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Atmospherw EnmronmentVol 29, No 16, pp 2075-2087, 1995 Copynght © 1995 Elsewer Setence Ltd Pnnted m Great Bntam All rtghts reserved 1352-2310/95 $9 50 + 000
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DEVELOPMENT OF DENSE GAS DISPERSION MODEL FOR EMERGENCY PREPAREDNESS M A N J U M O H A N , T. S. P A N W A R a n d M. P. S I N G H Centre for Atmospheric Soences, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India (Ftrst received 10 February 1993 and in final form 8 May 1994) Abstract--Mathematicalmodels are recognized as important tools for providing quantitative assessment of the consequences of the aeodental release of hazardous materials. In several accidental release situations, denser-than-air vapour clouds are formed which exhibit dispersion behavlour markedly different from that observed for passive atmospheric pollutants. The present work undertakes the development and validation of conceptually simple and computationally efficient dense gas dispersion models which could be used for emergency response. Here, IIT Heavy Gas Models I and II have been developed for instantaneous and continuous releases, respectively, of dense toxic materials in the atmosphere. Sensitivity tests have been performed to determine the various empirical coefficaentswhich are found to be quite different than those used in the earlier studies. Particular emphasis has been laid on model validation by comparing their performance against relevant field trial data (Thorney Island, Burro Series and Maplin Sands Trials) as well as with other models. On the basis of statistical evaluation, a good performance of the model has been established. The performance of the IIT Heavy Gas Model is close to the model showing the best performancc amongst 11-14 other models developed in various countries. Using the IIT Heavy Gas Model, the Safe disl ance/vulnerable zones can be easily estimated for different meteorological and release conditions for the; storage of various hazardous chemicals. Key word index: Gravity slumping, air entrainment, cloud heating, sensitivity analysis, model validation, statistical evaluation, vulnerable zones.
the cross wind plane. Quasi-three-dimensional solutions are obtained by using similarity profiles, i.e, by The increasing use of hazardous toxic substances and assuming a cross wind profile for the concentration the associated potential risk warrant development of and other cloud properties. Examples of this type of practical and well-tested mathematical models for es- model include SLAB, HEGADAS, and DEGADIS. timating vulnerable zones in relation to their acci- At the simplest level are the modified Gaussian plume dental release in the atmosphere. In many of the models. These models are usually used to simulate accidental release situations, denser-than-air clouds continuous releases and employ a variety of modificaare formed. The negative buoyancy modifies the dis- tions to include the effects of dense gas dispersion persion of a toxic gas cloud and its modelling requires within the Gaussian plume model for trace gas rean approach different from a positively buoyant or leases (Ermak et al., 1987). The intermediate class of models for heavy gas a passive gas cloud as it tends to hug the ground and does not readily (disperse. Gravity driven flow and release and dispersion has been identified by a variety stable stratification are the key factors making dense of names. Wheatly and Webber (1984) used the term gases behave differently when released into the atmo- "box models", Blackmore et al. (1982) "Slab models", sphere (Hunt et al, 1983). and Havens (1982) "box (top-hat profile) models". The The models which give the most physically com- results from these type of models have proved in the past plete description of dense gas dispersion are those that as the important ingredients for effective contingency are based on the three-dimensional, time-dependent planning, in-crisis remedial action and other decision conservation equations Examples of this type of measures. Hence the present work undertakes the model include FEM3, SIGMET, MARIAH, and development and validation of reasonably simple opZEPHYR (Ermak et al., 1987). At the intermediate erational heavy gas dispersion model which could be level of completeness and complexity are the sim- used for emergency response. The model is essentially ilarity type models. These type of models use simplifi- a numerical box type of model which includes all the ed forms of the conservation equations that are basic features tenable to dense gas dispersion in a realobtained by averaging the cloud properties over istic manner. In order to verify the accuracy of various 1. INTRODUCTION
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M. MOHAN
input parameters and empirical coefficients, sensitivity tests have been performed through several model simulations using the field data. The most essential part of the model development effort is to test the model against observed data as well as with other models already available for this purpose. In this regard, rigorous statistical tests have been performed which indicate a good model performance. Being computatlonally efficient, these models are well suited for emergency response purposes. One of the important aspects in these models is the appropnate transition from dense gas to passive phase. Often, matching of various parameters before and after transition lacks strong physical foundation. For example, in case of catastrophic/instantaneous release of toxic materials, appropriate dispersion parameters after transition are not available. Therefore, normally one resorts to the use of dispersion parameters which are tenable for continuous releases upto distances of 1 km from the source and for an averaging time varying 10-30 min. In the present work, an attempt has been made to incorporate formulation based on turbulent energy density and cloud dimensions after transition to the passive phase. Although it requires more in-depth study, it ensures continuity of the various parameters after the transition phase and gives more realistic results.
