at SciVerse ScienceDirect

Applied Thermal Engineering 59 (2013) 587e598

Contents lists available

Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

Mathematical modeling of cryogenic spills onto quiescent sea watersfollowed by pool fires of liquefied natural gas (LNG)

Alan Silva Esteves*, José Alberto Reis ParisePontifícia Universidade Católica do Rio de Janeiro, Department of Mechanical Engineering, Rio de Janeiro 22453-900, RJ, Brazil

h i g h l i g h t s

� More than 20 orifice models published since 1969 were reviewed.� Flow parameter adjusted with proxy equations for a*,max and t*v within 1/3 � 4 � 30.� Review of experimental of data for vaporization velocities covered since 1978.� The axial emissive power along the fire plume increases with vaporization velocity.� Plume height/diameter ratio of termal plume was nearly insensitive to the scale up of carrier cargo capacity.

a r t i c l e i n f o

Article history:Received 30 January 2013Accepted 11 June 2013Available online 21 June 2013

Keywords:Mathematical modelingCryogenic spillsLNG pool firesMaritime transportation

* Corresponding author. Tel.: þ55 21 9716 1965; faE-mail addresses: alan-esteves@esp.puc-rio.b

(A.S. Esteves), parise@puc-rio.br (J.A. Reis Parise).

1359-4311/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.applthermaleng.2013.06.01

a b s t r a c t

Spill and combustion of a pool as a result of a spreading of liquefied natural gas (LNG) at sea frompunctures on carrier hulls is presented. Models from literature combined mechanisms of flow thoroughan orifice, formation of a semicircular pool, vaporization of a cryogenic fluid by boiling and pool fireheating, ignition, non-premixed turbulent fire with variation with height of the emissive power of the‘visible’ plume, burning of fuel along the ‘luminous’ zone (fire base) and radiation emitted by gray gasesand soot particles from the combustion zone.

A review of the experimental data on vaporization velocity and burning rate is presented. Predictionsagreed well with existing experimental data and other models. The model simulated fires from 1 to 5 mdiameter holes in vessel geometries of 125,000 and 265,000 m3. Predictions are plausible, and robustenough to be applied in industrial practice.

The construction of an LNG terminal involves, among other parameters, the prediction of thermalradiation fields emitted by pool fires. This is to evaluate safe distances to vulnerable resources around thefacility.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

A growing demand for LNG, from all over the world, resulted inthe introduction of a number of new terminals (over 40) and largervessel carriers with capacities ranging from current 125,000 m3 [1]and to expected 265,000 m3 [2]. In this new context, spill accidentsare now more likely to occur.

Spills are caused by punctures, due to accidents or intentionalacts of terrorism, brought against broadsides of LNG carriers, andmay result in pool fires alongside the stricken tanker [1]. Over thelast years, works analyzed spills over water from large LNG carriers[2,3], reviewed the experiments and modeling of large-scale spills

x: þ55 21 3527 1165.r, esteves.alan@gmail.com

All rights reserved.6

[4], studied the liquid spread and evaporation of LNG [5], proposedsimilarity solutions for the spreading of liquid pools [6] andmodeled large LNG pools on the sea [7]. In the last five years, otherworks covered LNG releases, pool spreading and pool formation,pool fire description, pool fire radiant heat output and hazard dis-tance calculation procedures [8], reviewed the state-of-the-art ofsource term models which predict the development of a release ofLNG and presented an approach for assessing the adequacy of suchmodels, with main focus on pool spread and vaporization [9]. Poolfire models are also currently available, and can be divided into fivecategories [10] as follows: punctual source flame (semi-empirical)[11]; solid flame [12]; integral [13,14]; multi-zones [15e17]; andfield (involving CFD) [18]. These models are thoroughly reviewed inRefs. [19e22].

A number of works have studied the phenomenon of LNG spillfollowed by combustion [1e3,23e28]. One could mention an early

Nomenclature

Ah tear area alongside the carrier hull (m2)Ahcr

critical tear area (m2)AL specific soot extinction area (m2/kg)Apsc

semicircular pool area spilled onto the sea alongsidethe carrier (m2)

Amaxpsc

maximum semicircular pool area spilled onto the seaalongside the carrier (m2)

Amaxpsc;cr

critical value of the maximum semicircular pool area(m2)

Amaxpsc;ub

upper bound limit of the maximum semicircular poolarea (m2)

Amaxpci

maximum circular pool area converted from thesemicircular pool (m2)

At carrier cargo tank constant cross section area (m2)a*,max dimensionless maximum pool area (e)cpa

specific heat of air at constant pressure (assumed thesame for all gases) (J/kg.K)

Cd discharge coefficient (e)Cs concentration of smoke particles (soot) in the fire (kg/

m3)CVC LNG cargo vessel capacity (geometry) (m3)CTV volume of the membrane or prismatic cargo tank (m3)D diameter of the base of the fire plume (or liquid pool

diameter) (m)Dh puncture diameter (m)DR fully-loaded draft (vertical distance from thewater line

to the keel) (m)Dpsc

semicircular pool diameter (m)hDpsc

i average of several values of semicircular pool diameter(m)

Dpcicircular pool diameter, calculated from Eq. (16) (m)

hDpcii average of several values of circular pool diameter (m)

E mean SEP (surface emissive power) over the visible fireplume height (kW/m2)

Emax maximum emissive power at the base of the fireequivalent to a black blackbody temperature (kW/m2)

Es effective radiation emitted (emissive power) by thecylindrical nominal surface of the fire plume, obscuredby smoke (kW/m2)

E0 emissive power of the fire nominal surface near thebase (kW/m2)

FrC combustion Froude number (e)g module of the gravitational acceleration vector field

(m/s2)h any height of liquid inside cargo tank (m)h0 initial height of liquid inside cargo tank (m)h(t) height of liquid inside cargo tank, as a function of time

(m)Lbeam optical beam length for cylindrical fires (m)LC length (height) the bottom ‘clean’ burning zone (m)LI length (height) of intermittency zone (m)LV mean length (height) of visible fire plume (m)Ll spectral extinction coefficient for absorption of

thermal radiation by soot particles (m�1)_m00b boiling mass flow rate of fuel per unit area at the base

of fire (kg/m2.s)_md release mass flow rate (kg/s)_m00r radiation mass flow rate per of fuel per unit area at the

base of fire (kg/m2.s)_m00v overall vaporizationmass flow rate of fuel per unit area

at the base of fire (kg/m2.s)n quantity of carrier cargo tanks (e)

n adjustment power of a polynomial function (e)Pa air pressure (kPa)p(x) probability at height Z of having, at any time, on the

surface of the nominal cylinder, the emission from theinner core flame not obscured by smoke (e)

q00

thermal radiation flux emitted by the pool fire (J/m2)R pool area radius (m)r semicircular horizontal position (radial) of the pool

area slick (m)r air to fuel mass ratio for stoichiometric combustion (-)t time (s)td duration of the outflow from the cargo tank, discharge

time (s)Ta air temperature (K)Tb liquid normal boiling point (K)Tw sea water temperature (K)t*v dimensionless time required to vaporize the pool (-)tv vaporization time (s)htvi average of several values of vaporization time (-)tvcr critical value of the vaporization time (s)tvlb lower bound of the vaporization time (s)U* dimensionless wind speed (e)Uwind wind speed (m/s)Vp volume of liquid in the pool (m3)V0 initial spilled volume (or inside the cargo tank) (m3)Y smoke (soot) yield (%)w average regression (vaporization) velocity of the liquid

fuel in the pool (m/s)Z length along the fire axis (m)

Greek symbolsb empirical constant in axisymmetric pool spreading (e)D ratio of difference of seawater and LNG densities to the

sea water density (-)DHC heat of combustion of the fuel (J/kg.K)DHvl heat of vaporization of the liquid fuel (J/kg.K)x fraction of axial fire length (height) to mean length

(height) of visible fire plume (e)d time average LNG slick thickness (m)ε mean total hemispheric emissivity of fire (-)kl optical path length (thickness) consistent with the

type of fuel burning (m)ra density of air (kg/m3)rl density of liquid fuel (kg/m3)rw density of sea water (kg/m3)4 mass fraction of air that is entrained up to any height Z

that burns stoichiometrically with fuel (e)ss total hemispheric transmissivity of smoke (e)4 flow parameter used in LNG pool spreading modeling

(e)fcr flow parameter critical value (e)j ratio of ‘clean burn zone’ axial length to mean fire

plume length LC=LV (e)

AcronymsABS American Bureau of ShippingAGA American Gas AssociationAIAA American Institute of Aeronautics and AstronauticsAIChE American Institute of Chemical EngineersAMOP Arctic and Marine Oilspill ProgramCFD Computational Fluid DynamicsCLNG Compressed Liquefied Natural GasEES� Engineering Equation Solver of F-Chart SoftwareEFCE European Federation of Chemical Engineers

A.S. Esteves, J.A. Reis Parise / Applied Thermal Engineering 59 (2013) 587e598588

