# Studies on the Exergy Transfer Law for the Irreversible Process in the Waxy Crude Oil Pipeline Transportation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Field Equilibrium Equation and Entropy Generation Rate Equation

#### 2.1. Field Equilibrium Equation

_{e}supplied by the outside world and entropy generation dS

_{i}due to the irreversible process in the system.

#### 2.2. Entropy Generation Rate Equation of Waxy Crude Oil

_{i}” and its coupling force “X

_{j}” satisfy the linear relationship [17,18].

## 3. Waxy Crude Oil Pipeline Exergy Transfer Equation

#### 3.1. The Establishment of Exergy Transfer Model

#### 3.2. The Exergy Dynamics Transfer Equation

## 4. Waxy Crude Oil Pipeline Exergy Transfer Law

_{n}. Chemical potential gradient causes diffusion exergy transfer, so the generated flow is called chemical exergy flow.

## 5. Analysis of Influence Factors for Exergy Transfer in Waxy Crude Oil Pipeline Process

#### 5.1. Analysis of Pressure Exergy Transfer Influence Factors

^{3}/h, 75 m

^{3}/h, and 85 m

^{3}/h, as shown in Figure 4 and Figure 5.

#### 5.2. Analysis of Thermal Exergy Transfer Influence Factors

^{3}/h, 75 m

^{3}/h, and 85 m

^{3}/h, as shown in Figure 11 and Figure 12.

#### 5.3. Analysis of Diffusion Exergy Transfer Influence Factors

^{2}°C). The other pipeline operating parameters are the same above. The wax molecular concentration gradient, the diffusion exergy transfer coefficient and diffusion exergy flow density are calculated. The diffusion exergy transfer coefficient change curve and the diffusion exergy flow density change curve along the pipeline are shown in Figure 13:

^{3}/h, 75 m

^{3}/h, and 85 m

^{3}/h, as shown in Figure 15.

