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Predicting the vaporization rate of a spreading cryogenic liquid pool on concrete using an improved 1-D heat conduction equation

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Abstract

The accidental spilling of cryogenic liquid leads to formation of a spreading pool, which may result in pool fires, BLEVE(boiled liquid evaporate vapor explosion) or vapor cloud fire, such as liquefied natural gas, is flammable. The key aspect of evaluating the consequence of such a disaster is to predict vaporization rate of the spreading cryogenic liquid pool. In this study, an empirical function was established to predict the temperature gradient of concrete. Afterwards an improved 1-D heat conduction equation was established to predict heat conduction of the spreading cryogenic liquid, and then vaporization rate was measured. In addition, to validate accuracy of the improved 1-D heat conduction equation, small-scale experiments were conducted to calculate vaporization rate for a spreading cryogenic liquid pool. The resulting vaporization rate decreased with discharge time, and increased with spill rate. The established empirical function was used to predict the temperature gradient displayed satisfactory accuracy with absolute average relative errors (AAREs) less than 10%; the improved 1-D heat transfer model AAREs were less than 13% compared with the experimental value. In summary, the improved 1-D heat transfer model can be applied to predict vaporization rate if the spill rate and discharge time are confirmed.

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Abbreviations

r :

pool radius, m

u :

radial liquid velocity at the edge, m/s

q s :

spill rate, kg/s

\( {M}_s^{mass} \) :

weight of the released liquid , kg

Δt :

discharge time, s

t st :

starting time, s

t end :

end time, s

ρ :

liquid density, kg/m3

H :

depth of the pool, m

h c,∞ :

minimum depth of the pool, m

α i :

molecular weight liquid, kg/mol

p i :

vapor pressure above the pool, N/m2

u * :

atmospheric friction velocity above the pool, m/s;

n :

wind profile index

m m,V :

mole fraction of vapor above liquid pool surface, mol/mol;

v :

kinematic viscosity , m2/s;

D :

diffusion coefficient, m2/s.

T :

temperature

t :

time, s

q :

heat flux, W/m2

A :

pool area, m2

L C :

characteristic length, m

λ :

thermal conductivity, W/(K·m)

C p :

specific heat capacity of air, J/(kg·K)

η :

dynamic viscosity, Pa·s

L :

latent heat of vaporization, J/kg

a :

thermal diffusivity, m2/s

u w,10 :

wind speed at 10 m height, m/s

g :

Acceleration of gravity, 9.8m/s2

E :

vaporization rate, kg/(m2·s)

L :

Liquid phase

a :

Ambient

v :

Vapor phase

b :

Boiling point

w :

Concrete ground

t :

Turbulence flow

L :

Laminar flow

Nu :

Nusselt number

Re :

Reynolds number

Sc :

Schmidt number

Pr :

Prandtl number

References

  1. Thyer AM (2003) A review of data on spreading and vaporisation of cryogenic liquid spills. J Hazard Mater 99(1):31–40

    Article  Google Scholar 

  2. Gopalaswami N, Kakosimos K, Zhang B, Liu Y, Mentzer R, Mannan MS (2017) Experimental and numerical study of liquefied natural gas (LNG) pool spreading and vaporization on water. J Hazard Mater 334:244–255

    Article  Google Scholar 

  3. Drake EM, Reid RC (1975) How LNG boils on soils. Hydrocarb Process 54(5):191–194

    Google Scholar 

  4. Reid RC, Wang R (1978) The boiling rates of LNG on typical dike floor materials. Cryogenics 18(7):401–404

    Article  Google Scholar 

  5. Gopalaswami N, Véchot L, Olewski T, Mannan MS (2015) Small-scale experimental study of vaporization flux of liquid nitrogen released on ice. J Loss Prev Process Ind 37:124–131

    Article  Google Scholar 

  6. Luketa-Hanlin A (2006) A review of large-scale LNG spills: experiments and modeling. J Hazard Mater 132(2–3):119–140

    Article  Google Scholar 

  7. Webber DM, Grant SE, Ivings MJ, Jagger SF (2010) LNG source term models for hazard analysis. Health and Safty Laboratory for the Health and Safety Executive, Buxton: 1st edn, 2010

  8. Takeno K, Ichinose T, Hyodo Y, Nakamura H (1994) Evaporation rates of liquid hydrogen and liquid oxygen spilled onto the ground. J Loss Prev Process Ind 7(5):425–431

