Temperature effect on thermal-diffusivity and heat-capacity and derived values of thermal-conductivity of reservoir rock materials

  • Z. Z. Abdulagatova
  • S. N. Kallaev
  • Z. M. Omarov
  • A. G. Bakmaev
  • B. A. Grigor’ev
  • I. M. AbdulagatovEmail author
Original Article
Part of the following topical collections:
  1. Sustainable development and utilization of geothermal systems


A laser flash method (micro-flash apparatus LFA 457) and differential scanning calorimeter (DSC 204 F1) were employed to study of the temperature effect on the thermophysical properties (thermal diffusivity \(a\), heat capacity \(C_{\text{P}}\) and thermal conductivity \(\lambda\)) of the natural reservoir rock sample. A relationship between the thermophysical properties behavior and the physical–chemical processes (thermal decomposition of pore heavy oil and volatilization of pore fluids) occurring in the rock’s pore fluids during heating in distinct temperature ranges was established. The measurements of the thermal-diffusivity have been made over the temperature range from 295 to 774 K. The isobaric heat capacities (CP) of the same sample were measured in the temperature range from 308 to 768 K. Uncertainties of the measurements are 3% and 1% for \(a\) and \(C_{\text{P}}\), respectively. The significant effect of thermal decomposition on the measured values of heat-capacity of reservoir rock sample at high temperatures (above 680 K) was experimentally found. We experimentally observed temperature anomaly of the heat capacity of rock sample in distinct temperature ranges, around 380 K (low-temperature range) and 680 K (high-temperature range).We attribute these anomalies to the dehydration (evolution of the volatile matter, VM, devolatilization) and aromatization of the carbon (thermal decomposition), which are known to occur under heat treatment. This leads to unusual increasing the heat capacity at high temperatures. Measured values of thermal diffusivity (\(a\)) and heat capacity (\(C_{\text{P}}\)) together with density data (\(\rho = { 2210}\;{\text{kg}}\;{\text{m}}^{ - 3}\)) were used to calculate the derived key properties, thermal conductivities (\(\lambda\)) of the rock sample, using very well-known relation, \(\lambda = a\rho C_{\text{P}}\).


Density DSC Heat capacity Laser flash method Geothermal reservoir rock Thermal diffusivity Thermal conductivity 



The study has been support by Russian Scientific Foundation (Project # 19-08-00353).


  1. Abdulagatov IM, Emirov SN, Gairbekov KhA, Magomaeva MA, Sya Askerov, Ramazanova EN (2002) The effective thermal conductivity of fluid saturated porous mica-ceramics at high temperatures and high pressures. Ind Eng Chem Res 41:3586–3593CrossRefGoogle Scholar
  2. Abdulagatov IM, Emirov SN, Abdulagatova ZZ, Askerov SYA (2006) Effect of pressure and temperature on the thermal conductivity of rocks. J Chem Eng Data 51:22–33CrossRefGoogle Scholar
  3. Abdulagatov IM, Abdulagatova ZZ, Kallaev SM, Bakmaev AG, Ranjith PG (2015) Thermal-diffusivity and heat-capacity measurements of sandstone at high temperatures using Laser-Flash and DSC methods. Int J Thermophys 36:658–691CrossRefGoogle Scholar
  4. Abdulagatov IM,Abdulagatova ZZ, Kallaev SN, Omarov ZM, Ranjith PG (2016a) Heat-capacity measurements of sandstone at high temperatures. In: Ranjith PG, Zhao J (eds) Proceedings of international conference on geomechanics, geo-energy and geo-resources. Australia, Melbourne, September 28–29, IC3G 2016, pp 493–499Google Scholar
