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Journal of Loss Prevention in the Process Industries 31 (2014) 16e25

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Journal of Loss Prevention in the Process Industries

journal homepage: www.elsevier .com/locate/ j lp

New correlation for vapor cloud explosion overpressure calculation atcongested configurations

Jingde Li a, Madhat Abdel-jawad b, *, Guowei Ma a

a School of Civil and Resource Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australiab GexCon Australia, 8/64 Fitzgerald Street, Northbridge, WA 6003, Australia

a r t i c l e i n f o

Article history:Received 4 December 2013Received in revised form27 May 2014Accepted 29 May 2014Available online 21 June 2014

Keywords:ConfinementCongestionBlockage ratioObstacle diameterFlame path

* Corresponding author.E-mail addresses: jaden_li@hotmail.com (J. Li), ma

jawad), ma@civil.uwa.edu.au, guowei.ma@uwa.edu.au

http://dx.doi.org/10.1016/j.jlp.2014.05.0130950-4230/© 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

In this study, we present a newly developed correlation for the estimation of boundary overpressures inand around congested regions subjected to vapor gas explosions. The GAME correlation, which is basedon the MERGE, EMERGE experimental programs, shows rather moderate correlation with computationalfluid dynamics (CFD) results in homogeneously congested configurations, however, a greater level ofinaccuracy is found when it comes to the combination of a number of realistic scenarios. The newlydeveloped model (confinement specific correlation), which consists parameters of volume blockageration, the density of the gas, the flame path distance, the confinement ratio and the laminar flame speedof the flammable gas is proposed as a non-dimensional alternative and it shows a closer correlation withdetailed CFD simulation in general particularly for realistic geometries. A linear least square method isused to achieve the best fitting parameters by applying the validated commercial software FLACS. About400 CFD cases with homogenous congestions are modeled using FLACS for the purpose of testing boththe GAME correlation and the confinement specific correlation (CSC). In addition to those 400 CFD ho-mogenous cases, around 700 realistic cases in ten different module scenarios of a Liquefied Natural Gas(LNG) train along with three simplified models are simulated to validate the CSC; it is found that the CSCis applicable to both realistic modules with irregular obstacles and homogenous artificial modules.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Explosions and fires in the process industry (Mannan, Aldeeb, &Rogers, 2002) can result in large financial and environmentaldamages in addition to potential injury and loss of life. Typicalmajor industrial accidents include vapor cloud explosions (VCE),Boiling Liquid Expanding Vapor Explosions (BLEVEs) and dust ex-plosions. The VCE is defined as “an explosion resulting from anignition of a premixed cloud of flammable vapor, gas or spray withair, in which flames accelerate to sufficiently high velocities toproduce significant overpressure” (Mercx & van den Berg, 2005).Although analytical methods for the calculation of overpressuresarising from accidental inventory releases and subsequent delayedignition of resulting gas clouds leading to explosions have longbeen in use, these methods hold significant uncertainty becausethey do not adequately account for several important parameters,

dhat@gexcon.com (M. Abdel-(G. Ma).

particularly the role that congestion and confinement play in flameacceleration and hence the overpressures arising. In particular,methods such as the multi-energy method (MEM) can be in errorby more than an order of magnitude because they do not take intoaccount the geometry detail of most industrial layouts and also relyon estimates of explosion strength and congestion input by theengineer. Where such methods are applied conservatively, theestimated overpressure can be much higher than in a real event,leading to significant financial overspends. Conversely, where theseestimates are under-conservative (which is a possibility with thesemethods even when thought to be applied conservatively), theresults can be catastrophic.

Computational fluid dynamics (CFD) is by far the most detailedmethodology for quantifying the risk posed by this class of cata-strophic events. However, despite significant advances deployed inCFD, it remains computationally and labor intensive. There is,therefore, a need for the development of faster analytical modelsthat can be appliedwith far less effort yet still capture the dominantmechanisms for gas dispersion and flame propagation and flameacceleration. Here we present a correlation that better accounts forimportant details of complex geometries, which enables this

J. Li et al. / Journal of Loss Prevention in the Process Industries 31 (2014) 16e25 17

correlation to be more accurate that existing analytical methodswhile offering greater implementation speed compared to existingCFD methods.

