A Review of Mathematical Models for the Atmospheric Dispersion of Heavy Gases. Part I. A Classification of Models

Open access

A Review of Mathematical Models for the Atmospheric Dispersion of Heavy Gases. Part I. A Classification of Models

In this two part article in its first part models of heavy gas dispersion in the atmosphere are classified and the distinguished groups of models are characterised. In the second part the procedures for the model quality evaluation are described and the main results of model evaluation projects are summarised. Substances released to the atmosphere which have a density greater than the density of the atmospheric air are called heavy gases or dense gases. The dispersion of heavy gases is different from that encountered in the case of neutrally or positively buoyant gases. Specific models have been developed to describe it. The heavy gas dispersion models differ in the complexity and mathematical description. Based on these criteria four main groups of models are distinguished: simple/empirical models, intermediate/integral and shallow layer models, advanced/Lagrangian particle trajectory and Lagrangian puff dispersion models and sophisticated/Computer Fluid Dynamics (CFD) models. This classification is an extension of the classification proposed earlier in the literature.

Britter RE. Ann Rev Fluid Mech. 1989;21:317-344.

Rigas F, Sklavounos S. Computer simulation in consequence analysis and loss prevention. In: New research on hazardous materials. Warrey PB, editors. Nova Science Publishing Inc. 2007;161-209.

Hanna SR, Drivas PJ. Guidelines for use of vapour cloud dispersion models. New York: Center for Chemical Process Safety, Institute of Chemical Engineers; 1989.

Markiewicz M. A review of mathematical models for atmospheric dispersion of heavy gases. Part II: Procedures for the model quality evaluation and the main results on the model evaluation projects. Ecol Chem Eng. (in press).

Koopman RP, Ermak DL. J Hazard Mater. 2007;140:412-428.

Mercer A, Bartholome C, Carissimo B, Dujm NJ, Giesbrecht H. CEC Model evaluation group. Heavy Gas Dispersion Expert Group, Final Report, Directorate of Research, Sci Development. Brussels, Belgium: 1999.

Britter RE, McQuaid J. Workbook on the dispersion of dense gases. HSE Contract Research Report No. 17/1988. Sheffield, UK: Health and Safety Executive; 1988.

Britter R. E. Recent research on the dispersion of hazardous materials. CEC EUR 18198. Brussels, Belgium: CEC, Directorate General; 1998.

Britter R. E. A researcher's/consultant's view on advances in source and dispersion modelling. Proc from the CCPS International conference and workshop on Modelling and mitigation the consequences of accidental releases of hazardous materials. American Institute of Chem Eng/Center for Chemical Process Safety, 1995;67-76.

Emission and dispersion. In: Lees FP, editors. Loss prevention in the process industries. London: Butterworths; 1980.

Borysiewicz M, Furtek A, Potempski S. Guidance on risk assessment methods related to hazardous installations. Otwock: Institute of Atomic Energy; 2000 (in Polish).

Markiewicz M. Modelling the heavy gas dispersion in Poland. In: Pawłowski L, Dudzinska M, Pawłowski A, editors. Environ Eng. New York: Taylor and Francis; 2007;371-374.

Markiewicz M. Modelling of the heavy gas dispersion. In: Borysiewicz M, Potemski S, editors. Modelling and techniques for health and environment hazard assessment and management. Institute of Atomic Energy, Otwock: 2006, 279-302.

Blackmore DR, Herman MN, Woodward JL. J Hazard Mater. 1982;6:106-128.

Ermak DL, Rodean HC, Lange R, Chan ST. A survey of dense than air atmospheric dispersion models. UCRL-21024. Livermore, California: Lawrence Livermore National Laboratory; 1988.

Burgess DS, Zabetakis MG. Detonation of a flammable cloud following a propane pipeline break: the December 9, 1970, explosion in Port Hudson. Bureau of Mines Report of Investigations No. 7752, US Department of the Interior, 1973.

Clancey VJ. Liquid and vapour emission and dispersion. Course on Loss prevention in the process industries. Loughborough, UK: Department of Chemical Engineering, Loughborough University of Technology; 1976.

VDI Guidelines, VDI 3783 Part II Environmental Meteorology, Dispersion of heavy gases. Dusseldorf, Germany: Beuth Verlag Berlin/VDI; 1990 (in German).

