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Review

Toxic industrial chemical (TIC) source emissions modeling for pressurizedliquefied gases

Rex Britter a, Jeffrey Weil b, Joseph Leung c, Steven Hanna d,*

aMassachusetts Institute of Technology, Cambridge, MA, USAbUniversity of Colorado, Boulder CO, USAc Leung Inc., Rancho Palos Verdes, CA, USAdHanna Consultants, 7 Crescent Ave., Kennebunkport, ME 04046, USA

a r t i c l e i n f o

Article history:Received 23 February 2010Received in revised form15 August 2010Accepted 9 September 2010

Keywords:Chlorine releases to atmosphereHazardous chemicalsPressurized liquefied gas releasesSource emission modelsToxic industrial chemicalsTwo-phase jets

a b s t r a c t

The objective of this article is to report current toxic industrial chemical (TIC) source emissions formulasappropriate for use in atmospheric comprehensive risk assessment models so as to represent state-of-the-art knowledge. The focus is on high-priority scenarios, including two-phase releases of pressur-ized liquefied gases such as chlorine from rail cars. The total mass released and the release duration aremajor parameters, as well as the velocity, thermodynamic state, and amount and droplet sizes ofimbedded aerosols of the material at the exit of the rupture, which are required as inputs to thesubsequent jet and dispersion modeling. Because of the many possible release scenarios that coulddevelop, a suite of model equations has been described. These allow for gas, two-phase or liquid storageand release through ruptures of various types including sharp-edged and “pipe-like” ruptures. Modelequations for jet depressurization and phase change due to flashing are available. Consideration of theimportance of vessel response to a rupture is introduced. The breakup of the jet into fine droplets andtheir subsequent suspension and evaporation, or rainout is still a significant uncertainty in the overallmodeling process. The recommended models are evaluated with data from various TIC field experiments,in particular recent experiments with pressurized liquefied gases. It is found that there is typicallya factor of two error in models compared with research-grade observations of mass flow rates. However,biases are present in models’ estimates of the droplet size distributions resulting from flashing releases.

� 2010 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1. The type of rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2

2. Fluid property information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33. Release rate and exit thermodynamic conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.1. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43.2. Recommended approach where the liquid is subcooled referenced to the saturation temperature at both the storage pressure and

atmospheric pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53.3. Recommended approach where the vapor is superheated referenced to the saturation temperature at both storage and atmospheric pressure 53.4. Recommended approach for the release of material that is initially, or becomes, two-phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

3.4.1. Release from storage at saturated conditions as a liquid, as a gas or as a two-phase mixture of the two . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63.4.2. The non-equilibrium flow of a saturated liquid through a rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83.4.3. The release of a subcooled liquid through a rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .93.4.4. A non-equilibrium flow of a subcooled liquid through a rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.4.5. The effect of a rupture in a longer pipe connected to a vessel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.4.6. An exact alternative exact approach for the two-phase case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.5. The discharge coefficient CD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

* Corresponding author. Tel.: þ1 207 967 4478.E-mail address: [email protected] (S. Hanna).

Contents lists available at ScienceDirect

Atmospheric Environment

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

1352-2310/$ e see front matter � 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.atmosenv.2010.09.021

Atmospheric Environment 45 (2011) 1e25


4. Storage vessel response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .114.2. On level swell and discharge exit conditions during vessel blowdown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.2.1. Basic relations in level swell analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.2.2. Complete vaporeliquid (V/L) disengagement (top vent) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.2.3. Partial V/L disengagement (top vent) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.2.4. Exit conditions for side and bottom vents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5. Flow after exit from the storage vessel and coupling with an air flow and dispersion model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135.1. Jet depressurization to atmospheric pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145.2. Flashing of superheated liquid to vapor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145.3. Breakup of liquid to form small droplets and rainout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.3.1. Initial drop size and its distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166. Evaluation of the modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

6.1. Discharge conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .176.1.1. Evaluation of the modeling of the mass discharge rate: single-phase release . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .176.1.2. Evaluation of the modeling of the mass discharge rate: two-phase release . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186.1.3. Evaluation of the modeling of the thermodynamic state of discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196.1.4. Evaluation of the modeling of the exit velocity and momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

6.2. Evaluation of the modeling of jet breakup, droplet particle size and rainout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206.2.1. RELEASE model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206.2.2. RELEASE/CCPS experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206.2.3. RELEASE model results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216.2.4. JIP model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216.2.5. JIP model results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

7. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

1. Introduction

In this paper, models are addressed that can calculate toxicindustrial chemical (TIC) emission rates and other sourceparameters at the point where the emissions are “handed off” toatmospheric transport and dispersion models. A few representa-tive papers from this journal describing TIC transport anddispersion models are Anfossi et al. (2010), Hanna et al. (2009),Lee et al. (2007), Mohan et al. (1995), and Witlox and McFarlane(1994). These authors usually depend on someone else toprovide the TIC source emission rates and physical and chemicalconditions. In the case of two-phase TIC jets from pressurizedliquefied containers, the transport and dispersion model is usuallylooking for source input information after the velocity of themomentum jet has decreased to a value “close to” ambientvelocity.

Generally what are required are TIC source emissions modelsthat are of the right quality, i.e., models that are “fit-for-purpose”.This requirement refers to the incorporated physics and chemistry,to the mathematical coding and to a formal evaluation of theperformancemetrics of the model. In the 1996 AIChE Guidelines forVapor Cloud Modeling (Hanna et al., 1996), the available sourceemissions models are reviewed and recommendations made.However, since that time, there have been several advances inunderstanding the scientific issues concerning these types ofreleases, and concerns about pressurized liquefied gas releaseshave increased due to a few major railcar accidents and due toterrorism threats. The generic approach for the modeling of thesource term for a TIC release is outlined below.

There are various specific scenarios of interest and these dependupon the following factors:

The stored material e Each TIC material has its own thermody-namic, fluid mechanical and transport properties, and the degree ofdetail within various models may require more or less propertyinformation.

The type of storage (geometry) e Models may be required thatcan accommodate any shape of storage vessel. However twoparticular shapes are fairly common, that is the cylindrical storagevessel with either vertical or horizontal axis.

The type of storage (thermodynamic state) e Generally there areonly a limited number of cases and these are:

� Material stored as a vapor only; consequently the materialmust be saturated or superheated (with respect to the satu-rated state at the storage pressure); e.g., water vapor/steamstored at 120� C at 1 atm pressure. (See Glossary for the defi-nition of terms)

� Material stored as a liquid only (though typically stored undera pad gas (e.g., nitrogen) pressure); the material must besaturated or subcooled (with respect to the saturated state atthe storage pressure). This includes the case of material storedas a liquid at ambient temperature and pressure; e.g., waterstored at 20� C and 1 atm pressure. Alternatively it could bea material stored as a liquid at a pressure that is equal to orabove the saturated vapor pressure for the storage tempera-ture; e.g., water stored at 100� C and 1.2 atm pressure.

� Material stored as a vapor and liquid together at saturationcondition, that is at a pressure and temperature that lie on thesaturated vapor line; e.g., water and steam stored together at100� C and 1 atm pressure.

1.1. The type of rupture

There are five broad categories:

� Catastrophic failure� Those that resemble a sharp-edged orifice; the term “sharp-edged” refers to an idealized orifice type that is often consid-ered as a limiting case.

R. Britter et al. / Atmospheric Environment 45 (2011) 1e252


� Those that resemble many sharp-edged orifices� Those that resemble a short pipe. This last case may be pipe-like just because of the width of the wall of the containingvessel.

� Those from a rupture in a long pipe connected to a vessel

Three accidental chlorine releases from rail cars have beenstudied in some detail (e.g., Hanna et al., 2008). At theMacdona andGraniteville accidents the ruptures were jagged holes of roughdimension 10 cm by 30 cm. These would be classed as resemblingsharp-edged orifices unless the storage vessel wall was thicker than0.1 m. The storage vessel wall was estimated to be of the order of0.1 m for these accidents. For the Festus accident the rupture was atthe end of a long, narrow pipe connected to a storage vessel.

From knowledge of the stored material, the type of storage(geometrical and thermodynamic) and the type of rupture themodel(s) must calculate:

� The release rate and other characteristics of the release at therupture

� The resulting response of thematerial within the storage vesselfollowing the rupture

� The consequences of the near source depressurization toatmospheric pressure

� The partition of the material into vapor, suspended liquidaerosol and liquid rainout close to the release

Our approach requires the selecting, from the various availablemodels, models that will address adequately the processes above.An important issue here is to ensure that the selected models arewell-balanced in the sense that they all have similar accuracy andsimilar speeds and similar complexity or simplicity. These are oftenmatters of judgment and pragmatism and should be guided by theoverall model “purpose” and also by the current state of develop-ment or development intent of existing operational models.

Our detailed project reports (Britter et al., 2009; HannaConsultants, 2009) cover a comprehensive set of TIC source emis-sions equation recommendations, including evaporation fromliquid pools, evaluations of all equations with field and laboratorydata, and worked examples from eight categories of TIC scenarios.In this paper we focus on pressurized liquefied gases and considerthe following parts of the modeling process in turn:

� Fluid property information� Release rate and exit thermodynamic conditions� Vessel response� Flow after exit from the storage vessel

2. Fluid property information

The TICs are principally of concern as inhalation hazards. Thescale over which health effects occur will depend upon the toxicityof the material, the amount of material likely to be released in anincident, andwhether their boiling point is low enough so that theyrapidly become gases or suspended aerosols upon release. Thereare many toxic chemicals stored as gases and these must also beconsidered; however, the mass stored is likely to be much less thanfor the storage of liquefied gases. Hanna Consultants (2006) indi-cate the comparative health impacts in one particular region thatmay result from releases of various stored and transported TICstaking into account the above features. The “top 13” are:

Chlorine, Sulfur Dioxide, Ammonia (anhydrous), HydrogenChloride (anhydrous), Phosgene, Bromine, Acrolein, HydrogenCyanide, Chlorine Trifluoride, Methyl Chloroformate, Oleum (65%SO3), Hydrogen Fluoride, Phosphorus Trichloride

It is clear that common chemicals such as chlorine, ammoniaand sulfur dioxide top this list, reflecting the large amounts of thechemicals being stored and transported. Because many TICs ofinterest are commonly stored as liquids and will commonlydisperse as gases, the study of TIC releases will also commonlyinvolve the fluid mechanics and thermodynamics of multi-phaseflows. The material properties play an important role in such flows.

The nature of much of the fluid information required is obtainedwithin the liquidevapor phase diagram. Various forms of thisdiagram are available of which the most easily interpreted is thatusing pressure and specific volume (inverse of density) as axes andtemperature as the parameter. However, because pressure andtemperature are not independent in a two-phase region this formof phase diagram is less useful. The preferred version is the tem-peratureeentropy form with pressure as the parameter, shown inFig. 1, which applies to chlorine. The quantitative data are availablein tabular/electronic form from various standard sources and someof these are listed in the next section.

The lines shown are constant pressure lines in units of Mega-Pascals. The “hump” shape in the middle is the saturation linethat demarcates the two-phase region. A depressurization, ata commonly-assumed constant entropy, will produce a vertical lineindicating a temperature reduction. The area to the left of the“hump” is referred to as subcooled liquid while the area to the rightof thehump is referred to as superheatedvapor. These terms are usedhere solely to indicate that the material is a liquid or a vaporrespectively and is not within the two-phase region or on the satu-ration line. These terms are often used when referring to the state ofthe material within a storage vessel. To the left of the curve thestorage temperature is lower than the saturation temperature atthe same pressure while to the right the temperature is greaterthan the saturation temperature at the same pressure. Here we areusing the terms subcooled and superheated to describe the storageconditions. These terms are also used when the temperature of thefluid is compared with the saturation temperature at ambient(atmospheric) pressure also known as the normal boiling point. Thiswill affect the state of thematerial as it exits from the storage vessel.If the fluid temperature is above the normal boiling point then thefluid is superheated and will change phase upon depressurizationdown to atmospheric pressure. If the fluid temperature is less thanthe normal boiling point then the fluid is subcooled and will notchange phase upon depressurization down to atmospheric pressure.

Fig. 1. Temperatureeentropy diagram for chlorine. Dashed and dotted lines arepressure in units of MegaPascals.

R. Britter et al. / Atmospheric Environment 45 (2011) 1e25 3


So a material could be a subcooled liquid relative to saturationconditions at the storage pressure but a superheated liquid relativeto saturation conditions at atmospheric pressure. The terminologyused throughout this paper is to explicitly state whether thereference is to the saturation temperature at the storage pressure orat ambient pressure.

Because pressure and temperature are not independent variables(for single-componentfluids)when twophases are present, the two-phase region in Fig. 1 collapses to a single curve when the phasediagram is presented on pressureetemperature axes as in Fig. 2.

In this plot the “hump” of the two-phase region in Fig. 1 hascollapsed to the single line. Note that the red dot in Fig. 2 showsmaterial that is a subcooled liquid relative to the saturation line (atthe same pressure) but is a superheated liquid relative to thesaturation line (at ambient or atmospheric pressure).

Clearly it is important to have access to accurate values of TICproperties. The National Institute of Standards and Technology(NIST) database is currently used in many models for many mate-rials. Alternatively, DIPPR is a widely-used property database.Currently NIST is a sponsor of DIPPR 801 (BYU DIPPR 801 verwebsite). Where the chemical is not found in either NIST or DIPPR,then one has to resort to estimation methods. In this case signifi-cant discrepancies may arise depending upon how the estimationsare made. Properties of interest include.Antoine coefficients (forsaturation vapor pressure)

Molecular weightLiquid density (plus variation with temperature) Specific heats(liquid and vapor)Surface tension (for droplet deformation)Liquid viscosity (for droplet absorption into substrate)

3. Release rate and exit thermodynamic conditions

For most cases with a rupture of a container full of pressurizedliquefied gas, the mass release rate will vary strongly with time(Hanna et al., 1996). The optimum input for the dispersion model isthe release rate as a function of time with a resolution of a fewseconds or even smaller for large ruptures. However, manydispersion models cannot use that much detail, and the mass

release rate will, at best, be a set of piecewise constant values, witheach piece averaged over say 1e10 min or more. Some models cantake only a constant release rate (although perhaps for a finiteduration) or a single total mass released. Thus the total massreleased is also a major parameter. The thermodynamic state of thematerial at the exit of the rupture is required as an input to thesubsequent jet and dispersionmodeling. Also because the flowmaybe choked at the exit the pressure at the exit may be aboveatmospheric pressure. Consequently the jet material will accelerateafter the exit. This requires the calculation of the momentum flowrate of the jet including any acceleration due to an elevated pres-sure at the exit plane.

