Skip to main content
SpringerLink
Log in

Thermal-Diffusivity and Heat-Capacity Measurements of Sandstone at High Temperatures Using Laser Flash and DSC Methods

  • Published:
International Journal of Thermophysics Aims and scope Submit manuscript

Abstract

The well-known contact-free, laser-flash method was used for measurement of the thermal diffusivity \((a)\) of natural sandstone samples. The experimental procedure was conducted using the microflash apparatus (LFA 457). The measurements have been made over the temperature range from (302.9 to 774.3) K. The isobaric heat capacities \((C_P )\) of the same sample were measured over the temperature range from (308 to 763) K using DSC 204 F1. Uncertainties are 3 % and 1 % for \(a\) and \(C_P \), respectively. Measured values of \(a\) and \(C_P\) together with density data were used to calculate the thermal conductivity \((\lambda )\) of sandstone. Theoretically based correlations for the thermal diffusivity (damped harmonic oscillator, DHO) and heat capacity (Debye and Einstein theories) were adopted to accurately represent the measured data. Correlation equations for the thermal diffusivity and heat capacity have been developed using the well-known theoretical asymptotic behavior of \(a\left( T \right) \) and \(C_P \left( T \right) \) for various temperature ranges (low- and high-temperature limits). The microscopic nature of the effect of temperature on \(a\left( T \right) \) and \(\lambda \left( T \right) \) behavior of sandstone is discussed. Detailed interpretation and testing of the measured property data for sandstone using various existing theoretical and empirical models, in order to check their accuracy, predictive capability, and applicability, are provided.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. A.M. Hofmeister, Phys. Chem. Miner. 33, 45 (2006)

    Article  ADS  Google Scholar 

  2. F. Dubuffet, D.A. Yuen, E.S.C. Rainey, Geophysics 9, 1 (2002)

    Google Scholar 

  3. J.M. Branlund, M. Kameyama, D.A. Yuen, Y. Kaneda, Earth Planet. Sci. Lett. 182, 171 (2000)

    Article  ADS  Google Scholar 

  4. T.K.B. Yanagawa, M. Nakada, D.A. Yuen, Earth Planets Space 57, 15 (2005)

    Article  ADS  Google Scholar 

  5. A.P. Van den Berg, D.A. Yuen, E.S.G. Rainey, Phys. Earth Planet. Inter. 142, 283 (2004)

    Article  ADS  Google Scholar 

  6. J.W. Parker, J.R. Jenkins, WADD Technical Report 65–91, Directorate of Materials and Processes (1961)

  7. W.J. Parker, R.J. Jenkins, C.P. Butler, G.L. Abbott, J. Appl. Phys. 32, 1679 (1961)

    Article  ADS  Google Scholar 

  8. A.G. Whittington, A.M. Hofmeister, P.I. Nabelek, Nature 458, 319 (2009)

    Article  ADS  Google Scholar 

  9. G. Wei, X. Zhang, F. Yu, K. Chen, Int. J. Thermophys. 27, 235 (2006)

    Article  ADS  Google Scholar 

  10. P. Schoderböck, H. Klocker, L.S. Sigl, G. Seeber, Int. J. Thermophys. 30, 599 (2009)

    Article  ADS  Google Scholar 

  11. J.B. Holt, Earth Planet. Sci. 27, 404 (1975)

    Article  ADS  Google Scholar 

  12. R. Buttner, B. Zimanowski, J. Blumm, L. Hagemann, J. Volcanol. Geotherm. Res. 80, 293 (1998)

    Article  ADS  Google Scholar 

  13. A. Degiovanni, S. Andre, D. Maillet, in Thermal Conductivity, vol. 22, ed. by T.W. Tong (Technomic, Lancaster, PN, 1994), pp. 623–633