Simpler methods such as the TNT-equivalency method (Safety,1994) and TNO Multi-Energy Method (MEM) (Alonso et al., 2006;Gugan, 1979; Lobato, Canizares, Rodrigo, Saez, & Linares, 2006;Vandenberg, 1985), are often adequate for the estimation of farfield pressures where the explosion field displays little direction-ality. The TNT-equivalency method uses the blast generated by anequivalent amount of TNT to describe the strength of the vaporcloud explosion and the decay of the blast as a function of distance.However, it is inherently assumed that the overpressures generatedare equal in all directions with no accounting for directional effects,and it is hard to achieve the correlation between the quantity of fuelinvolved in the explosion and the equivalent-charge weight of TNTrequired to model its blast effect (Gugan, 1979). Therefore, thismethod has limited applicability in scenarios where the layouts aredirectionally irregular. Further, it is difficult to set up a standard toconvert the equivalent charge weight of TNT, in most cases, theeffects of VCE in the near field can be either overestimated orunderestimated.

The Multi-Energy Method (MEM), which is regarded as a morereasonable simple and practical method alternative (Mercx, vanden Berg, Hayhurst, Robertson, & Moran, 2000), is also only reli-able for the calculation of far field pressures. MEM uses over-pressure results phenomenologically derived from several fromsimplified numerical solutions of idealized gas explosions (vanWingerden, Hansen, & Foisselon, 1999). MEM has shortcomingssimilar to those of TNT equivalence method in that they both as-sume the gas pressure fields are radial. MEM is also ultimatelybased on a selected severity from 1 to 10 entirely at the discretion ofthe engineer applying the method with no mathematical basis forthe selection.

The shortcomings in MEM led to the development of a Guidancefor the Application of the Multi-Energy method (GAME) (Eggen,1995). GAME was designed to provide additional guidance and toextend its applicability to cases where MEM is designed to address.The phenomenological approach, which is effective for qualitativeresearch projects (Alfred,1976; Edmund,1989; Gurwitsch&Garcia-Gomez, 2009), is used to derive the GAME correlation based on theexperimental research programs performed during the MERGE andEMERGE projects (EMEG, 1997; Harris & Wickens, 1989; Mercx,Johnson, & Puttock, 1995; Schumann, Haas, & Schmittberger,1993; Wingerdenv, 1988, 1989) at the Dutch research institute TNO.

As seen in the report (Eggen, 1995), satisfactory correlation withlimited experiments were obtained by using GAME correlation, andthe it is a safe approach in the determination of the overpressure inmost situations characterized by artificially homogenous conges-tion and confinement.

To set up such experimental tests is a very expensive task andthere is a significant limit on the quality of possible tests in that it isvery difficult to create realistic fields of congestion and confine-ment at the appropriate scale. Further, the reliability and repeat-ability of the tests are often very difficult to achieve because somefactors such as initial turbulence, the stability of the wind directionand speed as well as the flexibility of some structural components isvery difficult to characterize or account for. Hence we have chosento compare the results from our new correlation as well as resultsfrom the GAME correlation against the highly validated well-established CFD software FLACS. This allows us to examine hun-dreds of cases including those for realistic geometries at realisticscales which would be impossible to set up without tens of years ofsignificant spend.

Our new correlation presented in this study is validated againstwidely-accepted CFD commercial software FLACS, which itself has

been the validated over the last 40 years against numerous ex-periments and previous work (Bleyer, Taveau, Djebaili-Chaumeix,Paillard, & Bentaib, 2012; Hansen, Gavelli, Ichard, & Davis, 2010;Middha, Hansen, Grune, & Kotchourko, 2010; Middha, Hansen, &Storvik, 2009). The FLACS CFD solvers account for the parameters ofthe congestion (Bakke, van Wingerden, Hoorelbeke, & Brewerton,2010; Davis & Hanen, 2010; Hansen, Hinze, Engel, & Davis, 2010;Huser, Foyn, & Skottene, 2009), the flame path distance and thelaminar flame speed of the flammable gas (Chen, Qin, Xu, Ju, & Liu,2007; Pfahl, Ross, Shepherd, Pasamehmetoglu, & Unal, 2000;Silvestrini, Genova, & Trujillo, 2008) which were derived by usingthe idealized experimental programs' data, the new correlationwasdeduced with a set of parameters by means of the linear leastsquare method to describe the obstructed region and the fuelproperties in the vapor cloud explosion.

By comparing the results from 1100 simulation cases carried outusing FLACS, we are able to compare the estimate the overpressuresfrom the new correlation and the GAME correlation for vapor cloudexplosions in realistically congested areas, taking into account thecomplexity of the geometry; and the congestion and confinementwith a well validated benchmark.

2. The GAME correlation and case studies

In this section, the GAME correlation is introduced and inves-tigated by comparing its results with those of FLACS for bothrealistic and idealized configurations from CFD simulations.

As originally derived from experiments, two variants of theGAME correlationwere given in the GAME project to determine thevapor cloud explosion overpressure (Eggen, 1995).