FERC The Federal Energy Regulatory CommissionFIRE2� Pool fire software of HSEHSE Health and Safety ExecutiveIChemE Institution of Chemical EngineersLLNL Lawrence Livermore National LaboratoryLNG Liquefied Natural GasLPG Liquefied Petroleum GasNAR Narrow angle radiometerNFPA National Fire Protection AssociationSRD Safety and Reliability Directorate

Sandia Sandia National LaboratoriesSEP Surface Emissive PowerTMS Technical & Management SystemsTNO The Netherlands Organization of Applied Scientific

ResearchUKAEA UK Atomic Energy AuthorityU.S. BuMines United States Bureau of MinesUSCG United States Coast GuardUSDOE United States Department of EnergyWAR Wide Angle Radiometer

A.S. Esteves, J.A. Reis Parise / Applied Thermal Engineering 59 (2013) 587e598 589

work [26] where a simple theoretical model for the spreading,evaporation and burning of an LNG pool on open water was per-formed. Experimental data was available for confirmation of thespill process only. More recently, quantitative estimates were car-ried out [27] for the spread rate and maximum slick size, burn rateand duration, effective thermal radiation and soot generation. Acomparison was performed between spill predictions for differenthydrocarbon fuels. Overall, it was concluded that LNG would burnfaster and at a higher temperature than a fuel oil fire. Two recentarticles refer to FERC’s models [24] to study the spillage conse-quences and their dependence on contributing variables [28] aswell as to conclude that the basic equations and principles in FERC’sLNG release, spreading and burning models could be applied toother flammable fluid releases [23].

Besides the important findings that have been consolidated ininitial review works [22,24,25], more recent works were recentlymade available in the literature, providing further information andunderstanding of the complete problem, from the cryogenicleakage to the thermal radiation field emitted from the fire sur-face [8], citing [1,7]. One can also find recommendations [29] on theprediction of thermal hazard distances resulting from large LNGpool fires (up to 50m) onwater for solid flamemodels, based on theresults obtained with large-scale LNG pool fire experiments [30].Studies were also developed [31] on the hazards posed by thermalradiation fields emitted by the thermal fire plume and flammablevapor dispersion, resulting from unconfined LNG spills on water,recalling references [1,24]. The study covered, among other aspects,the pool spreading semicircle format in assessment methods, citingexplicitly Fay’s model [1]. It was pointed out [7] that the effects ofocean wave interaction on the spread of an evaporating LNG poolwere only small or negligible. A validation protocol for LNG datasets used in dispersion models was also developed in Ref. [31].Industrial experience of classifiers societies, shipbuilders, agencies,engineering and risk consultants were also added as references tothis effort [32].

As far as modeling is concerned, a step forward is here taken bycoupling the spill model from Fay [1] to a non-premixed turbulentcombustion pool fire model from TMS [17] and Raj [33], taking intoaccount the existence of three different zones, with the surfaceemissive power (SEP) varyingwith the height of the thermal plume,and presenting numerical results with pool diameters varying from10 to 500 m, a range not covered previously, to the authors’knowledge, in literature. The main objective of the present work isto couple both spill and combustion calculation procedures into alow computational effort model, so that it can be easily applied inthe LNG industry.

2. Mathematical model

2.1. Semicircular pool spill and spreading

To reach the objectives of the present work, first, a suitable spill/spreading model had to be adopted. A protocol, with prescribed

criteria, was to be followed. The protocol here adopted, for itsconciseness and representativeness, was suggested in Ref. [8]. Acomparison was carried out between several models, underdifferent aspects which included modeling approach, focus,formulation, confidence interval, limitations, results, accuracies,strengths and weaknesses.

Amongst over a dozen alternatives, Fay’s standard [1] and su-percritical [7] models seemed to suit the purposes of the presentwork. To decide between one or another, a few requirements wereput forward, to meet LNG industrial needs, as follows: (i) to providea more accurate pool shape (semicircular) centered symmetricallyaround the tear point, alongside the carriers’ hull from bow tostern; (ii) to provide plausible predictions of maximum LNG spilledarea related to any tear area perpetrated against the hull,compatible with the reality of the LGN industry, varying from 1 to100 m2, according to the sizes recommended by FERC and SandiaNational Laboratories; (iii) to be robust enough to predictmaximum semicircle pool area poured onto the sea and its vapor-ization time, for any large volume spilled from cargo tanks varying12,500e41,000 m3 from current carriers, at any vaporization ve-locity; (iv) to be ease to handle and to use, reproducing well theresults published in the original reference, with the model imple-mented in a single user-friendly computer code; (v) to be reliable inpredicting results, vis a vis the requirements on mitigation mea-sures for exclusion zones around carriers and terminals, so thatlicensingwith authorities can be properly addressed; (vi) to be usedeven when the carrier geometry is scaled up to volumes currentlyconstructed; (vii) to be ease to couple and load the results of spill/spread modeling as input data for the pool burning model.

Between the two models [1,7], Fay’s standard model [1] waschosen as the best choice to meet all the above criteria. Besides, itsadoption is in line with the findings published by Refs. [8] statingthat pool spread and evaporation could be adequately representedusing the Fay [1] model. Furthermore, it expresses the maximumpool area and the vaporization time as functions of only one flowdimensionless parameter, 0� 4�þN, depending on the geometriccharacteristics of the ship and the vaporization rate of the pool inquiescent waters. Finally, Fay’s model [1] is consistent with thereality of carriers under construction nowadays, with capacitiesreaching 266,000 m3. The basic geometry of the damaged LNGcarrier is depicted in Fig. 1.

According to [8,32], LNG releases and spills on water stem fromthe position of the puncture: (i) above the water line e category I;(ii) at or close to the water line e category II, and (iii) below thewater line e category III. Category II is further divided by Ref. [8]into sub-category II.1, in which punctures in both hulls are justabove the water line, and II.2, in which the outer puncture ispartially underwater and the inner one is “slightly above orpartially below” the water line. A number of possible interactionsbetweenwater and LNG can be considered for categories II.2 and III,involving different phenomena, such as flash formation or waterinflow to the ballast space. Such phenomena may occur sequen-tially or concomitantly and, most probably, would be better

Fig. 1. Schematics of the cargo tank of an LNG carrier [1].

A.S. Esteves, J.A. Reis Parise / Applied Thermal Engineering 59 (2013) 587e598590

addressed by some sort of CFD analysis, not yet found in the liter-ature [8]. For the present purposes, it is understood [1,8] that, forcategories I and II.1, therefore assuming no water ingestion, theorifice equation would be sufficient to describe the outflow.

Fay [1] defines a time scale, td, which determines the timeelapsed of the outflow from the cargo tank tear. Orificemodels statethat the magnitude of the outflow velocity through the tear at, orclose to the water line [8,32] is

ffiffiffiffiffiffiffiffigh0

p, so that the magnitude of the

outflow volumetric flow rate of spilled LNG is given byffiffiffiffiffiffiffiffigh0

pAhtd

that, multiplied by the discharge time, td, gives a volume that, fromthe mass conservation, must equalize the volume dischargedV0 ¼ Ath0. The initial value of h(t) (function of time) inside the cargotank is h0, and both of themaremeasured fromabove thewater line,as depicted in Fig.1.When rupture occurs, the carrier is supposed tobe loaded at full capacity, operating in quiescent waters of a ter-minal. The whole cargo is assumed to be held in a carrier equippedwithmembrane or prismatic cargo tanks of constant cross sectionalarea,At. Due to intensivemeasures to fulfill authorities’ constructionand safety requirements, carriers are supposed to be equipped withmodern barriers and redundant equipment, so as to improve theprevention and mitigation measures to avoid, as far as possible,potential hazards for the industrial activity. On this account, anumber of simplifying hypotheses are assumed, which includesneglecting the occurrence of phenomena such as: (i) ullage pressureinside the cargo tank, usually less than w115 kPa (2 psig) [28]; (ii)vacuumbreaker and air entering the cargo tank through the breach;as well as (iii) rapid phase transitions (RPT), as a result of eventualwater entrance into the cargo and ballast tanks during the spill.Cargo tank pressure effects are considered as of low to mediumimportance [8] on the prediction of liquid outflow from the ship,although it could be considered as being altered due to the potentialpressure changes associatedwith the LNG release, flash of LNG, heatingress through the inner tank walls, etc. [8,32,34].

Therefore,

tdzAth0ffiffiffiffiffiffiffiffigh0

pAh

¼�At

Ah

� ffiffiffiffiffiffih0g

s(1)

The liquid pool vaporizes by a boiling or pool fire process, and itsdepletion cannot occur in a time shorter than td. The rate of loss ofthe liquid by vaporization is expressed by w, a function of themechanisms that vaporize the fluid [2]. According to Fay [1], Eqs.(2)e(5), below, describe the variation with time of the dischargeprocess from the carrier cargo tank, and subsequent pool formationand vaporization.

