Dispersion models and hydrogen fluoride predictions

Dispersion predictions

models

and hydrogen

f.luoride

J. S Puttockt, K. McFarlane, A. Pm&hero, F. J. Rees, P. T. Roberts, H. W. M. Witlox, and D. N. Blewitt* Shell Research Ltd, Thornton Research Centre, PO Box 1, Chester CHI 3SH, UK *Amoco Corporation, 200 East Randolph Drive, Chicago, Illinois 60601, USA

A set of models has been developed to simulate the dispersion of an accidental release of hydrogen fluoride. The system of programs is based on Shell’s HEGADAS model, which has been adapted to incorporate HF thermodynamics. Other developments are not specifically related to HF. Analysis of wind-tunnel data has led to the development of a new formulation for gravity spreading effects on dense gas dispersion. With this incorporated, it has been found that the HEGADAS parameterization of surface-roughness effects, through the friction velocity, correctly predicts dilution of the gas cloud for high-roughness as well as low-roughness surfaces. A jet/plume model (HFPLUME) has been developed that provides a unified representation of the stages of the flow from pressurized release, through elevated plume dispersion, to the touchdown of dense plumes and transition to ground-based dispersion. To provide a complete source and dispersion modelling package, the programs developed also include a source release-rate model, a pool evaporation model, and a far-field Gaussian plume model linked to HFPLUME. A range of experimental data have been used in the development and testing of the individual models; for HF, the system has been validated against the data from Goldfish experimental HF releases.

(Keywords: release: dispersion;

hydrogen

fluoride]

The thermodynamic behaviour of hydrogen fluoride when diluted with air, particularly moist air, is very different from that of a simple ideal gas. In particular, the gas-air mixture can, depending on conditions, be denser than air or significantly less dense than air. Such behaviour could have an important influence on the dispersion of HF in the atmosphere if it were accidentally released. In 1986 it was decided that, because of the special properties of this gas, data on its dispersion in the atmosphere were needed; so a series ‘of six atmospheric releases of superheated anhydrous hydrofluoric acid (HF) was performed at the Frenchman Flat spill test facility in Nevada by Amoco Oil Company and Lawrence Livermore National Laboratory. These experiments are known as the Goldfish Test SerieslT3. Existing dispersion models could not be expected to describe how humidity affects HF dispersion since they do not take into account the changes of molecular weight and temperature in I-IF/&O/air mixtures.

Received 2 AUEU.T~ 1990 tPresent add&s: Koninklijke/Shell-Laboratorium, Amsterdam, Postbus 3003,1003 AAAmsterdam,

The Netherlands

Presented at ‘Problem Clouds’ Symposium, 14 June 1990, Chester, UK

03504230/31/0!001613 0 1991 Buttenwrth-Heinemann

16

Ltd

J. Loss Prev. Process lnd., 1991, Vol4, January

Indeed, efforts to use existing models even to simulate the Goldfish experiments, where the influence of humidity was small, met with limited success. Consequently, as part of a cooperative exercise to develop assessment and mitigation techniques related to HF, a group of companies agreed to sponsor development of dispersion modelling techniques related to HF. The group was called the Ambient Assessment Group (AAG), a sub-committee of the Industry Cooperative HF Mitigation Assessment Group; the work was sponsored by 20 companies from the chemical and petroleum industries. In developing such a model the AAG felt that it should use as the starting point an existing public domain model (defined as a model for which the computer source code is available for a nominal fee). Following a review of models and proposals, the AAG selected the proposal of Shell Research Ltd to develop a system of programs based around the HEGADAS dense gas dispersiori model. The resulting models have been incorporated into a software package entitled HFSYSTEM. This paper describes the work carried out in the development of this set of models. Although part of this effort has been focussed on modelling the specific properties of HF, much of the programme has been concerned with developments in the general capabilities of the dense-gas and plume/jet models, and the

Dispersion

models and hydrogen

results obtained are thus also relevant for the dispersion of other gases. The major objectives of this study were to develop and validate computer-based models to calculate the release properties in addition to the jet and plume behaviour downwind of an accidental release of HF. It was decided that the models to be developed should have the following attributes: the ability to account for the I-IF/I-&O/air thermodynamics and cloud aerosol effects on cloud density (both positive and negative effects); the ability to simulate both pressurized (jet release, both vertical and horizontal) and non-pressurized (evaporating pool) releases; the ability to predict concentrations over a wide range of surface roughness conditions (possibly multiple roughness conditions); the ability to predict concentrations for any userspecified averaging period; the ability to consider steady state, time varying and finite duration releases; and the ability to compute crosswind and vertical concentration profiles.

fluoride predictions:

J. S. Puttocket

al.

predicted to remain denser than ambient air. However, at high relative humidities, when the surface heat effects are included, the predicted plume is slightly buoyant even though the plume was initially denser than air. The importance of including the LNG thermodynamics4 is illustrated in Table 1. This table indicates the observed distance to the lower flammable limit (LFL) for six of the Maplin Sands experiments. Also included in this table are HEGADAS predicted distances to the LFL with and without surface heat or water vapour transfer. As indicated in the table, when surface heat and water vapour effects are included, the model predictions fall within the range of the measured LFL with the exception of one experiment for which steady state conditions may not have been established. However, when these effects are not included in the model, there is little overlap between the observed and predicted data. It is important to note that the data presented in Table I centre

MIXTURE

TEMPERATUHE

40 _..

. .

The programme of work comprised developing an integrated suite of models to meet these objectives, to run on a personal computer. In addition, analysis of wind-tunnel data provided new findings about gravity-spreading of dense-gas plumes, which were incorporated into the models. Detailed reports of this project along with the computer code will be available through National Technical Information Service (NTIS).

