1. LONG TERM PERFORMANCE PREDICTION OF A
BOREHOLE AND DETERMINATION OF OPTIMAL
THERMAL RESPONSE TEST DURATION
MURAT AYDIN
ALTUG SISMAN
AHMET GULTEKIN
ISTANBUL TECHNICAL UNIVERSITY, ENERGY INSTITUTE
NEW ENERGY TECHNOLOGIES RESEARCH GROUP

2. BRIEF INFORMATION ABOUT GROUND SOURCE HEAT PUMP TEST AND
RESEARCH LABORATORY AT ITU ENERGY INSTITUTE
Laboratory facilities:
 Vertical Ground Heat Exchangers:
Horizontal Ground Heat Exchangers:
Boreholes having different
• Snail type (depth:2m, total length:100m)
• Depths (50m, 100m)
• Slinky
• Pipe diameters (Ø25, Ø32, Ø40)
• Number of U-tubes (1U, 2U, 3U)
• Shank spaces (LS97mm, LS135mm)
• Distance from each others (3m, 5m, 7m, 10m)
• Vertical (depth:2m, total length:100m)
• Horizontal (depth:2m, total length:100m)
• Helix
• Vertical (depth:1.5m-4.5m, total length:40m)
• Horizontal (depth:1.5m, total length:40m)

3. BRIEF INFORMATION ABOUT GROUND SOURCE HEAT PUMP TEST AND
RESEARCH LABORATORY AT ITU ENERGY INSTITUTE
 Ground Temperature Measurement System
 Depth:20m
 Some other sensors in ground for different aims
 For results : web.itu.edu.tr/murataydin/taso13.html
 Thermal Response Test System
Depth (m)
 Sensors: 15
Temperature (C)

4. CONTENT
 Thermal Response Test System
 Introduction of Analytical Model
 Experimental Results and Long Term Predictions
 Optimum Test Duration
 Conclusion

5. Thermal Response Test System

6. THERMAL RESPONSE TEST
 In Ground Source Heat Pump (GSHP) applications, 75-80% of heat transfered to the building
comes from ground,
 Determination of thermal properties of ground is an important issue,
 Thermal Response Test (TRT) is used to determine thermal properties and then the
longterm performance predictions of a borehole can be made for a GSHP application,
 Thermal Response Test Methods,
 Constant Heat Flux Method
 Constant Temperature Method

7. CONSTANT TEMPERATURE TRT
ADVANTAGES AND DISADVANTAGES
Advantages
• Flexible test temperatures
• Better accuracy
• Unlimited test duration
• Possibility of test of more than one boreholes simultaneously
Disadvantages
• High cost to build the test system

8. CONSTANT TEMPERATURE THERMAL RESPONSE TEST SYSTEM
WORKING DIAGRAM
7
Auto.Air Purge
PID
CONTROL
PANEL
5
Expansion Vessel
TO MEASURE UNDISTURBED GROUND TEMPERATURE
DATA
LOGGER
Valve with
temp.sensor Ø25
Boreh. 3 T
T
Boreh. 2
3
By pass line
2
Boreh. 1 T
Ground Inlet Collector
WATER TANK
500lt
PT1000
TEMPERATURE
SENSOR
Ground Return Collector
T
Borehole 3
T
Borehole 2
6
Filter
Borehole 1
Pump
T
4
Electrical Resistance 3 x 6kw
Flowmeters Ø25
Mini Pump
1
Valve with
temp.sensor Ø25

9. PID
CONTROL
PANEL
5
7
Auto.Air Purge
FOR PREPARING THE SYSTEM TO TEST
Expansion Vessel
CONSTANT TEMPERATURE THERMAL RESPONSE TEST SYSTEM
WORKING DIAGRAM
DATA
LOGGER
Valve with
temp.sensor Ø25
Boreh. 3 T
T
Boreh. 2
3
By pass line
2
Boreh. 1 T
Ground Inlet Collector
WATER TANK
500lt
PT1000
TEMPERATURE
SENSOR
Ground Return Collector
T
Borehole 3
T
Borehole 2
6
Filter
Borehole 1
Pump
T
4
Electrical Resistance 3 x 6kw
Flowmeters Ø25
Mini Pump
1
Valve with
temp.sensor Ø25

