Thermal Response Test (TRT) – System for Measurement of Thermal Response of Rock Massif

12th IFAC Conference on Programmable Devices and Embedded Systems The International Federation of Automatic Control September 25-27, 2013. Velke Karlovice, Czech Republic

Thermal Response Test (TRT) – System for Measurement of Thermal Response of Rock Massif R. Hajovsky*, P.Vojcinak*, M.Pies*, J. Koziorek* 

*Department of Cybernetics and Biomedical Engineering, VŠB-Technical University of Ostrava, Czech Republic (e-mail: {radovan.hajovsky|petr.vojcinak|martin.pies|[email protected]})

Abstract: The article describes an experimental system for measuring the temperature response of the rock massif known as the Thermal Response Test (TRT), its activity and usage patterns. The response of the rock mass is represented by the value of thermal conductivity of rocks λ, which characterizes the ability of rocks to conduct the heat. Determination of the value of λ is the most essential output of measurement. The measurement results are then used in the design of a complex system of boreholes for heat pumps providing heating or cooling of particular object. Keywords: Thermal conductivity, Measuring, Heat exchangers, Mathematical systems theory, Temperature measurement, Data processing, Renewable energy systems, Response measurement. 

1. INTRODUCTION Proper design of parameters of the boreholes used as energy sources for heat pumps requires knowledge of the basic thermal characteristics of the rock massif at the installation site. The most important of these include the thermal conductivity λ. Other variables, knowledge of which is important when designing a polygon, are the total thermal resistance in the borehole Rb and temperature of unaffected rock massif Tug. The values of these quantities are determined by experimental measurement of temperature response of the rock massif (Thermal Response Test, TRT). 2. APPARATUS FOR MEASUREMENT OF THERMAL RESPONSE (SYSTEM TRT) The main goal of TRT system is to determine the thermal characteristics of the rock massif at the planned depths of boreholes designed for heat pumps based on experimental measurements. Both in the past and at present all required physical properties are determined by tables or laboratory for smaller systems, based on the analysis of collected samples of rocks of the area. However this approach is highly inaccurate and suffers from some cons as follows:

For these reasons, the above mentioned special system allowing TRT experimental determination of the values of necessary physical quantities measured directly in the equipped boreholes has been designed. The first mobile system of this kind was developed and built in 1995 in Sweden and the USA. The thermal response test is carried out at a particular location in the testing borehole equipped in the same way as standard borehole for heat pump. The main objective of measuring the thermal response is to determine the basic thermal properties of the rock massif in the installation of boreholes. These experimentally determined values are then inserted into a special software that calculates the number of boreholes, their depth and geometry for given predefined parameters required for the desired object (heating or cooling performance). 3. TRT SYSTEM OPERATION Schematic block diagram of the apparatus of TRT for measuring the thermal response is shown in Fig. 1.

- The necessary physical properties of the rocks are determined only from the samples, regardless of some storage conditions (groundwater tributaries etc.) - Gathering samples by special boreholes is very expensive - It is not possible to evaluate the influence of the borehole equipment on heat transfer from borehole wall towards plastic exchanger (so called PE collector) Fig. 1. The block scheme of full TRT experiment.

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The equipment is connected to the borehole which has the same characteristics as the other planned boreholes in the polygon designed for heat pumps. Once the measurements are finished the apparatus is disconnected and such equipped borehole is then used as standard borehole providing energy exchange between the rock massif and heat pump.

initial time. With regard to the boundary conditions, there are several common possibilities, which are simply expressed in mathematical form. Because the heat equation is the second order one in the spatial coordinates, two boundary conditions must be expressed for each coordinate to describe the system (or model); Rohsenow, Hartnett, Cho (1998).

