accuracy. Large steps

reduce the required simulation time but decrease the accuracy of the results, because temperature

changes on a scale smaller than the scale of the corresponding time step cannot be taken into

account by the simulation, i.e. greater time steps underestimate fast changes in temperature.

The effects of time steps on production temperature were examined for both continuous and cycled

operations.

Production temperature Tout showed no differences for time steps of Δt = ½ sec and 3.6 sec, and a

minor initial deviation at Δt = 60 sec. The initially greater deviations of even larger time steps

vanished within hours (see figure 18). For continuous operation the deviation between Δt = 3.6 sec

and ½ h was virtually zero after 15 hours; between steps of Δt = ½ h and 24 h the deviation was

virtually zero after the 5th day, i.e. the 5th time step. The zero-deviation remained until the end of

the simulations.

The deviation of equal time steps was greater for larger volume flows. This can be explained by the

Fig. 18 Production temperature Tout against time steps at 5m³/h for different values of timesteps size Δt: There is only a small deviation between the small time steps. The deviations for larger time steps vanished within hours (λpipe= 0.05 Wm-1K-1).

Courant criterion (Eq. 19), which guarantees that during each time step no more heat or matter is

lost at each node than was available at the beginning of this time step [Clauser, 2003]:

Eq. 19 Co=v z ΔtΔz1

Eq. 20 t zv z

where Δt is the time step, Δz is the vertical resolution of the grid, and vz is the vertical flow rate of

the fluid.

The vertical flow rate vz is dependent on volume flow Q and cross sectional area A:

Eq. 21 v z=QA

In this study, the Neumann Criterion (Eq. 22), which guarantees that the numerical procedure does

not invert the temperature gradient by heat conduction alone [Clauser, 2003], is fulfilled whenever

the Courant criterion is fulfilled, because the flow rate of the fluid is much faster than the velocity of

heat diffusion.

Eq. 22 Ne z ,heat=λ Δt

ρ c Δz ²½

As stated before, very large time steps can be used only for simulations of long-term, continuous

operations. Simulations of cycled operations required short time steps for sufficient accuracy. This

results in extremely large computing times. But an interesting observation was made:

Figure 19 shows the 2nd and 365th cycles of two identical simulations, one run with a time step Δt of

60 sec, the other with a time step Δt of 600 sec. The curves of each simulation look similar, but also

the curves of each cycle look similar; e.g. maximum and minimum values of all curves calculated

with the same time step Δt occur about the same time.

I developed the following procedure to reproduce at least the values of maximum production

temperature Tmax and the duration of the time interval of production temperatures greater than 65°C t

(T>65°C) geometrically by parallel translation, as shown in figures 20 and 21:

To determine the maximum production temperature Tmax of the late (365th) cycle for the small time

step (Δt = 60s) do this:

1) draw a vertical line from the maximum production temperature of the late large time step curve 600sTmax(365th) to the maximum production temperature of the early large time step curve 600sTmax(2nd);

2) draw a line from 600sTmax(2nd) to the maximum production temperature of the early small time

step curve60sTmax(2nd);

3) draw a vertical line with the same length as line 1 from 60sTmax(2nd):

the resulting point 60sTmax(365th) is (at least very close to) the maximum temperature of the late

small time step curve.

To determine the points, at which the late (365th) cycle of the small time step curve (Δt = 60s)

intersect the line of 65 °C, and therefore to determine the time interval of production temperatures

above 65°C t(T>65°C) do this:

1) draw a vertical line from the point at which the late large time step curve intersects the line of

65 °C 600sT65°C(365th) to the early large time step curve, resulting in point 600sT(2nd);

2) draw a horizontal line from 600sT(2nd) to the early small time step curve, resulting in point 60sT(2nd);

3) draw a vertical line from 60sT(2nd) to the line of 65 °C:

the resulting point 60sT65°C(365th) is (at least very close to) the point, at which the late small scale

curve intersects the line of 65 °C.

The heuristic procedure worked on different cycles of different simulations with different time

steps. Although it does not work for every point it yields to a much better approximation of

maximum production temperatures Tmax and time intervals t(T>65°C) than one percentage value.

The topic should be further investigated, because it could allow precise long term simulations of

cycled operations in a reasonable amount of time.

The conclusions of the above described observations are:

Higher volume flows require smaller time steps, and cycled operations short time steps. Long-term

cycled operations can be simulated with long time steps if at least 2 cycles of the same simulation

are run with very small time steps for comparison.

Fig. 20 Illustration of the correction of rough time steps at a 5m³/h 6/18 cycle:Number 1 to 3 leads to the corresponding point on the fine curve (λpipe = 0.01 Wm-1K-1).

Fig. 19 Comparison of the 2nd and 356th cycle of a cycled operation, calculated with time steps Δt of 60 sec and 600 sec: all 4 curves look similar, e.g. minimum and maximum temperatures are at the same times and the difference between the curves of large and small time steps are similar (λpipe = 0.01 Wm-1K-1).

Fig. 21 Illustration of the correction of large time steps at a 4m³/h, 8 h operating-16 h recovering cycle:the arrows point from the large time step curve to the corresponding point on the smal time step curve (λpipe = 0.01 Wm-1K-1).

V.3 Effects of the Volume flow rate

Several volume flow rates were simulated for a continuous operation in order to determine suitable

volume flow rates for cycled operations: 1 m³/h, 3 m³/h, 4 m³/h, 5 m³/h, 6 m³/h, 7 m³/h, and 10 m³/h.

Figures 23 and 22 and table 2 show the results:

At a volume flow rate of 1 m³/h an almost constant production temperature Tout > 60 °C could be

obtained, while for the others the time interval of production temperatures above 65 °C t(T>65°C)

is about 9 h, 6 h, 4 h, and 1.5 h respectively. During t(T>65°C) mean thermal powers P of about 23

kW, 115 kW, 145 kW, 160 kW, and 310 kW respectively were obtained. The thermal power P

drops to zero in the beginning, because the temperature difference ΔT between increasing

production temperature (Tout starts at 10 °C) and inlet temperature (Tin = 40 °C) becomes zero. It

rises to maximum value when the hottest water from the deepest point of the borehole heat

exchanger reaches the surface. It drops again when the water from the annulus resurfaces. The

second rise at the 10 m³/h curve can be explained when looking at the residence time of the water in

each of the casing sections (table 2):

After 12 h, the water from the inlet with the initial temperature of 40 °C reaches the surface again

with a temperature of 54.25 °C. On the other extreme, at a rate of 1 m³/h it takes 117 h to complete

one circulation.

