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Heat Transfer in Sandstones at Low Temperature

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Abstract

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.

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Abbreviations

A s :

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)

Bi:

Biot number

c :

Specific heat

D :

Spreading coefficient

e :

Thickness of pre-melting liquid film

h :

Convection coefficient

k :

Thermal conductivity

L :

Latent heat

L c :

Characteristic length

m, n :

Coefficients describing the dependence of thermal conductivity on temperature

p :

Mercury pressure

r :

Pore radius

r i :

Smallest pore-access radius invaded by ice crystals

\({r_a}\) :

Given radius

R :

Correlation coefficient

S w, S i :

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

t :

Time

T :

Temperature

T i :

Initial temperature

T ∞ :

Environment temperature

T s :

Temperatures of the solid surface

T m :

Melting point at atmospheric pressure

V :

Volume

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

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

α :

Contact angle of ice–water interface

ρ :

Density

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

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

\(\nabla\) :

Gradient operator

θ i :

Volumetric fraction of ice

\(\phi\) :

Porosity

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

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

\(\xi\) :

Range of intermolecular forces

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

Interfacial tension of mercury

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Acknowledgements

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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Authors and Affiliations

  1. State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing, China

    Zhiqiang Liu, Linlin Wang, Bo Zhao, Jingyi Leng & Guangqing Zhang

  2. College of Petroleum Engineering, China University of Petroleum, Beijing, China

    Zhiqiang Liu, Linlin Wang, Bo Zhao, Jingyi Leng & Guangqing Zhang

  3. State Key Laboratory of Geomechanics and Geotechnical Engineering, IRSM, Chinese Academy of Science, Wuhan, China

    Diansen Yang

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  1. Zhiqiang Liu
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Correspondence to Linlin Wang.

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Liu, Z., Wang, L., Zhao, B. et al. Heat Transfer in Sandstones at Low Temperature. Rock Mech Rock Eng 52, 35–45 (2019). https://doi.org/10.1007/s00603-018-1595-x

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