10. PID
CONTROL
PANEL
5
7
Auto.Air Purge
TESTING PROCESS
Expansion Vessel
CONSTANT TEMPERATURE THERMAL RESPONSE TEST SYSTEM
WORKING DIAGRAM
DATA
LOGGER
Valve with
temp.sensor Ø25
Boreh. 3 T
T
Boreh. 2
3
By pass line
2
Boreh. 1 T
Ground Inlet Collector
WATER TANK
500lt
PT1000
TEMPERATURE
SENSOR
Ground Return Collector
T
Borehole 3
T
Borehole 2
6
Filter
Borehole 1
Pump
T
4
Electrical Resistance 3 x 6kw
Flowmeters Ø25
Mini Pump
1
Valve with
temp.sensor Ø25

11. CONSTANT TEMPERATURE THERMAL RESPONSE TEST SYSTEM
PICTURES

12. Analytical Model
For
Constant Temperature TRT

13. ANALYTICAL MODEL FOR CONSTANT TEMPERATURE TRT
Measured Quantities
r
θ
Tin
Tout
Borehole
Tb
Fluid Inlet Temperature : Tin
Fluid Outlet Temperature : Tout
rb
Flow-rate
Ground
Tin
Tout
Mean fluid temperature :

: m
T 
Tin  Tout
2
U-tube
L
 rb 

q

ln
Borehole wall temperature : Tb  T 
2 k g  2rp 


(Under steady state approx.)
Unit heat transfer rate

Q


: q'   mc p Tin  Tout 
L

14. ANALYTICAL MODEL - NONDIMENSIONALIZATION
To find the temperature distribution around the
borehole following expression should be solved
 2 T 1 T 1 T


2
r r  t
r
Nondimensionalization

T  Tb
r
t
; ~ ; ~ 2
r
t
T  Tb
rb
rb
 2 1  

 ~
r r
~ 2 ~ ~  t
r
Initial Condition
T(r,0 )  T
 ( ~ ,0 )  1
r
Boundary Conditions
T rb ,t   Tb
 (1, ~)  0
t
T(,t)  T
 (, ~)  1
t

15. ANALYTICAL MODEL - SOLUTION
Solution:
 ( ~ ,~ )  
r t

e  
2~
 0
t
J 0 ~ Y0    Y0 ~ J 0  d .  r J r Y    Y r J  dr 
r
r
0
0
0
2
2
r1 0
J 0    Y0  
2

2
 ( ~, ~ ) 
r t



 0
e
 2~
t
J 0 ~ Y0    Y0 ~ J 0  
r
r
d
2
2
 J 0    Y0  

16. ANALYTICAL MODEL - HEAT TRANSFER RATE (HTR)

q   2πkrb
Heat Transfer Rate (HTR) per unit borehole length
Nondimensionalization for unit HTR value
Dimensionless unit Heat Transfer Rate
~

q 
dT
dr
r  rb

q
dθ
 ~
2πk Tb  T  dr
~ dθ

q'  ~
dr
dθ

q  2πk T  Tb  ~
dr
~ 1
r
e  β t Y0  β J 1  β   J 0  β Y1  β 

d
2
2
β 0
~ 1
J 0  β   Y0  β 
r

2~


~ 1
r

17. ANALYTICAL MODEL - DATA FITTING
Fitting the model to the experimental data

q(t )
~  t 
 
q  2 k 
2 Tb  T 
 rb 
Model
Exp. Results
k (Thermal Conductivity)
 (Thermal Diffusivity)

18. ~

q
A REPRESENTATIVE EXPRESSION FOR
~ ~ 2  e β t Y0 β J1 β   J 0 β Y1 β 

d
Fitting process is a time consuming process due to numerical integration q  t   β 0
2
π
β   Y0 2 β 
β J0
2~