Q t(T>65°C) mean P Residence time in

standpipe

tcirculation

[m³/h] [h:mm] [kW] [h] [h]

10 01:51 311 1.0 11.76 04:05 163 1.6 19.55 06:16 146 1.9 23.44 09:27 118 2.4 29.33 19:00 86 3.2 39.01 n.a. n.a. 9.7 117.0

Table 2: Volume flow, useable time, mean power output, residence time and total time for one circulation; (values for 3 m³/h are underestimated because of a greater time step).

Although the layout of the planned deep borehole heat exchanger calls for a thermal power of 450

kW, I calculated the cycled operations with flow rates of 4 m³/h and 5 m³/h, because only their

thermal power can be supplied for at the least 8 h a day, even after some years of operation.

Fig. 23 Tout against volume flow; As shown, t(T>65°C) is about 1.5 h, 4 h, 6 h, and 9 h, while at 1 m³/h an almost constant Tout of above 60 °C can be achieved (Δt = 6 s, , λpipe = 0.01 Wm-1K-1).

Fig. 22 Thermal power against volume flow (Δt = 6 s, , λpipe = 0.01 Wm-1K-1).

V.4 Effects of the Thermal Conductivity of the Stand Pipe

The thermal conductivity of the standpipe λpipe has a significant influence on the production

temperature Tout. The effects were examined for continuous operation at volume flow rates of 5 m³/h

and 10 m³/h, and for cycled operations at 4 m³/h.

In general, the importance of a lower value of λpipe increases as the volume flow decreases. This

effect is due to the longer residence time of the water in the pipe. As shown in figure 24, a decrease

from 0.001 Wm-1K-1 – 0.0001 Wm-1K-1 results in an increase of maximum production temperature

Tmax < 1K, which cannot justify the effort. On the other hand, an increase to 0.01 Wm-1K-1 reduces

the time in which Tout is greater than 65 °C t(T>65°C) almost by half. According to Summa et al.

[2005], GRP7-pipes usually have a conductivity of 0.36 Wm-1K-1. At Weggis (Switzerland), a

double-walled steel pipe with a maintained vacuum of 0.02 MPa is at use; its minimum thermal

conductivity λpipe is quoted to 0.09 Wm-1K-1, i.e. it may be higher [Kohl et al. 2002]. It goes without

saying, the use of simple state of the art GRP-pipes with a thermal conductivity on the order of 0.36

Wm-1K-1 is out of the question. On the other hand, even with the best available insulation with a

thermal conductivity λpipe of about 0.1 Wm-1K-1 temperature losses of 15 K – 25 K occur (see figure

29). Therefore, at least the best available insulation has to be used and even better ones should be

developed.

7 GRP = Glass-fibre Reinforced Plastic

Fig. 24 Tout against λpipe. at 5m³ (dwell: 2 h);An improvement from 0.001 Wm-1K-1 to 0.0001 Wm-1K-1 shows an increase of Tmax < 1°C, which can not justify the effort. On the other hand, an increase to 0.01 Wm-1K-1 reduced the t(T>65°C) almost by half (Δt is 60 s).

V.5 Thermal Capacity of the Standpipe

To estimate the influence of the thermal capacity of the standpipe, values of thermal capacity ρc of

window glass, district heating network pipe, glass-fibre reinforced plastic and other were simulated.

Aside from unrealistic values, t(T>65°C) is not affected by variations (figure 25). Most simulations

were run with the value of the district heating network pipe Kusiflex [Anonymous, 2005].

Fig. 25 Tout against RHOCMpipe

Aside from extreme values, t(T>65°C) is not affect variations (Q is 5m³/h, Δt is 60 s, λpipe. is 0.01 Wm-1K-1).

V.6 Operating Cycle

The simulations described above showed, that in continuous operation the deep borehole heat

exchanger is not able to supply the required temperatures and power. Therefore, cycled operations

with daily periods of heat extraction and recover were simulated. The length of the time interval of

heat extraction was selected from figure 23 (page 41): at a volume flow rate of 5m³/h, t(T>65°C) is

about 6 h, therefore a phase of 6 h of heat extraction alternates with a phase of 18 h of recovery . At

a volume flow of 4 m³/h, the phases were of 8 h and 16 h, respectively.

Longer phases of extraction were of no use, because production temperatures lower than the

required minimum temperature will just result in unproductive cooling of the subsurface.

Shorter phases of extraction were of no use, because at least 1 h was needed to remove the cooled

water volume within the standpipe. In Chapter V.4 it was demonstrated that even the best available

insulation cannot prevent a significant heat loss and corresponding temperature drops.

Figure 26 (page 47) shows the result of a simulation with a volume flow rate of 5 m³/h in a daily

operation cycle consisting of 6 h pumping followed by 18h of recovery; λpipe was set to 0.01 Wm-1K-1

as this is the highest value which allowed a production temperature Tout above 65°C:

Tmax(2nd) = 70 °C, t(T>65°C)2nd = 4:10 h, mean P2nd = 150.8 kW.

Tmax(365th ) = 67 °C, t(T>65°C)365th = 2:00 h, mean P365th = 141.9 kW.

Already after one year the operation time of the conceptual climate control unit is reduced by half.

Figure 27 shows a long term simulation of a volume flow rate of 5 m³/h in a daily operation cycle

consisting of 6 h pumping followed by 18h of recovery with a thermal conductivity of the standpipe

λpipe = 0.001 Wm-1K-1. Simulated operation time is 22.5 years, calculated with time steps of 600 s.

As a result, even after 20 years of operation, the deep borehole heat exchanger did not stop loosing

efficiency. In the first three years, the decrease in thermal power output is greatest.

Figure 28 (page 48)shows a simulation with a volume flow rate of 4 m³/h with the thermal

conductivity pattern GM87. λpipe was again equal to 0.001 Wm-1K-1. The results are:

2nd day Tmax(2nd) = 74.5 °C, t(T>65°C)2nd = 7:04 h, mean P2nd = 130.1 kW;

191th day8 Tmax(191th) = 71.2 °C, t(T>65°C)191th = 5:50 h.

