Measuring and Estimating Thermal Properties of Porous Materials
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Transcript of Measuring and Estimating Thermal Properties of Porous Materials
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Measuring and Estimating Thermal Properties of Porous
Materials
Colin S. Campbell, Ph.D.Decagon Devices and
Washington State University
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Background About the presenter
Ph.D. in Soil Physics, 2000, Texas A&M University
VP of Research and Development, Decagon Devices
Adjunct Faculty in Environmental Biophysics, Washington State University
Supporting Scientist on TECP instrument for NASA 2008 Phoenix Mars Lander
2
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Outline Why measure thermal properties of
materials Thermal properties definitions Ranges and behaviour with density,
temperature and moisture Measurement methods Estimating thermal properties
Modeling Interpolation
Thermal properties on Mars
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Thermal Properties of Soil Impact Wind Power Generation
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Interesting applications for thermal properties Artificial skin and human corneas Nanofluids Cooking and sterilizing of foods Thermal properties of oils and coolants
Heat transfer Quality monitoring
Thermal greases and heat sink compounds
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Interesting soil and geotechnical applications Direct
Thermal resistivity of building materials Surface energy balance
Climate change research Geothermal (heat pump) exchangers
For a given volume of soil, how much heat can be stored? Buried power transmission lines
What is the thermal resistance between a buried power line and the external environment?
Burial of high level radio-active waste How hot will it get? How will it affect moisture patterns?
Indirect Water content of soil Water content of construction materials (concrete)
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Steady State Heat Flow: Fourier’s First Law
T1
T2
Dx
H
xTT
xTTkH
dxdTkH
D
D
2121 )(
H - heat flux density W m-2
k - thermal conductivity
W m-1 K-1
- thermal resistivity oC cm-1 W-1
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Steady State Thermal Properties
Thermal conductivity (k )Ratio of heat flux density to
temperature gradient – measures the amount of heat a material can transmit for a given temperature gradient
Thermal resistivity ( )Reciprocal of thermal conductivity –
used mainly in buried power cable applications
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Which is best, conductivity or resistivity?For soil, conductivity is almost always
preferable to resistivity:Better statistical propertiesMore correct for averagingMore linear with water contentA more correct perception of
significance
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An extreme exampleAssume two materials of equal area,
one with a conductivity of 1 and the other with a conductivity of zero. Resistivities would be 1 and infinity.
Averaging the conductivities would give ½. Averaging resistivities would give infinity.
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Transient Heat Flow: Fourier’s Second Law
zTk
zzH
tTC
T Dz
H1
For homogeneous material
H2
2
2
2
2
zTD
zT
Ck
tT
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Transient Thermal PropertiesVolumetric specific heat (C )
Heat required to raise the temperature of unit volume by 1 K (or C): J m-3 K-1
(product of density and sp. ht.) Thermal diffusivity (D )
Ratio of conductivity to heat capacity; measure of propagation rate of thermal disturbances: m2 s-1
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Applications of Fourier’s Second LawNeher-McGrath cable heat loss
calculations
2D and 3D numerical solutions to the differential equations (finite difference or finite element)
Line heat source equations for thermal properties measurement
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Modeling Soil Thermal PropertiesSoil is a mixture of solid, liquid (water)
and gas (air and water vapor)
The thermal properties of the soil depend on the thermal properties of the constituents, their volume fractions, and how they are mixed
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Thermal properties of constituents
From Campbell and Norman (1998)
k W m-1 K-1
R m K W-1
C MJ m-3 K-1
D mm2 s-1
Soil Minerals 2.5 0.40 2.3 1.09Granite 3 0.33 2.2 1.36Quartz 8.8 0.11 2.1 4.19Organic matter 0.25 4.00 2.5 0.10Water 0.6 1.67 4.18 0.14Ice 2.2 0.45 1.9 1.16Air 0.025 40.00 0.001 20.83
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Calculating volumetric heat capacity
The heat capacity of a mixture of air, water and solids is the sum of the volume fractions, each multiplied by its heat capacity
where C is heat capacityx – volume fraction of the constituents, w, and a refer to solids, water, and air
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Volumetric heat capacity example
For a mixture of 50% soil minerals, 25% air and 25% water the heat capacity is
Note: water is half of total and air is insignificant
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Heat capacity ranges
DryMJ m-3 K-1
SaturatedMJ m-3 K-1
Soil (50% voids) 1.2 3.2Concrete (17% voids) 1.9 2.6Granite 2.2
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Volumetric heat capacity: main points
Ranges from around 1 to 3 MJ m-3 K-1
Varies linearly with water content
Easy to compute from water content and density