3.1. Background

In order to calculate the mass flow rate from the storagecontainer and the thermodynamic condition of the releasedmaterial at the rupture plane it is common to consider the flowas inFig. 3. Within the storage container there exists essentially stagnantfluid and this accelerates towards the rupture plane. The pressure atthe rupture plane (or at the vena contracta if one exists) will beatmospheric pressure if the flow is unchoked or will be aboveatmospheric pressure if the flow is choked. The pressure at therupture plane is an important input to the subsequent jet modeling.

We are particularly interested in going from the stagnant(stationary, stagnation) conditions “o” to those at or just after therupture plane “1”. In all scenarios the pressure will reduce from thestorage pressure to atmospheric pressure. However this may occurdirectly to atmospheric pressure at the rupture plane or it mayoccur with an important intermediary pressure at the ruptureplane that is above atmospheric pressure (a “choking” condition).In this case there would be a further depressurization down toatmospheric pressure downstream of the rupture plane. The massflow rate of a compressible fluid through a rupture is often thoughtto depend upon the pressure difference across the rupture. Thisstatement is only partially correct.

For a fixed pressure in the storage vessel the mass flow rate doesincrease for smaller and smaller downstream pressures. Howeverthere is a limiting mass flow rate that beyond which the down-stream pressure has no influence. In this case the mass flow ratedepends on the pressure in the storage vessel and not on thedifference in pressure across the rupture. This condition is called“choked flow” and is commonly met in single-phase high speed gasdynamics. The maximum exit velocity will be the sonic velocity ofthe fluid (of the order of several 100’s of m s�1) at the thermody-namic conditions at the rupture plane. If the fluid is made up of gasand liquid then this can be considered a pseudo compressible fluidand will also experience a choking condition. Somewhat

Fig. 2. The saturation curve of pressure against temperature for chlorine; definition ofterms.

Fig. 3. Schematic diagram to illustrate nomenclature. Definition of flow planes “o”, “1”and “2”.



surprisingly themaximum exit velocity for a two-phase fluid can bemuch smaller than the sonic velocities of either phase individually.Physically this is because the “sonic” velocity depends on thecompressibility and the inertia (density) of the fluid. For the two-phase flashing fluid the phase-change process in effect increasesthe two-phase mixture compressibility, hence yielding a low sonicvelocity. Maximum exit velocities of the order of only several 10’s ofm s�1 are often found.

The types of releases are categorized as coming from containersin which material is stored as a:

1. Liquid in a subcooled state (with a storage temperature that islower than the saturation temperature at the storage pressure).This includes refrigerated liquefied gases (stored at atmo-spheric pressure) and pressurized and partially refrigeratedliquefied gases (often done with anhydrous ammonia). It isimportant to note that if the material is subcooled then, bydefinition, there must be an imposed pad gas.

2. Gas in a superheated state (with a storage temperature that ishigher than the saturation temperature at the storagepressure).

3. Either liquid or gas under saturation conditions (at the ends ofthe horizontal lines in Fig. 1) or liquid and gas together(somewhere along the horizontal lines in Fig. 1). The last case iscommonly met with both liquid and gas being present withinthe storage vessel. What is being considered specifically here isthat, during the release, part of the liquid and vapor within thevessel may mix and appear to be like a stored mixture atsaturation conditions.

It is useful to consider the list of TICs mentioned earlier andrefer to them in the three categories above. The 13 TICs on the listare inhalation toxics that are shipped in large quantities. Themost dangerous category of TICs includes those with low boilingpoints (i.e., they are gases at ambient conditions) that aretransported as pressurized liquids. The “top three” in this groupare chlorine, ammonia (anhydrous), and sulfur dioxide, which allhave boiling points less than �10� C and are shipped in largequantities in rail cars. Other high-priority TICs in this groupinclude chlorine trifluoride, hydrogen chloride anhydrous,hydrogen fluoride, and phosgene. As an example chlorine istypically stored under saturation condition with liquid and vaportogether. Consequently the pressure and temperature are notindependent. The pressure in the storage vessel will be thatdetermined by the temperature of the contents of the vessel. Ifthe contents increase in temperature due to heat transfer fromthe storage vessel to the contents then some of the contents willchange phase to a gas and thereby increase the pressure until thetemperature and pressure are back together on the saturationline. Some of these chemicals may be stored as partly pressurizedand partly refrigerated, and some may have a pad gas introducedunder particular situations.

A less dangerous category of TICs on the list includes those thatare liquids at ambient conditions (e.g., acrolein, bromine, hydrogencyanide, and methyl chloroformate), which are most likely to beemitted to the atmosphere primarily by evaporation from a liquidpool. The mass is emitted over a relatively long time period and thedownwind concentrations are relatively low. These four liquidswere selected for the high-priority list because of their relativelylow toxic concentration criteria and the fact that they are trans-ported in relatively large amounts. These are subcooled liquidsunder both storage conditions and ambient conditions.

Finally, two of the TICs on the list are also liquids at storage andambient conditions (e.g., oleum (65% sulfur trioxide) and phos-phorous trichloride) are in the category of “fuming liquid”, meaning

that they may react with water vapor in the atmosphere, with therelease of heat and conversion to secondary chemicals.

We see that only the first set of chemicals carries across tocategories 1 and 3 above. The source emission models for releasesof the other chemicals involve liquid pool formation and subse-quent evaporation.

Most importantly, it may well be the case that more than onetype of release may be evident in the one incident and the onerupture. During depressurization of the storage vessel the vesselmay contain regions of vapor only, liquid only and a two-phasevaporeliquid mixture. Depending on the geometric location of therupture different release types will occur. The evolution of theinternal state of the storage vessel during depressurization maymean that a fixed geometrical location of the rupture will experi-ence three or more different release types. For example, considera mid-level rupture in a storage vessel that contains material storedunder saturation conditions and predominantly liquid. Initially therupture will be in the liquid space. After rupture the tank contentsmight appear as a liquid phase at the bottom, a vapor phase at thetop and a liquidevapor mixture between the two. As time proceedsand the tank empties the released material (at the rupture plane)may be all liquid, a two-phase mixture and all vapor.

For the cases labeled 1) and 2) above (and provided the materialdoes not change phase prior to exiting the rupture) and when therelease process is one that always maintains thermodynamicequilibrium, the release problem is relatively straightforward.

3.2. Recommended approach where the liquid is subcooledreferenced to the saturation temperature at both the storagepressure and atmospheric pressure

In this case the liquid in the storage vessel is initially ata temperature below its normal boiling point (that is below thesaturation temperature at ambient pressure so there is no phasechange upon release). It must be stored under a pad gas which is ata pressure higher than ambient pressure. The relevant equation isthe Bernoulli equation

G ¼ CD�2�P0 þ rf gh� Pa

�rf

�1=2(1)

where G ¼ mass flow rate per unit rupture area (kg s�1 m�2)rf ¼ liquid density in storage tank (kg m�3) P0 ¼ storage pressure(N m�2) Pa ¼ atmospheric pressure (N m�2) CD ¼ discharge coef-ficient (dimensionless); discussed in detail in Section 3.5g ¼ acceleration due to gravity (m s�2) h ¼ height of liquid abovethe rupture position (m)

3.3. Recommended approach where the vapor is superheatedreferenced to the saturation temperature at both storageand atmospheric pressure

For the superheated vapor case, the relevant equations are thecompressible gas flow equations and these allow for the importantphenomenon of choked or critical flow. Consider a gas jet comingfrom a rupture in the vapor space of a pressurized liquid storagetank. When the rupture occurs, the velocity, and themass flow rate,of the exiting fluid will depend on the pressure inside and thepressure outside of the container. When these pressures are not toodifferent the flow is unchoked. However the gas can exit therupture only as fast as its sonic velocity and at larger pressuredifferences there is a “choked” condition at the exit. Choked flowsimply means that the gas is moving through the puncture at itsmaximum possible speed, namely the local speed of sound in thegas.



The discharge rate equations for an ideal (note that non-idealgas behavior may be expected when the flow approaches thesaturation curve) gas jet release are well known. Whether or notthe flow is choked depends on the ratio of atmospheric pressure totank pressure relative to the critical pressure ratio as definedbelow:

rcrit ¼�PaP0

�crit

¼�

2gþ 1

� gg�1

(2)

where P0 ¼ absolute tank (stagnation) pressure (N m�2)Pa ¼ absolute ambient atmospheric pressure (N m�2) g ¼ gasspecific heat ratio ¼ cp/cv (dimensionless)

For a typical gas, values of g range from 1.1 to 1.5, and rcrit valuesrange from 0.5 to 0.59. Thus, the releases of most diatomic gases(g ¼ 1.4) will be a choked or critical flow at a critical pressure ratioof 0.528 (i.e., a tank pressure above approximately twice atmo-spheric pressure). Note that the critical pressure ratio rcrit will begiven the symbol hc when addressing two-phase flow later.

For an ideal gas exiting through an orifice under isentropicconditions, the gas mass discharge rate is given by:

_m ¼ GAh (3)

G ¼ CD

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2�P0v0

�g

g� 1

"�PaP0

�2g

��PaP0

�gþ1g

#vuutfor subsonic or unchoked flows

�PaP0

� rcrit

�(4)

and

G ¼ CD

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�P0v0

�g

�2

gþ 1

�gþ1g�1

sfor choked flows

�PaP0

� rcrit

�(5)

where P0 ¼ absolute tank (stagnation) pressure (N m�2),Pa ¼ absolute ambient atmospheric pressure (N m�2), g ¼ gasspecific heat ratio ¼ cp/cv (dimensionless), _m ¼ gas discharge rate(kg s�1), CD ¼ discharge coefficient (dimensionless), Ah ¼ holeor rupture area (m2), n0 ¼ specific volume of gas within thevessel

Some care is needed when considering flows that come near tothe saturation curve. The use of perfect gas laws will not beapplicable even if there is no phase change. Furthermore if therelease changes phase (e.g., a superheated vapor cools as itdepressurizes), then it may condense and the condensation willaffect the flow. In addition caution should be shown by the userabout non-ideal gas behavior that will occur at high pressures. Notethat the u-method addressed in Section 3.4.1 can be used in thecase with condensation phenomena.

3.4. Recommended approach for the release of materialthat is initially, or becomes, two-phase

There are several approximatemethods available to describe thedepressurization of a material that is initially two phase or thatbecomes two phase during depressurization that do not havedemanding data requirements. Most of these rely on treating thetwo-phase fluid as a compressible pseudo-fluid whose compress-ibility can be determined based on the bulk properties of the two-phase fluid. Several scenarios can be envisaged for which a modelfor the source emission rate is required. The two main categoriesare: i) Storage at saturated conditions as a liquid, as a gas or asa mixture of the two, and ii) Storage as a liquid at subcooled

conditions but such that the material would be superheated atatmospheric pressure.

3.4.1. Release from storage at saturated conditions as a liquid,as a gas or as a two-phase mixture of the two

The model recommended here is the u-method (Leung, 1986,1990, 1996). This is a widely-used simple model and has beenextensively tested (e.g., see Richardson et al., 2006). The model canbe used for estimating flow rates and exit pressures. The initial statecan be all (saturated) liquid, all (saturated) vapor or a mixture of thetwo but saturated conditions must apply. The u-method was firstproposed for flashing two-phase flow in 1986, and in subsequentyears was extended to non-flashing two-phase flow (Leung, 1990),subcooled liquid flow (Leung and Grolmes, 1988), two-phase pipeflow (Leung and Grolmes, 1987; Leung and Ciolek, 1994), and thelocal speed of sound in two-phase mixture (Leung, 1996). The u-method is an (isentropic) homogeneous equilibrium model (HEM)for the flow of a saturated two-phase mixture initially at a storagepressure P0 equal to Pv(T0), the vapor pressure at the storagetemperature T0.

The “u-method” is based on three approximations orassumptions:

� The liquidevapor mixture is homogeneous; i.e., there is no slipbetween the phases

� The phases are in thermodynamic equilibrium� The expansion is isentropic. This last assumption will likely bevalid prior to the fluid exiting through the rupture; between“0” and “1” in Fig. 3.

It is applicable to cases where the initial state is two phase or onthe saturation line as a liquid or a vapor. For example it can treat thecase of a saturated vapor; a case in which condensation wouldoccur through the flow passage. As with Section 2.4 where thecompressible gas equations were appropriate, here the two-phasematerial might be considered as a type of “compressible gas”.Consequently the phenomenon of choking will also be relevant.That is, the flow may be choked (quite common for TIC releases) orunchoked depending upon the material properties and the storageconditions. Because the “sonic velocity” for a two-phase mixture istypically well below the speed of sound for either the liquid or thevapor phase, smaller exit velocities are expected for the two-phasescenario.

The critical or choked flow rate for various storage conditionscan be found once the pressure P versus specific volume (v) rela-tionship is available as tables or formulas. This can be obtainedfrom isentropic flashing calculations at varying pressure, as dis-cussed in the DARPA report (Hanna Consultants, 2006), in theAIChE/DIERS report (Fisher et al., 1992), and by Richardson et al.(2006). In fact, this is the essence of an exact approach for thetwo-phase case and an example of this is provided at the end of thisSection 3.4.6. However this exact approach requires fluid propertydata that may not be commonly available and adequately accuratefor a wide range of chemicals.

The “u-method” is based on a one-parameter approximation ofthe P versus v relationship using:

v

v0� 1 ¼ u

�P0P

� 1�

(6)

and

uha0

1� 2

P0vfg0hfg0

!þ T0cp0P0

v0

vfg0hfg0

!2

(7)



where the subscript “0” denotes the values in the tank at stag-nation condition, and, a0 ¼ volume fraction of TIC vapor, cp0 ¼ heatcapacity of the (liquid) material at T0 (J kg�1 K�1), hfg0 ¼ heat ofvaporization at T0 (J kg�1), P ¼ downstream pressure (N m�2),P0 ¼ stagnation (storage) pressure (N m�2), T0 ¼ storage tanktemperature (K), v ¼ specific volume of the material at P (m3 kg�1)vo ¼ specific volume of the material at Po (m3 kg�1) vfg0 ¼ specificvolume difference between liquid and vapor at T0 (m3 kg�1), andvo ¼ vfo þ xo vfgo where xo is the inlet vapor mass fraction or quality

Leung describes the parameter u as consisting of two distinctterms: the first reflects the compressibility of the two-phasemixture due to the existing vapor/gas volume, and the secondconcerns the compressibility due to phase change upon depres-surization or flashing. The larger the value of u, the more volumeexpansion or compressible behavior the mixture exhibits. As notedin Leung (1996), flashing flow occurs for u > 1 and non-flashingflow for 0 < u < 1. u depends only on conditions at stagnation inthe tank. The u-method is presented in the design chart in Leung(1986, 1990) and Fig. 4. The critical mass flux per unit rupturearea, Gc, and the critical pressure, Pc (the pressure at the exit planefor choked flow), can be found as follows:

1. Find u from its definition equation above2. Find hc from Fig. 4 or from a solution to the critical pressure

ratio hc

h2c þ uðu� 2Þð1� hcÞ2þ2u2 lnðhcÞ þ 2u2ð1� hcÞ ¼ 0 (8)

3. Find Gc* from Fig. 4 or

a) For choked flow simply use the following formula

G*c ¼ hc=

ffiffiffiffiu

p(9)

b) For unchoked flow where h > hc

G* ¼ ½�2ðuln hþðu�1Þð1�hÞÞ�0:5.�

u

�1h�1�þ1�

where h ¼ PaP0

(10)

4. Then Pc and Gc are found from

Pc ¼ hcP0 (11)

Gc ¼ G*c

ffiffiffiffiffiP0n0

s(12)

Note that explicit formulas for the critical pressure ratio havebeen advanced by Simpson (2003), and more recently by Moncalcoand Friedel (2010).