Aside from the theoretical λpipe the results indicate a possible long-term heat supply. Admittedly, an

increasing amount of time is needed until the standpipe starts discharging hot water, so either the

energy extracting periods – i.e. the time the climate control is powered by “green” energy – or the

recovering periods have to be shortened, which will result in an additional decrease in thermal

power.

Figure 29 shows different volume flows simulated for a cycled operation consisting of 6 h pumping

followed by 18h of recovery with a realistic thermal conductivity of the standpipe of

λpipe = 0.1 Wm-1K-1, the thermal conductivity pattern GM87, and the measured temperatures. The

corresponding depths of log and model were identified and the mean of the adjacent values was

taken. The missing values at the beginning became mean values between surface temperature and

first log value, while the missing last values were calculated using a gradient of 0.025 K/m.

Although the model was not in thermal equilibrium, 80 day simulations proofed a similar behaviour

as shown in figure 27. Therefore, the proposal of the result is clear.

The curves of the 1st cycles indicate the temperature loss due to the residence time:

Before the 1st cycle, bottom hole temperature was 79.6 °C. Depending on volume flow rate a

temperature drop of 15 K – 25 K or 19 % – 31 % was due to insufficient insulation;

the curves of the 2nd cycle show that the required minimum temperature of 65 °C is never achieved.

See next chapter (chapter VI) for the conclusion.

8Values were constructed using the procedure described in chapter V.2

Fig. 26 The 2nd and 365th cycle of a simulation with of volume flow of 5 m³/h at a daily operation cycle of 6 h pumping followed by 18h of recovery (Δt= 60sec, λpipe = 0.01 Wm-1K-1).

Fig. 27 The temperature pattern of 5 m³/h at a daily operation cycle of 6 h pumping followed by 18h of recovery with a simulated over 22 years; the upper and lower borders of the black region is composed of Tmax. and Tmin . Even after over 20 years, the deep borehole heat exchanger did not stop loosing efficiency (Δt= 600 s, λpipe = 0.001 Wm-1K-1).

Fig. 28 Simulation of 4 m³/h based on the thermal conductivity pattern GM87. λpipe was set to a next to optimum value of 0.001 Wm-1K-1:for the 2nd cycle: maximum production temperature 2nd Tmax = 74.5 °C, useable time interval t(T>65°C)2nd = 7:04 h, and mean thermal power P2nd = 130.1 kW;for the 191th cycle:191th Tmax and t(T>65°C)191th were constructed using the procedure described in chapter V.2 to 71.2 °C and 5:50 h.

Fig. 29 Production temperature vs. volume flow for a daily operation cycle of 6 h pumping followed by 18h ofrecovery and a realistic pipe of λpipe = 0.1 Wm-1K-1; bottom hole temperature was 79.6 °C.for the 1st cycles: a temperature loss of 15 K - 25 K is due to insufficient insulation.The minimum required temperature is never reached.The concept for the climate control unit has to be redesigned.

VI Conclusion

RWTH Aachen University will build a new student affairs building. To demonstrate the capabilities

on the field of renewable energies its climate control unit will be based on geothermal energy. The

current conceptual design required a thermal power of 450 kW at a minimum production

temperature of 65 °C for the next 30 – 40 years. The drill site in the centre of the university limited

the maximum depth of the deep borehole heat exchanger to about 2500 m, but enabled the easy

collection of nearly 2500 cutting samples. Additionally about 150 m of core was recovered.

Measurements on drill cuttings showed a correlation between density and thermal conductivity. At

greater depths higher thermal conductivities were measured and corresponded to high percentage of

quartz. The classification on the basis of compressional wave velocity and potassium content in

gamma radiation was confirmed by the temperature log. The prediction of thermal conductivity

based on the volume content of clay (VCLGR) from the of potassium signal in gamma radiation

was successful and could be further improved using (future) temperature logs. A detailed numerical

model which represented the real design of the deep borehole heat exchanger with a resolution of

0.005 m was designed and procedures for easy change of data were developed. The influence of

calculation parameters (time steps), design parameters of the standpipe (thermal capacity, thermal

conductivity), and operating parameters (volume flow, alternating cycles of heat extraction and

recovery) were examined:

It turned out that very large time steps could be used without loss of precision at long term

continuous operations and that short time steps were required for precise cycled operations. It was

observed that the 2nd cycle of a precise simulation of a cycled operation could be used to

approximate maximum production temperature Tmax and time interval of a required minimum output

temperature t(T>X °C) for any cycle of the same simulation calculated with larger time steps.

The research of the design parameters showed the importance of an optimum insulation of the

standpipe. The best available concept (a double walled steel pipe with a maintained vacuum) is still

clearly away from the theoretical optimum.

The research of the operating parameters with realistic values for the standpipe clearly showed that

even for a maximum estimate of the thermal properties, neither the required thermal power nor the

required production temperature could be reached or maintained. Even with an optimum insulated

standpipe, the thermal power of the RWTH-1 deep borehole heat exchanger varies from 90 kW –

150 kW, depending on flow rates, which is far less than the design value of 450 kW. Although

further simulations are necessary the present results recommended a redesign of the energy

exchange system, e.g. The use of heat pumps or the combined use of geothermal and district heat.

VII Appendix

VII.1 Principles

VII.1.1 Rotary Drilling

This section outlines the principle of rotary drilling in the style of [Howard, 1990].

There are two basic ways to attack rock mechanically: by

percussion and by rotation. The rotary roller-bit drilling

method mainly used for the RWTH-1 drill hole is a

combination of both. Causing rock to break is a matter of

applying sufficient force with a tool to exceed the

"drilling strength" of the rock. Drilling strength is the

resistance against penetration and not equivalent to any

of the well known strength parameters. Further, the

stress field created by the tool must be directed in such a

way as to produce penetration in the form of a hole of

the desired shape and size. As the bit turns, cutting teeth

mounted on each rotating cone alternately engage the

rock, impacting, indenting and chipping it (figures 31

and 30).

Fig. 30 cutting sequence of a rotary roller bit (after Cheatham and Gnirk, 1967).

Pic. 8 Rotary triple cone drill bit.

Fig. 31 cutting sequence of a percussion drill bit (after Hartman, 1959).