��v

vtðhAtÞ

�Ah;w

¼ffiffiffiffiffiffiffiffi2gh

pAh (2)

�vVp

vt

�¼

ffiffiffiffiffiffiffiffi2gh

pAh �wAmax

psc(3)

Ah;w

�v�pR2=2

�vt

�Ah;w

¼�vRvt

�Ah;w

¼�b

p

� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2pgVpD

q(4)

D ¼ rw � rlrw

(5)

Some correlations were proposed by Fay [1], assuming the ge-ometry of the cargo tank as prismatic, with V0 ¼ Ath0, and withconstant cross sectional area. A dimensionless flow parameter, f,correlating, b, D, w and the cargo tank geometry, was defined as:

f ¼ bffiffiffiffiffiffiffiffiffi2pD

pw

ffiffiffiffiffiffih0g

sA3=2t

A2h

(6)

For f > 30, dimensionless asymptotic values of 2.828, 1.414 and4 for a*,max, t*v and a*;max$t*v, respectively, are used. However, for fvalues within 1/3 and 30, differently to [1], the present work pro-poses, as an approximation, the use of continuous functions tocalculate f within that interval, as follows:

a*;max ¼ 0:43 ln fþ 1:184 (7)

t*v ¼ 0:8199f2 � 2:7431fþ 3:6982 (8)

By expressing Amaxpsc

and tv in terms of a*;max, t*v and f, onehas [1]:

Amaxpsc

¼ Ah

ffiffiffiffiffiffiffiffigh0

pw

!a*;max ¼

"b2ð2pDÞgðh0AtÞ3

w2

#1=4a*;maxffiffiffi

fp (9)

tv ¼�At

Ah

� ffiffiffiffiffiffih0g

st*v ¼

"h0At

b2ð2pDÞgw2

#1=4t*v

ffiffiffif

p(10)

The critical values of Ahcr, Amax

psc;crand tvcr are calculated as follows

[1], respectively:

Ahcr¼ 0:749

"b2ð2pDÞw2h0A3

tg

#1=4(11)

Amaxpsc;cr

¼ 1:071

"b2ð2pDÞgðh0AtÞ3

w2

#1=4(12)

tvcr ¼ 1:889

"h0At

b2ð2pDÞgw2

#1=4(13)

According to [1], these critical values distinguish betweenmostly quasi-steady and rapid unsteady outflows, respectively,from a small or large hole.

Upper and lower bounds for Amaxpsc

and tv can be calculated and,for the case of an instantaneous spill (f approaching 0), withb ¼ 4=

ffiffiffi3

pz2:31, one has [1]:

Amaxpsc;ub

� 2:58

"gDðh0AtÞ3

w2

#1=4(14)

tvlb � 0:785�h0At

gDw2

�1=4

(15)

A.S. Esteves, J.A. Reis Parise / Applied Thermal Engineering 59 (2013) 587e598 591

2.2. Transition from semicircular to a circular pool

The combustion model, next, assumes a circular pool, whereasthe spill is supposed to form a semicircular pool. Therefore, frommass, energy and momentum conservation principles andassuming constant density and slick thickness during transition,one has:

Amaxpsc

¼ Amaxpci

0Dpci¼ 1ffiffiffi

2p Dpsc

(16)

2.3. Non-premixed turbulent combustion pool fire

Current multi-zone models for pool fire simulation considerdifferent regions of combustion within the ‘visible’ height of theflame [16,17,32,33]. Results from such models have already beencalibrated and validated quantitatively against experimental datafrom Montoir LGN terminal fire tests with pools of 35 m diameter[33,35], used recently by the LNG community [8,17,33]. For theircompromise between simplicity and accuracy, these models havebeen chosen as reference for the present work. Following anassessment carried out on the available multi-zone models thepresent work is based on Raj’s model [33], also reported in Refs.[16,17]. A visualization of resulting thermal plume of the pool fire ispresented in Fig. 2.

The plume is composed by three zones that form: (i) the ‘visible’plume, e.g., the lowest part of the plume, where combustion isconsidered as ‘clean’; (ii) the middle zone, where the plume pul-sates intermittently, and the (iii) highest part, where combustionproducts are taken off from the fire column by buoyancy. This thirdregion is known as a time averaged geometric loci of the ‘visible’height of the thermal plume.

The equations for modeling the non-premixed turbulent com-bustion pool fire are presented next. Two factors contribute tovaporization: _m00

v, boiling the LNG pool due to the heat transferbetween the water and the LNG, i.e., _m00

b, and from the radiationemitted within the plume, _m00

r , so that [1,36]

_m00v ¼ _m00

b þ _m00r (17)

The relationship between w and _m00v is given by, for example, by

Ref. [25,36]

_m00v ¼ wrl (18)

Fig. 2. Thermal plume of a buoyant turbulent diffusion with different combustion andintermittency zones. Adapted from Refs. [17,33].

It becomes clear, at this point of the model presentation, thatadequate values ofw or _m00

v are fundamental to themodeling of poolformation and turbulent diffusion flames. Following, experimentaldata of wand _m00

v have been gathered, from different sources, inTable 1.

Based on Table 1, the present work adopted eight values of w, inm/s: 0.00021 [46], 0.0003 [2], 0.000324 [17,33], 0.000473 [23,25],0.000667 [24,25], 0.0008 [2], 0.000852 [24,25] and 0.0011 [4].Conversion between w and _m00

v was carried out with Eq. (18),assuming rl ¼ 422.5 kg/m3 for LNG at normal Tb ¼ 111.7 K andPa ¼ 102.3 kPa [24,25].

The equations used in themodel of TMS [17] and Raj [33], for thethermal plume of Fig. 2, are presented next. Wind effects are rep-resented [8,32,33] by:

U* ¼ Uwind�_m00v=ra

�gD1=3 (19)

and the combustion Froude number is defined as [8,17,32,33]:

FrC ¼ _m00v

raffiffiffiffiffiffigD

p (20)

Based on experiments, the following correlations were pro-posed [8,17,33,58] for the overall mean height (length) of the‘visible’ fire plume:

LVD

¼ 55Fr2=3C for U* � 1 (21)

LVD

¼ 55Fr2=3C

�U*��0:21

for U* > 1 (22)

Based on experimental data from 35 m-diameter Montoir LNGfire tests [8,35,45,59], the evaluation of L C near the fire base led to asmall value of around 15% (z10m) of the total ‘visible’ plume flame(66 m). Eqs. (23) and (24) were proposed [8,17,33] correlating LC, LIand LV with FrC.

j ¼ LCLV

¼�1� LI

LV

�¼ 0:70þ log10

hðFrCÞ1=4

i(23)

LI ¼ ð1� jÞLV (24)

Es is related to ss by E0 near the thermal plume base [33].

Es ¼ E0ss (25)

Total hemispheric transmissivity, independent of the wavelength, is given by Ref. [17,33]

ss ¼ e�ðALCsLbeamÞ (26)

For cylindrical fires, Lbeam should be considered as 63% of D[17,33]

Lbeam ¼ 0:63D (27)

and Cs in fire column is given by Ref. [8,17,32,33]

Cs ¼ raY1

1þ ðs=4Þ þ DHC=�cPaTa

� (28)

For petroleum fires of 0.1e17 m-diameters, Y was correlated[8,17,33,60] by:

Y ¼ 9:412þ 2:758 log10 ðDÞ (29)

Table 1LNG experimental and literature data of w and _m00

v.

Experiment/Study summary(description/premises considered)

Vaporization velocity [event](mechanism of heat transfer)hwia (m/s)

Vaporization massflow rate per areaunith _m00

vib (kg/m2.s)

Heat flux hq00i(kW/m2)

Remarks

Fay’s Study e Spill on water þ pool fire(Boiling þ thermal radiationto vaporize the pool) [1]

0.00019 [ConfinedLNG pool fire] (Fromwater only)

0.08 NAc NA

0.0005e0.0007 [Confined LNGspill on water] (Fromwater only)

0.21e0.29 NA NA

0.0008 [Unconfined LNG poolfire] (From water þ fire)

0.34 NA Spill volume (m3): 14,300Semicircular pool radius: 339 m

Analysis of vaporization velocities [2] 0.0002e0.0008 0.0845e0.338 NA Circular pool radius (m): > 100Sensitivity analysis of the variations of

thermal intensity level with distances [3]0.0003 0.1268 NA NA

Not ignited LNG pool on water. (Experimentsused markers in the pool and photography abovethe pool to record the spread rate and sizeof the pool over time. Determinationof’ h _m00

v i based on the measures of spill rateand pool area) [4]

0.0001e0.0004 [For all poolranges of the experiments]

0.0423e0.169[For all poolranges of theexperiments]

NA Ranges of the circularpools radius (m):1.97e3.630.75e6.067e14w10

Burning rate (vaporization mass flow rate per area unit)and heat flux analysis. (Three burning rates, one heatflux. Spread model considered: Webber) [24]