The following figure is assumed to apply to all two-phase fluids;an assumption supported by the data presented in Fig. 2 of Leung(1986); the figure covers chlorine, ammonia, carbon tetrachloride,water and several other chemicals.

The temperature along a saturation line (as shown in Fig. 2 forchlorine) can be found using the Clapeyron equation (Perry andGreen, 1997). That is

dT=dP ¼ vfgT=Rfg (13)

Thus the temperature Tc corresponding to Pc can be found.Additionally since most chemicals should have accurate vaporpressureetemperature relationships or correlations, one could infact bemore precise in using them for determining the temperatureTc corresponding to Pc at the choking location.

The vapor quality (vapor mass fraction), x, at temperature T ¼ Tcis:

x ¼ Thfg

�cpf ln

ToTþ x0

hfgoTo

�(14)

From the vapor mass fraction the density or the specific volumeof the two-phase fluid can be calculated.

vm ¼ ð1� xÞvf þ xvg ¼ vf þ xvfg (15)

If the chemical has reasonable enthalpy data, the flash calcula-tion can be performed directly without resorting to the aboveapproximate equation.

Note that x, the vapor mass fraction, is related to the vaporvolume fraction, a, by

a ¼ xvgv

(16)

In summary, we calculate u and then determine hc and Gc*. These

are then converted to the critical mass flow/unit rupture area Gc

and the exit plane pressure Pc which are the required unknowns.We can also calculate the temperature at the exit plane and thevapor mass fraction there, and thus the fluid density or specificvolume and finally the exit velocity at the rupture plane.

Note that there is no discharge coefficient in the above analysis.A discharge coefficient of unity could be assumed though see Leung(2004) and Section 3.5 for further guidance.

The above set of equations is generally applicable to releases ofmaterial under saturated conditions whether saturated liquid,saturated vapor or saturated two-phase storage.

There are several widely-used simplified methods such as theEquilibrium RateModel (ERM)model by Fauske and Epstein (1988).Though this approach is now thought to be less appropriate andmore limited than the u-method for the problems at hand theresults for that model are included here as they may be useful forvery simple calculations. The ERM can be derived from the “u”

method above with the initial vapor fraction (a0) set equal to zero.Fig. 4. Design chart for critical flow parameters of a two-phase mixture; that is,initially at saturation conditions.



GERMzhfgo.�

nfgo

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�Tocpfo

�r �¼ ðdP=dTÞsat

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�To=cpfo

�r(17)

where GERM ¼ mass flux for equilibrium rate model (kg s�1 m�2),hfgo ¼ heat of vaporization at To (J kg�1), vfgo ¼ difference in specificvolume between liquid and gas (¼vg e vf) at To (m3 kg�1),To ¼ storage tank temperature (K), cpfo ¼ liquid heat capacity at To(J kg�1 K�1)

provided that x <P0vfgoh2fgo

Tocpfo (18)

This provides a good estimate of the flow rate without the needto specify the liquid-to-vapor ratio involved in the discharge.However the only difference between “u” method (with the initialvapor fraction (a0) set equal to zero) and the ERM model is the hcvalue which ERM assumes 1.0. According to Fig. 4, for u > 10, i.e.,low-quality two-phase flow, hc is about 0.9. So the real difference isonly about 10% between the two models. Since ERM has otherlimitations, such as assuming the critical pressure ratio is 1.0 all thetime, the u-method is preferred.

The actual ERM follows from the original Henry and Fauske(1971) non-equilibrium flow model, and contains two parts in itsoriginal form. The part representing the flashing term would begoverning if eq. (18) were satisfied, which leads to the approxi-mation of eq. (17), the so-called approximate ERM equation.

3.4.2. The non-equilibrium flow of a saturated liquid througha rupture

When the length of the rupture is very short, say like a sharp-edged orifice, the stored liquid may be able to exit the storagevessel quickly enough so that thermodynamic equilibrium is notmaintained. There is not enough time for the material to changephase until well after the material has exited the vessel.

The non-equilibrium nature of the flow is often thought of interms of the “length” of the “orifice”, in that a sharp-edged orificewill have a small length and short residence time while the flowthrough a pipe-like orifice will have a long length and a long resi-dence time. The latter flow will appear more like an equilibriumflow and the former like a non-equilibrium flow. A delimiter ofa length of 0.1 m is often quoted.

The use of a dimensional criterion rather than a dimensionlessone is often queried. However experimental data support thedimensional result (Moody,1975; Fauske,1985). The residence timeis of primary importance, but other physical properties such assurface tension and Jakob number could play a part in the bubblegrowth dynamics. Moody argued that the bubble growth time istypically about 1 ms, and that that residence time would translateapproximately to a 0.15 m length. Among the short nozzle data,there are very few datasets that would allow one to examine theeffect of L (or L/D) in detail in the<0.1 m region; two exceptions areillustrated later in Figs. 7 and 8.

A model for this type of problem is sometimes called a Homo-geneous Non-Equilibrium (or Frozen) Model (HNEQ). There are alsomore complex homogeneous non-equilibrium models.

For flow lengths less than 0.1 m (the non-equilibrium regime),the flow rate increases strongly with decreasing length. As thelength approaches zero an all-liquid flow occurs and

Gc;L¼0 ¼ CD�2ðPs � PaÞ=vf0

�1=2(19)

where CD ¼ discharge coefficient (dimensionless and typically 0.6for an orifice), Ps ¼ vapor pressure at the stagnation/storagetemperature T0 ¼ P(T0) (N m�2), Pa ¼ ambient pressure (N m�2),nf0 ¼ specific volume of the liquid at saturation condition

This is the Bernoulli equation for an incompressible liquid withpressure drop, (Ps e Pa), available for flow. In this case thestorage pressure and the saturation pressure are equal so(Ps e Pa) ¼ (P0 e Pa).

Fig. 5 taken from Fauske (1985) shows the equilibrium and non-equilibrium results for the mass flux (for saturated conditions).When L is large the mass flow rates are small and the ERM is within20% of the more exact HEM. Much larger release rates are apparentwhen L is small and the flow near the rupture is a non-equilibriumone.

Fauske (1985) proposed an interpolation formula linking theERM model and the non-equilibrium model for the discharge rateof saturated liquid and produced the supporting Fig. 6 below:

A similar interpolationwas developed by Leung between the “u”method (as our recommended example of an HEM model) and theorifice model by defining a non-equilibrium parameter N in termsof the flow length L as:

N ¼ Gu=Gc;L¼0

2ð1� L=LEÞ þ L=LE for L � LE (20)

and

G ¼ Gu for L > LE (21)

G ¼ Gu=N1=2 for L � LE (22)

where Gu and Gc,L¼0 are mass flux per unit rupture area given by theu-method and by the all-liquid orifice model respectively. Forequilibrium flow to be attained, the flow length has to exceed 0.1 m(a relaxation phenomenon) and the corresponding CD is taken to be1.0 (i.e., with no vena contracta).

As first pointed out by Fletcher (1984) and Moody (1975), theproper scaling in this non-equilibrium region is the pipe length andnot the length-to-diameter ratio (L/D) of the pipe. A constantrelaxation length ranging from 75 mm to 150 mm has beenproposed by these early researchers. Figs. 7 and 8 illustrate thepresent correlation for the saturated discharge of water and Freon,respectively using a constant equilibrium length of 100 mm. Boththe equilibrium regime and the non-equilibrium region are illus-trated here. For the saturated water case, an inlet pressure Po of55 bar was used in the prediction (a lower Po would raise theprediction due to the higher liquid density).

When there is full non-equilibrium and L approaches zero thevelocity of the jet exiting the rupture plane will be determined

Fig. 5. Typically flashing discharge data of initially saturated water.



directly from the Bernoulli equation. There has been some argu-ment about what the pressure at the rupture plane (or the venacontracta) must be. It appears that it must be atmospheric pressure,with the exiting liquid in a non-thermodynamic equilibrium state.The important point is that the jet will not accelerate further due toany pressure excess at or downstream of the rupture plane. Therewill be an expansion, and hence acceleration, due to the subsequentflashing process. What the exit plane pressure will be in the regionwhere L is less than 0.1 m has not been clarified.

This would obviously be relevant if the rupture was to be in theform of a “short” pipe attached to the storage vessel; i.e., thebreakage of pipework attached to the storage vessel.

3.4.3. The release of a subcooled liquid through a ruptureThe u-method, as described earlier, is restricted to materials

that are initially at saturation conditions, be they vapor only, liquidonly or vapor and liquid together. The case of subcooled liquids isnot treatable with that approach. However Leung and Grolmes(1988) and Leung (1995) do provide a modified form of the u

method for subcooled liquids. Subcooled liquids may arise due tocooling of the material or to the “padding” of the stored materialwith another gas. The subcooled liquid release is of particularinterest since it is expected that even a moderate subcooling maycause a much larger mass flow.

The extension of the u-method to subcooled liquid discharge isfacilitated by removing the first term in equation 7 and defininga “saturated” u parameter as:

us ¼ CpoToPsvfo

vfgohfgo

!2

(23)

where Ps ¼ vapor pressure corresponding to inlet temperature To(N m�2), vfo ¼ liquid specific volume (m3 kg�1)

Again all the properties are to be evaluated at To, the inletstagnation temperature. The generalized solutions are divided intolow and high sub-cooling regions, delineated by a transition satu-ration pressure ratio (Ps/Po)t:

hsth

�PsPo

�t¼ 2us

1þ 2us(24)

In the low-subcooling regionwhere hs (¼Ps/Po)> hst or Ps> hstPo,the fluid attains flashing (two-phase) flow prior to the exit plane(throat) location and the dimensionless mass flux is given by

GffiffiffiffiffiffiffiffiffiffiffiffiffiPo=vfo

q ¼n2ð1�hsÞþ2

hushsln

�hsh

��ðus�1Þðhs�hÞ

io1=2us

�hsh�1

�þ1

(25)

and for choking conditions to occur, the following equation yieldsthe critical pressure ratio hc:

�usþ 1

us�2�

2hsh2c �2ðus�1Þhcþushsln

�hchs

�þ32ushs�1¼ 0 (26)

Note that above two equations, Eqs. (25) and (26) reduce exactlyto Eqs. (9) and (10) in Section 3.4.1, respectively, for the saturatedliquid inlet case with hs ¼ 1 (i.e., Ps ¼ Po).

In the high sub-cooling region where hs < hst or Ps < hstPo, novapor is formed until the exit plane is reached, and Eq. (25) reducesto a Bernoulli-type formula,

GcffiffiffiffiffiffiffiffiffiffiffiffiffiPo=vfo

q ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ð1� hsÞ

p(27)

or

Gc ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2rfoðPo � PsÞ

q(28)

where rfo ¼ 1/vfo, the inlet liquid density at To. The criticalpressure ratio is given by

Fig. 6. Saturated F-11 mass flux variation with L/D for D ¼ 3.2 mm.

Fig. 7. Prediction of saturated water discharge using present correlation (data aspresented in Fletcher, 1984).

Fig. 8. Prediction of saturated Freon discharge using present correlation (data aspresented in Fletcher, 1984).



hc ¼ PsPo

(29)

or choking simply occurs at the saturation pressure correspondingto the inlet temperature To. Fig. 9 illustrates the graphical solutionsfor inlet subcooled liquid discharge. The point of consequence hereis that the pressure at the rupture exit plane is the saturation vaporpressure corresponding to the storage temperature and this will bein excess of ambient pressure. Thus the phase change occursoutside the storage vessel.

In Fig. 9 all-liquid discharge will be expected where “high sub-cooling” is indicated. Where “low-sub-cooling” is indicated therewill be some phase change within the vessel and a reduced massflux discharge. Roughly speaking, if the storage pressure is morethan about 10% larger than the saturation pressure at the storagetemperature an all-liquid release is expected; reflecting themaximum discharge rate possible.

As the stagnation pressure approaches the saturation pressure atthe storage temperature the equation for the strongly sub-cooledmass flux is not consistent with that obtained based on an homo-geneous equilibrium model (HEM) or an (ERM) model for saturatedliquid storage conditions. A pragmatic solution to this is to use theinterpolation proposed by Fauske and Epstein (1988), where the“vector sum” is taken of, say, the ERMmodel and strongly sub-cooledmodel above. Fauske and Epstein (1988) present three experimentalresults that, they argue, support the formulas. However it is thoughtthat this may underestimate the flow rate for slightly subcooledliquids andDIERS/AIChE (Fisher et al.,1992) recommends themethodgiven in Leung and Grolmes (1988). But we note again that thesearguments and the interpolation will not produce an exit planepressure. Of considerable importance is that the u-method, whenextended to subcooled materials, provides both the discharge rateand the exit plane pressure, as well as a smooth transition. Of coursefor an all-liquid release that remains all liquid after the exit or onethat is not in equilibrium, then the pressure in the jet will be atmo-spheric at the vena contracta position for a sharp-edged orifice and islikely to be atmospheric at the exit plane for amore generic opening.

3.4.4. A non-equilibrium flow of a subcooled liquid througha rupture

A similar non-equilibrium correlation as suggested for thesaturated liquid discharge can be employed for the subcooled liquid

case. Here the equilibrium mass flux is evaluated using the sub-cooled liquid extension to the u method as presented in Section3.4.2, and is closely approached when L ¼ 0.1 m. When Lapproaches zero length the orificewill appear as a sharp-edged oneand a liquid discharge with a typical CD of 0.6 would be applicable.

3.4.5. The effect of a rupture in a longer pipe connected to a vesselIf the pipework was “longer” then calculation of the release rate

would need to account for frictional losses in the pipe and thesewould depend upon L/D and the reduction in flow rate due to thephase change occurring within the pipe rather than close to theend. Of course the exit pressures and velocities would be alteredalso. Fauske and Epstein (1988) provide simple estimates of theeffects of friction for modest pipe L/D on the mass flow rate fromthe storage vessel and the exit pressure that may be useful directlyor as an indicator of the magnitude of this effect.

