Lowest Required Surface Temperature for Thermal Spallation in Granite and Sandstone Specimens: Experiments and Simulations

  • Xiaodong Hu
  • Xianzhi SongEmail author
  • Yu Liu
  • Gensheng Li
  • Zhonghou Shen
  • Zehao Lyu
  • QingLing Liu
Original Paper


Thermal spallation may be economically advantageous for the drilling of deep wells and is of strong interest for the development of oil, gas and geothermal energy. The lowest required surface temperature (LRST) represents the minimal surface temperature that can induce the spallation of rock. A deeper understanding of the LRST can be used to determine when thermal spallation can be successfully initiated. However, to the best of our knowledge, comparisons of LRST in sandstone and granite have not been performed. Based on experiments and simulations, this study investigated the LRST of one type of granite and one type of sandstone in thermal spallation. First, we conducted thermal spallation experiments using rock specimens and measured the LRST by an infrared thermometer. Then, the heat flux was evaluated and compared between the sandstone and granite specimens. Meanwhile, a three-dimensional numerical model was built to simulate the heat transfer and stress distribution in the granite and sandstone specimens. The temperature and von Mises stress between the granite and sandstone specimens were compared, and then the breakage-probability factors were investigated to compare the experimental results and simulation results. This study clarifies the differences in LRST between one type of granite and one type of sandstone.


Thermal spallation Granite Sandstone Surface temperature Infrared measurements 

List of Symbols


Lowest required surface temperature


Slope of “best-fit” line (K/s1/2)


Heat capacity (J/(kg•K))


Breakage-probability factor (dimensionless)


Young’s modulus (Pa)


Body force (Pa)


Shear modulus (Pa)


Heat convective coefficient [(W/(m2 K)]


Thermal conductivity coefficient [W/(m K)]


Rock expansion index (Pa)


Heat flux on the rock surface (W/m2)


Convective heat transfer coefficient (W/m2)


Temperature in the rock (K)


Temperature on the boundary (K)


Temperature of ambient temperature (K)


Displacement (m)


Rock thermal diffusivity (m2/s)


Thermal expansion coefficient (/K)


Poisson’s ratio (–)

\({\varepsilon _{ij}}\)

Strain tensor (dimensionless)


Rock density (kg/m3)

\({\sigma _{ij,j}}\)

Stress tensor (Pa)

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

Yield strength (Pa)

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

Von Mises stress (Pa)

\({\sigma _1}\)

First principal stress (Pa)

\({\sigma _{\text{2}}}\)

Second principal stress (Pa)

\({\sigma _{\text{3}}}\)

Third principal stress (Pa)



The authors would like to acknowledge the financial support from the National Natural Science Foundation of China (no. U1562212 and no. 51504272) and National Key Research and Development Program of China (2016YFE0124600).


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Copyright information

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

Authors and Affiliations

  • Xiaodong Hu
    • 1
    • 2
  • Xianzhi Song
    • 1
    • 2
    Email author
  • Yu Liu
    • 1
    • 2
  • Gensheng Li
    • 1
    • 2
  • Zhonghou Shen
    • 1
    • 2
  • Zehao Lyu
    • 1
    • 2
  • QingLing Liu
    • 1
    • 2
  1. 1.China University of Petroleum-BeijingBeijingChina
  2. 2.State Key Laboratory of Petroleum Resource and ProspectingBeijingChina

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