Thermal Response Tests Using Optical Fiber Thermometers

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Thermal Response Tests Using Optical Fiber
Thermometers

• September 13, 2006
• Hikari FUJII, Hiroaki OKUBO, Ryuichi ITOI
• Graduate School of Engineering, Kyushu
  University, Japan

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Background

• At Ground Heat Exchangers (GHEs) drilled in
  heterogeneous formations, heat exchange rates may
  not be uniform due the variation of ground
  thermal conductivity (ls) with depth.
• Optical fiber thermometers, which measure
  continuous temperature distribution along optical
  fiber sensors, could be useful in the estimation
  of the distribution of ls.

High Capacity
Low Capacity
Estimated Vertical Distribution of Heat Exchange
Rates
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Contents

• To carry out Thermal Response Tests (TRTs) using
  optical fiber thermometers at GHEs in Kyushu
  Universitys campus in Fukuoka City, Japan.
• To develop procedures to estimate ls distribution
  on the basis of measured temperature data.

• Installation of Optical Fiber Sensors

Optical Fiber Thermometer (Hitachi Cable Ltd.
FTR-070) -Resolution 0.1K -Accuracy 1.0K
-Minimum Depth Interval 1.0m -Minimum
Time Interval 60sec
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Experimental Wells and Geological Column
Sensor Position
Sand and Gravel (Permeable)
Quaternary System
Unconformity (_at_-17m)
Siltstone and Silty Sandstone (Impermeable)
Tertiary System
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Temperature Distribution in Co-axial and U-tube
GHEs
(Co-axial GHE) Large temperature difference with
depth. Temperature change with depth needs to
be considered in the calculation of well
performance. (U-tube GHE) Nearly constant
temperature with depth. Well temperatures could
be treated as uniform.
Vertical Temperature Distribution (After 1 days
Circulation)
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Temperature Distribution in U-tubes during
Circulation
uw (m/s) qw (L/min) 0.55
35.0 0.33 21.0 ()Double
U-tube ID26mm
Photo of Wellhead
Measured Temperature
Average Temperature
Measured water temperatures in U-tubes showed
negligible differences with depth in Survey
No.1. Water temperature in U-tubes is considered
uniform under high circulation rates.
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Multi-layer Model
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Calculation of Temperature Distribution in
Co-axial GHE
(1) Heat transfer between tubing and annulus (q1)
and annulus and ground (q2) q1,nUtAt
(Ta,n-Tt,n) q2,nUaAa (Tro,n-Ta,n)
U Heat Transfer Coefficient ASurface Area (2)
Convective heat transfer in pipes
(Tt,n-Tt,n1) mwCpq1,n (Ta,n-Ta,n1)
mwCpq1,n -q,2,n mw Mass Flow Rate Cp
Specific Heat
Ta
Tt
n-1
Tro
q2
q1
n
n1
Energy Balance in Co-axial GHE
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Estimation of Thermal Conductivity
Estimate ls by minimizing objective function F
using a nonlinear regression method, the Polytope
method (Nelder and Mead, 1965).
Error in vertical temperature profile
Error in heat medium temperature
To Water temperature at well outlet (K) Tro
Outer face temperature of GHE (K) obs observed,
cal calculated nstep number of timestep,
nlayer number of layer ntest number of
comparison between measure and calculated
temperature profiles a Weighting factor (0.1)
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Conditions of TRTs
0.62(m/s)
0.31(m/s)
H-2 (U-tube GHE)
H-1 (Co-axial GHE)
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Interpretation of TRT No.1 (Co-axial, Reverse
Circulation)
Well Temperatures during Circulation
Outlet Temperatures of Heat Medium
Calculated temperature fitted measured data
reasonably well.
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Interpretation of TRT No.3 (Single U-tube)
Outlet Temperatures of Heat Medium
Well Temperatures (After Well Shut-in)
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Comparison of Estimated Thermal Conductivity
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Summary
Through interpretations of TRTs using optical
fiber thermometers, following results were
obtained The application of optical fiber
thermometers on TRTs will enable the optimization
of GHE length in heterogeneous formations.

• The estimated distribution of thermal
  conductivity agreed with the local geological and
  groundwater information.
• Co-axial and U-tube GHEs require different
  modeling approaches.

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Interpretation of TRT No.2 (Co-axial, Normal
Circulation)
Well Temperatures during Circulation
Outlet Temperatures of Heat Medium
Using same ls distribution as TRT No.1,
calculated temperature well matched measured data.
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Cylindrical Source Function
The cylindrical source function G (Ingersoll, et
al. 1954) was applied to calculate the heat
conduction in the ground.
Temperature difference between ground and GHE
Tff farfield
temperature, Tro outer face temperature of
GHE, nstep number of timestep, qgc heat
exchange rate, ls thermal conductivity of
soil, L well depth Cylindrical source
function G Z ast/r2 Pr/ro  
J0, J1, Y0, Y1, Y2 Bessel functions, as
thermal diffusivity of soil, ro outer
radius of the GHE
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Poor Performance of Double U-tube