The u-method has also been extended to similar discharges butthroughmore extensive pipework and for two-phase inlet conditionsincluding saturated liquid and subcooled liquid (Leung and Grolmes,1987; Leung and Ciolek, 1994). For the former the analytical resultscan be illustrated by Fig. 10 where the effect of L/D e shown inhorizontal axis as 4fL/D where f is the Fanning friction factor e is toreduce the mass flux Gc relative to the equilibrium nozzle case Goc.

As for the subcooled liquid pipe discharge, the bounding equilib-rium flow is given by a simple Bernoulli-type formula (Leung, 1995),

G ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2rfoðPo � PsÞ1þ 4fL=D

s(30)

By bounding it is meant that this will be the maximumdischarge rate; a maximumwhen the nucleation occurs at the veryend of the pipe and so it is essentially an all-liquid flow throughoutthe pipework.

3.4.6. An exact alternative exact approach for the two-phase caseAn interesting and possibly operationally useful approach has

been provided by Richardson et al. (2006), who made the veryimportant, though not new, observation that the simplifiedapproximate solutions for this problem as provided by Fauske andEpstein (1988) and, more substantially, by Leung (1996) may be anunnecessary approach. Direct and exact calculation may be just asefficient. The simplified approaches are of course extremely usefulfor directly determining the relative influence of the various inputvariables and for determining output trends with the input vari-ables. Simplified methods, like the u-method, were meant tocircumvent the hard-to-get thermodynamic properties for indus-trial chemicals. If detailed thermodynamic properties are available

Fig. 10. Critical two-phase pipe discharge based on u-method.Fig. 9. Critical discharge of inlet subcooled liquid based on u-method.



there be no need to use the “u-method ”, and a classical HEMcalculation such as this can be made.

All that is required for an exact solution is to satisfy threeconditions that connect the flow from the storage tank to therupture/exit plane. The conditions are:

� The specific entropy, s, is the same at both places (flow isreversible)

� The sum of the specific enthalpy, h, and ½ U2 is the same atboth places (flow is adiabatic)

� The velocity at the exit plane a0 is the “speed of sound” and isgiven by (vP/vr)�1/2 where the derivative is taken at constantentropy evaluated at the conditions at the exit plane (the flowis choked at the exit/rupture plane)

� If no solution is found then the flowwill be non-choking. In thiscase the condition at the rupture plane should be that thepressure is atmospheric.

The solution relies on an iteration based around the thermo-dynamic properties of the material. These should be accessible formany TICs. A solution procedure is referred to in Richardson et al.(2006). There is substantial concern regarding the need forconstant entropy flash calculations; the tools for this are available(a robust flash routine or simulation package such as ASPEN) andfurther consideration may be worthwhile depending, in part, onwhat particular scenarios are of interest.

Richardson states that the u-method (a homogeneous equilib-rium model, HEM) is within 1% of exact calculations. The recom-mendation here is that the use of an exact approach should beconsidered further; particularly the availability of the necessarychemical data. Of course, from an engineering standpoint, if the u-method is within 1%, there may be little good reason to useanything more complex!

3.5. The discharge coefficient CD

The dimensionless discharge coefficient, CD, accounts forreductions below the theoretical exit velocity due to frictionallosses arising in the flow near the rupture and the possibility of theflow area being smaller than the rupture area (a phenomenoncalled the vena contracta). The combination of these two compo-nents means that CD accounts for the reduction in flow rate due toboth the effect of friction and the reduction in the jet area beingsmaller than the rupture area. It depends upon nozzle shape andReynolds number, and graphical relationships of CD for varioustypes of orifices can be found in handbooks and fluid mechanicstextbooks (e.g., Perry and Green, 1997). In the context of thisdocument, CD is entirely due to the flow field or vena contractaeffect and is not affected by frictional loss or L/D.

CD is typically 0.6 for incompressible flow of liquids flowingthrough circular sharp-edged orifices. For thin slit orifices thetheoretical discharge coefficient is p/(pþ 2)¼ 0.61 (Batchelor,1967,p. 360). For sharp-edged orifices a discharge coefficient of 0.60 isrecommended.

For gas flows through orifices, the observed discharge coeffi-cient varies from 0.6 at low pressure drops (the incompressibleflow case) to slightly less than 0.9 at large pressure drops (thecompressible flow case).

Discharge coefficients for a comprehensive range of industriallyrelevant scenarios are available in Wirth (1983).

Leung (2004) presents results for discharge coefficients fororifice flow and its application to safety relief valves under two-phase conditions. He also provides theoretical results usingu-method for the discharge coefficient. It varies monotonicallyfrom 0.60 through 0.88 to unity as u varies from near zero (liquid

flow) through unity (near (compressible) gas/vapor flow) to verylarge (saturated liquid inlet). These results have been supportedby the work of Richardson et al. (2006). Leung (private commu-nication) argues that the saturated liquid case provides a morecompressible mixture due to its ability to flash and greatlyincrease its specific volume, yielding a lesser contraction at thevena contracta location; a plausible argument and consistent withthe u-method.

We recommend:

� the use of a value of CD ¼ 1 for all scenarios if a truly conser-vative estimate is essential

� If this is not the case and a more accurate result is desired thenwe recommend the use of CD ¼ 0.60 for all-liquid flows and forall-gas flows where incompressibility can be assumed (at Machnumbers less than 0.3) and the orifice resembles a sharp-edgedone

� For all other cases we recommend the use of CD ¼ 1

If more detailed information is required then the following maybe considered:

� The result from Leung (2004) above� Extensive research has been done on discharge coefficients forincompressible, compressible, two-phase fluids in various flowgeometries (Jobson, 1955; Bragg, 1960; Chisholm, 1983;Idelchik, 1986; Morris, 1989; Wirth, 1983).

� The effect of some other geometry can produce dischargecoefficients from below 0.50 for incompressible fluids.

� Wirth (1983) provides discharge coefficients for many differentshapes of orifices.

4. Storage vessel response

4.1. Introduction

Following a rupture of a storage vessel there will be a mass flowrate from the vessel and this may be gas, liquid or a mixture of gasand liquid depending upon the contents, their disposition and therupture position. The vessel response (called blowdown in thechemical engineering community) will depend upon the funda-mental equations for mass, momentum, enthalpy and entropyincluding heat transfer to or from the vessel contents, transfersbetween different phases within the storage vessel and the ther-modynamic equilibrium or not of the vessel contents. Thesechanges will lead to a change in the phase fractions in the vesseland the temperatures and pressure within the vessel.

The chemical engineering community defines blowdown as thetime-dependent (transient) discharge from a vent or hole ina pressurized vessel containing liquefied gas, as the tank depres-surizes to ambient conditions. Generally there are several differentscenarios that are considered based on the storage conditions, thethermodynamic properties of the stored material and the type ofrupture.

One specific scenario is of particular interest in the context ofthis study; the scenario where the material is stored under“saturated” conditions where both liquid and vapor are presentwithin the storage vessel (and are initially in thermal equilibrium).Under these conditions the storage pressure and the storagetemperature (both assumed uniform) are not independent;knowing the pressure or temperature determines the other (forexample, water boils at 100� C at 101,325 N m�2 pressure). Thisscenario is typical of several possible releases of concern. Arelated, though different, scenario is when the storage vessel alsocontains an inert “pad” gas, such as nitrogen. The nitrogen can be



used to keep the stored material as solely liquid by ensuring thatthe storage pressure is in excess of the saturated vapor pressurecorresponding to the storage temperature. Often tanks are pres-surized with N2 in order to unload the tank contents. Evidenceshows that if the blowdown is due to a top opening, then the“pad” gas will be vented out initially and subsequent blowdownwill follow the saturation curve. On the other hand, if the blow-down is from a bottom hole, then the “pad” gas will exert itsinfluence on the discharge rate e a subcooled liquid dischargeregime. Note that the “pad” gas pressure will continue to diminishdue to the increasing head space as inventory drops. This caneasily be accounted for in a simulation code.

When a tank ruptures or a hole develops in the tank, materialexits the tank and the pressure decreases within the tank. If thehole is well above the vapor/liquid interface then vapor will exitthe tank. If the hole is well below the vapor/liquid interface thenliquid will exit the tank. In both cases the material approachingthe hole, at the hole, and just downstream of the hole willmaintain its state of either vapor or of liquid. The decrease ofpressure within the tank will lead to the liquid within the tankchanging phase by nucleation and the liquid boils sometimesviolently. The region of two-phase fluid within the tank will benear to the initial position of the fluid interface. This region of thetank contents will swell. If the hole is within this two-phaseregion of the tank contents then there will be two-phase fluidapproaching, at and immediately downstream of the hole.Experimental data including those of the large-scale DIERSexperiments (500 gal or 2 m3) demonstrated that the void (orbubble volume) distribution is skew, more void at top than atbottom. However the void profile would very much depend onthe size of the rupture (opening) and location. A large opening atthe top can induce so much flashing (phase change) inside thetank as a result of rapid depressurization that can cause the levelswell to the top, resulting in a two-phase release.

For an arbitrary hole position and initial fluid interface positionvarious time-dependent flows will evolve. For example:

� A hole at the top of a tank, well above the vapor/liquid inter-face, will initially discharge vapor. As the pressure in the tankbegins to decrease, some of the liquid will vaporize (andeventually exit the tank) and slow the pressure decrease. Thismay be a substantial fraction of the tank mass. The vaporizingphase change within the tank cools the tank contents by autorefrigeration, and eventually the vapor pressure falls to atmo-spheric pressure and discharge ceases. More commonly therewill be a continued release after pressure has come down toequilibrate with the outside ambient pressure because of theheat transfer to the tank contents from the tank walls and fromoutside the tank. Note that heat transfer from the tank wallsmay influence the blowdown process but heat transfer fromoutside will be too slow to play an important role in theblowdown phase.

� With a hole at the bottom of a tank, well below the vapor/liquidinterface then the discharge will be all liquid. It will remain anall-liquid release until the two-phase region within the tankdescends to the position of the hole.

� If the hole is initially near the liquid/vapor interface there willbe a two-phase release closely following the rupture and thiswill remain so until the two-phase region within the tankdrops below the hole position.

The overall picture is best considered for a hole initially wellbelow the vapor/liquid interface. The sequence of events (at theplane of the rupture) would be an initial all-liquid release, thena two-phase release and then a single-phase release. The pressure

would remain relatively constant but slightly decreasing until allthe liquid had vaporized. The mass flow rates would be largest forthe all-liquid release, less for the two-phase release and smallest forthe single-phase vapor release. The exit velocities (and possibly themomentum fluxes) would be in the reverse order. The all-liquidrelease produces the smallest velocities and the all vapor releasesproduces the largest velocities.

The most prevalent release scenarios involve pressurized liq-uefied gas of TICs such as chlorine, anhydrous ammonia, and sulfurdioxide, which would lead to two-phase jet releases. Two-phaseflow stops when the inventory depletes sufficiently for the frothylevel to drop below the bottom of the puncture. The blowdownstops when the pressure in the tank reaches atmospheric.

An example of a particularly simple blowdown model (fromJoseph C. Leung) follows. This is included in this paper as indicativeof what might be developed.

4.2. On level swell and discharge exit conditions during vesselblowdown

The purpose of this section is to summarize the methodologyand underlying equations describing the level swell and thedischarge exit conditions during a vessel blowdown. The discussionis necessarily brief and should provide a good-enough firstapproximation to the rather complex in-vessel hydrodynamicbehavior during blowdown.

In this treatment the model assumptions are:

(1) Neglect transient level swell associated with pressure under-shoot or delayed bubble nucleation during the initialblowdown.

(2) Thermodynamic equilibrium between vapor and liquid phases.(3) One-dimensional model allowing vertical void distribution.(4) Constant cross-sectional area vessel.(5) Uniform vapor generation from blowdown (depressurization).(6) Churn-turbulent flow regime with Co (void distribution

parameter) of 1.0 in terms of the drift-flux model.(7) Uniform pressure and temperature in-vessel

4.2.1. Basic relations in level swell analysisThe level swell inside a vessel is a buoyancy-driven flow

phenomena where the rising of swarms of vapor bubbles throughthe liquid bulk results in the level swell. This phenomena is bestdescribed by the so-called drift-fluxmodel (Wallis, 1969; Zuber andFindlay, 1965). Applications of the drift-flux model can be found inblowdown analysis of nuclear reactor components and chemicalequipments. The DIERS work utilized the drift-flux model exten-sively in describing the hydrodynamics of both chemical runawayreactions and storage vessels during pressure relief conditions(DIERS report, 1983; Fisher et al., 1992). It suffices here to justsummarize the key results. During a vessel blowdown, the super-ficial vapor velocity at the top jgN and the average void fraction inthe liquid pool a are related via:

jgNUN

¼ 2a1� a

(31)

where UN is the individual bubble rise velocity (m sec�1) given byWallis (1969).

UN ¼ 1:53

"sg�rf � rg

�r2f

#1=4(32)



Here s is the liquid surface tension (N m�1), rf is the liquiddensity (kgm�3) and rg is the vapor density (kgm�3). In most cases,rg << rf such that Eq. (32) can be simplified to

UN ¼ 1:53

"sgrf

#1=4(33)

The void fraction at the top of the pool aT can be related to theaverage a via,

aT ¼ 2a1þ a

(34)

If one invokes a simple linear void distribution profile, the voidfraction at the bottom aB would be given by

aB ¼ 2a� aT (35)

Now define: Ho as the vessel height (m), HL as the collapsed liquidheight (m), and H2P as the two-phase swell height (m).

Here HL is related to the liquid mass ML (kg) via:

HL ¼ ML

rf Ax(36)

where Ax is the vessel cross-sectional area (m2). Also H2P is relatedto HL via:

H2P ¼ HL

1� a(37)

Finally the void fraction in the vessel ao is related to Ho and HL

via:

ao ¼ Ho � HL

Ho(38)

4.2.2. Complete vaporeliquid (V/L) disengagement (top vent)In a top-vented vessel, the complete V/L disengagement crite-

rion is simply stated as

a < ao (39)

It can be easily shown that this inequality requires that H2P < Ho

as expected, i.e., the two-phase swell height being less than thevessel height. Here the superficial vapor velocity jgN at the top ofthe liquid pool is related to the vapor discharge rate at the top hole,

rgjgNAx ¼ Wx1 ¼ Wg (40)

where x1 ,the exit quality, is 1.0 for vapor discharge, W is the massdischarge rate, andWg designates vapormass flow rate (kg s�1). ThisjgN is used in Eq. (31) to determine the level swell or a: On the otherhand, if a > ao, that would imply a level swell to the vessel topresulting inpartialV/Ldisengagement for a top-vented configuration.

4.2.3. Partial V/L disengagement (top vent)In a top-vented vessel when the level swell reaches the top vent,

the vessel exit quality or vapor mass fraction is given by Leung(1987):

x1 ¼

rgUNAx

Wþ rg

rf1� a

2aþ rg

rf

(41)

where W is the mass discharge rate (kg sec�1). Note that W isdependent on x1, the inlet quality to the hole opening, via

W ¼ CdAoGðx1Þ (42)

where Cd is the discharge coefficient, Ao is the hole area (m2) and Gis the discharge mass flux (kg m�2sec�1) with (x1) indicating itsdependency on x1 in above equation. Thus Eqs. (41) and (42) haveto be solved simultaneously for both W and x1. Numericallysuccessive substitution scheme for x1 has been found to converge ina few iterations.