HI? thermodynamics thermodynamic properties of mixtures of HF and moist air have a very strong influence on the dispersion of an HF cloud. Although the molecular weight of HF (monomer) is only 20, which is less than that of air, when released into the atmosphere HF forms polymers up to (I-IF),; this has a molecular weight of 160 gmol-' . As more air is entrained into the cloud the HF depolymeiizes. The mean molecular weight consequently decreases, but the process is endothermic and results in a cooling of the cloud. However, there is also a strongly exothermic reaction with water vapour in the air as that is mixed into the cloud. Thus there are competing mechanisms which influence cloud temperature and cloud density. Figure I demonstrates these effects in mixing I-IF and air at 25 “C. The dependence on humidity is very marked, with the mixture becoming buoyant as the cloud dilutes with air at high levels of humidity. I‘ nsight into the significance of thermodynamic effects in dispersion has been gained from the modelling of LNG clouds. In analyses of the Maplin Sands LNG releases4, it was found that if the effects of atmospheric humidity and surface heat transfer (and water vapour transfer) are ignored, the plume is

The

HF CONCENTRATION

MIXTURE

0.95

I-

1 E-3

’

’

’

’ ’ ’

“I

I

DENSITY

I

11,111

0.01

I

I

I,,,,

0.1

1

HF CONCENTRATION

Figure1 Cloud temperature concentration and humidity with moist air at 25 “C

and when

de& variations with HF HF vapour at 25°C is mixed

J. Loss Prev. Process Ind., 1991, Vol4, January

17

Dispersion

models and hydrogen

Table 1 Observed

and predicted

fluoride predictions:

distances to lower flammable

J. S. Puttocket

al.

limit for Maplin Sands continuous

LNG spills (surface release).

Distance to LFL (m)

Trial no.

Spill rate (m3 s-‘)

Wind speed (m s-‘)

Observed

Predicted*

Predicted b

%:

4.1 3.2

5.5

200 165 + 25 20

250 260

210 180

z 39 56

3.8 3.0 4.7 2.5

::: 9.8 4.1 5.1

180 170 zt k 25 30 130 + 20” 115+30

205 195 355 210

160 145 220 125

‘Initial model runs without surface heat or water vapour transfer, and using relative humidity observed at 10 m level bModel runs with surface heat and water vapour transfer, and using measured humidity of air at 1 m elevation “The full steadv plume may not have developed in the short time available for dispersion in trial 39, with a resulting distance

around distance rather than concentration. If this comparison were made in terms of concentration instead of distance, the effect of neglecting detailed thermodynamics in the model would be approximately a factor of two higher. HF in its monomer state has a molecular weight similar to methane; however, the influence of atmospheric water vapour is potentially greater than for methane since the thermodynamics now include the heat of reaction in addition to heat of condensation. The thermodynamic submodel used in HFSYSTEM is essentially the model first proposed and later revised by Schotte ‘s6. This determines the equilibrium concentrations of an ideal gas mixture containing air, water vapour, I-IF monomer, dimer (I-IF),, hexamer (HF),, octamer (I%),, the complex HF = H20, and the possible existence of liquid HF/water aerosol. The dispersion models in I-IF solve the non-linear equations of the thermodynamic submodel simultaneously with the differential equations for plume dispersion. Inclusion of the thermodynamic properties of the cloud in this manner allows the local cloud density to be determined ~accurately as a function of concentration and heat content.

18

J. Loss Prev. Process lnd., 1991, Wol4, January

LFL

phere. Where models can be linked, the first model calculates parameters which are required as input by the following model. For instance, the jet/plume model HFPLUME will calculate the touch-down of a dense plume, but, following touch-down and slumping, further calculations need to be performed by the ground-based dispersion model I-IEGADAS. Within HFPLUME, checks are made against criteria which determine when the calculation should be stopped. Relevant parameters are then written to a file of the same free-format ASCII type as those generated by the user.

The models in HFSYSTEM In developing the models in HFSYSTEM, it is important to provide enough detail in the near field or jet region, as well as the far field, so that reliable predictions of cloud properties may be estimated at the entrance to a mitigation device such as a water spray. In addition, to address the effectiveness of mitigation, dispersion calculations should be able to be started downwind of the mitigation device so that the reduction in the hazard zone can be determined. Furthermore, a means to calculate release rates should be included. Figure 2 provides a flow chart of the models contained in HFSYSTEM. These models are standalone computer programs which can be run separately or can be linked together to simulate all of the aspects of an accidental release of material into the atmos-

low observed

Fiiure

2 Models contained

in HFSYSTEM

Dispersion

models and hydrogen

Source models There are two models

in the package that may be used to estimate the rate of release of material into the atmosphere. The first of these is HFSPILL. This program is used to compute the amount of material that would be released into the atmosphere from pressurized storage. The second model is EVAP, which may be used to estimate the HF emissions from an evaporating liquid pool of HF. This latter model should only be used if the user is certain that storage pressure and temperature will be low enough to ensure that a pool will form. HFSPKL. The model HFSPILL is used to estimate the time dependent rate of release from a storage vessel during depressurization. In describing the reservoir conditions, HFSPILL assumes that the reservoir and fluid contents are in thermal equilibrium. Depressurization of the vessel and fluid loss are controlled by pipe-break mass flux expressed as a function of ambient and reservoir conditions and of elapsed time. The fluid in the reservoir is assumed to be either a pure liquid, pure vapour, or a mixture of liquid and vapour. The discharge is assumed to be either a liquid or vapour. Vapour/liquid phase equilibrium is determined by the Schotte thermodynamic submode1576. The mass release rate is determined by using empirical correlations which have been reported in the literature. By using such an approach the need for a detailed pipe and orifice discharge model is avoided. This approach is consistent with the level of accuracy of jet and dispersion models. For estimating the discharge of a liquid subcooled at storage, but superheated at ambient conditions, the correlation developed by Fauske and Epstein’ has been used. Otherwise, standard correlations for the discharge of ideal gas and subcooled liquid have been used’“. EVA P. The EVAP model was developed to estimate the steady-state or time-dependent spreading and evaporation of a liquid pool on land or water in conditions where evaporation is mass-transfer limited, i.e. the model does not consider the thermodynamic effects of heat transfer either from the substrate or air to the liquid pool. A relationship for mass transfer was adopted from the Shell SPrLLS model”. This relates pool evaporation to pool radius. The properties of HF are included in the model; for use with other compounds the user must input the chemical-specific properties. EVAP can take as an input a time-varying release rate of liquid and will calculate the pool radius and vapour flux, also as a function of time. This output can be used as input to the time-dependent dispersion model HEGADAS-T.