  14. Y.A. Popov, D. Pribnow, J.H. Sass, C.F. Williams, H. Burkhardt, Geothermics 28, 253 (1999)

    Article  Google Scholar 

  15. A.M. Hofmeister, Phys. Earth Planet. Inter. 170, 201 (2008)

    Article  ADS  Google Scholar 

  16. M. Pertermann, A.G. Whittington, A.M. Hofmeister, F.J. Spera, J. Zayak, Contrib. Mineral. Petrol. 155, 689 (2008)

    Article  ADS  Google Scholar 

  17. H. Mehling, G. Hautzinger, O. Nilsson, J. Fricke, R. Hofmann, O. Hahn, Int. J. Thermophys. 19, 941 (1998)

    Article  Google Scholar 

  18. R. Hofmann, O. Hahn, F. Raether, H. Mehling, J. Fricke, High Temp. High Press. 29, 703 (1997)

    Article  Google Scholar 

  19. E. Fried, in Thermal Conductivity, chap. 5, vol. 2, ed. by R.P. Tye (Academic Press, London, 1969), pp. 253–275

  20. E.J. Hanley, D.P. DeWitt, R.E. Taylor, in Proceedings of 7th Symposium on Thermophysical Properties, ed. by A. Cezairliyan (ASME, New York, 1977), p. 386

  21. K.M. Strack, A.W. Ibrahim, G.V. Keller, C.H. Stoyer, Geophys. Prospect. 30, 454 (1982)

    Article  ADS  Google Scholar 

  22. J.F. Schatz, G. Simmons, J. Geophys. Res. 77, 6966 (1972)

    Article  ADS  Google Scholar 

  23. J.F. Schatz, G. Simmons, J. Appl. Phys. 43, 2588 (1972)

    Article  ADS  Google Scholar 

  24. J. Zaug, E. Abransom, J.M. Brown, L.J. Slutsky, in High-Pressure, ed. by Y. Syono, M.H. Manghnani (Terra/AGU, Washington, DC, 1992), pp. 157–166

    Google Scholar 

  25. M. Chai, J.M. Brown, L.J. Slutsy, Phys. Chem. Miner. 23, 470 (1996)

    Article  ADS  Google Scholar 

  26. H. Kanamori, N. Fujii, H. Mizutani, J. Geophys. Res. 73, 595 (1968)

    Article  ADS  Google Scholar 

  27. A.M. Hofmeister, in Superlumes: Beyond Plate Tectonics, ed. by D.A. Yuen, S. Maruyama, S.I. Kavato, B.F. Windley (Springer, Dordrecht, 2007), pp. 269–292

    Chapter  Google Scholar 

  28. A.M. Hofmeister, in Infrared Spectroscopy in Geochemistry, Exploration Geochemistry, and Remote Sensing, ed. by P. King, M. Ramsey, G. Swayze (Mineralogical Association of Canada, Ottawa, 2004), pp. 135–154

  29. M. Pertermann, A.M. Hofmeister, Am. Mineral. 91, 1747 (2006)

    Article  Google Scholar 

  30. P.A. Geisting, A.M. Hofmeister, Phys. Rev. B 65, 144305-1 (2002)

    ADS  Google Scholar 

  31. A.M. Hofmeister, A.G. Whittington, M. Pertermann, Contrib. Mineral. Petrol. 158, 381 (2009)

    Article  ADS  Google Scholar 

  32. A. Hartmann, V. Rath, C. Clauser, Int. J. Rock Mech. Min. Sci. 42, 1042 (2005)

    Article  Google Scholar 

  33. F. Surma, Y. Geraud, Pure Appl. Geophys. 160, 1125 (2003)

    Article  ADS  Google Scholar 

  34. Y.A. Popov, in Proceedings of 4th World Congress on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics, vol. 1, ed. by M. Giot, F. Mayinger, G.P. Celeta (Brussels, Belgium, 1997), pp. 109–116

  35. C. Moyne, J.C. Batsale, A. Degiovanni, in Thermal Conductivity, vol. 21, ed. by J. Gremers (Plenum Press, New York, 1990), pp. 109–120

