Thermal properties + heat transfer

Size: px

Start display at page:

Download "Thermal properties + heat transfer"

Randolf Campbell
6 years ago
Views:

1 Thermal properties + heat transfer Daniel Pringle, Fall 2006, GEOS 692, University Alaska Fairbanks Heat capacity Thermal conductivity Variability -Rock type -Anisotropy -Pressure -Temperature Mineralogy Fabric/structure Conductivity mechanism

history borehole temperature profiles + climate reconstruction Engineering and geo-technical

2 Applications of Thermophysical Properties Geothermal heat flow: Earth s age and structure Rock genesis processes: rates of cooling, heat transfer Reconstruction of surface temperature history borehole temperature profiles + climate reconstruction Engineering and geo-technical applications: bore hole heat dissipation permafrost degradation stability of buried gas clathrates

3 Main thermo-physical properties Specific Heat c [J kg -1 K -1 ] Heat required to raise the temperature of unit mass of material by 1 degree. Q = mcδt cρ = c vol volumetric heat capacity ~ 2 MJ kg -1 K -1 Bulk property, scalar Thermal Conductivity k or λ [W m -1 K -1 ] Heat flow per unit temperature gradient. J Q = k T Transport property, tensor Thermal Diffusivity D or K or α [m 2 /s] Governs rate of spread of temperature disturbances. Latent heat, coefficient of thermal expansion. D = k cρ

Specific heat Usage: Q = mcδt Definition: c p = E T p c v = E T v Specific heat constant pressure, constant volume - Temperature kinetic energy within material - energy modes

4 Specific heat Usage: Q = mcδt Definition: c p = E T p c v = E T v Specific heat constant pressure, constant volume - Temperature kinetic energy within material - energy modes in electrically insulating crystals: lattice vibrations - lattice vibrations are quantized: phonons Collective excitations Quanta of lattice vibrations Sound version of photons

5 Phonons and specific heat E = hf = hv λ - statistics of phonons: Einstein and Debye theories: E(T) c(t) 3R T -3 θ D Debye temperature for each material θ D (Si) ~ 750 K, θ D (Ge) ~ 500 K,

6 Heat capacity of composites: easy! mass-weighted averages C vol, eff = v1c1ρ 1 + v2c2ρ v i volume fractions, ρ i, densities Specific heat,c [J kg -1 K -1 ] ( ~ 300 K) Cρ [MJ m -3 K -1 ] Air x 10-3 Water Ice 2100 (0 ºC) 2 Quartz Rock minerals ~ 2.3 ± 0.5 Roy, Clauser & Huenges

7 Sea ice heat capacity S = 12.5 ppt S = 8.5 ppt S = 6 ppt Trodahl et at. JGR, 2000.

8 Thermal Conductivity of Rocks Variability -Rock type -Anisotropy -Pressure -Temperature Mineralogy Fabric/structure Conductivity mechanism

9 Conductivity Variability Schön

mineral phase Metamorphic - anisotropy, dominant mineral phase Metamorphic

10 Rock type Analysis - Clauser & Huenges Rock Type Paramount Factors Sedimentary - porosity, anisotropy Volcanic - porosity Plutonic - dominant mineral phase Metamorphic - anisotropy, dominant mineral phase Metamorphic rocks; high/low quartz content Volcanic rocks; high/low porosity Clauser & Huenges

11 Porosity Hawaiian basalts k(water) ~ 0.6 Wm -1 K -1 k(air) ~ 0.02 Wm -1 K -1 Clauser & Huenges

12 Temperature Metamorphic k ~ T -1 Quartzite Quartz-poor (incl. marble, slate albitite, amphibolite) Volcanic Basalt glass, obsidian, diabase dolerite Basalt, rhyolite, dacite, tuff Many empirical fits for k(t): local areas, different rock types (see Schön, Clauser & Huenges) Clauser & Huenges

13 Heat transfer Q 1 A dq dt = k dt dx T h T c What is being transported, and how? Thermal (kinetic) energy transferred: conduction, radiation, convection. Radiative conductivity : k r T 3 / α opt T temperature [K] α optical absorption coeff. Basalt glass, obsidian, diabase dolerite Basalt, rhyolite, dacite, tuff Clauser & Huenges

14 Phonons again Electrical insulators as phonon gas Gas theory result applies! k = 1 c 3 ul c, specific heat u, phonon velocity l mean free path ~constant distance between scattering events Kittel