0.0005; 0.0007; 0.0009 0.20; 0.28; 0.36 265 Radius of the maximum pools(m): 120; 100; 93

Burning rate and heat flux analysis. (Three burning rates,one heat flux Spread model: NA) [25]

0.0005; 0.0007; 0.0009 0.20; 0.28; 0.36 265 Radius of the maximumpools (m): 90; 74; 66

Lehr’s Study (Spills comparison from refined oilproducts vs. LGN) [3,27]

0.0004e0.001 0.17e0.42 NA Spill volume (m3): 500

U.S. BuMines tests (‘Burro’ tests) [28] 0.0005; 0.0004 0.20; 0.17 85 NAU.S. Coast Guard LNG fire experiments on water

(‘China Lake’ tests, 1978) [3,36e40]0.0004e0.0011 0.17e0.465 220 � 50 Spill volume (m3): 3e5.5,

diameter of themaximum circular pool: 15 m

LNG fire experiments on water (‘MaplinSands’ tests, 1980) [3,41,42]

0.00021 Calculated 0.089 203 (average);178e248 (range)

Spill volume (m3):5e20; effectivepool diameter: 30 m

LGN fire experiments on water ‘Coyote’tests (1981) [43]

Not measured Not measured 150e340 Spill volume (m3): 14.6e28

LNG fire experiments on land (‘Maplin Sands’tests, 1982) [3,44]

0.000237 Measured 0.1 153 (Average),219 (Maxim)

Circular pooldiameter: 20 m

LNG fire experiments on land (‘Montoir’,three tests, 1989) [3,8,45]

0.00031 (From fire only)Measured

0.14 290e320 (NAR)d,257e273 (WAR)e

Spill volume (m3): 238; pooldiameter: 35 m

Quest’s Study (Release of GNL tanker atBoston Harbor) [3,46]

0.00071 0.3 NA Spill volume (m3): 12,500; Poolradius (m): 253 (No waves)

Vallejo’s Study (Spill from a ship tankconsider tears of 1 m and 5 mdiameter) [3,47].

0.00049 (From water only) 0.21 NA Spill volume (m3): 14,3000.0008 (From fire only) 0.34 NA

Unignited LNG pool on water [8,48](‘Thornton Center’ tests, LNGpoured onto a pond)

0.000068 0.029 NA Spill volume (m3):0.023e0.093 Poolradius (m) 1.97e3.63

Unignited LNG pool on water [8,49,50](‘U.S. BuMines’ tests)

0.00043 (From water only) 0.181 NA Spill volume (m3):0.0055e0.36 (pond)Pool radius (m): 0.75e6.1

Unignited LNG pool on water [8,51](‘Matagorda Bay’ tests)

0.00046 0.195 NA Spill volume (m3): 0.73e10.2Pool radius (m): 7e14

Unignited LNG pool on water [8,52](LNG inlet surroundedby a 300 m dyke)

0.0002 0.085 NA Spill volume (m3): 5e20Pool radius (m) w10

A.S.Esteves,J.A

.ReisParise

/Applied

Thermal

Engineering59

(2013)587

e598

592

Unignited

LNGpoo

lon

water

[8,53]

0.00

028

0.12

NA

Spill

volume(m

3):

4.2e

4.52

Pool

radius(m

):6.82

e7.22

Ignited

LNGpoo

lon

land[8,54]

(‘AGA’tests)

0.00

022

0.09

3NA

NA

Ignited

LNGpoo

lon

water

[8,55]

0.00

121

0.51

e0.14

5NA

Spill

volume(m

3):

3e5.7

Pool

radius(m

)w7.5

Spread

andva

porizationof

cryo

genic

liquidson

water

[8,56]

0.00

011e

0.00

045(From

water

only)

0.04

9e0.19

NA

Analytical

resu

lts

Spread

andva

porizationof

liquids[8,57]

0.00

049(From

water

only)

0.21

NA

Analytical

resu

lts

aQuan

tities

insidebracke

tsaretheav

erag

eof

seve

ralex

perim

ents.

bEx

perim

entan

dassessmen

tdatawereob

tained

byco

nve

rsion,a

ssuming[25]

r l¼

422.5kg

/m3@

P a¼

101.3kP

a,T a

¼29

3K;T b

¼11

1.7K;DHv l

¼50

9:3kJ=kg

;T w

¼29

3K.

cNot

available.

dNarrow

angleradiometer.

eW

idean

gleradiometer.

A.S. Esteves, J.A. Reis Parise / Applied Thermal Engineering 59 (2013) 587e598 593

In the intermittent zone, p(x) is assumed to be given by apolynomial variation of order n, calibrated (‘best fit’) to the exper-imental data from Refs. [8,17,32,33,35,59]

pðxÞ ¼ 1 for 0 � x � j (30)

pðxÞ ¼�1� x

1� j

�n

for j � x � 1 (31)

where

x ¼ ZLV

¼ length along the fire axisvisible fire plume length

� j (32)

Using the probability function p(x), it can be shown[8,17,32,33,35,59] that the mean SEP over the visible fire plumeheightE, can be given by:

EE0

¼ jþ"1þ ne�ðALCsLbeamÞ

1þ n

#ð1� jÞ (33)

The ‘best fit’ to the data from the 35 m-diameter Montoir LNGfire tests was obtained when n ¼ 3 [8,17,32,33,35,59]. Parameter εdepends on D, where kl is based on experimental data of the ChinaLake tests, as follows [17,33]:

ε ¼ 1� e�ðD=klÞ (34)

The value of Emax was found to be 325 kW/m2 [17,33], equivalentto a blackbody temperature of 1547 K [17,33]. With these empiricalparameters, E0 is calculated with kl ¼ 1=Ll [61], such as

E0 ¼ Emax 1� e� Dpci=klð Þh i

¼ Emax 1� e� DpciLlð Þh i

(35)

LNG pool fires are considered to be optically thick, irradiating asa blackbody in the region of higher thermal radiation, emitted nearthe substrate. The values obtained in Refs. [15e17,33] are used inthe present work.

3. Results and discussions

The resulting non-linear system of algebraic equations wassolved within the EES� platform. Studies on semicircular LNG poolsbehavior considered: Ah varying from 1 to 100 m2; Amax

pscand tv for

each. A specific Ah of 5 m2 was investigated with w ¼ 0.0008 m/s[2,3]. For the modeling of spill followed by combustion, twomembrane or prismatic carrier geometries were simulated:125,000 m3 and 265,000 m3 [1,2].

3.1. Comparison with existing pool spill/spreading models

3.1.1. Reproduction of results of Fay [1] ship geometryResults are presented in Fig. 3, Amax

pscand tv. Vessels with mem-

brane or prismatic tanks and constant cross section carrier wereconsidered [1]. As expected, a good agreement was obtained, as thepresent model only differs from Ref. [1] with the use of Eqs. (7) and(8) for the interval 1=3 � f � 30. The value of Amax

pscobtained for

Ah¼ 1m2 is around 40,000m2, comparing well to 39,900m2 in Ref.[1]. Similarly, for Ah ¼ 9.1 m2 (critical, in light gray color) and 20 m2

(maximum, in dark gray color), Amaxpsc

values of 184,000 m2 and214,000 m2, respectively, are close enough to 181,000 m2 and214,000 m2, from Ref. [1]. Similar agreement was obtained with tv.Finally, the ‘critical’ tear area is achieved when fcr assumes thevalue of 1.7825, against 1.784 found in Ref. [1]. These results sug-gests that Eqs. (7) and (8) did not influence the accuracy of results, ifcompared to Fay’s original model [1].

Fig. 3. Comparison of predictions of the present work with compilation of the originaldata obtained by Ref. [1]. Single membrane or prismatic cargo tank spill of an LNGcarrier with 14,300 m3, w ¼ 0.0008 m/s. Light gray: critical vaporization time andmaximum semicircular pool area. Dark gray: maximum vaporization time and peak ofmaximum area.

A.S. Esteves, J.A. Reis Parise / Applied Thermal Engineering 59 (2013) 587e598594

3.1.2. Comparison with the literature dataA sensitivity analysis was carried out, comparing results from

seven existing models with results of the present work, Tables 2and 3. The results of semicircular pool diameters obtained withthe application of Fay’s [1] model were converted to circular pooldiameters, Eq. (16), and were then used as input data to Raj’s [33]combustion model, so as to determine the variation of the surfaceemissive power (SEP) with the plume height.

Main parameters considered were Dpci, hDpci

i, tv and htvi ob-tained from other works considered [2,3,5,23e25,28,36]. Anaverage value of each parameter from those works was determinedand compared with the correspondent values found with the pre-sent model.