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Conductivity can’t be easily predicted from volume fraction
k = 0.5 x 2.5 + 0.5 x 0.025 = 1.26
1/k = 0.5/2.5 + 0.5/0.025k = 0.05
air min
heat heat
air
min
Parallel Series
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Thermally induced water flow in soil – soil as a heat pipe
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Temperature dependence of soil thermal conductivity
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Some consequences of thermally induced water flowUnsaturated soil will dry out around
heated objectsThermal runaway in buried cablesWater migration away from buried nuclear
waste
Take Home: Methods that heat the soil for long time periods can’t accurately measure conductivity of unsaturated porous media
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Response to Thermal Conductivity of Solids
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Response to Compaction
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Take-home Thermal conductivity of soil can range
over more than an order of magnitude (0.1 to 2 W m-1K-1)
Thermal conductivity of porous material depends on:
Composition Temperature Density Water content
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More Take-homeIf you want high conductivity (low
resistivity): Compacted is good, fluffy is bad Wet is good, dry is bad Quartz is good, organic is bad For a wet soil, high temperature is good. For
dry soil it doesn't matter.
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Outline Thermal properties definitions Ranges and behaviour with density,
temperature and moisture Measurement methods Estimating thermal properties
Modelling Interpolation
Thermal properties on Mars
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Equations for single and dual line heat source
Heating curve
Cooling curve
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Pulsed Infinite Line Source, Approximate Solution
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Heat capacity measurement: dual needle method
C proportional to inverse height of maximum
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Thermal conductivity: single needle method
k proportional to 1/slope
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Heated needles are transient line heat sources
IdeallySource is infinitely long and
infinitesimally smallTemperature is uniform and constantPerfect thermal contact between
needle and medium
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Real sensors: not infinitely long or infinitesimally small
10 cm long, 2.4 mm diameter
6 cm long, 1.27 mm diameter
3 cm long, 6 mm spacing
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Measurement problems for the line heat source
Ideal Source is infinitely
long and infinitesimally small
Perfect thermal contact between needle and medium
Temperature is uniform and constant
Reality Source is 3 cm - 120
cm long Contact resistance
between needle and medium
Temperature may vary in space and time
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Effect of finite needle size (30 s heating)
Thick needles must be heated longer for accurate measurements
Cond.W/(mK)
1.27 mmneedle
2.4 mmneedle
water 0.6 0.579 ± 0.006 0.852 ± 0.005
glycerol 0.29 0.277 ± 0.007 0.427 ± 0.002
oil 0.14 0.124 ± 0.0001 0.191 ± 0.003
foam 0.033 0.0157 ± 0.00002 0.033 ± 0.0001
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Contact resistance Poor thermal contact between needle and
medium of interest Dry soil or granular material Solid materials with pilot hole
Thermal conductivity can be significantly underestimated if short heating times used Longer heating times needed in these types of
materials
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Effect of Sample Temperature Drift on K Measurements
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Important points Small need with short heating time
preferred if no contact resistance
Must have longer heating time if: Larger needle used Dry or solid materials
Temperature drift during measurement causes serious errors in heating-only analyses
Must analyze heating and cooling data
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How does the KD2-Pro address these issues?
Heating time is optimized for needle size and material 30 s for small “liquids” needle 2.5 – 5 minutes for large “soil and solids” needle
Measure both heating and cooling phases to remove effects of temperature drift
Verify accuracy against known standards
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Outline Thermal properties definitions Ranges and behaviour with density,
temperature and moisture Measurement methods Estimating thermal properties
Modeling Interpolation
Thermal properties on Mars
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How can we get a dryout curve?Reliable mathematical models exist
relating conductivity to water content and other variables – use them to generate the dryout curve
Make measurements on a single sample as it dries
Mix up multiple samples and make measurements on them
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Dryout Curves - ModelingResistivity as a function of water
content, temp, compaction and composition
Determined using composition and compaction
Apply model for desired tempReferences
Bristow, K. 2002 . Thermal Conductivity, p1209-1226. Methods of soil analysis. Part 4. Physical Methods (Soil Science Society of America Book Series, Vol. 5). Soil Science Society of America. Madison, WI.
