\PERGAMON International Journal of Hydrogen Energy 13 "0888# 378Ð384

9259!2088:88:,19[99 Þ 0888 International Association for Hydrogen Energy[ Published by Elsevier Science Ltd[ All rights reservedPII] S 9 2 5 9 ! 2 0 8 8 " 8 7 # 9 9 9 7 6 ! 0

Safety assessment of hydrogen disposal on vents and ~arestacks at high ~ow rates

Pierre Benarda\�\ Vasile Mustafab\ D[R[ Hayb

a Institut de recherche sur l|hydro`e�ne\ Universite� du Que�bec a� Trois!Rivie�res\ Trois!Rive�res\ Que�bec\ Canadab Tektrend International\ Montre�al\ Que�bec\ Canada

Abstract

We compare the point source and solid ~ame models for assessing the thermal ~ux levels from hydrogen vent ~ares[Substantial disagreement exists between the solid ~ame approach and the point source model close to the base of the~are stack[ In this region\ the solid ~ame model is more reliable and may result in higher estimates of the maximumthermal ~ux from the ~are stack[ We use the solid ~ame model to determine restrictions on vent heights and the locationof buildings[ Þ 0888 International Association for Hydrogen Energy[ Published by Elsevier Science Ltd[ All rightsreserved[

0[ Introduction

The disposal of hydrogen through vent and ~are stacksmust comply with several requirements to ensure thesafety of personnel and equipment[ These restrictionscover the ~ow rate\ the diameter of the pipe\ the height ofthe stack and the location of nearby structures[ Hydrogen~ow rates of 9[990Ð9[991 kg s−0 may be vented directlyinto the atmosphere\ but ~ow rates larger than 9[0 kg:sshould be disposed of by ~aring ð0Ł[ Accidental de~a!grations and detonations are most likely to occur forsmall ~ow rates\ where signi_cant concentrations of aircan then be found inside ð1\ 2Ł the stack[ Small ~ow ratesmay also cause the ~ame to dip back into the stack[ The~ow rates must therefore remain above a lower limit\which is determined by the stack diameter[ On the otherhand\ the stream velocities of the out~ow in ~are stacksmust also remain below a lower limit "which is a functionof the fuel concentration and the gradient of the jet vel!ocity# in order to avoid a blow!o} of the ~ame ð3Ł[ Thiscould lead to dangerously high concentrations of hydro!gen close to the disposal system[ Finally\ restrictions mustbe imposed on the length of the stack[ Vents for liquidhydrogen must be long enough to allow the out~ow ofhydrogen vapor to warm up to a temperature above 70

� Corresponding author

K in order to prevent an in~ow of lique_ed air and theformation of a potentially combustible mixture of airand hydrogen within the stack[ Combustible mixture ofhydrogen and air in con_ned volumes are particularlydangerous since they are likely to result in a detonation[A _nal restriction on ~are stacks and vents is that theradiation ~ux resulting from the intentional or accidentalignition of the out~ow will not harm people or damagenearby buildings and structures[ In this paper we presentan analysis of the thermal ~ux emanating from ~arestacks and vents using the Apostrophe code\ which wasdeveloped by us as a tool to assess the hazards arisingfrom liquid and gaseous hydrogen out~ows[ The basicproperties of hydrogen ~ares are reviewed in the nextsection[ This is followed by a discussion on the thermal~ux estimation methods used by Apostrophe[ Finally\ wediscuss thermal level predictions for the solid ~ame modelin relation to established safety criteria as a function ofthe ~ow rate[

1[ Flow rates and ~ame lengths

The rate!limiting mechanism of a ~ame resulting fromthe ignition of a non!premixed out~ow of fuel is thedi}usion of hydrogen into the surrounding atmosphere[Di}usion ~ames can be turbulent or laminar\ dependingon the Reynolds number "Re#[ The Reynolds number is

