Characteristic overpressure–impulse–distance …

1 Journal of Hazardous Materials A137 (2006) 734 741 Characteristic overpressure impulse distance curves for vapour cloudexplosions using the TNO Multi-Energy modelFernando D az Alonsoa, , Enrique Gonz alez Ferrad asa, Juan Francisco S anchez P ereza,Agust n Mi nana Aznara, Jos e Ruiz Gimenoa, Jes us Mart nez AlonsobaGrupo de Investigaci on Seguridad e Higiene en la Industria , Departamento de Ingenier a Qu mica, Universidad de Murcia, Campus Universitario deEspinardo, 30100 Murcia, SpainbUnidad de Protecci on Civil, Delegaci on del Gobierno en Madrid.

2 C/Garc a Paredes, 65. 28010 Madrid, SpainReceived 20 February 2006; received in revised form 28 March 2006; accepted 1 April 2006 Available online 18 April 2006 AbstractA number of models have been proposed to calculate overpressure and impulse from accidental industrial explosions. When the blast is producedby ignition of a vapour cloud, the TNO Multi-Energy model is widely used. From the curves given by this model, data are fitted to obtain equationsshowing the relationship between overpressure , impulse and distance . These equations, referred herein ascharacteristiccurves, can be fitted bymeans of power equations, which depend on explosion energy and charge allow the determination of overpressureand impulse at each distance .

3 2006 Elsevier All rights : vapour cloud explosion; overpressure ; impulse ; TNO Multi-energy model; Industrial accident1. IntroductionVapour cloud explosions (VCEs) are serious hazards in refin-ing and petrochemical industries[1]. Since the 1970s, whenseveral devastating vapour cloud explosions occurred, a consid-erable degree of attention and research effort has been focussedon this subject[2]. A number of examples of VCE accidents canbe found in the literature[3,4], amongst them the Flixboroughexplosion of June 1, 1974, which was especially was caused by the uncontrolled leakage of about 30 tons ofcyclohexane at the Nypro plant in Flixborough, UK.

4 A few min-utes after the leakage started, the cyclohexane cloud ignitedand a violent explosion occurred, causing the death of 28 menand severe damage to on-site infrastructure[5]. Another seri-ous industrial accident occurred at Beek in The Netherlandson November 7, 1975, when a violent VCE occurred withina naphta-cracker installation. The explosion resulted in sev- Corresponding author at: Departamento de Ingenier a Qu mica, Facultad deQu mica, Universidad de Murcia, Campus Universitario de Espinardo, 30100 Murcia, Spain.

5 Tel.: +34 968 36 39 37/34 968 36 39 36; fax: +34 968 36 41 Alonso).eral fatalities, destroyed the installation and resulted in severedamage to the immediate surroundings with window break-age up to km from the source[6]. Apart from these twoexamples, many other VCEs have occurred and, unfortunately,these types of devastating accidents still happen. Regarding themagnitude of an explosion, the two most important and danger-ous factors are overpressure and impulse (the latter dependingon overpressure and positive phase time duration)

6 , which arechiefly responsible for injury to humans, and structural and envi-ronmental 1shows some damages for differentoverpressures and assess damage, models are necessary to calculate the mag-nitude of an explosion as a function of distance from the , with proper safety guidelines, appropriate struc-tural design and safe distance considerations, blast hazards fromVCEs could be reduced to acceptable levels[1].For vapour cloud explosions, the TNO Multi-Energy model isoften used to determine overpressure and positive phase durationtime as a function of distance [7].

7 Lees[3]makes referenceto this method in his textbook. The Multi-Energy concept isbased on the observation that the explosive potential of a vapourcloud is primarily determined by the obstructed and/or partiallyconfined parts of the cloud[8]. Some data have been obtained and0304-3894/$ see front matter 2006 Elsevier All rights Alonso et al. / Journal of Hazardous Materials A137 (2006) 734 741735 Nomenclatureaparameter used in fitted scaled overpressure equa-tion Eq.(8)bexponent of the fitted scaled overpressure equa-tion Eq.(8)cparameter used in fitted scaled impulse equation Eq.

8 (9)c0sound velocity in air (340 m/s)dexponent of the fitted scaled impulse equation Eq.(9)Eexpexplosion energy (J)iimpulse (Pa s)i scaled impulse (dimensionless)Kconstant overpressure value from Eq.(10)(Pa).Psside-on overpressure (Pa)P0atmospheric pressure (Pa)P scaled overpressure (dimensionless)R scaled distance (dimensionless)tppositive phase duration time (s)t pscaled positive phase duration time (dimension-less)zdistance to the explosion s centre (m)Greek symbols parameter used in Characteristic equation Eq.(11) exponent of the Characteristic equation Eq.

9 (11)analysed from explosion experiments[9,10]and several authorshave proposed methodologies to select the appropriate chargestrength[11 14]. The Multi-Energy model is widely used forconsequence analysis[15 19], also for domino hazards[20].This model uses the following parameters:P =PsP0(1)R =z(Eexp/P0)1/3(2)tp=t p(Eexp/P0)1/3c0(3)i=1/2 Pstp(4)whereP (dimensionless) is the scaled overpressure ;Ps(Pa) isthe side-on overpressure ;P0(101 000 Pa) is atmospheric pres-sure;R (dimensionless) is the scaled distance ;z(m) is thedistance from the explosion centre;c0(340 m/s) is sound veloc-ity in air;i(Pa s) is the wave s impulse ;tp(s) is the positivephase duration time.

10 T p(dimensionless) is the scaled positivephase duration time andEexp(J) is the explosion TNO Multi-Energy model does not solve the relationshipbetween impulse and scaled distance . Since this relationship isnecessary for the aim of this paper, Eqs.(1), (3)and(4)arecombined to obtain:i=1/2(P2/30E1/3exp/c0)P t p(5)A new dimensionless parameter calledscaled impulseisdefined, as follows:i =P t p(6)and from Eq.(5), the following is obtainedi =2[c0(P2/30E1/3exp)]i(7)showing the relationship between impulse (i) and scaled impulse (i ). From eachR value (corresponding to each distance ), thescaled impulse is calculated (Eq.)