Schatzmann M. Accidental releases of heavy gases in urban areas. In: Cermak JE, Davenport AG, Plate EJ, Viegas DX, editors. Wind climate in cities. Dordrecht, The Netherlands: Kluwer Academic Publishers; 1995;555-574.

Van Ulden AP: On the spreading of a heavy gas released near the ground. In: Bushmann CH, editors. Loss prevention and safety promotion in process industries. Delft, The Netherlands: Elsevier; 1974:221-226.

Kaiser GD, Walker BC. Atmos Environ. 1978;12:2289-2300.

Bradley CI, Carpenter RJ, Waite PJ, Ramsey CG, English MA. Recent development of a simple box type model for dense vapour cloud dispersion. In: Hartwig S, editors. Heavy gas and risk assessment. Dordrecht, The Netherlands: Reidel D. Publishing Company; 1979;77-89.

Eidsvik KJ. Atmos Environ. 1980;14:769-777.

Fay JA. Ranck DA. Atmos Environ. 1982;17:239-248.

Van Ulden AP. A new bulk model for dense gas dispersion of two dimensional spread in still air. In: Ooms G, Tennekes H, editors. Atmospheric dispersion of heavy gases and small particles. Berlin: Springer Verlag; 1984;419-440.

Fay JA, Zemba SG. Atmos Environ. 1985;19:1257-1261.

Van Ulden AP. J Hazard Mater. 1987;16:411-425.

Carpenter RJ, Cleaver RP, Waite PJ, English MA. J Hazard Mater. 1987;16:293-314.

Crabol B, Roux A, Lhomme V. J Hazard Mater. 1987;16:201-214.

Wheatley CJ, Prince AJ. J Hazard Mater. 1987;16:185-199.

Puttock JS. J Hazard Mater. 1987;16:439-455.

Britter R. E. GASTAR user manual. Cambridge, UK: Cambridge Environmental Research Center; 1990.

Cleaver RP, Cooper MG, Halford AR. J Hazard Mater. 1994;40:85-108.

Delvosalle C, Levert JM, Benjelloun F, Schayes G, Moyaux B, Ronday F, et al. Major industrial hazards: The SEVEX project: source terms and dispersion calculation in complex terrain. In: Grynning SE, Millan M, editors. Air pollution modelling and its application. New York: Plenum Press Publishing Corporation; 1993;357-365.

Webber DM, Jones SJ, Tickl GA, Wren T. A model of a dispersing dense gas cloud and the computer program DRIFT. SRD/HSE Reports R586, R587. Culcheth, Cheshire, UK: Health and Safety Executive, 1992.

Webber DM, Jones SJ, Martin D. J Hazard Mater. 1993;33:101-122.

Kunsch JP, Fannelop TK. J Hazard Mater. 1995;43:169-193.

Nielsen M. J Hazard Mater. 1994;48:251-258.

Mohan M, Panwar TS, Singh P. Atmos Environ. 1995;29:2075-2087.

Kunsch JP, Webber DM. J Hazard Mater. 2000;A75:29-46.

Kumar A, Mahukart A, Joshi A. J Hazard Mater. 2003;B101:157-177.

Galkowski A. A unified model for pollutant dispersion in atmosphere and for consequence assessment. In: Borysiewicz MJ, editors. Models and techniques for health and environmental hazard assessment and management. Otwock, Poland: Institute of Atomic Energy, 2006;95-113.

Ramsay SR. Dense gas dispersion in complex settings. Part I: The effects of obstacle, In: Cermak JE, Davenport AG, Plate EJ, Viegas DX, editors. Wind climate in cities. Dordrecht, The Netherlands: Kluwer Academic Publishers; 2001;575-605

Ramsay SR. Dense gas dispersion in complex settings. Part II: The effects of topography. In: Cermak JE, Davenport AG, Plate EJ, Viegas DX, editors. Wind climate in cities. Dordrecht, The Netherlands: Kluwer Academic Publishers; 2001;607-629.

Kukkonen J, Kulmala M, Nikimo J, Vesala T, Webber DM, Wren T. Atmos Environ. 1994;28:2767-2776.

Vesala T, Kukkoken J. Atmos Environ. 1992;26A:1573-1581.

Ditali S, Colombi M, Moreschini G, Senni SJ. Hazard Mater. 2000;71:159-197.