P[ Benard et al[ : International Journal of Hydrogen Energy 13 "0888# 378Ð384389

equal to Re � v9d9:m\ where v9 and d9 are respectively thecharacteristic velocity and length scale of the problem\and where m is the kinematic viscosity[ For ~ares\ d9 isthe pipe diameter "D# and v9 is the ~ow velocity of thegas\ given by the following expression]

v9 �3Q

pD1\ "0#

where Q is the volumetric ~ow rate of the gas[ For hydro!gen\ the Reynolds number of the gas ~ow at ambienttemperature can be as much as 19 times larger than the~ame\ because the kinematic viscosity increases with tem!perature[ Turbulent ~ames will occur for large out~owsand small pipe diameters[ Chemical kinetics and di}usionboth contribute to the rate limiting mechanism of tur!bulent ~ames[

In the laminar regime\ the shape of the ~ames is char!acterized ð5\ 6Ł by the Froude number Fr\ which measuresthe relative importance of momentum e}ects over buoy!ancy[ For low values of Fr\ the ~ame is buoyant andbecomes much wider than the pipe[ Large values\ onthe other hand\ lead to momentum!driven ~ames[ TheFroude number of the ~are problem is equal to v1

9:"`D#where ` is the acceleration of gravity "8[70 m s−1#[ Exper!imental and theoretical work ð5Ł on ~ares have shown thatthe ratio of the ~ame length "h# over the pipe diameter isexpected to be proportional to the Froude number Fr tosome power m

hD

� Frm[ "1#

The experimental data on ~are lengths has been cor!related ð5\ 6Ł with the following de_nition of Fr]

Fr �"Q:rD1#1

`D[ "2#

The exponent m is equal ð5Ł to 0:2 for Froude numbersin the ranging from 093Ð095 and drops to 0:4 for highervalues "095Ð098#[ For even larger values of Fr\ theexponent is believed to drop to 9[09 and then to zeroð6Ł[ The correlation of the NASA and Bureau of Minesexperiments with the Froude number show ð6Ł that theexponent m is respectively equal to 9[21 and 9[07 forlow and high Froude numbers\ in good agreement withtheory[ In the second regime\ where m � 0:4\ the ~amelength becomes independent ð4\ 5Ł of the pipe diameter D[

A piecewise power law _t of the h:D data summarizedin Ref[ ð6Ł as a function of the Froude number yields thefollowing correlation

hD

� 0[93Fr0:2 for Fr ³ 574\699

andhD

� 5[13Fr9[1 for Fr − 574\699[ "3#

The data used for this correlation covered the range 0[3kg:s to 21 kg:s[ Other experimental correlations havebeen developed for the ~ame length of ~ares from stacksand vents for ~ow rates in the second regime[ Schmitt|scorrelation ð7Ł predicts the following relationship betweenthe ~ame length\ the mass ~ow rate and the heat ofcombustion Hc]

h � 2[694×09−2"QHc#9[360 "4#

where Hc � 008[82 MJ:kg[ Hydrogen is thereforeexpected to have longer ~ames than hydrocarbonfuels\ because of its greater heat of combustion perunit of mass^ despite the fact that it requires a smalleramount of air ð8Ł[ When applied to hydrogen\ eqn "3#becomes

h � 12[546Q9[360[ "5#

The Schmitt correlation predicts a ~ame length of 7 mfor a ~ow rate of 9[0 kg:s[ Flames as high as 12 m can beexpected from ~ow rates of 0 kg s−0[ Expression "5# agreesð7Ł with the experimental results for hydrogen ~ow ratesranging from 0[3 kg s−0 to 4 kg s−0[ A second equationfor the ~ame length as a function of the ~ow rate wasproposed ð4Ł by Werthenbach]

h � 07[403Q9[3[ "6#

Figure 0 shows a comparison of the Werthenbach andSchmitt correlations using data taken from Ref[ ð7Ł[ TheWerthenbach correlation systematically underestimatesthe ~ame length[ The Schmitt correlation yields a better_t to the experimental values\ despite the fact that itconsistently predicts higher values[ The experimental

Fig[ 0[ Hydrogen ~ame height predictions as a function of ~owrate "Schmitt and Werthenbach models# compared with exper!imental data from Refs[ ð8Ł and ð00Ł[ A power law _t of the datayields h � 15[05Q9[3 "the exponent m is set to 9[3#[

P[ Benard et al[ : International Journal of Hydrogen Energy 13 "0888# 378Ð384 380

data is bracketed by the Schmitt and Werthenbachexpressions[ Flame length data from Ref[ ð01Ł also sup!port the Schmitt correlation[