    Article  Google Scholar 

  9. Olewski T, Mannan MS, Véchot L (2013) Validation of liquid nitrogen vaporisation rate by small scale experiments and analysis of the conductive heat flux from the concrete. J Loss Prev Process Ind 35:277–282

    Article  Google Scholar 

  10. Verfondern K, Dienhart B (2007) Pool spreading and vaporization of liquid hydrogen. Int J Hydrog Energy 32(13):2106–2117

    Article  Google Scholar 

  11. Basha O, Olewski T, Véchot L, Castier M, Mannan MS (2014) Modeling of pool spreading of LNG on land. J Loss Prev Process Ind 30:307–314

    Article  Google Scholar 

  12. Kim M, Nguyen D, Choi B (2016) Experimental study of the evaporation of spreading liquid nitrogen. J Loss Prev Process Ind 39:68–73

    Article  Google Scholar 

  13. Nguyen LD, Kim M, Choi B (2017) An experimental investigation of the evaporation of cryogenic-liquid-pool spreading on concrete ground. Appl Therm Eng 123:196–204

    Article  Google Scholar 

  14. Nguyen LD, Kim M, Choi B, Chung K (2019) Validation of numerical models for cryogenic-liquid pool spreading and vaporization on solid ground. J Heat Mass Transf 128:817–824

    Article  Google Scholar 

  15. Nguyen LD, Kim M, Choi B, Chung K, Do K, Kim T (2020) An evaluation of vaporization models for a cryogenic liquid spreading on a solid ground. J Heat Mass Transf 146:1188–1148

    Article  Google Scholar 

  16. van den Bosch CJH, Wetweings RAPM (2005). Methods for the calculation of physical effects (TNO Yellow Book CPR 14E), 348–361

  17. Gopalaswam N, Mentzer RA, Mannan MS (2015) Investigation of pool spreading and vaporization behavior in medium-scale LNG tests. J Loss Prev Process Ind 35:267–276

    Article  Google Scholar 

  18. Webber DM (2012) On models of spreading pools. J Loss Prev Process Ind 25(6):923–926

    Article  Google Scholar 

  19. ABS Consulting Inc (2004) Consequence assessment methods for incidents involving releases from liquefied natural gas carriers. ABS Consulting Risk Consulting Inc., Houston

    Google Scholar 

  20. Poling EB, Prausnitz MJ, O’Connell PJ (2006) The properties of gases and liquids, fifth edn. McGraw-Hill Education Co.

  21. Jaeger JC, Carslaw HS (1959) Conduction of heat in solids. Oxford University Press

  22. Folland GB (2011) Introduction to partial differential equations, second edn. Princeton University Press

  23. Fleischer MT (1980) Spills: an evaporation/air dispersion model for chemical spills on land. Shell Development Company, Houston

    Google Scholar 

  24. Design Institute for Physical Property Data (U.S.) (2005) DIPPR project 801. Evaluated Standard Thermophysical Property Values, Full Version

    Google Scholar 

  25. Véchot L, Olewski T, Osorio C, Basha O, Liu Y, Mannan MS (2013) Laboratory scale analysis of the influence of different heat transfer mechanisms on liquid nitrogen vaporization rate. J Loss Prev Process Ind 26(3):398–409

    Article  Google Scholar 

Download references

Acknowledgements

This paper was supported by a Nanchong Technology Bureau Project Award under grant number 18SXHZ0021 and the National Natural Science Foundation of China under grant number 51474184.

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Authors and Affiliations

  1. Institution for Disaster Management and Reconstruction, Sichuan University, Chengdu, 610207, China

    Jingya Dong

  2. School of Engineering, Southwest Petroleum University, Nanchong, 637001, China

    Jingya Dong

  3. College of Architecture and Environment, Sichuan University, Chengdu, 610065, China

    Chengjun Jing

  4. PetroChina Southwest Oil & Gas Field Company, Chengdu, 610056, China

    Hao Wen

  5. Luzhou China Resources Xinglu Gas Co. Ltd, Luzhou, 646000, China

    Min Tu

  6. Shu’nan Gas-mine Field, PetroChina Southwest Oil & Gas Field Company, Luzhou, 646000, China

    Jiajun Li

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  1. Jingya Dong
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  2. Chengjun Jing
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  3. Hao Wen
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Correspondence to Chengjun Jing.

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Dong, J., Jing, C., Wen, H. et al. Predicting the vaporization rate of a spreading cryogenic liquid pool on concrete using an improved 1-D heat conduction equation. Heat Mass Transfer (2021). https://doi.org/10.1007/s00231-021-03018-9

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