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Leakage of hydrocarbon liquids from tanks and reactors
Journal of Hazardous Materials 167 (2009) 1252
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Journal of Hazardous Materials journal homepage: www.elsevier.com/locate/jhazmat
Letter to the Editor Leakage of hydrocarbon liquids from tanks and reactors The article by Barmbilla and Manca [1] in a recent issue of this journal is concerned with leakage of hydrocarbon liquids from tanks. In this comment I wish to focus on their ‘Case study 4a: Pool spreading from a hole in a cylindrical tank’. Such a situation is surely easily treated by Bernoulii’s equation, and a reader will find full treatment of the application of Bernoulii’s equation to a leaking tank of liquid in Ref. [2]. The result of such an application is:
v=
2gh
where v is the exit velocity of liquid from the hole (m s−1 ), g is the acceleration due to gravity (9.81 m s−2 ) and h is the height of the hole above the base of the tank (m). The tank shape does not feature in the derivation. I am unaware of how if at all this relates to the analysis in Ref. [1]. We can however at least determine the value of h which corresponds to the ‘radial velocity’ in Ref. [1]. For leak through a hole in a cylindrical tank, a value of 0.92 m s−1 is given for this in Table 3 of Ref. [1], giving a value for h of: 0.922 = 0.043 m, 2g
4.3 cm
Case 4b, a ‘more rigorous’ treatment of the same problem, gives a value of the radial velocity of 1.3 m s−1 and the correspondingly greater value of 8.6 cm for the height. There is consistency between the approach in Ref. [1] and application of the Bernoulli equation in that in Ref. [1] the same value
0304-3894/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jhazmat.2009.01.095
of the ‘radial velocity’ applies to cylinder and parallelepiped where leakage is from a single hole. It is noted above that the Bernoulli treatment takes no note of the tank shape. It might be that in this commentary like is not being compared with like and that the velocities in Ref. [1] are for spread across the ground hence the absence of the acceleration due to gravity from the equations. If so it is presumably the case that any hole in the cylinder, parallelepiped or whatever is at ground level. This is in some degree supported by the fact that in the above calculations the heights calculated are small and holes at such heights would be close to the base of an actual hydrocarbon storage tank. Further clarification is however needed before it can confidently be asserted that this result brings the two approaches together. References [1] S. Barmbilla, D. Manca, On pool spreading around tanks: geometrical considerations, Journal of Hazardous Materials 158 (2008) 88–99. [2] J.C. Jones, Hydrocarbon Process Safety: A Text for Students and Professionals, Whittles Publishing, Caithness, 2003.
J.C. Jones School of Engineering, University of Aberdeen, Aberdeen AB24 1WT, UK E-mail address: [email protected] 9 January 2009 Available online 3 February 2009
Contents lists available at ScienceDirect
Journal of Hazardous Materials journal homepage: www.elsevier.com/locate/jhazmat
Letter to the Editor Leakage of hydrocarbon liquids from tanks and reactors The article by Barmbilla and Manca [1] in a recent issue of this journal is concerned with leakage of hydrocarbon liquids from tanks. In this comment I wish to focus on their ‘Case study 4a: Pool spreading from a hole in a cylindrical tank’. Such a situation is surely easily treated by Bernoulii’s equation, and a reader will find full treatment of the application of Bernoulii’s equation to a leaking tank of liquid in Ref. [2]. The result of such an application is:
v=
2gh
where v is the exit velocity of liquid from the hole (m s−1 ), g is the acceleration due to gravity (9.81 m s−2 ) and h is the height of the hole above the base of the tank (m). The tank shape does not feature in the derivation. I am unaware of how if at all this relates to the analysis in Ref. [1]. We can however at least determine the value of h which corresponds to the ‘radial velocity’ in Ref. [1]. For leak through a hole in a cylindrical tank, a value of 0.92 m s−1 is given for this in Table 3 of Ref. [1], giving a value for h of: 0.922 = 0.043 m, 2g
4.3 cm
Case 4b, a ‘more rigorous’ treatment of the same problem, gives a value of the radial velocity of 1.3 m s−1 and the correspondingly greater value of 8.6 cm for the height. There is consistency between the approach in Ref. [1] and application of the Bernoulli equation in that in Ref. [1] the same value
0304-3894/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jhazmat.2009.01.095
of the ‘radial velocity’ applies to cylinder and parallelepiped where leakage is from a single hole. It is noted above that the Bernoulli treatment takes no note of the tank shape. It might be that in this commentary like is not being compared with like and that the velocities in Ref. [1] are for spread across the ground hence the absence of the acceleration due to gravity from the equations. If so it is presumably the case that any hole in the cylinder, parallelepiped or whatever is at ground level. This is in some degree supported by the fact that in the above calculations the heights calculated are small and holes at such heights would be close to the base of an actual hydrocarbon storage tank. Further clarification is however needed before it can confidently be asserted that this result brings the two approaches together. References [1] S. Barmbilla, D. Manca, On pool spreading around tanks: geometrical considerations, Journal of Hazardous Materials 158 (2008) 88–99. [2] J.C. Jones, Hydrocarbon Process Safety: A Text for Students and Professionals, Whittles Publishing, Caithness, 2003.
J.C. Jones School of Engineering, University of Aberdeen, Aberdeen AB24 1WT, UK E-mail address: [email protected] 9 January 2009 Available online 3 February 2009