2. M O D E L F O R M U L A T I O N
The model developed is a numerical box model where governing equations take into account the relevant physical processes associated with dense gas dispersion, namely, gravitational slumping, entrainment of air, cloud heating, and finally, transition to the passive phase. The model consists of two versions; while IIT Heavy Gas Model-I is valid for instantaneous releases, liT Heavy Gas Model-II is suitable for continuous releases of dense gases. The governing model equations are solved numerically using forward finite difference scheme for IIT Heavy Gas Model-I and the Runge--Kutta method for IIT Heavy Gas Model-II. The models have been developed taking into account the work carried out earlier by Kaiser and Walker (1978), Cox and Carpenter (1979), Britter and McQuaid (1988), Van Ulden (1974), Britter and Griffiths (1982), Jagger (1983), Singh et al. (1991), and several other workers. Cloud geometry is considered to be cylindrical in the case of instantaneous release and rectangular in the case of continuous release in the conventional manner. The main input parameters to the mathematical model for dispersion calculations are the emission rates and the relevant meteorological parameters. Numerical solution of the equations evaluates the cloud characteristics, i.e. radius (length in the case of continuous release), height, density, temperature and amount of air entrained at each time step. An appropriate treatment for the cloud disper-
et al
sion parameters is made after transition to the passive phase. The concentration distribution is assumed to be Gaussian in nature.
2.1. Dense gas dispersion model for instantaneous release of toxic materials: IIT Heavy Gas Model-I The instantaneous release model described here is concerned mainly with the rapid releases of large quantities of toxic gases to the atmosphere and is thus intended to model "puff" releases. The characteristic features of dense gas dispersion included in the model are as follows. (a) Gravitational slumping. Assuming that the puff is in the form of a cylinder of height h and radius R, the velocity of the edge of the cloud is adequately described by the liquid column analogy (Cox and Carpenter, 1979; Eidsvik, 1980; Fay, 1983; Hanna and Drivas, 1987; McQuaid, 1987):
dR ,,[" , Ap'~1/2 --~=t~gn-~ ;
(1)
where t is the time after slumping has started, g is the acceleration due to gravity, p is the density within the cylinder and Ap = p - p , , p, being the density of ambient air and K is a constant. (b) Entrainment of air. Air is presumed to be entrained both at the edges and at the top of the cloud. Although some of the models consider only top entrainment based on Van Ulden's Dutch Freon experiments, in the present model we have considered both top and edge entrainment based on our model simulations and studies. The rate at which air is entrained into the cloud is given by (Cox and Carpenter, 1979; Hanna and Drivas, 1987; McQuaid, 1987):
dM'= P'(nR 2) U" + a* 2nRh p"
dR
(2)
where a* is a parameter which controls the rate of edge entrainment of air. U, is the top entrainment velocity which is a function of Richardson number Ri and the longitudinal turbulence velocity U~. The entrainment velocity Uc depends on U~ and Ri as follows: U e = or' U I R ! - 1
(2a)
where (gl,) Ap
R,= U""~
p'-~.
(2b)
Equation (2a) is valid when U, ~ 8.0
4.0 20-
1.0 ~ 0.125
• GPM
DEGADIS • HEGADAS GASTAR
0.25
• •
0.5
(Overpredictlon)
)_---.----4--AFTOX - SLAB - -
1.0 MG
2.0
4.0
8.0
(Underprediction)
Fig. 2. Model performance measures, geometnc mean bias (MG) and geometric variance (VG) for concentration predictions and observations for the continuous dense gas data from Burro Series and Maplin Sands Trials.
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this viewpoint also, the IIT Heavy Gas Model-II seems to perform well. In summary, considering the above discussion on the performance of the statistical measures of agreement alongwith the graphical representation of the observed and predicted concentration values in the form of scatter plots (Figs 3 and 4), it could be concluded that the IIT Heavy Gas Model performs well against field trials. 3.5. Intercomparison of model results with other dense oas dispersion models The performance of the IIT Heavy Gas Models will be further judged by mtercomparison of their results with those obtained from other dense gas dispersion models, namely, DEGADIS (DEnse GAs DISpersion) and • M E (Ontario Ministry of Environment) models. While • M E model represents a relatively simple model, the DEGADIS model is quite sophisticated and undertakes detailed treatment of the various phenomena associated with dense gas dispersion. The IIT Heavy Gas Models are developed from a viewpoint of having simple, inexpensive and operational models which are computationally efficient. The degree of sophistication involved in their development lies between the DEGADIS and • M E models. However, as shown during model validation, a higher level of sophistication in the model does not always indicate a comparable improvement in its performance. Here, intercomparison of results with the other models will further support the use of IIT Heavy Gas Models in finding safe distances for various toxic chemical releases. For the purpose of intercomparison of the results obtained from liT Heavy Gas, DEGADIS and OME Models, accidental release of various quantities of chlonne is considered and the distances to the IDLH
30 25 20 O
E
to
•
• ni
5
•
m~ •m
we m •
I 5
o•
I I0
I 15
I 20
I 25
I 30
C (observed) mole (%) Fig. 3. Scatter plot for observed vs predicted concentration for the instantaneous dense gas data from Thorney Island.