Quaranta N, DeMartini A, Bellasio R, Bianconi R, Marioni M. Environ Monit Softw. 2002;17:487-504.

Scenna NJ, Santa Cruz ASM. Reliab Eng Syst Saf. 2005;90:83-90.

Cox R, Roe D. A model of the dispersion of dense vapour clouds. In: Second international symposium on Loss prevention and safety promotion in the process industries. Heidenberg, Germany: 1977;359-366.

Cox R, Carpenter RJ. Further developments of a dense vapour cloud dispersion model for hazard analysis. In: Hartwig S, editors. Heavy gas dispersion. Dordrecht, The Netherlands: Reidel D, Publishing Company, 1979;55.

Fay JA, Zemba SG. Atmos Environ. 1986;20:1347-1354.

Jagger SF. Development of CRUNCH - a dispersion model for continuous releases of a denser than air vapour into the atmosphere. UK Atomic Energy, Culcheth, Warrington, UK: 1983.

Witlox HWM, McFarlane K. Atmos Environ. 1994;28:2947-2962.

Witlox HWM. Atmos Environ. 1994;28:2917-2932.

Witlox HWM. Atmos Environ. 1994;28:2933-2946.

Spicer TO, Havens JA. J Hazard Mater. 1984;11:237-260.

Colenbrander GW. A mathematical model for the transient behaviour of dense gas clouds. In: Third international symposium on Loss prevention and safety promotion in the process industries. Basel, Switzerland: 1980.

Colenbrander GW, Puttock JS. MAPLIN Sands experiments 1980: interpretation and modelling of liquefied spills on the sea. In: Ooms G, Tennekes H, editors. Atmospheric dispersion of heavy gases and small particles. Berlin: Springer Verlag; 1984;277-286.

te Riele PHM. Atmospheric dispersion of heavy gases emitted at or near ground level. In: Second international symposium on Loss prevention and safety promotion in the process industries. Heidenberg, Germany: 1977;347-357.

Ooms G, Mahiue AP, Zelis F. The plume path of vent gases heavier then air. In: Birschman CH, editors. Loss prevention and safety promotion in the process industries. Hague/Delft, The Netherlands: Elsevier Press; 1974;211-219.

Hoot TG, Meroney RN, Peterka JA. Wind tunnel tests of negatively buoyant plumes. Technical report. Fort Collins, Colorado: Colorado State University; 1973.

Woodward JL. J Loss Prevent Proc Ind. 1989;2:22-32.

Woodward JL, Cook J, Papadourakis A. J Hazard Mater. 1995;44:185-207.

Cleaver RP, Edwards PD. J Loss Prevent Proc Ind. 1990;3:91-96.

Epstain M, Fauske HK, Hauser GH. J Loss Prevent Proc Ind. 1990;3:280-290.

Tickle GA. Heat Transfer, AICHE Symp. Ser. No. 288. 1992;88:350-356.

Khan FI, Abassi SA. J Hazard Mater. 1999;A80:15-30.

Benerjee S, Martini R, Pattison MJ. J Hazard Mater. 1996;46:231-240.

Pattison MJ, Martini R, Benarjee S, Hewitt GF. TransIchem, 76, part B. 1998;31-40.

Bricard P, Friedel L. J Hazard Mater. 1998;59:287-310.

Ooms G, Dijum NJ. Dispersion of stack plume heavier than air. In: Ooms G, Tennekes H, editors. Atmospheric dispersion of heavy gases and small particles, Berlin: Springer Verlag; 1984;1-21.

Zeman O. Atmos Environ. 1982;16:741-751.

Morgan DL Jr, Morris LK, Ermak LR. SLAB - A time dependent computer model for the dispersion of heavy gases released in the atmosphere. UCRL-53383, Livermore, California: Lawrence Livermore National Laboratory; 1983.

Meroney RN. J Hazard Mater. 1984;9:139-157.

Meroney RN. J Hazard Mater. 1984;9:159-170.

Wurtz J. A transient one dimensional shallow layer model for dispersion of denser that air gases on obstructed terrain under non isothermal conditions. JRC Ispra Report EUR 15343, Ispra, Italy: 1993.

Wurtz J, Bartzis J, Venestanos A, Andronopoulos S, Statharas J, Nijsing R. J Hazard Mater. 1996;46:273-284.

Ott S, Nielsen M. Shallow layer modelling of dense gas clouds. Riso-R-90. Roskilde, Denmark: Riso National Labolatory; 1996.