  36. S.Q. Zeng, A. Hunt, R.J. Greif, Heat Transf. 117, 1055 (1995)

    Article  Google Scholar 

  37. U. Seipold, Tectonophysics 291, 161 (1998)

    Article  ADS  Google Scholar 

  38. U. Seipold, Scientific Technical Report STR01/13 (GFZ, Potsdam, 2001)

    Google Scholar 

  39. U. Seipold, J. Geodyn. 20, 145 (1995)

    Article  Google Scholar 

  40. U. Seipold, E. Huenges, Tectonophysics 291, 173 (1998)

    Article  ADS  Google Scholar 

  41. U. Seipold, High Temp. High Press. 34, 299 (2002)

    Article  Google Scholar 

  42. S. Fuchs, A. Förster, Chemie der Erde Geochem. 70, 13 (2010)

    Article  ADS  Google Scholar 

  43. D.G. Cahill, S.K. Watson, R.O. Pohl, Phys. Rev. B 46, 6131 (1992)

    Article  ADS  Google Scholar 

  44. R.G. Berman, T.H. Brown, Contrib. Mineral. Petrol. 89, 168 (1985)

    Article  ADS  Google Scholar 

  45. R.G. Berman, T.H. Brown, EOS 64, 875 (1983)

    Google Scholar 

  46. R.G. Berman, T.H. Brown, Geochim. Cosmochim. Acta 45, 661 (1984)

    Article  ADS  Google Scholar 

  47. J.M. Branlund, A.M. Hofmeister, Phys. Chem. Miner. 34, 581 (2007)

    Article  ADS  Google Scholar 

  48. S. Min, J. Blumm, A. Lindemann, Thermochim. Acta 455, 46 (2007)

    Article  Google Scholar 

  49. J. Blumm, J. Opfermann, High Temp. High Press. 34, 515 (2002)

    Article  Google Scholar 

  50. J.A. Cape, G.W. Lehman, J. Appl. Phys. 34, 1909 (1963)

    Article  ADS  Google Scholar 

  51. R.D. Cowan, J. Appl. Phys. 34, 926 (1963)

    Article  ADS  Google Scholar 

  52. L. Vozár, W. Hohenauer, Int. J. Thermophys. 26, 1899 (2005)

    Article  ADS  Google Scholar 

  53. L. Ray, H.J. Forster, F. Schilling, A. Forster, Earth Planet. Sci. Lett. 251, 241 (2006)

    Article  ADS  Google Scholar 

  54. H.D. Vosteen, R. Schellschmidt, Phys. Chem. Earth. 28, 499 (2003)

    Article  Google Scholar 

  55. M. Osako, E. Ito, A. Yoneda, Phys. Earth Planet. Inter. 143–144, 311 (2004)

    Article  Google Scholar 

  56. M. Osako, A. Yoneda, E. Ito, Phys. Earth Planet. Inter. 183, 229 (2010)

    Article  ADS  Google Scholar 

  57. M. Osako, E. Ito, Rev. High Press. Sci. Technol. 7, 110 (1998)

    Article  Google Scholar 

  58. A. Tommasi, B. Gilbert, U. Seipold, D. Mainprice, Nature 411, 783 (2001)

    Article  ADS  Google Scholar 

  59. A.M. Hofmeister, D.A. Yuen, J. Geodyn. 44, 186 (2007)

    Article  Google Scholar 

  60. A.M. Hofmeister, J.M. Branlund, M. Pertermann, in Treatise in Geophysics, Mineral Physics, vol. 2, ed. by G. Schubert (Elsevier, Amsterdam, 2007), pp. 543–578