For low ignition energy and no confinement in 3D flameexpansion conditions:

DPo ¼ 0:84$�VBR$Lf

D

�2:75

S2:7l $D0:7 (1)

For low ignition energy and confinement between parallelplates (2D expansion):

DPo ¼ 3:38$�VBR$Lf

D

�2:25

S2:7l $D0:7 (2)

where:

DPo ¼ the overpressure [barg],VBR¼ the volume blockage ratio, which is defined as the ratio ofthe total volume of the obstacles inside an obstructed region,Lf ¼ the maximum distance of flame propagation obtained byassuming Lf equal to the radius of a hemisphere with a volumeequal to the volume of the configuration [m],D ¼ the average obstacle diameter, which give a single averagevalue for the whole obstructed region by assuming a homoge-nous distribution of obstacle types and obstacle diameters [m],Sl¼ the laminar flame speed of the flammable gas by assuming ahomogenous stoichiometric flammable cloud in all assessment[m/s].

2.1. Modules tested in CFD simulations

CFD simulations were carried out to validate the results fromboth the GAME correlation and the newly developed correlation.The overpressures arising from the CFD simulations were extrac-ted for the purpose of comparison with results from bothcorrelations.

J. Li et al. / Journal of Loss Prevention in the Process Industries 31 (2014) 16e2518

The commercial software FLACS, which is a reliable tool forprediction of vapor cloud explosions in petrochemical process areaoffshore and onshore, is used here as the benchmark against whichthe GAME correlation and the newly developed correlation pre-sented here. FLACS is a specialized CFD solver developed especiallyto model dispersion of flammable or toxic gas, gas explosions andpropagation of blast and shock waves, in complex, large-scale,three-dimensional (3D) geometries.

The CFD simulations were performed for three artificial caseswith homogenous congestion along with five realistic and inho-mogeneous configurations as shown in Figs. 1 and 2. For the arti-ficial modules 1e3 (Fig. 1), all module sizes are 80 � 80 � 80 (m),and the obstacles in the configurations are arranged orthogonallyby filling the pipes of diameter of 0.5 m. The five realistic modulesare from a Liquefied Natural Gas (LNG) train. The explosions areconducted in the fractionation area, the pipe rack area and thecombination areas of the pipe racks and the mercury removal anddehydration areas, respectively (Fig. 2).

Overall, three artificial modules subjected to propane vaporexplosions, five methane vapor explosions of realistic modules andanother five propane vapor explosion of the same realistic modulescomposes the 13 module cases as seen in Table 1. And for all themodules, the values of volume blockage ratio, the laminar flamevelocity, the characteristic average obstacle diameter and the gascomposition, as shown in Table 1, are extracted to calculate theoverpressure in the following section.

2.2. Validation results of GAME correlation in case studies

By using the CFD configurations listed above, the applicabilityand accuracy of GAME correlationwere investigated in this section.Three models of modules with artificial configurations wereinitially created with a uniform distribution of cylinders similar tothose in the experiments upon which the GAME correlation wasdefined. Due to the homogeneity of the obstacle arrangement andmeshing grid, the CPU time for each calculation of the artificialconfiguration was relatively short (i.e. within 1 h).

The confinement of the modules was controlled with theinsertion of parallel plates, and hence equation (2) of the GAMEcorrelations was employed. It is seen in Fig. 3 that the values of thecorrelation R-squared factor (which indicates how well data pointsfit a line or curve), for the first two homogenous cases are 0.78 and0.51 respectively when applying the linear least square method.These values show that the GAME correlation is valid for congestionconfigurations that are filled with the regular-patterned pipeswithin a certain range of the confinement. However, as the area ofthe top plate decreases, negative R-squared values (�0.32) are seenin the homogenous case 3 with partially confined roof, Fig. 3. Themain reason is that the confinement effect is not accounted for inthe GAME correlation. By varying the confinement (Fig. 1) with the

Fig. 1. Artificial m

other parameters kept constant, the overpressures of those threehomogenous scenarios obtained in the GAME correlation remainthe same, while the pressures are reduced due to the decrease ofconfinement in the results of FLACS simulations, which means theoverpressures are overestimated by the GAME correlation in thelow confinement case.

The results given by the GAME correlation described abovedemonstrate that the lack of appropriate definition of confinementwithin the GAME equation result in an increasing error when thisparameter becomes important. They also show that GAME can onlygive satisfactory results when the confinement is within a certainrange.

In addition to these three artificial configurations, another 5realistic configurations (Fig. 2) were also investigated, for each ofthose realistic cases; the CPU time was increased to the range of1e3 h each due to the complexity of the geometries and longercalculation time of the flame turbulence development within theirregularly congested regions. As those realistic cases (case 4e13)were included in the comparison, the overall correlation betweenthe GAME results and FLACS data gives a poor value as seen in Fig. 4,which can be attributed to the geometric inhomogeneity of therealistic geometric configurations in addition to the lack of appro-priate modeling of confinement. The GAME correlations werederived from MERGE experiments which have a highly regularpattern of obstacles, all of which are idealized as cylinders andhomogeneously distributed in the obstructed region.

