This article proposed an analytic and finite element-combined modelling method for the investigation of temperature effects on bolt loads and variation in a bolted flange for subsea pipeline connection. With this method, the preloads of bolt in the bolted flange assembly were investigated under different medium liquid temperatures in the pipeline. The simulation results illustrate that the deviation of bolt loads can be increased due to the medium liquid temperature increasing. The final bolt load deviation increases along with the increasing of the initial deviation of bolt preloads in a constant medium liquid temperature. The final distribution of bolt loads can be affected by the initial condition of the bolts. When bolt preloads are staggered, the variance of the final bolt loads is minimized; when the bolt preloads are axisymmetric, the final bolt load variance is the maximum.

Due to the depletion of land oil reserves, more attention is being paid to offshore oil, especially deep-sea resources. As a safe and reliable transportation method, the subsea oil pipeline played a very important role in deep-water oil and gas exploitation. Flange connection is a common way to connect the deep-sea oil pipelines [

The temperature of the pipeline and the flange is not immutable. When the medium liquid goes through the pipeline, the temperature increases, then the bolt loads increase as well. In a bolted flange connection, elastic interaction happens; if a bolt is tightened, it leads to the other bolt loads’ increase or decrease. In 1985, Payne found that that the transient temperature change was a major cause of flange connection failure [

In fact, the distribution of bolt loads is very important for the sealing performance of the flange, which cannot be ignored. This paper proposed an analytic and finite element-combined modelling method; taking both temperature change and the elastic interaction into account, we obtained the distribution trend of bolt preload with the temperature change with a given initial bolt preload deviation.

As shown in Figure

The flange and the bolts.

The heat transfer model includes heat conduction, heat radiation, and heat convection. The calculation of heat radiation is highly nonlinear, including the material nonlinearity and geometric nonlinearity. Heat convection is usually temperature-dependent; it means that the heat convection coefficient cannot be directly calculated, so an appropriate heat transfer model is required. The heat transfer model can be simplified as an equivalent coefficient of thermal conductivity with a good calculation accuracy.

Although the heat transfer in the seawater layer is low, if it is fully ignored, the temperature difference between the bolt and the flange can be exaggerated. If the seawater layer is treated as a liquid thermal material with a conductivity, a big error can be introduced as well. The heat conduction is the easiest to be calculated on comparing with heat convection and heat radiation, and the coefficient of heat conductivity can be set in the material property in simulation. Therefore, the heat transfer can be treated as an equivalent coefficient of heat conductivity. With the setting of the temperature-dependent equivalent coefficient of heat conductivity, the heat radiation, heat convection, and heat conduction can be simulated. So the heat transfer can be idealized as a heat conduction process with a temperature-dependent equivalent heat conductivity coefficient.

As the real surface is not perfect, the nature of the surface can increase or decrease energy exchange. The direct energy flux between the two surfaces is expressed by an angular factor. The determination of the angle factor is to find the energy exchange between differential area elements of two surfaces and after that integrate it on the whole surface. The result relies on the geometric conditions. The angular factor represents only the percentage of the radiant energy that reaches the other surface, which is independent of the absorption capacity of the other surface. It is a parameter that depends on the size and position of the surfaces only. The heat exchange model between the hole and the bolt can be simplified as a heat exchange case between two concentric cylinders. The two concentric cylinders with the same length, _{2}, radiate directly to the outer surface of the inner cylinder with radius, _{1}. The angle factor of the hole radiation to the bolt can be obtained [

Considering the effects of heat radiation, the heat emissivity of the bolt and hole can be expressed as_{1} and _{2} denote the blackness of the bolt and hole.

As the materials of the bolt and flange are corrosion-resistant alloy and heat-resistant alloy, the corrosion of seawater also produces an oxidation layer on the surfaces for the long-term operation in deep water, so the blackness of all parts is selected as 0.8.

When the heat convection can be ignored, the heat transfers through the heat radiation and heat conduction of the seawater layer; then, the energy that transfers between the flange and the bolt is_{1-2} is the heat transfer of the seawater layer between the flange and bolt, J, _{1} is the bolt surface temperature, K, _{2} is the flange bolt hole temperature, K, _{0} is the blackbody emissivity, 5.67 W/(m^{2}·K^{4}), and ^{2} is the seawater thermal conductivity at _{2} [

Substitute equation (

The equivalent heat conductivity can be expressed as

Considering that the heat conductivity is a function of temperature, this equation is a coupling equation, which can be solved by the dichotomy method. The relation of the equivalent heat conductivity coefficient and temperature is plotted in Figure

The relation of the equivalent heat conductivity coefficient _{e1} and temperature.