As soon as the TRT system is connected to the borehole, the closed system is filled up with antifreeze media (usually a mixture of water and alcohol, or glycol) and vented so that there are no remaining air bubbles that might affect the heat transfer between the flowing liquid and rock massif. Then the media starts warming up via controlled immersion heater, storing the fluid temperature at the inlet and outlet, volume flow of media and input power of immersion heater. Measurements are usually performed over 2-4 days.

4.2 Line Source Theory

4. MATHEMATICAL BACKGROUND OF TRT Kelvin’s infinite line-source model is the most widely used approach to determining ground thermal conductivity. For large time values, finite size effects have to be taken into account; otherwise ground temperature changes all the time. This is not the case of the finite line-source – corresponding solution has been obtained and expressed as one-dimensional integral at zero temperature and at boundary of a semiinfinite medium. However, an analytical asymptotic form of the solution is highly desirable to improve estimating the essential parameters like effective ground thermal conductivity (λeff.) and borehole thermal resistance (RB) from acquired TRT data; Bandos et al. (2008).

The BHE is very long in relation to its small diameter. In 1948, Ingersoll & Plass introduced practical implications to evaluate the performance of the first BHE; Sass, Lehr (2011). So they had to define some simplifications, whereas this step requires a one-dimensional approach (i. e. parabolic type, sourceless heat equation with one space variable, cylindrical coordinate system, symmetric unsteady-state process, generalized form), thus; Polyanin (2002):  2T 1  2    T 1 T     . a t r r r 2

Where

T  T r ,  , z, t 



Where

(3b)

the initial condition (K) t  0 : T r , t  0   T r ,0   T r   f r  .

(4a)

the first boundary (Neumann) condition (K · m-1) r  rB :

 T r , t  q" t    Tr  g t   .   r r  rB

(4b)

the boundedness condition (K) r  0 : T r , t    .



T  T r , z, t 

arbitrary constant, (-).

These following IC/BC conditions are prescribed (for the second boundary value problem); Polyanin (2002):

(1)

temp. distribution, (K).

1  T  1    T   2T    2T 1  T  2T      r   2 .  2    2   r r a t  z   r  r   r   z    r

thermal diffusivity, (m2 · s-1),

This dimensional equation (K · m-2), see (3a), is encountered in problems of a diffusion boundary layer; Polyanin (2002). If we consider   0 , then (3a) has this form:

In case of axial symmetry, (1) may be written in this form, because  2T  2  0 ; Polyanin (2002):





temp. distribution, (K),

1 T 1   T   2T 1  T       r  . a t r r  r  r 2 r r

There are several fundamental formulae and equations, used for mathematical modelling. At first, let us consider a general four-variable function of temperature in the borehole neighbourhood - T(r, φ, z, t) - conforming to Fourier partial differential equation of heat transfer (i. e. parabolic type, sourceless heat equation with three space variables, cylindrical coordinate system, non-symmetric unsteady-state process), thus:

Where



a    cp

4.1 Formulation of Heat Equation

 1    T  1  2T  2T  T  a   3T  a     r    2  . 2 t  z 2   r  r   r  r  

T  T r, t 

(3a)

(2)

(4c)

Neumann solution has this form (K): T r , t  

rB

t

0

0

 f    G r ,  , t   d   a   g    G r , rB , t     d  .

(5)

temp. distribution, (K).

To determine a temperature distribution in a medium, it is necessary to solve the appropriate form of the heat equation. However, such a solution depends on physical conditions existing at boundaries of the medium and, if situation is time dependent, on conditions existing in the medium at some

The forms of the Green functions are as follows; Polyanin (2002): for the space variable

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  r     J 0   n  J 0   n  rB  rB 2  2    G r ,  , t   2  2   J 02  n  rB rB n 1 

2    a   n t 2   e rB . (5a)

for the time variable (at   rB ) 2 2  G r , rB , t       rB rB n 1

 r J 0   n  rB  J 0  n 

  

a   n2  t   rB2 e

T r , t   T0  g rB

Where



 1 1  1 1      0,   lim          ,    4  Fo    0   4  Fo  







 1    1   1    4  Fo   .   0,        ln   4  Fo  n 1 n!n  4  Fo 

T Fo   A  B     ln 4  Fo   O n 4  Fo .