  5. Abdulagatov IM, Abdulagatova ZZ, Kallaev SN, Magomedov M-RM, Abdullaev KhKh, Ranjith PG (2016b) Thermal expansion coefficient measurements and density of sandstone at high temperatures. In: Ranjith PG, Zhao J (eds) Proceedings of international conference on geomechanics, geo-energy and geo-resources. Australia, Melbourne, September 28–29, IC3G 2016, pp 500–506Google Scholar
  6. Abdulagatov IM, Abdulagatova ZZ, Kallaev SN, Omarov ZM, Bakmaev AG, Ranjith PG (2017) Thermal-diffusivity and heat capacity of black coal at high temperatures. In: Proceedings of V international conference on renewal energy: problems and prosperities, 23–26 October 2017, Makhachkala, Geothermal Research Inst Rus Acad Sci, Dagestan, pp 34–87Google Scholar
  7. Abdulagatov IM, Abdulagatova ZZ, Kallaev SN, Omarov ZM (2019) Heat-capacity measurements of sandstone at high temperatures. Geomech Geophys Geo-Energy Geo-Resour 5:65–85CrossRefGoogle Scholar
  8. Abdulagatova ZZ, Abdulagatov IM, Emirov SN (2009) Effect of temperature and pressure on the thermal conductivity of sandstone. Int J Rock Mech Min Sci 46:1055–1071CrossRefGoogle Scholar
  9. Abdulagatova ZZ, Abdulagatov IM, Emirov SN (2010) Effect of pressure, temperature, and oil-saturation on the thermal conductivity of sandstone up to 250 Mpa and 520 K. J Pet Sci Eng 73:141–155CrossRefGoogle Scholar
  10. Alishaev MG, Abdulagatov IM, Abdulagatova ZZ (2012) Effective thermal conductivity of fluid-saturated rocks. Experiment and modeling. Eng Geol 135–136:24–39CrossRefGoogle Scholar
  11. Barry-Macaulay D, Bouazza A, Singh RM, Wang B, Ranjith PG (2013) Thermal conductivity of soils and rocks from the Melbourne (Australia) region. Eng Geol 164:131–138CrossRefGoogle Scholar
  12. Berman RG, Brown TH (1984) A thermodynamic model for multicomponent melts, with application to the system CaO–Al2O3–SiO2. Geochim Cosmochim Acta 45:661–678CrossRefGoogle Scholar
  13. Berman RG, Brown TH (1985) Heat capacity of minerals in the system Na2O–K2O–CaOMgO–FeO–Fe2O2–Al2O3–SiO2–TiO2–H2O–CO2: representation, estimation, and high temperature extrapolation. Contrib Miner Petrol 89:168–183CrossRefGoogle Scholar
  14. Blumm J, Opfermann J (2002) Improvement of the mathematical modeling of flash measurements. High Temp-High Press 34:515–521CrossRefGoogle Scholar
  15. Born M, von Karman T (1912) On fluctuations in spatial grids. Phys Z 13:297–309zbMATHGoogle Scholar
  16. Bozlar M, He D, Bai J, Chalopin Y, Mingo N, Volz S (2010) Carbon nanotube microarchitectures for enhanced thermal conduction at ultralow mass fraction in polymer composites. Adv Mater 22:1654–1658CrossRefGoogle Scholar
  17. Branlund JM, Hofmeister AM (2007) Thermal diffusivity of quartz to 1000 °C: effects of impurities and the a-b phase transition. Phys Chem Miner 34:581–595CrossRefGoogle Scholar
  18. Branlund JM, Hofmeister AM (2008) Factors affecting heat transfer in SiO2 solids. Am Mineral 93:1620–1629CrossRefGoogle Scholar
  19. Buttner R, Zimanowski B, Blumm J, Hagemann L (1998) Thermal conductivity of a volcanic rock material (olivine-melilitite) in the temperature range between 288 and 1470 K. J Volcanol Geotherm Res 80:293–302CrossRefGoogle Scholar
  20. Cape JA, Lehman GW (1963) Temperature and finite pulse-time effects in the flash method for measuring thermal diffusivity. J Appl Phys 34:1909–1913CrossRefGoogle Scholar
  21. Chai M, Brown JM, Slutsy LJ (1996) Thermal diffusivity of mantle minerals. Phys Chem Miner 23:470–475CrossRefGoogle Scholar