Results obtained for Dpciwith Fay’s [1] model differ, to a certain

extent, from other results presented in Tables 2 and 3. Such

Table 2Comparison with other models of literature for near shore operations. Dh ¼ 1 m, one ca

Results found in the literature and simulations made in the present work using Fay [1

V0 ¼ 12,500 m3, Ah ¼ 0.78 m2

Description DatafromRef. [23]

DatafromRef. [36](1)

Datafrom Ref. [28]

Datafrom Ref. [5](2)

Vaporizationvelocity w (m/s)

0.0007 0.0003(4) 0.0004(5) NA

Thermal flux emittedby the pool q

0 0(kW/m2)

143 65(8) 86(9) NA

Release mass flowrate _md (kg/s)

2300(11) 1000(11) 1700(12) app. 2300

Total spill duration td (min) 51 1.5(13) app. 50(14) 30Circular pool

diameter Dpci(m)

140 108 180(15) 124

Average circular pooldiameter hDpci

i (m)163

Deviation from averagecircular pooldiameter (%)

�14 �34 þ10 �24

Vaporization time tv (min) 51 1.5 NA NAAverage vaporization

time htvi (min)36

Deviation from the averagevaporization time (%)

þ42 �96 NA NA

Obs.: (1)Ah ¼ 0.44 m2. Continuous spill of inventory above water line of (2/3) (40,000 mAh ¼ 1 m2 and Cd ¼ 0.6; (4)Used by Refs. [3]; (5)Recommended by Refs. [24]; (6)[24] inpu(9)Calculated from (0.0004 m/s) (422.5 kg/m3) (509.3 J/kg); (10)Calculated from (0.0007 mbased on [24,25]; (12)Computed in Refs. [28], assuming zero the final value; (13)LNG reachapp. 1.5 min; (14)Inferred from Ref. [28] for Dh ¼ 1 m; (15)From Ref. [28] for Dh ¼ 1 m, wdiameter in accordance with Eq. (16).

differences can be partly explained by the distinct flowmodels thathave been adopted elsewhere [1,3,5,24,25,28,37,62,63].

Nevertheless, Fay’s [1] model proved to be robust, providingconsistent results for the range of today’s most commonmembraneLNG carriers. This model takes into account all relevant phenom-ena, including cryogenic spill and pool spreading, as well asvaporization of the maximum area onto the sea. Results indicatethat the model is accurate enough to fit industry needs, although aclose agreement between works is still a distant objective. Due tothe limitations and scarcity of field tests data, there remains anumber of issues on mechanisms that are still controversial [64].

3.2. Comparison with existing non-premixed turbulent pool firemodels and experimental data

The results found for E and other correlated parameters of thepool fire model were compared with the corresponding values ofthe literature [17,33], experiments of Montoir (France) and ChinaLake (USA) that were used [35] to calibrate TMS [17] and Raj [33]solid flame models. Circular pool fires with diameters of 15, 20,35, 100 and 300 m were simulated, and agreement between theseresults and the present model was good. Indeed, the predictedbehavior of FrC, Y, Cs, j, ss and E as functions of Dpci

was verified, andgenerally coincided, with original results from Refs. [15,17,33].Overall, agreement with available literature and experimental dataof E, from Refs. [17,33] and present work, was reasonable.

Data for comparison can be summarized as follows: (i) ForDpci

¼ 15 m: 172 [17,33] and 185e224 kW/m2 [39] of China Laketests vs. 171 kW/m2; (ii) for Dpci

¼ 20 m: 183 kW/m2 [17,33] and140e180 kW/m2 [65] for large scale LNG pool fires vs. 184 kW/m2;(iii) forDpci

¼ 35 m: 177 [17,33] and 175 � 30 kW/m2 [58] ofMontoir tests vs. 178 kW/m2; (iv) forDpci

¼ 100 m: 113 kW/m2

[17,33] vs. 113 kW/m2; and (v) for Dpci¼ 300 m [estimated pool

size due to spill of 1/2 cargo tank content (12,500 m3 of LNG) froman LNG carrier]: 90 kW/m2 [17,33] vs. 89 kW/m2.

rgo tank breached.

] model with Eqs. (7) and (8)

Datafrom Ref. [24]

Datafrom Ref. [25]

Present workinput datafrom Ref. [24]

Present workinput datafrom Ref. [25]

DatafromRefs. [2,3](3)

0.0007 0.0007 0.0007(6) 0,0007(7) 0.0003

265 265 151(10) 151(10) 220

1700(11) 2600(11) 1700(11) 2600(11) NA

51 33 27 27 NA141(16) 200 213(16) 213(16) 148

�13 þ23 þ31 þ31 �9

51 33 38 38 40

þ42 �8 þ5 þ5 þ11

3) z27,000 m3; (2)Total volume of continuous spill: 10,000 m3; (3)Accidental event,t data; (7)[25] input data; (8)Present work: (0.0003 m/s) (422.5 kg/m3) (509.3 J/kg);/s) (422.5 kg/m3) (509.3 J/kg); (11)Average inferred between initial and final values,es the top of the hole and the pool fire reaches the maximum diameter of 108 m inith circular pool diameter converted in accordance with Eq. (16). (16) Circular pool

Table 3Comparison with other models of literature for near shore operations. Dh ¼ 5 m; one cargo tank breached.

Results found in the literature and simulations made in the present work using Fay [1] model with Eqs. (7) and (8).

V0 ¼ 12,500 m3; Ah ¼ 19.6 m2

Description Data fromRef. [23]

Data fromRef. [36]

Data fromRef. [28]

Present workinput datafrom Ref. [28]

Data fromRef. [24]

Data fromRef. [25]

Present workinput datafrom Ref. [24]

Present workinput datafrom Ref. [25]

Data fromRefs. [2,3](1)

Vaporization velocity w (m/s) NA NA 0.0004(2) 0.0004(2) 0.0007 0.0007 0.0007(3) 0.0007(4) 0.0003Thermal flux

to the pool q00 (kW/m2)NA NA 86(5) 86(5) 265 265 151(6) 151(6) 220

Release mass flow rate _md (kg/s) NA NA NA NA 43,000(7) 65,000(7) 43,000(7) 65,000(7) NATotal spill duration td (min) NA NA 2(8) 1 2 1.3 1 1 NACircular pool diameter Dpci

(m) NA NA 495(9) 589(10) 438(10) 260 525 525 512Average circular pool diameter

between the literatureand this work hDpci

i (m)

472

Deviation from averagecircular pool diameter, (%)

NA NA þ5 þ25 �7 �45 þ11 þ11 þ8

Vaporization time tv (min) NA NA NA 3.8 4.2 6.9 3 3 3.4Average vaporization

time htvi (min)4.2

Deviation around the averagevaporization time (%)

NA NA NA �9 0 þ64 �28 �28 �19

Obs.: (1)Intentional event, Ah ¼ 12 m2 with Dhz4 m; Cd ¼ 0.6; (2)Recommended by Refs. [24]; (3)[24] input data; (4)[25] input data; (5)Calculated from (0.0004 m/s) (422.5 kg/m3) (509.3 J/kg); (6)Calculated from (0.0007 m/s) (422.5 kg/m3) (509.3 J/kg); (7)Average inferred between initial and final values, based on [24,25]; (8)Inferred from Ref. [28] forDh ¼ 5 m; (9)From Ref. [28] for Dh ¼ 5 m, with circular pool diameter in accordance with Eq. (16); (10)Circular pool diameter in accordance with Eq. (16).

A.S. Esteves, J.A. Reis Parise / Applied Thermal Engineering 59 (2013) 587e598 595

Table 4 compares predicted values of LV=Dpci, from present work

and other models [58,67e71], with experimental results fromChina Lake (tests number 1 and 4), Maplin Sands and Montoir (testnumber 2) compiled from Refs. [2,36]. Good agreement is shownwith deviations of, þ7.1%, þ3.6%, þ16.3% and �13.6%, respectively.

Fig. 4 shows the behavior of E using Eq. (36), which is similar toEq. (35), with different w and Dpci

,

E0 ¼ Eh1� e�ðDpci

LlÞihEmaxh1� e�ðDpci

LlÞi (36)

Eq. (36) was recommended by Refs. [72], used on the SanClemente AGA tests [54]. Good agreement was obtained for di-ameters up to 10m. Amean SEP of 142 kW/m2 and an average Ll, of0.18 m-1, were suggested by Ref. [72]. They were based on theexperimental data reported by Ref. [73] in AGA’s test series andcited in Ref. [17] for fire tests with pools of 6.1 m of diameter.

The present work simulated eight values of Dpci, 1, 1.7, 3.1, 5.8,

9.2, 12, 14 and 18 m, compiled from Refs. [72], and also used four wof 0.00067, 0.0008, 0.000852 and 0.0011 m/s according to [25], andmaximum SEPs, based on [72]. These simulations presented goodagreement withWARmeasurements of E [72] with diameters up to10 m. The simulation was scaled up to Dpci

of 12 m, 14 m and 18 m,and the predictions trends are also consistent with experimentalWAR measurements, as depicted in Fig. 4.

Table 4Comparison of thermal plume geometry predictions with results of tests and valuescited in literature. Compiled and adapted from Refs. [2,8,32,66]. (A) [67] (B) [68] (C)[58] (D) [69] (E) [70] (F) [71] (G) Present work.