Where

(6)

characteristic borehole radius, (-), dimensionless position at  rB  r rB , (-).  rB Other possible particular solution, used for practical TRT data evaluation, has this form (for   0 , Carslaw & Jaeger, 1959); Polyanin (2002): e y  dy . y

A  T0

undisturbed temperature, (K),

B  qh B

4       Q 4      hB  , (K).

(7)

1  4  Fo n , (-). n  n ! n 1

On 4  Fo  

The thermal (transfer) resistance value, gotten by the TRT, it is valid at test conditions only. There are some dynamic partial resistances (e. g. mass flow depending upon BHE’s fluid and groundwater), which affect the thermal resistance value. The borehole thermal resistance is defined between heat carrier fluid (inside the BHE) and the borehole wall; Sass, Lehr (2011). If we consider the infinite line model, where temperature of the borehole wall is not dependent upon z-coordinate, arithmetic mean of inlet and outlet fluid temperatures is calculated (at the beginning of the TRT measurement); Bandos et al. (2008):

Where

Q t   qhB t   hB , (W),



(8)



T0  T f r , t  0   0.5  T f IN 0  T f OUT 0 , (K),

equation (for X  0 ):     Ei1   1 .   4  Fo  

It is reported, that the maximum error equals to 2.5 % at Fo  20 , and 10 % at Fo  5 .

Q t  Tˆ f r , t   T0  R B  q h B t   T B r , t   R B   T B r , t . hB

In (7), heat conduction process inside grout is simplified as one-dimensional. This model is characterized by its simplicity and it is proved to be appropriate for response to step heat rejection/extraction of a few hours to a few months; Incropera, DeWitt, Bergman, Lavine (2007). Because upper incomplete function gamma  , X  is closely related to exponential integral function Ei1   X  , we can write this  1 r2   0, X    4 4  a  t  Fo 





J 0  n  the first kind Bessel function with order value of 0, (-), Fourier number at ForB  a  t rB2 , based on ForB

Where

Euler constant, (-),

Fourier number at Fo  a  t r 2 , (-),



positive zeros of the first kind Bessel function (with order value of 1) at J1  n   0 , (-),

r 4  a t

(7e)

 1  , (-), ln4  Fo   ln 4  Fo1   ln   4  Fo 

n

2

  ' 1  0,577215665 Fo

B



(7d)

Finally, we get this borehole-known result:

K rB  2  ForB  0,25  0,5   r2 , (-),



(7c)

n

(5b)

.

 J 0 n   r   B  rB   K rB  2   2  exp   n2  Fo rB .  n 1  n  J 0  n  

 r 2  T r , t   A  B      0 ,  A B  4  a  t  

 . 

Using L’Hospital rule and feature of upper incomplete gamma’s derivative:

If the initial temperature of the cylinder is uniform, f(r) = T0, and its lateral surface is maintained all the time at a constant thermal flux, g(t) = grB, then the solution in (5) has this particular form (based on the Fourier number and dimensionless position, Carslaw & Jaeger, 1984); Polyanin (2002):



And

(7b)

T f r  rB , t   T f rB , t   T f t  , (K),

TB r  rB , t   TB rB , t   TB t  , (K).