4.2.4. Exit conditions for side and bottom ventsFor side and bottom vents, the exit conditions can be deter-

mined in accordance to the void distribution profile. For completeV/L disengagement, i.e., only vapor exiting the hole at an elevation Z(above vessel bottom), it requires the hole to be above the swellliquid level, i.e.,

Z > H2P orHL

1� a(43)

Otherwise for Z < H2P, i.e., vent located below swell liquid level,the local void fraction can be approximated by

aZ ¼ aB þ ðaT � aBÞZ

H2P(44)

where Z (m) is the elevation of the vent above the vessel bottomand aZ denotes the void fraction at elevation Z.

The exit quality x1 is simply 1 if Eq. (43) is satisfied, otherwise

x1 ¼ aZrgaZrg þ ð1� aZÞrf

(45)

Again sinceW depends on x1 via Eq. (42), both Eqs. (45) and (42)have to be solved simultaneously for both W and x1.

Here the superficial vapor velocity jgN at the top of the liquidpool is also related to the volumetric discharge rate via

jgNAx ¼ WaZrg þ ð1� aZÞrf

(46a)

or

rgjgNAx ¼ Wx1aZ

(46b)

The above two equations are identical but Eq. (46a) avoids thedivision by zero when aZ is 0.

5. Flow after exit from the storage vessel and coupling withan air flow and dispersion model

In all model systems, it is essential that total plume or pufffluxes be conserved at any transition from one model componentto another (such as from the source emission model to theatmospheric transport and dispersion model). The most impor-tant of these is the mass flux, since it is directly used to calculatethe concentrations. Other fluxes to be conserved are momentumflux, enthalpy flux, and aerosol drop mass flux and drop sizedistributions. For TICs such as chlorine, there is a significant jetthat extends from the hole in the storage tank to some downwinddistance (10’se100’s of meters) where the jet speed reduces andapproaches the ambient wind speed. Close to the rupture the jetmay be at pressures many times atmospheric and the material ina superheated state. Downstream the jet pressure reduces toatmospheric, the superheated material may flash as liquidchanges phase to gas and the jet will entrain ambient air. Theseprocesses are commonly artificially split into two distinct



processes. Very close to the rupture (within a few meters) theflashing and the depressurization of the jet down to atmosphericpressure occur but without any entrainment of ambient air.Subsequently the jet is assumed to be at atmospheric pressureand entrainment of ambient air takes place. Across these twoartificial processes the various fluxes are required to be contin-uous. Of great importance is that within the near rupture regionthe liquid that has not flashed will be forming small droplets dueto both mechanical shear and the thermodynamic flashingprocesses. Not all of these effects are included in all widely-usedmodels, and sometimes one or both parts of the jet are includedin a source model. Often the second part of the jet is included inthe atmospheric dispersion model. Consequently the transitionfrom the source model to the atmospheric dispersion modeloccurs at different locations for different models. Many publicly-available models ignore some of the jet effects or only roughlyparameterize them. For example, the Lagrangian particle modelfor dense gas dispersion described by Anfossi et al. (2010) doesnot simulate the initial dense jet but needs the jet precalculatedby another model for input to their model. However, theHGSYSTEM model described by Witlox and McFarlane (1994) hasa module for calculating certain types of jets, but not all possi-bilities. The CFD model used by Hanna et al. (2009) for simulatingthe transport and dispersion of chlorine releases in an urban areais looking for jet inputs from an independent source emissionmodel in the version in that paper. However, the CFD modeldevelopers now have an internal model for two-phase jetsincluded in their transport and dispersion model for TICs.

When the concentrations are needed very near the sourcelocation (say, within 100 m) it is necessary to account for more ofthe source details than if the concentrations are needed at fartherdistances (say beyond a few hundred meters). For example, by thetime the plume reaches a distance of 1 km, the aerosol generationand evaporation processes are much less important, as long as therainout (and reduction of plume mass flux) can be approximated.Sensitivity studies can assist in decided which details arenecessary.

The material exiting through the rupture plane will eventuallyform a conventional momentum jet at atmospheric pressure. Therequirement is to model the flow between the rupture plane andthe momentum jet at atmospheric pressure. This is commonlyattempted by finding an equivalent source condition for themomentum jet that is consistent with the conditions at the ruptureplane. If the flow is unchoked at the rupture plane then the pres-sure is atmospheric and there is no further depressurization. If theflow is choked at the rupture plane then there will be an acceler-ation of the released material as it depressurizes. Additionally thedepressurization will allow further liquid to change phase toa vapor and cool the jet. This process is commonly called “flashing”.Accompanying this process will be a breakup of the liquid part ofa jet into smaller droplets as a result of mechanical shear instabilityand the thermodynamic flashing process. Finally, there will also bemixing between the momentum jet and the surroundingatmosphere.

All these effects must be subsumed into an alternative initialcondition for the momentum jet at atmospheric pressure. This isoften done by assuming that there is a depressurization to atmo-spheric pressure and there is no mixing between the momentumjet and the surrounding atmosphere until after the depressuriza-tion has been accounted for.

In this section we are considering the processes between planes1 and 2 in Fig. 3, but not allowing any mixing of the surroundingatmosphere into the jet.

There are three distinct though related phenomena here, assummarized below.

5.1. Jet depressurization to atmospheric pressure

The first of these is the acceleration of the jet downstream of therupture as the fluid depressurizes to atmospheric pressure.Considering a flow from a hole (subscripted “1”) to the end ofexpansion (subscripted “2”), the following approaches are mostlyused in the literature:

Mass and Momentum Balance

_mu1 þ ðP1 � P2ÞA1 ¼ _mu2 (47)

u2 ¼ u1 þðP1 � P2ÞA1

_m¼ u1 þ

P1 � P2G1

(48)

where _m ¼ mass flow rate (kg s�1), G1 ¼ mass flux (kg m�2 s�1),u ¼ velocity (m s�1), P ¼ pressure (Pa), A ¼ flow area (m2)

Enthalpy Balance

H1 þ12u21 ¼ H2 þ

12u22 (49)

where H is enthalpy (expressed as cpT for ideal gases).It should be noted that the development above is commonly

used; however, one aspect of the analysis is open to question. Theargument presented is a one-dimensional one though the flow issketched to, and is observed to, diverge in the downstream direc-tion, particularly close to the source. Actually little detail is knownabout this flashing/mixing/depressurizing flow. Our methodology,which breaks the flow into a depressurization and accelerationregion and a following mixing region is a gross simplification. Onbalance the level of analysis used here is thought to be appropriatefor the problem at hand until further experimental information isavailable to support or negate it.

5.2. Flashing of superheated liquid to vapor

The second phenomenon is the phase change from liquid tovapor immediately downstream of the rupture plane. The massfraction that initially changes phase by flashing is determined bydirect thermodynamic calculations. The flash fraction arising froman all-liquid release is

xg ¼ CplðT0 � TbÞ=hfg (50)

where Cpl is the liquid specific heat, T0 and Tb are the temperaturesin the storage vessel prior to flashing and the boiling point of thematerial at atmospheric pressure respectively, hfg is the phase-change enthalpy at atmospheric pressure. This formulation may befound in Fauske and Epstein (1988) and may be traced back to theapplication of the steady flow energy equation while ignoring thekinetic energy terms. Their inclusion leads to

xg ¼ CplðT0 � TbÞ=hfg � 1=2�U21 � U2

2

�.hfg (51)

where U1 and U2 are the jet velocities at the rupture plane and afterany depressurization to atmospheric pressure has occurred. U2 willbe equal to or larger than U1 and thus the neglect of the velocityterms will lead to an overestimation of the flash fraction. The actualusage of this equation is influenced by whether or not the ½ U2

term is incorporated within the subsequent jet model or not.The equivalent result when there are two phases present at the

exit plane is:

xg � xg1 ¼ CplðTl � TbÞ=hfg � 1=2�U21 � U2

2

�.hfg (52)

where T1 is the temperature at the exit plane.



5.3. Breakup of liquid to form small droplets and rainout

The third phenomenon is the breakup of the remaining liquidinto small droplets with a particular probability density functionfor their sizes. The larger droplets will fall out to make a “pool” onthe ground while the smaller droplets remain suspended and willevaporate in the plume. The characteristic droplet diameter is oftento be determined from correlations. From this the rainout fractionmay be estimated though this should be influenced by the fluiddynamics of both the jet flow from the rupture and the ambientwind conditions.

An important aspect of this section and the next, in the contextof real scenarios, is that the release and jet may have many orien-tations and may hit and be influenced by various obstructions.Additionally they may not be directed into regions of clear air butmay be submerged within large clouds formed bymaterial releasedearlier and remaining near to the material source. This is verypossible when the local wind speed is small.

In the case of a flashing liquid jet, such as a release of chlorineor ammonia or HF from a pressurized container, the chemical willflash partially to vapor when released to atmospheric pressure asdescribed above. For ammonia, about 80% of the released massremains as liquid. Thus, the “quality”, or mass fraction that isvapor, is 100% � 80% ¼ 20%. The liquid component in the aerosol isoften parameterized to consist of spherical droplets with sizesdistributed around some mean diameter. The droplets areassumed to be surrounded by a mixture of air and evaporatedvapor. Some large liquid drops may rainout (i.e., may fall) imme-diately onto the ground, some drops may move under gravity anddrag force while vaporizing and may rainout later, and some mayremain in the plume as an aerosol. However, the fraction of liquidthat rains out versus the fraction that remains suspended in theplume as an aerosol is not well known. This fraction is importantbecause the greatest hazard range is likely to occur when all therelease remains suspended as is the maximum possible sourceemission rate for the subsequent dispersion modeling. Addition-ally the evaporation of the suspended aerosol produces anincreased negative buoyancy and this can affect the downwindplume greatly. The liquid that rains out is likely to form a boilingpool that will continuously evaporate and add vapor mass into thedispersing jet. The evaporation may continue long after the jetrelease ceases. This process is controlled by the heat transfer to theliquid pool.

The breakup of the liquid into droplets occurs by two mecha-nisms; a mechanical breakup dominant for releases that are sub-cooled relative to ambient conditions and a thermodynamicbreakup dominant for liquid or two-phase releases that aresuperheated relative to the ambient conditions though both effectsmay also occur together.

The modeling of these processes is complex and the results aretypically in the form of correlations. It is sometimes forgotten thatthe essential information required is the amount of releasedmaterial that rains out. Additionally knowledge of where therainout occurs may be required for input to the pool evaporationmodeling but pragmatically all that may be required is knowledgeof where the mean particle diameter rains out.

By definitionwhatever does not rainout must remainwithin thejet/plume and be subsequently be evaporated within the jet/plume.Most jet/plume models can accommodate this evaporation processeither in bulk due to air entrainment or by considering evaporationof individual droplets. In the latter case knowledge of the meandroplet diameter of the liquid in the jet/plume or the actual particlesize distribution is required. Whether such detailed knowledge ofthe evaporation process is required in operational models could beargued.

However the approach commonly taken is to determine a meanparticle diameter, assume a particle diameter distribution and thentrack the fate of particles within the jet/plume downstream of therupture; with some of the particles raining out and some evapo-rating. Of course this all hinges on whether an appropriate two-phase jet model is available and whether this is correctly linked tothe (possibly multi-phase) plume model.

The mean diameter and/or the size distribution of the liquiddrops have to be input to the models for droplet motion andvaporization. In somemodels, the droplet size is calculated based onan assumption of an aerodynamic or mechanical breakup mecha-nism (e.g., the shattering of initial drops into smaller droplets due toaerodynamic forces). The stable droplet size is determined by theratio of the disruptive hydrodynamic forces to the stabilizing surfacetension force. The ratio is the Weber number, We:

We ¼ rgu2reldps

(53)

where rg ¼ surrounding gas density (kg m�3), urel ¼ relativevelocity between the jet and gas (ambient air) (m s�1), dp ¼ dropletdiameter (m), s ¼ surface tension of the liquid (N m�1).

It is generally accepted that there is a critical Weber number,Wec, below which drop breakup does not occur. Fig. 11 shows thatthe Wec is approximately 12 for small Ohnesorge number, which isthe ratio of the viscous force to the surface tension force, and is alsoknown as the viscosity number. Drop breakup at higher Ohnesorgenumber is progressively more difficult and is ultimately impossible.

The assumption of a mechanical breakup mechanism leads tothe following estimate of the mean droplet diameter, dpm(m):

dpm ¼ Wecs

rgu2rel(54)

The TNO (1997) Yellow Book recommends values of between 10and 20 for Wec, and most models use 12.5.

For droplet size predictions, the RELEASE model (Johnson andWoodward, 1999) adopts Eq. (54) for the mechanical breakup andhas a separate formulation for treating the “flashing” breakup (seeSection 6.2.1 below). In addition, correlations of droplet size againstthermodynamic and other variables have been conducted by JohnsonandWoodward (1999) and others as discussed in the following.

The thermodynamic breakup occurs when the liquid is super-heated relative to atmospheric conditions, with a degree ofsuperheat defined as DTsh ¼ To e Tsat(Pa), where To is the temper-ature at stagnation, typically the storage temperature. The

10110-4 10-3 10-2 10-1 100

0

70

10

20

30

40

50

60Brodkey’sCorrelation

Ohnesorge Number (On)

Crit

ical

Web

er N

umbe

r (W

e C)

Fig. 11. Observations of critical Weber number as a function of Ohnesorge number(Brodkey, 1969).



superheat, if sufficient, nucleates bubbles which grow until theyagglomerate with neighbors, thereby breaking the liquid apart(Brown and York, 1962). This flashing droplet breakup is a domi-nant mechanism in releases of pressurized chlorine or ammonia. Amethod for estimating the size of the droplets formed by theflashingmechanism is given byWoodward (1995). After correlatingpublished experimental drop sizes against a number of differingparameters, he concluded that the partial expansion energy, Ep(J kg�1), was the most effective correlator for droplet size:

Ep ¼ �DH � vsðPs � PaÞ þ vsjP1 � Psj (55)

whereDH¼ Change in enthalpy from exit to expansion (from plane1 to plane 2 in Fig. 3) (J kg�1), Ps¼ saturation pressure at the storageor stagnation temperature (N m�2), vs ¼mixture specific volume atTs (Pa) (m3 kg�1), P1 ¼ exit pressure (N m�2)

The drop diameter, dp (m), based on the correlation is given by:

dp � 106 ¼ 1000 Ep < 0.1.dp � 106 ¼ 833e73.4 ln (Ep) 0.1 < Ep < 6000.dp � 106 ¼ 498e43.0 ln (Ep) 6000 < Ep < 15000.dp � 106 ¼ 0.85 15000 < Ep

where Ep has units of J kg�1.Fig. 12 shows diameters of liquid Cl2 drops in the CCPS experi-

ment versus Ep (Woodward, 1995; CCPS/AIChE, 1999). Unfortu-nately, the drop sizes were not measured in the CCPS experiment.Woodward (1995) assumed the drop sizes, as the y-axis title indi-cates, calculated the trajectories of the drops, compared calculatedamount of rainout against experimental liquid capture data.Therefore, the value of Ep as a correlator is demonstrated. But therelationship in the equation above is specific only to the models ofdrop motion and vaporization Woodward used in arriving at it.Witlox et al. (2007) has proposed similar correlations. But all thesecorrelations can only be used together with the droplet motion,vaporization, and rainout models the correlations are based on.