Jet/plume models: early plume dispersion

HFSYSTEM provides a single near-field jet/plume model HFPLUME governing the near-field dispersion following a pressurized release up to the establishment

fluoride predictions:

J. S. P&to&

et al.

of grounded or airborne advection. Control is then passed to the heavy-gas or passive advection models, HEGADAS-5, and PGPLUME. The HFPLUME model synthesizes and extends models developed for steady plume and two-phase jet dispersiong,“-16. The model capabilities include: HFPLUME.

allowance for HF thermodynamic@. A separate model (PLUME) capable of treating ideal gas releases is also available; an original, consistent, formulation based on the division of the plume into airbo&e, touchdown, and slumped regions; prediction is of cross-section averaged properties such as HF concentration, excess density, and temperature; the comprehensive representation of passive dispersion, jet entrainment, gravity slumping, plume/ ground impact, and momentum/buoyancy effeCts in each plume region, including gravity current collapse as introduced and supported under HEGADAS developments; a physically based transition to a passive or heavygas advection model, based upon a careful monitoring of the relative importance (in entrainment and in momentum balance) of mechanisms present or absent in the far-field advection models; user friendly input stream; highly modular code structure with extensive in-line comment permitting easy modification or generalization; separation of physical processes from numerical implementation. HFPLUME treats early dispersion external to any pipework or release path. Release (of pure anhydrous HF) may be at any angle to the ambient wind, and may be near to, or at a distance from, level ground. Formulation is in terms of cross-sectionally averaged (‘top-hat’) profiles of mass-concentration and excessdensity, with derived temperature, volume-concentration, and equilibrium phase-composition. The model is based upon a careful analysis of the difference between plume and undisturbed atmosphere”, and the assignment of appropriate plume coordinates following the plume centre of mass l1 . HFPLUME recognises three phenomenological regions of airborne, touchdown, and slumped plume. These regions correspond to circular, circular section, and semi-elliptic cross-sections; they permit the description within a single formalism of the descent to ground, ground-impact, and subsequent gravity-slumping of a dense gas plume. In particular, redistribution of material in response to ground impact and subsequent gravity-current slumping may be represented by a dynamically changing cross-sectional geometry, and an increase in the width-to-height aspect ratio. Pressure and drag forces act at the interfaces between plume and ground and between plume and undisturbed air. These are described in terms of the sectional mean properties and plume geometry so as to

J. Loss Prev. Process Ind., 7997, Vol4, January

19

Dispersion

models and hydrogen

fluoride predictions:

recover (in the appropriate limits) expected impact and plume slumping behaviour l7 . The formalism is applicable to buoyant as well as to dense plumes. To ensure compatibility with HEGADASJ, provision has been made within HFPLUME for the phenomenon of gravity-current collapse, and for the description of subsequent lateral spreading. Several features of the representation of touchdown and slumping are new, or at any rate new in this context; in particular the use of asymptotic analysis to deduce the pressure forces between ground and plume, and the representation of plume/ground interaction by changes in plume crosssectional geometry. Such geometry changes were in part anticipated by Brandsma and Sauer’s, and by Ermak”. In a pressurized liquid release the sudden drop in fluid pressure results in flash atomization of the released liquid, and promotes equilibrium aerosol evaporation accompanying subsequent air entrainment. During depressurization air entrainment is assumed to be negligible in response to the strong radial flows within the expanding jet. This initial flashing is followed by an isobaric dilution in which the jet core is progressively eroded by the ingress of entrained air. This flow establishment zone ends when conditions approximating self-similarity are established within the jet”. Both flashing and flow establishment zones may be bridged by means of a control volume analysis based upon fundamental conservation laws. Since these zones are short (of combined length perhaps 20 release diameters), errors arising from uncertainties in their length are generally negligible; HFPLUME therefore assumes that postflash conditions arise at the release orifice, and that entrainment within the establishment zone may be determined by the same functional forms as apply in the self-similar zone. mLUME monitors the contributions to entrainment of heavy-gas/passive mechanisms as a fraction of the plume total. In addition indices marking the influence of residual buoyancy and source momentum upon _the plume path are defined and calculated. If the residual effect of mechanisms not represented within the far-field advection models HEGADAS or PGPLUME is sufficiently small, transition is made to the appropriate model. Far-field model choice is based upon a prior assessment of the establishment of ‘advection’ , and a subsequent judgement based upon the relative importance of heavy-gas as distinct from purely passive entrainment at transition. If heavy-gas effects are important and the plume is grounded transition is made to HEGADAS, otherwise the calculation in HFPLUME is continued until either transition is made to the airborne passive advection model, PGPLUME, or the plume belatedly touches down. ‘Dispersion models In HFSYSTEM there are two models that can be used to describe plume dispersion downwind of a jet

20

J. Loss Prev. Process Ind., 1991, Vol4, January

J. S. Puttock et al. (region of excess velocity) or an evaporating pool. These models are HEGADAS-5 and PGPLUME. HEGADAS is used when the plume is at ground level and PGPLUME is used for cases when the plume is elevated. HEGADAS-5. The HEGADAS dense-gas dispersion mode1 was developed by Colenbranderzl. It treats both steady state and transient releases. A later version (HEGADAS4) included heat and water vapour effects u-23. During this project further enhancements have been added to the model, resulting in a new version called HEGADASJ; the .developments include: allowance for I-IF thermodynamics as an option in addition to the thermodynamics for an ideal gas; an improved gravity-driven crosswind-spreading formulation; verification of its ability to mode1 the effects of increased entrainment resulting from increased surface roughness/arrays of obstacles; an improved formulation of along-wind diffusion for transient releases or finite-duration releases; new options for lateral dispersion formulae (a,); provision of interfaces to other HFSYSTEM programs (i.e. HFPLUME and EVAP); and improved ‘user friendliness’, robustness and efficiency of the program. In simulating an accidental release of toxic material like HF it is important for the model to describe accurately both dense and trace (neutral density) dispersion and to be able to treat the transient nature of such releases. HEGADAS has these capabilities. For a steady state plume of a dense gas HEGADAS uses the following similarity profiles for the mean wind velocity (u,) and concentration (c): 24,