The heat convection between the outer surface of the seal ring and the seawater is much lower than the seawater heat conduction and heat radiation, so it can be ignored in simulation. The heat transfer between the flanges can be treated as the heat conduction and heat radiation, and we yield the following:_{e2} is the equivalent heat conductivity between the flanges, W/(m·K), _{k4} is the seawater heat conductivity at _{4} [_{3} is the seal surface temperature, K, _{4} is the seawater temperature, K, _{3} is the seal ring radius, and _{4} is the flange radius.

The corresponding temperature-dependent equivalent heat conductivity coefficient _{e2} is shown in Figure

The relation of the equivalent heat conductivity coefficient _{e2} and temperature.

As the flange is exposed to the seawater environment, the main heat transfer is natural convection heat exchange with the seawater, _{2}, and monomer radiation heat transfer, _{3}. The convective heat loss is defined as _{p}.

The radiative heat exchange between the external surface of the flange and the seawater can be replaced by the equivalent air convection heat exchanger in simulation and calculated as_{p} is the heat loss due to convection heat transfer, J, _{p} is the seawater natural heat transfer coefficient [^{−2}·K^{−1}, _{p} is the outer surface area of the flange, m^{2}, _{5} is the flange outer surface temperature, K, and _{6} is the seawater temperature, K.

In addition, the heat loss due to heat radiation _{R} is_{R} is the heat loss caused by heat radiation from the outer surface of the pressure ring, J, and

Introducing a temperature-dependent equivalent heat transfer coefficient of convection and heat radiation, _{e}, is

The relation of the equivalent heat transfer coefficient and temperature is plotted in Figure

The relation of the equivalent heat transfer coefficient _{e} and temperature.

The temperature-dependent conductivity coefficients and heat transfer coefficient acquired in Section

The material of the seal ring is 12Cr1MoV, and the material of flange and bolts is 060A35 (British Standards Institution). The material properties are listed in Table

Material behaviors.

Material | 12Cr1MoV | 060A35 | |
---|---|---|---|

Conductivity W/(m·K) | 293K | 35.6 | |

373K | 35.6 | 46.0 | |

473K | 35.6 | 48.2 | |

573K | 35.2 | 44.9 | |

Mass density ^{3} | 7.85 × 10^{−9} | 7.87 × 10^{−9} | |

Elastic | Young’s modulus MPa | 210000 | 210000 |

Poisson’ ratio | 0.3 | 0.3 | |

Expansion coeff. K^{−1} | 293K | 10^{−6} | |

373K | 1.125 × 10^{−6} | 1.245 × 10^{−6} | |

473K | 1.218 × 10^{−6} | 1.287 × 10^{−6} | |

573K | 1.249 × 10^{−6} | 1.350 × 10^{−6} | |

Specific heat mJ/( | 4.6 × 10^{8} | 4.8 × 10^{8} |

The boundary conditions.

Inprops in the interaction property.

Type | Inprop-1 | Inprop-2 | Inprop-3 | ||||||
---|---|---|---|---|---|---|---|---|---|

Contact | Contact | Film conduction | |||||||

Conductance W·m^{−2}·K^{−1} | Clearance mm | Temp. K | Conductance W·m^{−2}·K^{−1} | Clearance mm | Temp. K | Film coeff. W·m^{−2}·K^{−1} | Temp. K | ||