Hankin RKS, Britter RE. J Hazard Mater. 1999;A66:211-226.

Hankin RKS, Britter RE. J Hazard Mater. 1999;A66:227-237.

Hankin RKS. Atmos Environ. 2004;38:695-705.

Hankin RKS. Atmos Environ. 2004;38:707-714.

Hankin RKS. J Hazard Mater. 2003;102:1-10.

Venestanos AG, Bartzis JG, Wurtz J, Papailiou DD. J Hazard Mater. 2003;A 99:111-144.

Brambilla SB. Comp Aided Eng. 2009;26:1147-1152.

Brambilla SB, Manca D, Williams MD, Gowardhan A, Brown MJ. A Shallow water model for dense gas simulation in urban areas. In: Proc. from the symposium on Urban environment. Phoenix, Arizona: American Meteorological Society; 2009 (paper 14.6).

Schreurs P, Mewis J. Development of a transport phenomena model for accidental (heavy gas) releases in an industrial environment. Atmos Environ. 1987;21:765.

Gaffen DJC, Benocci JC, Olivari D. Atmos Environ., 1987;21:1285-1293.

Ermak DL. Dense gas dispersion advection-dfiffusion model. In: Proc. of the JANNAF Safety and environmental protection subcommittee meeting in Monterey, UCRL-JC-109697. Livermore, California: Lawrence Livermore National Laboratory; 1992.

Gopalakrioshnan SG, Sharan M. Atmos Environ. 1997;31:3369-3382.

Williams MD, Brown MJ. Adaptation of the QUIC-PLUME model for heavy gas dispersion. In: Proc. of the symposium on Atmospheric science and air quality. San Francisco: 2005 (session 8.6).

Lee Ch, Kim BG, Ko SY. Atmos Environ. 2007;41:7874-7886.

Brambilla SB. Comp Aided Eng. 2009;26:1147-1152.

Anfossi D, Tinarelli G, Trini Castelli S, Nibart M, Orly C, Commanay J. Atmos Environ. 2010;44:753-762.

Markiewicz M. Environ Prot Eng. 2005;33:75-86.

Markiewicz M. The fundamentals of air pollution dispersion modelling. Warsaw: Warsaw University of Technology Office; 2004 (in Polish).

Sykes RI, Cerasoli CP, Henn DS. J Hazard Mater. 1998;64:223-247.

Donaldson C, Du P. Atmospheric turbulence and the dispersion of atmospheric pollutants. In: Hangen DA, editors. American Meteorological Society Workshop on Micrometeorology. Boston: Science Press; 1973;31-380.

Lewellen LS. Use of invariant modelling. In: Frost W, Moulden TH, editors. Handbook of turbulence. New York: Plenum Press; 1972;237-280.

England WG, Teuscher LH, Hauser LE, Freedman BE. Atmospheric dispersion of a liquefied natural gas vapour cloud using SIGMET, a three dimensional hydrodynamic computer model. In: Crowe CT, Grasshandler WL, editors. Proc from the conference of Heat transfer and fluid mechanics institute. Paolo Alto, USA: Stanford University Press; 1978;4-20.

Havens JR. J Hazard Mater. 1982;6:181-210.

Deaves DM. Application of advanced turbulence models in determining the structure and dispersion of heavy gas clouds. In: Ooms G, Tennekes H, editors. Atmospheric dispersion of heavy gases and small particles. Berlin: Springer Verlag; 1984;93-103.

Deaves DM. J Hazard Mater. 1985;11:341-346.

Deaves DM. J Hazard Mater. 1987;16:427-438.

Ermak DL, Chan ST, Morgan DL, Morris LK. J Hazard Mater. 1982;6:129-160.

Chan ST, Ermak DL, Morris LK. J Hazard Mater. 1987;16:262.

Chan ST. FEM3 A finite element model for simulation of heavy gas dispersion and incompressible flow: User's manual. UCRL-53397. Livermore, California: Lawrence Livermore National Laboratory; 1983.

Taft JR, Ryn MS, Weston DA. MARIAH a dispersion model for evaluating realistic heavy gas spills scenarios. In: Proc of the American Gas Association Transmission Conference, Seattle: 1983.

Riou YJ. Hazard Mater. 1987;16:247-266.