=

uo

(1 -

z

lx

zo

For lyl > b

4x7 y, z) = c*(x)exp[-

(“‘S,(*h:“))’

- (&)‘+a]

For lyl < b

where x is the downwind distance, y is the crosswind distance and z is the vertical distance. The release, at ground level, is centred on n = 0, y = 0, z = 0. There are then four variables which need to be determined to predict the concentration at any point within the computational domain: c*(x), the ground-level centreline concentration; S,(X), a plume height parameter; b(x), the half-width of the middle part of the crosswind concentration profile; and S,(x), the width of the Gaussian edges of the crosswind concentration

Dispersion

models and hydrogen

profile. The solution of the model requires the numerical solution of ordinary differential equations for these four variables and for the heat and water content of the plume. The equations express the conservation of fluxes of gas, air, water and heat, subject to air entrainment and surface heat transfer (and possibly water-vapour transfer); these are supplemented by relations for turbulent lateral spread and gravity spreading of the plume. The thermodynamic subroutine determines volume, density and temperature from concentration and heat (and water) content. The formulation for vertical entrainment is a continuous function dependent on both cloud density and ambient stratification. Thus, no transition has to be used in progressing from dense gas to passive dispersion. As S, increases, b eventually becomes zero, and then the crosswind profile is Gaussian. In this region, the crosswind profile in the model replicates conventional Gaussian models when consistent assumptions on averaging times are made. The rate of increase of S, is related to the lateral growth of a passive plume (a,) with allowance for the extra width due to gravity spreading. u,, increases with averaging time owing to low frequencies in the turbulent spectrum (changes in wind direction). Using an expression of the form a,. = 6x(1 + /Ix)-‘~, 6 is taken to be proportional to averaging time to the power 0.2. This relationship for averaging time is used by many models of this type. As part of this study, compariGravity spreading. sons were made between predictions of HEGADAS and an extensive set of wind-tunnel simulations of dense-gas plumes. One finding from this was that the well-defined gravity-current head at the edge of such a plume can be destroyed by boundary-layer turbulence much sooner than had previously been thought. After the collapse, the velocity of lateral spread is typically reduced by an order of magnitude. Figure 3 shows two typical examples. Model predictions of plume half-width using the conventional gravity-

Figure 3 Effect of HTAG dispersion HEGADAS model. HEGADAS model ratio 3.9

fluoride prbdicrions:

J. S. Pmocket

al.

spread formula are shown as dashed lines. The data are compatible with these calculations for the first SO m (full-scale) or so of the dispersion in these cases; thereafter there is a considerable discrepancy. The collapse of a gravity current has been studied in the laboratory by Linden and Simp~on~~~. Using their work and an analysis of the wind-tunnel data of Petersen and Ratcliff=, a criterion for this collapse has been developed and implemented in the model. Details of this study have been published previously27*B. The link with the findings of Linden and Simpson, and success in explaining data from a low-wind propane release and the Goldfish releases, suggests that the observations were not just an artefact of wind-tunnel simulation. roughness effects. Previous verifications of HEGADAS and other dense gas dispersion models have been made using field experiments in which the surface roughness was small (0.03-0.00006 m). An application of concern is a release in an industrial complex where the surface roughness is 2 0.5 m. The assumptions, particularly relating to boundary layer profiles and turbulence, made in the development of HEGADAS are not strictly valid for a cloud whose height is comparable with the height of the obstacles on the surface. However, to discover whether, empirically, the model predictions still relate to observations of dispersion at high roughness length, HEGADAS predictions were compared with data collected in a boundary layer wind tunnelz6. The results indicated that the model predictions agreed well with experiments at both low and high roughness. Consequently, no change to the vertical entrainment formulation in HEGADAS was found necessary as a result of this study. Surface

Along-wind

dispersion.

a version (HEGADAS-T) releases. In this context

The HEGADAS

model has which simulates transient transient release implies a

changing the gravity spreading formulation in HEGADAS to describe the plume spread observed in the course of the experiments. The dashed lines show the plume widths and centreline concentrations prediaed by the original The HTAG data (squares) show a sharp reduction in the plume spread at about 99 m. The solid lines show the revised predictions that take this into account. Results are for the R3 roughness distribution: a, density ratio 1.4: b, density

J. Loss Prev. Process Ind., 1991, Vol4, January

21

Dispersion models and hydrogen

fluoride predictions:

release rate which is varying with time or a release rate which is constant but is terminated after a finite duration. It can be important to use the transient model for a steady release if the travel time to the concentration level of concern substantially exceeds the release duration, because the effects of alongwind dispersion may reduce concentrations below the steady state levels. Details of the time-dependent formulation used in HEGADAS are given by Colenbrander”. Dispersion in the n direction (along-wind) for a finite release duration is controlled by two physical phenomena. The first is turbulence in the x direction; this produces spread in the wind direction (a,) similar to av. The second cause of longitudinal dispersion is wind shear. The gas in the cloud furthest above ground moves faster, in the ambient wind velocity profile, than that closer to the ground, and therefore becomes separated from it. The rate of increase of crX depends on a complex interaction between the vertical variations in velocity (wind shear) and vertical diffusion. The wind speed profile is dependent on atmospheric conditions, in particular the atmospheric stability. In the original HEGADAS (transient) formulation, along-wind diffusion was accounted for by taking u, proportional to x. This did not take into account the effect of atmospheric stability. Following a review of the literature, a formulation based on the work of Wilson2’ and Chatwin3’ has been incorporated into the model. In this formulation a, is considered to be composed of the two independent components, turbulent spread (a,,) and wind shear (a,). These are combined by:

PGPLUME. Whether a plume falls to the ground or remains elevated depends on a number of factors. These include the release elevation and angle and details of the source conditions. For HF the atmospheric humidity also has a strong influence since it greatly affects the plume density. If the plume does not reach the ground, then once it has diluted sufficiently to behave as a trace gas, the detailed thermodynamic and jet entrainment calculations in HFPLUME are no longer required. It is appropriate to match the calculated plume to a Gaussian trace gas model to simulate dispersion further downwind. The model PGPLUME was developed for this purpose. The far field dispersion from PGPLUME is described by: c(b,

Y, 2)/c* = Q(y, z; UY’ cZ> zFo )

c* = dm/dt(mf12~U+uZ] WY, ev

z; uy> u,, (-Y2P+=p

zpo) = 1-h

-

zpd2/W

+ exp{--(z

where dx is the displacement

22

downwind

+

zp~Y/;?d~l of a virtual

J. Loss Prev. Process Ind., 1991, Vol4, January

J. S. Puttocket

al.

point-source of HF with mass flux dm/dt& at point (XP& 0, zro); c* is the centre-line mass concentration at displacement dx; uv and a, are the lateral and vertical dispersion standard deviations; and u, is the mean wind speed. The standard deviations in the vertical and horizontal planes are described by the Pasquill-Gifford dispersion curves for stability classes A to F31-33. The Pasquill-Gifford dispersion curves are based on experiments” for which the surface roughness was =3 cm and the averaging time of the measurements was =lO min. A correction is applied to uy in the model to account for averaging time (plume meander) in the same way as in HEGADAS. The model also has a correction to a, to account for the effects of increased entrainment into the plume as a result of increased surface roughness. The matching from HFPLUME to PGPLUME locates a virtual origin such that fluxes of entrained air, pollutant, excess momentum and energy are conserved at the transition plane. It is based on a rigorous and original asymptotic analysis of the conservation equations in the limit of large dilution, taking account not only of concentration but also of residual velocity differences. As in HEGADAS it is important for PGPLUME to be able to simulate finite release durations (i.e. non-steady state conditions). The approach taken in this model was outlined by Ermak (Ref. 19 and private communication, 1986) and Blewitt et al. 2.

Model validation

and sensitivity

analyses

In examining the results from HFSYSTEM it is important to keep in mind how the physics or fundamentals of the models were formulated. The models in HFSYSTEM were developed using experimental laboratory data. Parameters which quantify a particular physical process have been determined, where possible, from laboratory experiments which study that process in isolation. The models were then validated against independent field data to ensure that they correctly describe the effect of these various physical processes in combination. Thus an independence is maintained between the model formulation and the data which are used to verify the models (i.e. models are not tuned to any particular field data set). By using this approach, greater confidence can be given to the predictions from the models when applied to the simulation.of an accidental release. Results have been presented here which verify the Schotte thermodynamic submodel, and comparisons have been made with wind-tunnel data. In each of these cases one aspect of the model was quantified by the data sets described, and so these are not independent validations. However, they show the ability of each of the models, following the setting of one parameter, to simulate the variations of the observations over a wide range of experimental conditions. Thus, these results give added confidence in

Dispersion

models end hydrogen

the model predictions. In particular, the HEGADAS comparisons demonstrate the ability of this model to account for the differences in surface roughness between an industrial site and the environment in which the Goldfish experiments were performed. Verification

of the HF thermodynamic

fluoride predictions:

J. S. Puttock et al.

16

submodel

The thermodynamic submodel was verified by two methods. The first was to compare the model predictions with the original experiments conducted by Schotte5 and Vierweg35. In these experiments HF was mixed to a range of concentrations with air containing varying amounts of water vapour. The resulting temperature change was measured as a function of HF concentration and relative humidity. Figure 4 presents the observed temperatures for the mixing of HF with moist air. Also plotted are temperatures predicted using the original Schotte model and those predicted by the HFSYSTEM submodel, which is based on the revised Schotte modelb. It can be seen that the HF thermodynamic submodel contained in these data closely replicates the experimental data of Schotte. A second method of testing the HF thermodynamic submodel is to compare observed and predicted cloud temperatures for the Goldfish experiments. Figure 5 presents observed and predicted cloud temperatures for Goldfish 3. For this experiment the plume was transported down the centre of the sampling array and so the temperature sensors were exposed directly to the plume centreline.

.

-20 -24

t

-2a

1 0

Figup at 25-26

a

Measurad Predicted (Schcttef Predicted (this study)

I

I

I

2

4

6

Temperature “C

I

f

I

I

1

8 10 12 Total Male % HF

14

16

18

20

1

I

change during mixing of HF and moist air

HFPLUME verification The entrainment relationships within HFPLUME were

tested using several different data sets. One parameter in the model formulation was set by reference to these data. The first comparison was with observed rise from buoyant plumes using data from an experimental program 36 conducted in a wind tunnel to examine the rise and concentration decay of a vertical release into a crosswind flow. Figure 6 compares the predictions. from HFPLUME and the experimental data. The agreement between predicted and observed data is within 15%. The second experimental data set used to test HFPLUME was obtained by Hoot et al. 37. In these experiments a dense gas was formed by mixing air with Freon 12 and releases were made in the wind tunnel with the plume directed upward. Figure 7 presents a comparison between observed and predicted plume rise. In this figure the maximum observed and predicted rises are within about 10% of each other. These data were further analysed to examine the location of maximum rise and the touchdown, as shown in Figure 8.

Figur.5 Comparison of observed and predicted plume temperetures using HFPLUME/HEGADAS (steady state) for Goldfish 3 (HFPLUME mean temperature; HEGADAS ground temperature)

I

HEGADAS comparisons with wind-tunnel data The effect of changing the gravity spreading relationship in HECGADAS is indicated in Figure 3. This

figure presents model predictions from HEGADASJ

0.25

0.5 -

Figure6 Comparison of the plume rise height of plumes predicted by HFPLUME with the experimental Petersens

buoyant data of

J. Loss Prev. Process Ind., 1991, I/o/4, January

23

Dispersion

models and hydrogen

fluoride predictions:

A

J. S. Puttock et al. Table2 Summary of HEGADAS-5 performance against the Petersen and Ratcliff data= for small aree sources, showing geometric mean ratio of predicted to observed concentration

z % %

_ 0.25

Density

R3.