0.241 | 3 | 273 | 3.421 | 5 | 273 | 203.861 | 273 | ||

0.353 | 3 | 298 | 4.474 | 5 | 298 | 205.003 | 298 | ||

0.440 | 3 | 323 | 5.670 | 5 | 323 | 206.350 | 323 | ||

0.506 | 3 | 348 | 7.030 | 5 | 348 | 207.922 | 348 | ||

0.560 | 3 | 373 | 8.574 | 5 | 373 | 209.731 | 373 | ||

0.605 | 3 | 398 | 10.321 | 5 | 398 | 211.798 | 398 | ||

0.644 | 3 | 423 | 12.287 | 5 | 423 | 214.138 | 423 | ||

0.679 | 3 | 448 | 14.489 | 5 | 448 | 216.797 | 448 | ||

0.713 | 3 | 473 | 16.942 | 5 | 473 | 219.709 | 473 | ||

0.745 | 3 | 498 | 19.660 | 5 | 498 | 222.971 | 498 | ||

0.777 | 3 | 523 | 22.662 | 5 | 523 | 226.578 | 523 |

The temperature field of the flange is shown in Figure

The temperature distribution of the bolt is shown in Figure

Flange temperature distribution.

Bolt temperature distribution.

Because of the elastic interaction, the bolt preloads are not exactly the same. If the temperature of the flange changes, the bolt loads change as well. When the bolt loads change, the elastic interaction between the bolts further affects the uniformity of the bolt loads which affects the sealing of the flange in the final [

The simulation shows that when the bolts’ preload is uniform and the medium liquid temperature is 373 K (Condition 1), the bolt loads change are shown in Figure

The bolt loads change with time in Condition 1 (373 K).

When the bolt preloads are uniform, the medium liquid temperature is 473 K (Condition 2), and the bolt loads’ change is shown in Figure

The bolt loads change with time in Condition 2 (473 K).

When the bolts’ preload is uniform, the medium liquid temperature is 523 K (Condition 3), and the bolt loads’ change is shown in Figure

The bolt loads change with time in Condition 3 (523 K).

When the bolts’ preload variation is 1% and the temperature of the medium liquid is 523 K (Condition 4), the bolt loads’ change is shown in Figure

The bolt loads change with time in Condition 4.

When the bolts’ preload variation is 2% and the temperature of the medium liquid is 523 K (Condition 5), the bolt loads’ change is shown in Figure

The bolt loads change with time in Condition 5.

When the bolts’ preload variation is 5% and the temperature of the medium liquid is 523 K (Condition 6), the bolt loads’ change is shown in Figure

The bolt loads change with time in situation 6.

The bolt loads increase quickly from 0 to 2000 s and after that gently until stable.

Then, we can see that the high temperature of the medium liquid leads to a high increase of the bolt load, and the bolt loads are more scattered; meanwhile, a big bolt preload deviation leads to more scattered bolt loads; in order to study the effects of the distribution of the bolts’ preload on the bolt loads with the same deviation, define the standard deviation as_{i} is the bolt load of bolt _{F} is the average of the bolt loads.

When the bolt preload deviation is 5%, the temperature of the medium liquid is 523 K, and the bolts’ preload was axial symmetry (Condition 7), the standard deviation is shown in Figure

The standard deviation with time in Condition 7.

When the bolt preload deviation is 5%, the temperature of the medium liquid is 523 K, and the bolts’ preload was decreasing (Condition 8), the standard deviation is shown in Figure

The standard deviation with time in Condition 8.

When the bolt preload deviation is 5%, the temperature of the medium liquid is 523 K, and the bolt preloads are staggered (Condition 9), the standard deviation is shown in Figure

The standard deviation with time in Condition 9.

The bolt load peak deviations are around 6–6.4 kN, happen around 1000 s, and tend to be stable after 2000 s.

This research proposed an analytic and finite element-combined modelling approach to analyze the thermal-structural coupling for bolted flanges of pipeline connection. With the proposed method, a bolted flange was analyzed and the following conclusions can be drawn:

As the temperature of the liquid in the pipe increased, the temperature of the flanges and bolts increased as well, resulting in the bolt load increase. At the same time, as the temperature increased, the bolt loads’ standard deviation increased first and then decreased; the maximum standard deviation of the final load was 1.800 kN; the maximum standard deviation in the thermal process was 6.388 kN.

The temperature of the medium liquid also influenced the distribution of the bolt loads; a higher temperature of the medium liquid led to a more uneven final load distribution.

If the deviation of the bolt preloads was a constant, the distribution of bolts’ preload also affected the final load distribution of the bolts. When the bolts’ preload was staggered, the variance of the final bolt loads was minimized; when the bolt preloads decreased, the final bolt load variance increased, and the maximum standard deviation was about 6.388 kN.

The data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China, Grant no. 51779064.