Abstract
We discuss the baric and temperature dependences of the effective thermal conductivity of rocks (including sandstones) naturally occurring in the earth’s crust. We present the results of our experimental studies of the effective thermal conductivity of natural sandstone under hydrostatic pressure (up to 400 MPa) in the temperature range (273–523 K), performed by the absolute steady-state method of parallel plates with an uncertainty of 3–4% and summarize numerous our previous results as well as results by the authors. We have analyzed the general regularities of the thermal conductivity temperature dependence for crystalline and amorphous dielectrics and rocks and compared them with the data of other authors. The temperature dependence of thermal conductivity is derived to be described by the power law, where the degree ranges from − 0.5 to + 0.5 and it can be used as an indicator of orderliness. The experimental data show that the pressure affects the nature of the temperature dependence. The heat transfer in dielectrics and rocks is revealed to occur due to increment of the maximum frequency of atomic acoustic vibrations and the associated Debye temperature. Based on the Landau and Lifshitz theories, we also discuss the possibility of reversible second-order phase transitions. In brittle and blocky crystalline solids this effect is more pronounced because they acquire a new quality—plasticity, whereas in plastic dielectrics and rocks only insignificant quantitative change is observed. The rocks without irreversible structural changes restore the original volume when decreasing the pressure. The results contribute to theoretical models describing heat transfer in complex disordered structures which is important for solving a number of tasks in Earth sciences.
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Abbreviations
- λ :
-
Effective thermal conductivity
- λ m :
-
Thermal conductivity of transmitting pressure medium
- P :
-
Pressure
- T :
-
Temperature
- \(\vartheta\) :
-
Frequency
- \(\vartheta_{\max }\) :
-
Acoustic oscillation frequency
- \(\vartheta_{{{\text{opt}}}}\) :
-
Optical oscillation frequency
- \(\Theta\) :
-
Debye temperature
- h :
-
Planck constant
- K :
-
Boltzmann constant
- \(\gamma\) :
-
Grüneisen parameter
- n :
-
Exponent
- k :
-
Thermal diffusivity
- C p :
-
Isobaric heat capacity
- \(\rho\) :
-
Density
- \(\chi\) :
-
Isothermal modulus of compressibility
- a :
-
Interatomic distances
- q :
-
Heat flux density
- Q :
-
Quantity of heat
- Q los :
-
Thermal losses from the lateral surface of rock samples
- D :
-
Internal diameter of the high pressure chamber
- d :
-
Diameter of rock samples
- υ :
-
Velocity of ultrasonic waves
- V :
-
Volume
- M :
-
Molecular weight
- l :
-
Distance
- S :
-
Area
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Acknowledgements
This work was partially supported by the RFBR grants 18-08-00059A and 20-08-00319A.
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Emirov, S.N., Aliverdiev, A.A., Zarichnyak, Y.P. et al. Studies of the Effective Thermal Conductivity of Sandstone Under High Pressure and Temperature. Rock Mech Rock Eng 54, 3165–3174 (2021). https://doi.org/10.1007/s00603-020-02353-3
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DOI: https://doi.org/10.1007/s00603-020-02353-3