Campbell, G. S., J. D. Jungbauer, Jr., W. R. Bidlake and R. D. Hungerford. 1994. Predicting the effect of temperature on soil thermal conductivity. Soil Science 158:307-313.
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Dryout Curves - ModelingAdvantages
Relatively straight forwardUseful for understanding the effects of:
CompositionCompactionTemperature changesWater content
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Dryout Curves - Modeling
Knowing water content is crucial to accurate resistivity
measurements
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Dryout Curves - ModelingDisadvantages
No actual thermal resistivity measurements from specific sample
Have to knowMineralogyCompactionSoil texture Temperature
Lack of confidence in data
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Dryout Curves – Single SampleCore or repacked sample
Core for native materialsRepacked sample for backfill materials
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Dryout Curves – Single SampleMethod
Saturate with waterMeasurement takenWeigh sampleMeasurements over time (as sample dries)Oven dry, then cool to room tempMeasureWeighWater contents computedPlot dryout curve
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Dryout Curves – Single SampleAdvantages
No disturbance of soil (density stays constant)But, the sample could crack
Good on fully wet and fully dry but…
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Dryout Curves – Single SampleDisadvantages
Time and labor intensive
Samples don’t dry uniformlyCan be more
than 50% error
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Dryout Curves – Single Sample Disadvantages (cont.)
Weight gives average water content not water content at the point of the thermal resistivity measurement
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4-50
-40
-30
-20
-10
0
10
20
30
40
50
Average Column Water Content (m3/m3)
Perc
ent E
rror
in W
ater
Con
tent
Val
ue
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Dryout Curves – Multiple SampleMethod
Dry sample packed to desired bulk densityTake thermal resistivity measurementWeigh the sample or take subsample for water
content determinationAdd water, mix, repack, repeat measurements
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Dryout Curves – Multiple SampleAdvantages
Fast and easyDisadvantages
Can’t be used on undisturbed samplesDifficult to obtain desired bulk density
with dry samplesDrop hammer method won’t workCould use a press (no standard procedure)
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Dryout Curves – A Different ApproachCombination of Single Sample and
Modeling methodsPrepare and saturate sample (Single
sample method)Weight and measure
Oven dry, cool to room temp Weight and measure
Compute density and water contentPlot
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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
0.5
1
1.5
2
2.5
3
3.5
4
Dryout Curve
Series1
Moisture Content (m3/m3)
Resistivity
Dryout Curves – A Different Approach
)]1([8.2)1(
1)/(
wssdry
w
sat
w fff
WCm
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References for modelling soil thermal properties
Bristow, K. 2002 . Thermal Conductivity p1209-1226. Methods of soil analysis. Part 4 Soil Science Society of America, Inc. 677 South Segoe Rd. Madison, WI 53711-1086.
Campbell, G. S. and J. M. Norman. 1998. An Introduction to Environmental Biophysics, 2nd Ed. Springer Verlag, NY
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Field measurements A single measurement represents a point in
time and is nearly worthless for design
Continuously measuring thermal properties over a year or more will provide adequate information
Combining field measurements with modelling based on physical properties of material can be powerful
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Laboratory measurement on cores
Three reliable points are available on intact cores: field moist, saturation and fully dryDrying the sample to get intermediate
moisture values doesn’t work because the average water content of the sample isn’t the water content around the probe
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Laboratory measurement on cores
Repacked cores can be produced at a range of water contentsThermal properties depend on water
content, density, temperature, and mineralogy, all of which can be duplicated in the laboratory on repacked samples
Measurements on repacked samples are fast and reliable
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Conclusions
Thermal properties of soil and other porous materials vary widely over space and time Density Water content
Volumetric heat capacity can be predicted from the density and water content of soil Thermal conductivity is more difficult to predict,
but still possible
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Conclusions
Methods exist for easily and reliably measuring thermal properties of soil and other porous materials Best transient line heat source measurements
analyze heating and cooling data
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Phoenix Scout Mission to Mars June 25, 2008 – Oct., 2008
TECP: Thermal and electrical properties probe
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TECP Purpose Measure thermal and
electrical properties of Martian soil
Infer liquid water content, ice content, and pore size distribution
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TECP thermal properties results
Complete thermal characterization of soil at landing site
Results validated satellite-derived data
Measurements indicated dry, low density material