VII.1.2 Mud system

This section outlines the principle of the mud system in the style of [Lundershausen, 2004]

The mud system consists of the mud pump,

stand pipe swivel, contaminant-removing

equipment, and storage and mixing

facilities for additional substances. At the

RWTH-1 borehole, a water-based mud was

used. The main additional substances are

clay minerals to seal the borehole against

the rock and vice versa, barite or calcium

carbonate to increase the density of the

mud, polymers, salt minerals, special

substances to liquefy the mud, to reduce

foaming, to improve lubrication etc.

The circulation of the mud system is

illustrated in figure 32:

The mud is pumped into the drill string.

Forced through the nozzles of the drill bit,

the mud cools, cleans and lubricates the bit,

and takes the cuttings away from the bottom

hole. During flow up through the annulus, the mud transports the cuttings and the weight of the mud

stabilises the wall of the borehole. After leaving the hole, the mud enters the shale shakers

(reciprocating screens) where the cuttings are mechanically separated and returns to the mud pit for

further use.

Fig. 32 mud circle (after Moore, 1981)

VII.1.3 Sampling Procedure

This section outlines the sampling preparation procedure particularly developed for the hole

RWTH-1.

Samples were taken every other metre for the RWTH Aachen University and additionally every fifth

metre for the Geological Survey of NRW.

In order to obtain depth-related samples, the sampler recorded time and the current depth of the

borehole before and after the sampling and determined the mean time and depth. Due to the low

penetration rate (1–2 m/h) only a small amount of cuttings passes the screens. To obtain a

reasonable amount of material in a reasonable amount of time, a rubber band attached to the end of

the screens was bend into a hopper like form and directed all the oversized grain into a bucket

which was hung beneath it. When the bucket was half filled, the rubber band was released to allow a

regular filling of the container. The sampler sized and cleaned the recovered material from residuals

of mud using a water filled tube, a screen with a squarish mesh size of 2 mm and a hosepipe. A

second tube acted as slurry tank. After cleaning the remaining material was filled into a 5 L storage

box and a matchbox sized sample box, both serial numbered. After been measured by the author, all

of the cuttings were dried at 55 °C.

The drill cores were hydraulically pressed from the core barrel and flushed with water. Red and

yellow chalk lines were applied immediately for conservation of the depth orientation. After

measuring and photographing, the cores were stored in core boxes according to serial number an

depth.

VII.1.4 Matrix Density

This section outlines the measuring principle for measurements of matrix density according to

[Krug, 2003 and Linek, 2003].

Matrix density is measured with a helium gas pycnometer build by Micromeritics [Anonymous,

1997]. The device consists of a closed cylinder where the dried sample (spl) is placed (cylinder, cyl)

and a calibrated expansion cell (expansion cell, exp) connected with a valve.

At the beginning, the valve is closed and there is Helium gas at pressure Pa with temperature Ta in

both volumes. Next the pressure in the cylinder is raised to P1, balancing to:

Eq. 23 P1⋅V cyl−V spl =nz⋅R⋅T a

where nz is the number of gas molecules in the cylinder [mol] and R is the universal gas constant

[8.31 J/(K*mol)].

In the expansion cell where

Eq. 24 Pa⋅V exp=ne⋅R⋅T a ,

where ne is the number of gas molecules in the expansion cell [mol].

When the valve is opened, pressure P1 drops isothermally to P2, yielding:

Eq. 25 P2⋅V cyl−V splV exp=nenz⋅R⋅T a ,

and

Eq. 26V spl.=V cyl−

V exp

P1−Pa

P2−Pa−1

The procedure can be repeated many times, so that the result contains an error estimate. The usual

deviation is in the order of 1 kg/m³ – 0.1 kg/m³.

Pic. 9 schematic representation of the mode of functionality of Accupyc.

The matrix density ρm follow from:

Eq. 27 ρm=mdry

V spl,

where mdry is the mass of the dried sample, measured with a precision scale (accuracy 1%).

VII.1.5 Thermal Conductivity from Needle Probe Measurements

This section outlines the measuring principle for measurements of thermal conductivity on cuttings

with a needle probe [Howard, 2004]

The Tk04 Thermal Conductivity Measuring

System (picture 10), build by TeKa

Geophysical Instruments, determines thermal

conductivity based on a transient heat flow

method. A line source is heated with constant

power, and its temperature is recorded

simultaneously. Thermal conductivity is

calculated from the resulting heating curve.

The measuring and evaluation process is PC

controlled. A Special Approximation Method

(SAM) automatically detects disturbances and select the optimal part of the heating curve for

evaluation.

The measuring principle is based on heating a cylindrical source with infinite length, finite radius,

infinite thermal conductivity, and constant heating power in a homogenous and isotropic sample full

space for a finite measuring time. Thermal conductivity then is determined from the temperature

increase of the source. Assuming the given geometry, temperature depends on the radial distance

from the source only, i.e. the problem is axial symmetric and hence as two-dimensional. In this

model, thermal conductivity determined with a line source is a scalar value representing the plane

perpendicular to the source axis.

As the equation describing the temperature rise with time is still too complex to be used directly for

determining thermal conductivity from the heating curve, generally a simple first order

Pic. 10 TK04, PVC-pipe, Sample with needle probe, PC.

approximation of this solution is used. The resulting equation for the temperature rise in the source

(radius r = 0) can be solved for the thermal conductivity ka(t) of the full space, where (t1, t2) is a time

interval of the heating curve, T(t1) and T(t2) the corresponding source temperatures and q the heating

power:

Eq. 28 λa t =q

4⋅

ln t2−ln t1T t2−T t1

λa(t) is called apparent because the approximation is only valid for sufficiently large times.

Commonly, thermal conductivity λ is calculated from the largest time interval (t1, t2) of the heating

curve in which λa(t) remains constant.

By using a higher order approximation the SAM method can account for important parameters like

contact resistance and hence reaches a higher accuracy. If the SAM approximation formula is fitted

to the heating curve using a least squares fit, the thermal conductivity of the sample can be

calculated from the coefficients. The mathematical properties of the approximation calculated for a

given heating curve can be used to check the quality of the measured curve. The TK04 uses a

logarithmic measure for the position of the maximum, the LET-value (the logarithm of the time tmax

where the maximum λa(tmax) of the curve λa(t) is located):

Eq. 29 LET = Ln(Extreme Time) = ln(tmax)

If an approximation has a high LET value, this means that it corresponds well with the theoretical

heating curve, i.e. that the measured heating curve from which it was calculated can be regard as

undisturbed.