Circular pooldiameter ðDpci

Þ (m)Test ðLV=Dpci Þ(substrate)

Prediction of LV=Dpci

(A) (B) (C) (D) (E) (F) (G)

8.5, Test#1, China LakeUwind ¼ 6.2 m/s

2.8 (Water) 2.8 2.0 3.0 4.7 4.1 3.6 3.0

9.0, Test#4, China Lake,Uwind ¼ 2.2 m/s

2.8 (Water) 2.6 1.9 2.5 3.9 3.7 3.1 2.9

20.0, Maplin Sands,Uwind ¼ 6.2 m/s

2.15 (Land) 2.2 1.6 1.6 2.9 3.1 2.4 2.5

35.0, Test#2, Montoir,Uwind ¼ 9.0 m/s

2.2 (Land) 2.2 1.6 1.5 2.9 3.1 2.4 1.9

Results confirm that E peaks occur due to the increase in ther-mal plume emissivity, up to a level when the pool fire diametersurpasses 3.5 times its spectral optical thickness ðDpci

� 3:5klÞ.Beyond this value, the thermal plume may be considered as ablackbody, and the temporal total hemispherical emissivity ap-proaches unity, as observed in Montoir [59] and China Lake [15]tests. Beyond this diameter, the emissive power declines. As anexample, in Montoir tests, the thermal plume already with adiameter of 20 m, was considered to radiate at 1516 K, close toblackbody’s at 1547 K.

Raj’s [17,33] model considers the diameter dependence in Eq.(29) as a substitute to air mixing inefficiencies and low oxygencontents in the fire plume inner core, instead of the explicitdependence on burning rate. If the vapor flow rate inside the fire isincreased, for a given diameter, it is expected that a higher per-centage of fuel should be converted to smoke, due to increased fuelconcentration and proportional reduction of oxygen.

Therefore, based on Eq. (29), higher _m00v are expected to lead to

incomplete combustion, with a greater fraction of the fuel massconverted into unburned carbon particles. If this argument is true,LNG fires on water will result smokier when compared to fires ofthe same diameter on land. Also, one may also infer that the hazard

Fig. 4. Mean SEP vs. circular pool fire diameters from 1 m to 18 m.

Table 5Results of coupling of pool spill and spreading with pool fire.

Coupling of spill and spreading and turbulent combustion models e simulation results

Geometry Parameter Dh ¼ 1 m � Ah ¼ 0.78 m2 Dh ¼ 5 m � Ah ¼ 19.6 m2

w � 10�4 (m/s)

2.10 3.24 8.00 11.0 2.10 3.24 8.00 11.0

Fay [1],a td (min) 27.1 27.1 27.1 27.1 1.1 1.1 1.1 1.1tv (min) 38.3 38.3 38.3 38.3 5.4 4.4 3.0 2.7Amaxpsc

(m2) 118,560 78,845 31,122 22,634 405,919 334,761 214,460 183,511Dpsc

(m) 549 442 282 240 1017 923 739 684Dpci

(m) 388 313 199 170 719 653 523 483FrC (e) 0.001221 0.002098 0.006497 0.009665 0.000897 0.001453 0.004008 0.005734LC (m) e 9 58 83 e e 73 119LV (m) 244 282 381 424 368 461 726 851j ¼ LC=LV (e) e 0.03 0.15 0.20 e e 0.10 0.14LV=Dpci

(e) 0.63 0.90 1.91 2.49 0.51 0.70 1.39 1.76Cs (kg/m3 � 10�4) 4.26 4.19 4.10 4.0 4.4 4.4 4.3 4.3ss (e) 0.0000013 0.0000215 0.00135 0,00379 0 0 8.0 � 10�9 3.7 � 10�9

E (kW/m2) 74 89 119 130 66 79 106 115Sandia [2] (Q-max)b td (min) 70.1 70.1 70.1 70.1 2.8 2.8 2.8 2.8

tv (min) 99.1 99.1 99.1 99.1 7.7 6.6 4.0 4.1Amaxpsc

(m2) 147,056 95,314 38,602 28,074 967,597 785,065 451,263 362,350Dpsc

(m) 612 493 314 267 1570 1414 1072 961Dpci

(m) 433 348 222 189 1130 1014 766 685FrC (e) 0.001156 0.001990 0.00615 0.009167 0.000716 0.001166 0.003312 0.004815LC (m) e 7 60 87 e e 75 130LV (m) 262 303 410 455 497 618 936 1074j ¼ LC=LV(�) e 0.024 0.15 0,19 e e 0.08 0.12LV=Dpci

(e) 0.61 0.87 1.85 2.41 0.44 0.61 1.22 1.57Cs (kg/m3 � 10�4) 4.3 4.2 4.1 4,0 4.6 4.5 4.4 4.4ss (e) 0.00000024 0.0000059 0.000593 0.001933 0 0 0 0E (kW/m2) 73 87 118 128 60 73 101 111

a Carrier geometry [1] CVC ¼ 125,000 m3; CTV ¼ CVC/5 ¼ 25,000 m3; Assumed a carrier with n ¼ 5 membrane or prismatic cargo tanks with one cargo tank breached;V0 ¼ 12,500 m3; DR ¼ 11.8 m; h0 ¼ 13 m.

b Carrier geometry [2] CVC ¼ 265,000 m3 (Q-max); CTV ¼ CVC/5 ¼ 53,000 m3; Assumed a carrier with n ¼ 5 membrane or prismatic cargo tanks with one cargo tankbreached; V0 ¼ 41,000 m3; DR ¼ 12,5 m; h0 ¼ 20 m.

A.S. Esteves, J.A. Reis Parise / Applied Thermal Engineering 59 (2013) 587e598596

distance from LNG fires on water will be less than that from a landfire of the same diameter.

3.3. Coupling of spill and spreading and non-premixed turbulentpool fire models

A global study of the problem, encompassing the two modelssimultaneously, is presented in Table 5. It shows an overall con-sistency of results, as depicted in each geometry [1,2], using teararea values suggested in Refs. [2,3,25].

For w ¼ 0.000324 m/s, for example, Ah ¼ 0.78 m2 does not affectsubstantially FrC for both CVCs. Consequently, the pool fire geome-try, LV=Dpci

, as well as the values of LC, LV and j ¼ LC=LV are nearlythe same for both. In two CVCs, the axial emissive power along the‘visible’ thermal plume increases with the vaporization velocity,while Dpci

decreases as the plume geometry increases. Alternatively,LV=Dpci

decreases as Ah increases, in both carrier geometries.If the heat transfer mechanisms, radiation from the fire plume

and boiling by Liedenfrost effect (LNG film contact with sea water)are considered, w increases, thus reducing Amax

psc. This behavior is

consistent with trends forAmaxpsc

. When comparing the two geome-tries, it is expected that a nearly 2-fold increase in cargo volumewould produce an increase in td and tv. Taken into consideration thevariations of LC and LV, it is observed that LC contribution governsthe plume geometry, since this region concentrates most of theenergy radiated by the fire, which produces E. Therefore, the higherthe LC, the higher the values of LV, LV=Dpci

, ss and E will be in bothgeometries. On the other hand, Cs will rise slightly for an increase ingeometry, and will reduce with Dh. Larger cargo geometriesaugment td and tv substantially, whereas larger Ah reduces

drastically both times, although these variables are not significantlysensitive to the rise of w, in each geometry. However, if Dh rises, itrepresents a drastic reduction in td and tv, and, again, they are notsensitive to the increase ofw. Notwithstanding the fact thatDpsc

andDpci

increase with geometry, LV=Dpcidecreases as Dh rises, for each

corresponding value of w. The same reducing trend is observed forss and E, as Ah augments.

Table 5 shows that LV=Dpciwas nearly insensitive to the 2-fold

scale up of carrier capacity, which demonstrates the numericalrobustness and coherence of the spill-combustion model coupling.As an example, with w ¼ 0.000324 m/s and Dpci

¼ 300 m [17,33],found a SEP of 90 kW/m2 and j ¼ LC=LV ¼ 0:033. Coupling thetwo models, the results Dpci

¼ 313 m with Fay [1] geometry wereE ¼ 89 kW/m2 and j ¼ LC=LV ¼ 0:03, respectively. Sandia [2]geometry, with Dpci

¼ 348 m, provided E of 87 kW/m2 andj ¼ 0.024, i.e., the same order of magnitude.

The discussion above reveals that the coupling of both modelsprovides results that are consistent with expected trends.

