new methods to spatially extend thermal response test assessments

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IGSHPA Technical / Research Conference and Expo 2017

Denver, ColoradoMarch 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

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Thermal response test (TRT)

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11. G

roun

d wa

ter• 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

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TRT radius of influence

Raymond et al. 2014. ASHRAE Trans.

• Limited to ~1 - 2 m• Heterogeneous subsurface

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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

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1) Site scale extrapolation of thermal conductivity

Validated at an experimental site with 2 boreholes

Versaprofiles test site

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Measurement of temperature profiles

Submersible pressure and

temperature probe

Depth compensated by the rise in water level inside the U-pipe

𝐷∗(𝐿)=𝐷− ¿

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Numerical model development

Transient conductiveHeat transfer

tTc

yTλ

yxTλ

x

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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

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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

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Inverse numerical simulations to extent TRT assessmentRaymond et al. 2017. Renewable Energy

λ inversed = 3.2 W/mK λ TRT = 3.5 W/mK

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2) District scale extrapolation of thermal conductivity

Geothermal potential of an urban area with multiple projects

350 km2 zonein the northern

part of MontrealPerozzi et al. 2016. R1663

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4 TRTs with a heating cable

Wireless hub

Wireless switch

Variable transformer

Intelligent power meter

To power supply

To heating cable

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TRT analysis example

∆𝑇 (𝑡)∆ ln (𝑡)

= 𝑄4𝜋 λs𝐻

Q=V 𝐴

Infinite line source equation with the temporal superposition

principle for the recovery period

Slope method

∆𝑇 (𝑡c , 𝑡h)

∆ ln (𝑡 c+𝑡h𝑡 c

)= 𝑄4𝜋 λs𝐻

Test 3Thermal conductivity (W/mK)

Dep

th (m

)

Overburden

Bedrock

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10 lab measurements on outcrop samples

Transient plane source method

ctherm.com

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Measurements summary

Latitude LongitudeThermal

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

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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

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Sequential Gaussian simulations

To evaluate the spatial distributionof the host rock thermal conductivity

35 000 pixels 100 m × 100 m

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Single stochastic realization

Perozzi et al. 2016. R1663

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Mean of 10 stochastic realizations

Perozzi et al. 2016. R1663

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Perozzi et al. 2016. R1663

Standard deviation of 10 stochastic realizations

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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!

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Past and current TRT research - Field and analytical methods

The next challenge -Spatial limitation

Conclusions