At evaluating the TRT data, this TRT algorithm uses the form of (7e) (at the boundary r = rB), thus: T f r  rB , t   T0  R B  q h B 

Where



 

C1  T0  RB  qhB  B  ln 4  a rB2   , (K), C2  B  qhB

128

  4a     ln  2   ln t     .   4       rB    q hB

4       Q 4      hB  , (K).

(9)

IFAC PDeS 2013 Velke Karlovice, Czech Republic

5. TRT SYSTEM IN THE CZECH REPUBLIC The first experimental measurement of the thermal response test of the rock massif in the Czech Republic was performed with the aim of determination of the thermal characteristics of the basic parameters of the rock massif in the new assembly hall and the Centre for Information Technology (CIT) by VSB-TU Ostrava. At that time it was the largest installation of heating systems using heat pumps consisting of 110 boreholes and ten compressor heat pumps, ground-to-water (IVT model D70) with a planned thermal power of 700 kW. For such large systems it is necessary to obtain the necessary information yet by measurements and not only by the use of tabulated values. Measurements were performed and evaluated with the use of the apparatus borrowed from Mr. Hellstrom, an associate professor at the Technical University of Lund in Sweden (Fig. 2).

warming) with the application of heat pumps in New Auditorium + CIT VSB-TU Ostrava“ helped to purchase a professional TRT system supplied by the German company UBeG GmbH & Co. KG. Delivery includes a complete measuring equipment together with software for postprocessing of measured values and calculation of the thermal conductivity of rocks λ. Purchased equipment for the implementation of TRT methods is the only one of its kind in the Region and the Czech Republic (Fig. 3).

Fig. 2. The TRT apparatus from Sweden Measurements have been performed at two testing boreholes with a depth of 130m spaced about 100m. Both boreholes were standardly fitted with two-pipe PE collector of 40 mm diameter intended for subsequent connection to the heat pump. The parameters of the two boreholes are shown in the following table. Table 1. The boreholes parameters Parameter heating power  power output time of borehole heating temperature Tug heat conductivity of rock  thermal resistance Rb grouting

Borehole 1 8,2 kW 0,83 l/s 71,5 h

Borehole 2 7,6 kW 0,87 l/s 93,3 h

10,8 °C 2,2 W/mK

10,8°C 2,1 W/mK

0,16 K/Wm

0,12 K/Wm

cement+bentonit

Stuwatherm 2000Z

Fig. 3. The block scheme of UBeG TRT apparatus

Due to the unavailability of mobile apparatus designed for TRT purposes in Czech Republic, experts from the Department of Cybernetics and Biomedical Engineering (FEI), together with the staff of the Faculty of Mechanical Engineering (FME) and the Faculty of Mining and Geology (HGF) VSB-TU Ostrava in early 2008 decided to buy the mobile unit. Another reason was the fact that in the last few years there can be seen a sharply increasing interest in heat pumps and measuring methods of TRT. The previous project “Research of temperature changes of the rock mass (cooling -

It is capable of analysis of the characteristics of the rock massif and in particular to measure the thermal response. The results are especially important for the design of the layout of boreholes for heat pumps and for optimization of the number and depths of boreholes and their equipment. From the very beginning the apparatus has been assumed to be applied for the following purposes:

129



Research of thermal properties of the geological layers of rock massif



Research of the influence of heat pump operation on the temperature of the rock massif

IFAC PDeS 2013 Velke Karlovice, Czech Republic



Research of energy storage in rock massif (storage of waste heat from air conditioning units)



Usage for future installation of heat pumps in the completion of other objects by VSB-TU Ostrava,



Use of facilities in technical-research collaboration with industrial partners dealing with heat pumps, design of installation systems of heat pumps and the implementation of projects.

6. PROCESSING OF MEASURED DATA During the measurement data are automatically stored in two independent data loggers (MiniMEP-404s, Zenner S1 + PcRead). After the measurement data are imported from the logger to the evaluation program called Gert-CAL installed in the PC taking care of the processing. The results of processing are the waveforms of temperature and thermal conductivity of rocks, flow and power. An example of the resulting measurement protocol is shown in Fig. 6.