When the repeatability of obstacles, equal obstacle spacing andthe obstacle diameter were carefully chosen the GAME correlationproduced results moderately close to those predicted by CFD.However as seen in Fig. 4, for realistic modules with inhomoge-neous congested volumes, the GAME correlation has poor predic-tion of overpressures and the GAME correlation often over-predictsbut sometimes under-predicts the overpressures significantly.

In summary the GAME equations shows a very poor correlationto numerically simulated results when all realistic modules areincluded, it only gives a moderate R-squared value for the idealizedcase created with a homogenous distribution of congestion. Thelack of consideration of congestion inhomogeneity and the defini-tion criteria of confinement hinders the applicability of GAMEcorrelation in practical problems. Those issues are improved anddeveloped in the following section by introducing a newcorrelation.

3. Parametric studies and development of a new correlation

Confinement was introduced and defined in a confinementspecific correlation (CSC); other critical parameters were chosen tomodel other factors as was done for the GAME correlationdescribing the physical phenomenon of gas explosion. The deriva-tion of the CSC was based on the linear least square method with a

odules 1e3.

Fig. 2. Realistic modules 4e8.

Table 1Parameters in difference modules.

Case no. Gas composition D (m) VBR Sl(m/s)

Gas density(kg/m3)

Cm

1. Module 1 Pure propane 0.50 0.070 0.46 1.8 1.0002. Module 2 Pure propane 0.50 0.070 0.46 1.8 0.9253. Module 3 Pure propane 0.50 0.070 0.46 1.8 0.8884. Module 4 Pure methane 0.37 0.040 0.4 0.65 0.7165. Module 5 Pure methane 0.45 0.058 0.4 0.65 0.7076. Module 4 Pure propane 0.37 0.040 0.46 1.8 0.7167. Module 5 Pure propane 0.45 0.058 0.46 1.8 0.7078. Module 6 Pure methane 0.12 0.080 0.4 0.65 0.9179. Module 7 Pure methane 0.34 0.103 0.4 0.65 0.98010. Module 8 Pure methane 0.31 0.096 0.4 0.65 0.90311. Module 6 Pure propane 0.12 0.080 0.46 1.8 0.91712. Module 7 Pure propane 0.34 0.103 0.46 1.8 0.98013. Module 8 Pure propane 0.31 0.096 0.46 1.8 0.903

J. Li et al. / Journal of Loss Prevention in the Process Industries 31 (2014) 16e25 19

subset of the simulations. In order to appropriately isolate theimportant set of parameters, all the CFD cases in this subset(approximately 400 cases) were simulated as homogenous models;the distributions of pipes were arranged in regular patterns byhand.

3.1. Conceptual definition of confinement and congestion

Both confinement and congestion, which are parameters thataffect turbulence induced flame acceleration, which has a signifi-cant effect on overpressures (Bradley, Lawes, & Liu, 2008; Harrison& Eyre, 1987; Moen, Donato, Knystautas, & Lee, 1980; van den Berg& Mos, 2005).

For the GAME correlation, the congestion was defined using thevolume blockage ratio (VBR) divided by the average pipe diameter.This is a very useful parameter; however the manner in which it isapplied does not take into account the fact that changing the

(a)Case 1 (b) Case 2 (c) Case 3

y = xR² = 0.78

0123456

0 2 4 6

FLAC

S (B

arg)

GAME (Barg)

y = xR² = 0.51

0123456

0 2 4 6

FLAC

S (B

arg)

GAME (Barg)

y = xR² = -0.32

0123456

0 2 4 6

FLAC

S (B

arg)

GAME (Barg)

Fig. 3. The comparison of GAME correlation overpressure results vs. FLACS results for homogenous cases subject to propane vapor explosions.

J. Li et al. / Journal of Loss Prevention in the Process Industries 31 (2014) 16e2520

congestion inherently changes the confinement which is demon-strated in this section below. In addition, the manner in which thecongestion parameter was applied for the GAME correlation ap-pears to weight VBR and the characteristic pipe diameter equally.Here we investigate the isolation of a unique confinement param-eter and different weighting of VBR in relation to the characteristicpipe diameter as part of the overall congestion parameter.

We defined the conceptual confinement ratio as the totalblocked edge area of a space divided by the total volume of thespace, i.e. ABlocked/ATotal. Then for a cubic volume (of dimension1 m � 1 m � 1 m) with six open sides, the conceptual confinementratio ABlocked/ATotal ¼ 0/6 (m2/m2

), while the fully confined cube hasthe conceptual confinement ratio ABlocked/ATotal ¼ 6/6 ¼ 1 whichmeans the more the surface area being blocked the greater theconfinement of the cube. It follows that for a partially confinedvolume with 2 sides fully blocked; the ratio is 1/3.