Several hundred LET-values are calculated from time intervals matching selected requirements and

are drawn by the analysing software TkGraph on a LET-thermal conductivity chart. The more the

resulting point set matches the shape of a right angle, the higher the accuracy of the measurement

(figure 33).

The values for thermal conductivity provided by the TK04 were values for a mixture of cuttings and

water. A spread sheet provided by supervisor Lydia Dijkshoorn was used to calculate the thermal

conductivity of the cuttings.

In a first step the porosity Φ of the sample is calculated:

Eq. 30 =V spl−V mc⋅ρct−mspl−mmc

ρct−ρH2O⋅ 1

V spl−V mc

Vspl = displaced volume of measuring cup with sample

Vmc = displaced volume of empty measuring cup

ρct = density of cuttings

ρH2O = density of water

mspl = weight of of measuring cup with sample

mmc = weight of empty measuring cup

This formula is very sensitive to the water content: In order to measure the exact water content, the

irregular surface of the sample must be just covered with water when determining the weight.

Unfortunately, finding the right amount of water is difficult especially for the irregular surface of

Fig. 33 A good result of the TK04: The point set forms almost a right ankle. The most reasonable thermal conductivity of the sample is the vertical asymptote.

samples consisting of huge chippings.

The second step yields the thermal conductivity of the cuttings λct from the geometric mean:

Eq. 31 λct= λTK04

λH2O

11−

where λtk04 is the thermal conductivity of the sample and λH2O from water respectively.

VII.1.6 Thermal Conductivity from optical scanning

This section outlines the measuring principle for measurements of thermal conductivity at drill

cores in the style of [Kleiner, 2003].

The thermal conductivity of 27 drill

core samples were measured with a

thermal conductivity scanner (TCS)

(picture 11), build by Lippmann &

Rauen GbR [Anonymous, 2002].

A source of constant radiant power

moves outside the sample and its

light- and heat-radiation is focused

onto the surface, heating the sample.

A black coating along the scanning line provides constant absorption conditions. Infrared

temperature sensors, installed at defined distances before and after the source of radiation, measure

the temperature before and after the heating. The thermal conductivity can be calculated from the

difference of temperature. The maximum rise of temperature θ is defined as follows:

Eq. 32 θ= Q2 π⋅x⋅λ

where Q is the energy of the source in [W] and x the distance between source and sensor in [m].

If there is a comparative body with defined thermal conductivity λR and known temperature

difference θR on the same measuring length the thermal conductivity of the core sample can be

Pic. 11 TCS with laptop, controller, measuring device:from the left to the right: On the TCS there are two identical standards and a core sample. In the enlargement there is the "hot" sensor, the heat source and the "cold" sensor.

determined as follows:

Eq. 33 λP=λR⋅θ R

θ

At porous rock samples the filling of e.g. water has a significant influence on the thermal

conductivity. Tests on one sample from each (coring section) showed that variations between

directly from stock, dried and saturated are in the magnitude of the accuracy of the device only.

Therefore neither drying nor saturating were done.

The thermal conductivity can along the sample. This variation is expressed by the factor of

inhomogenity β.

34 β=λmax−λmin

λmin

The error of the measurement is < 3% [Popov et al, 1999].

VII.1.7 Multi Sensor Core Logger

This section outlines the measuring principle for measurements done with the multi sensor core

logger according to [Krug, 2003 and Linek, 2003]

The multi sensor core logger (shown in figure 34) build by Geotek Ltd.[Anonymous, 2000] is a

multifunctional measuring device designed for measurements at drill cores and unconsolidated

sediments. An important feature of this device is the non-destructive nature of the measuring

principles, i.e. measurements can be repeated on the same sample many times and the same sample

can be studied by other teams who required undisturbed samples. This device measures physical

properties like the compressional wave velocity vp, density ρb and magnetic susceptility χ. It works

with complete and split cores, which are pushed path several measuring devices in selectable

intervals. Sediments have to be placed in pipes, which disturb the measurements of vp. While the

measuring interval at borehole measurements is usually on the order of some dm, the multi sensor

permits core logger intervals as small as mm, resulting in a high resolution. Even though a computer

controls the measurements measurements require an experienced human supervisor. Calibration is

needed at the beginning of each set of continuous measurements.

Fig. 34 Multi Sensor Core Logger.

VII.1.7.i Density

Density is determined from gamma ray absorption of a radioactive source. Photons leaving the

source at a defined energy level are detected by a scintillator after travelling through the sample.

Usually 137Cs is used as source and NaI as scintillator. The aperture or collimator of the source can

be opened in 2 steps: 2.5 mm or 5 mm corresponding to an initial intensity I0 = 10000 cps or I0 =

30000 cps, respectively. 137Cs decays with a half-time of T½ = 30 a emitting i.a. photons at a fixed

energy level Eγ = 0.6616 MeV. These photons are used to determine the density of the sample.

While travelling through the sample, some of the photons are scattered at the crystal. At this energy

level (0.1 MeV < Eγ < 5 MeV) the Compton-scattering dominates.

The likeliness of such a scattering process depends on the density of electrons. Therefore, the

coefficient of mass absorption of the Compton-scattering µc is determined from

Eq. 35 µc=ZA⋅ρ [m²/kg]

where Z is the atomic number and A the nucleon number.

As a first approximation most of the rock forming elements have a constant ratio Z/A = 0.5.

Therefore the loss of radiation intensity could be used directly as a measure of the density of the

sample (Schoen, 1983).

Scattered photons loose energy. A calibrated multi-channel analyser is used to count only photons

with the original energy level of 0.6616 MeV, i.e. non-scattered ones. From the law of absorption,

which describes the interaction of radiation with matter, the bulk density ρb can be determined:

Eq. 36 ρb=1

µc⋅d⋅ln

I o

I [kg/m³]

where d is the thickness of the sample [m] and I the measured intensity [cps]

VII.1.7.ii Compressional Wave Velocity

To determine the compressional wave velocity vp, the travel time tot of ultrasonic impulses in the

sample between one transmitter and one receiver is measured. A short p-wave pulse is produced at

the transmitter, which propagates through the core and is detected.