15 Phonon mean free path l crystal size l ~ constant, phonon density increases as N ~ T c ~ T 3 k ~T 3 l ~ T -1 k ~ T -1 KCl single crystal

16 Phonon mean free path l crystal size l ~ constant, phonon density increases as N ~ T c ~ T 3 k ~T 3 l ~ T -1 k ~ T -1 KCl single crystal T > 300 K: crystalline solids: k ~ T -1, small crystallites and amorphous solids (eg. glasses) k ~ c Kittel

17 Quartz Conductivity T-dependence Ordered: l limited by phonon density k ~ c k ~ T -1 + k rad Disordered: mfp limited scale of disorder fused quartz l ~ 8 Å Si0 2 tetrahedra ~ 7 Å Parrott & Stuckes, Kittel

18 Thermal Conductivity of Rocks Variability -Rock type -Anisotropy -Pressure -Temperature Mineralogy Fabric/structure Conductivity mechanism Phonons + radiative

19 Thermal conductivity of minerals Uni. Leoben

20 Thermal conductivity of minerals Anisotropy (see Schon, Clauser & Huenges, pdf s on class web page) Graphite (300 K): k(in plane) ~ 2000 W m -1 K -1 ; k(perp) ~ 5 W m -1 K -1 Empirical correlations with density and mean atomic weight: Horai and Simmons (1969) 3 k = 5.5 x 10 ρ (20 m A ) Uni. Leoben

21 Thermal conductivity of composites: harder! Heat flow along paths of least resistance! Factor in geometry Arithmetic mean; harmonic mean

22 Simple composite models

23 Granite conductivity & mineralogy Quartz 7.7 W m -1 K -1 Geometric mean Orthoclase 2.4 W m -1 K W m -1 K -1 Plagioclase Measured, n=441 Canadian Shield Uniform distribution Jessop

24 Saturation + Porosity Fluid saturation Bottle-necks vs. open pore space Sandstones Granite Clauser & Huenges, web

25 Pressure 1. Closing bottlenecks 2. Reduction in intrinsic porosity Sandstone, dolomite, limestone, basalt, porphyry, granite + x 10 = [atm] Simple Fracture Model k k 1 exp p D 0 A p = m 0 (actually need two terms to fit data, here gneiss) Clauser & Huenges, Schön

26 Summary of Rock-type variations Rock Type Paramount Factors Sedimentary - porosity, anisotropy Volcanic - porosity Plutonic - dominant mineral phase Metamorphic - anisotropy, dominant mineral phase Clauser & Huenges

27 Thermal Conductivity of Rocks Different mixing models Variability -Rock type -Anisotropy -Pressure -Temperature Quartz content Mineralogy Fabric/structure porosity, saturation Conductivity mechanism Phonons + radiative

28 Anisotropy φ gneiss 70-90% water sat dry amphibolite Clauser & Huenges

29 References Clauser, C and E. Huenges, 1995, Thermal Conductivity of Rocks and Minerals, Rock Physics and Phase Relations, Ed. T. Ahrens, AGU. (pdf online) Discussion, data rocks and minerals, statistical analysis rock types Jessop, A.M., 1990, Thermal Geophysics, Elsevier. Broader picture Kittel, C, 1971, Introduction to Thermal Physics, Wiley & Sons. Theory Parrott, J.E. and A.D. Stuckes, 1975,Thermal Conductivity of Solids, Pion, London. Theory Roy, R.F, A.E.Beck and Y.S. Touloukian, 1981,Thermophysical Properties of Rocks, in Physical Properties of Rocks and Minerals, vol. 2, ed. Y.S.Touloukian et al. Brief discussion, properties, tables, graphs Schön, J.H., 1996, Physical Properties of Rocks: Fundamentals and Principles of Petrophysics, Permagon Press (reserve in GI/IARC library) Petrology, models, properties Google: Petrovsky and Uni. Leobden presentations.

Time & place: Fridays, 10:30-11:30am Natural Science Bldg 235, 1st meeting Friday Sept 8

GEOS 692, Transport Processes and Physical Properties of Rocks (1 CR) Time & place: Fridays, 10:30-11:30am Natural Science Bldg 235, 1st meeting Friday Sept 8 Instructor: Hajo Eicken, Geophysical Institute,