In the turbulent regime\ the ~ame length is expectedto become proportional to the diameter of the pipe[ Itbecomes comparable to hydrocarbon ~ares ð7Ł[ Anexpression due to Hawthorne\ Weddel and Hottel hasbeen used to estimate the ~ame length for fuels in thisregime ð4\ 8\ 02Ł[ Validated for Fourde numbers smallerthan 047\999\ the predicted L:D ratio ð4Ł for hydrogenwas found to be close to 049 and the ratio of the jet radius"R# to pipe diameter ð4Ł R:D is 03\ leading to a h:R ratioof 09[6[

Finally\ an important factor a}ecting the shape of ahydrogen ~are is the presence of a crosswind\ especiallyfor low values of the Froude number[ For a given dis!charge velocity and fuel jet diameter\ the total ~amelength of a hydrogen ~are is expected to increase withincreasing wind velocity\ in contrast with hydrocarbonfuels\ which have the opposite behavior ð8Ł[

2[ Estimation of the thermal ~ux from ~ares

The Apostrophe program can estimate the thermal ~uxfrom a ~are using either the point source or the solid~ame models[ The solid ~ame model is more reliable atcloser distances to the ~are[ The point source model\however\ can yield thermal ~ux estimates without anydetailed knowledge of the geometric features of the ~ame[

2[0[ Point source model

The point source model assumes that the thermal radi!ation emanates from a point ð02\ 03Ł[ It can be modi_edð7Ł for a ~are\ in which case it predicts that the incidentthermal ~ux at a horizontal distance d from a ~are oflength h on a stack of height l is given by the expression]

qý �hQHc

3p

d

"ð0¦h:1Ł1¦d1#2:1

� 8369hQd

"ð0¦h:1#1¦d1#2:1kW:m1\ "7#

where h is the fraction of the combustion energy releasedas thermal radiation[ Typical values of h range from 9[06Ð9[31 for hydrocarbon fuels ð02Ł[ For hydrogen\ estimatesof h ranging from 9[04 to 9[19 and 9[06Ð9[14 have beenreported ð3\ 7Ł[ The radiative output coe.cient h of gase!ous hydrogen di}usion ~ames is smaller ð03Ł "h � 8[4Ð05[8# than liquid supported di}usion ~ames "h � 9[14#[

2[1[ Solid ~ame model

The solid ~ame model ð01\ 02Ł is based on the assump!tion that the ~ame can be regarded as a uniformly rad!

iating surface[ The radiative heat transfer from a ~ameto a target is given by the expression

qflame:tar � Qflame:tar:Atar � tosFtar:flame "T3flame−T3

9#[

"8#

In this model\ the ~ame is assumed to be a uniformlyradiating cylinder whose temperature is equal to the aver!age ~ame temperature[ The view factor "or con_gurationfactor# for a cylindrical radiator to a small rectangularsurface facing in is given by the following expression]

Fverticaltar:cylinder "L\H# �

0pL 0 tan−0 0

H

zL1−01

¦H 0X−1L

zXYtan−0 XX"L−0#

Y"L¦0#−tan−0 XL−0

L¦011with L �

rR

\H �hR

\X � "0¦L#1¦H1

and Y � "0−L#1¦H1[ "09#

R is the average or typical radius of the ~ame\ and h isthe ~ame length "see Fig[ 1#[ For a ground level ~are\ eqn"09# can be used in eqn "8#[ As mentioned earlier\ thee}ect of a crosswind on ~ares can be important ð8Ł[ Inthis case\ the relevant view factor is that of a verticalobserver facing a tilted cylinder ð03Ł[ For a ~are of lengthh at a vent opening located at height l\ the view factor

Fig[ 1[ Parameters of the view factors for a ~are from a stack his the ~ame length\ l is the stack height\ r is the horizontaldistance between the target and the ~ame\ R is the radius of the~ame and D the pipe diameter[

P[ Benard et al[ : International Journal of Hydrogen Energy 13 "0888# 378Ð384381

from a cylinder at height l with respect to the groundlevel observer must be used ð03Ł[