For the same cube (dimension 1 m � 1 m � 1 m) with six opensides and with conceptual confinement ratio ABlocked/ATotal ¼ 0, byplacing a pipe with dimension of 1 m length and 0.4 m diameter inthe center of the cube, as seen in Fig. 5, the congestion volume inthe cube becomes 0.126m3 (the volume of the pipe) whereas it was0 m3 in the empty space. Commensurately, the volume blockageratio (VBR ¼ Vblockage/Vtotal) increased from 0/1 (m3/m3) to 0.126/1(m3/m3), meanwhile the conceptual confinement ratio of the cubeincreases from 0/6 (m2/m2) to 0.25/6 (m2/m2), 0.25 m2 is the totalarea of the top and bottom cross section of the pipewhich reach thesurfaces of the cube on two size. It is clear that a change incongestion influences the confinement of the configurationsimultaneously, the confinement and congestions should be

y = x

0.01

0.1

1

10

100

0.01 0.1 1 10 100

FLAC

S (B

arg)

GAME (Barg)

case 1case 2case 3case 4case 5case 6case 7case 8case 9case 10case 11case 12case 13

Fig. 4. Overall results of GAME correlation vs. FLACS simulation from all cases.

considered together as two interactional factors to determine theexplosion pressure.

3.2. Definition of parameters

Six parameters are taken into account in determining theoverpressure in a vapor could explosion event. They include theconfinement ratio, the volume blockage ratio, the characteristicobstacle diameter, the flame propagation path, the laminar flamespeed and the gas density. In order to investigate their relativeimportance in the determination of the overpressures from ex-plosions, parametric studies were conducted and compared to theoutput from CFD simulations using the software FLACS.

3.2.1. Confinement effectIn accordance with the 2D expansion of the GAME correlation,

simulations were conducted using a geometric configuration thathad parallel plates, the confinement was then defined as

Cm ¼ AB

AT(3)

The blocked area AB is the sum of obstructed areas on the topand bottom of the domain simulated; AT is the total area of the topand bottom surfaces. As seen in Fig. 1, the confinement parameterwas regulated by reducing the blocked surface on the top of thegeometries modeled using FLACS, while the averaged diameter andvolume blockage ratio as well as other parameters were fixed atcertain values. 24 CFD simulations with 6 different confinementlevels were performed to investigate the effect of the confinementparameter on overpressure. It is seen that the pressure varies withconfinement according to:

Po eexpð8:5$CmÞ (4)

where Po is the overpressure calculated at different monitor pointsin along the explosion flame path (Fig. 6).

Pipe (1m length, 0.4m diameter)1m*1m*1m Open air cube

Place a pipe inside

Fig. 5. Conceptual definition of confinement and congestion.

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.1 0.2 0.3

Pres

sure

from

corr

ela

on P

o (B

arg)

Confinement Exp(8.5*Cm)

Lf=64.3m

Lf=67.3m

Lf=70.9m

Lf=76.8

Lf=64.3mtrendlineLf=67.3mtrendlineLf=70.9mtrendlineLf=76.8mtrendline

Fig. 6. Simulation results of confinement effect and trendlines for the CFD cases.

J. Li et al. / Journal of Loss Prevention in the Process Industries 31 (2014) 16e25 21

3.2.2. Effects of VBR and the average obstacle diameter DThe GAME correlation uses the equally weighted volume

blockage ratio (VBR) and the characteristic obstacle diameter (D) asthe basic predictors of congestion. However, in order to address theissue of irregular congestion, the VBR was differently weighted inthe correlation developed here, and the averaged obstacle diameterwas investigated separately.

The volume blockage ratio here was defined as the ratio ofobstruction volume within the domain from the ignition point tothe target point to the total configuration volume, so for eachspecific target of interest, there is a unique VBR to calculate theoverpressure.

Applying the results from 8 cases with different VBR resulting ina total of 32 CFD cases, the parameter of VBRwas variedwhile otherparameters kept constant (e.g. constant Cm ¼ 1) to determine theeffect of VBR in correlation with overpressure. Similarly, 25 CFDsimulations with 5 different averaged obstacle diameters (D) wereconducted to investigate the relationship between overpressureand averaged obstacle diameter while the VBR and the other pa-rameters were fixed. The similar slopes are seen in Fig. 7(a) and (b)respectively, which indicates that for all cases the correlationamong overpressure, VBR and D are:

Po e1:6 lnðVBRÞ þ 6 (5)

(a) Parameter of VBR

0

0.5

1

1.5

2

2.5

3

3.5

1 2 3

Pres

sure

from

corr

ela

on P

o (B

arg)

Volume blockage ra o 1.6ln(VBR)+6

Lf=39.9m

Lf=42.3m

Lf=45.6

Lf=46.7m

Lf=39.9mtrendline

Lf=42.3mtrendline

Lf=45.6mtrendline

Lf=46.7mtrendline

Fig. 7. Simulation results and tr

Po e�DH

��1:5

(6)

where H is the height of the configuration.