Pulse timing is used to measure the travel time [Anonymous, 2000]. The travel time tot is composed

of the travel time through the rock tt and the travel time through transmitter and receiver Pto. After

the determination of Pto, where transmitter and receiver are directly contacted, the travel time tt is

determined by:

Eq. 37 tt = tot − Pto

The distance D is the core diameter measured with an accuracy of 0.1 mm. With Tt and the diameter

D the compressional wave velocity is determined to:

Eq. 38 v p=Dt t

VII.2 Formulae

The thermal conductivity of the cements were given in BTUh⋅ ft⋅° F

with 1 BTU = 1,05506 kJ follows

1 BTU/h = 0,293071 W;

with 1 ft = 12 in = 0.3048 m and

1°F = 5/9°C = 5/9 K follows

39[BTU ]

[h]⋅[ ft ]⋅[° F ]= 0,293071W

0,3048 m⋅59

K=1.73073 W

m , K

[http://www.metas.ch/de/scales/systemus.html]

VII.3 Data

VII.3.1 Cuttings

depth number of sample density thermal conductivity porosity of [m] [kg/m³] [W/(m,K)] prepared sample

65.56 sc-0030 2839 2.7 48.10%86.29 sc-0050 2742 3.9 45.10%86.29 sc-0050 WH 2742 4.0 45.97%132.81 sc-0100 2795 2.8 43.37%132.81 sc-0100 WH 2795 2.5 43.26%181.52 sc-0150 2787 2.8 42.46%181.52 sc-0150 WH 2787 2.9 44.28%231.30 sc-0200 2817 2.3 47.32%231.30 sc-0200 WH 2817 2.2 46.22%231.30 sc-0200 WH2 2817 2.3 46.75%285.40 sc-0250 2809 3.3 45.34%285.40 sc-0250 WH 2809 3.0 46.33%310.14 sc-0274 2764 3.2 42.59%310.14 sc-0274 WH 2764 3.2 42.30%336.05 sc-0300 2827 3.0 47.07%336.05 sc-0300 WH 2827 2.8 46.40%336.05 sc-0300 WH2 2827 2.9 45.27%341.00 sc-0305 2717 4.6 45.94%390.51 sc-0350 2768 3.2 44.02%421.17 sc-0380 2835 2.8 45.64%439.00 sc-0400 2791 3.2 44.07%491.90 sc-0450 2809 2.8 43.71%491.90 sc-0450 WH 2809 3.0 43.39%544.03 sc-0500 2786 3.0 45.66%491.90 sc-450_? 2809 2.9 43.39%544.03 sc-0500 WH 2786 3.5 45.27%544.03 sc-0500 WH2 2786 3.1 44.99%544.03 sc-0500 WH3 2786 3.2 45.05%593.50 sc-0550 2797 3.4 47.94%544.03 sc-500_? 2786 3.5 45.27%593.50 sc-0550 WH 2797 3.4 45.44%644.00 sc-0600 2759 3.6 45.34%644.00 sc-0600 WH 2759 3.5 45.27%694.05 sc-0650 2798 3.3 45.34%694.05 sc-0650 WH 2798 3.1 45.27%744.96 sc-0700 2760 4.0 45.34%744.96 sc-0700 WH 2760 3.1 45.27%795.02 sc-0750 2817 3.3 46.62%795.02 sc-0750 WH 2817 3.4 44.51%depth number of sample density thermal conductivity porosity of [m] [kg/m³] [W/(m.K)] prepared sample

795.02 sc-0750 WH2 2817 3.2 43.64%845.00 sc-0800 2789 3.1 46.47%845.00 sc-0800 WH 2789 3.1 45.30%894.00 sc-0850 2803 2.7 45.04%894.00 sc-0850 WH 2803 2.8 43.56%944.00 sc-0900 2790 3.5 43.98%997.00 sc-0950 2788 3.7 47.82%1046.00 sc-1000 2789 4.1 49.59%1098.00 sc-1050 2740 3.6 45.21%1146.98 sc-1100 2727 3.9 47.15%1197.99 sc-1150 2735 4.3 47.78%1247.99 sc-1200 2772 3.2 49.96%1296.12 sc-1250 2775 3.8 46.34%1296.12 sc-1250 WH 2775 4.2 45.66%1347.00 sc-1300 2787 3.5 48.55%1347.00 sc-1300 WH 2787 3.6 48.20%1392.00 sc-1346 2791 2.9 47.48%1405.00 sc-1359 2777 3.1 42.61%1517.60 sc-1441 2780 3.8 45.75%1526.07 sc-1450 2812 4.1 48.37%1578.98 sc-1500_100s 2814 3.7 42.40%1578.98 sc-1500_80s 2814 4.0 44.88%1636.18 sc-1550 WH 2778 5.0 42.11%1685.81 SC 1600 WH 2 2802 3.3 43.44%1636.18 sc-1550 2778 4.6 42.98%1685.81 SC-1600 WH 2802 3.7 42.80%1733.73 sc-1650 2796 3.5 40.98%1685.81 sc-1600 2802 3.4 42.96%1733.73 sc-1650 WH 2796 3.8 41.29%1784.99 sc-1700 2809 3.6 41.21%1835.05 sc-1750 2789 3.7 45.32%1884.30 sc-1800 2816 3.5 43.47%1925.80 sc-1850 2721 6.8 46.32%1976.10 sc-1900 2794 3.3 44.70%2024.02 sc-1950 2786 4.3 45.88%2073.04 sc-2000 2767 4.2 46.78%2119.70 sc-2050 2696 6.9 45.10%2160.95 sc-2100 2721 6.6 48.53%2124.30 sc-2058 2707 5.5 45.05%2125.80 sc-2059 0.8>x>0.063mm 2695 6.4 44.67%2125.80 sc-2059-nat 2708 7.6 46.31%2146.37 sc-2084 2696 7.6 44.79%2213.95 sc-2150 2771 4.3 46.02%2263.16 sc-2200 2779 4.2 42.32%2312.94 sc-2250 2753 5.8 47.49%2365.00 sc-2300 2782 3.6 43.61%2325.00 sc-2262 2660 7.2 43.68%2413.30 sc-2350 2759 4.9 42.41%depth number of sample density thermal conductivity porosity of [m] [kg/m³] [W/(m.K)] prepared sample