The transmittivity t\ which depends on the CO1 andH1O content of the ambient atmosphere\ can be con!servatively set to one[ The ~ame temperature for hydro!gen di}usion ~ames from leaks and spills is 0819 Kaccording to the Bowen report ð05Ł[ Values as low as0162Ð0262 K have been reported for ~ares ð7Ł[ Using avalue of 1207 K for the ~ame temperature will lead to athermal ~ux 1[02 greater than if a value of 0819 K hadbeen used[ The predicted centerline temperature forhydrogen ~ares is close to the adiabatic ~ame tem!perature of hydrogen in air ð00Ł[

In the solid ~ame model\ the total ~ux is a function ofthe h:R ratio\ where R is the average radius of the ~ame[In general\ the high burning rate of hydrogen is expectedto lead to large h:R ratio[ An estimate for the radius canbe obtained by using the Baron estimate for the maximumradius ð09Ł of a jet _re\ which is 05[56 times smallerthan the length of the ~ame[ For large h:R ratios\ theviewfactor for a cylindrical ~ame at ground level has thelimiting value]

Fverticaltar:cylinder"L\H : �# �

R1r

[ "00#

Close to the ~ame\ therefore\ the thermal ~ux is expectedto decrease more slowly than the 0:r1 behavior predictedby the point source model[ Equation "00# also showsthat the average ~ame radius is a crucial parameter forground!level ~ares[ Good agreement "better than 09)#is obtained between the thermal ~ux calculated usingeqns "09# and "00# for thermal ~uxes higher than 3 kW:m1\when the transmittivity\ the emissivity and the ~ame tem!peratures are set to 0[9\ 9[0 and 0819 K respectively[Larger values of the product to"T3

flame−T39# increases the

accuracy of the approximation and extends its range ofapplications[ Use of eqn "09# leads to the followingexpression for the thermal ~ux for a ground level ~are asa function of distance[

qflame:tar �1tos"T3

flame−T39#R

r"01#

The 0:r1 behavior will occur for large values of r:R[ Equa!tion "01# can be compared with the thermal ~ux data ð7Łfrom a ground level hydrogen out~ow ~ared from a poolof 079 m1[ Values of 19 kW:m1\ 09 kW:m1 and less than7 kW:m1 were observed at distances of 26[4 m\ 49 m and099 m respectively[ The ~ame length was about 099 m[The average radius of the pool "calculated from the sur!face area# was 6[45 m[ This corresponds to a ratio ofh:D � 5[5[ A _t of the above thermal ~ux data withexpression "09# yields an average value of1tos"T3

flame−T39#R equal to 509 kW:m[ Use of the value

0399 K as the average ~ame temperature leads to ane}ective ~ame radius of 03[1 m or a h:R ratio of 6[ Use

of eqn "01# with the average prefactor lead to thermal~ux values of 07 kW:m1\ 02[4 kW:m1 and 5[6 kW:m1 fordistances of 26[4 m\ 49 m and 099 m[ These values are inbetter agreement with experiments than the ones pre!dicted by the point source model ð7Ł[ For ground level~ares\ the solid ~ame model leads to more accurate esti!mates of the thermal ~ux than the point source modelused in Ref[ ð5Ł for ~ux values as close as nearly a thirdof the ~ame length\ without the need of the ~ame length[If the average radius of the ~are pool is taken as thecharacteristic radius of the ~ame\ a ~ame temperature of1252 K is obtained[ Although this result is close to theadiabatic ~ame temperature of hydrogen "1207 K#\ it ismuch larger than the measured ð7Ł infrared ~ame tem!perature of 0999Ð0099 C[

The thermal ~ux predicted by the solid ~ame and thepoint source models is shown in Fig[ 2[ The adiabatic~ame temperature leads to a much larger thermal ~uxthan the ~ux predicted by the point source model[ How!ever the value 0819 K leads to comparable levels at largedistances[ Both models predict a maximum value of thethermal ~ux at ground level[ The point source modelpredicts a maximum at a distance

d �X01 00¦

h11[

For the solid ~ame model\ the predicted maximum doesnot follow this simple relationship[ Since the validity ofthe point source model is restricted to distances largerthan the total length of the ~ame "h¦l#\ where the geo!metric features of the _re can be neglected\ predictionsfrom the point source model on the maximum thermal~ux are unreliable[