  22. Cowan RD (1963) Pulse method of measuring thermal diffusivity at high temperatures. Appl Phys 34:926–927CrossRefGoogle Scholar
  23. Debye P (1912) Zur Theorie der spezifischen Wärmen. Ann Phys 39:789–939zbMATHCrossRefGoogle Scholar
  24. Degiovanni A, Andre S, Maillet D (1969) Thermal characterization of anisotropic composite. In: Tong TW (ed) Thermal conductivity 22, vol 2. Academic Press, London, Chap 5, pp 253–275Google Scholar
  25. Degiovanni A, Andre S, Maillet D (1994) Phonic conductivity measurement of a semi-transparent material. In: Tong TW (ed) Thermal conductivity 22. pp 623–633Google Scholar
  26. Deng J, LiQW Xiao Y, Shu CM (2017) Experimental study of the thermal properties of coal during pyrolysis, oxidation, and re-oxidation. Appl Therm Eng 110:1137–1152CrossRefGoogle Scholar
  27. Eckert ER, Faghri M (1980) A general analysis of moisture migration caused by temperature differences in an unsaturated porous medium. Int. J. Heat Mass Transf 23:1613–1623zbMATHCrossRefGoogle Scholar
  28. Einstein A (1907) Die Plancsche Theorie der Strahlung und die Theorie der spezifischen Wärme. Ann Phys 22:180–190zbMATHCrossRefGoogle Scholar
  29. Fei Y, Saxena SK (1987) An equation for the heat capacity of solids. Geochim Cosmochim Acta 51:251–254CrossRefGoogle Scholar
  30. Feng Z, Zhao Y, Zhou A, Zhang N (2012) Development program of hot dry rock geothermal resource in the Yangbajing Basin of China. Renew Energy 39(1):490–495CrossRefGoogle Scholar
  31. Fuchs S, Förster A (2010) Rock thermal conductivity of Mesozoic geothermal aquifers in the Northeast German Basin. Chemie der Erde Geochem 70:13–22CrossRefGoogle Scholar
  32. Gallagher K, Ramsdale M, Lonergan L, Morrow D (1997) The role of thermal conductivity measurements in modeling thermal histories in sedimentary basins. Mar Pet Geol 14:201–214CrossRefGoogle Scholar
  33. Geisting PA, Hofmeister AM (2002) Thermal conductivity of disordered garnets from infrared spectroscopy. Phys Rev B 65(14):144305-1–144305-16Google Scholar
  34. Geisting PA, Hofmeister AM, Wopenka B, Gwanmesia GD, Jolliff BL (2004) Thermal conductivity and thermodynamics of majoritic garnets: implications for the transition zone. Earth Planet Sci Lett 218:45–56CrossRefGoogle Scholar
  35. Gopal ESR (1966) Specific heats at low temperature. Plenum Press, New YorkCrossRefGoogle Scholar
  36. Hadgu T, Lum CC, Bean JE (2007) Determination of heat capacity of Yucca Mountain stratigraphic layers. Int J Rock Mech Min Sci 44:1022–1034CrossRefGoogle Scholar
  37. Hartmann A, Rath V, Clauser C (2005) Thermal conductivity from core and well log data. Int J Rock Mech Min Sci 42:1042–1055CrossRefGoogle Scholar
  38. Hemingway BS, Robie RA (1990) Heat capacities and thermodynamic properties of annite (aluminous iron biotite). Am Mineralogist 75:183–187Google Scholar
  39. Herrin JM, Deming D (1996) Thermal conductivity of US coals. J Geophys Res 101:381–386CrossRefGoogle Scholar
  40. Hirono T, Hamada Y (2010) Specific heat capacity and thermal diffusivity and their temperature dependences in a rock sample from adjacent to the Taiwan Chelungpu fault. J Geohys Res 115(B5):B05313CrossRefGoogle Scholar
  41. Hofmann R, Hahn O, Raether F, Mehling H, Fricke J (1997) Determination of thermal diffusivity in diathermic materialsby the laser-flash technique. High Temp-High Press 29:703–710CrossRefGoogle Scholar