Therefore a representative expression is needed to fit the model to results in an easy and fast way
~

For a borehole, variation of q  with ~ is shown in the following figures:
t
0.24
0.22
0.20
~

q (W/m)
0.18
 0.0004 ln ( t / rb )  0.0156 ln ( t / rb
~

q   exp 
2
 0.2840 ln( t / rb )  0.0492

3
2
Representative exp. of
2
2
4
)



~

q
 
~

ln q   0.0004 ln 3 ( ~ )  0.0156 ln 2 ( ~ )  0.2840 ln ( ~ )  0.0492
t
t
t
2
 0
~

ln q
Fitting a cubic polynomial
expression
0.16
2
0.14
0.12
~  t r 2
0.10
t
0
b
4
200000 400 000 600000 800 000 1.0 106 1.2 106 1.4 106
0
2
4
6
8
10
12
14
ln ~ 
t

19. REPRESENTATIVE EXPRESSION FOR FITTING
Following figure shows a comparison of true and repr. equations
Repr.exp.
True expression
Repr. expression
Short term
experimental
data fitting

mc p T
~  t 
 
q  2 k 
2 Tb  T 
 rb 
Determining
k and α
0.24
0.22
Experimental Results
k , 
Long term
performance
prediction of
borehole
~  t 


q'  2k .( Tb  T )q  2 
r 
 b 
0.20
~

q (W/m) 0.18
0.16
0.14
0.12
0.10
0
200000 400 000 600000 800 000 1.0 106 1.2 106 1.4 106
~  t r 2
t
b
True exp.

20. Experimental Results and
Long Term Predictions

21. A TEST STUDY
Experimental Results

q' (W/m)
200
Properties of Borehole and Test Conditions
Borehole diameter
Borehole length
Total test duration
Ground inlet temperature
Ground avg. outlet temperature
Flow-rate
Average unit HTR value
150
100
50
0
0
10
20
Time [hours]
30
40
0.17
50
240
40.0
37.5
25.4
88.0
m
m
hours
oC
oC
lt/min
W/m

22. A TEST STUDY
DATA FITTING
200
150

q' (W/m)
keff= 3.8 W/mK
100
αeff=0.7x10-6m2/s
50
0
0
10
20
Time [hours]
30
40

23. A TEST STUDY
LONG TERM PERFORMANCE PREDICTION
12 days prediction

q' (W/m)
200
200
150
150
Fitted curve to test results
100
100
Prediction curve
50
0
0
4 months prediction

q' (W/m)
50
Experimental Results
50
100
150
Time [hours]
200
250
0
0
500
1000
1500
Time [hours]
2000
2500

24. Optimum Test Duration

25. OPTIMUM TEST DURATION
Variation of % Difference of Long Term
Predictions with Test Duration

q ' [W/m]
Test
Duration
2.50
% Difference
2.00
prediction of unit
HTR value after 4
months non-stop
working
% Difference of
predictions
24
0.00
24
48
72
96
120
144
Test Duration
Even 24 h test duration seems to be enough.
168
192
216
240
Reference
Test Duration
1.56
63.4
1.09
96
0.50
63.1
72
1.00
2.03
48
1.50
62.8
63.6
0.78
120
63.7
0.62
240
64.1
0

26. Conclusion

27. CONCLUSION
• A process to make long term predictions for unit HTR value of a borehole is developed,
• Optimum test duration is examined for constant temperature TRT and it seems that even
24h is enough,
• Long term predictions are made by using the experimental data for a single borehole,
• This process can be used to determine total length of boreholes for GSHP applications.

28. Thank You For Attention
This project is supported by
• BAYMAK A.Ş. and
• Republic of Turkey, Ministry of Science, Industry and Technology.

29. TB VARIATION DURING THE TEST
Tb
40.00
35.00
Temperature [C]
30.00
25.00
20.00
15.00
10.00
5.00
0.00
0.00
24.00
48.00
72.00
96.00
120.00
144.00
Time [hours]
168.00
192.00
216.00
240.00
264.00

30. SOME PICTURES