  61. A.M. Hofmeister, M. Pertermann, Eur. J. Mineral. 20, 537 (2008)

    Article  Google Scholar 

  62. A.M. Hofmeister, Science 283, 1699 (1999)

    Article  ADS  Google Scholar 

  63. A.M. Hofmeister, Am. Mineral. 86, 1188 (2001)

    MathSciNet  Google Scholar 

  64. P.A. Geisting, A.M. Hofmeister, B. Wopenka, G.D. Gwanmesia, B.L. Jolliff, Earth Planet. Sci. Lett. 218, 45 (2004)

    Article  ADS  Google Scholar 

  65. J.M. Branlund, A.M. Hofmeister, Am. Mineral. 93, 1620 (2008)

    Article  Google Scholar 

  66. M. Roufosse, P.G. Klemens, J. Geophys. Res. 79, 703 (1974)

    Article  ADS  Google Scholar 

  67. J.M. Ziman, Electrons and Phonons. The Theory of Transport Phenomena in Solids (Clarendon Press, Oxford, 1962)

    Google Scholar 

  68. X. Yu, A.M. Hofmeister, J. Appl. Phys. 109, 033516-1 (2011)

    ADS  Google Scholar 

  69. D. Mottaghy, H.D. Vosteen, R. Schellschmidt, Int. J. Earth Sci. 97, 435–442 (2003)

    Article  Google Scholar 

  70. Z.Z. Abdulagatova, I.M. Abdulagatov, S.N. Emirov, Int. J. Rock Mech. Min. Sci. 46, 1055 (2009)

    Article  Google Scholar 

  71. Z.Z. Abdulagatov, A.I. Abdulagatov, I.M. Abdulagatov, in Sandstones: Geochemistry, Uses and Environmental Impact, chap. 1, ed. by A.M. Kazerouni (Nova Sci. Pub., Inc., New York, 2013)

  72. YuS Sudenko, YuP Barskii, in Thermophysical Properties of Substances and Materials, vol. 10, ed. by V.V. Sychev (GSSSD, Moscow, 1976), pp. 246–259

  73. A.E. Beck, in Handbook of Terrastrial Heat Flow Density Determination, ed. by R. Haenel, L. Rybach, L. Stegena (Kluwer, Dordrecht, 1988), pp. 87–124

  74. A.M. Hofmeister, Geochim. Cosmochim. Acta 68, 4721 (2004)

    Article  ADS  Google Scholar 

  75. A. Einstein, Ann. Phys. 22, 180 (1907)

    MATH  Google Scholar 

  76. P. Debye, Ann. Phys. 39, 789 (1912)

    Article  MATH  Google Scholar 

  77. E.S.R. Gopal, Specific Heats at Low Temperature (Plenum Press, New York, 1966)

    Book  Google Scholar 

  78. S.W. Kieffer, Rev. Geophys. Space Phys. 17, 35 (1979)

    Article  ADS  Google Scholar 

  79. M. Born, T. von Karman, Phys. Z. 13, 298 (1912)

    Google Scholar 

  80. A.M. Hofmeister, H.K. Mao, Am. Mineral. 86, 622 (2001)

    Google Scholar 

  81. K.K. Kelley, S.S. Todd, R.L. Orr, E.G. King, K.R. Bonnickson, U.S. Bureau Mines Representative Investigation 4955 (1953)

  82. K. Kelly, US Bureau of Mines Bulletin 584 (U.S. Government Printing Office, Washington, DC, 1960)

  83. R.A. Robie, B.S. Hemingway, U.S. Geological Survey Bulletin 2131 (Washington, DC, 1995)

  84. M.A. Reiter, R.J.C. Tovar, Can. J. Earth Sci. 22, 1503 (1982)

    Article  Google Scholar 

  85. P.A. Giesting, A.M. Hofmeister, Phys. Rev. B 65, 144305-1 (2002)

    Article  ADS  Google Scholar 

  86. M. Roufosse, P.G. Klemens, Phys. Rev. B 7, 5379 (1973)

    Article  ADS  Google Scholar 

  87. C.L. Julian, Phys. Rev. A 137, 128 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  88. W.G. Spitzer, R.C. Miller, D.A. Kleinman, L.W. Howarth, Phys. Rev. 126, 1710 (1962)

    Article  ADS  Google Scholar 

  89. F. Wooten, Optical Properties of Solids (AP, San Diego, 1972)

    Google Scholar 

  90. D.P. Spitzer, J. Phys. Chem. Solids 31, 19 (1970)

    Article  ADS  Google Scholar 

  91. G. Leibfried, E. Schlömann, Nachr. Ges. Wiss. Goett. Math. Phys. KI. 2, 71 (1954)

    Google Scholar 

  92. I. Polmeranchuk, Russ. J. Phys. 7, 197 (1943)

    Google Scholar 

  93. A. Eucken, Allgemeine Geseteztmassig keitne für das Warmeleitvermogen Versciediner Stoffarten und Aggregatzustande. Forsch. Gebiete Ingenieur Ausgabe A, V.D.I. Forschnung 11, 6 (1940)