  42. Hofmeister AM (1999) Mantle values of thermal conductivity and the geotherm from phonon lifetimes. Science 283:1699–1706CrossRefGoogle Scholar
  43. Hofmeister AM (2001) Thermal conductivity of spinels and olivines from vibrational spectroscopy at ambient conditions. Am Mineral 86:1188–1208CrossRefGoogle Scholar
  44. Hofmeister AM (2004a) In: King P, Ramsey M, Swayze G (eds) Infrared spectroscopy in geochemistry, exploration geochemistry, and remote sensing. Mineralogical Association of Canada, Ottawa, Ontario, pp 135–154Google Scholar
  45. Hofmeister AM (2004b) Physical properties of calcium aluminates from vibrational spectroscopy. Geochim Cosmochim Acta 68:4721–4726CrossRefGoogle Scholar
  46. Hofmeister AM (2006) Thermal diffusivity of garnets at high temperatures. Phys Chem Miner 33:45–62CrossRefGoogle Scholar
  47. Hofmeister AM (2007) Thermal conductivity of the Earth’s deepest mantle. In: Yuen DA, Maruyama S, Kavato SI, Windley BF (eds) Superplumes: beyond plate tectonics. Springer, Dordrecht, pp 269–292Google Scholar
  48. Hofmeister AM (2008) Inference of high thermal transport in the lower mantle from laser-flash experiments and the damped harmonic oscillator model. Phys Earth Planet Interiors 170:201–206CrossRefGoogle Scholar
  49. Hofmeister AM, Mao HK (2001) Evaluation of shear moduli and other properties of silicates with the spinel structure from IR spectroscopy. Am Mineral 86:622–639CrossRefGoogle Scholar
  50. Hofmeister AM, Pertermann M (2008) Thermal diffusivity of clinopyroxenes at elevated temperatures. Eur J Miner 20:537–549CrossRefGoogle Scholar
  51. Hofmeister AM, Yuen DA (2007) Critical phenomena in thermal conductivity: implications for lower mantle dynamics. J Geodyn 44:186–199CrossRefGoogle Scholar
  52. Hofmeister AM, Branlund JM, Pertermann M (2007) Treatise in geophysics, vol 2. In: Schubert G (ed in chief) Mineral physics (GD Price, ed), Elsevier, Dordrecht, pp 543–578Google Scholar
  53. Hofmeister AM, Whittington AG, Pertermann M (2009) Transport properties of high albite crystals and near-endmember feldspar and pyroxene glasses and melts to high temperatures. Contrib Miner Petrol 158:381–400CrossRefGoogle Scholar
  54. Holt JB (1975) Thermal diffusivity of olivine. Earth Planet Sci 27:404–408CrossRefGoogle Scholar
  55. Jha MK, Verma AK, Maheshwar S, Chauhan A (2016) Study of temperature effect on thermal conductivity of Jhiri shale from Upper Vindhyan, India. Bull Eng Geol Environ 75:1657–1668CrossRefGoogle Scholar
  56. Kallaev SN, Gadzhiev GG, Kamilov IK, Omarov ZM, Sadykov SA (2004) Thermal conductivity and thermal expansion coefficient anomaly of segno-ceramics on the bases of PZT. Izv Russ Acad Sci ser Phys 68:981–983Google Scholar
  57. Kallaev SN, Gadzhiev GG, Kamilov IK, Omarov ZM, Sadykov SA, Raznichenko LA (2006) Thermohysical properties of segno-ceramics on the bases of PZT. Russ Solid State Phys 6:1099–1101Google Scholar
  58. Kanamori H, Fujii N, Mizutani H (1968) Thermal diffusivity measurement of rock-forming minerals from 300 to 1100 K. J Geophys Res 73:595–606CrossRefGoogle Scholar
  59. Kappelmeyer O, Haenel R (1974) Geothermic with special reference to application. Gebrueder Borntraeger, Berlin, p 238Google Scholar
  60. Kieffer SW (1979) Thermodynamics and lattice vibrations of minerals, 3, Lattice dynamics and an approximation for minerals with application to simple substances and framework silicates. Rev Geophys Space Phys 17:35–59CrossRefGoogle Scholar