3.2.3. Maximum distance of flame propagationThe maximum distance of flame propagation (Lf) in the CSC was

defined as the direct distance from the ignition location to thetarget point of overpressure in contradistinction to the assumptionin the GAME project that Lf was equal to the radius of a hemispherewith a volume equal to the volume of the configuration, whichmakes the CSC easier and more convenient to use. About 300 CFDsimulation cases were included in the investigation. The trendlinesfor all cases show similar slopes In Fig. 8 with the power of 2.2 ofthe maximum distance of flame propagation, namely:

Po e�LfH

�2:2

(7)

3.2.4. Mass density and laminar flame speed of gasFor these two parameters, 13 explosion scenarios consist of

approximately 1100 simulation cases were conducted by using twodifferent gases which were methane and propane with twodifferent mass densities and two different laminar flame speeds.The approach taken here was to use the phenomenological methodto analyze all the available data. The last correlation for massdensity and laminar flame speed with power of 0.5 and 2 wassubsequently found by minimizing the total variance of the com-plete correlation against CFD results.

3.3. New proposed correlation

With the parameters of confinement, volume blockage ratio, theaverage obstacle, laminar flame velocity and gas density derived inthe manner described above, the new dimensionless correlation(CSC) is given by:

DPoPair

¼ 0:037$e8:5Cm$½1:6 lnðVBRtÞ

þ 6�$�LfH

�2:2

$

�DH

��1:5

$

�rgas

rair

�0:5

$

�SlSs

�2

(8)

where:

(b) Parameter of D

0

2

4

6

8

10

12

14

0 5 10 15

Pres

sure

from

corr

ela

on P

o (B

arg)

Averaged obstacle diameter (D/H)-1.5 (m)

Lf=45.6m

Lf=48.7m

Lf=49.7m

Lf=51.7m

Lf=64.3m

Lf=45.6mtrendlineLf=48.7mtrendlineLf=49.7mtrendlineLf=51.7mtrendlineLf=64.3mtrendline

endlines for the CFD cases.

1

1.5

2

2.5

3

3.5

4

4.5

5

0 20 40 60 80

Pres

sure

from

corr

ela

on P

o (B

arg)

Maximum distance of flame propaga on (Lf/H) 2.2 (m)

Corner igni onCm=1

Corner igni onCm=0.925

Edge igni onCm=0.85

Corner igni onCm=1 trendline

Corner igni onCm=0.925trendlineEdge igni onCm=0.85trendline

Fig. 8. Simulation results of flame propagation maximum distance effect and trend-lines for the CFD cases.

Fig.to t

J. Li et al. / Journal of Loss Prevention in the Process Industries 31 (2014) 16e2522

DPo ¼ the escalation overpressure [barg],Pair ¼ 1 standard atmospheric pressure 101.325 kPa [1 barg],D ¼ the average obstacle diameter [m],Lf ¼ the direct distance from the ignition location to the targetpoint [m],Sl ¼ the laminar flame speed of the flammable gas [m/s],Ss ¼ the speed of sound [m/s],Cm ¼ the confinement ratio,VBRt ¼ the volume blockage ratio of configuration region fromthe ignition point to the target,rgas ¼ mass density of gas (kg/m3) (the gas density is assumedideally under one standard atmosphere pressure at normaltemperature 26� in this study),rair ¼ mass density of air (kg/m3),H ¼ the height of the configuration (m).

3.4. Validation of the new correlation

In the validation of CSC, about 1100 realistic and idealized vaporcloud explosion simulations from the modules in Figs. 1 and 2 wereconducted to compare the results of CSC with FLACS data. Theobstacle configurations were filled with equivalent stoichiometricflammable gas cloud in the simulations; methane and propanewere used as fuels in this study. The parameters are shown inTable 1.

