Abstract
Mathematical models and numerical approaches are applied to the thermal system coupling by the crude oil, pipeline and soil during the reverse pipelining of pipeline. On the basis of the above, five simulation cases are carried out to investigate the transient thermal characteristics of the thermal system. It can be concluded that the time evolution of crude oil temperature can be divided into three stages; among them, thermal performance in each stage is different due to the different dominating mechanisms. Based on the variation of the temperature profile along the pipeline, the crude oil pipeline can be divided into three regions. Among them, the temperature profile characteristics in each region are different due to the different dominating mechanisms. Further, the detailed evolution characteristics of thermal performance along the pipeline during the reverse pipelining are presented. So as to investigate the heat transfer mechanism of the thermal process, the temperature profile of soil around the pipeline is also presented. It can be concluded that the temperature of soil around the pipeline has the similar thermal characteristics as crude oil except the thermal hysteresis phenomena are presented. In addition, there exist two thermal influence regions around the pipeline during the reverse pipelining. One region is influenced by the reverse pipelining process. And another region is much larger and influenced by the crude oil pipeline. Furthermore, the effects of the outlet temperature and flow rate as well as the atmospheric temperature and pipeline diameter on the thermal characteristics of the pipeline system are also analyzed.
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Abbreviations
- \(A\) :
-
Sectional area of pipeline (m2)
- \(C_{\text{o}}\) :
-
Heat capacity of crude oil (J kg−1 °C−1)
- \(C_{\text{p}}\) :
-
Heat capacity of pipeline wall (J kg−1 °C−1)
- \(C_{\text{s}}\) :
-
Heat capacity of soil (J (kg−1 °C−1)
- \(C_{\text{i}}\) :
-
Heat capacity of insulating layer (J kg−1 °C−1)
- \(D_{0}\) :
-
Inner diameter of pipeline (m)
- \(f\) :
-
Coefficient of friction resistance of pipeline
- \(g\) :
-
Gravitational acceleration (m s−2)
- \(H_{\text{c}}\) :
-
Depth of the constant temperature surface of soil (m)
- \(H_{\text{t}}\) :
-
Buried depth of the pipeline (m)
- \(k_{\text{o}}\) :
-
Thermal conductivity of crude oil (W m−1 °C−1)
- \(k_{\text{p}}\) :
-
Thermal conductivity of pipeline wall (W m−1 °C−1)
- \(k_{\text{s}}\) :
-
Thermal conductivity of soil (W m−1 °C−1)
- \(k_{\text{i}}\) :
-
Thermal conductivity of insulating layer (W m−1 °C−1)
- \(L_{\text{R}}\) :
-
Pipeline length (m)
- \(p_{\text{i}}\) :
-
Average pressure of oil at point i (Pa)
- \(p_{\text{i}}^{0}\) :
-
Average pressure of oil at point i at previous time step (Pa)
- \(p_{{{\text{i}} - 1}}^{0}\) :
-
Average pressure of oil at point \({\text{i}} - 1\) at previous time step (Pa)
- \(p_{{{\text{i}} - 1}}^{{}}\) :
-
Average pressure of oil at point \({\text{i}} - 1\) (Pa)
- \(P\) :
-
Average pressure of oil (Pa)
- \(P_{\text{z}}\) :
-
Terminal pressure of the pipeline (Pa)
- \(Q\) :
-
Flow rate of crude oil during restart (m3 s−1)
- Q re :
-
Flow rate during the reverse pipelining (m3 s−1)
- \(q_{\text{o}}\) :
-
Amount of heat dissipation of crude oil in the unit wall area per unit of time (W m−2)
- \(q_{\text{i}}^{0}\) :
-
Amount of heat dissipation of crude oil in the unit wall area per unit of time at point i at previous time step (W m−2)
- \(R_{0}\) :
-
Inner radius of pipeline (m)
- \(R_{1}\) :
-
Inner radius of insulating layer (m)
- \(R_{2}\) :
-
External radius of insulating layer (m)
- \(r\) :
-
Radial position of pipeline and insulating layer (m)
- \(T_{ 0}\) :
-
Environment temperature (°C)
- \(T_{\text{i}}^{0}\) :
-
Temperature of crude oil point i at previous time step (°C)
- \(T_{\text{o}}\) :
-
Temperature of crude oil (°C)
- \(T_{\text{p}}\) :
-
Temperature of pipeline wall (°C)
- \(T_{\text{i}}\) :
-
Temperature of insulating layer (°C)
- \(T_{\text{i}}\) :
-
Temperature of crude oil point i (°C)
- \(T_{{{\text{i}} - 1}}^{0}\) :
-
Temperature of crude oil point \({\text{i}} - {\text{1}}\) at previous time step (°C)
- \(T_{\text{R}}\) :
-
Outlet temperature of the pipeline (°C)
- T re :
-
Outlet temperature during the reverse pipeline (°C)
- \(T_{\text{c}}\) :
-
Temperature of the constant temperature surface of soil (°C)
- \(T_{\text{a}}\) :
-
Atmospheric temperature (°C)
- \(T_{\text{s}}\) :
-
Temperature of soil (°C)
- \(t\) :
-
Operating time (s)
- \(v_{0}\) :
-
Average oil flow rate at the initial moment (m s−1)
- \(v_{\text{i}}\) :
-
Average oil flow rate at point i (m s−1)
- \(v_{\text{i}}^{0}\) :
-
Average oil flow rate at point i at previous time step (m s−1)
- \(v\) :
-
Average oil flow rate (m s−1)
- \(W_{\text{t}}\) :
-
Distance from center of pipeline to the heat influence boundary (m)
- \(x\) :
-
Horizontal direction (m)
- \(y\) :
-
Vertical direction (m)
- \(z\) :
-
Axial direction of the pipeline (m)
- \(\Delta t\) :
-
Time interval (s)
- \(\Delta z\) :
-
Space interval (s)
- \(\alpha\) :
-
Included angle between the flow direction of pipeline and horizontal direction
- \(\alpha_{\text{o}}\) :
-
Convection heat transfer coefficient at the inner surface of the pipeline wall (W m−2 °C−1
- \(\beta_{\text{o}}\) :
-
Expansion coefficient of crude oil (K−1)
- δ :
-
Thickness of the pipeline (mm)
- \(\theta\) :
-
Round curvature
- \(\rho_{\text{o}}\) :
-
Density of crude oil (kg m−3)
- \(\rho_{\text{p}}\) :
-
Density of pipeline wall (kg m−3)
- \(\rho_{\text{s}}\) :
-
Density of soil (kg m−3)
- \(\rho_{\text{i}}\) :
-
Density of insulating layer (kg m−3)
- a:
-
Atmosphere
- i:
-
Insulating layer
- o:
-
Oil
- p:
-
Pipeline wall
- s:
-
Soil
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Acknowledgements
This work was financially supported by the University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province of China (Grant No. UNPYSCT-2018039).
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Wei, L., Dong, H., Zhao, J. et al. Transient thermal characteristics of the buried crude oil pipeline system during the reverse pipelining. J Therm Anal Calorim 145, 2503–2524 (2021). https://doi.org/10.1007/s10973-020-09829-y
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DOI: https://doi.org/10.1007/s10973-020-09829-y