Fig[ 2[ Comparison of the thermal ~ux predictions of the pointsource and the solid ~ame models for a 6[5 m stack and a ~owrate of 9[0 kg s−0[ The ~ame temperature was set to 1207 K"dotted line# and 0819 K "dashed line#[ The full line shows thesolid ~ame model with h � 9[1[

P[ Benard et al[ : International Journal of Hydrogen Energy 13 "0888# 378Ð384 382

3[ Discussion

Because of its larger range of applicability\ the solid~ame model will be used to predict the maximum thermal~ux received by a human target at ground level[ We willconsider two criteria for safety assessment] the safe levelfor inde_nite exposures of humans to a thermal ~uxsource "0[3 kW m−1# and the minimum threshold to ignitewooden structures "01[5 kW m−1#[ The _rst criteria applyto human beings and the second to buildings and struc!tures[ The _rst criteria will set the absolute height ofthe stack\ and the second can be used to establish thecon_guration of nearby structures[ The absolute heightha is de_ned as the sum of the average height of the target"1 m# and of the relative height l required to establish amaximum ~ux level of 0[3 kW m−1[ The emissivity willbe set to 9[0 and the transmittivity to 0[9[ Figure 3 showsthe maximum thermal level for a ~ame temperature of1207 K as a function of the absolute height of the vent"ha#\ for three values of the ~ow rate] 9[0\ 0[9 and 4[9kg:s[ For a maximum thermal ~ux of 0[3 kW m−1\ ha

must be equal to 5[8\ 05[4 and 22 m\ respectively[ Theheight di}erence Dl between the top of the neighboringstructures and the vent opening must be greater than 9[5\0[4 and 2[1 m "respectively# in order for the incident ~uxto remain below 01[5 kW m−1[

Figure 4 shows ha as a function of the ~ow rate cal!culated using the Schmitt and Werthenbach models and~ame temperatures of 1207 K and 0819 K[ For large ~owrates\ the height restriction Dl is smaller by a factor of8[54\ which is roughly equivalent to the ratio of the ~uxlevels[ Although the ratio of the ~ame length to radius isthe same for the two models\ the choice of the modelto estimate the ~ame length is an important parameter[Variations of up to 49) can be observed between thetwo models at the same ~ame temperature[ These vari!

Fig[ 3[ Maximum thermal ~ux on a 1 m upright target at groundlevel as a function of the vent height for ~ow rates of 9[0\ 0 and4 kg s−0[

Fig[ 4[ Absolute height ha as a function of the ~ow rate calculatedusing the Schmitt and Werthenbach models and ~ame tem!peratures of 1207 K and 0819 K[ The emissivity was set to 9[0and the transmittivity to 0[9[

ations are of the same order of the di}erences between~ame length predictions themselves[ It is important topoint out that the variations between the models for the~ame length stem from the di}erent values of the average~ame radius that they predict[ Thus the model chosen toestimate the average radius of the ~ame is important[ For_xed values of R\ the incident ~ux will not depend muchon the ~ame length since the contribution of the cyl!indrical ~ame to the ground level ~ux decreases rapidlyalong the z!axis[ The average ~ame temperature\however\ has the greatest impact on the height estimates\due to the quartic dependence of the radiative ~ux onthe temperature of the ~ame[ For both the Schmitt andWerthenbach models\ the ratio of l at 1207 K to its valueat 0819 K is 0[80\ which is somewhat below the ratio ofthe temperatures to the fourth power "1[01#[

Figure 5 shows the ratio l:D for a maximum thermal~ux of 0[3 kW m−1 as a function of the Froude number[The ~ame length was calculated using the piecewise _tfrom the NASA and Bureau of Mines data "Eqn "3##[The ratio l:D for 01[5 kW m−1 is 8[54 times smaller thanthe corresponding value for 0[3 kW m−1[