4. Conclusion

The following conclusions can be withdrawn:

� More than 20 orifice models published since 1969 werereviewed, as well as several types of pool fire models: punctualsource flame [11], solid flame [12], integral [13,14], multi-zones[15e17], field (CFD) [18]. To the authors’ knowledge, no workhas been published to the present date coupling, explicitly,models of spill and spreading and turbulent diffusion pool fire;

A.S. Esteves, J.A. Reis Parise / Applied Thermal Engineering 59 (2013) 587e598 597

� A comprehensive review of experimental of data for w and _m00v,

since 1978, has been presented;� Results attest the robustness of both models. The present workcovered spill and spreading with Ah between 1 and 100 m2,possible to occur at in the current LNG industry, testing 20 holediameters with 8 vaporization velocities. The turbulent diffu-sion fire model covered circular pools from 1 to 500 m diam-eter, with 50 different diameters and 8 vaporization velocities.The model proved to be robust and reliable, simulating all therelevant phenomena and important mechanisms;

� Concerning flow parameter, f, it was adjusted by Eqs. (7) and(8) in the interval 1=3 � f � 30, with the adoption of acontinuous logarithm and the second order polynomial for‘best fit’ adjustment. Results indicated that the proposedadjustment did not affect substantially the values obtained;

� When compared to experimental measurements of mean SEPfromNAR radiometers, as presented in Table 5, along the plumeaxis, the model reproduced well the experiments of China Lake[40], large scale LNG pool fires [65] and Montoir [59].

Acknowledgements

The authors are indebted to CNPq (from the BrazilianMinistry ofScience and Technology) and to FAPERJ (State of Rio de JaneiroResearch Funding Agency) for the financial support.

References

[1] J.A. Fay, Model of spills and fires from LNG and oil tankers, J. Hazard. Mater. 96(2003) 171e188.

[2] A. Luketa, M.M. Hightower, S. Attaway, Breach and safety analysis of spillsover water from large liquefied natural gas carriers, in: Sandia National Lab-oratories (Ed.), Technical Report SAND2008-3153, U.S. Department of Energy(USDOE), Washington, DC; Albuquerque, NM; Livermore, CA, May 2008.

[3] M.M. Hightower, L. Gritzo, A. Luketa-Hanlin, J. Covan, S. Tieszen, G. Wellman,M. Irwan, M. Kaneshige, B. Melof, C. Morrow, D. Ragland, Guidance on riskanalysis and safety implications of a large liquefied natural gas (LNG) spillover water, in: Sandia National Laboratories (Ed.), Technical ReportSAND2004-6258, U.S. Department of Energy, Washington, DC; Albuquerque,NM; Livermore, CA, December 2004.

[4] A. Luketa-Hanlin, A review of large-scale spills: experiments and modeling,J. Hazard. Mater. A132 (2006) 119e140.

[5] Otterman, Analysis of large LNG spills on water. Part 1: liquid spread andevaporation, Cryogenics (1975) 455e460.

[6] D.M. Webber, P.W.M. Brighton, Similarity solutions for the spreading of liquidpools, in: UK Atomic Energy Authority, Safety and Reliability Directorate(UKAEA) (Ed.), Technical Report UKAEA SRD/R371, London (July 1987).

[7] J.A. Fay, Spread of large LNG pools on the sea, J. Hazard. Mater. 140 (2007)541e551.

[8] M.S. Mannan, B.R. Cormier, P. Lian, M. Rana, D. Startz, J.A. Suardin, J. Wang,Y. Zhang, LNG pool fire modeling e white paper, in: Mary Kay O’ConnorProcess Safety Center (Ed.), LNG Spread and Pool Formation Considerationsand Models, Artie McFerrin Department of Chemical Engineering Texas A&MUniversity System, College Station, TX, 2008.

[9] D.M. Webber, S.E. Grant, M.J. Ivings, S.F. Jagger, in: Health and Safety Labo-ratory (Ed.), LNG Source Term Models for Hazard Analysis: A Review of theState-of-the-art and an Approach to Model Assessment, HSE, Buxton, Derby-shire, 2010.

[10] R. Pula, F.I. Khan, B. Veitch, P.R. Amyotte, Revised fire consequence modelsfor offshore quantitative risk assessment, J. Loss Prev. Proc. Ind. 18 (2005)443e454.

[11] F.P. Lees, Loss Prevention in Process Industries, Hazard Identification,Assessment and Control, second ed., Butterworth-Heinemann, Oxford, UK,1996.

[12] P.J. Rew, H. Spencer, T. Madison, Sensitivity of Risk Assessment of Flash FireEvents to Modeling Assumptions, IChemE Symposium Series, 144, 1998,265e278.

[13] M. Vachon, M. Champion, Integral model of a flame with large buoyancy ef-fects, Combust. Flame 63 (1986) 269e278.

[14] D.C. Wilcox, Model for fires with low initial momentum and nongray thermalradiation, AIAA J. 13 (1975) 381e386.

[15] P.K. Raj, LNG fires: a review of experimental results, models and hazardprediction challenges, J. Hazard. Mater. 140 (2007) 444e464.

[16] J.A. Fay, Model of large pool fires, J. Hazard. Mater. B136 (2006) 219e232.[17] TMS. Technology & Management Systems, Inc, Spectrum of Fires in a LNG

Facility - Assessments, Models and Consideration in Risk Evaluations, Final

Technical Report, The U.S. Department of Transportation Pipeline & Hazard-ous Materials Safety Administration, Burlington, MA, 2006.

[18] A.D. Johnson, A model for predicting thermal radiation hazards from large-scale LNG pool fires, in: EFCE (Ed.), Major Hazards Onshore and Offshore,IchemE Symposium Series No. 130, European Federation of Chemical Engi-neers (EFCE) Event No. 470, EFCE Publication No. 93, EFCE, Manchester, UK,1992, pp. 507e524.

[19] J.F. Sacadura, Radiative heat transfer in the safety science, J. Quant. Spectr.Rad. Trans. 93 (5) (2005) 24.

[20] C.L. Beyler, Fire hazard calculations for large, open hydrocarbon fires, in:P.J. DiNenno (Ed.), Handbook of Fire Protection Engineering, third ed,, Na-tional Fire Protection Association (NFPA), Society of Fire Protection Engi-neering (SFPE), Quincy, MA, 2002.

[21] W.F.J.M. Engelhard, Heat flux from fires, in: , third ed,, in: C.J.H. Van den Bosch,R.A.P.M. Weterings (Eds.), Methods for the Calculation of Physical Effects Dueto Release of Hazardous Materials (Liquids and Gases) (‘Yellow Book’), Part 2,2 v, The Netherlands Organization of Applied Scientific Research (TNO), TheHague, 1997, pp. 6.1e6.130.

[22] K.S. Mudan, Thermal radiation hazards from hydrocarbon pool fires, Prog.Energy Combust. Sci. 10 (1984) 59e80.

[23] D.W. Johnson, J. Cornwell, Modeling the release, spreading, and burning ofLNG, LPG, and gasoline on water, J. Hazard. Mater 140 (2007) 535e540.

[24] United States. the Federal Energy Regulatory Commission (FERC), Notice ofAvailability of Staff’s Responses to Comments on the Consequence AssessmentMethods for Incidents Involving Releases from Liquefied Natural Gas Carriers,DC: Docket No. AD04-6-000, Washington, June 2004.

[25] ABS Consulting Group. Consequence Assessment Methods for IncidentsInvolving Releases from Liquefied Natural Gas Carriers, Technical Report toFederal Energy Regulatory Commission-ferc, 131e04 GEMS 1288209, Wash-ington, DC, May 2004.

[26] G. Opschoor, The spreading and evaporation of LNG- and burning LNG-spillson water, J. Hazard. Mater. 3 (1980) 249e266.

[27] W. Lehr, D. Simecek-Beatty, Comparison of hypothetical LNG and fuel oil fireson water, J. Hazard. Mater. 107 (2004) 3e9.

[28] Y. Qiao, H.H. West, M.S. Mannan, D.W. Johnson, J.B. Cornell, Assessment of theeffects of release variables on the consequences of LNG spillage onto waterusing FERC models, J. Hazard. Mater. 130 (2006) 155e162.

[29] A. Luketa, Recommendations on the prediction of thermal hazard distances fromlarge liquefied natural gas pool fires on water for solid flame models, in: SandiaNational Laboratories (Ed.), Technical Report SAND2011-0495, U.S. Departmentof Energy, Washington, DC; Albuquerque, NM; Livermore, CA, 2011.

[30] T. Blanchat, P. Helmick, R. Jensen, A. Luketa, R. Deola, J. Suo-Anttila, J. Mercier,T. Miller, A. Ricks, R. Simpson, B. Demosthenous, S. Tieszen, M. Hightower, ThePhoenix series large scale LNG pool fire experiments, in: Sandia NationalLaboratories (Ed.), Sandia Report SAND2010-8676, U.S. Department of Energy,Washington, DC; Albuquerque, NM; Livermore, CA, December 2011.

[31] H. Oka, Consequence analysis of large-scale liquefied natural gas spills onwater, in: Primoz Potocnik & InTech (Ed.), Natural Gas, National MaritimeResearch Institute, Croatia, Japan, 2010, pp. 549e570.