As seen in Fig. 9, the comparison of the overall results betweenthe pressures yielded by the CSC and the simulation results fromFLACS is remarkable the R-squared value yielded by this

y = xR² = 0.8395

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12 14 16

Pres

sure

in F

LACS

(Bar

g)

Cofinement Specific Correla on (CSC) calculated pressure (Barg)

9. Overall R-squared values of CSC vs. FLACS results for 13 simulation cases subjectwo types of gas vapor explosions.

comparison is 0.8395. For individual cases as shown in Fig. 10, thecorrelation factor R-squared is within the moderate range of0.44e0.90, which means the CSC applies to all realistic and ideal-ized modules very well. In terms of the homogenous case 1e3 withdifferent confinement, the factors of R-squared in CSC are 0.886,0.608, 0.464 respectively, which are closer to the CFD results thanfor the GAME correlation. Overall, the CSC equation correspondingto the confinement criteria can be effectively utilized to the prac-tical problems with different congestion and confinementconditions.

4. Discussion

Although the GAME correlation includes the volume blockageratio and the characteristic pipe diameter together in an attempt toaccount for congestion, the confinement of the combusting gas isnot thoroughly examined in the experimental programs. It isshown in Section 3 that a change in congestion necessarily affectsthe confinement, and the change can be significant. Confinementplays a major role in the evolution of combustion and the over-pressure magnitudes generated. In real explosion situations, thetwo parameters of confinement and congestion should be bothexplicitly accounted for in the calculation of explosionoverpressure.

Secondly, the acceptable results can only be obtained from theGAME correlation when it is used in the situations where obstaclesare homogeneously distributed; indeed the hydraulic averageobstacle diameter is taken into account to investigate the conges-tion effect on the overpressure calculation. However, in the prac-tical scenarios where there is inhomogeneous distribution ofobstructions, the explosion overpressure will vary significantly andthis will result in overpressure being overestimated as a result ofusing GAME correlation based on the averaged parameters ofobstacle diameter.

Another critical parameter to determine the vapor explosionpressure is the flame path length, which has, for the GAME corre-lation, been assumed to be equal to the radius of a hemispherewitha volume equal to the volume of the obstructed region (Mercx, vanden Berg, & van Leeuwen, 1998). Hence, for cases that ignition lo-cations at the edge/corner of the configurations and the aspect ratioof configurations larger than 1, it creates the question that how toconvert or determine the flame path length appropriately. Thisuncertainty results in an uncertainly in the overpressure throughthe use of the GAME correlation, which also makes the GAMEcorrelation difficult to be applied in realistic scenarios.

Finally, and interestingly, one notes that the GAME correlation isdimensionally unbalanced, i.e. the dimensions of the right handside of the equation do not match those for the left hand side. Thisindicates that there are either too few or too many parameters andindicates that there will also exist cases where this equation is notappropriately applicable.

On the other hand, the applicability of the newly developedcorrelation is greatly improved, and the issues about confinementand congestion are addressed.

The greatest difference between the two correlations is that theconfinement Cm which was not accounted for separately in theGAME correlation was introduced in CSC. In order to invoke twodifferent GAME equations to calculate the overpressure, the gasexplosions were classified into three categories, namely 1D, 2D and3D expansions depends on the degree of confinement. However,the way in which the GAME distinguishes between the 2D and 3Dflame expansion lacks detail; for instance, configurations with ex-plosion charge confined by parallel planes were deemed to be 2Dexpansion to enable Eq. (2) applying to all such cases, which resultsin very large errors for those cases with partially confined top.

(1) Case 1 (2) Case 2 (3) Case 3

y = xR² = 0.886

0

1

2

3

4

5

6

7

0 5

FLAC

S (B

arg)

CSC (Barg)

y = xR² = 0.608

0

1

2

3

4

5

6

0 5

FLAC

S (B

arg)

CSC (Barg)

y = xR² = 0.464

0

1

2

3

4

5

0 5

FLAC

S (B

arg)

CSC (Barg)

(4) Case 4 (5) Case 5 (6) Case 6 (7) Case 7

(8) Case 8 (9) Case 9 (10) Case 10 (11) Case 11

(12) Case 12 (13) Case 13

y = xR² = 0.441

0

0.005

0.01

0.015

0.02

0.025

0 0.02

FLAC

S (B

arg)

CSC (Barg)

y = xR² = 0.486

0

0.005

0.01

0.015

0.02

0.025

0.03

0 0.02

FLAC

S (B

arg)

CSC (Barg)

y = xR² 0.585

0

0.01

0.02

0.03

0.04

0.05

0 0.05

FLAC

S (B

arg)

CSC (Barg)

y = xR² = 0.767

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 0.05

FLAC

S (B

arg)

CSC (Barg)

y = xR² = 0.765

0

1

2

3

4

5

6

7

0 5

FLAC

S (B

arg)

CSC (Barg)

y = xR² = 0.485

0

1

2

3

4

5

6

7

0 5

FLAC

S (B

arg)

CSC (Barg)

y = xR² = 0.561

0

1

2

3

4

5

6

7

8

9

0 5

FLAC

S (B

arg)

CSC (Barg)

y = xR² = 0.644

02468

101214161820

0 10 20

FLAC

S (B

arg)

CSC (Barg)

y = xR² = 0.787

02468

101214

0 5 10

FLAC

S (B

arg)

CSC (Barg)

y = xR² = 0.90

02468

101214

0 5 10

FLAC

S (B

arg)

CSC (Barg)

Fig. 10. The comparison of CSC overpressure results vs. FLACS results for 13 cases subject to methane and propane vapor explosions.