The restrictions on the height of the vent and heightdi}erences between rooftops and the vent opening isshown in Table 0 as a function of the mass ~ow[ Flowrates larger than 9[0 kg s−0 are typical for low!pressurestorage systems[ The maximum diameter of the stack toprevent the ~ame from dipping back is 47 cm for this~ow rate[ A ~ow rate of about 9[2 can be expected fromthe gaseous out~ow of a liquid hydrogen storage unitwith a vent diameter of 5 cm[ Table 0 shows conservativerestrictions for hydrogen disposal system on the totalheight of the vent stacks and on the height di}erencebetween the nozzle and the rooftops based on thermal~ux emanating from a ~are[ The ~ame temperature\ the

P[ Benard et al[ : International Journal of Hydrogen Energy 13 "0888# 378Ð384383

Fig[ 5[ Renormalized height di}erence between ~ame and targetrequired to limit the thermal ~ux to 0[3 kW:m1\ as a function ofthe Froude number[ Expression "3# was used for the ~ame height[The ~ame temperature was 1207 K and the emissivity was 9[0[The height di}erence for a maximum thermal ~ux of 01[5 kWm−1 is 8[45 times smaller than the one shown on this graph[ Theright vertical axis shows the predicted height di}erence for astack with a pipe diameter of 05[34 cm[

Table 0Total vent height "Ha# and height di}erence "DH# between ventopening and rooftop of structures to achieve maximum thermal~uxes of 0[3 kW m−1 and 01[5 kW m−1\ respectively

Flow rate Ha "in m# DH "in m#"kg s−0# T~ame � 1207 K T~ame � 1207 K

9[2 09[1 9[740[9 05[4 0[41[4 13[2 1[214 21[8 2[10

emissivity and the transmittivity were set to 1207 K\ 9[0and 0[9 respectively[ The ~ame height was calculatedusing the Schmitt formula and the Baron maximumradius for the h:R ratio[

The NFPA standards for Gaseous and lique_ed hydro!gen systems at consumer sites "NFPA 49B and NFPA49B# recommend a minimum elevation of 6[5 m for ventsand pressure relief systems ð06\ 07Ł[ A human being atground level will face a maximum thermal ~ux of 1[11kW m−1 if the depressurization out~ow "9[2 kg s−0# froma vent 6[5 m high is ignited[ Although this level of thermal~ux is above 0[3 kW m−1\ a level of 3[9 kW m−1 must bereached for pain to be felt after 19 s[ The ignition of ahydrogen out~ow of 4 kg s−0 would result in a maximum~ux of 7[09 kW m−1 on a human being[ The maximum~ow rate for which the absolute height h � 6[5 m resultsin a maximum ~ux of 0[3 kW m−1 is 9[142 kg s−0[ The

maximum thermal ~ux at ground level will exceed 01[5kW m−1 for ~ow rates above 20[1 kg s−0[

4[ Conclusions

We have compared the point source and solid ~amemodels for assessing the thermal ~ux levels from hydro!gen vent ~ares using the Apostrophe program[ Althoughthe point source model is known to give good results farfrom the ~ame\ the geometric features of the ~ame mustbe taken into account in the high thermal ~ux regioncritical for safety assessment of people and structures[ Inthis region\ a simple form can be used for the viewfactorof ground level ~ares[ The thermal level predicted closeto the ~ame by the solid ~ame model are higher than theones expected from the point source approach[ At longdistances\ both models predict identical levels if a ~ametemperature of 0819 K is used[ The solid ~ame modelpredicts that the maximum value of the thermal ~ux onan average human target from a ~are with Q � 9[2 kgs−0 located 6[5 m above the ground are slightly above thesafety level for inde_nitely long exposure[ Other restric!tions must also be observed for the safe disposal of ventand ~are stacks[ In particular\ the distance from the ventoutlet to any ignition source must be maximized to avoidan unwanted ignition[ Furthermore\ vent outlets must beset in such a way that the out~ow can never enter acon_ned area or an intake[ Finally\ nearby structuresmust be separated from the vent by a distance greaterthan the expected ~ame length\ bearing in mind that thewind may have any direction\ so that the hydrogen ~ame"which is invisible# cannot impinge on nearby structures[

Acknowledgements

We wish to thank Professor Tapan K[ Bose for usefuldiscussions[ We gratefully acknowledge the support ofNatural Resource Canada and Tektrend Internationalin!house research and development[

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