## 6. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Abbreviations

A | an arbitrary variable (-) |

ε | A density (-) |

c | group element mass(kg) |

r | component i mass generation rate in chemical reaction |

η | mass fraction (-) |

E | exergy (kJ) |

W | flow velocity (m/s) |

L | phenomenological coefficient (-) |

T | temperature (K) |

V | molar volume (m^{3}) |

S | entropy (kJ/K) |

T | time (s) |

X | intensive variable (-) |

K | exergy transfer coefficient (-) |

j | flow (-) |

e | specific exergy (kJ/kg) |

p | pressure (kPa) |

ρ | density (kg/m^{3}) |

π | compressive stress tensor (-) |

τ | shear force tensor (-) |

Greek symbols | |

μ | viscosity coefficient (kg/m∙s) |

δ | unit tensor (-) |

Λ | mass calculation coefficient of component in chemical reaction (-) |

σ | entropy generation rate (-) |

Subscripts | |

0 | initial state |

i | component |

l | length |

Superscripts | |

ex | exergy |

## References

- Cheng, Q.L.; Liu, Y.; Xiang, X.Y. Exergy transfer analysis for thermal oil pipeline process. J. Therm. Technol.
**2005**, 4, 6–9. [Google Scholar] [CrossRef] - Xiang, X.Y. Engineering Exergy Analysis Method; Petroleum Industry Press: Beijing, China, 1990; ISBN 7-5021-0353-8/TE∙343. [Google Scholar]
- Gaggioli, R.A. The concept of available energy. J. Chem. Eng. Sci.
**1961**, 3, 45–52. [Google Scholar] [CrossRef] - Soma, J. Energy Transfer-A New Field of Energy Endeaver. Energy Eng.
**1985**, 82, 11–22. [Google Scholar] - Dunbrt, W.R. The Compont Equation of Energy and Exergy. J. Energy Resour. Technol.
**1992**, 114, 75–83. [Google Scholar] [CrossRef] - Wang, S.P.; Chen, Q.L. Transfer and inter-conversions between different forms of exergy in electromagnetic fluids. J. Chem. Ind. Eng.
**2007**, 58, 2964–2969. [Google Scholar] - Cheng, Q.L.; Liu, Y.; Xiang, X.Y. Formation of thoughts thread and development status quo for exergy transfer study. J. Chem. Ind. Eng. Prog.
**2012**, 9, 1936–1941. [Google Scholar] - Wang, S.P.; Chen, Q.L.; Yin, Q.H. Study on Exergy Transfer and Conversion Principle. J. South China Univ. Technol. (Nat. Sci.)
**1998**, 26, 27–32. [Google Scholar] - Wang, S.P.; Chen, Q.L.; Yin, Q.H. Exergy Transfer of Turbulent Flow through A Duct with Constant Mass Flux. J. Eng. Thermophys.
**2002**, 23, 405–408. [Google Scholar] - Qiao, C.Z. The Regulariy of Exergy Tansfer in the Heat Conduction and Application. Master’s Thesis, North East Petroleum University, Daqing, China, 2002. [Google Scholar]
- Qiao, C.Z.; Wu, Z.Y.; Xiang, X.Y. One dimensional regulariy and calculation of exergy transferring in steady heat conduction process. J. North China Electr. Power Univ.
**2003**, 30, 50–53. [Google Scholar] - Qiao, C.Z.; Xiang, X.Y.; Wu, Z.Y. Description of exergy transfer in the two dimensional thermal conduction process. J. Eng. Thermophys.
**2003**, 24, 202–204. [Google Scholar] - Qiao, C.Z.; Wu, Z.Y.; Xiang, X.Y. One dimensional regularity and calculation of exergy transfer in the unsteady heat conduction process. J. Therm. Sci. Technol.
**2003**, 2, 42–46. [Google Scholar] - Liu, Y.; Cheng, Q.L.; Xiang, X.Y. The Exergy Transfer Analysis on Pipeline Transportation Process. J. Oil Gas Storage Transp.
**2007**, 26, 5–7. [Google Scholar] - Cheng, Q.L.; Zhou, H.L.; Xiang, X.Y. The definition of exergy transfer coefficient and its influence mechanism. J. North China Electr. Power Univ.
**2009**, 36, 43–46. [Google Scholar] - Zeng, D.L. Nonequilibrium Dynamics of Engineering; Science Press: Beijing, China, 1991; ISBN 7-03-002263-7/TB∙69. [Google Scholar]
- Li, X.L. Analysis and Application Study of Irreversible Entropy Generation Characteristics in Waxy Crude Oil Piple-Transportation Process. Ph.D. Thesis, North East Petroleum University, Daqing, China, 2014. [Google Scholar]
- Sun, X.L. Analysis on Entropy Production Rate in Pipeline Process of Waxy Crude Oil. Master’s Thesis, North East Petroleum University, Daqing, China, 2013. [Google Scholar]
- Wang, S.P.; Yin, Q.H.; Chen, Q.L.; Hua, B. A Study on the Fundamental Theory of Exergy Transfer. J. South China Univ. Technol. (Nat. Sci.)
**1998**, 26, 30–36. [Google Scholar] - Wang, S.P.; Hua, B.; Chen, Q.L.; Yin, Q.H. Transformation relationship between energy, exergy, and axergy. J. Energy Res. Inf.
**1997**, 13, 27–30. [Google Scholar] - Gan, Y.F.; Cheng, Q.L.; Sun, W.; Su, W.K.; Liu, Y. Research Progress in the Chemical Exergy Composition and Application in Waxy Crude Oil Pipeline Transportation Process. J. Chem. Mach.
**2017**, 44, 375–381. [Google Scholar] - Su, W.K. The Comprehensive Composition of Exergy Flow and Exergy Loss Analysis in Waxy Crude Oil Transportation Process. Master’s Thesis, North East Petroleum University, Daqing, China, 2016. [Google Scholar]
- Cheng, Q.L.; Gan, Y.F.; Su, W.K.; Liu, Y.; Sun, W.; Xu, Y. Research on Exergy Flow Composition and Exergy Loss Mechanisms for Waxy Crude Oil Pipeline Transport Processes. Energies
**2017**, 10, 1956. [Google Scholar] [CrossRef] - Cheng, Q.L.; Ding, N.; Yi, X.; Zhao, Y.; Sun, W. Study of exergy transfer and conversion law of irreversible process in crude oil pipeline transportation. J. Therm. Sci. Technol.
**2015**, 14, 125–129. [Google Scholar] - Lucia, U.; Grisolia, G. Cyanobacteria and Microalgae: Thermoeconomic Considerations in Biofuel Production. Energies
**2018**, 11, 156. [Google Scholar] [CrossRef]

**Figure 1.**The pressure exergy transfer coefficient change curve and the pressure exergy flow density change curve of pipeline.