[32] J.L. Woodward, R.M. Pitblado, LNG pool fire modeling, in: LGN Risk BasedSafety, AIChE, John Wiley & Sons, Hoboken, NJ, 2010, pp. 222e274.

[33] P.K. Raj, Large hydrocarbon fuel pool fires, physical characteristics and ther-mal emission variations with height, J. Hazard. Mater. 140 (2007) 280e292.

[34] W.J. Lehr, Unique physics of LNG spills, in: Proceedings of the Thirtieth AMOPTechnical Seminar, Environment Canada, Ottawa, ON, 2007, pp. 637e644.

[35] H. Malvos, P.K. Raj, Thermal emission and other characteristics of large liq-uefied natural gas fires, Proc. Saf. Prog. 26 (3) (September 2007) 237e247.

[36] D.R. Hissong, Keys to modeling LNG spills on water, J. Hazard. Mater. 140(2007) 465e477.

[37] A.L. Schneider et al., U.S. Coast Guard Liquefied Natural Gas Research at ChinaLake, Gastech 78. Monte Carlo, France, 5e8 October 1978.

[38] P.K. Raj, et al., LNG Spill Fire Tests on Water: An Overview of the Results,American Gas Association (AGA), 1979, pp. T246eT251. Oper. Sect., Proc.

[39] P.K. Raj, K.S. Mudan, A.N. Moussa, Experiments Involving Pool and Vapor Firesfrom Spills of LNG onWater. Report #CG-D-55e79, NTIS AD077073, U.S. CoastGuard (USCG), Washington, DC, 1979, p. 20590.

[40] A.L. Schneider, Liquefied natural gas spills on water fire modeling, J. FireFlammabil. 12-4 (1980) 302e313.

[41] G.A. Mizner, J.A. Eyre, Radiation from liquefied gas fires on water, Comb. Sci.Tech. 35 (1983) 33e57.

[42] W.J.S. Hirst, J.A. Eyre, J.A. Maplin, Sands experiments 1980: combustion oflarge LNG and refrigerated liquid propane spills on the sea, Heavy Gas RiskAssess. (1983) 211e224.

[43] H.C. Rodean, W.J. Hogan, H.C. Urtiew, et al., Vapor Burn Analysis for the CoyoteSeries LNG Spill Experiments, UCRL-53530, Lawrence Livermore NationalLaboratory (LLNL), Livermore, CA, 1984.

[44] G.A. Mizner, J.A. Eyre, Large-scale LNG and LPG Pool Fires, EFCE Publ. Ser. 25(1982) 147e163. (European Federation of Chemical Engineering).

[45] D.J. Nedelka, J. Moorhouse, R.F. Tucker, The montoir 35 m diameter LNG poolfire experiments, in: Proceedings of the Ninth International Conference &Exposition on Natural Gas, LNG9, TRCP.3148R, Nice, France, 17-20 October,1989.

[46] Quest Consultants, Inc., Modeling LNG spills in Boston harbor, 2001, 2003, in:ABS Consulting Group (Ed.), Consequence Assessment Methods for IncidentsInvolving Releases from Liquefied Natural Gas Carriers, Technical Report to

A.S. Esteves, J.A. Reis Parise / Applied Thermal Engineering 59 (2013) 587e598598

The Federal Energy Regulatory Commission-FERC, 131-04 GEMS 1288209,Washington, DC: May 2004, 56 p.

[47] City of Vallejo, liquefied natural gas, in: Vallejo (Ed.), Health and Safety Issues,Final Report, LNG Health and Safety Committee, Vallejo, CA, January 2003.

[48] G.J. Boyle, A. Kneebone, Laboratory Investigation into the Characteristics ofLNG Spills on Water. Evaporation, Spreading and Vapor Dispersion, ShellResearch Ltd., Thornton Research Center, 1973.

[49] D. Burgess, J. Biordi, J. Murphy, Hazards of Spillage of LNG into Water, U.S.Bureau of Mines, Pittsburg, PA, 1972.

[50] D. Burgess, D.J. Murphy, M.G. Zabetakis, Hazards Associated with the Spillageof Liquefied Natural Gas on Water, U.S. Bureau of Mines, 1970.

[51] G.F. Feldbauer, J.J. Heigl, W. McQueen, R.H. Whipp, W.G. May, Spills of LNGonto Water: Vaporization and Downwind Drift of Combustible Mixture, EssoResearch and Engineering Co., 1972.

[52] J.S. Puttock, D.R. Blackmore, G.W. Colenbrander, Field experiments on densegas dispersion, J. Hazard. Mater. 6 (1-2) (1982) 13e41.

[53] R.P. Koopman, B.R. Bowman, D.L. Ermak, Data and Calculation of 5 M3 LNGSpills Tests. Technical Report UCRL-52976, Lawrence Livermore Laboratory(LLNL), Livermore, CA, 1979.

[54] American Gas Association, LNG safety program, in: AGA Interim Report onPhase II Work, IS-31, AGA, Arlington, VA, 1974.

[55] P.K. Raj, A.L. Moussa, K. Aravamudan, Experiments involving pool and vaporfires from spills of LNG on water, in: USCG (Ed.), U.S. Coast Guard (USCG)Report NTIS (National Technical Information Service) AD-107703, Arthur D.Little, Washington, DC, 1979.

[56] P.J. Waite, R.J. Whitehouse, E.B. Winn, W.A. Wakeham, The spread and vapor-ization of cryogenic liquids on water, J. Hazard. Mater. 8 (2) (1983) 165e184.

[57] F. Briscoe, P. Shaw, Spread and evaporation of liquid, Prog. Eng. Combust. Sci.6 (2) (1980) 127e140.

[58] P.H. Thomas, Fire Spread in Wooden Cribs: Part III, the Effect of Wind. FireResearch Station, Fire Research Note No. 600, Boreham Woods, England, June1965.

[59] H. Malvos, P.K. Raj, Details of 35 m diameter LNG fire tests conducted inMontoir, France, in 1987 and analysis of fire spectral and other data, in: AIChE(Ed.), Paper Presented in Session T6005 LNG VI, Risk & Safety, American Insti-tute of Chemical Engineers (AIChE)Winter Conference, Orlando, FL, April 2006.

[60] K.A. Notarianni, D.D. Evans, W.D. Walton, D. Madrzykowski, J.R. Lawson,Smoke production from large oil pool fires, in: Interscience CommunicationsLtd London (Eds.), Proceedings of the Interflam 1993 Fire Safety InternationalFire Conference, Oxford, UK, March 1993, pp. 111e119.

[61] R. Siegel, J.R. Howell, Thermal Radiation Heat Transfer, fourth ed., Taylor andFrancis, New York, 2001.

[62] C.J.H. Van den Bosch, Pool evaporation, third ed., in: C.J.H. Van den Bosch,R.A.P.M. Weterings (Eds.), Methods for the Calculation of Physical Effects Dueto Release of Hazardous Materials (Liquids and Gases) (‘Yellow Book’), Part 1,2 v, The Netherlands Organization of Applied Scientific Research (TNO), TheHague, 1997, pp. 3.1e3.126.

[63] A. Luketa-Hanlin, M. Hightower, On the Evaluation of Models for HazardPrediction for Liquefied Natural Gas (LNG) Spills on Water, Sandia NationalLaboratories, Albuquerque, NW, 2008.

[64] W.J. Lehr, Foreword, my natural gas bias, J. Hazard. Mater. 140 (2007) 411.[65] G.A. Mizner, J.A Eyre, Large scale LNG and LPG pool fires, in: Proceedings of the

Institution of Chemical Engineering Symposium, Series 71, Manchester, April,1982.

[66] M. Hightower, Suggestions on modeling LNG release from a ship, in: CLNGWorkshop on LNG Pool Fire Modeling, Washington DC, 2007.

[67] M.J. Pritchard, T.M. Binding, FIRE2�: a New Approach for Predicting ThermalRadiation Levels from Hydrocarbon Pool Fires. IChemE Symposium Series 130,1992, 491e505.

[68] D.J. Moorhouse, M.J. Pritchard, Thermal Radiation Hazards from Large PoolFires and Fireballs: a Literature Review, European Federation of ChemicalEngineering 25, IChemE Symposium Series, 71, 1982, 397e428.

[69] E.E. Zukoski, Properties of fire plumes. in: Combustion Fundamentals of Fire,Academic Press, G. Cox (Ed.), London, 195, pp. 101e219.

[70] F.R. Steward, Prediction of the height of turbulent diffusion buoyant flames,Combust. Sci. Technol. 2 (1970) 203e212.

[71] G. Heskestad, Dynamics of the fire plume, Phil. Trans. Royal Soc. London A 356(1998) 2815e2833.

[72] L.E. Brown, H.R. Wesson, J.R. Welker, Predict LNG fire radiation, HydrocarbonProc. (1974) 141e143.

[73] P.K. Raj, S. Atallah, Thermal radiation from LNG fires, Adv. Cryogen. Eng. 20(1974) 143e150.