This document describes two new methods for spatially extending thermal response test (TRT) assessments: 1) Inverse numerical modeling of temperature profiles from multiple boreholes at a site can be used to evaluate subsurface thermal conductivity beyond a single TRT well. 2) At a district scale, geostatistical simulation using thermal conductivity data from outcrops, boreholes, and multiple TRTs can provide stochastic realizations of subsurface properties to spatially interpolate between test locations. Both methods allow TRT assessments to be expanded beyond their typical limited spatial scope, creating new opportunities for evaluating ground source heat potential.

1. 1
IGSHPA Technical / Research Conference and Expo 2017
Denver, Colorado
March 15th, 2017
jasmin.raymond@inrs.ca
New Methods to Spatially Extend Thermal
Response Test Assessments
Jasmin Raymond, Michel Malo, Louis Lamarche, Lorenzo
Perozzi, Erwan Gloaguen & Carl Bégin

2. 2
Thermal response test (TRT)
Raymondetal.2011.Groundwater
• Evaluation of the subsurface
thermal conductivity
• To design ground coupled heat
pump (GCHP) systems
• Single test commonly carried
out for a commercial size
system
• Limited use because of
important cost

3. 3
TRT radius of influence
Raymond et al. 2014. ASHRAE Trans.
• Limited to ~1 - 2 m
• Heterogeneous subsurface

4. 4
How to extend TRT assessment beyond a single well?
1) Inverse numerical modeling of a
temperature profile – site scale, large project
2) Geostatistical simulation – district
scale, many small projects

5. 5
1) Site scale extrapolation of thermal conductivity
Validated at an
experimental site
with 2 boreholes
Versaprofiles test site

6. 6
Measurement of temperature profiles
Submersible
pressure and
temperature probe
Depth compensated by the rise
in water level inside the U-pipe
𝐷∗
(𝐿) = 𝐷 −
𝑉logger + 𝑉wire(𝐿)
2𝜋𝑟pipe,in
2

7. 7
Numerical model development
Transient conductive
Heat transfer
t
T
c
y
T
λ
yx
T
λ
x 























8. 8
PG-08-01: Evaluation of the Earth heat flux with
inverse numerical simulations
λ = 3.0 W/mK (TRT)
Squared residuals are
minimized to find q

9. 9
PG-08-02: Evaluation of the subsurface thermal
conductivity with inverse numerical simulations
q = 25 mW/m2 (inversion)
Squared residuals are
minimized to find λ

10. 10
Inverse numerical simulations to extent TRT assessment
Raymond et al. 2017. Renewable Energy
λ inversed = 3.2 W/mK λ TRT = 3.5 W/mK

11. 2) District scale extrapolation of thermal
conductivity
Geothermal potential of
an urban area with
multiple projects
11
350 km2 zone
in the northern
part of Montreal
Perozzi et al. 2016. R1663

12. 4 TRTs with a
heating cable
12
Wireless hub
Wireless
switch
Variable
transformer
Intelligent
power
meter
To power
supply
To heating
cable

13. TRT analysis example
13
∆𝑇(𝑡)
∆ ln(𝑡)
=
𝑄
4𝜋λs 𝐻
Q = V𝐴
Infinite line source equation with
the temporal superposition
principle for the recovery period
Slope method
∆𝑇(𝑡c, 𝑡h)
∆ ln(
𝑡c + 𝑡h
𝑡c
)
=
𝑄
4𝜋λs 𝐻
Test 3
Thermal conductivity (W/mK)
Depth(m)
Overburden
Bedrock

14. 14
10 lab measurements on outcrop samples
Transient plane source method
ctherm.com

15. 15
Measurements summary
Latitude Longitude
Thermal
conductivity
(W/mK)
Thermostratigraphic unit Measurement type
45.519249 -73.652824 2.10 T-BR-C Outcrop/TPS
45.519249 -73.652824 2.22 T-BR-C Outcrop/TPS
45.547637 -73.696752 2.90 T-BR-C Outcrop/TPS
45.60307 -73.656963 2.90 T-BR-C Outcrop/TPS
45.604803 -73.659649 3.15 T-BR-C Outcrop/TPS
45.605735 -73.661411 2.31 T-BR-C Outcrop/TPS
45.60307 -73.656963 2.60 T-BR-C Outcrop/TPS
45.602381 -73.658056 2.93 T-BR-C Outcrop/TPS
45.50964 -73.627682 2.24 T-BR-C Outcrop/TPS
45.604803 -73.659649 2.16 T-BR-C Outcrop/TPS
45.511454 -73.6518 2.39 T-BR-C Borehole/TRT cable
45.504581 -73.65772 2.39 T-BR-C Borehole/TRT cable
45.516988 -73.648486 2.81 T-BR-C Borehole/TRT cable
45.527392 -73.855424 4.20 Beauharnois Borehole/TRT cable

16. 16
Synthetic data
45 measurements
at the sedimentary
basin scale
Thermostratigraphy
of the St. Lawrence
Lowlands
Average thermal
properties
Thermal conductivity (W/mK)
Thermostratigraphic
unit
N Average
Standard
deviation
Trenton, Black River,
Chazy
23 2.67 0.44
Beauharnois 6 3.40 0.55
Raymondetal.2017.EnvironmentalEarthSciences

17. 17
Sequential Gaussian simulations
To evaluate the spatial distribution
of the host rock thermal conductivity
35 000 pixels 100 m × 100 m

18. 18
Single stochastic realization
Perozzi et al. 2016. R1663

19. 19
Mean of 10 stochastic realizations
Perozzi et al. 2016. R1663

20. 20
Perozzi et al. 2016. R1663
Standard deviation of 10 stochastic realizations

21. 21
Conclusions
Two methods are proposed to extend TRT
assessments:
• Inverse numerical modeling of
temperature profiles to extend at the site
scale beyond a first TRT
• Geostatistical simulations to interpolate
TRT assessments at the district scale
Can create new opportunities for TRT
assessments!

22. 22
Past and current TRT research -
Field and analytical methods
The next challenge -
Spatial limitation
Conclusions