**Figure 2.**Pipe axial pressure field distribution curves under different outbound pressure conditions.

**Figure 3.**(

**a**) Pressure exergy transfer coefficient change curves under different outbound pressure conditions. (

**b**) Pressure exergy flow density change curves under different outbound pressure conditions.

**Figure 5.**(

**a**) Pressure exergy transfer coefficient change curves under different flow conditions. (

**b**) Pressure exergy flow density change curves under different flow conditions.

**Figure 6.**The thermal exergy transfer coefficient change curve and the thermal exergy flow density change curve of pipeline.

**Figure 7.**Pipe axial temperature field distribution curves under different ambient temperature conditions.

**Figure 8.**(

**a**) Thermal exergy transfer coefficient change curves under different ambient temperature conditions. (

**b**) Thermal exergy flow density change curves under different ambient temperature conditions.

**Figure 9.**Pipe axial temperature field distribution curves under different outbound temperature conditions.

**Figure 10.**(

**a**) Thermal exergy transfer coefficient change curves under different outbound temperature conditions. (

**b**) Thermal exergy flow density change curves under different outbound temperature conditions.

**Figure 12.**(

**a**) Thermal exergy transfer coefficient change curves under different flow conditions. (

**b**) Thermal exergy flow density change curves under different flow conditions.

**Figure 13.**The diffusion exergy transfer coefficient change curve and the diffusion exergy flow density change curve of pipeline.

**Figure 14.**(

**a**) Diffusion exergy transfer coefficient change curves under different ambient temperature conditions. (

**b**) Diffusion exergy flow density change curves under different ambient temperature conditions.

**Figure 15.**(

**a**) Diffusion exergy transfer coefficient change curves under different flow conditions. (

**b**) Diffusion exergy flow density change curves under different flow conditions.

Crude Oil Specific Heat Capacity | 2.0 kJ/(kg·°C) | Pipeline Length | 10 km |
---|---|---|---|

Crude oil Density | 870 kg/m^{3} | Pipeline diameter | 219.1 mm |

Crude oil dynamic viscosity | 20.2 mPa·s (50·°C) | Pipeline external diameter | 207.9 mm |

Ambient temperature | 2·°C | Pipeline start point temperature | 75·°C |

Environmental pressure | 0.3 MPa | Pipeline start point pressure | 5 MPa |

Total heat transfer coefficient | 2.6 W/(m^{2}·°C) | Flow | 0.0208 m^{3}/s |

Condensation point | 28·°C | Average velocity | 0.6137 m/s |

Wax density | 900 kg/m^{3} | Wax content | 26.29% |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Cheng, Q.; Zheng, A.; Song, S.; Wu, H.; Lv, L.; Liu, Y. Studies on the Exergy Transfer Law for the Irreversible Process in the Waxy Crude Oil Pipeline Transportation. *Entropy* **2018**, *20*, 309.
https://doi.org/10.3390/e20050309

**AMA Style**

Cheng Q, Zheng A, Song S, Wu H, Lv L, Liu Y. Studies on the Exergy Transfer Law for the Irreversible Process in the Waxy Crude Oil Pipeline Transportation. *Entropy*. 2018; 20(5):309.
https://doi.org/10.3390/e20050309

**Chicago/Turabian Style**

Cheng, Qinglin, Anbo Zheng, Shuang Song, Hao Wu, Lili Lv, and Yang Liu. 2018. "Studies on the Exergy Transfer Law for the Irreversible Process in the Waxy Crude Oil Pipeline Transportation" *Entropy* 20, no. 5: 309.
https://doi.org/10.3390/e20050309