Rock Mechanics and Rock Engineering

, Volume 52, Issue 1, pp 35–45 | Cite as

Heat Transfer in Sandstones at Low Temperature

  • Zhiqiang Liu
  • Linlin WangEmail author
  • Bo Zhao
  • Jingyi Leng
  • Guangqing Zhang
  • Diansen Yang
Original Paper


This paper addresses experimental and modeling investigations of heat transfer in sandstones subject to low-temperature conditions. At low temperature, pore liquid (e.g., water) would freeze; thus, heat is transferred not only in the form of specific heat but also in the form of latent heat. Moreover, the melting point is not constant; it depends on the pore size. Considering these characteristics, a governing equation of heat transfer with phase transition is established using the equivalent heat-capacity method. To calculate the equivalent heat capacity, the relation between ice content and temperature is assessed by the pore-size distribution curve. Heating tests (from 77 to 293 K) of sandstone samples in three saturation conditions (water-saturated, oil-saturated, and dry) are conducted and simulated using the model established. The results reveal that the temperature sensitivity of the heat capacity of dry sandstone is more pronounced in the low-temperature regime than in the high-temperature regime. The thermal conductivity of dry sandstone increases with temperature in the low-temperature regime. This is different with the case of the high-temperature regime at which the thermal conductivity decreases with temperature. The temperature evolution curve for the water-saturated sample features a plateau regime, that is, the temperature remains quasi-constant with time. The analysis demonstrates that the position and length of this temperature plateau are governed by the pore-size distribution.


Freezing–thawing Sandstone Convective boundary Heat capacity Thermal conductivity Pore-size distribution 

List of Symbols


Convective area

\(a,{\text{ }}b,{\text{ }}{a_j},{\text{ }}{b_j}\)

Coefficients describing the dependence of heat capacity on temperature; j can be i (ice), w (water), s (solid) or o (oil)


Biot number


Specific heat


Spreading coefficient


Thickness of pre-melting liquid film


Convection coefficient


Thermal conductivity


Latent heat


Characteristic length

m, n

Coefficients describing the dependence of thermal conductivity on temperature


Mercury pressure


Pore radius


Smallest pore-access radius invaded by ice crystals


Given radius


Correlation coefficient

Sw, Si

Molar entropy of water (w) and ice (i)






Initial temperature


Environment temperature


Temperatures of the solid surface


Melting point at atmospheric pressure



\({\bar {V}_{\text{i}}},{\text{ }}{\bar {V}_{\text{w}}}\)

Molar volume of ice (i) and water (w)


Contact angle of ice–water interface



\({\rho _{\text{i}}},{\rho _{\text{w}}},{\rho _{\text{s}}}\)

Density of ice (i), water (w) and solid (s)


Gradient operator


Volumetric fraction of ice



\({\gamma _{{\text{iw}}}},{\gamma _{{\text{si}}}},{\gamma _{{\text{sw}}}}\)

Interface stress of ice–water (iw), solid–ice (si) and solid–water (sw)


Range of intermolecular forces

\({\sigma _{{\text{Hg}}}}\)

Interfacial tension of mercury



The authors gratefully acknowledge the support of the National Natural Science Foundation of China (Grant no. 51809275) and the Science Foundation of China University of Petroleum, Beijing (2462018BJC002).


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Petroleum Resources and ProspectingChina University of PetroleumBeijingChina
  2. 2.College of Petroleum EngineeringChina University of PetroleumBeijingChina
  3. 3.State Key Laboratory of Geomechanics and Geotechnical Engineering, IRSMChinese Academy of ScienceWuhanChina

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