R50

1.0 1.4 3.9

1.22b 0.70 0.94

1.00 0.91 1.03

r

i Y s ti _ 0.125

“R3 and R50 denote the nominal 3cm and 5Ocm (full-scale) roughness lengths bThe geometric standard deviations of the ratios varied from 1.13to 1.22

yo G e B 0.125 OBSERVED

0.25 PLUME RISE HEIGHT

Figure7 Comparison of the HFPLUME with experimental Hoot era/.37

im)

plume rise height dense

predicted by gas wind-tunnel data of

Figure8 Comparison of the point of plume touchdown predicted by HFPLUME with experimental (visible edge) touchdown data of Hoot et a!.”

and HEGADAS4 (which did not have the gravityspread transition) and data from two of the Peterson and Ratcliff experiments. It is clear that the revised model replicates the observed centreline concentration and the cloud width significantly better than the previous version of the model. The change in the gravity spreading relationship and the increase in entrainment as a result of higher surface roughness was tested using the Peterson and Ratcliff wind tunnel database. The results of the comparison between the measured and predicted concentrations are difficult to present succinctly. Goodness-of-fit has been assessed using both the horizontal and vertical distributions of concentration obtained at different downwind distances (between 80 and 320 m full scale) from the source. The measure of goodnessof-fit used is the ratio of the predicted to measured concentration at each location in the cloud. This is a very sensitive measure since, at the plume edges, large changes in concentration occur over a relatively short distance, so that small differences in plume shape can strongly affect the concentration ratio. Table 2 shows the geometric mean ratio of

24

J. Loss Prev. Process Ind., 1991, Vol4, January

predicted to measured concentrations for the experiments using a small area source. For the horizontal concentration distributions, data at an average of 34 points per experiment were used; the model predictions were within 22% of the observations for all runs. The vertical profiles showed similar agreement although there were fewer data points available. There is no significant difference between the results for the 0.03 m and the 0.5 m surface roughness. It thus appears to be possible to use the existing entrainment formulation in HEGADAS over a very wide range of surface roughness values. The model also correctly predicted the change in dispersion behaviour for each of the three source gas densities used. For reference, increasing the roughness from 0.03 m to 0.5 m decreased the observed concentrations by a factor of 3 for density ratio 1, a factor of 4 for density ratio 1.4, and a factor of 6 for density ratio 3.9. Further details of these analyses are given elsewhere27*28.

Comparison of results with the Gold)?.sh experimental data The Goldfish experiments comprised a series of releases of (flashing liquid) anhydrous HF at the spill test facility at Frenchman Flat in Nevada. Six releases were made, of which the first three were to study dispersion of HF, the others examined the mitigation potential of water sprays. Conditions for experiments 1, 2 and 3, which have been used to test the HFSYSTEM models, are summarized in Table 3. HF concentrations were measured using arrays of samplers at 300, 1000 and 3000 m downwind of the release point. The array, spread across the plume and at heights 1, 3 and 8 m gave a detailed cross-section of the plume at each distance. The averaging time of the HF measurements was -60 s. More details are given by Blewitt et al. ‘. For the simulations, both HFPLUME and HEGADAS were used with an interface between them. I-IFSPILL was not employed because the liquid spill rate was a measured parameter and a constant pressure was applied to the liquid storage vessel (i.e. the system was not allowed to depressurize). The EVAP model was also not applicable since no liquid pool was formed owing to the use of superheated HF. For Goldfish test number 1 the release duration was

Dispersion Tebk3

models and hydrogen fluoride predictions:

J. S. futtocket

Test condition for the Goldfish HF spill experiments

Atmospheric stability class

Ambient temperature (“CI

Dewpoint temperature (“Cl

D

37.0

-8.5

Purpose of

“0.

test

(kg

1

System check out and dispersion experiment Dispersion experiment Dispersion experiment

27.1

40

111

125

5.6

10.3

30

115

360

4.2

D

36.0

1.1

360

5.4

D

36.5

6.6

3

10.1

(“Cl

HF pressure Ipsig)

Duration (8)

Test

s-‘1

HF temperature

Mean wind speed tm s-l)

HFspill rate

2

al.

39

117

therefore, once the plume travelled much further than 700 m, a steady state model could not be used with confidence since the travel time of the plume exceeds the release duration. Thus for the 3000 and possibly the 1000 m sensors the use of a steady state model copld overstate the observed concentrations. The further downwind the simulation is carried the greater the deviation between steady state and finite release duration calculations. The remaining two tests had a release duration of 6 min. Steady state calculations were used in simulating tests 2 and 3. In making comparisons with the concentration data, both centreline concentrations and crosswind profiles have been compared. Figures 9, 10 and 11 present comparisons of observed versus predicted plume centreline concentrations. For Goldfish 2 the plume centreline was not observed at 3ooO m downwind because of a shift in the wind direction. All plume centreline concentration predictions are well within a factor of two of the observations. A full set of plume cross-section predictions and data comparisons are published elsewhere”. Figure 12 shows typical results for Goldfish 2 at 1000 m downwind.

These comparisons show that the model is predicting both the centreline (peak) concentration and the width of the cloud well.

Figureg Comparison of obaen!ed and predicted line concantretions using HFPLUMEBEGADAS for Goldfish 1

Figure 11 Comparison of observed and predicted line concentrations using HFPLUME/HEGADAS for Goldfish 3

2 min;

plume centre= (steady state)

Figure 10 Comparison of observed and predicted plume centreline concentrations using HFPLUME/HEGADAS (steady state) for Goldfish 2

plume centre(steady state)

J. Loss Prev. Process Ind., 1991, Vol4, January

25

Dispersion

models and hydrogen

fluoride predictions:

Figure 12 Comparison of observed and predicted plume crossGoldfish 2 at a downwind distance of 1000 m

section for

Model sensitivity The models in HFSYSTEM have been found to replicate the Goldfish experiments quite well, and have also been checked against other experimental data sets to verify thermodynamics, jet entrainment and the additional entrainment caused by larger roughness. A wider range of model predictions is now presented to illustrate differences in plume dispersion that would occur with, for example, a release in typical industrial or urban surroundings, in contrast to the Goldfish experiments. Figure 13 illustrates the effect of ambient humidity on plume centreline concentrations. After about 100 m relative humidity has a pronounced effect on predicted concentration. These trends are a result of the thermodynamic reactions which alter the cloud density. For relative humidity around 50%, the lower density reduces the gravity spreading in the early stages of dispersion, resulting in a plume which then dilutes more slowly than for a relative humidity of 10%. At higher relative humidities, this effect is counteracted by the enhanced vertical mixing resulting from the persisting additional buoyancy.

al.