  61. Krupka MK, Robie RA, Hemingway BS (1979) High-temperature heat capacities of corundum, pericllase, anortite, CaAl2Si2O8 glas, muscovite, pyrophyllite, KAlSi3O8 glas, grossular, and NaAlSi3O8 glass. Am Mineral 64:86–101Google Scholar
  62. Luchenbruch AH, Sass JH (1977) Heat flows in the United State. In: Heacock JG (ed) the earth’s crust. AGU, Washington, pp 626–675Google Scholar
  63. Mehling H, Hautzinger G, Nilsson O, Fricke J, Hofmann R, Hahn O (1998) Thermal diffusivity of semitransparent materials determined by the laser-flash method applying a new analytical model. Int J Thermophys 19:941–949CrossRefGoogle Scholar
  64. Miao SQ, Li HP, Chen G (2014) Temperature dependence of thermal diffusivity, specific heat capacity, and thermal conductivity for several types of rocks. J Therm Anal Calorim 115:1057–1063CrossRefGoogle Scholar
  65. Min S, Blumm J, Lindemann A (2007) A new laser flash system for measurement of the thermophysical properties. Thermochim Acta 455:46–49CrossRefGoogle Scholar
  66. Mostafa MS, Afify N, Gaber A, Abu Zaid EF (2004) Investigation of thermal properties of some basalt samples, Egypt. J Therm Anal Calorim 75:179–188CrossRefGoogle Scholar
  67. Mottaghy D, Vosteen HD, Schellschmidt R (2008) Temperature dependence of the relationship of thermal diffusivity versus thermal conductivity for crystalline rocks. Int J Earth Sci (GeolRundsch) 97:435–442CrossRefGoogle Scholar
  68. Nabelek PI, Hofmeister A, Whittington AG (2010a) The influence of temperature-dependent thermal diffusivity on the conductive cooling rate of plutons and temperature –time paths in contact aureoles. Earth Plan Sci Lett 317–318:157–164Google Scholar
  69. Nabelek PI, Whittington AG, Hofmeister A (2010b) Strain heating as a mechanism for partial melting and ultrahigh temperature metamorphism in convergent orogens: implications of temperature –dependent thermal diffusivity and rheology. J Geophys Res 115:B12417-17CrossRefGoogle Scholar
  70. Osako M, Ito E (1998) Simultaneous thermal diffusivity and thermal conductivity measurements of mantle materials up to 6 GPa. Rev High Press Sci Technol 7:110–112CrossRefGoogle Scholar
  71. Osako M, Ito E, Yoneda A (2004) Simultaneous measurements of thermal conductivity and thermal diffusivity for garnet and olivine under high pressure. Phys Earth Planet Inter 143–144:311–320CrossRefGoogle Scholar
  72. Osako M, Yoneda A, Ito E (2010) Thermal diffusivity, thermal conductivity and heat capacity of serpentine (antigorite) under high pressure. Phys Earth Planet Inter 183:229–233CrossRefGoogle Scholar
  73. Parker JW, Jenkins JR (1961) WADD technical report 65-91, Directorate of Materials and ProcessesGoogle Scholar
  74. Parker JW, Jenkins JR, Butler CP, Abbott GL (1961) Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity. J Appl Phys 32:1679–1684CrossRefGoogle Scholar
  75. Pertermann M, Hofmeister AM (2006) Thermal diffusivity of olivine-group minerals at high temperature. Am Miner 91:1747–1760CrossRefGoogle Scholar
  76. Pertermann M, Whittington AG, Hofmeister AM, Spera FJ, Zayak J (2008) Transport properties of low-sanidine single-crystals, glasses and melts at high temperatures. Contrib Miner Petrol 155:689–702CrossRefGoogle Scholar
  77. Popov YA (1997) In: Giot M, Mayinger F, Celeta GP (eds) Experimental heat transfer, fluid mechanics and thermodynamics. Proceedings of 4th world congress on experimental heat transfer, fluid mechanics and thermodynamics, vol 1. Belgium, Brussels, pp 109–116Google Scholar