The CCPS/AIChE performed experiments to gather data onaerosol rainout from superheated liquid release, so that these couldbe used to validate the CCPS RELEASE model (CCPS/AIChE, 1999).The tests were carried out in two phases, Phase 1 consisting ofwater and CFC-11 and Phase 2 of chlorine, monomethylamine(MMA) and cyclohexane (Cyc6) releases. The results reported byEnergy Analysts (1990) and Quest Consultants (1992) are availableon CD-ROM that was attached to the CCPS/AIChE (1999) report. Theexperimental data were later modified to allow for evaporation ofliquid drops during their flight and also evaporation in the liquidcapture pans. The experiments, in spite of some criticisms

(Ramsdale and Tickle, 2000), provide valuable data with which tovalidate rainout models. Apart from these experiments, very fewrainout data exist, except for the Rohm & Hass (R&H) MMA data(Lantzy et al., 1990) and the Hocquet et al. (2002) and Bigot et al.(2005) water data. Chemicals were released 1.22 m above theliquid capture pans in CCPS, 1.73 m in R&H experiments, and 1.5 min the Hocquet et al. and Bigot et al. experiments.

Fig. 13 shows the “corrected” rainout in the CCPS experimentversus “needed drop diameter” (Woodward, 1995; CCPS/AIChE,1999). Because drop sizes were not observed in the experiment,the term “needed drop diameter” refers to a parameterization ofthe expected drop diameter. This corroborated an independentanalysis by Melhem et al. (1995) of the same data, shown in Fig. 14.Except for water, the tested chemicals seem to show a similarcorrelation between rainout and droplet size, i.e., approximately45% rainout of liquid occurs for a droplet diameter of 300 micronsThe experimenters have questioned the quality of the CCPS waterdata because the water experiments were done in a semi-enclosedgreenhouse that might have become saturated with water vaporduring experiments. However, the Hocquet et al. and Bigot et al.experiments, conducted outdoors, showed a similar variation of theliquid water capture rate versus storage temperature as the CCPSexperiments. Thus, the water data in Figs. 13 and 14 require furtheranalysis to explain their difference from the other liquid datacorrelations in those figures.

5.3.1. Initial drop size and its distributionSuppose the dispersion model requires specification of the PSD,

the liquid mass fraction, and the temperature for all-liquid releases.At present, no deterministic models are available that can predictstable droplet sizes for various release conditions. Thus, correla-tions based on observations may be the best alternatives. Havingreviewed those in the literature, Melhem and Croce (1992) andMelhem et al. (1995) proposed the use of specific available energy,AE (J kg�1), as the correlation parameter:

dp ¼ f�rvsd

AE

�(56)

and

AE ¼ �DU � Paðv2 � voÞ ¼ �ðH2 � HoÞ � voðPo � PaÞ (57)

0

50

100

150

200

250

300

350

400

450

000010001001

Partial Expansion Energy (J/kg)

As

su

me

d D

ro

p S

ize

(μ

m)

Drop size calculated from CCPS data Equation (18)

Fig. 12. Drop size plotted versus partial expansion energy correlation for CCPS Cl2 data.

0

10

20

30

40

50

60

70

80

90

100

0 100 200 300 400 500 600 700

Needed Drop Diameter (μ m)

Rain

ou

t (%

)

H2OCFC-11Cl2MMACyc6

Fig. 13. Rainout % plotted versus needed (parameterized) drop diameter in CCPSexperiments.



where dp ¼ droplet diameter (m), rv ¼ vapor density at “2”(kg m�3), sd ¼ surface tension of the droplet liquid (N m�1),DU ¼ Change in internal energy from storage to expansion (J kg�1)

Later Woodward (1995) and CCPS/AIChE (1999) reviewed theliterature correlations for droplet size. They concluded that thepartial expansion energy, Ep (J kg�1), was the most effectivecorrelator for droplet size:

Ep ¼ �DH � voðPsðToÞ � PaÞ þ voðPo � PsðToÞÞ (58)

where DH ¼ Change in enthalpy from stagnation to expansion(J kg�1)

Both correlators, AE and Ep, are related to some measure ofkinetic energy “available” when the flashing liquid expands fromstagnation to ambient pressure. Previously we recommended themost effective Ep-based CCPS correlation for the Sauter meandiameter (SMD) of the droplet size:

dpx106 ¼ 833� 73:4 lnEp

(59)

A recent correlation (called here “DNV-JIP”) proposed byWitloxet al. (2007) is sometimes used. It has been recommended that theWitlox et al. correlation be carefully re-evaluated for the followingreasons:

� The DNV-JIP correlation uses the correlation developed byKitamura et al. (1986) to find the superheat for transition frommechanical breakup to flashing breakup. Witlox et al. howeveruse rv at To in place of the equilibrium vapor density at ambientpressure that Kitamura et al. have used. This would producesignificant errors in predicting drop size.

� Table 2 and Fig. 7 in Witlox et al. (2007) show the DNV-JIPcorrelation predicts much larger drop sizes, more rainoutaccordingly, than the CCPS/AIChE (1999) model. This is notexpected by the experimenters, industry experts, and accidentinvestigators.

� The DNV-JIP correlation is based on a few experimental data. Infact, the DNV-JIP research program has been completing moreexperiments (Phases III and IV), but the observations have notyet been made publicly available.

Once a model is implemented with proper droplet motion andvaporization models with the initial drop size discussed here, itmay be able to predict rainout. But at present, there is not anaccepted model that performs consistently well against the limitedset of experiments done by CCPS/AIChE (1999), Rohm and Haas(Lantzy et al., 1990), and Witlox et al. (2007). The lack of an

acceptable model may be also due to the need for more experi-mental data, especially for full-scale releases. CCPS/AIChE experi-mental data were useful but the range of scenarios should beexpanded.

It may be worthwhile to see what can be summarized as“known”.

� There is both mechanical and thermodynamic breakup.� Witlox has argued that the problem is generally more complexthan can be treated with very simple parameterizations; thismay be less important if only a small number of TICs are beingconsidered.

� Two approaches have been followed for rainout; direct corre-lations or following individual particles.

� In both cases the near rupture jet characteristics must playa part.

� The treatment of the liquid that is not rained out is relativelystraightforward and there are several levels of approximationthat have been used.

� Witlox and Holt (1999) argue that a case could be made that allparticles below 20 m would not rainout. Fig. 12 suggests thatmay be a figure of 100 m might be acceptable. Figs. 12 and 13suggest that “roughly” there is “always” some substantialrainout (around 80%) for all particles above 400 m. Are there notsome simple parameterizations hidden away here that couldbe operationally useful (given some set accuracy threshold)?

� There are several correlations for the probability densityfunction of droplet sizes together with the accompanyingcharacteristic diameter.

The breakup of the jet into fine droplets and their subsequentsuspension and evaporation, or rainout, is a significant uncertaintyin the overall modeling process. What has not yet been done is torecommend the RELEASE approach, the more recent and “stillbeing developed” Witlox effort or what can be discerned from thealso recent FLIE project. Weaknesses of the RELEASE model and thelack of completeness of the Witlox JIP experimental and modeldevelopment make it difficult to offer specific recommendations.What can be said is that there is nothing inherently poor about theWitlox JIP model and this model could be used though the uncer-tainty of this modeling process must be kept in mind.

6. Evaluation of the modeling

As stated in the introduction, this paper has focused on high-priority TIC scenarios such as two-phase releases of pressurizedliquefied gases. The evaluations described below first addresssingle-phase releases and then two-phase releases. Our detailedproject report (Britter et al., 2009) covers amore comprehensive setof scenarios, including evaluations of evaporation from liquid pools.

6.1. Discharge conditions

6.1.1. Evaluation of the modeling of the mass discharge rate:single-phase release

The evaluation is limited to only a few comparisons since thesingle-phase models have been evaluated elsewhere (e.g.,Richardson et al., 2006; Spicer et al., 2003), perform well, and arerather well understood. We first consider a compressible gas flowand then liquid flows through an orifice.

Richardson et al. (2006) carried out well-designed experimentsfor themeasurement of single- and two-phaseflows of hydrocarbonsthrough an orifice. The experiments, conducted for the UK EnergyInstitute,weremade for volatilemixturesof natural gas, propane, andcondensates and were aimed primarily at testing models for

200018002000 400 800600 1000 1200 1400 16000.0

1.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

CyclohexaneChlorineFreon 11Monomethylamine

WaterAmmonia

Droplet Diameter (Microns)

Frac

tion

at G

roun

d Su

rface

Fig. 14. Rainout, expressed as “fraction at ground surface”, versus drop diameter inCCPS experiments (Melhem et al., 1995).



restricted flow (through relief valves, etc.) in the oil and gas industry.The experiments were significant in their precise determination ofthe mixture composition, mass flow, and thermodynamic stateincluding the fluid temperature and pressure. Moreover, the appa-ratus used allowed higher flow rates (up to 4 kg s�1) than usuallypossible in laboratory-scale experiments and at storage pressuresapproaching 100 bar. Here, we only use their natural gas data fortesting mass flow based on the perfect gas law (Eq. (4)).

In addition to measurements, Richardson et al. calculated theflow rate for single- and two-phase flow using a simple modelbased on isentropic choked flow with the “sound speed” deter-mined for either a single- or two-phase fluid. A key component ofthis was an equation of state model for determining the pressure,temperature, and mixture composition based on a “principle ofcorresponding states,” which was purported to be more accuratethan a cubic equation of state model such as the Peng and Robinson(1976) approach. A more complete equation of state model isparticular useful for two-phase mixtures and at pressures near andabove the critical pressure Pc, where compressibility effects fornon-ideal gases become important.

For natural gas, an analysis of the simple emissions estimatebased on the perfect gas model (Eq. (4)) has been made by deter-mining the discharge coefficient, CD¼ observed flow rate/predictedflow rate, and comparing it with the Richardson et al. results andthe CD ranges discussed in Section 3.5. In the perfect gas formula-tion, the natural gas was assumed to be all methane, which shouldbe a good first approximation since natural gas is 90% methane, 9%ethane, and 1% propane by weight. In the natural gas experiments,the orifice diameter ranged from 8 to 15 mm, the pressure from 10to 82 bar, and the measured flow rate from 0.3 to 2.82 kg s�1.

Fig. 15 shows the discharge coefficient for the natural gas datawhere the open and enclosed circles are the results for the perfect

gas approach (Eq. (4)) and the Richardson et al. model, respectively.As can be seen, the Richardson et al. model leads to an approxi-mately constant CD ¼ 0.9 (average value), whether plotted versusthe measured mass flux or the pressure ratio P0/Pc. The perfect gasapproach (open circles) gives higher CD values that range fromabout 0.9 to 1.1, and this is believed due to two causes. The first isthe assumption that the natural gas is 100% methane, which mayexplain the higher CD values (average of 0.97) for the “lower”pressures P0/Pc < 1, where non-ideal gas effects are not a largeissue. Second, the CD’s show systematically higher values for thelarger pressure ratios (P0/Pc > 1) where non-ideal gas effects areprobably important. The CD’s are as much as 20% greater than theRichardson et al. CD (0.9) at P0/Pc ¼ 1.8, where P0 ¼ 82 bar. This isprobably due to the failure of the perfect gas law to performwell atsuch high pressures.

Leung (private communication) made a corroborative check onthe above speculated effect of pressure using a non-ideal gas flowmodel (Leung and Epstein,1988), which accounts for compressibilityat high pressure. Assuming the natural gas to be 100% methane, heobtained a theoretical mass flow rate of 2.85 kg s�1 versus themeasured value of 2.72 kg s�1 at the highest pressure (P0 ¼ 82 bar).This resulted in a CD ¼ 0.95, which is considerably closer to theRichardson et al. value (0.9) than the perfect gas model (CD ¼ 1.1) atthat pressure. Thus, the non-ideal gas model indeed explained mostof the difference between the perfect gas and Richardson et al. modelresults. Leung also found that for a mixture of 90% methane and 10%ethane, the CD was 0.93 or slightly closer to the reported 0.9 value.

In summary, the perfect gas model combined with the recom-mended CD ¼ 1 (Section 3.5) would slightly overestimate theRichardson et al. flow rate data for P0/Pc < 1 and underestimate theflow rate by about 10% at the highest pressures in those experi-ments. This accuracy is considered sufficient for TIC modeling.

For liquids, we evaluated the predicted mass flow rate ordischarge coefficient using experimental data collected in testing theRELEASE model (Johnson and Woodward, 1999). Since the CD (¼0.6)for liquid discharges iswell documented (Section 3.5), the evaluationwas only conducted for two of the liquids, water and CFC-11, used inthe RELEASE/CCPS experiments. The comparisons were expected tobe a confirmation of the above CD value. For these experiments, theliquids were released through an orifice connected to a heatedstorage tank, which was pressurized to ensure that the fluid in theorifice was 100% liquid. The release rate was determined from thechange with time of the liquid level in the tank. The water releaseswere conducted for storage temperatures ranging from 378 to 488 Kand orifice pressures of 184 to 2140 kPa, whereas the CFC-11 releasesinvolved lower temperatures (295e355 K) and pressures(162e554 kPa). The lower end of the temperature rangewas near theboiling point of the liquids. The measured release rates ranged from0.07 to 3.11 kg s�1 (water) and 0.27 to 0.67 kg s�1 (CFC-11).

Fig. 16 shows the discharge coefficient as a function of the pres-sure difference, P0 � Pa, driving the flow. The average CD’s for waterand CFC-11 are 0.59 and 0.61, respectively, and are in close agree-ment with the CD (¼ 0.6) reported for liquids in Section 3.5. Asidefrom three CD values (�0.69) for water, the individual CD’s exhibitrelatively little scatter and have small rms deviations about theaverage: 0.05 for water and 0.02 for CFC-11. The agreement betweenthe average CD’s and the expected one (0.6) is representative of thatfor the other liquids e chlorine, methylamine, and cyclohexane e inthe CCPS experiments. This was demonstrated by Spicer et al. (2003)in a comparison between the predicted and measured flow rates.