25
20 • O
ff
as
15 •
ass
•
wa
l0
& •
5
a•
,
,
,
10
15
20
"
,
25
C (observed)mole (%) Fig. 4. Scatter plot for observed vs predicted concentratlon for the c o n t m u o u s dense gas data from Burro Series and Maplin Sands Trials.
concentration are determined from these models. An intercomparison of the safe distances so obtained is used to assess the relative model performance. Table 7 gives the distances to IDLH concentration obtained from IIT Heavy Gas Model-I, DEGADIS and • M E models for the instantaneous release of 25, 100 and 500 tonnes of chlorine. These safe distances are estimated for some typical meteorological scenarios which correspond to various atmospheric stabilities and wind speeds. From Table 7, one can observe that the IIT Heavy Gas MOdeM results are comparable to the results from DEGADIS and • M E models under all stabilities for comparatively small storage amounts (e.g: 25 t of C12 storage) and for unstable and neutral stabilities for all the release amounts considered here. However, for stable atmospheric conditions (especially stability F), IIT model gives larger distances than those obtained from the other models and the difference between them increases with the increase in the storage quantity. It may be noted that in the IIT models, the dispersion in the vertical is limited by the mixing height (100m in stability F) in the conventional manner which would tend to increase the downwind distance to IDLH concentration whereas in DEGADIS and • M E models, dispersion in the vertical is not limited by the mixing height. Further, for the sake of comparison, model simulations have also been performed using the IIT Heavy Gas Model where the ~z is not limited by the mixing height (as is the case in DEGADIS and • M E models) and the results indicate that IDLH distances are reduced significantly for large release amounts under stable atmospheric conditions and they are now comparable to those obtained from the other two models. However, this concept of limiting az with mixing height in dispersion models, which seems physically sound and
B B C C D D E
F
F
2 3 4 5 6 7 8
9
10
2.80
5.34 (5.11) 5.93 (5.38)
1.97 2.45 2.66 3.03 3.21 3.68 3.81 4.16
1.19 1.19 2.70 1.19 2.70 1.19 2.70 2.80 1.35
IITHG-I
Wind speed (m/s) 1.44 1.84 1.88 2.27 2.30 2.78 2.78 2.99 3.97 4.16
1.74 2.05
3.03 4.26
3.24 ---
--
2.35
--
OME
DEGADIS
25t
3.06 3.79 4.18 4.72 5.01 5.71 5.90 7.48 (6.49) 11.05 (7.89) 11.96 (8.34)
IITHG-I
6.83
4.46
2.76 3.24 -3.70 -5.22 -6.25
DEGADIS
100t
8.31
6.61
2.27 2.92 2.96 3.64 3.63 4.52 4.38 5.30
OME
5.10 6.38 7.05 7.91 8.38 9.52 9.91 16.94 (10.85) 25.75 (13.12) 27.19 (13.90)
IITHG-I
11.45
7.42
4.68 5.52 7.01 6.36 8.44 8.95 10.73 11.84
DEGADIS
SOOt
18.58
13.55
3.88 5.06 5.01 6.44 6.16 8.21 7.47 11.84
OME
Note:--Indicates the cases for which IDLH distances could not be obtained from DEGADIS Model. ( # ) Indicates the IDLH distances obtained from the IITHG-I Model for simulations m which the sigma-z value is not hmlted by the mixing height.
A
1
S. No.
Stability category
Downwind distance to IDLH concentration (km) Quantity Released
Table 7. Comparison of IDLH distances obtained from IIT Heavy Gas Model-I, DEGADIS (transient) and OME models for various amounts of chlorine released under different meteorological conditions
Ix3
O
=o
g
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M. MOHAN et al.
is usually adopted, needs further investigation on the basis of dense gas field trials involving large release amounts. Despite the above mentioned point which needs further study, our comparisons are good with the other models. In summary, the performance of the l i T Heavy Gas models is comparable to that of the DEGADIS and OME models except under stable atmospheric conditions. It has been observed that in A, B,C, and D stability conditions, IITHG model over predicts downwind distances in the range 0.57-28.94% in comparison to the distances estimated by DEGADIS model and in the range 15.96-41.48% than the OME model. While in E and F cases the aforesaid percentage range of over prediction is 3.84-76.91 and 0.36-39.13, respectively. These ranges seem reasonable and over prediction keeps us on safer side in view of the calculations for industrial planning purposes. It may be pointed out that the l i T Heavy Gas Models incorporate all the basic phenomena associated with dense gas dispersion in a realistic manner and, at the same time, are computationally efficient. Moreover, model evaluation shows a good performance of the model. Therefore, from the operational point of view, the l i T Heavy Gas models are well suited for emergency response.
4. CONCLUSIONS The IIT Heavy Gas dispersion model is developed which is simple in concept, yet it predicts downwind vapour concentration with good accuracy. On the basis of statistical evaluation, its performance is comparable to the best amongst 11-14 other models developed elsewhere in the World. It is valid both for instantaneous and continuous releases of dense toxic material. Being computationaily efficient, it is well suited for operational purposes. Although the present model has some limitations, it certainly accounts well for the characteristic features of dense gas dispersion and can be utilized for providing guidelines for emergency response measures.
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