2466.20 sc-2400 2765 4.5 42.49%

2516.01 sc-2450 2793 3.4 46.93%2541.87 sc-2476 0.8>x>0.063mm 2798 3.3 44.37%2541.87 sc-2476-nat 2815 3.5 43.58%

# Mean Deviation Error Variation valid/invalid Power Control Quality[W/(m.K)] [%] measurements

0050 1.657 0.008 0.004 0.400 3/20 1.600 unusable0050_2 1.681 0.008 0.004 0.700 5/10 1.500 modified0100 1.358 0.020 0.007 1.900 9/15 1.500 modified0150 1.441 0.004 0.001 0.400 9/12 1.500 good0200 1.198 0.013 0.006 1.300 4/13 1.600 unusable0200_2 1.232 0.005 0.001 0.600 15/20 1.5(*) bad0250 1.514 0.006 0.003 0.400 3/5 (3W) unusable0250-2 1.424 0.007 0.002 0.800 10/13 1.5000274 1.573 0.037 0.014 3.400 7/15 1.500 bad0274-2 1.582 0.023 0.009 2.000 7/16 1.5000300 1.406 0.008 0.006 0.400 2/11 (3W) unusable0300-2 1.364 0.012 0.008 0.600 2/14 1.5* unusable0300-3 1.431 0.005 0.002 0.600 7/14 1.5000305 1.812 0.002 0.001 0.200 12/14 1.500 modified0350 1.519 0.007 0.002 0.900 9/15 1.5000400 1.520 0.006 0.002 0.700 8/15 1.5000450 1.423 - - - 0/8 (3W) unusable0450-2 1.496 0.015 0.007 1.200 5/10 1.5000500 1.430 0.013 0.006 1.000 4/10 (3W-5W-DC-P) unusable0500-2 1.580 0.006 0.003 0.400 4/10 1.500 unusable0500-3 1.475 0.008 0.004 0.600 4/10 1.5-1.6 bad0500-4 1.494 0.011 0.004 1.000 8/21 1.500 bad0550 1.490 0.008 0.005 0.400 2/5 (5W-DC-P) unusable0550-2 1.534 0.011 0.007 0.500 2/10 1.6000600 1.591 0.004 0.002 0.300 4/5 (4W)0600-2 1.567 0.011 0.005 0.800 5/12 1.5000650 1.418 0.001 0.001 0.000 2/10 (4W)0650-2 1.458 0.015 0.006 1.100 6/12 1.5000700 1.749 - - - 1/5 (4W) unusable0700-2 1.534 0.011 0.007 0.500 2/10 1.6000750 1.487 - - - 1/10 (4-2W) unusable0750-2 1.571 0.019 0.011 1.100 3/8 1.500 bad0750-3 1.542 0.010 0.003 1.000 10/21 1.5*0800 1.449 0.005 0.002 0.400 4/25 (2W) bad0800 1.453 - - - 1/25 (2W) unusable0800-2 1.483 0.012 0.005 1.100 6/10 1.5000850 1.368 0.007 0.003 0.800 7/50 1.7(2W)0850-2 1.421 0.037 0.017 3.100 5/17 1.500 unusable0900 1.615 0.062 0.025 4.600 6/43 1.5-1.60950 1.548 0.017 0.008 1.200 4/10 1.9001000 1.590 0.026 0.011 2.300 6/20 1.5001050 1.609 0.025 0.018 1.100 2/7 1.9-1.81100 1.624 0.020 0.010 1.400 4/10 1.8001150 1.684 0.021 0.010 1.500 4/12 1.8-1.91200 1.396 0.009 0.007 0.500 2/7 1.8001250 1.606 0.008 0.006 0.400 2/12 1.5-1.8 bad1250-2 1.721 0.005 0.002 0.400 9/12 1.500 good# Mean Deviation Error Variation valid/invalidPower Control Quality

[W/(m.K)] [%] measurements

1300 1.480 0.007 0.003 0.500 3/26 1.6-1.7 bad1300-2 1.511 0.005 0.002 0.600 8/12 1.6001346 1.361 0.008 0.003 0.800 8/17 1.5001359 1.553 0.006 0.002 0.700 12/17 1.500 modified1441 1.628 0.007 0.003 0.700 8/15 1.5001450 1.618 0.011 0.007 0.700 3/21 1.5001500 1.716 0.011 0.007 0.600 3/12 1.7-1.81550 1.924 0.026 0.015 1.300 3/7 1.500 bad1550-2 2.042 0.005 0.002 0.300 7/11 1.5(*)1600 1.617 - - - 1/10 1.6001600 1.618 0.021 0.006 1.200 9/10 1.600 unusable1600-2 1.692 0.035 0.024 1.400 2/11 1.500 bad1600-3 1.566 0.013 0.006 1.000 5/12 1.500 bad1650 1.691 - - - 1/10 1.500 unusable1650 1.709 0.020 0.006 1.800 10/10 1.500 unusable1650-2 1.773 0.042 0.013 3.900 10/20 1.5001700 1.734 0.010 0.005 0.600 4/10 1.5001750 1.624 0.010 0.003 1.000 9/18 1.5001800 1.639 0.005 0.002 0.400 7/13 1.5001850 2.213 0.010 0.004 0.600 7/29 1.6001900 1.547 0.013 0.008 0.800 3/10 1.8001950 1.738 0.023 0.012 1.600 4/10 1.5002000 1.699 0.002 0.001 0.100 3/10 1.5002050 2.300 0.025 0.012 1.300 4/14 1.6002058 1.948 0.030 0.015 1.700 4/14 1.500 unusable2058-2 2.029 0.011 0.005 0.700 5/14 1.5002059-n 2.348 0.010 0.003 0.700 11/13 1.500 modified2059-s 2.221 0.008 0.002 0.600 15/18 1.5002084 2.431 0.004 0.002 0.200 7/13 1.5002100 2.064 0.026 0.012 1.500 5/10 1.5002150 1.735 0.023 0.011 1.400 4/11 1.5002200 1.848 0.022 0.010 1.500 5/10 1.5002250 1.966 0.003 0.001 0.200 9/20 1.5002262 2.431 0.015 0.005 1.100 10/17 1.5002300 1.646 0.018 0.007 1.500 6/20 1.6002350 2.003 0.021 0.012 0.900 3/13 1.5002400 1.912 0.019 0.009 1.300 5/20 1.5002450 1.510 0.025 0.010 2.300 6/20 1.5-1.62450 1.519 0.013 0.006 1.200 5/20 1.5-1.62476-n 1.631 0.002 0.001 0.200 11/14 1.500 modified2476-s 1.543 0.006 0.002 0.600 7/17 1.500