J. S. Putrocket

Figure 24 presents plume trajectories from HFPLUME for varying relative humidities. This example is for a plume released horizontally at a height of 10 m. At low relative humidities the plume becomes dense and falls to the ground. However, at humidities > 70%) the plume initially becomes dense and then, as the heat of reaction between HF and water becomes more significant, the plume becomes buoyaht. This buoyant effect will result in substantially lower groundlevel concentrations. Figure 15 illustrates the effect of increasing surface roughness above the very low value pertaining to Frenchman Flat where the Goldfish experiments were performed. There is almost an order of magnitude difference between the concentrations observed during the Goldfish experiments and the dispersion predictions for an urban environment.

Computer implementation The HFSYSTEM group of programs has been designed to run with ease on an IBM or compatible personal computer. However, the programs are written in Fortran 77 and have been successfully ported to other operating systems (UNIX, IBM VM/CMS).

0.00 0.00 ? ,,.,

I

25.00

.,

,

,

,

SO.00 -No

,

,

,

,,

75.00

,

,,,

,

100.00 (U)

,

,

,

,

125.00

,

,

,

,

150.00

MPTANCE

Figure 14 Effect of relative humidity (rh) on plume trajectory for jet releases: 1, 10% rh; 2, 50% rh: 3,70% rh; 4, 80% rh; 5, 90% rh

Figure13 Effect of relative humidity (rh) on predicted HF concentrations: 1, 10% rh; 2, 50% rh; 3, 70% rh; 4, 90% rh: 5, 100% rh

26

J. Loss Prev. Process Ind., 1997, Vol4, January

Figure 15 Effect.of surface roughness (r) on predicted conwntrations: 1. 0.0002 m r (GoldfishI; 2, 0.03 m r (rural); 3, 0.5 m r (urban)

Dispersion models and hydrogen

Input files are free-format ASCII files consisting of keywords followed by values, which can be read and modified by standard editors. Because of the use of keywords, the order in which parameters are given is not important. In practice, the user normally generates an input file by modifying one of a number of standard input files available for each model. This process is aided by comments in the input files which explain the parameters and define units. A preliminary check is performed to ensure that input parameters are within predefined validity ranges. If not, an error message is written at the appropriate point in the input file; this is removed automatically on resubmission with corrected data. Where two models can be run in succession, the first model will calculate to the transition point and then output a file of the above type suitable for input to the next program (either on its own or concatenated with other necessary input data from another file). This process can be automated (on a PC) using the DOS batch tiles provided with HFSYSTEM. Thus the sequence of models can run without user intervention, or a series of runs with various permutations of, say, release conditions and meteorological conditions can be performed. Post-processing facilities are also provided to allow generation of files of data suitable for direct input to standard graphics packages. The aim was to provide a system which is ‘user-friendly’ for the new user but which can be used efficiently by an experienced user. The programs are documented in a Users’ Guide38, and a Systems Manua13’. The theoretical development of the package is fully described in the Technical Report on the project27. These documents and the programs on diskette will be available from the US National Technical Information Service (NTIS).

Conclusions The main aims of t&s project were to provide the ability to simulate the complex effects of HP thermodynamics on accidental dispersion, and also to address a number of other uncertainties related to dense-gas dispersion modelling. These particularly concerned the use of models in conditions of high roughness and the matching of jet/elevated plume calculations to dense-gas dispersion on the ground. -It was also felt that further consideration should be given to the formulation for lateral ‘passive’ dispersion, and for longitudinal dispersion in transient releases. The main models developed in this project were HPPLUME for calculation of the two-phase jet and early plume, and HEGADASJ for ground-based dense-gas dispersion. In addition, a source estimation front-end model, a pool evaporation model, and a linked far-field Gaussian model were added to provide a more complete source and dispersion modelling package. The models can be linked automatically

fluoride predictions:

J. S. Puttocket

al.

where appropriate. This package runs on an IBM or equivalent PC, and the programs have also been successfully ported to other operating systems. The main conclusions from the project are: the inclusion of I-IF thermodynamics into the model results in significant changes in plume dispersion, most particularly in conditions of high humidity; analysis of wind-tunnel and other data has led to a revised gravity-spreading relationship which has been implemented in HEGADAS-5 and HPPLUME; following the inclusion of the revised gravityspreading relation, the existing entrainment formulation in HEGADAS was found to be applicable over a very wide range of surface roughness without alteration; for finite duration releases, the formulation for dispersion in the along-wind direction has been improved. This accounts for wind shear, which is a function of atmospheric stability; a jet/plume model, HFPLUME, applicable for releases at any angle from direct downwind to vertical, has been developed. This also explicitly includes HF thermodynamics.