Betts PL, Harountunian V. Finite element calculations of transient dense gas dispersion. In: Puttock JS, editors. Stably stratified flows and dense gas dispersion. Oxford, England: Clarendon Press; 1988;349.

Bartzis JG. ADREA-HF: a three dimensional finite volume code for vapour cloud dispersion in complex terrain. Report EUR 13580. Ispra, Italy: CEC IRC Ispra; 1991.

Builtjes PH. Research on continuous and instantaneous heavy gas releases, TNO-ME Report 92-135, TNO, Appeldorn, Netherlands: 1992.

Bellasio R, Tamponi M. Atmos Environ. 1993;28:1633-1643.

Pereira JCF, Chen XQ. J Hazard Mater. 1995;46:253-272.

Burman J. J Wind Eng Ind Aerodynam. 1998;74-76:515-325.

Duijm NJ. Research on the dispersion of two phase flashing releases- FLADIS. Fladis final report R94-451. Appeldorn, The Netherlands: TNO Environmental and Energy Research; 1994.

Bayanow IM, Gilmullin MZ, Shagapov V. J Appl Mech Tech Phys. 2003;44:858-865.

Ohba R, Kouchi A, Hara T, Vieillard V, Nedelka D. J Loss Prev Proc Ind. 2005;17:325-337.

Scargiali F, Di Rienzo E, Ciofalo M, Grisafi F, Brucato A. Trans Ichem E, Part B - Proc Saf Environ Prot. 2005;83(B5):1-16.

Luketa-Hanlin A, Koopman RP, Ermak DL. J Hazard Mater. 2007;140:504-517.

Hanna SR, Chang JC. Atmos Environ. 2001;35:2231-2242.

Hanna SR, Hansen OR, Dharmavaran S. Atmos Environ. 2004;38:4675-4687.

Hanna SR, Hansen O, Ichard M, Strimatis D. Atmos Environ. 2009;43:262-270.

Sklavounos S, Rigas F. J Hazard Mater. 2004;A108:9-20.

Sklavounos S, Rigas F. Chem Eng Sci. 2006;61:1434-1443.

Sklavounos S, Rigas F. Chem Eng Sci. 2006;61:1444-1452.

Qi R, Ng D, Cormier BJ, Mannan MS. J Hazard Mater. 2010;183:51-61.

Cormier BR, Qi R, Yun G, Zhang Y, Mannan MS. J Loss Prevent Proc Ind. 2009;22:332-352.

Gavelli F, Bullister E, Kytomaa H. J Hazard Mater. 2008;159:158-168.

Gavelli F, Chernovsky MK, Bullister E, Kytomaa HK. J Hazard Mater. 2010;180:332-339.

Qiu TX, Guo YC, Lin WY. Large eddy simulation of heavy gas dispersion around obstacles. In: Zhuang FG, Li JC, editors. New trends in fluid mechanics research: Proc of the fifth international conference on fluid mechanics in Shanghai. Springer Verlag: 2008.

Murakami S, Mochida A, Tominaga Y. Numerical simulation of turbulent diffusion in cities Cermak JE, Davenport AG, Plate EJ, Viegas DX, editors. Wind climate in cities. Dordrecht, Netherlands: Kluwer Academic Publishers; 1995;681-702.

Smagorinsky J. Month Weather Rev. 1963;91:99-164.

Cowan RI, Britter RE. Direct numerical simulation of stable stratified turbulent boundary layer. In: First ERCOFTAC conference on Stably stratified flows. Guildfor, UK: 1992.

Hortel C, Michand M, Stein C. DNS of heavy gas dispersion in plane channel. In: Gavrilakis S, editors. Advances in Turbulence VI. Kluwer Academic Publishers, 1996;585-588.

Ivings MJ, Jagger SF, Lea CJ, Webber DM. Evaluating vapour dispersion models for safety analysis of facilities research project. HSE Report. Fire Protection Research Foundation: 2007.

Ecological Chemistry and Engineering S

The Journal of Society of Ecological Chemistry and Engineering

Journal Information


IMPACT FACTOR 2017: 0.7
5-year IMPACT FACTOR: 0.815

CiteScore 2017: 0.79

SCImago Journal Rank (SJR) 2017: 0.227
Source Normalized Impact per Paper (SNIP) 2017: 0.535

Cited By

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 648 637 31
PDF Downloads 181 179 20