VII.3.2 Cores

Sample Depth Gamma V_p Th_mean G β VGL9 VGL Nr weightdensity

# [m] [kg/m³] [m/s] [W/(m,K)] [-] [W/(m,K)] [g]

01-1-1 1391.6 2821 5714.29 2.7 3.301 0.165 2.861 1 468.701-1-1 1391.6 2821 5714.29 2.7 3.134 0.155 2.863 1 468.701-1-2 1391.7 2833 5544.44 2.8 2.870 0.124 2.863 1 399.701-1-2 1391.7 2833 5544.44 2.8 2.816 0.121 2.861 1 399.701-1-3 1391.8 2814 5702.86 2.8 2.486 0.102 2.863 1 355.001-1-3 1391.8 2814 5702.86 2.8 2.564 0.305 2.861 1 355.008-3-1 1410.9 - - 3.0 7.168 0.542 - - 2054.208-3-1 1410.9 - - 3.1 7.173 0.479 - - 2054.510-2-3 1415.9 2884 6060.98 2.8 2.807 0.174 2.884 1 1661.310-2-3 1415.9 2884 6060.98 2.8 2.932 0.163 2.913 1 1661.322-1-8b 1448.6 2835 4990.54 2.7 6.751 0.266 2.970 1 646.022-1-8b 1448.6 2835 4990.54 2.7 6.688 0.248 2.974 1 646.0I 1461.4 - - 3.7 6.238 0.352 2.954 1 1164.5I 1461.4 - - 3.7 6.702 0.330 2.910 1 1164.629-3-3 1469.7 2838 5231.53 2.5 4.960 0.230 2.953 1 698.429-3-3 1469.7 2838 5231.53 2.6 5.457 0.227 2.943 1 698.329-3-4.5b 1469.9 2858 5146.70 2.6 4.822 0.030 2.981 1 1293.629-3-4.5b 1469.9 2858 5146.70 2.6 4.948 0.288 2.951 1 1293.5II 1476.8 - - 2.8 4.011 0.189 2.942 1 854.2II 1476.8 - - 2.9 3.125 0.219 2.914 1 854.335-2-10 1485.58 2839 5155.76 2.9 4.574 0.259 - - 1996.135-2-10 1485.58 2839 5155.76 2.9 4.582 0.273 - - 1996.138-1-6 1492.4 2788 4963.73 3.3 6.911 0.325 2.976 1 778.838-1-6 1492.4 2788 4963.73 3.3 6.191 0.265 2.968 1 778.940-3-1ab 1498.1 2789 5125.27 2.3 4.449 0.222 2.990 1 797.340-3-1ab 1498.1 2789 5125.27 2.3 4.543 0.232 2.955 1 797.344-1-4 1506.7 2830 4719.01 2.7 7.175 0.286 2.934 1 900.344-1-4 1506.7 2830 4719.01 2.7 7.073 0.287 2.968 1 900.146-3-13 1515.2 2763 5403.23 3.3 6.246 0.272 3.004 1 725.646-3-13 1515.2 2763 5403.23 3.3 6.554 0.261 2.988 1 725.648-1-1 2131.3 2755 5657.14 3.3 4.692 0.113 2.947 1 475.748-1-1 2131.3 2755 5657.14 3.4 4.553 0.188 2.981 1 475.748-1-2 2131.5 2842 5370.56 2.8 7.910 0.354 2.969 1 1082.948-1-2 2131.5 2842 5370.56 2.8 8.126 0.347 2.933 1 1082.8III 2134.8 - - 2.9 3.419 0.165 2.943 1 761.3III 2134.8 - - 2.9 3.093 0.145 2.905 1 761.351-2-5a 2139.9 2812 6030.27 3.3 8.888 0.298 2.962 1 628.051-2-5a 2139.9 2812 6030.27 3.3 9.276 0.301 2.973 1 628.151-2-5b 2140.1 2798 5969.45 3.3 5.575 0.253 2.937 1 1193.951-2-5b 2140.1 2798 5969.45 3.4 5.898 0.296 2.985 1 1193.952-2-1 2141.7 2845 5799.79 3.2 4.943 0.226 3.002 1 1215.852-2-1 2141.7 2845 5799.79 3.2 5.465 0.285 2.943 1 1215.852-2-2 2141.8 2841 5779.31 2.8 2.071 0.105 2.960 1 524.752-2-2 2141.8 2841 5779.31 2.8 1.992 0.091 2.957 1 524.853-1-2 2537.0 2870 5325.62 2.6 3.577 0.180 2.949 1 3098.153-1-2 2537.0 2870 5325.62 2.6 3.797 0.153 2.969 1 3098.153-1-3 2537.3 2868 5596.79 2.9 6.548 0.332 2.992 1 4937.6Sample Depth Gamma V_p Th_mean G β VGL10 VGL Nr weight

9 VGL = thermal conductivity of the calibration block10 VGL = thermal conductivity of the calibration block

density# [m] [kg/m³] [m/s] [W/(m,K)] [-] [W/(m,K)] [g]

53-1-3 2537.3 2868 5596.79 3.0 6.569 0.311 2.954 1 4937.353-1-4 2537.5 2872 5622.01 2.9 3.884 0.145 2.948 1 2276.053-1-4 2537.5 2872 5622.01 2.9 3.791 0.165 - 1 2276.061-1-1 2543.11 2840 5743.28 3.5 11.171 0.467 2.942 1 3197.461-1-1 2543.11 2840 5743.28 3.5 11.985 0.539 2.984 1 3197.261-1-2 2543.4 2796 5768.72 4.8 - - - - -61-1-2 2543.4 2796 5768.72 4.8 16.779 0.699 - - -61-1-2 2543.4 2796 5768.72 4.9 16.190 0.768 - - 7121.261-1-2 2543.4 2796 5768.72 4.9 16.339 0.721 - - 7121.061-1-2 2543.4 2796 5768.72 5.0 16.820 0.697 - - -61-1-2 2543.4 2796 5768.72 5.0 16.229 0.713 - - -

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