J. Li et al. / Journal of Loss Prevention in the Process Industries 31 (2014) 16e25 23

Therefore, a criterion was established in the CSC, the confinementwas well defined by considering the ratio of blocked area to totalsurface area of the configuration, the improved correlation of theCSC equation's results and the FLACS data are seen in Fig. 10.

Secondly, in the CSC, the volume blockage ratio and the averagediameter were investigated separately with unequal weightings toquantify the congestion. Unlike the parameters D and VBR in GAMEcorrelation, the volume blockage ratio of configurationwas definedas it in the calculation volume from the ignition point to the target,the overpressure calculation in the configuration with inhomoge-neous congestion therefore can be accurate since for each specifictarget of interest, it has individual VBR to determine theoverpressure.

Moreover, the CSC is relatively easy to use by redefining themaximum distance of flame propagation (Lf) as the direct distancefrom the ignition location to the target point of overpressure,whereas in the GAME project that Lf was assumed to be equal to theradius of a hemisphere with a volume equal to the volume of theconfiguration, where for edge/corner ignition cases and the con-figurations with aspect ratio of larger than 1, the GAME correlationmay not be applicable. And thanks to the balanced inputs' dimen-sion to represent different fuels, the gasmass density was introduceas well as the laminar flame speed of gas (Sl) to improve the ac-curacy of the new correlation.

However, all the simulations conducted so far have usedmethane and propane as fuels for explosions. Further tests using

J. Li et al. / Journal of Loss Prevention in the Process Industries 31 (2014) 16e2524

different flammable gases and mixed gases are required to test andvalidate the CSC model for those cases.

It is noteworthy that for CFD, the advent of use of mixed gasesandmultiple species is a recent development and only 10 years ago,the use of pure propane or pure methane was the industrystandard.

The effect of Carbon Dioxide in these reactions is predominantlyas a thermal sink which can slow down the combustion rate andthereby reduce overpressures. However a notable effect requireslarge amounts of the gas to be present. The same is true for hu-midity (i.e. water in vapor form).

Hence the impact of air humiditywas not thoroughly consideredin the simulations. The cases we modeled here, and the currentcommon practice with CFD in industry has been to date, to ignorehumidity in the overwhelming majority of cases as its effect onoverpressure is considered to be relatively small. The exception isfor mitigation measures involving deluge, or events involving rainwhere the evaporation of thewater can have a significant effect. Theinclusion of this effect would make an interesting expansion to thecurrent work. But this requires detailed studies dedicated to thiseffect.

Similarly the effect of Carbon Dioxide mixed in with the re-actants has not been considered here. CO2 is also often ignored inCFD modeling of explosions unless it exists in significant quantitiesmixed with the reactants which is possible but not frequent.

5. Conclusions

In this paper, a new correlation to quantify the overpressure isdeveloped based on the linear least square method by using 400CFD simulations of homogenous geometries. The method is appli-cable only to propane and methane and represents a first step indeveloping robust rapid correlations.

The newly proposed correlation termed CSC has satisfactoryresults when it is applied to all scenarios consisting of realistic andidealized homogenous modules in two different explosion blastsources.

CSC consists of a relation between parameters describing theobstructed region (the average obstacle diameter, volume blockageratio and confinement) and describing the fuel properties. Datafromnumerical simulations using the CFD software FLACS served asa reference for comparison with the results of the CSC. The nu-merical results for approximately an additional 700 simulations onmore realistic geometries were comparedwith both GAME and CSC.

The difference between the two approaches relates to one sig-nificant parameter, confinement. Confinement is introduced in CSCto set up a reference in different confined scenarios. The concept toquantify congestion in an obstructed configuration as well as thevolume blockage ratio is redefined. Additionally, the gas massdensity is taken into account in the calculation and the CSC isderived as dimensionless.

Because the new correlation have been tested against over 1100simulation monitor points carried out using CFD it appears to haveless restriction on its applicability than does the GAME correlation.In any case, this correlation as well as GAME has applicability as abenchmarking tool only. However based on the discussion abovealso it is not recommended using the GAME correlation outside theconfines of the experiments from which it was derived.

Indeed it would be advantageous to test and develop this newlyproposed correlation by comparison to further experiments.

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