6.1.2. Evaluation of the modeling of the mass discharge rate:two-phase release

Richardson et al. (2006) also undertook an extensive set ofexperiments, again with what might be considered as sharp-edged

a Perfect gas modelRichardson et al. (2006) model

Average CDRichardson et el. model

0 0.5 1 1.5 2 2.5 30.8

0.9

1

1.1

1.2

Measured flow rate (kg/s)

Dis

char

ge c

oeffi

cien

t

b Average CD, Perfect gas modelP0/Pc < 1

0 0.5 1 1.5 20.8

0.9

1

1.1

1.2

Dis

char

ge c

oeffi

cien

t

P0 / Pc

Fig. 15. The discharge coefficient for the perfect gas and Richardson et al. (2006)emissions models for natural gas as a function of a) the measured flow rate, and b)the ratio of storage pressure to critical pressure. The flow rate measurements are fromRichardson et al. (2006).



orifices, using highly volatile mixtures of hydrocarbons at pressuresup to 100 bar and flow rates of up to 4 kg s�1 under saturationconditions. What is of particular interest for this report was thatRichardson et al. (2006) compared their experimental results withpredictions provided by an HEMmodel (described in Section 3.4.6).The expected flow rate was calculated from the exact iterativetechnique and comparedwith themeasured flowand the dischargecoefficient calculated as the ratio of the two. Several hundredexperiments were undertaken.

Richardson et al. (2006) also compared the results from theirHEM model and the u-method recommended in this report andconcluded that “for wide-boiling mixtures in which the upstreamcondition is two-phase . the u-method agrees with the exact,iterative method to within 1%.” Thus we can interpret thecomparisonmadewith the exact HEMmodel as being equivalent toa comparison made with the u-method. The liquid mass fractionsupstream of the orifice varied from 0.0 to 1.0.

However the u-method omega did produce significantly largererrors when the fluid stream is single phase at the orifice, but twophase within the throat.

There were two situations for which two particular (simple)model types were applicable

1. For flows of compressed volatile liquids, the incompressibleflow model provides a good approximation with a dischargecoefficient of 0.60. This simple model progressively breaksdown as the volatile gas content increases.

This is the Bernoulli equation approach.

2. For two-phase flows (that must of course be at the appropriatetwo-phase state) and the liquid mass fraction is below 0.8 thenthe homogeneous equilibrium model (HEM) provides a goodapproximation; with the discharge coefficient varying from

0.90 for a pure single-phase gas flow to about 0.98 when theupstream liquid fraction is 0.8.

3. The transition from incompressible flow to HEM is not sharp asthe upstream state crosses the saturation boundary.

Also of importance is the observation that the variability of thecalculated discharge rates using the above arguments seemed quitemodest (order 10%) compared with our accuracy requirements.

6.1.3. Evaluation of the modeling of the thermodynamic stateof discharge

There are little specific data to be used here presumably becauseof the strong assumption that the thermodynamic state will beprovided by basic thermodynamic relationships. The data fromRichardson et al. (2006) for two-phase releases was consistent withthat anticipated from the model used by Richardson et al. (2006) orby that anticipated from the use of the u-method, reflecting thatthe appropriate thermodynamics was being utilized.

Of interest from the FLADIS study of Nielsen et al. (1997) wasthat for a subcooled storage of ammonia and a discharge througha long nozzle (for which an equilibrium model would be appro-priate) then the pressure at the nozzle exit was well above atmo-spheric pressure and close to the saturated vapor pressure at thetemperature at the nozzle.

This is to be contrasted with the data from the studies of Spiceret al. (2003) that were for subcooled liquids and a sharp-edgedorifice release. In all these latter cases, the results were consistentwith the pressure at the vena contracta being atmospheric and theflow near the rupture being a non-equilibrium one.

6.1.4. Evaluation of the modeling of the exit velocityand momentum

There are little data to evaluate the modeling of the exit velocityandmomentum of the jet. The results fromNielsen et al. (1997) andfrom Spicer et al. (2003) for subcooled liquids indicates that thepressure at the exit plane would be atmospheric if the flow wasa non-equilibrium one and the saturated vapor pressure at thenozzle (or approximately the storage) temperature if the flow wasan equilibrium one. These differences will directly influence themomentum of the flow and the effective velocity of the release.

The modeling anticipates an increase of velocity during theflashing. This was not seen when studying droplet data at differentpositions downstream. However the question was then asked as towhether the flow acceleration had already taken place prior to themeasurements of the droplet velocities. The important comparisonwould be between the actual liquid exit velocity and the down-stream flow and droplet velocities.

In an interim calculation, an example was described of a dropletvelocity starting from 45 m s�1 at x/D ¼ 20, and decreasing to20e25 m s�1 further downstream. However other calculationsindicated that the liquid exit velocity was of the order of less than25 m s�1 for propane, and even less than this for butane. This wasthen rechecked. It was argued that, assuming all liquid at the orificeexit, that the velocity was 24 m s�1. The droplet velocitiesat x/D ¼ 20 (first measurement position) showed a mean dropletvelocity of 43 m s�1.

To complicate the issue it was found from the computations ofthe mass flow rate at the exit that the exit pressure is atmospheric(that is, the atmospheric exit pressure gives better results than thesaturation pressure at the stagnation temperature).

Additionally data fromVKI experiments do showan accelerationand this acceleration occurs before x/D ¼ 20 and this seemsconsistent with the FLIE result.

It is unclear whether this process is linked to “flashing” or theexcess pressure above ambient at the exit plane for choked flows.

Average CD

0 500 1000 1500 20000.4

0.5

0.6

0.7

0.8

0.9

Dis

char

ge c

oeffi

cien

t Heated water

CFC-11

0 100 200 300 400 5000.4

0.5

0.6

0.7

0.8

0.9

Dis

char

ge c

oeffi

cien

t

Po - Pa (kPa)

b

a

Fig. 16. The discharge coefficient for a) water and b) CFC-11 based on the mass flowrate obtained from the incompressible flow rate model (Eq. (1) with h ¼ 0). Themeasured flow rates are from the CCPS experiments (Johnson and Woodward, 1999).



The latter phenomenon is also anticipated for under expandedsingle-phase jets. The acceleration in that case is directly attributedto the excess pressure at the exit plane.

6.2. Evaluation of the modeling of jet breakup, droplet particlesize and rainout

6.2.1. RELEASE modelThe RELEASE model (Johnson and Woodward, 1999) for droplet

size and rainout is based on six key assumptions listed below.

1) The droplet size distribution is assumed to follow a lognormalprobability density function (PDF) with a geometric mean (GM)diameter, hereafter called themean diameter dpm, for given exitor orifice conditions and a constant geometric standard devi-ation (GSD), sG ¼ 1.8.

2) Themean diameter dpm is given by the smaller of two estimatesdpm ¼ Min(dp1, dp2) where dp1 is based on a mechanical oraerodynamic breakup model using the critical Weber number(Wec) criterion: dp1 ¼ Wec sL/(ra uexp2 ) and where Wec is set to12, ra is the air density, and uexp is the expansion velocity; theuexp ¼ u2 is the value at Section 2 in Fig. 3. The dp2 is based ona flashing breakup model using the same Wec but with ra anduexp replaced by rv and urel, respectively. Here, rv and urel arethe flash vapor density and the “relative velocity,” which isfound from uexp, the exit or discharge velocity u0, and a bubblevelocity (ub) in the drops: urel ¼ (ub2 þ (uexp e u0)2)1/2, whereu0 ¼ CD u0v and u0v ¼ [2(P0 e Pa)/rf]1/2.

3) The expansion velocity is found from the mass and momentumbalance discussed in Section 5.1: u2 ¼ u1 þ (P1 e P2)/G1, whereP2 is the ambient pressure. Johnson and Woodward (1999)effectively calculate uexp ¼ u2 from uexp ¼ u0 [1 þ 1/(2CD2)],where the velocity at the exit plane, u1, is assumed to be the u0above.

4) There is no evaporation of the rainout droplets along theirtrajectory to the surface.

5) The mass fraction of droplets that rainout is found by inte-grating over the droplet mass distribution or PDF froma droplet diameter d equal to the “critical diameter” dc to N.

6) As presented by Johnson and Woodward (1999), the criticaldrop size is the diameter (dc) with a critical settling velocity ucequal to the radial velocity ur of the spreading jet, whereur ¼ uexp tanqj, and qj is the jet spread angle which they take as4.46�. Droplets larger than dc will have greater settling veloci-ties and fall faster than uc and thus rainout.

We have comments on three of these assumptions. 1) Forassumption 2, there is no scientific basis given for the inclusion of(uexp e u0)2 in the urel term. In the applications below, the ub isnegligible and urel¼ uexpe u0, which is the reasonwhy the flashingmodel “works” for the CFC-11 droplet predictions (Section 6.2.3). 2)We believe that assumption 3 for the uexp calculation is flawed/questionable because of the assumption u1 ¼ u0, which means thatthe exit plane or “vena contracta” pressure is ambient. Thus, P1¼ P2in the above momentum balance and there should be no flowacceleration. However, for CD ¼ 0.6, the predicted uexp ¼ 2.4 u0,which is a rather large speed-up. We regard the inclusion of thisuexp as necessary to make the RELEASE model “work” although werecognize that flow speed-up from the orifice may occur as dis-cussed in Section 6.1.4; however, the magnitude and approach forobtaining it are in question. 3) Assumption 6 ignores the effects ofjet turbulence on the droplet trajectories and the distance depen-dence of the jet velocity following the expansion zone.

The RELEASE model also was used to determine the “neededdiameter” or an “observed” value to explain or match the rainout

data. The observed diameter was an inferred dpm found from thecalculated dc and the observed rainout. We developed an analyticalexpression for the rainout fraction R by integrating over the dropletmass distribution as indicated in 5) above and dividing the result bythe total mass. The expression is

R ¼ 0:5ð1� erfð4cÞÞ (60)

where erf is the error function,

4c ¼ lndc=dpm

.�21=2sm

��3$21=2=2

�sm (61)

and sm ¼ ln sG. Thus, given R one can find 4c, the ratio dc/dpm, andhence the “observed” dpm given the computed dc. This R expressionwas not given or used by Johnson and Woodward (1999), whopresumably used similar methods to obtain R in terms of dc/dpm andthus find the “observed” mean diameter, dpm obs or Dobs as usedbelow.

6.2.2. RELEASE/CCPS experimentsThe CCPS or RELEASE experiments for water and CFC-11 were

conducted in a greenhouse to shield the tests from any windeffects; the range of storage temperatures and pressures were givenin the references. For these experiments, the discharge orifice wasoriented horizontally and located 1.22 m above a 15.2-m longcapture system consisting of pans that collected the falling liquidand conveyed it to collection vessels, which were weighed todetermine the rainout mass. Note that the rainout depended on theparticular source e collection pan geometry, i.e., the source heightand the length of the collection pan. The orifice diameters rangedfrom 3.2 to 12.7 mm for water and was 6.4 mm for CFC-11. For theCFC-11 tests, the vessels were cooled, presumably to preventevaporation of the captured liquid since the CFC-11 boiling pointtemperature (297 K) was in the ambient temperature range.

For chlorine, cyclohexane, and methylamine, the experimentswere conducted using a similar test arrangement and the samegeometry as for water and CFC-11. However, the experiments wereperformed outdoors at the DOE Test Spill Facility in Nevada due tothe hazardous nature of these chemicals. Chlorine and methyl-amine have boiling point temperatures (Tboil ¼ 237 K and 264 K atlocal conditions) below the summer ambient temperatures inNevada, and thus, the liquid capture systemwas modified for thesechemicals. Chlorine and methylamine were captured using basicand acidic solutions, respectively, in the capture pans with subse-quent solution analysis determining the mass of the capturedchemicals. The cyclohexane rainout was found by draining itdirectly from the capture pans to the weighing vessels.

The liquid captured in the pans or rainout varied systematicallywith the isenthalpic flash fraction, xg (see Eq. (8a), Section 5.2) oressentially with the superheat, T0 e Tsat(pa) where Tsat(pa) ¼ Tboil.This is shown in Fig.17 for the five liquids where the liquid capturedis expressed as a percentage of the released mass. This figure alsoshows that the captured mass decreased systematically witha decrease in the boiling point temperature, which corresponds toan increase in the liquid volatility. Thus, the most volatile chemical,chlorine, exhibits the smallest capture and the least volatile, water,the highest. The liquid capture fractions in this figure are the raw or“uncorrected” values.

Two points should be made concerning the evaluation of theRELEASE model predictions of droplet size using the CCPS data.First, drop sizes were not measured in the CCPS experiments andinstead were inferred from the rainout measurements as noted inSection 6.2.1. Thus, evaluation of the RELEASE model using thesedata is not an independent test of the model, but is neverthelessuseful (e.g., to show model biases).



Second, the rainout data collected for chlorine, cyclohexane, andmethylamine were corrected by Johnson andWoodward (1999) forre-evaporation from the capture pans because the experimentswere conducted outdoors during the summer as alreadymentioned.For chlorine and methylamine, the correction accounted for thespreading, dissolution, and reaction of these chemicals in anaqueous solution. For cyclohexane, the correctionwas made for thecapture and spreading of the liquid in a dry pan, which was cooledfrom below to prevent or diminish the evaporation. In the case ofmethylamine and cyclohexane, the correctionswere relatively smallwith the ratio of corrected to uncorrected capture averaging1.14 0.038 for methyamine and 0.88 0.070 for cyclohexane.However, for chlorine, the ratio was large e 2.72 0.28 e and thusrepresented a significant correction to the original data.

6.2.3. RELEASE model resultsThe RELEASE model predictions of the mean diameter, dpm or

Dpred (Tables 10-1 to 10-5; Johnson and Woodward, 1999), arecompared with the observed diameters, Dobs (Tables 11-1 to 11-5),obtained from the corrected CCPS rainout data. We conducted spotchecks of the tabulated data to ensure consistency with theassumptions listed in Section 6.2.1. Given those assumptions, theaerodynamic model was applied for dp1/dp2 ¼ (rv/ra)(urel/uexp)2 ¼ (rv/ra)/(1 þ 2CD2)2 < 1 and the flashing model for a reversalof the inequality. Thus, with CD ¼ 0.6, the aerodynamic model wasadopted for rv/ra < 3 and the flashing model for rv/ra > 3. For theCCPS experiments, only CFC-11 satisfied the last inequality (i.e.,Dpred ¼ dp2). In all other cases, the minimum diameter was given bythe aerodynamicmodel although for chlorine, with rv/ra¼ 2.82, thepredictions for the two models were close.

The ratio Dpred/Dobs is analyzed for four data groupings: 1) chlo-rine, 2) CFC-11, methylamine, and cyclohexane, 3) water, and 4) allliquids. These groupings were selected because a) chlorine had thelargest correction to the observed rainout data, b) water was sus-pected of being much different from the other rainout data (Fig. 17)due to the high humidity in the greenhouse, the possibility ofcondensation onto droplets in the discharge jet (Johnson andWoodward, 1999), and thus higher rainout, and c) the CFC-11,methylamine, and cyclohexane exhibited similar trends ofDpred/Dobs.