The use of TRT is closely related to the issues of renewable energy sources and it will be one of further future activities developed by VSB-TU Ostrava in this area in the recent years. Workers of VSB-TU Ostrava nowadays work in the area of measurement of thermal response test of the rock massifs around the Czech Republic. The first contact with the complete TRT system by UBeG company, it mobile measuring apparatus and software for analysing measured values, was carried out in the company's headquarters in Wetzlar, Germany in July 2008. The delivery itself took place at the end of October 2008, including the demonstration of measurement and training of operating staff from the Department of Cybernetics and Biomedical Engineering by FEI, VSB-TU Ostrava. Verification tests and testing measurements for a detailed familiarity with the system, its installation and measurement processing techniques were carried out at testing boreholes that are part of the small research polygon (MVP) in Building Energy Research Center (VEC2) in the area of VSB-TU Ostrava. Small research polygon is especially designed for research activity related to the issue of heat pumps and measuring the thermal properties of the rock mass. It consists of two operating boreholes (connected to the heat pump) and a set of nine monitoring boreholes According to Bujok, P. et al. (2012). A view of TRT system during verification measurements at the test borehole is shown in Fig. 4 and 5.

Fig. 6. An example of TRT result 7. CHOSEN MEASUREMENTS IN THE CZECH REPUBLIC Our TRT device (produced by UBeG GmbH & Co. KG, Wetzlar – Nauborn, Germany; see Fig. 4) is able to carry out some analysis of rock massif properties and to measure its thermal response, too. This device is often used not only for research activities, but also for experimental measurements at specific localities. From the research viewpoint, these activities are mainly focused on:

Fig. 4. A view of experimental TRT test

    Fig. 5. A detailed view of TRT apparatus connection to the borehole 130

thermal properties of geological layers inside a rock massif, temperature influences of the rock massif at operation of heat pumps (HP), energy accumulation inside the rock massif, using this device for the TRT measurements of other HP installations at the district of VŠB – Technical University of Ostrava, where there are two research polygons with lots of vertical BHEs,

IFAC PDeS 2013 Velke Karlovice, Czech Republic



using this device for collaboration with industrial companies, centred on the HP installations,  using a TRT data evaluation for design of large geothermal systems including HPs,  using this device for solving own research projects. Between 2011 - 2013, several TRT measurements were performed at these localities in the Moravian -Silesian region, thus:  ID1 March 2011,  ID2 September 2011,  ID3 November 2011,  ID4 April 2012,  ID5 May 2012,  ID6 May 2012,  ID7 April 2013. Result values of selected geothermal parameters are summarized in Table 2. The values of the thermal conductivity and the thermal resistance are average, see Vojcinak et al. (2012). Table 2. Summarization of the selected TRT measurement results ID 1 2 3 4 5 6 7

ttest hours 52.33 71.17 71.67 74.17 71.83 68.33 62.33

Q W 7073 7420 6322 6992 6847 7658 7485

Test Parameters λ RB W·m-1·K-1 K·m·W-1 5.67 0.042 3.91 0.060 2.02 0.137 2.61 0.079 3.21 0.109 3.9 0.034 2.17 0.047

T0 °C 12.14 7.18 10.58 11.94 11.39 6.75 10.64

8. CONCLUSIONS The article focused on description of the system for measuring the thermal response of the rock massif by Thermal Response Test (TRT), which is an indispensable tool for responsible design of complex installation of heat pumps. At the end of 2008, the VSB-TU Ostrava was the only one subject in the Czech Republic that purchased a professional TRT system at the German company UBeG. This system is primarily used for research in the field of thermal properties of rock massifs and renewable energy sources. It can be applied in a wider scale in cooperation with industrial partners involved in the problems of design and implementation of systems for heating / cooling with heat pumps. Department of Cybernetics and Biomedical Engineering is able to use this system to offer and perform commercial measurement in the Czech Republic, including evaluation of the measured data. ACKNOWLEDGEMENT This work is supported by project SP2013/168, named “Methods of collecting and transfer of the data in distributed systems” of Student Grant Agency (VSB Technical University of Ostrava).

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