References 1 Blewitt, D. N., Yohn, J. F. and Brown, T. C. ‘International Conference on Vapour Cloud Modelling’, AIChE, New York, USA, 1987, pp. 1-38 2 Blew&, D. N., Yohn, J. F. and Ermak, D. L. ‘International Conference on Vapour Cloud Modelling’, AIChE, New York, USA, 1987, pp. 56-80 3 Blewitt, D. N., Yohn, J. F., Koopman, R. P., et al. ‘International Conference on Vapour Cloud Modelling’, AIChE, New York, USA, 1987, pp. 155-180 4 Puttock, J. S. ‘Development and use of HEGABOX/HEGADAS dispersion models for hazardous analyses’, AIChE, New York, USA, 1987, pp. 317-341 5 Schotte, W. Ind. Emg. Chem. Res. 1987,M, 300 6 Schotte, W. Thermodynamic model for HF fog formation: letter to C. A. Soczek 31 August 1988 7 Fauske, H. K. and Epstein, M. J. Loss Prev. Process fnd. 198&l, 75 8 Fox, J. A. in ‘An introduction to engineering fluid mechanics’, The MacMillan Press Limited, London, UK, Chapter 6, pp. 176-206 9 Raj, P. K. and Morris, J. A. ‘Source characterization and heavy gas dispersion models for reactive chemicals’, Technology & Management Systems Inc., Burlington, MA, USA, AFGL-TR88-0003 (I), December 1987 10 Fleischer, M. T. ‘SPILLS: An evaporation/air dispersion model for chemical spills on land’, Report of Shell Development Company, Westhollow Research Center, Houston, 1980 11 Ooms, G. Atmos. Environ. 1972,6,899 12 Schatnnann, M. J. Appl. Math. and Phys. (ZAMP) 1978,29,608 13 Schatzmann, M. Atmos. Environ. 1979,13,721 14 Wheatley, C. J. ‘A theoretical study of NH3 concentrations in moist air arising from accidental releases of liquified NHs, using the computer code TRAUMA’, Safety and Reliability Directorate, United Kingdom Atomic Energy Authority, SRD/ HSE/R 393,1987 15 Fomey, L. J. and Droescher, F. M. Atmos. Environ. 1985, 19, 879 16 McFarlane, K. ‘Proceedings ECMI Conference on the Application of Mathematics in Industry’, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1990, pp. 415-428

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Dispersion

models and hydrogen

fluoride predictions:

17 van Ulden, A. P. in ‘Atmospheric dispersion of heavy gas and small particles’, (Eds. G. Ooms and H. Tennekes). Springer-Verlag, Berlin, FRG, 1984, pp. 419-440 18 Brandsma, M. G. and Sauer, T. C. ‘Mud discharge model report and user’s guide: A model for predicting the fate of drilling fluid discharges in the marine environment’, Exxon Production Research Company, CO, USA, 1983 19 Ermak, D. L. ‘User’s manual for SLAB: An atmospheric dispersion model for denser-than-air releases’, Lawrence Livermore National Laboratory, Livermore, CA, USA, February 1989 20 Abramovich, G. N. in ‘The theory of turbulent jets’, MIT Press, Cambridge, MA, USA, 1963 21 Colenbrander, G. W. ‘Third International Symposium on Loss Prevention and Safety Promotion in the Process Industries’, Basle, Switzerland, September 1980 22 Colenbrander, G. W. and Puttock, J. S. ‘Fourth International Symposium on Loss Prevention and Safety Promotion in the Process Industries’, Pergamon Press, UK, Vol. I, pp. F66-F75 23 Colenbrander, G. W. and Puttock, J. S. ‘Dispersion of releases of dense gas: Development of the HEGADAS model’, HEGADAS Public Release Documentation, US Environmental Protection Agency, 1988 (distributed by the National Technical Information Chre (NTIS)) 24 Linden, P. F. and Simpson, J. E. J. Fluid Mechanics 1986, 172, 481 25 Linden, P. F. and Simpson, J. E. in ‘Stably stratified flow and dense gas dispersion’, (Ed. J. S. Puttock), Clarendon Press, Oxford, UK, 1988, pp. 97-113 26 Petersen, R. L. and Ratcliff, M. A. ‘Effect of homogeneous and heterogeneous surface roughness on HTAG dispersion’, C.P.P. Inc. Report 87-0417, August 1988 27 McFarlane, K., Prothero, A., Puttock, J. S., etnl. ‘Development and validation of atmospheric dispersion models for hydrogen fluoride’, Volume I, Technical Reference Manual, Shell Research

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al.

Limited, Thornton, Chester, Report TNER.90.015,1990 28 Roberts, P. T., Puttock, J. S. and Blewitt, D. N. ‘AICHE Health and Safety Symposium’, Orlando, FL, USA, 1990 29 Wilson, D. J. Atmos. Environ. 1981,15,489 30 Chatwin, P. C. Quart. 1. Roy. Met. Sot. 1968,94,350 31 Gifford, F. A. ‘Lectures on Air Pollution and Environmental Impact Analyses’, American Meteorological Society, Boston, MA, USA, 1976, Chapter 2, pp. 35-58 32 Pasquill, F. ‘Atmospheric dispersion parameters in Gaussian plume modelling, Part 2. Possible requirements for change in the Turner workbook values’, US Environmental Protection Agency, EPA-600/4-76-03Ob, 1976 33 Hanna, S. R. in ‘Engineering meteorology fundamentals of meterology and their application to problems in environment and civil engineering’, (Ed. E. J. Plate), Elsevier Scientific Publishing Company, New York, USA, Chapter 10, pp. 429-448 34 Hanna, S. R., Briggs, G. A. and Hosker, R. P. in ‘Handbook on US Department of Energy, DOE/ atmospheric diffusion’, TIC-11223 (DE92002045), 1982, pp. 22-35 35 Vierweg, R. Chem. Tech. 1963,12,734 36 Petersen, R. L. JAPCA 1978.37.1314 37 Hoot, T. G., Meroney, R. N. and.Peterka, J. A. ‘Wind tunnel tests of negatively buoyant plumes’, US Dept. of Commerce, Report PB-231-590, 1973 (distributed by National Technical Information Service) 38 Witlox, H. W. M., McFarlane, K., Rees, F. J., and Puttock, J. S. ‘Development and validation of atmospheric dispersion models for hydrogen fluoride’, Volume II, HFSYSTEM Program Users Manual, Shell Research Limited, Thornton, Chester, Report TNER.90.016,1990 39 Rees, F. J. ‘Development and validation (rr atmospheric dispersion models for hydrogen fluoride’, Volume III, HFSYSTEM Systems Manual, Shell Research Limited, Thornton, Chester 1990