  78. Popov YuA, Pribnow D, Sass JH, Williams CF, Burkhardt H (1999) Characterization of rock thermal conductivity by high-resolution optical scanning. Geothermics 28:253–276CrossRefGoogle Scholar
  79. Ramazanova AE, Abdulagatov IM, Ranjith PG (2018) Temperature effect on thermal conductivity of black coal. J Chem Eng Data 63:1534–1545CrossRefGoogle Scholar
  80. Ray L, Forster HJ, Schilling F, Forster A (2006) Thermal diffusivity of felsic to mafic granulites at elevated temperatures. Earth Planet Sci Lett 251:241–253CrossRefGoogle Scholar
  81. Reiter MA, Tovar RJC (1982) Estimates of terrestrial heat flow in Northern Chihuahua, Mexico. Can J Earth Sci 22:1503–1517CrossRefGoogle Scholar
  82. Richet P (2001) The physical basics of thermodynamics: with applications to chemistry. Kluwer Academic/Plenum Publishers, New YorkCrossRefGoogle Scholar
  83. Richet P, Fiquet G (1991) High-temperature heat capacity and premelting of minerals in the system MgO–CaO–Al2O3–SiO2. J Geophys Res 96:445–456CrossRefGoogle Scholar
  84. Robie RA, Hemingway BS (1995) Thermodynamic properties of minerals and related substances at 298.15 K and 1 Bar (105 Pascals) pressure and higher temperatures. US Geological Survey Bulletin 2131, Washington, DCGoogle Scholar
  85. Santa GD, Peron F, Galgaro A, Cultrera M, Bertermann D, Mueller J, Bernardi A (2017) Laboratory measurements of gravel thermal conductivity: an update methodological approach. Energy Proc 125:671–677CrossRefGoogle Scholar
  86. Sass JH, Lachenbruch AH, Munroe R, Greene G, Moses T (1971) Heat flow in the western United States. J Geophys Res 76:6376–6413CrossRefGoogle Scholar
  87. Saxena SK (1996) Earth mineralogical model: Gibbs free energy minimization computation in the system MgO-FeO-SiO2. Geochim Cosmochim Acta 60:2379–2395CrossRefGoogle Scholar
  88. Schatz JF, Simmons G (1972) Method of simultaneous measurement of radiative and lattice thermal conductivity. J Appl Phys 43:2588–2594CrossRefGoogle Scholar
  89. Schoderböck P, Klocker H, SiglL S, Seeber G (2009) Evaluation of the thermal diffusivity of thin specimens from laser flash data. Int J Thermophys 30:599–607CrossRefGoogle Scholar
  90. Seipold U (2001) Scientific Technical Report STR01/13. GFZ, PotsdamGoogle Scholar
  91. Seipold U (2002) Investigation of the thermal transport properties of amphibolites. I. Pressure dependence. High Temp High Press 34:299–306CrossRefGoogle Scholar
  92. Skauge A, Fuller N, Hepler LG (1983) Specific heats of clay minerals: sodium and calcium kaolinites, sodium and calcium montmorillonites, illite, and attapulgite. Thermochim Acta 61:139–145CrossRefGoogle Scholar
  93. Strack KM, Ibrahim AW, Keller GV, Stoyer CH (1982) A method for the determination of the thermal conductivity of sandstones using a variable state approach. Geophys Prospect 30:454–469CrossRefGoogle Scholar
  94. Sudenko YS, Barskii YP, Pavlov LP (1976) Thermophysical properties of substances and materials. In: Sychev VV (ed), GSSSD, vol 10, Moscow, pp 246–259Google Scholar
  95. Surma F, Geraud Y (2003) Porosity and thermal conductivity of the soultz-sous-forêts granite. Pure Appl Geophys 160:1125–1136CrossRefGoogle Scholar
  96. Tommasi A, Gilbert B, Seipold U, Mainprice D (2001) Anisotropy of thermal diffusivity in the upper mantle. Nature 411:783–786CrossRefGoogle Scholar
  97. Vosteen HD, Schellschmidt R (2003) Influence of temperature on thermal conductivity, thermal capacity and thermal diffusivity for different types of rock. Phys Chem Earth 28:499–509CrossRefGoogle Scholar