Fig. 18 presents the Dpred/Dobs versus the superheat for the fourgroups where one can observe the different character of the trendsin a)ec). The Dpred/Dobs ratio for chlorine has a mean value (1.6) thatis about double that of the other chemicals includingwater (see alsoFig. 20), and it exhibitsmuchmore scatter than the others especiallyCFC-11, methylamine, and cyclohexane. This difference may be dueto the large correction factor (2.7) applied to the original chlorinerainout data. With the exception of water, the chemicals exhibita trend of a decreasing Dpred/Dobs with an increase in the superheat.

Fig. 19 shows the Dpred/Dobs versus the calculated orifice velocityu0 and trends that look similar to those with the superheat e

a decrease in Dpred/Dobs with u0. The similarity in the trends is notsurprising since the u0 increases with the storage/orifice pressure,which increases with the superheat. For u0, the trend of decreasingDpred/Dobs with u0 is believed due to the dependence and sensitivityof the predicted and observedmean diameter on uexp, which in turndepends on u0 or u1. We cannot determine whether the trend in theDpred/Dobs is due to the predicted or observed diameter or both. Theresults in Fig. 19d with the Witlox et al. (2007) data appear to bea continuation of the trend found with the CCPS data.

In addition to the uexp accuracy, there are at least two otherfactors that would affect the prediction of dpm and its inferencefrom the rainout data: 1) the neglect of jet turbulence which affectsthe droplet trajectories and the amount/location of the rainout, and2) the jet axial velocity uj, which should decrease downstream ofthe expansion zone. The uj decrease should be ujf1=x for a turbu-lent jet (Schlichting, 1987), but in RELEASE the uj is taken as uexp,i.e., a constant. The above effects could be included with a simpledeposition model that incorporates a “tilted plume”. We note thatthe Cleary et al. (2007) laser measurements of water jets anddroplets clearly show the gravitational settling and “tilt” of thedroplet jet/plume.

Fig. 20 shows the statistics of the Dpred/Dobs for each of the CCPSchemicals. The behavior confirms the scatter plot results inshowing the overprediction of Dobs for chlorine, a mean Dpred/Dobs ¼ 1.6 0.93, and the large rms error. This mean ratio is abouttwice that for CFC-11, methylamine, cyclohexane, and water. ForCFC-11, methylamine, and cyclohexane, the rms errors are modestor about 30% of their respective mean values, but for water the rmsdeviation is 0.92 or about 1.2 times themean. The latter may be dueto the high humidity in the greenhouse as noted earlier.

6.2.4. JIP modelThe Joint Industry Project (JIP) model developed byWitlox et al.

(2007) is based on an empirical correlation from the laboratory-scale water jet experiments of Cleary et al. (2007). It predictsa Sauter mean diameter (SMD), designated here by dSMD anddefined by dSMD ¼ <d3>/<d2>, where the < > brackets denote anaverage over the droplet PDF. For a lognormal PDF, the dSMD ¼ dpmexp(2.5 sm

2). JIP is based on the following:

1) The dSMD is comprised of an aerodynamic breakup modelprediction dpa valid from a zero superheat to a transition “A”superheatDTA and a flashing droplet size dpC (¼dpA/2.4) achievedat a transition superheat DTC. For intermediate superheats(DTA<DT<DTC), the droplet size is assumed tovary linearlywithsuperheat. This continues until dSMD reaches the “fully flashed”diameter of 30 mm, after which it decreases at a very slow rate.

2) The aerodynamic model prediction is given by the dimen-sionless empirical correlation developed by Cleary et al. (2007):

dpa=do ¼ 64:73We�0:533Lo Re�0:014

Lo ðL=doÞ0:114; (62)

where WeLo ¼ rLuo2do/sL, ReLo ¼ u0do/no is the orifice Reynolds

number, L is the orifice wall thickness or pipe length (if there is

Tboil (°K)237264297353373

ChlorineMethylamineCFC-11CyclohexaneWater

0 10 20 300

20

40

60

80

100

Flash (%)

Rai

nout

(%)

Fig. 17. Dependence of the rainout expressed as a percentage of the released liquidmass on the flash fraction (xg) for the liquid discharges in the CCPS experiments(Johnson and Woodward, 1999).



one), and do is the orifice diameter. Although dimensionally correct,theWeLo is not really aWeber number since it is based on the orificediameter rather than a droplet diameter.

3) The superheat at the beginning (DTA) and end (DTC) of thetransition-to-flashing are found from

JaA4 ¼ 55We�1=7v and JaC4 ¼ 150We�1=7

v ; (63)

whereWev ¼ rvuo2do/sL is the vapor “pseudoWeber number” (again

not actually aWeber number due to the use of do), Ja¼ (cpL DTsh/hfg)(rL/rv) is the Jacob number, subscripts A and C on Ja denoteconditions at the superheats DTA and DTC, v denotes the vapor, andall variables (rL, rv, hfg, etc.) are evaluated at the orifice temperature.The transition state beginning (A) and end (C) are based on jetdroplet visualizations in the Cleary et al. experiments. The form ofthe Jacob number correlations are similar to the flashing correlationexpression of Kitamura et al. (1986), but differ in that the use ofWevin the latter is a true Weber number based on the droplet diameterin the post-expansion region and not the orifice diameter.

4) Evaporation of rainout droplets is not addressed as is the casefor the RELEASE model.

Some further comments on the JIP model are in order. First, thecorrelation for the aerodynamic diameter has a very weak depen-dence on the orifice Reynolds number, which results in only a smalldeviation of ReLo�0.014 from1 over a large ReLo range. For ReLo¼ 103 and106, the ReLo term only varies from 0.91 to 0.82 and could be taken as

its average or even 1 for simplicity. We note that the Reynoldsnumber for theWitlox et al. (2007) water jet data ranged from about9� 104 to 1.9� 105, whereas the ReLo in the CCPS water experimentswas about an order of magnitude larger, 1.6 � 105 to 1.1 � 106.

Second, the (L/do)0.114 term has a variation from 1 to 1.6 for L/do ¼ 1 to 50, which is the L/do range in the Cleary et al. (2007)experiments. If the (L/do)0.114 term were taken as some typicalvalue, say 1.3, the Cleary et al. correlation could be simplified to dpa/do¼ a1WeLo

�1/2, where a1 is a constant. Either this simple form or thefull form above for dpa/do shows that the dpa has a weaker depen-dence on u0 in the JIP model, dpaf1=uo, than the RELEASE model(dpaf1=u2o).

Third, as noted above, the Wev in the transition-to-flashingcorrelations is not a true Weber number but a dimensionlessvariable based on the orifice diameter. As a result, the Cleary et al.correlations must be regarded as specific to their particularexperiments and require extensive evaluation over a broad range ofconditions.

6.2.5. JIP model resultsThe JIP model was evaluated with the Witlox et al. (2007)

dataset and some of the measurements from the CCPS experi-ments. The Witlox et al. data contained droplet diameters (SMDs)from seven experiments including the two water jet tests of Clearyet al. and those from four other sources. The experiments includedflashing water, butane, and propane jets at storage pressuresranging from 3 bar to 11.5 bar, T0 from 23 K (butane) to 167 K(water), orifice diameters from 0.75 mm to 5 mm, and orificevelocities from 20 to 36 m s�1. The Cleary et al. droplet measure-ments were obtained using a phase Doppler anemometry system.

Ideal ratio

0 20 40 60 800

1

2

3

4

Dpr

ed/D

obs

b

CFC-11MethylamineCyclohexane

0 20 40 600

1

2

3

4

0 20 40 60 80 100 1200

1

2

3

4

ΔTSH (°K)

Dpr

ed/D

obs

Chlorine

Water Allc d

0 20 40 60 80 100 1200

1

2

3

4

ΔTSH (°K)

a

Fig. 18. Variation of the predicted-to-observed droplet diameter ratio, Dpred/Dobs, with the liquid superheat for the RELEASE model using the CCPS data; “observed” diameterdetermined from the rainout data (Johnson and Woodward, 1999; Tables 11-1 to 11-5).



Witlox et al. evaluated the JIP model using 10 tests from theCCPS experiments with two tests randomly chosen for each of thefive liquids. However, the “observed” CCPS diameters (dpm’s)differed from the values reported in Johnson and Woodward

(1999), and we replaced them with the Johnson and Woodwardvalues (their Tables 11-1 to 11-5) to maintain consistency with thedata used in Section 6.2.3. Since RELEASE and JIP predict the mean(dpm) and SMD diameters, respectively, we accounted for thesedifferences and the dSMD/dpm ratio (2.4 for the sG ¼ 1.8) in thefollowing comparisons. That is, RELEASE predictions were multi-plied by 2.4 for the Witlox et al. data, and JIP predictions weredivided by 2.4 when compared with the CCPS results.

Fig. 21a shows the Dpred/Dobs ratios for the JIP model as a func-tion of the superheat with the RELEASE model results shown forreference. Both models exhibit a weak trend of decreasing Dpred/Dobs with superheat. Overall, the models have similar results witha mean ratio of Dpred/Dobs of 0.89 1.49 for JIP and 0.87 0.59 forRELEASE, the main difference being the much greater scatter for JIPwhich is dominated by one point. By removing this case, the JIPmean Dpred/Dobs falls to 0.52 0.32, and the statistics are similar forboth datasets. In contrast, RELEASE has different statistics for thetwo datasets with a mean Dpred/Dobs of 1.14 0.65 for the CCPS dataand 0.52 0.23 for theWitlox et al. data. This difference is probablyrelated to the dependence on the orifice velocity (below).

Fig. 21b presents the Dpred/Dobs versus the orifice velocity for thetwo models and both datasets. For RELEASE, there is a noticeabletrend of a decreasing Dpred/Dobs with the velocity, which is consis-tent with the different statistics for the datasets: a mean Dpred/Dobs

for CCPS (lower velocities) that is about twice that for the Witloxet al. data (higher velocities). This trend is likely caused by a defi-ciency in themodel physics concerning the treatment of u0, and it isimportant to determine the cause of this and correct it. For JIP, thetrend is possibly weaker due to its weaker dependence on u0.

Ideal ratio

Chlorine

0 5 10 15 20 250

1

2

3

4

Dpr

ed/D

obs

b

CFC-11MethylamineCyclohexane

0 5 10 15 20 250

1

2

3

4

Water

0 10 20 30 400

1

2

3

4

U0 (m/s)

Dpr

ed/D

obs

AllWitlox et al. (2007)data

0 10 20 30 400

1

2

3

4

U0 (m/s)

a

c d

Fig. 19. Predicted-to-observed droplet diameter ratio, Dpred/Dobs, versus the orifice velocity for the RELEASE model using the CCPS and Witlox et al. (2007) data.

ChlorineMethylamineCFC-11CyclohexaneWater

0

0.5

1

1.5

2

2.5

3

⟨ Dpr

ed/D

obs

⟩

Fig. 20. Mean value and rms deviation of the predicted-to-observed droplet diameterratio, Dpred/Dobs, for the RELEASE model for each liquid used in the CCPS experiments.



7. Limitations

This review paper is a first attempt to suggest a comprehensiveset of operational TIC source emissions formulas based on a reviewof the recent literature. Opinions on the pros and cons of variousapproaches are those of the authors, and we are aware that othersmay have different opinions. We do recommend specific sourceemissions formulas for about ten categories of sources, but wemention alternate formulas that also might be appropriate.

As mentioned in the introduction, we have emphasizedformulas and models that are “fit-for-purpose”, where the“purpose” here is assumed to be operational use for planning andemergency response. For example, this set of formulas and meth-odologies could be used as the basis of the source emissionsmodule in a comprehensive TIC modeling software system.

We are fairly certain that no one else has carried out evaluationsof the suggested source emissions formulas using such a broad setof laboratory and field data. In particular, we have evaluatedalternate formulas from two different research groups for massemission rate and droplet formation in two-phase jets using datafrom two separate field studies. The results of the latter evaluationsreveal a few limitations of the models and we suggest wherefurther research is needed.

We encourage dialogue on the issues raised in this paper. Forexample, we would like to see alternate evaluations of the dropletformation models.

Acknowledgements

This research was funded by the Defense Threat ReductionAgency, with Rick Fry as project manager. Dr. Gene Lee of BakerRisk,Mr. Olav Hansen of Gexcon and Dr. Peter Drivas provided extensiveinputs and comments over the course of this study. Mr. HenkWitlox of DNV provided comments on the JIP field experiments andon his model for droplet formation.

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Superheat (°K)

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Orifice velocity (m/s)

Fig. 21. Predicted-to-observed droplet diameter ratio, Dpred/Dobs, as a function of liquid superheat and orifice velocity for the JIP and RELEASE models using the CCPS and Witloxet al. (2007) data.



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Glossary

Choked flow: is the condition of maximum flow rate that is achieved even withfurther lowering of the downstream pressure.

Enthalpy: denoted by the symbol H is given by U (internal energy) and PV (pressuretimes volume), a thermodynamic state function. h, u and v are the specificenthalpy, the specific energy and the specific volume respectively.

Entropy: denoted by the symbol S is a thermodynamic state function, its usefulnesslies in the entropy balance and the entropy change in reversible and irreversibleprocess analysis.

Flashing: vapor formation due to a reduction in pressure, in the case of storage ofa pressurized liquefied gas.

Flashing flow: vapor formation due to a reduction in pressure (a pressure drop) in theflow of a pressurized liquefied gas.

Saturation line: the locus of conditions (of pressure and temperature) at which vaporand liquid co-exist.

Saturation, saturated state: When vapor and liquid co-exist under thermodynamic(phase) equilibrium, the respective phases are termed saturated vapor andsaturated liquid.

Saturated vapor pressure: is the vapor pressure exerted by the co-existing liquid atthe saturation temperature.

Stagnation pressure: is the pressure when a flowing fluid is decelerated to zero viaa frictionless process; it generally refers to upstream inlet condition when thefluid velocity is small or possibly zero within a storage container.

Stefan (bulk) flow: transport phenomenon concerning the movement of a chemicalspecies induced by a process (e.g., evaporation, condensation, chemical reaction)at an interface.

Subcooled liquid: refers to liquid existing below its saturation temperature at theprevailing pressure.

Superheated vapor: refers to vapor existing above its saturation temperature at theprevailing pressure.

Vapor, Gas: vapor is a gas below its thermodynamic critical temperature, while gas isone above its critical temperature; though these terms are sometimes usedsynonymously.


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This paper might be a pre-copy-editing or a post-print ...senseable.mit.edu/papers/pdf/20110115_Britter_etal_ToxicIndustrial_Atmospheric...Jan 15, 2011 · Those thatresemble a short