  94. J.H. Sass, T.H. Lachenbruch, T.H. Moses, P. Morgan, J. Geophys. Res. 97, 5017 (1992)

    Article  ADS  Google Scholar 

  95. D. Pribnow, C.F. Williams, J.H. Sass, R. Keating, Geophys. Res. Lett. 23, 391 (1996)

    Article  ADS  Google Scholar 

  96. F.L. Madarasz, P.G. Klemens, Int. J. Thermophys. 8, 257 (1987)

    Article  ADS  Google Scholar 

  97. D.W. Lee, W.D. Kingery, J. Am. Ceram. Soc. 43, 594 (1960)

    Article  Google Scholar 

  98. S.P. Clark, in The Earth’s Crust and Upper Mantle, Geophysical Monograph Series, vol. 13, ed. by P.J. Hart (AGU, Washington, DC, 1969), pp. 622–626

  99. G. Buntebarth, Sci. Drill. 2, 73 (1991)

    Google Scholar 

  100. G. Buntebarth, in Equilibrium and Kinetics in Contact Metamorphism: The Ballachulish Igneous Complex and Its Aureole, ed. by G. Voll, D. Pattison, J. Topel, F. Seifert (Springer, New York, 1991), p. 377

  101. P.G. Klemens, in Thermal Conductivity, ed. by R.P. Tye (AP, New York, 1969)

  102. A.R. McBirney, J. Geophys. Res. 68, 6323 (1963)

    Article  ADS  Google Scholar 

  103. E.A. Ljubimova, Geophys. J. R. Astron Soc. 1, 115 (1958)

    Article  ADS  Google Scholar 

  104. I.T. Kukkonen, J. Jokinen, U. Seipold, Surv. Geophys. 20, 33 (1999)

    Article  ADS  Google Scholar 

  105. C. Clauser, E. Huenges, in Rock Physics and Phase Relations. A Handbook of Physical Constants, Rock Physics and Phase Relations, vol. 3, ed. by T.J. Ahrens (AGU, Washington, DC, 1995), pp. 105–126

  106. G. Zoth, R. Hänel, in Handbook of Terrestrial Heat-Flow Density Determination, ed. by R. Haenel, L. Rybach, L. Stegena (Kluwer AP, Dordrecht, 1988)

  107. A. Eucken, Forsch. Gehiete Ingenieurue B3, Forschnung 353, 16 (1932)

Download references

Acknowledgments

One of us (I.M.A.) thanks the Applied Chemicals and Materials Division at the National Institute of Standards and Technology (NIST) for the opportunity to work as a Guest Researcher at NIST during the course of this research.

Author information

Author notes

  1. I. M. Abdulagatov

    Present address: Applied Chemicals and Materials Division, National Institute of Standards and Technology, 325 Broadway, Boulder, CO, 80305-3337, USA

Authors and Affiliations

  1. Institute of Physics of the Dagestan Scientific Center of the Russian Academy of Sciences, M. Yaragskogo Str. 94, 367005, Makhachkala, Dagestan, Russia

    I. M. Abdulagatov, Z. Z. Abdulagatova, S. N. Kallaev & A. G. Bakmaev

  2. Deep Earth Energy Research Lab, Department of Civil Engineering, Monash University, Melbourne, VIC, 3800, Australia

    P. G. Ranjith

Authors
  1. I. M. Abdulagatov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Z. Z. Abdulagatova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. N. Kallaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. G. Bakmaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. P. G. Ranjith
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. M. Abdulagatov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abdulagatov, I.M., Abdulagatova, Z.Z., Kallaev, S.N. et al. Thermal-Diffusivity and Heat-Capacity Measurements of Sandstone at High Temperatures Using Laser Flash and DSC Methods. Int J Thermophys 36, 658–691 (2015). https://doi.org/10.1007/s10765-014-1829-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10765-014-1829-4

Keywords

Search

Navigation