  98. Vozár V, Hohenauer W (2005) Uncertainty of thermal diffusivity measurements using the laser flash method. Int J Thermophys 26:1899–1915zbMATHCrossRefGoogle Scholar
  99. Waples DW, Waples JS (2004) A review and evaluation of specific heat capacity of rocks, minerals, and subsurface fluids. Part 1: minerals and nonporous rocks. Nat Resour Res 13:97–122CrossRefGoogle Scholar
  100. Wei G, Zhang X, Yu F, Chen K (2006) Thermal diffusivity measurements on insulation materials with the Laser Flash method. Int J Thermophys 27:235–243CrossRefGoogle Scholar
  101. Wen H, Lu JH, Xiao Y, Deng J (2015) Temperature dependence of thermal conductivity, diffusivity and specific heat capacity for coal and rocks from coalfield. Thermochim Acta 619:41–47CrossRefGoogle Scholar
  102. Whittington AG, Hofmeister AM, Nabelek PI (2009) Temperature dependent thermal diffusivity of Earth’s crust and implications for magmatism. Nature 458:319–321CrossRefGoogle Scholar
  103. Williams CF, Sass JH (1994) The role of temperature-dependent thermal conductivity in heat transfer at the Geysers. In: Proceedings of international association of seismology and physics of the earth’s interior, 27th General Assembly, Wellington, New ZealandGoogle Scholar
  104. Yamano MS, Uyeda S, Aoki Y, Shipley TH (1982) Estimates of heat flow derived from gas hydrates. Geology 10:339–343CrossRefGoogle Scholar
  105. Yong W, Dachs E, Withers AC (2006) Heat capacity and phase equilibria of hollandite polymorph of KalSi3O8. Phys Chem Miner 33:167–177CrossRefGoogle Scholar
  106. Yong W, Dachs E, Withers AC, Essene EJ (2008) Heat capacity and phase equilibria of wadeite-type of K2Si4O9. Contrib Miner Petrol 155:137–146CrossRefGoogle Scholar
  107. Yong W, Dachs E, Benisek A, Withers AC, Secco RA (2012) Heat capacity, entropy, and phase equilibria of dmitryivanovite. Phys Chem Miner 39:259–267CrossRefGoogle Scholar
  108. Yu X, Hofmeister AM (2011) Thermal diffusivity of alkali and silver halides. J Appl Phys 109:033516-1–033516-20Google Scholar
  109. Zaug J, Abransom E, Brown JM, Slutsky LJ (1992) Elastic constants, equations of state and thermal diffusivity at high pressure. In: Syono Y, Manghnani MH (eds) High-pressure. Terra/AGU, Washington, pp 157–166CrossRefGoogle Scholar
  110. Zawilski BM, Iv RTL, Tritt TM (2001) Description of the parallel thermal conductance technique for the measurements of the thermal conductivity of small diameter samples. Rec Sci Instrum 72:1770–1774CrossRefGoogle Scholar
  111. Zhao D, Qian X, Gu X, Jajja SA, Yang R (2016) Measurement techniques for thermal conductivity and interfacial thermal conductance of bulk and thin film materials. J Electron Packag 138:040802CrossRefGoogle Scholar

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Authors and Affiliations

  • Z. Z. Abdulagatova
    • 2
    • 3
  • S. N. Kallaev
    • 3
  • Z. M. Omarov
    • 3
  • A. G. Bakmaev
    • 3
  • B. A. Grigor’ev
    • 4
  • I. M. Abdulagatov
    • 1
    • 2
    Email author
  1. 1.Geothermal Research Institute of the Dagestan Scientific Center of the Russian Academy of SciencesMakhachkalaRussian Federation
  2. 2.Dagestan State UniversityMakhachkalaRussian Federation
  3. 3.Institute of Physics of the Dagestan Scientific Center of the Russian Academy of SciencesMakhachkalaRussian Federation
  4. 4.Gubkin Russian State University of Oil and GasNational Research UniversityMoscowRussian Federation

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